What are the domain and the range of this function ?

D: _ _ X _ _

R: _ _ Y _ _

Answer:

\(\huge\boxed{y=\dfrac{4}{3}x-1}\)

Step-by-step explanation:

Let

\(k:y=m_1x+b_1\\l:y=m_2x+b_2\)

then

\(k\perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2\)

==========================================

We have:

\(y=-\dfrac{3}{4}x-3\to m_1=-\dfrac{3}{4}\)

Let

\(y=m_2x+b_2\)

Therefore

\(m_2=-\dfrac{1}{-\frac{3}{4}}=\dfrac{4}{3}\Rightarrow y=\dfrac{4}{3}x+b_2\)

Substitute

\((0,\ -1)\to x=0;\ y=-1\)

\(-1=\dfrac{4}{3}\cdot0+b_2\\\\b_2=-1\)

The mass of the solid Q of density rho = k is k(8π/√e).

To find the mass of the solid Q with density rho, we can use the triple integral formula in cylindrical coordinates. The density function rho is given as a constant k, which means it is independent of the coordinates. Therefore, the mass of Q is simply the product of its volume and density.

First, we need to determine the limits of integration in cylindrical coordinates. Since the solid Q is defined in terms of x, y, and z, we need to express these variables in terms of cylindrical coordinates.

In cylindrical coordinates, x = r cos(theta), y = r sin(theta), and z = z. Also, the condition x2 + y2 ≤ 16 corresponds to the cylinder of radius 4 in the xy-plane.

Thus, the limits of integration become:
0 ≤ z ≤ 8e^(-r^2)
0 ≤ r ≤ 4
0 ≤ theta ≤ π/2

Now, we can set up the integral to find the volume of Q:
V = ∭Q dV = ∫₀²π ∫₀⁴ ∫₀^(8e^(-r^2)) r dz dr dθ

Evaluating this integral, we get V = 8π/√e. Therefore, the mass of Q is:
M = ρV = kV = k(8π/√e).

The mass of the solid Q of density rho = k is k(8π/√e).

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Answer: D. Vertical

Step-by-step explanation:

Answer:

-3, -3

Step-by-step explanation:

Answer:

$29.70

Step-by-step explanation:

1. First, we have to find how much 10% of 33 is!

2. Okay, now that we know 3.3 is 10% of 33, we need to subtract 3.3 from 33 to get the amount Jen will pay for the dress.

Therefore, Jen will pay $29.70 for the dress.

Answer:

$29.70

Step-by-step explanation:

So, 10% of 33, which= 3.3

33- 3.3= 29.70

The expected value for a student to spend on lunch each day from the survey of 50 students is $5.18.

The expected value for a student to spend on lunch each day is derived from the survey of 50 students. This value is calculated by taking the total number of dollars spent by all of the surveyed students and dividing it by the total number of students surveyed. In this particular survey, the total number of dollars spent was $247, and the total number of students surveyed was 50. Dividing $247 by 50 gives us a value of $4.94. This value is then rounded up to the nearest cent to give us the expected value of $5.18. This expected value is the average amount of money that a student can expect to spend on lunch each day from the survey. It is important to note that this value is an estimate, as individual student spending habits may vary greatly.

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The squares represent a visual representation of equivalent fractions. Each square is divided into a certain number of equal parts, and the number of parts that are shaded in represents the numerator of the fraction. The total number of parts the square is divided into represents the denominator of the fraction.

In the first square, it is divided into 23 equal parts and 8 of them are shaded in. Therefore, the fraction represented by that square is 8/23.

In the second square, it is divided into 812 equal parts and 23 of them are shaded in. Therefore, the fraction represented by that square is 23/812. Since both squares are divided into the same number of equal parts, the fractions 8/23 and 23/812 represent the same quantity, just in different forms. Therefore, they are equivalent fractions.

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To test the researcher’s claim that on average high school students sleep less than middle school students, a two-sample t-test can be used.

Standard deviations are a measure of how spread out data points are from the mean. It is a measure of variability that is used to describe the distribution of data around the mean. Standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. It is used in statistical analysis to measure the spread of data points in relation to the mean.

The two-sample t-test tests the difference in means between two independent samples. The null hypothesis for the test states that the means of the two groups are the same, while the alternative hypothesis states that the means of the two groups are not the same.

To perform the two-sample t-test at the 5% level of significance, first the data needs to be organized into a two-sample t-test format. The mean and standard deviation of the middle school students is 7 hours and 0.2, respectively, and the mean and standard deviation of the high school students is 7.9 hours and 5, respectively.

Next, the two-sample t-test is conducted using a calculator or a computer program. The test statistic is calculated from the sample means, sample sizes, and standard deviations of the two groups. The p-value is calculated from the test statistic and degrees of freedom. If the p-value is below the 5% level of significance, then the null hypothesis is rejected and the alternative hypothesis is accepted.

In this example, the p-value of the two-sample t-test is 0.0007, which is below the 5% level of significance. This means that the null hypothesis can be rejected and the alternative hypothesis can be accepted, indicating that on average high school students sleep less than middle school students.

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Answer:

given a regular polygon which means that it's all sides are equal and all angles are equal

one angel of a polygon is 3x

the sum of all the angles of a polygon = 360°

3x + 3x + 3x + 3x + 3x + 3x = 360°

18x = 360°

x = 20°

Answer:

both numbers are negative

negative number is greater than the positive number

Step-by-step explanation:

In order to add two rational numbers and get a negative value, one of two scenarios should occur:

1- both numbers are negative.

2- negative number is greater than the positive number

The situation represents a function and the domain and range will be [0, 8] and [0, 56].

From the information, the drive-in movie theater charges $7 per person and your vehicle can hold a maximum of eight people.

It should be noted that the appropriate function will be:

y = 7x

To fund the domain, we simony have to solve the equation for f(x( to determine the independent variable. In this case, the vehicle can have 8 people. The domain will be [0, 8].

The range will be:

[0, (7 × 8)]

= [0, 56].

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Answer:

x = -2/3

Step-by-step explanation:

27^x=1/9

writing 27 as 3^3  and 1/9 as 3 ^-2

3^3^x = 3^-2

We know that a^b^c =a^(b*c)

3^(3x) = 3^-2

Since the bases are the same the exponents need to be the same

3x = -2

x = -2/3

The expected return is 13.90%, standard deviation is 21.90%, and coefficient of variation is 157.17%

The formulas for expected return, standard deviation and coefficient of variation (CV) are:

Expected return = Σ (pi * ri)

where pi is the probability of occurrence of return ri.

Standard deviation = √ [Σ pi * (ri - E (r))^2]

where E (r) is the expected return of an investment.

CV = (standard deviation / expected return) x 100

To calculate the standard deviation of the returns provided in the table above:

We first need to calculate the variance.

The formula for variance is:

Variance = Σ pi * (ri - E (r))^2

Substituting the given values, we have:

Variance = (0.1 * (0.30 - 0.139)^2) + (0.1 * (0.14 - 0.139)^2) + (0.3 * (0.11 - 0.139)^2) + (0.3 * (0.20 - 0.139)^2) + (0.2 * (0.45 - 0.139)^2)

= 0.047769

Then, the standard deviation is the square root of variance:

Standard deviation = √0.047769

                                = 0.2185612 or 21.90%

Finally, the coefficient of variation (CV) can be calculated as follows:

CV = (0.2185612 / 0.139) x 100

     = 157.17% (rounded to two decimal places)

Therefore, the expected return is 13.90%, standard deviation is 21.90%, and coefficient of variation is 157.17%

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Answer:

exponent of x is 33

exponent of y is 0

Step-by-step explanation:

you need to combine all powers (exponents) of x, and all exponents of y separately.

remember : x to the power of a divided by x to the power of b is x to the power of (a-b).

when multiplying, the "-" turns into a "+".

so, we have actually for x the exponent calculation :

8 - 14 -(-39) = 8 - 14 + 39 = 33

so, x³³ remains.

and for the y exponents

-26 -(-5) -(-21) = -26 + 5 + 21 = 0

so, all the y expressions eliminate each other and y⁰ remains.

The correct answer is option B which is (-4-√11) and (-4+√11).

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).

(-4 - √11)  = -4 -3.31 =-7.31

(-4 + √11) = -4 +3.31 = -0.68

Therefore the correct answer is option B which is (-4-√11) and (-4+√11).

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Answer:

5 hours and 2 minutes?

Step-by-step explanation:

5,10,15,20,25 + the two=27

Answer: 3 hours

Step-by-step explanation: First you add the one time fee to the first hour. Which you get $17. Then you keep adding $5 until you get $27

Answer:

By adding the gravity of the earth ang subtracting the number of the enumeration and multiply the square root of need to be the first divorcee you know that I love ckicen nuggets

Step-by-step explanation:

Me to mama o sige na kain na kau

Answer:

sum of terms: 55550

Explanation:

\(\sf S_n = \dfrac{n}{2} (u_{start}+u_{end}})\)

Here the number of terms:

1100 ÷ 11 = 100

Using the Formula:

\(\sf \dfrac{100}{2} (11+1100)\)

\(\sf 55550\)

We can evaluate the given iterated integral to be -πcos2(x) (z - 0 ).

We start with the innermost integral: 0 √1 − z2 0 z sin(x) dy. We can simplify this expression to 0  sin(x) ( √1 − z2  - 0 ). We then integrate this expression with respect to y, yielding sin2(x).

Next, we move on to the middle integral, which is sin2(x) dz. We can easily integrate this expression with respect to z and get sin2(x) (z - 0 ).

Finally, we take the outermost integral, which is sin2(x) (z - 0 ) dx. We can integrate this expression with respect to x and get -cos2(x) (z - 0 ).

Putting everything together, we can evaluate the given iterated integral to be -πcos2(x) (z - 0 ).

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The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm

The density of an object is the ratio of the mass of the object to its volume. Mathematically;

Density = mass/volume

Given the following

Mass of block = 82.8grams

Density = 0.69g/cm^3

volume = lwh
Volume = 20h

Substitute

0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120

h = 6cm

Hence the height of the block of sugar maple is 6cm

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6cm

Step-by-step explanation i can confirm that the answer is 6 ;}

To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

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After considering the given data we conclude that the value of \(x^2 dV\) in cylindrical coordinates is \((16/5) \pi.\)

To evaluate \(x^2 dV\) in cylindrical coordinates, where E is the solid that lies within the cylinder
\(x^2 + y^2 = 9,\)
above the plane z = 0, and below the cone \(z^2 = 9x^2 + 9y^2,\) we can use the following steps:
Express the solid E in cylindrical coordinates. Since the cylinder \(x^2 + y^2 = 9\) is symmetric about the z-axis, we can use cylindrical coordinates (r, \(\theta\), z) to describe the solid.
The cylinder has a radius of 3 in the xy-plane, so we have 0 <= r <= 3. The cone \(z^2 = 9x^2 + 9y^2\) can be expressed in cylindrical coordinates as \(r^2 = 9\), or r = 3. Therefore, the solid E can be described as \(0 < = r < = 3, 0 < = \theta < = 2\pi, and 0 < = z < = \sqrt(9 - r^2).\)
Express \(x^2\) in terms of cylindrical coordinates. Since \(x = r cos(\theta)\), we have \(x^2 = r^2 cos^2(\theta).\)
Express dV in terms of cylindrical coordinates. In cylindrical coordinates, we have \(dV = r dz dr d\theta.\)
Evaluate the integral \(x^2\) dV over the solid E. Substituting the expressions for \(x^2\) and dV, we get:
\(x^2 dV = r^4 cos^2(\theta) dz dr d\theta\)
Integrating over the limits of z, r, and\(\theta\), we get:
\(\int\int\int x^2 dV = \int 0^3 \int 0^2\pi \int 0^{\sqrt(9 - r^2) r^4} cos^2(\theta) dz dr d\theta\)
Integrating with respect to z, we get:
\(\int \int \int x^2 dV = \int 0^3 \int 0^2\pi r^4 cos^2(\theta) \sqrt(9 - r^2) dr d\theta\)
Integrating with respect to r, we can use the substitution \(u = 9 - r^2\), du = -2r dr, to get:
\(\int \int \int x^2 dV = \int 0^3 \int 0^2\pi (9 - u)^{(3/2)} cos^2(\theta) du d\theta\)
Integrating with respect to u, we can use the substitution v = 9 - u, dv = -du, to get:
\(\int \int \int x^2 dV = \int 0^3 \int 0^2\pi v^{(3/2)} cos^2(\theta) dv d\theta\)
Integrating with respect to \theta, we get:
\(\int \int \int x^2 dV = 2\pi \int 0^3 v^{(3/2)} cos^2(\theta) dv\)
Integrating with respect to v, we get:
\(\int \int \int x^2 dV = (16/5) \pi\)
Therefore, the value of \(x^2 dV\)in cylindrical coordinates is \((16/5) \pi.\)
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The lateral surface area of the can is approximately 2962.76 cm².

The lateral surface area (CSA) of a cylindrical can with a hemispherical lid can be calculated as follows:

CSA = 2πrh + πr²

Where:

r is the radius of the cylindrical part of the can

h is the height of the cylindrical part of the can

We know the height of the cylindrical part is 27 cm and the diameter of the hemispherical lid is 20 cm, so the radius is half the diameter or 10 cm.

So, the lateral surface area of the cylindrical part is:

CSA = 2πr × h = 2 × π × 10 ×:27 = 540 π cm²

And the surface area of the hemispherical lid is:

CSA = 4π × r² = 4 × π × 10² = 400π cm²

Therefore, the total lateral surface area of the can is:

CSA = 540π + 400π = 940π cm²

So the answer is approximately 2962.76 cm².

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The standard deviation of a beta distribution is calculated using the formula \(\(\sigma = \sqrt{\frac{\alpha \cdot \beta}{(\alpha + \beta)^2 \cdot (\alpha + \beta + 1)}}\),\) where \(\(\alpha\)\) and \(\(\beta\)\) are the parameters defining the shape of the distribution. It does not involve multiplying the sigma value by any fixed factor.

When calculating the standard deviation of a beta distribution, the denominator of the formula is not directly related to the sigma (standard deviation) parameter.

The standard deviation of a beta distribution depends on the alpha and beta parameters, which define the shape of the distribution.

The formula for the standard deviation of a beta distribution is:

\(\[ \sigma = \sqrt{\frac{\alpha \cdot \beta}{(\alpha + \beta)^2 \cdot (\alpha + \beta + 1)}} \]\)

Here, the standard deviation \((\(\sigma\))\) is calculated using the alpha and beta parameters of the beta distribution. It does not involve multiplying the sigma value by any particular factor or using a fixed denominator.

The denominator in the formula for the standard deviation of a beta distribution involves the alpha and beta parameters, which determine the shape and spread of the distribution.

It does not directly relate to the sigma value or involve multiplying sigma by a fixed factor.

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If 96 people divide into groups of eight, the following expression indicates that 12 groups are created.

Eight persons form groups made up of multiple people. a expression for how many groups made up of p people there are.

P = the number of groups.

12 groups out of 96

If there are 96 individuals, 12 groups are created.

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You need to adjust the tube of the microscope to 6.83cm in order to view the sample in focus with a completely relaxed eye

Given, Focal length of the eyepiece,  = 2.50 cm

The focal length of the converging lens, f = 1.00 cm

The distance of the object, p = 1.30 cm

Lens equation, \(\frac{1}{f} = \frac{1}{p} + \frac{1}{q}\)

Substitute the values in the above equation

\(\frac{1}{1.00} = \frac{1}{1.30} + \frac{1}{q}\)

q = 4.33 cm

now, the image is formed at the focal point of the eyepiece,

therefore, the distance between the objective and the eyepiece, d =  + q = 2.50 cm + 4.33 cm

d = 6.83 cm

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