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9 days ago

9

Write the quadratic equation whose roots are six and -2 and who’s leading coefficient is 3 use the letter X to represent the var

iable

1 answer:

babunello [11.8K]9 days ago

6 0

Response:

$3X^{2} - 12X - 36 = 0$

A quadratic equation has solutions of 6 and -2.

Thus, if the variable is denoted by X, the factors of the polynomial function will be (X - 6) and (X + 2).

Thus, the equation can be represented as

(X - 6)(X + 2) = 0

⇒

$X^{2} - 4X - 12 = 0$

If the leading coefficient is 3, we can express the equation as

(Response) $3X^{2} - 12X - 36 = 0$

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Manuel decides to build a fence to enclose an area for his dogs to play. The area is to be rectangular in shape. If he has 80 fe

PIT_PIT [12445]

Manuel has opted to construct a fence to define a play area for his dogs, which will be a rectangular shape. Since only three sides require fencing because his house acts as one side of the rectangle, we conclude that the optimal area configuration will consist of two shorter sides each measuring 20 feet and a longer side measuring 40 feet.

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18 days ago

Jenna works in an ice cream shop. When she starts her shift the tub of chocolate ice cream is 23 full. When she finishes her shi

tester [12383]

Answer:

$Rate = 1.1/hr$

Step-by-step explanation:

Given

$Start = 23$

$End = 16$

$Hours = 6\frac{1}{2}h$

Required

Calculate the hourly rate

First, we will determine the amount of ice cream that was sold

$Ice\ Cream = 23 - 16$

$Ice\ Cream = 7$

Next, calculate the average hourly rate:

$Rate = Ice\ Cream/Hours$

$Rate = 7/6\frac{1}{2}h$

$Rate = 7/\frac{13}{2}h$

$Rate = 7*\frac{2}{13h}$

$Rate = \frac{14}{13h}$

$Rate = 1.07692307692/hr$

$Rate = 1.1/hr$ -- Approximated

4 0

1 month ago

Read 2 more answers

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling

lawyer [12517]

Response:

Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

Detailed explanation:

Maureen McIlvoy, as the owner and CEO of a mail-order business specializing in windsurfing gear, is scrutinizing the order fulfillment processes in her warehouses. Her objective is to achieve a 100% shipment rate of orders within 24 hours. Upon examining her warehouse operations, she discovers that both the East coast and West coast warehouses have not met this goal, although the East Coast warehouse has consistently outperformed its counterpart.

To verify this finding, Maureen’s team randomly sampled 200 orders from the West Coast warehouse (population 1) and 400 from the East Coast warehouse (population 2).

Of the sampled 200 orders from the West Coast warehouse, 190 were delivered within the specified time. In contrast, 372 out of 400 orders from the East Coast warehouse were processed within 24 hours.

The hypotheses can be formulated as followed:

H₀: The proportion of timely shipments from the East Coast does not exceed that from the West Coast warehouse, thus, p₁ ≥ p₂.

Hₐ: The proportion of timely shipments from the East Coast warehouse is indeed greater than that from the West Coast warehouse, stated as p₁ < p₂.

Thus, Maureen's null hypothesis becomes, H₀: p₁ ≥ p₂.

8 0

21 day ago

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn w

Zina [12379]

Answer:

The number of standard deviations above the mean is $z_o = 1.4607$

Step-by-step explanation:

The question indicates that:

The average weight of the corn ears from each farm is $\mu=1.26$

The standard deviation for the corn ears from Iowa is $\sigma_1$

The standard deviation for the corn ears from Ohio is

$\sigma_2= 0.01 + \sigma_1$

A randomly chosen ear of corn from Iowa weighs x = 1.39 pounds

The standardized score is z = 1.645

The weight of a randomly chosen ear of corn from Ohio measures $x_1 = 1.39\ pound$

In general, the standardized score of corn weight from Iowa can be mathematically defined as:

$z = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $\sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}$

=> $\sigma_1 = 0.0790$

Conversely, the standardized score of corn weight from Ohio is expressed as:

$z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }$

=> $z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }$

=> $z_o = \frac{ 1.39 - 1.26 }{ 0.089}$

=> $z_o = 1.4607$

A positive value indicates this quantity represents the number of standard deviations above the mean.

4 0

1 month ago

In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.

tester [12383]

Answer:

128

Step-by-step explanation:

Imagine you have two jars and seven marbles.

The result is $2^{7}$ .

That totals 128

3 0

13 days ago