65 points!!!!
The angle of elevation from a park bench 778 feet from the base of the Gateway Arch. How tall is the Gateway Arch? Show all work.

The expression of the statement that is given above can be written as follows: 262144y³ + 27.

To determine how to express the given statement the following should be carried out.

When a number is said to be cubed, it means that the number should be times by itself three consecutive times.

That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,

= 64×64×64(y)³ + 3×3×3

= 262144y³ + 27.

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Answer:

L = 45 + D

Step-by-step explanation:

Examples

D = 2

L = 47 miles

D = 5

L = 50 miles

D = 10

L= 55 miles

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Answer:

Step-by-step explanation:

1) 1. AB ≅ CD                 Given

 2. AD ≅ CB                  Given

 3 . BD ≅ BD                  Reflexive property

 4. ΔABD ≅ ΔCBD         S S S congruent

2) 1. GH // JK                  Given

   2. ∠HGJ ≅∠KJG        Given

   3. GH ≅ JK                 Given

  4 . GJ ≅ GJ                    Reflexive property

   5. ΔHGJ ≅ ΔKJG         S A S congruent

3) ΔJNK ≅ ΔMNL             SSS congruent

  JK = ML                           CPCT

 JK = 160 ft

4) ΔRPS ≅ ΔTQS                A A S congruent

  RS ≅ TS

RS = 85 m

5)ΔDEF ≅ΔGHJ

 GJ  = DE       {CPCT}

6x - 13 = 3x + 2

6x = 3x + 2 + 13

6x = 3x + 15

6x - 3x = 15

3x = 15

 x = 15/3

x = 5

HJ = 5x = 5*5 = 25

Answer:

2

Step-by-step explanation: 1+1=2

Answer:

6 groups of 2, 4 groups of 3, 3 groups of 4, 2 groups of 6, and 1 group of 12 or 12 groups of 1.

Step-by-step explanation:

This question requires you to factor 12. This is because you need to find the numbers that multiply to 12, or its factors. After factoring, you get 1, 2, 3, 4, 6, and 12. When you use these numbers as the amount of groups, you can divide 12 by them to get the size of the groups.

Answer: Discrimant is -55

I think 2 real solutions

Step-by-step explanation:

Step-by-step explanation:

First, let's find the area of the rectangular sides using the dimensions given.

16 x 7 = 112 \(in^2\)

112 is just for one rectangle. We need to find the area for 3 rectangles.

112 x 3 = 336 \(in^2\)

Now, we need to find the area of the triangle. Using the formula let's find the area.

bh/2

7 x 8/2

56

Our answer is 56 as we find the area of two triangles and 28 x 2 equals 56.   To find the prism's total area, we have to add the areas altogether.

56 + 336 =

Answer: 392 \(in^2\)

The software company released 227 home versions and 723 professional versions.

Let  h represent the number of home versions sold and p represent the number of professional versions sold.

Since 1000 copies where sold, hence:

Also the revenue was $38075, hence:

Solving equations 1 and 2 simultaneously gives:

h = 227, p = 723

The software company released 227 home versions and 723 professional versions.

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Answer:

Position  is n = 16

Step-by-step explanation:

he explicit rule for the term in the sequence is given as:

f(n) = 2.5 n - 16

given that the term is 24, we need to find "n" (position). So we solve for "n" :

24 = 2.5 n - 16

24 + 16 = 2.5 n

40 = 2.5 n

n = 40/2.5

n = 16

Step-by-step explanation:

3^6  = 3 * 3^5

 = 3 * 243 =  729

Answer:

Pvalue = 0.1505

y = 0.550x1 + 3.600x2 + 7.300

Step-by-step explanation:

Given the data :

Study Hours GPA ACT Score

5 4 27

5 2 18

5 3 18

1 3 20

2 4 21

Using technology, the Pvalue obtained using the Fratio :

F = MSregression / MSresidual = 30.228571/ 8.190476 = 3.69

The Pvalue for the regression equation is:

Using the Pvalue from Fratio calculator :

F(1, 3), 3.69 = 0.1505

Using the Pvalue approach :

At α = 0.01

Pvalue > α ; Hence, we fail to reject H0 and conclude that ; There is not enough evidence to show that the relationship is statistically significant.

The regression equation :

y = A1x1 + A2x2 +... AnXn

y = 0.550x1 + 3.600x2 + 7.300

x1 and x2 are the predictor variables ;

y = predicted variable

"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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7

15

because there are a total of 15 grid and the question asked to pick the grid that doesn't shaded

Answer:

7/15

Step-by-step explanation:

We can count the grids to see that there are 15. This is the total, and will become our denominator. From there, we can count the non blue squares to get to 7, our numerator. We put our numerator, 7, over pur denominator, 15. This gives us 7/15.

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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\(\begin{cases} x=-7\implies &x+7=0\\ x=0\implies &x=0\\ x=1\implies &x-1=0\\ x=6\implies &x-6=0 \end{cases}\qquad \implies (x+7)(x)(x-1)(x-6)=\stackrel{y}{0} \\\\\\ (x+7)(x)\stackrel{using~\mathbb{FOIL}}{(x^2-7x+6)}=0\implies (x^2+7x)(x^2-7x+6)=0\)

\(\begin{array}{llll} x^2-7x+6\\ \qquad \times ~x^2\\\cline{1-1} x^4-7x^3+6x^2 \end{array}\qquad +\qquad \begin{array}{llll} x^2-7x+6\\ \qquad \times ~7x\\\cline{1-1} 7x^3-49x^2+42x \end{array} \\\\\\ (x^4-7x^3+6x^2)+(7x^3-49x^2+42x)=0 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x^4-43x^2+42x=y~\hfill\)

Answer:

29.5

Step-by-step explanation:

median number is the middle number

Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:

D. f(x) = x² and k(x) = x² - 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:

D. f(x) = x² and k(x) = x² - 6.

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The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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Answer:

The first one

Step-by-step explanation:

....................

Answer:

y = 1/4x

Step-by-step explanation:

The slope changes from 4 to 1/4

so,

y = 1/4x + b

Then, plug in (4,1) into the equation

1 = 1/4(4) + b

1 = 1 + b

b = 0

y = 1/4x + 0

y = 1/4x

Answer:

9/20

Step-by-step explanation:

0.45 = 45/100

45/100=9/20 (divide numerator and denominator by 5)

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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Answer:

\(\textsf{a)} \quad P=-20(x-2)^2+3380\)

b)  cost of ticket = $13

    max profit = $3380

    number of tickets sold = 260

Step-by-step explanation:

Profit equation:   \(P=20(15-x)(11+x)\)

Vertex form of quadratic equation:  \(y=a(x-h)^2+k\)

(where (h, k) is the vertex and \(a\) is some constant)

First, write the given profit equation in standard form \(ax^2+bx+c\):

\(\begin{aligned}\implies P&=20(15-x)(11+x)\\& = 20(165+4x-x^2)\\& = -20x^2+80x+3300\end{aligned}\)

Factor -20 from the first two terms:

\(\implies P=-20(x^2-4x)+3300\)

Complete the square:

\(\implies P=-20(x^2-4x+4)+80+3300\)

\(\implies P=-20(x-2)^2+3380\)

The vertex of the profit equation is (2, 3380).

Therefore, the cost of the ticket is when x = 2 ⇒ $11 + 2 = $13

The maximum profit is the y-value of the vertex:  $3380

The number of tickets sold at this price is:

⇒ max profit ÷ ticket price

= 3380 ÷ 13

= 260