Clare is paid $90 for 5 hours of work. At this rate, how long will it take her to save $360?

The required probability for event A is 1 / 2 and event B is  1 / 2.

Given that,
A marble is selected from a bag containing eight marbles numbered 1 to 8. The number on the marble selected will be recorded as the outcome.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total possible events = 1, 2, 3, 4, 5, 6, 7, 8 = 8
For Event A = 2, 3, 4, 5 = 4
Probability = 4 / 8 = 1 / 2
For event B = 1, 3, 5 ,7 = 4
Probability = 4 / 8 = 1/2

Thus, the required probability for event A is 1 / 2 and event B is  1 / 2.

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The third side of the triangle whose two sides are 11 cm and 19 cm can be between 9 and 29.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

The sides of triangles are 11 cm and 19 cm,

Let the third side of the triangle is x,

Since, a side of a triangle is greater than the difference of two sides and less than the sum of two sides,

implies that,

19-11<x<19+11

8 < x < 30

The possible range of third side is (9,29).  

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Answer:

8cm < x < 30cm

Step-by-step explanation:

To find the range of lengths for the third side of a triangle when two side lengths are known, first, assign a variable for the length of the third side.

Let x be the length of the unknown side.

Use the Triangle Inequality Theorem to write the three inequalities.

x + 11x > 19

x + 19 > 11

11 + 19 > x

Solve each inequality.

x > 8

x > -8

30 > x

Now find the range of values that satisfies all three inequalities.

The range between 8 and 30 satisfies all 3 inequalities. Therefore, this triangle's third side lengths range is 8cm < x < 30cm.

The probability cannot be negative, there must be an error in the given information. So, the correct answer is:
f) None of the above.

We are given the following probabilities: P(A) = 17/50, P(B) = 17/25, and P(A ∪ Bc) = 2/5. We are asked to find P(A ∩ Bc).

Using the formula for the union of two events: P(A ∪ Bc) = P(A) + P(Bc) - P(A ∩ Bc)

Since Bc is the complement of B, we have P(Bc) = 1 - P(B) = 1 - (17/25) = 8/25.

Now we can plug in the given probabilities into the formula:
2/5 = (17/50) + (8/25) - P(A ∩ Bc)

To solve for P(A ∩ Bc), we first find a common denominator for the fractions, which is 50. So, we have:
20/50 = (17/50) + (16/50) - P(A ∩ Bc)

Combine the fractions:
20/50 = 33/50 - P(A ∩ Bc)

Subtract 33/50 from both sides to isolate P(A ∩ Bc):
P(A ∩ Bc) = -13/50

Since the probability cannot be negative, there must be an error in the given information. So, the correct answer is:
f) None of the above.

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Answer:

never because they are continually increasing at the same rate without multiplying and dividing

if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.

A relation is a function if it has only One y-value for each x-value.

Given that f(x) = ax² + bx + c for all x and

if f( -3 ) = 0 and

f( 1) = 0

We need to find the value of b+c

f(-3)=a(-3)² + b(-3) + c

f(-3)=9a-3b+c=0

9a-3b+c=0

We need to find the value of b + c, which is equal to -a.

From equation (2), we have:

a = -b - c

Substituting this value of a in equation (1), we get:

9(-b - c) - 3b + c = 0

-12b - 8c = 0

3b + 2c = 0

b = -(2/3)c

Substituting this value of b in equation (2), we get:

a + (-(2/3)c) + c = 0

a = (1/3)c

Therefore, b + c = -(2/3)c + c = (1/3)c

Hence, if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.

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A rectangle with an area of 12x² - 3x - 15 can have dimensions of (3x - 5) and (4x + 3), or vice versa.

To find the dimensions of a rectangle with a given area, we need to factor the expression 12x² - 3x - 15. By factoring the expression, we can determine the two dimensions of the rectangle.

The given expression can be factored as follows:

12x² - 3x - 15 = (3x - 5)(4x + 3)

The dimensions of the rectangle are (3x - 5) and (4x + 3), or vice versa. This means that the length of the rectangle is 3x - 5, and the width is 4x + 3. Alternatively, the length could be 4x + 3, and the width could be 3x - 5.

For example, if we take the length as 3x - 5 and the width as 4x + 3, the area of the rectangle is obtained by multiplying these two dimensions:

Area = (3x - 5)(4x + 3)

= 12x² + 9x - 20x - 15

= 12x² - 11x - 15

Thus, we have determined that a rectangle with an area of 12x² - 3x - 15 can have dimensions of (3x - 5) and (4x + 3), or vice versa.

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Step-by-step explanation:

So in order to solve, you have to set the equation equal to zero by subtracting 27 from both sides. You'll end up with x^2 + 6x -27 = 0.

Now, we can use the quadratic formula to solve.

I attached it below.

Your a value will be 1, the b value is +6, and the c value is -27.

Plug into the formula and then solve. :)

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

C

Step-by-step explanation:

To convert from point-slope form to slope-intercept form, we can simplify and isolate the y.

We have the equation:

\(\displaystyle y-3=\frac{1}{2}(x-1)\)

Distribute the right-hand side:

\(\displaystyle y-3=\frac{1}{2}x-\frac{1}{2}\)

Add 3 to both sides:

\(\begin{aligned} \displaystyle y&=\frac{1}{2}x-\frac{1}{2}+3\\\\&=\frac{1}{2}x-\frac{1}{2}+\frac{6}{2}\\\\&=\frac{1}{2}x+\frac{5}{2}\end{aligned}\)

Our answer is C.

Answer:

A and E are right triangles

Triangles A and triangle E are the right-angle triangle, but triangles B, C, and D are not right-angle triangles.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

Applying in Pythagoras theorem in the triangle A:

(√5)² = (√2)²+ (√3)²

5 = 5

Triangle A is the right-angle triangle.

For triangle B:

(√5)² = (√4)²+ (√3)²

5 ≠ 7

Triangle B is not the right-angle triangle

For triangle C:

16 + 25 ≠ 36

triangle C is not a right-angle triangle

For  triangle D:

25 + 25 ≠ 49

triangle D is not a right-angle triangle

For triangle E:

100 = 36 + 64

It is a right-angle triangle.

Thus, triangles A and triangle E is the right angle triangle.

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The consumer expenditure for a certain item at a price of $18 is approximately $8.72 million dollars.

The demand function for a certain item is given by:

D(P) = 28e^(-0.25P)

where P is the price per unit, in dollars. The consumer expenditure is the amount of money spent by the consumers to buy a certain quantity of the item at a certain price. It is equal to the product of the quantity demanded and the price per unit: CE = P × Q

where CE is the consumer expenditure, P is the price per unit, and Q is the quantity demanded.

To find the consumer expenditure at a price of $18, we need to first find the quantity demanded at that price by substituting P = 18 into the demand function: D(18) = 28e^(-0.25×18)D(18) ≈ 12.42 million units

Next, we can compute the consumer expenditure at a price of $18 by multiplying the price per unit by the quantity demanded: CE = P × QCE = 18 × 12.42CE ≈ 221.56 million dollars

However, the question asks us to give the answer in million dollars, so we need to divide by 1000 to get the answer in million dollars: CE ≈ 221.56/1000CE ≈ 8.72 million dollars.

Therefore, the consumer expenditure at a price of $18 is approximately $8.72 million dollars.

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Answer:

Step-by-step explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

\(h^2= a^2+b^2.\)

and the perimeter is \(P=h+a+b\).

Since P=24 and a=6  we have these equations:

\(h^2=36+b^2\\24=h+6+b\)

From the last equation we have \(h=18-b\). Replace h in the first equation we get that

\((18-b)^2=36+b^2\)

\(18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8\)

and h=18-8=10

Answer:

80% 0f the bike cost.

Step-by-step explanation:

If the discounted is 20% of the Cost, you will pay 80% of the cost

because (100% of the cost - 20% = 80% of the cost)

The Average speed over the entire 360 km journey is approximately 66.67 kmph.

The average speed over the entire 360 km journey, we can use the formula:

Average Speed = Total Distance / Total Time

In this case, the total distance is 360 km (120 km from A to B and 120 km back from B to A).

Let's calculate the total time for the journey:

Time taken for the first leg (from A to B):

Distance = 120 km

Speed = 50 kmph

Time = Distance / Speed = 120 km / 50 kmph = 2.4 hours

Time taken for the return leg (from B to A):

Distance = 120 km

Speed = 40 kmph

Time = Distance / Speed = 120 km / 40 kmph = 3 hours

Total time for the journey = Time for the first leg + Time for the return leg = 2.4 hours + 3 hours = 5.4 hours

Now we can calculate the average speed:

Average Speed = Total Distance / Total Time = 360 km / 5.4 hours = 66.67 kmph

Therefore, the average speed over the entire 360 km journey is approximately 66.67 kmph.

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Main Answer:The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

Supporting Question and Answer:

How do we find points on a curve where the tangent line is horizontal or vertical?

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

Body of the Solution:To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

  Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

   Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Final Answer:Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

Horizontal tangent line: A horizontal tangent line occurs when the derivative of r with respect to θ is equal to zero.

 Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

Vertical tangent line: A vertical tangent line occurs when the derivative of θ with respect to r is undefined or infinite.

  Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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Answer:

10

Step-by-step explanation:

|-8| = 8

Answer:

10

Step-by-step explanation:

The absolute value is never negative and is shown by the vertical line.

|-8|=8 and |2|=2.

8+2=10

Here we have some given restrictions that affect the number of medals, using these, we want to find the maximum number of bronze medals that can be awarded.

We will find that:

The maximum number of bronze medals that can be awarded is 535

Now let's see how we can get that.

Let's define the variables:

G = number of gold medals.

S = number of silver medals.

B = number of bronze medals.

Now we can see what information we have.

There are 2021 participants.

The number of silver medals is at least twice the number of gold medals.

S ≥ 2*G

The number of bronze medals is at least twice the number of silver medals:

B ≥ 2*S.

The number of all medals is not more than 40% of the number of participants.

The total number of medals is (G + S + B)

40% of the total number of participants is:

(40%/100%)*2021 = 0.4*2021 = 808.4

Then we have:

G + S + B ≤ 808.4

We can rewrite the above inequality as:

G + S + B ≤ 808.

Then we have 3 inequalities:

S ≥ 2*G

B ≥ 2*S

G + S + B ≤ 808

Now we want to maximize the number of gold medals.

This means that the total number of medals should be exactly 808 (the maximum number of total medals) so we have:

G + S + B = 808.

Also, if we want to maximize the number of gold medals, then we need to minimize the number of silver medals and the number of bronze medals, such that we get:

S = 2*G

B = 2*S

Now we have 3 equations:

G + S + B = 808

S = 2*G

B = 2*S

Replacing the third equation in the first one, we get:

G + S + 2*S = 808

G + 3*S = 808

Now we can replace:

S = 2*G

in the above equation to get:

G + 3*(2*G) = 808

G + 6*G = 808

7*G = 808 =

G = 808/7 = 115.43

But we can have 0.43 of a gold medal, so we need to round down to the next whole number:

G = 115

Now, with this restriction, we want to find the maximum number of bronze medals.

This means that we need to minimize the number of silver medals, so we use:

S = 2*G = 2*115 = 230

And the number of bronze medals will be such that:

B + G + S  = 880

B + 115 + 230 = 880

B = 880 - 115 - 230 = 535

The maximum number of bronze medals that can be awarded is 535

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Answer:

\(\{r | r \ge -3 \}\)

Step-by-step explanation:

\( 7 - 9r - (r + 12) \le 25 \)

Remember that to deal with the negative sign to the left of the parentheses, you must think of it as a -1 multiplying the parentheses, and you distribute the -1 by multiply each term inside the parentheses by -1. That changes all the signs inside the parentheses.

\( 7 - 9r - r - 12 \le 25 \)

Combine like terms on the left side.

\( -10r - 5 \le 25 \)

Add 5 to both sides.

\( -10r \le 30 \)

We now divide both sides by -10. Remember that when you divide both sides fo an inequality by a negative number, the inequality sign changes direction.

\( r \ge -3 \)

Answer: \(\{r | r \ge -3 \}\)

Answer:

C. 7

Step-by-step explanation:

4 * Sum (i = 1 to 3) (1/2)^(i - 1) =

= 4 * [(1/2)^0 + (1/2)^1 + (1/2)^2]

= 4 * [1 + 1/2 + 1/4]

= 4 * [7/4]

= 7

Answer:

7

Step-by-step explanation:

because I'm smart like that

Given:

90 + 27

Let's apply the distributive property to factor out the greatest common factor.

First find greatest common factor of 90 and 27

Greatest common Factor of 90 and 27 = 9

Thus, we have:

Applying distribuive property, we could rewrite as: 9(10 + 3)

ANSWER:

9(10 + 3)

The 40 randomly selected teachers: sample.

The list of all teachers in the school district: frame.

The 245 teachers in the school district: population.

A sample is a subset of a population that is selected for research purposes. In this case, the school board has randomly selected 40 teachers out of the 245 teachers in the district as a sample to survey their opinions on the new professional development plan.

A population is the entire group of individuals or objects that researchers are interested in studying. In this case, the population is all 245 teachers in the school district.

A frame is the list or method used to define the population. In this case, the frame is the list of all 245 teachers in the school district that was used as the basis for selecting the random sample of 40 teachers.

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Given statement is True.

A system of equations can be represented in different forms, such as point form (showing the x and y values that make the equations true) or equation form (showing the equations in standard form, with variables on one side and constants on the other). A solve by substitution calculator can be used to find the solution to a system of two or three equations in both point form and equation form of the answer.

The process of solving a system of equations by substitution involves isolating a variable in one equation and then substituting it into the other equation(s) to find the values of the other variable(s). The calculator can display the solution in point form by showing the values of x and y (or x, y, and z for a system of three equations) that make the equations true. It can also display the solution in equation form by showing the equations with the variable(s) replaced by the values found in the solution.

In conclusion, solve by substitution calculator can find the solution to a system of two or three equations in both point form and equation form of the answer, it can be a helpful tool for solving systems of equations.

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Answer:

x = -2

Step-by-step explanation:

y + 2x = -1

y = 1/2 x + 4​

y + 2x= -1

(1/2x + 4) + 2x = -1

1/2x + 2x + 4 = -1

5/2x + 4 = -1

5/2x = -5

x = -2

Answer:

x = -2

Step-by-step explanation:

First, we need to represent y in terms of x by using the first equation. If we do this we will get the following...

y + 2x = -1

y = -1 - 2x

Now we substitute the "y" in the second equation with an equal value in terms of "x" that we got in the last equation, and we will get the follolowing equation...

\(y = \frac{1}{2} x + 4\\- 1 - 2x = \frac{1}{2} x + 4\\-2 -4x = x + 8\\-4x - x = 8 + 2\\- 5x = 10\\5x = -10\\x = 10 /5\\x = 2\)

Answer:

26741 and 12

Step-by-step explanation:

(1)

The area ( A) of a rectangle is calculated as

A = length × width , then

A = 221 × 121  = 26741

(2)

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) × base × height , then

A= \(\frac{1}{2}\) × 8 × 3 = 4 × 3 = 12

ANSWER:

STEP-BY-STEP EXPLANATION:

We have to rule for reflection about the line y = x is:

Therefore:

The typical height of a door, which is 96 inches, is equivalent to 243.84 centimeters when using the conversion factor of 1 inch = 2.54 cm.

To find the height of a door in centimeters, we need to convert the given height in inches to centimeters using the conversion factor of 1 inch = 2.54 cm

Height of the door = 96 inches

To convert inches to centimeters, we multiply the number of inches by the conversion factor of 2.54 cm/inch.

Height in centimeters = 96 inches * 2.54 cm/inch

Calculating the value:

Height in centimeters = 243.84 cm

Therefore, the height of the door in centimeters is 243.84 cm.

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After 20 years, the value of the fox population will be 640.

The population of the fox after 20 years is calculated as follows;

The given function is;

y = 40 x 4ˣ

Where;

how many 10 years period make up 20 years?

x = 2

The value of the fox population is calculated as follows

y = 40 x 4²

y = 40 x 16

y = 640

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