50 Points! Multiple choice geometry question. Photo attached. Thank you!

The solution is : the value of P(2≤X≤5) is 0.50.

Here, we have,

given that,

The graph show the probability distribution of a random variable.

we know that,

The probability distribution of a random variable X is P(X = xi) = pi for x = xi and P(X = xi) = 0 for x ≠ xi. The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 ≤ p(x) ≤ 1.

so, we have,

P(2≤X≤5)

=P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)

= 0.2+ 0.1 +0.05+0.15

= 0.50

Hence, The solution is : the value of P(2≤X≤5) is 0.50.

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If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).

The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).

To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.

The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).

To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.

The new coordinates of the vertices after the translation are:

A': (1, -2 - 5) = (1, -7)

B': (9, -2 - 5) = (9, -7)

C': (5, 2 - 5) = (5, -3)

Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).

In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).

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The equation of the line in point-slope form, using the point (-2, -1), is: y + 1 = -2(x + 2)

The equation of a line in point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and m represents the slope.

Given:

Slope (m) = rise/run = -2

Point (-2, -1)

Substituting the given slope and point into the equation, we have:

y - (-1) = -2(x - (-2))

y + 1 = -2(x + 2)

Therefore, the equation of the line is: y + 1 = -2(x + 2).

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Answer:

area=20ft^2

Step-by-step explanation:

3ft×4ft=12ft^2

12ft÷2=6ft is the area of the smaller triangle

7ft×4ft=28ft^2

28ft÷2=14ft is the area of the larger triangle

6ft+14ft=20ft^2

Answer: X = 8

Step-by-step explanation:

47 - 7 = 40

40 / 5 = 8

x = 8

Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

Answer:

(a) 44 (4 + 4 = 8), 62 (6 + 2 = 8)

(b) 165 (1 + 6 + 5 = 12)

The given function does not have an end behavior because it is not a polynomial function.

The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The end behavior of this function does not exist because this is not a polynomial.

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The slope of each line is given as follows:

58) -2.

59) 1.

60) -2/3.

61) 2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

When two lines are parallel, they have the same slope, which are the cases for itens 58 and 59, as the slope is given by the multiplier of x.

When two lines are perpendicular, we have that the multiplication of the slopes of the line is of -1, hence the slope for item 60 is given as follows:

3m/2 = -1

3m = -2

m = -2/3.

For item 61, the slope is given as follows:

-m/2 = -1

m = 2.

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The values of the angles x and y are ∠x = 110 and ∠y = 70

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

The lines (parallel, transversal and others)

The measure of angle 1 is calculated as

∠1 = 180 - 140 -- angle on a straight line

So, we have

∠1 = 40

Next, we have

∠2 = 180 - 40 - 80 --- corresponding angles

So, we have

∠2 = 60

This means that

∠y = 180 - 60 - 50 -- angle on a straight line

So, we have

∠y = 70

This also means that

∠x = 180 - 60 - 10 -- angle in a triangle

So, we have

∠x = 110

Hence, the values of x and y are ∠x = 110 and ∠y = 70

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The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.

To calculate vertical asymptote,

Putting the denominator equal to zero,

x²+2x+3 = 0

Using Quadratic formulae,

b² - 4ac

where,

b = 2

a = 1

c = 3

putting value,

4-12 = -8<0

therefore, the solution is negative

Hence, no vertical asymptote of the given equation exists,

To calculate the horizontal asymptote,

the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.

The coefficient of x² in the numerator is 1

Hence, the horizontal asymptote is y = 1.

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The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

We have,

We see that there are 10 marbles.

Now,

Number of blue marbles = 2

Number of green marbles = 4

Now,

The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.

After picking a blue marble, there will be 9 marbles left in the bag.

The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.

Now,

P(blue marble and green marble) = P(blue marble) x P(green marble)

= (2/10) x (4/9)

= 8/90

= 4/45.

Therefore,

The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

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The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

(2x - 13) + 123 = 180° {supplementary angles}

2x - 13 + 123 = 180°

2x + 110 = 180

2x = 180 - 110 {collect like terms}

2x = 70

x = 70/2 {divide through by 2}

x = 35

Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

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A function that has a degree of 5 must have the following: d. at least one real 0.

In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using specific mathematical operations.

Generally speaking, the degree of a polynomial function is sometimes referred to as an absolute degree and it is the greatest exponent (leading coefficient) of each of its term.

In conclusion, a function that has a degree of 5 is referred to as a quintic function and it is characterized by an odd degree, can't have more than 4 turning points, and must have at least one real zero.

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Answer:

27

Step-by-step explanation:

We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:

The / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.

Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.

Step 1:  Simplify inside the parentheses:

5 * 4 + (1 + 1) + 5

5 * 4 + 2 + 5

Step 2:  Multiply 5 and 4:

20 + 2 + 5

Step 3:  Add 20 and 2:

22 + 5

Step 4:  Add 22 and 5 to get your answer:

27

Thus, 5 *4 + (1 + 1) + 5 = 27

Answer:

  53%

Step-by-step explanation:

You want to know the depreciation of car value after 5 years if it is 14% per year.

The multiplier of value each year is ...

  1 + growth rate = 1 + (-14%) = 0.86

When the value has been multiplied by that 5 times, it has been multiplied by ...

  0.86^5 ≈ 0.4704

This represents a change in value from the original value of ...

  0.4704 -1 = -0.5296 = -52.96% ≈ -53%

Zara's car has depreciated by 53% after 5 years.

<95141404393>

Solving a simple equation, we can see that x = 35.

The 3 lines with an arrow that go to the left are parallel lines, thus, the relation between the sets of values in each of the sides must be the same ones.

Then we can take the quotients between the respective values, and these quotients must be equal, so we can write:

30/12 = x/14

And now we can solve that equation for x, we will get:

x = 14*(30/12)

x = 35

That is the value of x.

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The solution of the inequality equation is determined as y > 3.

A solution for an inequality in y is a number such that when we substitute that number for y we have a true statement.

For the given inequality equation, which is;

y + 5 > 8

The solution of the inequality equation is calculated as follows;

y + 5 > 8

Subtract 5 from both sides of the equation as shown below;

y + 5 - 5 > 8 - 5

y > 3

The solution of the inequality equation is determined as 3, so we can conclude that any value less than  3 is not true and the proposed solution of 1 is not true or correct for the inequality equation.

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After using ruler and following the steps described below

We get the standard position of 35 degree.

The given angle is = 35 degree

To draw standard position of angle:

We proceed it to draw by ruler

So, in order to get position,

Follow the following steps:

1: Draw a straight line with your ruler.

2: Place your protractor on the line and align the base of the protractor with the line.

3: Find the 35 degree mark on the protractor and make a small mark on the line at that point.

4: Move your protractor to the mark you just made.

5: Align the base of the protractor with the line and make another small mark on the line at the 35 degree mark.

6: Draw a straight line connecting the two points you just marked.

And there you have it! A 35 degree angle drawn on paper.

And after following these steps we get the standard potion angle 35 degree.

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The minor arcs of the circle C are given as follows:

The arcs of a circle can be classified as minor arcs or major arcs, depending on their angle measures, as follows:

The entire circumference of the circle is of 360º, hence we have that segment LN, connecting two points on the circumference of the circle through the center, represents the diameter of the circle, with an arc length of 180º.

Hence the minor arcs are all the arcs that are smaller than LN, given as follows:

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The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

On the basis of the quantity of checks written, we can compare the overall costs of the two accounts.

Let's calculate the total cost for each account based on the given information:

First Account:

Monthly fee: $12

Per-check fee: $0.10

Total cost = Monthly fee + (Per-check fee * Number of checks)

Second Account:

Monthly fee: $9

Per-check fee: $0.25

Total cost = Monthly fee + (Per-check fee * Number of checks)

We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:

$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)

Simplifying the equation

$12 - $9 < ($0.25 - $0.10) * Number of checks

$3 < $0.15 * Number of checks

Dividing both sides by $0.15:

$3 / $0.15 < Number of checks

20 < Number of checks

Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

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a) The rate of slower train is 110 km/hr

b) The speed of faster train is 112 km/hr

Given data ,

When two objects are moving towards each other, their combined rate is equal to the sum of their individual speeds.

So, the rate of the slower train as x km/hr. Since the faster train is traveling 12 km/hr faster, its rate will be ( x + 12 ) km/hr.

The combined rate of the two trains is x + (x + 12) = 2x + 12 km/hr.

We know that the trains travel a total distance of 696 km and meet in 3 hours. Using the formula distance = speed × time, we can set up the following equation:

(2x + 12) × 3 = 696

Simplifying the equation:

6x + 36 = 696

Subtracting 36 from both sides:

6x = 660

Dividing both sides by 6:

x = 110

Hence , the rate of the slower train is 110 km/hr, and the rate of the faster train is 110 + 12 = 122 km/hr.

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Step-by-step explanation:

To calculate the monthly payment for a mortgage, you can use the formula for a fixed-rate mortgage:

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Loan amount (in this case, the home cost minus the down payment)

r = Monthly interest rate (annual rate divided by 12 and converted to decimal)

n = Total number of payments (number of years multiplied by 12)

Given:

Home cost = $600,000

Down payment = 40% of the home cost = 0.4 * $600,000 = $240,000

Loan amount = Home cost - Down payment = $600,000 - $240,000 = $360,000

Annual interest rate = 3.00%

Loan term = 30 years

First, calculate the monthly interest rate:

Monthly interest rate = (Annual interest rate / 100) / 12 = (3.00 / 100) / 12 = 0.0025

Next, calculate the total number of payments:

Total number of payments = Loan term * 12 = 30 * 12 = 360

Now, substitute the values into the formula:

Monthly Payment = ($360,000 * 0.0025 * (1 + 0.0025)^360) / ((1 + 0.0025)^360 - 1)

After performing the calculations, the monthly payment for this mortgage is approximately $1,520.06.

I hope I was helpful

The scatter plot shows a [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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Answer:

220 in²

Step-by-step explanation:

surface area = [area of the 4 vertical faces] + area of the base + area of top.

surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)

= (80 + 100) + 20 +  20

= 220 in²

The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.

5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;

D. 205.8 cm squared

A composite figure is a figure that is composed two or more regular figures.

The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.

The area of the unshaded semicircle = π × 24²/8 = 72·π

The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144

Area of the square = 24 × 24 = 576

Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8

The area of the shaded region ≈ 205.8 cm squared

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The maximum volume of the box is 864 cubic inches.

Let side length of the square cut from each corner is x inches.

After cutting the squares from each corner, the remaining dimensions of the sheet metal will be:

Length: 24 - 2x inches

Width: 24 - 2x inches

Height: x inches

So, the volume of the box

V = (24 - 2x) (24 - 2x)  x

V = x(24 - 2x)²

To find the maximum volume, we can take the derivative of V with respect to x, set it to zero, and solve for x:

dV/dx = (24 - 2x)² - 2x(24 - 2x) = 0

4x² - 96x + 576 = 0

Solving the quadratic equation,

x = 6 and x = 12.

We can substitute x = 6 into the volume equation to find the maximum volume:

V = 6(24 - 2(6))²

V = 6(12)²

V = 6 x 144

V = 864 cubic inches

Therefore, the maximum volume of the box is 864 cubic inches.

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94.2 square feet is the surface area of the cylinder

The given cylinder has a height of 2 ft and radius of 3 ft

We have to find the surface area of cylinder

Surface area =2πrh+2πr²

Substitute the values of radius and height

=2πr(r+h)

=2×3.14×3(3+2)

=18.84(5)

=18.84×5

Surface area=94.2 square feet

Hence, the surface area of the cylinder is 94.2 square feet

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a) The area of the rectangular shaped bathroom floor is A = 30.375 feet²

b) The number of boxes of tiles = 25 boxes

Given data ,

Jordan is putting new tile on the bathroom floor. The width of the floor is 4 2/4 feet and the length is 6 3/4 feet

Now , Area of Rectangle = Length x Width

On simplifying , we get

Width = 4 2/4 feet = (4 x 4 + 2)/4 = 18/4 feet

Length = 6 3/4 feet = (6 x 4 + 3)/4 = 27/4 feet

Area = (18/4) x (27/4) = (18 x 27)/(4 x 4) = 30.375 feet²

Therefore , the area of bathroom floor is A = 30.375 feet²

Now , the number of boxes is given by

Number of boxes of tiles = Total area of bathroom floor / Area covered by each box of tiles

B = 30.375 / 5

B = 6.075

B = 6 tiles

Hence , the area of bathroom floor is A = 30.375 feet²

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Answer:

24

Step-by-step explanation:

For this problem, substitute the value -3 for x and solve. It would look like this:

[tex]4(-3)^2+2(-3)-6[/tex]

Using the order of operations (PEMDAS) we solve the exponent first.

[tex]-3^2=9[/tex]

Then solve the multiplication parts.

[tex]4(9)+2(-3)-6\\4*9=36[/tex]and        [tex]2*(-3)=-6[/tex]

Finally subtract to get the answer.

[tex]36-6-6=24[/tex]