Of 30 students, 1/3 play sports. Of those who play sports, 2/5 play soccer.

Jaime reads 36 pages of her novel in three nights. If Jaime continues to read at this rate, How many nights will it take for her

Lera25 [3.4K]

Nine days. You can divide 108 by 36, to get how many times she has to read 36 pages, which is 3. Then you multiply that by 3, because she uses 3days for every 36 pages. 3x3=9

7 0

3 years ago

Read 2 more answers

Please... I... need... HELP

Alja [10]

Here!
(x+4)+(x+2)+(x+5)= (x+1)+(x+1)+(x+3)+(x+3)
First you want to write the whole equation out. Make each perimeter equal to each other.
Then add both sides separately.
(x+4)+(x+2)+(x+5)
=3x+11

and

(x+1)+(x+1)+(x+3)+(x+3)
=4x+8

Now that you've simplified each side, solve like a normal equation.
3x+11 = 4x+8
-3x -3x
11 = x+8
-8 -8
3=x

7 0

3 years ago

Refer previous problem. Suppose that you wish to estimate the difference between the mean acidity for rainfalls at two different

aivan3 [116]

Answer:

Hence,we need at least 136 rainfall PH values in the sample i.e

n ≥ 136

Step-by-step explanation:

We are given that:

(σ1)^2 = (σ2)^2 = Population variance = 0.25

So, E < 0.1

Confidence coefficient (c) = 0.9

n = n1 = n2

For confidence level, 1 - α = 0.9,we'll determine Z (α /2) = Z 0.05 by looking up 0.005 using the normal probability table which i have attached.

So, Z (α /2) = 1.645

The margin of error E is given as;

E = Z (α /2)√[(σ1)^2)/n1] + [(σ2)^2)/n2]

= Z (α /2)√({(σ1)^2 + (σ2)^2}/n) < 0.1

Multiply both sides by √n to get;

Z (α /2)√(σ1)^2 + (σ2)^2} < 0.1√n

Divide both sides by 0.1;

{Z (α /2)√(σ1)^2 + (σ2)^2}}/0.1 <√n

When we square each side, we get

{Z (α /2)√(σ1)^2 + (σ2)^2}}/0.1} ^2 < n

We'll now fill in the known values and solve;

n > ( 1.645 x √{(0.25 + 0.25)/0.1}^2

n > 135.3 or approximately n > 136

Hence,we need at least 136 observations in the sample i.e

n ≥ 136

7 0

3 years ago

Maggie graphed the image of a 90 counterclockwise rotation about vertex A of . Coordinates B and C of are (2, 6) and (4, 3) and

Lemur [1.5K]

Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates $(x_A,y_A)$

Vectors AB and AB' are perpendicular, then

$\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0$

Vectors AC and AC' are perpendicular, then

$\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0$

Now, solve the system of two equations:

$\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.$

Subtract these two equations:

$5x_A-y_A-8=0\Rightarrow y_A=5x_A-8$

Substitute it into the first equation:

$x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2$

Then

$y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2$

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

8 0

3 years ago

The number of members on an organization increases by an average of 125 members annually. There were 3,875 members in 1971. Choo

Lena [83]

Answer:

B.

Mn = Mn-1 + 125 for n > 1 ; M1 = 3,875

Step-by-step explanation:

Since they tell us after 1970, the first data would be that of 1971 and also that if we started since 1970, we do not know the data of 1969, therefore answer B is correct.

Replacing:

Let M1 = 1971 then Mn-1, that is M0 = 1970, we know that the population of 1970 the population is 3750, because it would be 125 less than the subsequent year, and in 1975 there are 3875. Therefore:

in n = 1

M1 = M0 + 125

3875 = 3750 + 125

this gives an equality, thus fulfilling the equation.

8 0

3 years ago