Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an appropriate form so that a trigonometric substitution can be performed. 13 + 12x − x2

Answer:68

Step-by-step explanation:

angle sum property

56+y+y-12=180

44+2y=180

2y=180-44=136

y=136/2

=68

VERIFICATION :56+68+56

                         =180

Y =112°

remember the sum of angles in a triangle equals 180°

EDIT : previous answer is right, i messed up with the sign

Answer:

The probability that Joe will be accepted at one, and only one, university is 0.45 or 45%.

Step-by-step explanation:

We are given that Joe is considering pursuing an MBA degree. He has applied to two different universities.

The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.

Let the probability that Joe will be accepted for University A = P(A) = 0.25

Probability that Joe will be accepted for University B = P(B) = 0.40

Now, Probability that Joe will be accepted at one, and only one, university is given by ;

Accepted for University A but not for University B + Accepted for University B but not for University A

=  [P(A) [tex]\times[/tex] (1 - P(B))] + [P(B) [tex]\times[/tex] (1 - P(A))]

=  (0.25 [tex]\times[/tex] 0.60) + (0.40 [tex]\times[/tex] 0.75)

=  0.15 + 0.30 = 0.45

Hence, the probability that Joe will be accepted at one, and only one, university is 0.45.

The probability that Joe will be accepted at one, and only one, university is 0.45 or 45%.

Let us assume the probability that Joe will be accepted for University A = P(A) = 0.25

Now

Probability that Joe will be accepted for University B = P(B) = 0.40

Now,

= Accepted for University A but not for University B + Accepted for University B but not for University A

=  [P(A)  (1 - P(B))] + [P(B)  (1 - P(A))]

=  (0.25  0.60) + (0.40  0.75)

=  0.15 + 0.30

= 0.45

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Answer:

Roughly 15% hourly rate.

Step-by-step explanation:

This is an exponential function that relates to natural growth.

Use the formula A = P*e^(rt)

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer: D.

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

Step-by-step explanation:

Looking at the graph included in the answer, the graph is connected between four points.

It starts with a negative slope, then changes to a positive slope after (-2, 0), and then changes back to a negative slope after (2, 2).

To answer this, first we need to know what a one-to-one function is.

A one-to-one function is any function that only has one x-coordinate for every y-coordinate. If a function has two x-coordinates for one y-coordinate (for example, (5, 4) and (10, 4)), then the function is not one-to-one.

An example of a one-to-one function is the graph of y = x.

There is only one x-coordinate for every y-coordinate on the graph.

You can use the "horizontal line" test to determine whether a function is one-to-one. If a horizontal line is placed anywhere on a graph and intersects the function more than once, the function is not one-to-one

For the function given:

When a horizontal line is placed at "y = 1", it intersects the function three times. This means that the function IS NOT one-to-one.

Choice D is correct.

The coordinates between y = 0 and y = 2 are paired with multiple x-values, and this correctly explains why the function is not one-to-one.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Answer: The word "ensures" implies that it is certain.

In the case of the study, they simply found that the average salary is greater for college graduates. This doesn't mean that in every case the college graduate makes more money.

The problem is the word "ensures". Our study doesn't show certainty only a general pattern.

Step-by-step explanation:

Answer: the last 1/ 12 a < 18

Step-by-step explanation:

Answer:

Length = [tex]\frac{189}{4}\ m[/tex]

Width = 21 m

Area of garden = 992.25 [tex]m^{2}[/tex]

Step-by-step explanation:

Side of square = 1 cm

As per the given question figure, we can see that there are 11 square across the length of rectangular garden.

But the garden includes only 9 squares, the corner squares are not in the garden.

So, length of garden = 9 [tex]\times[/tex] 1 = 9 cm

Using the scaling given in the question,

[tex]\dfrac{2}{3}\ cm = 3\dfrac{1}{2}\ m\\[/tex][tex]\Rightarrow \dfrac{2}{3}\ cm = \dfrac{7}{2}\ m[/tex]

[tex]1 cm = \dfrac{\dfrac{7}{2}}{\dfrac{2}{3}} \ m \Rightarrow \dfrac{21}{4}\ m[/tex]

So, length of garden = [tex]\dfrac{21}{4} \times 9 \Rightarrow \dfrac{189}{4}\ m[/tex]

-------------

And, similarly width contains 4 squares, (Corner squares are excluded)

Width of garden = [tex]\dfrac{21}{4} \times 4 \Rightarrow 21\ m[/tex]

-------------

Area of garden = Length [tex]\times[/tex] Width

[tex]\Rightarrow \dfrac{189}{4} \times 21\\\Rightarrow \dfrac{3969}{4}\\\Rightarrow 992.25\ m^{2}[/tex]

Answer:

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]

[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]

[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]

And the 90% confidence interval would be given (0.131;0.169).

Step-by-step explanation:

We have the following info given:

[tex]n= 955[/tex] represent the sampel size slected

[tex] x = 812[/tex] number of students who read above the eighth grade level

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]

The confidence interval for the proportion  would be given by this formula

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

For the 90% confidence interval the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], with that value we can find the quantile required for the interval in the normal standard distribution and we got.

[tex]z_{\alpha/2}=1.64[/tex]

And replacing into the confidence interval formula we got:

[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]

[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]

And the 90% confidence interval would be given (0.131;0.169).

Answer:

The total amount of water needed is 540 cubic inches.

Step-by-step explanation:

A cubic prism has three dimension. Lenght l, width w and height h.

It's volume is:

[tex]V = l*w*h[/tex]

In this question:

[tex]l = 12.5, w = 6, h = 8[/tex]

Dimensions in inches, so the volume will be in cubic inches.

[tex]V = 12.5*6*8 = 600[/tex]

The volume is 600 cubic inches.

What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?

This is 90% of 600. So

0.9*600 = 540

The total amount of water needed is 540 cubic inches.

Answer:

Richard works for $9 per hour

Step-by-step explanation:

Answer:

The answer is proportional. He makes 9$ an hour

Step-by-step explanation:

Your welcome

Answer:

y^1/2/xz^2 option 3

Step-by-step explanation:

(x^1/2 y^-1/4 z)^-2= x^(-1/2*2) y^(1/4*2) z^-2= x^-1 y^1/2 z^-2= y^1/2/xz^2

Answer: C y^1/2/xz^2

Step-by-step explanation:

I checked with my calculator.

Answer:

Step-by-step explanation:

Given that:

X(t) = be the number of customers that have arrived up to time t.

[tex]W_1,W_2[/tex]... = the successive arrival times of the customers.

(a)

Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;

[tex]E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))[/tex]

[tex]= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}[/tex]

[tex]= 1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]

[tex]= 1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]

Now [tex]P(X(s) \leq 0) = P(X(s) = 0)[/tex]

(b)  We can Determine the conditional mean E[W3|X(t)=5] as follows;

[tex]E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\ = 1- P (X(s) \leq 2 | X (t) = 5 ) \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}[/tex]

Now; [tex]P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)[/tex]

(c) Determine the conditional probability density function for W2, given that X(t)=5.

So ; the conditional probability density function of [tex]W_2[/tex] given that  X(t)=5 is:

[tex]f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 ) \\ \\ = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)[/tex]

Answer:

hope this helps you

Answer:

a. The positive difference between Nelson's height and the population mean is: [tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: [tex] \\ z = -1.1739 \approx -1.174[/tex] (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since [tex] \\ -2 < -1.174 < 2[/tex].

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

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

Where

[tex] \\ z[/tex] is the z-score.

[tex] \\ \mu[/tex] is the population mean.

[tex] \\ \sigma[/tex] is the population standard deviation.

From the question, we have that:

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson​'s height and the​ mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

[tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].

That is, the positive difference is 2.7 in.

b. How many standard deviations is that​ [the difference found in part​ (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

[tex] \\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174[/tex]

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson​'s height to a z score.

Using formula [1], we have

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

[tex] \\ z = \frac{68\;in - 70.7\;in}{2.3\;in}[/tex]

[tex] \\ z = \frac{-2.7\;in}{2.3\;in}[/tex]

[tex] \\ z = -1.1739 \approx -1.174[/tex]

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Nelson​'s height usual or​ unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

[tex] \\ -2 < z_{Nelson} < 2[/tex]

[tex] \\ -2 < -1.174 < 2[/tex]

Then, Nelson's height is usual according to that statement.  

The probability that the women's team experiences 2 or more concussions is 0.0013.

We are given that;

The concussion rate = 0.63 per 1,000 participation hours

Now,

The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when these events occur with a known average rate and independently of the time since the last event.

The probability mass function of the Poisson distribution is given by:

[tex]$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$[/tex]

where X is the number of events occurring in the interval, k is a non-negative integer, and λ is the average rate of events per interval.

a. For collegiate men soccer players, the concussion rate is .41 per 1,000 participation hours.

Therefore, the average number of concussions per hour is λ = 0.41/1000 = 0.00041.

Let X be the number of concussions experienced by the men's team in an hour. Then X follows a Poisson distribution with parameter λ = 0.00041. We want to find P(X ≥ 2). Using the Poisson distribution formula,

[tex]$P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)$$= 1 - \frac{0.00041^0 e^{-0.00041}}{0!} - \frac{0.00041^1 e^{-0.00041}}{1!}$$= 1 - e^{-0.00041}(1 + 0.00041)$$\approx \boxed{0.0002}$[/tex]

b. For collegiate women soccer players, the concussion rate is .63 per 1,000 participation hours.

Therefore, the average number of concussions per hour is λ = 0.63/1000 = 0.00063.

Let Y be the number of concussions experienced by the women's team in an hour. Then Y follows a Poisson distribution with parameter λ = 0.00063. We want to find P(Y ≥ 2). Using the Poisson distribution formula,

[tex]$P(Y \geq 2) = 1 - P(Y < 2) = 1 - P(Y = 0) - P(Y = 1)$$= 1 - \frac{0.00063^0 e^{-0.00063}}{0!} - \frac{0.00063^1 e^{-0.00063}}{1!}$[/tex]

[tex]$= 1 - e^{-0.00063}(1 + 0.00063)$[/tex]

[tex]$\approx \boxed{0.0013}$[/tex]

Therefore, by poisson distribution formula answer will be 0.0013.

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Answer:

1. The chi-squared statistic = 10.36

The degrees of freedom = 17

The p-value for the test = 0.89

2. The range of the p-value from the Chi squared table = 0.75 < p-value < 0.90

Step-by-step explanation:

1. The Chi squared test is given as follows;

[tex]\chi ^{2} = \sum \dfrac{\left (Observed - Expected \right )^{2}}{Expected }[/tex]

Therefore,

                              UTI   No UTI    %     Total

Cranberry juice       8           42      84     50

Lactobacillus          19          30       61     49

Control                    18          30      60    50

The chi-squared statistic is given as follows;

[tex]\chi ^{2} = \dfrac{\left (8- 18\right )^{2}}{18} + \dfrac{\left (42 - 30\right )^{2}}{30} = 10.36[/tex]

The chi-squared statistic = 10.36

The degrees of freedom, df = 18 - 1 = 17 since the all of the expected count have a minimum value of 18

With the aid of the calculator we find the p value as p as follows;

[tex]p = 0.9 - \dfrac{10.36 - 10.085}{12.972 - 10.085} \times (0.9 - 0.75)[/tex]

The p-value for the test = 0.89  

2. The range of the p-value from the Chi squared table is given as follows;

0.75 < p-value < 0.90.

Answer:

m = 1/4

Step-by-step explanation:

We want to get the equation in slope intercept form

y = mx+b where m is the slope and b is the y intercept

x  -4y +3 =0

Add 4y to each side

x -4y+3 +4y = 0+4y

x-3 = 4y

Divide each side by 4

1/4x -3/4 =y

the slope is 1/4 and the y intercept is -3/4

Answer:

Step-by-step explanation:

The information given in the question can be represent in a table format for better understanding with the additional columns as follows:

Items          Weights Q₀         Prices P₀      Prices P₁        P₀Q₀        P₁Q₀

Cashew        1                        $12.50           $17.00        $12.50      $17.00

Pecans         1                         $4.00            $4.00         $4.00        $4.00

Almonds       1                         $5.50           $3.00          $5.50        $3.00

Total                                                                                 $22           $24

Can you say what happened to the overall "price level"?

The changes in overall price level can be a result of a condition termed as inflation rate

How might you construct a measure of the "change in price level"?

To construct a measure of the change in price level; we need to determine the consumer price index (CPI).

The consumer price index can be determined by using the relation:

[tex]=\mathbf{\dfrac{Sum \ of \ P_1Q_0}{Sum \ of \ P_oQ_o}*100 }[/tex]

[tex]= \mathbf{\dfrac{24}{22}*100 }[/tex]

= 109.0%

consumer price index (CPI) is 109.0% ; This implies that there is a 9.9% inflation in the economy.

Answer:

a. 9.9 cents

b. 26.5 dollars

Step-by-step explanation:

The first thing they mention to us is the cost of energy 11 cents / kwh

a) In the first point they ask us to calculate the daily cost of keeping the flashlight on for 12 hours, they tell us that it consumes 75 watts per hour, but this value must be passed to kW because the cost is given in kWh

to pass it, it would be: 75 watt * 1 kw / 1000 watt = 0.075 kw,

the formula to apply would be like this:

Daily cost = flashlight cost * time * energy cost

we all know them so we replace:

Daily cost = 0.075 kw * 12 h * 11 cents / kwh = 9.9 cents

b) Now, to know the annual savings, we must calculate the difference between the expense of the normal flashlight and the LED, let's calculate the daily cost of the LED, like this:

20 watt * 1 kw / 1000 watt = 0.02 kw

Daily cost = 0.02 kw * 12 h * 11 cents / kwh = 2.64 cents

Now by calculating the difference we multiply by 365 which are the days of a year.

Savings / year = (9.9 - 2.64) * 365 = 2649.9 cents = 26.5 dollars.

Answer:

A

Step-by-step explanation:

You can substitute 40 into c, work out the equation and you'll get $75 as the profit. Each candy bar is $2.5 so c would be the number of candy bars she sold.

Answer:

$75.58

The amount spent of $75.58 is most likely an outlier

Step-by-step explanation:

An outliers are unusual values in a dataset, they are data values that are extremely higher or extremely lower when compared to the other values in a data (data points that are far from other data points)

For the case above, give a dataset;

$32.92 $14.14 $30.80 $28.34 $75.58 $36.33 $33.51 $22.94

$75.58 is extremely far from other value. So $75.58 is an outlier in the given dataset.

Answer:

3600

Step-by-step explanation:

It consumes 3600 watt hours per day. Steps are included below.

We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.

Steps:

1: 24*15300/(4*24+6)=3600

Answer: 3600 watt hours per day

Hope this helps.

Answer:

3,600

Step-by-step explanation:

In the question, there is energy consumption and a rate but not in an easy way.

In order to find out how much watt-hours the light bulb consumes per day, the easiest way is to multiply by the hour to find out how much it uses in a day.

In 4 days and 6 hours there are 102 hours.

[tex]4 \times 24 = 96[/tex]

[tex]96 + 6 = 102[/tex]The hours for 4 days...

[tex]96 + 6 = 102[/tex]

4 days plus 6 hours. The total time...

Now make the watt-hours usage an hourly rate...

[tex]15300 + 102 = 150[/tex]

150 watts/hour...

Take the hourly rate and multiply it by 24 (number of hours in a day) to find out how many watt-hours the lightbulb uses in a day...

[tex]150 \times 24 = 3600[/tex]

Answer:

Yes the explanation satisfy the questions stated.

See below for explanation

Step-by-step explanation:

From the question, distance is said to be a function of time and the constant rate of change is 64.

y = 64x + 22

The above is in the form of a Linear equation:

y = mx + c

Where y = dependent variable (distance)

x = independent variable (time)

m = slope = distance/time

c = constant = 22

m = constant rate of change = 64

If x (time) = 4

y (distance) = 278 miles

y = 64(4) + 22

y = 256 + 22

y = 256 + 22

y = 278 miles

Answer:

nclude that distance is a function of time?

include that the constant rate of change, or slope, is 64?

include the equation y = 64x + 22?

say to substitute 4 in for x to get 278 miles?

Step-by-step explanation:

Answer:

Plot f(x)=x^4+x^3-8x^2-12x

Step-by-step explanation:

Answer:

If the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.

Step-by-step explanation:

When we performed a two-sided test and the null hypothesis failed to be rejected, when we perform a one-sided test we may reject or not the null hypothesis.

For instance, we have a 5% significance level test, where the test statistic is z=1.8.

For a two-sided test the critical values for α=5% are zc=±1.960. In this situation, the null hypothesis failed to be rejected.

But if we perform a one-sided test with the same significance level, we have a critical value z=1.645 and the conclusion is that the null hypothesis is rejected.

Then, if the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.

We are only sure that if a two-sided test rejects the null hypothesis, a one-side test with same significance level will always reject the null hypothesis.

Answer:

1.9730677676839334 or 1.97 (rounded)

Step-by-step explanation:

102-43=59

Answer:

Step-by-step explanation:

If you draw a horizontal line through the shaded triangle such that it intersects the left vertex, you see that it bisects the 60° angle at that vertex. The measure of x is the same as the measure of either half of that bisected angle, so is 30°.

The pitch associated in the table with an angle of 30° is 7.