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3 years ago

Find the remainder of the division of

Mathematics

2 answers:

Naily [24]3 years ago

7 0

Answer:

C) 77

Step-by-step explanation:

Using remainder theorem:

x = 7

7³ - 5(7)² - 4(7) + 7

katen-ka-za [31]3 years ago

6 0

<h3>Answer: C) 77</h3>

Remainder theorem: If p(x) is divided by (x-k), then the remainder is p(k)

In our case, p(x) = x^3-5x^2-4x+7 and k = 7

p(x) = x^3-5x^2-4x+7

p(7) = (7)^3-5(7)^2-4(7)+7

p(7) = 77

The remainder is 77

Side note: The nonzero remainder means x-7 is not a factor of x^3-5x^2-4x+7.

You can also use polynomial long division (see figure 1) or synthetic division (see figure 2). The figures are attached in the image below.

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In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Calculate the lower confidence

Lyrx [107]

Answer:

The 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

Step-by-step explanation:

In a random sample of 300 boards the number of boards that fall outside the specification is 12.

Compute the sample proportion of boards that fall outside the specification in this sample as follows:

$\hat p =\frac{12}{300}=0.04$

The (1 - α)% confidence interval for population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The critical value of z for 95% confidence level is,

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.04\pm1.96\sqrt{\frac{0.04(1-0.04)}{300}}\\=0.04\pm0.022\\=(0.018, 0.062)\\\approx(1.8\%, 6.2\%)$

Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

6 0

3 years ago

8y + 4x + 6y=? Plz help

postnew [5]

Answer:

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8 0

3 years ago

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Which of the following are solutions for x in the equation ax2 = bx? Select all that apply.

Brums [2.3K]

I uploaded it here as the answers Bc

Slkwowkneojw

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2 years ago

Given the quadratic function g(x)=x^2, find g(3x-2).

maxonik [38]

Answer:

$g(3x-2) = (3x-2)^{2}$

Step-by-step explanation:

$g(x)=x^{2}$

To do this, you must substitute $3x-2$ for x in the equation g(x)

$g(3x-2) = (3x-2)^{2}$

Simplified this would be

$9x^{2} -12x+4$

7 0

3 years ago

67. The line contains the point (4,0) and is parallel to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :