The length of a rectangle is nine inches more than its width. Its area is 486 square inches. Find the width and length of the rectangle.

Answer:

14

Step-by-step explanation:

Answer:

Both variables appear to have something in common.

Explanatory: crowd/sale

Response: win/loss

There are two possible effects of crowd size to this game one might be due to pressure and nervousness from crowd size or

Another factor( variable) which is related to crowd size and the outcome of the match.

Step-by-step explanation:

Given data:

Home games with sell out crowd

Win = 3

Loss = 15

Total = 18

Home games without sell out crowd

Win = 12

Loss = 11

Total = 23

Therefore:

Percentage of win with sellout crowd

= 3/18 * 100

= 0.166 * 100

= 16.7%

Percentage of win with smaller crowd

= 12/23 * 100

= 0.522 * 100

= 52.2%

Both variables appear to have something in common.

Explanatory: crowd/sale

Response: win/loss

There are two possible effects of crowd size to this game one might be due to pressure and nervousness from crowd size or

Another factor( variable) which is related to crowd size and the outcome of the match.

Answer:

1-5: Make it 5 units tall

6-10: Make it 4 units tall

11-15: Make it 2 units tall

16-20: Make it 0 units tall (Don't do anything to it)

21-25: Make it 4 units tall

Step-by-step explanation:

1-5: 2, 3, 3, 3, 5 (5 numbers)

6-10: 6, 6, 8, 10 (4 numbers)

11-15: 11, 13 (2 numbers)

16-20: (0 numbers)

21-25: 22, 23, 24, 24 (4 numbers)

Answer:

The heights of the missing bars are the following:

1- 5 ⇒ 5

6-10 ⇒ 4

11-15 ⇒ 2

16-20 ⇒ 0

21-25 ⇒ 4

Answer:

a. The distribution is bell-shaped and symmetric: True.

b. The distribution is bell-shaped and symmetric: True.

c. The probability to the left of the mean is 0: False.

d. The standard deviation of the distribution is 1: True.

Step-by-step explanation:

The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].

It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.

We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where [tex] \\ x[/tex] is the raw score that we want to standardize.

Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:

(a) True or False: The distribution is bell-shaped and symmetric

Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.

(b) True or False: The mean of the distribution is 0.

Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

If [tex] \\ x = \mu[/tex]

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

[tex] \\ z = \frac{0}{\sigma}[/tex]

[tex] \\ z = 0[/tex]

Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.

(c) True or False: The probability to the left of the mean is 0.

Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].

(d) True or False: The standard deviation of the distribution is 1.

Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.

In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].

In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.

Answer:

A: true

B: true

C: false

D: true

Answer:

There is enough evidence to support the claim that the proportion of brand awareness of female TV viewers and the gender of the spokesperson are not independent (P-value = 0.01537).

Step-by-step explanation:

The question is incomplete: the picture attached gives the missing sample data.

This is a hypothesis test for the difference between proportions.

The claim that is going to be stated in the alternative hypothesis is that the proportion of brand awareness of female TV viewers and the gender of the spokesperson are not independent. This means that the proportions differ significantly.

Then, the null and alternative hypothesis can be written as:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1 (Male celebrity), of size n1=150 has a proportion of p1=0.273.

[tex]p_1=X_1/n_1=41/150=0.273[/tex]

The sample 2 (Female celebrity), of size n2=150 has a proportion of p2=0.407.

[tex]p_2=X_2/n_2=61/150=0.407[/tex]

The difference between proportions is (p1-p2)=-0.133.

[tex]p_d=p_1-p_2=0.273-0.407=-0.133[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{41+61.05}{150+150}=\dfrac{102}{300}=0.34[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.34*0.66}{150}+\dfrac{0.34*0.66}{150}}\\\\\\s_{p1-p2}=\sqrt{0.001496+0.001496}=\sqrt{0.002992}=0.055[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.133-0}{0.055}=\dfrac{-0.133}{0.055}=-2.44[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=2\cdot P(z<-2.44)=0.01537[/tex]

As the P-value (0.01537) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of brand awareness of female TV viewers and the gender of the spokesperson are not independent (the proportions differ).

Answer:

Alternative hypothesis Ha; is that the average time to accelerate from 0 to 60 miles per hour is greater than 7.7 seconds.

H0: u > 7.7

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

Let u represent the average time to accelerate from 0 to 60 miles per hour

Null hypothesis H0; is that the average time to accelerate from 0 to 60 miles per hour is equal to 7.7 seconds.

H0: u = 7.7

Alternative hypothesis Ha; is that the average time to accelerate from 0 to 60 miles per hour is greater than 7.7 seconds.

H0: u > 7.7

Answer:

  41,850

Step-by-step explanation:

The 4th digit from the left is in the 10s place, so you need to round to that place. This requires rounding up, since the 1s digit is more than 4.

  41,850 . . . . to 4 significant figures

Answer:

Step-by-step explanation:

er

Answer:

x = 20

Step-by-step explanation:

4/2x - 10 =30

Divide 4/2.

2x - 10 =30

Add 10 to both sides.

2x = 30 + 10

2x = 40

Divide 2 into both sides.

2x/2 = 40/2

x = 20

Step-by-step explanation:

First we will Rearrange after replacing 9 with 6

1 3 3 6 6 6 6 6 8 8

Mode = 6

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ? [Hint: Let Y = the number among the 1000 intervals that contain μ. What kind of random variable is Y?]

(Round your answer to four decimal places.)

Answer:

The expected value is

[tex]E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980[/tex]

[tex]P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%[/tex]

There is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Step-by-step explanation:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients.

From the above information, we know that,

n = 1000

p = 0.98

How many of these 1000 intervals do you expect to capture the corresponding value of μ?

The expected value is given by

[tex]E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980[/tex]

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and p is also greater than 0.50.

n×p ≥ 10

1000×0.98 ≥ 10

980 ≥ 10  (satisfied)

n×(1 - p) ≥ 10

1000×(1 - 0.98) ≥ 10

20 ≥ 10 (satisfied)

Let Y be the random number among the 1000 intervals that contain μ

[tex]P(970 < Y < 990) = P(Y < 990) - P(Y < 970) \\\\P(970 < Y < 990) = P( Z < \frac{Y - \mu}{\sigma}) - P( Z < \frac{Y - \mu}{\sigma} )\\\\[/tex]

Where the mean is

[tex]\mu = 980[/tex]

and the standard deviation is

[tex]\sigma = \sqrt{n \times p(1-p)} \\\\\sigma = \sqrt{1000 \times 0.98(1-0.98)} \\\\\sigma = 4.4272[/tex]

Finally, the required probability is

[tex]P(970 < Y < 990) = P( Z < \frac{990 - 980}{4.4272}) - P( Z < \frac{970 - 980}{4.4272} )\\\\[/tex]

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution)  to approximate discrete probability distribution (Binomial distribution).

[tex]P(970 < Y < 990) = P( Z < \frac{989.5 - 980}{4.4272}) - P( Z < \frac{969.5 - 980}{4.4272} )\\\\P(970 < Y < 990) = P( Z < \frac{9.5}{4.4272}) - P( Z < \frac{-10.5}{4.4272} )\\\\P(970 < Y < 990) = P( Z < 2.15) - P( Z < -2.37 )\\\\[/tex]

From the z-table, the z-score corresponding to 2.15 is 0.9842

From the z-table, the z-score corresponding to -2.37 is 0.0089

[tex]P(970 < Y < 990) = 0.9842 - 0.0089\\\\P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%[/tex]

Therefore, there is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Answer:

974

Step-by-step explanation:

Initial × Increase percentage ^ Time

500 × (1 + 10%)^(70/10)

500 × 1.1^7

= 974.36

The population of the town in 70 years will be 974.

Step-by-step explanation:

Answer:

f (4) = -11

g(x) = 2, x = 0

you're welcome :)

Step-by-step explanation:

Answer:

The region where the inequality is valid is (x>-5) and (x<-9).

The graph is attached.

Step-by-step explanation:

We have a inequality and we have to determine the region in the xy-plane that inequality.

[tex]|x+7|-2>0\\\\|x+7|-2+2>0+2\\\\|x+7|>2[/tex]

We divide the inequality in two regions:

1) When (x+7)>0, we have:

[tex]x+7>2\\\\x+7-7>2-7\\\\x>-5[/tex]

2) When (x+7)<0, we have:

[tex]-(x+7)>2\\\\-x-7+7>2+7\\\\-x>9\\\\(-x)(-1)<9(-1)\\\\x<-9[/tex]

Then, the region where the inequality is valid is (x>-5) and (x<-9).

The graph is attached.

Answer:

B

Step-by-step explanation:

edg 2020

Answer:

a.) 8x + 6y

b.) 4x + 2y

Step-by-step explanation:

Simply add like terms together (x with x and y with y).

Answer:

7

Step-by-step explanation:

hh

ht

th

tt

so it's a 1/4 chance

1/4 * 28 = 7

Answer:

7

Step-by-step explanation:

The probability of both coins landing on heads is:

1/2 × 1/2 = 1/4

Multiply by 28.

1/4 × 28

= 7

Answer:

Y = 5x -3

Step-by-step explanation:

Let's look for the gradient to solve this question for.

We are given y= -1/5x-3

Any line perpendicular to the above line will have a graient of m'.

Where mm'= -1

m = -1/5 from the line equation

So

mm'= -1

-1/5m'= -1

m' =5

For the equation of point (1,2)

(Y-y1)/(x-x1) = m'

(Y-2)/(x-1)= 5

Y-2= 5x -5

Y = 5x -3

Answer:

if the net where to be folded into a cube number 6 will be opposite number 1.

Step-by-step explanation:

If the net where folded into a cube the number that will be opposite to number 1 will be 6 . The best way to know this is by simply cutting a paper similar to the shape of the net above and numbering them as required . Folding the paper to form a cube, you will discover that the number 6 is opposite the number 1 value.

Or from the picture you will notice when you close the number 5, the number 4 will be on top of number 1 and the 6 can then be bend  down which makes it opposite the number 1.

Answer: 66 possible combinations.

Step-by-step explanation:

To have a positive product we have 3 situations.

The 4 numbers are positive:

if the "order" of the selection does not matter, then we have only one solution here:

1, 2, 3 and 4.

Second case, we have two negative numbers and two positive numbers.

Here we can use the fact that in a group of N objects, the number of different combinations of K objects (where K ≤ N) is:

[tex]C = \frac{N!}{(N -K)!*K!}[/tex]

Here we have 5 negative numbers and we want to make groups of 2, so the possible combinations are:

[tex]C = \frac{5!}{3!*2!} = \frac{5*4}{2*1} = 2*5 = 10[/tex]

And we have exactly the same for the other two positive numbers, but in this case we have N = 4 and  K = 2.

[tex]C = \frac{4!}{2!*2!} = 6[/tex]

The total number of combinations is the product of those two:

C = 10*6 = 60 combinations

Now, the last option is that the 4 numbers are negative numbers, so here we have 5 negative numbers and we want to make groups of 4.

[tex]C = \frac{5!}{1!*4!} = 5[/tex]

So in total, we have: 1 + 60 + 6 = 66 possible combinations.

Answer:

3/10 gallons

Step-by-step explanation:

We know that the recipe for 1 serving calls for 3/5 gallons of milk.

We want to know what 1/2 a serving calls for. Let's set up a proportion:

(1/2) / 1 = x / (3/5) , where x is the amount of milk needed for 1/2 the recipe

Cross-multiply:

x * 1 = (1/2) * (3/5)

x = 3/10

The answer is thus 3/10 gallons.

~ an aesthetics lover

Answer:

3/10 gallon of milk

Step-by-step explanation:

The recipe needs 3/5 gallon of milk, half of the recipe requires half of the milk.

3/5 half is:

[tex]3/5 \times 1/2[/tex]

[tex]=3/10[/tex]

Answer:

The formula to compute the probability that at exactly x of the students scored over 650 points is:

[tex]P(X=x)={9\choose x}\ (0.30)^{x}\ (1-0.30)^{9-x}[/tex]

Step-by-step explanation:

Let the random variable X represent the number of students who scored above 650 in the college entrance exam.

The probability that a student scored above 650 in the college entrance exam is, p = 0.30.

A random sample of n = 9 students was selected.

The events of any student scoring above 650 in the college entrance exam  is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 9 and p = 0.30.

The probability mass function of X is:

[tex]P(X=x)={9\choose x}\ (0.30)^{x}\ (1-0.30)^{9-x};\ x=0,1,2,3...[/tex]

Thus, the formula to compute the probability that at exactly x of the students scored over 650 points is:

[tex]P(X=x)={9\choose x}\ (0.30)^{x}\ (1-0.30)^{9-x}[/tex]

Answer:

7

Step-by-step explanation:

Answer on learning curve

Answer:

Step-by-step explanation:

1) divide equilateral tri from the middle you will get two 30-60-90 triangles

2) by using pythagorean law & trigimintory, you will get two unknowns (height and side length) and two functions

Answer:

Mode

Step-by-step explanation:

Mean:

Before replacing = 464/8 = 58

After replacing 42 with 98 = 520/8 = 65

Mode:

Before replacing = 42

After replacing 42 with 98 = 98

Median:

25, 42 , 42 , 47, 55 , 59, 96,98

Before replacing =  47+55/2 = 51

25, 42 ,  47, 55 , 59, 96,98 , 98

After replacing 42 with 98 =  55+59/2 = 114/2 = 57

Answer:

Step-by-step explanation:

Degree of a polynomial is the highest sum of exponents for any one monomial of the polynomial.

[tex]-w^0[/tex]                           Degree : 0  

Degree of monomial 'w' = 0

[tex]36x^8-2x^9+8x^7[/tex]       Degree : 9

Highest degree term of the polynomial is 2x⁹,

Therefore, degree of polynomial = 9

[tex]\frac{rs}{3}+\frac{xy}{7}[/tex]                        Degree :  2

Degree of x + degree of y = 1 + 1 = 2

[tex]3x^4+9x^3-4x^5+1[/tex]   Degree : 5

Highest degree term of the polynomial is 4x⁵,

Therefore, degree of polynomial = 5

Answer:  4

Step-by-step explanation:

To fit the maximum amount of people in one row, you would have 3 couples and 1 single = 7 parents.

If we continue the maximum amount of people for 7 rows, we get 49 parents seated.

Since a total of 54 parents are seated, that leaves 54 - 49 = 5 parents remaining to be seated in the last row.  These parents can be seated as 2 couples and 1 single. If you put the single at the end of the row, there will be 4 seats between the couple and the single.

Couple, Couple, Open, Couple, Couple, Open, Open, Open, Open, Single

Answer: they are congruent

Answer:

congruent :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation: if you replace R1 with 1 and R3 with 0 you have -2(1)+0 which equals 0 and that matches matrix II. Repeat the process with the other numbers in R1 and R3 and they all come out equal therefor the answer is D.

The 4th operation i.e. -2R1 + R3 → R3 transformed matrix I to matrix II.

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.

Here, the R3 row is transformed. The elements of R3 in matrix I are 2, 7, 8, and 25. In matrix II, the elements of R3 are 0, 3, 6, and 15.

The elements of R1 in both matrices are 1, 2, 1, and 5.

Now, 2 - 1×2 = 2 - 2 = 0

7 - 2×2 = 7 - 4 = 3

8 - 1×2 = 8 - 2 = 6

25 - 5×2 = 25 - 10 = 15

Clearly, if we can perform the operation R3 - 2R1 in matrix I, we can get matrix II.

Therefore the 4th operation i.e. -2R1 + R3 → R3 transformed matrix I to matrix II.

Learn more about matrix here -

https://brainly.com/question/12563637

#SPJ2

Answer:

y = [tex]-9 \frac{1}{2}[/tex]

Step-by-step explanation:

9x-4y = 20

Given that x = -2

Putting in the above equation

9(-2) -4y = 20

-18 - 4y = 20

-4y = 20+18

-4y = 38

Dividing both sides by -4

y = [tex]-\frac{38}{4}[/tex]

y = [tex]-\frac{19}{2}[/tex]

y = [tex]-9 \frac{1}{2}[/tex]

Answer:

19/-2

Step-by-step explanation:

the answer is referred in the picture with the working out. hope it was helpful

Answer:

Step-by-step explanation:

A

The marble is red. There are 6 red marbles out of ten. So the answer is

6/10 = 0.60

B

Red: 1 3 5

Blue: 1 3

So there are 5 ways that you can draw an odd number. The problem is that they are not evenly distributed.

Red: 1/2 * 3/6 = 1/4 = 0.25

Blue: 1/2 * 2/4 = 0.25

Red + blue = 1/4 + 1/4 = 1/2

You could have gotten 1/2 by taking 5/10 but that won't always work.

C

Answer:

8:55 am.

Step-by-step explanation:

First we find the least Common Multiple of 25 and 35.

25 = 5 * 5

35 = 5 * 7

The LCM = 5 * 5 * 7 = 175 minutes

or 2 hours 55 minutes.

So the required time is 8:55 am.

Answer:

r < 37 or r ≥ 42

Step-by-step explanation:

the route, r?

than 37 minutes

she leaves after 7:00

then r= 37 or r ≥ 42

          or

r < 37 or r ≥ 42