If f(x) = square root of x, which equation describes the graphed function

a) The average rate of change on that interval is 0.1

b) as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1

For any function f(x), the average rate of change on an interval (a, b) is given by:

(f(b) - f(a))/(b - a)

In this case, the function is:

F(x) = −0.005x^2 + 0.8x + 12

And the interval is [60, 80]

Then we have:

F(60) =  −0.005*60^2 + 0.8*60 + 12 = 42

F(80) = −0.005*80^2 + 0.8*80 + 12 = 44

Then the average rate of change on that interval is:

R = (44 - 42)/(80 - 60) = 0.1

b) What does that rate means?

F(x) relates the fuel economy and x the speed of the vehicle.

This means that as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1.

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Answer: 2

Step-by-step explanation: 12 x 3 first becuase pemdas

Answer:

b⁶

Step-by-step explanation:

Where b is the variable, we multiply b by itself six times to represent its multiplications every 6 days.

Answer:

Step-by-step explanation:

all of the angles complete a circle so they must add up to 360 degrees.

230 + 38 + 52 + x = 360

320 + x = 360

x = 40 degrees

Answer:B

Step-by-step explanation:A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.

Hey there!

3% of $600.00

= 3% * $600.00

= 0.03 * 600

= 3/100 * 600/1

= 3(600) / 100(1)

= 1800/100

= 1800 ÷ 100 / 100 ÷ 100

= 18/1

= 18 ÷ 1

= 18

Therefore, your answer should be:

18

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one is relative to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent.A ratio divides two numbers to compare them.

a: The ratio of two mathematical expressions that is indicated.

b: the proportions of two or more items in terms of quantity, amount, or size: proportion.

based on the available facts;

2/6 for the first ratio can be converted to 1/3, as can 3/9 for the second ratio.

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Answer:

-10

Step-by-step explanation:

[tex]f(x) = 2 - 3x \\ [/tex]

So,

[tex]f(4) = 2 - (3 \times 4) = 2 - 12 = - 10[/tex]

Therefore, Option A is correct

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The area of the triangle is = 19.4 cm²

Triangle's area is equal to 1/2 (b × h) square units.

where the triangle's base and height, respectively, are denoted by b and h. Let's now examine how to use the provided formula to get a triangle's area.

Area of triangle = 1/2 × B × H

We will calculate the height of the triangle with the help of Pythagoras theorem.

Consider a straight line representing the height of the triangle.

⇒ base = 4cm, half of base = 2cm

⇒ hypotonus = 10cm

(h²) = b² + a²

⇒ 10² = 2² + a²

⇒ 100 = 4 + a²

⇒ √96cm = a

a = 9.7cm

area of triangle = 1/2 × 4  × 9.7

= 19.4 cm²

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The total amount saved by the James is: $330.

The relationship between two expressions is expressed by the word equation. It employs many mathematical symbols, including greater-than, less-than, and equal.

The amount James has saved, according to the query, is $15 each week.

It is now time to generate the table that shows how the variable "x" and the number of weeks relate to one another.

The following are the possible possibilities for the necessary parameters "x" and "y":

x = [1 2 3 4]

y = [15 30 45 60]

The last formula may now be written as y = 15x.

The formula will be y = 15x = 15x22 = 330 dollars after 22 weeks.

As a result, the James have saved $330.

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30 = m<1 = m<2

m<1 is equals to m<2 because these two angles are transitive property.

given that m<1 = 30° and m<2 = 30°.

m<1 = 30

m<2 equals to m<1

m<2 = 30 can be obtained by substituting 30 into the second equation.

The proof is now complete.

The Transitive Property of Equality can also be used, which asserts that if X = Y and Y = Z, then X = Y = Z. In other words, if one number is equal to another, and that other number is equal to a third, then all three numbers must be the same.

thus, 30 = m<1 = m<2, m<1 is equals to m<2 because these two angles are transitive property.

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Answer:

[tex]-\frac{3+\sqrt{5}}{4}[/tex]

Step-by-step explanation:

[tex]\sqrt{20} \leq 5 \implies f(\sqrt{20})=\frac{2}{\sqrt{20}-6} \\ \\ =\frac{1}{\sqrt{5}-3} \\ \\ =\frac{\sqrt{5}+3}{-4} \\ \\ =-\frac{3+\sqrt{5}}{4}[/tex]

Answer: lol

no question that is the station? so there's no question?

ok

Step-by-step explanation:

Answer: Turning your cell phone off or on silent can help you listen actively because you won't have the urge to look at it unless you hear a little notification.

But honestly, whose question is this, it's so random, and I think everyone can listen with their phones out, because I pay more attention when I'm doing something like on a phone or listening to music.

Answer:

104

Step-by-step explanation:

You would do this by diving 65 by 5, you get 13 then multiple that by 8.

Taking into account the definition of Scientific notation,  the correct answer is the first option: the total mass of the paperclips in the box is 4.338×10¹ mg.

Scientific notation is a quick way to represent a number using powers of base 10.

The numbers are written as a product:

a×10ⁿ

where:

Total mass of the paperclips

In this case, you know that:

To know the total mass of the paperclips in the box, you must multiply the number of paperclips in the box by the mass of each paperclip:

7.23×10⁴×6.0×10⁻⁴

To multiply numbers in scientific notation, you multiply the numbers that are not powers of 10 (the numbers previously called "a") and add the exponents of 10.

(7.23×6.0)×10⁴⁻⁴= 43.38×10⁰= 4.338×10¹ mg

Finally, the correct answer is the first option: the total mass of the paperclips in the box is 4.338×10¹ mg.

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Answer: 4,6

Step-by-step explanation:

The value of (fogoh)(x) is [tex]\sqrt{x^{3} }[/tex] + 6x + 12[tex]\sqrt{x}[/tex]

Here, we are given 3 functions as listed below:

f(x) = [tex]x^{3}[/tex] +8

g(x) = x - 2

and, h(x) = [tex]\sqrt{x}[/tex]

now, (fogoh)(x) can be written as follows-

f[g{h(x)}] = f{g([tex]\sqrt{x}[/tex])}

here, g([tex]\sqrt{x}[/tex]) = [tex]\sqrt{x}[/tex] - 2

Thus, f{g([tex]\sqrt{x}[/tex])} = f([tex]\sqrt{x}[/tex] - 2)

Substituting x = [tex]\sqrt{x}[/tex] - 2 in the function f(x) we get,

[tex](\sqrt{x} - 2)^{3}[/tex]+8

using the algebraic property [tex](a+b)^{3}[/tex] = [tex]a^{3} + b^{3}[/tex] + 3ab(a + b), we get-

= [tex]\sqrt{x^{3} }[/tex] - [tex]2^{3}[/tex] + 3[tex]\sqrt{x}[/tex](-2){[tex]\sqrt{x}[/tex] - 2} + 8

= [tex]\sqrt{x^{3} }[/tex] - 8 + 6x + 12[tex]\sqrt{x}[/tex] + 8

= [tex]\sqrt{x^{3} }[/tex] + 6x + 12[tex]\sqrt{x}[/tex]

Thus the value of (fogoh)(x) = [tex]\sqrt{x^{3} }[/tex] + 6x +12[tex]\sqrt{x}[/tex]

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Answer: Tane needs to work 8 hours per week while Pete needs to work 5 hours per week

Step-by-step explanation:

T=Tane. P=Pete

5*13=65

T+P=65

15T+16P=1000

T=65-P

15(65-P)+16P=1000

975-15P+16P=1000

975+P=1000

P=25 hours for 5 weeks

T=65-25

T=40 hours for 5 weeks

P: 25/5=5 hours per week

T: 40/5=8 hours per week

Tane needs to work 8 hours per week while Pete needs to work 5 hours per week

Answer: f'(11)=1/6

Step-by-step explanation:

f(x)=sqrt(x-2)

f(x)=(x-2)^1/2

f'(x)=1/2 * (x-2)^(1/2-1)

f'(x)=1/2 * (x-2)^(-1/2)

f'(11)=1/2 * (11-2)^(-1/2)

f'(11)=1/2 * (9)^(-1/2)

f'(11)=1/2 * (9)^(1/2 * (-1))

f'(11)=1/2 * (9^1/2)^(-1)

f'(11)=1/2 * (3)^(-1)

f'(11)=1/2 * 1/3

f'(11)=1*1/(2*3)

f'(11)=1/6

Using the definition of the derivative, we have

[tex]\displaystyle f'(11) = \lim_{x\to11} \frac{\sqrt{x-2} - \sqrt{11-2}}{x - 11} = \lim_{x\to11} \frac{\sqrt{x-2} - 3}{x - 11}[/tex]

Rationalize the numerator.

[tex]\displaystyle \frac{\sqrt{x-2}-3}{x-11} \cdot \frac{\sqrt{x-2}+3}{\sqrt{x-2}+3} = \frac{\left(\sqrt{x-2}\right)^2 - 3^2}{(x-11)\left(\sqrt{x-2}+3\right)} = \frac{x - 11}{(x - 11) \left(\sqrt{x-2} + 3\right)}[/tex]

If [tex]x\neq11[/tex], we can simplify the limit to

[tex]\displaystyle f'(11) = \lim_{x\to11} \frac{x-11}{(x-11)\left(\sqrt{x-2}+3\right)} = \lim_{x\to11} \frac1{\sqrt{x-2} + 3}[/tex]

The function in the remaining limit is continuous at [tex]x=11[/tex], so we end up with

[tex]\displaystyle f'(11) = \frac1{\sqrt{11-2} + 3} = \boxed{\frac16}[/tex]

The amount saved by repaying the loan early is $831.25

The amount of discount received by purchasing supplies is $3,500

The net amount saved by purchasing supplies rather than repaying loan is $2,668.75

What is ordinary interest?

Ordinary interest is the interest computation that is based on 360-day a  year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.

Amount saved in interest=$35,000*9.5%*90/360

Amount saved in interest=$831.25

Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000

Amount saved with discount=10%*$35,000

Amount saved with discount=$3,500

The difference between discount on supplies and interest saved=$3,500-$831.25

The difference between discount on supplies and interest saved=$2,668.75

The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies

Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates

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She can have 60 reading list to plan to read the 6 novels that she wants to read including the 'in the chest of a woman' in the list.

We are given that:

Number of novels that Julia wants to read = 6

She plans to read = 4

1 novel is fixed that is "in the chest of a woman' by Efo Kodjo"

We need to tell the number of possible reading list that she can have.

We will use permutation for it

By using permutation, we get that:

Number of reading list = 1 × 5 × 4 × 3

Number of reading list = 5 × 12

Number of reading list = 60 lists

Therefore, she can have 60 reading list to plan to read the 6 novels that she wants to read including the 'in the chest of a woman' in the list.

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Step-by-step explanation:

Given that

To find

So, according to the question

We have,

We know that,

Chebyshev's Theorem

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

          [tex]P = 100(1-\frac{1}{k^2} )[/tex]

Chebyshev's Theorem is used to determine that:

For the 1sr item, we have to find k at P = 56,

          [tex]P = 100(1-\frac{1}{k^2} )[/tex]  

          [tex]56 = 100(1-\frac{1}{k^2} )[/tex]

          0.56 = 1 - [tex]\frac{1}{k^2}[/tex]

            [tex]\frac{1}{k^2} = 0.44[/tex]

            k² = 1/0.44

            k = [tex]\sqrt{\frac{1}{0.44} }[/tex]

             k = 1.5  

The bounds are, therefore, within 1.5 standard deviations:

Ages 25 and 65 are both 2 standard deviations away from the mean, so:

Answer:

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The number that has a lesser value in the hundred thousands place than 6,318,219 is: 4,237,639.

Starting from the end of the number and moving left, the hundred thousands digit is the 6th digit of the number.

The values of the digit for each number are given as follows:

2 < 3, hence, the number that has a lesser value in the hundred thousands place than 6,318,219 is: 4,237,639.

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Answer:

can you take a picture of the sum

7 will go in the box. The full number would be 67.14.

work: 64.24 + 2.9 = 67.14.

Answer:

The break-even point in dollars is 1,344,000 and in units is 28,000. The break-even point is calculated by dividing the fixed costs by the contribution margin. In this case, 336,000 ÷ .25 = 1,344,000. The break-even point in units is then calculated by dividing the break-even point in dollars by the sales price. In this case, 1,344,000 ÷ 48 = 28,000.

Step-by-step explanation:

Give me brainliest if that helped :)

Answer:

Step-by-step explanation:

if you are trying to find x in the equation

3(2x+2)-3x= 6+3x you have to distribute the 3 (which you did correctly.)

6x+6-3x=6+3x

what you did wrong was canceling out the threes. you cannot cancel out the threes here because the one on the left is negative. What you should do is add 3x to each side like this.

6x+6-3x=6+3x

+3x +3x

6x+6=6+6x

since both sides are equal and we obtain 0=0, this means the equation is in fact an identity which is true for all values of x.

It should be noted that an algebraic expression will be equal to zero when the difference is between the same expressions.

It should be noted that an algebraic expression simply means the expression that's used to show the relationship between the variables

In this case, the should be noted that an algebraic expression will be equal to zero when the difference is between the same expressions.

An example is illustrated as:

= 2x - 2x

= 0

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The equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600

It is given in the problem that,

The total cost function C(x) = 76x + 3600 (in dollars)

Also,

The total revenue function R(x) = 376x (in dollars)

We need to find the equation of the profit function P(x) (in dollars) for this commodity

First we need to understand the following terms

Cost is the price of a commodity which is paid or charged in exchange of something. Example - 1 kg of apple are of 3 Dollars

Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations.

So,

The equation of the profit is given by = Total Revenue - Total Cost

P(x) = R(x) - C(x)

Putting values, we get

P(x) =  376x - (76x + 3600)

P(x) =  376x - 76x - 3600

P(x) = 300x - 3600

Hence, the equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600

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