Answer:
1.6
Step-by-step explanation:
4,4-2.8 = 1.6
6-4.4 = 1.6
7.6-6 = 1.6
Then common difference is 1.6
what is the sum of the series
Answer: 925
Step-by-step explanation:
This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.
Using the sum of an arithmetic series formula, we get the sum is:
[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]
perform the following operation.
-49 - +65 =
Answer:
Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45
Help please I need as quick as possible!
Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]
Step-by-step explanation:
This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.
To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.
For the top right, the first term is 4(0)+5=5, which does not match the first term of the given sequence.For the bottom right, the first term is 4(1)+5=9, which does match the first term of the given sequence.what is the number whose 10% is 12?
Answer:
120
Step-by-step explanation:
10%=12
20%=12x2
100%=12x10
=120
Answer:
Let the number be x.
Compute 10% of x and equate it to 12 to compute the value of x as follows:
[tex]x[/tex] x [tex]\frac{10}{100} = 12[/tex]
[tex]x[/tex] = 12 x [tex]\frac{100}{10}[/tex]
[tex]x[/tex] = 120
Thus, the number is 120.
Which of the following is a root of the polynomial function below?
In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)
How to determine the roots of a cubic equation
In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.
The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7
x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2
In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)
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how many lines of symmetry does the following figure have ?
Answer:
1
Step-by-step explanation:
It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.
Answer: 1
Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition.
The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The associative property states that when adding or multiplying it can be represented by:
(a + b) + c = a + (b + c)
For multiplication:
a * (b * c) = (a * b) * c
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A linear function contains these points: (0,-1) & (3,8)
What is the slope and y-intercept of this function?
Answer:
slope: 3
y-intercept: (0, -1)
Find slope:
[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given points are: (0, -1), (3, 8)
[tex]\rightarrow \sf slope : \dfrac{8-(-1)}{3-0} = \dfrac{9}{3} = 3[/tex]
When finding y-intercept, the value of x is 0. Here given y is -1 when x is 0.
y-intercept: -1 or (0, -1)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
If a linear function contains these points: (0,-1) and (3,8), what is its slope and y-int.?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Formula utilised, here [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
Put in the values,
[tex]\bf{\dfrac{8-(-1)}{3-0}}[/tex] | subtract on top and bottom
[tex]\bf{\dfrac{9}{3}}[/tex] | divide on top and bottom
[tex]\bf{3}[/tex]
The y-intercept is the second co-ordinate of the point (0,-1)
[tex]\bf{Which\;is\;-1}[/tex].
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{\begin{cases} \bf{Slope=3} \\ \bf{Y-int. -1} \end{cases}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1 \theta l}}[/tex]
A comedy club's nightly revenue from the sale of x tickets is given by R = 15x and its
nightly costs are given by C= 1.25x + 495. How many tickets need to be sold each night
to break even? In other words, when will revenue equal costs?
Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.
What is the break-even point?The break-even point is when the revenue and the costs are equal.
In this problem, the equations are given as follows:
R(x) = 15x.C(x) = 1.25x + 495.At the break-even point:
R(x) = C(x)
15x = 1.25x + 495
13.75x = 495
x = 495/13.75
x = 36.
36 tickets have to be sold each night to break even.
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Pre-Test Active
2 3
5 6
7
9 10
Which formula should be used to find the circumference of a circle?
O C-nd
O C-2nd
0 С-яг
OC-4
Save and Exit
Mark this and return
Next
TIME REMAINING
45:32
Submit
Answer:
C = 2√(πA) units
Step-by-step explanation:
Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time.
The recursive function that gives the number of books Ashley has at any time is
=
, starting at
.
The recursive formula would be: 100 - XN = B.
What is Recursive formula?
When a function calls itself and uses its own previous terms to define its subsequent terms, it is called a recursive function. It is the technical recursive function’s definition, i.e., a recursive function builds on itself.
X: represents how many weeks
N: represents books per week
B: represents books she has at anytime
So the recursive formula would be: 100 - XN = B
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Question in image, it asks to show your work
Answer:
• f(g(x)) = [tex]\sqrt{x^{2} + 1}[/tex] + 8
• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65
Step-by-step explanation:
• f(g(x)) = f(x² + 1)
= [tex]\sqrt{x^{2} + 1}[/tex] + 8
• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )
= [tex](\sqrt{x } + 8)^{2}[/tex] + 1
= x + 16[tex]\sqrt{x}[/tex] + 64 + 1
= 16[tex]\sqrt{x}[/tex] + x + 65
Please help! Solve the equation on the interval [0,2pi)
Answer:
[tex]\frac{5pi}{6}[/tex]
Step-by-step explanation:
Answer:
[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]
Therefore, the value of x in the interval [0, 2π) is:
[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]
please i need it so badl please
The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age. How old is Damien now?
Answer:
Damien is 74 years old now
Step-by-step explanation:
Define the variables:
Let d = age of DamienLet k = age of KeyannaGiven information:
The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age.From the given information, create 2 equations:
Equation 1: d + k = 100
Equation 2: d - 10 = 4(k - 10)
Rewrite Equation 1 to make k the subject:
⇒ k = 100 - d
Substitute this into Equation 2 and solve for d:
⇒ d - 10 = 4(100 - d - 10)
⇒ d - 10 = 400 - 4d - 40
⇒ d - 10 = 360 - 4d
⇒ d - 10 + 10 = 360 - 4d + 10
⇒ d = 370 - 4d
⇒ d + 4d = 370 - 4d + 4d
⇒ 5d = 370
⇒ 5d ÷ 5 = 370 ÷ 5
⇒ d = 74
Therefore, Damien is 74 years old now.
Which expression is the simplest form of - (4x³ + x²) + 2 (x³ − 3x²)?
OA. -2³ - 7x²
OB.
B. -2x³-5x2
O C.-6x³ - 2x²
OD. -6x³6x²
The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².
What is the simplest form of the expression?The expression given in the task content whose simplest form is to be determined is;
- (4x³ + x²) + 2 (x³ − 3x²)
Hence, upon opening up the parentheses, it follows that;
-4x³ - x² +2x³ -6x²
Upon collection and summing up of like terms; -2x³ -7x².
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Classify each of the following variables as quantitative or qualitative. For those which are quantitative, classify them further as continuous or discrete.
a) Weight of adult females
b) Street addresses in Addis Ababa
c) Years of professional experience of employees
d) Number of courses offered to students in AAU in this semester.
Answer:
a) quantitative - continuous
b) qualitative
c) quantitative - discrete
d) quantitative - discrete
Explanation:
A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.
A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.
As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 90 milligrams of Medication A with 72 milligrams of Medication B. However this week, the doctor said to only use 8 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
The Medication A mixed this week should be 10 milligrams.
We have,
Medications to be mixed in the proper proportions.
Last week's proportions as the doctor indicated ;
Medication A = 90 milligrams
Medication B = 72 milligrams
This week's proportions as doctor indicated;
Medication B = 8 milligrams
Let, Medication A = x milligrams
As we are instructed to mix the Medication in the proper proportions,
So,
According to the question,
90/72 = x/8
10/8 = x/8
⇒ x = 10 milligrams
Here, the Medication A mixed is 10 milligrams.
Therefore, the Medication A mixed this week should be 10 milligrams.
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multiplicity of F(x)= 4x^3+19x^2-41x+9
The multiplicity of the function is 1 for each term after factorization.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial function:
[tex]\rm F(x)= 4x^3+19x^2-41x+9[/tex]
After factorization:
[tex]\rm F(x) = \left(4x-1\right)\left(x^2+5x-9\right)=0[/tex]
[tex]\rm F(x) =(4x-1)^1(\:x-\frac{-5+\sqrt{61}}{2})^1(\:x+\frac{-5-\sqrt{61}}{2})^1[/tex]
The multiplicity of the function is 1 for each term.
Thus, the multiplicity of the function is 1 for each term after factorization.
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A car has a maximum speed of 355.7 feet/second. Convert this speed to miles/hour.
Answer:
242.5226626 mphStep-by-step explanation:
1 ft/s = 0.681818 mph
355.7 * 0.681818 = 242.5226626
355.7 ft/s = 242.5226626 mph
Given that log 2= 0.30103 and log 3= 0.47712. Evaluate log 12
Answer:
log12=log(2.2.3)
=log2+log2+log3
=0.30103+0.30103+0.47712
=0.60206+0.47712
=1.07918
(10^4)^4 as an expression (simplified)
[tex](10^4)^4[/tex]
[tex]10^8[/tex]
Therefore in simplified form [tex](10^4)^4[/tex] is [tex]10^8[/tex]
Point T is at (–16.8, 31.7) and point M is at (1.2, 12.5). Point M is the midpoint of the line segment whose endpoints are S and T. What are the coordinates of endpoint S? (–34.8, 50.9) (–7.8, 22.1) (19.2, –6.7) (20.4, –5.5)
Answer:
option c (19.2, -6.7) is correct
Step-by-step explanation:
Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.
if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is
given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]
according to question :
given : end point T(-16.8, 31.7) and mid point M(1.2, 12.5)
let coordinates of another end point S (a, b)
therefore, using mid point formula
1.2 = (-16.8 + a)/2
2.4= (-16.8 + a)
19.2 = a
and,
12.5 = (31.7 + b)/2
25 = 31.7 + b
-6.7 = b
so the option c (19.2, -6.7) is the correct answer
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Find the volume of a cone that has a diameter of 7 and a height of 8.
98/3 Pi
448/3 Pi
131 Pi
24 Pi
On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
A restaurant uses 80 pounds of potatoes per week. The restaurant owner buys the potatoes in 10-pound bags from a local farmer. How many bags will the owner need to buy this week?
Answer:
1. santina drove 14 more miles than carole
2. the owner will need to buy 8 bags this week
Step-by-step explanation:
1. 203-189= 14
2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds
1. 14
2. 8
3. 48
4. 318
5. 23
6. 4
7. a) 10 b) 60 c) 8 d) 107
8. $1,532
9. 1
10. $15.50
11. .95
Step-by-step explanation:
Piece Wise function Math...help!
The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.
What is a function?A function is a type of relation, or rule, that maps one input to a specific single output.
Given
Base salary = $2500 per month
Commision = 3% on Sales over 48000
Determine the function s(x) for sales over $48000
Let's Represent the total sales in a month with s.
So, the function s(x) is:
s(x) = Base Amount + Commission x Sales over $48000
s(x) = 2500 + 3% (s - 48000)
s(x) = 2500 + 0.03(s - 48000)
s(x) = 2500 + 0.03s - 1440
s(x) = 0.03s - 1060
Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.
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The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie? Express your answer as a simplified fraction or a decimal rounded to two places.
Need help with the following question
OLLEGE
>
For the given functions, find (fog)(x) and (gof)(x) and the domain of each.
f(x) = 4x + 1, g(x)=√x
(fog)(x) =
(gof)(x) =
The domain of fog is ☐.
(Type your answer in interval notation.)
The domain of g of is.
(Type your answer in interval notation. Use integers or fractions for any numbe
Part 1
[tex](f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1[/tex]
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is [tex]\boxed{[0, \infty)}[/tex]
Part 2
[tex](g \circ f)(x)=g(4x+1)=\sqrt{4x+1}[/tex]
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,
[tex]4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}[/tex]
Thus, the domain in interval notation is [tex]\boxed{\left[-\frac{1}{4}, \infty)}[/tex]
Value of x or y so that the line through the points has the given slope:
(X,9) and (9,-3), slope is -6/7
Sorry if it’s not worded great.
If we want the slope to be -6/7, then the value of x must be -5.
How to find the value of x?Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:
[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]
Where on the second line we multiplied and divided the right fraction by 2.
Comparing the fractions, we see that we must have:
9 -x = 14
9 - 14 = x
-5 = x
So the value of x must be -5.
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when finding the margin of error of the mean of a normally distributed population from a sample, what is the critical probability, assuming a confindence level of 58%
The critical probability, assuming a confindence level of 58% is 0.79.
How to calculate probability?From the information given, the confidence level is 58%. The alpha will be:
= 1 - (58/100)
= 1 - 0.58
= 0.42
The critical probability will be:
= 1 - (0.42/2)
= 1 - 0.21
= 0.79
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