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The probability that 16 randomly selected batteries will have a runtime of less than 27 hours is 0.0228.

Probability is a branch of mathematics that deals with the study of random events or outcomes. It involves the analysis of the likelihood or chance of a particular event occurring, given certain conditions or assumptions. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

Probability theory is used to analyze and understand random phenomena such as games of chance, weather patterns, financial markets, and many other areas of study. The main tools of probability theory include probability distributions, random variables, and statistical inference.

Probability distributions are mathematical functions that describe the probabilities of different outcomes for a particular event or experiment. Random variables are variables that take on different values based on the outcome of a random event, and they are used to calculate probabilities for a range of different scenarios.

We can use the central limit theorem to approximate the distribution of the sample means, where n=16. The sample mean, X', will also be normally distributed with a mean of μ = 30 hours and a standard deviation of σ/√n = 6/√16 = 1.5 hours.

Now, we need to find the probability that the sample mean is less than 27 hours:

P(X' < 27) = P(z < (27-30)/1.5) [converting to standard normal distribution using z-score]

P(X' < 27) = P(z < -2)

Looking up the z-table, we can find that the probability of a standard normal random variable being less than -2 is approximately 0.0228.

Therefore, the probability that 16 randomly selected batteries will have a runtime of less than 27 hours is 0.0228.

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Answer:

$3.47

Step-by-step explanation:

They are selling the container for $3.97 and it costs them $0.50 to make each. So that means they'll make a profit of $3.47.

1.0% is the percent error for his estimate .

What is percent error?

When compared to the actual value, the percent error is the difference between the estimated and actual values. The relative error is multiplied by 100 to calculate the % error, in other words. The difference between an estimated number and a precise value is measured in percent error.

the percent error = {exact error - approximate error} * 100%/exact error

                             = (9.9 - 10) * 100/9.9

                             = 0.1/9.9 * 100%

                             ≈ 1.0%

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Therefore, the perimeter P of the nonagon is 19.5 units.

Perimeter refers to the total length of the boundary or the outer edge of a closed figure or shape. It is the sum of the lengths of all the sides or edges that enclose the shape.

Here,

Since O is the center of the regular nonagon, all the sides of the nonagon are equal in length. Let the length of one side of the nonagon be s. Then, the perimeter P of the nonagon is given by:

P = 9s

To find s, we can use the fact that the sum of the interior angles of a nonagon is given by (9-2)×180° = 1260°. Since the nonagon is regular, each angle is equal to 1260°/9 = 140°.

Consider the triangle OAB, where A and B are two adjacent vertices of the nonagon. Since O is the center of the nonagon, angle AOB is equal to 360°/9 = 40°. Also, angle OAB and angle OBA are equal to half of (180° - 140°) = 20°.

Therefore, angle AOB is isosceles, and we can use the cosine rule to find s:

cos(20°) = (s/2) / s

cos(20°) = 1/2

s = 2 / cos(20°)

Using a calculator, we get s ≈ 2.165. Therefore, the perimeter P of the nonagon is:

P = 9s

≈ 19.5 (rounded to the nearest tenth)

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a) Using the formula for finance charge, we can find the balance after one year:

charge = r*(balance-payments+purchases)

Here, r = 16.73% = 0.1673 (as a decimal), payments = $300 per month = $3,600 per year, and purchases = 0 (since Chloe is not making any new purchases).

Let's assume that x is the balance after one year. Then, we can write:

0.1673*(7316.48-3600) = x - 3600

Simplifying and solving for x, we get:

x = $6,830.58

So, the credit card balance (to the nearest dollar) after one year would be $6,831.

b) If Chloe increases her monthly payment to $350 per month, then her payments for the year would be $4,200. Using the same formula as above, we can find the balance after one year:

0.1673*(7316.48-4200) = x - 4200

Simplifying and solving for x, we get:

x = $5,774.99

So, the credit card balance (to the nearest dollar) after one year with a $350 monthly payment would be $5,775.

Answer:

$ 922.25

Step-by-step explanation:

General equation for simple interest ... B(t)=B(0)[1+rt]B

(0)= inital amount r= simple annual interest rate t= number of yearsFor this problem,

B (2)=$850[0.0425×2}=850×1.085 =$922.25

Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint called the vertex. The rays or line segments are called the sides of the angle.

Angles are typically measured in degrees or radians, and they are denoted using the symbol ∠. The measure of an angle is the amount of rotation needed to bring one side of the angle into coincidence with the other. A full rotation is 360 degrees or 2π radians.

Angles can be classified into different types based on their measures and their relationships with other angles. Some common types of angles include:

Acute Angle: An angle whose measure is less than 90 degrees.

Right Angle: An angle whose measure is exactly 90 degrees.

Obtuse Angle: An angle whose measure is greater than 90 degrees but less than 180 degrees.

Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.

By definition of angle bisectors, we know that CD=DE and BD=DF.

Thus, the triangle congruence principle SAS (side-angle-side) allows us to deduce that Triangle BCD is congruent to Triangle ECD, since they share side CD, angle BDC and angle EDC.

Therefore, BC=CE (corresponding sides of congruent triangles are equal) and CE=EF (because CE bisects segment BF).

Thus, BC=EF, and we have proven that BC is equal to EF

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Town B will have a larger population than Town A in the year 2019.

To solve this problem, we can use a year-by-year approach to see when the population of town B surpasses that of town A.

Let's start with year 0 (2015):

Town A population: 9,000

Town B population: 8,000

In year 1 (2016):

Town A population: 9,500 (9,000 + 500)

Town B population: 8,720 (8,000 x 1.09)

In year 2 (2017):

Town A population: 10,000 (9,500 + 500)

Town B population: 9,504.8 (8,720 x 1.09)

In year 3 (2018):

Town A population: 10,500 (10,000 + 500)

Town B population: 10,360.232 (9,508.8 x 1.09)

In year 4 (2019):

Town A population: 11,000 (10,500 + 500)

Town B population: 11,292.653 (10,394.912 x 1.09)

From this calculation, we can see that in the year 2019, the population of Town B will be larger than that of Town A. Therefore, the answer is:

Town B will have a larger population than Town A in the year 2019.

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Answer: there

Step-by-step explanation:

exactly 1 solution

The angle that is congruent to ∠S after the given rotation transformation is: ∠M

A rotation is defined as a type of transformation whereby the object is rotated about a fixed point. The direction of the rotation can either be clockwise or anticlockwise.

Now, rotating a specific point that has the coordinates as (x, y) by 180° about the origin in either a clockwise or counterclockwise direction, will produce a new point that has the coordinates (−x,−y)

Thus, if Polygon KLMN is the image of polygon PQRS after a 180 degree rotation, then we can say that the new image formed will have ∠M congruent to ∠S

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Answer:

c) The Diameter is Half of the radius

Step-by-step explanation:

A) A diameter ALWAYS passes through the center of the circle, so EVERY diameter WILL pass through the Center of the circle, making this statement valid.

b) A center of a circle will ALWAYS lie in the interior of the circle. it is an Axiom

c) False, the RADIUS is half of the Diameter of a circle.

d) The Longest Chord IS the Diameter, which passes through the circle, so this statement is valid.

So the false option is (C)

Answer:

Step-by-step explanation:

50+40+15+40+85

=230

Rounding to the nearest whole number, the number of bacteria still present in the culture after 7 hours is approximately 3481.

How many whole numbers are there?

All natural numbers are added together to form whole numbers. both a fraction and neither a decimal. Integer 0 through 11: 2, 3, 5, 6, 7, 8, 9, & 10. 0 is a counting number or the opposite.

To determine the number of bacteria inside the culture at t hours, use the formula Pt = Po 2(t/d), in which Po is simply the initial population and d is the doubling time.

The values of Po are 870, d, and t are respectively 3 and 7. When we use the formula with these numbers, we get:

[tex]Pt = 870 * 2^{(7/3)}[/tex]

Pt ≈ 3480.5

Hence, the number of bacteria still present in the culture after 7 hours is approximately 3481.

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Using the prοbability cοncept, it is fοund that there is a 0.0887 = 8.87% prοbability all three marbles are the same cοlοr.

A prοbability is the number οf desired οutcοmes divided by the number οf tοtal οutcοmes.

The οrder in which the marbles are chοsen is nοt impοrtant, and they are alsο chοsen withοut replacement, which means that the cοmbinatiοn fοrmula is used tο find the number οf οutcοmes.

Tο find the prοbability that all three marbles selected are the same cοlοr, we need tο cοnsider three cases: selecting three red marbles, selecting three white marbles, οr selecting three blue marbles.

Let's first calculate the tοtal number οf ways tο select three marbles frοm the urn. This can be dοne using the cοmbinatiοn fοrmula:

C(19, 3) = 19! / (3! * 16!) = 969

Sο there are 969 pοssible ways tο select three marbles frοm the urn.

Nοw let's calculate the number οf ways tο select three marbles οf the same cοlοr:

Sο the tοtal number οf ways tο select three marbles οf the same cοlοr is:

20 + 10 + 56 = 86

Therefοre, the prοbability οf selecting three marbles οf the same cοlοr is:

86 / 969 = 0.0887 (rοunded tο fοur decimal places)

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Step-by-step explanation:

The first two are not equations, there is no ' = ' sign. Tey are expressions.

C) -3 + (5-4) = ) (-3+5) -4

     -3 +1   = 2 -4

         -2    = -2       True

D)  -5 -4 = -5 +( -4)

        -9    =   -9      True

I will assume the + sign is supposed to =   ( same key)

A)   -3 (5-4)  = -3(5) - 4

       -3  = -19     FALSE

B)  -5 + (-4) =  -4 + (-5)

        -9       =   -9    True

The conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.

What is conditional probability?

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

Here, we have

Given: Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played.

Let A be the event of a contestant playing acoustic guitar.

Let B be the event of a contestant wearing leather pants

The conditional probability of a contestant playing acoustic guitar given he wears leather pants, P(A|B) is-

P(A|B) = P(A∩B)|P(B)

Where,

P(A∩B) =  is the probability of simultaneous occurrence of events A and B.

P(A∩B) = 6

P(B) = no. of contestants wearing leather pants

P(B) = 15

P(A|B) = 6/15 = 2/5

Hence, the conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.

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Answer:

the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent.  option (C) √(2x² + x) is equivalent to the original expression √(2x) * √(x+3) when x > 0.

Step-by-step explanation:

To simplify the expression √(2x) * √(x+3), we can use the property of radicals that says:

√(a) * √(b) = √(a * b)

So, we have:

√(2x) * √(x+3) = √(2x * (x+3))

Multiplying out the terms inside the radical, we get:

√(2x * (x+3)) = √(2x² + 6x)

Therefore, the expression √(2x) * √(x+3) is equivalent to the radical expression √(2x² + 6x) when x > 0.

So, the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent:

√(2x² + 6x) = √(2x² + x + 5x) = √(x * (2x + 5)) = √x * √(2x + 5)

The period, phase shift, and cosine function of the graph are;

The period = π

The phase shift = π/8

The cosine function is; y = 2·cos(2·(x - π/8)) - 1

The period of the graph is the distance between two consecutive peaks of the wave.

The maximum value of the graph is 1 at x = π/8 and x = 9·π/8, and the minimum value of the function is; -3 at 5·π/8.

The vertical displacement can be obtained from half the sum of the max and min point as follows;

Vertical displacement = (1 + (-3))/2 = -1

The vertical displacement = -1

The amplitude = Half the distance between the max and min point of the graph

Amplitude, a = (1 - (-3))/2 = 2

The amplitude, a = 2

The period of the graph = 9·π/8 - π/8 = 8·π/8 = π

The period = 2·π/b

Therefore; 2·π/b = π

b = 2·π/π = 2

b = 2

The phase shift = π/8

The cosine function is therefore;

y = 2·cos(2·(x - π/8) - 1

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The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

The likelihood or chance that a specific occurrence or outcome will occur is quantified by probability. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. For instance, there are two equally likely outcomes (heads or tails), but only one of them is heads, hence the probability of flipping a fair coin and obtaining heads is 0.5 or 50%. By dividing the number of favorable outcomes by the total number of possible outcomes, one can calculate probability.

given

We can see that Nestor won a medal in 6 out of the 10 trials by counting the number of victories.

We can use the binomial distribution with parameters n=10 (number of trials) and p=0.79 to calculate the likelihood that this will occur (probability of success).

The following calculation can be used to determine the likelihood of at least 6 successes in 10 trials:

P(X>=6) = 1 - P(X<=5)

Using a calculator for the binomial distribution, we obtain:

P(X>=6) = 90.1%

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

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Answer:

Answer : 264.12cm²

Step-by-step explanation:

Area of a triangle : bh/2

47-18.6 = 28.4

28.4 x 18.6 = 528.24

528.24/2 = 264.12

Pls Mark Brainliest

Answer:

874.2 cm²

Step-by-step explanation:

The given shape is a parallelogram.

Here,

Base ( b ) = 47 cm

Height ( h ) = 18.6 cm

Formula : -

Area of parallelogram = bh

Area of parallelogram

= bh

= 47 x 18.6

= 874.2 cm²

Hence,

Area of the given parallelogram is 874.2 cm².

Step-by-step explanation:

For RIGHT triangles such as this one:

sin (60) = opposite LEG/ hypotenuse =  sqrt(3) / 2  / CB       solve for CB

tan (60°) =  opposite LEG / adjacent LEG = sqrt(3)/2  / AC    solve for AC

The Space Shuttle Discovery traveled 22.3 million miles more distance than the Space Shuttle Atlantis.

What is distance ?

To find how many more miles the Space Shuttle Discovery traveled than the Space Shuttle Atlantis, we can subtract the distance traveled by Atlantis from the distance traveled by Discovery:

148.2 million miles - 125.9 million miles = 22.3 million miles

Therefore, the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

What is Space Shuttle ?

The Space Shuttle was a reusable spacecraft designed and operated by NASA (the National Aeronautics and Space Administration) to carry astronauts and cargo into space. It was in service from 1981 until 2011, when the final mission was completed.

The Space Shuttle consisted of several components, including the orbiter, which was the main spacecraft, and the two solid rocket boosters and external fuel tank that provided the initial propulsion during liftoff. The orbiter was designed to carry up to seven crew members and could be used to deploy satellites, conduct scientific experiments, and perform other tasks in space.

The Space Shuttle was unique in that it could land like an airplane, allowing it to be reused multiple times. After completing a mission, the orbiter would re-enter Earth's atmosphere and glide to a landing on a runway.

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Complete question is: The space shuttle discovery traveled 148.2 million miles during its mission. The space shuttle Atlantis traveled 125.9 million miles. the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

One of the solutions for the given graph is (-5,-4).

What is a graph and how to plot the values?

In the given graph, a straight line intersects the parabola at two points i.e., (-5, -4) and (2, 0).

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The fractions equivalent to 2/5 are 4/10, 6/15, 8/20. The correct option is B.

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

Hence, the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

The fractions equivalent to 2/5 are 4/10, 6/15, 8/20,.

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Which of the lists below includes all of the above expressions that are equivalent to 2/5?

I, 2/6

II,  4/10

III, 6/15

IV. 10/20

V. 4 / 12

VI 8/20

A. I, III, V, VI

B. III, VI

C. II, III, VI

D. II, III, IV, VI

Answer:

To simplify the expression p/ab+2q/ac, we need to find a common denominator for the two fractions in the denominator. The common denominator is abc.

Thus,

p/ab + 2q/ac

= p*c/abc + 2q*b/abc (multiplying the first fraction by c/c and the second fraction by b/b)

= pc/abc + 2qb/abc

= (pc + 2qb) / abc

Therefore, the simplified expression is (pc + 2qb) / abc.

Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

We can start by finding the cost of cherries per pound:

2 3/5 pounds = (2 × 5 + 3) / 5 = 13/5 pounds

Cost of 13/5 pounds of cherries = $5.25

Cost of 1 pound of cherries = $5.25 ÷ (13/5) = $2

Now we can find the cost of 5.5 pounds of cherries:

Cost of 5.5 pounds of cherries = $2 × 5.5 = $11

Therefore, Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

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The probability that the student was NOT a female that got a “A” is given as follows:

p = 10/19.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that the student was NOT a female that got a “A” is obtained as follows:

p = 20/38

p = 10/19.

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Answer: 28/5

Step-by-step explanation:

each toy had a mass of 4/5 kilograms .there are 7 toys.so the total mass is

7 times 4/5=28/5 kilograms

hope it helps

A very simple explanation:

Solution;

Apperciation: 2.1%

Principal: 150,000

Time: 15 years

Now,

=((0.021×150,000)×15)+150,000

=(3,150×15)+150,000

=47250+150,000

=197,250$

Hence, the house would worth 197,250$ after 15 years

The value of x in right angle whose hypotenuse is given 74 m  one angle is 90° and other angle given is 30° to the nearest tenth is approximately 37 meters.

The branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles is known as Trigonometry. It involves studying the properties of trigonometric functions, which are mathematical functions that relate the angles of a triangle to the ratios of its sides.

In this triangle, the height is opposite the 30° angle and the hypotenuse is the longest side of the triangle. We can use the trigonometric function sine to relate the height and the hypotenuse:

sin(30°) = x / 74

To solve for x, we can multiply both sides by 74 and simplify:

x = 74 sin(30°)

x ≈ 37 (to the nearest tenth)

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