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frozen [14]
2 years ago
15

Tell whether the ordered pair is a solution to the equation. (1, 3); 4x – 3y = -5

Mathematics
1 answer:
Bumek [7]2 years ago
8 0

Answer:

Yes

Step-by-step explanation:

4(1)-3(3)=-5

4-9=-5

-5=-5

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In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S
lys-0071 [83]

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

8 0
2 years ago
- The four-digit number 1210 has an interesting property.
vampirchik [111]

Answer:

ABCDEFG = 3211000

Step-by-step explanation:

A counts the number of zeroes, and there are 3 zeroes (E, F, G), so A = 3.B counts the number of ones, and there are 2 ones (C, D), so B = 2.C counts the number of twos, and there is 1 two (B), so C = 1.D counts the number of threes, and there is 1 three (A), so D = 1.There is no four, five, six in, so E, F, G are all zeroes.

5 0
2 years ago
Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)
Juliette [100K]

Answer:

y=-4x-3

Step-by-step explanation:

Hi there!

We are given the following two points: (-2,5) and (-1,1)

We want to write the equation of the line that passes through these two lines in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope

The formula for the slope (m) calculated from 2 points is \frac{y_2-y_1}{x_2-x_1}, where (x_1, y_1) and (x_2, y_2) are points

We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion

x_1=-2\\y_1=5\\x_2=-1\\y_2=1

Now substitute into the formula

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{1-5}{-1--2}
Simplify

m=\frac{1-5}{-1+2}

Subtract

m=\frac{-4}{1}

Divide

m=-4

Now substitute -4 as m into the equation:

y=-4x+b

Now we need to find b

As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.

Taking (-2,5) for example:

Substitute -2 as x and 5 as y:

5=-4(-2)+b

Multiply

5=8+b

Subtract 8 from both sides

-3=b

Substitute -3 as b.

y=-4x-3

Hope this helps!

See more on this topic here: brainly.com/question/27304092

4 0
2 years ago
Whats the difference between coplanar and collinear
Sergio [31]
In terms of points, a point that is coplanar is one that lies anywhere on the given plane while a point that is collinear is a point that lies anywhere on the given line.
5 0
3 years ago
Read 2 more answers
Calculate the Average of...
lesantik [10]
You add them and then divide by how many numbers there are.

a. (3+43)/2 = 23
b. 0
c. -1
3 0
3 years ago
Read 2 more answers
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