A company has 9 male and seven female employees and needs to nominate two men and two women for the company bowling team how many different teams can be formed?

Answer:

1/6 -> 2/11 -> 4/7 -> 14/9

Step-by-step explanation:

Answer:

N1,052,800.

Step-by-step explanation:

The starting salary of the officer = N57,000

Increase per annum =N2,800

The given pattern forms an arithmetic sequence since the annual salary increases by a fixed amount.

We are to determine the total amount of money that the officer will earn in 14 years.​

Sum of an arithmetic sequence, \(S_n=\frac{n}{2}[2a+(n-1)d]$ ,where: \left\{\begin{array}{lll}$First term, a=57,000\\$Common difference, d=2,800\\$Number of terms, n=14\end{array}\right\)

\(S_{14}=\frac{14}{2}[2(57,000)+(14-1)(2,800)]\\=7[114,000+13*2800]\\=7[150,400]\\=1,052,800\)

At the end of 14 years, the total amount earned by the officer will be N1,052,800.

Answer:

The measure of angle wxz is 130°?

We will find the probability of getting each color of marble, and we will see that getting red and blue is equally likely, while getting green is less likely.

If we draw a marble at random from the box, all of them will have the same probability of being drawn.

Then the probability of getting a given color is given by the quotient between the number of marbles of that color and the total number of marbles.

Probability of getting red:

P = 11/25 =  0.44  This is really close to 50%, so this is equally likely.

Probability of getting blue:

P = 11/25 =  0.44  This is really close to 50%, so this is equally likely.

Probability of getting green:

P = 3/25 = 0.12 This is really close to 0%, so this is less likely.

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Answer:

10, -7, -35, 5

Step-by-step explanation:

f(9) = -5(-9 + 7) = 10

0 = -5(x + 7)

0 = x + 7

x = -7

f(0) = -5(0 + 7) = -35

-60 = -5(x + 7)

12 = x + 7

x = 5

Answer:

area of a rectangle is L × B

3.1m ×6m = 18.6 m

Answer:

Step-by-step explanation:

Point P is on line segment

O

Q

‾

OQ

​

. Given

O

P

=

6

,

OP=6,

O

Q

=

4

x

−

3

,

OQ=4x−3, and

P

Q

=

3

x

,

PQ=3x, determine the numerical length of

O

Q

‾

.

OQ

​

.

Label known information:

Label known information:

O

P

Q

6

3x

OQ = 4x – 3

O

P

+

P

Q

=

OP+PQ=

O

Q

OQ

6

+

3

x

=

6+3x=

4

x

−

3

4x−3

−

4

x

−4x=

−

4

x

−4x

−

x

+

6

=

−x+6=

−

3

−3

−

6

−6=

−

6

−6

−

x

=

−x=

−

9

−9

−

x

−

1

=

−1

−x

​

=

−

9

−

1

−1

−9

​

x

=

x=

9

9

Plug in value of

x

to find

O

Q

:

Plug in value of x to find OQ:

O

Q

=

4

x

−

3

=

4

(

9

)

−

3

=

33

OQ=4x−3=4(9)−3=33

You can plug

x

into each expression:

You can plug x into each expression:

O

P

Q

6

3(9)

OQ = 4(9) – 3

Simplify:

Simplify:

O

P

Q

6

27

OQ = 33

Final Answer:

Final Answer:

O

Q

=

33

OQ=33

Answer:

UHHHHHHHHHHHHHHHHHHH ion know

Step-by-step explanation:

Answer: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since, 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11, you can form a triangle with side lengths 11 mm, 21 mm, and 16 mm.

Step-by-step explanation:

Answer:

y = 2x + 16

Step-by-step explanation:

Remember: The slope of perpendicular lines are negative reciprocals of each other.

1. Find the slope using the given equation.

   y= -1/2x +  8      Using the slope- intercept form  y = mx + b, the slope is -1/2 because it is the coefficient of the x-term .

  The new line is perpendicular to the given line and their slopes are negative reciprocals of each other.  You will use a slope = 2

2. Substitute into the slope intercept form y = mx +b , the value of the slope, "m" and the given point (-6, 4)  and solve for "b"

y = mx + b

4 = 2(-6) + b

4 = -12 + b

16 = b

3.  General form of slope intercept form: y = 2x +16

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Answer:

12 minutes 40 seconds

Step-by-step explanation:

One keychain, 1 minutes 35 second = 1*60 + 35 = 95 seconds

8 keychains, 95 * 8 = 760 seconds = 760/60 = 12.66667 minutes

= 12 minutes 0.66667*60 seconds

= 12 minutes 40 seconds

Given:

Score in first round = 5 points

Score in second, third and fourth rounds was identical.

A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round.

To find:

The inequality for the given problem.

Solution:

Let p be the number of points, p, that Steward scored in each of the second, third, and fourth rounds.

Score in first 4 rounds = Score of 1st round + Score of 2nd round + Score of  1s 3rd round + Score of 4th round

Score in first 4 rounds \(=5 + p + p + p\)

                                     \(=5 +3p\)

A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. It means the total score in first 4 rounds must be greater than or equal to 30.

\(5+3p\geq 30\)

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

The required amount of water will be saved per year is 9594 gallons per year.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
With a rate of 2.3 gallons per minute, a person consumed 10764 gallons/yr.

Now, the same person replaces the shower head with a low-flow shower head that has a flow rate of 1.5 gallons per minute.
The amount of water that will be saved is given as,
= 10764 - (1.5 × number of weeks in year × time in a day the shower taken)
= 10764 - 1.5×52× 15
= 9594 gallons per year,

Thus, the required amount of water will be saved per year is 9594 gallons per year.

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Answer:

The answer is "0.081"

Step-by-step explanation:

Dimes \(= 55\)

Calculating total coins \(= (23+55+20+19) = 117\)

P(for a dime) \(= \frac{55}{117}\)

Calculating remaining coins \(= 116\)

Nickels \(= 20\)

P(for nickel draw in second) \(= \frac{20}{116}\)

P(for a dime after that a nickel, without replacement)

\(= \frac{55}{117} \times \frac{20}{116} \\\\= \frac{1100}{13572} \\\\=0.081\)

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

205.

Step-by-step explanation:

Answer:

Amadi: 20 years old

Chima : 4 years old

The y-coordinate of the center of the circle obtained by the completing the square method is; k = -2

The completing the square method is a technique used to rewrite a quadratic expression in the form (x + p)² + q.

The equation of a circle can be written in the standard form as (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius.

h = The x-coordinate of the center of the circle

k = The y-coordinate of the center of the circle

To find the y-coordinate of the center, we need to complete the square for the y-terms in the given equation. The given equation can be rewritten as x² - 6·x + y² + 4·y = c. We can group the y-terms together and complete the square as follows;

x² - 6·x + y² + 4·y = c

x² - 6·x + (y² + 4·y + 4) = c + 4

x² - 6·x + (y + 2)² = c + 4

Therefore, by comparison to the equation for a circle, (x - h)² + (y - k)² = r², we get;

- k = 2

k = -2

The y-coordinate of the center of the circle is -2

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Answer:

1. y= x- 15

2. 20

Step-by-step explanation:

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Answer:

a. 6

Step-by-step explanation:

We reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

Given that,

Consider an NFL team that says the average weight of its defensive players is 315 pounds. A opposing team believes that their defensive players' average weight is lower than the 315 pounds they state. Consider that they take 15 defensive players as a sample and discover that the average weight of the players is 300 pounds, with an 8-pound sample standard deviation.

We have to create a suitable hypothesis test, draw conclusions at significance level 0.08, and then. Suppose that the weights are evenly distributed.

We know that,

Weights are normally distributed.

We are given μ = 315 , n= 15 , x = 300, s = 8, α = 0.08

The hypothesis are :

H₀ : μ = 315   v/s  H₁ : μ ≠ 315

The test statistic is given by,

z=x-μ/σ/√15

=300-315/8/√15

=-7.26

The critical value = z(α)  = z(0.04) = -1.75 and z(1-α)  = z(1-0.04)  = 1.75

Here calculated value of z > critical value of z

Therefore, we reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

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Answer:

In my sketch the angle between their flights is 135°

So wouldn't we just have the cosine law??

x^2 = 120^2 + 150^2 - 2(120)(150)cos135°

carry on, take care with the cos135, since it will be negative

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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Answer:

s = the number of student tickets sold a = the number of adult tickets sold The drama class sold 25 more student tickets than adult tickets to the fall play s = a + 25 The class collected $660 from ticket sales: 6s + 3a = 660 divide both sides by 3 2s + a = 220 by solving the system of equations s = a + 25 2s + a = 220 we find s = 81.67 student tickets a = 56.67 adult tickets

Step-by-step explanation:

hope this helps

The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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Answer:

we need more information to be able to answer this

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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