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Answer:

The 90% confidence interval, C.I = (0.693, 0.7307)

Step-by-step explanation:

Catalysts 1 and catalyst 2 have the following statistical data;

Catalyst 1

The number of batches in the sample, n₁ = 12

The average yield by the 12 batches of catalyst 1, [tex]\overline x_1[/tex] = 85

The sample standard deviation, s₁ = 4

Catalyst 2

The number of batches in the sample, n₂ = 10

The average yield, [tex]\overline x_2[/tex] = 81

The standard deviation, s₂ = 5

F-test = s₂²/s₁² = 5²/4² = 1.5625

The degrees of freedom, df = n₁ + n₂ - 2

∴ df = 12 + 10 - 2 = 20

The critical-t at 90% confidence level = 1.725

The F-test < The critical-t, we pool the variance

The 90% confidence interval with the assumption of equal variance is given as follows;

[tex]The \ 90\% \ confidence \ interval= \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times (s_p) \times \sqrt{\dfrac{1^{2}}{n_{1}}+\dfrac{1^{2}}{n_{2}}}[/tex]

[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]

Therefore;

[tex]s_p[/tex] = √((12 - 1)×4² + (10 - 1)×5²)/(12 + 10 - 2)) ≈ 4.48

Therefore, we get;

[tex]C.I. = \left (85- 81 \right )\pm 1.725 \times 4.48 \times \sqrt{\dfrac{1}{12}+\dfrac{1}{10}}[/tex]

The 90% confidence interval, C.I = 0.693 < μ₁ - μ₂ < 7.307 = (0.693, 0.7307).

Answer:

(-3,-1)

Step-by-step explanation:

So we need to find a number, x=a, such that when we average that number and x=3, we get x=0.

Since we want x=0 to be middle and x=3 is 3 units right of 0, then we are looking for number 3 units left of 0 which is x= -3.

Since we want y=2 to be the middle and y=5 is 3 units above 2, then we are looking for a number 3 units below 2 which is y=-1.

The other endpoint is (-3,-1).

Let's average (-3,-1) and (3,5).

(-3+3)/2=0/2=0

(-1+5)/2=4/2=2.

Check mark.

Answer:

67 degrees

Step-by-step explanation:

All angles in a triangle add up to 180 degrees. So...

23 + x + 90 = 180

113 + x = 180

x = 67 degrees

Answer:

The answer is B! P(Y and R) = StartFraction (8 C 1) (5 C 1) Over 25 C 2 EndFraction

Answer:

The Second Option

Step-by-step explanation:

Edge '21

Answer:

10

Step-by-step explanation:

30/100*x=3

Multiply both sides by 100 and divide both by 30

You get the answer x=10

Answer:

10

Step-by-step explanation:

DO this 3x100/30 and you get 10

Answer:

60 ounces

Step-by-step explanation:

3 pounds = 48oz+12oz=60oz

Answer:

Step-by-step explanation:

[tex]circumference \: of \: circle \: = 2 \: \pi \: r[/tex]

38 = 2πr

r = 38/2π

r = 38÷6.28

r = 6 cm

Answer:

Step-by-step explanation:

[tex](10a^5b^4-15a^4b^5+5a^3b^3)\div(-5a^3b^3)=\dfrac{10a^5b^4-15a^4b^5+5a^3b^3}{-5a^3b^3}=\\\\\\=\dfrac{10a^5b^4}{-5a^3b^3}+\dfrac{-15a^4b^5}{-5a^3b^3}+\dfrac{5a^3b^3}{-5a^3b^3}=-2a^2b+3ab^2-1[/tex]

Answer:

cuz im Not very smarttt

Step-by-step explanation:

at all

Answer:

option C

Step-by-step explanation:

Answer:

[tex]2x + 12 = \frac{180}{2} = 90 \\ 2x = 78 \\ x = 39[/tex]

Fill in the given information then calculate the missing parts. See attached picture

Answer:

15

Step-by-step explanation:

The probability that the first number divided by the second number is greater than zero is 1/3

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Tiles are numbered -2,-1,1,2

So, possibility first number divided by the second number is greater than zero

-2/-1=2

-2/1=-2

-2/2=-1

-1/-2= 0.5

-1/1=-1

-1/2=-0.5

1/-2=-0.5

1/-1=-1

1/2=0.5

2/-2=-1

2/-1=-2

2/2=1

Probability the first number divided by the second number is greater than zero = 4/12=1/3.

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

Answer:

the sum of the interior angles = 360°

A kite has 4 sides.

This is the formula for the sum of the interior angles of any polygon:

N = number of sides

the sum of the interior angles = (N x 180°) - 360°

so, N = 4, then:

(4 x 180°) - 360° = 360°

Answer:

1/20 x 595

Step-by-step explanation:

1/20 is the lowest fraction in this situation so lower fractions and multiplying whole numbers will be lower than 1/2

Answer:

41.67 kg

72 books

Step-by-step explanation:

mass of 150 books = 150/108 × 30 kg

= 41.67 kg

number of books = 20/30 × 108 books

= 72 books

Answer:

12

Step-by-step explanation:

hi

Equation which describe relationship between total cost and number of t-shirt is    [tex]c(t)=75.93e^{0.06t}[/tex].

Data given are ,

Number of t-shirt (t)                  total cost c(t)

12                                            156

17                                             211

22                                            266

According to above table, exponential function best describes the relationship between the total cost, c(t), and the number of T-shirts, t.

Let,        [tex]c(t)=Ae^{kt}[/tex]

Substitute ,   t=12  and c(t) = 156

We get,     [tex]156=Ae^{12k}.......(1)[/tex]

Substitute ,  t=17 and c(t) = 211

We get,     [tex]211=Ae^{17k} ........(2)[/tex]

After solving above equations.

We get,    A = 75.93  and  k = 0.06

Thus,     [tex]c(t)=75.93e^{0.06t}[/tex]

Learn more:

https://brainly.com/question/12626186

Answer:

x = 12 degrees

Step-by-step explanation:

m < LNM = (70+136)/2

= 206 / 2

= 103 degrees

So 7x + 19 = 103

7x = 103 - 19 = 84

x = 84/7

x = 12.

Answer:

Hourly wage at the library = x = $7.5

Hourly wage at the coffee cart = y = $7

Step-by-step explanation:

Let

Hourly wage at the library = x

Hourly wage at the coffee cart = y

On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50.

Hence:

3x + 2y = 36.5.... Equation 1

On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50.

2x + 5y = 50...... Equation 2

Combining both Equations

3x + 2y = 36.5.... Equation 1

2x + 5y = 50...... Equation 2

We solve using Elimination method, Multiply Equation 1 by 2 and Equation 2 by 3 which are coefficients of x to eliminate x

6x + 4y = 73 .. Equation 3

6x + 15y = 150...... Equation 4

Subtract Equation 3 from Equation 4

11y = 77

y = 77/11

y = 7

Solving for x using Equation 2

2x + 5y = 50...... Equation 2

2x + 5 × 7 = 50

2x + 35 = 50

2x = 50-35

2x = 15

x = 15/2

x = 7.5

Therefore,

Hourly wage at the library = x = $7.5

Hourly wage at the coffee cart = y = $7

Answer:

yeah thats right good job keep up the good work and keep doing ur thing good job

Step-by-step explanation:

Answer:

3: 27

8; 512

6; 216

Step-by-step explanation:

Answer:

Step-by-step explanation:

For this problem use 3.14 for , and any non-integer answers should be entered as decimals rounded to the hundredths place. Lannon is designing a carnival game for a school event. She has a large wooden square and she needs to cut out a circle from the middle. The circumference of the circle that she plans to cut out is 56.52 inches. What is the radius

The formula for circumference of a circle = 2πr

Circumference = 56.52 inches

r = Circumference/2π

r = 56.52/2π

Given:

The given volume formulas to calculate the volume of a rectangular

pyramid.

To find:

The correct volume formula.

Solution:

The volume of a rectangular pyramid is:

[tex]V=\dfrac{1}{3}Bh[/tex]

Where, B is the base area of the rectangular pyramid and h is the vertical height of the rectangular pyramid.

Therefore, the correct volume of a rectangular pyramid is [tex]V=\dfrac{1}{3}Bh[/tex].

Note: In the given problem, the options are not in correct form.

Answer:

the two numbers are six and four

Step-by-step explanation: 6+4=10    6x4=24

Step-by-step explanation:

[tex]4 \times \frac{3}{8} [/tex]

[tex] \frac{4}{1} \times \frac{3}{8} [/tex]

=12/8

=1 4/8=

= 1 1/2