Write <, =, > to compare the decimals

Can someone please help me, i really will apreciate it

Allushta [10]

Answer:

i know this let me go find it

Step-by-step explanation:

5 0

3 years ago

Which side lengths form a right triangle?

olga nikolaevna [1]

Answer:

B, C

Step-by-step explanation:

A: √4 = 2, so the side lengths form an equilateral triangle, not a right triangle.

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B: √(9²+40²) = 41 . . . . these form a right triangle

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C: √(5² +10²) = √125 . . . . these form a right triangle

4 0

3 years ago

A fast-food restaurant claims that a small order of french fries contains 120 calories. A nutritionist is concerned that the tru

Pie

Answer:

Correct option is (C).

Step-by-step explanation:

The p-value is well defined as the probability, [under the null-hypothesis (H₀)], of attaining a result, of a statistical hypothesis test, equivalent to or greater than what was the truly observed.

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you reject the null hypothesis.

A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to reject the null hypothesis.

A nutritionist is concerned that the true average calorie count in the french fries served by a fast-food restaurant is higher than 120 calories.

The hypothesis to test this can be defined as:

H₀: The true average calorie count in the french fries is 120 calories, i.e. μ = 120.

Hₐ: The true average calorie count in the french fries is more than 120 calories, i.e. μ > 120.

The test statistic is:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}$

The sample mean calories in the sample of 35 small orders of french fries is,

$\bar x=155.6$

And the p-value is,

p-value = 0.00093

The p-value can be interpreted as the probability of getting a sample of 155.6 calories or greater when the population mean is 120 calories.

That is,

$\bar x-\mu=155.6-120=35.6$

The p-value can also be interpreted as probability of getting a sample of 84.4 calories or less when the population mean is 120 calories.

$\bar x-\mu=-35.6$ *

*Since the normal distribution is symmetric the P (Z < -z) = P (Z > z).

So,

$\bar x-\mu=-35.6$

$\\\bar x=-35.6+120\\\bar x=84.4$

Thus, the correct option is (C).

3 0

3 years ago

Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Constr

asambeis [7]

Answer:

a) Null hypothesis: $\rho = 0$

Alternative hypothesis: $\rho \neq 0$

b) The scatter plot is on the figure attached.

c) $t=\frac{0.874}{\sqrt{1-(0.874)^2}} \sqrt{9-2}=4.758$

$p_v = P(t_{7} >4.758) =
0.0010$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that the correlation coefficient is significant.

Step-by-step explanation:

Previous concepts

Pearson correlation coefficient(r), "measures a linear dependence between two variables (x and y). Its a parametric correlation test because it depends to the distribution of the data. And other assumption is that the variables x and y needs to follow a normal distribution".

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

Solution to the problem

In order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

Let X the Court Income and Y= Justice Salary, for this case we have that:

$n=9, \sum X= 3986, \sumY=398. \sumXY=265160, \sum X^2 =4076636, \sumY^2 =22074$

On this case we got that r =0.874

Part a

Null hypothesis: $\rho = 0$

Alternative hypothesis: $\rho \neq 0$

Part b

The scatter plot is on the figure attached.

Part c

In order to test a hypothesis related to the correlation coefficient we need to use the following statistic:

$t=\frac{r}{\sqrt{1-r^2}} \sqrt{n-2}$

Where n represent the sample size and the statistic t follows a t distribution with n-2 degrees of freedom:

$t \sim t_{n-2}$

On this case our value of n = 9 and the statistic is given by:

$t=\frac{0.874}{\sqrt{1-(0.874)^2}} \sqrt{9-2}=4.758$

And the degrees of freedom are given by df=9-2=7

And the p value for this case since we have a bilateral test is given by:

$p_v = P(t_{7} >4.758) =
0.0010$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that the correlation coefficient is significant.

3 0

3 years ago

Seven times a number is 20 more than five times that number. Find the number.

erastova [34]

Answer: 10

Step-by-step explanation:

$7a-20=5a\\7a-20-5a=5a-5a\\2a-20=0\\2a-20+20=0+20\\2a=20\\$

Divide both parts of the equation by 2:

$a=10$

6 0

2 years ago