What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48

Answer:

The expression 4a - 2(a + b) + 1 simplifies to -3 when a = 2 and b = 4.

Step-by-step explanation:

When a = 2 and b = 4, substituting the values into the expression gives:

4 * 2 - 2 * (2 + 4) + 1 = 8 - 2 * 6 + 1 = 8 - 12 + 1 = -4 + 1 = -3

So the expression 4a - 2(a + b) + 1 simplifies to -3 when a = 2 and b = 4.

Please mark me as brainiest if this helped

The value of  function f(-7) is 157.

Functions have the property that each input is related to exactly one output. The function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For the given situation,

The function is f(x) = 3 x^2 + 10

Then  f( - 7) becomes,

⇒ \(f(-7)=3(-7 )^{2} +10\)

⇒ \(f(-7)=147+10\)

⇒ \(f(-7)=157\)

Hence we can conclude that the value of  function f(-7) is 157.

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Answer:

x = 1, y = 46

Step-by-step explanation:

Since the triangles are congruent then corresponding sides and angles are congruent, then

DE = AB , that is

3x + 6 = 9 ( subtract 6 from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

and

∠ C = ∠ F

10x + y = 56 ( substitute x = 1 )

10(1) + y = 56

10 + y = 56 ( subtract 10 from both sides )

y = 46

nothing is shown as far as I can tell

edit: but the inner angles of a regular pentagon should always be 120°. maybe it helps

Step-by-step explanation:

can see any photo concerning the angle

Answer:

See answers in explanation

Step-by-step explanation:

For 1.)

A.)

\(x-y=7\\x+y=5\)

For elimination, attempt to remove one variable.  For these problems, the two equations can be added together without modification to remove y:

\(x-y=7\\+\\x+y=5\\2x=12\\\frac{2x}{2}=\frac{12}{2}\\x=6\)

Now, substitute x for 6 in equation 2:

\(6+y=5\\(6+y)-6=(5)-6\\y=-1\)

To check,

\(6-(-1)=7\\7=7\)

and

\(6+(-1)=5\\5=5\)

B.)

\(2m+5n=3\\-2m-n=5\\\\4n=8\\\frac{4n}{4}=\frac{8}{4}\\n=2\)

Substitute into equation 2:

\(-2m-(2)=5\\(-2m-2)+2=5+2\\-2m=7\\\frac{-2m}{-2}=\frac{7}{-2}\\m=-\frac{7}{2}\)

For part 2, a manipulation must be made for each problem to eliminate a variable:

A.)

\(x-y=15\\4x+2y=30\\\\2(x-y=15)\\4x+2y=30\\\\2x-2y=30\\4x+2y=30\\\\6x=60\\\frac{6x}{6}=\frac{60}{6}\\x=10\)

Substitute into equation 2:

\(4(10)+2y=30\\40+2y=30\\2(20+y)=30\\\frac{2(20+y)}{2}=\frac{30}{2}\\20+y=15\\(20+y)-20=(15)-20\\y=-5\)

B.)

\(2c+3d=17\\5c+6d=32\\\\-2(2c+3d=17)\\5c+6d=32\\\\-4c-6d=-34\\5c+6d=32\\c=-2\)

Substitute into equation 2:

\(5(-2)+6d=32\\-10+6d=32\\(-10+6d)+10=(32)+10\\6d=42\\\frac{6d}{6}=\frac{42}{60}\\d=7\)

For question 3, both equations in each system must be manipulated to eliminate a variable:

A.)

\(2x+3y=16\\5x-2y=21\\\\2(2x+3y=16)\\3(5x-2y=21)\\\\4x+6y=32\\15x-6y=63\\\\19x=95\\\frac{19x}{19}=\frac{95}{19}\\x=5\)

Substitute into equation 2:

\(5(5)-2y=21\\25-2y=21\\(25-2y)-25=(21)-25\\-2y=-4\\\frac{-2y}{-2}=\frac{-4}{-2}\\y=2\)

B.)

\(6s-7t=25\\15s+3t=42\\\\3(6s-7t=25)\\7(15s+3t=42)\\\\18s-21t=75\\105s+21t=294\\\\123s=369\\\frac{123s}{123}=\frac{369}{123}\\s=3\)

Substitute into equation 2:

\(15(3)+3t=42\\45+3t=42\\(45+3t)-45=(42)-45\\3t=-3\\\frac{3t}{3}=\frac{-3}{3}\\t=-1\)

I didn't write out all the checks, but all these answers satisfy their original equations.  Hope this will help you out.

Sample a is more surprising because there is more variability in smaller samples, making it less likely to obtain a sample mean that is as extreme as $2750.

Sample A is more surprising because there is more variability in smaller samples. The variability of sample means decreases as the sample size increases due to the central limit theorem.

The central limit theorem states that as the sample size increases, the distribution of sample means becomes more normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, sample A, which has a smaller sample size of 9, has a larger standard deviation and more variability in the mean award amount compared to sample B, which has a sample size of 36. It is less likely to obtain a sample mean of $2750 from a smaller sample with more variability than from a larger sample with less variability. Thus, sample A is more surprising than sample B.

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The correct Answer is D

s1 = s2 and r1 = r2

The two data sets have the same range. The first data set has a range of 88 − 56 = 32, and the second data set has a range of 112 − 80 = 32.

This relationship is sometimes referred to as the range rule for standard deviation. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.

The standard deviation is a more effective measure of variation than the range. Range of the data is a measure of variation which gives the difference in the maximum and the minimum observation of the dataset. It is only based on two observations, the maximum and the minimum.

Alternatively, it can be seen visually that the ranges are the same because the two dot plots are aligned, the scales of the graphs are the same, and the graphs have the same width. The two data sets have different standard deviations. Both dot plots show distributions that have a mean near the center value of the dot plot. The first dot plot shows most values clustered near the mean, while the second dot plot shows most values farther from the mean. Therefore, the standard deviations of the two data sets are not equal—the data represented by the second dot plot has a greater standard deviation.

Choices A, B, and C are incorrect because they incorrectly assert either that the standard deviations are the same or that the ranges are different.

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There is step to step calculation

Hope is helpful

Answer: b is correct

Step-by-step explanation:

The given triangle will be an obtuse triangle.

As the above mention criteria fulfill the requirement of obtuse triangle.

As, ab and <ACB=134.76° that is greater that 120 degree.

A triangle is a polygon with three edges and three vertices. it is one of the simple shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC. In Euclidean geometry, any 3 factors, when non- collinear, decide a unique triangle and concurrently, a completely unique plane.

A triangle is a 3-sided polygon, which has 3 vertices. The three sides are linked with each different end to quit at a point, which bureaucracy the angles of the triangle. The sum of all 3 angles of the triangle is equal to a hundred and eighty tiers.

Triangles are shapes with 3 aspects. There are extraordinary names for the kinds of triangles. A triangle's type relies upon on the length of its facets and the size of its angles (corners). There are three varieties of triangle primarily based on the period of the edges: equilateral, isosceles, and scalene.

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Answer:

47°

Step-by-step explanation:

Given that m<BOC = 6x + 29, m<AOB = 3x + 124, and m<AOC is a straight angle, therefore, m<AOC = 180°.

m<BOC +m<AOB = 180°

6x + 29 + 3x + 124 = 180

Solve for x

6x + 3x + 29 + 124 = 180

9x + 153 = 180

Subtract both sides by 153

9x = 180 - 153

9x = 27

Divide both sides by 9

x = 3

m<BOC = 6x + 29

Plug in the value of x

m<BOC = 6(3) + 29

m<BOC = 18 + 29 = 47°

Two equal-size vectors at right angles to each other have a resultant that is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

The magnitude of the resultant vector of two equal-size vectors at right angles to each other can be determined using the Pythagorean theorem.

Let's assume the magnitude of each vector is represented by "a".

According to the Pythagorean theorem, the magnitude of the resultant vector, denoted as "R", can be calculated as:

R =\(\sqrt{a^2 + a^2}\)

R = (\(\sqrt{2a^{2} )}\)

R = \(\sqrt{2}\) a

Therefore, the magnitude of the resultant vector is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

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Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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Step-by-step explanation:

Volume of a cylinder = pi r^2 h     <=====solve for 'h'

h = volume / (pi r^2)

  = 348.3 mm^3 / ( pi * 4.5^2)             ( I assumed the dimension mm^3 )

h = ~ 5.5 mm

Answer:

Step-by-step explanation:

Answer: A=38.48

Step-by-step explanation:

A=πr^2

7/2=3.5

3.5x3.5=12.25

12.25π

38.48

Hope this helps! :)

Answer:

The answer is all real numbers

Answer:b

Step-by-step explanation:

Answer:

simplified, it is 3m^3+6f+267

Answer:

10-30x=-20x,i hope i help u :)

Step-by-step explanation:

f(0)=8

Coordinate: (0,8)

y intercept,c: 8

f(4)=20

Coordinate: (4,20)

gradient, m

= (20-8)/(4-0)

=3

Y=mx+c

f(x)=3x+8

f(x)=3x+8 is the  linear function f with the values f(0) = 8 and f(4) = 20.

A linear function is a function that represents a straight line on the coordinate plane.

The given functions are f(0)=8 and f(4) =20

For f(0)=8

Coordinate: (0,8)

y intercept, c: 8

For f(4)=20

Coordinate: (4,20)

gradient or slope, m when x₁=0,y₁=8,x₂=4, y₂=20

=( y₂-y₁)/(x₂-x₁)

= (20-8)/(4-0)=12/4

=3

The linear equation is in the form, y=mx+c

So f(x)=3x+8, where 3 is the slope and 8 is y intercept.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Alessandra will pay $24, which is the second highest price. By making the winner pay the second highest price, the auction ensures that the winning bid is close to the true value of the item.

In an auction, the winner pays the second highest price, not their own bid. Since Alessandra's bid was $25 and the second highest bid was $24, she will pay $24. This is because the auction is designed to incentivize bidders to bid their true value for the item, as bidding too high could result in paying more than the item is worth, while bidding too low could result in losing the auction altogether. By making the winner pay the second highest price, the auction ensures that the winning bid is close to the true value of the item.

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The probability of exactly 4 households being in violation of the law out of a random selection of 10 households can be calculated using the binomial probability formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient. In this case, n=10, k=4, and p=0.2 (since 20% of households are in violation). Plugging in these values, we get P(X=4) = (10 choose 4) * 0.2^4 * 0.8^6 ≈ 0.2508. Therefore, the probability of exactly 4 households being in violation out of a random selection of 10 households is approximately 0.2508 or 25.08%.

To explain this further, we can break down the formula. The (10 choose 4) term represents the number of ways to choose 4 households out of 10. The 0.2^4 term represents the probability of exactly 4 households being in violation (since the probability of any given household being in violation is 0.2). The 0.8^6 term represents the probability of the remaining 6 households not being in violation. Multiplying these terms together gives us the probability of exactly 4 households being in violation out of a random selection of 10 households.

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The ratio of the number of boys to the number of girls in a choir is 3 to 4. There are 56 girls in the choir then there are 42 boys in the choir

We can use the ratio of boys to girls to determine how many boys are in the choir.

The ratio of boys to girls is given as 3 to 4, which means that for every 3 boys, there are 4 girls.

If we let x be the number of boys in the choir, then we can set up the following proportion:

3/4 = x/56

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

3 × 56 = 4 × x

168 = 4x

Divide both sides by 4

x = 42

Therefore, there are 42 boys in the choir.

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For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

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Answer:

z = 17.5

Step-by-step explanation:

To get the value of z, we use the bisector theorem

7/z = 6/15

6z = 7 * 15

6z = 105

z = 105/6

z = 17.5

Answer:

Step-by-step explanation:

A sum of was to be shared among three sidlings rambo nikita and kimroy in the ratio 3:7:9 if nikita and kimroy $2500 more than rambo evaluate the sum of money kimroys share

This question is incomplete. It lacks the amount of money that the 3 siblings share

Answer: The length is 9 inches.

Step-by-step explanation:

Find the length:

Answer:

The length is 9.

Step-by-step explanation: