question 3 and 4
- 10 points

Answer:

the probability is 0.0202

Step-by-step explanation:

The computation is shown below:

Given that

The Average life span = 17 hours

Standard deviation = 0.8 hours

Sample = 30 batteries

Sample mean = 16.7 hours

Now based on the above information

The probability is

[tex]P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202[/tex]

Hence, the probability is 0.0202

Answer:

The correct answer is "9.3%".

Step-by-step explanation:

The given values are:

Amount of interest,

= $590

Principle,

= $8,000

Time:

= 285

Let the interest rate will be "x".

Now,

⇒  [tex]Amount \ of \ interest=Principle\times Interest \ rate\times \frac{time}{No. \ of \ days \ in \ year}[/tex]

On substituting the values, we get

⇒                             [tex]590=8000\times x\times \frac{285}{360}[/tex]

⇒                             [tex]590=6333.33\times x[/tex]

⇒                                [tex]x=\frac{590}{6333.33}[/tex]

⇒                                   [tex]=9.3157 \ percent[/tex]

or,

⇒                                   [tex]=9.3[/tex]%

Answer:

56tt8989899999999×-×554545--455356788:988

Answer:

[tex]\bar x =29.7[/tex]

[tex]\sigma = 6.81[/tex]

[tex]Median = 30.5[/tex]

Step-by-step explanation:

Given

[tex]Data:20,38,24,39,27,40,28,37,29,35,30,31,32,19,33,18,34,21,36,23[/tex]

[tex]n = 20[/tex]

Solving (a): The sample mean

This is calculated as:

[tex]\bar x =\frac{\sum x}{n}[/tex]

[tex]\bar x =\frac{20+38+24+39+27+40+28+37+29+35+30+31+32+19+33+18+34+21+36+23}{20}[/tex]

[tex]\bar x =\frac{594}{20}[/tex]

[tex]\bar x =29.7[/tex]

Solving (b): The standard deviation

This is calculated as;

[tex]\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n}}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{928.2}{20}}[/tex]

[tex]\sigma = \sqrt{46.41}[/tex]

[tex]\sigma = 6.81[/tex]

Solving (c): The median

First, sort the data in ascending order

[tex]Sorted:18,19,20,21,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,40[/tex]

The position of the median is calculated as:

[tex]Median = \frac{n+1}{2}[/tex]

[tex]Median = \frac{20+1}{2}[/tex]

[tex]Median = \frac{21}{2}[/tex]

[tex]Median = 10.5th[/tex]

The 10.5th item represents the mean of the 10th and 11th item.

So, median is:

[tex]Median = \frac{30+31}{2}[/tex]

[tex]Median = \frac{61}{2}[/tex]

[tex]Median = 30.5[/tex]

Answer:

x = 3

Step-by-step explanation:

3*3*3 = 9*3 = 27

Step-by-step explanation:      

Let's solve your equation step-by-step.

[tex]x^3 =27[/tex]

Step 1: Take cube root.

[tex]x = (27)^(1/3)[/tex]

[tex]x=3[/tex]

Explanation in words (Short Form)

- Move the variable to the left and the other values to the right to determine the value of x. To ascertain the outcome, simplify the values.

- In this equation (x^3=27), we can solve this equation by taking the cube root and then ascertaining the outcome.  The answer will result as x = 3 at the end for the following equation: x^3=27 to finding the value for x.

Answer:  

[tex]x=3[/tex]

Hope this helps.

Answer:

x=2

Step-by-step explanation:

To solve this equation combine like terms and move all like terms to the same side. Then, isolate the variable.

First, combine like terms that are on the same side,

-10x+4=-2x-12

Next, move -10x to the other side by adding it to both sides,

4=8x-12

Then, add 12 to both sides as well,

16=8x

Finally, isolate x by dividing the whole equation by 8,

2=x

Answer:

x=2

Step-by-step explanation:

I know the answer is x=2.

First, I set up the equation.

-7x+4-3x=-2x-12

Next, I added like values on each side.

-10x+4=-2x-12

Then, I added 10x to both sides.

4=8x-12

Then, I added 12 to both sides.

16=8x

Next, I divided 8 on both sides.

2=x

To make sure 2 is the true value of x, I inserted 2 to all values of x in the equation. -7(2)+4-3(2)=-2(2)-12. Both sides of the equation are -16. So, 2 is the real value of x in this equation.

Answer:

1. right

2. acute

3. obtuse

4. obtuse

5. acute

6. acute

7. scalene

8. scalene

9. isosceles

10. equilateral

11. scalene

12. isosceles

Step-by-step explanation:

9514 1404 393

Answer:

  (d)

Step-by-step explanation:

The area of the semicircle is ...

  A = (1/2)πr²

  A = (1/2)(3.14)(4 m)² = 25.12 m²

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(12 m)(8 m) = 48 m²

Then the total area of the composite figure is ...

  total area = semicircle area + triangle area

  = 25.12 m² + 48 m² = 73.12 m²

_____

Additional comment

The areas of choices A-C are too small. Choice A represents the area of the full circle. Choice B represents the area of the triangle only. Choice C is completely irrelevant. Choice D is the sum of the first two choices, inappropriately using the full circle area.

You should talk to your teacher about this question. None of the offered choices is correct.

Answer:

exposed is another word for endangered

Answer:

The bowl can hold 2.094 L.

Step-by-step explanation:

We want to find the volume of the hemisphere to calculate how many liters the bowl can hold. To find the volume of a hemisphere, we use this equation:

V = (2/3)•(π)•(r)³

Let's plug in what we know.

V = (2/3)(π)(10)³

Evaluate the exponent.

V = (2/3)(π)(1000)

Multiply.

V = 666.667π

V = 2094.395 cm³

Remember that 1000 cm = 1 liter, and we want to know how many liters the bowl can hold.

= 2094.395/1000

= 2.094 L

The bowl can hold 2.094 L.

Hope this helps!

Answer:

4 x 10

Step-by-step explanation:

4 x 2 x 5

4 x 2 = 8

8 x 5 = 40

4 x 10 = 40

Answer:

the awnser is D) $41.25.

Answer:

basically, with each value of x, you replace it by x on the equation

Step-by-step explanation:

y=1/3(12)

y=4

--------

y=1/3(3)

y=1

--------

y=1/3(18)

y=6

-------

hope this helped!

Answer:

C.  80%

Step-by-step explanation:

Answer:

9.045 grams

Step-by-step explanation:

You add the 42.68+19.125=61.805

Then take 61.805- 52.76=9.045

The number of grams of mixture that the baker still has is 9.045 grams.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that,

A baker mixes 42.68 grams of flour and 19.125 grams of sugar in a bowl.

Total grams of flour and sugar = 42.68 + 19.125 = 61.805 grams

So,

Total weight of the mixture = 61.805 grams

The baker then uses 52.76 grams of the mixture in a cake.

Remaining grams of the mixture = 61.805 grams - 52.76 grams

                                                      = 9.045 grams

Hence the remaining mixture is 9.045 grams.

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Answer:

13 + 3x = 34

Variables:

x = random number

Answer: 4/5 = .8

cos adj/hyp of r is .8

HOWEVER...

I’m assuming it’s talking about angle R...

Answer:

C) [tex]\sqrt{90}[/tex]

Step-by-step explanation:

VY = base and leg

XY = height and leg

VX = hypotenuse (c)

VY:

9 - 6 = 3

Solving for VX(c):

a² + b² = c²

3² + 9² = c²

9 + 81 = c²

c² = 90

c = [tex]\sqrt{90}[/tex]

Answer:The answer would be C 90

Step-by-step explanation:

Answer:

ANSWER

step explanation:

The vertex of the parabola below is at the point (2,4), and the point (3,6) is on the parabola. What is the equation of the parabola? 10 (3,6) (2,4) TO 10 10 A. y= 2(x - 2)2 + 4 B. x = 4(y - 3)2 + 1 C. y= 6(x - 2)2 + 4 D. y = 3(x - 4)2 + 2

Answer:

4.8

Step-by-step explanation:

Since the scale is 2 feet and the real is 70 to find the cale factor you do 70/2. Since the answer to that is 35 the scale factor is 35. SO to find tha drawing scale factor in feet you do 168/35 to get 4.8,

Answer:

The required interest rate would be of 3.4% a year.

Step-by-step explanation:

The amount of money earned in compound interest, after t years, is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Peyton is going to invest $440 and leave it in an account for 5 years.

This means that [tex]P(0) = 440, t = 5[/tex]

So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 440(1+r)^5[/tex]

What interest rate, to the nearest tenth of a percent, would be required in order for Peyton to end up with $520?

This is r for which P(t) = 520. So

[tex]P(t) = 440(1+r)^5[/tex]

[tex](1+r)^5 = \frac{520}{440}[/tex]

[tex]\sqrt[5]{(1+r)^5} = \sqrt[5]{\frac{52}{44}}[/tex]

[tex]1 + r = (\frac{52}{44})^{\frac{1}{5}}[/tex]

[tex]1 + r = 1.034[/tex]

Then

[tex]r = 1.034 - 1 = 0.034[/tex]

The required interest rate would be of 3.4% a year.

Answer:

4n

Step-by-step explanation:

you multiply 4 x n= 4n

:')

Answer:

D) $5385.10

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the decay of an amount after t years is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

If you buy a motorcycle for $12,500 in 2015 and it depreciates (shrinks) in value by 15.5% every year

This means that [tex]A(0) = 12500, r = 0.155[/tex]

So

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]A(t) = 12500(1-0.155)^t[/tex]

[tex]A(t) = 12500(0.845)^t[/tex]

How much will it be worth in 2020?

2020 is 2020 - 2015 = 5 years after 2015, so this is A(5). So

[tex]A(5) = 12500(0.845)^5 = 5385.10[/tex]

The correct answer is given by option D.

Answer:

66 students prefer the zoo

Step-by-step explanation:

I got it correct :)

Answer:

the answer is 2400 cents

Step-by-step explanation:

if you have 48 candies and each cost 50 cents so u meltiply 48 with 50. so if u mutiply them u get 2400cents, but if u want them in dollar then 1 dollar is 100 cent so if 1 dollar = 100 cent

                   ?        = 2400 cent

you criss -cross them so when u do 2400 multiplyed by 1 is 2400 and 100 multiplyed by ? is 100?  

so your going to get this

2400 = 100?

so u divide both sides by 100 because u want "?" alone. so when u do 100 will vanish because you divided both sides with 100

so it will look something like this

2400/100 = ?

when u divide 2400 with 100 u get 24.

what does that mean? it mean 2400 cents are 24 dollars

do you get it?

Answer:

360 mi^3

Step-by-step explanation:

The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values

solid  1

length = 11 - 4 = 7 mi

base area = length x width = 7 x 4 = 28 mi^2

V = base area x height = 28 x 6 = 168 mi^3

solid 2

base area = 8 x 4 = 32 mi^2

V = 32 x 6 = 192 mi^3

total volume: 168 + 192 = 360 mi^3

The volume of the figure is 360 mi³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a figure where two rectangular boxes are put on top of each other.

Volume of a rectangular prism = L × W × H

Here L is the length, W is the width and H is the height.

The dimensions of the rectangular prism are :

Larger one having L = 11 mi, W = 6 mi and H = 4 mi

Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.

Volume of the figure = volume of larger box + Volume of smaller box

                                  = (11 × 6 × 4) + (4 × 6 × 4)

                                  = 264 + 96

                                  = 360 mi³

Hence the volume of the figure is 360 mi³.

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Step-by-step explanation:

Add the corresponding sides of the two equations

1.

2x=6

x=3

substitute for x

3+y=-1

y=-4

4.

5x=10

x=2

substitute for x

2(2)+2y=-2

2y=-6

y=-3

5.

12y=24

y=2

substitute for y

6x+5(2)=4

6x+10=4

x=-6

x=-1

Answer:

Q3. x = 3, y = -4

Q4. x = 2, y = -3

Q5. x = -1, y = 2

Step-by-step explanation:

Since the question is asking us to solve the system using elimination/adding, that's what I'll do.

To solve by adding, we add the like terms of both equations together.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1st question:

x + y = -1

x - y = 7

We add the first term together.

x + x = 2x

Then the second term.

y + -y = y - y = 0

Then the last term.

-1 + 7 = 6

Which becomes:

2x = 6

Then we solve the linear equation.

2x = 6

÷ 2  ÷ 2

x = 3

From the x value, we can then find y.

We can use either equation. In this example, I'll choose the first one.

x + y = -1

Substitute x = 3

3 + y = -1

-3         -3

y = -4

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2nd question:

2x + 2y = -2

3x - 2y = 12

We add the first term together.

2x + 3x = 5x

Then the second term.

2y + - 2y = 2y - 2y = 0

Then the last term.

-2 + 12 = 10

Which becomes:

5x = 10

Then we solve the linear equation.

5x = 10

÷5   ÷5

x = 2

From the x value, we can then find y.

We can use either equation. In this example, I'll choose the first one.

2x + 2y = -2

Substitute x = 2

4 + 2y = -2

-4           -4

2y = -6

÷2   ÷2

y = -3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3rd question:

6x + 5y = 4

-6x + 7y = 20

We add the first term together.

6x + -6x = 6x - 6x = 0

Then the second term.

5y + 7y = 12y

Then the last term.

4 + 20 = 24

Which becomes:

12y = 24

Then we solve the linear equation.

12y = 24

÷12   ÷12

y = 2

From the x value, we can then find y.

We can use either equation. In this example, I'll choose the first one.

6x + 5y = 4

Substitute y = 2

6x + 10 = 4

-10          -10

6x = -6

÷6   ÷6

x = -1

Answer:

Verdader

o

Step-by-step explanation: