y = 0.8x+ 7.2
20x + 32y = 48

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                          P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 94.3

            n = sample of car drivers = 16

            [tex]\mu[/tex] = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95

P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                   = [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]

                                   = [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Answer:  243/5 = 48.6

Step-by-step explanation:

  a₁,  375,  a₃,   a₄,  81 , a₆

First, let's find the ratio (r). There are three multiple from 375 to 81.

[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]

Next, let's find a₆ which is one multiple from 81.

[tex]a_6=81\bigg(\dfrac{3}{5}\bigg)^1\\\\\\.\quad =\large\boxed{\dfrac{243}{5}}[/tex]

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

Answer:

-17x + y = 128

Step-by-step explanation:

First, find the slope.

[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{9-(-8) }{-7-(-8)}\\m=\frac{9+8 }{-7+8}\\m=\frac{17}{1} \\m=17[/tex]

Now, use point-slope form to find the equation.

y - y = m(x - x)

y - 9 = 17(x - (-7))

y - 9 = 17(x + 7)

y - 9 = 17x + 119

y = 17x + 128

Since your equation needs to be in Ax + By = C form, rearrange the equation so that the x and y values are on the left side of the equation.

y = 17x + 128

-17x + y = 128

Answer:

4.167(10²)

Step-by-step explanation:

Step 1: Put number into proper decimal form

416.7 = 4.167

Step 2: Figure out exponent

Since we are moving the decimal places 2 places to the right, our exponent is 2

Answer:

4.167 × 10^2

Step-by-step explanation:

= 4.167 × 10^2

(scientific notation)

= 4.167e2

(scientific e notation)

= 416.7 × 10^0

(engineering notation)

(one)

= 416.7

(real number)

Answer:

[tex]y = -3/2x + 4[/tex]

Step-by-step explanation:

[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]

Answer:

x=-52

Step-by-step explanation:

1/3x=-17 1/3

x=-52

Answer:

SSA the only other right one missing is ASA

The greatest number is 6.23 times 10 superscript 12.

The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

We are given that the number so;

A.6.23 x 10^12 is equivalent to rolling the decimal 12 times to the right.

B.6.23 x 10^8 is equivalent to rolling the decimal 8 times to the right.

C.6.23 x 10^-6 is equivalent to rolling the decimal 6 times to the left.

D.6.23 x 10^3 is equivalent to rolling the decimal 3 times to the right.

This shows the 10 has been multiplied by itself thrice.

Learn more about scientific notation here:

https://brainly.com/question/3112062

#SPJ6

Answer:

A. 7√3 in

Step-by-step explanation:

We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:

tan60° = x/7

x = 7tan60°

x = 7√3

Answer:

It's A

Step-by-step explanation:

Answer:

yes, because they intercept the same arc

Step-by-step explanation:

Answer:

yes, because they intercept the same arc

Step-by-step explanation:

Answer:

d = 3 in

Step-by-step explanation:

Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.

Answer: a. 12.4 years

Step-by-step explanation:

Function to represent exponential growth continuously:

[tex]A=A_0e^{rt}[/tex]  ...(i)

, where [tex]A_0[/tex] = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.

As per given , we have

[tex]A_0=\$1300\\\\r=8\%=0.08\\\\ A=\$3500[/tex]

To find : t

Put all values in (i) ,

[tex]3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}[/tex]

Taking natural log on both sides

[tex]\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4[/tex]

Hence, it would take 12.4 years.

so, the correct option is a. 12.4 years .

Answer:

[tex]\frac{12}{x^2 +7x}[/tex]

Step-by-step explanation:

Simply multiply straight across which you get

12/X X × ( X +7 )

Then just multiply X into the parenthesis

Hope this helps :)

Answer:

2800

Step-by-step explanation:

2826 to the nearest hundred is 2800

Answer:

angle of bc= 180-168= 12°

length of bc= 12/360 × π × diameter

= 12/360 × 22/7 × 21

= 12/360 × 66

= 2,20 cm (b)

Answer:

13

Step-by-step explanation:

We can find the missing side length by using the pythagorean theorem

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

So, 13 is the missing side length.

Answer:

more info is needed

Step-by-step explanation:

Answer:

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean is significantly less than 5.4.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]

The significance level is 0.05.

The sample has a size n=44.

The sample mean is M=5.31.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=44-1=43[/tex]

This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]

As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Answer:

[tex]\begin{center}\begin{tabular}{ c c } n & T\\ 0 & 20 \\ 1 & 25 \\ 2 & 30 \\ 3 & 35 \\ 4 & 40 \\ \end{tabular}\end{center}[/tex]

Please refer to graph attached.

Step-by-step explanation:

Given that mass of each candy in the box is 5 gm.

Mass of empty box is 20 gm.

Total grams, [tex]T = 5n + 20[/tex]

To find: A table of values and graph of the relation.

Solution:

The given equation is nothing but a Linear equation in two variables.

Let us try to create a table of values by putting some values of 'n' and then finding the values for Total grams 'T'.

Let us put [tex]n = 0 \Rightarrow T =5\times 0 +20 = 20[/tex]

Let us put [tex]n = 1 \Rightarrow T =5\times 1 +20 = 25[/tex]

Let us put [tex]n = 2 \Rightarrow T =5\times 2 +20 = 30[/tex]

Let us put [tex]n = 3 \Rightarrow T =5\times 3 +20 = 35[/tex]

Let us put [tex]n = 4 \Rightarrow T =5\times 4 +20 = 40[/tex]

So, the table of values becomes:

[tex]\begin{center}\begin{tabular}{ c c } n & T\\ 0 & 20 \\ 1 & 25 \\ 2 & 30 \\ 3 & 35 \\ 4 & 40 \\ \end{tabular}\end{center}[/tex]

We can see that the value of T is increasing with increasing values of 'n'.

Please refer to the attached image for the graph of given equation.

As it is a linear equation in two variables, it will be a straight line. It will be an increasing positive slope graph.

The correct answer is $216

Explanation:

The chart shows the price users need to pay for visiting the museum or riding on the train. This includes a difference in price between adults and students. However, as the club includes only students (27 students) the price that should be considered are $3 for visiting the museum and $5 for the train ride. Additionally, you can know the total the student spend if you multiply the prices by the total number of students.

27 (number of students) x $3 (price for visiting the museum) =  $81 (total for visiting the museum)

27 (number of students) x $5 (price for the train ride) =  $135 (total for the train ride)

Additionally, you will need to add both results to know the total: $81 + $135 = $216

You can also get the same result if you consider each student will spend $8 (price for visiting the museum and for the train ride) and then multiply this by the number of students ($8 x 27 = $216)

Answer:

(n- 2/3)²

Step-by-step explanation:

We have:

It can be put as:

Here we consider n = a and -2/3 = b, then

Now we add 4/9 to a given binomial to make it perfect square:

So, added 4/9 and got a perfect square (n- 2/3)²

Question:

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

30

∑  (−3i+5)

i=1

Answer:

The first three terms are : 2, -1 and -4

The last term is: -85

The sum of the sequence is: -1245

Step-by-step explanation:

Given;

==================================

30

∑  (−3i+5)                    -------------------(i)

i=1

==================================

Where the ith term aₙ is given by;

[tex]a_{i}[/tex] = [tex]-3i + 5[/tex]         -------------------(ii)

(a) Therefore, to get the first three terms ([tex]a_1, a_2, a_3[/tex]), we substitute i=1,2 and 3 into equation (ii) as follows;

[tex]a_{1}[/tex] = [tex]-3(1) + 5[/tex] = 2

[tex]a_2 = -3(2) + 5 = -1[/tex]

[tex]a_3 = -3(3) + 5[/tex][tex]= -4[/tex]

Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;

[tex]a_{30} = -3(30) + 5 = -85[/tex]

(b) The sum [tex]s_n[/tex] of an arithmetic sequence is given by;

[tex]s_n = \frac{n}{2}[a_1 + a_n][/tex]   -----------------(iii)

Where;

n = number of terms in the sequence = 30

[tex]a_1[/tex] = first term = 2

[tex]a_n[/tex] = last term = -85

Substitute the corresponding values of n, [tex]a_1[/tex] and [tex]a_n[/tex] into equation (iii) as follows;

[tex]s_n = \frac{30}{2}[2 + (-85)][/tex]

[tex]s_n[/tex] = 15[-83]

[tex]s_n[/tex] = -1245

Answer:

Step-by-step explanation:

H0: mu is equal to $108.50

Ha: mu is not equal to $108.50

This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.

z = x-u / sd/√n

Where x is $112, u is $108.50 sd is $16 and n is 64

z = 112-108.50 / 16/√64

z = 3.5/(16/8)

z = 3.5/2

z = 1.75

To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50

Answer:

Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.

Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.

Step-by-step explanation:

Answer:

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

Step-by-step explanation:

Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.

If total cost = C(x, y)

Average cost = C(x, y) ÷ (x+y)

For this question, total cost function is

C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾

The average cost is simply this total cost function divided by the total number of units produced.

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.

Hope this Helps!!!

Here the l'Hospital's Rule is appropriate, as the limit is in the form [tex]\infty / \infty[/tex]. Take a look at the procedure below -

[tex]\lim_{x \to \infty} x^4e^{-x^3} = \lim_{x \to \infty} \frac{x^4}{e^{x^3}}[/tex],

At this point, one can conclude that the solution should " boil down " to the expression [tex]4 / \infty[/tex], and thus the solution is 0.

Hope that helps!

Answer:

Probability of answering 5out of 10 correctly= 0.246

Step-by-step explanation:

Total question answered= 2

Question answered correctly= 1

Probability of answered correctly= 1/2

Probability of answered correctly= 0.5

Probability of answered incorrectly = 0.5

Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)

Probability of answering 5out of 10 correctly= 0.246

Answer:

A

Step-by-step explanation:

For lines to be parallel, their slopes need to be the same.

For lines to be perpendicular, the product of their slopes needs to be -1.

None of these conditions are met since the slopes are 2 and 4 respectively.

Sooo.... The answer must be A! :)

Answer:

The lines given are neither perpendicular nor are they parallel.

Step-by-step explanation:

In order for two lines to be be parallel, they must have the same slope but different y-intercepts. In order for two lines to be perpendicular, one line has to have a slope that is the negative reciprocal of the other line.

We are given two line equations.

y = 2x

y = 4x + 1

These lines do not represent a perpendicular situation nor do they represent a parallel situation.