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Naddika [18.5K]

2 years ago

8

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than

30 inches of wood to use. Select the system of inequalities that represents the possible length, l, and the possible width, w, that her frame could have. A. l ≤ 12. 2l + 2w < 30 B. l > 12. 2l + 2w < 30 C. l ≤ 12. l + w < 30 D. l > 12. l + w < 30

1 answer:

svlad2 [7]2 years ago

5 0

The perimeter of a rectangle is
2l + 2w
This has to be less than 30 because she has less than 30 inches of wood altogether.
The length must also be "no more than", which means less than or equal to, 12 inches.
Option A satisfies both of these conditions.

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Karson drove from his house to work at an average speed of 35 miles per hour. The drive took him 20 minutes. If the drive took

Nastasia [14]

Answer:

Karson's average speed on his way home was 28 miles per hour.

Step-by-step explanation:

Since Karson drove from his house to work at an average speed of 35 miles per hour, and the drive took him 20 minutes, if the drive took him 25 minutes and he used the same route in reverse, to determine what was his average speed going home, the following calculation must be performed:

60 = 35

20 = X

20 x 35/60 = X

700/60 = X

11.666 = X

25 = 11,666

60 = X

60 x 11.666 / 25 = X

27.99 = X

Therefore, Karson's average speed on his way home was 28 miles per hour.

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Step-by-step explanation:

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2 years ago

myra swims 3/5 of a mile farther than luke.if luke swims 2 and 4/10 miles, how many milrs does myra swim?

Dmitry [639]

Myra swims 3/5 of mile so that is .6 miles

8 0

2 years ago

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An Article in the Journal of Sports Science (1987, Vol. 5, pp. 261-271) presents the results of an investigation of the hemoglob

ValentinkaMS [17]

Answer:

The 95% confidence interval for the population variance is $\left[0.219, \hspace{0.1cm} 0.807\right]\\\\$

The 95% confidence interval for the population mean is $\left [15.112, \hspace{0.3cm}15.688\right]$

Step-by-step explanation:

To solve this problem, a confidence interval of $(1-\alpha) \times 100%$ for the population variance will be calculated.

$$$Sample variance: $S^2=(0.6152)^2$\\Sample size $n=20$\\Confidence level $(1-\alpha)\times100\%=95\%$\\$\alpha: \alpha=0.05$\\$\chi^2$ values (for a 95\% confidence and n-1 degree of freedom)\\$\chi^2_{\left (1-\frac{\alpha}{2};n-1\right )}=\chi^2_{(0.975;19)}=8.907\\$\chi^2_{\left (\frac{\alpha}{2};n-1\right )}=\chi^2_{(0.025;19)}=32.852\\\\$

Then, the $(1-\alpha) \times 100%$ confidence interval for the population variance is given by:

$\left [\frac{(n-1)S^2}{\chi^2_{\left (\frac{\alpha}{2};n-1\right )}}, \hspace{0.3cm}\frac{(n-1)S^2}{\chi^2_{\left (1-\frac{\alpha}{2};n-1\right )}} \right ]\\\\$ Thus, the 95% confidence interval for the population variance is: $\\\\\left [\frac{(19-1)(0.6152)^2}{32.852}, \hspace{0.1cm}\frac{(19-1)(0.6152)^2}{8.907} \right ]=\left[0.219, \hspace{0.1cm} 0.807\right]\\\\$

On other hand,

A confidence interval of $(1-\alpha) \times 100%$ for the population mean will be calculated

$$$Sample mean: $\bar X=15.40$\\Sample variance: $S^2=(0.6152)^2$\\Sample size $n=20$\\Confidence level $(1-\alpha)\times100\%=95\%$\\$\alpha: \alpha=0.05$\\T values (for a 95\% confidence and n-1 degree of freedom) T_{(\alpha/2;n-1)}=T_{(0.025;19)}=2.093\\\\$Then, the (1-\alpha) \times 100$\% confidence interval for the population mean is given by:\\\\$

\ $\left[ \bar X - T_{(\alpha/2;n-1}\sqrt{\frac{\S^2}{n}}, \hspace{0.3cm}\bar X + T_{(\alpha/2;n-1}\sqrt{\frac{\S^2}{n}} \right ]\\\\$ Thus, the 95\% confidence interval for the population mean is: $\\\\\left [15.40 - 2.093\sqrt{\frac{(0.6152)^2}{19}}, \hspace{0.3cm}15.40 + 2.093\sqrt{\frac{(0.6152)^2}{19}} \right ]=\left [15.112, \hspace{0.3cm}15.688\right] \\\\$

5 0

2 years ago

Triangles O N M and S R Q are shown. Angles O N M and S R Q are congruent. The length of side N M is 10 and the length of side S

valina [46]

Answer:

Option C.

Step-by-step explanation:

In △ONM and △SRQ,

$\angle ONM\cong \angle SRQ$

$NM=10$

$SR=20$

$NO=8$

$QR=x$

We need to find the value of x that will make △ONM similar to △SRQ by the SAS similarity theorem.

According to SAS similarity theorem, two triangle are similar if two corresponding sides in both triangles are proportional and the included angle in both are congruent.

It is given that $\angle ONM\cong \angle SRQ$ . So, both triangles are similar by SAS if

$\dfrac{NO}{NM}=\dfrac{SR}{QR}$

Substitute the given values.

$\dfrac{8}{10}=\dfrac{20}{x}$

$8\times x=20\times 10$

$8x=200$

Divide both sides by 8.

$x=\dfrac{200}{8}$

$x=25$

Therefore, the correct option is C.

7 0

2 years ago

Read 2 more answers