Betty bought two bags full of books at an annual library book sale. If she
pays a total of $12.90 for both bags, of which $0.90 is tax, how much did
each bag of books cost?

Answer:

15.94490514

Step-by-step explanation:

First, work out the average, or arithmetic mean, of the numbers:

Count: 5(How many numbers)

Sum: 357(All the numbers added up)

Mean: 71.4(Arithmetic mean = Sum / Count)

Then, take each number, subtract the mean and square the result:

Differences:

4.6, -26.4, -7.4, 8.6, 20.6

(Every Number minus Mean)

Differences^2:

21.16, 696.96, 54.76, 73.96, 424.36

(Square of each difference)

Now calculate the Variance:

Sum of Differences2:1271.2(Add up the Squared Differences)

Variance:254.24(Sum of Differences2 / Count)

Lastly, take the square root of the Variance:

Standard Deviation:15.94490514 (The square root of the Variance)

Answer:

Below.

Step-by-step explanation:

To find the answer, you have to compare the two equations:

[tex]y=\frac{1}{10}x+60[/tex] and [tex]y=\frac{1}{5}[/tex]

So first, the graph looks different because the two slopes are different. The first one will be more vertical than the second one.

The second difference is the y - intercepts. The first equation starts at (0, 60) and the second starts at the origin.

Answer:

Acute and Scalene.

Step-by-step explanation:

By definition, an acute triangle is one that has three angles that are less than 90 degrees. This triangle falls under the category.

By definition, a scalene triangle is one that has three sides with different measurements. This triangle falls under the category.

Hope this helps!

Answer:

The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22

Step-by-step explanation:

We convert the equation to the form (x - h)² + (y - k)² = r²

Where:

(h, k) = Coordinates of the center of the circle

We therefore have;

x² + y² - 2·x + 3·y = 8 which gives;

x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8

(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8

(x - 1)² + (y + 3/2)²  = 8 +  1 + (3/2)² = 45/4

Therefore, the center = (1, -3/2) and the radius = √5 × 3/2

The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;

Midpoint between (1, -3/2) and  (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]

Which gives;

y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]

Which gives;

4·h -2·k -13 = 0.......(1)

Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles

Therefore;

The slope of the line, y = 2·x - 3 = 2, hence we have;

[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]

Which gives;

2·h -4·k -12 = 0.......(2)

Multiplying equation (2) and subtracting from equation (1) gives

4·h -2·k -13 - 2×(2·h -4·k -12) = 0

6·k + 11 = 0

k = -11/6

From which we have;

2·h -4×(-11/6) -12 = 0

Hence;

h = 7/3

Therefore, the center of the reflected circle = (7/3, -11/6)

The equation of the reflected circle is therefore;

(x - 7/3)² + (y + 11/6)² = 45/4

Which gives;

9·x² + 9·y² - 42·x + 33·y - 22 = 0

or x² + y² - 42/9·x + 33/9·y = 22/9.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The Whispering Lakes  Neighborhood Association is  having a hamburger cookout.  Each family can choose whether  to order the hamburgers or  bring their own. Use the  information in the table to solve  the number stories. Use  drawings, tables, or equations  to show what you did.

Mrs. Ward found 80-ounce packages of hamburger on sale. If she needs to make  2 of each size hamburger, how many packages of meat will she need to buy?

Answer:

The number of meat packages is

100/80 = 1.25 = 5/4

Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.

Number of meat packages = 2

Step-by-step explanation:

Please refer to the attached table where we are given size of hamburgers and the weight of corresponding hamburger patty in pounds.

small = 1/8 lb

medium = 1/4 lb

large = 1/2 lb

jumbo = 3/4 lb

king of burgers = 1 1/2 lb = 3/2 lb

To make 1 of each hamburger we need

Total weight of patty = 1/8 + 1/4 + 1/2 + 3/4 + 3/2

Total weight of patty = 25/8 = 3.125 lb

But she needs to make  2 of each size hamburger so,

Total weight of patty = (25/8)×2 = 25/4 = 6.25 lb

Mrs. Ward found 80-ounce packages of hamburger on sale

first we have to convert pounds into ounces

We know that 1 pound has 16 ounces

6.25×16 = 100 ounces

So the number of meat packages required is

100/80 = 1.25 = 5/4

Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.

Number of meat packages = 2

Answer:

1. (-1/4,0)(1.5,0)

2.(-1/2,2)(6/4,2)

Step-by-step explanation:

just locate the numbers on the graph

Answer:

Jason has 75 pencils.

Step-by-step explanation:

In order to get from 4 to 100, you must multiply by 25 (100/4 = 25). And in order to find the amount of pencils Jason has, you must have an equivalent ratio. So you have to also multiply 3 by 25, 3 * 25 = 75. Jason has 75 pencils.

Answer:

the slope is zero because

Step-by-step explanation:

this is a perfect horizontal line passing through y=-3

I've been thought

hope it helps

Answer:

Slope = 0

This is because the line does not go up or down. And the line is horizontal leading to the factor of the slope being 0.

Answer:

x = - [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{5}[/tex] (x - 2) = 4x

Multiply both sides by 5 to clear the fraction

2(x - 2) = 20x ( divide both sides by 2 )

x - 2 = 10x ( subtract x from both sides )

- 2 = 9x ( divide both sides by 9 )

- [tex]\frac{2}{9}[/tex] = x

Answer: 27 miles in 1 gallon

Step-by-step explanation:

297/11

The unit rate of 297 miles in 11 gallons will be 27 miles/gallons.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b, will be the denominator.

We will be used when division is not possible wholly

For example 4/2 is divisible so we write 2 instant of 4/2 while 1/3 is not divisible so we write 1/3 instant of 0.33.

Proportion is the relation of a variable with another. It could be direct or inverse.

The ratio is very useful to determine complex calculation where decimal number become tough to solve.

Given,

297 miles in 11 gallons

297 miles ⇔ 11 gallons

Divide by 11 on both sides

297/11 miles ⇔ 11/11 gallons

27 miles ⇔ 1 gallon

So, 27 miles in 1 gallon.

Hence unit rate is 27 miles/gallon will be correct.

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Answer:

1/4

Step-by-step explanation:

3 and 6 are both multiples of 3, so there is a 2/8 chance of spinning a multiple of 3, which can be simplified to 1/4.

Answer:

A

Step-by-step explanation:

17/12 = 1  5/12

1×12+5=17

Answer:

A

Step-by-step explanation:

Hyperbolic geometry is defined as a non-Euclidean geometry.

(invalidating the fifth postulate of Euclid's five fundamental postulates)

Choice B and D can be eliminated because this has nothing to do with perpendicular lines.

Choice C should be eliminated as well since that's exactly the fifth postulate of Euclid's five fundamental postulates

We are left with A by the process of elimination

Answer:

A. There are an infinite number of lines parallel to a given line through a given point.

Hope this Helps!

The volume is 15/16 cubic meters.

please see the attached picture for full solution

hope it helps

Answer:

Option B.

Step-by-step explanation:

We take a point D from the figure attached,

Coordinates for the point D → (-1.5, 3.5)

And coordinates of D' → (3.5, 1.5)

Coordinates of D when rotated about the origin,

Option A. Rotated by 270° clockwise.

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

Therefore, Option A. is incorrect

Option B. rotation by 90° clockwise

Rule to be followed

D(x, y) → D'(y, -x)

D(-1.5, 3.5) → D'(3.5, 1.5)

Therefore, Option B. is correct.

Option C. 90° counterclockwise

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

This option C is incorrect.

Option D. 180° counterclockwise

Rule to be followed,

D(x, y) → D'(-x, -y)

D(-1.5, 3.5) → D'(1.5, -3.5)

Therefore, option D is incorrect.

Answer:

B. 90 clockwise

Step-by-step explanation:

Answer:

x = -2, x= -5 , x= +5

Step-by-step explanation:

x^3 + 2x^2 -25x - 50 = 0

Factor by grouping

x^3 + 2x^2        -25x - 50 = 0

x^2(x+2)   -25( x+2) = 0

(x+2) ( x^2 -25) =0

Using the zero product property

x+2 =0     x^2 -25 =0

x=-2            x^2 = 25

x= -2            Taking the square root of each side

                     x = ±5

Answer:

y - 32 = 4(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 1 = 4(x + 3) ← is in point- slope form

with slope m = 4

Parallel lines have equal slopes.

Using m = 4 and (a, b) = (4, 32), then

y - 32 = 4(x - 4) ← equation of parallel line

Answer:

The solution is x=4.75  and   y = -22

Step-by-step explanation:

To find the solution to the system of equations, we will follow the steps below:

3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)

-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)

add equation (1) and equation (2)

1.6x =7.6

Divide both-side of the equation by 1.6 to get the value of x

1.6x /1.6 =7.6/1.6

x =4.75

substitute x = 4.75 into equation (1) and solve for y

3.2(4.75) + 0.5y = 4.2

15.2 + 0.5y = 4.2

subtract 15.2 from both-side of the equation

15.2 - 15.2 + 0.5y = 4.2-15.2

0.5y = -11

Divide both-side of the equation by 0.5

0.5y/0.5 = -11/0.5

y = -22

The solution is x=4.75  and   y = -22

Answer

x= 4.75       y=-22

Step-by-step explanation:

got it right on the unit test!!

Answer: angles 1 and 7

Answer:

A

Step-by-step explanation:

(-4-3, 7+7)

(-7, 14)

Answer: A

Step-by-step explanation:

Answer:

A,D

Step-by-step explanation:

I'm taking the test

The first and the fourth graph do not represent constant rates of change. Hence, option A and option D are correct.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the first and the fourth graph the function follows a curved graph because of it, it does not follow linearity. In the second and third graphs, the function follows a linear line, therefore, it shows a constant rate of change.

Hence, option A and option D are correct.

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x x y = (13 i + 4 j - 9 k) x (- i + 7 j - 4 k)

Distribute the cross product:

x x y = 13*(-1) (i x i) + 4*(-1) (j x i) + (-9)*(-1) (k x i)

........... + 13*7 (i x j) + 4*7 (j x j) + (-9)*7 (k x j)

........... + 13*(-4) (i x k) + 4*(-4) (j x k) + (-9)*(-4) (k x k)

x x y = -13 (i x i) - 4 (j x i) + 9 (k x i)

........... + 91 (i x j) + 28 (j x j) - 63 (k x j)

........... - 52 (i x k) - 16 (j x k) + 36 (k x k)

By definition of the cross product, we have

i x i = j x j = k x k = 0

i x j = k

j x k = i

k x i = j

and for any two vectors x and y, the product is anti-symmetric:

x x y = -(y x x)

This makes the products on the "diagonal" vanish, and we can condense terms using the anti-symmetry property:

x x y = (4 + 91) (i x j) + (9 + 52) (k x i) + (63 - 16) (j x k)

x x y = 95 k + 61 j + 47 i

x x y = 47 i + 61 j + 95 k

Answer:

4+2.4=6.4+1.44=7.84

The infinite geometric sum of 4+2.4+1.44+... will be 10.

At each point in the sequence, you multiply or divide by the common ratio. Divide two sets of phrases that follow one another to find it. Whichever pair of terms is picked, as long as they appear next to one another in the sequence, is irrelevant.

It is given that, the sequence is 4+2.4+1.44+...

The sequence is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is obtained that the common ratio is,

r=2.4/4

r=0.6

The Sum of an infinite geometric sequence is,

S = a / (1-r)

S=4 / (1-0.6)

S=10

Thus, the infinite geometric sum of 4+2.4+1.44+... will be 10.

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Answer:

60 possible sequences.

Step-by-step explanation:

That would be 6! / 3! 2!

   6*5*4*3*2*1

=  ------------------

     3*2*1*2*1

= 5*4*3

= 60.

Answer:

The answer is option 2.

Step-by-step explanation:

Given that the equation of a straight line is y = mx + c where m represents gradient and c is the y-intercept which touches the y-axis.

By looking at the graph, we know that it is a positive gradient and it touches -1 at y-axis.

Answer:

Answer:

[tex](\sqrt[2]{32})^{9}[/tex]=5931641.60152

Step-by-step explanation:

:)

Answer:

rectangles

Step-by-step explanation:

convenient to use rectangles for the individual areas because they will combine horizontally and vertically to make larger rectangles with no gaps.

Answer:

the difference would be 28 degrees.

Step-by-step explanation:

The question says difference so we subtract the two following temperatures 30 and -2 which would be 28 degreees.

Answer: The difference between the high and low temperature in the thermometer is 32°F.

Step-by-step explanation:

Given information: Highest temperature = 30°F and the lowest temperature = -2°F.

We need to find the difference between the high and low temperature in the thermometer.

Difference between the high and low temperature is

Difference = Highest temperature - Lowest temperature

Difference = 30°F - (-2°F)

Difference = 30°F + 2°F

Difference = 32°F

Answer:

X=4

Step-by-step explanation:

Solution: x equals 4

x/14-(6/21)=0

1. Simplify 2/7

x/14- 2/7 is 0

It’s too much steps