Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?

Answer:

[tex]y=32[/tex]

Step-by-step explanation:

[tex]\frac{7}{4}y=56\\\mathrm{Multiply\:both\:sides\:by\:}4\\4\cdot \frac{7}{4}y=56\cdot \:4\\\mathrm{Simplify}\\7y=224\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7y}{7}=\frac{224}{7}\\Simplify\\y=32[/tex]

Answer:

B

Step-by-step explanation:

The coordinates of quadrilateral Q'P'R'S' is

Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

To perform a dilation centered at the origin with a scale factor of 2, we need to multiply the x and y coordinates of each vertex by 2.

So starting with the coordinates of quadrilateral QPRS:

Q(2, 4), P(0, 0), R(-2, -4), S(4, -2)

Multiplying each coordinate by 2, we get:

Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4)

Therefore,

The coordinates of quadrilateral Q'P'R'S' is

Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).

Learn more about scale factors here:

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The complete question.

Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?

Where

The coordinates of PQRS are:

Q = (2, 4), P = (0, 0), R = (-2, -4), S = (4, -2).

Answer:

Option D

Step-by-step explanation:

A matched pairs t-test is appropriate for this experiment. It compares two means that are from the same individual; the before drug administration and the after drug administration. It compares the before-and-after observations on the same subjects.

The best and convincing statistical evidence of a change, on average, in blood pressure is the t test.

The test is one of the kinds of inferential statistics. It is deployed in decision making. As such, it involves the test to see if there is significant difference between the means of two groups, which may be related.

Hence, in this study, the best and convincing statistical evidence of a change, on average, in blood pressure is the t test.

Learn more about t test:https://brainly.com/question/15870238

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Answer:

-127

Step-by-step explanation:

u(x)=2x-2

w(x)= -2x^2+1

w(u(5))=?

---------

u(5)= 2*5-2= 8

W(8)= - 2*64+1= -127

Answer:

that was the wrong answer this site sucks

Answer:

Convert the age to a z-score:

Step-by-step explanation:

Let X be the random variable with mean 27.2 and standard deviation 3.8.

Here, the observation, x is 24.

The z-score of the winner's age is -1.56.

A negative z-score indicates that the value is below the mean.

The age of the winner is not considered unusual.

A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.

It measures the unusual or extreme a particular data point is compared to the rest of the distribution

We have,

(a)

To transform the age of the winner into a z-score, we use the formula:

z = (x - μ) / σ

where x is the value we want to transform, μ is the mean, and σ is the standard deviation.

So,

Substituting the values given,

z = (22 - 27.3) / 3.4

z = -1.56

The z-score of the winner's age is -1.56.

(b)

A z-score represents the number of standard deviations a data point is from the mean.

In this case, the winner's age is 1.56 standard deviations below the mean age of the winners.

A negative z-score indicates that the value is below the mean.

(c)

Compare the z-score to a threshold value.

A commonly used threshold for unusual values is z = ±2.

If the absolute value of the z-score is greater than or equal to 2, then the value is considered unusual.

So,

The absolute value of the z-score is less than 2 (|z| < 2), which means that the age of the winner is not considered unusual in the context of the distribution of the ages of the winners.

Thus,

The z-score of the winner's age is -1.56.

A negative z-score indicates that the value is below the mean.

The age of the winner is not considered unusual.

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Answer:

[tex]3.1/13[/tex]

Step-by-step explanation:

[tex]1.5/7 =0.214286[/tex]

[tex]2.7/10=0.27[/tex]

[tex]3.1/13 =0.238462[/tex]

Answer:

$104430

Step-by-step explanation:

Let's recall the formula

PRT/100 = interest I

Where

P = principal/initial amount

R = rate

T= period or time

P =( 100*I)/(RT)

P =( 100*1320)/(15*(30/356))

P = 132000/1.264

P = $104430

Answer:

=2v−20

Step-by-step explanation:

Let's simplify step-by-step.

v−2+v−18

=v+−2+v+−18

Combine Like Terms:

=v+−2+v+−18

=(v+v)+(−2+−18)

=2v+−20

Answer:

=2v−20

Answer:

x = 23/5 and y = 7/20

Step-by-step explanation:

2x + 8y = 12 and 3x - 8y = 11 are two given equations

Now,

Step 1:

2x + 8y = 12 ...(1)

3x - 8y = 11 ...(2)

Step 2:

From equation (2) we get the value of x

i.e.,

3x - 8y = 11

3x = 8y + 11

x = 8y + 11/3

Step 3:

Now,

Put the value of x = 8y + 11/3 in equation (1) we get,

i.e.,

2x + 8y = 12

2(8y + 11/3) + 8y = 12

16y + 22/3 + 8y = 12

16y + 22 + 8y(3)/3 = 12

16y + 22 + 24y/3 = 12

16y + 24y + 22 = 12 * 3

40y = 36 - 22

40y = 14

y = 14/40

y = 7/20

Step 4:

Now,

Substitute the value of y = 7/20 in equation (2) we get,

i.e.,

3x - 8y = 11

3x - 8(7/20) = 11

3x - 56/20 = 11

3x - 14/5 = 11

3x = 11 + 14/5

3x = 11 * 5 + 14/5

3x = 55 + 14/5

3x = 69/5

x = 69/3 * 5

x = 23/5

Answer:

22.05

Step-by-step explanation:

Answer:

122 miles per hour.

Step-by-step explanation:

Time:108 min ÷60 =1.8 hours

Speed = distance /time = 219/1.8 =122 miles per hour.

Hope this helps..

Answer:

No its 121.67 mph.

Step-by-step explanation:

Speed in miles per minute is 219/108 miles per minute

To convert to miles per hour we multiply by 60:

= 219 * 60 / 108

= 121.67 m p h.

Answer:

(a) [tex]A_1[/tex] and [tex]A_2[/tex] are indeed mutually-exclusive.

(b) [tex]\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}[/tex], whereas [tex]\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}[/tex].

(c) [tex]\displaystyle P(B) = \frac{9}{100}[/tex].

(d) [tex]\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}[/tex], whereas [tex]P(A_1 \; |\; B) = \displaystyle \frac{4}{9}[/tex]

Step-by-step explanation:

[tex]P(A_1 \; \cap \; A_2) = 0[/tex] means that it is impossible for events [tex]A_1[/tex] and [tex]A_2[/tex] to happen at the same time. Therefore, event [tex]A_1[/tex] and [tex]A_2[/tex] are mutually-exclusive.

By the definition of conditional probability:

[tex]\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}[/tex].

Rearrange to obtain:

[tex]\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}[/tex].

Similarly:

[tex]\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}[/tex].

Note that:

[tex]\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}[/tex].

In other words, [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive. Since [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive and mutually-exclusive at the same time:

[tex]\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}[/tex].

By Bayes' Theorem:

[tex]\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}[/tex].

Similarly:

[tex]\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}[/tex].

Using probability concepts, along with conditional probability and Bayes Theorem, it is found that:

a) [tex]P(A1 \cap A2) = 0[/tex], thus yes, A1 and A2 are mutually exclusive.

b) The probabilities are: P(A1 ∩ B) = 0.05, P(A2 ∩ B) = 0.04.

c) The probability of event B is: P(B) = 0.09.

d) The probabilities are: P(A1|B) = 0.5555 and P(A2|B) = 0.4445.

-----------

Conditional Probability  

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]  

-----------

Bayes Theorem:  

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

-----------

Item a:

Item b:

Using conditional probability.

A1 and B:

[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]

[tex]0.25 = \frac{P(A1 \cap B)}{0.2}[/tex]

[tex]P(A1 \cap B) = 0.25(0.2) = 0.05[/tex]

A2 and B:

[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]

[tex]0.05 = \frac{P(A1 \cap B)}{0.8}[/tex]

[tex]P(A1 \cap B) = 0.8(0.05) = 0.04[/tex]

Item c:

P(B) is given by:

[tex]P(B) = P(A1 \cap B) + P(A2 \cap B) = 0.05 + 0.04 = 0.09[/tex]

Item d:

Applying Bayes Theorem

[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.25(0.2)}{0.09} = 0.5555[/tex]

[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.8(0.05)}{9} = 0.4445[/tex]

A similar problem is given at https://brainly.com/question/22428992

Answer:

  13.5%

Step-by-step explanation:

The probability of interest is the cumulative probability of a binomial probability density function with 18 trials and a probability of success of 0.25. We are interested in the value for x ≤ 2.

Such a calculation can be done "by hand" by adding up the probabilities for 0, 1, and 2 people. (A calculator is needed for the arithmetic.) One may as well use the appropriate function of a calculator to find the probability:

  binomcdf(18, 0.25, 2) ≈ 0.135

The probability is about 13.5%.

the answer is in the photos

Answer:

Test statistic t=1.2531.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters (P-value=0.11).

Step-by-step explanation:

The question is incomplete: We need the gestation length of the population to perform the hypothesis test. We assume it to be 16 days (μ=16).

This is a hypothesis test for the population mean.

The claim is that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=16\\\\H_a:\mu> 16[/tex]

The significance level is 0.05.

The sample has a size n=27.

The sample mean is M=17.4.

The sample variance is s^2=33.7 days^2.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.7^(0.5)=5.81.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.81}{\sqrt{27}}=1.1172[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.4-16}{1.1172}=\dfrac{1.4}{1.1172}=1.2531[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=27-1=26[/tex]

This test is a right-tailed test, with 26 degrees of freedom and t=1.2531, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>1.2531)=0.11[/tex]

As the P-value (0.11) is bigger 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 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.

Answer:

279 m

Step-by-step explanation:

Work by friction = change in kinetic energy

Fd = ½ mv²

d ∝ v²

d / 29 m = (105.4 mph)² / (34.0 mph)²

d = 279 m

Answer:

[tex]=210[/tex]

Step-by-step explanation:

[tex]7\times \left(-150\right)\div \left(10-10-5\right)\\Follow\:the\:PEMDAS\:order\:of\:operations\\\mathrm{Calculate\:within\:parentheses}\:\left(10-10-5\right)\::\quad -5\\10-10-5\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\\10-10=0\\=0-5\\=0-5\\=-5\\=7\times \left(-150\right)\div \left(-5\right)\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:7\times \left(-150\right)\div \left(-5\right)\::\quad 210\\7\times \left(-150\right)\div \left(-5\right)[/tex]

[tex]\mathrm{Apply\:rule\:}-a\div \left(-b\right)\:=\:a\div \:b\\-1050\div \left(-5\right)=1050\div \:5=210\\=210[/tex]

Answer:

210

Step-by-step explanation:

7×{(-150)÷(10-10-5)}

remove the opposites

7×{(-150)÷(-5)}

divide

7×30

multiply

210

Answer:

F(2)=3

Step-by-step explanation:

The first term is -1.5= f(1).

So  F(1+1)=-2*f(1)= (-1.5)*(-2)=3

Answer:

Step-by-step explanation:

From the information given, their last meter reading was 123,692 and their present reading is 127,394. The difference between the last and the present meter reading is

127394 - 123692 = 3702

If the water meter measures its water usage in terms of 1 point in CCF, then the amount of CCF of water used is 3702. If the school is charged $0.36 per CCF of water, then for this usage, the charge would be

3702 × 0.36 = $1332.72

Therefore, it is false

Answer:

  C. F(x) = | x |

Step-by-step explanation:

The parent function has no adornments, shifts, multipliers, offsets, reflections, or anything else.

The absolute value of x is written |x|. That is the parent absolute value function.

  F(x) = |x|

Answer: C

Step-by-step explanation:

Answer:

x=5/4

Step-by-step explanation:

First, plug in 1 for y. Since a common denominator for the right side is 3, multiply both sides by 3 to get 3=x+11/5. Then multiply both sides by 5 to get 15=5x+11. Subtract 11 on both sides to get 4=5x. Finally divide by 5 to get x by itself and get x = 5/4.

Answer:

The confidence interval is ( 0.225952516, 0.474047484)

People will get different results because, the amount of sedans may be dependent on the area in which the data is taken.

No, the sample is not really a good representation of the whole population of vehicles, since only a certain area was sampled or experimented.

Step-by-step explanation:

Solution

Given that:

From the experiment we discovered that out of 40 vehicles, 14 of them were sedans.

Let us note that:

p^ = It is the point estimate of the population proportion

Where,

n=/n  = 0.35

We also check for the standard error of p, sp:

which is,

sp =√{p^ (1-p^)/n] =0.075415516

Thus,

for the the critical z, we have the following:

α/2 = 0.05

So,

z (α)/2 = 1.644853627

Thus,

For lower bound = p^ - z(α/2) * sp = 0.225952516

For upper bound = p^ + z(α/2)* sp = 0.474047484

Hence,

The confidence interval becomes: ( 0.225952516, 0.474047484)

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]3x - 7 = 8[/tex]

[tex]3x = 8+7[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Answer:

x=5

Step-by-step explanation:

Let's solve your equation step-by-step.

3x−7=8

Step 1: Add 7 to both sides.

3x−7+7=8+7

3x=15

Step 2: Divide both sides by 3.

3x/3=15/3

x=5

Answer:

The formulas that will appear in

C1 is =B$2

D1 is = C$2

E1 is = D$2

Step-by-step explanation:

Given

Formula in B1 is = A$2

Required

Formulas in C1, D1 and E1 when dragged from B1.

In Microsoft Office Excel, this is called absolute reference.

But this type of absolute reference requires that only the cell name will be changed or altered, the row number will always remain the same no matter where it's been dragged to.

Since the initial column name is A and the Initial row number is 2 (from A$2),

Cell C1 will take the formula = B$2

Cell D1 will take = C$2

Cell E1 will take = D$2

Notice that only the column name changed for each formula; the row number remain unchanged.

Answer:

=B$2, C$2, D$2

Step-by-step explanation:

Explanation:

1. a) Null hypothesis: There is no statistically significant relationship between the mouse grimace scale and the amount of pain felt by mouse.

b) Alternate hypothesis: There is a statistically-significant relationship between the mouse grimace scale and the amount of pain felt by mouse.

2. Yes, because a statistically significant data implies that there is sufficient evidence to believe the study, based on the results of the findings.

3. No, since the variables are different in this case. Here we are dealing with a non-painful solution so there may be no sample correlation as extreme as that found in the original study.

4. Possibly, because every hypothesis is an assumption until it is proven. Thus, in every statistical research, there may be different findings.

Answer:

9x-2

Step-by-step explanation:

Since you are adding the two functions, you should first start adding like terms. 4x + 5x is 9x. -8 + 6 is -2. Thus the value of (f+g)(x) is 9x-2.

Answer:

a) [tex]7.4-1.96\frac{1.9}{\sqrt{36}}=6.78[/tex]    

[tex]7.4+1.96\frac{1.9}{\sqrt{36}}=8.02[/tex]    

b) For this case we can conclude that at 95% of confidence the true mean for the lenght of all welleye fingerprints in a fish hatchery pond is between 6.78 and 8.02

c) For this case since the value of 7.5 is included in the confidence interval we don't have enough evidence to conclude that the true mean is actually higher than 7.5 inches

Step-by-step explanation:

Information given

[tex]\bar X=7/4[/tex] represent the sample mean

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

[tex]\sigma=1.9[/tex] represent the population standard deviation

n=36 represent the sample size  

Part a

The confidence interval for the mean is given by :

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

The Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]

Replacing the info we got:

[tex]7.4-1.96\frac{1.9}{\sqrt{36}}=6.78[/tex]    

[tex]7.4+1.96\frac{1.9}{\sqrt{36}}=8.02[/tex]    

Part b

For this case we can conclude that at 95% of confidence the true mean for the lenght of all welleye fingerprints in a fish hatchery pond is between 6.78 and 8.02

Part c

For this case since the value of 7.5 is included in the confidence interval we don't have enough evidence to conclude that the true mean is actually higher than 7.5 inches

Answer:

b < 13

Step-by-step explanation:

Idk what you're asking but I'll try.

[tex]\frac{b}{1}=b[/tex]

b < 13

Answer:

b > -27.

Step-by-step explanation:

b / -3 + 4 < 13

b/-3 < 13 - 4

b/-3 < 9

-b/ 3 < 9

Multiply both sides by -3 ( the inequality sign will flip):

b > -27

Answer:no it doesn’t vary

Step-by-step explanation:because if you count them up there is no possibility that they match