MATHEMATICS HIGH SCHOOL

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide, if the reduced diagram is 4 centimeters wide how long will it be?

Answers

Answer 1

Answer:

Answer:

12 cm

Step-by-step explanation:

This is a proportionality/similarity problem.

10 cm turned to 4 cm. So by how much has it decreased? In other words, 10 multiplied by WHAT is 4?

$10*x=4\nx=(4)/(10)\nx=0.4$

0.4 is also known as the scale factor from the large diagram to the small diagram.

So how much would 30 cm become? It would be 30 multiplied by the scale factor, which is 0.4.

$30*0.4=12$

Hence, the length of the reduced diagram would be 12 cm.

Answer 2

Answer: $x-length\n\nFrom\ proportion:\n\n(30)/(10)=(x)/(4)\n\n10x=120\ \ \ \ \ \ |:10\n\nx=12\n\nIt\ will\ be\ 12\ cm\ long$

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Zoe put in 80 hours of work in July for which she is entitled to $920.65. She also works 5 hours overtime. If she receives a paycheck of $1030.45 for the month, how much is she paid for an hour of overtime work?

Answers

Answer:

1951.1

Step-by-step explanation:

Just add her money up 920.65 + 1030.45= 1951.1

What is the distance between points A and B? please help!! WILL MARK BRAINLIEST!!!!

A. 29
B. 2 V 29
C. 3 V 14
D. V58

Answers

Answer:

The answer should be 7.615773...

or $\sqrt58$

Step-by-step explanation:

$\sqrt(x^(2) -x^(1) )^(2) +(y^(2) -y^(1) )^(2) \n\n\n\sqrt(11^(2) -4^(1) )^(2) + (7^(2) - 4^(1) )^(2)\n\n \n\sqrt58 = 7.61577310586...\n$

I hope this helps.

1. Anne wants to join five pieces of paper together. She plans to use 3 rectangular pieces of the same size and 2 square pieces of the same size. The length of each rectangular piece is 3 1/2 feet. The width of each rectangular piece, w, is the same as the length of each square piece. The expression below can be used to find the total surface area of the five pieces of paper. Anne decides that the width, w, of the rectangular pieces should be 2 feet. What is the total surface area, in square feet, of all five pieces of paper?

Answers

Answer and explanation:

Surface area of a rectangle = length * width

Surface area of a square = a² where a is length of a side

To find total surface area of the the five pieces of paper, we add up all the areas of all the shapes

Given that length of rectangle =3.5

And width = 2

Area of rectangle =3.5*2=7

Area of 3 rectangles given they are all equal = 7*3=21

Since width of rectangle equal to width of square and all sides of square are equal

Area of square = 2 *2 =4

Area of the two squares =4*2=8

Total surface area of the five plane shapes = 21+8= 29

Zhao Xue wants to buy milk and yogurt. She wants to buy a total of at least 6.5 gallons of dairy products (condition A), and she has a budget of $20 (condition B). The graph represents the constraints on the number of gallons of milk M and yogurt Y Zhao Xue buys. Zhao Xue buys 4 gallons of milk. how many gallons of yogurt can she buy to meet both her constraints? A.) Exactly 2.5 gallons
B.) At least 4 gallons and at most 6.5 gallons
C.) At least 2.5 gallons and at most 4 gallons
D.) Zhao Xue doesn’t have enough money left to buy any yofurt

Answers

Answer: The answer is (D). Zhao Xue doesn’t have enough money left to buy any yofurt

Step-by-step explanation: Given that Zhao Xue is buying buy milk and yogurt, a total of at least 6.5 gallons of dairy products and she has a budget of $20. The given graph represents the constraints on the number of gallons of milk 'M' and yogurt 'Y' Zhao Xue buys. Zhao Xue buys 4 gallons of milk. We need to calculate the number of gallons of yogurt she can buy to meet both her constraints.

From the graph, we can write

Condition A :

$M+Y\geq 6.5.$

Condition B :

$8M+5Y\leq40.$

Now, if she buys 4 gallons of milk, the the conditions become

$4+Y\geq 6.5~~\Rightarrow Y\geq 2.5,\n\n8* 4+5Y\leq 40~~\Rightarrow Y\leq 1.6.$

Here, there will be no solution to these constraints.

Therefore, she does not have enough money left to buy any yogurt.

Thus, the correct option is (D).

Answer: exactly 2.5 gallons

This is for khan academy.

F(x) = √6xg(x) = √24x
Find (f g)(x). Assume x ≥ 0.
OA. (f g)(x) = 72x
OB. (f.g)(x) = 12x
OC. (f.g)(x) = 12√√
OD. (f.g)(x) = √30x
Finds (f • g)(x) assume x >0
-

Answers

Answer:

$f(x) = √(6x)$

$g(x) = √(24x)$

$f(g(x)) = f( √(24x) ) = \sqrt{6 √(24x) } = √(6) \sqrt{ √(24) } \sqrt{ √(x) } = √(6) \sqrt{2 √(6) } \sqrt{ √(x) } =$

$√(12) \sqrt{ √(6x) }$

The correct answer is C.

$f(x)g(x) = √(6x) √(24x) = 12x$

A die is rolled 260 times. Predict how many times it will show a 3 or 5.

Answers

The chances of getting 3 or 5 by 260 times will be 87.

What is probability?

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that a die is rolled 260 times. The number of times it will show a 3 or 5 will be calculated as below:-

Sample = 6

Number of getting 3 = 1

Number of getting 5 = 1

Probability of getting 3 = 1 / 6

Probability of getting 5 = 1 / 6

Probability of 3 or 5 = ( 1 / 6 ) + ( 1 / 6 )

Probability of 3 or 5 = 2 / 6

Number of times of getting 3 or 5 = ( 2 / 6 ) x 260

Number of times getting 3 or 5 = 87

Therefore, the chances of getting 3 or 5 by 260 times will be 87.