The equation is true when x = 9,x = 9 is a solution to this equation.
To determine which equations have x = 9 as a possible solution, we need to check each equation individually. Here are the equations to consider:
3x - 18 = 15
Substituting x = 9, we have:
3(9) - 18 = 15
27 - 18 = 15
9 = 15
The equation is not true when x = 9. Therefore, x = 9 is not a solution to this equation.
2(x + 4) = 26
Substituting x = 9, we have:
2(9 + 4) = 26
2(13) = 26
26 = 26
The equation is true when x = 9. Therefore, x = 9 is a solution to this equation.
5x + 3 = 2x + 30
Substituting x = 9, we have:
5(9) + 3 = 2(9) + 30
45 + 3 = 18 + 30
48 = 48
The equation is true when x = 9
Based on the analysis, x = 9 is a possible solution for equations 2 and 3.
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what is the solution to the system of equations graphed below
The solutions to the system of equations is (a) (1, 5)
Selecting the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The graph
This point of intersection of the lines of the graph represent the solution to the system graphed
From the graph, we have the intersection point to be
(x, y) = (1, 5)
Hence, the solutions to the system is (1, 5)
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If g(x) = (7x¹ + 6)³ (4x³ + 1)5, find g'(x).
g'(x) =
g'(x) = 21(7x¹ + 6)² * (4x³ + 1)⁵ + (7x¹ + 6)³ * 60x²(4x³ + 1)⁴
Hence, g'(x) is the derivative of the given function g(x) and can be represented by the expression above.
To find the derivative of the function g(x) = (7x¹ + 6)³ (4x³ + 1)⁵, we can apply the product rule and the chain rule.
Let's start by applying the product rule. If we have two functions u(x) and v(x), the derivative of their product is given by:
(d/dx) [u(x) v(x)] = u'(x) v(x) + u(x) v'(x)
For our function g(x) = (7x¹ + 6)³ (4x³ + 1)⁵, we can consider u(x) = (7x¹ + 6)³ and v(x) = (4x³ + 1)⁵.
Now, let's find the derivatives of u(x) and v(x):
u'(x) = 3(7x¹ + 6)² * (7) = 21(7x¹ + 6)²
v'(x) = 5(4x³ + 1)⁴ * (12x²) = 60x²(4x³ + 1)
Now, we can apply the product rule to find g'(x):
g'(x) = u'(x) v(x) + u(x) v'(x)
= (21(7x¹ + 6)²) * (4x³ + 1)⁵ + (7x¹ + 6)³ * (60x²(4x³ + 1)⁴)
Simplifying further, we can expand the expressions:
g'(x) = 21(7x¹ + 6)² * (4x³ + 1)⁵ + (7x¹ + 6)³ * 60x²(4x³ + 1)⁴
Hence, g'(x) is the derivative of the given function g(x) and can be represented by the expression above.
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if p= the computer's original price in dollars, which algebric expression represents the reduced price?
The correct algebraic expression for the reduced price of the computer is p - 250, as stated in option B. It signifies subtracting $250 from the original price, 'p.' Option B
To determine the algebraic expression that represents the reduced price of a computer, let's consider the given information. It states that the original price of the computer was reduced by $250.
Let's represent the original price of the computer as 'p' in dollars. Since the price was reduced by $250, we need to subtract $250 from the original price.
The expression that represents the reduced price is obtained by subtracting $250 from 'p.' Therefore, the algebraic expression for the reduced price is p - 250, which corresponds to option B.
Option A, 250 + p, suggests adding $250 to the original price, which would result in a higher value, contrary to the information given.
Option C, 250 - p, represents subtracting the original price from $250, which is not correct as we are reducing the price, not subtracting it from a fixed value.
Option D, 250p, represents multiplying the original price by $250, which does not align with the given scenario of reducing the price by $250.
Option B
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Note: The complete question is:
The original price of a computer was reduced by $250.If p = the computer's original price in dollars, which algebraic expression represents the reduced price? A.250 + p B.p – 250 C.250 – p D.250p
Solve for x.
OA. 9
OB. 1
OC. 4
OD.7
The value of x in the secant intersection is 4.
How to find the length in a secant?If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
Therefore, let's find the value of x using the secant intersection theorem as follows;
4(4+x + 2) = 5(5 + x - 1)
4(6 + x) = 5(4 + x)
24 + 4x = 20 + 5x
24 - 20 = 5x - 4x
x = 4
Therefore,
x = 4
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use the basic concepts of probability to identify the following . show solution .
1: 1/5 rolling a die
The probability of rolling the specific outcome 1: 1/5 on a fair six-sided die is 1/6
To identify the probability of rolling a specific outcome on a fair six-sided die, we can use the concept of probability. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, we want to find the probability of rolling a specific outcome, which is 1 out of 5. Since there is only one specific outcome we are interested in, and the die has a total of 6 possible outcomes (numbers 1 to 6), the probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 6
Therefore, the probability of rolling the specific outcome you mentioned (1 out of 5) on a fair six-sided die is 1/6.
In conclusion, when rolling a fair die, each of the six possible outcomes has an equal chance of occurring, resulting in a probability of 1/6 for any specific outcome.
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Give the domain and range. x –3 0 3 y –6 0 6 a. domain {–3, 0, 3}, range: {–6, 0, 6} b. domain {–6, 0, 6}, range {–3, 0, 3} c. domain {3, 0, 3}, range {6, 0, 6} d. domain {6, 0, 6}, range {3, 0, 3} Please select the best answer from the choices provided A B C D
The domain of the given table is { -3, 0, 3 } and the range is { -6, 0, 6 }. Option A.
The given table represents a set of ordered pairs (x, y). The x-values are -3, 0, and 3, and the corresponding y-values are -6, 0, and 6. To determine the domain and range, we need to identify the set of all possible x-values and y-values.
Domain: The domain represents the set of all possible x-values in the given table. In this case, the x-values are -3, 0, and 3. Therefore, the domain is { -3, 0, 3 }.
Range: The range represents the set of all possible y-values in the given table. In this case, the y-values are -6, 0, and 6. Therefore, the range is { -6, 0, 6 }.
Based on the above analysis, the correct answer is:
a. domain { -3, 0, 3 }, range: { -6, 0, 6 }.
This option correctly identifies the values in the given table as the domain and range, matching the values -3, 0, 3 for the domain and -6, 0, 6 for the range. Therefore, option a is the best answer. Option A is correct.
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Which two of the following are not characteristics of surveys?
A. The study involves one or more treatment groups and a control
group.
B. The study compares two or more treatments.
C. Statistical analysis is applied to the results of the study.
D. Data are gathered during the course of the study.
Answer: A and B are not characteristics of surveys.
Step-by-step explanation: A survey is a type of research method that involves collecting data from a sample of individuals or groups, usually by asking them questions or observing their behavior. Surveys can be used to describe, compare, or explain various aspects of a population or phenomenon of interest.
Some of the common characteristics of surveys are:
They use a predefined set of questions or items that are standardized and consistent for all respondents or participants.They use a sampling technique to select a representative subset of the population or target group that is relevant to the research question or objective.They use a mode of data collection that is suitable for the type and format of the questions or items, such as face-to-face interviews, telephone interviews, mail questionnaires, online surveys, etc.They use statistical analysis to summarize, describe, compare, or infer the results of the data collected from the sample to the population or target group.Some of the types of research methods that involve one or more treatment groups and a control group, and that compare two or more treatments, are:
Experiments: Experiments are research methods that involve manipulating one or more independent variables (the treatments) and measuring their effects on one or more dependent variables (the outcomes). Experiments aim to establish causal relationships between variables by controlling for other factors that may influence the results. Experiments usually involve random assignment of participants to different treatment groups and a control group that receives no treatment or a placebo.Quasi-experiments: Quasi-experiments are research methods that resemble experiments but lack some of the features of true experiments, such as random assignment or manipulation of variables. Quasi-experiments aim to estimate causal relationships between variables by using natural or existing variations in the independent variables (the treatments) and comparing their effects on the dependent variables (the outcomes). Quasi-experiments usually involve non-equivalent groups that differ in their exposure to the treatments or in other characteristics that may affect the results.Observational Studies: Observational studies are research methods that involve observing and measuring existing phenomena without manipulating any variables. Observational studies aim to describe, compare, or correlate variables by using natural or existing data sources. Observational studies usually involve different groups that are selected based on their exposure to the variables of interest or based on other criteria that may affect the results.Hope this helps, and have a great day! =)
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
(D) 10 ft
Step-by-step explanation:
Given:
Height = Base + 6
Area = 160
Area = Base * Height
160 = x * (x + 6)
Expand and rearrange:
x^2 + 6x - 160 = 0
Factor:
(x + 16)(x - 10) = 0
Solve for x:
x = -16 or x = 10
Discard the negative solution:
x = 10
What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.
Answer here
Answer:
The area of this triangle is (1/2)(9)(8) = 36.
Is the following infinite sum defined?
0.69+1.38+2.76+5.52+…
Select the correct answer below:
The given infinite sum 0.16 + 0.4 + 0.1 + 0.25 + ... is defined as it converges to a finite value. Option A is the correct answer.
To determine whether the given infinite sum is defined, let's examine its pattern.
If we observe the terms in the sum, we can see that each term is obtained by dividing the previous term by 4. Specifically, each term is one-fourth the value of the previous term.
Let's verify this pattern:
Term 1: 0.16
Term 2: Term 1 / 4 = 0.16 / 4 = 0.04
Term 3: Term 2 / 4 = 0.04 / 4 = 0.01
Term 4: Term 3 / 4 = 0.01 / 4 = 0.0025
It appears that each term is one-fourth the value of the previous term. If this pattern continues, we can write the nth term as:
Term n = (1/4)^(n-1) * 0.16
To determine whether the sum is defined, we need to check whether the terms approach a finite value or converge to a specific value.
As n approaches infinity, the term (1/4)^(n-1) * 0.16 will approach zero since (1/4)^(n-1) approaches zero exponentially. Therefore, the sum of the infinite terms in this sequence will converge to a finite value. Hence, Option A is the correct answer.
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HELPPP PLEASE!!!!!!!!!
16. Taylor uses 2 sticks that are 13 feet long to make the slanted sides of
a tent. From the bottom poles, the opening is 10 feet long.
13 ft.
10 ft.
What is the height of the tent in feet?
Write the answer in the box.
feet
We may apply the Pythagorean theorem to calculate the height of the tent, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the total of the squares on the other two sides. So, the height of the tent is 8.3077 feet.
In this case, the two sticks form the slanted sides of the tent, and the opening at the bottom forms the base of the triangle. We can consider the height of the tent as the missing side, which is perpendicular to the base.
Let's denote the height of the tent as 'h.' Using the Pythagorean theorem, we have:
(10 ft.)² + (h)² = (13 ft.)²
Simplifying the equation:
100 + h² = 169
Now, subtracting 100 from both sides:
h² = 169 - 100
h² = 69
Taking the square root of both sides:
h = sqrt(69)
Therefore, the height of the tent is approximately 8.3077 feet (rounded to four decimal places).
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
[tex]\textsf{(C)} \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
To find the probability of a point chosen at random being in the shaded area of the given diagram, we first need to calculate the areas of the larger circle and the shaded circle.
The formula for the area of a circle is A = πr², where r is the radius.
Given the radius of the larger circle is 8 units:
[tex]\begin{aligned}\sf Area\;of\;the\;larger\;circle&=\pi (8)^2\\&=64 \pi \end{aligned}[/tex]
Given the radius of the shaded circle is 4 units:
[tex]\begin{aligned}\sf Area\;of\;the\;shaded\;circle&=\pi (4)^2\\&=16 \pi \end{aligned}[/tex]
Probability formula[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
To find the probability that a point chosen at random is in the shaded area, divide the area of the shaded circle by the area of the larger circle:
[tex]\sf Probability= \dfrac{16 \pi}{64 \pi}=\dfrac{1}{4}[/tex]
Therefore, the probability of a point chosen at random being in the shaded area is 1/4.
Answer:
[tex]\frac{x}{y}[/tex] 1 over 4 (one-fourth)
Step-by-step explanation:
Kubin Company's relevant range of production is 13,000 to 18,000 units. When it produces and sells 15,500 units, its average costs per
unit are as follows:
Direct materials
Direct labor
Variable manufacturing overhead
Fixed manufacturing overhead
Fixed selling expense
Fixed administrative expense
Sales commissions
Variable administrative expense
Average
Cost per
Unit
$7.40
$ 4.40
$ 1.90
$ 5.40
$ 3.90
$ 2.90
$ 1.40
$0.90
Required:
1 Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 15,500 units?
b. What is the total indirect manufacturing cost incurred to make 15,500 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of
its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the
company's sales representatives' compensation.
a. When the company sells 15,500 units, what is the total direct selling expense that can be readily traced to individual sales
representatives?
b. When the company sells 15,500 units, what is the total indirect selling expense that cannot be readily traced to individual sales
representatives?
1. a. The Total direct manufacturing cost is $212,350. b. The Total indirect manufacturing cost is -$128,650. 2. a. the total manufacturing cost directly traceable to the Manufacturing Department is $212,350. b. the total manufacturing cost that is an indirect cost is $83,700. 3. a. the total direct selling expense that can be readily traced to individual sales representatives is $21,700. b. the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
1. Assume the cost object is units of production:
a. The total direct manufacturing cost incurred to make 15,500 units can be calculated by multiplying the average cost per unit for each cost component by the number of units produced:
Total direct manufacturing cost = (Direct materials cost + Direct labor cost + Variable manufacturing overhead cost) × Number of units produced
Direct materials cost = $7.40/unit × 15,500 units = $114,700
Direct labor cost = $4.40/unit × 15,500 units = $68,200
Variable manufacturing overhead cost = $1.90/unit × 15,500 units = $29,450
Total direct manufacturing cost = ($114,700 + $68,200 + $29,450) = $212,350
b. The total indirect manufacturing cost incurred to make 15,500 units can be calculated by subtracting the total direct manufacturing cost from the average cost per unit for fixed manufacturing overhead:
Total indirect manufacturing cost = Fixed manufacturing overhead cost × Number of units produced
Fixed manufacturing overhead cost = $5.40/unit × 15,500 units = $83,700
Total indirect manufacturing cost = $83,700 - $212,350 = -$128,650
Note: The negative value indicates that the fixed manufacturing overhead cost is not fully utilized within the relevant range of production. It suggests that there may be unused capacity or fixed costs that are not being allocated to the production of 15,500 units.
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units:
a. The total manufacturing cost directly traceable to the Manufacturing Department is the sum of the direct manufacturing costs:
Total manufacturing cost directly traceable to the Manufacturing Department = Total direct manufacturing cost
Using the values calculated in part 1a, the total manufacturing cost directly traceable to the Manufacturing Department is $212,350.
b. The total manufacturing cost that is an indirect cost and cannot be easily traced to the Manufacturing Department is the fixed manufacturing overhead cost:
Total manufacturing cost that is an indirect cost = Fixed manufacturing overhead cost
Using the value calculated in part 1b, the total manufacturing cost that is an indirect cost is $83,700.
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of its total fixed selling expense on advertising, and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives' compensation:
a. When the company sells 15,500 units, the total direct selling expense that can be readily traced to individual sales representatives is the sales commissions:
Total direct selling expense = Sales commissions × Number of units sold
Sales commissions = $1.40/unit × 15,500 units = $21,700
Therefore, the total direct selling expense that can be readily traced to individual sales representatives is $21,700.
b. When the company sells 15,500 units, the total indirect selling expense that cannot be readily traced to individual sales representatives is the fixed portion of the company's sales representatives' compensation:
Total indirect selling expense = Total fixed selling expense - Total direct selling expense
Total fixed selling expense = $3.90/unit × 15,500 units = $60,450
Total indirect selling expense = $60,450 - $21,700 = $38,750
Therefore, the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The volume of the pyramid is 357.7 inches³.
The volume of the cone is 1230.9 yard³.
How to find the volume of a cone/pyramid?The volume of a pyramid can be represented as follows;
volume of the pyramid = 1 / 3 Bh
where
B =base areah = heightTherefore,
B = 10 × 8 = 80 inches²
Hence,
h² = 14² - 4²
h = √196 - 16
h = √180
h = √180 inches
volume of the pyramid = 1 / 3 × 80 × √180
volume of the pyramid = 357.7 inches³
Therefore, let's find the volume of the cone.
volume of the cone = 1 / 3 πr²h
h = √25² - 7²
h = √576
h = 24 yards
volume of the cone = 1 / 3 × 3.14 × 7² × 24
volume of the cone = 1230.9 yard³
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Which description is paired with its correct expression?
four less than the quotient of a number cubed and seven, increased by three; 4-2+3
five times the difference of a number squared and six; 5(6-n²)
nine more than the quotient of six and a number cubed, decreased by four; 8+²-4
9+
O twice the difference of nine and a number squared; 2(9-n²)
The correct pairings are:
a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
b) Five times the difference of a number squared and six: 5(n² - 6)
c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
d) O twice the difference of nine and a number squared: 2(9 - n²)
The correct pairings of descriptions and expressions are as follows:
Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.
Five times the difference of a number squared and six: 5(n² - 6)
This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.
Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.
O twice the difference of nine and a number squared: 2(9 - n²)
This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.
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What else would need to be congruent to show that ABC = DEF by AAS?
A. AC = DF
B.
C.
D. BC = EF
To prove that ABC = DEF by AAS, then (b) A = D
How to show that ABC = DEF by AAS?From the question, we have the following parameters that can be used in our computation:
The triangles ABC and DEF
The AAS theorem states that "If one side in one triangle is proportional to one side in another triangle and two corresponding angles in both are congruent, then the two triangles are similar"
From the figure, we have
E = B = 50 degrees
AB = DE = 10
So, another pair of angles must be congruent
In this case, the pair are (b) A = D
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
∠ G = 73° , ∠ H = 98°
Step-by-step explanation:
EFGH is a cyclic quadrilateral, its 4 vertices lie on the circle.
the opposite angles sum to 180°
A
∠ E + ∠ G = 180° , that is
11x + 8 + 8x + 1 = 180
19x + 9 = 180 ( subtract 9 from both sides )
19x = 171 ( divide both sides by 19 )
x = 9
Then
∠ G = 8x + 1 = 8(9) + 1 = 72 + 1 = 73°
B
∠ H + ∠ F = 180° , that is
6y - 4 + 5y - 3 = 180
11y - 7 = 180 ( add 7 to both sides )
11y = 187 ( divide both sides by 11 )
y = 17
Then
∠ H = 6y - 4 = 6(17) - 4 = 102 - 4 = 98°
Answer:
A) m∠G = 73°
B) m∠H = 98°
Step-by-step explanation:
The diagram shows a cyclic quadrilateral.
A cyclic quadrilateral is a four-sided shape drawn inside a circle, where every vertex touches the circle's circumference.
As the opposite angles in a cyclic quadrilateral add up to 180°, then:
m∠E + m∠G = 180°m∠H + m∠F = 180°We can use these equations to find the values of x and y.
m∠E + m∠G = 180°
(11x + 8)° + (8x + 1)° = 180°
11x + 8 + 8x + 1 = 180
19x + 9 = 180
19x + 9 - 9 = 180 - 9
19x = 171
19x ÷ 19 = 171 ÷ 19
x = 9
m∠H + m∠F = 180°
(6y - 4)° + (5y - 3)° = 180°
6y - 4 + 5y - 3 = 180
11y - 7 = 180
11y - 7 + 7 = 180 + 7
11y = 187
11y ÷ 11 = 187 ÷ 11
y = 17
Now we have found the values of x and y, substitute them back into the angle expressions to find m∠G and m∠H.
m∠G = (8x + 1)°
m∠G = (8(9) + 1)°
m∠G = (72 + 1)°
m∠G = 73°
m∠H = (6y - 4)°
m∠H = (6(17) - 4)°
m∠H = (102 - 4)°
m∠H = 98°
I Need fast!!! 20 POINTS
Answer:
(x + 3)(5x + 2) , (2x - 1)(3x + 5)
Step-by-step explanation:
given
A = 5x² + 12x + 6
consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 5 × 6 = 30 and sum = 17
the factors are + 15 and + 2
use these factors to split the x- term
5x² + 15x + 2x + 6 ( factor the first/second and third/fourth terms )
= 5x(x + 3) + 2(x + 3) ← factor out (x + 3) from each term
= (x + 3)(5x + 2)
then
length = x + 3 , breadth = 5x + 2 or indeed the other way round
-------------------------------------------------------------------------------
given
A = 6x² + 7x - 5
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × - 5 = - 30 and sum = + 7
the factors are - 3 and + 10
use these factors to split the x- term
6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )
= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term
= (2x - 1()3x + 5)
then
length = 2x - 1 , breadth = 3x + 5 or the other way round
You can make $ when you activate a prepaid device with equipment
When you activate a prepaid device with equipment, you may have the opportunity to earn money through various means.
Firstly, as a retailer or reseller, you can make a profit by selling the prepaid device and associated equipment at a higher price than your purchase cost. This markup allows you to earn a margin on each sale.
Additionally, some service providers or retailers offer commission-based programs where you earn a commission or referral fee for each prepaid device activation. By promoting and selling these devices, you can earn a percentage of the total sale value or a fixed amount per activation.
Furthermore, you might have the chance to upsell customers on additional accessories or services during the activation process. By offering relevant accessories like cases, screen protectors, or headphones, you can increase the overall sale value and earn extra income.
It's worth noting that the specific earning potential can vary depending on factors such as the popularity of the device, the commission structure, and the competitiveness of the market. It's advisable to research and understand the terms and conditions of any commission or referral programs before engaging in such activities.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The correct answer is (C) SSS Similarity. The ratio of AA' to AB will be constant and equal to the scale factor. Similarly, the ratio of A'B' to AB will also be equal to the scale factor.
The correct answer is (C) SSS Similarity.
In a dilation, the image of a figure is created by enlarging or reducing it while maintaining the same shape. The scale factor determines the ratio of the lengths of corresponding sides between the original figure and its image.
In the given problem, we have AABC as the original figure, and AA'B'C' as its image under a dilation with the center at (0,0). To determine the scale factor, we need to compare the corresponding side lengths of the two figures.
In SSS (Side-Side-Side) similarity, we compare the ratios of the corresponding side lengths. If all corresponding side lengths have the same ratio, the figures are similar. In this case, we can compare the lengths of AA', AB, and A'B' to determine the scale factor.
Since the center of dilation is at (0,0), AA' and AB are radii of the same circle centered at (0,0). Therefore, the ratio of AA' to AB will be constant and equal to the scale factor. Similarly, the ratio of A'B' to AB will also be equal to the scale factor.
Hence, by comparing the lengths of corresponding sides AA', AB, and A'B', we can determine the scale factor. If all three ratios are equal, which is the case for SSS similarity, then the scale factor remains constant.
Therefore, the correct answer is (C) SSS Similarity.The correct answer is (C) SSS Similarity.
In a dilation, the image of a figure is created by enlarging or reducing it while maintaining the same shape. The scale factor determines the ratio of the lengths of corresponding sides between the original figure and its image.
In the given problem, we have AABC as the original figure, and AA'B'C' as its image under a dilation with the center at (0,0). To determine the scale factor, we need to compare the corresponding side lengths of the two figures.
In SSS (Side-Side-Side) similarity, we compare the ratios of the corresponding side lengths. If all corresponding side lengths have the same ratio, the figures are similar. In this case, we can compare the lengths of AA', AB, and A'B' to determine the scale factor.
Since the center of dilation is at (0,0), AA' and AB are radii of the same circle centered at (0,0). Therefore, the ratio of AA' to AB will be constant and equal to the scale factor. Similarly, the ratio of A'B' to AB will also be equal to the scale factor.
Hence, by comparing the lengths of corresponding sides AA', AB, and A'B', we can determine the scale factor. If all three ratios are equal, which is the case for SSS similarity, then the scale factor remains constant.
Therefore, the correct answer is (C) SSS Similarity.
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An experiment was conducted in which a six-sided die was rolled 20 times. The outcomes of the experiment are listed
in the table below. Use the table to answer the questions.
Value of Die Frequency
1
5
2
3
4
5
6
Your answers should be exact decimal values.
The probability that a die will land on 5 is
The probability that a die will land on 1 is
If a probability is unlikely, then the probability is less than
4
1
2
4
4
The probability that a die will land on 5 is 0.1.
The statement "If a probability is unlikely, then the probability is less than 1/2" is true in this context.
To determine the probabilities, we need to calculate the relative frequency of each outcome by dividing the frequency of that outcome by the total number of rolls (20 in this case).
The frequency table provided is as follows:
Value of Die | Frequency
1 | 5
2 | 3
3 | 4
4 | 5
5 | 2
6 | 1
To find the probability that a die will land on 5, we divide the frequency of 5 by the total number of rolls:
Probability of landing on 5 = Frequency of 5 / Total number of rolls
= 2 / 20
= 0.1
Therefore, the probability that a die will land on 5 is 0.1.
Similarly, to find the probability of landing on 1:
Probability of landing on 1 = Frequency of 1 / Total number of rolls
= 5 / 20
= 0.25
Thus, the probability that a die will land on 1 is 0.25.
Now, if a probability is unlikely, it means the probability is less than 1/2. In this case, we need to compare the probabilities to 0.5.
Since the probability of landing on 1 is 0.25, which is less than 0.5, we can conclude that the probability of landing on 1 is unlikely.
Therefore, the statement "If a probability is unlikely, then the probability is less than 1/2" is true in this context.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The similar triangles and their statements are
A. Side-Side-Side (SSS) Similarity
B. Side-Angle-Side (SAS) Similarity
C. Hypotenuse-leg (HL) similarity
What is similarity statement?A similarity statement is a statement that expresses the similarity between two or more geometric figures or objects. It describes the relationship between corresponding angles and corresponding sides of the figures.
The general form of a similarity statement for two figures, let's say figure A and figure B, is:
"Figure A is similar to Figure B"
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Question 5 of 5
How does the diagram illustrate why the sum of the lengths of two sides of a
triangle cannot be less than the length of the third side of the triangle?
4221
12
OA. by showing the two sides with lengths 4 and 3 can always meet to
form a vertex
B. by showing the two sides with lengths 4 and 3 will only meet when
the angle between them is large
OC. by showing the two sides with lengths 4 and 3 can never meet to
form a vertex
D. by showing the two sides with lengths 4 and 3 will only meet when
they lie on the third side
SUBMIT
Answer:
The diagram illustrates that the two sides with lengths 4 and 3 can never meet to form a vertex, therefore the correct answer is C.
Sparx 4: Item A
Bookwork code: C20
Find the size of the angle marked n. Give your answer in degrees (°).
n
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52
1,326 XP
Not drawn accurately
Answer >
13 Jun
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The size of angle marked n is ≈26.67 degrees.
Sparx 4:
Item A, bookwork code C20 requires us to determine the size of angle marked n in degrees.
We can solve the given question by using the angles sum rule that states that the sum of the angles of a triangle equals to 180 degrees.
The given figure represents an isosceles triangle since the two base angles are equal in length.
Also, the top line is parallel to the bottom line.
Using the angles sum rule for a triangle, we get:angle ABC + angle BCA + angle CAB = 180 degreesx + 2n + 50 = 180 degreesx = 180 - 2n - 50x = 130 - 2nWe know that angles that are opposite to equal sides of an isosceles triangle are equal.
Therefore, angle ABC = angle CAB = n
Thus, the above equation becomes:130 - 2n = n + 50.
Simplifying the equation, we get:3n = 80n = 80 / 3n ≈ 26.67 degrees.
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Mr. John recently bought 2 cords of wood from a local contractor
(delivered in a dump truck). After the pile was dropped off, he stacked
the wood and wondered if he really received the 2 standard cords of
wood (see diagram) or if the company sold him less wood than he
ordered.
Note: a cord of wood if defined as 4ft X 4ft’ X 8ft stack
Mr. John ended up stacking to piles of wood this past week.
Mr. John ended up with two piles of wood with the following sizes
PILE #1: 72” X 167” X 16”
PILE #2: 65” X 266” X 16”
QUESTIONS:
1. Did Mr. John get more or less than 2 cords of wood (as defined in
the diagram above)?
2. If a standard piece of wood is 5” X 5” X 12”. How pieces of actual
wood did he receive based on his stacked piles?
3. If the cost for both cords of wood was actually $250/cord,
What was the cost per a standard piece of wood?
1. Mr. John received more than 2 cords of wood based on the sizes of the stacked piles.
2. Based on the stacked piles, Mr. John received approximately 11,974 pieces of actual wood.
3. The cost per standard piece of wood is approximately $0.0417.
1. To determine if Mr. John received more or less than 2 cords of wood, we need to calculate the volume of each pile and compare it to the volume of a standard cord of wood.
Calculating the volume of each pile:
PILE #1:
Volume = 72 inches * 167 inches * 16 inches = 1,523,584 cubic inches
PILE #2:
Volume = 65 inches * 266 inches * 16 inches = 2,068,480 cubic inches
Calculating the volume of a standard cord of wood:
Volume of a standard cord = 4 feet * 4 feet * 8 feet = 128 cubic feet
Since 1 foot = 12 inches, the volume in cubic inches is 128 * 12 * 12 * 12 = 221,184 cubic inches.
Comparing the volumes:
Pile #1: 1,523,584 cubic inches
Pile #2: 2,068,480 cubic inches
Standard cord: 221,184 cubic inches
It is evident that both piles have significantly more volume than a standard cord of wood. Therefore, Mr. John received more than 2 cords of wood.
2. To determine the number of standard pieces of wood received, we need to calculate the number of pieces that can be obtained from the total volume of the piles.
Total volume of the piles = Volume of Pile #1 + Volume of Pile #2
Total volume = 1,523,584 cubic inches + 2,068,480 cubic inches = 3,592,064 cubic inches
Volume of a standard piece of wood = 5 inches * 5 inches * 12 inches = 300 cubic inches
Number of standard pieces of wood received = Total volume of the piles / Volume of a standard piece of wood
Number of pieces = 3,592,064 cubic inches / 300 cubic inches = 11,973.55 pieces (rounded to the nearest whole number)
Therefore, Mr. John received approximately 11,974 pieces of actual wood based on his stacked piles.
3. To calculate the cost per standard piece of wood, we need to divide the total cost of the two cords by the number of standard pieces received.
Total cost for both cords of wood = 2 cords * $250/cord = $500
Cost per standard piece of wood = Total cost / Number of standard pieces
Cost per piece = $500 / 11,974 = $0.0417 (rounded to four decimal places)
Therefore, the cost per standard piece of wood is approximately $0.0417.
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Calcula el área de un círculo con radio de 5 cm.
The area of a circle with a radius of 5 cm is given as follows:
78.5 cm².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, and it's measure is given as follows:
r = 5 cm.
Hence the area of the circle is given as follows:
A = π x 5²
A = 78.5 cm².
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John's four brothers each have names that begin with the letter J, but none of the other
members of his family has a name that begins with J. If a person in John's family is randomly
selected, there is a 25% chance that the person's name will start with J. How many people are
in John's family?
Answer:16
Step-by-step explanation:
25/100 × x = 4
x = 4 × 4
x = 16
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.
What are the important variables in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. p for points, m for multiple choice
OB. s for short answer, t for test
OC. m for multiple choice, s for short answer
OD. t for test, q for questions
The important variables are the two types of test questions which can be represented as :
m for multiple choice, s for short answerVariables are used to represent unknown values which could be worked out in a mathematical expression or problem.
The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer
Therefore, the correct option is C. m for multiple choice, s for short answer
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