You need to rent a bowling lane. On Friday nights, you have two options. Option A is a $20 lane rental plus $3 per game. Option B is a $35 lane rental with a maximum of 10 games. For what number of games is the cost the same for each option?​

Answer:

The x-axis, it would be between quadrant 2 and quadrant 3

Option 1: $71.00 is the correct answer

Step-by-step explanation:

Let x be the money Karen started with:

Then

22% of x is $15.62

Mathematically writing

[tex]15.62 = 22\%\ of\ x\\15.62 = 0.22 * x\\x = \frac{15.62}{0.22}\\x = 71[/tex]

Hence,

Karen had $71.00 to start.

Option 1: $71.00 is the correct answer

Keywords: Percentage, percent

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Answer:

Part 1) [tex]-\sqrt{15}[/tex]

Part 2) [tex]x=\frac{b+ac}{2c-ab}[/tex]

Step-by-step explanation:

Part 1) we know that

To put factor back into the square root, we have to put squared value

we have

[tex]-5\sqrt{0.6}[/tex]

Remember that

[tex]5=\sqrt{5^2}[/tex]

substitute in the expression above

[tex]-5\sqrt{0.6}=-\sqrt{(5^2)(0.6)}=-\sqrt{25*0.6}=-\sqrt{15}[/tex]

Part 2) we have

[tex]\frac{2x-a}{b}=\frac{ax+1}{c}[/tex]

Solve for x

That means----> Isolate the variable x

Multiply in cross

[tex](2x-a)c=(ax+1)b[/tex]

Apply distributive property

[tex]2cx-ac=abx+b[/tex]

Group terms

[tex]2cx-abx=b+ac[/tex]

Factor x left side

[tex]x(2c-ab)=b+ac[/tex]

Divide by (2c-ab) both sides

[tex]x=\frac{b+ac}{2c-ab}[/tex]

There were 100 student tickets sold

Step-by-step explanation:

The given is:

We need to find how many student tickets were sold

Assume that the number of student tickets is x and the number of adult tickets is y

∵ The number of student tickets is x

∵ The number of adult tickets is y

∵ They sold 300 tickets

∴ x + y = 300 ⇒ (1)

∵ The price of the student ticket = $4

∵ The price of the adult ticket = $6

∵ The total sales = $1600

- Add the prices of the students tickets and the adult tickets

  and equate the sum by the total sales

∴ 4x + 6y = 1600 ⇒ (2)

Now we have a system of equation to solve it

Multiply equation (1) by -6 to eliminate y

∵ -6x - 6y = -1800 ⇒ (3)

- Add equations (2) and (3)

∴ -2x = -200

- Divide both sides by -2

∴ x = 100

There were 100 student tickets sold

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In this question, you're plugging in g(x) into f(x) to simplify.

You would plug the g(x) equation into the x variable in the f(x) equation.

Plug g(x) into f(x):

(2x+3)² - 1

Solve:

(2x+3)² - 1

Use FOIL:

F = First

O = Outsides

I = Insides

L = Last

4x² + 12x + 9 - 1

Combine like terms:

4x² + 12x + 8

Answer:

4x² + 12x + 8

Answer:

-13x + 6y

Step-by-step explanation:

combine like terms

-7x + 6y - 6x

-7x - 6x = -13x

-13x + 6y

Answer:

Step-by-step explanation:

-7x+6y-6x

Solution:

Put like terms together from left to right; that is the equation will assume a new order from -7x+6y-6x to

-7x-6x+6y

Sum the figures with like terms

= -13x+6y (answer)

The distance from the point (-6,8) to the line y=-3x+10 is calculated using the distance formula which yields a value of approximately 6.32, when rounded to the nearest hundredths.

The subject of this question is mathematics, specifically it pertains to finding the distance between a point and a line. The distance between a point (x1, y1) and a line ax + by + c = 0 can be calculated using the formula: distance = |ax1 + by1 + c|/sqrt(a²+b²). In your case, the given point is (-6,8) and the line is y = -3x + 10, which can be rewritten as 3x + y - 10 = 0. Therefore, a = 3, b = 1, c = -10, x1 = -6, and y1 = 8.

Substituting these values into the distance formula: distance = |3*(-6) + 1*(8) - 10|/sqrt((3)² + (1)²) = |-18 + 8 - 10|/sqrt(10) = |-20|/sqrt(10) = 20/sqrt(10) = 6.32, rounded to the nearest hundredths.

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Answer:

3a²  

Step-by-step explanation:

least common denominator of a² and 3a

a²  = a *a

3a = 3 * a

least common denominator = 3 * a*a =3a²  

Answer:

The answer is 3a², where a ≠ 0

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Rational expressions are 4/a² and 5/3a

2. Find the least common denominator for these two rational expressions.

Denominators of the expressions are:

a² and 3a ⇒ a² = a * a, 3a = 3 * a

The least common denominator will be:

3a², where a ≠ 0

3a²/a² = 3 and 3a²/3a = a

Answer:

Jamal  is correct.

Step-by-step explanation:

3:4 is equivalent to 9:12, not 18:12.

We can see that for 3:4, the left side is less than the right, but for 18:12, left side is greater than the right, which immediately tells us the ratios are not equivalent.

Jamal is correct. 18:12 and 3:4 are not equivalent ratios.

To determine if two ratios are equivalent, you can simplify them to their simplest form or find a common factor that divides both terms. In this case:

18:12 can be simplified by dividing both terms by their greatest common factor, which is 6:

18 ÷ 6 = 3

12 ÷ 6 = 2

So, 18:12 simplifies to 3:2.

Now, compare it to 3:4. Since they have different values (3:2 vs. 3:4), Jamal's statement is incorrect, and Margie is right; they are not equivalent ratios.

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The probability of drawing two green marbles, with replacement is [tex]\frac{9}{25}[/tex]

Given that There are 4 red and 6 green marbles in a jar

To find: probability of drawing two green marbles, with replacement

The probability of an event is given as:

[tex]\text {probability }=\frac{\text { number of favourable outcomes }}{\text { total number of possible outcomes }}[/tex]

Here total number of possible outcomes = 4 red + 6 green marbles = 10

Favourable outcome is drawing two green marbles with replacement

So favourable outcome = 6

So probabilty of choosing green marble:

[tex]probability = \frac{6}{10} = \frac{3}{5}[/tex]

Now given that with replacement, so we get

[tex]\text { probability }=\frac{3}{5} \times \frac{3}{5}=\frac{9}{25}[/tex]

Thus probability is [tex]\frac{9}{25}[/tex]

Answer:

d = 5

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a₂ - a₁ = a₃ - a₂ = [tex]a_{n}[/tex] - [tex]a_{n-1}[/tex]

Given

[tex]a_{n}[/tex] = 5n - 3

Generate the first 2 terms of the sequence by substituting n = 1, n = 2

a₁ = 5(1) - 3 = 5 - 3 = 2

a₂ = 5(2) - 3 = 10 - 3 = 7

d = 7 - 2 = 5

Answer:

Closed.

Step-by-step explanation:

a)The scale of the number line is 1 unit represents 8 units.

b) On both x and y axes 1 unit represents 4 units.

How to find scale of a graph.

a) The difference between 64 and 32 is

= 64 - 32 = 32

On the number line there are 4 divisions between 32 and 64

Each division = 32/4 = 8

Therefore,the scale of the number line is 1 unit represents 8 units.

b) vertical axis (y axis)

From 0 to 12 there are 3 divisions

Each unit of the division = 12/3 = 4

Therefore, 1 unit represents 4 units on the y axis.

Horizontal axis (x axis)

From 0 to 20, there are five divisions

Each division = 20/5 = 4

Therefore, each 1 unit of division represents 4 unit

Complete question

Scenario:

Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write an inequality that would be used to solve for the least amount of money he needs to deposit to avoid a fee.

Equation:

727.29 − 248.50 + x ≥ 500

Answer:

x  ≥  21.21

Answer:

For Tammi it is 6% interest Rate.

For Gloria it is 6 Years.

Step-by-step explanation:

Tammi:

Principal = $520

Time = 5 Years

Interest = $156

Interest Rate = Interest / (Principal x Time)

Interest Rate = $156 / ($520 x 5)

Interest Rate = $156 / $2,600

Interest Rate = 0.06

Hence Interest Rate is 6%

Gloria:

Principal = $500

Interest Rate = 7.5%

Interest = $225

Time = Interest / (Principal x Interest Rate)

Time = $225 / ($500 x 0.075)

Time = $225 / $37.5

Time = 6 Years

Hence it will take 6 Years

Answer:

6%

Step-by-step explanation:

We did percent and converting problems in class and we've been doing it since yesterday.

I hope this helps!

Answer:

Step-by-step explanation:

(2/5 * 30) * 6^2 - 3^2           Reduce 2/5 * 30

180 * 6^2 - 3^2                    Raise the bases of the power

180 *36 - 9                           Multiply 36 and 180

6480 - 9                               Subtract 9

6471

Answer:

Step-by-step explanation:

You could complete the square to do this, or you could just evaluate the h coordinate using the simple formula

[tex]h=-\frac{b}{2a}[/tex]

then find k by subbing that h value into the equation for x to find y which is the same as k.  In our quadratic, a = 4, b = -8, and c = -4.

[tex]h=\frac{-(-8)}{2(4)}=1[/tex]

Now sub that value into the quadratic to find y (k):

[tex]4(1)^2-8(1)-4=4-8-4=-8[/tex]

The vertex of the quadratic is (1, -8)

Answer:

Step-by-step explanation:

X={0,12,23}

Y={3,12,15}  

X \ Y = { 0 , 23}

X/Y means the element should be only in X. We have remove the element in X if it is in Y

In this 0 and 23 is only in X

12 is X and Y. So it wont come in X/Y

The set X \ Y represents the difference of two sets, indicating all the elements that are in set X but not in set Y. For X={0, 12, 23} and Y={3, 12, 15}, the elements that are in X but not in Y are '0' and '23', so X \ Y = {0, 23}.

In set theory, the notation X \ Y represents the difference of two sets. This indicates all the elements that are in set X but not in set Y. In this case:

X={0, 12, 23}, Y={3, 12, 15}

So the elements that are in X but not in Y are '0' and '23'.

Therefore, X \ Y = {0, 23}.

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Answer:

Equation: 178 - x = - 62

Explanation:

Start of the wee: 178

One withdrawal: x

End of the week: -62

178 - x = -62

Simplify both sides of equation

178−x=−62

178+−x=−62

−x+178=−62

Subtract 178 from both sides

−x+178−178=−62−178

−x=−240

Divide both sides by -1

-x / -1 = -240 / -1

x=240

Trevor withdrew $240 from his bank account. This was calculated by setting up an equation with his initial positive balance and final negative balance, and solving for the withdrawal amount.

To determine how much money Trevor withdrew from his bank account, we can set up an equation representing the transactions in his account. Let x represent the amount of money withdrawn. We start with Trevor's initial balance, subtract the withdrawal, and set that equal to his final negative balance:

Initial balance - Withdrawal = Final balance

178 - x = -62

To solve for x, we add x to both sides to get the withdrawal amount on its own and then add 62 to both sides to isolate x:

178 - x + x = -62 + x

178 = x - 62

178 + 62 = x

240 = x

So, Trevor withdrew $240 from his bank account.

Answer:

The value of car after 5 years of exponentially depreciation is $16,213.36  

Step-by-step explanation:

The initial amount of the car = i = $24,600

The depreciates rate of interest applied = r = 8%

Let The value of car after n years = A  

The number of years = n = 5 years

Now,According to question

The value of car after n years = initial price of car  × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The value of car after 5 years = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, $A = $24,600 × [tex](1-\dfrac{\textrm 8}{100})^{\textrm 5}[/tex]

Or, $A = $24,600 × [tex](0.92)^{5}[/tex]

Or, $A = $24,600 × 0.65908

Or, $A = $16,213.36

So, The value of car after 5 years = A = $16,213.36

Hence , The value of car after 5 years of exponentially depreciation is $16,213.36  . Answer

Answer:

f(6)

Step-by-step explanation:

Answer:

f(2)

Step-by-step explanation:

Answer:

B.) 0.95%

Step-by-step explanation:

19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4

27.9 − 26.95 = 0.95

The difference is 0.95%

The data is given as 19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4

Organize the Data:

Arrange the percentages in ascending order:

19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4

Find the Median of the 7 States:

Since there are 7 data points, the median will be the 4th value.

Median = 27.9

Calculate the Median for All 50 States:

The median for all 50 states is given as 26.95%.

Find the Difference:

Difference = Median for all 50 states - Median for 7 states

Difference = 26.95 - 27.9

Difference = 0.95

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Answer:

[tex]\large\boxed{slope=\dfrac{7}{2}=3.5}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (3, 1) and (5, 8).

Substitute:

[tex]m=\dfrac{8-1}{5-3}=\dfrac{7}{2}[/tex]

Answer:

[tex]\boxed{\bold{Slope \ \frac{7}{2} \ = \ 3.5 }}[/tex]

Explanation:

Slope Intercept Form: y = mx + b

Slope Formula: [tex]\bold{\frac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\bold{\left(x_1,\:y_1\right)=\left(3,\:1\right),\:\left(x_2,\:y_2\right)=\left(5,\:8\right)}[/tex]

[tex]\bold{m=\frac{8-1}{5-3}}[/tex]

[tex]\bold{m=\frac{7}{2}}[/tex]

[tex]\bold{Slope \ in \ fraction \ form: \frac{7}{2} }[/tex]

[tex]\bold{Slope \ in \ decimal \ form: \ 3.5}[/tex]

Answer:

For [tex]d=-2[/tex] rational expression will be undefined.

Step-by-step explanation:

Given function is [tex]\frac{6d-4}{d+2}[/tex]

We need to find for what value of variable [tex]d[/tex] this rational expression will be undefined.

The rational expression will be undefined if the denominator of the expression will become zero.

So, let us plug denominator equal to zero.

[tex]d+2=0\\\\Subtracting\ both\ side\ 2\\\\d+2-2=-2\\\\d=-2[/tex]

Hence, this rational expression will be undefined if the value of variable [tex]d=-2[/tex].

Answer:

The midpoints are ( 6, 5 ).

Step-by-step explanation:

Given that the endpoints are  A ( 3, 7) and B (9, 3)-

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex] then the mid points C are-  

C = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex], [tex]\frac{ y_{1} + y_{2}  }{2}[/tex]  )

Here,

A ( 3, 7 ) and B ( 9, 3 )-

Then the  midpoints C are-

C = ( [tex]\frac{ 3 + 9}{2}[/tex], [tex]\frac{ 7 + 3 }{2}[/tex] )

C= ( 12/2 , 10/2 )

C = ( 6, 5 )

Hence the midpoints are (6, 5).

Answer:

Step-by-step explanation:

Answer:

A ) The Original price of music player before it was marked down by  [tex]\dfrac{1}{4}[/tex]  is $512

B ) The price that store paid for player is $256

C ) The difference between discount price and price paid by store is $128

Step-by-step explanation:

Given as :

A ) The sale price of music player = $128

The music player is marked down by [tex]\dfrac{1}{4}[/tex] of original price

Let The original price = $x

Now, According to question

[tex]\dfrac{1}{4}[/tex] of original price = $128

i.e [tex]\dfrac{1}{4}[/tex] × $x = $128

Or, x = 128 × 4

∴ x = $512

So, The Original price of music player before it was marked down by  [tex]\dfrac{1}{4}[/tex]  is $512

B ) The music player is marked up by [tex]\dfrac{1}{2}[/tex] before it was placed on sales floor .

Let The price that store paid for player = $y

Now, According to question

∵ The original price of player = $512

So, The price that store paid for player = [tex]\dfrac{1}{2}[/tex]  × original price of player

i.e y =  [tex]\dfrac{1}{2}[/tex]  × $512

Or , y = $256

So,The price that store paid for player = $256

C ) Let The difference between discount price and price paid by store = $z

So, According to question

z = y - discount price

Or , z = $256 - $128

∴  z = $128

So, The difference = $128

Hence, A ) The Original price of music player before it was marked down by  [tex]\dfrac{1}{4}[/tex]  is $512

B ) The price that store paid for player is $256

C ) The difference between discount price and price paid by store is $128

Answer

Answer:

6^h=126

Step-by-step explanation:

6 to the power of h is just 6^h

Plug it into an equation with =126

Boom you have the equation 6^h=126