Cameron bought twelve pounds of candy corn for 79 cents a pound and eighteen pounds of M&Ms for $1.09 a pound, planning to make packages of candy for a fund-raiser. The two types of candy will be mixed and sold in one-pound bags. What is the least price that Cameron can charge for each of the thirty bags, in order to make at least a 25% profit.

Answer:

  15

Step-by-step explanation:

Put the given value of x where x is in the expression and do the arithmetic.

  4^3 -(3 +4)^2 = 64 -49 = 15

The value of the expression for x=4 is 15.

Final answer:

The expression x³ - (3 + x)² for x = 4 simplifies to 64 - 49, resulting in a final answer of 15.

Explanation:

The student has asked to evaluate the expression x³ - (3 + x)² for x = 4. To do this, we will substitute x with 4 and simplify the expression step by step. First, calculate the value inside the parentheses: (3 + 4) = 7. Then, we square this value to get 7² = 49. After that, subtract the squared value from 4³ (which is 64), to get the final answer.

The final answer is 15

Answer:

The answer to your question is  x = 0 and x = 1

Step-by-step explanation:

Equation

                       [tex]\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1[/tex]

1)

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

Expand

2)                  x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)

Simplify

3)                  2x² -2x + 2 = -1(x² + x - 2x - 2)

4)                  2x² - 2x + 2 = -x² + x + 2

Equal to zero

5)                  2x² - 2x + 2 + x² - x - 2 = 0

6)                  3x² - 3x = 0

Factor

7)                  3x(x - 1) = 0

8)                  3x₁ = 0                   x₂ - 1 = 0

9)                    x₁ = 0/3                x₂ = 1

10)                  x₁ = 0                    x₂ = 1

Answer:

x= −5621/201

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3 /7x+5 =  812/7772/7-7

3 /7x+5=  1/67+−7

3 /7x+5=(  1/67+-7)(Combine Like Terms)

3 /7x+5=  −468 /67

3 /7x+5= −468/67

Step 2: Subtract 5 from both sides.

3 /7x+5−5=−468/67−5

3 /7x=−803/67

Step 3: Multiply both sides by 7/3.

(  7/3)*(3/7x)=(7/3)*(−803/67)

x= −5621/201

Answer:

  OT, OU, OR

Step-by-step explanation:

Point O is the center of the circle, so will be one end of any radius. Segments are shown from point O to points T, U, and R on the circle. Each of those segments is a radius:

  OT, OU, OR . . . . are radii

_____

OS would also be a radius, but no segment is shown there, and it doesn't show in any answer choice.

Answer:

  16 mph

Step-by-step explanation:

The relationship between distance, speed, and time is ...

  speed = distance/time . . . . . "miles per hour"

Malcom's distance was 32 miles each way, for a total of 64 miles. Then his average speed was ...

  speed = (64 mi)/(4 h) = 16 mi/h

Answer:

The answer to your question is below

Step-by-step explanation:

See the graph below

Process

1.- Find the distance from A to B, B to C, C to D, A to D

Formula

d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

d AB = [tex]\sqrt{(1 + 3)^{2} + (6 - 5)^{2}}  = \sqrt{17}[/tex]

dBC = [tex]\sqrt{(-2 -6)^{2} + (3 - 1)^{2}}  = \sqrt{68}[/tex]

dCD = [tex]\sqrt{(-1 - 3)^{2} + (-3 +2)^{2}}  = \sqrt{17}[/tex]

dAD = [tex]\sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}}  = \sqrt{68}[/tex]

2.- Find the perimeter

Perimeter = 2[tex]\sqrt{17} + 2\sqrt{68}[/tex] = [tex]6\sqrt{17}[/tex] u

3.- Find the area

Area = [tex]\sqrt{17} x \sqrt{68}[/tex]

Area = [tex]\sqrt{17x68} = \sqrt{1156} = 34 u^{2}[/tex]

Answer:11.38

Step-by-step explanation:

290-257=33 /290=.11379 x 100=11.37  =11.38

Final answer:

To find the percentage of racers who did not complete the marathon, we add those who gave up and those who were disqualified, a total of 31 racers. The percentage is then calculated using the formula for percentage, resulting in 10.7% of racers not completing the marathon.

Explanation:

To find the percentage of racers who did not complete the marathon, we first need to determine the total number of racers who did not finish. This includes those who gave up and those who were disqualified. In this case, 27 racers gave up, and 4 were disqualified, giving us a total of 31 racers who did not complete the marathon.

To calculate the percentage, we use the formula:

Percentage = (Number of racers who did not complete / Total number of racers) × 100%

Plugging the numbers into the formula gives us:

Percentage = (31 / 290) × 100% = 0.1069 × 100% = 10.69%

Rounding to the nearest tenth of a percent, 10.7% of racers did not complete the marathon.

Answer:The faster person will do the job in 7.53hours

Step-by-step explanation:

Let t=faster person

Let t-1= the other person

The job to be done =1

Each person will do a fraction of the job

4/t+4/t-1=1

Multiply both sides wit t(t-1)

4(t+1)+4t=t(t-1)

4t+4+4t=t^2+t

8t+4=t^2+t

0=t^2+t-8t-4

t^2-7t-4=0

Use Almighty formular to solve d quadratic equation

X=-b+- rootb^2-4ac/2a

X=t,a=1,b=-7 c=4

Substituting the values you get:

t=-7 +- root 49+16/2

t=-7 +- root 65/2

t=7 +8.06/2=15.06/2

t=7.53 hours

Answer:

See below.

Step-by-step explanation:

x < 2   f(x) = |x|.

x ≥ 2   f(x) =  3.

Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%

Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz

b=1.2 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S,a and b into the equation

Y=32-32.3/1.2

Y=-0.25

Probability of bottles that have a volume less than 32 oz is

P(S<32)=P(Y<-025)= 0.40129

Percentage of bottles that have volume less than 32 oz will be

0.40127×100%=40.13%

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle shown,

AB represents the hypotenuse of the right angle triangle.

With 45 degrees as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine QR, we would apply trigonometric ratio

Sin θ = opposite side/hypotenuse side. Therefore,

Sin 45 = BC/6√2

√2/2 = BC/6√2

BC = √2/2 × 6√2

BC = 6

Answer:

The sale price of the car is $48000.

Step-by-step explanation:

i) let the sale price of the car be = $x

ii) the premium is given as 16%

  therefore the premium of the car will be equal to = 16% of $x

  the premium of the car will be = $0.16x

iii) therefore total price of car in terms of sale price x  = $x + $0.16x

           therefore total price = $1.16x

iv) total price is given as $55,680

Therefore   $55,680 = $1.16x,    therefore $x = [tex]\dfrac{55,680}{1.16} = \$\hspace{0.15cm}48000[/tex].

Therefore the sale price of the car is $48000.

See the attached picture:

Edited graph 4. I missed the negative sign in front of the one. The new graph is attached.

Final answer:

A chemist cannot achieve a 34% concentration by mixing 20% and 30% acid solutions, as it is outside the possible range of concentrations achievable by combining these two solutions, option no 4.

Explanation:

When a chemist is mixing two acid solutions, one with a 20% concentration and the other with a 30% concentration, they can obtain a range of concentrations between the two provided percentages by varying the proportions of each solution mixed. The concentrations that could not be obtained would be any value outside of the 20% to 30% range because the resulting mixture cannot exceed the concentration of the higher concentrated solution or be lower than the concentration of the less concentrated solution. Therefore, a 34% concentration could not be obtained by mixing a 20% solution with a 30% concentration.

Answer:

Side of 40 and height of 20

Step-by-step explanation:

Let s be the side of the square base and h be the height of the box. Since the box volume is restricted to 32000 cubic centimeters  we have the following equation:

[tex]V = hs^2 = 32000[/tex]

[tex]h = 32000/ s^2[/tex]

Assume that we cannot change the thickness, we can minimize the weight by minimizing the surface area of the tank

Base area with open top [tex]s^2[/tex]

Side area 4hs

Total surface area [tex]A = s^2 + 4hs[/tex]

We can substitute [tex]h = 32000/ s^2[/tex]

[tex]A = s^2 + 4s\frac{32000}{s^2}[/tex]

[tex]A = s^2 + 128000/s[/tex]

To find the minimum of this function, we can take the first derivative, and set it to 0

[tex]A' = 2s - 128000/s^2 = 0[/tex]

[tex]2s = 128000/s^2[/tex]

[tex]s^3 = 64000[/tex]

[tex]s = \sqrt[3]{64000} = 40[/tex]

[tex]h = 32000/ s^2 = 32000/ 40^2 = 20[/tex]

Answer:

8.

Step-by-step explanation:

5, 10, 12, 4, 6, 11, 13, 5

Arrange in ascending order:

4, 5, 5, 6, 10, 11, 12, 13.

The median is the mean of the 2 middle numbers:

= (6 + 10) / 2

= 8.

Step-by-step explanation:

the sum of angles in a triangle is 180°. so if a triangle is equivalent, each degree will be 180/3 = 60°

Answer:

$600

Step-by-step explanation:

Let the random variable [tex]X[/tex] denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of [tex]X[/tex] is given by

                        [tex]X : \begin{pmatrix}0 & 1000 & 5000 & 10\; 000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]

A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by

                    [tex]F(x) = \left \{ {{X+100, \quad \quad \quad \quad \quad \text{for} \; X = 0 } \atop {X-500+100} , \quad \text{for} \; X = 500,4500,9500} \right.[/tex]

For [tex]X = 0[/tex],  we have

                              [tex]F(X) = 0+100 = 100[/tex]

For [tex]X = 500[/tex],

                             [tex]F(X) = 500-500+100 = 100[/tex]

For [tex]X = 4500[/tex],

                            [tex]F(X) = 4500-500+100 = 4100[/tex]

For [tex]X = 9500[/tex],

                            [tex]F(X) = 9500-500+100 = 9100[/tex]

Therefore, the probability distribution of [tex]F[/tex] is given by

                           [tex]F : \begin{pmatrix} 100 & 100 & 41000 & 91000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]

To determine the premium amount that the company should charge, we need to calculate the expected value of [tex]F.[/tex]

[tex]E(F(X)) = \sum \limits_{i=1}^{4} f(x_i) \cdot p_i = 100 \cdot 0.81 + 100 \cdot 0.09 + 4100 \cdot 0.08 + 9100 \cdot 0.02[/tex]

Therefore,

                             [tex]E(F) = 81+9+328+182 = 600[/tex]

which means the $600 is the amount the should be charged.

Answer:

Voters can select their members in 10possible ways

Step-by-step explanation:

According to the question, the voters are to elect 3members out of 5 candidates, this means they are to select any 3 candidates of their choice from a pool of 5 candidates. Since "combination" has to do with selection, we use the combination formula.

To select 'r' objects from 'n' pool of objects, we have;

nCr = n!/(n-r)!r!

5C3 = 5!/(5-3)!3!

5C3 = 5!/2!3!

5C3 = 5×4×3×2×1/2×3×2

= 120/12

5C3 = 10

Candidates can therefore vote in 10 possible ways

Answer:

Ms. Thomas was driving at constant rate of 52 miles/hour.

Step-by-step explanation:

Given:

Total time to travel (t) = 45 minutes

Distance drove (d) = 39 miles

we need to find the constant rate in miles per hour at which she was driving.

Solution:

Now we know that;

We need to find constant rate at miles per hour;

But time is given in minutes.

So we will convert minutes into hour by dividing by 60 we get;

time [tex]t =\frac{45}{60}= 0.75\ hrs[/tex]

Now we know that;

Distance is equal to rate times time.

framing in equation form we get;

distance [tex]d =rt[/tex]

Or

rate [tex]r= \frac{d}{t} = \frac{39}{0.75}= 52 \ mi/hr[/tex]

Hence Ms. Thomas was driving at constant rate of 52 miles/hour.

It is 12 miles from house to school

Solution:

Given that, Jeff wants to know how many miles it is from his house to school

On a map, the scale is 0.5 inches = 2 miles

His house island school are 3 inches apart on the map

So, from the given scale,

0.5 inches = 2 miles

Distance between school and house in map = 3 inches

Therefore,

0.5 inches = 2 miles

Muliply both sides by 6

[tex]0.5 \times 6\ inches = 6 \times 2\ miles\\\\3\ inches = 12\ miles[/tex]

Thus, it is 12 miles from house to school

Answer:

3hr 31mins

Step-by-step explanation:

First we convert miles to kilometers

1 miles to km = 1.60934 km

26.2 miles = 26.2 x 1.60934 = 42.164708

A typical marathon approx = 42.165km

If our runner covers 12 km = 1 hr

then he'll cover 42.165km = 42.165/12 = 3.5137 hrs

= 3 hrs + (0.514 * 60 mins) = 3hrs + (30.84mins)

Allan going at that speed would complete the marathon in appox = 3hrs : 31mins.

Answer:

2.34m2

Step-by-step explanation:

boom

Answer:

Option D. -0.80

Step-by-step explanation:

A scatter plot that shows a set of data points having two properties

1). If the points are clustered close to the line that reveals the high correlation.

2). Data points are clustered close to the line having slope down to the right or negative slope.

Therefore, Option D. has the highest correlation with negative slope.

Answer:

0.5

Step-by-step explanation:

The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5

Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through

Answer:

Step-by-step explanation:

A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of $72000 in one week, it means that the amount of commission that was received by the salesperson would be

3/100 × 72000 = 0.03 × 72000 = $2160

Therefore, the total amount of pay that the salesperson would receive for the week would be

900 + 2160 = $3060

Answer:

x ≥ 120

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

    15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

answer

x ≥ 120

Step-by-step explanation:

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

   15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

Answer:

Malcolm is showing evidence of gambler's fallacy.

This is the tendency to think previous results can affect future performance of an event that is fundamentally random.

Step-by-step explanation:

Since each round of the roulette-style game is independent of each other. The probability that 8 will come up at any time remains the same, equal to the probability of each number from 1 to 10 coming up. That it has not come up in the last 15 minutes does not increase or decrease the probability that it would come up afterwards.

Answer:

yes

Step-by-step explanation:

because it is not a whole number so you cant tell

Answer:

1). 875 seats

2). 25 rows in each section

3). $8400

4). Saving of $360

5). 2105 tickets remained unsold

6). x = 16

Step-by-step explanation:

This question is incomplete; here is the complete question.

A stadium has 10,500 seats and 8 VIP boxes. The stadium is divided into 12 equal  sections: 2 premium sections and 10 standard sections. A seat at the premium section  costs $48 per game. A seat at the standard section costs $27 per game.

1. How many seats are there in each section?

2. If there are 35 seats in each row, how many rows are in each section?

3. If all the seats in the premium section are sold out for a game, how much will the  stadium get from those ticket sales?

4. There are 50 games in each season. A season pass costs $2,040. A season pass  holder can go to all the games and have a seat in the premium section. How much can a fan save by buying the season pass?

5. For the night game on Tuesday, 8,395 tickets were sold. How many tickets were  left?

6. Write an equation using “x” and then solve  the equation. Each VIP boxes can seat X  people. If all the seats and VIP boxes are  filled up, there are 10,628 audience in the stadium.

1). Number of seats in the stadium = 10500

Number of sections = 2 premium + 10 standard = 12

Number of seats in each section = [tex]\frac{10500}{12}=875[/tex]

2). If the number of seats in each row = 35

Then number of rows in each section = [tex]\frac{875}{35}=25[/tex]

3). Number of seats in 2 premium sections = 2×875 = 1750

Cost of 1750 seats at the rate of $48 per game = 1750 × 48 = $84000

4). Cost of one ticket in premium section = $48 per game

If the games planned in one season = 50

Then cost of the tickets = 48×50 = $2400

Cost of the season ticket = $2040

Saving on the purchase of one season ticket = 2400 - 2040 = $360

5). For a night game number of tickets sold = 8395

Total number of seats in the stadium = 10500

Tickets remained unsold = 10500 - 8395 = 2105

6). Number of seats in each VIP box = x

Number of VIP boxes = 8

Number of seats in 8 VIP boxes = 8x

Total number of tickets sold = 10500 + 8x

Total number of audience in the stadium = 10628

Then the equation will be

8x + 10500 = 10628

8x = 10628 - 10500

x = [tex]\frac{128}{8}=16[/tex]

The subject of this question is Mathematics, specifically dealing with seating capacity and pricing in a stadium. To determine the maximum seating capacity of the stadium, add up the number of seats in each section. To calculate the total revenue from a single game, multiply the number of seats in each section by the corresponding ticket price, and then sum up the results.

The subject of this question is Mathematics, specifically dealing with the concepts of seating capacity and pricing in a stadium.

To determine the maximum seating capacity of the stadium, we add up the number of seats in each section: 2 premium sections with 48 seats each, 10 standard sections with 900 seats each, and 8 VIP boxes with a capacity of 12 seats each. This gives us a total of 1116 seats.

To calculate the total revenue from a single game, we multiply the number of seats in each section by the corresponding ticket price, and then sum up the results. For the premium sections, the revenue is $48 per seat multiplied by 96 seats, and for the standard sections, the revenue is $27 per seat multiplied by 900 seats. Adding up these two amounts gives us the total revenue from a single game.

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Answer:

Total time spent by Tiwa to set up the computer and install software = 6 hours

Step-by-step explanation:

Given:

Time spent by Tiwa to set up  her computer = [tex]1\frac{1}{2}\ hours[/tex]

Time spent to install the software is 3 times the time she took to set up the computer.

To find the total time Tiwa took to set up her computer and install the software.

Solution:

Time spent by Tiwa to install the software can be given as:

⇒ [tex]3\times 1\frac{1}{2} \ hours[/tex]

In order to multiply mixed numbers we first change them to fractions.

We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.

So, [tex]1\frac{1}{2}=\frac{3}{2}[/tex]

So, we have:

⇒ [tex]3\times \frac{3}{2}\ hours[/tex]

⇒ [tex]\frac{9}{2}\ hours[/tex]

Total time spent by Tiwa to set up the computer and install software can be given as:

⇒ [tex]\frac{3}{2}\ hours+\frac{9}{2}\ hours[/tex]

Since denominators are same, so we simply add the numerators.

⇒ [tex]\frac{3+9}{2}\ hours[/tex]

⇒ [tex]\frac{12}{2}\ hours[/tex]

⇒ [tex]6\ hours[/tex]