Answer:
The value of f(-3) + f(5) is 10
Step-by-step explanation:
Given;f(x) = -2x + 7f(-3) + f(5)So,
f(-3) = -2x + 7
f(-3) = -2(-3) + 7
f(-3) = 6 + 7 = 13
f(5) = -2x + 7
f() = -2(5) + 7
f(5) = -10 + 7 = -3
Here, The value of f(-3) + f(5)
= f(-3) + f(5)
= 13 + (-3)
= 13 - 3
= 10
Thus, The value of f(-3) + f(5) is 10
A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model:
Salary = β0 +β1 Service + ε. The following ANOVA table below shows a portion of the regression results.
df SS MS F
Regression 1 555,420 555,420 7.64
Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value
Intercept 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
Which of the following is the monthly salary of an employee that has worked for 48 months at the bank?
rev: 11_17_2017_QC_CS-109762
$441.
$785.
$1,050.
$1,226.
The monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.
The given table is:
Df SS MS F
Regression 1 555,420 555,420 7.64
Residual 27 1,962,873 72,699
Total 28 2,518,293
Coefficients Standard Error t-stat p-value
Intercept 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
We have to find the monthly salary of an employee that has worked for 48 months at the bank.
Salary = β(0)+ β(1) Service
y = β(0)+ β(1)x
where, Service = x(in months)
Service = y(in $)
From the table
y = 784.92+9.19x
If x=48 months
Then, y = 784.92+9.19(48)
y = 784.92+441.12
y = 1226.04
Hence, the monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.
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Find the inverse of the equation
Y=5/x-1
The inverse of the equation is y = (5/x) + 1
How to determine the inverse of the equation?From the question, we have the following parameters that can be used in our computation:
y = 5/(x - 1)
Start by swaping the positions of x an dy
So, we have the following representation
x = 5/(y - 1)
So, we have
x(y - 1) = 5
Divide both sides by x
y - 1 = 5/x
Add 1 to both sides
y = (5/x) + 1
Hence, the inverse is y = (5/x) + 1
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In the United States about 7% of the male population and about 0.4% of the female population is red-green color blind ( that is they cannot distinguish red from green, or see red and green differently from how others do). The population in the United States consist of about 49% males and 51% females. A person is randomly selected.
Let M be the event that the person is male, let F be the event that the person is female, let CB be the event that the person is red-green color blind, and let NC be the event that the person is not red-green color blind
A. Find P(CB \mid M)
B. Find P(CB \cap M)
C. Find P(CB)
Find P(M \mid CB)
Ans (A) P(CB/M) is 0.07
Ans (B) P(CB ∩ M) is 0.0343
Ans (C) P(CB) is 0.03634
Ans (D) P(M/CB) is 0.94386
Let the population be 100.
Therefore,
No. of males (M) = 49
No. of females (F) = 51
No. of colourblind males =
[tex]\frac{7}{100} * 49 = \frac{343}{100} = 3.43[/tex]
No. of colourblind females =
[tex]\frac{0.4}{51} * 100 = 0.204[/tex]
Total colourblind people (CB) = 3.43 + 0.204 = 3.634
Ans (A)
P(CB/M) = P(CB ∩ M)/P(M) = 3.43/49 = 0.07
Ans (B)
P (CB ∩ M) = 3.43/100 = 0.0343
Ans (C)
P(CB) = 3.634/100 = 0.03634
Ans (D)
P (M/CB) = P(M ∩ CB)/P(CB) = 3.43/3.634 = 0.94386
These are the answers.
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Need answers for all parts.
(a) The balance be at the end of the year is $502.53.
(b) The Effective annual interest rate is 0.5%.
(c) The Effective annual interest rate must be less than 6%.
What is effective annual interest rate?
The percentage of interest on a loan or financial product that would apply if compound interest built up over a year without any payments would be called the effective interest rate, also known as the effective annual interest rate, annual equivalent rate, or simply effective rate.
Given:
P = $500, n = 12, r = 0.5% = 0.005, t = 1
So, the balance be at the end of year is,
[tex]A = P(1+\frac{r}{n})^n^t \\A = 500(1+\frac{0.005}{12})^1^2^*^1 \\A = 500(1.00042)^1^2\\A = 502.53[/tex]
Now to find the effective annual interest rate,
Effective annual interest rate = [tex]= (1+\frac{r}{n})^n-1 = (1+\frac{0.005}{12})^1^2 - 1= 0.005[/tex]
Effective annual interest rate = 0.5%
So, the Effective annual interest rate must be less than 6%.
Hence,
(a) The balance be at the end of the year is $502.53.
(b) The Effective annual interest rate is 0.5%.
(c) The Effective annual interest rate must be less than 6%.
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A set of data items is normally distributed with a mean of 300 and a standard deviation of 60. Why’d the data item in this distribution that corresponds to the given z-score
Z= 2.5
The data item that corresponds to the z-score of 2.5 is 450.
What is Standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.
A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Although less robust in practice, it is algebraically easier than the average absolute deviation. The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, makes it a valuable statistic.
As, x = z×s + u, where z=2.5, s=60, u=300
⇒ x = 2.5×60 + 300
⇒ x = 150 + 300
⇒ x = 450
The data item that corresponds to the given z-score is 450.
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I’ve been struggling on this question please help ASAP <333
actuarial math, see attached
The total accumulated value if $1000 is deposited starting from 2017: (a) using the investment year value is $1897 and (b) Using the portfolio method is $1280.50
How to calculate the value of investment?You should be aware that the investment year rates are divided into three. Therefore, sum the rates to get the total rate for the years
(a)
Using the investment year method
Total rate for the investment year is
10.0%+10.0%+9.9%=29.9%
The investment value is=$1000
=29.9%*$1000
=0.299*1000
=$299*3 years= $897
After three years = $(1000+897)
=$1897
(b) Using the portfolio method
rate=9.35%
Value=$1000
=9.35%*1000
0.0935*1000
=$93.5
After 3 years, from 2017 = $[1000+(3*93.5)]
=$(1000+20.5)
=$1280.5
In conclusion, the total accumulated value if $1000 is deposited starting from 2017: (a) using the investment year value is $1897 and (b) Using the portfolio method is $1280.50
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Evaluate the function when x = 3, x = 0, and x = -4. (Lesson 4.8)
14. f(x) = -4x + 3
12. h(x) = − 8x
13. g(x) = 5x - 9
16. h(x) = 1.4x
15. g(x)=-3x - 12
17. f(x) = 1/4x
12-17 please
Select the table that represents a liner function. (Use graph if necessary)
The table that represents a linear equation is the first one, and the line is:
y = 5x + 5
Which table represents a linear function?
To check which table represents a linear function, you need to identify the increases in x, and check that al the increases/decreases in y are constant.
For example, if you look at the last table:
x = 0, 1, 2, 3
y = 1, 2, 4, 8
First x goes from 0 to 1, so 1 unit increase.
y goes from 1 to 2, 1 unit increase.
Then x goes from 1 to 2, 1 unit increase.
y goes from 2 to 4, 2 units increase.
The increase is not constant, thus it is not a linear equation.
The tables 2 and 3 can be discarded because have both increases/decreases.
Table 1 is the one that represents a linear equation:
x: 0, 1, 2, 3
y: 5, 10, 15, 20
Where the increases in y are always of 5 units, and the linear equation is:
y = 5*x + 5
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The coordinates of C are ( 4 , 4 ) , and the midpoint of CD ¯ is at M ( - 2 , - 6 ) . What are the coordinates of point D
Answer:
D (-8, -16)
Step-by-step explanation:
(4+x)/2 = -2
4+ x = -2 · 2
4 + x = -4
x = -4 - 4
x = -8
(4 + y)/2 = -6
4 + y = -6 · 2
4 + y = -12
y = -12 - 4
y = -16
check the screenshot
Answer:
a = 1
h = 4
k = -4
Step-by-step explanation:
To find the slope of a curve at a given point, we simply differentiate the equation of the curve and find the first derivative of the curve, i.e., dy/dx.
To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result
The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line
To find the slope of the curve at a given point
First differentiate the given equation of the curve with respect to x
That is dy / dx.
The derivative of the equation of the curve is the slope of the curve.
In next step substitute the value of x in the slope of the curve
The result will be the slope of the curve at a given point
Therefore, these are the steps to find the slope of the curve
I have answered the question in general, as the given question is incomplete
The complete question is:
How to find the slope of a curve at a given point?
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t^2-t-6/t^2+6+9 • t+3/t^2-4
if the correlation coefficient r is equal to 0.726, find the coefficient of determination and the coefficient of nondetermination.
Coefficient of determination ([tex]r^{2}[/tex]) = 0.527 and Coefficient of non-determination ( [tex]1-r^{2}[/tex]) = 0.473
The coefficient of correlation is the “R” value which is given in the summary table in the Regression output. R square is also called the coefficient of determination. To find the value of R squared, multiply R by R. In other words, the square of the correlation coefficient is the coefficient of determination. The coefficient of determination is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable when predicting the outcome of a given event.
The Coefficient of Non-Determination explains the amount of unexplained, or unaccounted-for, variance between two variables, or between a set of variables (predictors) in an outcome variable.
Given,
r = 0.726
Coefficient of determination ([tex]r^{2}[/tex]) = 0.527
Coefficient of non-determination ( [tex]1-r^{2}[/tex]) = 0.473
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Information for Questions 5-7: The Annual Survey of Colleges in the U.S. also reports on the average amount of student loan debt by state. The most recent data by state showed an approximately normal shape with a minimum average amount of
$19,000
and a maximum average amount of
$38,000
. Use the minimum and maximum value and the normal shape to estimate the mean and standard deviation of the data for the 50 states. (Mean and standard deviation have been rounded to the nearest
$100
.) a. mean
=$25,000;
standard deviation
=$3,500
b. mean
=$26,800;
standard deviation
=$2,100
c. mean
=$26,800;
standard deviation
=$3,700
d. mean
=$28.500;
standard deviation
=$1,800
e. mean
=$28,500;
standard deviation
=$3,200
A federal study of student loan debt plans to focus on those states with the highest amounts of student loan debt. The study plans on targeting those states that fall in the top
2.5%
in terms of average student loan amounts. What is the cutoff point that would place a state in the top
2.5%
based on student loan debt? (Use the mean and standard deviation estimates from Question #5.) a.
$38,100
b.
$34,900
c.
$31,700
d.
$32,500
e.
$22,100
The correct answer is $34900.
X : Average amount of loan of student debt by state .
X = N ( μ = $28500 , σ² = ( 3200 )² )
To find : What is the cutoff point that would place a state in top 2.5%
Let it be X
P( X > x ) = 0.025
P(X-μ/σ > X - 28500/3200) = 0.025
P(z >Z ) = 0.025
1 - P(z<Z ) = 0.025
P(z<Z ) = 0.975
φ(z) = 0.975
Z = φ⁻¹(0.975)
X - 28500/3200 = 1.96
X = 34772
i.e; P(X > 34772) = 0.025
Since, it is nearly equal to $34900 option b is correct.
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A recipe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made using 2 gallons of milk?
Answer:
what we cookin ma boi
Step-by-step explanation:
write the square root function stretched by 2 then shifted so that its turning point is located at (3,-5)
Answer:
the square root function stretched by 2 and shifted so that its turning point is located at (3,-5) is h(x) = 2 * sqrt(x + 3) - 5.
Step-by-step explanation:
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x) = (4 - x)x^-3 for x > 0. (a) Find the t-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither for the function f. Justify your answer. (b) Find all intervals on which the graph of f is concave down. Justify your answer. (c) Given that f(1) = 2, determine the function f.
x=4 is the t-coordinate of the f's critical point. For the function f, ascertain whether the point is a relative maximum, relative minimum, or neither.
Given that,
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x) = (4 - x)/x³ for x > 0
We have to find
(a)Discover the t-coordinate of the f's critical point. For the function f, ascertain whether the point is a relative maximum, relative minimum, or neither.
We know that,
f'(x) = 4-x/x³ = 4/x³ - 1/x²
Critical point f'(x)=0
4-x/x³=0⇒x=4
Therefore, x=4 is the t-coordinate of the f's critical point. For the function f, ascertain whether the point is a relative maximum, relative minimum, or neither.
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8 ft 10 ft Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate . A = [?]ft? Notice that only half of the circle is included in the figure!
find the area of the rectangle;
w x l = 8 x 10 = 80ft^2
circle;
pi(r)^2
r = 4
pi(4)^2
pi(16) = 50.24
80 + 50.24 = 130.24
PLEASE HURRY HELP FAST ILL GIVE BRAINALIEST
The price of a video game is $32.99 before tax. Andre bought the video game for 20% off. He then paid 8% sales tax on the discounted price.
Part A: How much did Andre pay in sales tax? Show all work and steps in your solution.
Part B: What is the total amount that Andre paid for the video game? Show all work and steps in your solution
Answer: $28.50
Step-by-step explanation:
(a) 20% of $32.99 = 6.598 so the discounted price is $32.99 - $6.60 (rounded) = $26.39 then 8% of $26.39 = $2.11 so the sales tax is $2.11. (b) the total amount Andre paid for the video game is $26.39 + $2.11 = $28.50.
Pls Brainliest?
Answer:
Step-by-step explanation:
part A $32.91 $32.99-8% = 32.91
part B $32.71 ($32.99-20%)-8% = 32.71
Your family ate a delicious meal at Jimmies of Savin Rock. The meal itself cost $147.25, you want to leave 20% tip and there was 7.35% tax added
Answer:
27.29 honestly this is a wild guess
Step-by-step explanation:
7.35% of 147.25 = 10.82
147.25-10.82=136.43
20% of 136.43 = 27.286(27.29)
Consider the drawing and information below. The drawing is NOT to scale.
1.What is m < 2 show work and calculations.
2. What is m < 4 show your work and calculations.
Answer:
m∠2 = 110°
m∠4 = 110°
Step-by-step explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Transitive Property of Equality
If any angles are congruent to the same angle, then they are congruent to each other.
--------------------------------------------------------------------------------------
As line p is parallel to line q, according to the Corresponding Angles Postulate:
⇒ m∠2 = m∠10
According to the Vertical Angles Theorem:
⇒ m∠10 = m∠13
According to the Transitive Property of Equality:
⇒ m∠2 = m∠13
Therefore:
⇒ 8x + 14 = 10x - 10
⇒ 8x + 14 - 8x = 10x - 10 - 8x
⇒ 14 = 2x - 10
⇒ 14 + 10 = 2x - 10 + 10
⇒ 24 = 2x
⇒ 2x = 24
⇒ 2x ÷ 2 = 24 ÷ 2
⇒ x = 12
Substitute the found value of x into the expression for the measure of angle 2:
⇒ m∠2 = 8(12) + 14
⇒ m∠2 = 96 + 14
⇒ m∠2 = 110°
--------------------------------------------------------------------------------------
As line p is parallel to line q, according to the Corresponding Angles Postulate:
⇒ m∠12 = m∠4
⇒ 15y + 5 = 13y + 19
⇒ 15y + 5 - 13y = 13y + 19 - 13y
⇒ 2y + 5 = 19
⇒ 2y + 5 - 5 = 19 - 5
⇒ 2y = 14
⇒ 2y ÷ 2 = 14 ÷ 2
⇒ y = 7
Substitute the found value of y into the expression for the measure of angle 4:
⇒ m∠4 = 13(7) + 19
⇒ m∠4 = 91 + 19
⇒ m∠4 = 110°
HELPP!!!!! HURRY!!!! Function g(x) = |x − 9| is a transformation of function f(x) = |x|. What effect does the value 9 have on the graph of function f? A. It translates the graph 9 units to the left. B. It translates the graph 9 units to the right. C. It vertically compresses the graph by a factor of 9. D. It vertically stretches the graph by a factor of 9.
Answer:
C
Step-by-step explanation:
Answer:
B: It translates the graph 9 units to the right.
Step-by-step explanation:
The value 9 has the effect of translating the graph of function f(x) = |x| 9 units to the right. This is because the transformation g(x) = |x - 9| is obtained from f(x) = |x| by subtracting 9 from the argument of the absolute value function. This has the effect of shifting the graph of f(x) to the right by 9 units.
Therefore, the correct answer is B: It translates the graph 9 units to the right.
I’m confused on this question
Answer: 3 of the squares should go down then 8 to the right.
Step-by-step explanation:
it just wants you to say how it was translated so take the corresponding points like p and p’ then count of many tiles it move to the right and then down to get from p to p’ you’ll see that it’s 8 right and 3 down.
hope this helps!
Use a scatterplot and the linear correlation coefficient rr to determine whether there is a correlation between the two variables. (Note: Use software, and don't forget to look at the scatterplot!)
x| 0.8 1.6 2.7 3.3 4.2 5.8 6.5 7 8.9 9.3 10.8 11.3 12.4 13.7 14.9
y| 3.8 1.9 12.6 9.4 8.2 7.1 4.1 0.1 11.9 13.3 14.1 8.5 9.6 7.4 14.1
r=
For given data the scatterplot is shown below and the linear correlation coefficient is r = 0.4693
In this question we have been given a data.
We need to use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation between the two variables.
Given data is:
x| 0.8 1.6 2.7 3.3 4.2 5.8 6.5 7 8.9 9.3 10.8 11.3 12.4 13.7 14.9
y| 3.8 1.9 12.6 9.4 8.2 7.1 4.1 0.1 11.9 13.3 14.1 8.5 9.6 7.4 14.1
The scatter plot for given data is as shown below.
An equation of the line of best fit is: y = 0.4623x + 4.9176
And the coefficient of correlation is:
r = √0.2202
r = 0.4693
Therefore, the scatterplot of given data is shown below.
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using the empirical rule, approximate the percentage of newborn pigs that weight between 3.75 and 4 lbs.
Answer:
Answer: 0.4419
Step-by-step explanation:
Given: The birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7.
i.e.
Let X denotes the birth weight.
Then, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is given by :-
Hence, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is 0.4419 .
Step-by-step explanation:
If repeated samples of yogurt sales were taken, according to the Central Limit Theorem, the mean of those repeated samples would tend to be normally distributed if the sample size is large enough.
Because the sample population is ________, it is safe to apply the Central Limit Theorem, even if the sample size for each sample is 15.
a.)negatively distributed
b.)positively distributed
c.)normally distributed
Because the sample population is normally distributed, it is safe to apply the Central Limit Theorem, even if the sample size for each sample is 15.
(this means that option c is correct).
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample means with size n of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], with mean and standard error given as follows:
Mean: [tex]\mu[/tex]Standard error: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]The Central Limit Theorem can be applied when at least one of these two conditions is true.
Underlying population has a normal distribution.The sample size is greater than 30.In this problem, the sample size is of 15, which is less than 30, meaning that the Central Limit Theorem can be applied only because the underlying population is normally distributed, meaning that option c is correct.
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geometry midterm coming up and i need help on similar figures.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
By Pythagoras' theorem,
(20)²+(48)²=x²
400+2304=x²
2704=x²
x=52
As we know, area of a triangle = 1/2 × b×h
480= 1/2× 52 ×h
h=2×480/52
h= 18.46 = BD
What is geometry?
Geometry with arithmetic is one of the oldest branches of mathematics. It deals with spatial properties such as distance, shape, size, and relative position of shapes. Mathematicians working in the field of geometry are called geometers.
Until the 19th century, geometry was mostly devoted to Euclidean geometry, which included the concepts of point, line, plane, distance, angle, area, and curve as basic concepts.
In the 19th century, several discoveries dramatically expanded the scope of geometry. One of the oldest discoveries of this kind is Carl Friedrich Gauss's Theorem Egregium ("Remarkable Theorem"), which loosely asserts that the Gaussian curvature of a surface is independent of any particular embedding in Euclidean space. I'm here. This meant that surfaces could be studied intrinsically, i.e., as spaces themselves, and extended to manifold theory and Riemannian geometry.
Therefore, A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
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9
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Bonnie withdrew $1,200 from her savings account. She spent of the money on travel arrangements. She spent of the remaining amount at the
hardware store. Finally, she treated her friend to lunch with some of the remaining money. After lunch, Bonnie had $300.50 left. How much money did
Bonnie spend on lunch?
Bonnie spent $
on lunch.
Reset
Next
According to the given information $19.50 money did Bonnie spend on lunch.
What sort of equation would that be?The description of an equations in algebra is a quantitative expression that demonstrates the equality of two mathematical expressions. Thus instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which have been separated by the 'equal' sign.
Briefing:The amount withdrew by Bonnie is $1200.
1/5 of the money withdrawn is used for travel arrangements.
the hardware shop for 2/3 of the remaining sum.
After lunch Bonnie had left with 300.50.
spent 1/5 on travel : 1/5(1200) = 1200/5 = 240
1200 - 240 = 960
she spent 2/3 on the hardware : 2/3(960) = 1920/3 = 640
960 - 640 = 320
320 - lunch = 300.50
320 - 300.50 = lunch
19.50 = lunch
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16. The points graphed below show the how completing homework can affect a student's test scores.
What is the meaning of the slope of the line in
the context of the problem?
A student's test score goes down 20 points
every time they complete 2 homework
assignments
A student's test score goes up 9 points every
time they complete 1 homework assignment
A student's test score goes down 10 points
every time they complete 1 homework
assignment
A student's test score goes 80 points every
time they complete 1 homework assignment
The meaning of slope of the line in the context of the problem is a student's test score goes up 9 points every time they complete 1 homework assignment.
What is Slope?Slope of line is shows how much a line is inclined with respect to the X axis. In other words, it can also be defined as the change in y coordinates with respect to the change in x coordinates.
Slope of the line can be calculated if two points (x₁, y₁) and (x₂, y₂) are given as,
Slope = (y₂ - y₁) / (x₂ - x₁)
From the graph, take any two points on the line.
For instance, we take initial point (1, 20) and final point (10, 100).
Slope = (100 - 20) / (10 - 1)
= 80/9
≈ 9
From the definition of slope, slope equals 9 means y values goes 9 points up with respect to one unit up in the x values.
Hence we got that a student's test score goes up 9 points every time they complete 1 homework assignment.
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