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3 years ago

Factor the expression completely 21x-9

Mathematics

1 answer:

Ronch [10]3 years ago

3 0

Answer:

3(7x - 3)

Step-by-step explanation:

21x - 9

3(7x - 3)

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An educational psychologist wishes to know the mean number of words a third grader can read per minute.

Rama09 [41]

Answer: 208.

Step-by-step explanation:

The formula to find the minimum sample size is given by :-

$n= (\dfrac{z^*\times \sigma}{E})^2$ (1)

, where z* = critical z-value (two tailed).

$\sigma$ = Standard deviation ( from prior study ) and E = Margin of error.

As per given , we have

Margin of error : E= 0.29

Confidence level = 85%

Significance level = $\alpha=1-0.85=0.15$

Using z-table , the critical value (two -tailed)= $z^*=z_{\alpha/2}=z_{0.15/2}=z_{0.075}=1.439$

As per previous study , Variance = $\sigma^2=8.41$

$\sigma=\sqrt{8.41}=2.9$

Now, the required minimum sample size = $n= (\dfrac{(1.439)\times (2.9)}{0.29})^2$ [Substitute the values in formula (1)]

$n=(14.39)^2$

$n=207.0721\approx208$ [ Round to the next integer]

Hence, the minimum number of third graders that must be included in a sample = 208.

5 0

4 years ago

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

Fantom [35]

Answer:

<h2>If we placed the number 10 in the box, we obtain a system of equations with infinitely many solutions.</h2>

Step-by-step explanation:

The given system is

$y=2x-5\\2y-4x=a$

<em>It's important to know that a system with infinitely many solutions, it's a system that has the same equation</em>, that is, both equation represent the same line, or as some textbooks say, one line is on the other one, so they have inifinitely common solutions.

Having said that, the first thing we should do here is reorder the system

$y=2x-5\\2y=4x+a$

This way, you can compare better both equations. If you look closer, observe that the second equation is double, that is, it can be obtained by multiplying a factor of 2 to the first one, that is

$y=2x-5\\2y=4x-10$

So, by multiplying such factor, we obtaine the second equation. Observe that $a$ must be equal to 10, that way the system would have infinitely solutions.

Therefore, the answer is 10.

4 0

3 years ago

Place the numbers 0 to 8, inclusive, in the magic square so that the sum of the numbers in each row, column, and diagonal is the

ehidna [41]

Answer: See attached table

Step-by-step explanation:

$\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}$ +---+---+---+

| 1 | 8 | 2 |

+---+---+---+

| 6 | 4 | 2 |

+---+---+---+

| 5 | 0 | 7 |

+---+---+---+

<u>Proofs:</u>
First row: 1+6+5 = 12

Second row: 8+4+0 = 12

Third row: 2+2+7 = 12

First column: 1+8+2 = 12

Second column: 6+4+2 = 12

Third column: 5+0+7 = 12

Diagonal starting from top left to bottom right: 1+4+7 = 12

Diagonal staring from top right to bottom left: 2+4+5 = 12

6 0

2 years ago

5. From the choices below, choose an expression that is equivalent to the

blondinia [14]

Answer: -(22/4)

Step-by-step explanation:

8 0

3 years ago

PLEASEEE HELPPP!!! 55 POINTSSS!!

algol [13]

Answer:

min: -10

max: 18

minmax

Step-by-step explanation:

4 0

2 years ago