A company has developed a new battery, but the average lifetime of all of the batteries it makes is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a:

Answer:

2 apples Follow me if u have any more request next time

Step-by-step explanation:

5-3=2

Answer:

PK represents a radius. Radius only goes half way of the circle.

Answer:

B) chord

Step-by-step explanation:

N and M are two points on the circumference and the segment MN doesn't pass through the centre, so it's a chord

Answer:

1

Step-by-step explanation:

Volume of Cube = a³

a is the length of one side of cube

Volume = a³ = 1³ =1x1x1 = 1

Answer:

The surface area is 88*pi square units.

Step-by-step explanation:

The surface area of a cylinder is given by two times the area of the base plus the area of the sides. This is given bellow:

surface area = 2*(base area) + (side area)

base area = pi*r²

base area = pi*(4)²

base area = pi*16 = 16*pi

side area = 2*pi*r*h

side area = 2*pi*4*7

side area = 8*7*pi

side area = 56*pi

surface area = 2*(16*pi) + 56*pi

surface area = 32*pi + 56*pi

surface area = 88*pi

The surface area is 88*pi square units.

Answer:

112π cubic units

Step-by-step explanation:

The volume of a cylinder is the area of the base × height.

The area of a circle is πr to the 2nd power

So the area of the base is π × 4 to the second power = 16π

The height of the cylinder is 7, so the volume is 16π × 7 = 112π cubic units

Absolute value equations can equal zero but cannot equal a negative number. This is because the absolute value of a number is its distance from zero on the number line, which is always zero or positive.

In the field of mathematics, absolute value equations can indeed be equal to zero. The absolute value of a number is its distance from zero on the number line, irrespective of direction. Therefore, the only number whose absolute value (distance from zero) is zero, is zero itself.

One can encounter such a situation in an equation like |x|=0, where the solution is x=0, simply because 0 is the only number that is at zero distance from zero. However, for an absolute value equation to be equal to a negative number, this is impossible, because absolute value is a measurement of distance and cannot be negative. So, if your simplified equations are resulting in negative values, you might want to double-check your work.

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Answer:

x = 50.5°

Step-by-step explanation:

∠ BDC and ∠ BDA are adjacent and supplementary, thus

∠ BDC = 180° - 78° = 102°

Calculate ∠ BCD using the Sine rule in Δ ABC, that is

[tex]\frac{5.6}{sinC}[/tex] = [tex]\frac{9.3}{sin50}[/tex] ( cross- multiply )

9.3 × sinC = 5.6 × sin50° ( divide both sides by 9.3 )

sinC = [tex]\frac{5.6sin50}{9.3}[/tex] ≈ 0.4613, thus

C = [tex]sin^{-1}[/tex] (0.4613 ) ≈ 27.5°

The sum of the 3 angles in Δ BCD = 180°, thus

x = 180° - (102 + 27.5)° = 180° - 129.5° = 50.5°

The angle x is also 52 degrees.

To find the measure of angle x in triangle ABC, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Given that angle A is 78 degrees and angle B is 50 degrees, we can find angle C using the following equation:

Angle C + Angle B + Angle A = 180 degrees

Angle C + 50 degrees + 78 degrees = 180 degrees

Now, subtract the known angles from 180 degrees to find the measure of angle C:

Angle C = 180 degrees - (50 degrees + 78 degrees)

Angle C = 180 degrees - 128 degrees

Angle C = 52 degrees

Now that we know angle C is 52 degrees, we can use the fact that the angles in a triangle add up to 180 degrees to find angle x:

Angle A + Angle B + Angle x = 180 degrees

78 degrees + 50 degrees + Angle x = 180 degrees

Now, subtract the known angles from 180 degrees to find angle x:

Angle x = 180 degrees - (78 degrees + 50 degrees)

Angle x = 180 degrees - 128 degrees

Angle x = 52 degrees

So, angle x is also 52 degrees.

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48/6 = 8

He needs to buy 8 of the six pack size for a total of :

8 x 12.12 = $96.96

Or

48/ 4 = 12 Of the 4 packs for a total of

12 x 9.72 = $116.64

He would save

116.64 - 96.96 = $19.68 by buying 8 of the six packs.

Answer:

—————————————-

He saves $19.68

—————————————-

Hope this helps!!!!

—————————————-

Step-by-step explanation:

—————————————-

6 bottles for $12.12

Find the unit rate:

12.12/6

=2.02

This tells us that using this price, each bottle costs $2.02

—————————————-

4 bottles for $9.72

Find the unit rate:

9.72/4

=2.43

This tells us that using this price, each bottle costs $2.43

—————————————-

The first deal is better because you are paying less for each bottle.

—————————————-

So now you know which “deal to use,”

—the first one— (6 bottles for $12.12)

Since each bottle costs $2.02 here, you can multiply:

48 x $2.02 = $96.96

—————————————-

In the second deal, where 4 bottles cost 9.72 bucks,

Each bottle is for $2.43

48 x $2.43 = $116.64

—————————————-

How much does he save by going with the first deal?

$116.64 - $96.96 = $19.68

Answer:

Step-by-step explanation:

The tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.

It is given that Leah is measuring the weight of adult rhinos at the zoo.

It is required to find the unit of measurement she should use to eliminate the need to write the values in scientific notation.

Given options:

1) grams

2) feet

3) gallons

4) tons

It is defined as the numerical quantity that gives an idea about an object's weight, length, width, and many more. It can be used to compare two objects.

We know the feet are the unit of measuring the length and gallons are the unit of measuring the volume.

The grams and tons are the units of measuring the weight.

Grams would use to measure a small amount of weight whereas we would use the tons to measure a large amount of weight. Ton is a metric unit that equals 1000 kilograms.

Thus, the tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.

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Answer:

97

Step-by-step explanation:

83 and JKL form a straight line so they add to 180 degrees

83+ JKL = 180

Subtract 180 from each side

83-83+ JKL = 180-83

JKL = 97

Answer:

97°

Step-by-step explanation:

Interior + exterior angle = 180

Interior angle (JKL) = 180 - 83

97

Answer:

195¢

Step-by-step explanation:

1 inch of the wire costs

[tex]\frac{85}{17}[/tex] cents

So we just multiply by 39 to get the total cost.

[tex]\frac{85}{17} * 39 = 195[/tex]

Answer: 195 cents

Explanation:

17 inches cost 85 cent

Means 1-inch will cost 85/17 = 5 cents

At the same rate 39 inches will cost 39×5= 195 cents

Answer:

57

Step-by-step explanation:

the angles of a triangle together make 180 degrees.

using this, we can find the unknown angle is 115 degrees.

from here, we subtract 1 from both sides of 2d+1=115, then divide by 2, to get the d alone.

114/2=57

d=57

Answer:

d=57

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees

38 +27 +2d+1=180

Combine like terms

(38+27+1) +2d= 180

66+2d=180

Now, solve for d by isolating it

Subtract 66 from both sides

66-66 +2d=180-66

2d=114

Divide both sides by 2

d=57

Answer: -4

Step-by-step explanation:

[tex]3x-7x=x\\-4x=-4x[/tex]

Answer:

The answer is -4x.

Step-by-step explanation:

You can just substract easily by writing 7-3 but remember to add negative to the final value as 3 is smaller than 7 and lastly, you only have to add x to the final answer.

600 is the total number of pages in the book

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Joshua is reading a book for history class.

He has read 180 pages so far.

This number represents 30% of the total number of pages in the book.

We need to find  total number of pages in the book.

Let x be the number of pages in the book.

30% of x=180

Convert 30% to decimal

30/100x=180

0.3x=180

Divide both sides by 0.3

x=600

Hence, 600 is the total number of pages in the book

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Answer: On average, each country receives 2.93 inches of rain each day.

Step-by-step explanation:

Since we have given that

Palm Beach = 2.3

Broward = 3.5

Dade = 3.0

So,the average inches of rain each country would receive each day would be :

[tex]\dfrac{2.3+3.5+3.0}{3}=\dfrac{8.8}{3}=2.93\ inches[/tex]

Hence, on average, each country receives 2.93 inches of rain each day.

Answer:

[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]

[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]

[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]

[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]

Step-by-step explanation:

The equation needs to be rearranged in terms of one trigonometric function:

[tex]5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0[/tex]

[tex]5\cdot \tan 2\theta - 9 = 0[/tex]

[tex]5\cdot \tan 2\theta = 9[/tex]

[tex]\tan 2\theta = \frac{9}{5}[/tex]

[tex]\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)[/tex]

The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:

[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]

[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]

[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]

[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]

Answer:

1,500,000 gallons

Step-by-step explanation:

In this question, we are to calculate the total volume of the aquarium after installing a new dolphin tank.

Mathematically, to calculate this, we simply need to add the the volume of the new dolphin tank to the volume of the things in the aquarium before bringing the dolphin tank.

The volume of all the things in the aquarium before installing the dolphin tank is 1.25 * 10^6 = 1,250,000 gallons

now let’s add the volume of the dolphin tank which is 250,000 gallons

that would be 1,250,000 + 250,000 = 1,500,000 gallons or 1.5 * 10^6 gallons

Step-by-step explanation:

x3 - 9x2 + 5x - 45

x2 (x - 9) + 5(x - 9)

(x - 9) and (x2 + 5) are the factors

Answer:

C

Step-by-step explanation:

EDGE 20-21

Answer:

11 tshirts would cost £106.15

Step-by-step explanation:

67.55 divided by 7 = 9.65

9.65 x 11 = 106.15

Therefore the total would be £106.15.

Answer: 106.15

Step-by-step explanation:

Answer:

The value of x is 16°

Step-by-step explanation:

Using the formula, angle = 1/2(θ°-x°) :

Let θ = 96°, x = x°, angle = 40°,

1/2×(96°-x°) = 40°

96° - x° = 80°

-x° = 80° - 96°

-x° = -16°

x = 16°

Answer:

12 hours

Step-by-step explanation:

Let's call the Jennifer's speed J, and the Krystal's speed K.

If Jennifer works alone, she can do the job in 6 hours, so:

J*6 = 1000

J = 1000/6 = 500/3

If Jennifer and Krystal work together, they can do the job in 4 hours, so:

(J+K)*4 = 1000

J+K = 250

Using the value of J, we can find K:

500/3 + K = 250

K = 250 - 500/3 = 250/3

Now, to find the time that Krystal would take if she works alone:

K * time = 1000

250/3 * time = 1000

time = 1000/ (250/3) = 1000*3/250 = 12 hours

Answer:

12 hours

Step-by-step explanation:

please check the attached files for explanation

Answer:

8 + [tex]\frac{x}{4}[/tex]

Step-by-step explanation:

I'm assuming you want an answer to the top section of the question.

We can start with 8.

    8

When a problem asks for the sum, it's looking for addition, so we use the + sign.

    8 +

The problem says "a number," so let's represent that with x. Basically, x just means a number we don't know.

    8 + x

The "number" is divided by 4, so we'll just put x/4 as our second term.

   8 + [tex]\frac{x}{4}[/tex]

Answer:

B is filling the tank most quickly

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A, (7,2), the time goes slow, so it cannot be correct.

C, you can see is more lower than the other two. That means it is the slowest.

B, is going at a average rate, but faster than A and C. If you find a coordinate on B, for an example (2,2). 2 gallons in 2 minutes.

Answer:

  250 minutes

Step-by-step explanation:

a) Assuming all taps flow at the same rate, the time is inversely proportional to the number of taps. Using 3/5 of the total taps will take 5/3 of the time required when all taps are used.

For 3 taps, the time is ...

  (5/3)(150 minutes) = 250 minutes

__

b) An assumption being made in my working is that all the taps are flowing at the same rate.

a) It will take 250 minutes to fill the pool using 3 taps.  B) The assumption being made here is that all the taps are flowing at the same rate r and that they are all turned on at the same time, working in parallel to fill the pool.

Let's denote the rate at which each tap fills the pool as r liters per minute.

With 5 taps working together, it takes 150 minutes to fill the pool. Therefore, the combined rate of 5 taps is [tex]\( \frac{1}{150} \)[/tex]  of the pool per minute. We can express this as:

[tex]\[ 5r = \frac{1}{150} \][/tex]

 Now, we want to find out how long it will take to fill the pool using only 3 taps.

The combined rate of 3 taps will be 3r.

To find the time t it takes for 3 taps to fill the pool, we set up the equation:

[tex]\[ 3r = \frac{1}{t} \][/tex]

We can solve for r using the first equation:

[tex]\[ r = \frac{1}{5 \times 150} \][/tex]

Substituting this value into the second equation gives us:

[tex]\[ 3 \times \frac{1}{5 \times 150} = \frac{1}{t} \][/tex]

Solving for t

[tex]\[ t = \frac{1}{3 \times \frac{1}{5 \times 150}} \][/tex]

t = 250

 So, it will take 250 minutes to fill the pool using 3 taps.

b) The assumption being made here is that all the taps are flowing at the same rate r and that they are all turned on at the same time, working in parallel to fill the pool.

This implies that the flow rate of each tap does not change regardless of how many taps are being used simultaneously, and that there are no other factors (like water pressure changes) affecting the flow rate when fewer taps are used.

Given:

The diameter of the bicycle wheel is 27 inches.

We need to determine the circumference of the bicycle wheel.

Circumference of the bicycle wheel:

The circumference of the bicycle wheel can be determined using the formula,

[tex]C=\pi d[/tex]

where d is the diameter of the bicycle wheel.

Substituting d = 27 and π = 3.14, we have;

[tex]C=(3.14)(27)[/tex]

Multiplying, we get;

[tex]C=84.78 \ in[/tex]

Thus, the circumference of the bicycle wheel is 84.78 inches.

Step-by-step explanation:

40° + 90° + 90° + angle ACB = 360°

220° + angle ACB = 360°

angle ACB = 360° - 220°

Therefore angle ACB = 140°

Hope it will help :))

Answer:

the movie is 2 hours and 10 min long

no it will not be over by 8:45pm

Step-by-step explanation:

if the movie begins at 3:45 pm and the next begins at 6:25pm with a half hour break you need to take 30 min from 6:25 to see what time the movie ended which is 5:55pm then you figure the time between 3:45pm and 5:55pm which is 2hours and 10 min.

since thw movie is starting 20 min late from 6:25pm that is now a start time of 6:45pm if the movie is 2hours and 10 min it will not be over by 8:45pm since that is only 2 hours

Answer:

$3,245

Step-by-step explanation:

For a money saved at Simple Interest,

Amount =Simple Interest+Principal

Principal, P=$2750

Rate, r=3%

Time, T=6 Years

[TeX] Simple \: Interest= \frac{Principal X Rate X Time}{100}[/TeX]

[TeX] = \frac{2750X 3 X 6}{100}[/TeX]=$495

Therefore, Amount in Erin's Account after 6 years =2750+495

=$3,245

Answer:

x = -13/5 OR -2.6

Step-by-step explanation:

Take steps to isolate x:

-14 - 5 = -10x - 45

-19 = -10x -45

26 = -10x

x = 26/-10

x = -13/5 OR -2.6

Answer:X=-13/5 is the simplified answer

Step-by-step explanation:

-14-5=-10x-45

-19=-10x-45

-19+45=-10x-45(+45)

26=-10x

26/-10=x

x=-13/5

Answer:

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

Step-by-step explanation:

sin(2x) + sin(4x) = 0

Use double angle formula.

sin(2x) + 2 sin(2x) cos(2x) = 0

Factor.

sin(2x) (1 + 2 cos(2x)) = 0

Solve.

sin(2x) = 0, cos(2x) = -½

2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

Answer:

Perimeter: 36 m

Area: 60 m squared

Step-by-step explanation:

The perimeter is the sum of the exterior side lengths of the shape. Here, we see that there are two side lengths given, but we need to find the third one.

Notice that the triangle is split up into two right triangles, which means that we can use the Pythagorean Theorem to solve for half of the remaining side. The right triangles have hypotenuses of 13 and one leg of 12. That means the second leg will be [tex]\sqrt{13^2-12^2} =\sqrt{169-144} =\sqrt{25} =5[/tex].

So, the third side is made up of the two legs with length 5. This makes the length of the remaining side: 5 + 5 = 10.

Now, we can calculate the perimeter: P = 10 + 13 + 13 = 36 meters.

The area is calculated by the formula: [tex]A=\frac{1}{2} bh[/tex] , where b is the base and h is  the height. Here, the base is what we found above, 10, and the height is the length that makes a perpendicular with the base, which is 12. So, the area is: [tex]A=(1/2)*10*12=(1/2)*120=60[/tex]. So, the area is 60 square meters.

Hope this helps!

Answer:

36m

60m²

Step-by-step explanation:

Base of 1 right angle triangle:

sqrt(13² - 12²)

5

Base of the bigger triangle:

5 + 5 = 10

Perimeter = 13 + 13 + 10

36 m

Area = ½ × 10 × 12

60 m²