Find the value of x that makes each sentence true.

How many degrees there in 3/5 right angle A. 180 B. 90 C. 150 D. 54

Natalija [7]

Answer:

D. 54

Step-by-step explanation:

Right angle = 90°

3/5 of 90°

3/5 × 90°

270 ÷ 5 = 54°

8 0

3 years ago

Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? E

slamgirl [31]

Answer:

Diego is correct.

He has correctly divided 1 in groups of $\frac{5}{6}$ .

Step-by-step explanation:

The question 'How many groups of 5/6 are in 1?' means that we need to divided 1 into groups of $\\frac{5}{6}$ .

When we form groups from a given total, we divided the total by the size of the group.

If we are dividing $N$ number of people in groups of $x$ number of people, then the expression to find the number of groups formed can be given as:

⇒ $\frac{N}{x}$

For this question the data given is:

$N=1$

$x=\frac{5}{6}$

So, the number of groups formed can be given as:

⇒ $\frac{1}{\frac{5}{6}}$

When divisor is a fraction, then we multiply the reciprocal of the divisor with the dividend.

⇒ $1\times\frac{6}{5}$

⇒ $\frac{6}{5}$

In order to convert fraction to mixed number we will divide numerator with denominator and then write the quotient as whole number, remainder as numerator and the denominator remains as it is.

On dividing 6 by 5, the quotient =1 and remainder =1. Thus the mized number is:

⇒ $1\frac{1}{5}$

Thus, there are $\frac{6}{5}$ or $1\frac{1}{5}$ groups in 1. This matches with Diego's answer and hence he is correct.

3 0

3 years ago

An igneous rock may change into which of the following?

grin007 [14]

By going through the rock cycle igneous rock can change into any other type of rock, so A. any of the above

3 0

3 years ago

Read 2 more answers

Find the value of x in this figure. 50 40 30 60

devlian [24]

Put a picture so we can see

8 0

3 years ago

Read 2 more answers

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca

saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let put some notation

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as $d_i = y_i -x_i$ and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}$

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

$\bar d=-0.7$ represent the sample mean for the difference

$\mu_d$ population mean (variable of interest)

$s_d$ =1.32 represent the sample standard deviation

n=8 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}$ (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

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

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that $t_(\alpha/2)=2.306$

Now we have everything in order to replace into formula (1):

$-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776$

$-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376$

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

6 0

3 years ago