Write an equation of the circle given its center and radius

Long division (4b^3+10b^2-32b+15) divided by (4b-6)

MrMuchimi

Answer:

4b^3 + 10b^2 - 32b + 15

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2(2b - 3)

Step-by-step explanation:

Take out the greatest common factor of (4b - 6) which is 2 and 3.

8 0

2 years ago

Store A sells 6 totes for $53.70. Store B sells 8 of the same totes for $71.60. Which store sells the toes for the lower unit pr

Alenkasestr [34]

Divide 53.70 by 6 to give you 8.95 and divide 71.60 by 8 to give you 8.95 so they sell it for the exact same unit price

6 0

2 years ago

If one bag of grass seed will cover 225 square feet, what is the minimum number of bags the haney family will need to cover thei

Veronika [31]

Answer:

9 bags

Step-by-step explanation:

First we will need to calculate the area of their entire backyard, which has a shape of trapezium.

So the formula for the area of a trapezium is $A=\frac{(a+b)*h}{2}$

a and b are the lenghts of the parallel sides and h is the height.

From the picture $a=10*5=50\\b=9*5=45\\h=8*5=40$

Then we plug into our formula

$A=\frac{(a+b)*h}{2} =\frac{(50+45)*40}{2} = 1200$ square feet

To get the number of bags required we just simply divide the aree of their entire yard by the space that 1 bag covers. We get:

$\frac{1900}{225} =8.444...$ bags

This is more than 8 bags so they will need 9 bags to cover their entire yard.

8 0

2 years ago

An automobile company wants to determine the average amount of time it takes a machine to assemble a car. A sample of 40 times y

aksik [14]

Answer:

A 98% confidence interval for the mean assembly time is [21.34, 26.49] .

Step-by-step explanation:

We are given that a sample of 40 times yielded an average time of 23.92 minutes, with a sample standard deviation of 6.72 minutes.

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 average time = 23.92 minutes

s = sample standard deviation = 6.72 minutes

n = sample of times = 40

$\mu$ = population mean assembly time

Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, a 98% confidence interval for the population mean, $\mu$ is;

P(-2.426 < $t_3_9$ < 2.426) = 0.98 {As the critical value of z at 1% level

of significance are -2.426 & 2.426}

P(-2.426 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.426) = 0.98

P( $-2.426 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.426 \times {\frac{s}{\sqrt{n} } }$ ) = 0.98

P( $\bar X-2.426 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.426 \times {\frac{s}{\sqrt{n} } }$ ) = 0.98

98% confidence interval for $\mu$ = [ $\bar X-2.426 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.426 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $23.92-2.426 \times {\frac{6.72}{\sqrt{40} } }$ , $23.92+2.426 \times {\frac{6.72}{\sqrt{40} } }$ ]

= [21.34, 26.49]

Therefore, a 98% confidence interval for the mean assembly time is [21.34, 26.49] .

7 0

2 years ago

MARKING BRAINLIESTTT!!! PLUS 30PTS EARNED!! HELP ASAPP PLZZZ!!!!

Elza [17]

Answer:

1. 9 < s < 17

2. 5 < MN < 19

3. AD > BD

Step-by-step explanation:

1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:

the sum of the shortest two sides is greater than the length of the longest side
the length of any side lies between the sum and the difference of the other two sides

Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...

9 < s < 17

(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)

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2. Same as (1) using different numbers.

12 -7 < MN < 12 +7

5 < MN < 19

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3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:

AD > BD

7 0

2 years ago