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2 years ago

Write the quadratic equation whose roots are

1 answer:

maks197457 [2]2 years ago

5 0

The quadratic equation $y = ax^2 +bx+c$ can be written in the form:
$y = a(x-p)(x-q)$
Where p and q are the roots of the equation.
Given p = 4, q = -2, a = 3, the quadratic will look like this:
$y = 3(x-4)(x+2)$
Finally, distribute and combine like terms to put it in standard form.
$y = 3(x^2 - 4x+2x -8) \\ \\ y = 3(x^2 -2x-8) \\ \\ y = 3x^2 -6x -24$

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A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean le

borishaifa [10]

Answer:

$1000-1.96\frac{2}{\sqrt{4}}=998.04$

$1000+1.96\frac{2}{\sqrt{4}}=1001.96$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$1000-1.96\frac{2}{\sqrt{4}}=998.04$

$1000+1.96\frac{2}{\sqrt{4}}=1001.96$

5 0

2 years ago

Betty paints twice as fast as Dan. Working together, Dan and Betty can paint 2, 400 square feet in 4 hours. Another employee, Su

Natalija [7]

Answer:

2670 square feet. Option e.

Step-by-step explanation:

Dan and Betty can paint 2,400 square feet in 4 hours.

They can paint in one hour $\frac{2400}{4}$ = 600 square feet.

Since given that Betty paints twice as fast as Dan. Let us take an equation:

Let Betty = B, Dan = D and Sue = S

B = 2D

4(B+D) = 2400

4B + 4D = 2400

12D = 2400

D = 200 sq. ft.

B = 2D = 400 sq. ft.

Therefore, Dan can paint 200 square feet in 1 hour and Betty paints twice 400 square feet in 1 hour.

Now given three of them can paint 3,600 square feet in 3 hours.

3( B+D+S) = 3600

3B + 3D + 3S = 3600

3(400) + 3(200) + 3(S) = 3600

1200 + 600 + 3S = 3600

S = 600 Sq. ft.

Sue can paint 600 square feet in one hour.

So sue can paint in 4 hours and 27 minutes.

$(\frac{4+27}{60})$ × 600

= 2670 square feet. Option e.

8 0

2 years ago

your friend deposits $9500 in an investment account that earns 2.1% annual interest. what is the balance after 11 years when the

solmaris [256]

Answer:

The answer is "$ 11,961.43"

Step-by-step explanation:

Given values:

P = $ 9500

r= 2.1 %

time (t)= 11 year

total quarterly year =4

Formula:

$A= P (1+\frac{r}{n})^{nt}\\\\$

quarterly time = $4 \times 11$

$= 44$

$A= P (1+\frac{r}{n})^{nt}\\\\$

$A = 9500 ( 1+ \frac{0.021}{4})^{44}\\\\A = 9500(\frac{4+ 0.021}{4} )^{44} \\\\A = 9500(\frac{4.021}{4} )^{44} \\\\A= 9500 (1.00525)^{44}\\\\A= 9500(1.25909819)\\\\A= 11,961. 43\\$

8 0

2 years ago

A graph shows an x- and y-axis. The data line is in the shape of a "vee." The begins above the x-axis and to the left of the y-a

HACTEHA [7]

Answer:

As x increases, y decreases and then increases.

Step-by-step explanation:

You can see in the graph as the x values are moving to the right (increasing), the y values go down first (decreasing), then go up (increasing). So basically you can see that as x increases, y decreases first, then starts to increase.

5 0

2 years ago

Find the solution of this system of equations -2x + 8y = 14 -2x – 2y = -26

Elodia [21]

X cancels out, 8y + 2y is equal to 10y, and 26 + 14 is 40, so y=4

5 0

2 years ago

Read 2 more answers