Tickets to a play cost $4 in advance and $5 at the door. The theater club president wants to raise at least $400 from the ticket sales. If the club sells 40 tickets in advance, what is the least number of tickets the club needs to sell at the door to reach the president’s goal?

Answer:

B

Step-by-step explanation:

A

f(1) = 4*(1/2)^1 = 4/2 = 2

(1,1) is not the same thing.

B

B is the answer.

C

f(0)=4 not 2 C is incorrect. C is not the answer

D

Same problem as C

Put the value of slope to the equation of the function:

[tex]y=-\dfrac{1}{6}x+b[/tex]

Put the coordinates of the point B(12, 3) to the equation:

[tex]3=-\dfrac{1}{6}(12)+b[/tex]

[tex]3=-2+b[/tex]            add 2 to both sides

[tex]5=b[/tex]

Answer:

The value of b is 5.

Step-by-step explanation:

Consider the provided information.

It is given that the slope intercept form is, y = mx + b

Where m is the slope and b is the y intercept.

Also, it is given that the slope of the line is -1/6.

Line AB passes through points A(–6, 6) and B(12, 3).

That means Point A and B must satisfy the equation of line.

Substitute [tex]m=\frac{-1}{6}, x=-6\ \text{and}\ y = 6[/tex] in slope intercept form:

[tex]6=\frac{-1}{6}\times(-6)+b[/tex]

[tex]6=1+b[/tex]

[tex]5=b[/tex]

Thus, the value of b is 5.

Answer:

Area of the figure is 304 sq. units

Step-by-step explanation:

The area is divided into two identical trapezoids of height 8 units and bases 14 and 24 units.

Area of a trapezoid = (1/2) * (Sum of base lengths) * height

So, area of 1 one trapezoid = (1/2)*(14+24)*8=152

The area of the figure is twice the area of the trapezoid.

So, area of figure = 2 * 152 = 304 sq. units

∴ Area of the figure is 304 sq. units

Answer:

Your answer would require a 7 in the hundreds place

Step-by-step explanation:

1,273

The 1 is in the thousands place.  1 * 1000

The 2 is in the hundreds place.  2 * 100

The 7 in in the tens place.  7 * 10

 The 3 is in the ones place.  1 * 1

To get from 10 to 100, we would multiply by 10, so to get from the tens place to the hundreds place is 10 times greater.

Your answer would require a 7 in the hundreds place

In the number system, each place to the left is ten times the place to its right. Therefore, for the value of the 7 to be ten times greater than the 7 in 1,273, it must be in the tens place, such as in numbers like 702, 770, or 170.

The value of a digit in a number depends on its place or position. In the number system, each place is ten times the place to its right. Therefore, in the number 1,273, the value of the 7 is simply 7 (because it's in the units place). However, for the 7 in the new number to be ten times greater than the 7 in 1,273, it must be in tens place. Therefore, the new number could be 7x10 = 70 (with the 7 in the tens place). So, any number with 70 in the tens place (like 702, 770, or 170) has a 7 that's ten times the 7 in 1,273.

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Answer:

Step-by-step explanation:

1) 144 x $12 = $1728.00

2) $10 x 2 = $20       $20 x 3 = $60      $30 x 2 = 60;   $20+$60+$60 = $140

3)  $350 - $234 = $116.00

4) $225 ÷ $15 = 15 lawns will need to be cut

5) 2/4 = 1/2 = .50 = 50%  B

6) 0.99 + 1.19 + 1.50 + 0.99 =  $4.67

7)  B  90 seconds is = 1 minutes and 30 seconds  (1 minute = 60 seconds)

8) 4 weeks x 5 nights = 20 nights of studying

   20 nights x 30 minutes = 600 minutes

   600 minutes ÷ 60 (minutes in an hour) = 10 hours of studying  D

Answer:

? = 113

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.  Since the lines are parallel, the angles are equal.

? = 113

Answer:

y = 33/5 or 6.6

Step-by-step explanation:

7y + 44 = 12y + 11

      -11              -11

7y + 33 = 12y

-7y           -7y

33 = 5y

Divide both sides by 5

= 33/5 or 6.6

Answer:

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

Step-by-step explanation:

We are given the following equation for which we have to solve for y:

[tex]7y+44=12y+11[/tex]

So first of all, we will rearrange the terms by putting the like terms together (variables on one side of the equation and constants on the other side) to get:

[tex]12y-7y=44-11[/tex]

Then solving for y:

[tex]5y=33\\\\y=\frac{33}{5}[/tex]

Therefore, the value of y is equal to [tex]y=6\frac{3}{5}[/tex] (rewriting y in a mixed fraction form).

Answer:

2w

Step-by-step explanation:

you multiply 2 by how many hours you have worked (w)

Put the coordinates of the points to the inequality and check.

y > 2x + 1

for (1, 4):

4 > 2(1) + 1

4 > 2 + 1

4 > 3   CORRECT

for (1, 6):

6 > 2(1) + 1

6 > 2 + 1

6 > 3   CORRECT

for (3, 8):

8 > 2(3) + 1

8 > 6 + 1

8 > 7   CORRECT

for (2, 5):

5 > 2(2) + 1

5 > 4 + 1

5 > 5   FALSE

Answer:

a

Step-by-step explanation:

the mean = [tex]\frac{total score}{count}[/tex]

let the fifth score be x and count = 5, hence

[tex]\frac{86+82+72+69+x}{5}[/tex] = 79 ( multiply both sides by 5 )

309 + x = 395 ( subtract 309 from both sides )

x = 86

the student requires a score of 86% → a

Answer:

-3

Step-by-step explanation:

-3-16=-19

-19+16=-3

Answer:

-3

Step-by-step explanation:

Answer:

You should recruit a total of 525 subjects for the whole study.

Step-by-step explanation:

The question states that you want 175 subjects per group for 3 groups.  This indicates that we need to either multiply 175 times 3, or we can add 175 three times to get the total number of subjects we would need to recruit.  Group 1 should have 175, Group 2 should have 175 and Group 3 should have 175.  Whether we multiply 175 x 3 or add 175+175+175, we get a final anser of 525.

Answer:

y = 2x+2

Step-by-step explanation:

When we have 2 points, we can find the slope from

m = (y2-y1)/(x2-x1)

   = (6--6)/(2--4)

   = (6+6)/(2+4)

   = 12/6

  = 2

The slope is 2

We can use the point slope form of the equation for a line

y-y1 = m(x-x1)

y-6 = 2(x-2)

We need to get this in slope intercept form

Distribute the 2

y-6 = 2x-4

Add 6 to each side

y-6+6 = 2x-4+6

y = 2x+2

Answer:

y = 2x + 2

Step-by-step explanation:

the equation of a line in slope-intercept form is

y = mx + b ( m is the slope and b the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 6) and (x₂, y₂ ) = (2, 6)

m = [tex]\frac{6+6}{2+4}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence

y = 2x + b is the partial equation

to find b substitute either of the 2 points into the partial equation

using (2, 6), then

6 = 4 + b ⇒ b = 6 - 4 = 2

y = 2x + 2 ← equation in slope-intercept form

Answer:

10:45

Step-by-step explanation:

v...speed = 40 mph

s...distance = 60

t...time

if he was 15 min late he arrived at 12:15

v=s/t => t=s/v

t = 60/40 = 1.5 h = 1h and 30 min

if he arrived at 12:15 and he was driving for an hour and a half just substract

12:15 - 1:30 = 11:15 - 0:30 = 10:45

he left at 10 45

Answer:

x < [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

distribute the parenthesis on the right side

5x + 3 < 3x + 6 ( subtract 3x from both sides )

2x + 3 < 6 ( subtract 3 from both sides )

2x < 3 ( divide both sides by 2 )

x < [tex]\frac{3}{2}[/tex]

Answer:

x <  [tex]\frac{3}{2} \\[/tex]

Answer:

The answer is ASA.

Step-by-step explanation:

There is one other angle in the middle which is congruent to its self.

ASA (Angle-Side- Angle) method can we use to prove that the triangles are congruent

Two triangles are called to be congruent if their sides have the equal length and angles have equal measure.

Thus, two triangles can be superimposed side to side and angle to angle.

If any two angles and the side of the angles of triangle are equivalent to the corresponding, then the two triangles are said to be congruent by ASA rule.

There is one other angle in the middle which is congruent to its self

ASA (Angle-Side- Angle)

Learn more about congruent triangles here:

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Answer:

[tex]a=1,\ 2,\ 3,\ 6.[/tex]

Step-by-step explanation:

A whole number is any number of a set [tex]\{0,\ 1,\ 2,\ 3,...\}[/tex]

The equation [tex]ax=6[/tex] has a solution [tex]x=\dfrac{6}{a},\ a\neq 0.[/tex]

If [tex]a=1,[/tex] then [tex]x=\dfrac{6}{1}=6[/tex] is a whole number.

If [tex]a=2,[/tex] then [tex]x=\dfrac{6}{2}=3[/tex] is a whole number.

If [tex]a=3,[/tex] then [tex]x=\dfrac{6}{3}=2[/tex] is a whole number.

If [tex]a=6,[/tex] then [tex]x=\dfrac{6}{6}=1[/tex] is a whole number.

For all other values of [tex]a[/tex] equation  [tex]ax=6[/tex]  will have solution that is not a whole number.

Answer: 164.4 or 165

Step-by-step explanation: So, you do 226 x 3 and you get $678. So now that you know that you have $678 worth of student tickets, you want to find how much more you need for the adult tickets, so you do $1500-$678, and you get $822. Divide it by 5 and you get 164.4, so you wanna sell about 165 tickets. Check your work by multiplying 5 by 165 and you get $825, which meets your $1500 minimum

After calculating the revenue already obtained from the student tickets sold, the remaining revenue needed to reach $1500 is found. This amount is divided by $5 (the cost of an adult ticket) to find the minimum number of adult tickets needed. Since you can't sell fractions of tickets, we round up to the next whole number, which is 165 adult tickets.

The first step to solve this problem is to calculate how much revenue has already been raised from the student tickets sold, which is $3 x 226 = $678. Then subtract this amount from the total revenue target of $1500, which gives $1500 - $678 = $822.

The choir director now needs to raise $822 from selling adult tickets. As each adult ticket costs $5, we can calculate the minimum number of adult tickets that need to be sold by dividing the amount of revenue needed by the price of an adult ticket. This is $822 / $5 = 164.4.

Since you can't sell .4 of a ticket, we'll need to round up to the next whole number, giving a minimum of 165 adult tickets that need to sell in order to reach the revenue target.

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Answer:

4j-3 = j   is an equation

2 + 66÷11 -3*2  is an expression

g+h>f  is an inequality

Step-by-step explanation:

An equation has an equals sign    =

An expression has no equals sign or greater or less than signs

An inequality has (  ≤,≥,<,>)   greater than or equal to, less than or equal to, greater than, less than signs

Answer:

Ratio = 3 : 2 and value of m = 5.

Step-by-step explanation:

We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.

Let us assume that it cuts the line in k : 1 ratio.

Then, the co-ordinates of P = [tex]( \frac{-8k-3}{k+1},\frac{9k-1}{k+1} )[/tex].

But, [tex]\frac{-8k-3}{k+1}[/tex] = -6

i.e. -8k-3 = -6k-6

i.e. -2k = -3

i.e. [tex]k = \frac{3}{2}[/tex]

So, the ratio is k : 1 i.e [tex]\frac{3}{2} : 1[/tex] i.e. 3 : 2.

Hence, the ratio in which P divides the line is 3 : 2.

Also, [tex]\frac{9k-1}{k+1}[/tex] = m where [tex]k = \frac{3}{2}[/tex]

i.e. m = [tex]\frac{\frac{9 \times 3}{2}-1}{\frac{3}{2}-1}[/tex]

i.e. m = [tex]\frac{27-2}{3+2}[/tex]

i.e. m = [tex]\frac{25}{5}[/tex]

i.e. m = 5.

Hence, the value of m is 5.

Answer:

m=5

Step-by-step explanation:

Given: Point [tex]C(x_3,y_3)=(-6,m)[/tex] divides the join of point [tex]A(x_1,y_1)=(-3,-1)[/tex] and point [tex]B(x_2,y_2)=(8,9)[/tex]

Let the line AB divides by Point C in a ratio m:n=k:1

Then, Using section formula   [tex](x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}[/tex]

Applying formula,

[tex]x_3,y_3=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}[/tex]

[tex]x_3,y_3=\frac{-8k-3}{k+1},\frac{9k-1}{k+1}[/tex]

But, [tex]x_3=-6[/tex]

Therefore,  [tex]x_3=\frac{-8k-3}{k+1}[/tex]

[tex]-6=\frac{-8k-3}{k+1}[/tex]

[tex]-6k-6=-8k-3[/tex]

[tex]2k-3=0[/tex]

[tex]k=\frac{3}{2}[/tex]

Therefore, C divides line AB in 3:2

Now,  [tex]m=\frac{9k-1}{k+1}[/tex]  where, k=3/2

[tex]m=\frac{9\frac{3}{2}-1}{\frac{3}{2}+1}[/tex]

[tex]m=\frac{\frac{25}{2}}{\frac{5}{2}}[/tex]

[tex]m=\frac{25\times2}{2\times5}[/tex]

[tex]m=5[/tex]

Answer:

a1 = 8

a2 =10

a3 = 13

a4 = 17

Step-by-step explanation:

The first term is a1 = 8

The second term is a2 = a1 + n

                                       = 8+2

                                       = 10

The third term is a3 = a2 + n

                                       = 10+3

                                       = 13

The fourth term is a4 = a3 + n

                                       = 13+4

                                       = 17

Final answer:

The total interest cost of the loan is $28,999.

Explanation:

To find the total interest cost of the loan, we need to calculate the amount of interest paid over the 25-year period. First, we need to find the amount of the mortgage by subtracting the down payment from the purchase price. 20% of $230,000 is $46,000, so the mortgage is $230,000 - $46,000 = $184,000.

To calculate the interest cost, we can use the formula: Interest Cost = Total Repayment - Principal Amount.

Principal Amount = Mortgage Amount = $184,000.
Number of Payments = Number of years x Number of payments per year = 25 x 12 = 300.
Monthly Interest Rate = Annual Interest Rate / Number of payments per year = 8% / 12 = 0.00667.
Total Repayment = Monthly Payment x Number of Payments = [(Monthly Interest Rate x Principal Amount) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments)) ] x Number of Payments = [(0.00667 x $184,000) / (1 - (1 + 0.00667)^(-300))] x 300 = $526.67 x 300 = $157,001.
Interest Cost = Total Repayment - Principal Amount = $157,001 - $184,000 = $28,999.

Answer:

The coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).

Step-by-step explanation:

The vertices of triangle XYZ are X(-2,1), Y(-4,-3) and Z(0,-2).

It is given that the triangle translated by rule

[tex](x,y)\rightarrow (x-1,y+3)[/tex]

The coordinates of image of XYZ are

[tex]X(-2,1)\rightarrow X'(-2-1,1+3)[/tex]

[tex]X(-2,1)\rightarrow X'(-3,4)[/tex]

[tex]Y(-4,-3)\rightarrow Y'(-4-1,-3+3)[/tex]

[tex]Y(-4,-3)\rightarrow Y'(-5,0)[/tex]

[tex]Z(0,-2)\rightarrow Z'(0-1,-2+3)[/tex]

[tex]Z(0,-2)\rightarrow Z'(-1,1)[/tex]

Therefore coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).

Answer:

5.91%

Step-by-step explanation:

We are given an investment deposited fro 1 year compounded daily at an annual interest rate of 5.75%.

Compounding period per year, n: 365

The effective annual yield can be calculated by the following formula:

Effective Annual Yield = [tex] (1+\frac{r}{n})^{n}-1[/tex]

where n = 365

Interest rate, r= 5.75% = 0.0575

[tex]=(1+\frac{0.0575 }{365})^{365}-1[/tex]

= 0.059

The annual effective yield is 5.91%