find ∠AEC in the figure below.

Answer:

a. In the explanation.

b. The point estimate of the difference can be calculated as the difference between the sample mean and the population mean:

[tex]d=M-\mu=24.95-23.8=1.15[/tex]

c. Test statistic t = 0.90

P-value = 0.1932

The null hypothesis failed to be rejected.

Step-by-step explanation:

We have a sample, wich mean and standard deviation are calculated as:

[tex]M=\dfrac{1}{14}\sum_{i=1}^{14}(27.8+23.84+25.25+21+17.52+19.61+...+26.94+27.24)\\\\\\ M=\dfrac{349.34}{14}=24.95[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{14}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(27.8-(24.95))^2+(23.84-(24.95))^2+...+(27.24-(24.95))^2]}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(8.106)+(1.238)+...+(5.23)]}\\\\\\ s=\sqrt{\dfrac{304.036}{13}}=\sqrt{23.39}\\\\\\s=4.8[/tex]

This is a hypothesis test for the population mean.

The claim is that the consumption of milk in the Midwest is significantly higher than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=23.8\\\\H_a:\mu> 23.8[/tex]

The significance level is 0.01.

The sample has a size n=14.

The sample mean is M=24.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.8.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.8}{\sqrt{14}}=1.28[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{24.95-23.8}{1.28}=\dfrac{1.15}{1.28}=0.9[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=14-1=13[/tex]

This test is a right-tailed test, with 13 degrees of freedom and t=0.9, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>0.9)=0.1932[/tex]

As the P-value (0.1932) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the consumption of milk in the Midwest is significantly higher than the national average.

Answer:

[tex]\fbox{\begin{minipage}{5em}A = 18.3\end{minipage}}[/tex]

Step-by-step explanation:

Given:

Dan was thinking of a number.

Dan adds 10 to it, then doubles it and gets an answer of 56.6.

Solve for:

Dan's original number

Step 1: Clarify the problem:

Denote Dan's original number as A

Dan adds 10 to A => 10 + A, then

Dan doubles this sum => 2 x (10 + A), then

Dan gets an answer of 56.6 => 2 x (10 + A) = 56.6

Step 2: Solve for the defined equation:

2 x (10 + A) = 56.6

Let's divide both sides of equation by 2:

2 x (10 + A)/2 = 56.6/2

We simplify both sides after division:

10 + A = 28.3

Let's transfer all numbers to the right side, except A (the sign of 10 is changed from + to -)

A = 28.3 - 10

Let's perform the subtraction to get A:

A = 18.3

Hope this helps!

:)

Answer:

160 units and $6400

Step-by-step explanation:

We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2

the price per unit is 100, therefore revenue for each unit would be 100 * x

However:

profit = revenue - cost

p (x) = 100 * x - 20 * x - 0.25 * x ^ 2

for the maximum value profit we must derive and equal 0:

p '(x) = 100 - 20 - 0.5 * x

0 = 80 - 0.5 * x

0.5 * x = 80

x = 80 / 0.5

x = 160

Therefore, the maximum profit occurs when there are 160 units, replacing we have:

p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2

p (x) = 6400

that is to say that the $ 6400 is the maximum profit.

Answer:

2835

Step-by-step explanation:

(21×15)9=

(315)9=

2835

Answer:

Please show the graph choice it sounds linear xy (positive)

or parallel depending on how much pens and pencils were.

We know $18 purchased more than 1 pack so this divided by notebook shws us at least 6 per notepack paper or so many packs of pen that cost $18 ffor pens were ratio to 1 pack of paper. ie) if pens were £2 pack then while we understand it could have been as many as 9 we divide by how many we find or bought by the amount of notepaper books to determine the rate and distribution of the money.    

Step-by-step explanation:

$39 - $18 = $21 left over

21/3 = 7 packs of note paper can be purchased..

Answer:

D: <K = 35°

Step-by-step explanation:

<E = 55

<L = 90°

Now

<LKE = 180-90-55

<K = 35°

Answer:

[tex]\fbox{\begin{minipage}{8.8em}Option D is correct\end{minipage}}[/tex]

Explanation:

Here, we state again the definition of inscribed angle in circle:

(1) An inscribed angle has the vertex on the circle and the sides are chords.

=> In the picture shown, angle ELK is inscribed angle with vertex L and LE and LK are chords.

(2)An inscribed angle also creates an intercepted arc whose endpoints are on the angle.

=> Inscribed angle ELK creates intercepted arc EK.

(3) According to the Inscribed Angle Theorem, the measure of intercepted arc is twice as the measure of its inscribed angle.

=> Angle ELK = (1/2) arc EK

Arc EK, whose EK is diameter, is equal to measure of half of circle, or 180 degree, in other words.

=> Angle ELK = (1/2) x 180 = 90 deg

(4) As the property of sum of 3 angles inside a triangle, this sum is equal to 180 degree.

=> Considering triangle ELK:

ELK + LEK + LKE = 180 deg

or

90 + 55 + LKE = 180 deg

or

LKE = 180 - 90 - 55 = 35 deg

Hope this helps!

:)

Answer:

Step-by-step explanation:

a) Number of variables in the data set : 5

b) A quantitative variable is the one which can be quantitatively measured. i.e. it is a numerical value.

A categorical variable is the one that can take one value from a limited number of fixed values.

Exchange is a Categorical Variable. Price/Earnings Ratio is a Quantitative Variable. Gross Profit Margin (%) is a Quantitative Variable.

c. Out of the 25 stocks, AMEX is the exchange for 5 stocks. So percent frequency is 5/25 = 0.2 = 20%.

NYSE is the exchange for 3 stocks. So percent frequency is 3/25 = 0.12 = 12%.

OTC is the exchange for 17 stocks. So percent frequency is 17/25 = 0.68 = 68%.

These percentages are correctly shown in graph a. So the answer is a.

d) The frequency distribution is

Gross Profit Margin                Frequency

0-14.9                                        2

15-29.9                                      6

30-44.9                                     8

45.59.9                                    6

60.74.9                                    3

As we come across the Gross Profit Margin values in the table, we add a | next to its respective interval and build the above table. E.g. the first value in the table under Gross Profit Margin is 36.7 which lies in the interval 30–44.9. So we add one | in fromt of that interval and so on until we cover the entire table. The number of | shows the frequency distribution of the values.

The correct histogram is A.

e. The average price/earnings ratio is found by adding all the 25 values in the table and dividing the answer by 25.

= 505.40/25

Answer:

The mean of depth is 12.75cm.

The variance of depth is of 13.02 cm².

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

[tex]M = \frac{a+b}{2}[/tex]

The variance of the uniform distribution is given by:

[tex]V = \frac{(b-a)^{2}}{12}[/tex]

Uniform distribution on the interval (6.5, 19)

This means that: [tex]a = 6.5, b = 19[/tex]

So

Mean:

[tex]M = \frac{6.5+19}{2} = 12.75[/tex]

The mean of depth is 12.75cm.

Variance:

[tex]V = \frac{(19 - 6.5)^{2}}{12} = 13.02[/tex]

The variance of depth is of 13.02 cm².

Answer:D

Step-by-step explanation:

-2=4/5(0)-2

-2=0-2

-2=-2

-6/5=4/5(1)-2

-6/5=4/5-10/5

-6/5=4/5-10/5

-6/5=-6/5

Step-by-step explanation:

You can take the inverse of a function by replacing all x-values in the equation with y-values and vice versa and subsequently solving for y:

Equation given:

[tex]f(x) = \frac{-x}{x+2}[/tex]

Replace all x-values with y and all y-values with x:

[tex]x = \frac{-y}{y+2}[/tex]

Solve for y:

[tex]x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-\frac{2x}{x+1} =y[/tex]

This is the inverse of f(x), where x ≠ 2..

Answer:

24π

Step-by-step explanation:

If the diameter is 4, the radius is 2

V = [tex]\pi r^2 *h[/tex]

r = 2

h = 6

24π

Answer:

Step-by-step explanation:

diameter: 4 inch (Radius is 2)

V

If the diameter is 4, the radius is 2

V is  r^2*h

the radius is 6

so it’s 24

Answer

About 219-220

Step-by-step explanation:

Answer: $219.047619

Step-by-step explanation: 1150.00 ÷ 5.25 = 219.047619

Answer:

A

Step-by-step explanation:

We can see that Function A's y coordinate doubles every time. The function A = f(x) = 5(2)^x. It is an exponential growth function, and therefore y can never be 0. This means that A does not have an x-intercept.

Function B is a rational function. x cannot be 0, since that would result in an undefined number. This also means that B does not have an x-intercept.

Step-by-step explanation:

1039

This is the correct answer

Answer:

54

Step-by-step explanation:

A = (9*12)/2

A = 9*6

A = 54

Answer:54

Step-by-step explanation:

multiply 9 and 12 then divide by 2 because a triangle is half of a square

Step-by-step explanation:

work is shown and pictured

The discriminant of quadratic equation is,

⇒ D = 0

What is Quadratic equation?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:  ax² + bx + c = 0

We have to given that;

Quadratic equation is,

⇒ - 3 = x² + 4x + 1

Now, We can write as;

⇒ x² + 4x + 1 + 3 = 0

⇒ x² + 4x + 4 = 0

Hence, Discriminant of quadratic equation is,

⇒ D = b² - 4ac

⇒ D = (4)² - 4×1×4

⇒ D = 16 - 16

⇒ D = 0

Thus, The discriminant of quadratic equation is,

⇒ D = 0

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ7

Answer:

[tex]=3\frac{5}{6}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{2}+1\frac{1}{3}\\\mathrm{Add\:whole\:numbers}\:2+1:\quad 3\\\mathrm{Combine\:fractions}\:\frac{1}{2}+\frac{1}{3}:\quad \frac{5}{6}\\=3\frac{5}{6}[/tex]

Answer:40%

Step-by-step explanation:

For every 5 cars two are red. Percentage of red cars to blue is 2/5 * 100 = 40%

Answer:

1. Number of classes used are 7 with 5 class interval.

Step-by-step explanation:

Note: See the attached files for the tables and answers to questions 2, 3, 4 and 5.

Answer:

18, 13

Step-by-step explanation:

x=4+1/2y

x+y=31

4+1/y+y=31

3/2y=27

y=18

x=31-18=13

Answer:

13 & 18

Step-by-step explanation:

Create the formulas:

0.5x+4=y

x+y=31

0.5x+4=y

Multiply both sides by 2

x+8=2y

x+y=31

Subtract 31 from both sides

x+y-31=0

Subtract y from both sides

x-31= -y

Multiply both sides by -1

-x+31=y

Multiply both sides by 2

-2x+62=2y

Combine equations:

-2x+62=x+8

Add 2x to both sides

62=3x+8

Subtract 8 from both sides

3x=54

Divide both sides by 3

x=18

0.5x+4=y

Subtract y from both sides

0.5x-y+4=0

Subtract 0.5x from both sides

-y+4= -0.5x

Multiply both sides by -1

y-4=0.5x

Multiply both sides by 2

2y-8=x

x+y=31

Subtract y from both sides

x= -y+31

Combine equations:

2y-8= -y+31

Add y to both sides

3y-8=31

Add 8 to both sides

3y=39

Divide both sides by 3

y=13

Answer:

-2×h

Step-by-step explanation:

because it drops-2 by hour so multiply-2 by the difference of hours

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then

[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]

But perhaps you'd like the surface integral treatment. Parameterize the surface by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]

with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from

[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]

Take the normal vector to the surface to be

[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]

The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:

[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]

Then the area of the surface is

[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]

which reduces to the integral used in the surface-of-revolution setup.

Answer:

The equations are linearly independent so there is no parametric vector form

Step-by-step explanation:

I attached the solution.

Answer:

x>−6 and x<7

Step-by-step explanation:

Let's solve your inequality step-by-step.

|−2x+1|<13

Solve Absolute Value.

|−2x+1|<13

We know−2x+1<13and−2x+1>−13

−2x+1<13(Condition 1)

−2x+1−1<13−1(Subtract 1 from both sides)

−2x<12

−2x

−2

<

12

−2

(Divide both sides by -2)

x>−6

−2x+1>−13(Condition 2)

−2x+1−1>−13−1(Subtract 1 from both sides)

−2x>−14

−2x

−2

>

−14

−2

(Divide both sides by -2)

x<7

Answer:

x>−6 and x<7

Answer:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13        for the function.

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4         for the inverse.

Step-by-step explanation:

we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:

g(y) = x.

now we have

y=4x-3

y=(1/4)x+3/4

The only table that works for our first function is:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13

You can see this by replacing the values of x and see if the value of y also coincides.

Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.

The second table is that one:

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4

Answer: B and D

x:-23, -15, -3, 1, 13

y:-5, -3, 0, 1, 4

x:-5, -3, 0, 1, 4

y:-23, -15, -3, 1, 13

Step-by-step explanation:

answer: D) 439.85

Step-by-step explanation:

we are given the price of the bike which is $413.

we are also given the sales tax which is 6.5%.

sales tax is added to the original price to give us our total. so in order to find the total cost we need to find what the 6.5% sales tax is and add it to our original price. to find the sales tax number in dollars we need to set up our formula. The easiest formula is to use a proportion. X is out of 413 = 6.5% is out of 100%. X/413=6.5/100. We can then cross multiply then divide. 6.5 times 413=2,684.5. then divide 2684.5÷100= 26.845.

we need to round up to the nearest cent since we are working with dollars and cents 26.85. 26.85 is 6.5% of the price of the bike which is 413. Now we just simply add the tax to the original price and we get the cost. 413+26.85=439.85

Answer:    The answer is D) 439.85

Step-by-step explanation:

Answer:

( 5 ^ -2)^4

= 5 ^ -8

= 1 /5^8

= 1 / 390,625

Answer:

[tex](\frac{3}{8}\,in )^2=\frac{9}{64} \,in^2=0.140625\,\,i^2[/tex]

Step-by-step explanation:

Recall that the formula for the area of a square of side L is: [tex]Area=L^2[/tex]

Therefore, for this case:

[tex]Area=L^2\\Area = (\frac{3}{8} \,in)^2\\Area=\frac{9}{64} \,\,in^2\\Area=0.140625\,\,in^2[/tex]

Answer:

D.

Step-by-step explanation:

It's a right triangle so

[tex]x^2=40^2+9^2[/tex]

x = 41

Answer:

A . 0.85 + (0.15 +(-3)) = -2

B . [(-3)+(-3)]+(-3) = - 9

Step-by-step explanation:

Explanation:-

Associative  property with addition

(a+(b+c)) = (a+b) + c

A)

Given 0.85 + (0.15 +(-3)) = (0.85 +0.15)+(-3)

                                       = 1 - 3

                                       = -2

B)  Given [(-3)+(-3)]+(-3) = ( (-3)+[( -3)+(-3))]

                                     = ( -3 +[-3-3]

                                    =  -3 -6

                                    = -9

Final answer:-

A . 0.85 + (0.15 +(-3)) = -2

B . [(-3)+(-3)]+(-3) = - 9