Answer: The inner diameter of the ring is 16 mm.
Step-by-step explanation:
As we know that ,
Circumference of a circle = [tex]\pi d[/tex] , where d = diameter of the circle .
We are given that ,
The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm .
Now , if circumference of the inside the ring is 50 mm, then we have
[tex]50 = \pi d[/tex] , where d= diameter of the inner circle .
Then , [tex]d=\dfrac{50}{\pi}=\dfrac{50}{\dfrac{22}{7}}=\dfrac{50\times7}{22}\approx15.909090909\approx16\text{ mm}[/tex]
Hence , the inner diameter of the ring is 16 mm.
The diameter of the inner ring is 15.92mm
Circumference of a circleThe formula for calculating the circumference of a circle is expressed as:
C = πd
d is the diameter
Given the following parameters
C = 50mm
The diameter of the inner ring is given as:
d = C/π
d = 50/3.14
d = 15.92mm
Hence the diameter of the inner ring is 15.92mm
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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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Find the missing side length
Answer:
The answer to your question is b = 148.5
Step-by-step explanation:
To solve this problem, use trigonometric functions
tan Ф = [tex]\frac{opposite side}{adjacent side}[/tex]
opposite side = b
adjacent side = 60
tan Ф = tan 68° = 2.48
Opposite side = adjacent side x tan Ф
Opposite side = 60 x 2.48
Opposite side = b = 148.5
Answer: 24.24 (24 to the nearest whole number)
Step-by-step explanation:
Following trigonometric rule,
Tan tita = opposite side/ adjacent side
Tan 68° = 60 / b
2.475 = 60 / b
By cross multiplication,
2.475b = 60
Divide both sides by 2.475
2.475b/2.475 =60/2.475
b = 24.24
Hence, adjacent side = 24.24 (24 to the nearest whole number since opposite side is in whole number).
A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?
(1) y ≤ 8
(2) y ≥ 4
Answer:
a) y </= 8 is not sufficient
b) y >/= 4 is sufficient (y is not less than 3.5)
Step-by-step explanation:
Number of Red marbles = 8
Number of white marbles = y
Total number of marbles in the jar = 8+ y
Let Pr(R) be the probability of picking red marbles
Let Pr(W) be the probability picking white marbles
Pr(R) = 8/ (8+y)
Pr(W) = 7/(7+y)
Pr(RR) = Pr(R1) * Pr( R2)
= 8/(8+y) * 7/(7+y)
Pr(RW) = Pr(R1) * Pr(W2) + Pr(W1) * Pr(R2)
= 2[Pr(R1) * Pr(W2)
= 2[8/(8+y) * y/(7+y)]
The probability of having 2 red is greater than one marble of each color.
Pr(RR) > Pr( RW)
8/(8+y) * 7/(7+y) > 2[8/(8+y) * y/(7+y)]
7/(7+y) > 2(y/(7+y)
7/y > 2
7/2 > y
3.5 > y
y < 3.5
Therefore;
a) y </= 8 is not sufficient
b) y >/= 4 is sufficient (y is not less than 3.5)
help me figure out this problem!!
Answer:
4.47 years
Step-by-step explanation:
Fill in the given value of P and solve for t.
15390 = 19000·0.954^t
15390/19000 = 0.954^t
Taking logarithms ...
log(1539/1900) = t·log(0.954)
t = log(1539/1900)/log(0.954) ≈ 4.47 . . . years
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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A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides. Find the value of h that maximizes the volume of the box if
A = 7 and B = 12
Answer:
h = 1,743
Step-by-step explanation:
Volume of a box is
V(h) = ( A - 2h) * ( B - 2h)* h A = 7 B = 12
We have
V(h) = ( 7 - 2h) * ( 12 - 2h ) * h
V(h) = ( 84 - 14*h - 24*h + 4*h² ) * h
V(h) = ( 84 - 38*h + 4 *h² ) * h ⇒ V(h) = 84h - 38h² + 4h³
Taking derivatives both sides of the equation
V´(h) = 84 - 76h + 12x²
V´(h) = 0 84 - 76h + 12x² = 0 42 - 38h + 6x²
3x² - 19h + 24 = 0
Solving for h h1 = [ ( 19 + √(19)² - 288 ]/ 6 h1 = [ (19 + √73)/6]
h₁ = 4,59 we dismiss this value since 9,18 (4,59*2) > A
h₂ = [ 19 - √73)/6] h₂ = 1,743
h = 1.743 is h value to maximizes V
On the square baseball diamond shown below, the distance from first base to second base is 90 feet. How far does the catcher have to throw the ball from home plate to reach second base? Round your answer to the nearest 10th. Show your work
Answer:
127.3 ft
Step-by-step explanation:
The diagonal of a square is √2 times the length of one side. The distance from home plate to second base is ...
(90 ft)√2 ≈ 127.3 ft
The catcher at home has to throw the ball 127.3 ft to reach second base.
Please help me with my homework and explain to me how?
Answer:
350
Step-by-step explanation:
If x is the number of hamburgers and y is the number of cheeseburgers, then:
x + y = 764
y = x + 64
Solve the system of equations with substitution or elimination. Using substitution:
x + x + 64 = 764
2x + 64 = 764
2x = 700
x = 350
350 hamburgers were sold.
Suppose you begin a job with an annual salary of $32,900. Each year you are assured of a 5.5% raise. What its the total amount that you can earn in 15 years? A) $34,815 B) $51,751 C) $737,245 D) $1,682,920
Answer: The correct option is C
Step-by-step explanation:
You begin a job with an annual salary of $32,900
Each year you are assured of a 5.5%. If you get the same amount each year, that is a 100% payment. It is neither reducing nor increasing. But with an increase of 5.5% each year, it means you are getting (100+5.5)% each year. This equals 105.5%. So for each year, you get 105.5% of the previous year.
This is a geometric progression. To determine the total amount that you can earn in 15 years, we will find the sum of 15 terms, S15 of the series. The formula for sum of the nth term of a geometric progression is expressed as
Sn = [a(r^n - 1)] / r - 1
Where
Sn = sum of the nth terms of the series
a = the first term(salary of the first year
r = common ratio
n = number of years.
From the question,
a = 32900
n = 15
r = 105.5/100 = 1.055
S15 = [32900(1.055^15 - 1)] / 1.055 - 1
S15 = [32900(2.23247649224 - 1)] / 0.055
S15 = [32900 × 1.23247649224] / 0.055
S15 = $737245
Suppose you perform an ANOVA on 18 subjects divided evenly into three groups according to age. Reading speed is measured and averaged for each of the three groups. The reading speed for the Young Group is 10; for the Middle Group, 12; and for the Older Group, 13. Your F-obtained is 9.15. This is a significant F-obtained. Which of the following is the correct way to report this finding? A. The Older Group reads significantly faster than any other group. B. The Young Group reads significantly faster than any other group. C. There is a significant difference between the Older Group and the Middle Group. D. There is a significant difference among the reading speeds somewhere.
Answer:
D. There is a significant difference among the reading speeds somewhere.
Hope this helps!
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 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 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
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
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
Joe had eight sections of the fence to paint. He painted 2/3 of each section in one hour. How many hours did it take him to paint all the sections of fence?
Answer:
1.5 hours
Step-by-step explanation:
Since Joe painted 2/3 section (2 out of 3 sections) of each section, we can break up the sections into parts of "3".
So 8 sections would have total subsections of 8 * 3 = 24 subsections
He painted 2 subsections of each of the 8 sections, so number of subsections painted would be:
8 * 2 = 16 subsections
There are more 24 - 16 = 8 more subsections to paint
If 1 hour means 16 subsections,
1/16 hour = 1 subjection
Thus,
8 remaining subsections would take:
8 * 1/16 = 8/16 = 1/2 hour
So
Initially 1 hour, then 1/2 hour, so total of 1 + 1/2 = 1.5 hours
So, to paint all sections, he took 1.5 hours
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.
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
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
Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentive. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increase the average sales per salesperson.
a. Develop the appropriate null and alternative hypotheses.
b. What is the Type I error in this situation? What are the consequences of making this error?
c. What is the Type II error in this situation? What are the consequences of making this error?
The appropriate null and alternative hypotheses for the situation, the consequences of Type I and Type II errors in this context.
Explanation:a. Null Hypothesis (H0): The compensation plan does not increase the average sales per salesperson. Alternative Hypothesis (H1): The compensation plan does increase the average sales per salesperson.
b. Type I error occurs when the null hypothesis is rejected, but it is actually true. In this situation, it means concluding that the compensation plan increases the average sales per salesperson when it does not. The consequence is that the company may implement the compensation plan and incur unnecessary costs.
c. Type II error occurs when the null hypothesis is accepted, but it is actually false. In this situation, it means concluding that the compensation plan does not increase the average sales per salesperson when it actually does. The consequence is that the company may miss out on the benefits of the compensation plan and fail to motivate its salespeople effectively.
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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
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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Solve for x: 5/8=x-1/9
A. 37/8
B. 23/4
C. 11/2
D. 53/8
Answer:
53/72
Step-by-step explanation:
5/8 = x - 1/9
+1/9 +1/9
5/8 + 1/9 = x
9(5/8) + 8(1/9)
45/72 + 8/72
x= 53/72
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:
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.
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 physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 63 and a standard deviation of 6. Using the 68-95-99.7 rule, what is the approximate percentage of light bulb replacement requests numbering between 63 and 75? _________ % (Round your answer to the nearest tenth of a percent)
Approximately 81.5% of the daily light bulb replacement requests in the state university's physical plant can be expected to number between 63 and 75.
Explanation:The question is asking for the percentage of daily light bulb replacement requests numbering between 63 and 75 at a state university's physical plant. This can be answered using the 68-95-99.7 rule, also known as the Empirical Rule, which applies to a bell-shaped distribution.
Firstly, identify that a request count of 75 is two standard deviations above the mean (63 + 6*2 = 75), because the standard deviation here is 6. According to the Empirical Rule, approximately 95% of the data lies within two standard deviations of the mean.
However, we are only interested until the upper limit of 75 and not the lower limit (63 - 6*2 = 51). Therefore, we consider half of this 95%, which gives us 47.5%. However, don't forget to include the 34% that lies within the first standard deviation (from 63 to 69). Therefore, approximately 81.5% of the light bulb replacement requests should number between 63 and 75.
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the approximate percentage of light bulb replacement requests numbering between 63 and 75 is 47.5%.
Using the Empirical Rule:
Calculate the Z-scores for the given values: Z(63) = (63-63)/6 = 0 and Z(75) = (75-63)/6 = 2.Look up the percentage of data within these Z-scores: Between Z = 0 and Z = 2 is approximately 47.5%.Therefore, the approximate percentage of light bulb replacement requests numbering between 63 and 75 is 47.5%.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
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Help please I really need help I need it right now show work please
Answer:
ok with whuth do you need help with
Answer:
The right answer for question 1 is b) -14
Step-by-step explanation:
Since it's a decline, the amount will be negative.
your second question is not clear in the image
3.5 per day for 4 days so multiply 3.5 by 4, which equals: $14
so the overall change is -$14.00
Yesterday evening, Emily's journey home took 25% longer than usual, as she was stuck in a traffic jam. By what percentage was her average speed reduced compared to normal
Answer:
20%
Step-by-step explanation:
Time and speed are inversely proportional, so if Emily's time was 5/4 of normal, her speed was 4/5 of normal, or 1/5 = 20% below normal.