For your birthday you recieved a gift certificate from a music store for three CDs. There eight you would like to have. If you select the CDs at random, how many different groups of CDs could you select

Answer:

Step-by-step explanation:

a/b=4/5    b/c=2/9

Ration of a to c is

a/c=4/9

Answer:

[tex]\frac{8}{45}[/tex]

Step-by-step explanation:

[tex]\frac{a}{c}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{b}{c}[/tex]

                               = [tex]\frac{4}{5}[/tex] × [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{45}[/tex]

Answer:

90 minutes

Step-by-step explanation:

If Jim takes 30 minutes to write 10 sentences, we can write a proportion.

[tex]\frac{30}{10}=\frac{x}{30}[/tex]

Cross multiply so we get [tex]10x=900[/tex].

And simplify.

[tex]x=90[/tex]

Answer: There are 48 students in the class.

Step-by-step explanation:

Let the number of students = S

Let the number of benches = B

If 4 students sit on each bench, 3 benches are left vacant.

S = 4(B - 3)

S = 4·B - 12 } Equation 1

If 3 students sit on each bench, 3 students still standing.

S = 3·B + 3 } Equation 2

We can match the two equations because they both indicate the same number of students.

4B - 12 = 3·B + 3

on solving this

4·B - 3·B = 3 + 12

B = 15 → number of benches

That is the number of benches, therefore substituting the value for B in equation 1

S = 4·B - 12 Equation 1

S = 4·15 -12

S = 60 - 12 = 48 → number of students

Answer: There are 48 students in the class.

There are 48 students and 15 benches.

If 4 students sit on each bench, 3 benches are left vacant.

48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.

If 3 students sit on each bench, 3 students still standing.

15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Final answer:

By creating a system of equations from the given conditions, the number of students in the class is calculated to be 48.

Explanation:

To find the number of students in the class based on the provided scenario, we can set up a system of equations based on the given conditions:

If 4 students sit on each bench, 3 benches remain empty.

If 3 students sit on each bench, 3 students remain standing.

Let's use B to represent the total number of benches and S to represent the total number of students. The first condition tells us that when 4 students sit on each bench, there are B - 3 benches filled, which means 4(B - 3) students are seated. The second condition implies that if 3 students sit on each bench, all the benches are filled, and 3 more students are still standing, which can be represented by 3B + 3.

Therefore, we can write two equations as follows:

4(B - 3) = S

3B + 3 = S

Since both expressions equal S, we can set them equal to each other:

4(B - 3) = 3B + 3

Simplifying this equation, we can find the number of benches (B), and then substitute back to find the number of students (S).

4B - 12 = 3B + 3

B = 3 + 12 = 15 benches

Now we substitute B into one of our original equations to find S:

S = 4(B - 3)

S = 4(15 - 3)

S = 4 × 12

S = 48 students

Therefore, there are 48 students in the class.

Answer:

2-2/3y

Step-by-step explanation:

First, you rearrange the equation, to get 3x=6-2y.

Then, you would divide all of the terms by 3, in order to get the value of x

x=2-2/3y

Answer:

Second is the answer

Step-by-step explanation:

Slope = rise/run = y /x = m

Solve y to get y = mx

The slope of a line is rise over run, which would be Y over X.

The second answer is the correct one.

ANSWER

See below

EXPLANATION

To solve the triangle means to find all sides and angles.

The right triangle has an angle of 38 degrees and an opposite leg of 12 yards

The third angle is 90-38=52°

We use the sine ratio to find the hypotenuse, h.

[tex] \sin(38 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \sin(38 \degree) = \frac{12}{h} [/tex]

[tex]h = \frac{12}{ \sin(38) } [/tex]

[tex]h = 19.49[/tex]

The hypotenuse is 19.49 yards to the nearest hundredth.

We can find the adjacent leg using the cosine ratio.

[tex] \cos(38) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(38) = \frac{a}{19.49} [/tex]

[tex]a = 19.49 \cos(39) [/tex]

[tex]a = 15.36[/tex]

to the nearest hundredth.

Answer:

C

Step-by-step explanation:

Substitute 2x into the equation where x is located. G(x)= (2x)^2=4x^2. This will be a graph which has been vertically stretched has a very steep curve to it facing up. It is C.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of a distance between two points:

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

ΔABC:

A(2, 5), B(5, 5), C(5, 9)

[tex]AB=\sqrt{(5-2)^2+(5-5)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\AC=\sqrt{(5-2)^2+(9-5)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\BC=\sqrt{(5-5)^2+(9-5)^2}=\sqrt{0^2+4^2}=\sqrt{0+16}=\sqrt{16}=4[/tex]

ΔDEF:

D(-7, 8), E(-4, 8), F(-4, 4)

[tex]DE=\sqrt{-4-(-7))^2+(8-8)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\DF=\sqrt{(-4-(-7))^2+(4-8)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\EF=\sqrt{(-4-(-4))^2+(4-8)^2}=\sqrt{0^2+(-4)^2}=\sqrt0+16}=\sqrt{16}=4[/tex]

AB ≅ DE

AC ≅ DF

BC ≅ EF

Therefore ΔABC ≅ ΔDEF

Kyle was 1 minute and 47 seconds faster in a 3-mile race yesterday compared to his normal running time.

Kyle's normal time is 23 minutes and 25 seconds, which is (23 * 60) + 25 = 1405 seconds. Yesterday, Kyle's time was 21 minutes and 38 seconds, which is (21 * 60) + 38 = 1298 seconds.

Now, we subtract the faster time from the normal time: 1405 seconds - 1298 seconds = 107 seconds.

Thus, Kyle was 107 seconds faster yesterday than his normal time. To put it back into minutes and seconds, we divide by 60:  107  \ 60 = 1 minute and 47 seconds.

So, Kyle was 1 minute and 47 seconds faster yesterday.

Answer:

I think Christina caught 23 fish and Sarah caught 8 fish.

Step-by-step explanation:

If I did this right, we have to find the equation to represent this situation. Christina caught one less than 3 times as many as Sarah caught. Since we do not know how many Sarah has, we have to use a variable so let's go with x. One less than 3 times as many would be 3x - 1 because one less means subtracting 1 and 3 times means multiply by three. So we have x for Sarah and 3x - 1 for Christina. We add those together to get x + 3x - 1 = 31 (since they caught 31 fish, the total would be 31). We simplify it down to 4x - 1 = 31. Add one to both sides to cancel it out and we get 4x = 32. Divide by 4 on both sides and we get x = 8. Since Sarah was x, Sarah caught 8 fish. To find Christina we just plug in the 8. 3(8) -1. 3 times 8 is 24 and 24 minus 1 is 23. To check our answers we add 8 and 23 together which comes out to be 31.

Please correct me if I'm wrong! (Now I'm not sure what you mean by a 5D table but if this is right I hope it helps)

The number of fish caught by Sarah = 8

And, The number of fish caught by Christina = 23

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Christina and Sarah went on a fishing trip and caught 31 fish.

Now,

Let number of fish caught by Sarah = x

So, The number of fish caught by Christina = 3x - 1

Here, Christina and Sarah went on a fishing trip and caught 31 fish.

Hence, We get;

⇒ x + (3x - 1) = 31

⇒ 4x - 1 = 31

⇒ 4x = 31 + 1

⇒ 4x = 32

⇒  x= 8

Thus, The number of fish caught by Sarah = x

                                                                  = 8

So, The number of fish caught by Christina = 3x - 1

                                                                   = 3×8 - 1

                                                                   = 23

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Answer:

Option D

Step-by-step explanation:

we now that

The increase of the temperature is equal to the absolute value of the difference of the temperatures

Let

x-----> the increase of the temperature

[tex]x=\left|-8-23\right|=31\°F[/tex]

or

[tex]x=\left|23-(-8)\right|=31\°F[/tex]

The expression to represent the increase in temperature is 23 - (-8). To find the increase in temperature, we subtract the initial temperature (-8) from the final temperature (23).

The expression to represent the increase in temperature is 23 - (-8).

To find the increase in temperature, we subtract the initial temperature (-8) from the final temperature (23).

Therefore, the correct expression is 23 - (-8).

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Answer:

make all the numbers have the same denominator, then simply see what multiplies to equal both fractions. your answer should be -3/10(1/5k+1)

Step-by-step explanation:

Answer:

(2,8)

Step-by-step explanation:

Add them together to get rid of the y.

-6x = -4 - y

-7x = -22 + y

=

-13x = -26

Then solve for x.

-13x/-13 = -26/-13

x = 2

Now plug in the x value into either equation and solve for y.

-7(2) = -22 + y

-14 = -22 + y

-14 + 22 = -22 + 22 + y

8 = y

So...

x = 2

y = 8

(2,8)

Answer:

The solution is (-2, -16).

Step-by-step explanation:

-6x = -4-y  can be solved for y:  y = 6x - 4

-7x = -22 + y

In the second equation, substitute 6x - 4 for y:

-7x = -22 + 6x - 4

Grouping like terms:  0 = -22 + 6x + 7x - 4, or

                                   -26  = 13x

So x = -2.  If x = -2, we can obtain the value of y from y = 6x - 4 (see above).

y = 6(-2) - 4 = -16

The solution is (-2, -16).

Answer:

168

Step-by-step explanation:

you would times 3.75 by 82 and subtract the answer from 2071.50 and get 1764 then divide 1764 by 10.50 and get 168

Answer:

168 adult adult ticket were sold

Step-by-step explanation:

Hello

The tickets cost for adults is     $10.50

The tickets cost for students is $3.75

number of adult ticket sold:       A

number of student  ticket sold:  B

10.50A+3.75B=2071.50     Equation 1

B=82                                   Equation 2

replacing equation 2 in equation 1

10.50A+3.75(82)=2071.50

10.50A=2071.50-307.50

[tex]A=\frac{1764}{10.50} \\\\A=168\\\\\\[/tex]

168 adult adult ticket were sold

Have a great day.

Answer:

B

Step-by-step explanation:

A sum of cubes has the form

a³ + b³

8x³ = (2x)³ and 125 = 5³

Hence

8x³ + 125 = (2x)³ + 5³ ← a sum of cubes

Answer:

x = 1 + (i)5 and x = 1 - (i)5

Step-by-step explanation:

x^2-2x+26=0 can be rewritten by completing the square of x^2-2x, as follows:

x^2-2x+26=0

x^2-2x+ 1  - 1  +26=0 (this 1 comes from halving the coefficient of x (which is -2), obtaining -1, squaring the result, and then adding this 1 to and subtracting this 1 from x^2-2x)  →  x^2-2x+ 1  - 1  +26=0

Rewriting x^2-2x+ 1 as the square of a binomial, we get:

 (x - 1)²  - 1  +26=0, or  (x - 1)²  - 1  +26=0, or   (x - 1)² = -25

Taking the square root of both sides yields x - 1 = ±(i)5.

Thus, the roots are x = 1 + (i)5 and x = 1 - (i)5  (Answer C)

Since [tex]T_n[/tex] is arithmetic, it's given recursively by

[tex]T_n=T_{n-1}+c[/tex]

where [tex]c[/tex] is a fixed number and [tex]T_1[/tex] is the starting term in the sequence. We have

[tex]T_n=T_{n-2}+2c[/tex]

[tex]T_n=T_{n-3}+3c[/tex]

and so on, so that

[tex]T_n=T_1+(n-1)c[/tex]

We're told that [tex]T_4=16[/tex], so

[tex]16=T_3+c[/tex]

and

[tex]T_5=16+c[/tex]

so that

[tex]T_3-T_5=(16-c)-(16+c)=-2c=6\implies c=-3[/tex]

Then the first term in the sequence is [tex]T_1[/tex]:

[tex]T_4=T_1+3(-3)\implies T_1=25[/tex]

and the sequence has general formula

[tex]T_n=25-3(n-1)\implies\boxed{T_n=28-3n}[/tex]

The first negative term occurs for

[tex]28-3n<0\implies28<3n\implies n>\dfrac{28}3[/tex]

[tex]\implies n=10[/tex]

The first negative term in the sequence is [tex]T_{10}=28-3\cdot10=\boxed{T_{10}=-2}[/tex].

Answer: Infinitely many solutions

Step-by-step explanation:

The equation 9x-8=34x-12 is a linear equation which is solved by moving variables and numerals at the opposite sides of the equation. This simplifies to -25x = 4 and by dividing both sides by -25, the answer x=-0.16 is obtained.

The subject of your question is a linear equation, more specifically, the solution to the equation 9x-8=34x-12. To find the solution, firstly bring variables to one side and numerals to the other side of the equation. So, it becomes 9x - 34x = 12 - 8, which simplifies to -25x = 4.

Then, solve for 'x' by dividing both sides by -25. This yields x = -4/25 or x = -0.16. So, x=-0.16 is the solution to the original equation 9x-8=34x-12.

Such questions involve understanding the principles of algebraic manipulation and the resolution of linear equations, which are fundamental concepts in mathematics.

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Answer:

246.61 feet (rounded to 2 decimal places)

Step-by-step explanation:

We multiply 3/4 with previous minute traveling.

Minute #1: travels 75 feet

Minute #2: travels (3/4)*75 = 56.25 ft

Minute #3: travels (3/4)(56.25) = 42.19 ft

Minute #4: travels (3/4)(42.1875) = 31.64 ft

Minute #5: travels (3/4)(31.64) = 23.73 ft

Minute #6: travels (3/4)(23.73) = 17.80 ft

So, in 6 minutes, the car travels  75 + 56.25 + 42.19 + 31.64 +23.73 + 17.80 = 246.61 feet.

The required fraction 40/32 simplifies to 5/4.

To simplify the fraction 40/32, we can find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.

The prime factorization of 40 is 2³ * 5, and the prime factorization of 32 is 2⁵. The common factors between 40 and 32 are 2³, so the GCD is 2³ = 8.

Dividing both the numerator and denominator by 8, we get:

40/32 = (40 ÷ 8) / (32 ÷ 8) = 5/4

Therefore, 40/32 simplifies to 5/4.

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To simplify 40/32, find the greatest common divisor (GCD) of 40 and 32, which is 8. Divide both the numerator and the denominator by 8 to get the simplest form 5/4.

To simplify the fraction 40/32, we need to find the greatest common divisor (GCD) of the numerator (40) and the denominator (32). The GCD is the largest number that can evenly divide both the numerator and the denominator.

Thus, 40/32 simplified is 5/4.

f(g(x))  (you plug/substitute g(x) into x)

f(x) = 4x - √x

f(g(x)) = 4(g(x)) - √(g(x))      since g(x) = (x - 5)², you can do:

f(g(x)) = 4(x - 5)² - √(x - 5)²     The ² and √ cancel each other, leaving

f(g(x)) = 4(x - 5)² - (x - 5)      Next factor out (x - 5)² or (x - 5)(x - 5)

f(g(x)) = 4(x² - 10x + 25) - (x - 5)  Now distribute the 4 and the -

f(g(x)) = 4x² - 40x + 100 - x + 5   Simplify

f(g(x)) = 4x² - 41x + 105         Your answer is B

ANSWER

[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]

EXPLANATION

The given functions are:

[tex]f(x) = 4x - \sqrt{x} [/tex]

and

[tex]g(x) = {(x - 5)}^{2} [/tex]

To find

[tex]f(g(x)) = f( {(x - 5)}^{2} )[/tex]

[tex]f(g(x)) =4 {(x - 5)}^{2} - \sqrt{{(x - 5)}^{2} } [/tex]

We expand and simplify to obtain,

[tex]f(g(x)) =4 {( {x}^{2} - 10x + 25)} - (x - 5)[/tex]

[tex]f(g(x)) =4{x}^{2} - 40x + 100 - x + 5[/tex]

Combine similar terms to get;

[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]

The correct choice is B.

[tex]2\sqrt{10}[/tex]

1. Use Distance formula

Important to use distance formula in such problems, so keep this formula memorized for future use.

The formula to find distance amongst two points is

[tex]\sqrt{(x^2-x^1)^2 + (y^2 - y1)^2}[/tex]

2. Plug in the numbers into the formula:

1 -(-1)^2 + 3 - (-3)^2

[tex]2^2=4[/tex]

[tex]6^2 = 36[/tex]

36 + 4 = 40

3. Find the square root of 40.

[tex]\sqrt{40}[/tex]

Simplify further:

[tex]2\sqrt{10}[/tex]

The distance between two points (-1, -3) and (1, 3) in a 2-dimensional Cartesian system is √40 units or approximately 6.32 units.

The subject of this question relates to finding the distance between two points in a 2-dimensional Cartesian system. This can be done using the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. That is the square root of the sum of the squares of the differences of the x-coordinates and the y-coordinates of the two points respectively.

Here, we have points (-1, -3) and (1, 3). Substituting into the distance formula, we get:
d = √[(1--1)² + (3--3)²]
= √[(2)² + (6)²] = √[4 + 36] = √40
So the distance between the points (-1, -3) and (1, 3) is √40 units, which is approximately 6.32 units.

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6(2x-3)+4 = 16-(-18)

(6)(2x)+(6)(-3)+4 = 16+18

12+ -18+4 = 16+18

(12x)+(-18+4) = (16+18)

12x+ -14 = 34

12x-14 = 34

12x-14+14 = 34+14

12x = 48

12x/12 = 48/12

x = 4

The answer is B. Since there are no parenthesis around pi/2, it stating that the graph shifts up pi/2 units - which is incorrect. It is a phase shift of pi/2 units (not a vertical shift).

Answer:  [tex]\bold{B)\quad y=2\ sin2x+\dfrac{\pi}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]

In the given graph,

Option B shows the value of D as [tex]\dfrac{\pi}{2}[/tex], which is incorrect since there is no vertical shift up. If the parenthesis included that value, like Option C, then it would have been correct.

Answer: 175

Step-by-step explanation: I hope this helps!!

Answer:

D

Step-by-step explanation:

ACD is a straight angle, thus

∠ACB + ∠BCD = 180. thus

∠ACB  131 = 180 ( subtract 131 from both sides )

∠ACB = 49° → D

Answer:

There are a lot of combinations possible

Step-by-step explanation:

One of them would be that each roll of quarters is $10 and each roll of pennies is 50cents so she could have 12 rolls of quarters and 2 rolls of pennies

One of the possible combinations that Greta can have is 12 rolls of quarters and 2 rolls of pennies.

No. of quarters required to make $1 = 4 quarters

No. of coins in 1 roll of quarter = 40 coins = $10

If one roll of quarter is $10, then we can have 12 rolls which will give us $120.

Now we reached $120, we need $1 more to reach $121

No. of pennies to make $1 = 100 pennies

No. of coins in 1 roll of pennies = 50

So we need 2 rolls of pennies to make $1.

Hence, we need 12 rolls of quarters and 2 rolls of pennies to make $121.

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Answer:

56 oz

Step-by-step explanation:

1 pound = 16 ounces

16 * 3.5 = 56

3.5 pounds = 56 ounces

I hope I helped!

Let me know if you need anything else!

~ Zoe

16x3=48 half of 16 is 8 so 48+8=56 :)

Answer to this is 8. Letter B

If you left 3 blank and there's 4 options then a pretty big chance that you get it wrong....