a building 34.98 feet tall has a shadow that is 38.85 feet long. find the angle of elevation of the sun to the nearest hundredth of a degree.

Answer:

z ≈ 145.62

Step-by-step explanation:

using the sine ratio in the right triangle

sin18° = \(\frac{opposite}{hypotenuse}\) = \(\frac{45}{z}\) ( multiply both sides by z )

z × sin18° = 45 ( divide both sides by sin18° )

z = \(\frac{45}{sin18}\) ≈ 145.62 ( to the nearest hundredth )

Answer:

G: 98.96017

Step-by-step explanation:

Kus math

V=πr2h=π·32·3.5≈98.96017

Answer:

The answer is (G) 98.96 cm cubed

Step-by-step explanation:

You would use the formula V=πr2h or V=Bh to solve this. :)

Answer:

Perpendicular

Step-by-step explanation:

the slope of b is -3/4 and the slope of a is 4/3

Answer:

Perpendicular

Step-by-step explanation:

The lines are perpendicular because they meet at a right angle (90 degrees).

According to the Ricardian model, the difference in technology among nations causes output per worker in each country to differ.

The model is limited in several ways: 1. Having only 1 factor of production is way too simplistic a view of manufacturing. 2. In real world, almost no country produces only the goods in which they have a comparative advantage.

The Ricardian model assumes that labour is the only factor of production. Under this assumption, the only possible source of comparative advantage is differences between countries in labour productivity.

An important criticism leveled against Ricardian theory of rent concerns the relation between rent and price. According to Ricardo, price determines rent. The higher the price of corn, the higher will be the rent. The price of corn is determined by the cost of producing corn on the marginal land which is rent-free.

Therefore,

According to the Ricardian model, the difference in technology among nations causes output per worker in each country to differ.

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The total amount spent on gas is $9.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. Multiplication is the method that is used to add a number by itself a particular number of times. The sign used to denote multiplication is x. Other mathematical operations are subtraction, division and addition.

In order to determine the total amount spent on gas, multiply the cost of one gallon by the number of hours skied and the amount of galloons used per hour.

The total amount spent on gas = cost of one gallon of gas x number of hours skied x number of gallons used per hour

2 x 3 x $2.25 = $9

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Answer:

Step-by-step explanation:

The total amount spent on gas is $9.How much is spent on gas?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. Multiplication is the method that is used to add a number by itself a particular number of times. The sign used to denote multiplication is x. Other mathematical operations are subtraction, division and addition. In order to determine the total amount spent on gas, multiply the cost of one gallon by the number of hours skied and the amount of galloons used per hour. The total amount spent on gas = cost of one gallon of gas x number of hours skied x number of gallons used per hour 2 x 3 x $2.25 = $9To learn more about multiplication, please check:

Answer:

B

Step-by-step explanation:

The equation of the line;

Problem statement

Write the equation of the line; with the given properties, in slope-intercept form.

Slope (m)= -5 through (-5, 5)

Solution

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the

y-intercept.

Since (-5, 5 ) is a point on the line, we can "plug in" -5 for x and 5 for y into our equation to obtain

We now substitute for b now

The equation of the line;

AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE

Translation is a type of transformation that involve a linear movement.

The translation rule is gotten by comparing the points as below

preimage point A (1, 7) and B (5, 4)

image points D(-6, -2) and E(-2,-5)

x coordinate

using point A and D = -6 - 1 = -7

using point B and E = -2 - 5 = -7

y coordinate

using point A and D = -2 - 7 = -9

using point B and E = -5 -  = -9

Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B

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Answer:

8000

Step-by-step explanation:

Answer: Therefore, the number 8272 rounded to the nearest thousand is 8000

Step-by-step explanation:

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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Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The y intercept occurs when x = 0.

All you have to do is read the table until you come to x = 0.

When you do, read down to get the y value.

The answer is A (0,2)

Answer: 39. x= 37, 41. x=7, 43. x = 29

Step-by-step explanation:

39. 2x + 4 + 2x - 9 + x = 180

5x - 5 = 180

5x=185

185/5

x=37

41. 90 + 8x - 1 + 4x+7 =180

8x-1+4x+7=90

12x+6=90

12x=84

84/12

x=7

36+x=2x+7

36=x+7

29=x

Hope this helps.

Answer:

Hope this helps

Answer:

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term and \(q\) is the common ratio.

A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.

This means that:

\(q = 0.7, a_1 = 25*0.7 = 17.5\)

Then

\(a_n = a_1q^{n-1}\)

\(a_n = 17.5(0.7)^{n-1}\)

First 5 terms:

\(a_1 = 17.5\)

\(a_2 = 17.5(0.7)^{2-1} = 12.25\)

\(a_3 = 17.5(0.7)^{3-1} = 8.58\)

\(a_4 = 17.5(0.7)^{4-1} = 6\)

\(a_5 = 17.5(0.7)^{5-1} = 4.2\)

Find the total distance the ball has travelled after it hits the ground the 5th time.

\(T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53\)

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Step-by-step explanation:

125/1000=5/40=1/8

14/100=7/50

8/100=2/25

111.51 is the probability of the random sample of 15 people that 4 of them are left-handed.

P(exactly x out of n) = (n! ÷ (x! × (n - x)!)) × \(p^{x}\) × \((1 - p)^{n - x}\).

where n = number of trials = 15.

p = probability of selecting one lefty in one trial = 10% or 0.1

x = probability which needs to be deduced = 4.

P(exactly 4 out of 10) = (10! ÷ (4! × (10 - 4)!)) × \(1^{4}\) × \((1 - 0.1)^{10 - 4}\).

P(exactly 4 out of 10) = (10! ÷ (4! × 6!)) × \(1^{4}\) × \((0.9)^{6}\).

P(exactly 4 out of 10) = 210 × \(1^{4}\) × \((0.9)^{6}\).

P(exactly 4 out of 10) = 210 × 1 ×0.531

P(exactly 4 out of 10) = 111.51

The probability that 4 of them are left-handed is 111.51.

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Answer:

you multiply both side it gives you

-111.495

Answer:

Step-by-step explanation:

i cant see your pic to see what you are diling with

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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Answer:

Option (4)

Step-by-step explanation:

Option (1)

f(x) = 4x⁴- 7x²+ x + 25

Possible rational roots will be,

\(\frac{\pm \text{Factors of constant term '25'}}{{\pm \text{Factors of leading coefficient '4'}}}\)

For the given function,

Possible rational roots = \(\frac{\pm 1, 5, 25}{\pm 1,2}\)

                                      = \(\pm 1, \pm 5, \pm 25, \pm \frac{1}{2},\pm\frac{5}{2},\pm\frac{25}{2}\)

Therefore, \(-\frac{2}{5}\) is not the possible root.

Option (2)

f(x) = 9x⁴- 7x²+ x + 10

Possible rational roots = \(\frac{\pm 1,\pm 2,\pm 5,\pm10}{\pm 1,\pm3,\pm9}\)

Therefore, \(-\frac{2}{5}\) is not the possible root.

Option (3)

f(x) = 10x⁴- 7x²+ x + 9

Possible rational roots = \(\frac{\pm1, \pm3, \pm9}{\pm 1,\pm2,\pm5,\pm10}\)

Therefore, \(-\frac{2}{5}\) is not the possible root.

Option (4)

f(x) = 25x⁴- 7x²+ x + 4

Possible rational roots = \(\frac{\pm 1,\pm2,\pm5}{\pm1,\pm5,\pm 25}\)

                                      = \(\pm1,\pm2,\pm5,\pm\frac{1}{5},\pm\frac{1}{25},\pm\frac{2}{5},\pm\frac{2}{25}\)

Therefore, \(-\frac{2}{5}\) is the possible rational root.

Option (4) will be the answer.

Answer:

\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)

Answer: it looks correct to me!!!

Look at the attached picture above

(just from the top half, then apply this same thing to the rotated/reflected bottom half)

The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,

To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:

According to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).

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Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

Answer:

3 / 1352 ; 1 / 442

Step-by-step explanation:

Since it isn't stated if selection is done with replacement or not, we calculate the probability for the two scenarios :

Number of diamond face cards in a deck = 3

Number of black 2's in a deck = 2

Total number of catds in a deck = 52

Assume selection is done with replacement :

1st draw :

P(diamond face card) = 3 / 52 =

2nd draw :

P(black 2's) = 2 /52

P(1st draw) * P(2nd draw)

3/52 * 2 /52 = 6 / 2704 = 3 / 1352

Drawing without replacement :

P(diamond face card) = 3 / 52 =

2nd draw :

P(black 2's) = 2 /51

P(1st draw) * P(2nd draw)

3/52 * 2 /51 = 6 / 2652 = 1 / 442

Answer:

3 / 1352

Step-by-step explanation:

The change in electric potential energy of an alpha particle is:

1.3V/cm

"Information available from the question"

In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm.

At position y2=28 cm , the potential, v2, is 3. 9 v.

Now, According to the question:

Calculation of magnitude:

Since  V1 is 1.3 V at position y1=26 cm. At position y2=28 cm, the potential, V2, is 3.9 V

So, We know that

\(E =\frac{V_2-V_1}{Y_2-Y_1}\)

\(E=\frac{3.9-1.3}{28-26}\)

\(E=\frac{2.6}{2}\)

E = 1.3V/cm

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The given function is:y = −3 + (1/cos(xx - ²))³ = - 3 + (1/cos(x- ²))³The function is shifted 2 units to the right.Phase shift, P = 2 Final answer:Period: 2πAmplitude: 1 Phase shift: 2

Given function is

y = −3 + (1/cos(xx - ²))³Period:

Period is the distance after which the function will repeat itself. For finding the period of the given function, use the formula:

T = 2π/b

Where T = period and b is the coefficient of x Here the coefficient of x is 1 Period,

T = 2π/1 = 2πAmplitude:

Amplitude of the given function can be determined by observing the graph of the function or it can be calculated using the formula

A = |1/b|

Here b is the coefficient of cosx, which is 1.Amplitude, A = |1/b| = 1Phase Shift:The general form of cosine function is:

y = A cos (bx - c) + d

Here A is the amplitude, b is the coefficient of x, c is the phase shift and d is the vertical shift. Phase shift is the horizontal shift of the graph of the given function.The given function is:

y = −3 + (1/cos(xx - ²))³ = - 3 + (1/cos(x- ²))³

The function is shifted 2 units to the right.Phase shift, P = 2 Final answer:

Period: 2πAmplitude: 1 Phase shift: 2

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Step-by-step explanation:

Equation to find the sum of the first n terms :

\(S_{n}\) = \(\frac{n}{2}\) x (2\(a_{1}\) + (n - 1)d)

- where n is the first n terms

- where \(a_{1}\) is the first term in the sequence

- where d is the difference (To find the difference: \(a_{1}\) - \(a_{2}\))

How to find n for the given sum :

1. Using the previous equation, plug in all the numbers that you know

2. PEMDAS then combine all like terms

3. Distribute what's on the outside to the inside of the parenthesis

4. Move  \(S_{n}\) to the other side to make a quadratic equation

5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)

Question 1:

Sum of first 10 terms : \(S_{10}\) = \(\frac{10}{2}\) ( 2 x 2 + (10 - 1)6)

 \(S_{10}\) = \(\frac{10}{2}\) (4 + (9)6) = (4 + 54) = 58

 \(S_{10}\) = \(\frac{10}{2}\) x 58

Answer : 290

Find n for the given sum : 1704 =  \(\frac{n}{2}\) x (2 x 2 + (n - 1)6)

distribute 6 into (n-1)

1704 =  \(\frac{n}{2}\) x ( 4 + 6n - 6)

combine like terms

1704 =  \(\frac{n}{2}\) x ( -2 + 6n )

Distribute  \(\frac{n}{2}\) to ( -2 + 6n )

1704 = \(\frac{-2n}{2}\) - \(\frac{6n^{2} }{2}\)

Simplify fractions and move 1704 to the other side

-3\(n^{2}\) - n + 1704 = 0

Use a quadratic calculator to find the answer and use the answer with the whole number

Answer : -24

Question 2:

(i'm just gonna show you the answers for the rest of them-)

Sum of the first 14 terms: 490

Find n for the given sum: 33.65 (I'm gonna round it to 34)

Question 3:

Sum of the first 21 terms: 483

Find n for the given sum: 11.48 (rounded: 11)

Question 4:

Sum of the first 32 terms: -1328

Find n for the given sum: -9.34 (rounded -9)

really hope this helps in any way :D