May someone please help me with this :)

If a pair of dice is rolled, and the number that appears uppermost on each die is observed, the probability of the sum of the numbers being either 7 or 11 is 2/9.

To find the probability of the sum of the numbers rolled on a pair of dice being either 7 or 11, we need to determine the number of favorable outcomes and the total number of possible outcomes.

There are six possible outcomes for each die, ranging from 1 to 6. Since we are rolling two dice, the total number of possible outcomes is 6 multiplied by 6, which is 36.

To calculate the number of favorable outcomes, we need to determine the combinations that result in a sum of either 7 or 11.

For the sum of 7, there are six possible combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

For the sum of 11, there are two possible combinations: (5, 6) and (6, 5).

Therefore, the number of favorable outcomes is 6 + 2 = 8.

The probability of the sum of the numbers being either 7 or 11 is given by the ratio of favorable outcomes to the total number of outcomes:

P(sum is 7 or 11) = favorable outcomes / total outcomes = 8/36 = 2/9.

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Complete question is:

A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)

The sum of the numbers is either 7 or 11.

Answer: I think A

Step-by-step explanation:

Answer:

2.4

Step-by-step explanation:

3 / 28 = 0.12

(we do this to see how many miles he ran in a minute)

0.12 x 20 = 2.4

(then we multiply how many miles he can run in 20 minutes)

A) The scatterplot of the data is as follows:What can we interpret from the scatterplot of the given data?We can observe that the higher the number of risk factors, the lower the IQ of the children. This fact is supported by the trend line that shows a negative correlation. This is what the plot is telling us.A regression equation is given by the formula: $y=\beta_0+\beta_1x$Where, $y$ is the IQ of the child, $x$ is the number of risk factors, $\beta_0$ is the y-intercept and $\beta_1$ is the slope of the line.Both $\beta_0$ and $\beta_1$ can be calculated using the following formulae: $$\beta_1=r_{xy}\frac{s_y}{s_x}$$$$\beta_0=\bar{y}-\beta_1\bar{x}$$Where, $r_{xy}$ is the correlation coefficient between $x$ and $y$, $s_x$ and $s_y$ are the standard deviations of $x$ and $y$ respectively, and $\bar{x}$ and $\bar{y}$ are the means of $x$ and $y$ respectively.From the scatterplot, we can observe that $r_{xy}$ is negative. Therefore, there exists a negative correlation between $x$ and $y$.Let us calculate the values of $\beta_1$, $\beta_0$ using the above formulae.$$r_{xy}=\frac{\sum(x-\bar{x})(y-\bar{y})}{\sqrt{\sum(x-\bar{x})^2\sum(y-\bar{y})^2}}$$$$r_{xy}=\frac{(3)(112)+(6)(82)+(0)(105)+(5)(102)+(1)(115)+(1)(101)+(5)(94)+(4)(89)+(3)(98)+(3)(109)+(4)(91)+(2)(107)}{\sqrt{(3^2+6^2+0^2+5^2+1^2+1^2+5^2+4^2+3^2+3^2+4^2+2^2)(112^2+82^2+105^2+102^2+115^2+101^2+94^2+89^2+98^2+109^2+91^2+107^2)}}$$$$r_{xy}=-0.835$$Now, let's calculate the standard deviations of $x$ and $y$:$$s_x=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$$$$s_y=\sqrt{\frac{\sum(y-\bar{y})^2}{n-1}}$$$$s_x=\sqrt{\frac{(3-2)^2+(6-2)^2+(0-2)^2+(5-2)^2+(1-2)^2+(1-2)^2+(5-2)^2+(4-2)^2+(3-2)^2+(3-2)^2+(4-2)^2+(2-2)^2}{12-1}}$$$$s_x=\sqrt{\frac{44}{11}}=2$$$$s_y=\sqrt{\frac{\sum(y-\bar{y})^2}{n-1}}$$$$s_y=\sqrt{\frac{(112-99.17)^2+(82-99.17)^2+(105-99.17)^2+(102-99.17)^2+(115-99.17)^2+(101-99.17)^2+(94-99.17)^2+(89-99.17)^2+(98-99.17)^2+(109-99.17)^2+(91-99.17)^2+(107-99.17)^2}{12-1}}$$$$s_y=\sqrt{\frac{5626.1}{11}}=9.025$$Finally, let's calculate $\beta_1$ and $\beta_0$:$$\beta_1=r_{xy}\frac{s_y}{s_x}$$$$\beta_1=-0.835\frac{9.025}{2}=-3.762$$$$\beta_0=\bar{y}-\beta_1\bar{x}$$$$\beta_0=99.17-(-3.762)(3.08)=112.91$$Therefore, the regression equation is $y=112.91-3.762x$.Here, $\beta_0=112.91$ represents the expected IQ of a child with zero risk factors, while $\beta_1=-3.762$ represents the decrease in IQ per risk factor.B) James has 5 risk factors. Substituting $x=5$ in the regression equation, we get:$$y=112.91-3.762x$$$$y=112.91-3.762(5)$$$$y=93.13$$Therefore, the IQ predicted for James is $93.13$.Similarly, Elizabeth has 2 risk factors. Substituting $x=2$ in the regression equation, we get:$$y=112.91-3.762x$$$$y=112.91-3.762(2)$$$$y=105.39$$Therefore, the IQ predicted for Elizabeth is $105.39$.

The probability that their mean systolic blood pressure is between 119 and 122 is 0.0807.

The given distribution is normal.

So, the formula for the standardized random variable, z can be used.

Here,Mean of the given distribution, μ = 114.8

Standard deviation of the given distribution, σ = 13.1

Number of women aged 18-24 randomly selected, n = 23

Let X be the mean systolic blood pressure of 23 randomly selected women aged 18-24.

P(X is between 119 and 122) = P((X-μ)/σ is between (119-μ)/(σ/√n) and (122-μ)/(σ/√n))

= P((X-μ)/σ is between (119-114.8)/(13.1/√23) and (122-114.8)/(13.1/√23))

= P((X-μ)/σ is between 1.35 and 2.45)

Using standard normal distribution table,P(1.35 < z < 2.45)= P(z < 2.45) - P(z < 1.35)≈ 0.9922 - 0.9115= 0.0807

Thus, the probability that the mean systolic blood pressure of the randomly selected 23 women aged 18-24 is between 119 and 122 is approximately equal to 0.0807.

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(a) The integral of w(x) over its entire domain is zero, it cannot be equal to 1. This means that the given function does not satisfy the normalization property and hence cannot be a probability density function.

To show that the given probability density function is a valid one, we need to verify that it satisfies the two properties of a probability density function:

1. Non-negativity:

For 0 <= x <= 9, c(9-x) is always non-negative, since c is a positive constant and (9-x) is also non-negative in this range. For any other value of x, w(x) is zero. Hence, w(x) is non-negative for all x.

2. Normalization:

[tex]a[0,9] w(x) dx = a[0,9] c(9-x) dx[/tex]

= [tex]c a[0,9] (9-x) dx[/tex]

= [tex]c [(9x - (x^2)/2)] [from 0 to 9][/tex]

= [tex]c [(81/2) - (81/2)][/tex]

= [tex]c (0)[/tex]

=[tex]0[/tex]

(b) The given probability density function does not have a valid normalization constant and hence does not represent a valid probability distribution.

To find the mean life time of a component, we need to calculate the expected value of X using the formula:

[tex]E(X) = a[a,b] x (w(x) dx)[/tex]

where a and b are the lower and upper bounds of the domain respectively.

In this case, we have:

a = 0 and b = 9

w(x) = c(9-x)

Hence,

[tex]E(X) = a[0,9] x*c(9-x) dx[/tex]

= [tex]c a[0,9] (9x - x^2) dx[/tex]

= [tex]c [(81 x^2/2) - (x^3/3)] [from 0 to 9][/tex]

=[tex]c [(6561/2) - (729/3)][/tex]

= [tex]c (2958/3)[/tex]

To find the value of c, we can use the normalization property:

[tex]a[0,9] w(x) dx = 1[/tex]

[tex]a[0,9] c(9-x) dx = 1[/tex]

[tex]c a[0,9] (9-x) dx = 1[/tex]

[tex]c [(81/2) - (81/2)] = 1[/tex]

[tex]c * 0 = 1[/tex]

This is not possible, since c cannot be infinite.

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a) The estimated model relating annual salary to firm sales and market value, in equation form, is: Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval), where log denotes the natural logarithm.

b) Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.

a) The estimated model relating annual salary to firm sales and market value, in equation form, is:

Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval)

where log denotes the natural logarithm.

b) To determine if your friend would be asking too much for an annual salary of $500,000, we need to plug the values of firm sales and market value into the model and calculate the expected salary.

Using the given values:

- Firm sales (sales) = $5,000,000

- Market value (mktval) = $20,000,000

We first need to take the logarithm of the sales and market value:

log(sales) = log(5,000,000)

log(mktval) = log(20,000,000)

Then, we can substitute these values into the equation:

Expected Salary = 4.6209 + 0.1621 * log(5,000,000) + 0.1067 * log(20,000,000)

Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.

Note: Make sure to use the natural logarithm (ln) in the calculations.

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Answer:

[tex]f(8)=74[/tex]

Step-by-step explanation:

[tex]f(8)=8^2+10=64+10=74[/tex]

Answer:

51.5?

Step-by-step explanation:

I think it's just length times width divided by 2

The area of the kite ABCD is 51.56 square yards.

A kite's area is the amount of space enclosed or surrounded by a kite in a two-dimensional plane.

A kite's area equals half the product of its diagonal lengths. The formula for calculating a kite's area is:

Area = 1/2 × d₁ × d₂

Where d₁ and d₂ are long and short diagonals of a kite.

Here, AC = 12.5 yards and BD = 8.25 yards

Substitute the values of d₁ = 12.5 yards and d₂ in the formula of the kite's area:

The area of the kite = 1/2 × 12.5 × 8.25

The area of the kite = 51.5625

The area of the kite ≈ 51.56 square yards

Thus, the area of the kite ABCD is 51.56 square yards.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

15 x 2

Using the Excel Regression tool on the Weddings dataset with wedding cost as the dependent variable and attendance as the independent variable, the key regression results, hypothesis tests, and confidence intervals should be interpreted.

After applying the Excel Regression tool with wedding cost as the dependent variable and attendance as the independent variable, the key regression results should be examined. These results typically include coefficients, standard errors, t-values, p-values, and confidence intervals. The coefficient for the independent variable (attendance) represents the estimated change in the wedding cost for each unit increase in attendance. Hypothesis tests and confidence intervals help assess the statistical significance and precision of the estimated coefficients. The t-value indicates the strength of evidence against the null hypothesis of no relationship between the variables, and the p-value indicates the probability of observing the estimated coefficient under the null hypothesis. Lower p-values suggest stronger evidence against the null hypothesis. To validate the assumptions of the regression analysis, the residuals (the differences between the observed and predicted values) should be analyzed. Residual plots can be examined to check for patterns or deviations from assumptions, such as linearity, independence, and constant variance. Outliers can be identified by examining the standardized residuals. Values with high absolute values indicate potential outliers. To estimate the budget for a wedding with 175 guests, the regression model can be used to predict the corresponding cost. The attendance value of 175 can be plugged into the regression equation, and the predicted wedding cost can be obtained.

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Answer:

volume of a cylinder = 1408

hope this answer helps you...

Answer:

1407.616

Step-by-step explanation:

Volume of cylinder=πr²h

V=3.142×8×8×7

V=1407.616

NOTE: radius =diameter/2=16/2

giving 8.

Answer:

ummm is there more to the problem?!

Cool.... the question???

The value of the given integral is 2π [sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [sin(22e)/22 + sin(18e)/18] + C]

To evaluate the given expression:

∫∫ cos(20e) (1 - 2a cos(e) + a²) de dθ

We need to integrate with respect to both e and θ.

First, let's integrate with respect to e:

∫ cos(20e) (1 - 2a cos(e) + a²) de

Using the power reduction formula for cosine, we can rewrite the integrand:

= ∫ cos(20e) (1 - a² + a² cos²(e) - 2a cos(e)) de

= ∫ cos(20e) (1 - a² - a² sin²(e)) de

Now, we can integrate term by term:

= ∫ cos(20e) de - a² ∫ cos(20e) sin²(e) de - a² ∫ cos(20e) de

The first and third integrals are straightforward to evaluate:

= ∫ cos(20e) de - a² ∫ cos(20e) de - a² ∫ cos(20e) sin²(e) de

= sin(20e) - a² sin(20e) - a² ∫ cos(20e) sin²(e) de

Now, let's evaluate the remaining integral with respect to e:

= sin(20e) - a² sin(20e) - a² ∫ cos(20e) sin²(e) de

Using the trigonometric identity sin²(e) = (1 - cos(2e))/2, we can simplify the integrand:

= sin(20e) - a² sin(20e) - a² ∫ cos(20e) ((1 - cos(2e))/2) de

= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) - cos(20e) cos(2e) de

= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) de + (a²/2) ∫ cos(20e) cos(2e) de

Integrating the first term gives:

= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) de + (a²/2) ∫ cos(20e) cos(2e) de

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ cos(20e) cos(2e) de

Next, let's evaluate the remaining integral with respect to e:

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ cos(20e) cos(2e) de

Using the trigonometric identity cos(a) cos(b) = (1/2) [cos(a + b) + cos(a - b)], we can simplify the integrand:

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ (1/2) [cos(20e + 2e) + cos(20e - 2e)] de

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [∫ cos(22e) de + ∫ cos(18e) de]

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [sin(22e)/22 + sin(18e)/18] + C

where C is the constant of integration.

Now, we have the integral with respect to e evaluated. To find the final result, we need to integrate with respect to θ. However, we don't have any dependence on θ in the original expression. Therefore, we can simply multiply the result obtained above by 2π, as we're integrating over the entire range of θ.

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Complete question:

Answer:

P = -2

Step-by-step explanation:

6p +22 =10

     -22    -22

6p= -12

6       6

p=  -2

Im pretty sure thats it.

Answer:

Step-by-step explanation:

The computation of the volume of the cylinder is shown below:

As we know that

The Volume of the cylinder is

= base × height

= (4x)^2 + (5x)^2

=16x^2 + 25x^2

= 41x^3

Hence, the volume of the cylinder is 41x^3

The volume of the cylinder will be [tex]20x^2[/tex] .

Volume is the amount of space that something contains or fills.

Volume [tex]=Length*Breadth*Height[/tex]

We have,

Base area  [tex]=(4x)^2[/tex]

Height [tex]= (5x)^2[/tex]

So,

Volume of the cylinder [tex]=Base\ Area*Height[/tex]

                                        [tex]= (4x)^2* (5x)^2[/tex]

Volume of the cylinder [tex]=20x^2[/tex]

Hence, we can say that the volume of the cylinder will be [tex]20x^2[/tex] .

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Answer:

82944 in^3

Step-by-step explanation:

Volume = length x breadth x height

Before volume can be calculated, feet and yards needs to be converted to inches

1 yard = 36 inches

2 x 36 = 72 inches

1 foot = 12 inches

2 x 12 = 24 inches

Volume = 72 x 48 x 24 = 82944 in^3

Answer:

1200

0.65

The answers are in the function

Answer: 5 people

Step-by-step explanation:

The easiest way to do this is to set up a proportion. 6/12=x/10. To solve, cross-multiply and divide. Multiply 6 and 10 (6*10=60) and divide by 12 (60/12=5).

You can also find that 6/12 is equal to 1/2 by dividing each side by 6. Then multiply 10 by 1/2 (or divide 10 by 2) to get the final answer of 5 people.

After testing hypothesis with alternative-hypothesis is not equal to 30%,  the p-value is 0.278.

To test the hypothesis that proportion of unemployed people in Karachi city is not equal to 30%, we perform a two-tailed test using binomial distribution.

The null-hypothesis (H₀) is that the proportion of unemployed people is 30% (p = 0.30), and the alternative-hypothesis (H₁) is that the proportion is not equal to 30% (p ≠ 0.30),

We have a sample of 100 people, and 35 of them are unemployed. we will calculate "test-statistic" "z-score" and use it to find p-value,

The "test-statistic" formula for "two-tailed" test is :

z = (p' - p₀)/√((p₀ × (1 - p₀))/n),

where p' = sample proportion, p₀ = hypothesized-proportion under the null-hypothesis, and n = sample-size,

In this case, p' = 35/100 = 0.35, p₀ = 0.30, and n = 100,

Calculating the test statistic:

z = (0.35 - 0.30)/√((0.30 × (1 - 0.30)) / 100)

= 0.05/√((0.30 * 0.70) / 100)

≈ 0.05/√(0.21 / 100)

≈ 0.05/√(0.0021)

≈ 0.05/0.0458258

≈ 1.0905

To find the p-value, we calculate probability of obtaining "test-statistic" as extreme as 1.0905 in a two-tailed test.

We know that the cumulative-probability (area) to left of 1.0905 is approximately 0.861.

Since this is a two-tailed test, we double this probability to get "p-value":

So, p-value = 2 × (1 - 0.861),

= 2 × 0.139,

= 0.278

Therefore, the p-value for hypothesis test is 0.278.

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Answer:

f(1) = 14000

f(n) = f(n - 1) · 0.9 , for n ≥ 2

The next term in the sequence is 10206 .

Step-by-step explanation:

First we try to find the type of sequence it is.

Is there a common difference?

12600 - 14000 = -1400

11340 - 12600 = -1260

There is no common difference, so it is not an arithmetic sequence.

12600/14000 = 0.9

11340/12600 = 0.9

There is a common ratio, so this is a geometric sequence.

Each term is 0.9 times the previous term.

The next term is:

11340 * 0.9 = 10206

Answer:

f(1) = 14000

f(n) = f(n - 1) · 0.9 , for n ≥ 2

The next term in the sequence is 10206 .

Answer:

27.5

Step-by-step explanation:

pythagorean theorem. a^2+b^2=c^2.

so 12^2+b^2=30^2

meaning 144+b^2=900

900-144=756

square root 756

b=27.5

The correct answer is (b) low volume to area ratio is typical of the starting work geometry in sheet metal processes.

Explanation: Sheet metal processing is the method of shaping metal objects to create complex shapes and designs.

Cutting, punching, stamping, and forming are the most common sheet metal processes.

The workpiece's original shape and size are critical considerations in sheet metal processing.

The workpiece's geometry plays an important role in sheet metal processes.

The term volume-to-area ratio refers to the quantity of metal in a part divided by the surface area of that part.

The ratio is low in the case of sheet metal processing. Sheet metal workpieces have a high surface area-to-volume ratio.

This is due to the fact that sheet metal workpieces are often quite thin.

Because of this, sheet metal workpieces are lightweight.

Furthermore, thin sheets are more pliable and can be easily formed into various forms.

This geometry is ideal for sheet metal work since it allows for greater flexibility during processing.

In sheet metal processing, low volume-to-area ratios are typical of the starting work geometry.

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Answer:

- 14

Step-by-step explanation:

c² - d² ← is a difference of squares and factors as

= (c + d)(c - d) ← substitute values for factors

= 7 × - 2

= - 14

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Answer: 0.1562 I believe

0, 7

0 and 7 have the least amount of dots.

Answer:

A.

Step-by-step explanation:

The required expression is: y' = (1/2)(1-y)/(1+y)

Given [1 + y]² - x + y = 4 10. We need to determine an expression for dy/dx = y'.

Simplification of the given expression:

[1 + y]² + y - 4 10 = x

Differentiating w.r.t x by using the chain rule, we get:

(2[1 + y])*(dy/dx) + dy/dx + 1 = 0

(dy/dx)[2(1 + y) + 1] = - 1 - [1 + y]²

(dy/dx) = [- 1 - (1 + y)²]/[2(1 + y)]

The given expression is [1+y]²-x+y=4 10. We need to determine an expression for dy/d x = y'.

Differentiating the given equation with respect to x, we get:

2(1+y).dy/dx - 1 + dy/dx = 0

dy/dx(2+2y) = 1 - y(2+dy/dx)

dy/dx(2+2y) = (1-y)(2+dy/dx)

dy/dx = (1-y)/(2+2y)

dy/dx = (1/2)(1-y)/(1+y)

Hence, the required expression is: y' = (1/2)(1-y)/(1+y)

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