3. Beth finished 40% of her weekly biking workout. She has traveled 24 miles. How long is her
workout for the entire week?

Answer:

21.21

Step-by-step explanation:

Area of a circle is A = π r^2

Variables:

r = 18/2 = 9

θ = 30 deg

Find the area:

A = π r^2

A = π 9^2

A = 254.47

Find the area of the sector:

θ/360 * A

= 30/360 * 254.47

= 21.21

To determine the number of terms we need to add in order to find the sum of the series with an error less than or equal to 0.002, we can use the concept of the Alternating Series Estimation Theorem.

The Alternating Series Estimation Theorem states that for an alternating series with terms decreasing in absolute value, the error in approximating the sum of the series by the sum of a finite number of terms is less than or equal to the absolute value of the next term.

In the given series, ∑n=1[infinity](−1)n−1n^2, the terms are decreasing in absolute value as n increases, so we can apply the Alternating Series Estimation Theorem.

The next term in the series, which determines the error, is given by (-1)^n * (n+1)^2. To ensure the error is less than or equal to 0.002, we need to find the smallest value of n such that:

|(-1)^n * (n+1)^2| ≤ 0.002

We can solve this inequality by testing values of n until we find the smallest value that satisfies it. Starting with n = 1:

|(-1)^1 * (1+1)^2| = 4 > 0.002

The inequality is not satisfied for n = 1.

Let's continue testing values of n:

|(-1)^2 * (2+1)^2| = 9 > 0.002

|(-1)^3 * (3+1)^2| = 16 > 0.002

|(-1)^4 * (4+1)^2| = 25 > 0.002

|(-1)^5 * (5+1)^2| = 36 > 0.002

|(-1)^6 * (6+1)^2| = 49 > 0.002

...

After testing a few values, we can see that the smallest value of n that satisfies the inequality is n = 9:

|(-1)^9 * (9+1)^2| = 100 > 0.002

Therefore, we need to add at least 9 terms in order to find the sum of the series with an error less than or equal to 0.002.

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Answer:the left one

Step-by-step explanation:

Answer:the third one I suppose

Step-by-step explanation:

Answer:

3(t-y)

Step-by-step explanation:

difference means subtractions

3*(t-y)

Answer:

3 × (t - y)

Step-by-step explanation:

three times = 3×

the difference between t and y = t - y

Now that we have separated the key information in the word expression, you can now piece together the expression.

3 × (t - y)

Hope this helped.

the control limits for the x-bar chart are 9.7439 minutes (LCL) and 11.0561 minutes (UCL), and the control limits for the R chart are 0 minutes (LCL) and 2.0529 minutes (UCL).

To compute the control limits for the x-bar (mean) and R (range) charts, we'll use the following formulas:

For the x-bar chart:

Upper Control Limit (UCL) for x-bar = x-double-bar + A2 * R-bar

Lower Control Limit (LCL) for x-bar = x-double-bar - A2 * R-bar

For the R chart:

Upper Control Limit (UCL) for R = D4 * R-bar

Lower Control Limit (LCL) for R = D3 * R-bar

Where:

x-double-bar = Overall mean of the sample means

R-bar = Overall mean of the sample ranges

A2 = Constant from the control chart constants table

D4 = Constant from the control chart constants table

D3 = Constant from the control chart constants table

For sample sizes of 4, the control chart constants are as follows:

A2 = 0.729

D4 = 2.281

D3 = 0

Given the information you provided:

Overall mean (x-double-bar) = 10.4 minutes

Average range (R-bar) = 0.9 minutes

Let's calculate the control limits:

For the x-bar chart:

UCL for x-bar = 10.4 + 0.729 * 0.9

             = 10.4 + 0.6561

             = 11.0561 minutes

LCL for x-bar = 10.4 - 0.729 * 0.9

             = 10.4 - 0.6561

             = 9.7439 minutes

For the R chart:

UCL for R = 2.281 * 0.9

         = 2.0529 minutes

LCL for R = 0

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The solution to the equation 9(b - 2) = -7 + 0 is b = 11/9.

Given the equation in the question:

9( b - 2 ) = -7 + 0

To solve the equation, first apply distributive property to remove the poarenthesis:

9( b - 2 ) = -7 + 0

9×b + 9×-2 = -7 + 0

9b - 18 = -7 + 0

Next, we simplify the right side of the equation:

9b - 18 = -7

To isolate the variable 'b,' we need to get rid of the constant term (-18) on the left side. We can do this by adding 18 to both sides of the equation:

9b - 18 + 18 = -7 + 18

Simplifying further:

9b = -7 + 18

Add -7 and 18

9b = 11

Now, we want to solve for 'b,' so we divide both sides of the equation by 9:

9b/9 = 11/9

b = 11/9

Therefore, the value of b is 11/9.

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The value of the linear equation is 1.2

A linear equation is an algebraic equation for a straight line, where the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0, where x is a variable, A is a coefficient, and B is a constant

The given equation is 9(b-2) = -7 + 0

Opening the brackets we have

9b -18 = -7 + 0

Collecting like terms

9b = -7+18

9b = 11

Dividing both sides by 9 we have

b = 11/9

b = 1.2

Therefore the value of b is 1.2

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Answer:

From the graph, the y-intercept is 9 and the slope is -1 so the equation is y = -x + 9. We know the slope is -1 because when x goes up by 1, y decreases by 1.

Step-by-step explanation:

When we know both the x- and y-intercepts of a line, we can conveniently use the intercept form.

Let

A=x-intercept=9

B=y-intercept=9

the intercept form of the equation is therefore

x/A + y/B =1

substituting numerical values,

x/9 + y/9 =1  ..........................(1)

Factoring the identical denominators

(x+y)/9 = 1

Cross multiply

x+y = 9  ...............................(2)

Both (1) and (2) are valid forms of equation of the given line.

Using pythagoras' theorem in the right angled triangle, x = 2√10 in simplest radical form

A right angled triangle is a triangle in which one of the angles is 90 degrees.

To find the value of x in the figure, we proceed as follows

First we notice that the top right angled triangle has its hypotenuse side as the side length of the rectnagle.

So, using Pythagoras' theorem, we find the side length, L of the rectangle.

By Pythagoras' theorem L = √(4² + 2²)

= √(16 + 4)

= √20

= 2√5

Now in the rectangle, he diagonal of length 10 units divides the rectangle into two right angled triangles of sides L and x

So, by Pythagoras' theorem 10² = L² + x²

So, making x subject of the formula, we have that

x = √(10² - L²)

= √(10² - (√20)²)

= √(100 - 20)

= √80

= √(10 × 4)

= √10 × √4

= 2√10

So, the value of x = 2√10

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Answer:

Step-by-step explanation:

Nothing further can be done with this topic.  

f ( x ) = 3 x 2 − 10 x − 9

Answer:

D = b²-4ac

so, now put in Formula

Discriminate, D = 16-56 = -40

hope it helps you....

Answer: 7&8

Step-by-step explanation:

Answer:

B. y = -3/4x is the answer

Step-by-step explanation:

(0,0) and (4,-3) are the given points.

so,

slope = (-3-0)/(4-0) = -3/4

Now,

y = mx + b

or, 0 = -3/4 * 0 + b

or, 0 = 0 + b

so, b = 0

Now,

y = mx + b

or, y = -3/4x + 0

y = -3/4x

The equation of the line is y = (-3/4)x which is shown in the given graph. The correct answer is B.

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

For the equation of the line passing through two shown points, we use the point-slope formula:

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, and m is the slope of the line.

We can find the slope using the formula:

m = (y₂- y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the given points (0,0) and (4,-3), we have:

m = (-3 - 0) / (4 - 0) = -3/4

Now we can use the point-slope formula with the point (0,0):

y - 0 = (-3/4)(x - 0)

Simplifying, we get:

y = (-3/4)x

Thus, the equation of the line is y = (-3/4)x.

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Without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

To calculate a 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B, we can use the least squares means estimates provided in the JMP output.

According to the JMP output, the estimate for the mean time required to stabilize emergency condition 4 using display panel B is 10.375000.

To calculate the confidence interval, we need to find the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, we need to find the critical value for a 95 percent confidence interval. Since we have a sample size of 24 (as mentioned in the question), we can use the t-distribution with (24-1) degrees of freedom to find the critical value.

Looking up the critical value in the t-distribution table, with (24-1) degrees of freedom and a confidence level of 95 percent, we find that the critical value is approximately 2.064.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / √(sample size)

The standard deviation is not provided in the given information. Therefore, we cannot calculate the standard error or the confidence interval without this information.

In summary, without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

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Answer:

11z+ 13

Step-by-step explanation:

22z - 11z = 11z

11z+ 13

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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Answer:

430

Step-by-step explanation:

Given :-

And we need to find out the CP .So ,

Let :-

According to the Question :-

\(:\implies\) 460 = x + y ( Profit)

\(:\implies\) 400 = x - y ( Loss)

Adding both :-

\(:\implies\) 460 + 400 = x + y + x - y

\(:\implies\) 860 = 2x

\(:\implies\) x = 860/2

\(:\implies\) x = 430

Hence the Cost price of the watch is 430 .

The difference in the values of the two cars when they are each 7 years old is equal to $6,000.

In order to determine the difference in the values of the two cars, we would have to write an equation that models the price of the cars after a length of time, by using the data points shown in the graph above.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For Car A, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (9 - 12)/(4 - 2)

Slope, m = -3/2

Slope, m = -1.5

At point (4, 9), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 9 = -1.5(x - 4)

y = -1.5x + 15

In 7 seven years, the value of Car A is given by:

y = -1.5x + 15

y = -1.5(7) + 15

y = $4,500

Note: The negative sign indicates that the value of the car is depreciating.

For Car B, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (10 - 18)/(5 - 1)

Slope, m = -8/4

Slope, m = -2

At point (5, 1), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 1 = -2(x - 5)

y = -2x + 11

In 7 seven years, the value of Car B is given by:

y = -2x + 11

y = -2(7) + 3.5

y = $10,500

Now, we can determine the difference as follows:

Difference = $10,500 - $4,500

Difference = $6,000.

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The measure of angle ∠1 is 55 degrees if Andrew constructed a triangle so that the measurement of ∠1 and ∠2 were congruent.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

Andrew constructed a triangle so that the measurement of ∠1 and ∠2 were congruent.

The measure of the angle 3 = 70 degrees

As we know, in the triangle; interior angles add up to 180°.

∠1 + ∠2 + ∠3 = 180

∠1 = ∠2

∠3 = 70 degrees (given)

∠1 + ∠1 + 70 = 180

2∠1 = 180 - 70

2∠1 = 110

∠1 = 110/2

∠1 = 55 degrees

Thus, the measure of angle ∠1 is 55 degrees if Andrew constructed a triangle so that the measurement of ∠1 and ∠2 were congruent.

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Answer:

it's the Option 2

Explanation;

since x has to be greater than 6 the line would go to the right or towards the greater side.

Then it's a open circle because it's strickly greater than

This is False in light of the stated statement. Due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

How is regression calculated?

Y = mX + b, where X is the predictive (independent) factor, m is really the approximately slope, and b is the expected intercept, is the methodology for simple linear regression.

The relationship between scattered data points in any set is shown by a regression line. When there is a linear pattern, it displays the relationship between the dependent y variable and independent x variables.

The correlation between the independent variables (IVs) and the dependent variable is described by a linear regression equation (DV). The DV for the IV values you indicate can also be predicted for new values.

Hence we get the required answer.

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This is the answer to your problem

Answer:

12 - 0 = 12.

Step-by-step explanation:

If you substitute all x values for 0, then you get 12 - 8(0) = 3(0+4). Combine like terms and you will arrive at 12 - 0 = 3(4). Which then goes to 12 - 0 = 12. Since 0 has no value, just remove it from the equation. You are left with 12 = 12.

Answer:

it is x= 0

Step-by-step explanation:

you distribute the numbers in the parentheses first so your new equation would be 12 - 8x = 3x + 12 (basically multiply 3 by what was in the parentheses)

then cancel equal terms so 12 - 8x = 3x + 12 becomes -8x = 3x

after that move the variable and the 3 to the left while changing the sign from + to - (the + sign is implied since it's a positive number) your new equation becomes -8x - 3x = 0

next collect like terms so the numbers with the same variable meaning subtract -8x - 3x also known as -8x + -3x creating the equation -11x =0

finally divide both sides of the equation -11x = 0 by -11 creating x=0

Answer:

603.9

Step-by-step explanation:

100+10=110

110÷100=1.1

1.1 x 549=603.9

Answer:

(2x^(3)y^(2))^(3) the little ^ means "sub"

Step-by-step explanation:

Use the power rule to distribute the exponent.

Raise 2 to the power of 3

Multiply the exponents in (x^3)^3

Multiply the exponents in (y^2)^3

Answer:

-3

Step-by-step explanation:

In the slope-intercept form of linear equation (y=mx+b) the slope is the number next to the x, here represented with the letter m.  In your equation, y =-3x+7, the m is replaced by -3, so the slope here is -3.  

The solution of the equations (-5x + 2) / 7 = -4 and 17 - 3(w + 5) = 6(w + 5) - 2w will be 6 and negative 4, respectively.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

A. The equation is given below.

(-5x + 2) / 7 = -4

Simplify the equation, then we have

(-5x + 2) / 7 = -4

-5x + 2 = -28

-5x = - 30

x = 6

B. The equation is given below.

17 - 3(w + 5) = 6(w + 5) - 2w

Simplify the equation, then we have

17 - 3(w + 5) = 6(w + 5) - 2w

17 - 3w - 15 = 6w + 30 - 2w

2 - 3w = 4w + 30

- 7w = 28

w = - 4

The solution of the equations (-5x + 2) / 7 = -4 and 17 - 3(w + 5) = 6(w + 5) - 2w will be 6 and negative 4, respectively.

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The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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