What is the probability that both events will occur? Two dice are tossed. Event A: the first die is a 5 or 6. Event B: The second die is not a 1

The arc length of arc AB is approximately 8.3076π units.

To find the arc length of arc AB, we need to know the angle subtended by the arc and the radius of the circle. In this case, we are given that angle AB is 115 degrees and the radius BC is 13 units.

The formula for the arc length (L) of a circle is given by L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius of the circle.

Substituting the given values into the formula, we have:

L = (115/360) × 2π(13)

Simplifying this expression:

L = (0.3194) × 2π(13)

L ≈ 0.3194 × 26π

L ≈ 8.3076π

So, the arc length of arc AB is approximately 8.3076π units.

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The solutions to the equation 8x^3 - 1 = 0 are x = 1/2, x = (-2 + 2√2i)/8, and x = (-2 - 2√2i)/8.None of the given Values is NOT a solution of the equation.

The solution(s) of the equation 8x^3 - 1 = 0, we need to determine the values of x that satisfy the equation. We can solve this equation by setting it equal to zero and factoring:

8x^3 - 1 = 0

(2x)^3 - 1^3 = 0

(2x - 1)(4x^2 + 2x + 1) = 0

Now we can find the values of x that make each factor equal to zero:

2x - 1 = 0

x = 1/2

4x^2 + 2x + 1 = 0

Using the quadratic formula, we can solve for x and find two additional solutions:

x = (-2 ± √(-8))/8

x = (-2 ± 2√2i)/8

Therefore, the solutions to the equation 8x^3 - 1 = 0 are x = 1/2, x = (-2 + 2√2i)/8, and x = (-2 - 2√2i)/8.None of the given values is NOT a solution of the equation.

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Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer: Answer in explanation

Step-by-step explanation:

Based on the info you've given me I would say this:

t = time in years

P = principle (starting value)

r = rate (decimal value)

Length of the base of the building from the wall is, 1.68 m

We have to given that;

A ladder 8 m long leans against the wall of a building.

And, the foot of the ladder makes an angle of 78 degrees with the ground.

Now, We know that;

cos x = Base / Hypotenuse

Here, Hypotenuse = 8 m

And, Length of the base of the building from the wall = Base = x

Hence, We get;

cos 78 = x / 8

0.21 = x / 8

x = 0.21  x 8

x = 1.68 m

Thus, Length of the base of the building from the wall is, 1.68 m

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Answer:

8750

Step-by-step explanation:

It  had started at (0,120) and ran for 40 minutes, Coordinates would be approximately (60.00, 103.92).

a) To find the coordinates after 20 minutes of running counter-clockwise starting at (120,0), we need to determine the distance covered in that time period.

Since you are running at a speed of 3 meters per second, in 20 minutes (or 20 * 60 = 1200 seconds), you would have covered a distance of 3 * 1200 = 3600 meters.

Given that the equation of the circular track is x^2 + y^2 = 14400, which represents a circle with a radius of 120 units (since the radius squared is 14400), we can determine your new position on the track.

Starting from (120,0) and moving counter-clockwise, you would have traveled a distance of 3600 meters along the circumference of the circle. This corresponds to a fraction of 3600 / (2 * π * 120) = 15 / π of the circle's circumference.

Using this fraction, we can calculate the angle in radians by multiplying it by 2π. Therefore, the angle is 2π * (15 / π) = 30 radians.

To find the new coordinates, we can use the polar coordinates formula:

x = r * cos(θ)

y = r * sin(θ)

Plugging in the values:

x = 120 * cos(30) ≈ 103.92

y = 120 * sin(30) ≈ 60.00

So, after 20 minutes of running counter-clockwise, your coordinates would be approximately (103.92, 60.00).

b) If you had started at (0,120) and ran for 40 minutes, the process is similar. Since you are running at a speed of 3 meters per second, in 40 minutes (or 40 * 60 = 2400 seconds), you would have covered a distance of 3 * 2400 = 7200 meters.

Using the same circle equation x^2 + y^2 = 14400, we determine the new position on the track.

Starting from (0,120) and moving counter-clockwise, you would have traveled a distance of 7200 meters along the circumference of the circle. This corresponds to a fraction of 7200 / (2 * π * 120) = 30 / π of the circle's circumference.

The angle in radians is given by 2π * (30 / π) = 60 radians.

Using the polar coordinates formula:

x = r * cos(θ)

y = r * sin(θ)

Plugging in the values:

x = 120 * cos(60) ≈ 60.00

y = 120 * sin(60) ≈ 103.92

So, if you had started at (0,120) and ran for 40 minutes, your coordinates would be approximately (60.00, 103.92).

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The first quartile is 19, the second quartile (median) is 25, and the third quartile is 39 for the given data set A.

We have,

To find the first quartile, second quartile (which is also the median), and third quartile of a data set, we need to arrange the data in ascending order first.

Arranging the data set A = {15, 19, 23, 25, 37, 39, 43} in ascending order:

15, 19, 23, 25, 37, 39, 43

First, let's find the second quartile (median):

Since there are 7 data points, the median will be the value in the middle, which is the fourth value in the sorted data set:

Median = 25

Next, let's find the first quartile:

To find the first quartile, we need to find the median of the lower half of the data set. In this case, the lower half of the data set is {15, 19, 23}:

Since there are 3 data points in the lower half, the median will be the second value in the lower half:

First Quartile = 19

Finally, let's find the third quartile:

To find the third quartile, we need to find the median of the upper half of the data set. In this case, the upper half of the data set is {37, 39, 43}:

Since there are 3 data points in the upper half, the median will be the second value in the upper half:

Third Quartile = 39

Therefore,

The first quartile is 19, the second quartile (median) is 25, and the third quartile is 39 for the given data set A.

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When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

[tex]\textsf{1)} \quad f(x)=-\dfrac{1}{4}(x-2)^2+\dfrac{1}{2}[/tex]

[tex]\textsf{2)} \quad g(x)=-\dfrac{1}{4}(x+2)^2+\dfrac{1}{2}[/tex]

[tex]\textsf{3)} \quad h(x)=\dfrac{1}{4}(x-2)^2-\dfrac{1}{2}[/tex]

[tex]\textsf{4)} \quad p(x)=\dfrac{1}{4}(x+2)^2-\dfrac{1}{2}[/tex]

Step-by-step explanation:

From inspection of the given graph, function f(x) is a parabola that opens downwards. Its vertex is (2, 1/2) and its y-intercept is (0, -1/2).

To determine the equation of f(x), we can use the vertex formula:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Substitute the vertex (2, 1/2) and the y-intercept (0, -1/2) into the formula to determine the value of a:

[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies -\dfrac{1}{2}&=a(0-2)^2+\dfrac{1}{2}\\\\-1&=4a\\\\a&=-\dfrac{1}{4}\end{aligned}[/tex]

Substitute the found value of a and the vertex into the formula to create an equation for f(x):

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

[tex]\hrulefill[/tex]

To reflect a function in the y-axis, negate the x-value of each point, but leave the y-value the same:

Therefore, if g(x) is f(x) reflected in the y-axis, replace x with -x:

[tex]\begin{aligned}g(x)&=f(-x)\\\\&=-\dfrac{1}{4}(-x-2)^2+\dfrac{1}{2}\\\\&=-\dfrac{1}{4}(x+2)^2+\dfrac{1}{2}\end{aligned}[/tex]

The vertex of g(x) is (-2, 1/2) and its y-intercept is (0, -1/2).

[tex]\hrulefill[/tex]

To reflect a function in the x-axis, negate the y-value of each point, but leave the x-value the same:

Therefore, if h(x) is f(x) reflected in the x-axis, then:

[tex]\begin{aligned}h(x)&=-f(x)\\\\&=-\left(-\dfrac{1}{4}(x-2)^2+\dfrac{1}{2}\right)\\\\&=\dfrac{1}{4}(x-2)^2-\dfrac{1}{2}\end{aligned}[/tex]

The leading coefficient is positive, so the parabola opens upwards.

The vertex of h(x) is (2, -1/2) and its y-intercept is (0, 1/2).

[tex]\hrulefill[/tex]

If p(x) is g(x) reflected in the y-axis, then:

[tex]\begin{aligned}p(x)&=-g(x)\\\\&=-\left(-\dfrac{1}{4}(-x-2)^2+\dfrac{1}{2}\right)\\\\&=\dfrac{1}{4}(-x-2)^2-\dfrac{1}{2}\\\\&=\dfrac{1}{4}(x+2)^2-\dfrac{1}{2}\end{aligned}[/tex]

The leading coefficient is positive, so the parabola opens upwards.

The vertex of p(x) is (-2, -1/2) and its y-intercept is (0, 1/2).

Answer:the probability that event A or event B takes place is 12/19.

Amanda will catch up to Ben after approximately 36 minutes.

To determine how long it will take for Amanda to catch up to Ben, we can set up an equation based on their respective speeds and the time difference.

the distance traveled by Ben is given by:

Distance = Speed * Time

Distance = 2 mi/h * (t + 1.5) h

the distance traveled by Amanda is given by:

Distance = Speed * Time

Distance = 7 mi/h * t h

equating both distances

2(t + 1.5) = 7t

2t + 3 = 7t

3 = 5t

t = 3/5

Therefore, it will take Amanda 3/5 of an hour (or 36 minutes) to catch up to Ben.

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The  Amount of wet food and dry food together, dog would receive a total of 3 cups of food for dinner.

The total amount of food Elena's dog gets for dinner,  the amount of wet food and dry food together.

Elena mixes 1 cup of wet food with x cups of dry food.

The total amount of food for dinner is then given by:

Total = Wet food + Dry food

Total = 1 cup (wet food) + x cups (dry food)

the dog gets 1 cup of wet food plus x cups of dry food for dinner.

the specific value of x, representing the amount of dry food, is not provided in the information provided. To determine the exact total amount of food, we would need to know the value of x.if Elena mixes 1 cup of wet food with 2 cups of dry food, the total amount of food would be:

Total = 1 cup (wet food) + 2 cups (dry food)

Total = 3 cups

the dog would receive a total of 3 cups of food for dinner.

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The marginal distribution of girls based on the percentages will be 58.3%.

The number for boys is given as:

= 50 + 30 + 45

= 125

The number of females is given as:

= 50 + 80 + 45

= 175

The percentage of females will be:

= 175/(125 + 175) × 100

= 175/300 × 100

= 58.3%

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Answer:

120

61+97+82=240 There are 360 degrees in a rectangle. 360-240 is 120

The logarithmic eqaution log₂ 4 + log₂ (c-9) = 5 has its solution to be 17

From the question, we have the following parameters that can be used in our computation:

log₂ 4 + log₂ (c-9) = 5

Apply the product rule of logarithm

So, we have

log₂(4 * (c-9)) = 5

This can then be expressed as

(4 * (c-9)) = 2⁵

Divide both sides by 4

c - 9 = 2³

So, we have

c - 9 = 8

When evaluated, we have

c = 17

Hence, the logarithmic eqaution has its solution to be 17

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Answer:

The 10th term of the sequence is 60.

Step-by-step explanation:

The given sequence is arithmetic because each term is obtained by adding 6 to the previous term. To find the 10th term, we use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_1 is the first term, d is the common difference, and n is the term number we want to find.

For this sequence, a_1 = 6 and d = 6, so we have:

a_10 = 6 + (10-1)6

a_10 = 6 + 54

a_10 = 60

Therefore, the 10th term of the sequence is 60.

1/25 is the probability that a randomly selected male student plays both basketball and football

Let A be the  Male students who play football

B be Male students who play basketball

We are looking for the probability of P(A ∩ B), which represents the probability that a male student plays both basketball and football.

Using the formula for the probability of the intersection of two events:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

First, we need to find the probability of P(A ∪ B), which represents the probability that a male student plays either basketball or football.

Since we know the total number of male students who play either sport (90), we can calculate it as follows:

P(A ∪ B) = Total number of male students who play either basketball or football / Total number of male students

P(A ∪ B) = 90 / 200

P(A ∪ B) = 9/20

Next, we can calculate the probability of P(A) and P(B) individually:

P(A) = Number of male students who play football / Total number of male students

P(A) = 58 / 200

P(A) = 29/100

P(B) = Number of male students who play basketball / Total number of male students

P(B) = 40 / 200

P(B) = 1/5

Now, we can substitute the values into the formula to find P(A ∩ B):

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

P(A ∩ B) = 29/100 + 1/5 - 9/20

P(A ∩ B) = 29/100 + 20/100 - 45/100

P(A ∩ B) = 4/100

P(A ∩ B) = 1/25

Therefore, the probability that a randomly selected male student plays both basketball and football is 1/25.

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With a budget of less than $75, you can buy a maximum of 5 DVDs.

If all DVDs at the store are priced at $15 and you want to spend less than $75, we can calculate the maximum number of DVDs you can buy.

To determine the number of DVDs, we divide the maximum budget by the price of each DVD.

The maximum budget is $75 and each DVD costs $15.

Dividing the maximum budget by the price of each DVD, we get:

$75 / $15 = 5 DVDs

The price of each DVD remains constant and that you will not exceed your budget.

If there are any additional costs such as tax or shipping, you should take those into account to ensure you stay within your desired budget. Additionally, it's always a good idea to check the store's policies and any potential discounts or promotions that may affect the final price.

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Answer:

2.4*18 = $43.2

stock price is $43.2

Step-by-step explanation:

The area of the given rectangular frame is: 352 in²

The formula for the area of a rectangle is expressed as:

A = L * W

Where:

A is Area

L is Length

W is width

Now, we are told that the parameters are:

Width of frame = 16 inches

Length of frame = 22 inches

Thus:

Area of frame = 22 * 16

Area = 352 in²

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Harvey bought a frame in which he put his family's picture. Frame is 16 inches wide and 22 inches length. Picture area is 12 inches wide and 18 inches length. What is the area of the frame