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nlexa [21]
3 years ago
6

Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.

Mathematics
1 answer:
zepelin [54]3 years ago
4 0

see the attached figure with letter to better understand the problem    

we know that

If triangle ABC is similar to triangle PQR

then

the ratio of the corresponding sides are proportional

so

substitute the values

therefore

the answer is the option C

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My favorite recipe for lemonade calls for 4 cups of water to 3/4 cups sugar. How
Nikolay [14]

Answer and Step-by-step explanation:

To find the unit rate, divide the 4 cups of water and the \frac{3}{4} cups sugar by 4 to get a unite rate for 1 cut of water.

<u>4 divided by 4 equals 1.</u>

<u />

<u />\frac{3}{4}<u> divided by 4 equals </u>\frac{3}{16}<u>.</u>

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<u>Now, we multiply </u>\frac{3}{16}<u> by 6.</u>

<u></u>\frac{9}{8}<u> is how many cups of sugar that needs to be measured for 6 cups of water.</u>

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8 0
2 years ago
In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine
zimovet [89]

Answer:

(a)  0.2650

(b)  0.0111

(c)  0.0105

(d)  0.0006

Step-by-step explanation:

Given that:

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.

Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15.       &;

If the area of the agar plate is 75cm²;

what is the probability  of observing fewer than 4 CFUs in a 25 cm² area of the plate.

We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;

75cm²/25cm² = 3

Since;

mean  μ = 15  

mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs

Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:

= P(X < 4)

Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )

we have ;

P(X < 4) = 0.2650

b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?

Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates =  15×5 = 75 CFUs

The probability is therefore = P( X > 95 )

= 1 - P(X ≤ 95)

= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)

= 0.0111

c) Repeat the probability calculation in part (b) but now use the normal approximation.

Let assume that the mean and the variance of the poisson distribution are equal

Then;

X \sim N (\mu = 75 , \sigma^2 = 75)

We are to repeated the probability calculation in part (b) from above;

So:

P( X > 95 )

use the normal approximation

From standard normal variable table:

P(Z > 2.3094)

Using normal table

P(Z > 2.3094) = 0.0105

(d)  Find the difference between this value and your answer in part (b).

So;

the difference between the value in part c and part b is;

=  0.0111 - 0.0105

= 6*10^{-4}

= 0.0006 to four decimal places

5 0
3 years ago
How do you interpret slope and y- intercept from a table?​
Ivahew [28]

Answer:

graph the table and fine the rise over run

8 0
3 years ago
A rain gutter is to be made of aluminum sheets that are 16 inches wide by turning up the edges 90. See the illustration.
goblinko [34]

Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.

<h3>How much can the maximum cross-sectional area?</h3>

Assuming that the depth is x, the area would be:

= x (16 - 2x)

= 16x - 2x²

The maximum of the parabola is:

x = -b / 2a

= - 16 / (2 x -2)

= -16 / -4

= 4 inches

Find out more on using a parabola to solve for height at brainly.com/question/2274171

#SPJ1

7 0
1 year ago
Can someone help me asap​
Sholpan [36]

Answer: The second one. Sorry if it's wrong

Step-by-step explanation:

8 0
3 years ago
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