A chore of a circle is l cm long the distance of the circle is h in cm and the radius of the circle is r cm express r in terms of l and b

Answer: How Many Apples did Bethany Pick?

Step-by-step explanation:

Bethany picked 17 apples.

Let x be the number of apples that Catherine picked. Then Alice picked 2x apples, and Bethany picked (2x + 7) apples.

We know that Bethany picked 5 fewer apples than Catherine, so:

2x + 7 = x + 5

Solving for x, we get:

x = 2

Therefore, Catherine picked 2 apples.

We also know that Alice picked twice as many apples as Catherine, so:

2x = 4

Therefore, Alice picked 4 apples.

Finally, we know that Bethany picked 7 fewer apples than Alice, so:

2x + 7 = 4 - 7

2x + 7 = -3

Therefore, Bethany picked -3 apples. However, this is impossible, so we must have made a mistake.

Going back to our equations, we see that we made an error in the equation:

2x + 7 = x + 5

It should be:

2x = x + 5 - 7

2x = x - 2

Solving for x, we get:

x = 2

Therefore, Catherine picked 2 apples.

We also know that Alice picked twice as many apples as Catherine, so:

2x = 4

Therefore, Alice picked 4 apples.

Finally, we know that Bethany picked 7 fewer apples than Alice, so:

2x - 7 = 4 - 7

2x - 7 = -3

2x = 4

x = 2

Therefore, Bethany picked (2x - 7) = (2(2) - 7) = -3 apples. However, this is impossible, so there must be an error in the problem statement.

{Hope This Helps! :)}

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (6)^2}{360} \\\\\\ A=\cfrac{9\pi }{2}\implies A=\cfrac{9(3.14) }{2}\implies A=14.13~yd^2[/tex]

Answer:

flavor of candies in each box

Step-by-step explanation:

Check the picture below.

Answer: C

Step-by-step explanation: Plug -2 in for x for each answer option and see which inequality correctly applies. If the "mouth" of the inequality is pointed to the right, that means that the answer when you plug in x is less than the answer value. If the mouth is pointed to the left, that means that when you plug in x, the answer is greater than the resulting value.

Answer: -8

Step-by-step explanation:

13x+22=x-34+5x

13x+22=6x-34 (combine like terms)

13x-6x+22=6x-6x-34 (subtract 6x on each side)

7x+22=-34

7x-22+22=-34-22 (subtract 22 on each side)

7x=-56

7x/7x = -56/7 (divide 7 on each side)

x=-8

1. 24=4times6;24=6 times 4 is represented by  apple orchard

2. 45=9 times 5; 45 = 5 times 9 is represented by  classroom of students

3.  36= 3 times12; 36 =12 times 3  is represented by A construction site

4. 60 =12 times 5; 60 = 5times 12 is represented by A grocery store

1. An apple orchard is comparing the productivity of two of its workers in terms of the number of baskets of apples picked. Worker A picked 4 baskets in 6 hours, while Worker B picked 6 baskets in 2 hours.

The situation can be represented by the equations 24 = 4 x 6 and 24 = 6 x 2, where 24 represents the total number of baskets picked.

2. Another example is a classroom of students comparing the number of pencils each student has. In one row, there are 9 students and each student has 5 pencils. In another row, there are 5 students and each student has 9 pencils. This situation can be represented by the equations 45 = 9 x 5 and 45 = 5 x 9, where 45 represents the total number of pencils in each row.

3. A construction site is comparing the efficiency of two workers in terms of the number of bricks they can lay in a certain amount of time. Worker A can lay 3 bricks in 12 minutes, while Worker B can lay 12 bricks in 3 minutes. The situation can be represented by the equations 36 = 3 x 12 and 36 = 12 x 3, where 36 represents the total number of bricks laid.

4. A grocery store is comparing the size of two crates of oranges. Crate A contains 12 rows of oranges, with 5 oranges in each row. Crate B contains 5 rows of oranges, with 12 oranges in each row. This situation can be represented by the equations 60 = 12 x 5 and 60 = 5 x 12, where 60 represents the total number of oranges in each crate.

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Answer:

0.09 l

Step-by-step explanation:

Given:

900 ml ⇒ 10s

Required:

Liters per second

Analyze:

Let the unknown amount be x.

900 ml ⇒ 10s

         x ⇒ 1s

Solve:

Use cross multiplication

900 × 1 = 10 × x

    900 = 10x

Divide both sides by 10.

90 ml = x

To covert the answer into liters divide it by 1000.

0.09 l = x

Paraphrase:

We breathe 0.09 liters of air per second

according to question the surface integral is (32π - 192)/15.

To evaluate the surface integral, we need to parameterize the surface and find the surface element ds.

Let's consider the parameterization:

x = y^2 + z^2

y = y

z = z

The surface element can be found as:

ds = √(1 + (dx/dy)^2 + (dx/dz)^2) dy dz

ds = √(1 + 4y^2) dy dz

Now, we can rewrite the integral as:

∫∫s z^2 ds = ∫∫R (y^2 + z^2)^2 √(1 + 4y^2) dy dz

where R is the projection of the surface S onto the yz-plane, which is the region 0 ≤ y ≤ 2, -√(4 - y^2) ≤ z ≤ √(4 - y^2).

Let's evaluate the integral:

∫∫s z^2 ds = ∫0^2 ∫-√(4-y^2)^√(4-y^2) (y^2 + z^2)^2 √(1 + 4y^2) dz dy

Using cylindrical coordinates, we can rewrite the integral as:

∫0^2 ∫0^π/2 ∫0^2r (r^2 cos^2θ + r^2 sin^2θ)^2 r √(1 + 4r^2 sin^2θ) dr dθ dy

Simplifying and solving the integral, we get:

∫∫s z^2 ds = (32π - 192)/15

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To calculate the average number of employees per dealership, we need to first find the total number of employees working in both the dealerships and the head office. Let's assume that the total number of employees in August 2020 was 1000.

If 1.5% of the total number of employees worked at the head office, then the number of employees working in the head office would be 0.015 x 1000 = 15. To find the number of employees working in dealerships, we can subtract the number of employees working in the head office from the total number of employees, which is 1000 - 15 = 985.

Next, we need to calculate the average number of employees per dealership. To do this, we can divide the number of employees working in dealerships by the number of dealerships. Let's assume there are 10 dealerships in total. Therefore, the average number of employees per dealership would be 985/10 = 98.5.

So, on average, each dealership would have approximately 98.5 employees in August 2020.

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The graph of the equation y = -4 + 4 cos²θ represents a cardioid, which is a heart-shaped curve.

To convert the polar equation r = -4 sin θ to rectangular form, we can use the following relationships between polar and rectangular coordinates:

x = r cos θ

y = r sinθ

Substituting the given polar equation into these equations, we have:

x = -4 sinθ cosθ and y = -4 sinθ sinθ

x= -4 sinθ cosθ and y = -4 sin²θ

Since sin²θ = 1 - cos²θ, we can rewrite the equation for y as:

y = -4 (1 - cos²θ)

y = -4 + 4 cos²θ

Now we have the rectangular form of the equation, with x and y in terms of cosθ.

The graph of the equation y = -4 + 4 cos²θ represents a cardioid, which is a heart-shaped curve.

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When you graph a quadratic function, its shape is called a parabola.

Option C is the correct answer.

We have,

A parabola is a curve that is formed when graphing a quadratic function.

It is a U-shaped curve that can open upwards or downwards, depending on the coefficients of the quadratic equation.

A quadratic function is a polynomial function of degree 2, which can be expressed in the form y = ax² + bx + c, where a, b, and c are constants and x represents the variable.

The coefficient a determines whether the parabola opens upwards or downwards.

If coefficient a is positive, the parabola opens upwards, and if coefficient a is negative, the parabola opens downwards.

The vertex of the parabola is the highest or lowest point on the curve, depending on the orientation.

Thus,

A parabola is a specific shape that is formed when graphing a quadratic function, characterized by its U-shape.

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Answer:

400

Step-by-step explanation:

V= [tex]\frac{1}{3}[/tex]Bh

the base is a square, so B= [tex]10^{2}[/tex] or 100

h= 12

B= 100

Bh= 1200

[tex]\frac{1200}{3}[/tex] = 400

V=400

A type II error would occur if the candidate is actually a drug user, but the drug test incorrectly classifies them as a nonuser.

A type II error occurs when the null hypothesis is not rejected, even though it is false.

In this case, the null hypothesis is that the job candidate is not a drug user.

Therefore, a type II error would occur if the candidate is actually a drug user, but the drug test incorrectly classifies them as a nonuser.

In other words, a type II error would occur if the drug test fails to detect drug use in a job candidate who is actually a drug user.

This means that the organization would mistakenly hire a drug user, which could have negative consequences for the workplace and potentially put the safety of others at risk.

To minimize the risk of type II errors, organizations should use drug tests that are as accurate as possible and consider using multiple types of tests or follow-up testing to confirm results.

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When one increases the confidence level (1-α) from 0.90 to 0.95, it means they are becoming more certain about the estimate of the population parameter.

In statistical inference, the confidence level indicates the probability of the true population parameter falling within the confidence interval calculated from the sample data. So, a higher confidence level implies a wider confidence interval.

For example, if a confidence interval for a mean is calculated at the 90% confidence level, then we can say that we are 90% confident that the true population mean falls within the interval. However, if we increase the confidence level to 95%, the interval becomes wider, but we can say that we are now 95% confident that the true population mean falls within this wider interval.

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Answer:

(a) $ 7000

(b) $ 5600

Step-by-step explanation:

discount = 20%

20% = $1400

1% = 1400/20

original price = 100%

= 1400/20 × 100

= $7000

sale price = 80%

= 1400/20 × 80

= $5600

The total number of possible values of k is 13

The sum of two sides of a triangle is more than the third side

11 + 15 > k

26 > k   ..(1)

difference between the two sides of a triangle is less than the third side

15 - 11 < k

4 < k   ...(2)

From (1) and (2)

4 < k < 26

Triangle to be obtuse

Either 11² + 15² < k²

or 11² + k² < 15²

For 11² + 15² < k²

k = 19, 20, 21, 22, 23, 24, 25

For 11² + k² < 15²

k = 5, 6, 7, 8, 9, 10

The total number of possible values of k is 13

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Answer:

Step-by-step explanation:

To determine the number of different ratings combinations possible, we can use the combination formula. Since there are five possible ratings (very poor, poor, fair, good, and excellent) and 29 students in the class. Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.

The formula we can use is:
nCr = n! / r!(n-r)!
where n is the total number of items (in this case, the number of ratings), and r is the number of items we are choosing (in this case, the number of students).
Using this formula, we can find the number of different ratings combinations possible by plugging in the values:
nCr = 5! / 29!(5-29)!
nCr = 5! / 29!(-24)!
nCr = 5 x 4 x 3 x 2 x 1 / (29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
nCr = 657,800
Therefore, there are 657,800 different ratings combinations possible for the 29 students in the statistics class.
In this scenario, there are 29 students and a 5-point scale for rating their instructor. To determine the number of different rating combinations possible, we will use the concept of combinations with repetitions allowed.
In this case, the formula for combinations with repetitions is given by:
C(n+r-1, r) = C(n+r-1, n-1), where n is the number of ratings (5) and r is the number of students (29).
Using the formula, we get:
C(5+29-1, 29) = C(33, 29) = 33! / (29! * 4!)
Calculating the factorials and simplifying the expression, we get:
C(33, 29) = 46,376
Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.

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The equation of f(x) is given as follows:

f(x) = (x + 2)(x - 3).

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

The roots for this problem are given as follows:

Hence the function in factored form is defined as follows:

f(x) = a(x + 2)(x - 3)

From point (2,-4), when x = 2, f(x) = -4, hence the leading coefficient a is obtained as follows:

-4 = a(4)(-1)

-4a = -4

a = 1.

Hence the function is:

f(x) = (x + 2)(x - 3).

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The Percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

To find the percentage error, we need to calculate the difference between the recorded value and the true value, then divide that difference by the true value and multiply by 100 to get a percentage.

True value = 1,500

Recorded value = 900

Difference = True value - Recorded value

Difference = 1,500 - 900

Difference = 600

Percentage error = (Difference / True value) x 100

Percentage error = (600 / 1,500) x 100

Percentage error = 40

Therefore, the percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

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Answer:

x = 113

Step-by-step explanation:

x and 67 are a linear pair and sum to 180° , that is

x + 67 = 180 ( subtract 67 from both sides )

x = 113

the general solution of the given differential equation is:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

To find the general solution of the given differential equation:

(x^2 - 4) dy/dx + 4y = (x + 2)^2

We can rearrange the equation to isolate the derivative term:

dy/dx = [(x + 2)^2 - 4y] / (x^2 - 4)

First, let's simplify the numerator:

[(x + 2)^2 - 4y] = (x^2 + 4x + 4) - 4y

= x^2 + 4x + 4 - 4y

= x^2 + 4x - 4y + 4

Now, substitute this simplified expression back into the differential equation:

dy/dx = (x^2 + 4x - 4y + 4) / (x^2 - 4)

This is a first-order linear homogeneous differential equation. To solve it, we can use the integrating factor method.

First, let's write the equation in the standard form: dy/dx + P(x)y = Q(x)

dy/dx + (4x / (x^2 - 4))y = (x^2 + 4x + 4) / (x^2 - 4)

The integrating factor is given by the exponential of the integral of P(x):

μ(x) = exp ∫ (4x / (x^2 - 4)) dx

To find the integral, we can use substitution. Let u = x^2 - 4, then du = 2x dx:

μ(x) = exp ∫ (2x dx) / (x^2 - 4)

= exp ∫ (du / u)

= exp(ln|u|)

= |u|

Substituting back u = x^2 - 4:

μ(x) = |x^2 - 4|

Now, multiply the entire differential equation by the integrating factor:

|x^2 - 4| dy/dx + (4x / (x^2 - 4)) |x^2 - 4|y = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

The left side can be simplified using the product rule for differentiation:

d/dx [ |x^2 - 4|y ] = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

Now, integrate both sides with respect to x:

∫ d/dx [ |x^2 - 4|y ] dx = ∫ (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4) dx

Integrating the left side gives:

|x^2 - 4|y = ∫ (x^2 + 4x + 4) dx

= (1/3) x^3 + 2x^2 + 4x + C1

where C1 is the constant of integration.

Finally, divide both sides by |x^2 - 4| to solve for y:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

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The probability that the sample mean will be between 295 and 305 can be determined using the Central Limit Theorem and the properties of the normal distribution.

According to the Central Limit Theorem, for a large sample size (n ≥ 30), the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. In this case, since the sample size is 64, we can assume that the sample mean will follow a normal distribution.

To find the probability that the sample mean will be between 295 and 305, we need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the given range (295 to 305), μ is the population mean (300), σ is the population standard deviation (12), and n is the sample size (64).

By calculating the z-scores for the lower and upper limits of the range and referring to the standard normal distribution table, we can find the corresponding probabilities. The probability can be calculated by subtracting the cumulative probability corresponding to the lower limit from the cumulative probability corresponding to the upper limit.

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Answer:

  248.5 mm³

Step-by-step explanation:

Given similar shapes with a smaller : larger surface area ratio of 95 mm² : 245 mm², you want the larger volume if the smaller is 60 mm³.

The scale factor for the two shapes is the square root of the ratio of areas:

  larger : smaller = √(245 : 95) ≈ 1.60591

The ratio of volumes is the cube of the scale factor for the two shapes:

  larger volume : smaller volume = (1.60591 : 1)³ ≈ 4.14156 : 1

Then the larger volume is ...

  larger volume = smaller volume × 4.14156 = (60 mm³)(4.14156)

  larger volume ≈ 248.5 mm³

__

Additional comment

You don't need to compute the actual scale factor. The ratio of volumes is the 3/2 power of the ratio of areas. That fact is used in the calculation shown in the attachment.

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Answer:

3/28

Step-by-step explanation:

5 + 3 = marbles in total.

P(first blue) = 3/8

P(second blue) = (3-1) / (8-1)  = 2/7

P(selecting 2 blue) = (3/8) X (2/7) = 6/56 = 3/28