endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. what is the probability that an endure all battery selected at random will last more than 610 hours? a) 0.0228 b) 0.9970 c) 0.0030 d) 0.9965 e) 0.0035 f) none of the above.

We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.

Given that,

Let R be the relation defined on A as follows, and let A be the set of all statement forms in the three variables p, q, and r. S R T⇔ S and T have the same truth table for all S and T in A. substantiate the equivalence of R.

We have to demonstrate that it satisfies each of the properties you choose.

We know that,

By reflexive property,

S ≅ S  means that S has the same truth table as S.

T≅ T denotes that T and T have the same truth table.

By symmetric property,

S ≅T denotes that S and T share the same truth table.

At that time, T and S share the same truth table.

So, T ≅ S

By transitive property,

S≅T and T≅V and V≅W

S shares a truth table with S. Truth table between T and T W's truth table is the same for V and V.

S, T, V, and W all have the same truth table as a result.

S specifically has the same truth table as W.

Then S≅T≅V≅W ---> S≅W

Therefore, We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.

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The following ratio is the simplest form of 32 min: 36 min is 8: 9. The correct option is a.

If two quantities of a ratio (i.e., antecedent and consequent) have no common factor (i.e., antecedent and consequent are co-prime), the ratio is said to be in its simplest form or in the lowest term.

The simplest form of the fraction is also known as the reduced form of a fraction. For instance, 34 is the simplest form of a fraction with a common component of one.

32/36 = 8:9. It is divided by 2.

Therefore, the correct option is a. 8:9.

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Answer:

The answer is D

Step-by-step explanation:

I hope it helps!

a)The 7-year growth factor for the amount on the loan is $4285.71.

b)  7-year percentage change for the amount is 6.25%.

c) 1-year growth factor for the amount $612.244.

d) 1-year percent change for the amount is 0.894%.

a)We know very well that growth factor is ratio of difference of principal amount and loan amount to the time taken, or

Growth factor=(Final loan amount-Initial loan amount)/Total time

=>Growth factor=(78,000-48,000)/7

=>Growth factor=30,000/7=$4285.71

b)To find the percentage change in amount, we need to use initial loan amount and the difference between two amounts, or

  percentage change=((78000-48000)/48000)×100

=>percentage change=[(30000)/48000)]×100

=>percentage change=300/48=6.25%

c)Now, we have already find the growth factor for 7 years, we need to find growth rate in 1 year. So, we use unitary method to find it

=>In 7 years growth factor is=$4285.71

   ∴In 1 years growth factor is=$4285.71/7=$612.244

d)In 7 years percentage change for the given amount is =6.25%

∴In 1 year percentage change for the given amount=6.25/7=0.894%

Hence, answers are a)$4285.71 b)6.25% c)$612.244 d)0.894%

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Probabilities of Q are 1,4, 16, 64 are 312 2 8181818 , E(Q)=20.88 and 12.5% information revealed. Wheel is spin twice 0.2815.

When we are not sure about the outcome we can make possible probabilities about the situation. Therefore, it is the maximum and possible chances of something to be happen.

Step 1

Angle of one complete spin = 360°

Q=16=90° Q=6490"

Q=4-450

Q=1=135°

Here

P(Q16) = P(Q= 64)

=90/36

=1/4

Step 2

Expected value E(Q) = xP(x) E(Q) = 1x+4x+16x+64 x2/8

Step 3

c)

We learn Q=4

P(Q=4)=1/8=0.125

12.5 %  information is revealed.

Please refer to solution in this step.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=8\pi \\ r=2 \end{cases}\implies 8\pi =\cfrac{\pi (2)^2 h}{3}\implies 8\pi =\cfrac{4h\pi }{3} \\\\\\ 24\pi =4h\pi \implies \cfrac{24\pi }{4\pi }=h\implies 6=h[/tex]

1. The amount that the employee make in 5 months will be $7500.

2. The number of months that the gym employee have made $19,500 is 13 months.

3. The equation to represent the constant of proportionality is C = 1500m

The constant of proportionality simply shows the ratio of two proportional values that possess a constant value.

Since after working for 3 months, he had earned $4,500. The amount per month will be:

= $4500 / 3

= $1500

The amount in 5 months will be:

= $1500 × 5

= $7500

The number of months that the gym employee have made $19,500 will be:

= $19500 / $1500

= 13 months.

The equation to represent the constant of proportionality is c = 1500m. In this case, c = total amount earned and m = number of months.

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Answer: 20 nickels and 6 quarters.

Step-by-step explanation:

           Let q be equal to quarters and n be equal to nickels. We will write a system of equations to help us solve.

      First, we know each quarter is $0.25 and each nickel is $0.05.

0.25q + 0.05n = 2.5

      Next, we know there are 14 more nickels than quarters.

n = q + 14

      We will plug the second equation into the first and solve.

0.25q + 0.05n = 2.5

0.25q + 0.05(q + 14) = 2.5

0.25q + 0.05q + 0.7 = 2.5

0.3q = 1.8

q = 6

      Joan has 6 quarters. We know he has 14 more nickels than quarters, so we will use addition.

6 + 14 = 20 nickels

Set S should contain 137 number of integers so that at least 35 integers in S have same remainder when divided by 4.

According to the pigeonhole principle in mathematics, at least one container must hold more than one item if n things are placed into m containers, where n > m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

Given: Set S = {}, least number of integers having same remainder when divided by 4=35

As we know, any number when divided by 4 has following remainder = 0, 1, 2, 3.

Least number of integers having same remainder when divided by 4 = 35.

∴ Number of integers in set S = 35×4

                                                =  140

but 3 is to be subtracted from 140 as it is the last different remainder after which the remainders repeat in manner 0, 1, 2 & 3.

∴ Total number of integers in set S = 140-3  

                                            = 137                                                

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The approximate probability that the sample mean is within 48 and 51 is 0.82.

n = sample size = 81

σ = standard deviation = 9

μ = population mean = 50

Probability is a chance of something event can occur, for this case the probability measure of the chance of sample mean is between 48 and 51 can occur. So, the probability of the sample mean is between 48 and 51 is,

P(48 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])

= P([tex]\frac{48-50}{\frac{9}{\sqrt{81}}}[/tex]≤ z ≤ [tex]\frac{51-50}{\frac{9}{\sqrt{81}}}[/tex])

= P(-2 ≤ z ≤ 1)

= P(z ≤ 1) - P(z ≤ -2)

using z table and we get,

= 0.8413 - 0.0228

= 0.8185

= 0.82

Thus, the probability is 0.82 for the sample mean is within 48 and 51.

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Answer:

3 cupcakes per person

Step-by-step explanation:

first we need to find the total number of cupcakes so in order to do that we need to multiply the number of mixes and the number of cupcakes each mix would make so:

total number of cupcakes = 6 * 12 = 72

now we can divide it by the total number of people who attended the party  so:

72/24 = 3 cupcakes per person

Exercise needs to be consistent and done at regular times. The body can adjust more effectively and swiftly when there is consistency. Exercise should ideally be performed 3-5 times per week.

Exercise is any physical activity done to increase one's physical or mental fitness.

Exercise and physical activity not only aid to enhance physical health but also help to promote mental health.

A healthy mind follows from a healthy body.

By lowering body weight, frequent physical activity lowers the risk of developing serious conditions like heart attack, cardiovascular disease, diabetes, and high blood pressure. Regular exercise revitalizes the body and the mind.

Additionally, it raises energy levels, mood, and sleep quality.

Hence, Exercise must be performed consistently and at regular intervals. When there is consistency, the body can adjust more quickly and efficiently. The ideal number of times to exercise per week is three to five.

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If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg according to given standard deviation.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = x- υ/σ

Given that μ = 55, σ = 6;

For x = 49:

z = 49 - 55/6

z = -1

If the dog has a z-score of -1.09, his weight is:

-1.09 = x -55/6

x - 55 = -6.54

x = 48.46

If the dog has a z-score of 1.09, his weight is:

1.09 = x - 55/6

x -55 = 6.54

x = 61.54

Hence ,If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg

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The solution to the system of equation (x, y) is -3/4 and -7/2

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

The equations given are

y = -2x - 5 ...eq(i)

y = 2x - 2 ..eq(ii)

Solving this equation,

x = -3/4, y = -7/2

Using a graph to solve this problem, the point of intersection (x, y) is the solution to the equation.

Kindly find attached graph below

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The number of people who preferred alaber juice is 9 people

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether

Those who preferred alaber juice will be:

= 75% × 12

= 0.75 × 12

= 9

The number of people is 9.

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Check the picture below.

Answer:

f (5) = 4

Step-by-step explanation:

First we need to find f(x)

To do this we can find the gradient of the line then plug it into the formula for an equation of a line.

using the points on the line, (3,0) (0,-6)

gradient, m :

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

[tex] \frac{0 - ( - 6)}{3 - 0} = \frac{6}{3} = 2[/tex]

therefore the gradient was found to be 2.

Equation of a line:

y - y1 = m( x - x1)

y - 0 = 2( x - 3)

y = 2x - 6

Therefore the function of the line was found to be:

f(x) = 2x -6

so to find f(5) we substitute 5 in the place of x:

f(5) = 2(5) - 6

f(5) = 10 - 6

f(5) = 4

The equation that Hugo can use to find the number of days d he can feed Pickles from the bag is 4d = 24.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this situation, Hugo is going on vacation and taking his dog Pickles along. Pickles eats 4 cups of Hungry Hound dog food each day. Hugo wants to know how many days he can feed Pickles from a 24-cup bag of Hungry Hound.

Therefore, the equation to illustrate this will be:

(4 × d) = 24

4d = 24

d = number of days

d = 24/4

d = 6

The number of days is 6.

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Answer:8,800

Step-by-step explanation:

1760 times 5 = 8,800

Answer:

= –179/9

or –19 ^8/9

Step-by-step explanation:

–19²/9 –4¹/9 –(–3⁴/9)

–(173/9) –37/9 + 31/9

=L.c.m = 9

–173–37+31/9

= –210+31/9

= –179/9

or –19 ^8/9

i hope i was able to helped

Integer polynomials p and q fulfill that for an unlimited number of inputs of integers x, p (x)/q (x) is an integer. q (x) does not necessarily divide p. (x)

Sums of terms of the form k^xn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.This section covers the ideas of degree, standard form, monomial, binomial, and trinomial.

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By using the concept of growth, it can be calculated that

Number of turkeys after 10 years  = 57

It took 10 years for the number of turkeys to double

What is growth?

Growth is the increase in the value of an asset or cost or population at a certain rate over a certain period of time.

Original number of turkeys = 45

Rate of growth = 2.3 %

Time  = 10 years

Number of turkeys after 10 years = [tex]45 \times (1 + \frac{2.3}{100})^{10}[/tex]

                                                       = 57

Now,

New number of turkeys = 45 [tex]\times[/tex]2 = 90

[tex]90 = 45 \times (1 + \frac{2.3}{100})^n[/tex]

[tex](1 + \frac{2.3}{100})^n = \frac{90}{45}\\\\1.023^n = 2\\n\ ln (1.023) = ln( 2)\\n \times 0.023 = 0.693\\n = \frac{0.693}{0.023}\\n = 30.1 \ years[/tex]

It took 10 years for the number of turkeys to double

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Answer:

1. Polygons are flat figures formed by a closed polygonal line and its interior. Any plane figure that is made up of “straight sides” is a polygon.

2.A 100-sided polygon is called a hectogon, centagon or 100-gon. In general, any n-sided polygon with over 12 sides is called an n-gon. While there are other conventions for naming polygons with any number of sides, it is most common to use the n-gon form.

Step-by-step explanation:

A substantial interaction between age and educational status was discovered by a researcher who was creating a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) (x3)

A dummy variable, educational status has the values 0 for no college degree and 1 for a college degree.

The regression formula is y = 0 + 1x1 + 2x2 + 3x1x2 where 0 is the intercept, 1 is the age regression coefficient, 2 is the educational status regression coefficient, and 3 is the regression coefficient for the interaction between age and educational status.

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Answer:y=2x+-1

Step-by-step explanation:

y= slopex + y-intercept, the y-intercept is at the point (0,-1) as the y-intercept is when the x coordinate is 0 and the y coordinate gets touched by the y axis, therefore 2x+-1

50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.

What is confidence interval?

A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used.

Because the standard error is reduced as sample size increases, confidence intervals are narrower.

Therefore, we may state that when the population standard deviation rises, the width of the confidence interval will also rise.

Hence, 50 million people instead of 25 million people make up the population. The degree of assurance is reduced from 95% to 90%.

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The probability that the people came for the match live were born within 30 miles be, 0.197

Given, while watching a basketball game of lakers in a cafe near L.A live, we observe someone who is clearly supporting lakers in the game.

we have to find the probability that the person we observed born within 30 miles of L.A downtown.

As, the area of L.A downtown is 15.13 km².

1.6 km = 1 mile

2.56 km² = 1 miles

15.13 km² = 5.91 miles

Probability that the person was born within 30 miles be,

P = favorable area / total area

P =5.91/30

P = 0.197

Hence, the probability that the people came for the match live were born within 30 miles be, 0.197

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Answer: √6 -8√5

or 15.43905

Step-by-step explanation: