Hi please help I’m so confused .this is worth 13points

Answer:

Grace jumps for 9 minutes.

Zoe jumps for 12 minutes.

Step-by-step explanation:

Let the time for which Grace jumps the rope = \(x\) minutes

Let the time for which Zoe jumps the rope = \(y\) minutes

As per question statement:

\(x+y=21 ..... (1)\)

Number of times Grace jumps in one minute = 66

Number of times Zoe jumps in one minute = 56

Number of times Grace jumps in \(x\) minutes = 66

Number of times Zoe jumps in \(y\) minutes = 56

As per question statement:

\(66x+56y=1266 ...... (2)\)

Multiplying equation (1) with 66 and subtracting equation (2) from it:

\(10y = 1386 - 1266\\\Rightarrow 10y=120\\\Rightarrow y =\bold{12\ min}\)

By equation (1):

\(x=21-12=\bold{9\ min}\)

Therefore, the answer is:

Grace jumps for 9 minutes.

Zoe jumps for 12 minutes.

The right triangles among the given lengths of sides are options A, B, and C.

To determine the right triangles among the given lengths of sides, we need to apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's analyze each option:

Option A: √2, 5, A

We can check if this forms a right triangle by using the Pythagorean theorem:

√2^2 + 5^2 = A^2

2 + 25 = A^2

27 = A^2

Since there is no perfect square that equals 27, option A does not represent a right triangle.

Option B: √5, √4, 6

Again, we use the Pythagorean theorem to check if it forms a right triangle:

(√5)^2 + (√4)^2 = 6^2

5 + 4 = 36

9 ≠ 36

Option B does not represent a right triangle either.

Option C: 6, 8, 5

Applying the Pythagorean theorem:

6^2 + 8^2 = 5^2

36 + 64 = 25

100 = 25

Since 100 is equal to 25, option C represents a right triangle.

Therefore, the right triangles among the given lengths of sides are options A, B, and C.

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Margo is raising money for her club by selling boxes of nuts. She discovers that cashews are sold in three out of every seven cartons of nuts. The ratio, y=3/7, is the proportion of cashew boxes sold to all boxes sold.

Describe ratio:

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other. A ratio between two quantities, let's say 'a' and 'b,' is typically expressed as a: b.

Three out of every seven boxes of nuts, according to Margo, are cashews. These steps can be used to determine the ratio of two quantities: Before we can calculate the ratio, we must first figure out the values for both instances. There are three cashews and seven boxes present in this scenario. As a fraction, write it as a/b. Therefore, we express it as y= 3/7. As a result, the ratio of the number of cashew boxes to the total number of boxes sold is given as y=3/7.

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The method for including the garage square footage in the total depends on national standards, with some including it in the total and others excluding it.

When including the garage square footage in the total square footage of a home, there are different ways to do it depending on the national standards used.

Generally speaking, there are two main methods:

Including the garage in the total square footage, or excluding the garage from the total square footage.

If the garage is included in the total square footage, then Bob would add the square footage of the garage (600 square feet) to the square footage of the living spaces in the home (e.g., bedrooms, bathrooms, kitchen, living room, etc.).

This would give him the total square footage of the home, including the garage.

This method is commonly used in some areas of the United States.

On the other hand, if the garage is excluded from the total square footage, then Bob would only count the square footage of the living spaces in the home.

This method is commonly used in other areas of the United States, as well as in other countries.

It is important to note that the method used to calculate the total square footage can affect the perceived value of the home, as well as the taxes and insurance premiums associated with it.

Therefore, it is important for Bob to consult with a local real estate professional or appraiser to determine the most appropriate method for his area.

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Answer:

(5, 1)

Step-by-step explanation:

Substitute:

\(3x - 7*1 = 8\\3x - 7 = 8\\3x = 15\\x = 5\)

so the solution is (5, 1)

The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).

In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.

A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.

When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.

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Answer:

5

Step-by-step explanation:

BECAUSE 5*4 = 20

and there you go

Answer:y=1/380

Step-by-step explanation:

if you are trying to do y divided by 12 it would be 4560x12

The coordinates of the image point C after the given transformations are (-5, -3).

The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0).

To apply the given transformations to point A, we need to follow these steps:

Translate the point along vector (-8, -3) to get a new point B.

Reflect the point B across the line y=x to get the final image point C.

Let's first translate point A to get point B. To do this, we add the components of the translation vector to the coordinates of point A:

B = A + (-8, -3)

B = (5, -2) + (-8, -3)

B = (-3, -5)

So, point B is located at (-3, -5).

Next, we reflect point B across the line y=x to get the final image point C. To do this, we switch the x and y coordinates of point B:

C = (y, x)

C = (-5, -3)

Therefore, the coordinates of the image point C after the given transformations are (-5, -3).

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A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.

A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.

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Complete question:

Describe Bivariate Probability Distribution.

Decision B, keeping the park open when the lead levels are in excess of the allowed limit, would constitute making a Type I error in this situation.

A Type I error occurs when the null hypothesis is true, but it is rejected based on the sample data. In this case, the null hypothesis would be that the lead levels in the park are within the allowed limit.

B. Keeping the park open when the lead levels are in excess of the allowed limit would constitute a Type I error. This decision would mean that the department fails to detect the high lead levels and mistakenly keeps the park open, even though it should have been closed due to the elevated lead levels. This error can have potential consequences for public health and safety.

On the other hand, decision A (closing the park when the lead levels are within the allowed limit) would be a correct decision since it aligns with the null hypothesis and does not result in a Type I error. Decision C (closing the park when the lead levels are in excess of the allowed limit) is the correct action to take when the lead levels are actually high, so it does not constitute a Type I error.

Decision D (keeping the park open when the lead levels are within the allowed limit) is also a correct decision as it aligns with the null hypothesis and does not lead to a Type I error.

Decision E (closing the park because of increased noise level in the neighborhood) is unrelated to the lead levels and does not pertain to the hypothesis being tested, so it is not relevant to Type I error in this situation.

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To find the cubic function f(x) given the conditions f(5) = 100, f(-5) = f(0) = f(6) = 0, we need to solve the system of linear equations formed by substituting the values into the general cubic function f(x) = ax^3 + bx^2 + cx + d. Once the values of a, b, and c are determined, the formula for f(x) can be expressed as f(x) = ax^3 + bx^2 + cx.

To find a formula for a cubic function f(x) given the conditions f(5) = 100, f(-5) = f(0) = f(6) = 0, we can start by assuming that the cubic function takes the form f(x) = ax^3 + bx^2 + cx + d.

Using the given conditions, we can create a system of equations to solve for the coefficients a, b, c, and d:

1. f(5) = 100: 100 = a(5)^3 + b(5)^2 + c(5) + d

2. f(-5) = 0: 0 = a(-5)^3 + b(-5)^2 + c(-5) + d

3. f(0) = 0: 0 = a(0)^3 + b(0)^2 + c(0) + d

4. f(6) = 0: 0 = a(6)^3 + b(6)^2 + c(6) + d

Simplifying these equations, we get:

1. 100 = 125a + 25b + 5c + d

2. 0 = -125a + 25b - 5c + d

3. 0 = d

4. 0 = 216a + 36b + 6c + d

From equation 3, we find that d = 0. Substituting this value into equations 1, 2, and 4, we have:

1. 100 = 125a + 25b + 5c

2. 0 = -125a + 25b - 5c

4. 0 = 216a + 36b + 6c

We can solve this system of linear equations to find the values of a, b, and c. Once we have those values, we can express the formula for f(x) as f(x) = ax^3 + bx^2 + cx + d, where d is already determined to be 0.

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The first-order Taylor formula for f(x, y) at (0, 0) is:

f(x, y) ≈ f(0, 0) + ∂f/∂x(0, 0)x + ∂f/∂y(0, 0)y

The second-order Taylor formula for f(x, y) at (0, 0) is:

f(x, y) ≈ f(0, 0) + ∂f/∂x(0, 0)x + ∂f/∂y(0, 0)y + (1/2)∂²f/∂x²(0, 0)x² + ∂²f/∂x∂y(0, 0)xy + (1/2)∂²f/∂y²(0, 0)y²

The first-order Taylor formula is an approximation of a function using its first derivatives.

In this case, the function f(x, y) is approximated at the point (0, 0) using the first partial derivatives ∂f/∂x and ∂f/∂y evaluated at (0, 0).

The formula consists of the function value at (0, 0) plus the partial derivatives multiplied by the corresponding variables x and y.

The second-order Taylor formula extends the approximation to include second partial derivatives.

In addition to the terms in the first-order formula, it includes the second partial derivatives ∂²f/∂x², ∂²f/∂x∂y, and ∂²f/∂y².

These terms account for the curvature of the function and provide a more accurate approximation near the point (0, 0).

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a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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When an aircraft with speed v m/s make a turn with angle of turn θ, its radius of turn can be approximated by r ≈  v² / (g sin θ).

Correct parameters from the given problem:

The resulted radius of turn is given by:

r = (v² / g) tan (π/2 - θ)

Where:

v = aircraft's speed

θ = angle of turn

g = acceleration due to gravity, or 9.8 m/s²

Use the trigonometric property:

tan (π/2 - θ) = cot θ = 1 / tan θ

Hence,

r = v² / (g tan θ)

For relatively small θ, tan θ can be approximated as sin θ.

Therefore:

r = v² / (g tan θ) ≈  v² / (g sin θ)

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Answer:

$ 12 × 40/hr = $ 480

$ 588- $ 480 = $ 108 left over

12 × 1.5 = $ 18 OT rate

108 ÷ 18 = 6 hrs of OT

Answer:

5

Step-by-step explanation:

In this scenario, the independent variable influences the dependent variable in either a positive or negative way.

In statistical analysis, the independent variable is the variable that is manipulated or controlled by the researcher, and the dependent variable is the variable that is measured or observed and is influenced by changes in the independent variable.

The direction of influence, whether positive or negative, depends on the specific nature of the variables and the relationship between them. When the independent variable has a positive influence on the dependent variable, it means that as the value of the independent variable increases, the value of the dependent variable also increases. Conversely, when the independent variable has a negative influence on the dependent variable, an increase in the independent variable leads to a decrease in the dependent variable.

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Answer: 3/40

Step-by-step explanation:

Number of A's = 4

Number of B's = 5

Number of C's = 6

Number of D's = 5

Total number of letters tiles = 20

Probability of selecting C = 6/20 = 3/10

Probability of selecting D = 5/20 = 1/4

P( C and D)= 3/10 × 1/4 = 3/40

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

M = 0.65146579

t=0

simplified = M ( t ) = 0.65146579 t

Step-by-step explanation:i really hope this helps you

Answer:

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

\(f(x)=-16x^2+64x+5\)

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

\(10=-16x^2+64x+5\)

Subtracting 10 from both sides:

\(-16x^2+64x-5=0\)

For simplicity, divide both sides by -1:

\(16x^2-64x+5=0\)

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Substitute:

\(\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}\)

Evaluate:

\(\displaystyle x=\frac{64\pm\sqrt{3776}}{32}\)

Simplify the square root:

\(\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}\)

Therefore:

\(\displaystyle x=\frac{64\pm8\sqrt{59}}{32}\)

Simplify:

\(\displaystyle x=\frac{8\pm\sqrt{59}}{4}\)

Approximate:

\(\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08\)

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

Answer:

Circumference of circle = 18π inches

Step-by-step explanation:

Given the following data;

Area of circle = 81π in²

To find the circumference;

First of all, we would find the radius of the circle using the area of circle formula.

Area of circle = πr²

Substituting into the formula, we have:

81π = πr²

Dividing both sides by π, we have;

81 = r²

Taking the square root of both sides, we have;

r = 9 inches

Now, to find the circumference of the circle;

Circumference of circle = 2πr

Circumference of circle = 2*π*9

Circumference of circle = 18π inches.

The correct properties of the normal curve are:

A. The high point is located at the value of the mean.

C. The area under the normal curve to the right of the mean is 1.

F. The graph of a normal curve is symmetric.

Analyzing each of the options we can see that:

The normal curve is symmetric, with the highest point (peak) located exactly at the mean.

It has a bell-shaped appearance.

The area under the entire normal curve is equal to 1, representing the total probability. The area under the normal curve to the right of the mean is 0.5, or 50% of the total area, as the curve is symmetric.

The normal curve is not skewed right; it maintains its symmetric shape. The value of the standard deviation does not determine the location of the high point of the curve.

Then the correct options are A, C, and F.

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The following are properties of the normal curve: A. The high point is located at the value of the mean, C. The total area under the normal curve is 1 (not just to the right), and F. The graph of a normal curve is symmetric.

Based on the options provided, the following statements are properties of the normal curve:

Other options do not correctly describe the properties of a normal curve. For instance, normal curves are not skewed right, the high point does not correspond to the standard deviation, and the area under the curve to the right of the mean is not 0.5.

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Answer:

10(6)

Step-by-step explanation:

Hope it's right.....

The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = \(\frac{x}{100} *1 pound\)

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so \(\frac{x}{100} * y = 31/2\)

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Answer:

20.84

Step-by-step explanation:

$25.36 - $4.52 = $20.84

Hope this helps