You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.

Part 1 Choosing a Band

Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.

Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.

Part 2: Choosing a Caterer

A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.

Part 3: Analyzing cost

Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.

Part 4: Choosing Flowers

You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.

Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.

Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.

Therefore , the solution of the given problem of surface area comes out to be standard heptagon's perimeter is 89.25 inches as a result.

By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.

Here,

By dividing the length of one side by the heptagon's total number of sides, which is seven, one can determine the perimeter of a standard heptagon with sides measuring 12.75 inches in length.

The circumference P is thus:

=> P = 7(12.75)

=>  89.25 inches at P.

The standard heptagon's perimeter is 89.25 inches as a result.

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If Gopal, Krishna and Govind are partners sharing profits and losses in the ratio of 5 4 3. The gaining ratio will be: (a) 5:3.

Since Krishna is retiring, her share of profit will now be divided between Gopal and Govind in the same ratio as their existing profit-sharing ratio.

The total amount paid to Krishna is 1,20,000. Out of this, Gopal has paid 80,000 and Govind has paid 40,000.

So, the share of profit purchased by Gopal is:

5/12 x 120,000 = 50,000

And the share of profit purchased by Govind is:

3/12 x 120,000 = 30,000

Now, the total profit sharing ratio of the remaining partners (Gopal and Govind) will be:

5:3 + 3:3 = 8:3

Therefore, the gaining ratio will be:

Gopal = 50,000 / (50,000 + 30,000) = 5/8

Govind = 30,000 / (50,000 + 30,000) = 3/8

So, the gaining ratio of Gopal and Govind will be 5:3, which is option (a).

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Answer:

11 and 22

Step-by-step explanation:

radius is

r = 11 cm

diameter is

d = 2r = 2×11 = 22cm

Therefore, A grain silo has a cylindrical shape the answer is: 12,689 ft³ (cubic feet).

Percentage is a way of expressing a proportion or a part of a whole as a fraction of 100. It is represented by the symbol % (per cent), which means "per hundred". For example, if you say that 50% of a group of 100 people like chocolate, it means that 50 out of 100 people or 0.5 (50/100) of the total group like chocolate. Percentages are commonly used in many fields, including finance, business, mathematics, and statistics.

The formula for the volume of a cylinder is:

V = π[tex]r^{2}[/tex]h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

[tex]V = 3.14 *9^2 *49[/tex]

[tex]V = 12,689.46[/tex]

Rounding to the nearest whole number, the volume of the silo is approximately 12,689 cubic feet.

Therefore, the answer is:

12,689 ft³ (cubic feet)

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Answer:

1.P(9,then 3) = (1/10)*(1/10)=1/100

Step-by-step explanation:

hope it helps and no explanation

Answer:

f(g(x))=3x+8

g(f(x))=3x-2

Step-by-step explanation:

f(x)=3x-7, g(x)=x+5

f(g(x))=f(x+5)

=3(x+5)-7

=3x+15-7

=3x+8

g(f(x))=g(3x-7)

=3x-7+5

=3x-2

The blend of minimum cost with an octane rating of at least 90 is 11.11% type A gasoline and 55.56% type B gasoline, with a cost per liter of $0.6917.

What is the blend of minimum cost with an octane rating of at least 90?

Let x be the fraction of type A gasoline and y be the fraction of type B gasoline in the blend.

Since we want the blend to have an octane rating of at least 90, we can set up the following equation:

80x + 92y ≥ 90(x + y)

Simplifying this equation,

10x ≥ 2y

y ≤ 5x

We also want to minimize the cost of the blend, which can be expressed as 0.83x + 0.98y

Now we can use the inequalities we've established to find the minimum cost.

We know that y ≤ 5x

So we can substitute y = 5x into the cost equation 0.83x + 0.98(5x)

Simplifying and we get,

5.85x

This is the cost per liter of the blend, so we want to minimize this expression. To do so, we can use calculus and take the derivative with respect to x,

d/dx (5.85x) = 5.85

Setting this equal to zero to find the minimum value of the expression, we get:

5.85 = 0

This is not possible, so we know that the minimum value occurs at the boundary of the feasible region. That is, either x = 0 or y = 5x.

If x = 0, then the cost per liter is simply 0.98y, which we want to minimize subject to the constraint that 92y ≥ 90y, or y ≥ 45. We also have the constraint that y ≤ 1 (since we can't have more than 100% type B gasoline in the blend). So the minimum cost occurs when y = 1, and the cost per liter is 0.98.

If y = 5x, then the cost per liter is 0.83x + 4.9x = 5.73x. We want to minimize this subject to the constraints that 80x + 460x ≥ 90(1 + 4x), or x ≥ 0.0278, and that x ≤ 1. We can also use the inequality y ≤ 1 to get,

5x ≤ 1

x ≤ 0.2

So the feasible range for x is 0.0278 ≤ x ≤ 0.2. We can now calculate the cost of the blend for each value of x in this range and choose the minimum. This is a straightforward calculation, and we find that the minimum cost occurs when x = 0.1111 and y = 0.5556, and the cost per liter is $0.6917.

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The rate of inflation used to make this calculation is 4%

The equation

y = 100(0.96)^x

represents the purchasing power of $100 after x years of inflation. In this equation, 0.96 is the inflation rate.

This means that the purchasing power of $100 decreases by 4% each year due to inflation.

To understand this better, let's take an example. Suppose you have $100 today and the inflation rate is 4%. This means that the purchasing power of $100 will be reduced by 4% after one year. So, after one year, the value of $100 will be $96. If the inflation rate remains the same, after two years, the value of

$100 will be $92.16 ($96 * 0.96)  and so on.

It is important to note that inflation rates can vary over time and across countries, and can have a significant impact on the economy and the purchasing power of consumers. Understanding inflation and its effects is crucial for making informed financial decisions.

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Since the dividend per share is computed as Quarterly Dividend Payment / Shares, $1.52 is the yearly dividend for each share of Merck.

One of the four crucial steps in the division process is the dividend. It is necessary to divide the entire into several equal sections. For instance, if the result of the division of 10 by 2 is 5, then 10 is the dividend, which is split into two equal pieces, and 2 is the divisor. The result of the division is 5, the quotient, and the remainder is 0.

Given: The following steps can be taken in order to obtain the dividend per share for the quarterly payment:

Dividend per share is determined using the formula Quarter Dividend Payment / Shares.

The dividend equals $0.38 per share when $1,140 is divided by 3,000 shares.

To calculate the annual dividend per share, multiply the dividend paid every three months per share times the number of quarters in a year:

The annual dividend per share is equal to the quarter dividend per company multiplied by the total number of quarters in a year.

The annual dividend per share is calculated as $0.38 multiplied by four quarters, or $1.52 per share.

Since the calculation for the dividend per share is Periodic Dividend Payment / Shares, the annual dividend for each share of Merck is $1.52.

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The measures of the angles are:

m ∠GAL = 90°

m ∠LAO = 71°

m ∠CAO = 109°

m ∠KAC = 71°

From the question, we are to determine the measure of the angles

m ∠GAL = 90° (Right angle)

m ∠LAO

m ∠LAO + m ∠GAL + 19° = 180° (Sum of angles on a straight line)

m ∠LAO + 90° + 19° = 180°

m ∠LAO = 180° - 90° - 19°

m ∠LAO = 90° - 19°

m ∠LAO = 71°

m ∠CAO

m ∠CAO = m ∠KAL (Vertically opposite angles)

m ∠KAL = m ∠GAL + 19°

m ∠KAL = 90° + 19°

m ∠KAL = 109°

Therefore,

m ∠CAO = 109°

m ∠KAC = m ∠LAO (Vertically opposite angles)

m ∠LAO = 71°

Therefore,

m ∠KAC = 71°

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the total area of the figure is 412.16 yd² and closest option is 272.64 yd²,.

To find the area of a composite figure, we need to break it down into simpler shapes and add up their individual areas. In this case, we can divide the figure into a rectangle and two right triangles.

First, let's calculate the area of the rectangle. The base of the rectangle is 21.3 yards and the height is 12.8 yards. Therefore, the area of the rectangle is:

Area of rectangle = base x height

= 21.3 yd x 12.8 yd

= 272.64 yd²

Next, let's calculate the area of the right triangles. We can find the height of each triangle using the Pythagorean theorem.

For the triangle on the right side, we know the base is 6.4 yards and the hypotenuse is 21.3 yards (the same as the base of the rectangle). We can solve for the height (h) using the Pythagorean theorem:

h² + 6.4² = 21.3²

h² = 21.3² - 6.4²

h² = 410.45

h = √410.45

h ≈ 20.26 yards

The area of this triangle is:

Area of right triangle = (1/2) x base x height

= (1/2) x 6.4 yd x 20.26 yd

= 64.96 yd²

For the triangle on the left side, we know the base is 14.9 yards and the hypotenuse is also 21.3 yards. We can solve for the height (h) using the Pythagorean theorem:

h² + 14.9² = 21.3²

h² = 21.3² - 14.9²

h² = 99.94

h = √99.94

h ≈ 9.997 yards (rounded to three decimal places)

The area of this triangle is:

Area of left triangle = (1/2) x base x height

= (1/2) x 14.9 yd x 9.997 yd

= 74.56 yd²

Now, we can find the total area of the figure by adding up the areas of the rectangle and the two triangles:

Total area = area of rectangle + area of right triangle + area of left triangle

= 272.64 yd² + 64.96 yd² + 74.56 yd²

= 412.16 yd²

Therefore, the total area of the figure is 412.16 yd².

However, none of the given answer choices match this result. The closest option is 272.64 yd², which is the area of the rectangle only. This suggests that there may be an error in the problem statement or answer choices. If we assume that the area of the figure is intended to be the area of the rectangle only, then the answer is indeed 272.64 yd².

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or Part A, we can use the formula n = (Z^2 p q) / E^2 to calculate the sample size needed. Here, Z is the z-value for a 90% confidence level, which is 1.645, p is the estimated proportion of jets with the wiring problem (15/19 = 0.7895), q is 1-p, and E is the maximum error of the estimate in decimal form (0.06). Plugging in these values, we get n = (1.645^2 0.7895 0.2105) / 0.06^2, which is approximately 138. Therefore, a sample size of at least 138 aircraft would be needed to estimate the true proportion of jets with the wiring problem with 90% confidence and an error of 6%.

For Part B, it would depend on the airline's decision-making process and resources. Conducting further sampling could provide more accurate and reliable results, but it would also require more time and resources. Inspecting all the planes could provide a comprehensive solution, but it may not be feasible or cost-effective, especially if the planes are scattered across different locations. Ultimately, the airline would need to weigh the costs and benefits of each option and make the best decision for their specific situation.

Answer:

  $7734.82

Step-by-step explanation:

You want to know the amount that will result in $20,000 after 20 years when 4.75% interest is compounded continuously.

The formula for account value is ...

  A = P·e^(rt)

We want to find P when A=20,000, r=0.0475, and t=20.

  20000 = P·e^(0.0475·20)

  P = 20000·e^(-0.0475·20) ≈ 7734.82

You would have to deposit $7734.82 in the account to have $20,000 in 20 years.

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or Part A, we can use the formula for confidence intervals:

CI = p ± Zsqrt((pq)/n)

where p is the proportion of almonds found in the sample (13/100 = 0.13), q is 1-p, Z is the z-value for a 99% confidence level (2.576), and n is the sample size (100). Plugging in these values, we get:

CI = 0.13 ± 2.576sqrt((0.130.87)/100)

which simplifies to:

CI = (0.045, 0.215)

Therefore, we are 99% confident that the true proportion of almonds in the population of planters mixed nuts is between 0.045 and 0.215.

For Part B, we can use the Central Limit Theorem to assume normality if the sample size is large enough. Since n = 100 is greater than or equal to 30, we can assume normality.

For Part C, we can use the formula n = (Z^2 p q) / E^2 to calculate the sample size needed. Here, Z is the z-value for a 99% confidence level (2.576), p is the estimated proportion of almonds (0.13), q is 1-p, and E is the maximum error of the estimate in decimal form (0.05). Plugging in these values, we get:

n = (2.576^2 0.13 0.87) / 0.05^2

which simplifies to approximately 276. Therefore, a sample size of at least 276 planters mixed nuts would be needed to estimate the true proportion of almonds with 99% confidence and an error of 0.05

The value of x that satisfies the equation log(2x) = 2 is 50, which is obtained by applying the definition of logarithms and simplifying the resulting equation.

The given equation is log(2x) = 2. To solve this equation for x, we first use the definition of logarithms, which states that log(base a)(b) = c is equivalent to [tex]a^c = b[/tex]. In this case, the base of the logarithm is not specified, so we assume it is base 10.

To solve for x in the equation log(2x) = 2, we first need to use the definition of logarithms, which states that log(base a)(b) = c is equivalent to [tex]a^c = b[/tex].

In this case, we have:

log(2x) = 2

Using the definition of logarithms, we can rewrite this as:

[tex]10^2 = 2x[/tex]

Simplifying, we get:

100 = 2x

Dividing both sides by 2, we get:

50 = x

Therefore, the value of x that satisfies the equation log(2x) = 2 is 50.

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The monthly payment for this mortgage is $1,757.26.

The following can be deduced from the information:

P = $250,000

r = 0.03/12 = 0.0025

It should be noted that since APR is an annual rate, we need to divide it by 12 to get the monthly rate.

n = 15 × 12 = 180

Since the mortgage is for 15 years and there are 12 months in a year

Monthly payment will be:

= 250000 × (0.0025 × (1 + 0.0025)^180) / ((1 + 0.0025)^180 - 1)

= $1,757.26

Therefore, the monthly payment for this mortgage is $1,757.26.

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Answer:

3

Step-by-step explanation:

If blue, then 60%. 2/5 are red and 1/3 are blue. Two redfish and three bluefish are present. if the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.

Answer:

103.34 degrees

Step-by-step explanation:

The sum of angles in a triangle always equals 180 degrees. In other words, 40+(2x-30)+(x+20) = 180. Next, add the figures in both brackets so it becomes (2x-30+x+20), and then group like terms. (2x+x-30-20) which is 3x -50, because -30-20 is -50. The whole equation becomes 40+3x-50 = 180.

Group like terms again, so it becomes 30-50+3x = 180 which is -20+3x=180. Group like terms again but move the -20 to the side of the 180, and since it crosses the equal to sign, the - becomes + so it's 3x=180+20, resulting in 3x=200. Now to make x stand alone, we divide both sides by 3. 3x/3 is x and 200/3 is 66.6 recurring or 66.67. Now we know that x = 66.67, we substitute it in the formula for the angle at B. It becomes (2 times 66.67-30) which is 133.34 - 30, which becomes 103.34 as the answer. If told to round, it becomes 103 degrees.

GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.

First, we will show that GF is linear. Let u, v be vectors in V and c be a scalar in K. Then we have:

[tex]GF(cu + v) = G(F(cu + v)) = G(cF(u) + F(v)) = G(cF(u)) + G(F(v))= cG(F(u)) + G(F(v)) = c(GF(u)) + GF(v)[/tex]

Thus, GF is linear.

Next, we will show that GF is bijective. Since F and G are isomorphisms, they are both invertible. Let[tex]F^-1[/tex]and [tex]G^-1[/tex] denote their respective inverses. Then for any u in U, we have:

[tex](GF)^-1(u) = F^-1(G^-1(u))[/tex]

This shows that GF is invertible, and hence bijective.

Finally, we will show that GF preserves the identity and addition operations. Let v1, v2 be vectors in V. Then we have:

[tex]GF(v1 + v2) = G(F(v1 + v2)) = G(F(v1) + F(v2)) = G(F(v1)) + G(F(v2))= GF(v1) + GF(v2)[/tex]

Also, since F and G are isomorphisms, they preserve the identity operations:

[tex]GF(0v) = G(F(0v)) = G(0w) = 0u\\GF(v) = G(F(v)) = G(0w) = 0u if v=0v[/tex]

Thus, GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.

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Answer:

Step-by-step explanation:

32

As given the value of y varies directly from the cube of x so after solving the equation and finding the constant of proportionality:

when x=4, y is equal to 160.

The constant of proportionality is a value that relates two variables that are directly proportional to each other. In a mathematical equation where one variable is directly proportional to another, the constant of proportionality represents the ratio between the two variables.

If the value of y varies directly from the cube of x, then we can write:

y = kx^3

where k is a constant of proportionality. To find the value of k, we can use the given information that y=20 when x=2:

20 = k(2^3)

20 = 8k

k = 20/8

k = 2.5

Now that we have the value of k, we can use the equation to find y when x=4:

y = 2.5(4^3)

y = 2.5(64)

y = 160

Therefore, when x=4, y is equal to 160.

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Answer:

The answer to your problem is,

[tex]\frac{1}{5} n = l\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5} * n = l \frac{1}{2}[/tex]

[tex]\frac{1}{5} n = l\frac{1}{2}[/tex]

Thus the answer to your problem is, [tex]\frac{1}{5} n = l\frac{1}{2}[/tex]

There is nothing more to show. But I have picture I did it:

Answer:

x = 29

Step-by-step explanation:

The whole circle is 360°.

Theorem regarding angles inside a circle says that the angle is one half of the arc it encompasses. So m∠S = 0.5 * arc PQR. Also m∠Q = 0.5 * arc PSR.

Think about this, arc PQS + arc RQS = 360°. We have a formula for each of these arc measurements in terms of x.

The arc that corresponds to ∠R is some part of the circle, and the arc that corresponds to ∠P is the other part of the circle.

(5x + 20) + (7x - 8) = 360

12x + 12 = 360

12x = 348

x = 29

Answer:

-79

Step-by-step explanation:

-7(x+6) + 12                       x = 7

-7( 7 + 6) + 12

-7(13) + 12

-91 + 12

-79

So, the answer is -79

the company can pack 224 basketballs into each truck.

To calculate the number of basketballs that can be packed into the truck

Number of basketballs = Volume of truck / Volume of each basketball package

first calculate the volume of the truck

The volume of the truck is:

Volume = Length x Width x Height

Volume = 10.5 ft x 8 ft x 9 ft

Volume = 756 cubic feet

The volume of each basketball package  is:

Volume = Side x Side x Side

Volume = 1.5 ft x 1.5 ft x 1.5 ft

Volume = 3.375 cubic feet

Now, we can calculate the number of basketballs :

Number of basketballs = Volume of truck / Volume of each basketball package

Number of basketballs = 756 cubic feet / 3.375 cubic feet

Number of basketballs = 224

Therefore, the company can pack 224 basketballs into each truck.

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Since Olivia's fruit salad contains more apples than Amadou's, it will have a more apple-like flavour based on percent laws.

We must compute the percent of apples in each fruit salad in order to determine which salad will taste most apple-like.

Nine cups of melon plus ten cups of apples equals 19 cups of fruit in Amadou's fruit salad. Therefore, the fruit salad Amadou made contains:

10 cups of apples divided by 19 cups of fruit equals 100% of the percentage of apples in Amadou's fruit salad, or 52.63%.

2 cups of melon and 3 cups of apples total 5 cups of fruit for Olivia's fruit salad. So, there are: in Olivia's fruit salad.

3 cups of apples divided by 5 cups of fruit equals 100% of the percentage of apples in Olivia's fruit salad, which comes out to 60%.

When we compare the percentage of apples in the two fruit salads, we can observe that Olivia's salad contains more apples than Amadou's. Olivia's fruit salad will therefore taste more apple-like.

In conclusion, we can figure out which fruit salad will taste more appley by figuring out the percentage of apples in each salad. As there are more apples in Olivia's fruit salad than in Amadou's, it will taste more apple-like.

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Answer:

Step-by-step explanation:

Let's denote the time that Adrian traveled on the bike at 13 mph by "t" and the time that he walked at 3 mph by "9 - t" (since the total trip took 9 hours).

Since we know that the total distance traveled was 87 miles, we can write the equation:

distance traveled on bike + distance traveled walking = 87

Using the formula distance = rate x time, we can express the distance traveled on the bike and walking in terms of time:

13t + 3(9 - t) = 87

Simplifying this equation:

13t + 27 - 3t = 87

10t = 60

t = 6

Therefore, Adrian traveled on the bike for 6 hours (at 13 mph) and walked for 3 hours (at 3 mph).

The fractions as 50/15 and 6/15, respectively, and subtract them to obtain w = 44/15. This can be further simplified to the mixed number 2 14/15 or the decimal approximation 2.933.

To solve the equation w + 2/5 = 3 1/3, we need to isolate w on one side of the equation by subtracting 2/5 from both sides, finding a common denominator, and simplifying the resulting expression to obtain w.

w + 2/5 = 10/3

To isolate w, we need to move the constant term on the right-hand side of the equation to the left-hand side by subtracting 2/5 from both sides.

Subtracting 2/5 from both sides:

w = 10/3 - 2/5

To add these fractions, we need to find a common denominator, which is 15. So we can rewrite the fractions as:

w = (50/15) - (6/15)

Combining like terms:

w = 44/15

Therefore, w = 2 14/15 or approximately 2.933.

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