A random sample of 16 apartments in NYC showed that the average rent is $2,850 with standard deviation of $50. Assume normal distribution. Test the claim that the average rent has increased at α= 0.05

Answer:

im guessing thats on khan so 4=4  and 8 = 2:)

Step-by-step explanation:

Answer: Both

Step-by-step explanation: Both equal y intercept

Answer:

[tex]a. \quad 8\left(x+a\right)\\\\b. \quad 8\left(2x+h\right)[/tex]

Step-by-step explanation:

Best Regards!

Answer:  (a) 8(x  + a)   -->    8x + 8a

               (b) 8(2x + h)  -->   16x + 8h  

Step-by-step explanation:

f(x) = 8x²

f(a) = 8a²

[tex]\dfrac{f(x)-f(a)}{x-a}\quad = \quad \dfrac{8x^2-8a^2}{x-a}\quad = \quad \dfrac{8(x-a)(x+a)}{x-a}=\large\boxed{8(x+a)}[/tex]

f(x + h) = 8(x + h)²

           = 8(x² + 2xh + h²)

           = 8x² + 16xh + 8h²

f(x) = 8x²

[tex]\dfrac{f(x+h)-f(x)}{h} = \dfrac{(8x^2+16xh+8h^2)-8x^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{16xh + 8h^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{8h(2x + h)}{h}\\\\\\.\qquad \qquad \qquad \quad =\large\boxed{8(2x+h)}[/tex]

Answer:

  The discriminant is 0.

Step-by-step explanation:

The discriminant is zero if there is only one real solution to the quadratic equation.

__

A positive discriminant indicates 2 distinct real solutions; a negative discriminant indicates 2 distinct complex solutions.

Answer:

The Answer is C

Step-by-step explanation:

Answer:

mean of the sample μ₁ = $0.27

Standard deviation of the sample σ₁ = $0.83

Step-by-step explanation:

Step(i):-

given mean of the population 'μ' = $19.67

Mean of the sample

                            [tex]= \frac{mean}{n} = \frac{19.67}{72} = 0.27[/tex]

Mean of the sample  μ₁ = 0.27

Step(ii):-

Given standard deviation of the  population  (σ) =  $7.02

Standard deviation of sample

                             [tex]= \frac{mean}{\sqrt{n} } = \frac{7.02}{\sqrt{72} } = 0.827[/tex]

Standard deviation of sample = 0.827≅ 0.83

Final answer:-

mean of the sample μ₁ = $0.27

Standard deviation of the sample σ₁ = $0.83

Answer: if he/she tosses the coin 9 times i am pretty sure he/she out of 5/9 he/she will get heads

Step-by-step explanation:

1 if he flips the coin 9 times and it spins and it flips i am pretty sure a couple times he/she will get tails or heads 2 but there is a way for him/her to get heads it flips and spins he/she is most likey to get heads 3 if he/she flips the coin and the coin keeps going the coin will flip and he/she will get heads hope this helps you :)

Answer:

4a²

Step-by-step explanation:

(2a)²

Distribute the square to all the terms in the bracket.

2²a²

Solve the powers if possible.

4a²

Answer:

4a²

Step-by-step explanation:

=> [tex](2a)^2[/tex]

=> [tex](2^2*a^2)[/tex]

=> 4 * a²

=> 4a²

Answer:

4.92% probability that the third strike comes on the seventh well drilled

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution 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.

20% chance of striking oil.

This means that [tex]p = 0.2[/tex]

What is that probability that the third strike comes on the seventh well drilled

2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]

Strike during the 7th drill, with 0.2 probability. So

[tex]P = 0.2P(X = 2)[/tex]

In which

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

[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]

Then

[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]

4.92% probability that the third strike comes on the seventh well drilled

Answer:

The numbers are 2 and 8.

Solution,

Let the numbers be X and 4x

[tex] \frac{1}{x} + \frac{1}{4x} = \frac{5}{8} \\ or \: \frac{1 \times 4 + 1}{4x} = \frac{5}{8} \\ or \: \frac{4 + 1}{4x} = \frac{5}{8} \\ or \: \frac{5}{4x} = \frac{5}{8} \\ or \: 5 \times 4x = 5 \times 8(cross \: multiplication) \\ or \: 20x = 40 \\ or \: x = \frac{40}{20} \\ x = 2 \\ again \\ 4x \\ = 4 \times x \\ = 4 \times 2 \\ = 8[/tex]

hope this helps...

Good luck on your assignment..

Answer:

  (a) b = (4/7)c

  (b) Bill: 40 shingles/hour; Chip: 70 shingles/hour

Step-by-step explanation:

Let b and c represent Bill's and Chip's rates in shingles per hour, respectively. Then we have ...

  7b = 4c

  c - b = 30 . . . . shingles per hour difference in rates

(a) Bill's rate in terms of Chip's rate can be found by dividing the first equation by 7

  b = (4/7)c . . . . . Bill's rate is 4/7 of Chip's rate

__

(b) To find the rates, we can multiply the second equation by 7 and substitute using the first equation:

  7c -7b = 210

  7c -4c = 210

  c = 210/3 = 70

  b = (4/7)(70) = 40

Bill's rate is 40 shingles per hour; Chip's rate is 70 shingles per hour.

Answer:

Step-by-step explanation:

Hello!

The Psychomotor Development Index (PDI) has an average value of μ= 100

The Mental Development Index (MDI) has an average value of μ= 100

At an approximate age of 1 year of normal healthy infants.

Using the group data set heart = 1 for all calculations (see attachment for complete table), you can define two variables of interest and obtain the descriptive statistics:

X₁: PDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₁= 69

X[bar]₁= 97.61

S₁= 14.73

X₂: MDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₂= 69

X[bar]₂= 106.33

S₂= 14.67

a)

You have to test the hypothesis that the average PDI for kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

H₀: μ₁ = 100

H₁: μ₁ ≠ 100

α: 0.05

[tex]Z= \frac{X[bar]_1-Mu_1}{\frac{S_1}{\sqrt{n_1} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{97.61-100}{\frac{14.73}{\sqrt{69} } } = -1.347[/tex]

p-value: 0.17798

Using this approach the decision rule is:

The p-value is greater than the level of significance, the decision is to not reject the null hypothesis. Then the average PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

b)

H₀: μ₂ = 100

H₁: μ₂ ≠ 100

α: 0.05

[tex]Z= \frac{X[bar]_2-Mu_2}{\frac{S_2}{\sqrt{n_2} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{106.33-100}{\frac{14.67}{\sqrt{69} } } = 3.584[/tex]

p-value: 0.000338

Using this approach the decision rule is:

The p-value is less than the level of significance, the decision is to reject the null hypothesis. Then the average MDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is different from 100.

c)

[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

95% CI for PDI

X[bar]₁ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_1}{\sqrt{n_1} }[/tex]

97.61 ± 1.96 * [tex]\frac{14.73}{\sqrt{69} }[/tex]

[94.134; 101.086]

95% CI for MDI

X[bar]₂ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_2}{\sqrt{n_2} }[/tex]

106.33 ± 1.96 * [tex]\frac{14.67}{\sqrt{69} }[/tex]

[102.869; 109.791]

The CI for the mean PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life contains 100, this is to be expected since the null hypothesis in the hypothesis test made at complementary confidence level, was not rejected.

I hope this helps!

Answer:

The height of the flagpole = 4.50m (3signifiant figures)

Question:

A tree and a flagpole are on the same

horizontal ground. A bird on top of the

tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, Calculate Correct to 3 significant figures the height of the flagpole.

Step-by-step explanation:

First we have to represent the above information with a diagram to enable us solve the question.

Then label them for easy identification.

To determine the distance between the tree and flagpole, we would apply tangent rule.

Let their distance = x

Tan60 = opposite/adjacent

Tan60 = 10.65/y

Tan60 × y = 10.65

y = 10.65/Tan60

y = 10.65/1.7321

y = 6.15m

See attachment for the concluding part

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution 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.

Random voting:

So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]

15 members:

This means that [tex]n = 15[/tex]

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

[tex]p = P(X = 0) + P(X = 15)[/tex]

In which

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

[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]

[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]

So

[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]

0.006% probability that the final vote count is unanimous.

Answer:

[tex]\dfrac{3x^2+34x+51}{2x^2+12x+18}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x+9}{2x+6}+\dfrac{8x+12}{x^2+6x+9}= \\\\\\\dfrac{3(x+3)}{2(x+3)}+\dfrac{8x+12}{(x+3)(x+3)}[/tex]

To add these two fractions, you need to make the denominators equal:

[tex]\dfrac{3(x+3)(x+3)}{2(x+3)(x+3)}+\dfrac{16x+24}{2(x+3)(x+3)}= \\\\\\\dfrac{(3x^2+18x+27)+(16x+24)}{2(x+3)(x+3)}= \\\\\\\dfrac{3x^2+34x+51}{2(x+3)(x+3)}= \\\\\\\dfrac{3x^2+34x+51}{2x^2+12x+18}[/tex]

Hope this helps!

Answer:

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex] = 1

Step-by-step explanation:

You have to calculate the following limit:

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex]

To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}= \lim_{x \to \infty}\frac{x(1+\frac{6}{x})}{x(1+\frac{7}{x})}=\lim_{x \to \infty}\frac{1+6/x}{1+7/x}=\frac{1+0}{1+0}=1[/tex]

Hence, the limit is 1, L = 1

Answer:

25 pencils.

Step-by-step explanation:

You have 30 blue pencils and 15 green ones. To find how many pencils of other colors are in the bag, we can solve: 70-15-30=25

So, there are 25 pencils of other colors in the bag.

Answer:

15 cm

Step-by-step explanation:

Median means middle number

10,15,15,18,20

Answer:

15 cm

Step-by-step explanation:

The median is the number in the middle of a data set.

First, arrange the data from least to greatest.

10 cm, 15 cm, 15 cm, 18 cm, 20 cm

Now, take one number off each end of the data set until the middle number is reached.

10 cm, 15 cm, 15 cm, 18 cm, 20 cm

15 cm, 15 cm, 18 cm

15 cm

Therefore the median of the set of measurements is 15 cm.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

[tex] ME=0.03[/tex] the margin of error desired

[tex]Conf= 0.95[/tex] the level of confidence given

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

the critical value for 95% of confidence is [tex] z=1.96[/tex]

We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Answer:

Dear Yates

Answer to your query is provided below

Total Price for her vehicle will be $20600

Step-by-step explanation:

Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:

$22750 - $8000 = $14750.

Now, add the package upgrade ($5050) and the delivery charge ($800).

$14750 + $5050 + $800 = $20600.

The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The initial cost of the vehicle is = $ 22,750

Now , Edith has asked for an upgrade to a premium package for which the cost is $5050

So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800

Now , the delivery charge of the vehicle = $ 700

And , the updated total price = $ 27,800 + $ 700 = $ 28,500

Now , the dealer has offered her $8000

So , the final price of the vehicle = updated total price - $ 8000

On simplifying the equation , we get

The final price of the vehicle A = $ 28,500 - $ 8,000

The final price of the vehicle A = $ 20,500

Hence , the final price of the vehicle is $ 20,500

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Answer: yes is it a function

Step-by-step explanation:

A graph is a function when there is only one y value for each x value. You can also use the vertical line test. This example is a “quadratic function”.

Answer:

A. 12

Step-by-step explanation:

If we split an equalateral triangle down, it will become 2 30-60-90 triangles. Remember your 30-60-90 triangle rules.

6√3 = x√3, so x = 6

2(6) (for hypotenuse) = 12

Since the hypotenuse is one side of the bigger triangle, we have our final answer of 12.

Answer:

The value of the test statistic is:

t = -1.112

Step-by-step explanation:

In this case a paired difference test is to be performed.

The hypothesis can be defined as follows:

H₀: There is no difference between the two population means, i.e. d = 0.

Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.

The significance level of the test is, α = 0.10.

Use MS-Excel to perform the analysis.

Consider the output attached below.

The value of the test statistic is:

t = -1.112

The p-value of the two-tailed test is:

p-value = 0.303.

Decision rule:

Reject the null hypothesis if the p-value is less than the significance level.

p-value = 0.303 > α = 0.10.

The null hypothesis was failed to be rejected at 10% level of significance.

Conclusion:

There is not enough evidence to support the claim that there is a difference between the two population means.

Answer:

(x + 3)(x + 2)

Step-by-step explanation:

Given

x² + 5x + 6

Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)

The factors are + 3 and + 2 , since

3 × 2 = 6 and 3 + 2 = 5 , thus

x² + 5x + 6 = (x + 3)(x + 2)

Answer:

Mean, median and mode are measures of central tendency. The median is a better measure of central tendency when the given data contains outliers.

Step-by-step explanation:

Mean, median and mode are all measures of central tendency. These are statistical information that gives the middle or centre of a set of data. Since the values are central, they usually represent the entire distribution.

The mean is the obtained by dividing the sum of all the scores by the number of scores. The median is the middle value when numbers are arranged in increasing or decreasing order of magnitude. The mode is the most frequently occurring score in a distribution.

Let us see an example of the median as a measure of central tendency. Given the set of values; 4, 10, 12, and 26, the median is obtained from the average of the two middle numbers in the set of values which are 10 and 12 as seen from the set of values above. Hence the median of this set of values is 11.

The median can be a very good measure of central tendency, even better than the mean mostly in situations where there are outliers, or extreme values.

Answer:

Third option.

Step-by-step explanation:

The triangles below are similar, because they have congruent corresponding angles.

Angle N is 105 degrees and angle Q is 105 degrees.

Answer:

Step-by-step explanation:

Let the volume of tank be x

In 18 hours volume of tank filled = x

we have to find the volume of tank which is filled in 1 hours.

For that we divide LHS and RHS by 18

In 18/18 hours volume of tank filled = x/18

In 1 hours volume of tank filled = x/18

In 30 hours volume of tank emptied = x

we have to find the volume of tank which is emptied in 1 hours.

For that we divide LHS and RHS by 30

in 30/30 hours volume of tank filled = x/30

In 1 hours volume of tank filled = x/30

If tank is empty and one starts to fill it, two things will happen

it will start filling at rate of x/18 hours

But there is leak which will start to empty the tank at  x/30 hours

So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank

In 1 hour volume of tank filled if both filling and leaking takes place simultaneously =  x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45

In 1 hour volume of tank filled = x/45

in 1*45 hour volume of tank filled = x/45*45 = x

Thus, it will take 45 hours to fill the leaky tank  .

Answer:

Choice D.

Step-by-step explanation:

The number of points is obtained by the number of points of each multiple choice question times the number of multiple choice questions added to the number of points of each short answer question times the number of short answer questions.

Since the total number of points is 50, then the number of points from the multiple choice questions plus the number of points from the short answer questions add up to 50 points.

Answer: Choice D.

Answer:

D

Step-by-step explanation:

The number of points is 50, and short answer questions are 3 pts. Multiple choices are 1 pts.

So we have 3s+m=50

Answer:

b) 0.0608

Step-by-step explanation:

As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed

Therefore the rain probability is

[tex]= \frac{T}{24}[/tex]

where,

T = Length of the time interval

Plus, as we know that rain is independent

So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes

i.e

= 5.91666 hours long.

So, P1 should be

[tex]= \frac{5.91666}{24}[/tex]

= 0.2465

Now we assume the probability of rain on day 2 is P2

So it would be same  i.e 0.2465

Since these events are independent

So, the total probability is

[tex]= 0.2465 \times 0.2465[/tex]

= 0.0608

Hence, the b option is correct

Answer:

14

Step-by-step explanation:

630÷45=14

Answer:

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

We multiply 42 × 3= 126

The measure of the angle is 126.

The measure of angle will be 66°.

What is Complementary angle?

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

Given that;

The measure of the supplement of an angle is 42 more than 3 times the measure of the complement of an angle.

Now,

Let the measure of angle = x

So, We can formulate;

⇒ (180 - x) = 42 + 3 (90 - x)

Solve for x as;

⇒ 180 - x = 42 + 270 - 3x

⇒ 180 - x + 3x = 312

⇒ 2x = 312 - 180

⇒ 2x = 132

⇒ x = 66

Thus, The measure of angle will be 66°.

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Answer:

  see below

Step-by-step explanation:

The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.