A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?

The domain of the function is (-∞, ∞).

Definition of function

A function is an expression that shows the relationship between variables as well as numbers.

The domain of a function is the set of all possible inputs for the function.

From the graph, the domain is the set of all x values, hence:

Domain = (-∞, ∞)

The domain of the function is (-∞, ∞).

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Using a system of equations, it is found that Tripp weighs 42 pounds and Rico weighs 7 pounds.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Tripp weighs exactly 35 pounds more than Rico, hence:

x = 35 + y.

Together, they weigh exactly 49 pounds, hence:

x + y = 49

35 + y + y = 49

2y = 14 -> y = 7

x = 35 + y -> x = 42

Hence, Tripp weighs 42 pounds and Rico weighs 7 pounds.

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The graph of g(x) will be the same as the graph of f(x) shifted vertically downwards by 5 units because k=-5 represents a vertical shift, not a horizontal one. There is no horizontal shift involved.

When considering the functions [tex]f(x)=2^x[/tex]and g(x)=f(x)+k, with k=-5, we look at how the graph of g(x) compares to the graph of f(x).

Since the value of k is negative, it implies that a constant is being subtracted from the function f(x). This means that the graph of g(x) will not be shifted horizontally, but rather vertically downwards by 5 units.

Therefore, option c is the correct answer: the graph is not shifted horizontally from the graph of f(x).

Whenever we have been given to find the product of two square roots, the two roots cancel out each other. This is because [tex] (\sqrt{number} )^2 = number [/tex]

The power of two and the square root cancel out each other

In the given problem we have to multiply the square root 10 by itself, we have

[tex] \sqrt{10} * \sqrt{10} [/tex]

Now, the next step will be

[tex] (\sqrt{10})^2 [/tex]

Now the square root and the power of 2 cancel each other an d the result will be 10

Answer : 10

The tennis player must consecutively land 10 more first serves in bounds to raise their success rate from 62.5% to 70%.

First, let's define the variables:

x = number of additional successful serves needed

40 + x = total number of serves after additional successful serves

25 + x = total number of successful serves after additional successful serves

We set up the equation with the desired success rate of 70%:

(25 + x) / (40 + x) = 0.70

To solve this equation, follow these steps:

Multiply both sides by (40 + x):

25 + x = 0.70 * (40 + x)

Distribute 0.70 on the right side:

25 + x = 28 + 0.70x

Isolate the variable x by subtracting 0.70x from both sides:

25 + x - 0.70x = 28

Combine like terms:

0.30x = 3

Solve for x by dividing both sides by 0.30:

x = 10

Thus, the tennis player must land 10 more consecutive first serves in bounds to increase her success rate to 70%.

The greatest possible error when measuring to the nearest quarter of an inch is:

1/8 in.

Error in measurement is the difference between the measured value of a quantity and its true value. It is an inevitable part of any measurement, and there are many different sources of error.

The greatest possible error when measuring to the nearest quarter of an inch is 1/8 of an inch.

This is because the smallest measurement interval is 1/4 of an inch, and the greatest possible error is half of the smallest measurement interval.

Therefore, the greatest possible error when measuring to the nearest quarter of an inch is 1/8 in.

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Normal Distributions

I couldn't see the whole graph in the answer above, but using the quartiles, I chose graph A and that was right.

1. b. mean=75.8, median=76.5, mode=63

2. a. dots at 50, 53.5, 58, 62.5, and 67

3. c. 30th percentile=105, 90th percentile=176.

This is a controversial question because some of the numbers repeat, but as of 5/19, answer c is right.

4. d. mean=8, variance=18.3, standard deviation=4.3

5. a. 2

6. b. 22%

7. d. a^6-30d^5+375d^4-2,500d^3+9,375d^2-18,750d+15,625

8. a. 93%

9. b. 16%

10. c. 84%

For 52/9 to be expressed as a decimal, you need to divide the fraction.

52/9 = 5.78 (rounded by the 1hundreds in the decimals place).

Answer:

140 m

Step-by-step explanation:

A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length.

The perimeter of the kite is the sum of the length of all its sides. So, the perimeter of kite ABCD can be expressed as:

[tex]\sf Perimeter = AB + BC + CD + DA[/tex]

As BC = AB and CD = DA, then:

[tex]\sf Perimeter = BC + BC + CD + CD\\\\Perimeter = 2(BC + CD)[/tex]

Therefore, to find the perimeter of kite ABCD, we need to determine the lengths of sides BC and CD.

The diagonals of a kite intersect to form two pairs of congruent right triangles, where the sides of the kite are the hypotenuses of these triangles.

in kite ABCD:

The longer diagonal of a kite always bisects the shorter diagonal at a right angle.

Let M be the point of intersection of the diagonals. Therefore:

AM = MC = 24 m

Side BC is the hypotenuse of right triangle BMC, with legs measuring 18 m and 24 m, while side CD is the hypotenuse of right triangle CMD, with legs measuring 32 m and 24 m.

To find the lengths of sides BC and CD, we can use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two legs.

[tex]\sf BC^2=18^2+24^2 \\\\BC^2=324+576 \\\\BC^2=900\\\\BC=\sqrt{900}\\\\BC=30\; m[/tex]

[tex]\sf CD^2=32^2+24^2 \\\\CD^2=1024+576 \\\\CD^2=1600\\\\CD=\sqrt{1600}\\\\CD=40\; m[/tex]

Now we have determined the length of sides BC and CD, we can substitute them into the perimeter formula:

[tex]\sf Perimeter = 2(30+40) \\\\ Perimeter = 2(70) \\\\ Perimeter = 140 \; m[/tex]

Therefore, the perimeter of kite ABCD is:

[tex]\LARGE\boxed{\boxed{\sf 140\; m}}[/tex]