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1 year ago

Which statement could be used in step 2 when proving

Mathematics

1 answer:

Vinil7 [7]1 year ago

5 0

In proving that x = 30, the statement that could be used in step 2 is: A. ∠ORP and ∠ORN are a linear pair.

<h3>What is a Linear Pair?</h3>

When two angles lie on a straight line, they form a linear pair.
The sum of the two angles that form a linear pair = 180 degrees.

Thus:

∠ORP and ∠ORN are angles on a straight line, and they form a lienor pair.

Therefore, in proving that x = 30, the statement that could be used in step 2 is: A. ∠ORP and ∠ORN are a linear pair.

Learn more about linear pair on:

brainly.com/question/13218054

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HELP PLZ

ollegr [7]

Answer:

a. ∠D'A'B'

Step-by-step explanation:

From the graph it is clear that the transformation doesn't affect the size and shape of the figure ABCD.

Only the coordinates of the points are changed with the length of each side remaining the same.

Hence the corresponding angle values will also remain unaltered.

∴ ∠DAB = ∠D'A'B'

5 0

3 years ago

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some o

noname [10]

Answer: He should invest $44000 in fund A and $11000 in fund B.

Step-by-step explanation:

Let x represent the amount which he invested in fund A.

Let y represent the amount which he invested in fund B.

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some of the money into Fund A that earns 2% per year and the rest in Fund B that earns 10% per year.. This means that

x + y = 55000

The formula for determining simple interest is expressed as

I = PRT/100

Considering fund A,

P = $x

T = 1 year

R = 2℅

I = (x × 2 × 1)/100 = 0.02x

Considering fund B,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

The interest that he wants to earn on the total amount in a year is 3.6%. The interest would be

I = (55000 × 3.6 × 1)/100 = 1980

Therefore,

0.02x + 0.1y = 1980 - - - - - - - - - -1

Substituting x = 55000 - y into equation 1, it becomes

0.02(55000 - y) + 0.1y = 1980

1100 - 0.02y + 0.1y = 1980

- 0.02y + 0.1y = 1980 - 1100

0.08y = 880

y = 880/0.08

y = 11000

x = 55000 - y = 55000 - 11000

x = 44000

4 0

3 years ago

According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction.

klemol [59]

Answer:

a) the expected number of tweets with no reaction is 71 tweets

b) the variance is 20.59 tweets² ( ≈ 21 tweets )and the standard deviation is

4.537 tweets (≈ 5 tweets)

Step-by-step explanation:

we can use the binomial probability distribution

P(x, N, p ) = N!/[(N-x)!x!] * p^x * (1-p)^(N-x)

where

x = number of successful events

N = population total

p = probability for success for every individual and independent event

P = probability for x successful events

in our case p = 71% = 71/100 (probability of a tweet without reaction) , N = 100 tweets

a) the expected number of tweets

E(x) = N* p = 100 tweets * 71/100 = 71 tweets

b) the variance is

V(x) = N * p * (1-p)

V = 100 * 71/100 * (1-71/100) = 71* 29/100 = 20.59 tweets² ( units of variance are [N²] )

the standard deviation is

s = √V = √20.59 tweets² = 4.537 tweets

6 0

3 years ago

All the cubes below have a different image on each side.

-BARSIC- [3]

Answer:

Figure G

Explanation:

The figure labeled A cannot be because the cross and the line are not oriented in the same relative position as in X.

The figure labeled B cannot be because the line and the the image with the three lines are not oriented in the same relative position as in X.

You cannot tell about the figures labeled C because you do not see the images of the cross and the line.

The figure labeled E cannot be because the image with the three lines is not oriented in the same relative positiion with respect to the other two as in X.

You cannot tell about the figure labeled F because the image of the cross and with the three lines are not shown.

The figure labeled G is correct: you can just rotate the cube labeled X 90 degrees counterclockwise about a vertical axis that passes through the center of the cube and get the cube labeled G.

3 0

3 years ago

What is the slope of the line on the graph?

erma4kov [3.2K]

Answer:

$m=\frac{1}{2}$