27.) What shape do you create if you cut a square in
half horizontally or vertically?

Answer:

64k^2 - 16k +1

Step-by-step explanation:

We can rewrite this as

(-8k+1) ^2

We know that (a+b)^2 = a^2 +2ab +b^2

Let a = -8k  and b = 1

(-8k+1) = (-8k)^2 +2*(-8k)(1) + 1^2

           =64k^2 - 16k +1

Answer:

64k² - 16k + 1

Step-by-step explanation:

(−8k+1)(−8k+1)

64k² - 8k - 8k + 1

64k² - 16k + 1

b.

If it's a (+,+) it's the 1st quadrant. If it's a (-,+) it's the 2nd quadrant. If its a (-,-) it's the 3rd quadrant. And if it's a (+,-) it's the 4th quadrant

Answer:

B

Step-by-step explanation:

Answer:180cm^2

Step-by-step explanation:

A1=25×20=500

A2=16×20=320

A1-A2

500-320=180

Answer:

By the Central Limit Theorem, the mean of the average scores you get will be close to 1012.5.

Step-by-step explanation:

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.

Mean score of the population:

1012.5

If you do this many times, the mean of the average scores you get will be close to

By the Central Limit Theorem, the mean of the average scores you get will be close to 1012.5.

Answer:

481

Step-by-step explanation:

Given:

Variance = 1.44

S.d = √1.44 = 1.2

C.I = 80%

Margin of error, E = 0.07

Mean = 3.6

Using Z table, the Z score for 80% confidence interval, Zc = 1.28

To find the sample size, n, we have:

[tex] n= [\frac{Z_c * s.d}{E}]^2 [/tex]

Substituting figures in the formula, we have:

[tex] n = [\frac{1.28 * 1.2}{0.07}]^2 [/tex]

n = 21.94286²

n = 481.49

Approximately, n = 481

Answer:

The population consists of the 201 people who bought tires last month.

The sample consists of the 51 people who responded.

Step-by-step explanation:

In statistical analysis, the population is a set of all values that can be considered for an experiment. It is a set of observations from which a sample is selected. The sample is a subset of the population.

In this case, it is provided that a tire company sends an email survey to all customers who purchase new tires each month.

The number of tires sold last month was N = 201.

The email survey was sent to 100 of these 201 people and 51 responded.

In this case, since the survey is done every month, the population consists of all the people who bought tires the previous month.

So, the population consists of the 201 people who bought tires last month.

The number of people who responded was, n = 51.

The sample consists of these 51 people because the data from these 51 people would be used to conduct and draw conclusion about the survey.

So, the sample consists of the 51 people who responded.

Answer:

k = 37

Step-by-step explanation:

[tex]k = 13t - 2 \\ \therefore \: k = 13 \times 3 - 2 \\ \therefore \: k = 39 - 2 \\ \huge \red{ \boxed{ \therefore \: k = 37}}[/tex]

Answer:

We conclude that the calibration point is set too low.

Step-by-step explanation:

We are given that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be σ = 2.3. They weigh this weight on the scale 49 times and read the result each time. The 49 scale readings have a sample mean of x = 999.0 grams.

The calibration point is set too low if the mean scale reading is less than 1000 grams.

Let [tex]\mu[/tex] = mean scale reading

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 1000 grams     {means that the calibration point is not set too low}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 1000 grams     {means that the calibration point is set too low}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                         T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean = 999 grams

            [tex]\sigma[/tex] = population standard deviation = 2.3 grams

            n = sample of scale readings = 49

So, test statistics  =  [tex]\frac{999-1000}{\frac{2.3}{\sqrt{49} } }[/tex]  

                              =  -3.04

The value of z test statistics is -3.04.

Now, P-value of the test statistics is given by the following formula;

         P-value = P(Z < -3.04) = 1 - P(Z [tex]\leq[/tex] 3.04)

                                              = 1 - 0.99882 = 0.00118

Since, the P-value is less than the level of significance as 0.01 > 0.00118, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the calibration point is set too low.

Answer:

A.) 2 x minus 4 y = 8. x + y = 7.

Step-by-step explanation:

A.) 2 x minus 4 y = 8. x + y = 7.

2x-4y = 8

x+y=7

This has one solution

B.) 3 x + y = negative 1. 6 x + 2 y = negative 2.

3x+y = -1

Multiply by 2

6x +2y = -2

This is the second equation  so it has infinite solutions

C.) 3 x + 3 y = 3. Negative 6 x minus 6 y = 3.

3x+3y =3

Multiply by -2

-6x-6y = -6

The equation is the same but the constant, which means they are parallel lines, they have zero solutions

D.) 3 x minus 2 y = 4. Negative 3 x + 2 y = 4.

3x -2y = 4

Multiply by -1

-3x +2y = -4

The equation is the same but the constant, which means they are parallel lines, they have zero solutions

Answer:

A.) 2 x minus 4 y = 8. x + y = 7.

Step-by-step explanation:

A.) 2 x minus 4 y = 8. x + y = 7.

2x - 4y = 8

x - 2y = 4

x = 4 + 2y

x + y = 7

4 + 2y + y = 7

3y = 3

y = 1

x = 4 + 2

x = 6

Only solution: (6,1)

Answer: The alternative hypothesis represents the claim

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 0.38

For the alternative hypothesis,

µ > 0.38

Considering the population proportion, probability of success, p = 0.38

q = probability of failure = 1 - p

q = 1 - 0.38 = 0.6

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 176

n = number of samples = 400

P = 176/400 = 0.44

We would the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.44 - 0.38)/√(0.38 × 0.62)/400 = 2.47

Recall, population proportion, P = 0.38

The difference between sample proportion and population proportion(P - p) is 0.44 - 0.38 = 0.06

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.38 - 0.06 = 0.32

the p for the right tail is 0.38 + 0.06 = 0.44

These proportions are higher and lower than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above z is 1 - 0.9932 = 0.0068

We would double this area to include the area in the left tail of z = - 2.47. Thus

p = 0.0068 × 2 = 0.014

Since alpha, 0.01 < than the p value, 0.014, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the​ null hypothesis

Answer:

a) [tex]\vec v_{B} - \vec v_{C} = 3\, i - 17\,j[/tex], b) [tex]\theta = 79.992^{\textdegree}[/tex] (clockwise)

Step-by-step explanation:

The resultant velocity of the boat must be:

[tex]\vec v_{B} = 15\,i[/tex]

Likewise, the velocity of the current is:

[tex]\vec v_{C} = 2\,i + 17\,j[/tex]

a) The intended velocity of the boat is:

[tex]\vec v_{B} - \vec v_{C} = (15-2)\,i + (0-17)\,j[/tex]

[tex]\vec v_{B} - \vec v_{C} = 3\, i - 17\,j[/tex]

b) The direction of the boat is:

[tex]\theta = \tan^{-1}\left(\frac{17}{3} \right)[/tex] (clockwise)

[tex]\theta = 79.992^{\textdegree}[/tex] (clockwise)

Answer:

41

Step-by-step explanation:

PEMDAS parentheses equation multiplication division adding subtraction

Answer:

2

Step-by-step explanation:

Answer: 9?

Step-by-step explanation: I think.

Answer:

4  to 5

Step-by-step explanation:

20 footballs to 25 footballs

Divide each term by 5

20/5  to 25/5

4  to 5

Given:

The height of the the tree from where the tree was broken = 13 ft

The distance from the foot of the tree to the broken top = 36 ft

To find the height of the tree.

Formula

By Pythagoras theorem we get,

h² = l²+b²,

where, h be the hypotenuse

b be the base and

l be the other side of the triangle along the right angle.

Now,

Putting, l =13 and b = 36 we get,

[tex]h^{2} =36^{2} +13^{2}[/tex]

or, [tex]h^{2} = 1296+169[/tex]

or, [tex]h^{2} =1465[/tex]

or, [tex]h=\sqrt{1465}[/tex]

or, [tex]h = 38.3[/tex]

Therefore,

The height of the tree is about = 13+38.3 ft = 51.3 ft

Hence,

The height of the tree is about 51.3 ft.

Simplfied Answer: [tex]6b-4[/tex]

Combine Like Terms

[tex]8b+-2b+-4\\(8b+-2b)+(-4)\\6b+-4[/tex]

Answer:

[tex]8b - 2b - 4 \\ 6b - 4 \\ = 2(3b - 2)[/tex]

Answer:

[tex] ME = 1.653 *\frac{7.9}{\sqrt{300}}= \pm 0.75[/tex]

±0.75 ounce

Step-by-step explanation:

Assuming this complete question: The Wisconsin Dairy Association is interested in estimating the mean weekly consumption of milk for adults over the age of 18 in that state. To do this, they have selected a random sample of 300 people from the designated population. The following results were recorded: xbar=34.5 ounces, s=7.9 ounces Given this information, if the leaders wish to estimate the mean milk consumption with 90 percent confidence, what is the approximate margin of error in the estimate?

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=34.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=7.9 represent the sample standard deviation

n=300 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=300-1=299[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,199)".And we see that [tex]t_{\alpha/2}=1.653[/tex]

And the margin of error is given by:

[tex] ME = 1.653 *\frac{7.9}{\sqrt{300}}= \pm 0.75[/tex]

±0.75 ounce

Answer:

The approximate margin of error in the estimate is ±0.75 ounces.

Step-by-step explanation:

The question is incomplete:

The following results were recorded: xbar=34.5 ounces, s=7.9 ounces.

The sample size is n=300.

We will use the sample standard deviation to estimate the population standard deviation, so we will use the t-statistic.

To develop a confidence interval, we first have to calculate the degrees of freedom, and then look up in a t-students distribution table the critical value for a 90% confidence interval.

The degrees of freedom are:

[tex]df=n-1=300-1=299[/tex]

The critical value for a 90% CI is t=1.65.

Now, we can calculate the margin of error of the confidence interval as:

[tex]E=t\cdot s/\sqrt{n}=1.65*7.9/\sqrt{300}=13.035/17.32=0.75[/tex]

The lower and upper bounds of the confidence interval will be:

[tex]LL=\bar x-t\cdot s/\sqrt{n}=34.5-0.75=33.75\\\\UL=\bar x+t\cdot s/\sqrt{n}=34.5+0.75=35.25[/tex]

The confidence interval is (33.75, 35.25)

Final answer:

The events A and B are mutually exclusive. The events A and C are not mutually exclusive. Two events A and B are independent events.

Explanation:

The events A and B are mutually exclusive because they cannot happen at the same time. P(A AND B) = 0.

No, A and C are not mutually exclusive because they can occur at the same time. In fact, C includes all of the outcomes of A; if the card chosen is blue it is also (red or blue). P(A AND C) = P(A) = 20.

Two events A and B are independent events if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are not independent, then we say that they are dependent events. Sampling may be done with replacement or without replacement. With replacement: If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.

Answer:

  6

Step-by-step explanation:

Put the given point into the equation and solve for a.

  f(-2) = a(-2 +3)² -4 = a -4 = 2

  a = 6 . . . . . add 4

The a-value in the equation is 6.

Answer:

170

Step-by-step explanation:

Hello!

Let's represent a decimal as a fraction. That will help.

Since division is multiplication by the reciprocal, we can represent 0.01 as 1/100 which will be 100 when we divide.

1.7 * 100 = 170.0 (when we move one spot over.)

Thus, we see that [tex]\boxed{170}[/tex] is the answer.

Hope this helps!

The correct hypotheses to be tested are:

H0: p = 0.5 (The proportion of songs loaded by Rina is 0.5, meaning Ed and Rina loaded an equal proportion of songs.)

Ha: p = 0.5 (The proportion of songs loaded by Rina is not equal to 0.5, meaning Ed and Rina loaded different proportions of songs.)

To determine how strong the evidence is that Ed and Rina have each loaded a different proportion of songs into the player, we can perform a hypothesis test. The test statistic for a proportion in a binomial setting is given by:

[tex]\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \][/tex]

where:

- [tex]\(\hat{p}\)[/tex] is the sample proportion of successes (in this case, the proportion of songs by Rina),

- [tex]\(p_0\)[/tex] is the hypothesized proportion under the null hypothesis (0.5),

- [tex]\(n\)[/tex] is the sample size (53 songs).

Given that 35 out of 53 songs were by Rina, we calculate [tex]\(\hat{p}\)[/tex] as:

[tex]\[ \hat{p} = \frac{35}{53} \approx 0.660 \][/tex]

Now we can calculate the test statistic [tex]\(z\)[/tex] :

[tex]\[ z = \frac{0.660 - 0.5}{\sqrt{\frac{0.5(1-0.5)}{53}}} = \frac{0.160}{\sqrt{\frac{0.25}{53}}} \approx \frac{0.160}{\sqrt{0.004717}} \approx \frac{0.160}{0.0686} \approx 2.33 \][/tex]

The P-value for a two-tailed test is the probability of observing a test statistic as extreme as or more extreme than the one observed, under the assumption that the null hypothesis is true. We can find the P-value by looking up the z-score in a standard normal distribution table or using a calculator:

[tex]\[ P\text{-value} = 2 \times P(Z > |2.33|) \approx 2 \times 0.0099 \approx 0.0198 \][/tex]

Since the P-value (0.0198) is less than the significance level of 0.05, we reject the null hypothesis in favour of the alternative hypothesis. This means there is strong evidence to suggest that Ed and Rina have each loaded a different proportion of songs into the player.

Before we conclude, we must check the conditions for the use of this test:

1. The samples are independent. Each song selection is made independently of the others.

2. The number of successes and failures are each at least 10. In this case, Rina's songs (35) and Ed's songs (18) are both greater than 10, so this condition is satisfied.

3. The sample size is less than 10% of the population size. The population size is 3476 songs, and the sample size is 53 songs, which is much less than 10% of the population, so this condition is also satisfied.

Since all conditions are met, we can confidently conclude that there is strong evidence that Ed and Rina have each loaded a different proportion of songs into the player.

Answer: C. Because the graphs of the two equations overlap each other.

Step-by-step explanation: I took the test its right! Hope this helps

[tex]\text{Solve the equation to make it into slope intercept form}\\\\\text{Slope intercept form: y = mx + b}\\\\\text{Solve:}\\\\-2y=6(2x-2)\\\\\text{Distribute the 6 to the variables inside the parenthesis}\\\\-2y=12x-12\\\\\text{Divide both sides by -2}\\\\y=-6x+6\\\\\text{The slope would be -6 and the y intercept would be 6}\\\\\boxed{\text{Slope: -6 y-intercept: 6}}[/tex]

Answer:

a.

The random variable has binomial distribution with parameters p = 0.25, n=5.

b.

[tex]P(Y=2) = {5 \choose 2} (0.25)^2(0.75)^3 = 0.264\\P(Y<1 ) = P(Y = 0 ) = (0.75)^5 = 0.237[/tex]

Step-by-step explanation:

a.

Remember what a random variable with binomial distribution is. It is a random variable that counts the number of successes and in n trials of an experiment.

In this case, if you have  0,1,2,3,4,5  bottles of water, your success is that  the bottle has tap water, and the probability of that success is p = 0.25. and the number of trials is n = 5.

b.

Using the formula for the binomial distribution you get that

[tex]P(Y=2) = {5 \choose 2} (0.25)^2(0.75)^3 = 0.264\\P(Y<1 ) = P(Y = 0 ) = (0.75)^5 = 0.237[/tex]

Answer:

8π yards

Step-by-step explanation:

A circle subtends a total angle of 360 ° from its center.The length of an arc is directly proportional to the angle it subtends from the circle's center. The arc's length can therefore be calculated as:

C=πd=2πr

Where C is circumference, d is diameter and r is radius. Given r as 16 yards then the arc length which is equivalent to circumference is given as

[tex]C=\frac {90}{360}*2*\pi*16=8\pi[/tex]

Answer:

2,144.7 i just answered the other one is wrong

Step-by-step explanation:

Answer:

a) 0.3889

b) 0.5

c) 0.8333

d) The mean is 250 and the standard deviation is 51.96.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability of finding a value of X higher than x is:

[tex]P(X > x) = 1 - \frac{x - a}{b-a}[/tex]

The probability of finding a value of X between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The mean and the standard deviation are, respectively:

[tex]M = \frac{a+b}{2}[/tex]

[tex]S = \sqrt{\frac{b-a}^{2}{12}}[/tex]

A random variable follows the continuous uniform distribution between 160 and 340.

This means that [tex]a = 160, b = 340[/tex]

a)

[tex]P(220 \leq X \leq 290) = \frac{290 - 220}{340 - 160} = 0.3889[/tex]

b)

[tex]P(160 \leq X \leq 250) = \frac{250 - 160}{340 - 160} = 0.5[/tex]

c)

[tex]P(X > 190) = 1 - \frac{190 - 160}{340 - 160} = 0.8333[/tex]

d)

[tex]M = \frac{160 + 340}{2} = 250[/tex]

[tex]S = \sqrt{\frac{340 - 160}^{2}{12}} = 51.96[/tex]

The mean is 250 and the standard deviation is 51.96.

Answer:

 x < 3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    4*x-7-(5)<0

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  4x - 12  =   4 • (x - 3)

Equation at the end of step  1  :

Step  2  :

2.1    Divide both sides by  4

Solve Basic Inequality :

2.2      Add  3  to both sides

            x < 3

By solving the given inequality "[tex]4x-7<5[/tex]", we get the answer "[tex]x <3[/tex]". A complete solution is below.

The given equation of inequality is:

Now,

By adding "7" both sides of the equation, we get

→ [tex]4x-7+7<5+7[/tex]

→              [tex]4x< 12[/tex]

→                [tex]x < \frac{12}{4}[/tex]

→                [tex]x < 3[/tex]

Thus the above solution is correct.

Learn more about inequality here:

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To determine the scale of a drawing, you need the dimensions on the drawing or map as well as the actual dimensions of the object. The scale is then calculated as the ratio of these two sets of dimensions. However, without the dimensions of the drawing in this case, it is not possible to determine the exact scale.

The scale of a drawing is a ratio that compares the dimensions of the physical object to the dimensions on the drawing or map. In this case, the physical object is a pool that measures 30 feet by 66 feet. To find the scale, you would need additional information such as the dimensions of the pool in the drawing.

For example, if the pool is drawn as 2 inches by 4.4 inches on the paper, then the scale of the drawing would be 1 inch = 15 feet (for length) and 1 inch = 15 feet (for width), as 30 feet / 2 inches = 15 feet per inch and 66 feet / 4.4 inches = 15 feet per inch respectively.

Without this additional information, it is not possible to provide the exact scale of the drawing.

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The scale for the drawing shown is 1 in = 6 feets

Using the parameters given ;

Actual dimension :

Drawing dimension :

To calculate the scale of the drawing : Take the ratio of equivalent sides of the two drawings ;

Now we have ;

Hence the scale drawing is :

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