Please help!!!! Answer question!

With regard to mathematics, what is an accepted statement of fact that is used to prove other statements

spayn [35]

In mathematics, a proof is a deductive agruement for a mathematical statement.In the argument,other prevoiusly establised statements, such as theroms, an be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.

5 0

3 years ago

Suppose you are conducting a survey about the amount grocery store baggers are tipped for helping customers to their cars .for a

ELEN [110]

Using the Empirical Rule and the Central Limit Theorem, we have that:

About 68% of the sample mean fall with in the intervals $1.64 and $1.82.

About 99.7% of the sample mean fall with in the intervals $1.46 and $2.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

<h3>What does the Central Limit Theorem state?</h3>

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem, the standard deviation of the distribution of sample means is:

$s = \frac{0.657}{\sqrt{50}} = 0.09$

68% of the means are within 1 standard deviation of the mean, hence the bounds are:

1.73 - 0.09 = $1.64.

1.73 + 0.09 = $1.82.

99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:

1.73 - 3 x 0.09 = $1.46.

1.73 + 3 x 0.09 = $2.

More can be learned about the Empirical Rule at brainly.com/question/24537145

#SPJ1

5 0

2 years ago

In a survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for th

marysya [2.9K]

Answer:

The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).

Step-by-step explanation:

The formula for estimating the population proportion by a confidence interval is given by:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}$

Where:

$\hat{p}$ is the sample's proportion of success, which in this case is the people that regularly lie during surveys,

$z_{\alpha /2}$ is the critical value needed to find the tails of distribution related to the confidence level,

$n$ is the sample's size.

<u>First</u> we compute the $\hat{p}$ value:

$\hat{p}=\frac{successes}{n}=\frac{98}{603}=0.1625$

<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):

$z_{\alpha /2}=2.576$

Now we can replace in the formula with the obtained values to compute the confidence interval:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}=0.1625\pm 2.576\times\sqrt{\frac{0.1625\times(1-0.1625)}{603}}=(0.1238, 0.2012)$

5 0

3 years ago

4x + 5y = 10

Vika [28.1K]

Answer:

For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.

Step-by-step explanation:

Given equations are:

4x + 5y = 10

Ax + By = 16

The general form of linear equation in two variables is given by:

$ax+by = c$

Here a, b and c are constants and x,y are variables.

In the given equations, after comparing with the general form

$a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16$

"In order for a system of equations to have infinity many solutions,

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ "

Putting the values we get

$\frac{4}{A} = \frac{5}{B} = \frac{10}{16}\\\frac{4}{A} = \frac{5}{B} = \frac{5}{8}\\Now\\\frac{4}{A} = \frac{5}{8}\\\frac{A}{4} = \frac{8}{5}\\A = \frac{8}{5} * 4\\A = \frac{32}{5}\\And\\\frac{5}{B} = \frac{5}{8}\\\frac{B}{5} = \frac{8}{5}\\B = 8$

Hence,

For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.

5 0

3 years ago

Subtract the two expressions. 3x - 4 from -2x + 8

Margarita [4]

-2x - 3x = -5x
8 - 4 = 4
-5x + 4

5 0

3 years ago