A rotation in the origin is shown. The angle of rotation appears to be A) 30°. B) 45°. C) 60°. D) 90°.

Answer: 5 1/4 x 1 1/5 = 7 1/2 + 3/8 -> 7 7/8

The answer is 7 and 7/8

Answer:

The answer is 5

Answer:

the information is in the theorem itself and to prove it set up an equation in the same format the theorem uses and test it.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

40-24=16

16/4=4

4 tanks

The total cost of painting and tiling a community hall shaped as a cuboid with the given dimensions is £972. This is based on calculating the surface area for paint and the floor area for tiles, then multiplying by the respective costs per m².

To solve this problem, we first need to figure out the total surface area of the cuboid, which will include the floor area for the tiles, and all sides for the paint.
Surface area of the cuboid involves calculating area for all six sides, which totals to 2*(lb + bh + hl), where l is length, b is breadth, and h is height.
Substituting the values given, the total surface area of the cuboid is 2*(40*15 + 15*3 + 3*40) = 2*(600 + 45 + 120) = 2*765 = 1530m2.
The floor area is length * breadth i.e., 40m * 3m = 120 m2.

Next, we calculate the cost of painting and tiling. We know 10 liters of paint covers 25 m2 and costs £10.
So, 1 litre covers 25/10 = 2.5m2 and similarly costs £10/10 = £1.
Therefore, the paint costs for 1530 m2 are 1530/2.5 = 612 litres * £1/litre = £612.

For tiling, the cost for 1m2 is £3, so for a 120 m2 floor, the cost will be 120m2*£3/m2 = £360.
Therefore, the total cost for paint and tiles is £612 + £360 = £972.

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Answer:

10 goody bags.

Step-by-step explanation:

We are asked to find the largest number of identical goody bags that can be using 50 bouncy balls and 110 pokemon cards.

In order to solve our problem we will use GCF (Greatest common factor). Let us find out GCF of 50 and 110.

The factors of 50 are: 1, 2, 5, 10, 25, 50.

The factors of 110 are:  1, 2, 5, 10, 11, 22, 55, 110.

We can see that GCF of 50 and 110 is 10 as 10*11=110 and 10*5=50.

Therefore, the largest number of identical goody bags is 10 with 5 bouncy balls and 11 pokemon cards in each goody bag.

Answer:

168 = x

Step-by-step explanation:

mean  = u=132

standard deviation =sigma = 20

z score =z=1.8

The formula is

z = (x-u)/ sigma

Substituting what we know

1.8 = (x-132)/20

Multiply by 20

1.8*20 = (x-132)/20 *20

36 = x-132

Add 132 to each side

36+132 = x-132+132

168 = x

Multiply the standard deviation by the z-score and add that to the mean:

Value = 132 + (20*1.8) = 132 + 36 = 168

The value would be 168.

By rearranging the formula for the volume of a cylinder to solve for height, and substituting the given values for volume and radius, we find that the height of the can is 5 inches.

To solve for the height h of the cylinder, we need to rearrange the formula for the volume of a cylinder, V =
2h, to solve for h. This is done by dividing both sides of the equation by
2, thus isolating h on one side of the equation.

The rearranged formula becomes:

h = V / (2)

Using the given volume of the can, 62.8 cubic inches, and the given radius of 2 inches, we plug these values into our formula:

h = 62.8 / (3.14 × 2²)

h = 62.8 / (3.14 × 4)

h = 62.8 / 12.56

h = 5 inches

Therefore, the height of the can is 5 inches.

Answer:

(-3, -1)

Step-by-step explanation:

As its reflected across the y-axis  the y coordinate remains the same but the new x-coordinate is the opposite value.

First, let's ignore the answer choices and solve for a value of x ourselves.

2(8 - x) < 4

Distributive property.

16 - 2x < 4

Subtract 16 from both sides.

-2x < -12

Divide both sides by -2 (and flip the inequality sign)

x > 6

The value of x is going to be greater than 6, and so, we can observe the answer choices, and whichever value is greater than 6, is the correct answer.

Answer:

d x=10

Step-by-step explanation:

Answer:

a is less than or equal to -5

Step-by-step explanation:

Answer:

a ≤-5

Step-by-step explanation:

a-3 ≤-8

Add 3 to each side

a-3 +3≤-8+3

a ≤-5

Answer

  [tex]y = -3x^2-4x+3[/tex]

Explanation

The standard form of a parabola is

  [tex]y = ax^2 + bx + c,[/tex]

where [tex]a \ne 0[/tex], and [tex]a,b,c[/tex] are real numbers.

If it passes through (0,3) then when x = 0, y = 3 so this means that

  [tex]3 = a(0)^2 + b(0) + c \implies c = 3[/tex]

so [tex]y = ax^2 + bx + 3[/tex].

If it passes through (1,-4), then when x = 1, y = -4 so

  [tex]\begin{aligned}-4 &= a(1)^2 + b(1) + 3 \\a+b+3 &= -4 \\a+b &= -7 && \text{(I).}\end{aligned}[/tex]

If it passes through (-1,4) then when x = -1, y = 4 so

  [tex]\begin{aligned}4 &= a(-1)^2 + b(-1) + 3 \\a-b+3 &= 4 \\a-b &= 1 && \text{(II).}\end{aligned}[/tex]

Because both (I) and (II) need to be satisfied, we have the system of equations,

  [tex]\begin{cases}a+b &= -7\qquad\text{(I)}\\a-b &= 1\qquad\text{(II)}\end{cases}[/tex]

which we can easily solve by adding the two equations up to get

  [tex]\begin{aligned}(a+a) + (b-b) &= -7 + 1 \\ 2a&= -6 \\a &= -3.\end{aligned}[/tex]

Then we take any of the previous equations to solve for b:

  [tex]\begin{aligned}a+b &= -7\\-3 + b &= -7 \\ b &= -4\end{aligned}[/tex]

Thus the parabola in standard form is

  [tex]y = -3x^2-4x+3.[/tex]

So with the three points that are given to us, we will plug them into the standard form formula that I had mentioned earlier. Firstly, plug (0,3) into the equation since the 0 will cancel out the a and b variable:

[tex]3=a*0^2+b*0+c\\3=c[/tex]

Now we know that the value of c is 3.

Next, plug (1,-4) into the standard form formula and simplify (Remember to plug 3 into the c variable):

[tex]-4=a*1^2+1*b+3\\-4=a+b+3\\-7=a+b[/tex]

Next, plug (-1,4) into the standard form formula and simplify:

[tex]4=a*(-1)^2+b*(-1)+3\\4=a-b+3\\1=a-b[/tex]

With the last two simplified equations, we will create a system of equations:

[tex]-7=a+b\\1=a-b[/tex]

With this, I will be using the elimination method. Add the two equations together, and the following equation is the result:

[tex]-6=2a[/tex]

From here we can solve for a. For this, just divide both sides by 2:

[tex]-3=a[/tex]

Now that we have the value of a, plug it into either equation to solve for b:

[tex]-7=-3+b\\-4=b\\\\1=-3-b\\4=-b\\-4=b[/tex]

Now, plug the obtained values in our standard form equation and your final answer will be:

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

Answer:

35% off, deducts $15.05

Step-by-step explanation:

The sale price was $27.95 and is 65% of the original price. This means the sale was 100%-65%= 35% off the original price.

We can create a proportion to find the original price to see how much was deducted. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the prices and percents.

[tex]\frac{27.95}{x} =\frac{65}{100}[/tex]

We begin solving by cross multiplying numerator to denominator of each fraction.

[tex]27.95(100)=65(x)\\2795=65x\\\frac{2795}{65}=\frac{65x}{65}  \\43=x[/tex]

So the original price was $43. The sale price deducts 43-27.95= 15.05

Answer:

He will earn 13.91 after his raise.

Step-by-step explanation:

13 x .07 = .91

13.00 + .91 = 13.91

The amount Curtis earns per hour after his raise is 13 * (1 + 7%)

From the question, we have the following parameters that can be used in our computation:

Initial = $13

Raise =7%

using the above as a guide, we have the following:

New = Initial * (1 + raise)

So, we have

New = 13 * (1 + 7%)

Hence, the expression is 13 * (1 + 7%)

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Answer:

The answer is $10.80

Step-by-step explanation:

It goes up $0.70 every mile and the flat fee is $3.10.

The equation 3.1 + 0.7(x) when x is the number of miles traveled.

Substitute 11 for x and get  3.1 + 0.7(11).

The answer is $10.80

Answer:

Step-by-step explanation:

160miles • 330miles= 52,800square miles

Now it wants the population density in people per square miles, so you need to divide the population by the number of square miles.  

4779736/52800=90.5 which is about 91people per square mile.  

The population density of Colorado is 48.09 people per mile²

Population density is the concentration of individuals within a specific area. It is given by:

Population density = number of people / land area

Land area = length  * width = 280 * 380 = 106400 mile²

Population density = 5,116,800 / 106400 = 48.09 people per mile²

The population density of Colorado is 48.09 people per mile²

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Answer:

[tex]\frac{5}{18}[/tex] square feet.

Step-by-step explanation:

We have been given that the length of a rectangular piece of wood is 5/12 foot and width is 2/3 foot.

Since area of a rectangle is width times length, so to find the area of piece of wood we will multiply 5/12 by 2/3.

[tex]\text{Area of wood}=\frac{5}{12}\times \frac{2}{3}[/tex]

[tex]\text{Area of wood}=\frac{5}{6}\times \frac{1}{3}[/tex]

[tex]\text{Area of wood}=\frac{5}{6\times 3}[/tex]

[tex]\text{Area of wood}=\frac{5}{18}[/tex]

Therefore, area of piece of wood will be [tex]\frac{5}{18}[/tex] square feet.

Step 1.

Calculate measure of angle α:

[tex]47^o-38^o=9^o[/tex]

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]

Step 3.

Calculate the circumference of the Earth (circle):

[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]

Step 4.

The length of arc is equal 1/40 of the circumference:

[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]

[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]

The distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is approximately 628 miles, calculated using the formula for arc length of a sphere, considering the Earth's radius and the difference in degrees of latitude.

The question revolves around the concept of calculating the arc length in degrees, which is a topic in mathematics, specifically trigonometry.  

The formula for calculating the arc length of a sphere is arc length = radius x angle (in radians).

We already know the radius of the earth (4000 miles) and the difference in latitude between Seattle and San Francisco (47°-38°=9°).

However, in the formula, we need the angle to be in radians. To convert degrees to radians, we use the formula 1 degree = π/180 radians.

So, 9° equals 9*(π/180) = 0.157 radians.

Now, we substitute the values into the formula: arc length = 4000 miles * 0.157 radians. This gives an answer of approximately 628 miles.

Therefore, the distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is about 628 miles.

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Answer:

          7 sqrt(3) =x

Step-by-step explanation:

We know that sin 60 = opposite / hypotenuse

                       sin 60 = x/14

Multiply both sides by 14

                          14 sin 60 = x

                        14 * (sqrt(3)/2) =x

                      7 sqrt(3) =x

The answer is B. 80.8

Answer:

The average of the whole class is 80.8.

The correct answer is B)

Step-by-step explanation:

To solve this problem, it is very important to understand the phrase: "Ten students had an average of 88". Let's see an example.

Imagine that three students in the class took a test and their scores were: 80, 89 and 95. To calculate the average of they three we must divide the sum of the scores by the total number of scores.

[tex]average=\frac{80+89+95}{3}=\frac{264}{3}=88[/tex]

The previous value is the average of the three students. Now, if we say that each student got 88, the average would be 88.

[tex]average=\frac{88+88+88}{3}=\frac{264}{3}=88[/tex]

The previous expression could be simplified as:

[tex]average=\frac{88\times 3}{3}[/tex]

Where, the number 3 means the number of students.

With that in mind, the phrase "Ten students had an average of 88" could be written as:

[tex]average_{10\, \, students}=\frac{88+88+88+88+88+88+88+88+88+88}{10}[/tex]

[tex]average_{10\, \, students}=\frac{88\times 10}{10}=88[/tex]

On the other hand, the phrase "The other students had an average of 76" means that from the 25 students, 15 students got 76 (25 - 10 = 15), and could be written as:

[tex]average_{15\, \, students}=\frac{76+76+76+76+76+76+76+76+76+76+76+76+76+76+76}{15}[/tex]

[tex]average_{15\, \, students}=\frac{76\times 15}{15}=76[/tex]

Finally, to calculate the total average of the 25 students we must divide the sum of the scores of all students by the total number of scores. The sum would be: 88+88+88+88+88+88+88+88+88+88+76+76+76+76+76+76+76+76+76+76+76+76+76+76+76, which equals [tex]88\times 10+76\times 15[/tex]. The total number of scores would be: 25.

[tex]average_{total}=\frac{88\times 10 + 76\times 15}{25}[/tex]

[tex]average_{total}=\frac{880 + 1140}{25}[/tex]

[tex]average_{total}=\frac{880 + 1140}{25}[/tex]

[tex]average_{total}=\frac{2020}{25}[/tex]

[tex]average_{total}=80.8[/tex]

Thus, the average of the whole class is 80.8. The correct answer is B)

Answer:

The hourly rate of pay for:

Jude =$5 an hour

Ben = $4 an hour

Step-by-step explanation:

Let x represents Judy and y represents Ben.

As per the statement:Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80.

⇒[tex]8x + 10y =80[/tex]                     ......[1]

Also, it is given that When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65.

⇒[tex]9x+5y=65[/tex]                         .....[2]

Multiply equation [2] by 2 both sides we get;

[tex]2(9x+5y)=2 \cdot65[/tex]

18x + 10y = 130                                      .....[3]

Subtract [2] from [3] to eliminate y and solve for x;

18x + 10y -8x -10y = 130 -80

Simplify:

10x = 50

Divide both sides by 10 we get;

x = 5

⇒ Judy gets paid $5 an hour

Substitute value of x in [1] we get;

8(5) + 10y = 80

40 + 10y = 80

Subtract 40 from both sides we get;

40 + 10y - 40 = 80 -40

Simplify:

10 y = 40

Divide both sides by 10 we get;

y = 4

⇒Ben gets paid $4 an hour

(x, y) → (x, y + n) - translate the graph n units up

(x, y) → (x, y - n) - translate the graph n units down

(x, y) → (x - n, y) - translate the graph n units left

(x, y) → (x + n, y) - translate the graph n units right

---------------------------------------------------------------------------

(x, y) → (x + 2, y)

translate the graph 2 units right.

Answer:

A

B

Q

D

Step-by-step explanation:

Answer:168

Step-by-step explanation:

56 x 3 = 168

Answer:

The larger number is 52.

Step-by-step explanation:

To find this number, we have to create a statement for both of the equations that are given.

x + y = 96

x - y = 8

Now we can add them together to solve for x (which is the larger number).

x + y = 96

x - y = 8

-------------

2x = 104

x = 52