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2 years ago

Alice has a 4-inch by 5-inch photo of your school’s championship girls’ ice hockey team. To celebrate their recent

Mathematics

1 answer:

Pachacha [2.7K]2 years ago

7 0

Alice should pick the enlarged-photo with dimensions of 8-inch by 10-inch.

Step-by-step explanation:

Step 1:

In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.

We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.

Step 2:

The original photo was a 4-inch by 5-inch photo.

Option 1 is 7-inch by 9-inch, so the ratios are

$\frac{7}{4} = 1.75, \frac{9}{5} = 1.8.$ The ratios are different so this cannot be the enlarged photo's dimensions.

Option 2 is 8-inch by 10-inch, so the ratios are

$\frac{8}{4} = 2, \frac{10}{5} = 2.$ The ratios are the same so this can be the enlarged photo's dimensions.

Option 3 is 12-inch by 16-inch, so the ratios are

$\frac{12}{4} = 3, \frac{16}{5} = 3.2.$ The ratios are different so this cannot be the enlarged photo's dimensions.

So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.

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Jin’s soccer team has 4 coaches and 22 players, and his twin sister’s team has 2 coaches and 11 players. If the relationship bet

nikklg [1K]

Question : Jin’s soccer team has 4 coaches and 22 players, and his twin sister’s team has 2 coaches and 11 players. If the relationship between the number of players and coaches is proportional throughout the league, which ordered pair could represent the total number of coaches and players in the entire league?

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Answer :

B :

26 coaches and 143 players

4 0

2 years ago

Read 2 more answers

Two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2)

NeTakaya

Answer:

Step-by-step explanation:

Hello!

You have a sample of 200 people, they were asked their primary source of news, categorized in (1) Television, (2) Radio, (3) Internet and (4) Other.

And your objective is to test if the proportions in this sample follow the known frequencies 10%, 30%, 50%, and 10%.

The propper statistic test to use to probe if the sample follows the known or historical distribution is Chi-Square goodness of fit test. In this test, what you state in the null hypothesis is the model or distribution you want to test. In this case, you've to write down the proportions for each category:

H₀: P(1)= 0.10; P(2)= 0.30; P(3)= 0.50; P(4)= 0.10

I hope you have a SUPER day!

7 0

2 years ago

A rectangular portrait measures 50cm by 70cm. It is surrounded by a rectangular frame of uniform width. If the area of the frame

snow_tiger [21]

Let us assume uniform width = x cm wide.

Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.

Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.

And width of rectangle made by frame = 70+x+x = (2x+70) cm.

We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.

Total area of the rectangle made by frame would be = (2x+50) * (2x+70)

We know,

Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.

We also given "the area of the frame is the same as the area of the portrait."

We can setup an equation now,

3500 = (2x+50) * (2x+70) - 3500.

Subtracting 3500 from both sides, we get

3500-3500 = (2x+50) * (2x+70) - 3500-3500.

0 = (2x+50) * (2x+70) -7000.

FOIL (2x+50) * (2x+70), we get

0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.

0 = 4x^2 +140x +100x +3500 -7000.

4x^2 +240x -3500 = 0.

Dividing whole equation by 4, we get

x^2 +60x - 875 =0

Applying quadratic formula $=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , we get

$=\frac{-60\pm \sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}$

$x=\frac{-60+\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}=5\left(\sqrt{71}-6\right)$

$x=\frac{-60-\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}:\quad -5\left(6+\sqrt{71}\right)$

We cant take negative value.

So, $x=5\left(\sqrt{71}-6\right)=12.13$

We could take approximately 12 cm.

7 0

2 years ago

Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyron

scoray [572]

18 x 40 = 720 per week.....720 x 4 = 2880 per month earnings

net pay = 0.72(2880) = 2073.60 <=== cash inflow.

how much he spends per month is his cash outflow.

3 0

2 years ago

Read 2 more answers

An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24

enot [183]

Answer:

16 in.

Step-by-step explanation:

We have the ratio

How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

Now we need to know how many inches there would be if the number of feet is 24:

Cross multiply to get

3x = 48 so

x = 16 in.

7 0

2 years ago