According to the stem-and-leaf plot above, how many trees are between 610

Suppose a baker claims that the average bread height is more than 15cm. Several of this customers do not believe him. To persuad

laila [671]

Answer:

$17-2.262\frac{1.9}{\sqrt{10}}=15.641$

$17+2.262\frac{1.9}{\sqrt{10}}=18.359$

So on this case the 95% confidence interval would be given by (15.641;18.359)

And since the lower limit for the confidence interval is higher than 15 we can conclude that at 5% of significance the true mean is higher than 15 cm

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".

$\bar X=17$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.9 represent the sample standard deviation

n=10 represent the sample size

Confidence interval

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=10-1=9$

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(0.025,9)".And we see that $t_{\alpha/2}=2.262$

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

$17-2.262\frac{1.9}{\sqrt{10}}=15.641$

$17+2.262\frac{1.9}{\sqrt{10}}=18.359$

So on this case the 95% confidence interval would be given by (15.641;18.359)

And since the lower limit for the confidence interval is higher than 15 we can conclude that at 5% of significance the true mean is higher than 15 cm

4 0

3 years ago

Write an explicit formula for An, the nth term of the sequence 7, -42, 252, ....

erik [133]

Answer:

$A_n = 7(-6)^{n-1}$

Step-by-step explanation:

Key skills needed: Explicit formula, Geometric sequence

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7 or 252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

$a_n = a_1(r)^{n-1}$

--> r means the constant (or common ratio) that is being multiplied.

--> $a_1$ means the first term

--> $a_n$ means the "nth" numbered term (so $a_3$ is the 3rd term, $a_{10}$ is the 10th term and so on).

--> $n-1$ is just the "n" in $a_n$ minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> $r = -6$ (Since we got -6 as the constant/common ratio).

--> $a_1 = 7$ (Since 7 is the 1st term)

This means that our formula would be --> $A_n = 7(-6)^{n-1}$

Hope you understood and have a nice day!! :D

8 0

3 years ago

What is the reason for each step in the solution of the inequality?

Citrus2011 [14]

step 1: Given

step 2: Distributive Property

step 3: Combine Like terms

step 4: Subtraction Property of Order

step 5: Addition property of order

step 6: Division property of order

Step-by-step explanation:

We are given the inequality: $-38-3(x+5)>6x-17$

We need to match each step with the reasons.

The given steps are:

1.

−38−3(x+5)>6x−17

So, Reason for step 1: Given

2.

−38−3x−15>6x−17

So, Reason for step 2: Distributive Property

3.

−3x−53>6x−17

So, Reason for step 3: Combine Like terms

4.

−9x−53>−17

So, Reason for step 4: Subtraction Property of Order

5.

−9x>36

So, Reason for step 5: Addition property of order

6.

x<−4

So, Reason for step 6: Division property of order

Keywords: Solving inequalities

Learn more about Solving inequalities at:

#learnwithBrainly

7 0

3 years ago

Can someone help me with this? Right answer gets brainliest!! :)

Sedbober [7]

I have 2 answers in mind

Answer #1:

$\frac{y}{z}$

Step-by-step explanation:

quotient means the answer to 2 things being divided so the quotient of y and z would be $\frac{y}{z}$ because there is no numerical value.

Answer #2:

1

Step-by-step explanation:

Usually, when a letter is left by itself in an equation it usually has an invisible one in front of it. so when dividing y by z it would equal 1/1 which is equal to one.

Hope this helps :)

6 0

3 years ago

What is an equation of the line that passes through the point (-6, -7) and is

Alexandra [31]

Answer:

Step-by-step explanation:

Product of slope of perpendicular lines = -1

6x + 5y = 30

Write this equation in y = mx + b form

5y = -6x + 30

y = $\frac{-6}{5}x+\frac{30}{5}$