Answer:
80% of all sample proportions in the sampling distribution of sample proportions of size 45 will be above 0.6988.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = \frac{64}{85} = 0.7529, n = 45, \mu = 0.7529, s = \sqrt{\frac{0.7529*0.2471}{45}} = 0.0643[/tex]
Above what proportion will 80% of all sample proportions be in the sampling distribution of sample proportions of size 45.
Above the 100 - 80 = 20th percentile, which is X when Z has a pvalue of 0.2. So X when Z = -0.842.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]-0.842 = \frac{X - 0.7529}{0.0643}[/tex]
[tex]X - 0.7529 = -0.842*0.0643[/tex]
[tex]X = 0.6988[/tex]
80% of all sample proportions in the sampling distribution of sample proportions of size 45 will be above 0.6988.
A survey was conducted among people who visit swimming pools. 209 people were asked about the preferences in water sanitizing. 112 respondents reported they prefer pools with mechanical methods of water sanitizing, and 97 respondents reported they do not have any preferences. Construct a test for a difference in proportions for this survey to find out if the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences, if it is possible. A :
Answer:
The claim that needs to be tested is that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences. This can be expressed as the population proportion of people who prefer mechanical methods of water sanitizing is significantly higher than 0.5.
This is a hypothesis test for a population proportion.
The test will have null and alternative hypothesis:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
Test statistic z = 0.972
P-value = 0.166
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.
Step-by-step explanation:
We have to construct a hypothesis test for the population proportion. We need to test the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.
As the survey is done as a yes/no question, the null hypothesis would state that the amount of people who prefer mechanical methods of water sanitizing is not significantly different from the proportion of people who have no sanitizing methods preferences. That can be expressed as the population proportion equals 0.5, so both proportions are equal.
The alternative hypothesis would state that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences. This could be expressed as the population proportion significantly bigger than 0.5.
Then, the null and alternative hypothesis are written:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=209.
The sample proportion is p=0.536.
[tex]p=X/n=112/209=0.536[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{209}}\\\\\\ \sigma_p=\sqrt{0.001196}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.536-0.5-0.5/209}{0.035}=\dfrac{0.034}{0.035}=0.972[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.972)=0.166[/tex]
As the P-value (0.166) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of people who prefer mechanical methods of water sanitizing truly exceeds the proportion of people who have no sanitizing methods preferences.
Which expression is equal to -3b(6b^-8)
Answer:a^2/b
Step-by-step explanation:
(a^6b^−3)1^/3
a^6 ^ 1/3 b ^ -3 ^ 1/3
using the power of power rule we can multiply the exponents
a ^ (6*1/3) b ^ (-3* 1/3)
a^ 2 b ^ -1
the negative exponent flips it from the numerator to the denominator
a^2* 1/ b^1
a^2/b
Answer:
A. -18b^-4
second answer is B. -18/b^-4
Step-by-step explanation:
There is 0.3 probability that a group of insured motorists have an accident in a decade.
If there are 640 insured motorists, what is the mean number of accidents in a decade?
Answer:
192
Step-by-step explanation:
to find the mean you have to use this formula: mean= N(total number of trials) times P( probability of "success")
n=640
p=0.3
640x0.3= 192
Preciso de ajudaa! Resolução também! - Considere as funções f e g tais que f(x)= x³+1 e g(x)= x-2 Determine: a)(fog)(0) b)(gof)(0) c)(fof)(1) d)(gog)(1)
Answer:
(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).
So, if f(x) = x^3 + 1 and g(x) = x - 2.
we have:
a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7
b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1
c) (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9
d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3
How is 6x² + 7 written in words
Answer:
six x squared plus seven
Step-by-step explanation:
um..
Answer:
The way to write 6x² + 7 in words is six x squared plus seven
Step-by-step explanation:
I hope your happy with your answer
Find the indicated probability. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220. Group of answer choices 0.1554 0.2257 0.3811 0.0703
Answer:
The probability of a rating that is between 170 and 220 is 0.3811
Step-by-step explanation:
According to the given data we have the following:
μ=200
σ=50
To calculate the probability of a rating that is between 170 and 220 we would have to use the following formula:
z=x-μ/σ
Therefore, 170-200/50=-0.60
220-200/50=0.40
Using normal cdf formula we get normal cdf(-0.60,0.40)
=0.3811
Therefore, the probability of a rating that is between 170 and 220 is 0.3811
PLEASE I NEED HELP ASAP sally drives for 2 hours at an average speed of 70 m/h. she then drives for half an hour at an average speed of 40 m/h work ot the total distance that sally has travelled
Answer:
Total Distance = 160 m
Average speed = 64 m/hr
Step-by-step explanation:
For first 2 hours:
Distance = Speed × Time
D = 70 × 2
D = 140 m
For the next half hour:
Distance = Speed × Time
Distance = 40 × 0.5
Distance = 20 m
Now total Distance:
Total Distance = 140+20
Total Distance = 160 m
After that,
Average Speed = Total Distance Covered/ Total Time taken
Average Speed = 160 m / 2.5 hours
Average speed = 64 m/hr
help i give u brainliest
It is a 4 : 1 ratio of color to white
or a 1 : 4 white to colored
Explanation:
1cm = 10mm
1.2cm = 12mm
12 : 48 --> 1 : 4
Answer:
1:4
Step-by-step explanation:
1.2 cm of white fabric per 48 mm of colored fabric:
1.2 cm : 48 mm= 12 mm: 48 mm= 1:4
The ratio is: 1:4
A biologist conducting an experiment starts with a culture of 300 E. coli bacteria. 72 hours later the culture consists of 600,000 bacteria. What is the average increase in the number of E. coli bacteria per hour
Answer:
2,000
Step-by-step explanation:
if you divide 600,000 by 300 you get 2,000.
A lake has a large population of fish. On average, there are 2,400 fish in the lake, but this number can vary by as much as 155. What is the maximum number of fish in the lake? What is the minimum number of fish in the lake?
Answer:
Minimum population of fish in lake = 2400 - 155 = 2245
Maximum population of fish in lake = 2400 + 155 = 2555
Step-by-step explanation:
population of fish in lake = 2400
Variation of fish = 155
it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.
For example
for increase
population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc
but it cannot be beyond 2400 + 155.
It cannot be 2400 + 156
similarly for decrease
population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc
but it cannot be less that 2400 - 155.
It cannot be 2400 - 156
Hence population can fish in lake can be between 2400 - 155 and 2400 + 155
minimum population of fish in lake = 2400 - 155 = 2245
maximum population of fish in lake = 2400 + 155 = 2555
The diameter of a sphere is 4 centimeters, which represents the volume of the sphere?
Answer:
10 2/3π or 33.51
Step-by-step explanation:
the volume of a sphere is 4/3πr^3
if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51
Answer:
32π/3 cubic cm
Step-by-step explanation:
i will give mor points ans please
Answer:
Step-by-step explanation:
| − | = | + 9I
THERE ARE TWO POSSIBILITIES
2x-1=4x+9 and 2x-1=-4x-9
2x-4x=9+1 and 2x+4x=-9+1
-2x=10 and 6x=-8
x=-5 and x=-8/6
x=-5 and x=-4/3
SOLUTION SET ={-5,-4/3}
[tex]\frac{2x-1}{3}-\frac{3x}{4}=\frac{5}{6}\\ taking LCM\\\frac{8x-4-9x}{12}=\frac{5}{6}\\\frac{-1x-24}{12}=\frac{5}{6}\\ by cross multiplication\\6(-1x-4)=12*5\\-6x-24=60\\-6x=60+24\\-6x=84\\\\x=-14\\soltion set {-14}[/tex]
[tex]10+\sqrt{10m-1}=13\\\sqrt{10m-1}=13-10\\\\\sqrt{10m-1}=3\\ taking square on both sides\\10m-1=3^2\\10m-1=9\\10m=9+1\\10m=10\\m=1[/tex]
the number of solution to a linear equation is 1
2(x - 4) = 6 then x is ----7
Solution of | + | = − is ---------13/3,5/3
Consider the quadratic function:
f(x) = x2 – 8x – 9
Vertex: ( negative b Over 2a, f ( negative b Over 2 a))
What is the vertex of the function? ( , )
Answer:
(4, -25)
Step-by-step explanation:
The function is put into this form: f(x)= Ax^2 + Bx + C
In the equation x^2 - 8x - 9, A is 1, B is -8 and C is -9
The negatives cancel for negative B so 8 is positive.
8/ 2(1) = 4
Now we plug 4 into the function as x to find the y value
4^2 - 8(4) - 9
-25
add or subtract negative numbers
[tex]9+(-2)\\9-2\\=7[/tex]
[tex]-6+(-3)\\-6-3\\=-9[/tex]
[tex]4+(-9)\\4-9\\=-5[/tex]
Answer:
see below
Step-by-step explanation:
9 + -2 =
9 -2 = 7
-6 + -3
-6 - 3 =-9
4 + - 9
-9 +4 = -5
If I use my debit card at the gas pump, I get a five-cent discount. Which of the following statements is
accurate?
(a) The absolute change in price is the same for all grades ofgas; the relative change in price for Regular (the cheapest) is the greatest.
(b) The absolute change in price is the same for all grades ofgas; the relative change in price for Premium (the most expensive) is the greatest.
(c) The relative change in price is the same for all grades ofgas; the absolute change in price for Regular (the cheapest) is the greatest.
(d) The relative change in price is the same for all grades of gas; the absolute change in price for Premium (the most expensive) is the greatest.
Answer:
(d) The relative change in price is the same for all grades of gas; the absolute change in price for premium (the most expensive) is the greatest.
Step-by-step explanation:
The debit card holders are offered discount if they use debit card for a payment. When the gas pump offers the discount the relative change in price is same. The banks offers discounts to its customers to encourage cashless payments.
A restaurant borrows from a local bank for months. The local bank charges simple interest at an annual rate of for this loan. Assume each month is of a year. Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Complete Question:
A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.
Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Answer:
a) Interest that will be owed after 4 months , I = $131.48
b) Amount owed by the restaurant after 4 months = $16231.48
Step-by-step explanation:
Note that the question instructs not to round any intermediate computations except the final answer.
Annual rate = 2.45%
Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]
R = 0.20416666666%
Time, T = 4 months
Interest, [tex]I = \frac{PRT}{100}[/tex]
[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]
b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)
Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)
Amount owed by the restaurant after 4 months = 16100 + 131.48
Amount owed by the restaurant after 4 months = $16231.48
According to Brad, consumers claim to prefer the brand-name products better than the generics, but they can't even tell which is which. To test his theory, Brad gives each of 199 consumers two potato chips - one generic, and one brand-name - then asks them which one is the brand-name chip. 92 of the subjects correctly identified the brand-name chip.
Required:
a. At the 0.01 level of significance, is this significantly greater than the 50% that could be expected simply by chance?
b. Find the test statistic value.
Answer:
a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
b. Test statistic z=-1.001
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]
The significance level is 0.01.
The sample has a size n=199.
The sample proportion is p=0.462.
[tex]p=X/n=92/199=0.462[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]
As the P-value (0.16) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
Which of the following are point-slope equations of the line going through (3,
6) and (1,-2)? Check all that apply:
Answer:
y+2=4(x-1)
y-6=4(x-3)
Step-by-step explanation:
Slope between (3, 6) and (1, -2)
6-(-2)/3-1
8/2
4
y+2=4(x-1)
y-6=4(x-3)
Which expanded expressions represent the exponential expression (–4)3 · p4? Select all that apply. (–4) · (–4) · (–4) · (–4) · p · p · p p · p · p · p · (–4) · (–4) · (–4) p · (–4) · (–4) · p · (–4) · p p · p · (–4) · (–4) · p · p · (–4) (–4) · p · p · p · (–4) · (–4) · (–4) (–4) · (–4) · p · (–4) · p · p · p
The expanded form of the given exponential expression is (-4)×(-4)×(-4)×p×p×p×p.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is (-4)³·p⁴.
Here, (-4)³= (-4)×(-4)×(-4)
p⁴=p×p×p×p
So, (-4)×(-4)×(-4)×p×p×p×p
= -64×p×p×p×p
Therefore, the expanded form is (-4)×(-4)×(-4)×p×p×p×p.
To learn more about an exponents visit:
https://brainly.com/question/15993626.
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Question from quadratic equation .
solve.
(x-3)(x+7)=0
Answer:
x = 3, -7
Step-by-step explanation:
Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:
x - 3 = 0
x + 7 = 0
x = 3, -7
Answer:
3 or -7
Step-by-step explanation:
For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.
Find f(-11/5) if f(n) = 5n + 6
Answer:
f(-11/5) = -5
Step-by-step explanation:
f(n) = 5n + 6
Let x = -11/5
f(-11/5) = 5*-11/5 +6
= -11 +6
= -5
2(3y+6)−3(−4−y) simplified
Answer:
9y+24
Step-by-step explanation:
2(3y+6)-3(-4-y)
Expand the brackets.
6y+12+12+3y
Rearrange.
6y+3y+12+12
Add like terms.
9y+24
Answer:
9y+24solution,
[tex]2(3y + 6) - 3( - 4 - y) \\ = 6y + 12 + 12 + 3y[/tex]
Collect like terms,
[tex]6y + 3y + 12 + 12[/tex]
Simplify
[tex]9y + 24[/tex]
hope this helps...
Good luck on your assignment..
the mean of the prime factors of 24 is
Answer:
bad words
Step-by-step explanation:
it is your shet
Answer:
2.25
Step-by-step explanation:
Prime Factors of 24 is 2 x 2 x 2 x 3
2 + 2 + 2 + 3 = 9
9/4 = 2.25
In the diagram below, $RT:TS = 1:2$ and $SR = PQ = 20$. Find $UV$.
It's pretty easy not college levlel just some simple high school geomerty.
Answer: 12
Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.
Because $ST/SR = 2/3$ and $PQ = SR$, we have
\[\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\]Since $UQ/US = 3/2$, we have $UQ/QS = 3/5$.
We have $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.
in a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......
a).all men.
b).3men and 2 women
Answer:
a) Probability that a 5 member committee will have all men = 0.0065
b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Step-by-step explanation:
Number of men = 8
Number of women = 10
Total number of members = 10 + 8 = 18
Probability = (Number of possible outcomes)/(Total number of outcomes)
Number of ways of selecting a 5 member committee from 18 people = [tex]^{18}C_5 = \frac{18!}{(18-5)!5!} = \frac{18!}{13!5!}[/tex] = 8568 ways
a) Probability that a 5 member committee will have all men
Number of ways of selecting 5 men from 8 men
= [tex]^8C_5 = \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!}[/tex] = 56 ways
Probability that a 5 member committee will have all men = 56/8568
Probability that a 5 member committee will have all men = 0.0065
b)probability that a 5 member committee chosen randomly will have 3men and 2 women
Number of ways of selecting 3 men from 8 men
= [tex]^8C_3 = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!}[/tex] = 56 ways
Number of ways of selecting 2 women from 10 men
= [tex]^{10}C_2 = \frac{10!}{(10-2)!2!} = \frac{10!}{8!2!}[/tex] = 45 ways
Number of ways of selecting 3 men and 2 women = 56*45
Number of ways of selecting 3 men and 2 women = 2520
Probability of selecting 3 men and 2 women = 2520/8568 = 0.294
probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y= -x+5
y=x-3
Answer:
X+5= -x-3
2x = 2
X=1
then y1 is 4
y2 is -1
Answer:
Answer is 4, 1. If you graph the lines, they intersect at 4, 1.
Step-by-step explanation:
On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units. Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not? Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds Yes, because both figures are rectangles and all rectangles are similar. No, because the center of dilation is not at (0, 0). No, because corresponding sides have different slopes
Answer:
Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds.
Step-by-step explanation:
Dilation is a transformation process in which the dimensions of a given figure are resized to produce an image with the same shape. This is done with respect to a scale factor and center of dilation.
In the given question, the center of dilation is at the middle of side DC of rectangle ABCD (i.e on side DC).
Given that the scale factor is [tex]\frac{4}{3}[/tex],
EF = HG = [tex]\frac{4}{3}[/tex] × AB = [tex]\frac{4}{3}[/tex] × 6 = 8 units
FG = EH = [tex]\frac{4}{3}[/tex] × BC = [tex]\frac{4}{3}[/tex] × 3 = 4 units
Therefore, rectangle EFGH is the result of dilation of ABCD.
Answer:
A. Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds
Step-by-step explanation:
The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.
Answer:
9.233 ft, 23.233 ft
Step-by-step explanation:
If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...
x^2 + (x +14)^2 = 25^2
2x^2 +28x +196 = 625
x^2 +14x = 214.5
x^2 +14x +49 = 263.5
(x +7)^2 = 263.5
x = -7 +√263.5 ≈ 9.23268
The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.
Answer: 9 ft, 23 ft
Step-by-step explanation:
We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.
(x-14)²+x²=25²
(x²-28x+196)+x²=625
2x²-28x+196=625
2x²-28x-429=0
When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].
Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.
Which of the following fractions has the greatest value 6/10, 2/3, 5/8, 7/12
Answer:
2/3
Step-by-step explanation:
[tex]6/10=3/5=0.6[/tex]
[tex]2/3 \approx 0.66666667[/tex]
[tex]5/8=0.625[/tex]
[tex]7/12 \approx 0.583333333[/tex]
The fraction 2/3 has the greatest value.
The greatest of the fractions will be 2/3.
What is mean by Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
All fractions are;
6/10 , 2/3, 5/8, and 7 /12
Now, Find the greatest factor in the above fractions as;
Solve the fraction by dividing.
The value of the first fraction is;
6 / 10 = 0.6
The value of the second fraction is;
2/3 = 0.667
The value of the third fraction is;
5/8 = 0.625
The value of the fourth fraction is;
7 / 12 = 0.583
Clearly, In all the fractions the fraction 2/3 has the greatest value.
Therefore, The greatest of the fractions will be 2/3.
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The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it? 10 weeks 13 weeks 15 weeks 21 weeks
Answer: 13 weeks
Step-by-step explanation:
y = -24x + 379
67 = -24x + 379
24x = 379 - 67
x = 312 / 24
x = 13
Answer:
the answer is 13 weeks
Step-by-step explanation:
y = amount left
y = 67
67 = -24x+379
-312 = -24x
x = -312 / -24
x = 13