What is the Domain?


What is the Range?

Answer:

C) 1.4

Step-by-step explanation:

The probability of choosing 2 good ones is 7/10·6/9 = 42/90.

The probability of choosing 1 good one is 7/10·3/9 +3/10·7/9 = 42/90.

The probability of choosing 0 good ones is 3/10·2/9 = 6/90

The expected value is the sum of the product of number of good ones and their probability:

... 2·42/90 +1·42/90 +0·6/90 = (2+1)·42/90 = 42/30 = 1.4

Answer:

c) an = -13+7(n-1)

Step-by-step explanation:

We can use the formula for arithmetic sequences

an =a1+d(n-1)

where a1 is the first term in the sequence

d is the common difference

and n is the term number

a1 is -13

d is found by taking the second term and subtracting the first term

d = -6--13

  = -6+13

d=7

We are adding 7 each time

Substituting what we know,

an = -13 + 7(n-1)

The answer is:

Let us Represent the Line A in the Standard form : y = mx + c

where : m is the Slope of the Line and c is the y-intercept

Given : Equation of Line A is 2x + 3y = 10

[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]

Comparing with the Standard form, We can notice that :

Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]

We know that : Parallel lines have Same Slope

Given : Line A and Line B are Parallel

⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]

Given : Line B passes through the Point (-6 , 8)

We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)

Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]

Equation of Line B is :

[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]

⇒ 3y - 24 = -2x - 12

⇒ 2x + 3y = 12

Answer:

1. [tex]\sqrt[3]{4^2}[/tex]

2. Answer A

Step-by-step explanation:

1. A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.

[tex]4^{\frac{2}{3} }[/tex]

[tex]\sqrt[3]{4^2}[/tex]

2. An exponential always crosses at (0,1) This function crosses at (0.6) meaning it has shifted up 5 units or +5. These means only answer options A and D are possible solutions. Also, since the graph starts high and ends low and leveling out, this means the base is less than 1. Only 3/4 is less than 1. Answer A is the solution.

Answer:

x = 22 tan 31

x is approximately equal to 13.22

Step-by-step explanation:

We know from trigonometric functions that

tan A = opposite side/ adjacent side

tan 31 = x / 22

Multiply each side by 22

22 tan 31 = x

13.2189332

x is approximately equal to 13.22

Speed is the rate of change of distance over time.

It will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.

The given parameters are:

[tex]\mathbf{Speed = 1.17 \times 10^7 miles/mins}[/tex]

[tex]\mathbf{Distance = 3670000000 miles}[/tex]

Speed is calculated as:

[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]

Make Time the subject

[tex]\mathbf{Time = \frac{Distance}{Speed}}[/tex]

Substitute values for Speed and Distance

[tex]\mathbf{Time = \frac{3670000000\ miles}{1.17 \times 10^7 miles/mins}}[/tex]

[tex]\mathbf{Time = \frac{3670000000\ mins}{1.17 \times 10^7 }}[/tex]

Rewrite as:

[tex]\mathbf{Time = \frac{3.67\times 10^9\ mins}{1.17 \times 10^7 }}[/tex]

Apply law of indices

[tex]\mathbf{Time = \frac{3.67\times 10^{9 - 7}\ mins}{1.17}}[/tex]

Divide

[tex]\mathbf{Time = 2.20 \times 10^{2}\ mins}[/tex]

Hence, it will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.

Read more about speed and rates at:

https://brainly.com/question/359790

Answer:

After 33 weeks.

Step-by-step explanation:

Let w be number of weeks.

We have been given that Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. So the balance after w weeks will be 20w+40.

To figure out number of weeks Gina will have exactly $700 in her account, we will equate the balance after w weeks to 700.

[tex]20w+40=700[/tex]

Let us subtract 40 from both sides of equation.

[tex]20w+40-40=700-40[/tex]

[tex]20w=660[/tex]

Upon Dividing both sides of our equation by 20 we will get,

[tex]\frac{20w}{20}=\frac{660}{20}[/tex]

[tex]w=\frac{660}{20}[/tex]

[tex]w=33[/tex]

Therefore, after 33 weeks Gina will have exactly $700 in her account, excluding interest.

Answer:

(–6, –4)

Step-by-step explanation:

After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)

Answer:

(–6, –4)

Step-by-step explanation:

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.

It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.

Using the substitution method, make y the subject in the first equation

y = 5x + 26

substitute into the second equation

2x -7(5x + 26) = 16

-33x - 182 = 16

-33x = 16 + 182

-33x = 198

x = 198/-33

x = -6

since y = 5x + 26

y = 5(-6) + 26

= -30 + 26

= -4

hence (x,y) = (-6,-4)

Answer:

axis of symmetry   x=3/2

vertex  (3/2, 0)

Step-by-step explanation:

to find the axis of symmetry we use h = -b/2a

where ax^2 + bx+c

h = -(-12)/2(4)

h= 12/8

h = 3/2

the axis of symmetry is x = 3/2

the x coordinate of the vertex is h x=3/2

to find k, the y coordinate of the vertex, substitute x=3/2 into the equation

y=4x^2-12x+9

y=4(3/2) ^2-12(3/2)+9

 = 4 (9/4)  - 6*3 +9

  = 9-18+9

  = 0

the vertex (3/2, 0)

[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{The domain:} x\neq-4\ and\ x\neq1\\\\canceled\ (x+4)\\\\f(x)=\dfrac{x+3}{-(x-1)}=-\dfrac{x+3}{x-1}\ for\ x\neq-4\ and\ x=1[/tex]

Answer:

We have

seats x ( 62 / 100 ) = (seats - 17,100);

seats x 62 = 100 x (seats - 17,100);

seats x 62 = seats x 100 - 1710000;

1,710,000 = seats x 38;

seats = 1,710,000 ÷ 38;

seats = 45,000;

The correct answer is c. 45,000 seats;

Step-by-step explanation:

45, 000 A for plato users

Step-by-step explanation:

Trust me im Master chief

The first hexagon: 2, 2, 3, 4, 6, 7

The second hexagon: 3, 3, a, b, c, d

The hexagons are similar. Therefore the sides are in proportion.

[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex]     multiply both sides by 3

[tex]a=\dfrac{3}{2}=4.5[/tex]

[tex]\dfrac{b}{4}=\dfrac{3}{2}[/tex]    multiply both sides by 4

[tex]b=\dfrac{3}{2}\cdot4=6[/tex]

[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex]     multiply both sides by 6

[tex]c=\dfrac{3}{2}\cdot6=9[/tex]

[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex]    multiply both sides by 7

[tex]d=\dfrac{21}{2}=10.5[/tex]

The perimeter:

[tex]P=4.5+6+9+10.5=30[/tex]

Answer:

36

Step-by-step explanation:

The previous answerer forgot to add the two 3's to the sum so the correct answer it 36

Answer:

(B): (x - 2)/(x + 1)

Step-by-step explanation:

The numerator is x^2 + 5x - 14. That is equal to (x - 2)(x + 7).

The denominator is x^2 + 8x + 7. That is equal to (x + 1)(x + 7).

You can then eliminate (x+7) to get (x - 2)/(x + 1).

Answer: B

Step-by-step explanation:

 [tex]\dfrac{x^{2}+5x-14}{x^{2}+8x+7}[/tex]

[tex]=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}[/tex]

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

Hey there!

"Which is equivalent to [tex]80\frac{1}{4}[/tex]?"

In order for you to solve this particular equation, you multiply the front number from the denominator, then whatever that outcome is, add to the nominator

So,  

[tex]80\frac{1}{4}[/tex]

[tex]80(4) = 320[/tex]

[tex]320 +1 = 321[/tex]

[tex]4[/tex] stays the same

[tex]\boxed{Answer: \frac{321}{4}}[/tex]

If you want the decimal form, simplify the  the mixed  to a improper then you should get a outcome of: [tex]80.25[/tex]

For percentage do the fraction out of [tex]100[/tex] then solve it from there ([tex]0.8025[/tex]) would be the percentage form

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

[tex]80\frac{1}{4}[/tex] is equivalent to the decimal number 80.25, which can also be expressed as the improper fraction 321/4.

The question asks for an equivalent of the number [tex]80\frac{1}{4}[/tex].  To find this, we can convert the mixed number to an improper fraction or decimal. Since 1/4 is a standard fraction that is equivalent to 25 percent, we can express 1/4 as 0.25. Adding this to 80, we get an equivalent decimal number of 80.25. Another way to express 80 1/4 would be as an improper fraction, which would be [tex]\frac{321}{4}[/tex] because 80 times 4 equals 320, plus the numerator 1 equals 321.

Answer:

a. -1, odd; 2, even

b. [tex](x+1)(x-2)^2[/tex]

c. odd likely 3

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -1,2

We can write them in intercept or factored form as (x+1) and (x-2).  

Because the graph crosses the x-axis at -1, it's multiplicity is odd likely 1. However, the graph does not cross at 2 and has an even multiplicity likely 2.

The graph is ends up and is a sideways s so is positive with an odd degree.

This means the function has a degree of 3 or higher with the degree being odd.

Answer: P = 4w + 4

Step-by-step explanation:

width (w) = w

length (L) = w + 2  (2 more than its width)

Perimeter (P) = 2L + 2w

P = 2L + 2w

  = 2(w + 2) + 2(w)

  = 2w + 4   +  2w

  = 4w + 4

Answer:

4. 8.8 years

5. 8.6 meters

Step-by-step explanation:

4. The process of solving the equation f(x) = g(x) gives rise to a 4th-degree equation. Those are best solved using some sort of machine solver. A graphing calculator is often a good place to start. If you're going to do that anyway, you may as well start with a graphical solution to the question.

A plot of the two curves finds they intersect at about x = 8.8. (See the first attachment.) This avoids the extraneous solutions introduced by the process of eliminating the radical.

___

5. Analytical solution is simpler here, but the graphing calculator is faster yet. It shows the two rocks are at the same height at 8.6 meters (if they're launched at the same time).

... f(x) = g(x)

... -4.9x^2 +17 = -4.9x^2 +13x

... 17 = 13x . . . . . add 4.9x^2

... 17/13 = x . . . . time when rocks meet

... f(17/13) = -4.9(17/13)^2 +17 = -1416.1/169 +17 ≈ 8.62071

... f(17/13) ≈ 8.6 . . . . height at which rocks meet

Answer:

sin = √2/2, cos = -√2/2, tan = cot = -1

csc = √2, sec = -√2

Step-by-step explanation:

Angle runs around unit circle (where x^2+y^2=1)

from (1,0) to (-√2/2,√2/2)

Answer:

1. Translation 6 units to the right.

2. Stretch by a factor 5.

3. Translation 2 units up.

Step-by-step explanation:

Consider parent function [tex]f(x)=x^2.[/tex]

1. Translate the graph of the function 6 units to the right. Then you get the function [tex]f_1(x)=(x-6)^2.[/tex]

2. Stretch the graph of the function  [tex]f_1(x)=(x-6)^2[/tex] by a factor 5 and get the function [tex]f_2(x)=5(x-6)^2.[/tex]

3. Translate the graph of the function [tex]f_2(x)=5(x-6)^2[/tex]  2 units up to fet the function [tex]h(x)=5(x-6)^2+2.[/tex]

Answer:

66

Step-by-step explanation:

divide 264/4=66

Answer:

C) 66 jumps

Step-by-step explanation:

Dana can jump 264 times in 4 minutes

Divide 364 by 4 to see how many times she can jump in one minute

264/4 = 66

Answer:

You will want to set up the ratio for each and set them equal to each other. Then you can cross multiply to verify if you get the same answer. Another strategy is to set up each ratio and then reduce to lowest terms to see if you get the same fraction.

Step-by-step explanation:

Answer:

-24-36x-5x

-24-41x

or -41x-24

Step-by-step explanation:

Let's do the usual thing and make t the years since 1950.   We'll just abbreviate a billion B.

f(1950-1950)=39.4 B

f(2000-1950) =2025.2 B

Our exponential form for f will be

[tex]f = a e^{kt}[/tex]

[tex]39.4 \textrm{ B} = a e^{ 0 k} = a[/tex]

[tex]2025.2 \textrm{ B} = a e^{50 k}[/tex]

Dividing

[tex]\dfrac{2025.2}{39.4} = e^{50 k}[/tex]

[tex]50 k = \ln \dfrac{2025.2}{39.4}[/tex]

[tex]k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932[/tex]

Our function is

[tex]f = 39.4 \textrm{ B } e^{0.0787932 t }[/tex]

Since [tex]e^{0.0787932} \approx 1.08198[/tex]

[tex]f = 39.4 \textrm{B } 1.08198^t }[/tex]

around 8.2 % annualized growth.

Final answer:

An exponential function modeling U.S. federal budget growth between 1950 and 2000 is based on the formula f(t) = a ×[tex]b^t[/tex], where 'a' is the initial value in 1950 ($39.4 billion) and 'b' is the growth factor, calculated from the data in 2000 ($2025.2 billion). Solving the equations gives us the function [tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Explanation:

We can model the growth of the U.S. federal budget using an exponential function, given the data from 1950 and 2000. First, we identify the years as our variable 't' where t=0 corresponds to the year 1950. We'll use the formula for exponential growth, which is f(t) = a × b^t, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in years.

From the question, we have two data points: the budget in 1950 (t=0) is $39.4 billion, which gives us our 'a' value. In 2000 (t=50), the budget is $2025.2 billion. Plugging these values into our exponential function, we get two equations:

f(0) = 39.4 = a × [tex]b^0[/tex] which simplifies to a = 39.4.

f(50) = 2025.2 = 39.4 × b^50.

To find the value of 'b', we solve the second equation:

2025.2 = 39.4 ×  [tex]b^{50[/tex]
Divide both sides by 39.4:
51.4 = [tex]b^{50[/tex]
Take the 50th root of both sides:
b =[tex]51.4^(1/50).[/tex]

Now that we know both 'a' and 'b', we can write the exponential function that models the federal budget from 1950 to 2000:

[tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Keep in mind that this model does not account for complexities like inflation or changing economic conditions. It provides a simplified view of the growth of the federal budget over this particular time period.

Answer:

11x+8 cm = Perimeter

Step-by-step explanation:

A triangle has 3 sides.  We add up all three sides to get the perimeter.

s1+s2+s3 = Perimeter

(x+4) +( 3x+1) + (7x+3) = Perimeter

Combine like terms

11x+8 = Perimeter

Answer:

P = 11x + 8 cm

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of the three sides.

... P = s1 + s2 + s3

... P = (x +4 cm) +(3x +1 cm) +(7x +3 cm) . . . . substitute for s1, s2, s3

... P = x(1 +3 +7) + cm(4 + 1 + 3) . . . . . . collect terms

... P = 11x + 8 cm

Answer:

The answer is C)

Step-by-step explanation:

In order to fully solve a system of equations, you need both variables, x And y. Therefore he has to go back and solve for x

Answer:

SSS can be used to prove that the given triangles are congruent.

Step-by-step explanation:

In the given two triangles ΔADC and ΔABC,

Hence, ΔADC ≅ ΔABC by Side-Side-Side (SSS) congruence.

SSS congruence-

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.