Find the value of
3k-7 if k=-4

The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Lucinda will buy 2 kewpie dolls and 1 beanie baby if she were rational.

According to the question,

Given the table below compares the marginal benefit Lucinda gets from Kewpie dolls and Beanie Babies. The image of the table is attached.

If Lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6,

Lucinda will buy the combination for which the marginal benefit is the same.

Therefore, Lucinda will buy 2 kewpie dolls and 1 beanie baby, if she were rational.

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The complete question is:

If Lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would Lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies

The estimated probability that all four randomly selected young American men are 68 inches or shorter is approximately 0.004 or 0.4%.

To calculate the probability that all four randomly selected young American men are 68 inches or shorter, we need to consider the probability for each individual man and multiply them together.

Let's assume that the probability of an individual young American man being 68 inches or shorter is p. Since we are selecting four men at random, the probability of each man being 68 inches or shorter is the same, and we can multiply their probabilities together.

The probability of one man being 68 inches or shorter is p. Therefore, the probability of all four men being 68 inches or shorter is p × p × p × p = p^4.

However, we are not given the specific value of p in the problem statement. If we assume that the height of young American men follows a normal distribution, we can look up the corresponding z-score for a height of 68 inches or shorter and use the standard normal distribution to estimate the probability.

For example, if we find that a height of 68 inches corresponds to a z-score of -1.0, we can use a standard normal distribution table or a calculator to determine the probability of a z-score less than or equal to -1.0. Let's say this probability is approximately 0.1587.

Therefore, the estimated probability that all four randomly selected young American men are 68 inches or shorter would be (0.1587)^4 = 0.004.

Thus, the probability is approximately 0.004 or 0.4% rounded to three decimal places.

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For a clinical trial (study) on the mean GPA of night students, the appropriate null and alternative hypotheses would be given by:

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

For a clinical trial (study) on the mean GPA of night students, the appropriate null and alternative hypotheses would be given by:

In conclusion, we can infer and logically deduce that this test would be right-tailed.

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Answer:

B and D

Step-by-step explanation:

I think this is the answer

To determine the price the student-athlete should charge for each hot dog to break even, we need to consider the total costs she incurs, including the vendor fee, equipment cost, and the cost per hot dog. By dividing the total costs by the anticipated number of hot dogs sold, we can find the price per hot dog that would allow her to break even.

The total costs for the student-athlete include the vendor fee of $3000 and the equipment cost of $4500, which sums up to $7500 for the season. Additionally, she incurs a cost of $0.35 per hot dog sold. With an anticipation of selling 2000 hot dogs, the total cost for the hot dogs would be 2000 x $0.35 = $700.

To break even, the total revenue from selling the hot dogs should cover the total costs. Therefore, the price per hot dog should be set in such a way that the revenue from selling 2000 hot dogs equals $7500. Dividing the total costs ($7500) by the number of hot dogs (2000), we find that the student-athlete should charge $3.75 per hot dog in order to break even. This price per hot dog would allow her to cover all her expenses and reach the break-even point.

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The current yield of the bond is approximately 5.81%.

The current yield of a bond is calculated by dividing the annual coupon payment by the current market price of the bond. In this case, the bond pays semiannual coupons, so we need to adjust the coupon payment and then calculate the current yield.

Market price of the bond = $981.45

Semiannual coupon payment = $28.50

Par value of the bond = $1,000

First, we need to calculate the annual coupon payment by doubling the semiannual coupon payment:

Annual coupon payment = 2 * $28.50 = $57.00

Next, we can calculate the current yield using the formula:

Current yield = (Annual coupon payment / Market price) * 100

Current yield = ($57.00 / $981.45) * 100

Current yield ≈ 5.81%

Therefore, the current yield of the bond is approximately 5.81%.

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Answer:

680

Step-by-step explanation:

Jose's income in 2hours = $34

in 1 hour = 34 divide by 2 = 17

income made in 40 hours = 17 multiplied by 40 = $680

Answer:

8.5 hrs? direct variation

Step-by-step explanation:

60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator

600/60 =10

600/70 = 8.5

and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure

The general form of the equation 2/3(x - 4)(x + 5) = 1 is 2x^2 + 2x - 43 = 0

and the coefficients of general form a = 2, b= 2 and c = -43

To find the general form of the given equation, we need to simplify and expand the equation.

First, we can simplify the left-hand side of the equation by multiplying 2/3 into the brackets

2/3(x - 4)(x + 5) = (2/3)(x^2 + x - 20)

Next, we can multiply both sides of the equation by 3 to eliminate the fraction

2(x^2 + x - 20) = 3

Expanding the left-hand side, we get

2x^2 + 2x - 40 = 3

Simplifying further, we get

2x^2 + 2x - 43 = 0

So, the coefficients of the general form of the equation are

a = 2

b = 2

c = -43

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The given question is incomplete, the complete question is:

Give the values of a, b, and c needed to write the equation's general form. 2/3(x - 4)(x + 5) = 1

The true statements about the functions are:

The function is given as:

f(x) = 25000 * 0.96^x

Set x = 0 to determine the initial value of the function

f(0) = 25000 * 0.96^0

Evaluate

f(0) = 25000

This means that the population of the city in 2010 is 25000 i.e. option (B) is correct

Also, we have:

f(x) = 25000 * 0.96^x

The rate at which the population decreases every year is calculated as:

r = 1 - 0.96

Evaluate the difference

r = 0.04

Express as percentage

r = 4%

This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct

The population after 5 and 10 years are:

f(5) = 25000 * 0.96^5

f(5) = 20384

f(10) = 25000 * 0.96^10

f(10) = 16621

Divide these populations by the initial population in 2010

20384/25000 = 82%

16621/25000 = 66%

This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.

So, options (d) and (e) are false

Lastly, because the population function is an exponential decay function;

The function value would approach 0 as it decreases

This means that option (f) is correct

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1) The property P that we need to prove by induction is as P(p) = length p = length (rem R p) + numR p. 2) For the base case, we need to prove P([]) = length [] = length (rem R []) + numR []. 3) Inductive hypothesis is P(p) = length p = length (rem R p) + numR p. 4) For the step case, we need to prove P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p).

1) The property P that we need to prove by induction is as follows:

For all lists of directions p, the property P(p) is defined as:

P(p) = length p = length (rem R p) + numR p

If we can prove this property P by induction, it implies the goal of the exercise, which is to show that length p = length (rem R p) + numR p.

2) Base case goal:

For the base case, we need to prove the following goal:

For an empty list of directions p = [], the property P(p) holds:

P([]) = length [] = length (rem R []) + numR []

Proof:

P([]) simplifies to:

length [] = length (rem R []) + numR []

Using the definition of the length function and rem function, we have:

0 = length [] + numR []

Since the length of an empty list is 0, and there are no occurrences of R in an empty list, numR [] is also 0. Therefore, the base case goal holds.

3) Inductive hypothesis:

Assuming that the property P holds for a list p, we assume the following inductive hypothesis:

P(p) = length p = length (rem R p) + numR p

4) Step case goal:

For the step case, we need to prove the following goal:

Assuming P(p), we need to show that P(L:p) holds:

P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p)

Proof:

Using the definition of the length function and rem function, we have:

length (L:p) = length (L:(rem R p)) + numR (L:p)

Expanding the length and rem functions, we get:

1 + length p = 1 + length (rem R p) + numR (L:p)

Since L is not equal to R, numR (L:p) remains unchanged:

1 + length p = 1 + length (rem R p) + numR p

By canceling out the common terms on both sides, we get:

length p = length (rem R p) + numR p

This matches the property P(p), so the step case goal holds.

By proving the base case and the step case, we have proven the property P(p) by induction, which implies that length p = length (rem R p) + numR p for all lists of directions p.

Correct Question :

length []=0

length (x:xs)=1+ length xs

​−L1

−L2

Consider the following data types and functions: data Direction =L∣R numR : [Direction] -> Int

numR []=0

numR (L:p)= numR p

numR (R:p)=1+ numR p

Answer the following questions:

1. What precisely should we prove by induction? Specifically, state a property P, including possible quantifiers, so that proving this property by induction implies the (above) goal of this exercise.

2. State (including possible quantifiers) and prove the base case goal.

3. State (including possible quantifiers) the inc्acuctive hypothesis of the proof.

4. State (including possible quantifiers) and prove the step case goal.

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Answer:

x=√2 or x=−√2

Let's solve your equation step-by-step.

6=3x2

Step 1: Subtract 3x^2 from both sides.

6−3x2=3x2−3x2

−3x2+6=0

Step 2: Subtract 6 from both sides.

−3x2+6−6=0−6

−3x2=−6

Step 3: Divide both sides by -3.

−3x2

−3

=

−6

−3

x2=2

Step 4: Take square root.

x=±√2

x=√2 or x=−√2

Answer:

1. \(x^2-6x+8=0\)

2. \((x-4)(x-2)=0\)

3. \(x=4 \text{ and } x=2\)

4. \(x=4 \text{ and } x=2\)

Step-by-step explanation:

1. When using substitution all we do would be is substituse the y for a 3.

This leaves us with the equation:

\(3=-x^2+6x-5\)

Rewriting it we get:
\(0=-x^2+6x-8\)

or if we shift the 0 to the other side:

\(x^2-6x+8=0\)

2. In order to factor the equation we can use the butterfly method:

\(\left[\begin{array}{ccc}1&-4\\1&-2\end{array}\right]\)
So it factors out to:

\((x-4)(x-2)=0\)
You can also use the quadratic formula.

3. To find the solutions we just set each factor to 0
\(x-4=0\\\text{and}\\x-2=0\)
So the x-values would be:
\(x=4 \text{ and } x=2\)

4. To find the solution to the system we just plug in the values and it turns out to be the same numbers as before.

Step-by-step explanation:

angle 2 = 2x + 10 deg (corresponding angles) or 180 - 4x + 46 deg (angles on a straight line are supplementary)

therefore,

2x + 10 = 226 - 4x

6x = 216

x = 36

hence,

angle 2 = 2(36) + 10 = 82deg

Topic: Angles

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Answer:

B

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

because it is asking what minus 9 is equal to -4

Answer:

5

Step-by-step explanation:

5 - 9= - 4

I don't know if this is confusing but you could also just subtract 5 from 9 (9-5) which is 4 and then put a - in front of it

The equation of the line that is perpendicular to line y = 7x/4+7 is y = -4x/7+12/7 and the equation of the line that is parallel to this line is y = 7x/4+11.

According to the question,

We have the following information:

y = 7x/4+7

Now, the slope of this line is 7/4 which will be the slope of the parallel line and the slope of the perpendicular line will be -4/7 (-1/m).

Points through line is passing = (-4,4)

x' = -4 and y' = 4

Now, we know that following formula is used to find the equation of the line:

(y-y') = m(x-x')

Perpendicular line:

y-4 = -4/7(x+4)

y-4 = -4x/7-16/7

y = -4x/7-16/7+4

y = -4x/7+12/7

Parallel line:

y-4 = 7/4(x+4)

y-4 = 7x/4+7

y = 7x/4+7+4

y = 7x/4+11

Hence, the equation of the line that is perpendicular to line y = 7x/4+7 is y = -4x/7+12/7 and the equation of the line that is parallel to this line is y = 7x/4+11.

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Every graph with 2 or more nodes contains two nodes with the same degree.

Let's assume the opposite, that every node in the graph has a unique degree. We know that the degree of a node is the number of edges connected to that node. In a graph with n nodes, the maximum degree a node can have is n-1 (when it's connected to all other nodes). Similarly, the minimum degree a node can have is 0 (when it's not connected to any other node).

Now, let's consider two cases:

Case 1: All nodes have different degrees except one.
In this case, there must be a node with degree 0 (not connected to any other node) and a node with degree n-1 (connected to all other nodes). But since we assumed that every node has a unique degree, this is a contradiction. Therefore, this case cannot be true.

Case 2: All nodes have different degrees except two.
In this case, we have two nodes with degrees that are different from all other nodes. Let's call these nodes A and B, and let's assume without loss of generality that deg(A) < deg(B) (i.e., A has a smaller degree than B). Since every node has a unique degree, A is connected to some subset of the nodes that are connected to B. Let's call this subset C. Now, the maximum number of edges that can exist between C and B is deg(B)-deg(A) (since B cannot be connected to any node in C that is already connected to A). But since deg(B)-deg(A) is a positive integer, there must be at least one node in C that is connected to B and A (otherwise deg(A) would not be unique). But this node has the same degree as A, which contradicts our assumption. Therefore, this case cannot be true either.

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In 2026, the $5,000 in 2021 dollars would be worth $6,224.80 in 2021 terms. This is calculated by multiplying $5,000 by the inflation rate of 396%, which is 1.396, for five years. So $5,000 x 1.396 = $6,224.80.

Multiplying is the process of taking two or more numbers, called factors, and multiplying them together to find the product. It is one of the four basic operations in mathematics. Multiplying numbers can be done in many different ways, such as using a multiplication table, a calculator, or a pencil and paper.

The result of multiplying two numbers is called a product. Multiplying can also be used to solve equations and multiply fractions. Multiplying numbers is an important part of basic math, and it is essential for more advanced math topics, such as algebra and calculus.

The inflation rate of 396% is an annual rate, so to calculate the amount of money in 2021 terms you have after five years, you have to multiply the original amount with the inflation rate for five years. This is done by multiplying the inflation rate (1.396) by itself five times.  This gives you the total amount of money you will have in 2021 terms after five years.

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Answer:

2

Step-by-step explanation:

first you take the 1 and add the other 1 to it so it equals 2

The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie can be calculated using the following formula:
Confidence Interval = Sample Proportion ± Margin of Error

First, we need to calculate the sample proportion. In this case, the sample proportion is equal to the percentage of respondents who chose chocolate pie, which is 48%.

Sample Proportion = 48% = 0.48

Next, we need to calculate the margin of error. The margin of error depends on the confidence level and the sample size. In this case, the confidence level is 90%, which corresponds to a z-score of 1.645 (obtained from a z-table). The sample size is 22.

Margin of Error = z * sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
                = 1.645 * sqrt((0.48 * (1 - 0.48)) / 22)
                = 0.229

Now we can calculate the confidence interval.
Confidence Interval = Sample Proportion ± Margin of Error
                          = 0.48 ± 0.229
                          = (0.251, 0.709)

The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie is (0.251, 0.709) at a 90% confidence level.

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The test statistic for this sample can be calculated using the formula for the difference in sample proportions:

Test statistic = (pp1 - pp2) / sqrt[(pp(1-pp)/n1) + (pp(1-pp)/n2)]

where pp1 and pp2 are the sample proportions, n1 and n2 are the sample sizes, and pp is the pooled sample proportion.

In this case, the sample proportion for the first population is pp1 = 638/658 = 0.970, and the sample proportion for the second population is pp2 = 411/443 = 0.928. The sample sizes are n1 = 658 and n2 = 443.

To calculate the pooled sample proportion, we use the formula:

pp = (x1 + x2) / (n1 + n2)

where x1 and x2 are the total number of successes in each population.

In this case, x1 = 638 and x2 = 411, so pp = (638 + 411) / (658 + 443) = 1049 / 1101 = 0.952.

plugging in the values into the formula for the test statistic, we have:

Test statistic = (0.970 - 0.928) / sqrt[(0.952(1-0.952)/658) + (0.952(1-0.952)/443)] ≈ 1.932

The D-value for this sample refers to the p-value, which is the probability of observing a test statistic as extreme as the one calculated (or more extreme), assuming the null hypothesis is true.

To find the p-value, we can compare the test statistic to the critical value(s) based on the significance level α.

If the p-value is less than or equal to α (0.005 in this case), we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.

To determine the p-value, we would need to consult a statistical table or use software to calculate it based on the test statistic and the appropriate distribution (usually the standard normal distribution for large sample sizes). Without the actual values, we cannot provide the specific p-value for this sample.

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The probability that the satellite system operates adequately is 0.7056.

The probability that a component is not functional is 0.4. Therefore, the probability that a component is functional is 1-0.4=0.6.
Using the rule of combinations, there are 6 possible combinations of functional and non-functional components:
1. All 4 components are functional: (0.6)^4=0.1296
2. 3 components are functional: (0.6)^3(0.4)=0.3456
3. 2 components are functional: (0.6)^2(0.4)^2=0.2304
4. 1 component is functional: (0.6)(0.4)^3=0.0256
5. No components are functional: (0.4)^4=0.0256
6. At least 2 components are functional: P(2 or 3 or 4) = 0.1296 + 0.3456 + 0.2304 = 0.7056
Therefore, the probability that the satellite system operates adequately is 0.7056.

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A bar chart is a graph that shows the differences in frequencies or percentages among categories of a nominal or an ordinal variable.

A bar chart is a commonly used graphical representation to display the distribution of data in different categories. It is particularly useful when working with nominal or ordinal variables, where the categories are distinct and unordered or have a specific order.

In a bar chart, each category is represented by a rectangular bar whose length corresponds to the frequency or percentage associated with that category. The height of the bar represents the magnitude or count of the variable in each category, allowing for easy visual comparison between the categories.

The bars in a bar chart can be arranged horizontally or vertically, depending on the preference or nature of the data. The chart may also include labels or annotations to indicate the category names or additional information.

By examining the lengths or heights of the bars in a bar chart, it becomes easy to identify the categories with the highest or lowest frequencies or percentages, as well as to compare the relative magnitudes among the different categories. This graphical representation aids in visualizing and interpreting the distribution of a nominal or an ordinal variable effectively.

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The answer is that \($\bar{X}-\bar{Y}$\) is normal with mean 0 and standard deviation \($5 / 9$\). None of the given options match this result exactly, but the closest one is "normal with mean 0 and standard deviation \($5 / 6^{\prime \prime}$\).

The mean of \($\bar{X}$\) and \($\bar{Y}$\) are:

\(E(\bar{X})=E\left(\frac{1}{16} \sum_{i=1}^{16} X_i\right)=\frac{1}{16} \sum_{i=1}^{16} E\left(X_i\right)=\frac{1}{16}(16 \times 15)=15\)

and

\($$E(\bar{Y})=E\left(\frac{1}{9} \sum_{i=1}^9 Y_i\right)=\frac{1}{9} \sum_{i=1}^9 E\left(Y_i\right)=\frac{1}{9}(9 \times 15)=15$$\)

The variance of \($\bar{X}$\) and \($\bar{Y}$\) are:

\($$\{Var}(\bar{X})=\{Var}\left(\frac{1}{16} \sum_{i=1}^{16} X_i\right)=\frac{1}{16^2} \sum_{i=1}^{16} \{Var}\left(X_i\right)=\frac{1}{16^2}(16 \times 4)=\frac{1}{4}$$\)

and

\($$\{Var}(\bar{Y})=\{Var}\left(\frac{1}{9} \sum_{i=1}^9 Y_i\right)=\frac{1}{9^2} \sum_{i=1}^9 \{Var}\left(Y_i\right)=\frac{1}{9^2}(9 \times 4)=\frac{4}{81}$$\)

Now, we have:

\(E(\bar{X}-\bar{Y})=E(\bar{X})-E(\bar{Y})=0\)

and

\(\{Var}(\bar{X}-\bar{Y})=\{Var}(\bar{X})+\{Var}(\bar{Y})=\frac{1}{4}+\frac{4}{81}=\frac{25}{81}\)

Therefore, \($\bar{X}-\bar{Y}$\) follows a normal distribution with a mean 0 and a standard deviation:

\($$\sqrt{{Var}(\bar{X}-\bar{Y})}=\sqrt{\frac{25}{81}}=\frac{5}{9}$$\)

So, the answer is that \($\bar{X}-\bar{Y}$\) is normal with mean 0 and standard deviation \($5 / 9$\). None of the given options match this result exactly, but the closest one is "normal with a mean 0 and standard deviation \($5 / 6^{\prime \prime}$\).

Definition: To distribute a product is to make it available to a wide audience so that they can purchase it. These actions are involved in distribution: 1. A reliable transportation system to deliver the commodities to various locations.

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