Twice a number plus four equals 6. what is the number

A study is done to find the 95% confidence interval for the difference in means between the ACT scores between two schools in a

Kitty [74]

Solution :

95% confidence interval for the difference between the means of ACT scores between two schools, is given by :

$[(\overline X_1 - \overline X_2)-ME, (\overline X_1 - \overline X_2)+ME]$

$\overline X_1 = 25.90 , \ \ \ \overline X_2 = 27.70$

$S_1=3.49, \ \ \ S_2 = 2.47$

$n_1=39, \ \ n_2=37$

M.E. , Margin of error,

$=t_{n_1+n_2-2,0.025} \times \left( s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$

$s^2 = \frac{(n_1-1)S_1^2+(n_2-1)S^2_2}{n_1+n_2-2}$

$=\frac{38(3.49)^2+36(2.47)^2}{39+37-2}$

= 9.222

s = 3.03

$t_{74,0.05} = 1.99$

$M.E. = 1.99 \times 3.03 \times \sqrt{\frac{1}{39}+\frac{1}{37}}$

= 1.4

Therefore, 95% CI = [(25.90-27.70) - 1.4 , (25.90-27.70) + 1.4]

= [-3.2, -0.4]

Therefore, the lower bound is -3.2

7 0

2 years ago

Find the perimeter of a square with side a. Are the perimeter of the square and the length of its side directly proportional qua

erik [133]

Answer:

The perimeter is 8 cm.

Yes, the perimeter of a square is directly proportional to its side length.

Step-by-step explanation:

Given:

The side length of the square is, $a=2\ cm$

The perimeter of a square is the sum of all of its side lengths. The perimeter of a square of side length 'a' is given as:

$P=a+a+a+a=4a$

Plug in $a=2\ cm$ and find perimeter, 'P'. This gives,

$P=4\times 2=8\ cm$

Therefore, the perimeter is 8 cm.

Now, two quantities are directly proportional only if their ratio is a constant.

Let us find the ratio of 'P' and 'a'.

We have, $P=4a$

Dividing both sides by 'a', we get:

$\frac{P}{a}=\frac{4a}{a}\\\frac{P}{a}=4(Constant)$

Therefore, the ratio of perimeter and side length is a constant. Hence, these are directly proportional quantities.

6 0

3 years ago

Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 times

Kryger [21]

Answer:

8 and - 2

Step-by-step explanation:

let x be the larger number and y the smaller , then

x = 5y + 18 → (1)

3x + 4y = 16 → (2)

substitute x = 5y + 18 into (2)

3(5y + 18) + 4y = 16 ← distribute parenthesis and simplify left side

15y + 54 + 4y = 16

19y + 54 = 16 ( subtract 54 from both sides )

19y = - 38 ( divide both sides by - 19 )

y = - 2

substitute y = - 2 into (1)

x = 5(- 2) + 18 = - 10 + 18 = 8

then larger number is 8 and smaller is - 2

8 0

2 years ago

Alussa took a math test with 20 questions

anastassius [24]

Answer:

Step-by-step explanation: 100 divided by 20 is 5 therefore, each question is worth 5%. take how many questions she got right and multiply by 5. then determine if her score is less than or greater then 90%.

8 0

3 years ago

Answer Questions and show all of your work.

Dmitriy789 [7]

Answer:

X= 35

Z=90

Step-by-step explanation:

sorry I don’t know how else to help

6 0

2 years ago