Using Arithmetic progression(A.P.), the value of a22 will be 107
The formula to calculate A.P. is a + (n-1)d
The value of a5 = 5a1
a1 = 23
a5 = -5a1
a5 = 5 (23)
a5 = 115
a22 = a + (n-1)d
a22 = 23 + (22-1)d
a22 = 23 + 21d ................(1)
a5 = 115
115 = a + (n-1)d
115 = 23 + (4)d ...................(2)
from (1) and (2)
a5 = a + 4d
d = 23
a22 = 107
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HELP ASAP
(−2x − 13) + (19 + 5x)
Answer:
3x+6
Step-by-step explanation:
Let's simplify step-by-step.
−2x−13+19+5x
=−2x+−13+19+5x
Combine Like Terms:
=−2x+−13+19+5x
=(−2x+5x)+(−13+19)
=3x+6
Melanie spent half of her allowance going to the movies. She washed the family
car and earned nine dollars. What is her weekly allowance if she ended with
seventeen dollars?
Answer:43
Step-by-step explanation:
(9+17)x2
How do I Evaluate 16 2/3?
Answer:
6.34960 correct to 5 decimal places.
Step-by-step explanation
16 ^ 2/3
= cube root of 16^2
∛(16^2)
= ∛(256)
= 6.349604208.
The 2 in the 2/3 means the square of 16, and the 3 in 2/3 mean 16^1/3
which is the same as the cube root.
The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex] in improper fractions using the simplification rule is [tex]\dfrac{50}{3}[/tex].
The combination of a proper fraction and a whole number is called a mixed fraction.
When the numerator is greater than the denominator, such type of fraction is called an improper fraction.
To evaluate [tex]16 \dfrac{2}{3}[/tex] , convert the mixed number to an improper fraction and then simplify it.
Multiply the whole number [tex](16)[/tex] by the denominator [tex](3)[/tex] and add the numerator [tex](2)[/tex].
[tex](16 \times 3 )+ 2 \\= 48 + 2\\ = 50[/tex]
The sum is written with the denominator [tex]3[/tex] as [tex]\dfrac{50}{3}[/tex] .
The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex] in improper fractions is [tex]\dfrac{50}{3}[/tex].
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Look at the expression y - 2x + 7, and identify the following... coefficient(s) constant(s) variable(s)
In the given expression y - 2x + 7 y and x are the variables, -2 is the coefficient of x and 1 is the coefficient of y and 7 is the constant.
What is a coefficient ?
Any component of a product that is taken into account in relation to another component, particularly a constant component of a term as opposed to a variable.
What is an a variable?
Any qualities, quantity, or number that can be gauged or counted qualifies as a variable. A variable may alternatively be called a data piece. Examples of variables include age, sex, business income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle type.
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Simplify: (3^2x4^2)^5
Hey there!
Assuming:
(3^2 * 4^2)^5
If so,
(3^2 * 4^2)^5
= (3 * 3 * 4 * 4)^5
= (9 * 16)^5
= (144)^5
= 144^5
= 144 * 144 * 144 * 144 * 144
= 20,736 * 20,736 * 144
= 429,981,696 * 144
= 61,917,364,224
Therefore, your answer should be:
61,917,364,224
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Write an algebraic expression.
7. Bobby ran 4 miles and will run 3 miles a day from now on. Jack ran 6 miles and will
run 5 miles a day from now on.
a. Create an algebraic expression that represents the amount of miles that Bobby & Jack
will run together. Simplify, if possible.
b. Determine how many miles they will run after 8 days.
From the situation described, it is found that:
a) The linear function that represents the amount of miles that Bobby & Jack will run together is T(x) = 2(4x + 5).
b) They will have run 74 miles after 8 days.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For both Bobby's and Jack's function, we have that:
The amount that they have ran is the intercept.The daily amount that they will run is the slope.Hence the functions for the number of miles they will have run after x days are given by:
B(x) = 4 + 3x.J(x) = 6 + 5x.The total amount is:
T(x) = B(x) + J(x)
T(x) = 4 + 3x + 6 + 5x
T(x) = 8x + 10.
T(x) = 2(4x + 5).
After 8 days, the number of miles they will have run is:
T(8) = 2(4 x 8 + 5) = 2 x 37 = 74.
They will have run 74 miles after 8 days.
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The table shows the number of Calories José and Natalie burned after 1, 2, and 3 minutes of running. Graph the relationship between the number of minutes running and the number of Calories burned for each person. By which ordered pair is a unit rate represented?
Time (min) 0 1 2 3
Calories Burned
José 0 8 15 23
Natalie 0 5 10 15
A unit rate is represented by the second pair. The graph is also displayed.
A pair made consisting of two sections written inside parantheses and separated by commas is referred to as an ordered pair. For instance, an ordered pair with "x" as the first component and "y" as the second element is shown by the symbol (x, y). These items have unique names and, depending on the situation, can either be variables or constants.
The element order in an ordered pair has some bearing. It suggests that (x, y) could not always equal (y, x).
A coordinate geometry ordered pair is used to specify where a point is on the coordinate plane in relation to the origin.
Therefore, the graph is attached and the second pair represents the unit rate.
Graph is attached at end.
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Complete question -The table shows the number of Calories José and Natalie
burned after 1, 2, and 3 minutes of running. Graph the
relationship between the number of minutes running and
the number of Calories burned for each person. By which
ordered pair is a unit rate represented?
Calories Burned
X
Time (min) 0 1 2 3
Calories Burned
José 0 8 15 23
Natalie 0 5 10 15
Number of Calories
40 30 20 10 0 Calories Burned
Ryker goes to the golf driving range every Saturday morning. The cost is a flat fee of $10, plus $2.50 per bucket of golf balls. One Saturday morning, Ryker spent $52.50. Write and solve an equation to find out how many buckets Ryker used.
A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.
C - 2.75b + 4
sorry if i didn't answer it right
In Colorado Springs, the fine for illegally parking in a zone reserved for people with disabilities is $350
This is $200 higher than the fine in Denver.
How much is the fine in Denver? Use x as your variable.
The cost of the fine in Denver is $100.
How much is the fine in Denver?The mathematical operation that would be used to determine the cost of the fine in Denver is subtraction. Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to denote subtraction is - . Other mathematical operations are addition, division and multiplication.
In order to determine the cost of the fine in Denver, subtract $200 from the cost of the fine in Colorado Springs.
The equation that represents the cost of the fine in Denver is:
Cost of the fine in Colorado Springs = $200 + cost of the fine in Denver
$350 = $200 + x
In order to determine the value of x, subtract $200 from both sides of the equation.
$350 - $200 = x
x = $100
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A shipping container will be used to transport several 130-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 26500
kilograms. Other shipments weighing 7700 kilograms have already been loaded into
the container. What is the greatest number of 130-kilogram crates that can be loaded
into the shipping container?
The maximum number of 130 kg crates that can be loaded into the shipping container is 137 which is calculated using linear inequality.
A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in a linear inequality. It displays non-equal data in graph style.
An example of linear inequality is : 2x+8>18
Linear inequality can be represented using several symbols such as:
<,>,≥ and ≤.
Let us consider there are x number 130 kg crates.
The shipping container can take a maximum weight of 26500 Kilogram.
There is already 7700 kilograms of shipment loaded
Therefore we can write an linear inequality in x such as:
130x+7700 ≤ 256500
Subtracting 7700 from both sides we get:
130x+7700-7700 ≤ 25600-7700
or,130x ≤ 17900
Dividing both sides by 130
or, x ≤ 137.69....
Now we can say as the crates must be whole therefore the maximum number of 130 kg crates that the shipping container can hold is 137.
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Which expression is equivalent to 11(45−21)?
Answer:
11×45-11×21
Step-by-step explanation:
multiply the number outside the bracket with the each number inside the bracket
angle a = 2x-10 and angle b = 4x+16
solve for x
Answer:
29
Step-by-step explanation:
2x-10+4x+16=180
6x+6=180
6x=174
x=29
What do the meter, liter, and gram all have in common? they are all units of mass. they are all units of capacity. they are all basic units of measure in the customary system. they are all basic units of measure in the metric system.
Meter, liter, and gram are all basic units of measure in the metric system.
The U.S. customary system and the metric system are the two major systems of measurement. The system of measurement that uses the meter, liter, and gram as the base units of length (distance), capacity (volume), and weight (mass) is referred as Metric system.
Most of the countries use the metric system but in the United States, the US Customary system is used where the things are measured in feet, inches, and pounds. Meter, liter, and gram are all basic units of measure in the metric system.
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Answer:
It is D
Step-by-step explanation: I am verifying the persons answer. You're welcome.
Please help with the rest asap
The equations are listed below:
2 · x + 3 = 93 · x - 5 ≤ 64 · (x + 3) < 9x / 5 = x - 86 - 9 · x ≥ 12(1 / 4) · x + 8 = 329 · (x - 1) ≥ 223 - 2 · x ≤ 137 + 2 · x > 154 · x - 9 ≥ 10(x + 2) / (3 · x) = 53 · x ≤ x - 8(x + 3) / 8 = 189 · (x - 7) ≤ 19How to describe a sentence into mathematical equations
In this problem we find fourteen cases of sentences that must be translated into mathematical expressions, that is, expressions that involve constants, variables and operators. Now we proceed to present the result of each case:
Three more than twice a number is nine: 2 · x + 3 = 9Five less than three times a number is at most 6: 3 · x - 5 ≤ 6The product of 4 and the sum of a number and 3 is less than 9: 4 · (x + 3) < 9The quotient of a number and 5 is equivalent to 8 less than the number: x / 5 = x - 8Six decreased by the product of 9 and a number has a minimum of 12: 6 - 9 · x ≥ 12The total of one-fourth of a number and 8 is 32: (1 / 4) · x + 8 = 32The product of 9 and the difference of a number and 1 is at least 22: 9 · (x - 1) ≥ 22The difference of 3 and twice a number has a maximum of 13: 3 - 2 · x ≤ 13Seven increased by double a number is greater than 15: 7 + 2 · x > 15Nine subtracted from the product of 4 and a number is no less than 10: 4 · x - 9 ≥ 10The ratio of a number increased by 2 and the product of 3 and the same number equals 5: (x + 2) / (3 · x) = 5Triple a number is at most 8 fewer than the number: 3 · x ≤ x - 8Three more than a number divided by 8 yields 18: (x + 3) / 8 = 18The product of 9 and the difference of a number and 7 is no more than 19: 9 · (x - 7) ≤ 19To learn more on algebraic equations: https://brainly.com/question/953809
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The ratio of the measure of the angles of a triangle is 1: 2: 3 . The length of the shortest side is 8 . What is the perimeter of the triangle?
The perimeter of the triangle is 37.86
Given,
The ratio of the measure of the angles of triangle = 1:2:3
Let the angles be taken as x, 2x, 3x.
Total angle of a triangle is 180°.
We can now find x.
x + 2x + 3x = 180°
6x = 180°
x = 180°/6 = 30°
x = 30°
2x = 2 × 30° = 60°
3x = 3 × 30° = 90°
Let the sides of the triangle be a, b, c.
The length of the shortest side is given = 8
Lets take a as 8.
We can use Trignometric Formulas here:
Trignometric Formulas:
sin θ = [tex]\frac{opposite side}{hypotenuse}[/tex]
cos θ = [tex]\frac{adjacent side}{hypotenuse}[/tex]
tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
By using sin rule we can find other sides.
That is,
sin 30° = opposite side / hypotenuse
sin 30° = a/b
sin 30° = 8/b
b = 8 × sin 30°
b = 16
Next,
sin 60° = opposite side / hypotenuse
sin 60° = c/16
c = sin 60° × 16
c = 13.86
Now we can find the perimeter of the triangle = a + b + c
= 8 + 16 + 13.86
= 37.86
The perimeter of the triangle is 37.86
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The smallest camera in world is 0.99 millimeters in diameters is the diameter less than or greater than 0.1
99 is bigger than 10 therefore stating the video camera has a greater diameter than .1 .
What is an example of diameter?
If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.The diameter of this camera is greater than .1 millimeter because On a ruler, .99 millimeter is farther to the right than .10 millimeters.
Also, and easier way to look at this is taking away the decimal.
99 is bigger than 10 therefore stating the video camera has a greater diameter than .1 .
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What is the algebraic expression for "the sum of a number and 4"?
A. 4-z
B. 4/z
C. z+4
Answer:
C. z + 4
Hope this helps :)
Step-by-step explanation:
When it says "sum," it means the answer to 2 number that you add. The first number will be unknow which z will stand for, and the second number is 4 since it was stated in the statement, "the sum of a number and 4."
ASB is fundraising for their annual carnival to raise money for prom. They have Decided to sell lemonade for $2 per cup and orange drinks for $3 per cup.
Question 1: Suppose their goal is raise $240 and have sold 60 cups of lemonade, how many cups of orange drink would they need to sell to reach their goal?
Question 2: If the fundraising goal is to make $2500, what equation represents this scenario?
Question 3: Rewrite the equation form part d to express the number of orange drinks as a function of the number of lemonade drinks.
1. The number of cups of orange drink that ASB would need to sell to reach their goal of raising $240 after selling 60 cups of lemonade is 40 cups.
2. To raise $2,500, the equation representing the scenario is 2L + 3D = 2,500.
3. Rewriting the equation from part 2 above to express the number of orange drinks as a function of the number of lemonade drinks is F(D) = (2,500 - 2L)/3.
What is a mathematical function?A mathematical function is a mathematical expression, rule, or law, defining the value relationship between the independent variable and the dependent variable.
For instance, when we state that the number of orange drinks is a function of the number of lemonade drinks, it means that the number of orange drinks to be sold depends on the number of lemonade drinks sold.
Data and Calculations:Lemonade Orange Drink
Selling price per cup $2 $3
Expected total revenue = $240
Number of cups sold 60
Total revenue $120 ($2 x 60) $120 ($240 - $120)
Number of cups to be sold 40 ($120/$3)
2. The equation is:
2L + 3D = 2,500
Where:
L is the number of Lemonade
D is the number of Orange drinks sold.
3. The rewritten equation is:
F(D) = (2,500 - 2L)/3
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One reason a sample may fail to represent the population of interest is _____.
a. population proportion
b. measurement error
c. statistical inference
One reason a sample may fail to represent the population of interest is sampling error.
A sample is often used in the place of a very large population to carry out studies. Also a sample can be selected in multiple ways. Some of the systems used for this process are random sampling and systematic samplings.
But if there is an error in the selection of the sample, it may not represent the population properly. This error is referred as sampling error. sampling error affects the credibility of the sample selected nd thus affects the population interest in studies.
Sampling error is occurs when a statistician fails to select the appropriate sample representing the whole population. So it is basically a statistical error.
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A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
a. Explain how the surveyor can use the triangles formed to find AB.
The surveyor can find AB if he finds CD as CD = AB.
What actually means by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are readjusted, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
First, connect B and D and make a square ACDB with BC as a diagonal.
In triangle ACB and DCB:So, ACB ≅ DCB under SAS condition.
Therefore, the surveyor can find AB if he finds CD as CD = AB.
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If 35% of a number is 63 and 60% of the same number is 108, find 25% of that number.
Given the following triangle, find c.
1. 12
2. 18/17
3. 6/17
4. 3√34
Answer:
Step-by-step explanation:
4.
do A squared plus B squared equal C squared, you should get [squared root[ of 306 then simplify it to 3 squared root 34 by using the family tree
Find the missing terms in the sequence.
4, 6, 10, 16, 24, 34, __, 60, 76, __, 114
Answer:46 and 94
Step-by-step explanation:
Let S = {3, {1, 4}, 2}. The number of elements in power set of S will be:
A) 6
C) 12
B) 8
D) 16
S has 3 elements - 3, {1, 4}, and 2 - so its power set will contain 2³ = 8 elements. (B)
A board must be cut so that its length is 40.50 cm. The tolerance is 0.25 cm . Which inequality describes the allowable lengths for the board?
(A) |x-0.25| ≤ 40.50
(C) |x-40.50| ≤ 0.25
(B) |x+0.25| ≤ 40.50
(D) |x-0.25| ≤ 40.75
The inequality that describes the allowable lengths for the board is |x - 40.50| ≤ 0.25
How to determine which inequality describes the allowable lengths for the board?The given parameters are
Length = 40.50 cm
Tolerance = 0.25 cm
The inequality that describes the allowable lengths for the board is represented as:
|x - Length| ≤ Tolerance
This gives
|x - 40.50| ≤ 0.25
Hence, the inequality that describes the allowable lengths for the board is |x - 40.50| ≤ 0.25
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a. A supermarket displays cans in a triangle. Write an explicit formula for the sequence of the number of cans.
Explicit expressions help represent all members of a sequence in one expression. The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and each term in the sequence can be computed without knowing the other terms in the sequence.
In general, an explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.
Explicit expressions are always used to represent any term in a sequence without describing any other term in the sequence. The meaning of "explicit" is direct, which can be found directly without knowing the other terms in the sequence.
The explicit formula for the sequence of cans will be,
an=a+(n-1)
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CUANTO ES 4:5=16:20 ????? AYUDA PORFIS SE LOS VOY A AGRADESER MUCHISIMO
The total entrance fee for a group of 4 adults and 3 children to a water park is $220.
The total fee for a group of 2 adults and 1 child is $98. Determine the entrance fee for
an adult and the entrance fee for a child.
What does the solution represent in terms of this situation?
The entrance fee in the water park for the adult $37 and for the child are $24.
What basically is a two-variable linear equation?The maximum power of a variable in a linear equation of two variables is one.
A linear equation with two variables raised the same power is a two-variable equation.It is written as ax + by + c = 0, where a, b, and c have all become real numbers, but a and b remain not equal to zero.3x + 9y = 5 and -x + 8y = 6 are both two-variable linear equations.Now, for the question's given condition;
Let the cost for the adult is 'x'.
Let the cost for the child is 'y'.
The total cost for entrance fee is $220.
The group of 4 adults and 3 children costs 220.
4x + 3y = 220 ........equation 1
The group of 2 adults and 1 child costs $98.
2x + y = 98 .........equation 2
Use elimination method to solve the equations;
x = 37 and y = 24.
Therefore, the entrance fee in the water park for the adults is $37 and for the child us $24.
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for the love of GOD PLS ONLY ANSWER IF YOU ARE SURE.
I NEED quick and CORRECT answer ASAP I have been working all day and I feel so stressed and upset ... tbh I have overworked myself. AND THERES STILL MORE GOD JESUS. So please, PLEASE help me. and SERIOUSLY help me and don't just take advantage of the fact I offered a lot of points... thank you brainly community
Answer:
Check the attached screenshot! :)
Step-by-step explanation:
Check the attached screenshot! Let me know if you have any questions! :)
Answer:
1 - 3 -2 -4
Step-by-step explanation:
expand them all
.000000092
.058
.0544
2400 so you can see the least to greatest is 1 3 2 4
Simplify the expression.
-11-4 / 12-(-9)
The simplified form of expression is -5/7.
To simplify the expression, we will solve the equation to convert them in smallest divisible fraction.
For this, firstly solving the numerator of fraction and then solving the denominator of fraction.
Solving numerator -
Numerator = -11 -4
We will perform addition along with keeping the answer with negative sign
Numerator = -15
Solving denominator -
Denominator = 12 - (-9)
Here two negative signs are present, so we will perform addition. Also, the sign of result will also be positive
Denominator = 12 + 9
Performing addition
Denominator = 21
Now, representing in fraction form to simplify the expression -
Expression = -15/21
Dividing the fraction by 3
Expression = -5/7
Hence, the simplification of given expression is -5/7.
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