For each growth rate, find the associated growth factor.
1. 30% increase
2. 30% decrease
3. 2% increase
4. 2% decrease
5. 0.04% increase
6. 0.04% decrease
7. 100% increase

Solution:Given, the mean speed of the cars racing = 158.9 mph standard deviation = 6.7 mph

To find:What speed represents the 30th percentile for speeds of race cars at Talladega?

We need to find the z-score for the 30th percentile.From the standard normal distribution table, the z-score for the 30th percentile is -0.52.Using the formula for z-score we havez=(x-μ)/σwhere x is the speed of the carsμ is the mean speed = 158.9σ is the standard deviation = 6.7Substituting these values in the above equation we have-0.52=(x-158.9)/6.7Rearranging we get,x - 158.9 =[tex]-0.52 × 6.7x - 158.9 = -3.524x = 158.9 - 3.524x = 155.376[/tex]The speed that represents the 30th percentile for speeds of race cars at Talladega is approximately 155.38 mph.

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The probability of a printer failure given hardware problems is 0.9, given software problems are 0.2, and given any other type of problem is 0.5. The customer should diagnose the printer failure by looking for a hardware issue.

The probability of printer failure is dependent on three problem types, hardware, software, and others (like connectors). The respective probabilities are 0.1_, 0.6, and 0.3_.

We have hardware problems, the probability of printer failure is 0.9, given software problems the probability is 0.2, and given any other problem type the probability is 0.5. By using Bayes' theorem, the most probable cause of the failure can be determined.

Let A represent the cause of the problem, and B is the evidence that the customer sees. Let's calculate the probability that A = hardware given B, which is P(A|B) = P(B|A)*P(A)/P(B).

Here, P(A) is the prior probability of the cause being hardware,

P(B|A) is the likelihood of observing the evidence given the cause being hardware, and P(B) is the probability of observing the evidence.

Given hardware problems, the probability of printer failure is 0.9, while the probability of observing this evidence given hardware problems is 0.9. Since there are three problem types, each of them having a prior probability of 1/3, we get P(A) = 1/3.

The probabilities of observing the evidence in the case of other types of problems and software problems are 0.5 and 0.2, respectively. Therefore, the most likely cause of printer failure is hardware problems.

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Answer: 31 pizzas

Step-by-step explanation:

add them together

The mean, variance, and standard deviation for those who have purchased online goods or services are 72, 46.08, and 6.8, respectively.

That 36% of adult internet users have purchased products or services online and for a random sample of 200 adult internet users, we need to find the mean, variance, and standard deviation for the number who have purchased goods or services online.

Therefore, the mean, variance, and standard deviation for the number who have purchased goods or services online are 72, 46.08, and 6.8, respectively.

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Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

The domain of discourse of the propositional function P(x) is {1,2,3,4}, by using negation, disjunction, and conjunction are:

a)  "there does not exist an x in the domain for which P(x) is false."

b) "there exists an x in the domain for which P(x) is false."

c)  "there exist exactly three x's in the domain for which P(x) is true."

d) -(E. P(x)) can be rewritten as “Every x is not P(x)”

We are given that the domain of discourse of the propositional function P(x) is {1, 2, 3, 4}. We need to rewrite each propositional function below using only negation, disjunction, and conjunction.

a) The propositional function "Vx P(x)" means "for all x in the domain, P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

-(Ex -P(x)), which means "there does not exist an x in the domain for which P(x) is false."

b) The negation of "Vx P(x)" is "there exists an x in the domain for which P(x) is false." Using De Morgan's law again, we can rewrite this as:

Ex -P(x).

c) The propositional function "3x P(x)" means "there exist exactly three x's in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can break it down into two statements:

Using the symbols for negation, disjunction, and conjunction, we can write this as:

(Ex_1 P(x_1) ∧ Ex_2 P(x_2) ∧ Ex_3 P(x_3)) ∧ -(Ex P(x)).

d) The propositional function "-(E. P(x))" means "it is not true that there exists an x in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

Ax -P(x),

which means "for all x in the domain, P(x) is false."

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Answer: 11

Step-by-step explanation:

Turn it into an improper fraction so 8 from 8 1/4 to 33/4

Then just divide by 3/4

This will give you 11

Answer: 201.06

Step-by-step explanation:

A=πr2=π·8^2≈201.06193

The solution for the other variable, according to the stated statement, is[tex]X = 6^y[/tex] and [tex]y = 21 * 2^X[/tex]

Exponential numbers are represented by an, where an is multiplied by itself n times. An easy example is 8=2³=222. In exponential notation, an is known as the base, whereas n is known as the power, exponent, or index. Scientific notation is an example of an exponential number, with 10 usually typically serving as the base number.

Exponential functions are often employed in the biological sciences to describe the amount of a certain quantity over time, such as population size. Experiment data graphs are often created with time on the x-axis and amount on the y-axis.

a. y = log6(X)

[tex]6^y = X[/tex]

[tex]X = 6^y[/tex]

b. [tex]X = log2(y/21)[/tex]

[tex]2^X = y/21[/tex]

[tex]21 * 2^X = y[/tex]

[tex]y = 21 * 2^X[/tex]

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A fast food restaurant estimate that 45% of their customers buy drinks with their purchases. Last week, 6200 customers did not buy soft drinks. They have a total of 11272 customers.

when in a percentage we take 100%

if 45% take soft drinks with their purchases

then the other 55% did not take soft drinks with their purchases

therefore, we have 6200 customers who did not buy soft drinks with their purchases.

now we know that 11272 are there total customers

therefore, now we have to subtract 6200 from 11272

we get 5072.

therefore 5072 customers who buy soft drinks with their purchases.

A fast food restaurant estimate that 45% of their customers buy drinks with their purchases. Last week, 6200 customers did not buy soft drinks. They have a total of 11272 customers

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Answer:

-15

Step-by-step explanation:

4.1.60 - (15) + (-13) = 32

4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

A sampling distribution is normal only if the population is normal. This  statement is false because A sampling distribution is normal only if n≥30.

If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values ​​above 30, but after a certain threshold the x(bar) distribution is effectively "normal".

Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.

In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.

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As a result, Lara made a $6,262.71 initial deposit into her savings account.

A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.

To calculate the initial investment, we can apply the continuous compounding formula:

A = Pe(rt)

Where:

A = the current balance ($7,000.00)

P = the initial deposit (unknown)

r = the annual interest rate (11% or 0.11 as a decimal)

t = the time in years (1 year)

Plugging in these values, we get:

$7,000.00 = Pe(0.11 * 1)

A shorter version of the exponential expression:

$7,000.00 = Pe0.11

$7,000.00 = P * 1.1166 (rounded to 4 decimal places)

Dividing both sides by 1.1166:

P = $6,262.71 (rounded to the nearest cent)

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In the equation A’ = 364V relating the surface area A and the volume V of a spherical balloon. We are also given that the volume is increasing at a rate of 18 cubic inches per second.so the rate at which the surface area of the balloon is increasing is 6552 square inches per second

We want to find the rate at which the surface area is increasing when A = 153.24 square inches and V = 178.37 cubic inches.

To find the rate of change of A with respect to time, we can use the chain rule of differentiation:

dA/dt = dA/dV × dV/dt

We know that dV/dt = 18 cubic inches per second, so we just need to find dA/dV and then we can find dA/dt.

To find dA/dV, we differentiate the equation A’ = 364V with respect to volume V:

dA/dV = 364

Now we can find dA/dt:

dA/dt = dA/dV × dV/dt ⇒ 364 × 18 ⇒ 6552 square inches per second

So the rate at which the surface area of the balloon is increasing is 6552 square inches per second when A = 153.24 square inches and V = 178.37 cubic inches.

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The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.

Firstly convert the mixed fraction to fraction.

Length of neck of giraffe = (4×2)+1/2

Length of neck = 9/2 feet

Now, let us assume the height of giraffe be x. So, equation will be -

30% × x = 9/2

Rewriting the equation

30/100 × x = 9/2

Cancelling zero

3x/10 = 9/2

Again rewriting the equation

x = 90/6

Performing division on Right Hand Side of the equation

x = 15 feet

Thus, height of giraffe is 15 feet.

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Given: ,8^2x= 32^x+3

a: (2³)^2x = (2⁵)^x+3

b: Solving, we get

2^6x = 2^5x+15

Since bases are same, we have

=>6x=5x+15

=> x = 15

Answer:

We need to prove that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

Let's consider an isosceles triangle ABC where AB = AC. We draw the altitude from A to BC and call the point where it intersects BC as D.

Now, we need to prove that AD is the angle bisector, median, and altitude to the base BC.

To prove AD is the angle bisector:

We need to prove that the angle ADB and ADC are equal. We know that angle ABD and angle ACD are right angles because BD and CD are altitudes. We also know that AB = AC because the triangle is isosceles. Therefore, the triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion.

Thus, angle ADB = angle ADC, which means that AD is the angle bisector of angle BAC.

To prove AD is the median:

We need to prove that BD = CD. Since AB = AC and AD is perpendicular to BC, triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion. Therefore, BD = CD, which means that AD is also the median to the base.

To prove AD is the altitude:

We need to prove that angle BAD and angle CAD are right angles. This is true because AD is perpendicular to BC, and BD and CD are also perpendicular to BC. Therefore, AD is also the altitude to the base BC.

Hence, we have proved that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

The followings A, C, D, and F subsets of P₂ are subspace of P₂.

The subsets of P₂ that are subspace of P₂ are A, C, D, and F.

A.{p(t) | p'(t)+1p(t)+6=0} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

B.{p(t) | p('t)='p(t) for all t} is not a subspace of P₂ because the derivative of p(0) does not equal p(4).

C. {p(t) | p(4)=7} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

[tex]{p(t) | \int_{-1}^{7}p(t)dt=0[/tex] is constant } is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

E. {p(t) | '(8) = p(0)} is not a subspace of P₂ because the derivative of p(8) does not equal 0.

F. {p(t) | p(3)=0} for all t} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

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The product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

WHAT IS BOX METHOD ?

The box method, also known as the grid method, is a visual method used to multiply two numbers or two binomials. It involves creating a grid or box and filling it in with the products of the digits in each row and column. The method works for both single-digit and multi-digit numbers.

To use the box method for multiplying two numbers, we draw a box with two rows and two columns. We write one number along the top row and the other number along the left column. Then, we multiply the digits in each row and column and write the products in the corresponding cell of the box. Finally, we add the numbers in each cell of the box to get the product of the two numbers.

The box method can be used to multiply two binomials, such as (4x + 7) and (3x - 8). To use the box method, we draw a box with four cells, and we write the two binomials along the top and left sides of the box, like this:

     |  4x  |  7

-------------------

 3x  |      |

-------------------

    |      |

Then, we fill in the four cells of the box by multiplying the corresponding terms. For example, the top-left cell is filled by multiplying 4x and 3x, which gives 12x². The other cells are filled in a similar way:

     |  4x  |  7

-------------------

 3x  | 12x² | 28x

-------------------

    | -21x | -56

Next, we combine the terms in each row and column of the box, and write the final answer as the sum of these terms:

12x² + 28x - 21x - 56

Simplifying this expression gives:

12x² + 7x - 56

Therefore, the product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

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To form a parallelogram, the opposite sides of the quadrilateral should be parallel. Let's find the coordinates of point D such that AB is parallel to DC.

The slope of line AB = (yB - yA) / (xB - xA) = (6 - 1) / (-2 - 3) = -1

Therefore, the slope of line DC should also be -1.

Let's assume the x-coordinate of point D is xD.

The slope of line CD = (yD - yC) / (xD - xC)

Since the slope of CD is -1, we can write:

(yD - yC) / (xD - xC) = -1

yD - yC = -(xD - xC)

yD = -(xD - xC) + yC

Substituting the coordinates of points C and A, we get:

yD = -(xD - 6) + 4

yD = -xD + 10

Therefore, the coordinates of point D are (xD, -xD + 10).

To find the x-coordinate of point D, we can use the fact that BC is parallel to AD.

The slope of line BC = (yC - yB) / (xC - xB) = (4 - 6) / (6 + 2) = -1/4

Therefore, the slope of line AD should also be -1/4.

The slope of line AD = (yD - yA) / (xD - xA)

Substituting the coordinates of points A and D, we get:

(yD - 1) / (xD - 3) = -1/4

yD - 1 = -(xD - 3) / 4

yD = -(xD - 3) / 4 + 1

yD = -xD/4 + 5/4

Substituting the equation we found for yD in terms of xD, we get:

-xD/4 + 5/4 = -xD + 10

3/4 xD = 35/4

xD = 35/3

Therefore, the coordinates of point D are (35/3, -35/3 + 10) = (35/3, 5/3).

We can now plot the points A, B, C, and D on the coordinate axes, and verify that they form a parallelogram.

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Answer:

1

----

20

Step-by-step explanation: Total there are 20 Combinations as 5*4 = 20 ab>0 when b

Answer:

36 × 10^6 m²

Step-by-step explanation:

Given the side length of a square = 6 × 10³m,

To solve for the area of a square, use the following formula:

A = S² where:

S = side of the square

Substitute the given value for the side into the formula:

A = S²

A = (6 × 10³)²

A = 36000000 or 36 × 10^6 m²

NOTE:

6 × 10³ is also the same as 6 × 1000 = 6000,

(6 × 10³)² is essentially 6,000² = 36,000,000

Therefore, its area in square meters is 36 × 10^6

Answer: Let's start by using algebra to represent the given information.

If we let "a" be Anita's current age, then we know that Sarun's current age is 3a (since he is thrice as old as Anita).

According to the problem, if we subtract 5 years from Anita's age and add 7 years to Sarun's age, then Sarun will be 5 times Anita's age. In other words, we have the equation:

3a + 7 = 5(a - 5)

Simplifying and solving for a, we get:

3a + 7 = 5a - 25

32 = 2a

a = 16

So Anita is currently 16 years old, and Sarun is 3 times as old, or 48 years old.

To find out how old they were three years ago, we simply subtract 3 from their current ages:

Anita was 13 years old three years ago (16 - 3), and Sarun was 45 years old (48 - 3).

Step-by-step explanation:

Answer:<x=105

Step-by-step explanation:

180-75=105

Answer:

Step-by-step explanation:

We can set up a proportion to solve this problem:

(height of boy) / (length of boy's shadow) = (height of man) / (length of man's shadow)

We are given that the boy is 3 feet tall and his shadow is 7 feet long. Let's use "h" to represent the height of the man. We are also given that the man's shadow is 14 feet long. Substituting these values into the proportion, we get:

3/7 = h/14

To solve for h, we can cross-multiply and simplify:

3 × 14 = 7h

42 = 7h

h = 42/7

h = 6

Therefore, the man is 6 feet tall.

The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.

Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]

Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]

To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.

Probability of getting [tex]3[/tex]:

Outcome = [tex]3[/tex]

Probability of getting = [tex]^3P(3) = 0.3[/tex]

So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].

Probability of getting [tex]5[/tex]

So, the outcome of [tex]5[/tex]

Probability of getting [tex]^5P(5) = 0.2[/tex]

So, the possible probability of getting 5 is 0.2.

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In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.

The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:

Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977

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From the given information provided, the area of the shaded region inside the circle is 22.58

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.

The space enclosed by the sector of a circle is called the area of the sector.

the radius of the circle is 5cm.

area of arc =  radius² × θ/2

area of the arc is =  5² × 4π/9 = 25 × 4/9 = 34.88

area of the triangle inside circle = a×b × sin(y)/2

area of triangle = 5×5 × sin(80°)/2 = 25 × 0.492

area = 12.3

area of the shaded region is = 34.88 - 12.3 = 22.58

Hence, the area of the shaded region is 22.58

Question - Find the area of the shaded region in the circle if the angle of the arc is 80 degree radius is 5cm.

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