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6 days ago

A camera is selling for $7.50 off the regular price. It was marked down 15%. A student used the equation:

Mathematics

2 answers:

babunello [3.6K]6 days ago

8 0

Answer:

A camera is discounted by $7.50 off its original price and had a 15% markdown.

Let the original price be represented as x

The solution proceeds as follows:

$x-0.15x=7.50$

=> $0.85x=7.50$

=> x = 8.82

The actual original price comes to $8.82.

A student used the equation:

15(7.5) = Original price

and calculated the camera's original price to be $112.50.

This calculation was incorrect. The student mistakenly calculated 15% of the selling price instead of the original price.

He should have calculated 15% of the original price to equal the selling price.

lawyer [4K]6 days ago

4 0

Answer:

The student should have divided the amount after the discount by the percentage expressed as a decimal.

Step-by-step explanation:

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if a student scored 78 points on a test where the mean score was 84.5 and the standard deviation was 3.1. the student's z score

Inessa [3926]

Answer:

(value - mean)/standard deviation.

Now substitute 78 for the value, 84.5 for the mean, and 3.1 for the standard deviation.

Step-by-step explanation:

5 0

3 days ago

Students have organized

tester [3938]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

$D_E$

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

4 0

11 days ago

Erika is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She begins by assigning coordinates

Leona [4187]

Answer:

Option C is the right choice.

Step-by-step explanation:

The given coordinates define a rectangle, and our objective is to show that the diagonals JL and KM are congruent.

We know that rectangles possess four right angles.

To prove the congruence of the diagonals JL and KM, we will utilize the Pythagorean theorem.

In triangle KLM, KL has a length of b units while LM has a length of a units. By applying the Pythagorean theorem $\sqrt(a^{2}+b^{2})=KM$

In triangle JML, JM is b units long, and LM remains a units long. We again can apply the Pythagorean theorem $\sqrt(a^{2}+b^{2})=JL$

Thus, we find that $\sqrt(a^{2}+b^{2})=KM=LM$ and option C is the correct choice.

7 0

4 days ago

Read 2 more answers

Estimate the value of 9.9 squared x 1.79

PIT_PIT [3949]

9.9 squared times 1.79
Calculating 9.9^2 gives 98.01
Then multiplying 98.01 by 1.79 results in 175.4379

7 0

12 days ago

Read 2 more answers

The owners of Expo Company John Smith and Susan Jones invested $240,000 and $160,000 into the business respectively. What percen

tester [3938]

Answer:

40%

Detailed solution:

John Smith and Susan Jones have contributed $240,000 and $160,000 respectively toward Expo Company. We are tasked with determining the proportion of the business owned by Susan.

First, calculate the total investment by summing both contributions.

$\text{Total money invested in business}=\$240,000+\$160,000$

$\text{Total money invested in business}=\$400,000$

Next, find what percentage $160,000 is of the total $400,000.

$\text{Percentage of business Susan own}=\frac{160,000}{400,000}\times 100$

$\text{Percentage of business Susan own}=0.4\times 100$

$\text{Percentage of business Susan own}=40$

Thus, Susan's share in the company is 40%.

5 0

14 days ago