A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. (a) What is the probability that both grapes are green? (b) What is the probability that Henry eats a red grape then a green grape?

Answer:

\((14 + 7) + 12 = 14 + (7 + 12)\)

Step-by-step explanation:

Given

\((14 + 7) + 12\) --- [Missing in question]

Required

Select equivalent expression

\((14 + 7) + 12\)

Associative property states that:

\((a + b) + c = a + (b + c)\)

In this case:

\(a = 14\)

\(b = 7\)

\(c = 12\)

So, we have:

\((a + b) + c = a + (b + c)\)

\((14 + 7) + 12 = 14 + (7 + 12)\)

B. is correct

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

60= per hour ....which is 1 hrs

so 120= 2 hrs

60+60

120

2hr is the answer

Answer:

3.5 hours

Step-by-step explanation:

\(speed \: = 60 \\ distance = 210 \\ time = \\ speed \: = \frac{distance}{time} \)

\(time = \frac{distance}{speed} \\ time = \frac{210}{60} \\ time = \frac{7}{2} \)

\(time = 3.5 \: hours\)

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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The formula rise/run can be used to determine the slope of a graph by choosing any two points on it. Picking two locations and using the equation (y2 - y1) / (x2 - x1) will also get the answer. A horizontal line's slope is always zero. A vertical line has an unknown slope at all times.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").

The unit rate will be represented by the graph's slope.

The cost for one minute is the unit rate.

The rate is $3.20 according to the graph at x = 1.

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The solutions to the function y = -x^2 - 8x + 8 are (-8.9, 0) and (0.9, 0)

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

y = -x^2 - 8x + 8

To solve using a graphing calculator, we enter the equation in a graph and write out the solution

Having said that we have

When y = -x^2 - 8x + 8 is plotted, the soluton is (-8.9, 0) and (0.9, 0)

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Answer:

E

Step-by-step explanation:

=160*250*80

=3200000cm^3

also 1000cm =1 litres

therefore 3200000cm3 =3200litres

that's all ....... have fun

Answer:

9

Step-by-step explanation:

In this question we are working with ratios!

We will set up the ratio as "Hershey : lollipops." Fill in the numbers - 2 : 3

Since there are six Hershey bars in one bag, we have to figure out how much the Hershey side of the ratio was multiplied by so we can do the same to the lollipop side.

2 : 3

6 : ?

2 times 3 equals 6, so both sides are multiplied by 3. Now, we can multiply the number of lollipops by 3. (3 times 3 equals 9)

6 : 9 is the ratio we now have. Therefore, there are 9 lollipops in the bag.

Answer:

hope it helps you.........

Answer:

72

Step-by-step explanation:

9² - √81

= (9 × 9) - √9 × 9

= 81 - √9²

= 81 - 9

= 72

Answer:

-6 is the numeral cofficient

Answer:

Step-by-step explanation:

is a rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

Area = 1/2 b * h

Area =1/2 7 * 4

Area = 3.5 * 4

Area = 14 in²

So we have 7 in. and 4 in. so we just will mutilply It, So what we do here Is mutilply so we will do 7 x 4 = 28

So we have 28 then we mutilpy all of chocies to see which one Is 28.

A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

11 x 2=22 ❌ Not 28                                      

14 x 2 = 28 ✅ Is 28                                                                                                                                                            

22 x 2 = 44  ❌ Not 28

28 x 2 = 56  ❌ Not 28

A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

Area = 1/2 b * h ❌

 Area = 3.5 * 4  ❌            

 Area = 3.5 * 4  ❌      

 Area = 14 in²   ✅

Answer:

hi  hahahah

Step-by-step explanation:

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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Answer:

A

Step-by-step explanation:

Answer:

option  (a) is correct.

2 + m - 1 + m is an equivalent expression  to the given expression  3m+1-m

Step-by-step explanation:

Given expression  3m+1-m

We have to choose an equivalent expression from given options.

Equivalent expression are those expression that looks different but are same.

Like 4+2 = 6  and 3+ 3 = 6

Both have same value but looks differently.

Like terms are term having same variable with same degree.

Consider the given expression  3m+1-m

Simplify by adding like terms,

3m + 1 - m = (3-1) m + 1

Thus, (3-1) m + 1  = 2m + 1

Also 2m + 1 can be written as m + m + 2 - 1

Thus, option  (a) is correct.

Answer:

y = 0.01(3ˣ)

Step-by-step explanation:

Answer:

2.5 us dollars

Step-by-step explanation:

The employee's net pay after taxes if he works 52.5 hours in one week is $616.875.

The net pay is the difference between the gross periodic pay or earnings less statutory deductions, including income taxes.

Normal hourly rate = $15

Normal weekly hours = 40 hours

Overtime rate = 1¹/₂ of $15 = $22.50

Income tax rate = 30%

Total hours worked in one week = 52.5 hours

Overtime hours = 12.5 (52.5 - 40)

Normal weekly gross pay = $600 ($15 x 40)

Overtime pay = $281.25 ($22.50 x 12.5)

Total pay for the week = $881.25

Income tax = $264.375 ($881.25 x 30%)

Net pay = $616.875 ($881.25 - $264.375)

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To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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The value of a and b for the given quadrilateral to be a parallelogram is a = 16 and b = 4.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

We know that the opposite sides of a parallelogram are equal in length so we can equate the two sides as follows:

For a:

2a + 6 = 3a -10

Isolate the value of a by moving all the values having a to one side:

2a + 6 = 3a -10

3a - 2a = 6 + 10

a = 16

For b:

6b - 3 = 5b + 1

Isolate the value of b by moving all the values having b to one side:

6b - 3 = 5b + 1

6b - 5b = 1 + 3

b = 4

Hence, the value of a and b for the given quadrilateral to be a parallelogram is a = 16 and b = 4.

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A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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To be 95% confident that the estimate of the Percentage of computers with a new operating system is in error by no more than 4 percentage points, the programmer needs to survey at least 601 computers.

The sample size (n) needed to estimate the percentage of computers using a new operating system with a 95% confidence level and an error margin of no more than 4 percentage points, we need to use the formula for sample size estimation for proportions.

The formula is:

n = (Z^2 * p * (1-p)) / E^2

Where:

- n is the sample size

- Z is the z-score corresponding to the desired confidence level (for 95% confidence level, the z-score is approximately 1.96)

- p is the estimated proportion (since nothing is known about the percentage of computers with the new operating system, we assume p = 0.5 for maximum variability)

- E is the desired margin of error (in this case, 4 percentage points, which is 0.04 in decimal form)

Now, let's substitute the values into the formula and calculate the sample size (n)

n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2

n = (3.8416 * 0.25) / 0.0016

n = 0.9604 / 0.0016

n ≈ 600.25

Since the sample size must be a whole number, we round up to the nearest integer.

n = 601

Therefore, to be 95% confident that the estimate of the percentage of computers with a new operating system is in error by no more than 4 percentage points, the programmer needs to survey at least 601 computers.

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The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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Answer:

a. n=5

Step-by-step explanation:

The 4 of numerator cancels each other. So, 1/5=1/n is what you finally have.

Therefore, n=5.

Hope this helps!!

Answer:

788

Step-by-step explanation: