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The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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Answer:

Step-by-step explanation:

The quadratic formula is y=ax^2+bx+c

If we move everything to the left side of the equation,

-6x^2=-9x+7 becomes

-6x^2+9x-7=0

a=-6, b=9, c=-7, so the third answer choice

Answer:

try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is

The data set has two outliers, namely the points (2, 225) and (8, 75).

Based on the given information about the scatterplot, we can observe that most of the points are grouped closely together and show a slight increase.

There are two points that lie outside of this cluster, specifically (2, 225) and (8, 75).

To determine if these points are outliers, we need to consider their deviation from the general pattern exhibited by the majority of the data points.

If these points deviate significantly from the overall trend, they can be considered outliers.

In this case, since (2, 225) and (8, 75) lie outside of the cluster of closely grouped points and do not follow the general pattern, they can be considered outliers.

These points are noticeably different from the majority of the data points and may have influenced the overall trend of the scatterplot.

The data set has two outliers, namely the points (2, 225) and (8, 75).

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Answer:

Step-by-step explanation:

This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?

Answer:

W = V/(LH)

Step-by-step explanation:

All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation

The linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].

In a linear equation, the y-intercept is where the line crosses the y-axis.

It is represented by the constant term in the equation.

So, to determine which linear function has the greatest y-intercept, we need to look at the constant term of each equation.

Let's consider each equation: [tex]y = 6x + 1[/tex]

The constant term in this equation is 1.

So, the y-intercept is 1.

On a coordinate plane, a line goes through points (0, 2) and (5, 0).

To find the equation of this line, we can use the point-slope form:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is a point on the line.

Using the points (0, 2) and (5, 0), we get:

[tex]m = \frac{(0 - 2)}{(5 - 0)} =-\frac{2}{5}[/tex]

So, the equation of the line is:

[tex]y - 2 = (\frac{-2}{5} )(x - 0)[/tex]

[tex]y = (\frac{-2}{5} )x + 2[/tex]

The constant term in this equation is 2.

So, the y-intercept is 2.

On a coordinate plane, a line goes through points (1, 2) and (0, -3).

To find the equation of this line, we can use the point-slope form:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is a point on the line.

Using the points (1, 2) and (0, -3), we get:

[tex]m = \frac{ (-3 - 2) }{(0 - 1)} = -5[/tex]

So, the equation of the line is:

[tex]y - 2 = (-5)(x - 1)y = -5x + 7[/tex]

The constant term in this equation is 7.

So, the y-intercept is 7.

[tex]y = 3x + 4[/tex]

The constant term in this equation is 4.

So, the y-intercept is 4.

Therefore, we can see that the linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].

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Answer:

Step-by-step explanation:

The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.

In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;

y = 3.01x + 89.63

Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;

y = 3.01x + 89.63

y = 3.01(24.5) + 89.63

y = 163.375 ≈ 163.38 centimeters.

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Combining the results of a given triangle, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.

To find the value of 'x' in a triangle with side lengths 'x', 37, and 15, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, we have:

x + 37 > 15 (Sum of x and 37 is greater than 15)

x + 15 > 37 (Sum of x and 15 is greater than 37)

37 + 15 > x (Sum of 37 and 15 is greater than x)

From the first inequality, we can subtract 37 from both sides:

x > 15 - 37

x > -22

From the second inequality, we can subtract 15 from both sides:

x > 37 - 15

x > 22

From the third inequality, we can subtract 15 from both sides:

52 > x

Combining the results, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.

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Answer:

Part A:

The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:

A. 100 - 2 × (22 - 19)

Part B:

To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.

If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.

Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.

Yes, she has enough pencils to give each of her students 2.

She has 18 more than she needs.

Answer:

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis, we can use the method of cylindrical shells.

The formula for the volume of a solid obtained by rotating a region bounded by the graph of a function f(x), the x-axis, x = a, and x = b about the y-axis is given by:

V = 2π ∫[a, b] x * f(x) dx

In this case, the function f(x) = (x - 4)^3, and the bounds of integration are a = 0 and b = 5.

Substituting these values into the formula, we have:

V = 2π ∫[0, 5] x * (x - 4)^3 dx

To evaluate this integral, we can expand the cubic term and then integrate:

V = 2π ∫[0, 5] x * (x^3 - 12x^2 + 48x - 64) dx

V = 2π ∫[0, 5] (x^4 - 12x^3 + 48x^2 - 64x) dx

Integrating each term separately:

V = 2π [1/5 x^5 - 3x^4 + 16x^3 - 32x^2] evaluated from 0 to 5

Now we can substitute the bounds of integration:

V = 2π [(1/5 * 5^5 - 3 * 5^4 + 16 * 5^3 - 32 * 5^2) - (1/5 * 0^5 - 3 * 0^4 + 16 * 0^3 - 32 * 0^2)]

Simplifying:

V = 2π [(1/5 * 3125) - 0]

V = 2π * (625/5)

V = 2π * 125

V = 250π

Therefore, the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis is 250π cubic units.

Answer:

Where lines cross over each other. The lines have a common point.

Answer:

[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

[tex]\cos(105\°)[/tex]

Using the angle sum identity for cosine.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]

Now applying the identity.

[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]

Now utilizing the unit circle.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]

[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]

Now simplifying...

[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]

The given statement "An event with probability 3/4 is more likely to happen than an event with probability 4/5" is true.

The reason why we say an event with a higher probability is more likely to happen is because probability is the measure of how often an event will occur during a large number of trials.

Therefore, when we compare the probabilities of two events, we can expect that the one with the higher probability will occur more often and therefore is more likely to happen.For instance, in the context of a coin flip, the probability of getting heads is 1/2 while the probability of getting tails is also 1/2.

Therefore, both events are equally likely to happen. On the other hand, if we were to compare the probability of rolling a six-sided die and getting a 1, which has a probability of 1/6, with the probability of rolling the die and getting a number less than or equal to 4, which has a probability of 4/6 or 2/3, we can say that the latter is more likely to happen since it has a higher probability.

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[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]

Sum up ;

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]

So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years

Answer:

Sydney= 20, Devaughn= 60

Step-by-step explanation:

Let Sydney's age be 'x'

Devaughn's age = 3 times x = 3x

We Know That

The sum of their ages is 80.

So,

3x + x = 80

4x = 80

If we shift the 4 to the 80 side

x = 80/4

x = 20

So, Sydney's age is 20

Therefore, Devaughn's age =

3x = 3 times x

= 3 times 20

= 60

HI Your answer is 42

I have calculated it you can trust me

Well you have marked right in the pic

PLEASE MARK AS BRAINLIEST

The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.

The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).

In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:

g(x) = f(x) + c

In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).

It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).

Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

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Answer: 3

Step-by-step explanation: just 3

Edge 2020

The best measure of center of the data is (a) mean; because the data are close together

From the question, we have the dataset of 10 values

In the given dataset, we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

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Answer:

Step-by-step explanation:

The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.

We have,

The monthly basic salary of the married Chief Secretary of Nepal Government is given as Rs 74,000.

This is the fixed amount he receives as his base salary every month, before any additional allowances or deductions are considered.

Now,

In this case, the dearness allowance of Rs 2,000 is added to the basic salary.

This allowance is provided to compensate for the rising cost of living and is a fixed amount added to the basic salary.

Additionally, he receives 1 month's basic salary as a festival allowance. Since his monthly basic salary is Rs 74,000, his festival allowance would also be Rs 74,000.

Therefore, his total monthly salary can be calculated as follows:

Basic salary + Dearness allowance + Festival allowance

= Rs 74,000 + Rs 2,000 + Rs 74,000

= Rs 1,50,000

Thus,

The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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Answer:

5) tan A = 0.42

6) Acute angle is less than 90°

7) Right angle is exactly 90°

8) Obtuse angle is greater than 90° but less than 180°

9) Straight angle is exactly 180°

10) Complementary angles add up to 90°

11) Supplementary angles add up to 180°

Step-by-step explanation:

tan A = opposite / adjacent

= 5/12

= 0.42

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

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The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.

To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:

10f - 5f + 8 + 6g + 4

Combining the terms with 'f', we have:

(10f - 5f) + 8 + 6g + 4

This simplifies to:

5f + 8 + 6g + 4

Next, we can combine the constant terms:

8 + 4 = 12

Thus, the simplified expression is:

5f + 12 + 6g

This expression is equivalent to 10f - 5f + 8 + 6g + 4.

In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.

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Answer:

(-4,4)

Step-by-step explanation:

You rewrite the terms:

(x + 4)^2 => [x - (-4)]^2

(y - 4)^2 => [y - (4)]^2

so h = -4 and k = 4

so center of ellipse is (h,k) or (-4,4)

Answer:

Center = (-4, 4)

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h, k) is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

The given equation is:

[tex]\dfrac{(x+4)^2}{25}+\dfrac{(y-4)^2}{9}=1[/tex]

Comparing the given equation with the standard form, we can see that h = -4 and k = 4. Therefore, the center (h, k) of the ellipse is (-4, 4).

Answer:

Step Reason

∠NYR and ∠RYA form a linear pair

∠AXY and ∠AXZ form a linear pair Given

∠RYA≅∠AXY Given

∠NYR and ∠RYA are supplementary Definition of Linear Pair

If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair

∠NYR and ∠AXY are supplementary Transitive Property of Equality

m∠NYR+m∠RYA=180

m∠AXY+m∠AXZ=180 Definition of Supplementary Angles

m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality

m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality

m∠RYA=m∠AXZ Subtraction Property of Equality

∠NYR and ∠AXY are supplementary Definition of Supplementary Angles

m∠NYR+m∠AXY=180

m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality

m∠RYA=m∠AXY Subtraction Property of Equality

∠NYR≅∠AXY Definition of Congruent Angles.

Answer:

i believe by creating radii of equal lengths.

Step-by-step explanation:

it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.

Wish you good luck.