Elijah made 14 quarts of punch for a party. How many gallons of punch did he make?

[tex]\displaystyle|\Omega|=6^3=216\\A=\binom{3}{2}\cdot5=3\cdot5=15\\|A|=\dfrac{15}{216}=\dfrac{5}{72}\approx0.069[/tex]

And

Check

Hence

Or

Option C

Both the first and second statements are true and therefore Option D is the correct answer .

A function can be defined as the equation that identifies relation between a dependent variable and an independent variable.

A function always has a defined range and domain.

In the following statements

I. If f '(c) = 0, then f has a local maximum or minimum at x = c.

f'(c) = 0

It means that the slope of f(x) = 0 at x = c

If f has a local maximum or minimum at x = c  It is a True statement

II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].

If f'(x) = 0 on (a, b),

then f is neither increasing nor decreasing

and therefore is constant on [a, b]

So it is a True statement.

III. The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [−1, 1].

No the theorem cannot be applied as, f is neither continuous nor differentiable at x = 0

It is a False Statement.

Therefore Option D is the correct answer.

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A viable argument showing how it is reflected by the Cost Function for Wichita’s factory is; The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.

From the given options, the best statement is;

The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

A cost function is a formula used to predict the cost that will be experienced at a certain activity level. Thus, the cost function for the best option is;

The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.

The missing options are;

___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.

___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

___ Overtime wages were required to produce at levels above 25,000 units.

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Answer:

  23.20°, 71.57°, 85.24°

Step-by-step explanation:

The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the  vectors when they are placed tail-to-tail.

__

vector definition

The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...

  a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)

The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.

dot product definition

The definition of the dot product of vectors A and B is ...

  A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors

Solving for the angle, we find it to be ...

  [tex]\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)[/tex]

__

Because of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.

The spreadsheet shown in the first attachment does the necessary computations.

As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)

The interior angles of the triangle are 23.20°, 71.57°, 85.24°.

_____

Additional comment

Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.

Answer:

8.3 minutes

Step-by-step explanation:

93,000,000 m/186,000 m/s = 500 s

500/60 = 8.333333

The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³

Surface Area to Volume Ratio = 43/28

Given Data

Rectangular prism A

Length = 2 inches

Width = 7 inches

Height = 8 inches

Surface Area

A=2(wl+hl+hw)

A=2(7*2+8*2+8*7)

A=2(14+16+56)

A= 172 inches²

Volume

Volume = L*W*H

Volume = 2*7*8

Volume = 112 inches³

Surface Area to Volume Ratio

= 172/112

= 43/28

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Answer:

6.36 years (the .36 repeats), so rounded is 6.4.

Step-by-step explanation:

First, I'm going to convert all measurements to meters.

Since 1000 mm = 1 m, divide 44 by 1000.

44/1000 = 0.044 m

Since 100 cm = 1 m, divide 72 by 100.

72/100 = 0.72 m

Next, I'm going to setup an equation using y = mx + b.

b is the beginning amount which is 0.72.

m in the equation represents the rate which is 0.044.

y represents the total which is 1.

Plugin the numbers and solve for x.

1 = 0.044x + 0.72

1 - 0.72 = 0.044x + 0.72 - 0.72

0.28 = 0.044x

0.28/0.044 = 0.044x/0.044

6.36 = x

Answer:

25.13cm

Step-by-step explanation:

formula for circumference of a circle is (2r)π with r being the radius

since the problem gave us the diameter already we can change the formula to 8π (2r is equal to the diameter since diameter is twice as long as the radius)

this gives us the circumference of 25.13

Answer:

x = 5.

Step-by-step explanation:

x^3 - x = 120

We first guess the value of x and calculate the left side.

Take x = 4:-

4^3 - 4 = 64-4 = 60  

This is < 120 so try x = 5:

5^3 - 5 = 125 - 5 = 120.

So one solution is x = 5.

Answer:

[tex]\displaystyle \frac{-11}{9}[/tex]

Step-by-step explanation:

       We will use the equation of change in y over change in x to solve for the slope of the line. Then, we will simplify.

[tex]\displaystyle \frac{y_{2}-y_1 }{x_2-x_1}[/tex]

[tex]\displaystyle \frac{-8-3}{6--3}[/tex]

[tex]\displaystyle \frac{-8-3}{6+3}[/tex]

[tex]\displaystyle \frac{-11}{9}[/tex]

The area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have given a rhombus with diagonals.

The length of the long diagonal p = 2×52 = 104 m

The length of the short diagonal q = 2×8 = 16 m

Area = pq/2 = (104×16)/2 = 832 square m

Thus, the area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

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Answer:

152

Step-by-step explanation:

If you substitute the 6, the expression will look like this-

8( 3(6) + 1 )

You can then times 3 by 6, this makes 18. You then add the one, this equals 19.

19 times 8 = 152.

I hope this helps, have a lovely day.

The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

The dataset is given as:

21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1

The sample mean is:

[tex]\bar x = 22.1[/tex]

The significance level is

α = 0.010

Start by calculating the degrees of freedom using:

df = n - 1

Where n represents the sample size (n = 7)

So, we have:

df = 7 - 1

df = 6

Using the table for t critical values for a two-tailed test, we have:

Critical value = ±3.7074

Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

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200 is the median (50%) of the data represented in the box plot. The fraction of the books has 200 or fewer pages is: 1/2.

In a box plot, the median is indicated as the value marked by the vertical line that divides the rectangular box of the box plot.

The median is the middle of the data and represents the 50th percentile. That is 1/2 the data.

In the box plot given, 200 pages is the median. Therefore, the fraction of the books that have 200 or fewer pages is: 1/2.

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Answer:

24 ft sq

Step-by-step explanation:

find area of triangles

6×4=24

24/2=12

add areas together

12+12=24

Answer:

The number is 8

Step-by-step explanation:

Let x be the number

3x+4 = 28

Subtract4 from each side

3x+4-4 = 28-4

3x= 24

Divide by 3

3x/3 =24/3

x = 8

Answer:

2.25x 10^-6

Step-by-step explanation:

In order to find out which is the scientific notation you would want to count how many zeros are in front of the number in this case it has 6 zeros before the series of numbers meaning that it would be 10^-6

The new dimension of the rectangle are as follows;

The new dimension of the rectangle can be found as follows;

The sides of a square are equal.

Therefore,

let the side of the square = x

Hence,

length = x + 3

width = x + 1

area of rectangle = lw

where

Therefore,

24 = (x + 3)(x + 1)

24 = x² + x + 3x + 3

24 = x² + 4x + 3

x² + 4x + 3 - 24

x² + 4x - 21 = 0

(x - 3)(x + 7)

Therefore,

x = 3 or -7

It can't be negative. Hence, x = 3 ft

Therefore, the new dimension of the rectangle are as follows;

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Answer:

3840

Step-by-step explanation:

Given expression:

4(x+5)(x+1)(x+3)(x - 3)

To:

Evaluate the expression ; for x = 5.

Solution:

Evaluate x = 5 :

Simplify using PEMDAS rule:

P : Parentheses

E : Exponents

M : Multiplication

D : Division

A : Addition

S : Subtraction

Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to evaluate

[tex]\large\pmb{4(x+5)(x+1)(x+3)(x-3)}[/tex] for x=5.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's what PEMDAS stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

So, let's start computing...

///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\//\\\///\\\///\\\///\\\\///\\\\///\\\///\\\///\

                                   Evaluating the expression

First, substitute 5 for x:

[tex]\star~\large\pmb{4(5+5)(5+1)(5+3)(5-3)}[/tex]

Now, use the Order of Operations.

The first operation here is:

[tex]\dag[/tex] P=Parentheses

So we need to perform the operations inside the parentheses first:

[tex]\star~\large\pmb{4(10)(6)(8)(2)}[/tex]

The next operation is multiplication, since we don't have any exponents here:

[tex]\star~\large\pmb{40\times6\times8\times2}[/tex]

Multiply!

[tex]\star~\Large\pmb{3840}~~\square\!\!\!\!\!\checkmark[/tex]

That's the value of the expression 4(x+5)(x+1)(x+3)(x-3) for x=5.

Hope it helps you out! :D

Ask in comments if any queries arise.

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1. Mean of the data: 8

2. Median: 8

3. IQR = 4

4. Members that use the facility 10 days a month is: 2.

See reasons below.

Mean = sum of all values ÷ number of data values (easily solved using a dot plot

Median = middle value (easily found using a box plot).

Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).

1. Mean of the data: use the dot plot.

Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8

2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.

Median = 8

3. IQR = Q3 - Q1 = 10 - 6

IQR = 4

4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.

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Answer:

SORRY I DONOT KNOW THE ANSWER

Step-by-step explanation:

i am sorry i do not know the amswer

Answer:

F(x) = (x+2)(-x+3)(x-2)^2. I think answer should be like this

Answer:

[tex]m\angle B = 28^{\circ}[/tex]

Step-by-step explanation:

All angles in a triangle must add up to [tex]180^{\circ}[/tex]

We can solve for [tex]\angle B[/tex] using this knowledge

[tex]\angle B + 40 + 112 = 180\\\angle B + 152 = 180\\\boxed{\angle B = 28}[/tex]

That is the answer

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Answer:

9

Step-by-step explanation:

Because 3 letter to find that just do 3 times 3 which = 9

Hope This Helped

Answer:

64

Step-by-step explanation:

There are 4 options to choose from:

Each has a 1/4 chance of being picked.

For 3 times in a row, we would multiply the chance of being picked for one option, by whatever the other option's chance is.

As they all have the same chance, and it is 3 times in a row, we would do the following:

1/4 x 1/4 x 1/4

This is:

1/16 x 1/4

Which is:

1/64

Therefore, any possible combination has a 1/64 chance of occurring, meaning that there are 64 possible combinations that could be created.

Offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:
2 bags for £35

2 bags means 50 kg (2×25)

Each kg cost = 35/50 = £0.7 per kg

3 bags for £92.50

3 bags means 150 kg

Each kg cost = 92.50/150 = £0.61 per kg

As we can see, offer B has a low cost per kg

Thus, offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.

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Answer:

Circle D

Step-by-step explanation:

The circumference of a circle can be calculated by multiplying the diameter by π.  Therefore, the circle with the greatest circumference will be the circle with the greatest diameter.

The only circle for which we have been told the radius is Circle D.  The diameter of a circle is twice the radius, therefore the diameter of Circle D is 50 in × 2 = 100 in

There are 12 inches in 1 ft.

Therefore, the circumferences of the circles in order from smallest to largest is:  B < C < A < D

Proof

Diameters

Answer:  Check out the screenshot below for the answers

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

Explanation:

For each column, we divide the values by the sum of each column.

The sum of the first column is 6+8 = 14, and the sum of the second column is 7+3 = 10.

Column 1:

Those values are approximate to two decimal places.

Column 2:

Those values are exact.

The values in bold are then filled in the table as you see below.

A result like 0.43 means that 43% of those who play a sport also play an instrument. The other values are interpreted in a similar fashion.

The predicted number of plants with aphids is 109.

The predicted number of plants with aphids is the ratio of the random plants with aphids to total number of random plants selected multiplied by the number of plants in the nursery.

Predicted number = (7/50) x 780 = 109.

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Answer:

mean = 3.5

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{1+2+3+4+5+6}{6}[/tex] = [tex]\frac{21}{6}[/tex] = 3.5

Answer:

The mean of 1 , 2 , 3 , 4 , 5 , 6 is 3.5

Given :

The observations 1 , 2 , 3 , 4 , 5 , 6

To find :

The mean of 1 , 2 , 3 , 4 , 5 , 6

Solution :

Step 1 of 2 :

Calculate sum of the observations

Here the given observations are 1 , 2 , 3 , 4 , 5 , 6

Number of observations = 6

Sum of the observations

= 1 + 2 + 3 + 4 + 5 + 6

= 21

Step 2 of 2 :

Find the mean

The required mean