Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:

n_1 = 10
x_1 = 87.6
σ_1 = 1
n_2 = 12
x^2 = 74.5
σ_2 = 1.5.

Required:
If μ _1 and μ _2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the difference in mean strength.

Hey there! I'm happy to help!

Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.

10x+50y=1080

x+y=28

We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.

x+y=28

Subtract x from both sides.

y=28-x

Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.

10x+50(28-x)=1080

We use distributive property to undo the parentheses.

10x+1400-50x=1080

We combine like terms.

-40x+1400=1080

We subtract 1400 from both sides.

-40x=-320

We divide both sides by -40.

x=8

Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.

Have a wonderful day! :D

Answer:

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Step-by-step explanation:

The rate is -1 4/5 lbs  per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6  3/10

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Answer:

-6 3/10 pounds

Step-by-step explanation:

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10

Answer:

1/30

Step-by-step explanation:

The probability of getting ”E” is 1/6.

There is only 1 “E” out of 6 letters.

There is no replacement.

There are now 5 letters without “E”.

”A”, “B”, “C”, “D”, “F”

The probability of getting ”B” is 1/5.

There is only 1 “B” out of 5 letters.

⇒ 1/6 × 1/5

⇒ 1/30

Answer:

15.625 m³

Step-by-step explanation:

The volume of a cube has a formula: V = a³

V = volume

a = side length

The side length is given 2.5 meters.

V = 2.5³

Solve for V.

V = 15.625

The volume is 15.625 cubic meters.

Answer:

15.625cm^3

Step-by-step explanation:

Formula:

V=lxwxh

Given:

l=2.5m

w=2.5m

h=2.5m

Answer:

V=lxwxh

V=2.5m*2.5m*2.5m

V=6.25m^2*2.5m

V=15.625m^3

Hope this helps :)

Answer:

Step-by-step explanation:

Let, present age of son be 'x'

present age of father be 'y'

y = 4x→ equation ( i )

After five years,

Son's age = x + 5

father's age = y + 5

According to Question,

[tex]y + 5 = 3(x + 5)[/tex]

Put the value of y from equation ( i )

[tex]4x + 5 = 3(x + 5)[/tex]

Distribute 3 through the parentheses

[tex]4x + 5 = 3x + 15[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S. and change its sign

[tex]4x - 3x = 15 - 5[/tex]

Collect like terms

[tex]x = 15 - 5[/tex]

Calculate the difference

[tex]x = 10[/tex]

Now, put the value of X in equation ( i ) in order to find the present age of father

[tex]y = 4x[/tex]

plug the value of X

[tex] = 4 \times 10[/tex]

Calculate the product

[tex] = 40[/tex]

Therefore,

Present age of son = 10

present age of father = 40

Hope this helps..

Best regards!!

Answer:

Number is yellow box=3

Step-by-step explanation:

We know this because the way we get that number is subtracting the two numbers above it, which is 8 and 5, which give us 3.

if you appreciated this, please consider giving me brainliest, it will help me a lot

Thank you,

Have a good day! :)

Answer:

B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.

Step-by-step explanation:

Inductive reasoning uses logic and uses more evidence to draw conclusions. In deductive reasoning, WE decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. But some deductive reasoning may appear to make sense without pointing to a truth

Answer:

The answer is D. Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.

Step-by-step explanation:

I took the test

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

[tex] a^n = a ( n-1 ) * r [/tex]

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

Third term: a³ = 15 * ½ = 7.5

Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

Answer:

[tex] A = 50.7 [/tex] (to nearest tenth)

Step-by-step explanation:

Use the Law of Cosines to find the value of angle A as follows:

[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]

Where,

a = 7 in

b = 5 in

c = 9 in

Plug in the values into the formula

[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]

[tex] cos(A) = \frac{57}{90} [/tex]

[tex] cos(A) = 0.6333 [/tex]

[tex] A = cos^{-1}(0.6333) [/tex]

[tex] A = 50.7 [/tex] (to nearest tenth)

Answer:  see below

Step-by-step explanation:

1) Foci is plural for Focus.  Since a hyperbola has two focus points, they are referred to as foci.  The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

    a)  does the hyperbola open up or to the right?

    b)  what is the center (h, k) of the hyperbola?

    c)  What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]

Answer:

No solutions

Step-by-step explanation:

14(z + 3) = 14z + 21

Expand brackets.

14z + 42 = 14z + 21

Subtract 14z on both sides.

42 = 21

There are no solutions.

Answer:

No solution

Step-by-step explanation:

First, We have to simplify the right side.

Distribute 14, 14z+42.

Now the equation stands as 14z+42=14z+21

Subtract 14z from both sides,

this makes it 42=21.

We know when the solution is #=#, our answer is no solution.

Answer:

6227020800

Step-by-step explanation:

There are 13 ways to choose the first person in the first group, 12 ways to choose the second person in the first group and so on until we get 1 way to choose the second person in the last group so the answer is 13 * 12 * 11 * ... * 3 * 2 * 1 = 13! = 6227020800.

It's 1000 charges and not 1.000 charges

Answer:

A)Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = 1.4286

C) p-value = 0.15628

D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges

Step-by-step explanation:

We are given;

x = 1002 charges

s = 14

μ = 1000 charges

n = 100

degree of freedom = n - 1 = 100 - 1 = 99

A) The hypotheses are;

Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = (x - μ)/(s/√n)

(1002 - 1000)/(14/√100) = 1.4286

C) From the t-score calculator results attached, the p-value is approximately 0.15628

D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.

Answer:

Step-by-step explanation:

The surface area of a cone is:

● Sa = Pi*r^2 +Pi*r*l

r is the radius and l is the slant heigth

The diameter of this cone is 12 inches so the radius is 6 (12/2=6).

●Sa = Pi*36 +Pi*6*10

●Sa = 301.59 in^2

Answer:

pi (6) * 10+ pi ( 6)^2

Step-by-step explanation:

The surface area of a cone is given by

SA =  pi rl +pi r^2  where r is the radius and l is the slant height

We know the diameter is 12 so the radius is 12/2 = 6

SA =  pi (6) * 10+ pi ( 6)^2

Answer:

No correlation

Step-by-step explanation:

Hey there! :)

This has no correlation because all the points are spread out throughout the graph making no correlation.

Answer:

D no correlation

Step-by-step explanation:

too many scattered dot all over the place if its some going up down its NO CORRELATION!!!

Answer:

the answer is A) h=3V/(Pi*r^2)

Step-by-step explanation:

This question is asking to solve for h, the equation is allready solved for V.

to solve for h means to get h by itself on one side of the equation.

1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation

2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.

3) (3*V)/(pi*r^2)=h. Simplify.

4) 3V/(Pi*r^2)=h.

According to the given situation, the computation of two number in a given ratio is shown below:-

We assume the numbers is x and y

Given that

[tex]\frac{x}{y} = \frac{3}{1}[/tex]

x = 3y

and

[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]

With the help of above formula we will put the value and be able to find the values of x and y

x - y = 6

3y - y = 6

2y = 6

y = 3

x = 3y = 9

x = 9, y = 3

Therefore the correct answer is x = 9 where as y = 3

Answer:

A. Cone

D. Rectangular Prism

E. Cylinder

F. Sphere

Step-by-step explanation:

Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.

Answer:

-5 < x < 0

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:  6 feet from the pivot point

Step-by-step explanation:

Girl's weight x distance from center = Boy's weight x distance from center

65 (7) = 75x

[tex]\dfrac{65(7)}{75}=x[/tex]

6.066 = x

The boy needs to be placed 6 feet from the center (aka pivot point) which is the same as saying 1 foot from the end of the seesaw.

Answer:

6<y<∞

Step-by-step explanation:

Logarithmic curves can never go left to 0 and go on forever to the right.

x=6 would make the function 0, so 6 is the lower limit and infinity would be the upper limit.

Answer:

-4.3a + 4.1

Step-by-step explanation:

Well in the given expression,

2.5a - 7 - 6.8a + 11.1

We need to combine like terms,

2.5a + -6.8a = -4.3a

-7 + 11.1 = 4.1

Ans: -4.3a + 4.1

Thus,

the answer is -4.3a + 4.1

Hope this helps :)

The simplification form of given expression is -4.3a + 4.1

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

The given expression,

⇒ 2.5a - 7 - 6.8a + 11.1

Combine like terms in expression,

⇒ 2.5a  - 6.8a + 11.1- 7

Apply the arithmetic operations

⇒ -4.3a + 4.1

Hence, the simplification form of given expression is -4.3a + 4.1

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ5

Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

Answer:

[tex]\boxed{x = 7}[/tex]

Step-by-step explanation:

75 = 11x-2 (Corresponding angles are equal)

11x -2 = 75

Adding 2 to both sides

11x = 75+2

11x = 77

Dividing both sides by 11

x = 7

Answer:

[tex]\left[\begin{array}{ccc}\\x = 7\\\end{array}\right][/tex]

Step-by-step explanation:

Well to find x we can set up the following equation,

11x - 2 = 75

So we have to single out x.

+2 to both sides

11x = 77

Divide 11 by both sides

x = 7

Thus,

x = 7.

Hope this helps :)

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.

approximately 36.633 cm if you use pi = 3.14

approximately 36.6519 cm if you use the calculator's stored value of pi

Work Shown:

L = arc length, r = radius, x = central angle in degrees

L = (x/360)*2*pi*r

L = (300/360)*2*pi*7

L = (35/3)pi .... exact arc length in terms of pi

L = (35/3)*3.14

L = 36.633 .... approximate arc length

Keep in mind that I used pi = 3.14 which isn't that great an approximation for pi. If you want to use more digits of pi, then use your calculator's built in version of it to get (35/3)*pi = 36.6519; of course it will depend on which option your teacher prefers.

Answer:

[tex]\r p = 0.11[/tex]

[tex]\r q = 0.89[/tex]

n = 2000

[tex]E = \pm 5[/tex]

p - population proportion

[tex]\alpha = 5[/tex]%

Step-by-step explanation:

From the question we are told that  

   The  sample size is  [tex]n = 2000[/tex]

   The  proportion of the population for chocolate pie is  [tex]p_c = 0.11[/tex]

   The  margin of error is  [tex]E = \pm 5[/tex]%  

Now in the question we are asked to provide the meaning of  

       [tex]\r p , \r q , n , E , and\ p[/tex]

Now  [tex]\r p[/tex] is the sample proportion of the population that those  chocolate​ pie as  favorite pie of   which is given from the question as 0.11

Now

         [tex]\r q[/tex] is the sample  proportion of the population that choose other pies apart from chocolate pie as their favorite and it is evaluated as

      [tex]\r q = 1 - \r p[/tex]

      [tex]\r q = 1 - 0.11[/tex]

       [tex]\r q = 0.89[/tex]

       n is the sample size which is given as  n =  2000

       E is the margin of  error which given as  [tex]E = \pm 5[/tex]%

       p is the population proportion

Given that the confidence level is  95 %  then the level of significance is  mathematically evaluated as

        [tex]\alpha =(100 - 95)[/tex]%

        [tex]\alpha =[/tex]5%

Answer:

Step-by-step explanation:

Can you please include a image?

Thanks!!!

Answer:

3057.6 cm³

Step-by-step explanation:

You have a cylinder and a rectangular prism.  Solve for the area of each separately.

Cylinder

The formula for volume of a cylinder is V = πr²h.  The radius is 7, and the height is 7.

V = πr²h

V = π(7)²(7)

V = π(49)(7)

V = 343π

V = 1077.57 cm³

Rectangular Prism

The formula for volume of a rectangular prism is V = lwh.  The length is 20, the width is 11, and the height is 9.

V = lwh

V = (20)(11)(9)

V = (220)(9)

V = 1980 cm³

Add the areas of the two shapes.

1077.57 cm³ + 1980 cm³ = 3057.57 cm³

Round to the nearest tenth.

3057.57 cm³ ≈ 3057.6 cm³