​=
The solution set is
​ 1/2(10x+16)-13=-3/5(15x-35)

Answer:

Step-by-step explanation:

[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]

[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]

the b) part is easy do it!

Answer: 32 room

Step-by-step explanation:

[tex]7\frac{3}{4} =\frac{4(7)+3}{4} =\frac{28+3}{4} =\frac{31}{4}=7.75[/tex]

If 1 room = 7.75 yd of carpet ⇒ x rooms = 250 yd of carpet

Use proportions & cross-multiply to solve:

[tex]\frac{1}{7.75} =\frac{x}{250}\\7.75x=250\\x=\frac{250}{7.75} =32.258[/tex]

So 250 yd of carpet can cover about 32 rooms.

Answer:

2w<23

Step-by-step explanation:

The product of w and 2 mean that w multiplied by 2

Answer:

[tex]A"B" = \frac{AB}{2}[/tex]

Step-by-step explanation:

Given

[tex]k = \frac{1}{2}[/tex] --- scale factor

Required

Relationship between AB and A"B"

[tex]k = \frac{1}{2}[/tex] implies that the sides of A"B"C" are smaller than ABC

i.e.

[tex]A"B" = k * AB[/tex]

[tex]A"B" = \frac{1}{2} * AB[/tex]

This gives:

[tex]A"B" = \frac{AB}{2}[/tex]

Answer:

Domain: (-∞, 1]

Range: (-∞, 3]

Step-by-step explanation:

The function starts at point (1, 3) and goes to the left and down forever.

Domain: (-∞, 1]

Range: (-∞, 3]

Answer:

Domain: [tex](-\infty, 1][/tex]

Range: [tex](-\infty, 3][/tex]

Step-by-step explanation:

The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].

The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.

The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.

Answer:

x= -3

Step-by-step explanation:

2x+14= 8

2x= -6

x = -3

Answer:

-3

Step-by-step explanation:

According to the question,

[tex]\longrightarrow[/tex] CE = CD + DE

[tex]\longrightarrow[/tex] 8 = (x + 10) + (x + 4)

[tex]\longrightarrow[/tex] 8 = x + 10 + x + 4

[tex]\longrightarrow[/tex] 8 = 2x + 14

[tex]\longrightarrow[/tex] 8 ― 14 = 2x

[tex]\longrightarrow[/tex] ―6 = 2x

[tex]\longrightarrow[/tex] ―6 ÷ 2 = x

[tex]\longrightarrow[/tex] –3 = x

Therefore, the value of x is ― 3.

Step-by-step explanation:

Since an interior angle is 150 degrees, its adjacent exterior angle is 30 degrees.  Exterior angles of any polygon always add up to 360 degrees.  With the polygon being regular, we can just divide 360 by 30 to get 12 sides.

Answer:

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Step-by-step explanation:

To solve these questions, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.

This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]

Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

This is 1 subtracted by the p-value of Z when X = 40. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

1 - 0.8997 = 0.1003

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

[tex]\mu = 266, \sigma = 16[/tex]

1. What is the probability a randomly selected pregnancy lasts less than 260 days?

This is the p-value of Z when X = 260. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{260 -  266}{16}[/tex]

[tex]Z = -0.375[/tex]

[tex]Z = -0.375[/tex] has a p-value of 0.3539.

0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 20[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]

[tex]Z = -1.68[/tex]

[tex]Z = -1.68[/tex] has a p-value of 0.0465.

0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 50[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]

[tex]Z = -2.65[/tex]

[tex]Z = -2.65[/tex] has a p-value of 0.0040.

0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.

X = 276

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = 2.42[/tex]

[tex]Z = 2.42[/tex] has a p-value of 0.9922.

X = 256

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

0.9922 - 0.0078 = 0.9844

0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Answer:

the answer is c

Step-by-step explanation:

the answer is c

Answer:

150 dollars. if I am wrong correct me

Answer:

C and D

Step-by-step explanation:

15 to 30 galons at $9.95 to $21.00

the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25

the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630

there are 2 choices that are between 149.25 and 630, C, and D

Answer:23

Step-by-step explanation:

Answer:

H0 : ρ = 0

H1 : ρ ≠ 0

Test statistic = 1.197

Pvalue = 0.2335

There is no correlation between the two variables

Step-by-step explanation:

The null and alternative hypothesis :

H0 : No correlation exist,

H1 : Correlation exist

H0 : ρ = 0

H1 : ρ ≠ 0

Test statistic, T = r / √(1 - r²) / (n - 2)

T = 0.067 / √(1 - 0.067²) / (320 - 2)

T = 0.067 / √(0.995511 / 318)

T = 0.067 / 0.0559512

T = 1.197

The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335

α = 5% = 0.05

The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.

[tex]f(x)=\sqrt{x} -2[/tex] is the correct option

Step-by-step explanation:

I think substitution would be the easiest since you already have one of the variables solved for.

[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]

(You can just set the equations equal to each other since they both equal y).

Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)

[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]

So, your final points are:

(4,5) and (-1,0)

Answer: A

Step-by-step explanation:

We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.

-x²+4x+5=x+1        [subtract both sides by x]

-x²+3x+5=1            [subtract both sides by 1]

-x²+3x+4=0

Now that we have the equation above, we can factor it to find the roots.

-x²+3x+4=0           [factor out -1]

-1(x²-3x-4)=0         [factor x²-3x-4]

-1(x+1)(x-4)=0

This tells us that x=-1 and x=4.

We can narrow down our answer to A, but let's plug in those values to be sure it is correct.

-(-1)²+4(-1)+5=(-1)+1      [exponent]

-1+4(-1)+5=-1+1              [multiply]

-1-4+5=-1+1                    [add and subtract from left to right]

0=0  

-------------------------------------------------------------------------------------------

-(4)²+4(4)+5=(4)+1      [exponent]

-16+4(4)+5=4+1           [multiply]

-16+16+5=4+1              [add and subtract from left to right]

5=5

Therefore, we can conclude that A is the correct answer.

Answer:

19.3 miles per gallon

Step-by-step explanation:

First, subtract 54,042.8-53,737.7. The answer is 305.1

Then, find the unit rate. 305.1/15.8

You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.

That's your answer!

Answer:

0.2305 = 23.05% probability that exactly 2 workers say yes.

Step-by-step explanation:

For each worker, there are only two possible outcomes. Either they say yes, or they say no. The probability of a worker saying yes is independent of any other worker, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

5% of workers in the US use public transportation to get to work.

This means that [tex]p = 0.05[/tex]

You randomly select 25 workers

This means that [tex]n = 25[/tex]

Find the probability that exactly 2 workers say yes.

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305[/tex]

0.2305 = 23.05% probability that exactly 2 workers say yes.

Answer:

1. Find the GCF of all the terms in the polynomial.

2. Express each term as a product of the GCF and another factor.

3. Use the distributive property to factor out the GCF.

Answer:

It has a side that is 9 units long.

Step-by-step explanation:

Answer:

B) It has a side that is 9 units long.

Step-by-step explanation:

Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.

Answer:

a) The margin of error for a 98% confidence interval is of 3.388 people.

b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the hypergeometric distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]

In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.

Question b:

The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people

The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.

The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Answer:

A is that answer

A) y<2x-3

Answer:

1/2 or 50-50

Step-by-step explanation:

1/4 +1/4 = 1/2 or 50-50

Answer:

8(1/x) = 4(1/10)

Step-by-step explanation:

lets say the number is x

eight times the reciprocal of a number equals 4 times the reciprocal of 10

  8       *                       1//x                            =        4    *         1/10

8/x = 4/10 ,  cross multiply

4x =8*10, divide both sides by 4

x= 80/4

x= 20

Answer:

A saturated fat is a type of fat in which the fatty acid chains have all or predominantly single bonds. A fat is made of two kinds of smaller molecules: glycerol and fatty acids. Fats are made of long chains of carbon atoms. Some carbon atoms are linked by single bonds and others are linked by double bonds.

Saturated fats: a type of fat containing a high proportion of fatty acid molecules without double bonds, considered to be less healthy in the diet than unsaturated fat

Unsaturated fats: a type of fat containing a high proportion of fatty acid molecules with at least one double bond, considered to be healthier in the diet than saturated fat.

what's the difference between both?: saturated fats Contains a single bond, Excessive consumption leads to heart diseases,High melting point and Solid state in room temperature. While Unsaturated Contains at least one double bond, Good for consumption, but excessive may increase cholesterol,Low melting point and Liquid state in room temperature.

Answer:

Range: { 0,3,5,7,9}

Step-by-step explanation:

The range is the values that y takes

Range: { 0,3,5,7,9}

Now we have to find,

The range of the table of values,

→ Range = ?

Then the range will be the numbers that is in the Y column.

→ Range = ?

→ Range = (value that Y takes)

→ Range = 0,3,5,7,9

Therefore, the range is 0,3,5,7,9.

Answer:

(D.) 3x^2 + 6x

Step-by-step explanation:

the other options aren't complete and some don't even create a parabola.

Answer:

The answer is the third one below

Step-by-step explanation:

For an equation of form Ax + By = C, we are given A, B, and C.

The x intercept is when the line/equation is on the x axis, or when y=0.

Therefore, if we plug y=0 into the equation Ax+By=C, and anything multiplied by 0 is equal to 0, we can say that

Ax + 0 = C

Ax = C

divide both sides by A

x  = C/A

Therefore, the x intercept is equal to C/A

Similarly, for the y intercept, or when the line is on the y axis (or when x=0), we have

A*0 + By = C

By = C

divide both sides by B

y= C/B at the y intercept

Answer:

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.

This means that [tex]p = 0.0746[/tex]

Random sample of 318 independent returns

This means that [tex]n = 318[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]

What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]

[tex]Z = -0.26[/tex]

[tex]Z = -0.26[/tex] has a p-value of 0.3974.

1 - 0.3974 = 0.6026

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Answer:

True

Step-by-step explanation:

The statistic is a numerical value which describes the characteristic of a particular sample data. The sample is a set of data which represents a smaller subset randomly selected from the population or a larger dataset.

The sample mean, refers to the mean or average value of a sample data, therefore, a sample mean is a numerical characteristic of the sample dataset and it is therefore a statistic. On the other hand, numerical characteristics of a population data is called the parameter.