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3 years ago

Find the measure of each angel if m angle 8 = 115º

Mathematics

1 answer:

zalisa [80]3 years ago

7 0

Lines p and q are parallel.
Corresponding angles are congruent.
Each two adjacent angles are supplementary.
Vertical angles are congruent.

Angles 7 and 8 are adjacent, supplementary angles.
m<7 + m<8 = 180
m<7 + 115 = 180
m<7 = 65

Angles 6 and 8 are corresponding angles and congruent.
m<6 = m<8
m<6 = 115

Angles 1 and 6 are vertical angles and congruent.
m<1 = m<6
m<1 = 115

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Plz answer if you know it....

kap26 [50]

Sales tax is charged on the subtotal (amount before tax).

First, find the subtotal by adding up all of the amounts.

4(675) + 2(110) + 5(41) + 6(135) + 230(2.50)

2700 + 220 + 205 + 810 + 575

Total = 4510

Next, we need to find 7% of 4510. That number is the sales tax.

0.07 x 4510 = 315.70

Sales Tax = $315.70

Total Amount (with tax) = $4825.70

Hope this helps!! :)

7 0

3 years ago

Given a cube with a volume of 36 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?

Schach [20]

A square pyramid, if it fit perfectly in a cube, would be 1/3 of its volume.

V(square pyramid)=1/3(volume of cube)
V(square pyramid)=1/3(36)
V(square pyramid)=12cm³

7 0

3 years ago

Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and

lana [24]

Answer:

Expected profit policy 1 = $40

Expected profit policy 2 = $20

Expected profit policy 3 = $10

Step-by-step explanation:

X values | Probability P(x)

0 | 0.80

1,000 | 0.08

5,000 | 0.10

10,000 | 0.02

A particular company offers three different policies:

Policy 1: $200 deductible with a $780 premium

Policy 2: $500 deductible with a $700 premium

Policy 3: $1000 deductible with a $590 premium

The company pays X - Y in damages if X > Y and 0 otherwise.

So the expected profit is given by

Expected profit = Premium amount - Expected payout

Expected profit = Premium amount - [ (X - deductible) × P(x) ]

Expected profit Policy 1:

E(x) = $780 - [ 0×0.80 + (1,000 - 200)×0.08 + (5,000 - 200)×0.10 + (10,000 - 200)×0.02 ]

E(x) = $780 - [ 0 + 64 + 480 + 196 ]

E(x) = $780 - $740

E(x) = $40

Expected profit Policy 2:

E(x) = $700 - [ 0×0.80 + (1,000 - 500)×0.08 + (5,000 - 500)×0.10 + (10,000 - 500)×0.02 ]

E(x) = $700 - [ 0 + 40 + 450 + 190 ]

E(x) = $700 - $680

E(x) = $20

Expected profit Policy 3:

E(x) = $590 - [ 0×0.80 + (1,000 - 1,000)×0.08 + (5,000 - 1,000)×0.10 + (10,000 - 1,000)×0.02 ]

E(x) = $590 - [ 0 + 0 + 400 + 180 ]

E(x) = $590 - $580

E(x) = $10

Therefore, the expected profits for the three policies are:

Expected profit policy 1 = $40

Expected profit policy 2 = $20

Expected profit policy 3 = $10

8 0

3 years ago

Stephanie has an aquarium that is in the shape of a right rectangular prism, 50 centimetres long, 25 centimetres wide and 30 cen

Bess [88]

To solve this, we are going to use the volume formula for a rectangular prism: $V=lwh$
where
$V$ is the volume of the prism
$l$ is the length of the prism
$w$ is the width of the prism
$h$ is the height of the prism

We are also using the volume of a sphere formula: $V= \frac{4}{3} \pi r^{3}$
where
$V$ is the volume of the sphere
$r$ is the radius of the sphere

Part A: Since she wants a layer of marbles in the bottom of the tank about 5 centimeters deep, the height of this little rectangular prism will be 5 centimeters, so $h=5$ . Since the other measures of our little rectangular prism are the same as the aquarium, $l=50$ and $w=25$ . Lets replace those values in our volume formula:
$V=lwh$
$V=(50)(25)(5)$
$V=6250 cm^{3}$
Now that we know that she wants to cover a volume of 6250 $cm^{3}$ with marbles, lets find the volume of each marble.
We know that the diameter of each marble is 1 cm. Since the radius is of a sphere is half its diameter, $r= \frac{1}{2} =0.5$ . Lets replace that value in our volume formula:
$V= \frac{4}{3} \pi r^{3}$
$V= \frac{4}{3} \pi (0.5)^{3}$
$V=0.52 cm^{3}$
Now, let $x$ the number of marbles she will need to cover a volume of 6250 $cm^{3}$ :
$0.52x=6250$
$x= \frac{6250}{0.52}$
$x=12019.23$
Since we know that each bag of marbles has 500 marbles, we are going to divide the number of marbles she will need by the number of marbles in each bag:
$\frac{12019.23}{500} =24.03$

We can conclude that to fill a layer of 5 cm with marbles, she will need 24 bags of marbles.

Part B: We know that she already have 5 cm of her aquarium filled with marbles, and that she also added water until it’s level is 3 centimeters below the top of the tank, so to find the height of this new rectangular prism, we are going to subtract 5 cm plus 3 cm from the original height of her aquarium:
 $h=30-(5+8)$
$h=30-13$
$h=17cm$
Since the other measures of our little rectangular prism are the same as the aquarium, $l=50$ and $w=25$ . Lets replace those values in our volume formula:
$V=lwh$
$V=(50)(25)(17)$
$V=21250cm^{3}$
Remember that $1litre=1000cm^{3}$ . So:
$(21250cm^3)( \frac{1litre}{1000cm^{3})} =21.25liters$

We can conclude that there are 21.25 liters of water in the tank.

6 0

3 years ago

In your own words, explain why C=2πr, where C is the circumference of a circle of radius r. Include a description of the number

schepotkina [342]

Answer:

Pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi(3.1415).

There are two radii in one diameter. The formula for circumference is pi*d when using diameter which explains the two in front of the formula given by your teacher.

Step-by-step explanation:

7 0

3 years ago