2. The area of this trapezoid is 24.5 ft².
3 ft
4 ft
What is the height of the trapezoid? Write the formula first then SHOW YOUR WORK

Plssss I need the answer fasttttt

The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.

Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)

P(x > 77.83) = 1 - P(x < 77.83)

P(x > 77.83) = 1 - 0.9234

P(x > 77.83) = 0.0766

When the radius is 136 in. and the height is 110 in., the volume of the cone is changing at a rate of 109.76 in³/s.

The volume of a right circular cone is given by the formula V = (1/3)*πr²h, where r is the radius and h is the height. Thus, when the radius is increasing at a rate of 1.6 in/s and the height is decreasing at a rate of 2.5 in/s, the rate of change of the volume (dV/dt) is given by:

dV/dt = (1/3)*π(1.6r + 2.5h)

Substituting r = 136 in. and h = 110 in., we get

dV/dt = (1/3)*π(216 + 275) = 109.76 in³/s

Therefore, when the radius is 136 in. and the height is 110 in., the volume of the cone is changing at a rate of 109.76 in³/s.

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The experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.

The experimental probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.

In this case, the event is "getting a hit" and the number of times it occurred is 11. The total number of trials is 44, which represents the number of times Roberto was at bat.

Experimental probability of getting a hit = Number of times Roberto got a hit / Total number of times at bat

Experimental probability of getting a hit = 11 / 44

Experimental probability of getting a hit = 0.25 or 25%

Therefore, the experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.

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Answer:

There are several ways to make 45 cents using different coins:

Nine nickels

Four dimes and one nickel

Three dimes and six nickels

Two dimes and one quarter

One dime, two nickels, and three pennies

One quarter and two dimes

One quarter, one dime, and four nickels

One quarter, three nickels, and five pennies

45 pennies

So there are 9 ways to make 45 cents.

I Hope This Helps!

Fatouma lifted 1 kg during the first week and 120 kg during the tenth week. Fatouma lifted 120 kg in 10 weeks, increasing by 2 kg each week.

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0

Say the mass Fatouma lifted during the first week "x". According to the problem, she increases the weight she lifts by 2 kg every week. So, the mass of second week is "x + 2" kg, during the third week is "x + 4" kg, and so on.

Since there are 10 weeks of training, the mass she lifted during the 10th week is:

x + (10 - 1) × 2 = x + 18

We also know that during the 10th week, she lifted 120 kg. So, we can set up an equation:

x + 18 = 120

Solving for x, we get:

x = 102

Thus, Fatouma lifted 102 kg during the first week of training.

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The dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).

The perimeter of the bottom of a rectangular swimming pool is 60 meters, and the area is 221 square meters.

To find the dimensions of the pool, we can use the formula P = 2(l + w) where P is the perimeter and l and w are the length and width of the pool respectively. We can rearrange this formula to solve for either l or w, so we'll solve for l.

2(l + w) = 60
2l + 2w = 60
2l = 60 - 2w
l = (60 - 2w)/2

Now, we can use the formula A = l*w to solve for w.

221 = l*w
221 = (60 - 2w)/2 * w
221 = (60w - 2w^2)/2
442 = 60w - 2w^2
2w^2 - 60w + 442 = 0

Using the quadratic formula, we get w = 16.45 or 7.55.

Now that we know the width, we can use the formula l = (60 - 2w)/2 to find the length. For w = 16.45, l = 21.55, and for w = 7.55, l = 28.45.

Therefore, the dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).

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A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.

From the problem, we know that:

4b + 5t = 13 (for Clark)

5b + 3t = 13 (for Bruce)

We want to determine the cost of a burrito, so we can solve for "b" using the second equation:

[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]

Now we can substitute this expression for "b" into the first equation:

[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]

So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":

[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]

Therefore, a burrito costs $2 at Taco Hut.

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Answer:

19. sqrt{305}

20. 3*sqrt{7}

Step-by-step explanation:

You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.

Step-by-step explanation:

hope this will gel help u

The scale factor used to create the dilated polygon is 4.

What is scaler factor?

Scale factor is a numerical ratio that describes how much a geometric figure has been enlarged or reduced. It is the ratio of the length of a side, diagonal, or any other linear dimension of the new (dilated) figure to the corresponding dimension of the original figure.

The distance between two points can be calculated using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.[/tex]

To determine the scale factor, we need to compare the distances between corresponding points in the original and dilated polygons. Let's start by finding the distance between points A and B in the original polygon:

[tex]$d_{AB}=\sqrt{(3-1)^2+(-1+1)^2}=\sqrt{4}=2$[/tex]

Now let's find the distance between corresponding points A' and B' in the dilated polygon:

[tex]$d_{A'B'}=\sqrt{(12-4)^2+(-4+4)^2}=\sqrt{64}=8$[/tex]

To find the scale factor, we divide the corresponding distances:

[tex]$scale\ factor=\frac{d_{A'B'}}{d_{AB}}=\frac{8}{2}=4$[/tex]

Therefore, the scale factor used to create the dilated polygon is 4.

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We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.

an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.

X + 4 corresponds to a value in the second column and top row.

The third row's value is equal to the first column's value plus two.

(Third row, second column) The value is 12 at the bottom right corner.

First row and the first column, top left, represents value as B.

It reads 8, first row, second column, in the upper right corner.

C is the value located on the bottom left (third row, first column).

We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:

X plus 4 = 8

When we take 4 away from both sides, you get:

X = 4

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A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex]  .

The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that  [tex]ZF = ZD + DF = 24 + 28 = 52[/tex]  and [tex]FH = ZG = 30 and ZH = 36.[/tex]

As a result, Fard ZH's perimeter is as follows:

perimeter = [tex]= ZF + FH + ZH + ZG[/tex]

perimeter  [tex]= 52 + 30 + 36 + 30[/tex]

perimeter  [tex]= 148[/tex]

So the perimeter of Fard ZH is [tex]148[/tex]  .

(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:

[tex]V = (xB - xA, yB - yA)[/tex]

Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.

Plugging in the given values, we get:

[tex]V = (5 - 10, 2 - 14)[/tex]

[tex]V = (-5, -12)[/tex]

Therefore, The V's direction is [tex](-5, -12)[/tex] .

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The bread recipe calls for 2 more cups of flour per cup of sugar than the cookie recipe.

========================================================

Explanation:

I'll use this shorthand

Something like "2 cups of sugar" will shorten to "2s".

The cookies need 3s for every 6f.

Therefore we get this ratio

3s : 6f

And we can divide both sides by 3 to end up with

s : 2f

Meaning "each cup of sugar needs 2 cups of flour".

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

Meanwhile, the bread recipe calls for 2s for every 8f.

2s : 8f

2s/2 : 8f/2 .... divide both sides by 2

s : 4f

When making bread, each cup of sugar needs 4 cups of flour. In other words, the amount of flour is quadruple that of the sugar.

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

Recap

These ratios are reduced so that we have "s" on the left side without any numbers attached to it. In other words, we have 1s.

We can see that the bread needs 2 more cups of flour compared to the cookies (since 4f - 2f = 2f). It's important that we reduce those ratios so that we're talking about the same amount of sugar for each food item.

This is why  choice B   is the final answer.

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

An example:

Each food item will use 1 cup of sugar.

The cookies need twice the amount of flour, so the cookies require 2 cups of flour (because of the ratio s:2f mentioned earlier).

The bread needs quadruple the amount of flour compared to sugar. Meaning the bread needs 4 cups of flour (because of the ratio s:4f).

Then subtract to get

(4 cups flour for bread) - (2 cups flour for cookies) = 2 cups flour

The difference between cardinality and join type is that cardinality describes the relationship between two data tables, while join type is the specific method used to combine the two tables.

Cardinality defines the maximum number of records that can exist in one table for a relationship with another table. Cardinality can be either one-to-one, one-to-many, or many-to-many.

A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. For example, a customer can have multiple orders. In this situation, a one-to-one join type is often used because it is the most efficient way to retrieve the related data. This is because one-to-one join type only requires that one record be searched, while a one-to-many join type would require that multiple records be searched in order to find the related records. Additionally, a one-to-one join type ensures that no duplicate records will be returned in the result.

In summary, cardinality describes the relationship between two tables while join type is the specific method used to combine the two tables. A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. To efficiently retrieve the related data, a one-to-one join type is often used. This is because it only requires that one record be searched and it ensures that no duplicate records will be returned in the result.

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The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.

What is an extraneous solution?

An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

We are given two equations as f(x) = [tex]\frac{-1}{2}[/tex]x + 6 and f(x) = √x - 4.

Now, on equating both the equations, we get

⇒ [tex]\frac{-1}{2}[/tex]x + 6 = √x - 4

On squaring both sides, we get,

⇒ [tex](\frac{-1}{2}x + 6)^{2}[/tex]= x - 4

⇒ [tex]\frac{1}{4}x^{2}[/tex] + 36 - 6x = x - 4

⇒ [tex]\frac{1}{4}x^{2}[/tex] + 40 = 7x

⇒ [tex]\frac{1}{4}x^{2}[/tex] -7x + 40 = 0

⇒ [tex]x^{2}[/tex] -28x + 160 = 0

⇒ x = 20 , 8

For point of intersection, we will substitute x = 20 in both the equations.

So, we get

⇒ f(x) = [tex]\frac{-1}{2}[/tex] (20) + 6

⇒ f(x) = -10 + 6

⇒ f(x) = -4

Similarly,

⇒ f(x) = √20 - 4

⇒ f(x) = √16

⇒ f(x) = 4

Since both the solutions are not same so this is an extraneous solution.

Hence, the extraneous solution which arises is 10.

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The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.

To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.

In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.

Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.

By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.

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The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.

The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.

Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.

So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

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The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.

To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.

In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.

Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.

By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.

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The skewness coefficient is a measure of asymmetry in a distribution that can be used to compare means and compare one sample to a known reference distribution, but it is not typically used to compare standard deviations or compare two samples with different measurement units.

The skewness coefficient is a measure of the degree of asymmetry in a probability distribution. It indicates the direction and degree of skewness in a distribution, and can be used to compare means and compare one sample to a known reference distribution.

A positive skewness coefficient indicates that the distribution has a longer tail on the right side and that the mean is greater than the median, while a negative skewness coefficient indicates that the distribution has a longer tail on the left side and that the mean is less than the median.

The skewness coefficient can be useful in detecting departures from normality and in identifying outliers that might affect statistical inference.

However, the skewness coefficient is not typically used to compare standard deviations or to compare two samples with different measurement units.

Comparing standard deviations involves analyzing the variability in the data, whereas comparing means and comparing one sample to a known reference distribution involves analyzing the central tendency of the data.

Additionally, comparing two samples with different measurement units requires converting the measurements to a common scale, which is not related to skewness.

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To make a stable structure, the method of joints can be used to calculate the force BD in the truss shown.

This method uses the equations of equilibrium to determine the forces in the members of a truss. To calculate the force BD, one needs to sum the moments about point A and equate them to zero.

The moment is given by M = FxD, where F is the force, and D is the perpendicular distance from the point of interest to the line of action of the force. Therefore, the force BD can be calculated using the equation:

MAB = 0 = (BD)(2) - (AE)(5)

BD = 5AE/2

To find the forces in members CD and CE using the method of sections, one needs to cut through the truss along a line passing through points C and E.

Then, the force in member CD can be found by using the equation of equilibrium, where the sum of the forces in the x-direction and the sum of the forces in the y-direction must be equal to zero. Similarly, the force in member CE can also be calculated using the same method.

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Answer:

3,984.375 tons

Step-by-step explanation:

First, let's convert the weight of one box from ounces to tons:

0.51 oz = 0.51/16 = 0.031875 lbs

1 lb = 0.0005 tons (since 1 ton = 2000 lbs)

0.031875 lbs = 0.031875 x 0.0005 = 0.0000159375 tons

Next, let's calculate the total weight of cardboard needed for 250 million boxes:

Total weight of cardboard = weight of one box x number of boxes

Total weight of cardboard = 0.0000159375 tons x 250,000,000

Total weight of cardboard = 3,984.375 tons

Answer: 7x - 7y + 21

Step-by-step explanation:

7( x - y + 3) = 7x - 7y + 21

Answer:

  60.3°

Step-by-step explanation:

You want the measure of angle B in right triangle ABC with leg BC = 8 and leg AC = 14.

The tangent relation is ...

  Tan = Opposite/Adjacent

Applying this to the given triangle, we have ...

  tan(B) = 14/8

The arctangent function gives you the angle from the tangent.

  B = arctan(14/8) ≈ 60.3°

The measure of angle B is about 60.3°.

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The value 3.915 represents the y-intercept or the initial or baseline water lily population when there are no changes in the independent variable (x). the coefficient 1.106 represents the slope of the regression line or the rate of change in the dependent variable (y).

In the regression equation y = 3.915(1.106)x, the coefficient 3.915 represents the y-intercept or the value of y when x is 0. In the context of the water lily population change, this means that when there are no changes in the independent variable (x), the predicted value of the dependent variable (y) is 3.915, which represents the initial or baseline water lily population.

The coefficient 1.106 represents  rate of change in the dependent variable (y) per unit change in the independent variable (x) or the  the slope of regression line . In the context of the water lily population change, this means that for every unit increase in the independent variable (which could be time, environmental factors, or any other relevant variable), the predicted value of the dependent variable (y) increases by a factor of 1.106. In other words, the water lily population is expected to grow by 1.106 times for every unit increase in the relevant variable.

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____The given question is incomplete, the complete question is given below:

The regression equation you found for the water lilies is y = 3.915(1.106)x.

In terms of the water lily population change, the value 3.915 represents:

The value 1.106 represents:

Answer:

The value of 3.915 is the initial number

of water lilies. It is approximately 4, which matches

the data.

The value 1.106 is the growth rate. The rate represents growth for each day. The percentage growth each day is 10.6%

Step-by-step explanation:

Answer:

2/3 is the answer .......mmm..

5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.

We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:

p = 0.45

Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.

The formula for X's mean or expected value is:

E(X) = np

When we change the values of n and p, we obtain:

E(X) = 12(0.45) = 5.4

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The true statements for the graph of y=(x+2)²2+4 are:, The vertex of the parabola is at the point (-2, 4)., The graph opens upwards, since the coefficient of the squared term is positive., The y-intercept of the graph is at the point (0, 9)., The x-coordinate of the vertex is -2, which is also the axis of symmetry of the parabola., The graph is a parabola, which is a U-shaped curve.

What is graph?

In mathematics, a graph is a visual representation of a set of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs are used to model relationships between objects or to represent data in a visual way.

In the context of coordinate geometry, a graph is a visual representation of a function or relation, which shows the relationship between the input values (x-axis) and output values (y-axis). The graph is typically a set of points plotted on a Cartesian plane, where each point represents a unique input-output pair.

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Complete Question:

Select the statements that are true for the graph of y = (x+2)²2 + 4.

a) The vertex of the parabola is (-2, 4).

b) The parabola opens upward.

c) The y-intercept of the parabola is 4.

d) The x-intercepts of the parabola are (-4, 0) and (0, 0).

e) The axis of symmetry of the parabola is a vertical line through x = -2.

Answer:

Step-by-step explanation:

holy mocacrise

four is the minimal because you want to draw all four to the four of a kind

Answer:

To calculate the total milk yield in one year, we need to multiply the number of dairy cows by the amount of milk each cow produces per year:

Total milk yield = 2650 dairy cows × 2320 gallons of milk per cow per year

Total milk yield = 6,188,000 gallons per year

To write this answer in scientific notation, we need to express the number 6,188,000 as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left until we have a number between 1 and 10, and counting the number of decimal places we moved. In this case, we need to move the decimal point 6 places to the left:

Total milk yield = 6.188 × 10^6 gallons per year

Therefore, the dairy farm yields 6.188 × 10^6 gallons of milk per year.

One way to do this is to subtract 1.8x from both sides of the equation, which gives:

x - 1.8x = 32

Simplifying the left-hand side, we get:

-0.8x = 32

To solve for x, we can divide both sides of the equation by -0.8:

x = 32 / (-0.8)

Simplifying, we get:

x = -40