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2 years ago

5

the ratio of 7th graders to 8th grader at a school dance is 3 to 2. there are 54 7th graders at a dance. how many 8th graders ar

e at the dance?

1 answer:

Georgia [21]2 years ago

6 0

I just want u to know that u are loved

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Each side of a 7-sided shape is 3 feet long. What is the perimeter of this shape?

bearhunter [10]

Answer:

21 feet

Step-by-step explanation:

You could either do

3 + 3 + 3 + 3 + 3 + 3 + 3 = 21

or

3 x 7 = 21

8 0

2 years ago

Read 2 more answers

Each pair of figures below is similar. Find the lengths of all unknown sides

lions [1.4K]

Answer:

a) w = 8; y = 5.25

b) x = 10; z = 7.2

Step-by-step explanation:

a) Dimensions on the smaller figure are FA/F'A' = 3/4 times those on the larger figure.

6 = (3/4)w

w = 24/3 = 8

y = (3/4)·7 = 21/4 = 5.25

__

b) Dimensions on the smaller figure are ER/E'R' = 9/15 = 3/5 times those on the larger figure.

6 = (3/5)x

x = 30/3 = 10

z = (3/5)12 = 36/5 = 7.2

7 0

2 years ago

A rectangle with an area of 5/8 ft² is dilated by a factor of 8. What is the area of the dilated rectangle?

gulaghasi [49]

Answer:

40 ft²

Step-by-step explanation:

Let the length of the original rectangle be L and original Breadth be B

it is given that the original area is 5/8 ft²

i.e.

Original Length x Original Breadth = Original Area, or,

LB = 5/8 ft² ------------------(1)

Given that the dilation factor is 8,

Hence,

New Length = 8L and New Breadth = 8B

THerefore,

New Area = 8L x 8B

= 64 LB (from (1) above , we know that LB = 5/8 ft², substitute into expression)

= 64 (5/8)

= 40 ft²

4 0

3 years ago

A ship traveling east at 45 mph is 15 mi from a harbor when another ship leaves the harbor traveling east at 60 mph. How long do

Harman [31]

Answer:

1 hour

Step-by-step explanation:

I find these easiest to work by considering the initial difference in distance and the speed at with that gap is closing.

__

The gap is 15 miles, the distance the first ship is from harbor when the second ship starts.

The rate of closure is the difference in the speeds of the two ships:

60 mph -45 mph = 15 mph

Then the closure time is ...

time = distance/speed

time = (15 mi)/(15 mi/h) = 1 h

It will take the second ship 1 hour to catch up to the first ship.

7 0

2 years ago

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 144 millimeters,

valentinak56 [21]

Answer:

The probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The information provided is:

<em>μ</em> = 144 mm

<em>σ</em> = 7 mm

<em>n</em> = 50.

Since <em>n</em> = 50 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample mean.

$\bar X\sim N(\mu_{\bar x}=144, \sigma_{\bar x}^{2}=0.98)$

Compute the probability that the sample mean would differ from the population mean by more than 2.6 mm as follows:

$P(\bar X-\mu_{\bar x}>2.6)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}} >\frac{2.6}{\sqrt{0.98}})$

$=P(Z>2.63)\\=1-P(Z$

*Use a <em>z</em>-table for the probability.

Thus, the probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.

8 0

2 years ago