In many applications it is necessary to write expressions in the form cxn where c is a constant and n is an integer. Write the following expression in this form.
5/2x6

The answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called a function.

Given that, the function f(x) = 3x + 10 represents the number of animals adopted at one shelter, and the function g(x) = x + 5 represents the number of animals adopted at another shelter, where x is the number of months.

a) (f+g)x = f(x) + g(x)

= 3x+10 + x+5

= 4x+15

∴ (f+g)x = 4x+15

b) (f + g)(6)

Put x = 6 in (f+g)x = 4x+15

∴ (f + g)(6) = 4(6)+15

= 24+15

= 39

c) It means, the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

Hence, the answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

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Answer:

Step-by-step explanation:

Part A: (f + g)(x) = 4x + 15.

My work for Part A:

Step 1: Write the functions without the parentheses: x + 5 + 3x + 10 .

Step 2: Rewrite the function so like terms are next to each other: x + 3x + 5 + 10.

Step 3: Combine like terms: x + 3x = 4x, and 5 + 10 = 15.

Step 4: Write the final function in standard form: (f + g)(x) = 4x + 15.

Part B: (f + g)(6) = 39.

My work for Part B:

Step 1: Write the first function substituting x for 4: f(6) = 6 + 5.

Step 2: Solve the function: f(6) = 6 + 5 = 11.

Step 3: Write the final answer for the first function: f(6) = 11.

Step 4: Write the second function substituting x for 4: g(4) = 3 x 6 + 10.

Step 5: Solve the function: g(4) = 3 x 6 = 18, and 18 + 10 = 28.

Write the final answer for the second function: g(4) = 28.

Step 6: Add the output answers together: 11 + 28 = 39.

Step 7: Write the final output answer for both functions: (f + g)(4) = 39.

Part C: 39 represents the total number of animals adopted at two shelters in 6 months.

The simplest form of the ratio is given as 15 cm : 106 mm

We would have to divide the values by  a factor that is common to both the numerator and the denominator.

Hence we would have to divide through both sides of the equation by 10

150 / 10 : 1060 / 10

= 15 : 106

The ratio 150 cm: 1060 mm can be written as 15:106 in its simplest form. To simplify the ratio, both numbers are divided by the greatest common factor which is 10 in this case.

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Answer:

10

Step-by-step explanation:

find GCF for both numbers

150=2*3*5*5

1060=2*2*5*53

multiply all common ones:2*5=10

Answer:

Let y be the amount of money in the bank account after t years, where t >= 0.

The exponential function for this situation is:

y = 5000 * (1 + 0.027)^t

This function models the amount of money in the bank account after t years, given the initial deposit of $5,000 and an annual interest rate of 2.7%.

Step-by-step explanation:

In 120 different ways can the sequence of songs be played.

The art of arranging sound is called music. It is one of the defining characteristics of all human societies' cultures. Styles that highlight, de-emphasize, or exclude common components of organized sound, such as rhythm, loudness, and pitch, can be used to characterize the music.

Tempos and meters can be used to specify rhythm, and pitch variation and juxtaposition are frequently coordinated.

Individual sounds have timbres or textures that significantly affect the music's overall personality.

Music player:

A tool or program that plays digital audio files.

Solution -

To find the ways, multiply  5×4×3×2 .

⇒   20 × 3 × 2

⇒ 120

Therefore, songs can be played in 120 ways.

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All the roots of the function will be -5, 5, and -10. Then the correct option is D.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The function is given below.

f(x) = x³ + 10x² - 25x - 250

Factorize the equation, then we have

f(x) = x³ + 10x² - 25x - 250

f(x) = x²(x + 10) - 25(x + 10)

f(x) = (x² - 5²)(x + 10)

f(x) = (x + 5)(x - 5)(x + 10)

Then the roots of the function are given as,

f(x) = 0

(x + 5)(x - 5)(x + 10) = 0

x = -5, -10, 5

All the roots of the function will be -5, 5, and -10. Then the correct option is D.

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[tex]\huge\begin{array}{ccc}\left(\frac{f}{g}\right)(x)=x\sqrt{3x+3};&x\in[-1,\ \infty)\end{array}[/tex]

We have:

[tex]f(x)=\sqrt{3x+3}[/tex]

and

[tex]g(x)=\dfrac{1}{x}[/tex]

Create the domains:

[tex]D_f:\\\\3x+3\geq0\\\\3x+3-3\geq0-3\\\\3x\geq-3\\\\\dfrac{3x}{3}\geq\dfrac{-3}{3}\\\\\boxed{x\geq-1\to x\in[-1,\ \infty)}[/tex]

[tex]D_g:\\\\x\neq0\\\\\boxed{x\in\mathbb{R}-\{0\}}[/tex]

Solution:

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{\sqrt{3x+3}}{\frac{1}{x}}=\sqrt{3x+3}\cdot\dfrac{x}{1}=x\sqrt{3x+3}[/tex]

The  probability that they both take shapes 3 / 8.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that there are five shapes, Four of the shapes are squares and one of the shapes is a circle, One square is black, three squares are white, circle is black.

Jasmine takes a shape at random from the bag 150 times

3 / 5 ×150 = 90 times.

If Alec takes a shape at random from the bag and does not replace it, there are now 4 shapes left in the bag.

The probability that they both take a square is 3 / 4 × 3 / 3 = 3 / 4.

The probability that Bashir takes a square is 2 / 4 = 1 / 2.

If Alec takes a circle, the probability that Bashir takes a square is 3 / 4. The overall probability that they both take shapes

(3 / 4) × (1 / 2) + (1 / 4)× (3 / 4) = 3 / 8.

Hence, the  probability that they both take shapes 3 / 8.

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The area of a circle is [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle.

Prefix: Self - referring to one's self or own self;

Suffix: -produce - to create, make or cause something;

Word Root: Color - the sensation of light that is seen by the eye;

Prefix: Both/Double - referring to two or more;

Suffix: -single - indicating one only;

Prefix: Without/Lack of/Not - indicating the absence of something;

Word Root: Body - referring to the physical structure or anatomy of a living organism;

Word Root: Chromosomes - a thread-like structure made up of DNA found in the nucleus of cells;

Suffix: -small - indicating a size that is lesser than the average.

For example, let's say we want to calculate the area of a circle. We can use the formula [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle. We can plug in the numbers to calculate the area: [tex]A = 3.14 × 42 = 50.24 cm2[/tex]. This formula allows us to calculate the area of the circle with accuracy, and also allows us to use it for different shapes

The formula and calculation used to calculate the area of a circle is [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle.

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The variance of P + Q or  Var(P + Q) for given random variables is 14.

Since X and Y are independent N(0,1) random variables, we have Variance of X = 1 and Variance of Y = 1.

Given, P = 3X + XY

Variance of P = Variance of 3X + Variance of XY

= 9 + Variance of X * Variance of Y + 2 * Covariance(X,Y)

= 9 + 1 * 1 + 2 * Covariance(X,Y)

= 10

Given, Q = 2X

Variance of Q = Variance of 2X

= 4 * Variance of X

= 4

Variance of P + Q = Variance of P + Variance of Q

= 10 + 4

= 14

Therefore, the variance of P + Q = 14.

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Answer:

The formula for calculating the sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides.

Since an octagon has 8 sides, Shane needed to use the formula (8 - 2) * 180 to get 1080.

The only way Shane could have gotten 1440 is by inputting 10 for n since (10 - 2) * 180 = 1440.

The factors of the cubic function f(x) = 27x³ + 8 are ( 3x + 2) and ( 9x² - 6x + 4 ).

Given the function in the question;

f(x) = 27x³ + 8

To determine the factors, first rewrite 27x³ as (3x)² and 8 as 2³

27x³ + 8

(3x)² + 2³

Since both terms are perfect cubes, factor using the sum of cubes formula.

a³ + b³ = (a+b)(a² - ab + b² )

Here, a = 3x and b = 2

Plug in these values

(a+b)(a² - ab + b² )

( 3x + 2)( (3x)² - (3x)×2 + 2² )

Simplify

( 3x + 2)( (3x × 3x) - (3x)×2 + 2² )

( 3x + 2)( 9x² - 6x + 4 )

Therefore, the factors are ( 3x + 2) and ( 9x² - 6x + 4 ).

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Mean is 121.4, standard ,the deviation is 13. 21, variance is 175.47, minimum is 95, median is 118.

Here is an estimate of the order of a given intelligence level:

a. mean (normal):

mean can be found by including all scores and dividing by the number of scores:

mean = (141 + 139 + 126 + 122 + 125 + 130 + 95 + 110 + 118 + 118)/10 = 121.4

center:

b. median

if the scores are ordered ascending, center is the center score:

95, 110 , 118, 118, 122 , 125, 126, 130, 139, 141

Median = 118

c. Standard Deviation:

The standard deviation indicates how spread out the information is. Here's a recipe for finding the standard deviation:

Standard Deviation = sqrt(Variance)

d. Variation:

Variation is the proportion of variation in the set of information. The recipe for determining the change is:

Variance = (amount of ((each score - average)^2)/(number of scores - 1)

connect the numbers obtained:

Variance = (( ( amount of each score - ) 121.4)^2)/(10 - 1)

Variance = 1579.

24/9 = 175.47

standard deviation = sqrt(variance) = sqrt(175.47) = 13.21

e. minimum:

base is information gathering minimum:

minimum = 95

so, mean is 121.4, standard The deviation is 13. 21, difference is 175.47, base is 95, middle is 118

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The complete question is:

Below are the iq test scores of 10 randomly chosen fifth-grade students. 141 139 126 122 125 130 95 110 118 118. calculate a. mean b. median c. standard deviation d. variance e. minimum.

This differential equation states that the rate of change of the amount of salt in the tank is equal to the difference between the rate at which brine containing salt is being added to the tank.

(a) The initial amount of salt in the tank is 50 lbs.

(b) The initial volume of solution in the tank is 100 gal.

(c) The concentration of salt being added to the tank is 1 lb of salt per gallon of brine.

(d) The rate at which the solution is being added to the tank is 5 gal/s.

(e) The rate at which the solution is being removed from the tank is 3 gal/s.

(f) The volume of the solution in the tank at time t can be represented by V(t) = 100 + (5 - 3)t = 100 + 2t gal.

(g) The concentration of salt in the tank at time t can be represented by C(t) = x(t) / V(t), where x(t) represents the number of pounds of salt in the tank at time t.

(h) A differential equation with initial conditions that models this mixture problem is:

dx/dt = 5 - 3 = 2 (lb/s), where x(0) = 50 lbs.

This differential equation states that the rate of change of the amount of salt in the tank is equal to the difference between the rate at which brine containing salt is being added to the tank and the rate at which brine is being removed from the tank. The initial condition x(0) = 50 lbs states that the initial amount of salt in the tank is 50 lbs. The units in this differential equation make sense as the rate of change of the amount of salt in the tank is in lbs/s and the amount of salt in the tank is in lbs.

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The equation which represents Rob's debt  is -$15 + -$3 = -$18

Directed numbers, also known as integers, are numbers that have a direction or sign, either positive (+) or negative (-). They are used to represent quantities that have direction, such as temperature, height, weight, etc.

Rob borrows 15 dollars first

He later borrows 3 dollars.

Since we are to drag numbers to write an equation using NEGATIVE integers only,

We have -$15 + -$3 = -$18 which is Rob's debt

If numbers may be used more than once, the equation is

-$5 + -$3 + -$5 + -$2 + -$3 = -$18 which is Rob's debt.

Hence Rob owes his father $18. The debt is represented by the negative sign "-"

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Answer:

162

Step-by-step explanation:

The expected value of the number of rolls necessary to roll a specific number is 6. This is because each roll has an equal probability of rolling the desired number, which is 1/6.

The expected value of the number of rolls necessary to roll a specific number can be calculated by multiplying the probability of rolling the desired number by the total number of rolls. In this case, since the random number generator is a six-sided die, the probability of rolling a specific number, such as a six, is 1/6. Therefore, the expected value of the number of rolls necessary to roll a six would be 6 (1/6 x 6 = 6). This is because each roll has an equal probability of rolling the desired number. To calculate the expected value for any number, simply multiply the probability of rolling the desired number (1/6) by the total number of rolls. For example, if the desired number is a five, the expected value would be 5 (1/6 x 5 = 5). If the desired number is a three, the expected value would be 3 (1/6 x 3 = 3). Thus, the expected value of the number of rolls necessary to roll a specific number is equal to the number itself.

The complete question: Given a discrete random number generator, such as a six-sided die, what is the expected value of the number of rolls necessary to roll a specific number (e.g. a six)?

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Systematic sampling involves selecting every nth item from a list, potentially with bias and non-random results, so choose carefully.

The method used to choose the sample in this study is called "systematic sampling". This involves selecting a starting point (in this case using a random number generator) and then selecting every nth item (in this case, every 3rd person) from a list to form the sample. This type of sampling can introduce biases in the sample if the list has some pattern or structure, so it's important to be aware of these potential issues when using this method.

In systematic sampling, the selection of each member of the sample is based on a fixed and systematic rule. The advantage of this method is that it is easy to implement and cost-effective. The disadvantage is that if the list has any pattern or structure, such as alternation or clustering, the sample may not be representative of the population. It's important to carefully consider the list and choose an appropriate starting point and interval to reduce the potential for bias.

It's also worth noting that systematic sampling may not result in a random sample, as the sample members may not be independent of each other. This can have implications for the validity of inferences made from the sample to the population. Therefore, it's important to carefully consider the properties of the population and the goals of the study when choosing a sampling method.

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Answer:

its 2 i think

Step-by-step explanation:

Answer:

  (d)  ρ = 0.83 g/cm

Step-by-step explanation:

You want the density of a piece of driftwood that has a mass of 25 g and a volume of 30 cm³.

Use the given formula with the given numbers, and do the arithmetic.

  ρ = m ÷ V

  ρ = (25 g)÷(30 cm³) = (25/30) g/cm³ = 0.83 g/cm³

The solution is Option D.

The density of the driftwood is given by the equation D = 0.83 kg/cm³

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the density of the material be represented as D

Now , the equation will be

The mass of the material = m

The value of m = 25 grams

The volume of the material = v

The value of v = 30 cm³

So , density D = m / v

Substituting the values in the equation , we get

Density of driftwood D = 25/30

On simplifying the equation , we get

Density of driftwood = 0.83 kg/cm³

Hence , the equation is D = 0.83 kg/cm³

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The maximum flight height for a Bar headed Goose is 29,000 feet.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Maximum height that Rüppel's Vulture can fly = 37,000 feet

It is given that this height is 8,000 feet more than a Bar-headed Goose.

Let x be the maximum flight height of Bar-headed Goose.

We can write the equation as,

x + 8000 = 37000

Solving this,

x = 37000 - 8000

x = 29,000

Hence a Bar-headed Goose can fly to a maximum height of 29,000 feet.

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The equation representing the number of beads varies directly with the number of inches of the string is y = 9x.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The number of beads varies directly with the number of inches of string.

Therefore, y ∝ x.

y = kx.

From the table,

18 = 2k.

k = 9.

So, y = 9x.

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After checking the conditions are met, you perform a significance test of H0: μ = 1 versus Ha: μ≠ 1. You obtain a P-value of 0.022. the correct option is

A P-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. In this case, the P-value of 0.022 means that there is a 2.2% chance of observing the test statistic if the null hypothesis (μ = 1) were true.

A confidence interval, on the other hand, provides a range of values that are believed to contain the true population mean with a certain level of confidence. The confidence level (e.g. 95%) indicates the degree of certainty that the interval contains the true mean.

A low P-value suggests that the data provide strong evidence against the null hypothesis, and a confidence interval that does not contain the null value supports the alternative hypothesis. However, it is not guaranteed that a 95% or 99% confidence interval will include the value 1 or 0 just based on the P-value obtained from a hypothesis test. The confidence interval depends on multiple factors such as sample size, variability of the data, and estimation method used.

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The angle ∠Bm is equal to the measure of the angle in degrees rounded to the nearest degree.

The angle is the amount of deviation from a straight line. It is measured in degrees, with a full circle being 360 degrees. Angles can be either acute, obtuse, right, or reflex. An acute angle is less than 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, a right angle is exactly 90 degrees, and a reflex angle is greater than 180 degrees but less than 360 degrees. Angles can be used in a variety of ways, from measuring distances and directions to constructing shapes and figures. They are an important part of mathematics and can provide a useful way of understanding the world around us.

To find this, calculate the measure of the angle in degrees and then round it to the nearest degree.

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Find m∠B

Note that

m∠B is acute. Round to the nearest degree.

Answer:

The first five terms of the recursive sequence are:

an = 3an-1 + 3

a1 = 9

a2 = 3a1 + 3 = 3 * 9 + 3 = 30

a3 = 3a2 + 3 = 3 * 30 + 3 = 93

a4 = 3a3 + 3 = 3 * 93 + 3 = 282

a5 = 3a4 + 3 = 3 * 282 + 3 = 849

So the first five terms are: 9, 30, 93, 282, 849.

Step-by-step explanation:

a) The probability that the married couples will have 0, 1, 2, 3, or 4 preferences in common is as follows:

b) Yes, the probabilities add up to 1.

c) The above result does make sense. The table values add up to 375 as the probabilities sum up to 1.

d) The sample space in this problem is C. 0, 1, 2, 3, 4 personality preferences in common.

Probability refers to the odds, chance, or likelihood of an expected outcome occurring given many possible outcomes.

Probability is a fractional value, lying between 0 and 1, in most instances, except when it is 100% uncertain or certain.

Random Sample = 375 married couples

Number of Similar     Number of              Probability of

  Preferences        Married Couples   Common Preferences

     All four                        26                       6.93% (26/375)   or 0.07

     Three                         120                    32.00% (120/375) or 0.32

     Two                            113                     30.13% (113/375)   or 0.30

     One                             61                     16.27% (61/375)     or 0.16

    None                           55                     14.67% (55/375)    or 0.15

Total                               375                     100%                      or  1  

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Answer: no

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

It's not a linear function because

3 and 5  have the same y and its not a linear function

X + Y is continuous with density function fx+y(t) = |sx.x(8,6-u)|dxdy.

Let X and Y be jointly continuous random variables with joint density function fx,y(x,y). The density function of the sum of X and Y, X + Y, is given by the convolution of fx,y(x,y) and is denoted by fx+y(t). The convolution of fx,y(x,y) is calculated as follows:

fx+y(t) = ∫∫infinityfX,Y(x,y)dydx

= ∫∫∞fX,Y(x,y)dxdy

= ∫∫∞fX,Y(x,y)sx.(x(8,6-u))dxdy

= ∫∫∞|sx.x(8,6-u)|dxdy

Hence, X + Y is continuous with density function fx+y(t) = |sx.x(8,6-u)|dxdy.

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