Mario has 1 gallon of milk. He pours 4 cups of milk for him and his 3 siblings to have with their breakfast. How much milk is left ? Simplify your answer .

The equation which represents exponential growth is y = (1.2)* and equation which represents exponential decay is y = (.71)*,  y = 0(6.3)* represents a constant function.

Consider the function:

[tex]y = a(1\pm r)^m[/tex]

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %

If there is negative sign, then there is exponential decay happening by r fraction or 100r %

We are given that;

c. y = (1.2)*

d. y = 0(6.3)*

e. y = (.71)*

a.) The equation and graph that show exponential growth is y = (1.2)x. This is because the base of the exponent (1.2) is greater than 1, so as x increases, the value of y increases at an increasing rate. The graph of y = (1.2)x is an upward-curving curve that gets steeper as x increases.

b.) The equation and graph that show exponential decay is y = (0.71)x. This is because the base of the exponent (0.71) is between 0 and 1, so as x increases, the value of y decreases at a decreasing rate. The graph of y = (0.71)x is a downward-curving curve that flattens out as x increases.

Therefore, exponential growth shows y = (1.2)* whereas y = (.71)* show exponential decay.

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the answer is x+10 i think bye

Answer:

24

Step-by-step explanation:

This is a division problem.

0.72/0.03 = 7.2/0.3 = 72/3 = 24

The volume of the composite solid is 5104 cubic ft.

A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.

The area of a triangular prism is given as:

V = 1/2(bhl)

Here, h = 22 - 12 = 10 ft.

Substituting the values we have:

V = 1/2(13)(10)(32)

V = 2080 cubic ft.

The volume of the rectangular prism is given as:

V = lwh

V = (28)(9)(12)

V = 3024 cubic ft.

The volume of the composite solid is:

V = V1 + V2

V = 2080 + 3024

V = 5104 cubic ft.

Hence, the volume of the composite solid is 5104 cubic ft.

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The matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].

Assuming that A is a matrix with three rows, we can find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= by following these steps:

1. Start with the identity matrix, I, which is a matrix with ones along the main diagonal and zeros everywhere else:
I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

2. Apply the first row operation, 3R3​+R1​⇒R1​, to the identity matrix by adding three times the third row to the first row:
I = [[1+3(0), 0+3(0), 0+3(1)], [0, 1, 0], [0, 0, 1]]
I = [[1, 0, 3], [0, 1, 0], [0, 0, 1]]

3. Apply the second row operation, −7R2​⇒R2​, to the identity matrix by multiplying the second row by -7:
I = [[1, 0, 3], [0*(-7), 1*(-7), 0*(-7)], [0, 0, 1]]
I = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]

4. The resulting matrix, I, is the matrix B that we are looking for:
B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]

Therefore, the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].

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The two linear functions that have a minimum value but no maximum value are:

f(x) = 10 - 3x over the domain x ≤ 9

f(x) = 5x - 1 over the domain x ≥ -7

From the question, we are to determine the linear function that have minimum value but no maximum value

The decreasing function f(x) = 10 - 3x over the domain x ≤ 9 has a minimum value but no maximum value.

Domain: x ≤ 9

This function is decreasing since the slope is negative.

The minimum value occurs at x = 9, where f(9) = 10 - 3(9) = -17.

Since the slope is negative, the function continues to decrease without bound as x approaches negative infinity.

The decreasing function f(x) = 5x - 1 over the domain x ≥ -7 has a minimum value but no maximum value.

Domain: x ≥ -7

This function is increasing since the slope is positive.

The minimum value occurs at x = -7, where f(-7) = 5(-7) - 1 = -36.

Since the slope is positive, the function continues to increase without bound as x approaches positive infinity.

Hence, the functions are:

f(x) = 10 - 3x over the domain x ≤ 9

f(x) = 5x - 1 over the domain x ≥ -7

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The transformation between the points is (x, y) = (x, -y + 10)

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

G(9, 12), H(−2, −15), J(3, 8) and

G'(9, -2), H'(-2, 25), J'(3, 2)

We can see that the x coordinates of the image and the preimage are equal

However, the relationship between the y-coordinates is

y' = -y + 10

This means that

(x, y) = (x, -y + 10)

The above rule is a translation transformation

Translation transformation is a transformation that moves each point in a figure or object by a fixed distance in a specified direction.

Hence, the transformation is (x, y) = (x, -y + 10)

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Complete question

26. G(9, 12), H(−2, −15), J(3, 8) and G'(9, -2), H'(-2, 25), J'(3, 2)

Write out the transformation rule from GHJ to G'H'J'

The initial population is 4001 and the maximum population is 4000

The given population growth model is [tex]12000/3+e^{-0.02(t)}.[/tex]

To find the initial population, we need to plug in t=0 into the equation.

[tex]12000/3+e^{-0.02(0)}[/tex]

= [tex]12000/3+1[/tex]

= [tex]4000+1[/tex]

= [tex]4001[/tex]

So the initial population is 4001.

To find the maximum population, we need to find the limit of the equation as t approaches infinity.


= [tex]12000/3+0[/tex]

= [tex]4000[/tex]

So the maximum population is 4000.

In conclusion, the initial population is 4001 and the maximum population is 4000.

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The value of x and y are

x=100° y=100°

In an equilateral triangle,

Each angle = 60°

∴ a + a + 100° = 180°

⇒ 2a + 100° = 180°

⇒ 2a = 180° – 100° = 80°

∴ a = 80°/2 = 40° ∴ x = 60° + 40° = 100°

And y = 60° + 40° = 100°

An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle. Equilateral triangles have the same area, perimeter, and height formula as other kinds of triangles.

An equilateral triangle has a predictable shape. By combining the words "Equi" (which means equal) and "Lateral," which refers to sides, the word "Equilateral" is created. Due to the equality of its sides, an equilateral triangle is also known as a regular polygon or regular triangle.

from the question:

In an equilateral triangle,

Each angle = 60°

Let each base angle = a

∴ a + a + 100° = 180°

⇒ 2a + 100° = 180°

⇒ 2a = 180° – 100° = 80°

∴ a = 80°/2 = 40° ∴ x = 60° + 40° = 100°

And y = 60° + 40° = 100°

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complete question

Apply the properties of equilateral triangles and find the values of x and y in the given figure

In this case, the point (3/2, 0) is the optimal solution, which matches the solution we found using the simplex method.

To solve the problem using the simplex method, we first need to convert the inequalities to equations by adding slack variables. Then we can set up the initial tableau and use the simplex method to find the optimal solution. Finally, we can verify the solution using the graphical method.

Convert inequalities to equations by adding slack variables
-X1 + X2 >= -1 becomes -X1 + X2 + S1 = -1
4X1 + 3X2 <= 12 becomes 4X1 + 3X2 + S2 = 12
2X1 <= 3 becomes 2X1 + S3 = 3

Set up the initial tableau
| -1 | 2 | 1 | 0 | 0 | 0 |
| -1 | 1 | 1 | 0 | 0 | -1 |
| 4 | 3 | 0 | 1 | 0 | 12 |
| 2 | 0 | 0 | 0 | 1 | 3 |

Use the simplex method to find the optimal solution
We first need to choose the pivot column, which is the one with the most negative coefficient in the objective row. In this case, it is the first column. Then we need to choose the pivot row, which is the one with the smallest positive ratio of the right-hand side to the pivot column coefficient. In this case, it is the third row. We can then use the pivot element to eliminate the other coefficients in the pivot column and repeat the process until we have no negative coefficients in the objective row.

After performing the simplex method, we get the following final tableau:
| 0 | 5/4 | 1 | 1/4 | 0 | 3 |
| 0 | 7/4 | 1 | 1/4 | 0 | 3 |
| 0 | 3/4 | 0 | 1/4 | 0 | 3 |
| 1 | 0 | 0 | 0 | 1/2 | 3/2 |

The optimal solution is X1 = 3/2, X2 = 0, and Z = -3/2.

Verify the solution using the graphical method
We can graph the constraints and find the feasible region. Then we can graph the objective function and find the point where it intersects the feasible region that gives the maximum or minimum value. In this case, the point (3/2, 0) is the optimal solution, which matches the solution we found using the simplex method.

Extra Credit:
To solve the problem using the simplex method, we first need to convert the inequalities to equations by adding slack variables. Then we can set up the initial tableau and use the simplex method to find the optimal solution. Finally, we can verify the solution using the graphical method.

Convert inequalities to equations by adding slack variables
-X1 + X2 >= -1 becomes -X1 + X2 + S1 = -1
4X1 + 3X2 <= 12 becomes 4X1 + 3X2 + S2 = 12
2X1 <= 3 becomes 2X1 + S3 = 3

Set up the initial tableau
| -1 | 2 | 1 | 0 | 0 | 0 |
| -1 | 1 | 1 | 0 | 0 | -1 |
| 4 | 3 | 0 | 1 | 0 | 12 |
| 2 | 0 | 0 | 0 | 1 | 3 |

Use the simplex method to find the optimal solution
We first need to choose the pivot column, which is the one with the most negative coefficient in the objective row. In this case, it is the first column. Then we need to choose the pivot row, which is the one with the smallest positive ratio of the right-hand side to the pivot column coefficient. In this case, it is the third row. We can then use the pivot element to eliminate the other coefficients in the pivot column and repeat the process until we have no negative coefficients in the objective row.

After performing the simplex method, we get the following final tableau:
| 0 | 5/4 | 1 | 1/4 | 0 | 3 |
| 0 | 7/4 | 1 | 1/4 | 0 | 3 |
| 0 | 3/4 | 0 | 1/4 | 0 | 3 |
| 1 | 0 | 0 | 0 | 1/2 | 3/2 |

The optimal solution is X1 = 3/2, X2 = 0, and Z = -3/2.

Verify the solution using the graphical method
We can graph the constraints and find the feasible region. Then we can graph the objective function and find the point where it intersects the feasible region that gives the maximum or minimum value. In this case, the point (3/2, 0) is the optimal solution, which matches the solution we found using the simplex method.

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Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).

To use synthetic division to find the result of the given polynomial division, we need to follow these steps:

1. Write the coefficients of the dividend polynomial in a row: 2 10 8 1 24
2. Write the constant term of the divisor with the opposite sign in front of the row: -2 | 2 10 8 1 24
3. Bring down the first coefficient: -2 | 2 10 8 1 24
         -----------
            2
4. Multiply the first coefficient by the divisor's constant term and write the result under the second coefficient: -2 | 2 10 8 1 24
         -----------
            2 -4
5. Add the second coefficient and the result from step 4: -2 | 2 10 8 1 24
         -----------
            2  6
6. Repeat steps 4 and 5 for the remaining coefficients: -2 | 2 10 8 1 24
         -----------
            2  6  4 -6
7. The last number in the row is the remainder. If it is 0, the division is exact. If not, we need to express the result in the form: quotient + (remainder)/(divisor)

In this case, the quotient is 2x^(3)+6x^(2)+4x-6 and the remainder is 36. So the result of the division is:
2x^(3)+6x^(2)+4x-6+(36)/(x+2)

Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).

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Jimmy will leave a $33.32 tip for the great service.

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

To calculate the tip, we need to first find 20% of the total cost of the meal (before sales tax):

20% of 166.60 = 0.20 x 166.60 = 33.32

Therefore, Jimmy will leave a $33.32 tip for the great service.

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Answer:

The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.

Plugging x=0 into the given function, we get:

f(0) = 320(0.90)^0 = 320(1) = 320

Therefore, the initial price of the store item was $320.

The probability of the spinner not landing on A is 0.47.

To find the probability that the spinner does not land on A, we need to add up the frequencies of the outcomes where A does not appear, which are (B,B), (B,C), (C,B), and (C,C):

Frequency of not landing on A = Frequency(B,B) + Frequency(B,C) +  Frequency(C,B) + Frequency(C,C)

Frequency of not landing on A = 15 + 17 + 13 + 14 = 59

The total number of outcomes is 125, so the probability of not landing on A is:

P(not A) = Frequency of not landing on A / Total number of outcomes

P(not A) = 59 / 125 = 0.47

Therefore, the probability of the spinner not landing on A is 0.47.

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Answer:

(2,-3)

Step-by-step explanation:

Answer:

  (a)  8 : 3

  (b)  1 7/8 cups

Step-by-step explanation:

Given a recipe that calls for 2 cups of flour and 3/4 cup of water, you want to know the ratio in simplest terms, and the amount of water for 5 cups of flour.

The ratio can be written and simplified as a fraction. Fractions are divided in the usual way.

  2/(3/4) = 2 ÷ 3/4 = 2 × 4/3 = 8/3 = 8 : 3

If we multiply each term in this ratio by 5/8, we can find the recipe that uses 5 cups of flour:

  (5/8)·8 : (5/8)·3 = 5 : 15/8 = 5 : 1 7/8

Naomi uses 1 7/8 cups of water with 5 cups of flour.

Answer:

Step-by-step explanation:

[tex](a)[/tex]

[tex]2:\frac{3}{4}[/tex]

Multiply both sides by 4 to remove fraction:

[tex]2\times4:\frac{3}{4} \times 4[/tex]

[tex]8:3[/tex]     (this is simplest form because no number goes into both 8 and 3)

[tex](b)[/tex]

5 cups of flower:

[tex]8 \times \frac{5}{8} : 3 \times \frac{5}{8}[/tex]   (I chose [tex]\frac{5}{8}[/tex] to turn the 8 into 5)

[tex]5:\frac{15}{8}[/tex]

5 cups flour needs [tex]\frac{15}{8}[/tex] ([tex]=1\frac{7}{8}[/tex]) cups water

The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.

To find the y-intercept and slope of the linear equation x  +y=-6 1/2, we

need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's isolate y by subtracting x from both sides of the equation:

x + y = -6 1/2

y = -x - 6 1/2

Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.

Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.

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It can be inferred that milk chocolate does have a lower melting point than dark chocolate and that the rate at which chocolate melts is influenced by a number of variables, including composition, temperature, as well as humidity.

According to the facts provided, it is anticipated that within 64 seconds, half of the milk chocolate brands will melt. According to their composition as well as melting point, different milk chocolate brands may melt sooner or later than 64 seconds.

However, it is believed that none of the dark chocolate brands are expected to melt before 64 seconds have passed and that their melting time actually begins after 200 seconds.

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The x intercept and y intercept of the equation is 8 and 200 respectively.

x intercept is the point on the line where it touches the X axis.

y intercept is the point on the line where it touches the Y axis.

Given equation is,

y = 200 - 25x

where y is the total amount in Amanda's school lunch account after purchasing lunches for x weeks.

x intercept is the point on X axis. Any point on x axis has y coordinate 0.

So x intercept is the x coordinate when y coordinate is 0.

0 = 200 - 25x

25x = 200

x = 8

This means that the amount in the account will become 0, after purchasing lunch for 8 weeks.

y intercept is the y coordinate when x coordinate = 0.

y = 200 - (25 × 0)

y = 200

This indicates the amount in the account at the start before purchasing any lunch.

Hence the x intercept is 8 and y intercept is 200.

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Your question is incomplete. The complete question is as follows.

Amanda has $200 in her lunch account. She spends 25$ each week on lunch. The equation y=200-25x represents the total amount in Amanda's school lunch account, y for x weeks of purchasing lunches.

Find the x and y intercepts and interpret their meaning in the context of the situation.

Babe and Ruth are 675 miles apart and headed straight toward each

other. If Babe is traveling at 40 mph and Ruth is traveling at 35

mph, it will take 9 hours before they meet.

To determine the time it will take for Babe and Ruth to meet, we need to use the formula:

time = distance / rate

Since they are traveling towards each other, we can add their speeds to get the combined speed at which they are approaching each other.

combined speed = Babe's speed + Ruth's speed

combined speed = 40 mph + 35 mph

combined speed = 75 mph

Now we can plug in the values we have into the formula:

time = distance / combined speed

time = 675 miles / 75 mph

time = 9 hours

Therefore, it will take 9 hours before Babe and Ruth meet.

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Mr stove's final balance after 10 years if he invested 1500 on a bank account that would give him 3. 7% compounded monthly is $2,170.37

A = P(1 + r/n)^nt

Where

P = $1500

r = 3.7% = 0.037

n = monthly = 12

t = 10 years

So,

A = P(1 + r/n)^nt

A = 1,500.00(1 + 0.037/12)^(12×10)

A = 1,500.00(1 + 0.0030833333333333)¹²⁰

A = $2,170.37

Ultimately, Mr stove will have $2,170.37 as his balance after 10 years.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3 }{ 4 }[/tex]

If the values of A and B make the equation 35x – 29/x²-3x+2 = A/x-1 +b/x-2 true for all values of x for which it is defined, A+B is 35.

The given equation is 35x - 29/(x² - 3x + 2) = A/(x - 1) + B/(x - 2).

We can simplify the denominator of the second term on the left hand side by factoring it:

35x - 29/[(x - 1)(x - 2)] = A/(x - 1) + B/(x - 2)

Now, we can multiply both sides of the equation by (x - 1)(x - 2) to get rid of the fractions:

35x(x - 1)(x - 2) - 29 = A(x - 2) + B(x - 1)

Expanding the left hand side gives us:

35x³ - 70x² + 35x - 29 = A(x - 2) + B(x - 1)

Now, we can compare the coefficients of x on both sides of the equation to find the values of A and B. The coefficient of x on the left hand side is 35, and on the right hand side it is A + B. Therefore, A + B = 35.


Therefore, the values of A and B make the equation 35x – 29/x^2-3x+2 = A/x-1 +b/x-2 true for all values of x for which it is defined is 35.

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After 21 minutes the location of BO in the wheel is EO

The location of BO after 21 minutes is solved using the data:

It takes 4 minutes for the wheel to make one complete rotation

hence in 21 minutes the rotation covered is

= 21 / 4

= 5.25

This is 5 complete rotations and 0.25 (a quarter rotation).

0.25 rotation is

=0.25 * 360

= 90

Each gap in the wheel is

360 / 12 = 30 degrees

hence three steps from B which is EO

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Answer:

DE = 3

Step-by-step explanation:

A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of [tex]\frac{1}{2}[/tex] means that the new shape is half the size of the original.

To solve for a missing length, we can use this expression:

Inserting our numbers into the expression:

Subtract 64 from each side:

Therefore, the missing side length is 6.

Looking at the side CB, it is 10 units long. If the new shape is 5 units long, that means that the scale factor from shape 1 to 2 is [tex]\frac{1}{2}[/tex], meaning it is half its size. If the new shape is half its size, we can use this expression to solve for the missing length:

Therefore, the measure of DE is 3.

Answer:

AAS

Step-by-step explanation:

Answered this question before on Acellus.

The value of k that makes the remainder of the polynomial equal to -6 when divided by x + 1 is k = 5.

To find the value of k that makes the remainder of the polynomial P(x) = kx3 - 4x2 + x + 4 equal to -6 when divided by x + 1, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial P(x) is divided by x - a, the remainder is P(a).

In this case, we are dividing by x + 1, so we can rewrite this as x - (-1). Therefore, a = -1 and we can plug this value into the polynomial to find the remainder:

P(-1) = k(-1)3 - 4(-1)2 + (-1) + 4

Simplifying this equation gives us:

P(-1) = -k - 4 - 1 + 4

P(-1) = -k - 1

Since we want the remainder to be -6, we can set P(-1) equal to -6 and solve for k:

-k - 1 = -6

-k = -5

k = 5

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The probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826. The score the employer will use to decide job offers is 123.3 to decide job offers for potential "high flyers."

The IQ test is designed to have a mean of 100 and a standard deviation of 10. This means that the test follows a normal distribution with a mean of 100 and a standard deviation of 10.

(a) The probability that a randomly selected individual from the population will score between 90 and 110 on this test can be found using the standard normal distribution table. We need to find the z-scores for 90 and 110 and then use the table to find the corresponding probabilities.

The z-score for 90 is (90 - 100) / 10 = -1
The z-score for 110 is (110 - 100) / 10 = 1

Using the standard normal distribution table, we find that the probability for a z-score of -1 is 0.1587 and the probability for a z-score of 1 is 0.8413.

The probability that a randomly selected individual will score between 90 and 110 is the difference between these two probabilities:

0.8413 - 0.1587 = 0.6826

So the probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826.

(b) The employer wants to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, we need to find the z-score that corresponds to the top 1% of the population.

Using the standard normal distribution table, we find that the z-score that corresponds to the top 1% of the population is 2.33.

Now we can use the z-score formula to find the corresponding IQ score:

z = (x - mean) / standard deviation

2.33 = (x - 100) / 10

Solving for x, we get:

x = (2.33 * 10) + 100 = 123.3

So the employer will use a score of 123.3 to decide job offers for potential "high flyers."

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Therefore, after 10 payments, Jeff owes $1160.

Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.

A mathematical equation, such as 6 x 4 = 12 x 2, can be used to compare two amounts or values. a significant noun. An equation is employed when it's required to integrate two or more elements in order to understand or fully explain a situation.

To determine whose furniture costs more, we need to compare the amounts owed by Jeff and Ella for the same number of payments.

Jeff's equation is y = -108x + 2240, which gives the amount owed after x payments.

Ella's graph does not have an equation provided, but we can see that after 10 payments, she owes approximately $2200.

To compare the amounts owed after 10 payments, we can substitute x = 10 into Jeff's equation:

y = -108(10) + 2240

y = -1080 + 2240

y = 1160

Therefore, after 10 payments, Jeff owes $1160.

Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.

Answer: Ella's furniture costs more than Jeff's.

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Height of a trapezoid with Pythagorean theorem is = √{Hypotenuse ^2 - Base ^2}

Trapezoid has two parallel sides and two non parallel sides. The length of the parallel sides are unequal but the length of the non parallel sides are equal.

Thus the trapezoid can be divided into three parts where one is rectangle ( which has length equal to the shortest length of the parallel sides) and two triangles which are equal ( having equal base, height and hypotenuse).

The Pythagoras theorem on the triangular part of the trapezoid can be stated as ,

Hypotenuse ^2 = Base ^2 + Height ^2

⇒ Height ^2 = Hypotenuse ^2 - Base ^2

⇒ Height = √{ Hypotenuse ^2 - Base ^2}

where, Height of the triangle is equal to that of the trapezoid it belongs to;

Hypotenuse of the triangle is the non parallel but equal side of the trapezoid;

Base of the triangle is = {(length of the longest side of parallel sides of trapezoid) -   (length of the shortest side of parallel sides of trapezoid) }/2

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