mustafas soccer team is planning a school dance as a fundraiser. the dJ charges $200 and decorations cost $100. the team decides to charge each student $5.00 to attend the dance. if n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit


A. 5n - 300 = 1,500

B. 5n + 300 = 1,500

C. 5n - 200 + 100n = 1,500

D. 5n - 109 - 200n = 1,500​

The value of CD is 4 cm.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Since GH bisects CF, therefore:

CD = (1/2) CF

3y - 11 = (1/2) (2y -2)  

(multiply both sides by 2)

6y - 22 = 2y - 2

6y - 2y = -2 + 22

4y = 20

y = 5

Now, Substitute with the value of y in the equation of CD, you get:

CD = 3y-11

CD = 3(5) - 11

CD = 15 - 11

CD = 4 cm

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50 small cabinets and 15 large cabinets should be packed by Lee in the truck  and these value is obtaied after solving the equations given below.

Given : Weight of large cabinet and small cabinet is 40 and 25 pounds respectively

Total load weight allowed in the truck = 1850 pounds  - (i)

Total cabinets allowed in the truck = 65            - (ii)  

Let Lee pack x number of large cabinet and y number of small cabinet

Using equation (i):

40*x + 25*y = 1850          - (iii)

Using equation (ii):

x + y = 65       - (iv)

multiply by 40 on the both side so the equation changes to :

=> 40*x + 40*y = 65*40

=> 40*x + 40*y = 2600       - (v)

Subtracting equation iii from iv :

40*y - 25*y = 2600 - 1850

=> 15*y = 750

=> y = 50

Using (iv) :

x = 65 - y = 65 - 50 = 15

So, 50 small cabinets and 15 large cabinets should be packed by Lee in the truck

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Answer:

\(\frac{11}{2}\)

Step-by-step explanation:

To obtain the inverse of f(x)

let y = f(x) and rearrange making x the subject, that is

y = 2x - 1 ( add 1 to both sides )

y + 1 = 2x ( divide both sides by 2 )

\(\frac{y+1}{2}\) = x

Change y back into terms of x with x = \(f^{-1}\)(x) , thus

\(f^{-1}\)(x) = \(\frac{x+1}{2}\)

Evaluate g(3) and substitute the value obtained into \(f^{-1}\)(x)

g(3) = 3² + 1 = 9 + 1 = 10, then

\(f^{-1}\) (10) = \(\frac{10+1}{2}\) = \(\frac{11}{2}\)

Answer:

83505

Step-by-step explanation:

It's already in the expanded form...

Therefore, T(-6+12t) = [6, 2, -14]'.

Since T is a linear transformation from P1 to R^3, we know that it maps polynomial expressions of degree at most 1 to vectors in R^3. In particular, any such polynomial expression can be written as at + b for some real numbers a and b.

We are given that T(3+2t) = [(1), (-1), (5)]' and T(1+6t) = [(4), (3), (-2)]'. We want to find T(-6+12t).

To do this, we first express -6+12t as a linear combination of 3+2t and 1+6t. We have:

-6+12t = (-2)(3+2t) + (1+6t)

Therefore, we can write:

T(-6+12t) = T[(-2)(3+2t) + (1+6t)]

         = T((-2)(3+2t)) + T(1+6t)      (by linearity)

         = (-2)T(3+2t) + T(1+6t)

         = (-2)[(1), (-1), (5)]' + [(4), (3), (-2)]'

         = [2, -1, -12]' + [4, 3, -2]'

         = [6, 2, -14]'

Therefore, T(-6+12t) = [6, 2, -14]'.

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i³³ simplified is i.

What is the Complex Number?

A complex number is a number in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

When raising a complex number to a power, we can use the property \((a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n\)

It is also possible to simplify the powers of complex numbers using De Moivre's Theorem:

\((a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n\)

Where \((a + bi)^n = r^n * (cos(n\theta) + i*sin(n\theta))\)

Where r is the magnitude, θ is the argument, and n is an integer.

For example, if we raise i to the power of 3, we can use De Moivre's Theorem:

i³ = (cos(90) + isin(90))³ = cos(270) + isin(270) = -i

So, i³ = -i

When raising complex numbers to powers, the magnitude will be raised to the power of n while the argument will be multiplied by n.

i² = -1, so i³³ can be written as (i²)¹⁶ * i = (-1)¹⁶ * i = i

Therefore,  i³³ simplified is i.

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Hello,

Let's say y= log(x) in base 10.

\(\\y=log(x)\\\\log^2(x)-3log(x)-4=0\\\\y^2-3y-4=0\\\\\Delta=9+16=5^2\\\\y=4\ or\ y=-1\\\\log(x)=4 \Longrightarrow x=10^4\\\\or\\\\log(x)=-1 \Longrightarrow x=10^{-1}=0.1\\\)

IQR for the data {1, 3, 4, 8, 20} is 5.

Interquartile Range(IQR) for a data is defined as the difference between third quartile and first quartile.

denoted by  IQR=Q₃-Q₁              (Q₃ is third quartile and Q₁ is first quartile)

The five number summary of a data set is represented as

{minimum, first quartile , second quartile , third quartile , maximum}..…(1)

According to the question

{1, 3, 4, 8, 20}

On comparing it with equation   …(1)

minimum=1

Q₁ =3    , Q₂=4 , Q₃=8 , maximum =20

IQR=Q₃-Q₁

Substituting the values we get

IQR=8-3=5.

Therefore , Interquartile Range for the data {1, 3, 4, 8, 20} is 5.

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Answer:

Add all the outer lines and they may add up to be the perimeter, if you need the area multiply 4 times 8 and add that to 5.6*4/2 +4.5*4/2 plus four times eight

Step-by-step explanation:

Answer:

I remember these form when I was like 10 but ok.

Step-by-step explanation:

pretty sure you multiply the base times the height. But first you have to take out all triangwkes which leaves you with two of them.

so 8x4 for the top one and then 14x4.5 for the bottom one.

then for the triangles the one on the left is 5.6x4

the right one is 4.5x14

then divide both triangles answers into two. That should be the triangle areas. Then add the two triangles pieces together.

once don’t add the squares areas with the triangles and that’s THE AREAAAA

im sry I’m a lil rusty so if it’s wrong pwease forgive me :/

Answer: 96%

Step-by-step explanation:

Morgan's average grade was 92% after the third test.

Lets say all the tests were out of 100 to help you understand.

We can say that she got 92 out of 100 on all three tests.

Her total point would be 92 * 3 which would be 276, out of 300 points available.

Now she takes her fourth test and she wants an average of 93

Out of 100, if she gets a score of X, her total point after the fourth test would be 276 + X out of 400 points available.

so the percentage of 276 + X / 400 should be 93%.

( 276 + X / 400 ) * 100% = 93%

multiply 400 on each side,

( 276 + X ) * 100 % = 93 * 400 %

now divide each side by 100

276 + X = 93 * 4

93 * 4 = 372

Subtract each side by 276

X = 96

So she needs to get a 96 out of 100 or higher, which is 96%.

Answer:

x=3 and y=2

Step-by-step explanation:

Rewrite equations:

3x−y=7;2x+y=8

Step: Solve3x−y=7for y:

3x−y=7

3x−y+−3x=7+−3x(Add -3x to both sides)

−y=−3x+7

−y

−1

=

−3x+7

−1

(Divide both sides by -1)

y=3x−7

Step: Substitute 3x−7 for y in 2x+y=8:

2x+y=8

2x+3x−7=8

5x−7=8 (Simplify both sides of the equation)

5x−7+7=8+7 (Add 7 to both sides)

5x=15

5x5

=

15/5

(Divide both sides by 5)

x=3

Step: Substitute 3 for x in y=3x−7:

y=3x−7

y=(3)(3)−7

y=2(Simplify both sides of the equation)

Equations can be represented on graphs by plotting the corresponding x and y values. The graph of \(y = \frac{3}{2}x^2 + 4x - 2\) is option (B).

Given that:

\(y = \frac{3}{2}x^2 + 4x - 2\)

First, we check the y intercept of \(y = \frac{3}{2}x^2 + 4x - 2\)

This is when \(x = 0\)

So, we have:

\(y = \frac{3}{2}x^2 + 4x - 2\)

\(y = \frac{3}{2} \times 0^2 + 4\times 0 - 2\)

\(y = - 2\)

This point is represented as: \((0,-2)\)

Next, check the equation when \(x = 1\)

So, we have:

\(y = \frac{3}{2}x^2 + 4x - 2\)

\(y = \frac{3}{2} \times 1^2 + 4\times 1 - 2\)

\(y = 3.5\)

This point is represented as: \((1,3.5)\)

From the list of given options (see attachment).

Only graph B has the \((0,-2)\) and \((1,3.5)\) on its curve.

Hence, option (B) is correct.

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Answer:

Equations can be represented on graphs by plotting the corresponding x and y values. The graph of is option (B).

Step-by-step explanation:

y intercept is -2y = 3/2x^2 + 4x – 2y = 3/2(0^2) + 4(0) – 2 = -2and x intercepts are0 = 3/2x^2 + 4x – 2aboutx =  0.43050087, -3.09716754

Answer:

Step-by-step explanation:

The exterior angles of any n-gon is 360 degrees. Remember that we are talking about convex polygons.

The exterior angles of quadrilateral is going to be 360 degrees

Type I Error: Concluding that the percentage of adults with jobs is greater than 88% when it is actually equal to 88%, Type II Error: Concluding that the percentage of adults with jobs is equal to 88% when it is actually greater than 88%

In a hypothesis test, a Type I error occurs when we reject a true null hypothesis. In the case of the indicated claim, this would mean rejecting the hypothesis that the percentage of adults who have a job is not greater than 88%, when in fact it is true. This would be a serious mistake as we would be making a false claim.

On the other hand, a Type II error occurs when we fail to reject a false null hypothesis. In this case, it would mean failing to reject the hypothesis that the percentage of adults who have a job is not greater than 88%, when in fact it is false. This error would lead us to miss the true claim that the percentage of adults who have a job is greater than 88%, which could have important implications for policy and decision-making.

Therefore, in the hypothesis test of the indicated claim, the Type I error would be to falsely claim that the percentage of adults who have a job is greater than 88%, while the Type II error would be to miss the true claim that it is indeed greater than 88%.

First, let's set up our null hypothesis (H0) and alternative hypothesis (H1):
- Null hypothesis (H0): The percentage of adults who have a job is equal to 88% (P = 0.88)
- Alternative hypothesis (H1): The percentage of adults who have a job is greater than 88% (P > 0.88)

Now, let's identify the Type I and Type II errors for this hypothesis test:

1. Type I Error: This occurs when we reject the null hypothesis (H0) when it is actually true. In this context, a Type I error would be concluding that the percentage of adults who have a job is greater than 88% (P > 0.88) when, in reality, it is equal to 88% (P = 0.88).

2. Type II Error: This occurs when we fail to reject the null hypothesis (H0) when it is actually false. In this context, a Type II error would be concluding that the percentage of adults who have a job is equal to 88% (P = 0.88) when, in reality, it is greater than 88% (P > 0.88).

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Answer:

$78.84

Step-by-step explanation:

$26.28 multiplied by 3 is $78.84

Answer:

The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

Step-by-step explanation:

Let be \(d(s) = 0.0056\cdot s^{2} + 0.14\cdot s\), where \(d\) is the stopping distance measured in metres and \(s\) is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.

The procedure to find the speed related to the given stopping distance is described below:

1) Construct the graph of \(d(s)\).

2) Add the function \(d = 7\,m\).

3) The point of intersection between both curves contains the speed related to given stopping distance.

In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

An expression that represents the area of the gift shop, in terms of x is 720x² + 464x - 480.

An expression that represents the perimeter of the gift shop, in terms of x is 720x² + 464x - 480.

If the perimeter is going to be 176 feet, the dimensions of the building are 54 feet by 34 feet.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangular gift shop = (20x + 24) × (36x - 20)

Area of rectangular gift shop = 720x² - 400x + 864x - 480

Area of rectangular gift shop = 720x² + 464x - 480

Perimeter of rectangular gift shop = 2(20x + 24 + 36x - 20)

Perimeter of rectangular gift shop = 2(56x + 4)

Perimeter of rectangular gift shop = 112x + 8

176 = 112x + 8

112x = 168

x = 1.5

Length, L = 20(1.5) + 24 = 54 feet.

Width, W = 36(1.5) - 20 = 34 feet.

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Answer:

8.5

Step-by-step explanation:

The competitors in the first race ran 19.5 miles and the competitors in the second race ran 11.

I hope this helps and makes sense! :)

Examples of such data include stock prices, economic indicators, and meteorological data such as temperature, wind speed, and barometric pressure.

These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.

1. Data where the difference between data values has meaning but there is no defined starting point can be defined as data that is not linearly dependent.

2. Examples of such data include stock prices, economic indicators, and meteorological data. These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.

3. Stock prices, economic indicators, and meteorological data all have different scales and can move in different directions, making it difficult to track the exact difference between data points.

4. Despite this, these types of data still allow for meaningful analysis and can be used to make predictions and draw conclusions.

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The sample mean is significantly different from 10 at a 0.1 significance level.

The null hypothesis is a statement about the population parameter that we are testing, and the alternative hypothesis is the complement of the null hypothesis. The significance level is the probability of rejecting the null hypothesis when it is true.

In this case, we can use the following null and alternative hypotheses:

Null hypothesis: The population mean is equal to 10.

Alternative hypothesis: The population mean is not equal to 10.

We will use a two-tailed test because the alternative hypothesis is not directional.

We can use the t-test to test the null hypothesis. The t-test statistic is calculated as follows:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case:

\(t = (11 - 10) / (3.2 / \sqrt{10} ) = 1.58\)

We need to find the critical value of t at the 0.1 significance level with 9 degrees of freedom (10 - 1 = 9). We can use a t-table or a statistical software to find this value. The critical value is ±1.833.

Since the calculated t-value of 1.58 is not greater than the critical value of ±1.833, we cannot reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is different from 10 at the 0.1 significance level.

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a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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The line passing through the points (1, 0, 1) and (5, -2, 5) intersects the plane x + y + z = 14 at the point (3, -1, 11).

To find the intersection point, we can first find the direction vector of the line by subtracting the coordinates of the two given points.

The direction vector is (5 - 1, -2 - 0, 5 - 1) = (4, -2, 4).

Next, we can substitute the coordinates of one of the points (1, 0, 1) into the equation of the plane x + y + z = 14 to find the value of the parameter t at that point. By substituting the values into the equation, we get 1 + 0 + 1 = 14, which simplifies to 2 = 14. This implies that t = 2.

Finally, we can find the coordinates of the intersection point by substituting t = 2 into the parametric equations of the line. The x-coordinate is given by x = 1 + 4t = 1 + 4(2) = 9.

y-coordinate is y = 0 + (-2)t = 0 + (-2)(2) = -4. The z-coordinate is z = 1 + 4t = 1 + 4(2) = 9. Therefore, the intersection point is (9, -4, 9).

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Answer:

Step-by-step explanation:

a + c = 321

6a + 4c = 1590

c = 321 - a

6a + 1284 - 4a = 1590

2a = 306

a = 153

c = 168

The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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Answer:

1*3*3*3*3*3*3=729. For each term you multiply the previous term by three.

Answer:

2187

Step-by-step explanation:

To find the 8th term, we can find and use the explicit formula.

The standard form of the explicit formula for a geometric sequence is:

\(x_n=a(r)^{n-1}\)

Where a is the initial term, r is the common ratio, and n is the nth term.

From the sequence, we can see that the first term is 1, and each term is 3 times the previous term. Thus, the common ratio is 3.

Substituting these into our equation, we will have:

\(x_n=1(3)^{n-1}\\x_n=(3)^{n-1}\)

So, to find the 8th term, substitute 8 for n:

\(x_8=(3)^{8-1}\)

Subtract:

\(x_8=(3)^7\)

Evaluate:

\(x_8=2187\)

So, the 8th term is 2187.

And we're done!

Answer:

Step-by-step explanation:175.42x .20=35.08  35.08Divided by 11=3.19

so each would pay 3.19 tip

total each would pay for bill would be 175.42+35.08=210.50

210.50divided by 11 =19.14

Answer:

No solution.

Step-by-step explanation:

The two lines are parallel and will never meet. Therefore, they have no solution.