If Harry flies to the moon at 4000 miles per hour, but returns at 6000 miles per hour, what
is Harry’s average speed of the trip?

For the given data, current value of the gold in which Shelby invested is $1548.60 per ounce which is 38.9% more than its original value then the original purchase price is equal to $1114.90 per ounce.

As given in the question,

Current value of the gold is $1548.60 per ounce

Let x be the original purchase price of the gold invested by Shelby

Current value is 38.9% more than the original value of the gold

Required equation to represent the relation between current value and purchase price is given by:

x + (38.9 x/100) = 1548.60

⇒ ( 100x + 38.9x) /100 = 1548.60

⇒ 138.9x /100 = 1548.60

⇒ x = (1548.60 × 100 ) / 138.9

⇒ x = 1114.90 per ounce

Therefore, for the given data, current value of the gold in which Shelby invested is $1548.60 per ounce which is 38.9% more than its original value then the original purchase price is equal to $1114.90 per ounce.

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Answer:

y > 1/3 x - 3

Step-by-step explanation:

First, it would be easiest to find the equation of the line from the two integer points given, which are (0, -3) and (3, -2).

Find the change of y over the change of x to get the slope of the line.

(-2 - (-3))/(3 - 0) = 1/3

Since the line intercepts the y axis at (0, -3), the equation of the line would be

y = 1/3x - 3

We can see that the shaded portion is above the line, (and that the line is dotted) so this graph represents

y > 1/3 x - 3

Answer:

work is shown and pictured

Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

The annual rate of return on this motorcycle vending machine investment is 7.67%.

To determine the annual rate of return on a motorcycle vending machine that costs $187,400 and generates $2,832 in monthly cash flows for 84 months, follow these steps:

Calculate the total cash flows by multiplying the monthly cash flows by the number of months.

$2,832 x 84 = $237,888

Find the internal rate of return (IRR) of the investment.

$187,400 is the initial investment, and $237,888 is the total cash flows received over the 84 months.

Using the IRR function on a financial calculator or spreadsheet software, the annual rate of return is calculated as 7.67%.

Therefore, the annual rate of return on this motorcycle vending machine investment is 7.67%.

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Answer:

  A  f(x) = x/((x+5)(x-2))

Step-by-step explanation:

The vertical asymptotes at +2 and -5 indicate that (x -(+2)) and (x -(-5)) are factors of the denominator.

The zero at x=0 indicates (x -0) is a factor of the numerator.

The simplest function that will give a graph like this is ...

  f(x) = x/((x +5)(x -2))

we have the expression

we have that

Using the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer.

so

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Answer:

\(x + 2 = - 3x\)

\( - 4x = 2\)

\(x = - \frac{1}{2} \)

\( - 3( - \frac{1}{2} ) = \frac{3}{2} = 1 \frac{1}{2} \)

So the lines intersect at (-1/2, 1 1/2), or

(-.5, 1.5).

Step-by-step explanation:

We're going to be evaluating if we can round 2. (Values in the 10's place)

The value in the 'ones' place has to be greater than or equal to 5 in order to round up 2.

Since 8 is greater than 5, we can round up 2.

Rounded answer:

38830

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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Answer:

124 degrees warmer

Step-by-step explanation:

i think

Answer:

It’s 122 because 80 and -40 is 122.

Step-by-step explanation:

hope this helps

If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch

The area of a triangle is 96 sq. inches

Let base be b

Its altitude is 2 inches greater than five times its base.

a=5b+2

ab/2=A

(5b+2)b/2=96

(5b+2)b=192

5b²+2b=192

5b²2+2b-192=0

On solving the quadrartic equation,

we get

b=6

a=32

Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs

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1) Note that the condition that proves that a quadrilateral is a parallelogram are:

2) The statements from the above list that are specific to a Rhombus are:

3) The figures below that are parallograms are:

Option A

Option B; and

Option D.

A parallelogram is a type of quadrilateral with some special properties. Here are all the qualities of a parallelogram:

Opposite sides are congruent: This means that the two pairs of opposite sides have the same length.

Opposite sides are parallel: This means that the two pairs of opposite sides are always parallel to each other.

Opposite angles are congruent: This means that the two pairs of opposite angles have the same measure.

Consecutive angles are supplementary: This means that any two angles that are adjacent or consecutive to each other add up to 180 degrees.

Diagonals bisect each other: This means that the two diagonals of a parallelogram intersect at their midpoint, and each diagonal divides the parallelogram into two congruent triangles.

Diagonals are not congruent: This means that the two diagonals of a parallelogram have different lengths.

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Answer:

\( \sqrt{50} \)

Step-by-step explanation:

Step 1: Put the line in slope intercept form,

\(x + 7y = 7\)

\(7y = - x + 7\)

\(y = - \frac{x}{7} + 1\)

Step 2: The line that contains the point must be perpendicular to the original line.

So the slope of this line must be 7, and pass through (6,-7).

So we have

\(y + 7 = 7(x - 6)\)

\(y + 7 = 7x - 42\)

\(y = 7x - 49\)

Step 3: Find where the lines intersect at:

Now, we set that equal to -x/7+1

\( \frac{ - x}{7} + 1 = 7x - 49\)

\( - x + 7 = 49x - 343\)

\(350 = 50x\)

\(7 = x\)

So the two lines intersect at (7,y).

To find y, plug in 7 for any function

\( \frac{ - 7}{7} + 1 = 0\)

So y=0.

So the two lines intersect at (7,0).

Step 4: Use distance formula,

Find the distance between (7,0) and (6,-7).

\(d = \sqrt{ (- 7 - 0) {}^{2} + (6 - 7) {}^{2} } \)

\(d = \sqrt{ - 7) {}^{2} + ( - 1) {}^{2} } \)

\(d = \sqrt{50} \)

So the distance to the line root of 50.

The term factored form is an algebraic expression with the product of its factors

Here we need to define the factored form in math.

The factored form in math is known as the process of expressing a given number or algebraic expression as the product of its factors is called factoring.

The following three ways are used to convert any quadratic expression into factored form, that is

1) Finding GCD

2) Use identify that is a² - b²

3) Using the identity (x + a) (x + b).

Basically the factored form of a quadratic equations are very helpful in finding its roots or solutions.

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The temperature variations is represented on the graph attached with the answer.

What is graph?

A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

At 6am it is 56°.For the next 5hours it increases to 61° since it is 1° per hour and after 4 hours again it will increase to 69° because it is 2° per hour and it stayed steady till 6pm and it dropped the next 3 hours which the temperature now reduces to 66° and dropped steadily to 62° at midnight

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Answer:

I am pretty sure it is B

Step-by-step explanation:

1169 sq.rt.=34.190642

34.190642 times 4 =136.7

round to 137

From the calculation that we have done;

Angle B =   80.2°

Angle C = 59.8°

Side c =  20.3

The sine rule, often referred to as the law of sines, is a geometrical concept that links the sines of a triangle's opposite angles to the lengths of its sides. It claims that for all triangle sides and angles, the ratio of a side's length to the sine of its opposite angle is constant.

We have to apply the sine rule in the calculation;

We know that;

a/Sin A = b/SinB

Hence;

15/Sin 40 = 23/SinB

15 Sin B = 23Sin 40

B = Sin-1( 23Sin 40/15)

B = 80.2°

Angle C =

180 - (80.2 + 40)

= 59.8°

Then Side c

c/Sin 59.8 = 15/Sin 40

cSin40 = 15 Sin 59.8

c = 15 Sin 59.8/Sin 40

= 12.96/0.64

= 20.3

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Answer:

$8573.75

Step-by-step explanation:

The value of the car as a function of the number of years (t) is

V = $10,000(1.00-0.05)^t

which, after 3 years, comes to V = $10,000(1.00-0.05)^3 = $8573.75

The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

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The FOIL method, which stands for First, Outer, Inner, Last, is a technique commonly used to multiply binomials.

It involves multiplying the First terms, then the Outer terms, then the Inner terms, and finally the Last terms, and then combining the results. While the FOIL method works well for multiplying binomials, it is not applicable for multiplying all polynomials.

The reason the FOIL method cannot be used to multiply all polynomials is that it only applies to the specific case of multiplying two binomials with two terms each. When dealing with polynomials that have more than two terms or polynomials of higher degrees, the FOIL method does not provide a systematic approach to handle the multiplication.

For example, consider multiplying the polynomial (x + 2) with the polynomial (x^2 + 3x - 4). Applying the FOIL method, we would only multiply the First terms (x * x^2), the Outer terms (x * 3x), the Inner terms (2 * x^2), and the Last terms (2 * -4). However, this approach overlooks the multiplication between the terms of different degrees (e.g., x * 3x or 2 * x^2) and fails to account for all possible combinations.

To multiply more complex polynomials, we typically use more advanced methods such as the distributive property, grouping, or the use of matrices. These methods provide a systematic and comprehensive approach to handle polynomial multiplication in general, accommodating polynomials with any number of terms or degrees.

In summary, while the FOIL method is a helpful technique for multiplying binomials, it cannot be used for multiplying all polynomials due to its limited applicability. For more complex polynomials, alternative methods are necessary to ensure accurate and comprehensive multiplication.

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If 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

Given:

Volume of cube=64cm³

Hence:

Volume of the cube = a³

Volume of the cube, a³= 64 cm³

Using this formula

Cube edge length =∛(side)³

Let plug in the formula

Cube edge length =∛(64cm³)

Cube edge length=4cm

Therefore if 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

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The interval in which the function h(x) = 5x³ - 3x^5 is increasing is given as follows:

(−1,0)∪(0,1).

The function in this problem is defined as follows:

h(x) = 5x³ - 3x^5.

To obtain the intervals for increase of decrease, the critical points of the function need to be obtained, which are the values of x for which the derivative is of zero.

The derivative of the function in this problem is given as follows:

h'(x) = 15x² - 15x^4.

Hence the critical points of the function are given as follows:

15x² - 15x^4 = 0

15x²(1 - x²) = 0.

Hence:

Then the signals of the derivative in each interval is given as follows:

The function is increasing when the derivative is positive, hence the interval is given as follows:

(−1,0)∪(0,1).

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Answer:

it's 4.

Step-by-step explanation:

Answer:

4

Step-by-step explan

cus

1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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The solution of the linear expression is (x, y) = ( -3, -1/2)

option A.

The values of x and y in the given linear expression is calculated by applying the following formula.

y = ¹/₂ˣ  + 1

y = ³/₂ˣ + 4

solve the two equations together to determine the value of x ;

³/₂ˣ + 4 =  ¹/₂ˣ  + 1

³/₂ˣ -   ¹/₂ˣ   = 1 - 4

x = - 3

Now, solve for y as show below;

y = ¹/₂ˣ  +  1

y =   ¹/₂(-3)  + 1

y = -3/2 + 1

y = -1/2

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Answer: Mari earns 320 and jen earns 160

The base area of the second container is 281.25. Two right prism containers each hold 75 gallons of water. The height of the first container is 20 inches, and the height of the second container is unknown.

Given that the base area of the first container is known, we need to find the base area of the second container.

A right prism is a three-dimensional shape that has two parallel and congruent polygonal bases connected by rectangular sides. The volume of a right prism is given by the product of the base area and the height of the prism. Since both containers hold the same volume of water, their heights are inversely proportional to their base areas. Let the base area of the first container be A, and the height of the second container be h. Then we have:

75 = A * 20 and 75 = h * B

where B is the base area of the second container. Solving for A and B, we get:

A = 75/20 = 3.75 square inches and B = 75/h

Multiplying the two equations, we get:

A * B = 75/20 * 75/h = 281.25/h

Thus, the base area of the second container is 281.25 divided by its height in inches. Note that the units of A and B are square inches since they represent areas of the bases.

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