Consider the function f(x)=8x+3x-1. For this function there are four important intervals: ( [infinity], A], [A, B),(B, C], and [C, [infinity]) where A, and C - are the critical numbers and the function is not defined at B.
Find A, B, and C

There are 2 tablespoons in an ounce. So for 2 ounces, you will need 4 tablespoons, for 4 ounces 8 tablespoons, and so on.

A tablespoon is a unit of volume measurement in United States, and some other countries. It is equal to approximately 15 milliliters (0.51 fluid ounces). One tablespoon can be further divided into three teaspoons, meaning that one tablespoon is equal to three teaspoons.

In the United States, one tablespoon is equal to 0.5 ounce, which is equal to 14.3 grams. This is slightly different in the UK, where one tablespoon is equal to 0.6 ounces (which is equal to 17.7 grams). To convert tablespoons to ounces, you can use the following formula is 1 tablespoon = 0.5 ounces.

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the probability that it rains in Spain when hurricanes happen in Hartford is approximately 0.2192.

what is bayes theorem ?

Let’s use Bayes’ theorem to solve this problem. Let A be the event that it rains in Spain and B be the event that hurricanes happen in Hartford. We want to find P(A|B). We know that P(B|A) = 0.08 and P(B|A’) = 0.03 where A’ is the complement of A (i.e., it does not rain in Spain). We also know that P(A) = 1/13 and P(A’) = 12/13.

Bayes’ theorem states that:

P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|A’) * P(A’)]

Substituting the values we have:

P(A|B) = (0.08 * 1/13) / [(0.08 * 1/13) + (0.03 * 12/13)] = 0.2192 (rounded to four decimal places)

Therefore, the probability that it rains in Spain when hurricanes happen in Hartford is approximately 0.2192.

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Answer:

y – 5 = m(x – 6)

Step-by-step explanation:

using y =mx +c as our guide line

Step 1 : identification of coordinates

(6,5) ;x1= 6,y1 = 5

step 2 : applying the formula

y – y1 = m(x – x1)

y – 5 = m(x – 6)

The correct answer is "Bus 18, with merely an IQR of 16." The range is also smaller for Bus 18, but range is a less robust measure of variability and can be influenced by outliers.

What is IQR?

The IQR (interquartile range) provides a measure of the spread of the central 50% of the data, and is often used to identify outliers or to compare the variability of different datasets.

What is range?

Finding the variable's highest observed number (maximum) and deducting its minimum observed value yields the variable's range (minimum). Variational limits or a potential range: various steel prices; numerous styles; The scope or size of a method or action: understanding. the utmost or anticipated range of the a weapon's projectile. The number between both the lowest and maximum is known as the range of the a list or set. Align all of the numbers before determining the area. Next, subtract (subtract) the lowest number first from greatest number. The answer includes the list's range. The range of the list is given in the answer.

To compare the consistency of the travel times for Bus 18 and Bus 47, we need to use a measure of variability. Two common measures of variability are range and interquartile range (IQR) (interquartile range)

The range represents the discrepancy between the dataset's maximum and minimum values. The IQR  (interquartile range) is a measure of the spread of the middle 50% of the data, and is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1).

Looking at the graphs, we can see that Bus 18 has a smaller range than Bus 47 (16 vs. 24), but we cannot compare the IQRs just by looking at the graphs.

To calculate the IQR (interquartile range)  for each bus, we need to find the values of Q1 and Q3 for each dataset. We can do this by ordering the data and finding the median of the lower and upper halves. Using the values in the problem as a guide:

For Bus 18:

Q1 = median of {6, 6, 8, 9, 10, 10, 12, 14} = 9

Q3 = median of {16, 18, 18, 20, 22} = 18

So the IQR for Bus 18 is 18 - 9 = 9.

For Bus 47:

Q1 = median of {6, 10, 12, 12, 14, 14, 16, 16, 18} = 14

Q3 = median of {22, 22, 28, 28} = 25

So the IQR for Bus 47 is 25 - 14 = 11.

Based on these calculations, we can see that Bus 18 has a larger IQR (interquartile range)  than Bus 47, indicating that its travel times are more consistent. As a result, "Bus 18, with just an IQR of 16" is the right response. The range is likewise narrower for Bus 18, although range is a less reliable indicator of variability and is susceptible to outlier effect. The IQR  (interquartile range) is a better measure of spread for this comparison because it is less sensitive to outliers.

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Answer:

D: 922.3682

Step-by-step explanation:

First you take 1000 and subtract 20 from it.( 2% of 1000 = 1000x0.02x2=20).

You could do this on a calculator by entering 1000 and then subtracting 2% by clicking minus then, 2 then percent, then equals. you get 980. do the same to 980. (click minus, then 2, then percent, then equals). you get 960.4. do the same to 960.4. you get 941.192. do the same one more time since it says t=4  and you get 922.36816 which rounded to the nearest ten-thousandths is 922.3682.

hope this helped!

Answer: B

Step-by-step explanation: Skeletons serve as a scaffold which supports organs, anchors muscles, and protect organs such as, the brain, lung, heart, and spinal cord.

Therefore, if there were 40 dogs and the ratio stayed the same, there would be 120 cats at the pet daycare.

If the ratio of dogs to cats stays the same, then the ratio of dogs to cats in the two situations will be equal.

The initial ratio of dogs to cats is:

dogs : cats = 20 : 60

= 1 : 3

To maintain the same ratio, the new number of cats (C) can be found by setting up the proportion:

dogs : cats = 40 : C

Using the initial ratio of dogs to cats, we can substitute and simplify:

1 : 3 = 40 : C

Cross-multiplying gives:

C = (3 x 40) / 1

= 120

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Answer:

It wont load for me sorry

Step-by-step explanation:

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

I’m good LOVE

Step-by-step explanation:

Answer:

Good thank u for asking how abt u! xD

The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.

To calculate the circumference of a circle, the formula that should be used would be given below.

That is;

circumference of circle= 2πr

The radius = 31½

circumference = 2×π × 31½

= 2×π× 63/2

= 63π

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The height of Tree A t years after being planted can be represented by the equation:

A = 30 + 2t

This equation states that the initial height of the tree (30 inches) plus the annual growth of the tree (2 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.

The height of Tree B t years after being planted can be represented by the equation:

B = 15 + 5t

This equation states that the initial height of the tree (15 inches) plus the annual growth of the tree (5 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.

To determine which tree is taller after 6 years, we can substitute t = 6 into each equation and compare the results:

A = 30 + 2(6) = 30 + 12 = 42 inches

B = 15 + 5(6) = 15 + 30 = 45 inches

Tree B is taller than Tree A after 6 years because 45 inches is greater than 42 inches.

Answer:

literal equation

Step-by-step explanation:

The type of equation that is being described is known as a literal equation. Like mentioned these hold different variables and or can be a combination of variables and numbers. The best example or representation of a literal equation would be most formulas in geometry. For example, the area of a circle which is the following

A=πr2   ... in which A and r are both variables but also mixed with 2

Answer:

9

Step-by-step explanation:

Integer

Answer:

A rotation

The center of the rotation is (0,0)

With an angle of 90°

The range of the given function is {-5,-1,4} which is the B option.

Given function:-

\(f(x) = x^2+4x-1\)

Domain = {-2,0,1}

We have to find the range of the given function for the given domain.

Putting x = -2 in the given function, we get,

\(f(-2) = (-2)^2+4(-2)-1\)

f(-2) = 4 - 8 - 1 = -5

Putting x = 0 in the given function, we get,

\(f(0) = (0)^2+4(0)-1\)

f(0) = 0 + 0 -1 = -1

Putting x = 1 in the given function, we get,

\(f(1) = (1)^2+4(1)-1\)

f(1) = 1 + 4 - 1 = 4

Hence, the range of the given function is {-5,-1,4}.

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a) Alexandra's fortnightly repayments would be approximately $345.85.

b) The outstanding balance on the loan after 6 fortnights would be approximately $1,726.17.

To calculate Alexandra's fortnightly repayments and the outstanding balance on the loan after 6 fortnights, we need to use the formula for calculating the repayment amount and the formula for the outstanding balance.

a) Fortnightly Repayments:

First, we need to calculate the interest rate per fortnight. The annual interest rate is 8.12%, so the fortnightly interest rate would be (8.12% / 26) = 0.3123%.

The formula to calculate the repayment amount on a loan is:

Repayment Amount = \(P \times (r \times (1 + r)^n) / ((1 + r)^n - 1)\)

Where:

P = Principal amount of the loan ($2000)

r = Interest rate per fortnight (0.3123%)

n = Number of fortnights (6)

Plugging in the values:

Repayment Amount = \(2000 \times (0.003123 \times (1 + 0.003123)^6) / ((1 + 0.003123)^6 - 1)\)

Repayment Amount ≈ $345.85

b) Outstanding Balance after 6 Fortnights:

The formula to calculate the outstanding balance on a loan is:

Outstanding Balance = \(P \times ((1 + r)^n) - (A \times (((1 + r)^n) - 1) / r))\)

Where:

P = Principal amount of the loan ($2000)

r = Interest rate per fortnight (0.3123%)

n = Number of fortnights (6)

A = Repayment amount ($345.85)

Plugging in the values:

Outstanding Balance = \(2000 \times ((1 + 0.003123)^6) - (345.85 \times (((1 + 0.003123)^6) - 1) / 0.003123)\)

Outstanding Balance ≈ $1,726.17

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The probability that the sample mean is greater than 18 as calculated  is 0.8413.

Given data,

n = 36, sample size

μ = 17, population mean

σ = 6, population standard deviation

when x = 18

z = (18 - 17)/1 = 1

P(x <18) = 0.8413

Therefore , the probability = 0.8413

A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.

While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.

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The angle you would observe between the two ends of the meter stick if the pool is Part A empty is 18.92 degrees.

To determine the angle you observe between the two ends of the horizontal meter stick when the pool is empty, you can use the concept of similar triangles. The meter stick is 1.0 meter long and is centered at the bottom of the pool, so each half is 0.5 meters. The pool is 3.0 meters deep and 3.0 meters wide.

To find the angle, you can use the tangent function:

tan(θ) = opposite / adjacent

In this case, the opposite side is the half-length of the meter stick (0.5 meters), and the adjacent side is the depth of the pool (3.0 meters). So,

tan(θ) = 0.5 / 3.0

Now, to find the angle, use the inverse tangent function (arctan):

θ = arctan(0.5 / 3.0)

θ ≈ 9.46 degrees

Since there are two equal angles formed by the meter stick (one on the left and one on the right), the total angle you observe between the two ends of the meter stick would be:

Total angle = 2 * 9.46 ≈ 18.92 degrees

So, when the pool is empty, you observe an angle of approximately 18.92 degrees between the two ends of the horizontal meter stick.

Note: The question is incomplete. The complete question probably is: A horizontal meter stick is centered at the bottom of a 3.0-m-deep, 3.0-m-wide pool. Suppose you place your eye just above the edge of the pool, looking along the direction of the meter stick. What angle do you observe between the two ends of the meter stick if the pool is Part A empty? Express your answer with the appropriate units.

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Answer:

134.73

Step-by-step explanation:

Solving for m:

243 = m + 108.27

243 - 108.27 = m + 108.27 - 108.27

134.73 = m

Answer:

to find this we need to subtract 108.27 by 243 which we get 134.73

Step-by-step explanation:

so your answer is 134.73:)

brainliest is appreciated: D

Answer:

x = -8

Step-by-step explanation:

3.2 - 1/2(x + 4) = 4.8x + 2 - 5.2x

3.2 - 0.5x - 2 = - 0.4x + 2

1.2 - 0.5x = -0.4x + 2

1.2 - 0.1x = 2

-0.1x = 0.8

x = -8

Answer: 6.8 = 1.6

Step-by-step explanation:

3.2-1/2 (+4)                         4.8+2-5.2

2.8+4                                   6.8-5.2

6.8                      =                    1.6

Answer:

Solving steps:

Question:5 boys and 4 girls are randomly arranged to sit in a row. find the probability that all girls sit together.

Find:the probability that all girls sit together.

Solution: 5 boys and 4 girls, 9 kids in all, can be seated in a row in 9! ways. In order to find the number of ways, where the 4 girls are seated together, we place them in an imaginary group Z, so that they are not separated in the seating arrangements. Now we have 6 entities, namely 5 boys and one group of girls, and the number of ways of their seating is 6!. For each of these 6! ways, the 4 girls can be seated within the group Z in 4! ways. So the number of ways in which the 4 girls are seated together, is 6!/4!.

So the probability, as requested, is (6!4!)/9! = 24/(7x8x9) = 1/21

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Given:

2x + 4y = 14

4x + y = 20

Required:

We need to find the equivalent to the given system.

Explanation:

Consider the equation

Multiply both sides of the equation by -4, it will not affect the equations of the system

Final answer:

The equivalent system of the equation is

Answer:

Hey there!

The robot moves 63 cm in 9 seconds. Then in 1 second, it moves 7 cm.

If it goes 49 cm, it will take 7 seconds.

Let me know if this helps :)

Answer:

line B is the best model of data

Step-by-step explanation:

Line be is the best model for this since it runs through the data acting as an average.

Answer:

3.2

Step-by-step explanation:

Formula to find the simple interest rate :

S.I. = \(\frac{PRT}{100}\)

Formula to find R (simple interest rate) :

R = \(\frac{100*S.I.}{P*T}\)

Since you have I (interest amount), we can use this formula instead :

R = \(\frac{I}{PT}\)

R = \(\frac{320}{4,000*2}\) = 4%/year or 0.04

Now plug this into the first formula

S.I. = \(\frac{4,000*0.04*2}{100}\) = 3.2

i haven't done this in a while so hope this helps !!

Answer:

x = 4.5

Step-by-step explanation:

By geometric mean theorem:

\( {3}^{2} = 2 \times x \\ \\ 9 = 2x \\ \\ x = \frac{9}{2} \\ \\ x = 4.5\)

The slope of line is -3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

A line intersects the points (7, 6) and (11, -6).

So, the slope is

= \((y_2 - y_1)/ (x_2 - x_1)\)

= (-6 - 6) / (11 - 7)

= -12 / 4

= -3

Hence, the slope is -3.

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