A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 43 cables and apply weights to each of them until they break. The 43 cables have a mean breaking weight of 774.3 lb. The standard deviation of the breaking weight for the sample is 15.4 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable.

Let's solve

Using Pythagorean theorem

[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]

[tex]\\ \sf\longmapsto c^2=8^2+5^2[/tex]

[tex]\\ \sf\longmapsto c^2=64+25[/tex]

[tex]\\ \sf\longmapsto c^2=89[/tex]

[tex]\\ \sf\longmapsto c=\sqrt{89}[/tex]

[tex]\\ \sf\longmapsto c\approx 9.22[/tex]

Answer:76

Step-by-step explanation:

something amazing

Answer:

67°

Step-by-step explanation:

● cos<PQR = adjacent/hypotenus

● cos<PQR = 5/13

● cos< PQR = 0.384

Using a calculator:

● cos^-1(0.384) = 67°

● <PQR = 67°

Answer: If the question is to solve for A: A= [tex]\frac{15x+1-B}{3x-1}[/tex]

If the question is to solve for B: B= 15x+1-3xA+A

Step-by-step explanation:

A: Move terms to the left.

B: Simplify both sides.

Answer:

a=8x^2+3x+1-b/3x-1  -x^2;  xdoes not equal 1/3

Step-by-step explanation:

hope this helps

Answer:

see explanation

Step-by-step explanation:

Using the sum to product identity

cosx + cosy = 2cos([tex]\frac{x+y}{2}[/tex] )cos( [tex]\frac{x-y}{2}[/tex] )

Consider left side

(cos5A +cos3A) + (cos15A + cos7A)

= 2cos([tex]\frac{5A+3A}{2}[/tex] )cos([tex]\frac{5A-3A}{2}[/tex] ) + 2cos( [tex]\frac{15A+7A}{2}[/tex]) cos( [tex]\frac{15A-7A}{2}[/tex] )

= 2cos([tex]\frac{8A}{2}[/tex]) cos([tex]\frac{2A}{2}[/tex]) + 2cos([tex]\frac{22A}{2}[/tex] )cos([tex]\frac{8A}{2}[/tex] )

= 2cos4AcosA + 2cos11A cos4A ← factor out 2cos4A from both terms

= 2cos4A( cos11A + cosA) ← repeat the process

= 2cos4A( 2cos([tex]\frac{11A+A}{2}[/tex] )cos([tex]\frac{11A-A}{2}[/tex] )

= 2cos4A(2cos([tex]\frac{12A}{2}[/tex])cos([tex]\frac{10A}{2}[/tex] )

= 2cos4A(2cos6A cos5A)

= 4cos4Acos5Acos6A

= right side , thus verified

4 fries + 6 cheeseburgers = $52

3 fries + 2 cheeseburgers = $24

9 fries + 6 cheeseburgers = $24×3

= $72

$72-$52=$20

5 fries = $20

1 fries = $20÷5

= $4

1 cheeseburger = [$24 - (3×$4)]÷2

= $6

Answer:

(2, 2 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ) , [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]

Here (x₁, y₁ ) = (A(5, 8) and (x₂, y₂ ) = B(- 1, - 4) , thus

midpoint = [ [tex]\frac{1}{2}[/tex] (5 - 1), [tex]\frac{1}{2}[/tex] (8 - 4 ) ] = (2, 2 )

Answer:

The graph of x=4 is a vertical line parallel to y-axis and having a x-intecept:(4,0) and having no y-intercept

Step-by-step explanation:

So I think that the answer would be this, which means answer 1!! Hope this helps

Answer:

136+(4n-8)=180

136+4n-8=180

4n+128=180

4n=52

n=13

Step-by-step explanation:

please mark me as brainliest

Answer:

48 different ways

Step-by-step explanation:

To solve this question, we use the Fundamental Counting Principle technique.

Fundamental Counting Principle can be defined as the way by which we determine the possibility or the number of possible outcomes for an event.

If we have event X and event Y and event Z, then the number of possible outcomes = X × Y × Z

For the above question, we have 3 events

Event 1 : 4 students ( Stephanie, Charles, Tim, and Rachel)

Event 2: 3 subjects ( Math, Reading, And Science)

Event 3 : 4 tutors.

Therefore,the many different ways can the students, tutors, and subjects can be be uniquely combined is:

= 4 × 3 × 4

= 48 different ways

Answer:

30 km/h car

Step-by-step explanation:

From analysis the   car traveling at 30 km/h has greater kinetic energy

we can deduce it from the expression of kinetic energy which is

[tex]KE=\frac{1}{2} mv^2[/tex]

Assuming the mass m= 1 kg

For the 30 km/h

[tex]KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J[/tex]

For the 15 km/h

[tex]KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J[/tex]

Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE

Answer:

The answer is none.

Step-by-step explanation:

Hope this helps....

Have a nice day!!!!

Answer:

Empirical formula= COOH

Step-by-step explanation:

Molecular mass of the elements

Carbon= 12

Oxygen= 16

Hydrogen= 1

We divide the elements each with their molecular formula

Carbon= 2.4/12

Carbon= 0.2

Oxygen= 6.4/16

Oxygen= 0.4

Hydrogen= 0.2/1

Hydrogen= 0.2

Now we divide with the smallest result which is 0.2

Carbon= 0.2/0.2

Carbon = 1

Oxygen= 0.4/0.2

Oxygen= 2

Hydrogen= 0.2/0.2

Hydrogen= 1

So we have

Carbon 1, oxygen 2, hydrogen 1

Empirical formula= COOH

Answer:

11.21157846 =x

Step-by-step explanation:

We know log b (a) = c  can be written as b^c =a

log 3 (x) = 2.2

3^2.2 = x

11.21157846 =x

Answer:

[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]

Step-by-step explanation:

[tex]\large \sf log_3 (x)=2.2[/tex]

Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:

[tex]\large \sf log_b(y)=x[/tex]

[tex]\large{\sf y=b^x}[/tex]

Apply the relationship.

[tex]\large \sf log_3 (x)=2.2[/tex]

[tex]\large \sf x=3^{2.2}[/tex]

[tex]\large \sf x=11.21157845...[/tex]

[tex]\large \sf x \approx 11.21[/tex]

[tex]\rm \large \implies \: \: 3m \: + \: 3m[/tex]

[tex]\rm \large \implies \: \: 6m[/tex]

Answer:

6m

Step-by-step explanation:

those are like terms so you just have to add them

3m+3m=6m

i hope this helps

Answer:

Can you solve #18 from practice test 5 calculator section? ... years old and a pin oak tree with a diameter of 12 inches is ... because on the test you would have figured these mechanics out on ... Now, note that the concept of a “growth factor” as provided in the table ... That's a difference of about 1.3 inches.

Step-by-step explanation:

Answer:

  y = 5x

Step-by-step explanation:

The revenue (y) is 5 dollars for each car washed. The number of cars washed is x, so the revenue equation is ...

  y = 5x

_____

Additional comment

At the end of the exercise of writing revenue and cost and profit equations, you will find that the break-even number of cars is the ratio of fixed cost (start-up cost in this case) to the profit contribution of each car (per-car charge in this case). That is, it will take 75/5 = 15 cars to break even. Each additional car will contribute a positive profit.

Answer:

Equation INCLUDING the setup cost:   y = 5x - 75

Equation EXCLUDING the setup cost:   y = 5x

Step-by-step explanation:

It spent a total of $75 to set up the car wash.

It is charging $5 per car.

y = amount collected in $

x = number of cars washed

=> We can make an equation INCLUDING the setup cost and EXCLUDING the setup cost.

=> INCLUDING the setup cost.

=> y = 5x - 75

=> I subtracted 75 from 5x because they spent a total of $75 to set up the car wash.

=> I wrote 5x because they get $5 for each car so if they wash 10 cars they get 5 * 10 = $50.

An EXAMPLE  from the above equation:

y = 5x -75

=> y = 5*14 - 75

=> y = 70 - 75

=> y = -5

=> This means that if they wash 14 cars, they still have a debt of 5 dollars.

An equation EXCLUDING the setup cost will look like:

=> y = 5x

I wrote this because, they didn't spend any money so they will get 5 dollars per car. How many cars they wash, the answer will be 'number of cars x 5'.

An EXAMPLE from the above equation is:

=> y = 5x

=> y = 5 * 14

=> y = $70

=> This means that if they wash 14 cars, they get $70.

The first four terms of the given sequence are 18, 10, 6, and 4 respectively.

A sequence is an ordered list object which related and connected by a common value.

There are many sequences. They are Arithmetic sequence, Geometric sequence, and so on.

It is given that,

The first term of the sequence is a1 = 18

And the terms of the sequence are related by,

a(n + 1) = (2 + an)/2

For n = 1;

a(1 + 1) = (2 + a1)/2

⇒ a2 = (2 + 18)/2 = 10

For n = 2;

a(2 + 1) = (2 + a2)/2

⇒ a3 = (2 + 10)/2 = 6

For n = 3;

a(3 + 1) = (2 + a3)/2

⇒ a4 = (2 + 6)/2 = 4

Thus, the first four terms of the given sequence are a1 = 18, a2 = 10, a3 = 6, and a4 = 4.

Learn more about a sequence here:

https://brainly.com/question/6561461

#SPJ1

Answer:4.2 cups

Step-by-step explanation:

Just do 63 cups, divided by the 15 puppies which equals 4.2 cups! pls mark brainliest

Answer:

4.2 cups

Step-by-step explanation:

I am in the assiment and i just got it right on the assiment

Answer:

Step-by-step explanation:

The general form of a quadratic equation is ax²+bx+c = 0

Given the quadratic equation x²+4x+9=0 in its standard form, on comparing with the general equation we can get the value of the constant a, b and c as shown;

ax² = x²

a = 1

bx = 4x

b = 4

c = 9

The quadratic formula is given as x = -b±√(b²-4ac)/2a

Substituting the constant;

x = -4±√(4²-4(1)(9))/2(1)

x = -4 ±√(16-36)/2

x = -4±√-20/2

x = -4±(√-1*√20)/2

Note that √-1 = i

x = -4±(i√4*5)/2

x = (-4±i2√5)/2

x = -4/2±i2√5/2

x = -2±i√5

The solution to the quadratic equation are  -2+i√5 and  -2i-√5

Answer:

I think that the answer is 1 to1

Choice A would be true if it was for 8 years, and not 8 months. The value of t is in years. We would need to convert 8 months to years like so

12 months = 1 year

1 month = 1/12 of a year

8 months = 8/12 of a year

8 months = 2/3 of a year after dividing both parts by 4

So we'll go for choice B as the final answer

Answer:

x=12

Step-by-step explanation:

This is a right triangle, so the Pythagorean theorem can be used. The Pythagorean theorem states that [tex]C^2=a^2+b^2[/tex] where C is the hypotenuse and a and b are legs. In this question, we are given a and C. So, plugin 13 for C and 5 for a and solve for b. Once you rearrange the equation you get, [tex]b=\sqrt{13^2-5^2}[/tex]. Next, solve what is under the root to get, [tex]b=\sqrt{144}[/tex]. Finally, square root 144 for the final answer b=12.

Answer:

x = 12

Step-by-step explanation:

c² = a² + b²

13² = 5² + b²

169 = 25 + b²

b² = 169 - 25

b² = 144

b = 12

Step-by-step explanation: Ants are one of the most abundant insects on our planet and the reasons are their eusocial, complex societal behaviors and their ability to survive in many and various ecosystems. Like most other animal societies, reproduction is one of the core reasons why ants are so prevalent.

Acrobat Ant

Reproduction for ants is a complex phenomenon that involves finding, selecting and successfully fertilizing females to ensure that the eggs laid are able to survive and molt through the successive stages of the ant’s life cycle – larvae, pupae and adults.

Answer:

81

Step-by-step explanation:

Start: 50

After 1 day: 50 * 1.1

After 2 days: 50 * 1.1 * 1.1 = 50 * 1.1^2

After 3 days: 50 * 1.1^2 * 1.1 = 50 * 1.1^3

...

After 5 days: 50 * 1.1^5 = 80.53

Answer: 81

Answer:

see below

Step-by-step explanation:

25x + 200 > 1,200

Subtract 200 from each side

25x + 200-200 > 1,200-200

25x> 1000

Divide by 25

25x/25 >1000/25

x>40

Answer:

OPTION A AND B.

AS OPTION A IS 3/5=6/10=60%

Option C=60/100=60%

Answer:

the first and the last option

Step-by-step explanation:

In the first option 3/5 of the rectangle are filled in. if you divide 3 by 5, you will get 0.6, which when converted in to percent is equal to 60%

3/5 = 0.6

0.6 = 60%

*to convert decimals into percent, you just have to move the decimal point 2 places to the right and add the present sign*

in the second option 5 out of the 10 rectangles inside the square are filled in. that means that 5/10 of the square are filled in, the model shows 50%

5/10 = 1/2 = 0.5 = 50%

in the third model 6 out of the 10 rows in the square are filled in. that means that 6/10 of the square are filled in which is equal to 60%

6/10 = 0.6 = 60%

hope this helps! if you have any questions, let me know!

C.P. = $95000

S.P. = $280000

a. Profit

= S.P. - C.P.

= $280000 - $95000

= $185000

b. Let the profit% of C.P. be x.

(x/100) × $95000 = $185000

=> x/100 = $185000/$95000

=> x/100 = 37/19

=> x = (37/19) × 100

=> x = 3700/19

=> x = 194 14/19

So, profit percent of buying price is 194 14/19%.

c. Let the profit% of S.P. be x.

(x/100) × $280000 = $185000

=> x/100 = $185000/$280000

=> x/100 = 37/56

=> x = (37/56) × 100

=> x = 3700/56

=> x = 925/14

=> x = 16 1/14

So, profit percent of selling price is 16 1/14%.

d. Buying price percentage profit sounds better as far as Ella is concerned.

Answer:

i think A

Step-by-step explanation: