4. A choir is made up of 9 sopranos, 8 altos, 8 tenors, and 5 basses. What is the probabilitythat if two people were picked out of the choir that the first student is a tenor and the secondan alto?

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

66

Step-by-step explanation:

If there are  n  students, then the number of pairs is \(\frac{n(n-1)}{2}\).

With 12 students, \(\frac{12(12-1)}{2} = \frac{132}{2}=66\) pairs can be formed.

The reason the formula works is this:  Each of the 12 students can be paired with 11 other students (no student is paired with him/her self).  But counting 12 x 11 = 132  counts each pair twice.  Example: student A can be paired with student B,..., student B can be paired with student A.  The pair was counted two times.

See the attached image that shows pairings of 5 students.  There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.

The categories and their  Percentages on the circle graph would be as follows:

Cape: 25%

Garrison: 40%

Split: 35%

To represent the distribution of house types in a town containing 25,000 houses on a circle graph, we need to determine the percentage of each category.

The given data provides the following frequencies for each house style:

Cape: 6,250 houses

Garrison: 10,000 houses

Split: 8,750 houses

To calculate the percentage for each category, we divide the frequency of each house style by the total number of houses in the town (25,000) and multiply by 100.

Percentage for Cape: (6,250 / 25,000) * 100 = 25%

Percentage for Garrison: (10,000 / 25,000) * 100 = 40%

Percentage for Split: (8,750 / 25,000) * 100 = 35%

Therefore, the categories and their respective percentages on the circle graph would be as follows:

Cape: 25%

Garrison: 40%

Split: 35%

These percentages represent the proportion of each house style in the town and can be visually represented on a circle graph to provide a clear visualization of the distribution of house types.

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Answer:B

Step-by-step explanation:

A reflection of the line segment across the line y = - x, will produce an image with endpoints at (- 4, 1) and (- 1, - 4).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know, A reflection across the 180° about the origin transforms

(x, y) to (-x, - y)

Therefore A line segment has endpoints at (-1, 4) and (4,1) will have an image at  (- 4, 1), and (- 1,- 4) is a reflection of the line segment across the line y = - x.

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Answer:

12

Step-by-step explanation:

25 is 1/4 of 100, so you do 3 x 4 and you would get 12! Hope this helps!

Answer:

12 players

Step-by-step explanation:

Multiply the 3 players that are sick by 4, as 25*4 is 100.

we get that the circumference is

7.18° the angle which the road makes with the horizontal.

Define Trigonometric functions

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given,

Height of hill = 250 feet

Length of the slope = 2000 feet

find the angle,

we know, sin(x) = perpendicular / hypotenuse

sin(x) = 250 / 2000

x = sin^-1 (0.125)

x = 7.18°

Hence, 7.18° the angle which the road makes with the horizontal.

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The area of the rectangle will be 16 square cm.

The area is the space occu[ied by any shape in a two-dimensional space. The area of the rectangle is defined as, the product of the length and the width of the rectangle and is measured in square units.

Given that, the rectangle is having a width of 2 cm and a length of 8 cm. The area of the rectangle will be calculated as,

Area of rectangle = Length x Width

Area of rectangle = 8 x 2

Area of rectangle = 16 square units

Therefore, the area of the rectangle is 16 square cm.

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The complete question is given below.

What is the area of the rectangle with a length of 8 cm and a width of 2 cm?

Answer:

(x – 4)^2 + (y + 7)^2 = 16

Step-by-step explanation:

The formula of a circle is:

(x – h)^2 + (y – k)^2 = r^2

(h, k) represents the coordinates of the center of the circle

r represents the radius of the circle

If you plug in the given information, you get:

(x – 4)^2 + (y – (-7))^2 = 4^2

which simplifies into:

(x – 4)^2 + (y + 7)^2 = 16

Answer:

4n=10-n

n=2

Step-by-step explanation:

add n to both sides

5n=10

divide both sides by 5

n=10/5

n=2

Answer:

10

Step-by-step explanation:

Here it's given that the area of the shaded region is 48 u² and we need to find out the value of x .

The given figure is made up of two rectangles where the smaller one is inscribed into the bigger one .

So that ,

\(\longrightarrow\) ar(bigger) - ar(smaller) = 48

\(\longrightarrow\) [ (x+3) (x-4)] - 3(x) = 48

\(\longrightarrow\) [ x² - 4x +3x -12 - 3x ] = 48

\(\longrightarrow\) x² -4x -12 -48 = 0

\(\longrightarrow\) x² - 4x - 60 = 0

\(\longrightarrow\) x² - 10x + 4x - 60 = 0

\(\longrightarrow\) x( x -10) +4(x -10) = 0

\(\longrightarrow\) (x +4)(x-10) = 0

\(\longrightarrow\) x = -4,10

\(\longrightarrow\) x = 10

Define a square

A sqaure a plane figure that is closed, two dimensional shape with four equal straight sides and four right angles. It is a quadrilateral

Write out the formula for finding the area of a square

Find the area of the square with side 6 yards

Hence, the area of the square with side 6 yards is 36 yards squared

a) Where the above conditions are given, this means that we can not reject the null hypothesis since the t-value = 0.31 and is greater thand the t-value which is 2.26

b) there is 95% confidence that the true mean lenght of novels written duing the pandemic falls within the range of 338 - 352 pages.

To test the above hypothesis , we used the two tailed t -test with a 95% confidence level.

T- value is computed as follows:

t = (sample mean - population mean)/ (sample Standard deviation/ √sample size)

Using the given values, we have:

t = (345/320)/(11/√10)
t = 0.31

Hence at 95% confidence leve, we have 2.26 as critical value.

Since 0.31  is less than the critical value, we cannot reject the null hypothesis.


B) to compute the 95% confidence interval for the mean lenght of the novels written during the pendemic:

Sample  ± (t-value x standard error)

Where:
Standard Error is given as = Sample Standard Deviation / √Sample size

Thus:

Standard Error = 11/√10
SE = 3.48

The 95% confidence interval therefore is:

345 ± (2.26 x 3.48
= 339.1, 351.9
≈ 339, 352.


Hence, it is correct to state that there is 95% confidence that the true mean length of novels written during the pandemic falls within the range of 338 - 352 pages.

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Answer:

1.5 in or 3/2 in

Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

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Answer:

f(100) = 160.

Step-by-step explanation:

Linear function:

The equation of a linear function has the following format:

\(y = mx + b\)

In which m is the slope(how much f(x) changes when x changes by 1) and b is the y-intercept(value of f(x) when x = 0).

Finding the slope:

Suppose we have two points. The slope is the change in the output divided by the change in the input.

In this question, we have points (45,50) and (60,80).

Change in the output: 80 - 50 = 30

Change in the slope: 60 - 45 = 15

Slope: 30/15 = 2

So

\(y = 2x + b\)

Point (45,50)

This means that when \(x = 45, y = 50\). We use this to find the value of b.

\(y = 2x + b\)

\(50 = 2(45) + b\)

\(b = -40\)

So

\(y = 2x - 40\)

With y = f(x)

What is the value of f(100)?

This is y when x = 100. So

\(f(100) = 2(100) - 40 = 200 - 40 = 160\)

f(100) = 160.

Answer:

b.

Step-by-step explanation:

Answer:

35 cubic inches

Step-by-step explanation:

The volume of a pyramid is \(\frac{1}{3} bh\), where b = base and h = height. To find the area of the base, we multiply 3 by 5 and then divided by 2.

Next, we multiply 7.5 by 14.

Lastly, we divide by 3.

Therefore, the answer is 35 cubic inches.

Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

Answer: 10q-20

10(q-2)

factor out 10 as it is a common factor

Step-by-step explanation: this did not help please comment to contact please

The approximate area of the shaded region of the circle is 191 metres squared.

The radius of the circle below is given as 9 metres. The approximate area of the shaded region of the circle can be found as follows:

area of the shaded region = area of the circle - area of the sector uncoloured

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = π × 9²

area of the circle = 81π m²

Hence,

area of the sector uncoloured = ∅ / 360 × πr²

where

Therefore,

area of the sector uncoloured = 90 / 360 × π × 9²

area of the sector uncoloured = 1 / 4 × π × 81

area of the sector uncoloured = 81 / 4 π

Hence,

area of the shaded region = 81π  - 20.25π

area of the shaded region = 60.75π

area of the shaded region = 190.755

area of the shaded region = 191 m²

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Answer:

me too (help)

Step-by-step explanation:

The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

60 in²

Step-by-step explanation:

Area of parallelogram = base x height

= 10 in x 6 in

= 60 in²

The area of the parallelogram is 60in².

Answer:

Statistic

Step-by-step explanation:

a parameter describes a percentage of the whole population. For example. if the total population of guests were interviewed and 21% indicated they were staying at the hotel, it would have been a parameter

A statistic summarises data from a sample

Answer:

Step-by-step explanation:

50

Answer:  x = -3/2

Step-by-step explanation: