A planet travels 5.782× 10⁸ km in its orbit each day .How far will it travel in 800 years ? Use 1 year ≈ 365.25 days.​

The key features of f(x) = 2√[x + 7] - 1 are

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

f(x) = 2√[x + 7] - 1

The graph of the function is attached, where we have the following features

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1.) The probability that the spinner will land on C would be = 1/8

2.) The probability of not spinning on C would be = 7/8

To calculate the probability the formula that should be used would be as follows;

Probability = possible outcome/sample space.

For question 1.)

sample space = 8

possible outcome = 1

probability = 1/8

For question 2.)

sample space = 8

possible outcome = 7

probability = 7/8

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Answer: What is a Distributive Law?

Step-by-step explanation:

Distributive law, also called distributive property, in mathematics, the law relating the operations of multiplication and addition, stated symbolically as a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac. From this law it is easy to show that the result of first adding several numbers and then multiplying the sum by some number is the same as first multiplying each separately by the number and then adding the products.

{Hope This Helps :)}

Multiplying a number by a group of numbers adding together is called distructive law

When the volume of the triangular block is 4 cubic inches, the approximate length of y is 2.8 inches.

volume = 1/2 x A x C x H = 4 cubic inches

Because the volume of the triangular block is 4 cubic inches.

Formula:

A x C = Base x Height

= 2.8 inches will be the approximate lenght of the y.

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a) The probability of picking a blue tile = 1/5

b) The probability of picking a yellow tile = 1/2

c) The probability of picking a red tile = 3/10

Given data ,

Let the total number of tiles in the bag = 10 tiles

The number of blue tiles = 2

The number of red tiles = 3

The number of yellow tiles = 5

So , probability of picking a blue tile = 2/10 = 1/5

Now , probability of picking a yellow tile = 5 / 10 = 1/2

And , probability of picking a red tile = 3/10

Hence , the probability is solved

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The value of the product is 1/4

To determine the value of the product, we need to take note that fractions are described as the part of a whole number, element, or variable.

In mathematics, there are different types of fractions, namely;

From the information given, we have that;

1/4 × 25/25

Now, multiply the numerators

25/4(25)

Multiply the denominators

25/100

Divide the values

1/4

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Answer: 60 seconds

Step-by-step explanation:

Answer:

Step-by-step explanation:

60 seconds

The equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x-0)² + (y-3)² = 6²

The standard form for finding the equation of a circle is expressed as;

(x-a)² + (y-b)²=r²

where;

(a, b) is the center of the circle

r is the radius of the circle

Given the following diameter = 12 units

radius = 12/2 = 6 units

If the centre lies on the y-axis, the center will be at (0, 3)

Substituting into the formula, we will have (x-0)² + (y-3)² = 6² equivalent to x²+ (y-3)² = 36

Hence, the equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x-0)² + (y-3)² = 6²

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In statistical analysis, variables are often used to describe and explain relationships between different variables or to predict outcomes based on certain variables.

In statistics, a variable is a characteristic or attribute that can take on different values or levels for different individuals or objects being studied. Variables can be classified as either quantitative or qualitative.

Quantitative variables are numerical in nature and can be further classified as discrete or continuous. Discrete variables can only take on specific values (such as the number of children in a family), while continuous variables can take on any value within a certain range (such as a person's height or weight).

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Answer:

Hope this helps!

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

Answer:

1) The sum of the distances between the points on the ellipse and the foci is constant, whereas the difference between the distances between the points on the hyperbola and the foci is constant.

2) The equation of an ellipse is in the form (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axes, respectively. In contrast, the equation of a hyperbola is in the form (x^2/a^2) - (y^2/b^2) = 1, where a and b are also the lengths of the semi-major and semi-minor axes, respectively, but the difference between a and b determines the shape of the hyperbola.

Step-by-step explanation:

The number of djembe drum sold is 8

Profit is the money you have left after paying for business expenses. This means after deducting the money of expenses from the selling price , the remainder is profit.

Therefore , profit = selling price - cost price

set of claves = $5

set of maracas = $14

a drum = $16

Selling price of drum = 16 × x =16x

selling price of claves = 6×5 = 30

selling price of maracas = 14 × 12 = 168

total selling price =$( 16x+30+168)

cost price = 326-( 16x+30+168)

Therefore,

326 = 16x+30+168-(326-16x-30-168)

326 = 16x +30+168-326+16x+30+168

326 = 32x+60+336-326

326+326-336-60 = 32x

32x = 256

divide both sides by 32

x = 256/32

x = 8

Therefore the number of drums sold is 8

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a. The solution to the equation f - 13 = 51 is f = 64.

b. The solution to the equation x/10 = 4 is x = 40.

a. f - 13 = 51

Step 1: Add 13 to both sides to isolate f.

f - 13 + 13 = 51 + 13

Step 2: Simplify.

f = 64

Step 3: Check the answer by substituting f = 64 back into the original equation.

64 - 13 = 51

51 = 51

The answer checks out.

b. (x/10) = 4

Step 1: Multiply both sides by 10 to isolate x.

10(x/10) = 4(10)

Step 2: Simplify.

x = 40

Step 3: Check the answer by substituting x = 40 back into the original equation.

40/10 = 4

4 = 4

The answer checks out.

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The data plot in the line plot are skewed right

Given data ,

Let the data be shown in the graph be a line plot

Now , A line plot, also known as a dot plot, is a graphical representation of data where data points are shown as dots along a number line.

A right-skewed line plot would have more dots towards the lower end of the number line, with fewer dots towards the higher end.

From the line plot , we can see that most data points are placed on the lower end of the line plot

Hence , the data is skewed right

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a) The total amount of money earned is 7.30 dollars.

b) Max is wrong, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.

a) To find the total amount of money earned, we need to convert the number of quarters and dimes to dollars.

6 quarters = 6 * 0.25 = 1.50 dollars

8 dimes = 8 * 0.10 = 0.80 dollars

The total amount of money earned is:

5 dollars + 1.50 dollars + 0.80 dollars = 7.30 dollars

b) Max is incorrect. The total amount of money earned is an odd number ($7.30), which means it is impossible to divide it equally between two people in whole dollar amounts. However, it is possible to divide the total amount equally if we allow for fractions of a dollar.

For example, if we split the money equally, Gwen and Max would each get $3.65. This means that Gwen would get 3 dollars and 65 cents, while Max would also get 3 dollars and 65 cents.

Therefore, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.

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Answer:

2

Step-by-step explanation:

Slope, the measure of the steepness of the line created by these 2 points, is calculated by taking the difference in "y"s divided by the difference in "x"s. The equation is (y2-y1)/(x2-x1) 2 being the coordinate in the second point, and 1 the coordinate in the first point.

((-12)-(-4))/((-1)-3)

The -(-4) turns into +4, so the top is (-12+4)

(-8)/(-4) = 2

a. If Jennifer has begun construction on the home and plans to live in it in 12 months from the time construction began, the interest she pays on the loan can be treated as deductible mortgage interest.

This is because the IRS allows interest on loans for the construction or purchase of a second home to be deductible if the home will be used as a qualified residence within 24 months.

b. If Jennifer hasn't begun construction on the home but plans to live in it in 15 months, the interest she pays on the loan can still be treated as deductible mortgage interest. As long as she starts construction and completes it within 24 months, making the home a qualified residence, the interest remains deductible.

c. If Jennifer has begun construction on the home but doesn't plan to live in it for 37 months from the time construction began, the interest on the loan is not deductible as mortgage interest. This is because the home won't be used as a qualified residence within the 24-month time frame allowed by the IRS.

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The number of seconds where the football hit the ground is 2 seconds

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

The graph

The number of seconds where the football hit the ground is when the graph intersects with the x-axis at the second time

In this case, the point is (2, 0)

Also, the seconds is represented by x

So, we have

x = 2

Hence, the seconds the football hits the ground is 2

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The nature of the roots of a quadratic equation in which case, the discriminant is; 81 is; The roots are 2 distinct real roots.

It follows from the task content that the nature of the roots of a quadratic equation in which case, the discriminant is 81 is to be determined.

Recall; when the discriminant of a quadratic equation is greater than 0; the equation is said to have two real distinct roots.

Ultimately, for the given equation in discuss whose discriminant is 81 is such that; it has two real distinct roots.

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Therefore, the statement is false in general, and the equality Dkf(x, y, z) = fz(x, y, z) holds only when k = z.

The symbol Dk denotes the k-th partial derivative with respect to the variable k, so Dkf(x, y, z) denotes the partial derivative of f(x, y, z) with respect to the variable k.

On the other hand, fz(x, y, z) denotes the partial derivative of f(x, y, z) with respect to the variable z.

These two partial derivatives are generally not equal. For example, consider the function f(x, y, z) = x² + y² + z². Then:

Dxf(x, y, z) = 2x

Dyf(x, y, z) = 2y

Dzf(x, y, z) = 2z

In this case, we have Dzf(x, y, z) = fz(x, y, z) = 2z, so the statement is true when k = z.

However, if we consider k = x or k = y, then the statement is false in general. For example, when k = x, we have:

Dkf(x, y, z) = Dxf(x, y, z) = 2x

fz(x, y, z) = partial derivative of f with respect to z = 2z

Since 2x is generally not equal to 2z, the statement is false when k = x.

Similarly, the statement is false when k = y, because Dyf(x, y, z) is generally not equal to fz(x, y, z).

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(–2, 6) are the points that justify the shaded area

We can substitute the values of x and y from each point into the inequality and check if the inequality is satisfied or not.

Let's check each point:

For points (12, 6):

[tex](y+1)^2/6 -(x+2)^2/24\\ = (6+1)^2/6 - (12+2)^2/24 \\= 49/6 - 196/3 \\= -57.33[/tex]

Here, the value of the expression is less than 1, so this point does not justify the shaded area.

For points (–2, 6):

[tex](y+1)^2/6 -(x+2)^2/24\\ = (6+1)^2/6 - (-2+2)^2/24 \\= 49/6[/tex]

Here, the value of the expression is greater than or equal to 1, so this point does justify the shaded area.

For points (8, –6):

[tex](y+1)^2/6 -(x+2)^2/24 \\= (-6+1)^2/6 - (8+2)^2/24 \\= 25/6-100/24[/tex]

Here, the value of the expression is greater than or equal to 1, so this point does not justify the shaded area.

For point (–1, –2):

[tex](y+1)^2/6 -(x+2)^2/24 \\= (-2+1)^2/6 - (-1+2)^2/24 \\= 1/6 - 1/24 \\= 1/8[/tex]

Here, the value of the expression is less than 1, so this point does not justify the shaded area.

Therefore, the points that justify the shaded area are (–2, 6).

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a. The prime numbers in this list are 5 and 7. b. There are no prime numbers in this list. c. The prime numbers in this list are 31 and 17. d. The prime numbers in this list are 61 and 2.

a. In the list 5, 7, 12, 11, the prime numbers are 5, 7, and 11. Prime numbers are numbers greater than 1 that have only two factors, 1 and themselves.

b. In the list 14, 6, 3, the prime number is 3. The other numbers have more than two factors, making them not prime.

c. In the list 31, 17, 9, 15, the prime numbers are 31 and 17. The numbers 9 and 15 have more than two factors, so they are not prime.

d. In the list 782, 61, 2, the prime numbers are 61 and 2. Number 2 is the smallest prime number, and 61 has only two factors, 1 and 61. The number 782 has more than two factors, so it is not prime.

To summarize, the prime numbers in each list are: a. 5, 7, 11; b. 3; c. 31, 17; d. 61, 2.

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Answer:

If a = -2 and b = 3, then b^a can be calculated as follows:

b^a = 3^(-2)

To find the value of 3^(-2), we can use the rule that says:

a^(-b) = 1 / a^(b)

Thus,

3^(-2) = 1 / 3^2 = 1 / 9

Therefore, the value of b^a, or 3^(-2) is 1/9.

Step-by-step explanation:

The lengths of the longest sides of the triangles are 40 and 16.

The lengths of each side of the triangle is calculated as follows;

Let the longest side of the similar triangle = L

then the longest side of the triangle = 3L - 8

The value of L or the longest side is calculated by applying congruency theorem for the similar triangles.

L/6 = (3L - 8)/15

15L = 6 (3L - 8)

15L = 18L - 48

15L - 18L = -48

-3L = -48

L = 48/3

L = 16

The second triangle, = 3L - 8

= 3 x 16 - 8

= 40

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1. Shade Tolerance: The blend needs to score at least 300 points for shade tolerance.
Total: x * Shade Tolerance points + y * Shade Tolerance points ≥ 300
2. Traffic: The blend needs to score at least 400 points for traffic.
Total: x * Traffic points + y * Traffic points ≥ 400
3. Drought Resistance: The blend needs to score at least 750 points for drought resistance.
Total: x * Drought Resistance points + y * Drought Resistance points ≥ 750

To determine the number of pounds of each seed that should be in the blend, we need to use a system of equations. Let x be the number of pounds of type A seed and y be the number of pounds of type B seed in the blend.

The shade tolerance score for the blend can be expressed as:

x(80) + y(200) ≥ 300

The traffic score for the blend can be expressed as:

x(120) + y(100) ≥ 400

The drought resistance score for the blend can be expressed as:

x(200) + y(150) ≥ 750

We also know that the total amount of seed in the blend is x + y.

We want to minimize the costs of the blend, so we can set up the following equation for the total cost:

1x + 2y = Total cost

Now we can solve this system of equations using any method we prefer. One common method is to use substitution.

First, we can use the shade tolerance equation to solve for y in terms of x:

y ≥ (300 - 80x)/200

Next, we can substitute this expression for y in the traffic equation:

x(120) + ((300 - 80x)/200)(100) ≥ 400

Simplifying and solving for x, we get:

x ≥ 1.5

So the minimum amount of type A seed needed in the blend is 1.5 pounds. We can use this value to solve for y:

y ≥ (300 - 80(1.5))/200 = 1.05

So the minimum amount of type B seed needed in the blend is 1.05 pounds.

Since we want to minimize costs, we want to use the minimum amount of each seed necessary to meet the requirements. Therefore, we should use 1.5 pounds of type A seed and 1.05 pounds of type B seed in the blend.

We need the values for Shade Tolerance, Traffic, and Drought Resistance points for both Type A and Type B seeds to set up the inequalities. Please provide the points for each seed type, and I can help you determine the number of pounds needed for each seed in the blend.

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To construct the incenter of a triangle, construct the angle bisectors of each angle of the triangle. Here are the steps to construct the incenter of a triangle:

Draw the three sides of the triangle using a straightedge.

Choose one of the angles of the triangle and draw its bisector. To do this, place the point of your compass on the vertex of the angle, and draw an arc that intersects both sides of the angle. Without changing the width of your compass, place it on each of the two points where the arc intersects the sides of the angle, and draw two more arcs that intersect. The point where these two arcs intersect is the point where the angle bisector meets the opposite side of the triangle.

Repeat step 2 for the other two angles of the triangle. You should now have three lines that intersect at a single point.

The point where all three angle bisectors intersect is the incenter of the triangle.

Note that the incenter of a triangle is the center of the circle that can be inscribed inside the triangle.

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The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.

Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
 To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.

Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25

Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211

Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709

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Answer:

3 yards or option D.

Step-by-step explanation:

We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

We are given that the volume of the shower is 7.5 cubic yards, and the area of the base is 2.5 square yards. We can use the area of the base to find the length and width of the shower, since the base is a rectangle.

Area of base = length x width

2.5 = length x width

We are not given the length or width, but we can solve for one of them in terms of the other:

length = 2.5/width

Now we can substitute this expression for length into the formula for volume:

Volume = length x width x height

7.5 = (2.5/width) x width x height

Simplifying, we can cancel out the width terms:

7.5 = 2.5 x height

Dividing both sides by 2.5, we get:

3 = height