The base of a right triangular prism is right angle triangle if the height of the prism is 12 cm and the longer side of the base is 5 cm while the shortest side is 3 cm then find A)The lateral surface area B)The total surface area

The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.

The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.

In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.

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The graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.

y≤-1/2x² + 4x + 7

The inequality is a quadratic function in standard form.

To graph it, we can find the vertex and the x-intercepts.

The vertex is at the point (h, k) where h = -b/2a and k = f(h), and f(x) = -1/2x² + 4x + 7.

a = -1/2, b = 4, and c = 7,

so h = -b/2a = -4/(-1) = 4, and

k = f(h) = -1/2(4)² + 4(4) + 7 = 15.

So the vertex is at (4, 15).

Now let us find the x-intercepts by setting y value as 0 and solve for x:

0 ≤ -1/2x² + 4x + 7

1/2x² - 4x - 7 ≤ 0

x² - 8x - 14 ≤ 0

We find roots by using the quadratic formula

x = (8 ± √8² - 4(1)(-14))) / 2

x = 4 ± √18

So the x-intercepts are  0.34 and 7.66.

Hence, the graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.

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Explain the graph of the inequality y≤-1/2x² + 4x + 7?

To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.

Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.

Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.

To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:

d/dx (2πr^3) = 6πr^2 = 0

This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.

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The piecewise function graphed in this problem is defined as follows:

A piece-wise function is a function that has different definitions, depending on the input of the function.

The definitions for this problem are given as follows:

For the function up to x = 1, the function is a linear function with slope of 1 and intercept of 6, hence:

y = x + 6, x ≤ 1.

For the function greater than x = 1, the quadratic function y = x² + 3 is defined, hence:

y = x² + 3, x > 1.

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Answer:

1 cup

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for the total number of cups used, we need to first convert each fraction to have a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

As of now, each fraction looks like this:

Looking at each of the denominators, we can see that 12 is a multiple of both 4 and 3!

So, let's convert [tex]\frac{1}{3}[/tex].

Now that we have the denominator, we need to multiply the numerator by the same amount, so it stays equivalent.

Now let's convert [tex]\frac{1}{4}[/tex].

4 can be multiplied by 3 to get 12.

1 can be multiplied by 3 to get 3.

Now, each fraction looks like this:

Adding up the numerators:

Adding that back on top of the denominator:

So, [tex]\frac{4}{12}+ \frac{3}{12}+ \frac{5}{12} = \frac{12}{12}[/tex] or 1.

Therefore 1 cup of flour was used that day.

Answer:

the answer is lateral area

We can match the terms in the left column to the correct bolded examples as follows:

Sum: 1 + 1 = 2

Difference: 7 - 2 = 5

Term: 2x

Product: 9 * 9 = 81

Factor: 81 ÷ 9 = 9

Quotient: 81 ÷ 9 = 9

Coefficient: 7x - 8y

Variable: 5x + 3

To match the correct expression, an understanding of the mathematical terms is essential. The sum is the addition of terms and in the list, 1 + 1 is an example of a sum. Also, the product is the multiplication of numbers and 9 * 9 = 81 is an example of a product.

Coefficients are numbers that are matched with letters in algebra. A variable is a letter beside a number in an expression. In the option, x is the variable besides 5.

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Answer:

A, C

Step-by-step explanation:

For A, it's correct because they both start with 865.4, but the number in the problem has numbers after the 4, so A is right. B, is not because they both have 865.47, but the one in the problem has a 3, and C has 5, so no. C, is right, because the the problem's thousandths place is greater than C's. D, is not, because it's ones place is greater than the original number.

Answer:

Step-by-step explanation:

it is 83/49 because I searched it up.

To determine the order in which Harry Potter should visit the 4 places and return to Gryffindor in the least amount of time, we need to look at the graph provided by Hermione.

We can start by looking for the shortest distances between each location. Once we have identified the shortest distances, we can then use this information to determine the most efficient order for Harry to visit each place.
It's important to note that there may be multiple routes that Harry can take to visit all 4 places, but we want to find the one that will take the least amount of time. To do this, we can start by identifying the shortest distance between two locations and continue to do this until we have identified the shortest path to all 4 locations.
Once we have determined the order in which Harry should visit each location, we can then calculate the amount of time it will take for him to travel between each place and return to Gryffindor. This will give us a total time for the entire journey.
We can say that determining the most efficient route for Harry to visit the 4 places and return to Gryffindor in the least amount of time requires careful analysis of the graph provided by Hermione. By identifying the shortest distance between each location and using this information to create the most efficient route, we can minimize the amount of time Harry spends traveling between each place. Once we have identified the order in which Harry should visit each location, we can then calculate the amount of time it will take him to travel between each place and return to Gryffindor. By doing this, we can determine the total amount of time it will take for Harry to complete his journey.

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To find the dimensions of the rectangle, we need to use Cramer's rule, which is a method for solving systems of linear equations.

   Let's start by defining the variables:

Let x be the width of the rectangle in cm.

Let y be the length of the rectangle in cm.

According to the problem, we have two equations:

y = 3x - 6 (the length is 6cm less than three times the width)

2(x + y) = P (the perimeter of the rectangle is P)

We can rewrite the second equation as:

2x + 2y = P

To solve for x and y, we need to set up a matrix and apply Cramer's rule. The matrix is:

| 0 1 | | x | | -6 |

| 2 2 | x | y | = | P |

Using Cramer's rule, we can solve for x and y as follows:

x = (|-6 1| / |-2 1|) = 9

y = (|0 -6| / |-2 1|) = 12

Therefore, the width of the rectangle is 9 cm and the length of the rectangle is 12 cm.

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The sampling design used in this scenario is cluster sampling.

Cluster sampling involves dividing the population into groups or clusters (in this case, the 15 towns) and randomly selecting entire clusters to be included in the sample. In this case, the intern randomly selected 20 customers from each town, which means that the clusters were the towns themselves.

Cluster sampling is a practical and efficient sampling method when it is difficult or expensive to access individual elements of the population. By selecting entire clusters, the sampling process becomes more manageable, and it can reduce costs and logistical challenges.

However, it's important to note that cluster sampling introduces the possibility of within-cluster similarity, meaning that individuals within the same cluster may have similar characteristics or behaviors. This can affect the variability of the sample and the generalizability of the findings to the entire population. It is important to consider this potential bias and account for it in the data analysis and interpretation.

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The small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.

To determine the distance that the small submarine must travel to reach 180 feet below sea level, we need to use some basic math.
First, we need to determine the distance between the current position of the submarine (-1,320 feet) and its target depth (-180 feet below sea level). To do this, we subtract the target depth from the current depth:
-1,320 ft - (-180 ft) = -1,140 ft
This means that the submarine needs to travel 1,140 feet down in order to reach its target depth.
Next, we need to figure out how long it will take the submarine to travel that distance. We know that it has 60 minutes to do so, so we can use the formula:
distance = rate x time
We know the distance (1,140 feet), so we need to solve for rate. Rearranging the formula, we get:
rate = distance / time
Plugging in the values we know, we get:
rate = 1,140 ft / 60 min = 19 ft/min
So the small submarine needs to travel at a rate of 19 feet per minute in order to reach its target depth of 180 feet below sea level in 60 minutes.
In summary, the small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.

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The approximated value of the logarithm expression is 0.5646  + 4log(b)

From the question, we have the following parameters that can be used in our computation:

log, 2≈ 0.3562,

log, 3≈ 0.5646, and

log, 5 ≈ 0.8271

Also, we have

logb (3b⁴)

Using the logarithms property, we have

logb (3b⁴) = logb (3) + log(b⁴)

This gives

logb (3b⁴) = logb (3) + 4log(b)

Substitute the known values in the above equation, so, we have the following representation

logb (3b⁴) = 0.5646  + 4log(b)

Hence, the approximated value is 0.5646  + 4log(b)

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Given 20% of the pupils are girls and the rest are boys. So, there are a total of 1785 pupils in the school.

To solve this problem, we can start by using the information that 20% of the pupils are girls to find the total number of girls and boys in the school. If there are a total of x pupils, then 0.2x are girls and 0.8x are boys.

Next, we can use the fact that the ratio of the number of pupils who wear spectacles to those who do not wear spectacles is 1:5 to find the number of pupils who wear spectacles. Let the number of pupils who wear spectacles be y, then 1/6y are girls who wear spectacles and 5/6y are boys who wear spectacles.

We also know that there is an equal number of girls and boys who wear spectacles, so we can write:

1/6y = 5/6y / 4

where 4 is the ratio of boys to girls who wear spectacles.

Solving for y, we get y = 357 * 24 = 8568. Therefore, the total number of pupils in the school is:

x = 0.2x + 0.8x = 1785

Hence, there are 1785 pupils altogether in the school.

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To find two numbers that multiply to -63 and add to -18, we can start by listing all the factors of -63:

We can see that -9 and 7 are the only two factors that add up to -2.

Therefore, the two numbers that multiply to -63 and add to -18 are -9 and 7.

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Obsa will need 2 smaller prisms to fill the larger prism, with each smaller prism having a volume of 4/3 cubic feet.

To find out how many smaller prisms it would take to fill the larger one, we need to first determine the volume of the larger prism. We know that the larger prism has a volume of 2 1/3 cubic feet, which can also be expressed as 7/3 cubic feet.
Next, we need to find out how many of the smaller prisms will fit into the larger one.

To do this, we can divide the volume of the larger prism by the volume of the smaller prism.

The smaller prism has a volume of 4/3 cubic feet, so:
(7/3 cubic feet) / (4/3 cubic feet) = 7/4
This means that it will take 7/4 smaller prisms to fill the larger prism.

However, since we can't have a fraction of a prism, we need to round up to the nearest whole number.
Therefore, it will take 2 smaller prisms to fill the larger prism. One prism will fill up 4/3 cubic feet, and the other will fill up 4/3 cubic feet, totaling to 8/3 cubic feet, which is just a bit more than the 2 1/3 cubic feet of the larger prism.
This means that it takes 1 and 3/4 smaller prisms to fill the larger container.

However, since we cannot have a fraction of a prism, we need to round up to the nearest whole number, which is 2.

Therefore, it would take 2 smaller prisms to fill the larger prism-shaped container.

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the series ex2 converges for all real values of x.

The general term of the series ex2 = 1 + x^2 + x^4/2! + x^6/3! + x^8/4! + ... is given by:

an = xn/(n!) for n ≥ 0, where n is an even integer.

Here, xn represents the term with exponent n in the series.

Therefore, the range of values for the index n is all even non-negative integers starting from 0.

Note that n! (n factorial) in the denominator of the general term ensures that each term after the first term (which is 1) is smaller than the preceding term, as n increases.

what is integer?

An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals. Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on. The set of integers is denoted by the symbol Z.

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The level of accounts receivable will be $479,452.05.

If Harley-Davidson Inc. reduces its DSO to 35 days by pressuring more of its customers to pay their bills on time, the company’s average sales will fall by 15%. To calculate the level of accounts receivable following this change, we need to use the formula for DSO:

DSO = (Accounts Receivable / Average Daily Sales) x Number of Days in Period

We know that the current DSO is 55 days, and the company wants to reduce it to 35 days. Therefore, we can assume that the current average daily sales are:

Average Daily Sales = Annual Sales / 365
DSO = (Accounts Receivable / Average Daily Sales) x Number of Days in Period
55 = ($750,000 / (Annual Sales / 365)) x 365

Solving for Annual Sales, we get:

Annual Sales = $1,095,890.41

If the company’s average sales will fall by 15%, then the new Annual Sales will be:

New Annual Sales = $931,507.85 ($1,095,890.41 - 15%)

Using this new Annual Sales figure, we can now calculate the new level of accounts receivable following the change:

35 = (New Accounts Receivable / (New Annual Sales / 365)) x 365
New Accounts Receivable = $479,452.05

Therefore, if Harley-Davidson Inc. reduces its DSO to 35 days by pressuring more of its customers to pay their bills on time and its average sales fall by 15%, the level of accounts receivable will be $479,452.05.

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The 75th percentile of the wait time in a restaurant, assuming it follows an exponential distribution with a mean of 10 minutes, can be found using the inverse of the exponential cumulative distribution function.

In an exponential distribution, the probability density function (PDF) is given by f(x) = λe^(-λx), where λ is the rate parameter. The mean of the exponential distribution is equal to 1/λ. In this case, we are given that the mean is 10 minutes, so λ = 1/10.

To find the 75th percentile, we need to find the value x for which P(X ≤ x) = 0.75. In other words, we want to find the value of x such that 75% of the wait times are less than or equal to x.

Using the exponential cumulative distribution function (CDF), we can solve for x by setting P(X ≤ x) = 0.75 and solving for x. The formula for the exponential CDF is F(x) = 1 - e^(-λx).

Setting 1 - e^(-λx) = 0.75, we can solve for x to find the 75th percentile of the wait time.

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Mike has under 1/4 of a tank of gas, and he decides to fill up his gas tank. his gas tank holds 16 gallons. the gas cost $3.59 per gallon. It will cost Mike $43.08 to fill up his car.

To help you with your question, we first need to determine the amount of gas Mike needs to fill up his car. Since he has less than 1/4 of a tank, let's assume he has exactly 1/4 of a tank for simplicity.
Mike's car has a 16-gallon gas tank, so:
1/4 * 16 gallons = 4 gallons already in the tank.
To fill up the tank, Mike needs to add:
16 gallons - 4 gallons = 12 gallons.
The gas costs $3.59 per gallon, so to find the total cost:
12 gallons * $3.59 = $43.08.
Approximately, it will cost Mike $43.08 to fill up his car.

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Answer:

(-0.8, 2.2)

Step-by-step explanation:

Where the two lines intersect is the solution to the System of Equations.

Answer:

the answer would be (-0.8, 2.2) since it hasn't hit -3 yet and if it were to be -1 it would be in the bottom left

To convert the vertex form of a quadratic equation to standard form, we need to expand the squared term and simplify the expression.

Starting with the vertex form of the equation of a parabola:

y = 2(x - 3)^2 + 5

We can expand the squared term using the square of a binomial formula:

y = 2(x^2 - 6x + 9) + 5

Next, we distribute the coefficient 2:

y = 2x^2 - 12x + 18 + 5

Simplifying the constant terms:

y = 2x^2 - 12x + 23

This is the standard form of the equation of the parabola.

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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The value of the measure of each sides indicated are:

The measurement of the indicated side can be obtain as illustrated below:

1. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 20 = x / 11

Cross multiply

x = 11 × Tan 20

Value of x = 4

2. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 27 = 5 / x

Cross multiply

x × Sine 27 = 5

Divide both sides by Sine 27

x = 5 / Sine 27

Value of x = 11

3. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 27.2 = 10 / x

Cross multiply

x × Sine 27.2 = 10

Divide both sides by Sine 27.2

x = 10 / Sine 27.2

Value of x = 21.9

4. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 25 = 15 / x

Cross multiply

x × Tan 25 = 15

Divide both sides by Tan 25

x = 15 / Tan 25

Value of x = 32.2

5. The value of x can be obtain as follow:

Cos θ = Adjacent / Hypotenuse

Cos 64 = 4 / x

Cross multiply

x × Cos 64 = 4

Divide both sides by Cos 64

x = 4 / Cos 64

Value of x = 9.1

6. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 33 = x / 14

Cross multiply

x = 14 × Tan 33

Value of x = 9.1

7. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 49.6 = 5.6 / x

Cross multiply

x × Sine 49.6 = 5.6

Divide both sides by Sine 49.6

x = 5.6 / Sine 49.6

Value of x = 7.4

8. The value of x can be obtain as follow:

Cos θ = Adjacent / Hypotenuse

Cos 40 = x / 10.2

Cross multiply

x = 10.2 × Cos 40

Value of x = 7.8

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To compute the trimmed mean for the given data, we need to first delete the smallest and largest observed values, which are 0.76 and 0.96 respectively. Then we calculate the mean of the remaining 28 values.

The trimmed data set after deleting the smallest and largest values is:

0.81 0.88 0.82 0.90 0.84 0.84 0.91 0.94 0.86 0.86 0.88 0.87 0.89 0.91 0.86 0.87 0.88 0.83 0.91 0.91 0.86 0.89 0.84 0.88 0.88 0.89 0.83 0.90 0.88 0.92 0.85 0.84 0.86

The sum of these values is 24.39, and the trimmed mean is 24.39/28 = 0.871 (rounded to three decimal places).

The trimmed mean is considered to be a resistant measure of central tendency because it is less affected by extreme values compared to the mean. In this case, even though we deleted the smallest and largest values, the resulting trimmed mean is very close to the mean of the original data set (which is 0.8716). Therefore, the trimmed mean is resistant to changes in extreme values in the given data.

The answer is (b) yes, because changing the extreme values does not change the trimmed mean.

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Answer:

3 ways

Step-by-step explanation:

Using the arrows that they gave us, (which are the directions). The only possible ways are 3. Which I have shown in the screenshot attached below.

If we were to try to do it another time using the directions, it wouldn't work and we would most likely skip a step

Hope I helped!

The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.

To find the angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12), follow these steps:
Step 1: Determine the coordinates of the given point. In this case, it is (-5, 12).
Step 2: Calculate the horizontal (x) and vertical (y) distances from the origin (0, 0) to the point. The horizontal distance is -5 and the vertical distance is 12.
Step 3: Calculate the angle using the arctangent function (tan^(-1)). The arctangent function takes the ratio of the vertical distance to the horizontal distance as its argument. So, angle = tan^(-1)(12 / -5).
Step 4: Compute the arctangent value using a calculator or an online tool. Angle ≈ tan^(-1)(-2.4) ≈ -67.38 degrees.
Step 5: Convert the angle to a positive value measured counterclockwise from the positive x-axis. Since the angle is measured in the second quadrant, subtract the angle from 180 degrees: 180 - 67.38 ≈ 112.62 degrees.
The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.

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Therefore, the polynomial that passes through the given points is: f(x) = 6 - 38x - 6x^2 + 4x^3 + 3x^4.

To find the polynomial that passes through the given points, we can use the method of interpolation. Since we have five points, we can use a fourth-degree polynomial to fit the data.

Let's assume that the polynomial is of the form:

f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4

We can find the coefficients a0, a1, a2, a3, and a4 by substituting the given points into the equation and solving the resulting system of linear equations.

Substituting (-4, 89) into the equation, we get:

89 = a0 - 4a1 + 16a2 - 64a3 + 256a4

Substituting (-3, 7) into the equation, we get:

7 = a0 - 3a1 + 9a2 - 27a3 + 81a4

Substituting (-1, -1) into the equation, we get:

-1 = a0 - a1 + a2 - a3 + a4

Substituting (1, -1) into the equation, we get:

-1 = a0 + a1 + a2 + a3 + a4

Substituting (4, 329) into the equation, we get:

329 = a0 + 4a1 + 16a2 + 64a3 + 256a4

Now we have five linear equations with five unknowns, which we can solve using any method of linear algebra. One possible way is to use matrix inversion. After solving for the coefficients, we get:

a0 = 6

a1 = -38

a2 = -6

a3 = 4

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