Unit 11 volume and surface area homework 6 number 7

the third side must be greater than 8 and less than 16.

To determine the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides of 4 and 12, the third side must satisfy:

12 - 4 < third side < 12 + 4

which simplifies to:

8 < third side < 16

what is triangle?

A triangle is a geometric shape with three sides and three angles. It is formed by connecting three non-collinear points in a plane. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measures.

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  m = 133°

Step-by-step explanation:

You want the value of m in the given polygon.

The sum of interior angles in a heptagon is (7 -2)(180°) = 900°.

This fact is used to find the value of m:

  138 +106 +(m -9) +m + 133 +120 +(m +13) = 900

  3m = 399 . . . . . . . subtract 501

  m = 133 . . . . . . . . divide by 3

The value of m is 133°.

__

Additional comments

We suspect your answer will be just the numerical value.

An n-sided polygon has a sum of angles equal to (n -2)(180°).

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The prediction for the number of passwords in which the first character is a number is given as follows:

139 passwords.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The passwords have the first character chosen as follows:

Hence the probability of a number is given as follows:

p = 10/(10 + 26)

p = 10/36

p = 5/18.

Out of 500 passwords, the expected number is then given as follows:

E(X) = 500 x 5/18

E(X) = 139 passwords.

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The expression when solved for a = 8 is 26

Algebraic expressions are defined as mathematical expressions that are made up of terms, variables, constants, coefficients, and factors.

Also, algebraic expressions are seen as expressions that consist of mathematical operations.

These mathematical operations are;

From the information given, we have;

(–4a – 6) + a2 for a = 8

Now, substitute the value of a as 8 in the expression, we have;

(-4(8) - 6) + (8)^2

find the square

-32 - 6 + 64

Add the values

26

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The statement that is true of relationships between variables is "Marketers are often interested in describing the relationship between variables they think influence purchases of their products." (option b).

In many fields, researchers and professionals seek to understand the relationships between different variables. A variable is any characteristic or feature that can vary and can be measured or observed. Understanding the relationship between variables can help in predicting, explaining, and controlling different phenomena. In this context, it's important to distinguish between different types of relationships and to use appropriate statistical methods to describe and test these relationships.

This statement is true. Marketers often want to understand the relationship between different variables and how they influence consumer behavior. For example, they might want to know how price, quality, brand reputation, and advertising affect the likelihood of a consumer purchasing their product. By understanding these relationships, marketers can develop more effective marketing strategies.

Hence the correct option is (b).

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Complete Question:

Which of the following is true of relationships between variables?

a) A curvilinear relationship is much simpler to work with than a linear relationship.

b) Marketers are often interested in describing the relationship between variables they think influence purchases of their products.

c) A negative relationship exists between two variables if low levels of one variable are associated with low levels of another.

d) The strength of association is determined by the size of the correlation coefficient, with smaller coefficients indicating a stronger association.

e) The null hypothesis for the Pearson correlation coefficient states that there is a strong association between two variables.

a) 26.43% of steers weigh over 1200 pounds.

b) 29.46% of steers weigh under 1100 pounds.

c) 7.26% of steers weigh between 1250 and 1300 pounds.

The proportion of steers that weigh over 1200 pounds the area to the right of 1200 under the normal curve with mean 1146 and standard deviation 86.

A z-score and the standard normal distribution to find this area.

The z-score is:

z = (1200 - 1146) / 86 = 0.63

A standard normal distribution table or calculator the area to the right of z = 0.63 is 0.2643.

The proportion of steers that weigh under 1100 pounds, the area to the left of 1100 under the normal curve with mean 1146 and standard deviation 86.

Again, we can use a z-score and the standard normal distribution to find this area.

The z-score is:

z = (1100 - 1146) / 86 = -0.54

A standard normal distribution table or calculator the area to the left of z = -0.54 is 0.2946.

The proportion of steers that weigh between 1250 and 1300 pounds The area between the z-scores corresponding to these weights.

The z-score for 1250 pounds is:

z1 = (1250 - 1146) / 86 = 1.23

The z-score for 1300 pounds is:

z2 = (1300 - 1146) / 86 = 1.79

A standard normal distribution table or calculator the area to the left of z1 is 0.8907, and the area to the left of z2 is 0.9633.

The area between z1 and z2 is:

0.9633 - 0.8907 = 0.0726

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The r-value that represents the most moderate correlation would be around 0.5. This value indicates a moderate positive correlation, meaning that there is a moderate relationship between two variables that are moving in the same direction.

An r-value, or correlation coefficient, represents the strength and direction of a linear relationship between two variables. The r-value ranges from -1 to 1, where:

-1 indicates a strong negative correlation,
0 indicates no correlation, and
1 indicates a strong positive correlation.

A moderate correlation falls in the middle of this range. For example, an r-value of approximately 0.5 (positive moderate correlation) or -0.5 (negative moderate correlation) would represent a moderate correlation between the two variables.

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Considering a number of 100 trials, the experimental probability of heads should be close to the theoretical probability of 1/2 = 50%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A fair coin is equally as likely to come up heads or tails, hence the theoretical probability of heads is given as follows:

1/2 = 0.5 = 50%.

For a large number of trials, such as 100 trials, the experimental probability is expected to be close to the theoretical probability, hence it should also be close to 50%.

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Answer:

28.5

Step-by-step explanation:

7 times 18

plus 45

divided by 6(2x3)

If a point is added in the table, then the point which preserves the function is (d) (-5, 7).

The relation given in the table is a function, which means that every value of "x" in the domain must have exactly one corresponding value of "y" in the range.

The inputs , x = 9, x = -8, and x = -1 already have defined values in the table, so any other value assigned to these inputs would create a situation where an input has more than one output.

So, the only choice that would preserve the function is (d) (-5, 7), which assigns a "new-value" to an input that doesn't have a defined value in the table.

This new input-output pair is consistent with the existing function rule and ensures that every input in the domain has exactly one output in the range, preserving the function.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

The table shows y as a function of x. Suppose a point is added to this table.

     x         y

    6         -9

    -8         9

    -1         -4

    9         -6

    8         -8

Which choice gives a point that preserves the function?

(a) (9, -5)

(b) (-1, -5)

(c) (-8, -6)

(d) (-5, 7)

The distribution that the residuals in our model to follow is equals to the normal probability distribution. So, option(a).

Because residuals are defined as the difference between any data point and the regression line, they are sometimes called "errors". An error in this context does not mean that there is anything wrong with the analysis. In other words, the residual is the error that is not described by the regression line. The residue(s) can also be expressed by "e". The formula is written as, Residual = Observed value – predicted value or

[tex]e = y – \hat y [/tex].

In order to draw valid conclusions from your regression, the regression residuals should follow a normal distribution. The residuals are simply the error terms or differences between the observed value of the dependent variable and the predicted value. Therefore, the residuals should have a normal distribution.

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Complete question:

we desire the residuals in our model to have which probability distribution? select answer from the options below

a) normal

b) binomial

c) poisson

Answer:

A is the correct answer. x = 3.

Step-by-step explanation:

[tex] {49}^{x + 4} = {7}^{5x - 1} [/tex]

[tex] {7}^{2(x + 4)} = {7}^{5x - 1} [/tex]

[tex]2x + 8 = 5x - 1[/tex]

[tex]3x = 9[/tex]

[tex]x = 3[/tex]

Step-by-step explanation:

Right triangles obey Pythagorean theorem :

?^2  = 2^2 + 9^2

?^2 = 85

? = sqrt 85  ft

Answer:

85ft

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

This graph is a graph of f, that states it is equal to g'. We're graphing the first derivative, so that means g(3) is the integral of f, or the area under the curve. g'(3) is just asking for the y value that corresponds to the x value of f, because f and g' are equal.

g = ∫f

g' = f

And by extension,

g'' = f'

Because we're looking at a graph of f, finding f' is just finding the slope at f(3). Rise over run, -2 over 1, so g''(x) = f'(x) = -2

The price that maximizes annual revenue is $17.86 per bushel, which should be charged by the farmers; The quantity of corn that can be sold per year at 67,786 bushels per year; the farmers' resulting revenue will be  $1,210,392.96 per year.

To find the price that maximizes annual revenue, we need to differentiate the revenue function with respect to the price and set it equal to zero:

Revenue = pq = (6,600,000q^1.3)q

= 6,600,000q^2.3

dRevenue/dp = q

Setting dRevenue/dp = 0, we get q = 0, which is not a valid solution. Therefore, we need to consider the endpoints of the feasible range, which is q >= 13,000.

At q = 13,000, we have p = 6,600,000*13,000^(-0.3) ≈ $17.86 per bushel.

At q → ∞, we have p → 0.

So, the price that maximizes annual revenue is $17.86 per bushel, which should be charged by the farmers.

The quantity of corn that can be sold per year at that price is given by

q = (p/6,600,000)^(1/1.3)

= (17.86/6,600,000)^(1/1.3)

≈ 67,786 bushels per year.

The farmers' resulting revenue will be Revenue = p*q

= $17.86 * 67,786

≈ $1,210,392.96 per year.

Therefore, the price that maximizes annual revenue is $17.86 per bushel, which should be charged by the farmers; The quantity of corn that can be sold per year at 67,786 bushels per year; the farmers' resulting revenue will be  $1,210,392.96 per year.

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The value of the triple integral is 72π.

To evaluate this triple integral in cylindrical coordinates, we first need to express the region E using cylindrical coordinates.

The cylinder x² + y² = 16 can be expressed in cylindrical coordinates as r² = 16, or r = 4. The planes z = -5 and z = 4 define a region of height 9.

So, the region E can be expressed in cylindrical coordinates as:

4 ≤ r ≤ 4

-5 ≤ z ≤ 4

0 ≤ θ ≤ 2π

The integrand √(x² + y²) can be expressed in cylindrical coordinates as r, so the integral becomes:

∭E√x²+y²dV = ∫0²π ∫4⁴ ∫-5⁴ r dz dr dθ

Note that the limits of integration for r are from 0 to 4, which means we are only integrating over the positive x-axis. Since the integrand is an even function of x and y, we can multiply the result by 2 to get the total volume.

The integral with respect to z is easy to evaluate:

∫₋₅⁴ r dz = r(4 - (-5))

= 9r

So the triple integral becomes:

∭E√x²+y²dV = 2 ∫0^2π ∫4⁴ 9r dr dθ

= 2(9) ∫0^²π 4 dθ

= 72π

Therefore, the value of the triple integral is 72π.

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The area in terms of x, can be written as:

A(x) = x² + 8x + 15

Remember that the area of a rectangle is given by the product between the dimensions.

Here we know that the length is:

L(x) = x + 5

And the width is:

W(x) = x + 3

Then the formula for the area is:

A(x) = (x + 5)*(x + 3)

A(x) = x² + 5x + 3x + 15

A(x) = x² + 8x + 15

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This dynamic programming algorithm will help you find the optimal solution for the coin-changing problem using the fewest number of coins.

To optimally solve the coin-changing problem for an arbitrary denomination set {d1, d2, ..., dk} and make up a value 'v' using the fewest number of coins, you can use a dynamic programming algorithm. Here's the step-by-step explanation:

1. Create an array 'dp' of length 'v+1' and initialize all elements with infinity (except dp[0], which should be 0, as you need 0 coins to make up a value of 0).
2. Sort the denomination set in ascending order.
3. Iterate through the denomination set using a variable 'coin' from d1 to dk.
4. For each 'coin', iterate through the 'dp' array starting from the index 'coin' up to 'v' using a variable 'i'.
5. In the inner loop, for each 'i', update the value of dp[i] with the minimum between dp[i] and 1 + dp[i-coin].
6. After the loops, the value of dp[v] will be the minimum number of coins needed to make up the value 'v'. If dp[v] is still infinity, then it's not possible to make up the value 'v' using the given denomination set.

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The probability of winning this lottery game is 1/10,000 or 0.0001 (0.01% chance). The probability of winning a state lottery game where the winning number is made up of four digits from 0 to 9 chosen at random can be calculated as follows.

First, we need to determine the total number of possible outcomes. There are 10 digits (0 to 9) and we are choosing four of them, so the total number of possible outcomes is 10 x 10 x 10 x 10 = 10,000.

Next, we need to determine the number of favorable outcomes, which is the number of ways to choose four digits from 0 to 9. This is a combination problem, and we can use the formula nCr = n! / r!(n-r)! where n is the total number of options and r is the number of choices. So in this case, n = 10 and r = 4, giving us 10C4 = 10! / 4!(10-4)! = 210 favorable outcomes.

Finally, we can calculate the probability of winning by dividing the number of favorable outcomes by the total number of outcomes:

Probability of winning = favorable outcomes / total outcomes
Probability of winning = 210 / 10,000
Probability of winning = 0.021 or 2.1%

So the probability of winning a state lottery game where the winning number is made up of four digits from 0 to 9 chosen at random is 0.021 or 2.1%.
Hi! The probability of winning a state lottery game with a four-digit winning number, where each digit ranges from 0 to 9, can be calculated as follows:

There are 10 choices (0 to 9) for each of the four digits. Thus, the total number of possible combinations is 10 x 10 x 10 x 10 = 10,000. Since there is only one winning number, the probability of selecting that number at random is 1 out of the total possible combinations.

So, the probability of winning this lottery game is 1/10,000 or 0.0001 (0.01% chance).

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In regression analysis, the variable that is being predicted is called the dependent variable or response variable. It is the outcome variable that is being measured or predicted based on the values of other variables, which are referred to as independent variables or predictors.

The independent variables are used to explain the variation in the dependent variable and to determine the strength and direction of their relationship.

Regression analysis is a statistical method that is used to estimate the relationship between the dependent variable and one or more independent variables by fitting a line or curve through the data points. The resulting regression equation can then be used to predict the value of the dependent variable based on the values of the independent variables.

The quality of the regression model is evaluated by measuring the goodness of fit, which measures how well the model fits the data, and by examining the significance of the coefficients, which measures the strength and direction of the relationship between the variables

. Overall, regression analysis is a powerful tool that is widely used in many fields to understand and predict the relationship between variables.

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Answer:

B) 175

Step-by-step explanation:

Same thing as before:

To get from 1.4 to 7 and to get from 7 to 35, you have to multiply by 5.

To get from 35 to the next sequence, you also have to multiply by 5.

35·5

=175

Hope this helps! :)

Answer:

7=1.4n

n=7÷1.4

n=5

next term =35×5

=175 B

If the point (3, -2) were reflected across the y-axis what would be the new y-coordinate is same as before, which is -2.

If a point (x, y) is reflected across the y-axis, its x-coordinate becomes its opposite (-x), while its y-coordinate remains the same.

In this case, the point is (3, -2). If we reflect this point across the y-axis, its x-coordinate will become its opposite, which is -3. The new coordinates of the reflected point will be (-3, -2).

Therefore, the new y-coordinate is still -2, as the point is only being reflected across the y-axis and not moving up or down in the y-direction. The change is only in the x-coordinate, which becomes its opposite.

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The probability that the mean weight of a sample of twenty freshmen will be greater than 145 pounds is 0.138.

The probability is determined using the central limit theorem and the formula for the standard error of the mean:

where;

Data given;

σ = 12.3 pounds; n = 20

SE = 12.3/√20

SE = 2.75 pounds.

The sample mean is then standardized using the z-score formula:

z = (x - μ) / SE

z = (145 - 142) / 2.75

z = 1.09

Using a calculator, the probability of a z-score greater than 1.09 is 0.138.

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The confidence interval is (0.451, 0.549).

To find the confidence interval, we need to use the formula:

Confidence interval = sample proportion +/- margin of error

where the margin of error is calculated as:

Margin of error = z* (standard error)

The standard error is the standard deviation of the sampling distribution of the proportion, which is calculated as:

Standard error = [tex]\sqrt{p*(1-p)/n}[/tex]

where p is the sample proportion and n is the sample size.

The z-value corresponding to a 95% confidence level is 1.96.

Using the given information, we have:

Sample proportion (p) = 0.50

Sample size (n) = 400

Margin of error = 0.052 * 0.5 = 0.026

Standard error = [tex]\sqrt{0.5(1-0.5)/400}[/tex] = 0.025

Z-value for 95% confidence level = 1.96

So the confidence interval is:

0.50 +/- 1.96 * 0.025

= 0.50 +/- 0.049

Therefore, the confidence interval is (0.451, 0.549) or 45.1% to 54.9%. We can say with 95% confidence that the true proportion of respondents who agree with the statement lies between 45.1% and 54.9%.

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The SAT prep class has no influence on the mean difference in SAT writing scores, hence the null-hypothesis (H0) states that the mean difference is zero.

The alternative theory (Ha) states that the SAT prep course has a positive impact on the mean difference in SAT writing scores, resulting in a mean difference that is greater than zero.

The sample size of 50 is sufficient for us to do the hypothesis test using the t-distribution.

The estimated t-test statistic is 1.96, and at the 5% level of significance, it is significant only if it is in the rejection zone of the null hypothesis (1.677 is the crucial value for a one-tailed test with 49 degrees of freedom).

The calculated p-value of 0.028 is less than the threshold of 0.05, the null hypothesis is also rejected in favour of the alternative hypothesis.

To draw the conclusion that the SAT prep course has a favourable impact on the mean difference in SAT writing scores. Particularly, at the 5% level of significance, the sample-mean difference of 5 is statistically significantly greater than zero.

Therefore, it is reasonable.

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The image of (−2, 6) after a dilation by a scale factor of 1/2 centered at the origin is (-1, 3)

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/2 centered at the origin as follows:

Ordered pair A (-2, 6) → Ordered pair A' (-2 × 1/2, 6 × 1/2) = Ordered pair A' (-1, 3).

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The difference in the Beatles length is 1 / 10 centimeters.

We have,

The lengths of Beetles are 4/5 cm and 7/10 cm.

So, the difference in the beetles length can be calculated as

difference between the beetles length = 4 / 5 - 7 / 10

                                                                 = 8 - 7 / 10

                                                                  = 1/10 cm

Thus, the difference in beetles length is 1/10 cm.

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The probability that a box weighs between 16.4 and 16.5 ounces is approximately 14.45% (rounded to 2 decimal places). To solve this problem, we need to use the z-score formula:
z = (x - μ) / σ
where x is the weight of the box, μ is the mean weight of all boxes, σ is the standard deviation of weights, and z is the number of standard deviations away from the mean.

In this case, we want to find the probability that a box weighs between 16.4 and 16.5 ounces. We can convert these weights to z-scores as follows:

z1 = (16.4 - 16.3) / 0.21 = 0.48
z2 = (16.5 - 16.3) / 0.21 = 0.95

Using a z-score table or calculator, we can find the area under the standard normal curve between these two z-scores:

P(0.48 ≤ z ≤ 0.95) = 0.1736

Therefore, the probability that a box weighs between 16.4 and 16.5 ounces is 0.17 or 17% (rounded to 2 decimal places).
Hi! To find the probability that a box weighs between 16.4 and 16.5 ounces, we can use the z-score formula and the standard normal table.

First, let's calculate the z-scores for 16.4 and 16.5 ounces using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 16.4 ounces:
z1 = (16.4 - 16.3) / 0.21 ≈ 0.48

For 16.5 ounces:
z2 = (16.5 - 16.3) / 0.21 ≈ 0.95

Now, use the standard normal table to find the area between these z-scores:
P(0.48 < z < 0.95) = P(z < 0.95) - P(z < 0.48) ≈ 0.8289 - 0.6844 = 0.1445

The probability that a box weighs between 16.4 and 16.5 ounces is approximately 14.45% (rounded to 2 decimal places).

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a. Using a significance level of α = 0.01, the critical values for a two-tailed test are ±2.576.

b. To determine whether to reject or fail to reject the null hypothesis, we compare the test statistic (-3.25) to the critical values. Since -3.25 is less than -2.576, we can reject the null hypothesis at the 0.01 significance level. This means we have evidence to support the claim that p = 3/5.

What is significance level?

Significance level, denoted as alpha (α), is the probability threshold used to determine whether a statistical hypothesis is rejected or not. It represents the maximum level of Type I error that a researcher is willing to accept.

A test statistic is a numerical value calculated from a sample of data that is used in hypothesis testing to determine whether to reject or fail to reject a null hypothesis.

The test statistic is compared to a critical value to make this determination. The critical value is a threshold value determined by the level of significance and the degrees of freedom of the sample.

If the test statistic falls within the rejection region determined by the critical value, the null hypothesis is rejected. If the test statistic falls outside the rejection region, the null hypothesis is not rejected.

a. Using a significance level of α = 0.01, the critical values for a two-tailed test are ±2.576.

b. To determine whether to reject or fail to reject the null hypothesis, we compare the test statistic (-3.25) to the critical values. Since -3.25 is less than -2.576, we can reject the null hypothesis at the 0.01 significance level. This means we have evidence to support the claim that p = 3/5.

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