The length of a rectangle is 4ft longer than it’s width. If the perimeter of the rectangle is 68ft, find it’s length and width.

The ratio of the sides of a triangle is 2 6 7 if the perimeter of the triangle is 195 meters

timama [110]

Answer: 91m

Step-by-step explanation:

We set three sides of the triangle equal to 2x,6x,7x; because there is the ratio 2:6:7, which x is a common factor of these three sides.

P = a + b + c

2x + 6x + 7x = 195

15x = 195

x = 13

7x suppose be the longest side of the triangle, we plug in 13 for x, then:

7x = 7(13) = 91 m

6 0

3 years ago

How do you help children with their homework?

marishachu [46]

Answer:

Figure out how their teacher, teaches them and try to mimic that learning style. So the child's learns with one way and not multiple.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What is the square root of -1?

Mice21 [21]

Answer:

the square root of -1 is actually "i"

Step-by-step explana

3 0

4 years ago

Read 2 more answers

Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows:

netineya [11]

Answer:

a. A point estimate of the mean pull-force of all connectors in the population is approximately 75.7385

The point estimate for the mean used is the sample mean

b. The point estimate of the pull force that separates the weakest 50% of the connectors from the strongest 50% is 74.3131 N

c. The point estimate of the population variance is approximately 2.8577

The point estimate for the population standard deviation is approximately 1.6905

d. The standard error of the mean is approximately 0.3315

e. The point estimate of a proportion of the connectors are;

(72.7, 0.0385) , (73.8, 0.0769) , (73.9, 0.0385) , (74, 0.0385) , (74.1, 0.0385) ,(74.2, 0.0385), (74.6, 0.0385) , (74.7, 0.0385) , (74.9, 0.0385) , (75.1, 0.0769) , (75.3, 0.0385) , (75.4, 0.0385) , (75.5, 0.0385) , (75.6, 0.0385) , (75.8, 0.0385) , (76.2, 0.0385) , (76.3, 0.0385) , (76.8, 0.0385) , (77.3, 0.0385) , (77.6, 0.0385) , (78, 0.0385) , (78.1, 0.0385) , (78.2, 0.0385) , (79.6, 0.0385)

Step-by-step explanation:

The given data for the pull-force (pounds) for connectors used in an automobile engine are presented as follows;

Pull-force (pounds); 79.6, 75.1, 78.2, 74.1, 73.9, 75.6, 77.6, 77.3, 73.8, 74.6, 75.5, 74.0, 74.7, 75.8, 72.7, 73.8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9, 78.0, 75.1, 76.8

a. A point estimate of the mean pull-force of all connectors in the population is the sample mean given as follows;

$Mean, \ \overline x = \dfrac{\Sigma x_i}{n}$

$\Sigma x_i$ = The sum of the data = 1966.6

n = The sample size = 26

Therefore, the sample mean, $\overline x$ = 1966.6/26 ≈ 75.7385

The point estimate for the mean is approximately 75.7385

The sample mean was used as the point estimate for the mean because it is simple and representative of the sample

b. The weakest 50% of the connectors are;

72.7, 73.8, 73.8, 73.9, 74, 74.1, 74.2, 74.6, 74.7, 74.9, 75.1, 75.1, 75.3

The sum of forces that separates the weakest 50%, $\Sigma x_{i}_{50 \%}$ = 966.2

The point estimate of the pull force that separates the weakest 50% of the connectors from the strongest 50% = $\Sigma x_{i}_{50 \%}$ /13 = 966.2/13 = 74.3131 N

c. The estimate of the population variance is the sample variance, given as follows;

$s^2 =\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n - 1}}$

Where;

${\sum \left (x_i-\overline x \right )^{2} }$ ≈ 71.4415

Therefore;

$s^2 =\dfrac{71.4415 }{25}} \approx 2.8577$

The point estimate of the population variance, s², is 2.8577

The point estimate for the population standard deviation, σ, is tha sample standard deviation, 's', given as follows;

s = √s² = √2.8577 ≈ 1.6905

The point estimate for the population standard deviation ≈ 1.6905

d. The standard error of the mean is given as follows;

$SE_{\mu_x} = \dfrac{s}{\sqrt{n} }$

Therefore, we have;

$SE_{\mu_x}$ = 1.6905/√(26) ≈ 0.3315

The standard error indicates the likely hood of the difference between the sample mean and the population mean

e. The point estimate of a proportion of the connectors are;

(Number of sample with a given pull-force value)/(Sample size (26))

Therefore, using Microsoft Excel, we have

(72.7, 0.0385) , (73.8, 0.0769) , (73.9, 0.0385) , (74, 0.0385) , (74.1, 0.0385) ,(74.2, 0.0385), (74.6, 0.0385) , (74.7, 0.0385) , (74.9, 0.0385) , (75.1, 0.0769) , (75.3, 0.0385) , (75.4, 0.0385) , (75.5, 0.0385) , (75.6, 0.0385) , (75.8, 0.0385) , (76.2, 0.0385) , (76.3, 0.0385) , (76.8, 0.0385) , (77.3, 0.0385) , (77.6, 0.0385) , (78, 0.0385) , (78.1, 0.0385) , (78.2, 0.0385) , (79.6, 0.0385)

8 0

3 years ago

Complete the square to put he equation in convenient form for graphing. Then graph the conic section

Maslowich

First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.

You'll basically complete the square for two equations at the same time. Set it up like this:

(16x^2 + 96x) + (9y^2 - 18y) = 9

Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.

(x^2 + 6x) + (y^2 - 2y) = 9/144

then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.

For instance the first one will be 6/2 = 3^2 = 9

The next one will be 2/2 =1^2 = 1

Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.

(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1

Then find a common denominator on the right side of the equals sign and add them all together to get:

(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144

Factor out the two polynomials

(x+3)^2 + (y-1)^2 = 1449/144

the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17

8 0

3 years ago