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Bogdan [553]
3 years ago
7

In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. If the perimeter of MNPQ is 68 inches, t

hen determine the length of NP. Show how you solved for your answer.
Mathematics
1 answer:
Svetlanka [38]3 years ago
6 0

Answer: NP = 9 inches

Step-by-step explanation:

In a parallelogram, the opposite sides are equal.

If the length of the longer side is MN, it means that the length of the two opposite longer sides is 2MN.

If the length of the shorter side is NP, it means that the length of the two opposite shorter sides is 2NP.

The perimeter is 2MN + 2NP

If the perimeter of MNPQ is 68 inches, it means that

2MN + 2NP = 68- - - - - - - - - - - -1

In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. It means that

MN = 2NP + 7- - - - - - - - - - -2

Substituting equation 2 into equation 1, it becomes

2(2NP + 7) + 2NP = 68

4NP + 14 + 2NP = 68

4NP + 2NP = 68 - 14

6NP = 54

NP = 54/6

NP = 9 inches

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Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= <u> X[bar] - μ </u>~ N(0;1)

       σ/√n

The formula for the interval is:

X[bar] ± Z_{1- \alpha /2} * (σ/√n)

Z_{1- \alpha /2}= Z_{0.90} = 1.28

3.15 ± 1.28 * (0.33/√15)

[3.04; 3.26]gr

The margin of error (d) of a confidence interval is hal its amplitude (a)

a= Upper bond - Lower bond

d= (Upper bond - Lower bond)/2

d= \frac{(3.26-3.04)}{2} = 0.11

2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= Z_{1- \alpha /2} * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= Z_{1- \alpha /2} * (σ/√n)

\frac{d}{Z_{1- \alpha /2}}= σ/√n

√n * \frac{d}{Z_{1- \alpha /2}}= σ

√n = σ * \frac{Z_1- \alpha /2}{d}

n = (σ * \frac{Z_1- \alpha /2}{d})²

n=  (0.33 * \frac{1.28}{0.08})²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

4 0
3 years ago
Y=3 - 2x<br> 3x + 4y = 1
PolarNik [594]

Answer:

{y,x} = {17/2,-11}

Step-by-step explanation:

7 0
3 years ago
How many strings are there of four lowercase letters that have the letter x in them?
borishaifa [10]
We can subtract from the number of strings of length 4 of lower case letters the number of string of length 4 of lower case letters other than x. Thus the answer is 264 − 254 = 66,<span>351</span>
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3 years ago
50+25 POINTS!!! PLZ HELP WILL GIVE BRAINLIEST!!!
frosja888 [35]

3x-2 if x is less an or greater than 1,  will be a negative y value.

-2x+3 when x is greater than 1 will also be a negative y value.


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5 0
3 years ago
Read 2 more answers
Which points of the following points are solutions to the equation 3x-4y-8=12
Natali [406]

Answer:

(0, -5), (4, -2), (-16, -17)

Step-by-step explanation:

I attach your full question in the image below

The equation is

3x-4y-8=12

Which can be rewritten as

3x-4y =12 +8

3x-20 = 4y

y = (3/4)*x - 5

We need to check each individual case

(0,-5)

y = (3/4)*(0) - 5  

y = -5

True

(4,-2)

y = (3/4)*(4) - 5  

y = -2

True

(8,2)

y = (3/4)*(8) - 5  

y = 1

False

(-16,-17)

y = (3/4)*(-16) - 5  

y = -17

True

(-1,-8)

y = (3/4)*(-1) - 5  

y = -23/4

False

(-40,-34)

y = (3/4)*(-40) - 5  

y = -35

False

(0,-5) (4,-2) and (-16,-17) are the solutions

8 0
3 years ago
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