Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3

The following function won't produce the intended composite function:

f(x) = 8/x + 4

g(x) = 1/x²

A method or connection known as a function connects each element of a non-empty set A to at least one element of a second non-empty set B. A function in mathematics is a relation f between a set A (the function's domain) and a different set B (the function's co-domain).

In the given question,

When f(x) = 8/x + 4 and g(x) = 1/x²

Then (f o g(x)) = 8/1/x² + 4

= 8x² + 4

As a result, the following function would not produce the intended composite function:

f(x) = 8/x + 4

g(x) = 1/x²

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Answer:

Step-by-step explanation:

So your slope intercept is on the y line to you will go to your y line and find the -7

Once you find your -7 you rise 1 and run 4 which mean go up by 1 and right by 4

Hope this helps!!

Answer: To complete the recursive formula for g(n) = -50 - 15n, we need to find an expression for g(n) in terms of previous terms of the sequence.

One way to do this is to notice that g(n) can be obtained by subtracting 15 from the previous term, g(n-1):

g(n) = -50 - 15n

= -50 - 15(n-1) - 15 (adding and subtracting 15)

= g(n-1) - 15

Therefore, the recursive formula for g(n) is:

g(0) = -50 (base case)

g(n) = g(n-1) - 15 (recursive step)

This means that to find g(n), we need to first find g(n-1) and then subtract 15 from it. We can use this recursive formula to generate any term in the sequence of g(n).

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

step by step you will learn

In response to the query, we have that Hence, the following are the answers to this equation: 5x - 2 = 0 or x - 1 = 0 Thus, x = 2/5 or x = 1.

A quadratic equation in a single variable is x ax2+bx+c=0, a form of quadratic equation. a 0. The fact that this polynomial is of second sample guarantees that it comprises at least one solution according to the Basic Theorem of Algebra. Solutions might be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least single word in it has to be rounded. The formula "ax2 + bx + c = 0" constitutes one of the widely used solutions for complex numbers. where the undefined variable "X" is represented by the numerical values or constants a, b, and c.

2x² - 9x - 18 = 0

Secondly, we must identify two integers whose total is -9 and whose product is 2(-18)=-36. These are the numbers -12 and +3. Hence, we may say:

2x² - 9x - 18 = (2x + 3)(x - 6) = 0

Hence, the following are the answers to this equation:

2x + 3 = 0 or x - 6 = 0

Thus, x = -3/2 or 6.

8x² + 2x - 3 = 0

8x² + 2x - 3 = (4x - 3) (4x - 3)

(2x + 1) = 0

Hence, the following are the answers to this equation:

4x - 3 = 0 or 2x + 1 = 0

Thus, either x = 3/4 or x = -1/2.

5x² - 11x + 2 = 0

5x² - 11x + 2 = (5x - 2)(x - 1) = 0

Hence, the following are the answers to this equation:

5x - 2 = 0 or x - 1 = 0

Thus, x = 2/5 or x = 1.

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Answer:

Bases

Step-by-step explanation:

The Simple Interest is $10

Simple Interest is  the method of calculating the interest amount for some principal amount of money. It is also finding the product of the principal amount borrowed or lent, the rate of interest and the term or repayment period of the loan.

Where the Principal is the borrowed money which is given for a specific period.

Simple Interest = P * R * T/100

Where P = Principal = $1000

R = Rate = 2%

T = Time = 6 months

When 6 months converted to year = 6/12 = 1/2 = 0.5 year

SI = 1000 * 2 * 0.5/100

SI = 1000/100

SI = $10

Therefore, the Simple Interest is $10

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Answer:

Step-by-step explanation:

Simple Interest formula = P * R * T/100

p  = $1000

r = 2%

t = 6 months (0.5 year)

so, SI = 1000 * 2 * 0.5/100

SI = $10

hope this helps :))

The standard deviation is 0.67 metric tonnes, and the mean of the sampling distribution of the sample mean impact force is 30 metric tonnes.

What is the mean and standard deviation of the sampling distribution of the sample mean impact force?

a. The following formulas can be used to determine the mean and standard deviation of the sampling distribution of the sample mean impact force:

30 metric tonnes are the population's mean and the sampling distribution's mean.

Standard deviation of the sample distribution is equal to the square root of the population's standard deviation.

= [tex]2 / sqrt(9) (9)[/tex]

= 0.67 tonnes in metric

As a result, the standard deviation is 0.67 metric tonnes, and the mean of the sampling distribution of the sample mean impact force is 30 metric tonnes.

What is the probability of a sample mean impact force being less than 28.7 metric tons?

b. Using the z-score calculation and common normal distribution tables, we can determine the likelihood that the sample mean impact force will be less than 28.7 metric tonnes. The z-score equation is:

(Sample Mean - Population Mean) = Z (standard deviation of sampling distribution)

= (28.7 - 30) / 0.67 = -2

We discover that the probability of a z-score less than -2 is 0.0228 using the usual normal distribution table. Consequently, 0.0228 or 2.28% of the time, the sample mean impact force will be less than 28.7 metric tonnes.

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Answer:

[tex]3[/tex]×[tex]5[/tex][tex]=15[/tex]

[tex]15+1=16[/tex]

Answer:

2289.12

Step-by-step explanation:

Answer:

2289.12

Step-by-step explanation:

the sum of 897.23 and 39.89 is 937.12

937.12+1352=2289.12

Answer:

Step-by-step explanation:

The formula for Sn of a geometric series with first term a and common ratio r is:

Sn = a((1-r^n)/(1-r))

In this case, the first term a is $1,000, the common ratio r is 1.02 (since she's depositing 2% more each year), and n is 30 (since we're looking for the amount deposited after 30 years).

Plugging in these values, we get:

Sn = 1000((1-1.02^30)/(1-1.02))

Sn ≈ $87,453

Therefore, the answer is D. $87,453.

Answer:

2 ( 10 + 3 )

Step-by-step explanation:

An arithmetic sequence with a common difference d = -3 include the following: D. 43,40,37,34,31.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 40 - 43

Common difference, d = -3

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The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.

Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

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Work Shown:

The notation f(-1) = 30 tells us that (x,y) = (-1,30) is a point on the exponential curve.

Plug in x = -1 and y = 30 and solve for 'a'

y = a*b^x

30 = a*b^(-1)

30 = a*(1/b^1)

30 = a/b

a = 30b

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

Now plug that into the equation to get

y = a*b^x

y = 30b*b^x

y = 30b^1*b^x

y = 30b^(1+x)

Afterward, plug in x = 4 and y = 85 to solve for b.

85 = 30b^(1+4)

85 = 30b^5

b^5 = 85/30

b = (85/30)^(1/5)

b = 1.23157122757057

We can then determine the value of 'a'

a = 30b

a = 30*1.23157122757057

a = 36.947136827117

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

To summarize,

both of which are approximate.

Since we want f(3) to the nearest hundredth, we don't really need to go too overboard with precision. Let's round 'a' and b to 4 decimal places.

We then get

This means

y = a*b^x

turns into

y = 36.9471*(1.2316)^x

As a check, plug in x = -1 to get y = 29.999269; we'll have rounding error since we rounded those 'a' and b values earlier. But when rounding 29.999269 to the nearest hundredth, we get y = 30.

Also, plug x = 4 into the equation to get y = 85.00785875 which rounds to 85.

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

The last step is to plug x = 3 into the equation

y = 36.9471*(1.2316)^x

y = 36.9471*(1.2316)^3

y = 69.0222951885528

y = 69.02 which is the final answer

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If you were to use those more accurate values of 'a' and b, then x = 3 would lead to y = 69.0175266335801; that rounds to 69.02 when rounding to the nearest hundredth (aka 2 decimal places). So this shows we can stick with the less accurate 'a' and b values while still getting the correct final answer.

GeoGebra and Desmos are great tools to help quickly verify the answer.

Answer:

f(3) = 69.02  (nearest hundredth)

Step-by-step explanation:

An exponential function is used to calculate the exponential growth or decay of a given set of data.  In an exponential function, the variable is the exponent.

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given:

Substitute these values into the general form of an exponential function to create two equations in terms of a and b:

[tex]\begin{aligned}\implies f(-1)&=30\\ab^{-1}&=30\end{aligned}[/tex]

[tex]\begin{aligned}\implies f(4)&=85\\ab^{4}&=85\end{aligned}[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\begin{aligned}\implies \dfrac{ab^4}{ab^{-1}}&=\dfrac{85}{30}\\\\\dfrac{b^4}{b^{-1}}&=\dfrac{85}{30}\\\\\end{aligned}[/tex]

Solve for b:

[tex]\begin{aligned}\implies \dfrac{b^4}{b^{-1}}&=\dfrac{85}{30}\\\\b^{4-(-1)}&=\dfrac{17}{6}\\\\b^{5}&=\dfrac{17}{6}\\\\b&=\sqrt[5]{\dfrac{17}{6}}\end{aligned}[/tex]

Substitute the found value of b into ab⁴ = 85:

[tex]\implies a\left(\sqrt[5]{\dfrac{17}{6}}\right)^4=85[/tex]

Solve for a:

[tex]\implies a=\dfrac{85}{\left(\sqrt[5]{\dfrac{17}{6}}\right)^4}[/tex]

[tex]\implies a=\dfrac{85}{\sqrt[5]{\dfrac{17^4}{6^4}}}[/tex]

[tex]\implies a=\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}[/tex]

Substitute the found values of a and b into the exponential function formula to create an exponential equation for the given parameters:

[tex]f(x)=\left(\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}\right)\cdot \left(\sqrt[5]{\dfrac{17}{6}}\right)^x[/tex]

To find the value of f(3), substitute x = 3 into the equation:

[tex]\begin{aligned}\implies f(3)&=\left(\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}\right)\cdot \left(\sqrt[5]{\dfrac{17}{6}}\right)^3\\\\&=69.0175266...\\\\&=69.02\; \;\sf (nearest\;hundredth)\end{aligned}[/tex]

Therefore, the value of f(3) to the nearest hundredth is 69.02.

Therefore , the solution of the given problem of function comes out to be the ball can  reach a height of 74 feet, to the closest foot.

The study of mathematics includes topics such as numbers, symbols, and their component components, as well as anatomy, building, and that both true and fictitious geographic locations. A function describes the relationships between different components that all lead to the same result. A function is made up of several variable  distinct components that, when placed together, produce specific outputs for every input.

Here,

The starting height (h0) is 4 feet, and the initial speed (v0) is 75 feet per second.

The ball's vertical movement is modelled by the formula h(t) = 16t2 + v0t + h0.

When we change the numbers, we obtain:

h(t) = −16t2 + 75t + 4

The vertex of the parabolic function marks the height of the spheroid at its greatest height.

The vertex's t-value is determined by:

t = −v0/2a

where a represents the t2 component in the h-function (t).

When we change the numbers, we obtain:

t = −75/(2(−16)) = 2.34375

2.34375 seconds pass after the ball is thrown before it hits its highest point.

Given is the utmost height:

h(2.34375) = −16(2.34375) (2.34375)

2 + 75(2.34375) + 4 = 74 feet

The ball can therefore reach a height of 74 feet, to the closest foot.

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Step-by-step explanation:

factors of 14: 1, 14, 2, 7

factors of 22: 1, 22, 2, 11

factors of 30: 1, 30, 2, 15, 3, 10, 5, 6

factors of 25: 1, 25, 5, 5

Answer:

Factors 14 : 1, 14, 2, 7
Factors 22 : 1, 22, 2, 11
Factors 30 : 1, 30, 2, 15, 3, 10, 5, 6
Factors 25 : 1, 25, 5

Answer:

The 2nd graph

Step-by-step explanation:

We know

The solution is (0,5)

Looking at the options, we only see graph 2 has two lines intersecting at the solution point (0,5). So, the answer is graph 2.

Answer:

The practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.

Step-by-step explanation:

The practical domain of the function is limited by the given constraints: Joe can purchase up to 8 boxes of hot dogs, and he cannot purchase partial boxes. Therefore, the number of boxes he can purchase is a whole number between 0 and 8, inclusive.

Substituting the values from 0 to 8 into the function, we get:

f(0) = 48(0) + 20 = 20

f(1) = 48(1) + 20 = 68

f(2) = 48(2) + 20 = 116

f(3) = 48(3) + 20 = 164

f(4) = 48(4) + 20 = 212

f(5) = 48(5) + 20 = 260

f(6) = 48(6) + 20 = 308

f(7) = 48(7) + 20 = 356

f(8) = 48(8) + 20 = 404

Therefore, the practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.

Answer:

20=2g

g=10

20/2=10

g=10

The required number line shows that the four numbers between 10 and 20 that have a remainder of 2 when divided by 3.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

To show the numbers between 10 and 20 that have a remainder of 2 when divided by 3, we need to start with the first number in that range that has a remainder of 2 when divided by 3, which is 11. Then, we can add 3 to that number to get the next number that has a remainder of 2 when divided by 3, which is 14.

We can continue adding 3 to each previous number to get the rest of the numbers that meet this condition:

11, 14, 17, 20

So, these are the four numbers between 10 and 20 that have a remainder of 2 when divided by 3. We can plot them on the number line as shown.

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Answer: To find how much greater the beetle's length is than its width, we need to subtract the width from the length:

Length - Width

Substituting the given values, we get:

2/5 inch - 1/5 inch

Simplifying the expression by finding the common denominator of 5, we get:

(2/5 - 1/5) inch

= 1/5 inch

Therefore, the beetle's length is 1/5 inch greater than its width.

Step-by-step explanation:

Answer:

[tex] \tan G = \dfrac{3\sqrt{6}}{2} [/tex]

Step-by-step explanation:

tan G = opp/adj

[tex] \tan G = \dfrac{\sqrt{54}}{2} [/tex]

[tex] \tan G = \dfrac{\sqrt{9 \times 6}}{2} [/tex]

[tex] \tan G = \dfrac{3\sqrt{6}}{2} [/tex]

Answer:

-csc^2 θ = dθ/dt = 1/5 (dx/dt)

or

3.49 km/min

Step-by-step explanation:

dx/dt

- 5cosec^2 θ * (rate of change of angle of elevation)

- 5 cosec^2 (π/3) * (-π/6)

(5π/6) * (4/3)

= 10π/9 km/min. = 3.49 km/min

Answer:

72; Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer