Final answer:
Upon setting up an equation with the given information, we find that the shop sold 275 hamburgers on Sunday.
Explanation:
To find out how many hamburgers were sold on Sunday when the hamburger shop sold a combined total of 498 hamburgers and cheeseburgers, we can set up an equation. Let's denote the number of hamburgers as H and cheeseburgers as C. We are given that there were 52 fewer cheeseburgers sold than hamburgers, so we can express this as C = H - 52.
Since the total number of burgers sold was 498, we can also set up the following equation: H + C = 498. Substituting for C, we get H + (H - 52) = 498. Solving this equation, we get 2H - 52 = 498. Adding 52 to both sides gives us 2H = 550, and dividing by 2 gives us H = 275.
Therefore, the shop sold 275 hamburgers on Sunday.
An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3
Answer:
easey
Step-by-step explanation:
ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of A after both reflections?
(-2, -7) (-2, 7) (7, -2) (7, 2)
Answer:
option C) (7, -2)
Step-by-step explanation:
By the graph, the initial coordinates of point A are ( -5, -4)
first reflection along the line x=1, only the x coordinate will change.
the new x coordinate is = x = 7
thus the point becomes (7, -4)
similarly, reflection along y= -3, only the y coordinate will change.
the new y coordinate is = y = -2
thus the final coordinates are (7, -2)
A certain component is critical to the operation of an electrical system and must be replaced immedi- ately upon failure. If the mean lifetime of this type of component is 100 hours and its standard devi- ation is 30 hours, how many of these components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least .95?
Answer:
n=23
Step-by-step explanation:
Answer explained in the attachment .
The equation d=11cos(8pi/5 t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance. A. 0.625 seconds B. 0.8 seconds C. 1.25 seconds D. 1.6 seconds
Answer:
The time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Step-by-step explanation:
Given the equation
[tex]d = 11cos( \frac{8\pi}{5}*t)[/tex]-----------Equation 1
where d, in inches of the pendulum of a grandfather clock from the center.
Comparing with the standard equation of an oscillating pendulum bob.
[tex]d = Acos (wt + \alpha )[/tex] ----------Equation 2
where ω = angular velocity
t = time taken
α = The angular displacement when t = 0
Comparing equation 1 and 2,
α = 0
[tex]w =\frac{8\pi }{5}[/tex]
Recall that [tex]w = 2\pi f
Therefore,
[tex]2\pi f = \frac{8\pi }{5} \\\\f = \frac{4}{5}[/tex][/tex]
f = 0.8 Hertz
Recall that [tex]f = \frac{1}{T}[/tex]
[tex]T = \frac{1}{0.8}[/tex]
T = 1.25 seconds
Therefore, the time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:
Select one:
a. -2.101
b. -1.980
c. -1.960
d. -1.728
Answer:
lyrics d - 1.782
Step-by-step explanation:
Assume Normal Distribution
we have μ₀ = 40 (from Dullco claims)
And from sample μ = 37.8 and standard deviation of 5.4
random sample n = 18
We have to use t-student for testing the hypothesis
and we have a one tail test (left) since Dullco claims : " at least" meaning (always bigger or at least ) not different.
Then
t (s) =( μ - μ₀) / (σ/√n) ⇒ t (s) = [(37.8 - 40 )* √18 ]/5.4
t (s) = - 1.7284
Using the t-distribution, as we have the standard deviation for the sample, it is found that the test statistic is given by:
d. -1.728
What are the hypothesis tested?At the null hypothesis, it is tested if the batteries last at least 40 hours, that is:
[tex]H_0: \mu \geq 40[/tex]
At the alternative hypothesis, it is tested if they last less than 40 hours, that is:
[tex]H_1: \mu < 40[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In this problem, the parameters are given by:
[tex]\overline{x} = 37.8, \mu = 40, s = 5.4, n = 18[/tex]
Hence:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{37.8 - 40}{\frac{5.4}{\sqrt{18}}}[/tex]
[tex]t = -1.728[/tex]
Hence option d is correct.
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Please answer this question correctly I need it today please show work
Answer:
1: C(n) = 2.50 + 16n
2: $66.50
Step-by-step explanation:
Part 1
Each ticket costs $16 per person. If tickets for n persons were purchased, the total cost would be 16n.
There is also a one-time service fee of $2.50 that must be paid. Thus, for n tickets the total cost is
C(n) = 2.50 + 16n
Part 2
For n = 4, the expression evaluates to
C(4) = 2.50 + 16 (4) = $66.50
Pattern A follows the rule "add 2" and Pattern B follows the rule "subtract 2." Pattern A: 1, 3, 5, 7, 9 Pattern B: 10, 8, 6, 4, 2 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4)
Answer:
B, E, F
Step-by-step explanation:
Simply write the terms out and match them.
Final answer:
The correct ordered pairs formed from combining a term in Pattern A with its corresponding term in Pattern B are:
(1, 10), (5, 6), and (7, 4), which are Options B, E, and F, respectively.
Explanation:
The question involves creating ordered pairs from two different number patterns, Pattern A and Pattern B. To find the correct ordered pairs, we match each term in Pattern A with its corresponding term in Pattern B.
Pattern A: 1, 3, 5, 7, 9Pattern B: 10, 8, 6, 4, 2To identify the corresponding terms, we look at the positions: the first term in Pattern A pairs with the first in Pattern B, the second with the second, and so on. Here are the resulting pairs:
(1, 10)(3, 8)(5, 6)(7, 4)(9, 2)Based on the above matching, we evaluate the given options:
Option A: (1, 3) - Incorrect because the first term from Pattern A should be paired with the first term from Pattern B, which is 10.Option B: (1, 10) - Correct as it matches the first term in Pattern A with the first term in Pattern B.Option C: (3, 6) - Incorrect because the second term in Pattern A is 3, but the corresponding second term in Pattern B is 8, not 6.Option D: (5, 4) - Incorrect because the third term in Pattern A is 5, and the corresponding third term in Pattern B is 6, not 4.Option E: (5, 6) - Correct as it matches the third term in Pattern A with the third term in Pattern B.Option F: (7, 4) - Correct as it matches the fourth term in Pattern A with the fourth term in Pattern B.Therefore, the correct ordered pairs when combining a term from Pattern A with its corresponding term from Pattern B are Option B, Option E, and Option F.
A truck costs $16,000 with a residual value of $1,000. It has an estimated useful
life of five years. If the truck was bought on July 3, what would be the book
value at the end of year 1 using straight-line rate?
A. $1,500
B. $16,000
C. $12,500
D. $14,500
Answer:
Option D.
Step-by-step explanation:
Cost of truck = $16000
Residual value after 5 years = $1000
Depreciated value of a truck in 5 year is
[tex]Depreciation=16000-1000=15000[/tex]
In straight-line method, the value of a fixed asset depreciate by a constant rate.
Since depreciation of truck in 5 years is $15000, therefore, the depression of one year is
1 year Depreciation = [tex]\dfrac{15000}{5}=3000[/tex]
From July 3 to end of fist year = 1/2 year
1/2 year Depreciation = [tex]\dfrac{3000}{5}=1500[/tex]
So, the value at the end of year 1 using straight-line rate is
[tex]Value=16000-1500=14,500[/tex]
Therefore, the correct option is D.
A model rocket has upward velocity v(t) = 10t2 ft/s, t seconds after launch. Use the interval [0, 6] with n = 6 and equal subintervals to compute the following approximations of the distance the rocket traveled. (Round your answers to two decimal places.
(a) Left-hand sum = _____ ft
(b) Right-hand sum = _____ ft
(c) average of the two sums = ______ ft
Answer:
a)550
b)910
c)730
Step-by-step explanation:
The given model is
[tex]v(t) = 10t^2 ft/s[/tex]
Use the interval [0,6], with n=6 rectangles
Then, the interval width is
[tex]\Delta t = \frac{b-a}{n}[/tex]
[tex]\Delta t = \frac{6-0}{6}[/tex]= 1
so, the sub intervals are
[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]
Now evaluating the function values
[tex]f(t_0)= f(0) = 0[/tex]
[tex]f(t_1)= f(1) = 10[/tex]
[tex]f(t_2)= f(2) = 40[/tex]
[tex]f(t_3)= f(3) = 90[/tex]
[tex]f(t_4)= f(4) = 160[/tex]
[tex]f(t_5)= f(5) = 250[/tex]
[tex]f(t_6)= f(6) = 360[/tex]
a) left hand sum is
L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]
=[tex]1 [0+ 10+40+90+160+250][/tex]
= 550
b) right hand sum
R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]
= [tex]1 [10+40+90+160+250+360][/tex]
= 910
c) average of two sums is
[tex]\frac{L_5+R_5}{2}[/tex]
= [tex]\frac{550+910}{2}[/tex]
=730
Use the formula to find the length of the radius if the area is 25 square centimeters.
Round your final answer to the nearest tenth of a centimeter. [tex]\sqrt{\frac{a}{\pi }[/tex]
A circle has radius r. The area of this circle can be found using the formula
[tex]A=\pi r^{2}[/tex]
Answer:r = 2.81 centimeters
Step-by-step explanation:
The area of this circle can be found using the formula
A=πr^2
Where r = radius of the circle
π is a constant whose value is 3.14
We are given the area of the circle to be 25 square centimeters. To determine the length of the radius of the circle , we will make r the subject of the formula
r^2 = A/π
Taking square root of both sides of the equation,
r = √A/π
Since A = 25 and π = 3.14,
r= √25/3.14
r = 2.82166323992
Approximating to the nearest tenth of a centimeter,
r = 2.81 centimeters
A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.
Answer:
Part a) [tex]120\pi\ \frac{rad}{min}[/tex]
Part b) [tex]960\pi\ \frac{in}{min}[/tex]
Step-by-step explanation:
we have
60 rev/min
Part a) Find the angular speed in radians per minute
we know that
One revolution represent 2π radians (complete circle)
so
[tex]1\ rev=2\pi \ rad[/tex]
To convert rev to rad, multiply by 2π
[tex]60\ \frac{rev}{min}=60(2\pi)=120\pi\ \frac{rad}{min}[/tex]
Part b) Find the linear speed in inches per minute
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=8\ in[/tex] ----> given problem
substitute
[tex]C=2\pi(8)[/tex]
[tex]C=16\pi\ in[/tex]
Remember that
One revolution subtends a length equal to the circumference of the circle
so
[tex]1\ rev=16\pi\ in[/tex]
To convert rev to in, multiply by 16π
[tex]60\ \frac{rev}{min}=60(16\pi)=960\pi\ \frac{in}{min}[/tex]
Final answer:
The angular speed of the pulley is 120π radians per minute, and the linear speed is 960π inches per minute.
Explanation:
The question pertains to angular and linear speeds related to circular motion. Given that a belt runs a pulley with a radius of 8 inches at 60 revolutions per minute (rpm), we are tasked with finding both the angular speed in radians per minute and the linear speed in inches per minute.
Calculating the Angular Speed
The angular speed (ω) in radians per minute can be calculated using the formula ω = 2π×rpm, where rpm is the number of revolutions per minute and 2π radians is the equivalent of one full revolution.
ω = 2π × 60 = 120π radians/minute
Calculating the Linear Speed
The linear speed (v) can be determined from the radius (r) and angular speed (ω) using the formula v = r×ω. The radius of the pulley is 8 inches, so:
v = 8 inches × 120π radians/minute = 960π inches/minute
The radius of a spherical is decreasing at a constant rate of 3 cm per second. Find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5cm.
The rate of change of the volume of a ball when the radius is 5cm is -300π cubic centimeters per second.
Explanation:To find the rate of change of the volume of a ball, we can use the formula for the volume of a sphere, which is V = (4/3)πR³. We are given that the radius is decreasing at a constant rate of 3 cm per second. So, the rate of change of the volume can be found using the derivative of the volume function with respect to time.
First, we differentiate the volume function with respect to time:
dV/dt = (4/3)π×3R²×(-3)
dV/dt = -12πR²
Then we substitute the given value of the radius when it is 5 cm:
dV/dt = -12π×5²
dV/dt = -12π×25
dV/dt = -300π
Therefore, the rate of change of the volume of the ball when the radius is 5 cm is -300π cubic centimeters per second.
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What percent of 71 is 90?
of 71 is 90.
Answer: 126.76056338%
Step-by-step explanation: To answer the question what percent of 71 is 90, we translate the question into an equation.
We have "what percent" which we can represent by the variable X. Next we have "of 71" which means "times 71" and "is 90" means "equals 90."
Now to solve for x, since x is being multiplied by 71, we need to divide by 71 on both sides of the equation.
On the left side of the equation the 71's cancel and we have x. On the right side of the equation we have 90 divided by 71 which is 1.2676056338.
Now, remember that we want to write our answer as a percent. To write 1.2676056338 as a percent, we move the decimal point two places to the right and we get 126.76056338%.
Answer:
78.89%
Step-by-step explanation:
An electric sale gives a reading equal to the true weight plus a random error that isnormally distributed with mean 0 and standard deviationσ=.1 mg. Suppose that the results of fivesuccessive weightings of the same object are as follows:_______ 3.142, 3.163, 3.155, 3.150, 3.141.(a) Determine a 95 percent confidence interval estimate of the true weight.
(b) Determine a 99 percent confidence interval estimate of the true weight.
Answer:
a) 95% confidence interval estimate of the true weight is (3.026, 3.274)
b) 99% confidence interval estimate of the true weight is (2.944, 3.356)
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
M is the mean of five successive weightings (3.150)ME is the margin of error from the meanAnd margin of error (ME) can be calculated using the formula
ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where
t is the corresponding statistic in the given confidence level and degrees of freedom(t-score) s is the standard deviation of the random error (0.1)N is the sample size (5)Using the numbers 95% confidence interval estimate of the true weight is:
3.150±[tex]\frac{2.776*0.1}{\sqrt{5} }[/tex]≈3.150±0.124
And 99% confidence interval estimate of the true weight is:
3.150±[tex]\frac{4.604*0.1}{\sqrt{5} }[/tex]≈3.150±0.206
On October 1, 2014, Hess Company places a new asset into service. The cost of the asset is $80,000 with an estimated 5-year life and $20,000 salvage value at the end of its useful life. What is the book value of the plant asset on the December 31, 2015, balance sheet assuming that Hess Company uses the double-declining-balance method of depreciation?
Answer:
$43,200
Step-by-step explanation:
Data provided in the question:
Cost of the asset = $80,000
Useful life of the machine = 5 years
Salvage value at the end of useful life = $20,000
Now,
Using the double declining method of depreciation
Annual depreciation rate = 2 × [1 ÷ useful life ]
= 2 × [ 1 ÷ 5 ]
= 2 × 0.2
= 0.4 or 40%
thus,
The depreciation from October 1, 2014 to December 31, 2014
= Annual Depreciation rate × duration × Book value for 2014
= 0.4 × 3 months × $80,000
= 0.4 × 0.25 year × $80,000
= $8,000
Book value for 2015
= Cost - depreciation till December 31, 2014
= $80,000 - $8,000
= $72,000
Therefore,
Depreciation for the year 2015
= Annual Depreciation rate × Book value for 2015
= 0.4 × $72,000
= $28,800
Therefore,
the book value of the plant asset on the December 31, 2015
= Book value for 2015 - Depreciation for the year 2015
= $72,000 - $28,800
= $43,200
Choose the word or phrase that completes each sentence. helps businesses allocate resources for their best and most productive uses. The more a resource, the more costly it will be. A manufacturer that requires scarce and costly resources is likely to charge for its products.
Answer:
1. Value helps businesses allocate resources for their best and most productive uses.
2. The more Scarce a resource, the more costly it will be.
3. A manufacturer that requires scarce and costly resources is likely to charge more for its products.
Step-by-step explanation:
Given:
Three sentences are given we need to add a word or phrase to complete it
First Sentence:
helps businesses allocate resources for their best and most productive uses.
It the above sentence Value will be the word which will complete the sentence because when a resource is valued for his work he provides his best in his work and can be assured as productive too.
Hence we can say,
Value helps businesses allocate resources for their best and most productive uses.
Second Sentence:
The more a resource, the more costly it will be.
It the above sentence Scarce will be the word which will complete the sentence because Scarce Resource always considered to be more costly.
Hence we can say;
The more Scarce a resource, the more costly it will be.
Third Sentence.
A manufacturer that requires scarce and costly resources is likely to charge for its products.
It the above sentence more will be the word which will complete the sentence because A manufacture who has Scarce and costly resource is said to have less production and hence its product would be more costly too.
Hence we can say;
A manufacturer that requires scarce and costly resources is likely to charge more for its products.
Answer: Value, scarce , more
Step-by-step explanation:
those are correct
Help those 3 multiple choice questions correctly and show work please I need it today
A circular cloud of poison gas from a factory explosion is expanding so that t hours after the explosion the radius of the cloud is R(t)=50+20t meters. How fast is the area of the cloud increasing 5 hours after the explosion?
Answer:
6000π m²/h
Step-by-step explanation:
Area of the circular cloud =πr²----------------------------------------- (1)
Radius as a function of time = R(t)=50+20t------------------------ (2)
dA/dt = (dA/dr) x (dr/dt)-----------------------------------------------------(3)
dA/dr = 2πr
dr/dt = 20
After 5 hours, the radius of the cloud will be :
R(5)=50+20(5)
= 150 meters
Substituting into (3)
dA/dt = 2π(150) x 20
= 6000π m²/h
The radius of a circular disk is given as 25 cm with a maximal error in measurement of 0.3 cm. Use differentials to estimate the following. (a) The maximum error in the calculated area of the disk. (b) The relative maximum error. (c) The percentage error in that case.
Answer with Step-by-step explanation:
We are given that
Radius of circular disk=r=25 cm
Maximal error in measurement of radius =[tex]\Delta r=[/tex]0.3
We know that
Surface area of circle =A=[tex]\pi r^2[/tex]
Differentiate w.r.t r
a.Maximum error=[tex]dA=2\pi rdr[/tex]
Substitute the values then we get
[tex]dA=2\times 3.14\times 25\times 0.3=47.1 cm^2[/tex]
Hence, the maximum error in area of disk=[tex]47.1 cm^2[/tex]
b.
Relative error in A: [tex]\frac{\Delta A}{A}=\frac{2\pi r\Delta r}{\pi r^2}[/tex]
Substitute the value in the formula
Then ,we get
Relative maximal error in area of disk=[tex]\frac{2\cdot 25}{(25)^2}(0.3)=0.024[/tex]
Hence, the relative maximum error in area of disk=0.024
c.Relative error percentage in area of disk=[tex]\frac{\Delta A}{A}\times 100[/tex]
Substitute the values then we get
Relative error percentage in area of disk=[tex]0.024\times 100=2.4[/tex]%
Hence, the percentage error in area of disk=2.4%
To estimate the maximum error in the calculated area of a disk, use differentials. The maximum error in the area is approximately 15π cm². The relative maximum error is 0.24 and the percentage error is 24%.
Explanation:To estimate the maximum error in the calculated area of the disk, we can use differentials. The formula for the area of a disk is A = πr², where r is the radius. Taking the differential of this equation gives dA = 2πr dr. Since the maximum error in the radius is 0.3 cm, we substitute dr = 0.3 cm into the equation to find the maximum error in the area. Thus, the maximum error in the calculated area of the disk is approximately 2π(25 cm)(0.3 cm) = 15π cm².
The relative maximum error is the ratio of the maximum error in the area to the actual area. Therefore, the relative maximum error can be calculated as (15π cm²) / (π(25 cm)²) = 15 / 25² = 0.24.
To calculate the percentage error, we multiply the relative maximum error by 100%.
Thus, the percentage error is 0.24 * 100% = 24%.
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If anyone knows this can you please help i have about an hour left to submit this (:
Find the area of a triangle with the given vertices.
Part I: Graph the following points on the coordinate grid below.
(1, -3), (3, -1), (5, -3)
Part II: Find the area of the triangle. Show your work.
Answer:
Part 1 : Figure show the graph of triangle
Part 2 : The area of triangle is 4 sqaure units
Step-by-step explanation:
Given points A(1, -3), B(3, -1) and C(5, -3) make triangle.
Part 1:
Figure show the graph of triangle with A(1, -3), B(3, -1) and C(5, -3) as vertices.
Part 2: Find the area of the triangle.
The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]
From figure, Take base as length of AC
Length of line is given by L=[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]
Now, Base = length of AC
Base =[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]
=[tex]\sqrt{(1-5)^{2}+((-3)-(-3))^{2}}[/tex]
=[tex]\sqrt{(-4)^{2}+(0)^{2}}[/tex]
=[tex]\sqrt{16}[/tex]
=4units
and Height as difference of y-component of point A and point B
Height = (y of component of point B)- (y of component of point A)
= (-1)- (-3)
= 2units
Therefore, The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]
A=[tex]\frac{(4)(2)}{2}[/tex]
A=4 sqaure units
How does the graph of g(x) = (x − 1)3 + 5 compare to the parent function f(x) = x3?
g(x) is shifted 1 unit to the right and 5 units up.
g(x) is shifted 5 units to the right and 1 unit up.
g(x) is shifted 1 unit to the left and 5 units up.
g(x) is shifted 5 units to the right and 1 unit down.
Answer:
A
Step-by-step explanation:
Given:
- The original function is:
f(x) = x^3
Find:
How does the graph of g(x) = (x − 1)3 + 5 compare to the original function.
Solution:
- We have a general form of the new function relating to parent function.
g(x) = a*( x +/- b )^n + c
Where; a, b and c are constants.
- The constant a magnitude denotes steepness of the graph relative to 1 and the sign of a will determine the mirror image of the graph about line y = 0.
- The constant b magnitude denotes shifts of the graph of every x value sign of b will determine the direction of shifts. + b : shift left , - b shift right.
- The constant c magnitude denotes shifts of the graph of every y value. sign of c will determine the direction of shifts. + c : shift up , - b shift down.
- In our g(x). a = 1 , b = -1 , c = + 5
Hence, g(x) is shifted 1 unit to the right and 5 units up.
The graph of g(x) = (x - 1)^3 + 5 is shifted 1 unit to the right and 5 units up compared to the parent function f(x) = x^3.
Explanation:The graph of g(x) = (x - 1)3 + 5 is obtained by shifting the graph of f(x) = x3 one unit to the right and five units up. Shifting a function horizontally is done by replacing x with (x - h), where h is the amount of units you want to shift.
In this case, g(x) = (x - 1)3 + 5 is equivalent to f(x - 1) + 5. So the graph is shifted 1 unit to the right. Shifting a function vertically is done by replacing f(x) with f(x) + k, where k is the amount of units you want to shift.
Since f(x - 1) + 5 is obtained by shifting f(x) one unit to the right and five units up, the correct answer is: g(x) is shifted 1 unit to the right and 5 units up.
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A banana farm received a total of 271 millimeters of rain in March and April. If 118 millimeters of rain fell on the farm in March, how many millimeters of rain fell on the farm in April
Final answer:
The amount of rain that fell on the banana farm in April is 153 millimeters.
Explanation:
To find the amount of rain that fell on the banana farm in April, subtract the amount of rain that fell in March from the total rainfall. The total rainfall in March and April is 271 millimeters, and the amount of rain that fell in March is 118 millimeters. So, the amount of rain that fell in April is 271 millimeters - 118 millimeters = 153 millimeters.
A rectangular piece of sheet metal has a length that is 10 10 in. less than twice the width. A square piece 5 5 in. on a side is cut from each corner. The sides are then turned up to form an uncovered box of volume 1210 1210 in. cubed in.3 Find the length and width of the original piece of metal.
Answer:
length: 32 inwidth: 21 inStep-by-step explanation:
If the width of the original piece of sheet metal is x, then the length is 2x-10. Subtracting a 5" square from each corner makes the bottom of the box have dimensions (x-10) and (2x-20). The volume of the box is then ...
5(x -10)(2x -20) = 1210 . . . . . . volume is the product of the dimensions
10(x -10)² = 1210 = 10(11²) . . . . factor the equation
(x -10)² = 11² . . . . . . . . divide by 10
x = 11 + 10 = 21 . . . . . .take the square root, add 10
The length and width of the original piece of sheet metal were 32 inches and 21 inches, respectively.
If the coefficient of determination is a positive value, then the regression equation a. must have a negative slope b. must have a positive slope c. could have either a positive or a negative slope d. must have a positive y intercept
If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.
Explanation:If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.
The coefficient of determination, denoted as r², is equal to the square of the correlation coefficient, r. It represents the percentage of variation in the dependent variable, y, that can be explained by variation in the independent variable, x, using the regression line. When r² is positive, it indicates a positive relationship between x and y, but it does not specify the direction of the slope.
Therefore, if the coefficient of determination is positive, the regression equation could have either a positive or a negative slope.
A particular type of 4th grade Achievement Test provides overall scores that are normally distributed with a mean of 50 and a standard deviation of 10.
What is the probability that a randomly selected student earns a score between 33 and 48?
Answer:
The probability that a randomly selected student earns a score between 33 and 48 is 0.3761
Step-by-step explanation:
We compute the z-score related to some value x as [tex]z=\frac{x-50}{10}[/tex]. The z-score related to 33 is given by [tex]z_{1}=\frac{33-50}{10}=-1.7[/tex] and the z-score related to 48 is given by [tex]z_{2}=\frac{48-50}{10}=-0.2[/tex]. Therefore, the probability that a randomly selected student earns a score between 33 and 48 is given by P(-1.7 < Z < -0.2) = P(Z < -0.2) - P(Z < -1.7) = 0.4207 - 0.0446 = 0.3761.
The probability is 0.3761 (a) that a student scores between 33 and 48 on the 4th grade Achievement Test.
To find the probability that a randomly selected student earns a score between 33 and 48 on the 4th grade Achievement Test, we need to use the properties of the normal distribution.
Step 1 :**Standardize the Scores**:
First, we need to standardize the scores using the formula for z-score:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
where:
- ( x ) is the score we want to find the probability for,
- [tex]\( \mu \)[/tex] is the mean (50 in this case),
- [tex]\( \sigma \)[/tex] is the standard deviation (10 in this case).
For the lower score [tex]\( x = 33 \)[/tex]:
[tex]\[ z_{\text{lower}} = \frac{33 - 50}{10} = -1.7 \][/tex]
For the upper score [tex]\( x = 48 \)[/tex]:
[tex]\[ z_{\text{upper}} = \frac{48 - 50}{10} = -0.2 \][/tex]
Step 2:**Find the Probability**:
Once we have the standardized scores, we can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores.
From the z-table or calculator, we find:
- For [tex]\( z_{\text{lower}} = -1.7 \)[/tex], the corresponding probability is approximately 0.0446.
- For [tex]\( z_{\text{upper}} = -0.2 \)[/tex], the corresponding probability is approximately 0.4207.
Step 3 :**Calculate the Probability Between the Scores**:
To find the probability between the two scores, we subtract the probability corresponding to the lower score from the probability corresponding to the upper score:
[tex]\[ \text{Probability} = \text{Probability}(x < 48) - \text{Probability}(x < 33) \][/tex]
[tex]\[ \text{Probability} = 0.4207 - 0.0446 \][/tex]
[tex]\[ \text{Probability} = 0.3761 \][/tex]
So, the correct option is: a) .3761
Complete Question :
A particular type of 4th grade Achievement Test provides overall scores that are normally distributed with a mean of 50 and a standard deviation of 10. What is the probability that a randomly selected student earns a score between 33 and 48?
a) .3761
b) .4207
c) .4653
d) .0446
Abigail is making flower bouquets. She has 16 roses and 20 carnations. She wants to make identical bouquets and use all the flowers.What is the greatest number of bouquets she can make?
Answer:
four bouquets
Step-by-step explanation:
The way of solving this problem is tell Abigail to keep the relation between flowers constant, that is
We have 16 roses and 20 carnations
16 2 16 = 2⁴ 20 2 20 = 2² * 5
8 2 10 2
4 2 5 5
2 2 1
1
So we will make bouquets of 4 roses and 5 carnations
so we will have 4 bouquets using all flowers
How much is a $26,000 automobile car worth after 1 year if the depreciation is 15% per year
Answer:
The worth of the automobile after an year with 15% depreciation is $22,100.
Step-by-step explanation:
The current cost of the automobile car = $26,000
The percentage of depreciation = 15%
Now, calculating the depreciated amount:
15% of $26,000 = [tex]\frac{15}{100} \times 26,000 = 3,900[/tex]
So, the depreciated amount of the car in the next year = $3,900.
Now, the worth of the car after an year
= CURRENT WORTH - THE DEPRECIATED AMOUNT
= $26,000 - $3,900.
= $22,100
Hence, the worth of the automobile after an year is $22,100.
If 2/5 cup of coconut shavings covers 1/4 of a cake, then how much coconut shavings are needed for one cake? A. 3/5 cup B. 5/8 cup C. 1 3/5 cup D. 10 cups
The right answer is Option C.
Step-by-step explanation:
Given,
2/5 cup of coconut shavings covers 1/4 of a cake,
[tex]\frac{2}{5}\ coconut\ shavings=\frac{1}{4}\ of\ cake[/tex]
For one whole cake, we will multiply both sides with 4;
[tex]4*\frac{2}{5}=\frac{1}{4}*4\\\frac{8}{5} = 1\ cake[/tex]
Writing in simplified fraction form;
[tex]1\ cake = 1\frac{3}{5}\ cups[/tex]
The right answer is Option C.
Keywords: fractions, multiplication
Learn more about fractions at:
brainly.com/question/3617539brainly.com/question/3638399#LearnwithBrainly
A stone is thrown straight up from the edge of a roof, 775 feet above the ground, at a speed of 16 feet per second. A. Remembering that the acceleration due to gravity is −32ft/sec2, how high is the stone 4 seconds later?
Final answer:
The stone is approximately 583 feet high 4 seconds later.
Explanation:
To find the height of the stone 4 seconds later, we can use the equation of motion for an object in free fall:
h = h0 + v0t + (1/2)gt^2
Where:
h = height at time t
h0 = initial height
v0 = initial velocity
g = acceleration due to gravity
t = time
Substituting the given values:
h = 775 + 16(4) + (1/2)(-32)(4)^2
h = 775 + 64 - 256
h = 583 feet
Therefore, the stone is approximately 583 feet high 4 seconds later.
One of the roots of the equation 2x^2−bx−20=0 is −2.5. Find the other root
Answer:
The answer to your question is x = 4
Step-by-step explanation:
2x² - bx - 20 = 0
One root is -2.5
Process
Get the value of the equation when x = -2.5
2(-2.5)² - b(-2.5) - 20 = 0
2(6.25) + 2.5b - 20 = 0
12.5 + 2.5b - 20 = 0
2.5b = 20 - 12.5
2.5b = 7.5
b = 7.5 / 2.5
b = 3
Then
2x² - 3x - 20 = 0
Factor the polynomial
2 x -20 = -40
2x² -8x + 5x - 20 = 0
2x(x - 4) + 5(x - 4) = 0
(x - 4)(2x + 5) = 0
x₁ - 4 = 0 2x₂ + 5 = 0
x₁ = 4 x₂ = -5/2
x₂ = -2.5
Answer:
The "other" or "second" root is 4.
Step-by-step explanation:
We are told that -2.5 is a root of the equation. The coefficient b of the x term is unknown, and must be determined. Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.
Setting up synthetic division, we arrive at:
-2.5 / 2 -b -20
-5 +12.5 + 2.5b
-------------------------------------
2 -5-b -7.5 + 2.5b
The remainer, -7.5 + 2.5b, must be zero (0). Thus, 2.5b = 7.5, and b = 3.
Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.
The other factor is 2x - 8, which, if set equal to 0, yields x = 4. This is the "other root."