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3 years ago

Solve using perfect square factoring patterns. y2 + 14y + 49 = 0

1 answer:

4 0

Y² + 14y + 49 = 0

We know a² + 2ab + b² = (a + b)²
(y)² + 2 x 7 x y + (7)² = 0
(y + 7)² = 0
y = -7

y = -7

Correct option C

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What is the area of this?

Vanyuwa [196]

$area = lw \\ area = (7.5)(6) \\ area = 45 {feet}^{2}$

$area = \frac{1}{2} bh \\ area = \frac{1}{2} (6)(4) \\ area = \frac{1}{2} (24) \\ area = 12 {feet}^{2}$

total area = 45 + 12

total area = 57 feet²

6 0

3 years ago

The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir

Paha777 [63]

Answer:

95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time = 5.15 years

$\sigma$ = sample standard deviation = 1.68 years

n = sample of college graduates = 4400

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } }$ , $5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } }$ ]

= [5.10 , 5.20]

Therefore, 95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0

3 years ago

A can of orange juice has a circular base with an area of 156 square centimeters. The height of the can is 20 centimeters.

docker41 [41]

A Because if you do 156 x 20 it equals 3120. It’s A because the volume formula is Length x Width x height, And 156 and 20 were the only numbers given.

4 0

4 years ago

it is 3 kilometers from Linda's house to the nearest mailbox. How far is it in meters? Be sure to include the correct unit in yo

tester [92]

Answer:

1km=1000m... thats basically the answer so the nearest mail box is 3000M

3 0

3 years ago

Solve the system by substitution. 3x-6y=2 4x+3y=-1

crimeas [40]

Answer:

y = -1/3

x = 0

Step-by-step explanation:

3x-6y = 2 then 3x = 2+6y, x=(2+6y)/3

4x+3y = -1

substitute for x

4(2/3+2y)-6y = 2

8/3+8y-6y = 2

reduce

2y = 2-8/3

2y = -2/3

divide both sides by 2

y = -1/3

4x+3(-1/3) = -1

4x = 0

x = 0

8 0

3 years ago