1. Find f(-2) if : *
f (x) = 4 |x – 4| + 2
-20
28
32
26 ​

Answer:

2

4

6

8

10

12

Step-by-step explanation:

all together it equals 42

The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

For the team with the homecourt advantage, let \(Wi\) and \(Li\) denote whether the game '\(i\)' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P [H] = P [\(W1W2\)] + P [\(W1L2W3\)] + P [\(L1W2W3\)]

        = \(p(1-p)\) + \(p3\) + \(p(1-p){2}\)

Note that P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

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For the team with the homecourt advantage, let  and  denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

Answer:

5301

Step-by-step explanation:

There are 9 companies that needed to print 589 coupons each. Multiply the two numbers:

9 * 589 = 5301

Answer:

360-137+x+y

Step-by-step explanation:

Answer:

The answer is 6

Step-by-step explanation:

it can be written as 9/X = x/4

when you cross multiply, it gives you xsquare = 36

Therefore, X is 6

Answer:

The mean absolute deviation of the data set is 2.5

Step-by-step explanation:

We need to find mean absolute deviation of the data set:

10,8,10,6,6,2,10,4

First we will find mean of the given data set.

The formula used is: \(Mean=\frac{Sum\:of\:all\:data}{Number\:of\:data}\)

Sum of all data = 10+8+10+6+6+2+10+4 = 56

Number of data = 8

So, mean will be:

\(Mean=\frac{Sum\:of\:all\:data}{Number\:of\:data}\\Mean=\frac{56}{8}\\Mean=7\)

Now, we will calculate the absolute difference between mean and each data value.

|10-7| = 3

|8-7| = 1

|10-7| = 3

|6-7| = |-1| = 1

|6-7| = |-1| = 1

|2-7| = |-5| = 5

|10-7| = 3

|4-7| = |-3| = 3

Now, we will find mean of 3,1,3,1,1,5,3,3

Sum of all data = 3+1+3+1+1+5+3+3 = 20

Number of data = 8

So, mean will be:

\(Mean=\frac{Sum\:of\:all\:data}{Number\:of\:data}\\Mean=\frac{20}{8}\\Mean=2.5\)

So, the mean absolute deviation of the data set is 2.5

Therefore, the general solution of the given second-order differential equation is y = c1 e^(-x/4) + c2, where c1 and c2 are constants.

To find the general solution of the given second-order differential equation 4y'' + y' = 0, we can use the method of separation of variables.

Let us assume that the solution to the equation is of the form y = e^(rx), where r is a constant.

Differentiating with respect to x, we get y' = re^(rx) and y'' = r^2e^(rx).

Substituting these expressions into the given differential equation, we get:

4y'' + y' = 4(r^2e^(rx)) + (re^(rx)) = 0

Simplifying and factoring out e^(rx), we get:

e^(rx)(4r^2 + r) = 0

This equation holds for all values of x if and only if the coefficient of e^(rx) is zero. Therefore, we get:

4r^2 + r = 0

Solving for r using the quadratic formula, we get:

r = (-b ± sqrt(b^2 - 4ac))/(2a)

where a = 4, b = 1, and c = 0. Substituting these values, we get:

r = (-1 ± sqrt(1^2 - 4(4)(0)))/(2(4)) = (-1 ± sqrt(1))/8

Therefore, the two solutions to the differential equation are:

y1 = e^(-x/4)

y2 = Ce^0 = C

where C is a constant of integration

The general solution to the differential equation is then given by the linear combination of these two solutions:

y = c1 e^(-x/4) + c2

where c1 and c2 are constants of integration that depend on the initial conditions of the problem.

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Answer:: the equation is 7m + 19

Step-by-step explanation:

The factored form of 4x^2 + 9 = (2x)^2 - (3i)^2 = (2x + 3i) (2x - 3i).

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = -1 and both a and b are real values.

Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely genuine, the other entirely fantastical.

Given that the expression is 4x^2 + 9.

We know that x^2 is greater than equal to 0 for all the real values of x, that is 4x^2 + 9 will be greater than equal to 9 for all real values of x.

However, for 4x^2 + 9 there are no linear factors with real coefficients, It contains complex coefficients.

Consider the identity:

a^2 - b^2 = (a - b) (a + b)

In conjunction i^2 = -1 thus:

4x^2 + 9 = (2x)^2 - (3i)^2 = (2x + 3i) (2x - 3i)

Hence, the factored form of 4x^2 + 9 = (2x)^2 - (3i)^2 = (2x + 3i) (2x - 3i).

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In this question, we are given that common blood types are determined genetically by the three alleles A, B, and O. A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous.

The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is modeled by P(p,q,r)=2pq+2pr+2qr where p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population and p+q+r=1 (the sum of the three must equal 100%).We are to use the fact that p+q+r=1 to show that the maximum proportion of heterozygous individuals in any population is 2/3.In the given expression:$$P(p, q, r) = 2pq + 2pr + 2qr$$We know that p + q + r = 1The number of alleles per person is 2 since we have a diploid genome (one set of chromosomes from each parent).So, the total of all the individual allele frequencies must be 2.

We have:p + q + r = 1A person with two alleles (homozygous) has a frequency of:p² or q² or r²Similarly, a person with one allele of each type (heterozygous) has a frequency of:2pq or 2pr or 2rqTo show that the maximum proportion of heterozygous individuals in any population is 2/3, we will use the AM-GM inequality which states that the arithmetic mean is greater than or equal to the geometric mean.\($$ AM \geq GM $$\)The AM-GM inequality can be rewritten as:\($$ \frac{a+b}{2} \geq \sqrt{ab} $$\)where a and b are any two positive numbers.

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Answer:

C. 3

Step-by-step explanation:

One of the (many) properties of definite integrals is
\(\mbox{\large \int\limits _{a}^{b}f(x)\,dx + \int\limits _{b}^{c}f(x)\,dx = \int\limits }_{a}^{c}f(x)\,dx\)

Therefore
\(\mbox{\large \int\limits _{-2}^{5}f(x)\,dx + \int\limits _{5}^{2}f(x)\,dx = \int\limits }_{-2}^{2}f(x)\,dx\)

Given

\(\mbox{\large \int\limits _{-2}^{5}f(x)\,dx = 11}}}\para\)

and

\(\mbox{\large \int\limits _{-2}^{2}f(x)\,dx = 14}}\)

We get

\(\mbox{\large 11+ \int\limits _{5}^{2}f(x)\,dx} = 14\)

Subtracting 11 from both sides we get

\(\mbox{\large \int\limits _{5}^{2}f(x)\,dx} = 14 - 11 = 3\\\)

Answer: Choice C which is 3

Answer:

Step-by-step explanation:

d/t=mph

Billy's friend's house is 20 miles away from him.

What is Speed?

The ratio of the distance travelled by an object to the time required to travel that distance.

Given that when Billy moves with his normal speed, it takes 40 min for him to reach his friend's house and if he slows his speed to 20 mph he takes 2 hours to reach the same distance.

We know, Speed = Distance/time

Let x be Billy's normal speed,

Therefore, 2x/3  = 2 (x - 20)

2x/3 = 2x - 40

x = 3x - 60

x = 30

Therefore, Billy's normal speed is 30 mph

Distance covered by him = 2 (30 - 20) = 20 mi

Hence, Billy's friend's house is 20 mi far.

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We can prove that S(n+1,k)=S(n,k−1)+kS(n,k).

To prove that S(n+1,k)=S(n,k−1)+kS(n,k), we will use combinatorial argument.

Consider the set {1,2,...,n+1}. We want to partition this set into k unlabelled nonempty parts. There are two cases to consider:

Case 1: The element n+1 belongs to a part of size 1.

In this case, we have n elements to partition into k-1 parts. The number of ways to do this is S(n,k-1) since we are partitioning n elements into k-1 parts.

Case 2: The element n+1 belongs to a part of size m>1.

In this case, we have n elements to partition into k parts, with one part having size m-1. There are k ways to choose the part of size m-1, and m-1 ways to choose the element of that part that will be n+1. The remaining n-m+1 elements are partitioned into k-1 parts. The number of ways to do this is k(m-1)S(n-m+1,k-1).

Therefore, the total number of partitions of {1,2,...,n+1} into k unlabelled nonempty parts is S(n,k-1)+kS(n,k), which proves the desired formula S(n+1,k)=S(n,k−1)+kS(n,k).

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The length of side AB rounded to 3 significant figures is 8.86 cm.

The figure on the image is a right triangle.

From the image;

using the trigonometric ratio, we determine the length of side AB.

Sine = Opposite / Hypotenuse

sin( 41 ) = AB / 13.5

AB = sin( 41 ) × 13.5

AB = 8.86 cm

Therefore, the side AB has a length of 8.86 cm.

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Answer:

C is the Answer

Follow me please

Mark brainliest

Answer:

Since PQRS is a rectangle and the area of PQRS is 84 cm², then:

PQ x PS = 84

Since PQRS is a rectangle, PS = QR, so we can substitute PS for QR:

PQ x QR = 84

We also know that XY is parallel to PS, so triangle RXY is similar to triangle RQS:

RY/QS = XY/PS

9/QS = XY/PS

QS = 9XY/PS

The area of PXYS is 21 cm², so:

XY x PS = 21

Substitute QS for 9XY/PS:

XY x (9XY/QS) = 21

Simplify:

9XY²/QS = 21

XY² = 21QS/9

Substitute QS for PQ, since PQ = QS:

XY² = 21PQ/9

Substitute 84/PQ for PQ in the above equation:

XY² = 21(84/PQ)/9

XY² = 196/PQ

Now we can substitute PQ for 84/XY in the equation PQ x QR = 84:

(84/XY) x QR = 84

QR = XY

Substitute QR for PS in the equation XY x PS = 21:

XY² = 21/XY

Multiply both sides by XY:

XY³ = 21

XY = ∛21

Since RY = 9 cm, we can find QS:

9/QS = ∛21/PS

QS = 9PS/∛21

Now we can substitute QS and XY into the equation XY x PS = 21 and solve for PS:

(∛21) x PS = 21/((9/∛21))

PS = (21/((9/∛21)))/∛21

PS = 7∛21

Finally, we can solve for a and b:

a = PQ - XY = (84/PQ) - (∛21)

Substitute PQ for 84/XY:

a = (XY²/84) - ∛21

Substitute XY for ∛21:

a = (∛21²/84) - ∛21

a = 1/4 - ∛21

b = RY - QS = 9 - (9PS/∛21)

Substitute PS for 7∛21:

b = 9 - (9(7∛21)/∛21)

b = -54/∛21 + 9∛21

Step-by-step explanation:

Answer:

alternate interior angles

Step-by-step explanation:

We are looking at angles <3 and <6

which are on opposite sides of a transversal (line crossing through 2 parallel lines)

meaning that those 2 angles are congruent and are alternate interior angles are they are on the inside of this figure.

*Can we see the answer choices?  I'm not sure what they are, meaning I cannot fully help you*

Hope this helps a little! :)

Answer:

1757.50

Step-by-step explanation:

First determine the amount of the discount

1850 * 5%

1850 * .05

92.50

Subtract this from the price

1850-92.50

1757.50

Answer:

$1757.5

Step-by-step explanation:

The way I like to do problems like this is by taking the  % and putting it into this formula 100- x =

Then move it down to 2 decimal places and multiply it by the original cost. Then you have your answer.

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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Answer:

y=10x

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

y−y1=m(x−x1)  to find the line parallel to y=10x−45

.

Step-by-step explanation:

Putting values of x and y.

5(6) / 3(-4) + 6

30 / - 12 + 6

10 / - 4 + 6

5 / - 2 + 6

= 3.5

9514 1404 393

Answer:

  True

Step-by-step explanation:

We assume your equation is intended to be ...

  \(\sqrt{x+56} =x\)

The usual method of solution squares both sides, then solves the resulting quadratic.

  \(x+56=x^2\\\\x^2-x-56=0\\\\(x-8)(x+7)=0\longrightarrow x=\{-7,+8\}\)

Considering the initial problem, we require x ≥ 0, so the x=-7 solution is extraneous.

__

A graphical solution shows there is only one value of x that satisfies the equation. The other "solution" arises from considering the negative square root. It is introduced when the equation is squared.

Answer: Given that a, b, and c form an arithmetic sequence, so they are equally spaced, meaning the difference between each of them is constant. Let's denote the common difference between a, b, and c as d.

So, we have:

a = b - d

c = b + d

Using these two equations, we can prove that 2^a, 2^b, and 2^c form a geometric sequence.

We have:

2^a = 2^b / 2^d

2^c = 2^b * 2^d

Since the product of two powers of the same base is equivalent to the power of the base with the sum of the exponents, we have:

2^a * 2^c = 2^b * 2^b * 2^d * 2^d = 2^(b+b+d+d) = 2^(2b+2d)

So, we have:

2^a * 2^c = 2^(2b+2d) = 2^(2b) * 2^(2d) = 2^b * 2^b * 2^d * 2^d = 2^b * 2^c

This means that 2^a, 2^b, and 2^c form a geometric sequence, with the common ratio of 2^d.

Step-by-step explanation:

Answer:

128 (character filter filler here)

Step-by-step explanation:

64+8^2 is 128

The mean of the set is : 16

The Slandered deviation of set : 5.8689389538863

Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.

Average x = 16

Count n = 9

Sum     Sum =144

Average = Sum / Count

= 144 / 9

= 16

Standard Deviation, σ: 5.8689389538863

Count, N = 9

Sum, Σx: = 144

Mean, μ:  = 16

Variance, σ²: = 34.444444444444

Calculating slandered devotion:

\(\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}\)

\(\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}\)

\(=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}\)

= 310/9

=  34.444444444444

σ =  √34.444444444444

σ =   5.8689389538863

The mean of the set is : 16

The Standard deviation of set : 5.8689389538863

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Answer:

9)  C = 6\(\pi\) units

standard form : (x + 7)² +(y + 5)² = 9²

12) C = 8√5 \(\pi\) units

standard form : (x + 3)² +(y + 2)² = ( \(\sqrt{80}\))²

Step-by-step explanation:

Examples of random variables are option A: the weight of a bag of a dozen apples, and option C: the number of dots uppermost of rolling a pair of dice.

Because they can only have a finite number of values, discrete random variables include things like the weight of a bag of twelve apples and the number of dots that appear on top of a pair of dice.

Examples of continuous random variables are the length of an airline flight and the quantity of drive-through clients at a bank on a particular day since they might have any value within a specified range.

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Correct question:

Choose the random variables from this set that are discrete. select all that apply. multiple select question.

the weight of a bag of a dozen apples.

the travel time of an airline flight.

the number of dots uppermost of rolling a pair of dice.

number of drive-thru customers to the bank on a given day.

Answer: width is 5/4 miles

Step-by-step explanation:

area = length x width

5/8=1/2 x (w)

0.625=0.5 x (w)

0.625/0.5=1.25

1.25=w

1.25=5/4 2