what property tells us that m

Answer:

Step-by-step explanation:

Given a graph of a probability density function, you want the probabilities ...

The probability of a given range of values of X is the area under the density curve for those values of x.

The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:

  A = 1/2bh

  A = 1/2(16)(0.08) = 0.64

The probability is P(X<16) = 0.64.

The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...

  A = 1/2(b1 +b2)h

  A = 1/2(0.06 +0.10)(8) = 0.64

The probability is P(X>12) = 0.64.

we are given the following expression:

The greatest common factor between 12, 6, and 8 is 2. And the greatest common factor between the variables is:

Therefore, the factorization is:

Remember that

z =(x - μ)/σ

we have

μ=85

σ=5

For x=73

Find out the value of Z1

z1=(73-85)/5

z1=-2.4

For x=76

Find out the value of Z2

z2=(76-85)/5

z2=-1.8

using a z-scores table values

we have that

Let's make a diagram to visualize the problem.

First, let's find angle A.

Then, we use the law of sines to find AB.

To calculate the hypotenuse of a right angled triangle as shown in the diagram, we can apply the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (the longest side) 28 units, AB is one of the other two sides, 23 units and BC is the third side.

We can now re-write the formula as follows;

28^2 = 23^2 + BC^2

784 = 529 = BC^2

Subtract 529 from both sides of the equation

255 = BC^2

Add the square root sign to both sides of the equation and you have

BC = 15.9687

BC is approximately 16 units

The probability is 0.57

What is meant by probability?

Probability is a discipline of mathematics that deals with appropriate units of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number ranging from zero and 1, where 0 denotes the event's feasibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.

Probability of using the pool = 97/225 = 0.43

Probability that they do not use the swimming pool = 1 - 0.43 = 0.57

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Solution

Option 1:

- The owners asking the first 100 people they see would mean that they would see only those around them. This could be anyone at all from workers in the amusement park to people outside the park; these would not be random, and would not necessarily be a family but the survey is talking about randomly choosing 100 families. Because of these reasons, this is not the best way to randomly choose 100 families.

Option 2:

- Choosing a neighborhood near the amusement park would mean that they go to a neighborhood with families that might visit the amusement park and there would be many families to randomly choose from.

- This option seems like a good choice to randomly choose these 100 families that might visit the amusement park.

Option 3:

- Asking the first 100 families that enter the amusement park on a busy weekend would definitely bias the survey since families that you find in the amusement park are families that definitely want to be there and if they are there on a busy weekend, they certainly would not mind extending the season

A is angle opposite by the vertex with the angle of 104 degrees, that is why it also measure 104 degrees

The three inner angles of any triangle add 180 degrees, then 56 + A + B = 180

Solving for B: B = 180 - 56 - A = 180 - 56 - 104 = 20

In the right triangle of sides a, b, and c

Since a = 12 and c = 20

Substitute them in the given rule

Subtract 144 from both sides

Take a square root for both sides

The answer is b = 16

We are asked to evaluate the expression:

when x = 1 and y = -7

so we replace them as shown below, making sure we include them inside parenthesis to keep clear that the expressions in x and in y are multiplying each other:

So we see that x^2 becomes 1 and the factor y stays as -7. The final expression cancels out the negative sign in numerator (from -7) and in denominator (from -9) and gives 7/9.

Given the points:

(x1, y1) ==> (1, -4)

(x2, y2) ==> (-3, 8)

To find the slope, use the slope formula below:

Therefore, the slope is -3.

ANSWER:

-3

We need find the tax on the first 7500

7500 * 10%

7500 * .10 = 750

Now we find the tax on what is over 7500

20000 -7500 =12500

The tax rate for this amount is 16%

12500 * 16%

12500 * .16

2000

Add the tax for both amounts together

750 + 2000

2750

The total tax paid is 2750

Based on the information given in the exercise, you know that the shaded region has this area:

And the area of each square region in the corners is:

Since there are four square regions, you can multiply that the area of any of them by 4, in order to find the total area of them:

Then, in order to find the total area of the figure, you must add the area of the shaded region and the total area of the square regions:

Therefore, the total of the figure is:

Consider the following table for interval notation:

First row:

x<0 is the same as:

And the interval notation for that inequality is:

Second row:

-2

The graph of this inequality is:

The interval notation is:

Third row

The inequality that is represented by that interval is:

Its graph is:

Fourth row

The interval represented in that graph is:

The inequality represented by that interval is:

Given:

Area of a shaded region of a rectangle is given.

Area of the rectangle is twice the area of the triangle given.

The law of sines states that:

where alpha is the opposite angle to side a, beta is the opposite angle to side b and gamma is the opposite angle to side c.

For the triangle given we notice that:

Angle x is opposite to side 2.5.

Angle 28° is opposite to side 3.

Therefore the expression to find x is:

SOLUTION

Given the image on the answer tab;

Explanation;

The two angles are said to be adjacent angles when they share the common vertex and side.

Considering our question;

Given the function

Finding the derivative we have

Also

Finally

3x + 7y= 14

3x+7y= 10

Subtract the second equation to the first.

3x +7y= 14

-

3x + 7y= 10

_________

0x +0y = 4

0 = 4

0 is no

According to the graph, the value of the function g(-3) is 4 and g(10) is out of view

Graphs are graphical representations of equations, ordered pairs, tables of a relation

From the question, the function is represented by the attached graph

Also from the question, the function to calculate is given as g(10) and g(-3)

This means that we calculate the values of the function, when x = 10 and -3

i.e.

We calculate g(x), when x = -3

We calculate g(x), when x = 10

So, we look at the graph for this function value

From the graph of values, we have

When x = -3, g(x) = 4

When x = 10, g(x) = not visible

This means that

g(-3) = 4

g(10) = out of view

Hence, the function g(-3) has a value of 4 and g(10) is out of view

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First, rewrite all the mixed fractions as impropper fractions:

Next, multiply the rate of chocolate production over time by the the operating time of the machines to find the total amount of pounds of chocolate frogs produced in one day:

Then, the chocolate factory can produce 16 1/2 pounds of chocolate frogs per day.

Since 16 1/2 is greater than 10 1/2, then the chocolate factory will meet their goal with the total being over 10 1/2 pounds of chocolate frogs produced.

Linear Optimization

It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.

We'll use the graphic method to solve the problem.

The problem is as follows:

Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.

The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:

x + y ≤ 130 (1)

She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:

3.75x + 6y ≥ 600

Multiply this inequality by 4:

15x + 24y ≥ 2400

And divide it by 3:

5x + 8y ≥ 800 (2)

We are given a final condition that she can sell a minimum of 80 burritos, thus:

y ≥ 80 (3)

There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:

x ≥ 0 (4)

y ≥ 0 (5)

Let's put this all together:

x + y ≤ 130 (1)

5x + 8y ≥ 800 (2)

y ≥ 80 (3)

x ≥ 0 (4)

y ≥ 0 (5)

The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).

We need to graph all five lines in one common grid. It's shown below.

According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos

The quadrilateral ABCD was dilated by a scale factor of 3/4 to form the quadrilateral A'B'C'D'

This means that each side of the quadrilateral was multiplied by 3/4 to make the dilation.

You know that the scale factor is 3/4 and the length of D'A' is equal to 30 units, then:

Multiply both sides by the reciprocal of 3/4

The length of side DA is 40 units.

From the situation described in this problem, it is found that:

A. The composite function is: f(s(w)) = 36w + 30.

B. The unit of measurement of the composite function is: flowers.

C. After 36 weeks, Daisy can expect to bloom 1326 flowers.

For a composite function, the output of the inner function serves as the input of the outer function.

In the context of this problem, the functions are given as follows:

Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:

f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.

The unit of measurement of the composite function is the unit of the outer function, which is flowers.

After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:

f(s(36)) = 36(36) + 30 = 1326 flowers.

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Answer:

The slope is 3/5 and the equation is:

Explanation:

Given the points (0,2) and (5, 5)

The slope of a line is the ratio of the difference between the y coordinates to the x coordinates. The x coordinates are 0 and 5, the y coordinates are 2 and 5.

The equation of a straight line is given as:

y = mx + b

Where m is the slope and b is the y-intercept

Using any of the given points, we can find b

Use (0, 2), with x = 0, y = 2

2 = (3/5)(0) + b

b = 2

Now the equation is:

The situations that describe a proportional relationship are:

Jackson saves $10 in the first month and $30 in the next 3 months.

Mia saves $8 in the first 2 months and $4 in the next month.

Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.

A relation is proportional if the rate of change of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.

Is Jackson's saving proportional?

Average of the amount saved in the next 3 months: $30 / 3 = $10

The relationship is proportional because the amount saved in the first month and the average is equal.

Is Mia's saving proportional?

Average of the amount saved in the first 2 months: $8 / 2 = $4

The relationship is proportional because the amount saved in the thir month and the average is equal.

Is Piyoli's spending proportional?

Average of the amount spent in the first 2 days: $2 / 2 = $1

Average of the amount spent in the next 5 days = $5 / 5 = $1

The relationship is proportional because the averages are equal.

Is Robert's spending proportional?

Average of the amount spent in the first 3 days: $2 / 3 = $0.67

Average of the amount spent in the next 4 days = $5 / 4 = $1.25

The relationship is not proportional because the averages are not equal.

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The angle x has a measure of 13 degrees

Angles are the measure of space between lines

The figure represents the given parameter

On the figure, we have the following parameters:

Angle 1 = 54

Angle 2 = 11x - 7

Angle 5

From the figure, angles 1 and angle 5 are corresponding angles

Corresponding angles are congruent angles

So, we have

Angle 1 = Angle 5

This gives

Angle 5 = 54

Also, we have

Angle 5 and Angle 2 are supplementary angles

This means that

Angle 5 + Angle 2 = 180

Substitute the known values in the above equation

So, we have

54 + 11x - 17 = 180

Evaluate the like terms

11x = 143

Divide both sides by 11

x = 13

Hence, the value of x is 13 degrees

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The CLOSEST correct answer regarding "x" is the first one (answer A), since x is 79. The correct answer is: X measures 79 because it is an alternate external angle between parallel lines to the one labeled 79 in the picture.

To solve this problem, the first thing we must do is find the Z-Score of the given costs: $5265 , $6735 , $4530 ,and $7470

Then we proceed to find the percentages for each interval based on the graph

z-score for $5265 )

z-score for $6735 )

z-score for $4530 )

z-score $7470 )

now, let's analyze the intervals

a ) between $5265 and $6735

This interval goes from (μ-σ) to (μ+σ)

if we look at the graph we find that this corresponds to a percentage of 68%

b) above $6735

This corresponds to what is to the right of (μ+σ)

This is a percentage of 16%

c ) below $4530

This corresponds to what is to the left of (μ-2σ)

This is a percentage of 2.5%

d ) between $5265 and $7470

This interval goes from (μ-σ) to (μ+2σ)

This is a percentage of 81.5%