A 210-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.

Exponential functions have the form f(x)=b^x. What type of an exponential function would you have (increasing or decreasing) if

adoni [48]

Answer:

Increasing

Step-by-step explanation:

Let's see what happens if we choose a value for b greater than 1.

Let's try b=2.

$f(x)=2^x$ .

I'm going to keep increasing x. If y increases, the the function is increasing. If y decreases, the function is decreasing.

Let's start with x=1.

$y=2^1=2$

Now x=2.

$y=2^2=4$

The y's got higher as you increased x so the function is increasing.

8 0

3 years ago

Consider the accompanying data on breaking load (kg/25mm width) for various fabrics in both an unabraded condition and an abrade

WITCHER [35]

Answer:

The critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998.

The test statistic (t=1.729) is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.

Step-by-step explanation:

We have a matched-pair t-test for the difference.

We have the null and alternative hypothesis written as:

$H_0: \mu_d=0\\\\H_a: \mu_d>0$

We have n=8 pairs of data. We calculate the difference as:

$d_1=U_1-A_1=36.4-28.5=7.9$

Then, with this procedure we get the sample for d:

$d=[7.9,\, 35,\, 5.5,\, 4.2,\, 6.7,\, -3.7,\, -0.9,\, 3.3]$

The sample mean and standard deviation are:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(7.9+35+5.5+. . .+3.3)\\\\\\M=\dfrac{58}{8}\\\\\\M=7.25\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((7.9-7.25)^2+(35-7.25)^2+(5.5-7.25)^2+. . . +(3.3-7.25)^2)}\\\\\\s=\sqrt{\dfrac{985.08}{7}}\\\\\\s=\sqrt{140.73}=11.86\\\\\\$

Now, we can perform the one-tailed hypothesis test.

The significance level is 0.01.

The sample has a size n=8.

The sample mean is M=7.25.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.86.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{11.86}{\sqrt{8}}=4.1931$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.25-0}{4.1931}=\dfrac{7.25}{4.1931}=1.729$

The degrees of freedom for this sample size are:

$df=n-1=8-1=7$

This test is a right-tailed test, with 7 degrees of freedom and t=1.729, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t>1.729)=0.0637$

As the P-value (0.0637) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.

If we use the critical value approach, the critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998. The test statistic is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.

8 0

3 years ago

We decided that the movie night will last four hours each movie takes 1.75 hours and we want to make sure we leave a half hour f

Naddik [55]

2 movies
4 hours - .5 popcorn -1.75-1.75=0 Easier terms 4 hours minus 30 min is 3 hours and 30 min left each movie is 1 hour and 45 min plus 1 hour 45 min i that's 2 hours and 90 min 90 min are one hour and 30 min. So 2 hours plus one hour and 30 min is the 3 hours and 30 min are we're left

4 0

2 years ago

YOU RRR MEH HEROOOZZ! PUHLEASZEEE ITS 10:30pm!!

avanturin [10]

Answer:

$x(35)\approx 11.8$

Step-by-step explanation:

<u>Modeling With Functions </u>

We have a table of values of speeds vs distance taken for a car to stop. We are required to find a model that uses the square root and fits the given data to predict other values of d as a function of v.

By the nature of the problem, we can know that for v=0, d must be 0 too. So our model won't include a vertical shift or independent term. Being v the speed of the car and x the distance it takes to stop, we use the following model

$x(v)=A\sqrt{v}$

We must find A to make the function fit the data. Let's use the first point (v,x); (20,9)

$9=A\sqrt{20}$

Solving for A

$\displaystyle A=\frac{9}{\sqrt{20}}$

$A\approx 2$

Then we have

$x(v)=2\sqrt{v}$

Evaluating for v=35

$x(35)=2\sqrt{35}=11.83$

$\boxed{x(35)\approx 11.8}$

Last option

8 0

3 years ago

2 cm green square is painted on a triangle with a base of 6 and a height of 7. A dot will be randomly placed on the triangle. Wh

agasfer [191]

The area of the triangle is
(1/2)*(6)*(7) = 21 cm²

The area of the square is
(2)(2) = 4 cm²

The area of the triangle that is not covered by the square is
21 - 4 = 17 cm²

The probability that the dot will be placed outside the square is
17/21

Answer: 17/21 (or 0.81)

7 0

3 years ago

A 210​-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.

A 210-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.