Factor a number, vairable, or expression out of the polynomial shown below.<br> x(8x-3)+ 7(8x-3)

40. A catering chef is making a large quantity

ivann1987 [24]

The chef can plan on making 32 servings.

6 0

3 years ago

A student is trying to calculate the density of a ball. She already knows the mass, but she needs to determine the volume as wel

mario62 [17]

<h2>Answer and Explanation:</h2><h2 />

The density of a substance is defined as its mass per unit volume. In a mathematical language, this can be written as follows:

$\rho=\frac{m}{V} \\ \\ \\ Where: \\ \\ \rho: \ density \\ \\ m:mass \\ \\ V:Volume$

From the problem, a student is trying to calculate the density of a ball. She already knows the mass, but is facing a problem because she also needs to find the volume. From geometry, we know that the volume of a sphere is:

$V=\frac{4}{3} \pi r^{3}$

Since a ball is a sphere, then the student can use this formula. She just need to measure the radius of the ball and compute the Volumen, then she have to plug both the value of the mass and the value of the Volume in the equation $\rho=\frac{m}{V}$ . An easy way to find the radius is to take the measure of the diameter of the ball and divide that value by 2.

6 0

4 years ago

Random samples of students were compared to see whether or not there was a difference in the proportion favoring the university'

Nimfa-mama [501]

Answer:

There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the proportion of residents and commuters who prefer the switch.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1 (residents), of size n1=200 has a proportion of p1=0.4.

$p_1=X_1/n_1=80/200=0.4$

The sample 2 (conmuters), of size n2=200 has a proportion of p2=0.6.

$p_2=X_2/n_2=120/200=0.6$

The difference between proportions is (p1-p2)=-0.2.

$p_d=p_1-p_2=0.4-0.6=-0.2$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{80+120}{200+200}=\dfrac{200}{400}=0.5$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.5*0.5}{200}+\dfrac{0.5*0.5}{200}}\\\\\\s_{p1-p2}=\sqrt{0.0013+0.0013}=\sqrt{0.0025}=0.05$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.2-0}{0.05}=\dfrac{-0.2}{0.05}=-4$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z$

As the P-value (0.00008) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.

5 0

4 years ago

.Write the equation of the line with m = 3 going through the point (–2, –5). Put your answer in Slope–Intercept Form.

OverLord2011 [107]

Answer:

$y = 3x +1$

Step-by-step explanation:

Given

$m = 3$

$(x_1,y_1) = (-2,-5)$

Required

The equation

This is calculated as:

$y = m(x - x_1) + y_1$

So, we have:

$y = 3(x - -2) -5$

$y = 3(x +2) -5$

Open bracket

$y = 3x +6 -5$

$y = 3x +1$

7 0

3 years ago

Miguel ordered a rectangular print for his bedroom. The print is 7/8 ft wide and 1 3/5 ft long. What is the area of the print as

blagie [28]

The answer is 1 2/5 ft²

The area (A) of the rectangle with width w and length l is:
A = w * l

We know:
w = 7/8 ft
l = 1 3/5 ft = 1 + 3/5 = 5/5 + 3/5 = (5 + 3)/5 = 8/5 ft

A = 7/8 * 8/5
A = 7/5 = (5+2)/5 = 5/5 + 2/5 = 1 + 2/5 = 1 2/5 ft²

7 0

3 years ago

Factor a number, vairable, or expression out of the polynomial shown below. x(8x-3)+ 7(8x-3)