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3 years ago

The Quadratic Formula gives which roots for the equation 2x2 + 7x = -2?

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

7 0

Answer:

B. (-7 +/-√33) / 4

Step-by-step explanation:

2x2 + 7x + 2 = 0

x = [-7 +/- √(7^2 - 4*2*2)] / 2*2

x = -7/4 +/- √(33) / 4

= (-7 +/-√33) / 4

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A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

GenaCL600 [577]

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

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

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean income = $\frac{\sum X}{n}$ = $4.70

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = $1.83

n = sample of parking meters = 10

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

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

P(-2.262 < $t_9$ < 2.262) = 0.95 {As the critical value of t at 9 degrees of

freedom are -2.262 & 2.262 with P = 2.5%}

P(-2.262 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.262) = 0.95

P( $-2.262 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu$ < $2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }$ , $4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }$ ]

= [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error = $2.262 \times {\frac{s}{\sqrt{n} } }$

= $2.262 \times {\frac{1.83}{\sqrt{10} } }$ = 1.31

4 0

3 years ago

Translate the following words to algebra symbols, using "n" as the variable. The product of six and a number is 24.

sveta [45]

So n will be the unknown, and the expression is:
6n = 24
from where we can find the number n:
n = 24/6
n = 4

7 0

3 years ago

Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.

luda_lava [24]

Answer:

286.97

Step-by-step explanation:

find the area of the rectangle first

14*15=210

Find the area of a circle

πr^2=a

the radius of the circle is half the height of the rectangle

π*(7*7)=a

a=153.94

Now

Divide the area by two

153.94/2=76.97

Now add the two areas

76.97+210

7 0

3 years ago

Read 2 more answers

You estimate that a box contains 141 envelopes the actual number of envelopes is 150 find the percent error

S_A_V [24]

0.0094% error

Divide 150/141. You get 0.94, then you need to find the percentage of that by clicking the percent button of your calculator

7 0

3 years ago

write the slope-intercept form of the line that passes through the point (1,0) and is parallel to x-y=7. type your answer in the

Brilliant_brown [7]

Parallel lines have the same slope but different y intercepts.
turn x-y=7 into slope intercept form by isolating y which would be -y=-x+7
divide the equation by -1 in order to make y positive and you get y=x-7
So rewrite the equation with the same slope but this time solving for b
y=x+b
plug in your coordinates
0=1+b
subtract 1 from both sides
-1=b
so your equation would be
y=x-1

7 0

3 years ago

Read 2 more answers