Suppose you have a bag that contains 2 black and 8 striped marbles. You select one marble, replace it, and then select another. Find the probability that you will select two black marbles in a row.

P(black & black) =

The center of gravity (x¯, y¯) of the wire is approximately (2.546, 2.546).

To find the center of gravity (x¯, y¯) of the wire, we can use the concept of geometric centroids. For a quarter of a circle in the first quadrant, the center of gravity will coincide with the centroid of the quarter-circle.

The centroid coordinates (x¯, y¯) of a quarter-circle with radius R can be found using the following formulas:

x¯ = (4R)/(3π)

y¯ = (4R)/(3π)

In this case, the radius of the quarter-circle is 6. Plugging this value into the formulas, we get:

x¯ = (4 * 6) / (3 * π)

= 24 / (3 * 3.14159)

≈ 2.546

y¯ = (4 * 6) / (3 * π)

= 24 / (3 * 3.14159)

≈ 2.546

Therefore, the center of gravity (x¯, y¯) of the wire is approximately (2.546, 2.546).

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Answer:

x equals to -1

Step-by-step explanation:

x-4x :3

-3x : 3

so x: -1

The probability that a number chosen randomly from 10 through 99, inclusive, will have zero as at least one digit is 0.18 or 18/100.

To find the probability, we can count the total number of possible numbers from 10 through 99, which is 90. Of these 90 numbers, the numbers with at least one zero are 19: 10, 20, 30, ..., 90 and 01, 02, 03, ..., 09. Therefore, the probability of randomly choosing a number with at least one zero is 19/90, which simplifies to 0.21 or 21/100. However, we need to subtract the probability of choosing the number 10, which has two zeros, to get the probability of choosing a number with at least one zero as a digit. So the final probability is (19-1)/90 = 18/100 or 0.18.

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Answer:

16, 8, 36

Step-by-step explanation:

x = 4y

y = 4, x = 16

y = 2, x = 8

y = 9, x = 36

Answer:

-127

Step-by-step explanation:

Answer:

A. (0,4)

Step-by-step explanation:

You can calculate the y intercept when x = 0.

Substitute 0 for x:

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

= 0 + 4

= 4

To find the conversion factor for converting from one unit to another involving squares or cubes, we need to use the relationship between the units that are being converted and the appropriate power of the conversion factor.

The conversion from yards to feet and vice versa involves the concepts of squares and cubes.

There are 3 feet in 1 yard, so the number of feet squared in one square yard is (3 feet)² = 9 square feet (because 3² = 9). This is why there are 9 square feet in 1 square yard.

Similarly, there are 3 feet in 1 yard, so the number of feet cubed in one cubic yard is (3 feet)³ = 27 cubic feet (because 3³ = 27). This is why there are 27 cubic feet in 1 cubic yard.2.

To find conversion factors involving squares or cubes, we need to use the relationship between the units that are being converted.

For example, to convert from square feet to square yards, we know that there are 9 square feet in 1 square yard. So the conversion factor is:1 square yard / 9 square feet

Similarly, to convert from cubic feet to cubic yards, we know that there are 27 cubic feet in 1 cubic yard. So the conversion factor is:1 cubic yard / 27 cubic feetIn general, to find the conversion factor for converting from one unit to another involving squares or cubes, we need to use the relationship between the units that are being converted and the appropriate power of the conversion factor.

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A yard is equivalent to 3 feet. Hence, a square yard is equivalent to 9 square feet (3^2) and a cubic yard is equivalent to 27 cubic feet (3^3). Conversion factors for squares or cubes are found by squaring or cubing the base conversion factor.

In terms of measurement conversion, 1 yard is equivalent to 3 feet. When dealing with square units like square feet and square yard, we square this conversion factor, thus 1 square yard is equivalent to 3^2 or 9 square feet.

Similarly, for cubic measurements, we cube the conversion factor. Therefore, 1 cubic yard is equivalent to 3^3 or 27 cubic feet.

To find conversion factors involving squares or cubes, you typically square or cube the base conversion factor. For example, if converting inches to feet, the base conversion is 1 foot is 12 inches. For square inches to square feet, you'd square the conversion so 1 square foot is 144 (12^2) square inches. Finally, for cubic feet to cubic inches, you'd cube the base conversion thus 1 cubic foot is 1728 (12^3) cubic inches.

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Answer:

Step-by-step explanation:

The dotted line is the apothem, which is the height of the triangle with the base same as the side of the pentagon.

There are 5 same triangles.

Total area:

Correct choice is c.

To find two numbers that have a sum of 138 and a difference of 54, we can use a system of equations.

Let x be the larger number and y be the smaller number. Then we have:

x + y = 138 (equation 1)

x - y = 54 (equation 2)

We can solve this system of equations by adding equation 1 and equation 2:

2x = 192

Dividing both sides by 2, we get:

x = 96

Substituting x = 96 into equation 1, we get:

96 + y = 138

Subtracting 96 from both sides, we get:

y = 42

Therefore, the two numbers that have a sum of 138 and a difference of 54 are 96 and 42.

The amount the firm needs to deposit in the account now is 9,640.11. Given that the company has purchased a life truck with a useful life of 5 years, the maintenance costs for the truck during the first year are 2,000.

Also, maintenance costs are expected to increase at a rate of 300 per year over the remaining life, which is for four years. Assume that the maintenance costs occur at the end of each year.

The future maintenance costs for the truck can be calculated as shown below:

Year 1:\($2,000Year 2: $2,300Year 3: $2,600Year 4: $2,900Year 5: $3,200\)The maintenance account that earns 10% interest per year has to be set up, and all future maintenance expenses will be paid out of this account. The future value of the maintenance costs, i.e., the amount that the firm needs to deposit now to earn 10% interest and pay the maintenance costs over the next four years is given by:

\(PV = [C/(1 + i)] + [C/(1 + i)²] + [C/(1 + i)³] + [C/(1 + i)⁴] + [(C + FV)/(1 + i)⁵]\),where PV is the present value of the future maintenance costs, C is the annual maintenance cost, i is the interest rate per year, FV is the future value of the maintenance costs at the end of year 5, which is $3,200, and 5 is the total number of years, which is

5.Substituting the given values in the above equation:

\(PV = [2,000/(1 + 0.1)] + [2,300/(1 + 0.1)²] + [2,600/(1 + 0.1)³] + [2,900/(1 + 0.1)⁴] + [(3,200 + 3,200)/(1 + 0.1)⁵] = 9,640.11\)Therefore, the firm needs to deposit 9,640.11 in the account now. Hence, option (A) is the correct answer.

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We have the following linear equation:

5x - 2y = -10

In the standard form, we have:

-2y = -5x - 10

y = 5x/2 - 5

For x = 0, we have y = -5, and, for y = 0, we have x = 2

Therefore, to graph this equation, we just need to draw a line passing through (0,-5) and (2,0).

The null and alternative hypotheses are:

H0: β1 = 0 (The slope is not significant.)

H1: β1 ≠ 0 (The slope is significant.)

Here,β1=0.0943seβ1=0.107α=0.05

Test the slope significance and find the t-test statistic.

We need to find the t-test statistic so that we can compare it with the t-distribution, whose distributional properties we know, to determine if we can reject or fail to reject the null hypothesis.t-test statistic is calculated by dividing the value of β1 by its standard error (seβ1) and taking the absolute value of this quotient.

t-test statistic = | β1/seβ1 | = |0.0943/0.107| = 0.881

The degrees of freedom (df) associated with this t-test are df = n - 2, where n is the sample size for the explanatory variable x.

In this problem, the decision rule and conclusion are as follows:

Decision Rule: Reject the null hypothesis if |t-test statistic| > tc where tc is the critical value obtained from the t-distribution with df degrees of freedom and a significance level of α/2 in each tail.

Conclusion: The slope is not significant if we fail to reject the null hypothesis, but the slope is significant if we reject the null hypothesis. Since the t-test statistic (0.881) is less than the critical value (1.987), we fail to reject the null hypothesis. Therefore, we conclude that the slope is not significant.

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Answer:Find the vol of the sphere:

radius of the sphere = 3 in

V = %284%2F3%29%2Api%2A3%5E3

V = 97.858

:

Find the vol between the sphere and cube:

216 - 97.858 = 118.142 cu/in

Step-by-step explanation:

\(\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y) \\\\\\ \sin(x+y)=\sin(x)\left( \cfrac{\sqrt{2}}{2} \right)\cos(x)\left( \cfrac{\sqrt{2}}{2} \right) \\\\[-0.35em] ~\dotfill\\\\ \cos(y)=\sin(y)=\cfrac{\sqrt{2}}{2}\hspace{5em}\cos\left( \frac{\pi }{4} \right)=\sin\left( \frac{\pi }{4} \right)=\cfrac{\sqrt{2}}{2}\hspace{5em}y=\cfrac{\pi }{4}\)

Answer:

c

Step-by-step explanation:

You are consuming approximately 275 grams of carbohydrates each day, based on a daily calorie intake of 2200 kcal and a diet consisting of 50% carbohydrates.

To calculate the number of grams of carbohydrates you are consuming, you need to convert the percentage into a decimal and multiply it by the total calorie intake. Since carbohydrates provide 4 calories per gram, you can divide the calorie intake by 4 to get the number of grams.

In this case, 50% of 2200 kcal is 1100 kcal. To convert this into grams, divide 1100 kcal by 4, which equals 275 grams. Therefore, you are consuming 275 grams of carbohydrates each day.

It's important to note that this calculation assumes that each gram of carbohydrates provides 4 calories, which is a general estimate. The actual caloric value may vary depending on the specific types of carbohydrates consumed.

Additionally, individual dietary requirements and preferences may also affect the distribution of macronutrients in a person's diet. It's always recommended to consult with a healthcare professional or registered dietitian for personalized nutritional advice.

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Answer:0,0.5

Step-by-step explanation:

The coordinates of the intersection of the diagonals of the parallelogram will be (0, 0.50).

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

The coordinates of the parallelogram are given below.

Q(-1,3), R(5,2), S(1, - 2), and T(-5, -1)

The equation of the QS diagonal line is given as,

(y - 3) = [(3 + 2) / (- 1 - 1)](x + 1)

y - 3 = - 2.5 x  - 2.5

y = - 2.5 x + 0.5       ...1

The equation of the RT diagonal line is given as,

(y - 2) = [(2 + 1) / (5 + 5)](x - 5)

y - 2 = 0.3 x  - 1.5

y = 0.3 x + 0.50       ...2

From equations 1 and 2, then we have

0.3 x + 0.50 = - 2.5 x + 0.50

x = 0

Then the value of y is calculated as,

y = 0.3 (0) + 0.50

y = 0.50

The coordinates of the intersection of the diagonals of the parallelogram will be (0, 0.50).

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Answer:

a = 45

b = 45

c = 73

The order doesn't matter as long as we have two copies of 45 and one copy of 73.

============================================================

Explanation:

If a,b,c are all different values, then there's no way to have a mode since the mode is the most frequent item. We need 45 to repeat itself more than once.

This means either a,b,c are the same value (45) or exactly two of those variables are equal (either a = b, b = c or a = c) to 45.

Let's assume that a = b = c = 45. If so, then

{41,46,a,b,c}

would update to

{41,46,45,45,45}

Adding those items up and dividing by 5 gets us

(41+46+45+45+45)/5 = 44.4

We don't get the mean of 50 we want. So all three a,b,c values cannot be 45.

---------------------------------

Instead, we have the case that exactly two of a,b,c are 45 and the third is something else.

Without loss of generality, let's say a = b = 45 and c is something else.

The set {41,46,a,b,c} updates to {41,46,45,45,c}

Add those values up, divide by 5, and set the result equal to the target goal of 50. The idea is to solve for c.

(41+46+45+45+c)/5 = 50

(177+c)/5 = 50

177+c = 5*50

177+c = 250

c = 250-177

c = 73

As a check,

(41+46+45+45+73)/5 = 50

which works out.

---------------------------------

So that's how we arrive to a = 45, b = 45, c = 73

The order of the letters doesn't matter. We could easily have a = 45, c = 73 and b = 45; or we could have a = 73, b = 45, c = 45.

All that matters is exactly two of the a,b,c are 45 and the third variable is 73.

Answer:

1) 7 because there are 7 dots on 60 minutes and 65 minutes combined.  

2) 26 because you just count all the dots.

Answer:

2

Step-by-step explanation:

y = mx + b

y = 2x + 3

m is the slope. So of we look in the equation 2 is in the m place so 2 is the slope. Hope this helps, thank you :) !!

Answer: x = 2

Step-by-step explanation:

3x - 5 = 1

add 5 to both sides

3x - 5 (+5) = 1 (+5)

3x = 6

divide by 3 on both sides

3x/3 = 6/3

x = 2

Answer:

1) at the highest Point

KE= 0  PE=2116.8 N

2) 3 m above the ground

PE= 529.2 N KE=1587.6 N

3) at the ground

KE= 2116.8 N and PE=0

Step-by-step explanation:

The potential energy is given by

PE= mgh   where m is the mass , g is the acceleration due to gravity which is equal to 9.8 m/s² and h is the height.

The kinetic energy is given by KE= 1/2 mv² where m is the mass of the body and v is the velocity.

1) at the highest Point

Now at the highest point the  velocity is zero

KE= 1/2 mv²

KE= 0

PE = mgh

PE= 18 *9.8* 12= 2116.8 N

Total Energy = KE + PE= 0 + 2116.8 N= 2116.8 N

2) 3 m above the ground

At 3 m above the ground

PE= mgh

PE= 18 *9.8* 3= 529.2 N

According to law of conservation of energy the total energy ( sum of KE and PE)  remains the same at every point.

Total Energy = KE + PE

2116.8 N-529.2N= 1587.6N

KE=1587.6 N

3) at the ground

at the ground the height will be zero

PE= mgh

PE= 18 *9.8* 0= 0 N

According to law of conservation of energy the total energy ( sum of KE and PE)  remains the same at every point.

Total Energy = KE + PE

2116.8 N=2116.8 N + 0

KE= 2116.8 N

or

KE= 1/2 mv²

KE = 1/2* 18 *(15.36)²= 2116.8

The domain of the function f(x) when defined as all real numbers greater than or equal to 3 includes all real numbers to the right of 3 on the number line, while excluding any numbers to the left of 3.

The domain of a function refers to the set of all possible input values for which the function is defined.

The domain for the function f(x) is defined as all real numbers greater than or equal to 3.

We say that the domain is all real numbers greater than or equal to 3, it means that any real number that is greater than or equal to 3 can be used as an input for the function.

This includes all the numbers on the number line to the right of 3, including 3 itself.

If we have an input value of 3, it would be included in the domain because it satisfies the condition of being greater than or equal to 3.

Similarly, any real number larger than 3, such as 4, 5, 10, or even negative numbers like -2 or -5, would also be part of the domain.

Numbers less than 3, such as 2, 1, 0, or negative numbers like -1 or -10, would not be included in the domain.

These numbers are outside the specified range and do not satisfy the condition of being greater than or equal to 3.

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The probability that a  randomly selected bolt will have a diameter greater than 19.705 mm is 0.9812.

Given that:

mean = 19.0

standard deviation = 0.3

P(18.295 < x < 19.705)

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

= P[(18.295 - 19.0)/0.3) < (x-mean)/standard deviation < (19.705-19.0)/0.3)]

= P(-2.35 < z < 2.35)

= P(z<2.35)-P(z<-2.35)

= 0.9906 - 0.0094

= 0.9812

Probability = 0.9812

Hence we get the required probability.

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Answer:

The cosine of angle P = opposite / adjacent = 39 / 80

Step-by-step explanation:

The volume of the triangular prism is 216 ft³.

The prism above is a triangular base prism. Therefore, the volume of the prism can be calculated as follows:

volume of the triangular prism = Bh

where

Therefore,

B = 1 / 2 bh

B = 1 / 2 × 12 × 2

B = 24 / 2

B = 12 ft²

Therefore,

volume of the triangular prism = 12 × 18

volume of the triangular prism = 216 ft³

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Answer: x = 6

Step-by-step explanation:

2x = 7 + 5

x = 12/2 = 6

Answer:

P=106

Step-by-step explanation:

A=a2

P=4a

Solving forP

P=4A=4·702.25=106

Answer:

C

Step-by-step explanation:

702.25 / 4 = 175.5625

Round 175.5625 to 175.56

(sorry if this is confusign)