You want to pick a four-player tennis team. There are eight players to choose from. How many
different teams can you form?
​

[tex]\text{The angle from the right is 30}^\circ \\ \\ \text{We use sinus theorem:}\\\\ \dfrac{y}{\sin(60)^{\circ}} = \dfrac{8}{\sin(30)^{\circ}} \Rightarrow \dfrac{y}{\dfrac{\sqrt{3}}{2}} = \dfrac{8}{\dfrac{1}{2}} \Rightarrow y = \dfrac{\sqrt 3}{2}\cdot 16\Rightarrow \boxed{y = 8\sqrt 3}[/tex]

Answer:

y = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex], hence

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{8}[/tex]

Multiply both sides by 8

8 × tan60° = y, so

y = 8[tex]\sqrt{3}[/tex] ← exact value

Answer:

[tex]d=\sqrt{73}[/tex]

Step-by-step explanation:

Use the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the points.

8 - 0 = 8

8^2 = 64

5 - 8 = -3

-3^2 = 9

64 + 9 = 73

[tex]d=\sqrt{73}[/tex]

Hello there!

An equation to model the number is: n - 7 x 2 = 2

To find the equation, break apart the question.

twice the difference of a number and 7 equals 2. - "Twice" means we are multiplying by 2, or x 2

twice the difference of a number and 7 equals 2. "The difference of a number and 7" means we are subtracting n - 7, and this is being multiplied by 2 so we have n - 7 x 2 so far.

twice the difference of a number and 7 equals 2. "Equals two" means the equation is equal to 2, or = 2, so our equation is n - 7 x 2 = 2.

The value of the number based on the information given is 8.

Let the number be represented by x.

Since we are given the equation that twice the difference of a number and 7 equals 2, the equation to solve this will be:

2(x - 7) = 2

2x - 14 = 2

2x = 2 + 14

2x = 16

x = 16/2

x = 8

The value of the number is 8

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Answer:

B

Step-by-step explanation:

Corresponding angles are not always congruent

Corresponding angles are congruent.

Answer is B.

Answer:

C

Step-by-step explanation:

[tex] \frac{ - 1}{3} \times a = -1[/tex]

then

[tex]a = 3 \: where \: a \: is \: our \: line \: slope[/tex]

Answer:

[tex]\boxed{\text{C. } y - 2 = 3(x - 6)}[/tex]

Step-by-step explanation:

The slope of the perpendicular line m₂ must  be the negative reciprocal of the slope m₁ of the first line.

[tex]m_{2} = -\dfrac{1}{m_{1}} = -\dfrac{1}{-\frac{1}{3}} = 3[/tex]

The only equation with m = 3 is  

[tex]\boxed{\textbf{C. } y - 2 = 3(x - 6)}[/tex]

This is the point slope form of the equation for a straight line through (6, 2) with slope = 3.

Answer:

-6 I think

Step-by-step explanation:

Answer:

1. true

2.True

3.False

4.false

Step-by-step explanation:

A is the correct answer I believe

Answer:

Perimeter of Total Area = 18.4(2) + 32.5(2) = 101.8 meters

Area of Seating Space = 178 squared meters

Step-by-step explanation:

Perimeter of Total Area = 18.4(2) + 32.5(2) = 101.8 m

Seating Space = 18.4*32.5 = 598

Basketball Court = 15*28 = 420

598 - 420 = 178

Area of Seating Space = 178 squared meters

Answer:

C. 9P6

Step-by-step explanation:

Given choices are :

A. 8P5

B. 9P1

C. 9P6

D.8P1

Now we need to find about which below is largest when evaluated.

So let's evaluate them using formula:

[tex]nPr=\frac{n!}{\left(n-r\right)!}[/tex]

[tex]8P5=\frac{8!}{\left(8-5\right)!}=\frac{8!}{\left(3\right)!}=6720[/tex]

[tex]9P1=\frac{9!}{\left(9-1\right)!}=\frac{9!}{\left(8\right)!}=9[/tex]

[tex]9P6=\frac{9!}{\left(9-6\right)!}=\frac{9!}{\left(3\right)!}=60480[/tex]

[tex]8P1=\frac{8!}{\left(8-1\right)!}=\frac{8!}{\left(7\right)!}=8[/tex]

Largest value among those numbers is 60480.

Hence correct choice is C. 9P6

Let [tex]x=m\widehat{EY}=m\widehat{YI}[/tex]. By the inscribed angle theorem, we have

[tex]m\angle EJI=\dfrac12m\angle EOI=\dfrac12m\widehat{EI}=\dfrac{m\widehat{EY}+m\widehat{YI}}2=x^\circ[/tex]

Then

[tex]m\angle KJE=(180-x)^\circ[/tex]

Also by the inscribed angle theorem, we have

[tex]m\angle ELY=\dfrac12m\angle EOY=\dfrac12m\widehat{EY}=\left(\dfrac x2\right)^\circ[/tex]

so that

[tex]m\angle KLX=\left(180-\dfrac x2\right)^\circ[/tex]

Angles EXY and LXJ form a vertical pair so they are congruent and both have measure [tex]80^\circ[/tex].

The sum of the interior angles to any quadrilateral is [tex]360^\circ[/tex], so for quadrilateral KLXJ we get

[tex]25^\circ+\left(180-\dfrac x2\right)^\circ+(180-x)^\circ+80^\circ=360^\circ\implies x^\circ=70^\circ[/tex]

So,

[tex]m\widehat{EI}=2x^\circ=\boxed{140^\circ}[/tex]

Answer:

Step-by-step explanation:

Let . By the inscribed angle theorem, we have

Then

Also by the inscribed angle theorem, we have

so that

Angles EXY and LXJ form a vertical pair so they are congruent and both have measure .

The sum of the interior angles to any quadrilateral is , so for quadrilateral KLXJ we get

So,

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Answer:

14.14

Step-by-step explanation:

You can find the value of x using the trig ratio Sine = opposite/hypotenuse.

The sin 45 = 10/x. Solve for x.

x= 10/ sin45

x = 10/0.707

x = 14.14

ANSWER

C

E

F

EXPLANATION

The result of the synthetic division is :

3 -1 0

The last number is the remainder which is 0

The first two numbers are the coefficients of the quotient.

Therefore the quotient is 3x -1

Since the remainder is 0, x-4 is a factor of

[tex]f(x) = 3 {x}^{2} - 13x + 4[/tex]

This also means that:

[tex](3 {x}^{2} - 13x + 4) \div (x - 4) = 3x - 1[/tex]

This again means that x=4 is a root of

[tex]f(x) = 3 {x}^{2} - 13x + 4[/tex]

The correct choices are C,E and F.

Answer:

Option C is false.

Step-by-step explanation:

The correct answer is:

C. Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.

This is false because sometimes when we divide polynomials, one polynomial does not gets completely or evenly divided by the other.  

In such cases, we get a remainder which is not a monomial as the variable has a negative power. This means the quotient is not a polynomial.

We can show this by example : suppose we want to divide

[tex]x^{-6}[/tex]by [tex]x^{2}[/tex]

=> [tex]\frac{x^{-6} }{x^{2} }[/tex]

=> [tex]x^{-6-2}[/tex] =>[tex]x^{-8}[/tex]

This is not a polynomial. So the closure property does not hold true for division of polynomials.

Answer:

There are 40 total questions on his text.

Step-by-step explanation:

To find this, divide the number of questions he got right by the percentage of the total they represent.

32/80% = 40

Answer:

40?

Step-by-step explanation:

Answer:

[tex] x = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

Step-by-step explanation:

Let the numbers be x and y.

We now have a system of equations.

x + y = 5

xy = -3

Solve the second equation for x.

x = -3/y

Now substitute x in the first equation with -3/y.

-3/y + y = 5

Multiply both sides by y.

-3 + y^2 = 5y

y^2 - 5y - 3 = 0

Use the quadratic formula to solve for y.

[tex] y = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] y = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-3)}}{2(1)} [/tex]

[tex] y = \dfrac{5 \pm \sqrt{25 + 12}}{2} [/tex]

[tex] y = \dfrac{5 \pm \sqrt{37}}{2} [/tex]

[tex] y = \dfrac{5 + \sqrt{37}}{2} [/tex]   or   [tex] y = \dfrac{5 - \sqrt{37}}{2} [/tex]

[tex] y = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]   or   [tex] y = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

We get 2 solutions for y. Now for each solution for y, we need to find a corresponding solution for x.

Solve the first equation for x.

x + y = 5

x = 5 - y

Substitute each y value to find the corresponding x value.

[tex] x = 5 - (\dfrac{5}{2} + \dfrac{\sqrt{37}}{2}) [/tex]

[tex] x = 5 - \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{10}{2} - \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

This give one solution as:

[tex] x = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

Now we substitute the other y value to find the other x value.

[tex] x = 5 - (\dfrac{5}{2} - \dfrac{\sqrt{37}}{2}) [/tex]

[tex] x = 5 - \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{10}{2} - \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

This give the second solution as:

[tex] x = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

Answer: Option a) 3

Step-by-step explanation:

The formula for calculating combinations is as follows

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

Where "n" is the amount of items in a set and you can choose "r" from them

3C1 reads as: The combination of 1 in 3. You have a set of 3 elements and choose 1 of them.

[tex]n = 3\\\\r = 1[/tex]

So :

[tex]3C1=\frac{3!}{1!(3-1)!}\\\\3C1=\frac{3!}{1!*2!}\\\\3C1=\frac{3*2*1}{1*2*1}\\\\3C1=3[/tex]

Answer:

Last Option

[tex]P (B) = 0.6[/tex]

Step-by-step explanation:

We have the Venn diagram that shows the probabilities of occurrence of 3 events A, B and C

In this case, since events A and B and B and C are non-disjoint events, then the probability of occurrence B is the sum of the probability that only B will occur plus the probability of occuring A and B plus the probability that B and C occur

This is:

[tex]P (B) = 0.1 +0.3 +0.2[/tex]

[tex]P (B) = 0.6[/tex].

Answer:

i think this is it

Step-by-step explanation:

the answer i got is just 55

Answer:

0

Step-by-step explanation:

The slope of a line is   Change in y

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

                                       change in x

y does not change

                                    0

                                   ------

                                    change in x

Slope = 0

Horizontal lines have 0 slope

Vertical lines have undefined slope

$3.468.15

I just subtracted 1.89% from $183,500

$3,468.15.

To calculate Patrick's annual property taxes on his new home, we need to apply the property tax rate of 1.89% to the value of the home. The formula to calculate this is:

Property Taxes = Home Value  imes Tax Rate

In this case, Patrick's home value is $183,500 and the tax rate is 1.89%. So, the calculation would be:

Property Taxes = $183,500 times 0.0189

When we perform this multiplication, we get:

Property Taxes = $3,468.15

Therefore, the property taxes on Patrick's new home are $3,468.15.

Answer:

The slope is 1

Step-by-step explanation:

The slope of the line is also its gradient. A gradient is basically rise/run

In this case the rise is one and the run is also one if you look at the graph...therefore 1/1 equals 1

Just by eyeballing the graph, you could see that the slope is 1: whenever x increases by 1, y will also increase by 1. Since the slope is defined as the ratio of the increments along the y and x axis, we have 1/1=1.

If you want to be more formal, you can pick any two points on the line, for example (0,1) and (3,4), and use the formula

[tex]m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{4-1}{3-0} = 1[/tex]

Answer:

Step-by-step explanation:

look at the picture

The answer is 29 degrees.

Answer:

The variation equation is

[tex] f = \frac{k.m_1.m_2}{ {r}^{2} } [/tex]

step-by-step explanation:

From the question, the two masses are

[tex]m_1 \: and \: m_2[/tex]

This implies that the product of the two masses

[tex] = m_1 \times m_2 = m_1.m_2[/tex]

Moreover, the force,f varies directly with the products of the two masses

[tex] \implies \: f\propto m_1.m_2....eqn.1[/tex]

Also, the force varies inversely with the square of the distance,r

[tex] \implies \: f\propto \frac{1}{ {r}^{2} }.......eqn.2[/tex]

Joining equation 1 and 2, we got

[tex] \implies \: f\propto \frac{1}{ {r}^{2}} \times m_1.m_2[/tex]

[tex] \implies \: f \propto\frac{m_1.m_2}{ {r}^{2}}[/tex]

But the constant of variation is k

Multiplying the right hand side of the equation by k, we got

[tex] \implies \:f=\frac{k.m_1.m_2}{ {r}^{2}}[/tex]

Answer:

No correlation

Step-by-step explanation:

With the information provided, we have to conclude there is no correlation, since there is no apparent link between the two information.

It would be a positive correlation for example if we knew that the more apples Juan eats, the more he sleeps (or vice-versa).

It could be a negative correlation if we found that the more apples he eats, the less hours of sleep he has (or vice-versa).

But in this instance, we don't have any data indicating there is any form of correlation between those two numbers.

Answer:

9

Step-by-step explanation:

The number of possible lunch combinations of sandwich and juice are 9.

If we have to choose r objects out of n objects and then arrange them among themselves, then we first choose the objects in ⁿCr ways and then arrange them in  ways.

This can be used to find the number of different combinations possible of the sandwiches and juices.

Ways to select the sandwiches from 3 options = ³C₁ = 3!/1!(3-1)!

Ways to select the juice from 3 options = ³C₁ = 3!/1!(3-1)!

= ³C₁ = 3!/1!(3-1)!

Now, the total types of possible lunch combinations that can be created as  3×3=9

Hence, the number of possible lunch combinations of sandwich and juice are 9.

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Answer:

r = √98

Step-by-step explanation:

angle A and the diameter form an isosceles right triangle, with OA as the hypotenuse and r as the other sides. You can then make and solve an equation from the Pythagorean Theorem:

r^2 + r^2 = 14^2

2r^2 = 14^2

2r^2 = 196

r^2 = 98

r = √98

Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The angle A is 90 degree.

The side OA is 14.

There will be a right triangle formed.

So, Using Pythagorean theorem,

[tex]r^2+r^2=14^2[/tex]

[tex]2r^2=196[/tex]

Dividing 2 in both sides

[tex]r^2=\frac{196}{2}=98[/tex]

[tex]r=\sqrt{98}[/tex]

[tex]r=7\sqrt{2}[/tex]

So,the answer is [tex]7\sqrt{2}[/tex]     :     Answer

Hope it will help :)

Answer: Option B

2 is NOT in the domain of f ° g

Step-by-step explanation:

First we must perform the composition of both functions:

If [tex]g(x) = \sqrt{x-9}[/tex] and not [tex]\sqrt{x} -9[/tex]

[tex]f (x) = 4x + 3\\\\g (x) = \sqrt{x-9}\\\\f (g (x)) = 4 (\sqrt{x-9}) + 3[/tex]

The domain of the composite function will be all real numbers for which the term that is inside the root is greater than zero. When x equals 2, the expression within the root is less than zero

[tex]f (g (x)) = 4 (\sqrt{2-9}) + 3\\\\f (g (x)) = 4 (\sqrt{-7}) + 3[/tex]

The root of -7 does not exist in real numbers, therefore 2 does not belong to the domain of f ° g

The answer is Option B.

Note. If   [tex]g(x) = \sqrt{x}-9[/tex]

So

[tex]f(g(x)) = 4(\sqrt{x})-36 + 3[/tex]   And  2 belongs to the domain of the function

Buffalo Bills has the lowest price per wing. To find the answer divide the number of wings by the price to see how much it is per wing.

Buffalo Wild Wings offers the lowest cost per wing at $0.833, compared to $0.875 at Buffalo Bills and $0.85 at Fingers.

Comparing these values, Buffalo Wild Wings offers the lowest cost per wing at $0.833.

Answer:

Q1. is 628 cm

Q2 18.84 cm

Step-by-step explanation:

Q1. 400 / 2 = 200 to get the radius

3.14 * 200 = 628

Q2. 12 / 2 = 6 to get the radius

31.4 * 6 = 18.84

Answer:

This is exponential growth

Step-by-step explanation:

The amount by which the function is increasing from point to point is increasing, so it must be a quadratic or exponential function. If it was a quadratic, the amount it increases by would be increasing by a steady amount. (Ex. x^2 increases by how much it increased the last time + 2). But because this is not what the data shows, the function must be exponential.

Answer:  Exponential

Step-by-step explanation:

Find the slope of each tier:

2.654      6.290     14.909     35.335

           ∨             ∨              ∨              

        3.636      8.619        20.426       ← not equal so not linear

                    ∨             ∨

                4.983      11.807                  ← not equal so not quadratic

We have run out of slopes to compare so the options are either exponential or logarithmic.

Refer to the graph below that contains the given coordinates.  Since there is no apparent asymptote, it appears to be exponential.