A group
of friends wants to go to the amusement park. They have no more than $245
to spend on parking and admission. Parking is $9.25, and tickets cost $25.75 per
person, including tax. Which inequality can be used to determine p, the maximum
number of people who can go to the amusement park?

We are looking for the value of t when d(t) equals 250. So:

\(d(t)=250\\-16t^2+400t=250\)

So let's solve for t. The best way to do this is by using the Quadratic Formula. This evaluates quadratic equations. Quadratic equations are trinomials with a degree of two.

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\-16t^2+400t=250\\-16t^2+400t-250=250-250\\-16t^2+400t-250=0\\\\t=\frac{-400\pm\sqrt{400^2-4(-16)(-250)}}{2(-16)}\\t=\frac{-400\pm\sqrt{160000-4(4000)}}{-32}\\t=\frac{-400\pm\sqrt{160000-16000}}{-32}\\t=\frac{-400\pm\sqrt{144000}}{-32}\\t=\frac{-400\pm379.47}{-32}\\t=\frac{-20.53}{-32},\frac{-779.47}{-32}\\t=0.641,24.36\)

So the projectile will be at a height of 250ft at 0.641 seconds and 24.36 seconds.

When rolling a fair die 100 times the probability of rolling a 4 exactly 25 times is 0.01.

Therefore, the answer is 0.01.

Let us solve this by using Binomial probability distribution. Let us consider getting 4 as a successful trial when rolling a die. The possible number of outcomes when rolling a fair die is 6. The probability of getting 4 when rolling a die is p = 1/ 6 = 0.167.

The total number of trial is 100 and the number of successful trial is 25. The probability of rolling a 4 exactly 25 times can be obtained by

P = nCx × p^{x} × (1 - p)^{n - x}

P = 100C25 × 0.167^{25} × (1 - 0.167)^{100 - 25}

P = 100!/ (25! × (100 -25)!) × 0.167²⁵ × 0.833⁷⁵

P = 0.01

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When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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Answer: 3 1/4 inches

Step-by-step explanation:

9 3/4 - 6 1/2

I turned 6 1/2 into an easier fraction so it can be easier to subtract. Now the expression is:

9 3/4 - 6 2/4

6 2/4 is equivalent to 6 1/2

I then got 3 1/4

The perimeter of the quadrilateral is 46 units, so the correct option is d.

The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.

Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:

L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)

The length between the first two vertices: (−6, −2), (0, −10)

L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10

The length between the second two vertices:  (0, −10), (5, 2)

L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13

The length between the third two vertices:  (5, 2), (−1, 10)

L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10

The length between the fourth two vertices:  (−1, 10), (−6, −2)

L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13

Then the perimeter is:

P = 10 + 13 + 10 + 13 = 46

The correct option is D.

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Answer:

I believe the answer is B

Step-by-step explanation:

The graph with Vertical Asymptotes: x=-3 and Horizontal Asymptotes: y=3 is given below.

The given function is \(r(x)=2+\frac{x+1}{x+3}\).

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The graph for the given function is

Find the asymptotes.

Vertical Asymptotes: x=-3

Horizontal Asymptotes: y=3

No Oblique Asymptotes

The graph with Vertical Asymptotes: x=-3 and Horizontal Asymptotes: y=3 is given below.

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Answer:

h(-2) = -6, h(a) = 12/a

Step-by-step explanation:

h(-2)

It says that you are supposed to do 12 divided by the number in the parentheses, so you have 12 / -2 = -6.

h(a)

Again, you have to do 12 divided by the number in the parentheses, so you have 12/a.

To determine the amount of salt in the tank after 60 minutes, we need the concentration of salt in the solution entering the tank.

The information provided, which is the salt concentration in terms of "zib salt /gal," is incomplete and does not specify the actual value of zib.

If you can provide the concentration of salt in the solution entering the tank (in terms of a specific numerical value), I can help you calculate the amount of salt in the tank after 60 minutes.

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a tank contains 100 gal of pure water inirially. a solution containing zib salt /gal enters into the tank at the vate of 3 gal/min. also a drain is open so that qhe volume of the solution is constant. tow much after salt is in the tank after 60 mins?

The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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Answer:

z = 124 degrees

Step-by-step explanation:

If it is a parallelogram, opposite angles are congruent. So, z = 124 degrees

Answer:

opposite angles are equal so z=124°

Answer:

Use the given functions to set up and simplify .

2

x

+

7

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x

−

1

=

−

3

x

+

7

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x

−

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2

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−

1

−

1

=

x

−

3

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(

−

5

+

x

)

=

x

=

2

10

=

x

+

6

+

2

x

=

=

3

x

+

6

3

+

3

x

−

(

x

−

2

)

=

3

x

+

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=

x

=

1

−

4

+

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2

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1

Step-by-step explanation:

Answer:

n = -6

Step-by-step explanation:

Divide both sides by 2.

1. n+5=−1

Subtract 5 from both sides.

2. n=−1−5

Simplify  -1 − -5  to −6.

3. n = −6

Answer:

y= -1x + 4

Step-by-step explanation:

I think it's that because you would do x2-x1 over y2-y1 and get 5/-5 which you can simplify to get -1. Then I just put the equation in desmos I won't lie and found out it went through those two points.

Answer:

  j(0, 2)

Step-by-step explanation:

You want to know the coordinates of point J in parallelogram GBJF, given G(-4, 1), B(-2, 3), F(-2, 0).

In a parallelogram, the diagonals bisect each other. This means their midpoints are the same.

  (G +J)/2 = (B +F)/2 = M

  G +J = B +F . . . . . . . . multiply by 2

  J = B +F -G

  J = (-2, 3) +(-2, 0) -(-4, 1)

  J = (-2-2+4, 3+0-1) = (0, 2)

The coordinates of point J are (0, 2).

<95141404393>

We can use the given points to solve.

Slope formula: y2-y1/x2-x1

3-(-3)/-4-2

6/-6

-1

Best of Luck!

(2, -3) and (-4, 3)

The slope of the line through (2, -3) and (-4, 3).

y2 - y1 / x2 - x1

3 + 3 / -4 - 2

= 6 / -6

= -1

-1

Answer:

16 / 3 = 5.33333....

Step-by-step explanation:

its the accurate answer

pls brainliest

Answer: 37.7un^3

Step-by-step explanation:

Volume = 1/3πr^2h

=1/3×π×22×9

=12π

= 37.699111843078 feet3

The range of the graph shown is

range { y | y < 0 }

When a figure is transported from one place to another without changing its size, shape, or orientation, a translation takes place.

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The graph's entire range, from lower to upper numbers vertically, represents the range.

The translation downwards, means that the graph moved down and considering the image of the attached graph, the effect of the translation means that the range to be numbers less than zero

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Answer:

8.6 I think

Step-by-step explanation:

d=√((x_2-x_1)²+(y_2-y_1)²)

Answer:

\( - 18 + 18 \\ = 0 \\ thank \: you\)

Answer:

\( \longmapsto18 + ( - 18) = 18 - 18 = \boxed{0}✓\)

Answer:

-30

Step-by-step explanation:

i am not sure just remember getting taught it.

Answer:

h= -28

Step-by-step explanation:

h+14=-14 isolate h by subtracting 14 on both sides

h= -28

Answer:

h=-28

Step-by-step explanation:

k byeeeeeeeeeeeeee:)

Answer:

Point Form:

(9,12)

Equation Form:

x = 9

y = 12

Step-by-step explanation:

Answer:

\(\fbox{x = 9, y = 12}\)

Step-by-step explanation:

\(\textsf {Let's solve by substitution.}\)

\(\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}\)

\(\textsf {Substitute for x in the first equation of the system.}\)

\(\implies \mathsf {-5(2y-15)+4y=3}\)

\(\implies \mathsf {-10y+75+4y=3}\)

\(\implies \mathsf {-6y=-72}\)

\(\implies \textbf {y = 12}\)

\(\implies \mathsf {x = 2(12) - 15}\)

\(\implies \mathbf {x = 9}\)

\(\textsf {The solution is : x = 9, y = 12}\)

Answer:

An infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, ...}. Examples of infinite sequences are N = (0, 1, 2, 3, ...) and S = (1, 1/2, 1/4, 1/8, ..., 1/2 n , ...)

Answer:

2 x − y = 4

this is in standard

Answer:

2x-y=4

Step-by-step explanation:

Let S be the subspace of P3 consisting of all polynomials p(x) such that p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) The two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b) The two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c) The vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

We have the information from the question:

Let S be the subspace of \(P_3\) consisting of all polynomials p(x).

We have:

p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) S is all polynomials of the form p(x) = \(ax^2 + bx\) where a, b are

real numbers.

p(0) = \(a(0)^2 + b(0)\) = 0 for all a, b.

I propose that {x, \(x^{2}\)} forms a basis for S.

We must show that:

The vectors x and \(x^{2}\) are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1(x^2) + \alpha _2(x) = 0(x^2) + 0(x)\)

Only has the solution :

\(\alpha _1=\alpha _2=0\)

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span S we must show that any element

in S which I will represent by p(x) = ax^2 + bx can be written as:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

where, \(\alpha _1,\alpha _2\) are scalar  vectors.

Upon grouping the terms we find that:

\(\alpha _1=a\\\\\alpha _2=b\)

With this solution we have:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

which means the two vectors span S.

Thus, the two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b)T is all polynomials of the form :

\(q(x) = a(x - 1)(bx + c) =abx^2 + acx - abx - ca = ab(x^2) + (ac - ab)x - ac\)where a, b, c are real numbers.

This is because q(1) = a(1 − 1)(b + c) = 0 for all a, b, c.

Let s = ab and t = ac.

Now we have that T is all polynomials of the form

\(q(x) = sx^2 + (t - s)x - t\)

\({(x - 1),(x - 1)^2}\)forms a basis for S.

In order to confirm this we must show that the vectors x − 1 and \((x - 1)^2\)are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1((x -1)^2) + \alpha _2(x - 1) = 0(x - 1)(0(x) + 0)\)

only has the solution α1 = α2 = 0

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span T we must show that any element

in T which I will represent by \(q(x) = sx^2 + (t - s)x - t\) can be written as:

\(\alpha _1((x - 1)^2) + \alpha _2(x - 1) = sx^2 + (t - s)x - t\)

Where, \(\alpha _1,\alpha _2\) are scalars.

Upon grouping the terms we find that:

\(\alpha _1=s\\\\\alpha _2=s+t\)

With this solution we have:

\(sx^2 + (t - s)x - t = sx^2 + (t - s)x - t\)

which means the two vectors span T

Thus, the two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c)  S∩T is all polynomials of the form \(c(x) = a(x-1)(bx) = abx^2-abx\)

where a, b are real numbers.

This is because \(c(0) = a(0 - 1)^2\)

(b(0)) = 0 and

c(1) =\(a(1 - 1)^2\)

(b(1)) = 0 for all a, b.

Let ab = t

This means S∩T is all polynomials of the form \(c(x) = tx^2-tx = tx(x-1).\)

I propose that {x(x − 1)} forms a basis for S ∩ T.

Now, we must show that the vector x(x − 1) is linearly independent and spans S ∩ T.

To show it is linearly independent we must show that:

\(\alpha _1\)(x(x − 1)) = 0(x(x − 1))

only has the solution \(\alpha _1\) = 0.

Upon grouping the terms we find:

\(\alpha _1\) = 0

Thus the two vectors are clearly linearly independent.

Now to show that the vector spans S ∩ T we must show that any element

in S ∩ T which I will represent by c(x) = tx(x − 1) can be written as:

\(\alpha _1\)(x(x − 1)) = tx(x − 1).

where \(\alpha _1\) is a scalar.

Upon grouping the terms we find that:

\(\alpha _1\) = t

With this solution we have:

tx(x − 1) = tx(x − 1)

which means the vector spans S ∩ T.

Thus, the vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

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It would cost $40 to fence a single property with an area of one square mile, assuming a cost per unit length of $10.

To calculate the cost of fencing a square property with an area of one square mile, we need to know the cost of fencing per unit length. The total length of the fence needed can be found by calculating the perimeter of the square.

Since the property is perfectly square and each side is one mile long, the perimeter is equal to four times the length of one side. In this case, the perimeter would be 4 miles.

To calculate the cost, we need to multiply the perimeter by the cost per unit length. Let's assume the cost per unit length is $10.

Therefore, the cost of fencing the property would be:
4 miles (perimeter) * $10 (cost per unit length) = $40

So, it would cost $40 to fence a single property with an area of one square mile, assuming a cost per unit length of $10.

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Answer:

$5.58

Step-by-step explanation:

Because divide 12 by 67:

67 ÷ 12 = 5.58

5.58 is the answer

Hope this helped! Pls Brainliest!

Answer:

$5.58

Step-by-step explanation:

$67.00÷12=$5.58

Hope this helps!

Answer:

the answer is A because the height is 40 feet and the ground is 26°

Answer:

r = 1

Step-by-step explanation:

We need to isolate r, so first subtract 1 from both sides to get 19r = 19. Divide both sides by 19 to get r = 1