What is the sum?
7/2+(-3/5)

The average rate of change of f(x) over the interval [-1, 1] is 5.

To find the average rate of change of f(x) over the interval [-1, 1], we use the formula:

[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]

First, we find the change in f(x) over the interval [-1, 1]. The function values at x = -1 and x = 1 are f(-1) = -5 and f(1) = 5 respectively. So, the change in f(x) is 5 - (-5) = 10.

Next, we find the change in x over the same interval. The interval [-1, 1] has a width of 1 - (-1) = 2.

Finally, we divide the change in f(x) by the change in x to get the average rate of change:

[tex]\[ \text{Average Rate of Change} = \frac{10}{2} = 5 \][/tex]

So, the average rate of change of f(x) over the interval [-1, 1] is 5.

Final answer:

To round 16.2 to the nearest whole number, check the first digit after the decimal. It's less than 5, so round down to 16.

Explanation:

When rounding 16.2 to the nearest whole number, you need to look at the first digit after the decimal point, which is 2 in this case. If that digit is 5 or greater, you would round up. If it is less than 5, you round down. Since 2 is less than 5, we round down, so the whole number that 16.2 gets rounded to is 16.

The horizontal component of the velocity of a ball thrown at a 30 degree angle above the horizontal with an initial speed of 10 ft/s will remain approximately 8.66 ft/s after 0.50s, assuming no air resistance.

A ball is thrown at a 30 degree angle above the horizontal with a speed of 10 ft/s. After 0.50s the horizontal component of its velocity will remain the same, assuming no air resistance, because horizontal velocity in projectile motion is constant if air resistance is ignored. The vertical component will change due to gravity, but that does not affect the horizontal component.

To find the horizontal component of the velocity, we can use the cosine of the launch angle:
Horizontal velocity (v_x) = initial speed * cos(launch angle)
So, v_x = 10 ft/s * cos(30 degrees)

= 10 ft/s * (√3/2)

≈ 8.66 ft/s

As there is no horizontal acceleration in ideal projectile motion, after 0.50s, the horizontal component of the ball's velocity will still be approximately 8.66 ft/s.

The expressions equivalent to 10x are 50x/5 and (50/5)x as they both simplify to 10x. The other options do not simplify to 10x. Hence option D and E are correct.

To determine which expressions are equivalent to 10x, we need to simplify each option. Let us consider the options one by one:

To solve this a simple division is required.

⇒ (50x/5x)= 10÷(1) = 10

⇒ 10 is not equivalent to 10x.

⇒ 100x - 10

This is not equivalent to 10x.

⇒  10 • 10x • 10 = 100x+10 (Not equivalent to 10x)

⇒ (50/5)x = 10x (Equivalent to 10x)

The correct answers are D and E, both of which simplify to 10x.

The rate of change in miles per gallon for a car trip represents the number of miles the car can travel per gallon of gasoline used. The ordered pairs (0, 2), (1, 2), (2, 3), (1, 4), (3, 1) accurately correspond with the values provided in the given table.

In the given situation, the rate of change of a graph showing the miles per gallon of gasoline a car uses on a trip would represent the number of miles traveled for every one gallon of gas used. This is because the rate of change in this context quantifies how much distance can be covered (in miles) using one unit of gasoline (in gallon). For instance, if the rate of change is 30, it indicates that the car can travel 30 miles using just one gallon of gasoline.

For the second part of your question, matching the ordered pairs with the table, the correct match would be (0, 2), (1, 2), (2, 3), (1, 4), (3, 1). This set of pairs corresponds accurately to the values given in your table for x and y. To understand this, you can match each x value with its corresponding y value in the table. For example, when x is 0, y is 2 - and this gives you the ordered pair (0, 2).

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Answer:

7^4

Step-by-step explanation:

The value of the phrase is 5/8.

A subfield of mathematics known as arithmetic operations deals with the study and application of numbers to all other subfields of mathematics. Operations like addition, subtraction, multiplication, and division make up the bulk of them.

We use these fundamental mathematical operations every day (plus, minus, and). Arithmetic operations are used in every aspect of our lives, whether we need to figure out the annual budget or divide something equally among several people.

Given a phrase half of 1 and 1/4 cups,

1 and 1/4 = 1 + 1/4 = 5/4

and half of 5/4 is

1/2(5/4)

1/2 x 5/4 = 5/8

Hence the value is 5/8.

Learn more about arithmetic operators;

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Answer:

The absolute value parent function is symmetric with respect to the y-axis.  

The graphs of f(x) = 2|–x| and f(x) = 2|x| are identical because the absolute value of negative x is a reflection across the y-axis.  

If you substitute the three given points into both functions, they produce true statements.

Step-by-step explanation:

Answer:

none there would be an answer if it was 3√7

Step-by-step explanation:

The quotient is -3x² + 3x + 8.

To find the quotient when [tex]\(-3x^3 + 5x + 14\)[/tex] is divided by x - 2, we can use polynomial long division.

The dividend is [tex]\(-3x^3 + 0x^2 + 5x + 14\)[/tex] (since there is no [tex]\(x^2\)[/tex] term) and the divisor is x - 2.

1. Divide the first term of the dividend by the first term of the divisor: [tex]\(-3x^3 \div x = -3x^2\)[/tex].

2. Multiply the divisor by the result of step 1: [tex]\((-3x^2)(x - 2) = -3x^3 + 6x^2\).[/tex]

3. Subtract the result of step 2 from the dividend: [tex]\((-3x^3 + 0x^2 + 5x + 14) - (-3x^3 + 6x^2) = -6x^2 + 5x + 14\).[/tex]

4. Repeat the process with the new dividend [tex]\(-6x^2 + 5x + 14\)[/tex].

Continuing the division process, we find the quotient:

[tex]\[ \frac{-3x^3 + 5x + 14}{x - 2} = -3x^2 + 3x + 8 \][/tex]

So, the quotient is -3x² + 3x + 8.

Since, probability of selecting a blue candy and anything but a blue candy are mutually exclusive events, the probability of selecting anything but an blue candy at random from a large bag = P(Not blue) = 0.76

In logic and probability theory, two events are mutually exclusive or disjoint if they cannot both occur at the same time.

P(Blue) + P(Not blue) = 1 (mutually exclusive events)

0.24 + P(Not blue) = 1

P(Not blue) = 1 - 0.24 = 0.76

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1/4 divided by 5 results into '0.05'

Given that we need to find 1/4 divided by 5

Thus let the required answer be denoted as "A"

Thus using basic definitions of divisions and fractions we can find out the resultant value

[tex]A=\frac{\frac{1}{4} }{5} \\A=\frac{1}{4*5} \\A=\frac{1}{20}[/tex]

Thus '1/20' is  the required answer

Now the resultant value can also be simplified to get a decimal value

[tex]A=\frac{1}{20} \\A=\frac{1}{2*10} \\A=\frac{1}{2} *\frac{1}{10} \\A=0.5*0.1\\A=0.05[/tex]

Thus '0.05' is the final answer

The answer is provided in the image attached.