!!!!!!! Why isn't A the correct answer? I am having trouble to reason why A is wrong so please help if can!

Answer:

We conclude that the pulse rate for smokers and non-smokers is equal.

Step-by-step explanation:

We are given that a medical researcher wants to compare the pulse rates of smokers and non-smokers.

A sample of 75 smokers has a mean pulse rate of 76, and a sample of 73 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 9 for smokers and 10 for non-smokers.

Let [tex]\mu_1[/tex] = true mean pulse rate for smokers

[tex]\mu_2[/tex] = true mean pulse rate for non-smokers

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]    {means that the pulse rate for smokers and non-smokers is same}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]    {means that the pulse rate for smokers and non-smokers is different}

The test statistics that will be used here is Two-sample z-test statistics because we know about the population standard deviations;

                       T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2}} }[/tex]  ~  N(0,1)

where, [tex]\bar X_1[/tex] = sample mean pulse rate of smokers = 76

[tex]\bar X_2[/tex] = sample mean pulse rate of non-smokers = 72

[tex]\sigma_1[/tex] = population standard deviation of the pulse rates of smokers = 9

[tex]\sigma_2[/tex] = population standard deviation of the pulse rates of non-smokers = 10

[tex]n_1[/tex] = sample of smokers = 75

= sample of smokers = 73

So, the test statistics =  [tex]\frac{(76-72)-(0)}{\sqrt{\frac{9^{2} }{75}+\frac{10^{2} }{73}} }[/tex]

                                    =  2.56  

The value of the z-test statistics is 2.56.

Also, the P-value of the test statistics is given by;

                P-value = P(Z > 2.56) = 1 - P(Z [tex]\leq[/tex] 2.56)

                              = 1 - 0.9948 = 0.0052

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0052 = 0.0104.

Now, at a 0.01 level of significance, the z table gives a critical value of -2.58 and 2.58 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the pulse rate for smokers and non-smokers is equal.

Answer:

y = x - 1

Step-by-step explanation:

Answer: c2 - a2 = b2

Step-by-step explanation: to isolate b2 you have to subtract a2 from both sides to get c2 - a2 = b2

Answer:

D

Step-by-step explanation:

w² - 9 can be factored as (w + 3)(w - 3) using the difference of squares. To factor w² - 4w - 21, we need to find 2 integers that have a sum of -4 and product of -21; these integers are -7 and 3 so the factored form is (w + 7)(w - 3). Therefore, the expression becomes:

(w + 3)(w - 3) / (w + 7)(w - 3)

Both the numerator and denominator have a factor of (w - 3) so that cancels out, leaving us with (w + 3) / (w + 7).

Answer:

110 cupcakes are left

Step-by-step explanation:

200-90 is 110

Answer:

110 cupcakes

Step-by-step explanation:

If you have 200 cupcakes and you give away 90, that means you only have [tex]200-90[/tex] cupcakes left.

[tex]200 - 90 = 110[/tex]

So you have 110 cupcakes left.

Hope this helped!

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]

Div and Curl:

Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]

First, let's define what we are given:

[tex]\displaystyle \text{F} = x^2 \hat{\i} + y^2 \hat{\j} + z \hat{\text{k}}[/tex]

Region D is the solid cube cut by coordinate planes and planes [tex]x = 2[/tex]. [tex]y = 2[/tex], and [tex]z = 2[/tex]

In order to use the Divergence Theorem, we first must find div F. We use partial differentiation and differentiation properties found under "Calculus" to attain div F:

[tex]\begin{aligned}\nabla \cdot \text{F} & = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial z}(z) \\& = 2x + 2y + 1 \\\textbf{div} \ \text{F} & = \boxed{2x + 2y + 1}\end{aligned}[/tex]

∴ [tex]\displaystyle \boxed{ \textbf{div} \ \text{F} = 2x + 2y + 1 }[/tex]

In order to find the outward flux of F across region D, we now must use the Divergence Theorem. Substitute our knowns into the Divergence Theorem Formula listed under "Multivariable Calculus":

[tex]\displaystyle \iiint_D \nabla \cdot \textbf{F} \, dV = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz[/tex]

We can now evaluate the Divergence Theorem integral using basic + advanced integration techniques listed under "Calculus" and learned from "Multivariable Calculus":

[tex]\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dz \, dy \, dx \\& = \int\limits^2_0 \int\limits^2_0 {(2x + 2y + 1)z \bigg| \limits^2_0} \, dy \, dx \\& = 2 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dy \, dx \\& = 2 \int\limits^2_0 {\bigg( 2xy + y^2 + y \bigg) \bigg| \limits^2_0} \, dx \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = 2 \int\limits^2_0 {4x + 6} \, dx \\& = 2 \bigg[ 2x^2 + 6x \bigg] \bigg| \limits^2_0 \\& = 2(20) \\& = \boxed{40} \\\end{aligned}[/tex]

∴ the integrals evaluates to 40.

[tex]\displaystyle \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz = \boxed{40}[/tex]

___

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Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

Answer:

1/204

Step-by-step explanation:

6/18 * 5/17 * 4/16 * 3/15

= 1/3 * 5/17 * 1/4 * 1/5

= 1/204

Step-by-step explanation:

[tex]y = a {(x - h)}^{2} + k[/tex]

[tex]vertex = (h \: \: \: k)[/tex]

from the table

[tex]vertex = ( - 2 \: \: \: 4)[/tex]

therefore

[tex]h = - 2 \: \: and \: \: k = 4[/tex]

[tex]y = a {(x + 2)}^{2} + 4[/tex]

when x= 0, y = 3

[tex]3 = a {(2)}^{2} + 4[/tex]

[tex]3 = 4a + 4[/tex]

[tex]a = \frac{ - 1}{4} [/tex]

therefore equation of the function

[tex]y = - \frac{1}{4} {(x + 2)}^{2} + 4[/tex]

Answer:

0.083

Step-by-step explanation:

To solve the above question, we use the combination method.

C(n, r) = nCr = n!/r!(n - r)!

Probability of answering (all 5 correctly)

= Probability of answering ( 5 out of 7 correctly)/ Probability of answering (5 out of 10 problems)

Probability of answering ( 5 out of 7 correctly) = 7C5

nCr = n!/r!(n - r)!

= 7!/5! (7 - 5)!

= 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (2 × 1)

= 21 ways

Probability of answering (5 out of 10 problems) = 10C5

nCr = n!/r!(n - r)!

= 10!/5! (10 - 5)!

= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (5 × 4 × 3 × 2 × 1)

= 252 ways

Probability of answering (all 5 correctly)

= 21/252

= 0.0833333333

Approximately = 0.083

Answer:

The correct answer is: (x,y)↦(x+ 8 ,y+ 16)

Hoped I helped

Answer:

13791

Step-by-step explanation:

Take 96,537 and divide by 7

The required value of the triple integral is (16/3)π.

To evaluate the triple integral ∫∫∫E z dV, where E lies above the paraboloid z = x² + y² and below the plane z = 2y, we can use cylindrical coordinates.

In cylindrical coordinates, we have:

x = r cosθ

y = r sinθ

z = z

To determine the limits of integration, we need to find the bounds for r, θ, and z.

The paraboloid z = x² + y² can be expressed in cylindrical coordinates as z = r².

The plane z = 2y can be expressed in cylindrical coordinates as z = 2r sinθ.

To find the bounds for r, we set the two equations equal to each other:

r^2 = 2r sinθ

Simplifying the equation, we have:

r = 2 sinθ

Since the paraboloid lies above the xy-plane, the lower bound for r is 0.

To find the bounds for θ, we need to determine the range of θ that corresponds to the region of interest. This can be done by plotting the two surfaces and visualizing the region. From the equations, we can see that the region lies within the range 0 ≤ θ ≤ π.

To find the bounds for z, we need to determine the range of z between the two surfaces. The paraboloid is below the plane, so the lower bound for z is the equation of the paraboloid, z = r^2. The upper bound for z is the equation of the plane, z = 2r sinθ.

Therefore, the limits of integration are as follows:

0 ≤ r ≤ 2 sinθ

0 ≤ θ ≤ π

r² ≤ z ≤ 2r sinθ

Now, we can evaluate the triple integral:

∫∫∫E z dV = ∫[0,2π] ∫[0,∞] ∫[r²,(2r sin θ)] (r cos(φ) sin(θ)) dz dr dθ
               = (16/3)π

Therefore, the value of the triple integral is (16/3)π.

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Answer:

m∠OKG = 95°

Step-by-step explanation:

In the given question,

Angle OKL and angle OKG are the linear pairs.

And we know that sum of linear pair of angles is 180°.

Therefore, m∠OKL + m∠OKH = 180°

85° + m∠OKH = 180°

m∠OKH = 180° - 85°

              = 95°

Therefore, measure of angle OKG = 95° will be the answer.

Answer:

Step-by-step explanation:

Step 1: the first term a is 13

Which means a=13 let's make this equation i

And the third term ar^3-1 = 1208

= Ar²= 1208 let's make this equation ii

Step 2: subtititute equation i into equation ii

= 13r²=1208

Divide both sides by 13 it gives us

13r²/13 = 1208/13

r²= 92.92

r= 9.64

So the second term ar^2-1

=ar

= 13. 9.64

= 125.32

Answer: p = 13.9

Step-by-step explanation: 7(p-9) = 34.3 multiply 7 into p and -9

7p - 63 = 34.3  add 63 into both sides

7p = 97.3  divide 7 into both sides.

p = 13.9

This question can be solved in  two ways

the equation given is  7(p-9)=34.3

The first step to take is to divide both sides of the equation by 7

p - 9 = 34.3 / 7

p - 9 = 4.9

The second step is to combine similar terms

p = 4.9 + 9 = 13.9

A second method

the equation given is  7(p-9)=34.3

1. expand the bracket

7p - 63 = 34.3

2. Combine similar terms

7p = 34.3 + 63

7p = 97.3

3. Divide both sides of the equation by 7

p = 13.9

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Answer:

The answer is not complete. I will explain the concept of profit to you.

Step-by-step explanation:

We can determine profit deducting direct costs (cost price) of commodities from sales (selling prices) of the commodities.

Profit = Selling Price - Cost Price

Example:

A trader buys some dresses for #2,500 in May and agrees to pay for it in three months’ time. He sells off all the dresses in August for #4,500. The profit for the month is #2,000.

The formula for percentage profit is [tex]\frac{profit * 100}{cost price}[/tex]

The formula for gross profit is Revenue – Cost of Sold Items

Profit Margin =  [tex]\frac{Total Income}{Net Sales}[/tex] * 100

While Gross Profit Margin can be calculated as [tex]\frac{Gross Profit}{Net Sales}[/tex] * 100

Any of these formulas can be used to calculate profit-related questions.

Answer:

Associative

Step-by-step explanation:

Answer:

13 weeks

Step-by-step explanation:

V = -15 x + 200 x 213.33 weeks 6 = -15x + 200 after 13 weeks.

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

The number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.

Given,

Micah was given $200 for his birthday.

Each week he spends $15 on comic books.

We need to find in how many weeks will his birthday money be gone.

We need to make sure we get the required value on the left side.

If 1 week = 7 days

Find how many days in 2 weeks

2 weeks = ​2 x 7 days = 14 days

We have  2 weeks on the left side.

If 2 items = $5

5/2 x 2 items = 5/2 x $5

5 items = $25/2 = $12.5

Find the total amount Micah has.

= $200

Find the amount spend each week.

= $15

Find how many weeks she must spend to spend $200.

We have,

$15 = 1 week

Multiply 200/15 on both sides.

200/15 x $15 = 200/15 x 1 week

$200 = 13.33 weeks

This means 13 weeks.

Thus the number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.

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Answer:

False

Step-by-step explanation:

Torricelli once carried out a tube and mercury experiment to test the scientific claim that nature abhors a vacuum.

In his experiment, he used glassblowers to make a long glass tube which was 4 ft long with a closed end.

He filled the tube with mercury and put his finger over the open end. Thereafter, he turned the tube upside down, dipped the open end in a bowl of mercury, and then removed his finger from the open end. He discovered that the mercury in the tube didn't completely run out as it fell to around 30 inches above the bowl before it stopped.

The gap between the sealed top end of the tube and the top end of the fallen mercury was an empty space which is a vacuum.

The hypothesis that "nature abhors a vacuum" would have implied that the vacuum would have pulled the mercury and held it up in the tube. However, that wasn't the case with his experiment and it proves that nature doesn't abhor a vacuum.

Thus, it is false.

Complete Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between   0  and   7  minutes. Find the probability that a randomly selected passenger has a waiting time  greater than 1.25  minutes.

Answer:

The probability is  [tex]P(X > 1.25) = 0.8214[/tex]    

Step-by-step explanation:

From the question we are told that

    The start time is  a  = 0 minutes

     The end time is  b =  7 minutes

Generally the probability that a randomly selected passenger has a waiting time  greater than 1.25  minutes is mathematically represented as

      [tex]P(X > 1.25) = 1 - P(X \le 1.25)[/tex]  

=>    [tex]P(X > 1.25) = 1 - \frac{1.25 - a}{ b- a }[/tex]  

=>    [tex]P(X > 1.25) = 1 -0.1786[/tex]

=>   [tex]P(X > 1.25) = 0.8214[/tex]    

The critical t-value for a confidence level of 98% with a sample size of 30 is approximately 2.756.

To find the critical t-value for a confidence level of 98% with a sample size of 30, we'll use the t-distribution table or a statistical calculator. Here's how you can calculate it:

Determine the degrees of freedom (df) for the t-distribution. For a sample size of 30, the degrees of freedom will be df = n - 1 = 30 - 1 = 29.

Look up the critical t-value in the t-distribution table using the desired confidence level and the degrees of freedom. In this case, for a 98% confidence level, we're interested in the critical value that leaves 1% in the tails of the t-distribution. Since the distribution is symmetric, we divide the 1% by 2 to get 0.5% for each tail.

Locate the row in the t-distribution table corresponding to the degrees of freedom (29 in this case). Then, look for the column that corresponds to the desired significance level (0.005 or 0.5% in this case).

Using a statistical calculator or t-distribution table, we find that the critical t-value for a 98% confidence level and 29 degrees of freedom is approximately 2.756.

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The critical t-value for a confidence level of 98% is 2.756.

Given data:

To find the critical t-value for a confidence level of 98% with a sample size of 30,  use a t-distribution table or a calculator.

Since the sample size is small (less than 30) and the population standard deviation is unknown, we use the t-distribution instead of the standard normal distribution.

The critical t-value is determined based on the confidence level and the degrees of freedom (df), which is equal to the sample size minus 1.

For a 98% confidence level, the corresponding significance level (α) is 1 - 0.98 = 0.02. Since it's a two-tailed test, divide this significance level by 2 to find the area in each tail: 0.02 / 2 = 0.01.

With a sample size of 30, the degrees of freedom is 30 - 1 = 29.

Using a t-distribution table or a calculator, we find the critical t-value with a cumulative probability of 0.01 (in each tail) and 29 degrees of freedom.

The critical t-value for a confidence level of 98% with a sample size of 30 is approximately ±2.756.

Hence, the critical t-value is 2.756.

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Answer:

[tex]\frac{1716}{132600}[/tex]

Step-by-step explanation:

Assuming they removed the jokers there are 52 cards in a deck and 13 hearts

You can calculate the odds of something by multiplying the odds together, because you don't put back the card you drew you have to subtract 1 from both the numerator and denominator

[tex](\frac{13}{52})(\frac{12}{51})(\frac{11}{50})=\frac{1716}{132600}[/tex]

Therefore the probability of pulling 3 cards that are all hearts are [tex]\frac{1716}{132600}[/tex]

Answer:

 The  test statistics is [tex]t = -1.40[/tex]

  The critical value is  [tex]Z_{\alpha } = 2.33[/tex]

   The null hypothesis is rejected

Step-by-step explanation:

From the question we are told that

   The sample size  for men is  [tex]n_1 = 80[/tex]

    The sample  proportion of men that own a cat is  [tex]\r p _M = 0.40[/tex]

     The  sample  size for  women is [tex]n_2 = 80[/tex]

     The sample  proportion of women that own a cat is  [tex]\r p_F = 0.51[/tex]

     The level of significance is  [tex]\alpha = 0.10[/tex]

   The  null hypothesis is  [tex]H_o : \r p _M = \ r P_F[/tex]

    The alternative hypothesis is  [tex]H_a : \r p _M < \r p_F[/tex]

Generally the test statistic is mathematically represented as

        [tex]t = \frac{(\r p_M - \r p_F)}{\sqrt{\frac{(p_M*(1-p_M)}{n_1 } } + \frac{p_F*(1-pF)}{n_2 } }[/tex]

=>  [tex]t = \frac{(0.40 - 0.51)}{\sqrt{\frac{(0.40 *(1-0.41)}{80} } + \frac{0.51*(1-0.51)}{80 } }[/tex]

=>   [tex]t = -1.40[/tex]

The critical value of  [tex]\alpha[/tex]  from the normal distribution table is

     [tex]Z_{\alpha } = 2.33[/tex]

The p-value  is obtained from the z-table ,the value is  

    [tex]p-value = P( Z < -1.40) = 0.080757[/tex]

=>    [tex]p-value = 0.080757[/tex]

Given that the [tex]p-value < \alpha[/tex] then we reject the null hypothesis

Answer:

directrix: y=4

focus: (-3,2)

vertex: (-3,3)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We need to first rewrite the equation the proper way.

(-2x+4x²+5)-(x²+3x)

We need to distribute the negative thought the 2nd set of parenthesis.

-2x+4x²+5-x²-3x

combine the same terms

3x²-5x+5

Answer:

b. [tex]\displaystyle Law\:of\:Cosines[/tex]

Step-by-step explanation:

You would use this law under two conditions:

Hence, you have your answer.

* Just make sure to use the inverse function towards the end, or elce you will throw your answer off!

_______________________________________________

Now, you would use the Law of Sines under three conditions:

* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.

I am delighted to assist you at any time.

Answer:

Conditions for SINE RULE:

Conditions for COSINE RULE:

Step-by-step explanation:

Side is the number in m/cm.

Angle is the number with degree/in degree. Like this: ° ° °

With all these, it means you should COSINE rule.

Answer:

1.1% decrease

Step-by-step explanation:

Use the formula, % change = (difference/original) x 100

Plug in the values:

% change = ((9.69 - 9.58) / 9.69) x 100

= 1.1% decrease

Answer:

10.9 liters

Step-by-step explanation:

cubical tank size = 30 x 30 x 30

filled with 6 cm x 30 cm x 30 cm = 5400 cu.cm

then added 5500 cu.cm.

total volume on a cubical tank = 5400 cu.cm + 5500 cu.cm

total volume on a cubical tank = 10,900 cu.cm x 1 cu.cm/0.001 liters

total volume on a cubical tank = 10.9 liters

Answer:

Step-by-step explanation:

= 10.9 liters

Answer: 0.8

Step-by-step explanation:

Given the following :

Sum of Square Error Error (SSE) = 100 which is the difference between the actual and predicted value.

Sum of Square due to regression (SSR) = 400

The Coefficient of determination (R^2) :

(Sum of Square Regression(SSR)) / Sum of Squared total (SST))

Sum of Squared total (SST) = SSE + SSR

Sum of Squared Total = (100 + 400) = 500

R^2 = 400 / 500

R^2 = 0.8