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2 years ago

The quantities xxx and yyy are proportional.

Mathematics

1 answer:

Valentin [98]2 years ago

5 0

Answer:

The answer is 0.5

Step-by-step explanation:

If you do 4.5 divided by 9 you get 0.5

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A student raises her grade average from a 75 to a 90. What was the percent of increase

son4ous [18]

This can be solved algebraically. Before we start, as context, to find a percentage you multiply by the percentage/100.

$75*x=90 \\ x= \frac{90}{75} \\ \\ \boxed{x=1.2}$

This tells us that 90 is 120% of 75. However, your question wants us to find the <em>increase</em>, therefore we don't need that 100.
Therefore, the increase is 20%.

4 0

2 years ago

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

8 1

2 years ago

Read 2 more answers

The number of pages that Allen, Kevin, Roneisha, and Ben can read in a day is shown below. Allen read 15% of his 56-page book. K

grandymaker [24]

It would be “Allen” since his percentage is far more grater then the rest, even Roneisha because even though her percentage is 1% greater, she has less pages, Ben has more pages but has 1% less.

Basically it’s like 2 bikers racing, 1 biker is faster but can’t go 5 miles, but the other is not that fast but can go 5+ miles.

Now who can go further, it would be the slow one.

3 0

1 year ago

Read 2 more answers

Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned i

jolli1 [7]

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

0.3·X = $3,600

X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

Therefore, the amount invested at 7% = $12,000 and the amount invested at 10% = $8,000.

7 0

2 years ago

Read 2 more answers

Which of the following uses estimation to check 267 – 154 = 113?

Arturiano [62]

Estimation is taking the general values of an equation to find an answer that is close to the actual answer.

Round the numbers in the equation to their tens places by checking their ones value:

267
7 > 5
267 -> 270

154
4 < 5
154 -> 150

Subtract these two rounded values:

$270 - 150 = 120$

The answer that has this equation is D.

5 0

2 years ago