A zoologist recorded the speed of two cheetahs. Cheetah A ran 18 miles in 16 minutes. Cheetah B ran 54 miles in 50 minutes. Which statement is correct?

Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50.
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is less than 54 over 50.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Both cheetahs have the same ratio of miles per minute.

Answer:

7

Step-by-step explanation:

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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Answer:

a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°

Answer:

Step-by-step explanation:

eur / riu8 / + |5x5| = 9

0

2

0

4

3

6

Y-Intercept = 9

LL

8

Answer:

3n+3

Step-by-step explanation:

First, we can see that there is a "-" sign before the values in parenthesis.  This means there is an "invisible" 1 there, so we have to distribute this -1 to all numbers in parenthesis, or in simple terms, we have to flip the signs of the numbers in parenthesis.

7n - 4n + 3

We can combine like terms, 7n and -4n to get 3n.

3n + 3

This is the answer, hope this helps! :)

The calculated value of x and the measure of angle c are 29 and 93, respectively

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

The triangle (see attachment)

The sum of angles in a triangle is 180 degrees

So, we have

3(x + 2) + 35 + 52 = 180

Evaluate the like terms

So, we have

3(x + 2) = 93

Divide through by 3

x + 2 = 31

So, we have

x = 29

From the figure, we have

C = 3(x + 2)

This means that

C = 3(29 + 2)

Evaluate

C = 93

Hence, the value of x and the measure of angle c are 29 and 93, respectively

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For the triangle, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles of a triangle.

The correct option (d): a ≈ 14.9, C ≈ 24.1, B ≈ 104.9.

We have,

A = 51° (angle opposite side a)

b = 14

c = 6

Using the Law of Sines, we have:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values, we get:

a/sin(51°) = 14/sin(B) = 6/sin(C)

To find angle B, we can use the equation:

sin(B) = (b * sin(A))/a

sin(B) = (14 * sin(51°))/a

Now, let's calculate the values using the options:

a) No triangles possible: This option can be eliminated since the given side lengths satisfy the triangle inequality.

b) a ≈ 14.9, C ≈ 28.1, B ≈ 100.9:

Using the equation sin(B) = (14 * sin(51°))/a, we find sin(B) ≈ (14 * sin(51°))/14.9 ≈ 0.725.

Taking the arcsin of 0.725, we find B ≈ 46.3°.

c) a ≈ 11.2, C ≈ 24.1, B ≈ 104.9:

Using the equation sin(B) = (14 * sin(51°))/a, we find sin(B) ≈ (14 * sin(51°))/11.2 ≈ 1.022.

Since the sine value cannot exceed 1, this option can be eliminated.

d) a ≈ 14.9, C ≈ 24.1, B ≈ 104.9:

Using the equation sin(B) = (14 * sin(51°))/a, we find sin(B) ≈ (14 * sin(51°))/14.9 ≈ 0.725.

Taking the arcsin of 0.725, we find B ≈ 46.3°.

Therefore, the correct answer is option (d): a ≈ 14.9, C ≈ 24.1, B ≈ 104.9.

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If Q is directly proportional to r, when r is 45, the value of Q is 171.

If Q is directly proportional to r, we can express this relationship using the formula Q = k x r, where k is the constant of proportionality. To find the value of k, we can use the given information that Q is 76 when r is 20.

Substituting these values into the formula, we have:

76 = k x 20

To solve for k, we divide both sides of the equation by 20:

k = 76 / 20

k = 3.8

Now that we know the value of k, we can use it to find Q when r is 45:

Q = k x r

Q = 3.8 x 45

Q = 171

Therefore, when r is 45, Q is 171.

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Using a z-table or calculator, the p-value is approximately 0.2266. This represents the probability of observing a z test statistic of -0.75 or less, assuming the null hypothesis is true.

Based on the information provided, you are conducting a left-tailed test for the null hypothesis H0: π1 - π2 ≥ 0.20, and the z test statistic is -0.75. To find the p-value for this test, you'll need to look up the corresponding probability in a standard normal (z) distribution table or use a calculator with a built-in function.
The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the one calculated, given that the null hypothesis is true. Since this is a left-tailed test, you will look up the probability of getting a z-score of -0.75 or lower.
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The probability histogram to the right represents the number of live births by a mother 51 to 54 years old who had a live birth in 2012 to have had 1.75 live births (rounded to one decimal place). This means that on average, we would expect these mothers to have had between one and two live births.

(a) To find the probability that a randomly selected 51- to 54-year-old mother who had a live birth in 2012 has had her fourth live birth, we need to look at the histogram and locate the bar for the fourth live birth. We can see that the height of this bar is 0.1. Therefore, the probability is 0.1 or 10% (as a decimal).

(b) To find the probability that a randomly selected 51- to 54-year-old mother who had a live birth in 2012 has had her fourth or fifth live birth, we need to add the heights of the bars for the fourth and fifth live births. The height of the fourth live birth bar is 0.1 and the height of the fifth live birth bar is 0.05. Therefore, the probability is 0.1 + 0.05 = 0.15 or 15% (as a decimal).

(c) To find the probability that a randomly selected 51- to 54-year-old mother who had a live birth in 2012 has had her sixth or more live birth, we need to add the heights of the bars for the sixth or more live births. The height of the bar for six or more live births is 0.05. Therefore, the probability is 0.05 or 5% (as a decimal).

(d) To find how many live births we would expect a randomly selected 51- to 54-year-old mother who had a live birth in 2012 to have had, we need to find the mean of the distribution. We can do this by multiplying each number of live births by its corresponding probability and adding up the products.

Expected value = (0 x 0.2) + (1 x 0.15) + (2 x 0.15) + (3 x 0.2) + (4 x 0.1) + (5 x 0.05) + (6 x 0.05)
Expected value = 1.75

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1. f(216) is equal to 3.

2. The solution x = 3 is valid.

3. p(x) = x⁴ - 2x³ - 14x² - 2x - 15, the maximum number of real roots is 4.

1. To find f(216) when f(x) = log(x), we substitute 216 for x in the function:

f(216) = log₆(216)

= log₆(6³)

= 3 log₆(6)

= 3 x 1

= 3

Therefore, f(216) is equal to 3.

2. To solve the equation √(6x - 3) = √(4x + 3), we can square both sides of the equation to eliminate the square roots:

(√(6x - 3))² = (√(4x + 3))²

6x - 3 = 4x + 3

6x - 4x = 3 + 3

2x = 6

x = 3

Since both sides of the equation are equal, the solution x = 3 is valid.

3. For the function p(x) = x⁴ - 2x³ - 14x² - 2x - 15,

we can determine the maximum number of real roots by examining the degree of the polynomial.

The highest power of x in the polynomial is 4, which means the polynomial is of degree 4.

Therefore, in the given polynomial p(x) = x⁴ - 2x³ - 14x² - 2x - 15, the maximum number of real roots is 4.

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The standard form of the equation of a parabola with a vertical axis of symmetry is (x-h)^2 = 4p(y-k), where (h,k) is the vertex and p is the distance from the vertex to the focus/directrix.

In this case, the vertex is at (0,9) (since the directrix is a vertical line and the focus is above it) and the distance from the vertex to the focus/directrix is 9.
Therefore, p = 9 and the equation is (x-9)^2 = 36(y-9).
Note that the directrix being a vertical line means the parabola is opening upwards. The standard form of the equation of a parabola with a focus at (h, k) and a directrix at x = d is given by (x - h)^2 = 4p(y - k), where p is the distance between the focus and directrix.
In this case, the focus is at (9, 9) and the directrix is at x = -9. The distance between them, 2p, is 9 - (-9) = 18, so p = 9. Thus, the standard form of the equation of the parabola is:
(x - 9)^2 = 4(9)(y - 9)
Simplified, this becomes:
(x - 9)^2 = 36(y - 9)
This is the standard form of the equation of the parabola with the given characteristics.

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The relationship between the number of months after the first year and the amount remaining on the card is y = - 2.5 x + 25.

The independent variable is number of months after the first year.

The dependent variable is the amount remaining on the card.

The relationship between the number of months after the first year would be:

Amount remaining = Starting value - ( Amount decreasing by x Number of months )

y = 25 - ( 2. 50 x )

This can be written as:

y = - 2. 50 x + 25

The independent variable is the x value and as shown above, this is the number of months after the first year. This then means that the dependent variable would the amount remaining.

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The average speed of Renee over the last 2 hours of her trip is 9 miles/hour.

Let the average speed of Renee in 2 hours in between 6th and 8th hour be x miles / hours.

So the distance covered by Renee in 6 hours is = 6x

So the distance covered by Renee in 8 hours is = 8x

So the distance covered by Renee in this 2 hours in between 6th and 8th hours is = 8x - 6x

So according to the information the distance covered by Renee in this same 2 hours = 74 - 56 = 18 miles.

The equation best situated to the situation is,

8x - 6x = 18

2x = 18

x = 18/2

x = 9

Hence the average speed of Renee over the last 2 hours of her trip is 9 miles/hour.

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The value of a is 1.2 if the function f(x)= (5x-2)((a/x) +3)  is an odd function

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

f(x)= (5x-2)((a/x) +3)

The function is an odd function

So, we have

−f(x) = f(−x)

Using the above as a guide, we have the following:

f(-x)= (5(-x) - 2)((a/-x) + 3)

-f(x)= -(5x-2)((a/x) +3)

When equated, we have

(5(-x) - 2)((a/-x) + 3)  = -(5x-2)((a/x) +3)

So, we have

(-5x - 2)(-(a/x) + 3)  = (-5x + 2)((a/x) + 3)

Open the brackets

5a - 15x + 2a/x - 6 = -5a - 15x + 2a/x + 6

Evaluate the like terms

5a - 6 = -5a + 6

So, we have

10a = 12

Divide

a = 1.2

Hence, the value of a is 1.2

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A credit score is a measure of the ability to repay a debt. Like any usual unit of measurement, the more the credit score, the better it is.

A credit score ranges from 300 to 900 points. It is usually placed on a scale that is categorized from bad to good. A good credit score increases the chances of an individual to avail of loans and credit services. The better the score, the better the services.

If the score lies between 350-549, it is considered a low score and need urgent action to improve. If the score is between 550-649, the approval probability is doubtful and turbulent. If the score is between 650-699, it is considered satisfactory. If the score is between 700-749, it is considered good. If it is between 750-900, it is an excellent credit score.

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The answer of the given question is Integration testing.

Integration testing is a form of testing that involves linking all of the individual components together and testing them as a group to uncover any defects between individual components.

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Integration testing is a form of testing that involves linking all of the individual components together and testing them as a group to uncover any defects between individual components.

Integration testing focuses on the interactions between different components of a system. It aims to identify any issues that may arise when the components are combined, such as communication errors, data discrepancies, or incorrect functional behavior. This type of testing is typically performed after unit testing, which tests individual components in isolation, and before system testing, which evaluates the entire system's functionality.

In summary, integration testing is a crucial step in the software testing process that ensures individual components work together seamlessly, helping to identify and resolve defects that may occur when these components are connected.

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Answer:

  vertical asymptote: x = 3

  slant asymptote: y = x+5

Step-by-step explanation:

You want the vertical and slant asymptote of the graph of the rational function ...

  y = (x² +2x -3)/(x -3)

Using synthetic division (see the first attachment), we find the quotient to be (x+5) and the remaining rational function term to be 12/(x-3).

There is a vertical asymptote at the value of x where the denominator is zero: x = 3.

The slant asymptote is the polynomial part of the quotient:

  y = x +5

The asymptotes are the orange dashed lines in the second attachment.

<95141404393>

The region in the first quadrant bounded above by the curve [tex]y = x^2[/tex] and y = 4 is the area between the x-axis, the curve [tex]y = x^2[/tex], and the horizontal line y = 4.

In the first quadrant, the curve [tex]y = x^2[/tex] is a parabola that opens upward. The line y = 4 is a horizontal line parallel to the x-axis. To determine the region bounded above by these two curves, we need to find the x-values where the curve [tex]y = x^2[/tex] intersects with the line y = 4.

Setting[tex]y = x^2[/tex] equal to y = 4, we have x² = 4. Solving for x, we find two solutions: x = 2 and x = -2. However, since we are interested in the first quadrant, we consider only the positive solution, x = 2.

Thus, the region in the first quadrant bounded above by the curve[tex]y = x^2[/tex]and y = 4 is the area between the x-axis and the curve [tex]y = x^2[/tex], from x = 0 to x = 2. This region can be visualized as the space beneath the curve [tex]y = x^2[/tex] and above the line y = 4 in the first quadrant.

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Value after t years: V4(t) =[tex]24500 \times (0.8636)^t[/tex]

To determine the value of each car after a given amount of time, we can use the depreciation formula:

Value = Initial Value * (1 - Depreciation Rate)^n

where "Initial Value" is the starting value of the car, "Depreciation Rate" is the rate at which the car depreciates, "n" is the number of time periods elapsed.

Let's calculate the value of each car after "t" amount of years:

Car 1:

Initial Value: $15,000

Depreciation Rate: 5% annually

Value after t years: V1(t) =[tex]15000 \times (1 - 0.05)^t[/tex]

Car 2:

Initial Value: $11,250

Depreciation Rate: 1.2% quarterly

Since the depreciation rate is quarterly, we need to adjust it to match the number of years:

Adjusted Depreciation Rate: (1 - 0.012)^4 = 1 - 0.0488 = 0.9512

Value after t years: V2(t) = [tex]11250 \times(0.9512)^t[/tex]

Car 3:

Initial Value: $16,999

Depreciation Rate: 1.5% monthly

Adjusted Depreciation Rate: (1 - 0.015)^12 = 1 - 0.1779 = 0.8221

Value after t years: V3(t) = 16999 * (0.8221)^t

Car 4:

Initial Value: $24,500

Depreciation Rate: 2.5% bimonthly

Adjusted Depreciation Rate: (1 - 0.025)^6 = 1 - 0.1364 = 0.8636

Value after t years:[tex]V4(t) = 24500 \times (0.8636)^t[/tex]

These equations can be used to calculate the value of each car after a specific number of years, "t".

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Answer:

Step-by-step explanation:

your mom

The Ordering them from least to greatest: -3.75, -3, 3.1, 3.5, 31/5

To evaluate the given expressions and order them from least to greatest in value:

|3.1|

= 3.1 (since the absolute value of a positive number is the number itself)

-3

-3.75

|-3 1/2| = 3.5

(since the absolute value of a negative number is the positive value of that number)

|-31/5| = 31/5

(since the absolute value of a fraction is the positive value of that fraction)

Ordering them from least to greatest:

-3.75, -3, 3.1, 3.5, 31/5

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Answer:

36

Step-by-step explanation:

.04(900) = 36

4% is .04 as a decimal

Helping in the name of Jesus.

Answer: To find the perimeter of a parallelogram, we need to find the lengths of its sides. The sides of the parallelogram can be determined by calculating the distance between the given points.

Using the distance formula, the lengths of the sides can be calculated as follows:

Side IJ:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((-4 - (-4))^2 + (-3 - 5)^2)

Distance = √(0^2 + (-8)^2)

Distance = √(0 + 64)

Distance = √64

Distance = 8

Side JK:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((5 - (-4))^2 + (-8 - (-3))^2)

Distance = √((5 + 4)^2 + (-8 + 3)^2)

Distance = √(9^2 + (-5)^2)

Distance = √(81 + 25)

Distance = √106

Distance ≈ 10.3 (rounded to the nearest tenth)

Side KL:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((5 - 5)^2 + (0 - (-8))^2)

Distance = √(0^2 + 8^2)

Distance = √(0 + 64)

Distance = √64

Distance = 8

Side LI:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((-4 - 5)^2 + (5 - 0)^2)

Distance = √((-9)^2 + 5^2)

Distance = √(81 + 25)

Distance = √106

Distance ≈ 10.3 (rounded to the nearest tenth)

Now, we can calculate the perimeter by adding up the lengths of all four sides:

Perimeter = IJ + JK + KL + LI

Perimeter = 8 + 10.3 + 8 + 10.3

Perimeter ≈ 36.6 (rounded to the nearest tenth)

Therefore, the perimeter of the parallelogram IJKL is approximately 36.6 units.

The ratio that shows the square feet per the flower is 14 / 1.

Kristina has an area of 70 square feet for a flower garden. she plants 5

varieties of flowers equally in her garden.

Therefore, the ratio that shows the square feet per the flower type can be calculated as follows:

ratio = square feet / flower type

ratio = 70 / 5

Therefore,

ratio of the square feet per flower  = 70 / 5

ratio of the square feet per flower  = 14 / 1

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The equation that would best be solved using completing the square is:

2x² + 15x = 6.

Option A is the correct answer.

We have,

Completing the square is a useful technique to solve quadratic equations, particularly when the coefficient of the x² term is not 1.

In this case,

The equation 2x² + 15x = 6 is a quadratic equation with a coefficient of 2 for the x² term.

To solve this equation using completing the square, we follow these steps:

- Move the constant term to the other side of the equation:

2x² + 15x - 6 = 0.

- Divide the entire equation by the coefficient of the x² term (2) to make the coefficient 1:

x² + (15/2)x - 3 = 0.

- Take half of the coefficient of the x term (15/2) and square it:

(15/2) / 2 = 15/4,

(15/4)² = 225/16.

- Add the calculated value to both sides of the equation:

x² + (15/2)x + 225/16 - 3 = 225/16,

x² + (15/2)x + 201/16 = 225/16.

- Rewrite the left side of the equation as a perfect square trinomial:

(x + (15/4))² = 225/16.

- Take the square root of both sides of the equation, considering both the positive and negative square roots:

x + (15/4) = ±√(225/16).

Solve for x:

x = -15/4 ± √(225/16).

Therefore,

The equation 2x² + 15x = 6 is best solved using completing the square.

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Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

The measures of position that divide a set of data into four equal parts are called quartiles.

Quartiles are statistical measures that divide a dataset into four equal parts, each containing approximately 25% of the data. These quartiles are denoted as Q1, Q2, and Q3.

Q1, also known as the first quartile or the 25th percentile, represents the value below which 25% of the data falls. It splits the lowest 25% of the dataset from the rest.

Q2, also known as the second quartile or the 50th percentile, is the median of the dataset. It represents the value below which 50% of the data falls, dividing the dataset into two equal parts.

Q3, also known as the third quartile or the 75th percentile, represents the value below which 75% of the data falls. It separates the highest 25% of the dataset from the rest.

These quartiles are useful in analyzing the distribution and dispersion of data, providing insights into the spread and central tendency.

They are commonly used in box plots, where the box represents the interquartile range (IQR), which is the range between Q1 and Q3, while the line inside the box represents the median (Q2).

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Properties 1, 2, 3, and 4 apply to the function y = 3x + 1.

The function y = 3x + ln(e) can be simplified to y = 3x + 1 because ln(e) = 1. Now, we can analyze the properties:

1. The function is increasing for −∞ < x < ∞, because the coefficient of x is positive (3).
2. The domain of the function is (−∞, ∞) as there are no restrictions on x.
3. The range of the function is (−∞, ∞) as the output can take any real value.
4. The function is one-to-one, as it is a linear function with a non-zero slope.
5. The graph does not have an asymptote, since it is a linear function without restrictions.
6. The function is not decreasing for −∞ < x < ∞, as it is increasing.
7. The function is not a polynomial function, because the ln(e) term is a constant that comes from the natural logarithm function, which is not a polynomial.
8. The function does not have a turning point, as it is a linear function with a constant slope.

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