What is the value of 5 in 42.05

Answers

Answer 1

Answer: The 5 in 42.05 is 5 hundredths

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Solve the equation for the indicated variable. A = bh; h

Answers

Answer:

h = $(A)/(b)$

Step-by-step explanation:

given

A = bh ( isolate h by dividing both sides by b )

$(A)/(b)$ = $(bh)/(b)$ ( cancel b on numerator and denominator )

$(A)/(b)$ = h

Answer and Step-by-step explanation:

We're asked to solve the equation $\bf{A=bh}$ for $\bf{h}$ .

To solve it for h, we'll divide both sides by b.

$\bf{\cfrac{A}{b}=h}$

It's now solved for h.

◈⋆◈⋆◈⋆◈⋆

Note: Solving for h means we're isolating h on one side of the equation. To do it we'll use basic algebra.

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PLEASE HELP!!!!!! Which expressions are equivalent to 1/81 ? Check all that apply.8^ -1

9^ -2

9^ 8/9^4

9^8/9^10

9^ -6 · 9^3

9^5 · 9^ -7

Answers

Answer:

$9^(-2)\n\n(9^(8))/(9^(10))\n\n9^(5)*9^(-7)$

Step-by-step explanation:

Let's evaluate the answers.

Think of numbers with negative exponents as numbers on the wrong side of the fraction. So if you have a negative exponent, you put it at the bottom of the fraction or up and then you remove the negative sign.

So let's take the first answer:

$9^(-2) \:is\:actually\:equal\:to\: (1)/(9^(2))\n\n(1)/(9^(2)) = (1)/(81)}$

Now the next one, according to the law of exponents, when dividing we subtract the exponents. (But this only applies if the coefficients are the same!)

$(m^(x))/(m^(y)) = m^(x-y)$

Applying this rule to the second answer:

$(9^(8))/(9^(10)) = 9^(8-10) = 9^(-2)=(1)/(9^(2)) = (1)/(81)$

The third one:

$9^5*9^(-7) = (9^5)/(9^(7)) = 9^(5-7) = 9^(-2) = (1)/(9^2) = (1)/(81)$

If you apply the same rules to the rest of the choices, you wil find that they are not equivalent to 1/81.

The expressions that are equivalent to 1/81 are $9^(-2)$ , $(9^8)/(9^(10))$ , and $9^5 \cdot 9^(-7)$ .

To determine which expressions are equivalent to 1/81, we can simplify each expression and check if it equals 1/81.

$8^(-1)$ : This expression is equivalent to 1/8, not 1/81. Therefore, it is not equivalent. $9^(-2)$ : This expression is equivalent to 1/9², which simplifies to 1/81. Therefore, it is equivalent to 1/81. $(9^8)/(9^4)$ : This expression simplifies to $9^((8-4)) = 9^4$ , which is not equal to 1/81. Therefore, it is not equivalent. $(9^8)/(9^(10))$ : This expression simplifies to $9^((8-10)) = 9^(-2)$ , which is equivalent to 1/9². Therefore, it is equivalent to 1/81. $9^((-6)) \cdot 9^3$ : This expression simplifies to $(1)/(9^6) \cdot 9^3 = 1/729$ . Therefore, it is not equivalent. $9^5 \cdot 9^((-7))$ : This expression simplifies to $9^((5-7)) = 9^((-2))$ , which is equivalent to 1/9². Therefore, it is equivalent to 1/81.

Thus, the expressions that are equivalent to 1/81 are $9^(-2)$ , $(9^8)/(9^(10))$ , and $9^5 \cdot 9^(-7)$ .

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Last year the enrollment of genoa middle school was 465 students. this year the enrollment is 525.

Answers

Answer:

The amount of change is 60

The percent of change is 13%, increase.

Step-by-step explanation:

Consider the provided information.

Last year the enrollment of genoa middle school was 465 students. this year the enrollment is 525.

The amount of change is: 525-465=60

That means this yr 60 more student get enrollment.

Now find the percentage change.

$\text{Percent of change}=\frac{\text{Amount of change}}{\text{Orignal amount}}$

Substitute the respective values:

$\text{Percent of change}=(60)/(465)\approx0.13$

$\text{Percent of change}=13\%$

Hence, the percent of change is 13% and percentage is positive so this is a percent of increase.

The enrollment Count Went Up By 60 Student Enrollments :3

Please help 50 pts and brainliest if correct

Answers

Answer:

Step-by-step explanation:

it makes sense yah?

Answer:

C) Three fourths of the fish he caught were less than 50.5 pounds

What is the sum of the geometric series in which a1 = −2, r = 3, and an = −1,458?Sn = −2,186
Sn = −728
Sn = 2,186
Sn = 728

Answers

Sn= -2186
Detailed solution is attached

Final answer:

The sum of a geometric series is calculated using the relevant formula from a1, r, and an. The unknown n can be calculated from the given an, a1 and r. These are then substituted into the sum formula.

Explanation:

The given is a geometric series where first term a1 = -2, common ratio r = 3, and last term an = -1458. The sum of a geometric series, Sn, can be calculated using the formula $Sn = a1 * (1 - r^n) / (1 - r)$ , where n is the number of terms in the series. However, in this case, we don't know n directly, but we do know the nth term (an) using the formula $an = a1 * r^(n-1)$ , you can rearrange to solve for n: n = log((an/a1))/log(r) + 1. Plug this value of n and the given a1, r into the sum formula to get the sum.

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A beach has to enclose a rectangular area, because some endangered species are nesting there. They have 200 feet of rope to rope off the area with. What is the maximum area that they can rope off?

Answers

Area is equal to length times width. The perimeter (the amount of rope) has to equal twice the length added to twice the width so we're left with:
A = l * w
200 = 2l + 2w
solve for either l or w
l = 100 - w
plug into the area equation to get one equation with two variables
A = w(100 - w)
A = -w^2 + 100w
take the derivative
A' = -2w + 100
set the derivative equal to zero
0 = -2w + 100
2w = 100
w = 50
This is the width that maximizes the area
with a width of 50, the length must also be 50 to have a perimeter of 200
therefore, they can rope up to 50 * 50 = 2500 ft^2

Final answer:

The maximum area that can be roped off with 200 feet of rope is 2500 square feet by making the roped off area a square.

Explanation:

The question deals with the optimization of area given a fixed perimeter, which involves the principles of geometry and algebra. Since the area needs to be roped off is a rectangle, and you have 200 feet of rope, your rectangle will have dimensions length (L) and width (W) such that 2L + 2W = 200.

To maximize the area of a rectangle given a fixed perimeter, the rectangle should be a square. So, for a maximum area, the length and width should be equal. Thus, each dimension (length and width) would be 200/4 = 50 feet.

Finally, to find the maximum area, we multiply the length by the width: 50 feet * 50 feet = 2500 square feet. So, the maximum area that they can rope off with 200 feet of rope is 2500 square feet.

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