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Mathematics

1 answer:

NISA [10]2 years ago

8 0

Answer:

Step-by-step explanation:

First, we are decreasing the number so it has to be a decrease.

Next, we divide 7/31 and get around 0.23, which also represents 23 percent.

This only shows that 7 is 23 percent of 31, so we need to find the decrease by seeing the difference of 100 and 23.

We get 100 - 23 = 77, and because it is a decrease we get B.

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Solve the system of equations two ways: 3x+y=5 and x-2y=4 A) using substitution B) using elimination

Vedmedyk [2.9K]

A. solve for 1 variable
let's solve for x in 2nd equation
add 2y to both sides
x=2y+4
sub 2y+4 for x in other equation
3(2y+4)+y=5
6y+12+y=5
7y+12=5
minu12 both sides
7y=-7
divide 7
y=-1
sub back
x=2y+4
x=2(-1)+4
x=-2+4
x=2
(2,-1)

B. eliminate
eliminate y's
multiply first equation by 2 and add to first

6x+2y=10
<u>x-2y=4 +</u>
7x+0y=14

7x=14
divide by 7
x=2
sub back
x-2y=4
2-2y=4
minus 2
-2y=2
divide -2
y=-1
(2,-1)

(2,-1) is answer

5 0

3 years ago

4. A statistician working for the National Basketball Association supplies the television announcers with interesting statistics

Sonbull [250]

Answer: 0.038

Step-by-step explanation:

Given: Total games : n= 375

Number of games won by the team that was winning the game at the end of the third quarter. = 300

The proportion (p) of the team that was winning the game at the end of the third quarter: $p=\dfrac{300}{375}=0.8$

Critical z-value for 90% confidence: z* = 1.645

Margin of error = $z^*\sqrt{\dfrac{(1-p)p}{n}}$

The margin of error in a 90% confidence interval estimate of p $=1.645\sqrt{\dfrac{0.2\times0.8}{300}}\\= 1.645\times\sqrt{0.00053333}\\\\=1.645\times0.0231\\\\=0.0379995\approx$$0.038$