What is the value of X? A 57 B 48 C 38 D 28

aliina [53]

7 1/8 is greater than 7.025 because if you convert it into a decimal (8 * 7 = 56 + 1 = 57/8 =....) you get 7.125, which is obviously bigger (1>0)

3 0

3 years ago

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John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages

oksano4ka [1.4K]

Answer:

John’s age is 8 years

Step-by-step explanation:

Let

x -----> John’s father's age

y -----> John’s age

z -----> John’s sister's age

we know that

$x=5y$ -----> equation A

$y=2z$

$z=y/2$ -----> equation B

$(x+2)+(y+2)+(z+2)=58$

$x+y+z+6=58$

$x+y+z=52$ -----> equation C

Substitute equation A and equation B in equation C and solve for y

$5y+y+y/2=52$

Multiply by 2 both sides to remove the fraction

$10y+2y+y=104$

$13y=104$

$y=8$

Find the value of x

$x=5(8)=40$

Find the value of z

$z=8/2=4$

therefore

John’s father's age is 40 years

John’s age is 8 years

John’s sister's age is 4 years

7 0

3 years ago

there were 50 cars parked at the airport car rental lot. Of those 50 cars, 10% were red. How many cars were red?

solmaris [256]

10% of the 50 were red.

10% * 50

(10/100) * 50

(1/10) * 50

= 5

5 were red.

8 0

2 years ago

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How to write 100,203 in standard form

True [87]

This is standard form

8 0

3 years ago

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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