There are 10 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible

Answer:

Step-by-step explanation:

For equation:  y = 2x + 3 , 2x - y = 5

Compare equation y = 2x + 3 with y = m x + c then we get slope 'm' is 2.

Now, put x = 0 in y = 2x + 3 to get y-intercept

y = 2(0)+ 3

y = 0 + 3

y =  3

so, the y-intercept is 3 .

Re-write this equation 2x - y = 5 in the slope intercept form;

Subtract 2x from both the sides of 2x - y = 5

2x - y - 2x = 5 - 2x

- y = - 2x + 5

Multiply both the sides by '-1'

y = 2x - 5

so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .

Now, put x = 0 in y = 2x - 5 to get y-intercept

y = 2(0) - 5

y = 0 - 5

y =  - 5

so, the y-intercept is - 5 .

Equation y = 2x + 3 and  2x - y = 5 are parallel (since there slope are equal 'm = 2').

There is no solution to this system of equations.

For equation:  3x - y = 5 , 2x + y = -3

Re-write this equation 3x - y = 5 in the slope intercept form;

Subtract 3x from both the sides of 3x - y = 5

3x - y - 3x = 5 - 3x

- y = - 3x + 5

Multiply both the sides by '-1'

y = 3x - 5

so, when we compare above equation with y = m x + c then we get slope 'm' is 3 .

Now, put x = 0 in y = 3x - 5 to get y-intercept

y = 3(0) - 5

y = 0 - 5

y =  - 5

so, the y-intercept is - 5 .

Re-write this equation 2x + y = -3 in the slope intercept form;

Subtract 2x from both the sides of 2x + y = -3

2x - y - 2x = -3 - 2x

- y = - 2x - 3

Multiply both the sides by '-1'

y = 2x + 3

so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .

Now, put x = 0 in y = 2x + 3 to get y-intercept

y = 2(0) + 3

y = 0 + 3

y =  3

so, the y-intercept is 3 .

Equation 3x - y = 5 and 2x + y = -3 are intersecting lines (since their slope are not equal).

There is one solution to the system of equations (since the lines are intersect).

For equation:   y  = x + 4 , y  = x + 4

Compare equation y = x + 4 with y = m x + c then we get slope 'm' is 1.

Now, put x = 0 in y = x + 4 to get y-intercept

y = 0+ 4

y =  4

so, the y-intercept is 4 .

since equation of line are same therefore slopes are also equal

Equation  y  = x + 4 and y  = x + 4 are parallel lines.

There are infinite solutions to the system. ( Since equivalent equation)

As far as I can tell, the definition of margin of error involves more than you're given in this exercise (for example, you should know how many people were surveyed, the standard deviation, etc etc).

So, I assume that you're looking for a "simplified" interpretation of the margin of error: the estimate are around 80%, with a margin of 4% up or down.

So, you would be claiming that 80% of people is satisfied, with a margin of uncertainty of 4% (so it can be a minimum of 80-4=76 and a maximum of 80+4=84)

Answer:

(x + 1)^2 + (y - 2)^2 = 3^2 = 9

Step-by-step explanation:

The standard equation of a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2.

Here, h = -1, k = 2 and r = 3, so the equation of this particular circle is

(x + 1)^2 + (y - 2)^2 = 3^2 = 9.

Answer:

  c.  30.0 minutes

Step-by-step explanation:

Max mows 1/45 lawns per minute.

Jan takes twice as long (90 minutes per lawn), so mows 1/90 lawns per minute.

Working together, they mow ...

  (1/45 + 1/90) lawns per minute = (2/90 +1/90) lawn/min = 3/90 lawn/min

  = 1/30 lawn/min

Then for one lawn, it takes ...

  (1 lawn)/(1/30 lawn/min) = 30 min

Answer:

A

Step-by-step explanation:

30 min

To solve this equation, you need to isolate/get the variable (d) by itself, to do so, you should add 8 on both sides

d - 8 = 9

d - 8 + 8 = 9 + 8

d = 17       The 2nd option is your answer

Answer:

The distance of the dot above the ground is 28.9 in

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The triangle ABC is an isosceles triangle

CA=CB=15 in ------> is the radius of the circle

∠ACD+112°=180° ---> because the diameter divide the circle into two equal parts

∠ACD=180° -112°=68°

In the right triangle ACD

Find AD we have sin(68°)=AD/AC AD=AC*sin(68°) substitute the value AD=15*sin(68°)=13.9 in

Find the distance AB

AB=2*AD AB=2*13.9=27.8 in

The diameter is equal to

2*15=30 in

The distance of the dot above the ground is equal to

AB+(30-27.8)/2

27.8+1.1=28.9 in

90 speed in meters

:explenation step by step

1. 5× =450

2. 450÷5=90

3.5×90=450

Final answer:

Janice's swimming speed is calculated by dividing the distance she swims, 450 meters, by the time it takes, 5 minutes, resulting in a speed of 90 meters per minute.

Explanation:

To calculate Janice's swimming speed in meters per minute, you divide the distance she swims by the time it takes her to swim that distance. Janice swims 450 meters in 5 minutes.

Swimming speed = Distance ÷ Time.

Swimming speed = 450 meters ÷ 5 minutes = 90 meters per minute.

Therefore, Janice's swimming speed is 90 meters per minute.

Answer:

  C.  10

Step-by-step explanation:

The values on the left are proportional to the values on the right. You can write the ratios different ways, but the one I chose is ...

  6/15 = x/25

  6·25/15 = x = 150/15 = 10

The value of x is 10.

Well this series is neither arithmetic or geometric as said in the other solution but since there are addition signs I will find the sum

The sum is 522.24

Answer: D. 846 units squared

Step-by-step explanation:

12x9=108

108x2=216

15x9=135

135x2=270

12x15=180

180x2=360

360+270+216=846 units squared

The surface area of the rectangular prism is 846 sq.units

A rectangular prism is a three dimensional figure with rectangle at its base. It can also be called as a Cuboid .

A rectangular prism is given with

length 12 units

Width 15 units

Height 9 units

The surface area of the rectangular prism is given by

A = 2 * l * w + 2 * l * h + 2 * w * h

A = 2 * 12 * 15 + 2 * 9 * 12 + 2 * 15 * 9

A = 360 +  216 + 270

A = 846 sq.units

Therefore the surface area of the rectangular prism is 846 sq.units

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The normal distribution is symmetric about its mean. For any symmetric distribution, the mean is the same as the median. So the answer is B.

In a normal distribution, the mean and median are equal due to its symmetrical nature. Therefore, if the mean is 315, then the median is also 315.

The question asks about the relationship between the mean and median in a normal distribution. In a normal distribution, the mean, median, and mode are all equal. This is due to the symmetrical nature of the normal distribution around its mean. So, if the mean of the normal distribution is 315, the median is also 315.

The answer to the student's question is: B.315.

The relationship does not show a direct linear variation best describes f(x)=x−12. Option D is the correct choice.

A function is a specific mathematical relationship with a predefined domain and range, where each value in the domain corresponds to one value in the range.

In the given function, f(x) = x - 12, the slope of the line represents how much 'y' increases as 'x' increases.

A constant slope means that the increase in 'y' is uniform across the entire line. In this case, the slope (m) is 1.

However, this function doesn't exhibit a direct linear variation, as it also has a y-intercept of -12.

The presence of the y-intercept at -12 indicates that the line does not pass through the origin, and therefore, it doesn't show a direct linear variation.

Hence, the linear function f(x) = x - 12 does not display a direct linear variation, making option (D) the correct choice.

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Question:-

Which answer choice best describes f(x)=x−12?

A. The relationship shows a direct linear variation with a constant of variation of −12 .

B. The relationship shows a direct linear variation with a constant of variation of 1.

C. The relationship shows a direct linear variation with a constant of variation of 12.

D. The relationship does not show a direct linear variation

Patti swam a total of 5 hours and 25 minutes over the three days—1 hour and 15 minutes on Monday, 2 hours and 30 minutes on Tuesday, and 1 hour and 40 minutes on Wednesday.

Patti went swimming for 1 hour and 15 minutes on Monday. To find out how long she swam over the three days, we need to calculate the time for each day and then sum them up.

On Tuesday, she swam twice as long as she did on Monday, which means she swam 2 * (1 hour and 15 minutes) = 2 hours and 30 minutes.

On Wednesday, she swam 50 minutes less than the time she swam on Tuesday, which means she swam (2 hours and 30 minutes) - 50 minutes = 1 hour and 40 minutes.

To find the total time Patti spent swimming during the three days, we add up Monday's, Tuesday's, and Wednesday's swimming times:

The total is 5 hours and 25 minutes.

You're buying two items, we can represent them as X. First you set one of the X's to be the dryer, and since we know that the washer costs 46 more than the dryer, that can be represented as X + 46. The equation can be written as follows:

x + (x + 46) = 696

2x + 46 = 696

2x = 650

x = 325

Therefore, the dryer costs $325, and the washer costs $371

The cost of the dryer is found by setting up an equation where x represents the dryer's cost and solving for x. The calculation steps reveal that the dryer costs $325.

The student is asking how to find the cost of a dryer when given the combined cost of a washer and dryer, and that the washer costs $46 more than the dryer. To solve this, we first let the cost of the dryer be x dollars. Therefore, the cost of the washer would be x + $46. We are told that combined they cost $696.

Setting up the equation: x + (x + $46) = $696.

Combine like terms: 2x + $46 = $696.

Subtract $46 from both sides: 2x = $696 - $46.

Calculate the remaining balance: 2x = $650.

Divide both sides by 2 to find the cost of the dryer: x = $325.

Therefore, the cost of the dryer is $325.

Answer:

25150

Step-by-step explanation:

First, we have to see that this is an arithmetic sequence... since to get the next element we add 5 to it.  (a geometric sequence would be a multiplication, not an addition)

So, we have a, the first term (a = 4), and we have the difference between each term (d = 5), and we want to find the SUM of the first 100 terms.

To do this without spending hours writing them down, we can use this formula:

[tex]S = \frac{n}{2} * (2a + (n - 1) * d)[/tex]

If we plug in our values, we have:

[tex]S = \frac{100}{2} * (2 * 4 + (100 - 1) * 5) = 50 * (8 + 99 * 5)[/tex]

S = 50 * (8 + 495) = 50 * 503 = 25150

Answer:

Sum of 100 terms = 25150

Step-by-step explanation:

Formula:-

Sum of n terms of an AP

Sₙ = n/2[2a + (n - 1)d]

Where n - number of terms

a - first term and d - common difference

To find the sum of 100 terms

here, n = 100, a = 4 and d = 5

S₁₀₀ =  n/2[2a + (n - 1)d]

       = 100/2[2*4 + (100 - 1)5]

       = 50[8 + 99*5]

       = 25150

Answer:

B 0.34

Step-by-step explanation:

If 34% of all people are expected to get the flu, then that means 34% of any sample size should also expect to be infected.  If they choose 1 person at random from either the population or a preselected random sample, then that person has a 34% chance of getting the flu.  0.34 is the decimal corresponding to 34%. So the probability is 0.34

Convert the percentage to a decimal. The answer is 0.34.

Answer:

  x = [-1 | 5, 2 | 1]

Step-by-step explanation:

We assume your notation is used to describe 2×2 matrices.

Solve for x:

  2x -k = m

  2x = m + k . . . . add k

  x = (1/2)(m +k) . . . . multiply by 1/2

Fill in the values:

  x = 1/2[2+(-4) | 8 +2, -2+6 | 5+(-3)]

  x = [-1 | 5, 2 | 1]

The correct answer is B, or the graph attached.

Just got it right on edge 2020, hope this helps!! :)

Answer:

  740

Step-by-step explanation:

If x and y represent the numbers of cans Cannon and Haslyn collected, respectively, then the expression x+y represents the total number of cans the two of them collected. The problem statement tells you that, together, they collected 740 cans. The value of x+y is 740. The first equation gives that value the name "A", which means ...

  A = 740

the answer for this question is all are not polynomials

Answer:

The first, second, and last ones are polynomials, the others are not.

Step-by-step explanation:

The width is 3 3/4. you just have to divide 5 5/8 by 1 1/2.

let's firstly convert those mixed fractions to improper fractions and then proceed.

[tex]\bf \stackrel{mixed}{5\frac{5}{8}}\implies \cfrac{5\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\ \cline{1-1} L=\frac{3}{2}\\ A=\frac{45}{8} \end{cases}\implies \cfrac{45}{8}=\cfrac{3}{2}w\implies \cfrac{45}{8}=\cfrac{3w}{2}\implies 90=24w \\\\\\ \cfrac{90}{24}=w\implies \cfrac{15}{4}=w\implies 3\frac{3}{4}=w[/tex]

Answer:

4%

Step-by-step explanation:

Answer:

+/- 4%.

Step-by-step explanation:

That would be +/- (84-76)/2

= +/- 8/2

= +/-4%.

Answer:

The area of the triangular garden is [tex]173\ ft^{2}[/tex]  

Step-by-step explanation:

we know that

The equilateral triangle has three equal sides and three equal internal angles (the measure of each internal angle is 60 degrees)

The area of a triangle applying the law of sines is equal to

[tex]A=\frac{1}{2}(a)(b)sin(C)[/tex]

In this problem we have a equilateral triangle

therefore

[tex]a=b=20\ ft[/tex]

[tex]C=60\°[/tex]

substitute

[tex]A=\frac{1}{2}(20)(20)sin(60\°)[/tex]

[tex]A=\frac{1}{2}(20)(20)\frac{\sqrt{3}}{2} \\ \\A=100\sqrt{3}\ ft^{2}\\ \\A=173\ ft^{2}[/tex]

Answer:

-x^2+3x

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using Euler's formula for Polyhedra, that is

F + V - E = 2

where F is faces, V is vertices and E is edges

1

Rearrange formula for E

F + V - E = 2 ( add E to both sides )

F + V = 2 + E ( subtract 2 from both sides )

E = F + V - 2

  = 25 + 17 - 2 = 40

-------------------------------------------------

2

Rearrange formula for F

F + V - E = 2 ( add E to both sides )

F + V = 2 + E ( subtract V from both sides ) F = 2 + E - V, so

F = 2 + 34 - 11 = 25

-----------------------------------------------------

3

Rearrange formula for V

F + V - E = 2 ( add E and subtract F from both sides )

V = 2 + E - F

  = 2 + 36 - 22 = 16

Answer:

1. use Euler's formula to find the missing number f=25 vertices=17 Edges=?

40

2. Mario's company makes gemstones Faces=12 vertices=? edges=20

10 vertices

3. Pierre built the model shown in the diagram for a social studies project

pentagon

4. A jewelry store buys small boxes find the surface area of the box to the nearest whole number

266 cm^2

5. Find the lateral area of the prism below Round your answer to the nearest whole number

322 m^2

6. Find the surface area of the cylinder in terms of pi

350pi cm^2

7. Allison is planning to cover the lateral surface of a large cylindrical can diameter 3 feet height 3.5 feet

33. ft^2

8. Find the surface area of the regular pyramid shown to the nearest whole number

740 m^2

9. is the figure below drawn in one point or 2 point perspective

Answer:

A and E

Explanation:

A.the space the bottom of a tent takes up- Area

B.the distance around the outside of a tent- Perimeter

C.the measure from the top to the bottom of a tent- Height

D.the measure from the top to the bottom of a flat sleeping bag-length

E.the space a flat sleeping bag takes up-area

F.the distance around the outside of a flat sleeping bag- perimeter

Explanation:

Use the Pythagorean identity, cancel common factors, and divide numerator and denominator by cos(x). Equivalently, multiply numerator and denominator by sec(x).

[tex]\dfrac{\sin^2{x}+2\cos{x}-1}{\sin^2{x}+3\cos{x}-3}=\dfrac{1-\cos^2{x}+2\cos{x}-1}{1-\cos^2{x}+3\cos{x}-3} \qquad\text{replace $\sin^2$ with $1-\cos^2$}\\\\=\dfrac{\cos{x}(2-\cos{x})}{(\cos{x}-1)(2-\cos{x})}=\dfrac{\cos{x}}{\cos{x}-1}=\dfrac{1}{\dfrac{\cos{x}}{\cos{x}}-\dfrac{1}{\cos{x}}}=\dfrac{1}{1-\sec{x}}[/tex]

Answer:

you don't know the answer?! Come on folk you tweaking.

Step-by-step explanation:

Answer:

5.90551

Step-by-step explanation:

1cm in inches - 0.3937008in

30cm in inches - 11.81102in = approx. 1 foot (1 ft = 12")

Answer:

B

Step-by-step explanation:

Let length of Green Route be g and length of Blue Route be b

From 1st bullet point we can write the equation:

6g+5b = 52

From 2nd bullet, we can write:

12g + 13 b = 119

We can solve for b of the 1st equation as:

[tex]6g+5b = 52\\5b=52-6g\\b=\frac{52-6g}{5}[/tex]

Now we can put this value of b into 2nd equation and solve for g (as shown below):

[tex]12g+13b=119\\12g+13(\frac{52-6g}{5})=119\\12g+\frac{676-78g}{5}=119\\\frac{60g+676-78g}{5}=119\\60g+676-78g=5*119\\60g+676-78g=595\\-18g=-81\\g=\frac{-81}{-18}=4.5[/tex]

Hence, the green route is 4.5 miles, B is right.

5 people , 1 wall ~ 20/5 = 4 minutes

1 person, 1 wall ~ 4/5 minutes

9 people, 1 wall ~ (4/5) x 9 = (36/5) minutes

Therefore 9 people, 9 walls ~ (36/5) x 9

= 64.8 minutes

= 1h 4 min 48 s

Answer:

It takes 20 minutes :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I love these!  Ok, the expanded formula you need for this is

[tex]6(cos\frac{5\pi }{6}+sin\frac{5\pi }{6}i)[/tex]

From the unit circle we get the cos and sin of that angle and fill them in:

[tex]6(-\frac{\sqrt{3} }{2}+\frac{1}{2}i)[/tex]

Distributing through the parenthesis gives you

[tex]-\frac{6\sqrt{3} }{2}+\frac{6}{2}i[/tex]

which simplifies to

[tex]-3\sqrt{3}+3i[/tex]

To convert 6cis (5pi)/6 from polar form to rectangular form, use the formula r*cos(theta) + r*sin(theta)*i. The magnitude (r) is 6 and the angle (theta) is 5pi/6. The rectangular form results to be B. -3 Square root of 3 +3i.

The student is asked to convert the complex number 6cis (5pi)/6 from polar form to rectangle form. In polar form, a complex number can be represented as rcis(theta), where r is the magnitude and theta is the angle. To convert this to rectangular form, we use the formula r*cos(theta) + r*sin(theta)*i. In this case, r=6 and theta=5pi/6. Therefore, the rectangular form of the given number is (6*cos(5pi/6)) + (6*sin(5pi/6))*i which equals -3 +

3 square root

of 3*i. Hence, the correct answer is B. -3 Square root of 3 +3i.

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