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zlopas [31]
3 years ago
11

a rectangular picture measuring 5 in. by 7 in. is surrounding by a frame with uniform width x. Write a quadratic function in sta

ndard form to show the combined area of the picture and frame.​
Mathematics
2 answers:
9966 [12]3 years ago
8 0

Answer:

(4x² + 24x + 35) in²

Step-by-step explanation:

(5+2x)(7+2x)

35 + 14x + 10x + 4x²

4x² + 24x + 35

ale4655 [162]3 years ago
7 0

Answer: A(x) = 4x² + 24x + 35

Step-by-step explanation:

Let x represent the width of the rectangular frame.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The measurement of the rectangular picture is 5 in. by 7 in.

If the width is 5 inches, then the combined width of the picture and frame is 5 + x + x = (5 + 2x) inches

The combined length would be

7 + x + x = (7 + 2x) inches

Therefore, a quadratic function in standard form to show the combined area of the picture and frame would be

(5 + 2x)(7 + 2x)

35 + 10x + 14x + 4x²

A(x) = 4x² + 24x + 35

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About 9% of the population has a particular genetic mutation. 900 people are randomly selected. Find the standard deviation for
timama [110]

Answer:

The standard deviation is of 8.586.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a genetic mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

About 9% of the population has a particular genetic mutation.

This means that p = 0.09

900 people are randomly selected.

This means that n = 900

Find the standard deviation for the number of people with the genetic mutation in such groups of 900.

\sqrt{V(X)} = \sqrt{900*0.09*0.91} = 8.586

The standard deviation is of 8.586.

3 0
2 years ago
If the pattern below follows the rule “starting with two, every consecutive line has a number that is one less than twice the pr
erastovalidia [21]

Answer: the answer is 33

 

7 0
3 years ago
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 3-i, squ
SVEN [57.7K]
Real coefients
if a+bi is a root then a-bi is also a root
since 3-i is a root then 3+i s also a root

also the √7, so if √7 is a root then -√7 is also a root
so

f roots are r1 and r2 then the factored form is
f(x)=(x-r1)(x-r2)

roots are 3-i, 3+i and √7 and -√7

f(x)=(x-(3-i))(x-(3+i))(x-√7)(x-(-√7))
expanded
f(x)=x⁴-6x³+3x²+42x-70
8 0
3 years ago
How many degrees does the hour hand move from 3:00 to 5:30?
hodyreva [135]

now, keeping in mind that a circular clock has 360° total, and there are 12 hours labeled on it evenly, so the angle between each hour label is 360 ÷ 12 = 30.

so, from 3pm to 5pm, it moved by 30° + 30° = 60°.

from 5pm to 5:30, that's only half an hour, so it moved half 30°, or 15°.

60° + 15° = 75°.

4 0
3 years ago
Five milliliters of a children s medicine contains 400 mg of the drug amoxicillin. How many mg of amoxicillin does 25 ml contain
Nonamiya [84]

Answer:

ok, so pretty much you can set up an equation for this. You can use fractions to find this out.

Step-by-step explanation:

<h2>\frac{5}{400} =\frac{25}{x}</h2><h2 /><h2>what you do is multiply 400*25 and then divide by 5. It should be 2000</h2>
4 0
2 years ago
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