Graph g(x) = - 2 + 3) - 2​

Answer:The simplified expression is 12√3.

Step-by-step explanation:

\( \begin{aligned} \sqrt{6} \: ( \sqrt{18} + \sqrt{8} )&= \sqrt{6} \: ( \sqrt{2 \times 9} + \sqrt{2 \times 4} ) \\ &= \sqrt{6} \: (3 \sqrt{2} + 2 \sqrt{2} ) \\ &= \sqrt{6} \: (5 \sqrt{2} ) \\&=5 \sqrt{12} \\ &=5 \sqrt{3 \times 4} \\ &=5 \times 2 \sqrt{3} \\ &= \bold{10 \sqrt{3} } \\ \\ \small{ \blue{ \mathfrak{That's \:it\: :)}}}\end{aligned}\)

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since we are working with tenths all we have to do is add the numerators of each fraction.

4 + 3 + 1 + 1 = 9

9/10

Answer:

5

Step-by-step explanation:

Polynomial are expressions. The equivalent four-term polynomial of x²+16x+48 is x²+12x+4x+48.

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

In order to find the equivalent four-term polynomial of the given quadratic equation, we will break constant b(16) into two parts such that the sum of the parts is 16, while their product is equal to the product of the constant a(1) and c(48).

Therefore, the solution of the polynomial is,

\(x^2+16+48\\\\= x^2 + 12x+4x+48\)

Hence, the equivalent four-term polynomial of x²+16x+48 is x²+12x+4x+48.

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Answer:

9hrs

Step-by-step explanation:

72 x 9 = 648

The correct option is (B) generated randomly from probability distributions.

The values for random variables in a Monte Carlo simulation are generated randomly from probability distributions.

A frequency distribution that has been idealized is a probability distribution. An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value of a variable appears. The probability of occurrence of a value determines how frequently it appears in a sample.

A random variable can have any number of alternative values and likelihoods within a particular range, and a probability distribution is a statistical function that captures all of these possibilities. This range will be constrained by the minimum and maximum possible values, but the location of the possible value on the probability distribution will rely on a number of other variables.

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Answer:

Im not really sure but i think is D

Step-by-step explanation:

Plz let me know if its wrong

i hope it helped <3

The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.

The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.

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The interval will their systolic pressure be lowest is 4p.m. to 6p.m.

Given that

the effects on the systolic

145-6t if 0≤t≤5

function: S(t)

115 if 5 52+7t if 9≤t≤12

where t= time

the blood pressure medication takes at 7 a.m.

first of all we have to nknow about the Interval.

What is interval?

An interval is a distinct measure of time or the physical or temporal distance between two things.

From the function given above, the lowest systolic pression can be seen from 5 and 8 hours after taken the medication.

Therefore, this will fall into or between the interval of  2pm to 5pm.

And as such,  looking at the question, the option that best fit into this time range is 4pm to 6pm.

Therefore,  Based on the above, the interval will their systolic pressure be lowest is 4pm to 6pm.

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Answer:

\(y = \frac{5}{4} x - 5\)

r = number of reptiles on the endangered species list

2r = twice that number

2r < 127 since the 127 is more than twice the number of reptiles

Solve for r by dividing both sides by 2

2r < 127

r < 127/2

r < 63.5

If r is a positive whole number, then r could be anything from this set: {1, 2, 3, ..., 62, 63}

Unfortunately there isn't enough information to fully pin down what r is.

I would ask your teacher for further clarification.

The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Once we have a sketch of the region ω, we can determine the limits of integration for each variable by looking at the boundaries of the region. We can then change the order of integration by switching the order in which we integrate the variables.

Step 1: Sketch the region ω
To do this, we need the information about the limits of the repeated integral. However, since no specific integral is provided, let's use a general example to illustrate the process. The region ω is typically defined by a set of inequalities that describe the boundaries of the region. These boundaries can be plotted on a graph to give us a visual representation of the region.

Example:
Let's consider a double integral:
∬ ω f(x,y) dy dx, with the limits of integration for y as (g₁(x) ≤ y ≤ g₂(x)), and for x as (a ≤ x ≤ b).

To sketch region ω, we need to plot the bounding curves y = g₁(x), y = g₂(x), x = a, and x = b on a coordinate plane.

Step 2: Change the order of integration
To change the order of integration, we need to express the limits of integration in terms of x.

1. Find the inverse functions of g₁(x) and g₂(x), which are h₁(y) and h₂(y) respectively.
2. Determine the range of y, which will be the new limits of integration for the outer integral.
3. Rewrite the double integral with the new order of integration:
∬ ω f(x,y) dx dy, with the limits of integration for variable x as (h₁(y) ≤ x ≤ h₂(y)), and for y as (c ≤ y ≤ d).

Now, we have successfully sketched the region ω and changed the order of integration for the repeated integral.

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Answer:

It's b

Step-by-step explanation:

It is out of 8. Each circle has 8 sections. A full section would be 8/8 which is = to 1/1. This is because 8 divided by 8 is 1. In the second circle, three out of the 8 are shaded. This would make it 3/8. The / works as "out of". So 3 out of 8. Thus B. is 1 and 3/8

Answer:

The correct answer is B.

Step-by-step explanation:

As you can see one full circle is shaded in. This accounts for the whole number, 1, that we need. In the second image you can see a circle with 8 triangles, three of which are shaded in. This as fraction would look like 3/8.

Add up 1 + 3/8 and you get 1 and 3/8.

Thus, your answer is B.

La esculturas triangulares tendrán las siguientes medidas 16.66 cm, 40 cm y 23.32 cm.

Es la suma total de los lados del triángulo, en este caso el perímetro total es de 80.

Se pueden calcular usando el total y la información sobre cada lado:

Finalmente calcule cada lado:

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Answer:

It's number 12

Step-by-step explanation:

I just did the math.

Conducting a greater number of tosses will provide a better estimate of the true probability based on observed outcomes.

The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

To obtain an experimental probability closer to the theoretical probability, it is recommended to increase the number of trials or repetitions. In this case, the pair of coins was tossed 20 times, resulting in two heads coming up only 2 times. Since the experimental probability is determined by the ratio of favorable outcomes to the total number of trials, increasing the number of trials will help provide a more accurate estimation.

If you want to achieve a closer approximation to the theoretical probability of 0.25, you can increase the number of tosses. For example, you could try tossing the pair of coins 100 times or even 1000 times. By doing so, you would have a larger sample size, and the experimental probability would likely converge towards the theoretical probability of 0.25.

Remember that experimental probability tends to approach theoretical probability as the number of trials increases. Therefore, conducting a greater number of tosses will provide a better estimate of the true probability based on observed outcomes.

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The students who took the survey were concerned about social desirability.

Social desirability bias occurs when research participants provide responses they consider socially acceptable or desirable, rather than accurately representing their true beliefs, attitudes, or behaviors. . In this case, students may be reluctant to admit that they watch a lot of reality TV, believing that it may be viewed negatively by others, and may underestimate their actual reality TV viewing habits.

This leads us to underestimate the true percentage of students who watch more than four hours of reality TV per week.

It is important to note that social desirability bias can be a problem in any kind of survey or research study and can affect the validity and reliability of results. To minimize the effects of desirability bias, researchers can use a variety of techniques, including:  Anonymous surveys, double-blind study designs (where neither the researcher nor the participants know the true purpose of the study), or indirect measures of sensitive behaviors or attitudes

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The value of k(standard deviation) is 9.2649

Eight encoders were given a typing test,

The dataset is 8, 12, 15, 14, 19, 21, 24, 38.

The sample standard deviation is  \(s={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}\)

s=sample standard deviation

N=the number of observations

\(x_i\)=the observed values of a sample item

\(\overline {x}\)=the mean value of the observations

\($$\begin{aligned}& \overline{\mathrm{x}}=\frac{\sum \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}=\frac{8+\ldots+38}{8}=18.875 \\& \mathrm{~s}=\sqrt{\frac{\sum\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2}{\mathrm{n}-1}} \\& \mathrm{~s}=\sqrt{\frac{\left((8-18.875)^2+\ldots \ldots+(38-18.875)^2\right)}{8-1}}=9.2649493\end{aligned}$$\)

Therefore, the sample standard deviation(k) is 9.2649.

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Number of possible ways 5 card poker hands with exactly 3 aces can be dealt from a standard deck of 52 card is 4512

Total number of cards in a standard deck = 52 cards

Number of cards in poker's hand = 5 cards

We need to find the possible ways of 5 card poker hands with exactly 3 aces can be dealt from a standard deck of 52 card.

Here we have to use the combination

Total number of possible ways = 4C3 × 48C2

Expand the terms

= [4! / (4-3)!× 3! ] × [48! / (48-2)!×2!]

= [4! / 1! × 3!] × [48! / 46! × 2!]

= 4 × 1128

= 4512

Therefore, there are 4512 possible ways

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Answer:

\( \dfrac{1}{2} \)

Step-by-step explanation:

we are given a limit

and we want to simplify it

notice that, the numerator is in a sequence of sum of natural number

recall that,

\( \rm \displaystyle \: 1 + 2 + 3 + \dots {\dots }+ n = \frac{n(n + 1)}{2} \)

so substitute:

\(\displaystyle \lim_{n\to \infty } \frac{ \dfrac{n(n + 1)}{2} }{ {n}^{2} } \)

now recall L'Hôpital's rule

\( \displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} \)

first simplify the complex fraction:

\(\displaystyle \lim_{n\to \infty } \frac{n+ 1}{2n} \)

apply L'Hôpital's rule:

\(\displaystyle \lim_{ n\to \infty } \frac{ \dfrac{d}{dn} n+ 1}{ \dfrac{d}{dn} 2n} \)

simplify:

\( \dfrac{1}{2} \)

and we are done:

Step-by-step explanation:

solution given:

The given expression takes a form\( \frac{ \infty }{ \infty } \)

when n=\( \infty \)

so,

\( \displaystyle \lim_{n\to \infty } \frac{1 + 2 + 3 + \dots {\dots} +n }{ {n}^{2} } \)

\( \displaystyle \lim_{n\to \infty }\frac{n(n+1)}{ 2{n}^{2} }\)

\( \displaystyle \lim_{n\to \infty }\frac{n+1}{ 2n}\)

\( \frac{1}{2} \)

\( \displaystyle \lim_{n\to \infty }[1+\frac{1}{ n}]\)

=\( \frac{1}{2} \)(1+\( \frac{1}{ \infty }) \)

=\( \frac{1}{2} \) is your answer

The angle between \(\(\vec{a}\) and \(\vec{b}\) is \(60^\circ\).\)

To find the angle between two vectors\(\(\vec{a}\) and \(\vec{b}\)\), we can use the dot product formula:

\(\(\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos(\theta)\),\)

where \(\(|\vec{a}|\) and \(|\vec{b}|\)\) are the magnitudes of the vectors and\(\(\theta\)\)is the angle between them.

Given that \(\(\vec{a} \cdot \vec{b} = \sqrt{3}\),\) we can rewrite the equation as:

\(\(\sqrt{3} = |\vec{a}| |\vec{b}| \cos(\theta)\).\)

We are also given that \(\(\vec{a} \times \vec{b} = \langle 1, 2, 2 \rangle\),\)which represents the cross product of the vectors.

The magnitude of the cross product is given by:

\(\(|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(\theta)\).\)

Substituting the given values, we have:

\(\(|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(\theta) = |\langle 1, 2, 2 \rangle| = \sqrt{1^2 + 2^2 + 2^2} = \sqrt{9} = 3\).\)

We can rearrange the equation to solve for \(\(|\vec{a}| |\vec{b}| \sin(\theta)\):\(3 = |\vec{a}| |\vec{b}| \sin(\theta)\).\)

Now, we have two equations:

\(\(\sqrt{3} = |\vec{a}| |\vec{b}| \cos(\theta)\),\(3 = |\vec{a}| |\vec{b}| \sin(\theta)\).\)

To eliminate the magnitudes \(\(|\vec{a}|\) and \(|\vec{b}|\)\), we can square both equations and add them together:

\(\((\sqrt{3})^2 + 3^2 = (|\vec{a}| |\vec{b}|)^2 (\cos^2(\theta) + \sin^2(\theta))\)\).

Simplifying, we get:

\(\(3 + 9 = (|\vec{a}| |\vec{b}|)^2\).\(12 = (|\vec{a}| |\vec{b}|)^2\).\)

Taking the square root of both sides:

\(\(\sqrt{12} = |\vec{a}| |\vec{b}|\).\(\sqrt{12} = |\vec{a}| |\vec{b}| = |\vec{a}| |\vec{b}| \sqrt{\cos^2(\theta) + \sin^2(\theta)}\).\)

Since \(\(\cos^2(\theta) + \sin^2(\theta) = 1\)\), we have:

\(\(\sqrt{12} = |\vec{a}| |\vec{b}| \cdot 1\).\(\sqrt{12} = |\vec{a}| |\vec{b}|\).\)

Now, we can substitute this back into the first equation:

\(\(\sqrt{3} = \sqrt{12} \cos(\theta)\).\)

Simplifying, we get:

\(\(\cos(\theta) = \frac{\sqrt{3}}{\sqrt{12}} = \frac{\sqrt{3}}{2\sqrt{3}} = \frac{1}{2}\).\)

To find the angle \(\(\theta\)\), we take the inverse cosine (

arc cosine) of \(\(\frac{1}{2}\):\)

\(\(\theta = \cos^{-1}\left(\frac{1}{2}\right)\).\)

Using the unit circle or trigonometric identities, we find that\(\(\theta = \frac{\pi}{3}\) or \(60^\circ\).\)

Therefore, the angle between \(\(\vec{a}\) and \(\vec{b}\) is \(60^\circ\).\)

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The arc length of the curve x =\(y^4/4 + 1/8y^2\), for 1 <= y <= 5, is approximately 33.93 units.

To find the arc length of the curve, we use the formula for arc length integration. Given the equation x = \(y^4/4 + 1/8y^2\) and the interval 1 <= y <= 5, we want to determine the length of the curve within this range.

First, we differentiate the equation with respect to y to obtain dx/dy. In this case, dx/dy = \(y^3 + 1/4y\). Then, we use the formula for arc length:

L = ∫[a,b] \(\sqrt{(1 + (dx/dy)^2)}\) dy

Plugging in the values from the given interval, a = 1 and b = 5, we integrate the expression \(\sqrt{(1 + (y^3 + 1/4y)^2)}\) with respect to y. Evaluating this integral gives us the arc length of the curve within the specified interval, which is approximately 33.93 units.

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Answer:

80

Step-by-step explanation:

20% of a number is 16 so we can set up the equation like this

0.2n = 16

you then divide each side by 0.2

and you get 80

Answer: 80

Step-by-step explanation:

\(Rate = \frac{Percent}{Base} = \frac{16}{20} = \frac{4}{5} = 0.8 *100=80\)

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Answer:

4x^2-3x

Step-by-step explanation:

3x(2x+5) = 6x^2+15x

2x(x+9) = 2x^2+18x

(6x^2+15x)-(2x^2+18x) = 4x^2-3x

Answer:

11x

Step-by-step explanation:

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The number of different orders of top-three finishers in the free throw contest depends on the total number of participants. The specific number of participants is not provided in the given information.

To determine the number of different orders of top-three finishers, we need to know the total number of participants in the free throw contest. The order of finishers can be calculated using the concept of permutations, where the order matters.

If there are "n" participants, the number of different orders of top-three finishers can be calculated using the formula nP3, which represents the number of permutations of "n" objects taken 3 at a time. However, since the total number of participants is not provided in the given information, we cannot determine the exact number of different orders of top-three finishers.

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