To confirm that two function f and g are inverses, verify that f[g(x)]=x. True or False???​

The confidence interval would have been different if the only change had been  (a) A larger standard deviation among the sample sleeping times.

Confidence Interval:

A confidence interval (CI) is an estimated range for an unknown parameter. Calculates a confidence interval at a specified confidence level; a confidence level of 95% is the most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-term proportion of the CI (at a given confidence level) that theoretically contains the true value of the parameter. For example, of all the intervals calculated at the 95% level, 95% of them must contain the true value of the parameter.

Standard Deviation:

Standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

The standard deviation can be abbreviated SD, and is often used in mathematical texts and equations by the lowercase Greek letter σ (sigma) for population standard deviation, or the Latin letter s for standard deviation of the sample.

As mentioned earlier, the average sleep duration per night was 6.9 hours with a standard deviation of 1.2 hours. Thus, people who sleep between 4.5 and 9 hours.

3 hours is ± 2.4 hours or 2 standard deviations from the mean.

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The square of z varies inversely as the square root of e. If z=36 when w=16, then value of z is 24 when w=81.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The square of z varies inversely as the square root of e.

If z=36 when w=16

The value of z when w is 81 we need to find

z²=k/√e

where k is a proportionality constant

36²=k/√16

36²=k/4

Apply cross multiplication

1296(4)=k

5184=k

Now let us find when k is 5184 and w is 81

z²=5184/9

z²=576

Take square root on both sides

z=24

Hence, the value of z is 24 when w is 81.

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Answer:

no rocky

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

I think it's C and I am always right so it is C! You're welcome!

The interquartile range of the data set is 127 So, I disagree with Louis's calculation of the interquartile range which is 175..

The spread or dispersion of a dataset is measured by the interquartile range (IQR). It is described as the difference between the dataset's first and third quartiles (Q1 and Q3).

To determine whether Louis's calculation of the interquartile range (IQR) as 175 is correct, we first need to find the quartiles of the given data set.

To do this, we can first order the data set from smallest to largest:

{428, 452, 496, 518, 537, 579, 603}

The median is the middle value of the dataset, which is 518. We can then find the median of the lower half of the data (also known as the first quartile, Q1) and the median of the upper half of the data (also known as the third quartile, Q3).

Q1 = median({428, 452, 496}) = 452

Q3 = median({537, 579, 603}) = 579

The interquartile range (IQR) is then the difference between Q3 and Q1:

IQR = Q3 - Q1 = 579 - 452 = 127

Therefore, the interquartile range of the data set is actually 127, not 175 as Louis calculated. So, I would disagree with Louis's calculation of the interquartile range.

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Answer:

-10m-9

Step-by-step explanation:

-3(4m+3)+2m

combine like terms

-12m-9+2m

-10m-9

Based on the study, the researcher may develop a hypothesis that smoking is associated with an increased risk of depression.

An explanation that is put up for a phenomena or a group of facts is called a hypothesis. It is a speculative explanation that needs more testing and improvement because it is supported only by a small body of data. A hypothesis is not a tested theory, but rather a point of departure for more research. A hypothesis is examined in scientific study by testing and observationit. The purpose of hypothesis testing is to evaluate the likelihood that the suggested explanation is accurate and to spot any discrepancies or holes in the available data. The act of testing and improving hypotheses is a crucial component of the scientific method since it ensures that scientific ideas are supported by reliable data.

How to solve?

This hypothesis can then be tested through further research, such as conducting a larger study with more participants, or conducting experiments to evaluate the potential mechanisms by which smoking may affect the development of depression.

The researcher may also use statistical methods to analyze the data collected from the study, in order to determine the significance of the relationship between smoking and depression.

If the hypothesis is supported by the evidence, the researcher may conclude that smoking is a risk factor for depression, and may recommend interventions or preventative measures to reduce the risk of depression among smokers.

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Answer:

y=3x

2y=x

Step-by-step explanation:

N/A

big brain award pls

Answer:

143 i think

Step-by-step explanation:

45+ 106= 151

151 - 8 = 143

Answer:

$143

Step-by-step explanation:

106+45= 151

151-8=143

We can list out some of the ways to show 45 with tens and ones and see how many there are:

4 tens and 5 ones (i.e., 40 + 5 = 45)

3 tens and 15 ones (i.e., 30 + 15 = 45)

2 tens and 25 ones (i.e., 20 + 25 = 45)

What is probability?

Probability is a measure of the likelihood of an event occurring.

To answer the question, we first need to understand what it means to "show 45 with tens and ones." In this context, we are likely referring to different ways of expressing the number 45 as a sum of tens and ones.

For example, one way to show 45 with tens and ones is to write it as 4 tens and 5 ones (i.e., 40 + 5 = 45). Another way is to write it as 3 tens and 15 ones (i.e., 30 + 15 = 45). We can continue this pattern to find other ways of expressing 45 as a sum of tens and ones.

Now, let's consider Lester's and Anya's claims. Lester says there are 4 ways to show 45 with tens and ones, while Anya says there are 5 ways. Without knowing the specific ways they are counting, it's difficult to say who is correct.

However, we can list out some of the ways to show 45 with tens and ones and see how many there are:

4 tens and 5 ones (i.e., 40 + 5 = 45)

3 tens and 15 ones (i.e., 30 + 15 = 45)

2 tens and 25 ones (i.e., 20 + 25 = 45)

1 ten and 35 ones (i.e., 10 + 35 = 45)

0 tens and 45 ones (i.e., 0 + 45 = 45)

We can see that there are indeed 5 ways to show 45 with tens and ones, so Anya is correct.

In general, it's important to be specific about what we mean when we ask questions or make claims. In this case, it's possible that Lester and Anya were counting different things, which led to their different answers.

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Answer:

33.6 degrees F

Step-by-step explanation:

8000/1000 = 8

8(1.9) = 15.2 degree drop

48.8 - 15.2 = 33.6 degrees F

Answer:

me either I also need help in that one

Answer:

39°

Step-by-step explanation:

BE dusects CBD

-> CBE=EBD=20°

CBD = 40°

ABC = 79°-40°= 39°

Answer:

167

Step-by-step explanation:

the change between 276 and 109 is 167

Answer:

x^3 − 5x^2 + 8x − 6

Step-by-step explanation:

The standard form of "18 hundreds 11 tens" is 1910.

To write "18 hundreds 11 tens" in standard form, we need to convert the given number into its numerical representation.

We know that 1 hundred is equal to 100, and 1 ten is equal to 10.

So, to find the numerical value of "18 hundreds 11 tens," we multiply the respective values by their place values and then add them together.

18 hundreds = 18 x 100 = 1800

11 tens = 11 x 10 = 110

To find the standard form, we add the two values:

1800 + 110 = 1910

Therefore, "18 hundreds 11 tens" in standard form is 1910.

In standard form, numbers are written using digits, without any reference to place value units like hundreds or tens.

The standard form of a number represents its numerical value directly. So, the numerical value of "18 hundreds 11 tens" is 1910, which is its standard form.

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There will be no change in the price of the car.

A number line is a representation of a graduated straight line used to abstract real numbers in elementary mathematics. Its points are considered to correspond to real numbers and vice versa.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Let the sticker price = x, Price reduced by $300

Hence the new price is,

N= x-$300

The cost of additional features = $900

Hence the new price for selling will be.

=x-$300+$900

=x+$600

Dealer also provides a discount of $600

Hence Final  selling price will be

=x+$600-$600

Hence there seems to be no change in the sticker price as the sticker price and the final selling price are the same.

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Answer:

\(\frac{13\pi }{2}\) cm^2

Step-by-step explanation:

im a highschool student but we are doing this stuff and this is how i learned it: calculate the area of the larger sector (\(\frac{64\pi }{6}\)) and subtract the smaller sector(\(\frac{25\pi }{6}\)) from it to get  \(\frac{39\pi }{6}\)  which can be simplified to \(\frac{13\pi }{2}\).

Answer:

.

Step-by-step explanation:

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer:

14 square centimeters

Step-by-step explanation:

You gotta add the area of the first and second triangle.

First Triangle:

(1/2)x 4 x 4= 8cm

Second Triangle:

(1/2)x 4 x 3= 6cm

FINAL ANSWER: 6+8= 14cm

The answer of the question based on remainder and factor theorem is (1) The correct answer is (C) f(5) = -1. , (2)  The correct answer is (d) h(-3) = 10. , (3) (a) = True , (b) =False , (c) True , (d) = True.

The factor theorem is a theorem in algebra that states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. In other words, if a is a root of the polynomial (i.e., if (x - a) is a factor), then substituting a for x in the polynomial will result in a value of 0.

(1) The correct answer is (C) f(5) = -1.

The remainder theorem states that when a polynomial f(x) is divided by (x-a), the remainder is equal to f(a). Therefore, in this case, when f(x) is divided by (x-5), the remainder is -1, which means that f(5) = -1.

(2) The correct answer is (d) h(-3) = 10.

When h(x) is divided by (x+3), the remainder theorem states that the remainder is equal to h(-3), which can be found by substituting -3 for x in the expression for h(x) and simplifying.

(3) Based on the completed synthetic division provided, we can check the following statements:

The quotient is equal to -2x²+2x-5. (True)

The quotient is equal to 2x² - 2x + 5. (False)

(x-1) must be a factor of the starting function. (True, since the final remainder is zero after synthetic division by (x-1))

If the starting function is f(x), then f(-1) = 0. (True, since (-1) is one of the divisors used in the synthetic division, and the final remainder is zero)

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The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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Answer:

x = 18 y = 10

Step-by-step explanation:

let the first number be x

let the second number be y

x = y + 8..... equation 1

2x + y = 46.... equation 2

x is the larger number

y is the smaller number.

Rearrange the equation and add equation 1 to equation 2.

x - y = 8

+ 2x + y = 46

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

3x + 0 = 54

3x = 54

divide both sides by 3

x = 54/3

x = 18

Substitute x = 18 into equation 1

x = y + 8

18 = y + 8

collect like terms

y = 18-8

y = 10

The two numbers are 18 and 10

From the question, One number is 8 more than another

Let the first number be x and the second number be y

∴ x = y + 8 ------ (1)

From the second statement, the sum of the smaller number and twice the larger number is 46

That is,

y + 2x = 46 ----- (2)

Now, we will solve the two equations simultaneously

From equation (1)

We have x = y + 8

Substitute this into equation (2)

y + 2x = 46

y + 2(y+8) = 46

Then, clear the bracket

y + 2y + 16 = 46

3y + 16 = 46

Collect like terms

3y = 46 - 16

3y = 30

∴ y = 30 ÷ 3

y = 10

Substitute the value of y into equation (1)

x = y + 8

x = 10 + 8

x = 18

∴ x = 18 and y = 10

Hence, the two numbers are 18 and 10

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Given:

A baseball player get a hit in 31% of his at-bats.

To find:

The probability that he will  get a hit 5 at-bats in a row.

Solution:

Since, a baseball player get a hit in 31% of his at-bats, therefore

Probability that he get a hit = \(\dfrac{31}{100}\)

                                           = \(0.31\)

Now, the probability that he will  get a hit 5 at-bats in a row is

\(P=0.31\times 0.31\times 0.31\times 0.31\times 0.31\)

\(P=(0.31)^5\)

\(P=0.0028629151 \)

Therefore, the required probability is \((0.31)^5\) and it can be written as 0.0028629151 .

The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The equation has 2 terms in it which means 2 is the answer.

Answer: Number of games lost = 23 and Number of games won = 59.

Step-by-step explanation:

Let x = Number of games lost, y = Number of games won.

y = 13 + 2x    (i)

x+ y = 82    (ii)

Substitute value of y from (i) in (ii) , we get

x+ 13 + 2x  = 82

⇒ 3x= 82-13

⇒ 3x = 69

⇒  x= 23      [Divide both sides by 3]

Put value of x in (i), y= 13+2(23) = 13+46=59

Hence, Number of games lost = 23 and Number of games won = 59.