All categories

3 years ago

Drag a reason to each box to complete the proof.

Mathematics

1 answer:

Anna [14]3 years ago

6 0

To start off with, DF=EG's reason is given, since you stated it was given.

Next, DE+EF = EF+FG's reason is because of the substitution property of equality. Think "if a = c, b = c, then a = b"

Lastly, DE = FG's reason is because of the Subtraction property of equality. If you subtract EF on one side, you must do it on the other side.

You might be interested in

What is the answer to 10k-9=9k + 10?

oee [108]

K=19 which would leave the equation 181=181. The first step to solving this is subtracting 9k from each side.
after you do that it should be k-9=10
now you add 9 to both sides leave k=19. plug k into the equation and get 181=181

7 0

3 years ago

A sweater that normally costs $32.00 is on sale for $24.00. What is the percent

Vlad1618 [11]

Answer:

25 %

Step-by-step explanation:

Percentage is given by :

$\%=\dfrac{\text{original value-new value}}{\text{origial value}}\times 100$

Original cost of sweater is $32 and sale cost is $24. So,

$\%=\dfrac{32-24}{32}\times 100\\\\=25\%$

Hence, 25 % is the markdown on the sweater.

6 0

2 years ago

Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad. What percentage of the apples are b

stellarik [79]

I believe the answer is 25% because 6/24 is 1/4 and 1/4= 25%

3 0

3 years ago

Distribute and simply 7-2(x-5)+3x

KonstantinChe [14]

The given expression is

$7-2(x-5)+3x$

First, we use the distributive property to get rid of the parenthesis.

$7-2x+10+3x$

Then, we reduce like terms. -2x and 3x are like terms, also 7 and 10 are like terms.

$3x-2x+10+7=x+17$ <h2>Therefore, the simplest form of the given expression is <em>x + 17</em>.</h2>

4 0

9 months ago

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an incr

ss7ja [257]

Answer:

a) There is a 12.11% probability that exactly 1 man has the marker.

b) There is a 85.07% probability that more than 1 has the marker.

Step-by-step explanation:

There are only two possible outcomes: Either the men has the chromosome, or he hasn't. So we use the binomial probability distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem, we have that:

30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure, so $\pi = 0.30$

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

10 men, so $n = 10$

We want to find P(X = 1). So:

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{10,1}.(0.30)^{1}.(0.7)^{9} = 0.1211$

There is a 12.11% probability that exactly 1 man has the marker.

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

That is $P(X > 1)$

We have that:

$P(X \leq 1) + P(X > 1) = 1$

$P(X > 1) = 1 - P(X \leq 1)$

We also have that:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{10,0}.(0.30)^{0}.(0.7)^{10} = 0.0282$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0282 + 0.1211 = 0.1493$

Finally

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1493 = 0.8507$

There is a 85.07% probability that more than 1 has the marker.

3 0

3 years ago