A football stadium holds 17,700 seats. The lower level has 300 seats less than 4 times the number of seats in the upper level. The middle level has 500 more seats than twice the number of seats in the upper level. Let x represent the seats in the upper level. Which equation can be used to find the number of seats in the upper level?
7 x + 200 = 17,700
6 x + 200 = 17,700
7 x minus 200 = 17,700
6 x minus 200 = 17,700

Answer:

D*1.2        (OR)      1.2D

Step-by-step explanation:

Because the new menu has one hundred percent of the original menu (D), plus twenty percent, the new menu is 120%, or 1.2

You can then multiply the number of items on the original menu (D), by the new menu's value, which is 1.2 (or 120%).

This brings you to the answer of 1.2D

Answer:

f(-3) = -6

Step-by-step explanation:

f(x) = x^2 + 4x - 3

f(-3) means to put -3 in place of x and then do the calculation.

f(-3)

= (-3)^2 + 4(-3) - 3

= 9 - 12 - 3

= -3 - 3

= -6

First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.

f(-3) = -6

The surface area of the regular pyramid as given in the task content is; 16m².

The task content requires that the surface area of the pyramid be determined. This surface area can therefore be evaluated as follows;

Surface area = (2×2) + 4((1/2)×2×3) = 4 + 12 = 16m².

The surface area of the regular pyramid is therefore; 16m².

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Answer:

tickets: $14

popcorn: $10

total: $24

Step-by-step explanation:

2 movie tickets at $7 each is 2*7 which is $14

2 buckets of popcorn at $5 each is 2*5 which is $10

adding these together we get a total spending of $24

Answer:

Step-by-step explanation:

Remark

This is a proportion question. A proportion is 2 equal ratios that requires you to solve the 4th part when you know the other 3.

Givens

1 foot scale model length

5 feet of actual length

x = length of model

65 feet of actual length

Formula

1 foot / 5 feet = x / 65 feet

Solution

1/5 = x / 65                          Cross multiply

5x = 65                                Divide by 5

5x/5 = 65/5

x = 13

Answer

The model is 13 feet long

Answer: [tex]\sqrt{109} \text{ m }[/tex]

Step-by-step explanation:

If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.

Answer:

The answer is on the image, which is color coordinated with the how i got it

answer: 195cm

the photo should explain

The middle term of the expansion of (√x + √y)⁸ is; B: 70 * x² * y²

We want to expand the expression;

(√x + √y)⁸

Now, according to binomial expansion, we know that;

(x + y)ⁿ = ⁿC₀ xⁿ y⁰ + ⁿC₁ xⁿ ⁻ ¹ y¹ + ⁿC₂ xⁿ ⁻ ² y² + ..... + ⁿCₙ x⁰ yⁿ.

Now, for an 8 power binomial, the coefficient of each term from formula are respectively;

1      8      28      56      70     56     28    8      1

The mid term is the fifth term and so, we have;

(⁸C₄ * (√x)⁽⁸ ⁻ ⁴⁾ * (√y)⁴)

⇒ 70 * x² * y²

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The key features are (1) both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.

The functions are given as:

f(x) = 4 - x

[tex]g(x) = -\sqrt{x - 4}[/tex]

Using a graphing calculator:

By comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)

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Answer:

B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

Step-by-step explanation:

b is correct

The solution to this system of inequalities x + y>4  , x + y <3 is Option A

The complete question is

Which graph shows the solution to this system of inequalities? x + y>4 x + y <3

The image are attached with the answer.

When an expression is equated with another expression by an Inequality operator (< , >  < etc) then the mathematical statement formed is called Inequality.

The inequalities are

x+y>4

x + y <3

After plotting both the inequalities in the graph the following graph that is attached with the answer is obtained.

Therefore the correct answer is Option A

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The attached figure represents the sketch of the graph

The complete question requires that we sketch the graph that follows the given parameters

The given parameters are:

To start with, we plot the points on an empty coordinate plane.

Next, we connect the points using a rough curve

Lastly, the points are labelled

See attachment for the sketch of the graph

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The equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

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

We have a triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).

The slope of the segment AB:

[tex]\rm m =\dfrac{4-9}{8-2}[/tex]

m = -5/6

The slope of the line perpendicular to AB:

Let M is the slope of the line:

mM = -1

(-5/6)M = -1

M = 6/5

The line:

y = Mx + c

y = (6/5)x + c

The line passing through the point C(-3, -2)

-2 = (6/5)(-3) + c

c = 8/5

y = (6/5)x + 8/5

5y = 6x + 8

Thus, the equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.

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Answer: 36 m, 144 m

Step-by-Step Explanation:

a = 14 m

b = 12 m

c = 10 m

Perimeter = a + b + c

Therefore,

= a + b + c

= 14 + 12 + 10

= 26 + 10

=> 36

Perimeter = 36 m

Length of Fence required for Fencing 4 times = Perimeter * 4

Therefore,

= Perimeter * 4

= 36 * 4

= 144

Length of Fence required for Fencing 4 times = 144 m

The dimensions the rug should have is 20 by 29

The dimension of the rug is given as:

22 ft by 31 ft

The area of the carpet is given as:

Area = 580

Represent the length of the empty space with x.

So, the dimension of the carpet is:

22 - 2x by 31 - 2x

The area is calculated as:

Area = (22 - 2x) * (31 - 2x)

Expand

Area = 682 - 62x - 44x + 4x^2

Evaluate the difference

Area = 682 -106x + 4x^2

Substitute Area = 580

682 -106x + 4x^2 = 580

Subtract 580 from both sides

102 -106x + 4x^2 = 0

Rewrite as:

4x^2 - 106x +102 = 0

Using a graphing calculator, we have:

x = 1 and x = 22.5

Substitute these values in 22 - 2x by 31 - 2x

So, we have:

Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23

Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14

The dimensions cannot be negative.

So, we have:

Length = 20 and Width = 29

Hence, the dimensions the rug should have is 20 by 29

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Answer:

your mom fat as he'll that way you are adopted

Using the uniform distribution, considering that the novel has 435 pages, the probability that the page is numbered something between 21 and 31 is:

[tex]p = \frac{10}{435}[/tex]

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Researching the problem on the internet, it is found that the novel has 435 pages, hence a = 0, b = 435, and the probability that the page is numbered something between 21 and 31 is given by:

[tex]P(21 \leq X \leq 31) = \frac{31 - 21}{435 - 0} = \frac{10}{435}[/tex]

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The sentence that correctly compares the two numbers is 5385 > 5.395

Here are inequality signs and what they mean:
Note that

5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.

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Answer:

36 cm

Step-by-step explanation:

See attached image

Answer:

Step-by-step explanation:

A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).

The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

For a situation to be fair, the probability of every outcome must be equal.

We can now analyze each option using the above highlight

Situation 1

The probabilities of vowels and consonant are not equal.

Hence, this situation is not fair

Situation 2

People = 4

P(Each) = 1/4

The probability of each participant is equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

The probability of each cousin is equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

The probabilities of prime and composite numbers are not equal.

Hence, this situation is not fair

Situation 5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

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Answer:

4*64=256

256+1=256

there fore 64 1/4 is equivalent to 257/4

Answer:

Graph of Modulus

The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,

where,

(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),

And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.

Given to us

y = |x-3|

On the coordinate plane

The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.

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Step-by-step explanation:

Answer:

C

Step-by-step explanation:

edge 23

inflation means, the same item costs more however is the same item, so if a tomato in January 1st costs $1 and by December 31st it costs $2, the price went up by twice, however is same tomato, it didn't become twice as large, anyhow, inflation eats away value and thus is a Decay case.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A=100(1 - 0.04)^{15}\implies A=100(0.96)^{15}\implies A\approx 54.21[/tex]

now, we can look at this value reduction as value that was eaten away from the original.

we can also see the inflationary effect as the new value of the tomato in money terms, that means the tomato went up in price, exponentially by 4% per year, so we can see that as a Growth case in terms of money spent on it.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A = 100(1 + 0.04)^{15} \implies A \approx 180.09[/tex]

now, this is how much the tomato will be priced in money terms in 15 years.

The difference is "You have to pay interest on credit cards but not on charge cards" , Option B

The cards is a financial tool generally issued by banks which let you to borrow money for expenses and make payments afterward in installments.

Credit cards and charge cards differ in two important ways. One is the method of payment

The other difference is

You have to pay interest on credit cards but not on charge cards, as in credit card the person gets lot of time for the payment and the payment can be made in installments and so for this facility extra charge in terms of interest.

Therefore Option b is the correct answer.

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Answer:

$105.04

Step-by-step explanation:

First add $56 plus 45$ and you will get $101, then times $101 and 1.04 together.

Your answer should be $105.04.

Step-by-step explanation:

4 + 4 = 8 is one of the two closest double to 3 + 4

W.K.T(we know that )..

4 is 1 more than 3 this means ;

4 + 4 will be 1 more than 3 + 4

4 + 4 = 8 ,so finding 1 Less ;

3 + 4 = 7

here is the answer hope It helped U

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Answer:

(0, 9]

Step-by-step explanation:

√81 = 9

We must take positive numbers into consideration here.