Problem # 1: (10pts) If P(A) = 0.3 and P(B) = 0.2 and P(An B) = 0.1. Determine the following probabilities: a) P(A¹) b) P(AUB) c) P(A'n B) d) P(An B') e) P(AUB') f) P(A' UB)

The features of the function g(x) = f(x + 4) + 8 are:

To analyze the features of the function g(x) = f(x + 4) + 8, we need to consider the effects of each transformation applied to the original function f(x) = log2 x.

Translation: f(x + 4)

This transformation shifts the graph of f(x) horizontally to the left by 4 units. It means that every x-coordinate in f(x) is decreased by 4 units.

Vertical Shift: f(x + 4) + 8

After the horizontal translation, the graph is shifted vertically upward by 8 units. This means that every y-coordinate in f(x + 4) is increased by 8 units.

Based on these transformations, we can identify the features of the function g(x):

Y-intercept: The y-intercept of the function g(x) = f(x + 4) + 8 is (0, 10). This means that the graph intersects the y-axis at the point (0, 10).

Domain: The domain of the function g(x) = f(x + 4) + 8 is (4, ∞). The original function f(x) = log2 x has a domain of (0, ∞), but after the horizontal translation of 4 units to the left, the new domain starts from x = 4.

Range: The range of the function g(x) = f(x + 4) + 8 is (8, ∞). The original function f(x) = log2 x has a range of (-∞, ∞), but after the vertical shift of 8 units upward, the new range starts from y = 8.

Vertical Asymptote: The vertical asymptote of the function g(x) = f(x + 4) + 8 is x = -4. This vertical asymptote is the result of the original function f(x) = log2 x having a vertical asymptote at x = 0. After the horizontal translation of 4 units to the left, the asymptote also shifts 4 units to the left and becomes x = -4.

X-intercept: The x-intercept of the function g(x) = f(x + 4) + 8 is (1, 0).

This means that the graph intersects the x-axis at the point (1, 0).

Learn more about Translation here:

https://brainly.com/question/29712965

#SPJ1

Step-by-step explanation:

LCM of 20 and 40 is 40

So,

60/40+30/40

90/40.... Answer

hope it helps

Answer:

1/2 x 1/5 = 1/10.

Step-by-step explanation:

Answer : fraction of the sheet of paper she use to make the flower is 1/10

To estimate the number of baskets the player can make if he is standing ten feet from the net, we can use the best-fit line or regression line based on the given data.

The best-fit line represents the relationship between the distance from the net and the number of baskets made. Assuming we have the data points plotted on a scatter plot, we can determine the equation of the best-fit line using regression analysis. The equation will have the form y = mx + b, where y represents the number of baskets made, x represents the distance from the net, m represents the slope of the line, and b represents the y-intercept.

Once we have the equation, we can substitute the distance of ten feet into the equation to estimate the number of baskets the player can make. Since the specific data points or the equation of the best-fit line are not provided in the question, it is not possible to determine the exact estimate for the number of baskets made at ten feet. However, if you provide the data or the equation of the best-fit line, I would be able to assist you in making the estimation.

Learn more about data here

https://brainly.com/question/30459199

#SPJ11

Answer:

p=10

Step-by-step explanation:

86+p=96

Subtract 86 from both sides

86+p-86=96-86

Simplify;

p=10

Answer:

\( \sqrt{16} \)

Step-by-step explanation:

If you count the squares diagonally to the other point, you will get 16 units.

Answer:

yes!

Step-by-step explanation:

The images of the coordinates of the quadrilateral are A'(x, y) = (0, 0), B'(x, y) = (2, - 5), C'(x, y) = (- 5, - 5) and D'(x, y) = (- 3, 0). (Correct choice: B)

In this problem we have the coordinates of the four ends of a quadrilateral, whose images must be found by rotation formula:

P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

If we know that A(x, y) = (0, 0), B(x, y) = (5, 2), C(x, y) = (5, - 5), D(x, y) = (0, - 3) and θ = 270°, then the coordinates of the images are, respectively:

A'(x, y) = (0 · cos 270° - 0 · sin 270°, 0 · sin 270° + 0 · cos 270°)

A'(x, y) = (0, 0)

B'(x, y) = (5 · cos 270° - 2 · sin 270°, 5 · sin 270° + 2 · cos 270°)

B'(x, y) = (2, - 5)

C'(x, y) = (5 · cos 270° + 5 · sin 270°, 5 · sin 270° - 5 · cos 270°)

C'(x, y) = (- 5, - 5)

D'(x, y) = (0 · cos 270° + 3 · sin 270°, 0 · sin 270° - 3 · cos 270°)

D'(x, y) = (- 3, 0)

To learn more on rotations: https://brainly.com/question/1571997

#SPJ1

Answer:

x = 9

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + 6² = (\(\sqrt{117}\) )²

x² + 36 = 117 ( subtract 36 from both sides )

x² = 81 ( take square root of both sides )

x = \(\sqrt{81}\) = 9

Regression analysis is a statistical technique used to predict the value of a quantitative variable based on another quantitative variable i.e., the given statement is true.

Regression analysis is widely used when there is an interest in understanding how one quantitative variable, known as the dependent variable or response variable, is influenced by another quantitative variable, known as the independent variable or predictor variable.

The goal is to establish a mathematical relationship between the variables that can be used for prediction and inference.

In regression analysis, a model is built based on the observed data to estimate the relationship between the variables. The model takes into account the variability in the data and provides insights into the strength and direction of the relationship.

By analyzing the model's coefficients, such as the slope and intercept, predictions can be made about the dependent variable's values for different levels of the independent variable.

Regression analysis allows for the assessment of the significance of the relationship, the quantification of the effect of the predictor variable on the response variable, and the estimation of the prediction accuracy.

It provides a valuable tool for making informed decisions, conducting research, and understanding the underlying factors that contribute to the variability of the dependent variable.

Therefore, it is true that regression analysis is useful when predicting the value of a quantitative variable based on another quantitative variable.

Learn more about Regression analysis here:

https://brainly.com/question/31873297

#SPJ11

The radical expression 5√(12 * 50) when simplified is 50√6

Given that

5√(12 * 50)

First, we can simplify the expression inside the square root:

12 and 50 have a common factor of 2:

12 * 50 = 2 * 6 * 5 * 5 * 2 * 5 = 2^2 * 5^2 * 6

So, 5√(12 * 50) becomes:

5√(12 * 50) = 5√(2^2 * 5^2 * 6)

5√(12 * 50) = 5 * 2 * 5 * √6

5√(12 * 50) = 50√6

Therefore, 5√(12 * 50) simplifies to 50√6.

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The measure of the arc XYZ is 210°.

Given is a circle with an inscribed angle XYZ measuring 75°.

We need to find the measure of the arc XYZ,

So, using the Inscribed Angle Theorem.

The Inscribed Angle Theorem states that an inscribed angle in a circle is equal in measure to half the central angle that subtends the same arc.

So,

m arc XZ = 75° x 2 = 150°

Since the whole circle measures 360° so,

m arc XZ + m arc XYZ = 360°

m arc XYZ = 210°

Hence the measure of the arc XYZ is 210°.

Learn more about arcs click;

https://brainly.com/question/31612770

#SPJ1

The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).

What is Translation of graph?

A graph can be horizontally translated by moving the base graph to the left or right in relation to the x-axis. Each point on a graph is moved by k units in order to translate it horizontally.

To graph triangle LMN and its image after the composition of a 90 degree rotation about the origin and a translation of (x, y) (x-3, y+2), we can first plot the vertices of triangle LMN on the coordinate plane.

pair L = (1,6);

pair M = (-2,4);

pair N = (3,2);

Next, we can apply the 90 degree rotation about the origin to the vertices of the triangle. The rotation matrix for a 90 degree rotation about the origin is given by:

[cos(90) -sin(90)][x] [y]

[sin(90) cos(90)][y] = [-x]

Substituting the coordinates of the vertices into the rotation matrix, we get:

[cos(90) -sin(90)][1] [6]

[sin(90) cos(90)][-2] = [4]

[3] [2]

Therefore, the image of triangle LMN after the rotation is triangle L'M'N' with vertices L'(-6,1), M'(4,-2), and N'(-2,3).

Finally, we can apply the translation of (x, y) (x-3, y+2) to the vertices of the rotated triangle to get the final image of triangle LMN. The translation matrix is given by:

       \([1 \ 0][x] [y][-3 \ 2][y] = [x-3]\)

Substituting the coordinates of the rotated vertices into the translation matrix, we get:

[1 0][-6] [1]

[-3 2][4] = [-1]

[-2] [3]

Therefore, The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).

To know more about Translation of graph visit,

https://brainly.com/question/26238840

#SPJ1

Step-by-step explanation:

we know that midpoint of a segment is found from formula

x=(x1+x2)/2

and y=(y1+y2)/2

in this case x=3 and y=4 x2=-1 and y2=2

so x1=2x-x2 =2*3-(-1)=6+1=7

y1=2y-y2=2*4-2=8-2=6

the other endpoint is (7,6)

Answer:

2 distance

Step-by-step explanation:

you solve it and see it's easy know first try I will do it

The value of x for the given triangle is x = 7.4.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that the angle is 33 and the adjacent side is x and the hypotenuse is 8.8.

The measure of value x will be calculated below,

\(\cos(33)^\circ=\dfrac{\text{Adjacent}}{\text{Hypotenuse}}\)

\(\cos(33)^\circ=\dfrac{\text{x}}{8.8}\)

Multiply the value by 8.8 by cos(33) and solve for x,

\(\text{x}=\cos(33)^\circ\times8.8\)

\(\text{x}=7.380\)

\(\bold{x=7.4}\)

Therefore, the value of x will be 7.4.

To know more about trigonometric functions, visit:

https://brainly.com/question/31425947

Answer:

slope = -3

Step-by-step explanation:

Hope this helps! Have a great day!

The slope of the parent function f(x) determines how steep the line is at any given point on the graph.

The slope is defined as the change in y divided by the change in x, or the rise over run. The parent function is a basic or fundamental function that is used as a starting point for creating more complex functions.

In general, the slope of the parent function is constant, meaning it does not change as x increases or decreases. However, the slope of any transformed function, or function that has been shifted or stretched, will be different.

Understanding the slope of the parent function is important in calculus and other mathematical applications, as it helps determine rates of change and other important variables.

To know more about Parent function visit:

https://brainly.com/question/17939507

#SPJ11

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

Learn more about probability on:

https://brainly.com/question/23417919

Given:

Height of the tree

To find the height of the tree, we use ratio/proportion.

So, we let x be the height of the tree and use the formula:

Height of man/length of man's shadow = x/length of the tree's shadow

Therefore ,the height of the tree is 20 ft.

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

Learn more about graph from

https://brainly.com/question/19040584

#SPJ11

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

To learn more about derivative, click here: brainly.com/question/23819325

#SPJ11

Step-by-step explanation:

LHS= 1 + cot^2A/1+cosecA

=(1+cosecA + cot^2A)/1+cosecA

{By using basic trigonometric theorem cot^2A = cosec^2A - 1}

=(1+cosecA + cosec^2A - 1)/(1+cosecA)

=(cosecA + cosec^2A)/(1+cosecA)

=[cosecA (1+cosecA)]/(1+cosecA)

{Cancelling 1+cosecA}

=cosecA

The best choice for making a profit will be making 80 pies and selling them for $10 each. The total earning will be $800.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that when you made 160 pies, you sold them all at $6 per pie. When you made 80 pies, you sold them all for $10 each. Your principal has allowed you to use the school cafeteria kitchen for a one-time, non-refundable fee of $300, and the ingredients for each pie cost $2.

The profit when 160 pies are made:-

Investment = 300 + 2 = $302

Cost of one pie = 302 / 160 = $1.88

The selling price of one pie = $6

Profit = $6 - $1.88 = $4.12

The profit when 80 pies are made:-

Investment = 300 + 2 = $302

Cost of one pie = 302 / 80 = $3.775

The selling price of one pie = $10

Profit = $10 - $3.775 = $6.225

Here we can see he can earn $6.225 on each pie.

The total earning would be:-

Earning = 6.225 x 80

Earning = $498

To know more about an expression follow

https://brainly.com/question/11434706

#SPJ1

Answer:

Step-by-step explanation#1

Answer:

B. 38

Step-by-step explanation:

Area of the trapezoid = 48

Area of the triangle = 10

Subtract the triangle area 48 - 10 = 38

The top line tells you this two figure is similar.

What does this mean? Similar figures have the exact same corresponding angles and proportionate sides.

You can find their side ratio with 38 and 15.2.

38 ÷ 15.2 = 2.5

To find x, use 55 ÷ 2.5 and you get 22 as your answer.

The gap is approximately 259,854.9 inches wide.

What is the circumference of a circle?

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.

The Earth's equator has a circumference of about 24,901 miles. The new circular band has a circumference of 25,036 inches.

When the steel band was cut and spliced, it increased the circumference by 36 inches. Since the circumference is directly related to the diameter, the new band is also larger in diameter than the original band.

We can use this increase in circumference to find the increase in diameter:

25,036 inches / 2π = 3957.1 inches

24,901 miles * 12 inches/mile = 298,812 inches

The gap is the difference between the two diameters:

298,812 inches - 3957.1 inches = 259,854.9 inches

Hence, The gap is approximately 259,854.9 inches wide.

To learn more about the circumference of a circle visit,

https://brainly.com/question/18571680

#SPJ1

Answer:

+24

Step-by-step explanation: