Standing on top of a 200 m building with the estimation angle of depression from the top of the building to a park bench on the ground to be 54°

How far is the park bench is from the foot of the building

the equation representing amount paid by Peggy and Daniel for songs is

the cost per download for members and for non-members

from the question the following information can deduced

Daniel is not a member of the club and downloaded 85 at rate of $0.35

total amount paid by Daniel

= 85 * 0.35

= 29.75

Peggy is a member and downloaded 105 songs at a rate of $x

Total amount paid by Peggy

= 105 * $x

= 105x

equating both amounts

105x = 29.75

cost of downloading a song for members, x0.28

105x = 29.75

x = 29.5 / 105

x = 0.28

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[tex]\frac{3}{4}[/tex] of a 6-ounce glass will be drink by Logan in one hour.

What is Quantity?

Quantity is any number or variable and any algebraic combination of other quantities.

Define Average?

The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values .

Explanation for the answer:

Given time [tex]= \frac{2}{3}[/tex] of hours

                =  [tex]\frac{2}{3}\times 60[/tex] ([tex]\because[/tex] 1hrs = 60min)

                [tex]= \frac{120}{3}[/tex]

               = 40 minutes

Given quantity of water [tex]=\frac{1}{2}\ of\ 6\ ounce[/tex]

                                       [tex]= \frac{1}{2}\times6\\ =3 ounce[/tex]

So,

In 40 mins, water intake is 3 ounce

In 1 min, water intake is [tex]\frac{3}{40}[/tex]

 In 60 mins, water in take is  [tex]\frac{3}{40}\times 60 = 4.5\ ounce[/tex]

Quantity of water intake in 60 mins:

4.5 ounce or 3/4 of 6-ounce glass

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Greek mathematicians, who were first influenced by the Egyptians, would go on to produce innovations like Pythagoras' theory of right-angled triangles and, by concentrating on the abstract, bring accuracy and clarity to venerable mathematical conundrums.

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Answer:90 t shirts

Step-by-step explanation: 20:30 is the ratio and if they make 60 sweatshirts, they would have to make 90 tshirts as well. this would keep the same ratio

Using the properties of ratio we calculate that the largest land inheritance was sold at $825000 .

The ratio in which the land is divided is 2:3:5

Let the common ratio be x .

Hence the land is divided which has a combined area of 2750 acres.

Now, 2x+3x+5x = 2750

or, 10x = 2750

or, x = 275

Now the person with the highest inheritance will be having land:

= 5× 275

= 1375 acres

Cost of the land at $600 per acre

= 600 × 1375

= $825000

therefore the cost of the land is  $825000

A ratio can therefore be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value represented by this fraction.

Ratios of counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of two numbers is a dimensionless number when they are measured using the same unit, which happens frequently.

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Answer:

Carmen will have her loan paid back in 20 months

Answer:

0, 6 * 0,6 = 0.36

Step-by-step explanation:

Keyword is AND.First AND second matches both. It means you need to use *.

The probability of winning both matches is 0.36 or 36%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Since the outcome of each match is independent, we can use the multiplication rule of probability to find the probability of winning the next two matches:

P(win both matches) = P(win first match) x P(win second match)

The probability of winning a single match is given as 0.6.

Therefore, the probability of winning the first match is 0.6.

Now, assuming you won the first match, you still have a probability of 0.6 of winning the second match.

Therefore, the probability of winning both matches is:

P(win both matches) = P(win first match) * P(win second match)

= 0.6 x 0.6

= 0.36

Therefore,

The probability of winning both matches is 0.36 or 36%.

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The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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Answer:

x = - 7 , x = 10

Step-by-step explanation:

(x - 10)(x + 7) = 0

equate each factor to zero and solve for x

x - 10 = 0 ⇒ x = 10

x + 7 = 0 ⇒ x = - 7

The value of k so that the system of equation has no solution is k = -4

Since we have the system of equations

kx + 6y = 6

y = 2/3x - 4

For the system of equations to have no solution, the determinant coefficient matrix must be zero.

Re-arranging the equations, we have

kx + 6y = 6

-2/3x  + y = - 4

So, the coefficient matrix is

[tex]\left[\begin{array}{ccc}k&6\\-2/3&1\end{array}\right][/tex]

So, the determinant D = k × 1 - (-2/3) × 6

= k + 2/3 × 6

= k + 2 × 2

= k + 4

Since the determinant must be zero for the system of equations to have no solution, we have that

D = 0

k + 4 = 0

k = -4

So, the value of k = -4

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Answer:

  16 square inches

Step-by-step explanation:

You want the largest rectangle that can be inscribed in a semicircle with radius 4 inches.

The equation of a circle centered at the origin with radius 4 is ...

  x² +y² = 16

The height (y) of a rectangle whose corner is on the circle will be ...

  y = √(16 -x²)

The width of such a rectangle is 2x, so the area of it is ...

  A = WH = (2x)√(16 -x²)

The maximum area will be had when the derivative of the area with respect to x is zero.

  A' = 2√(16 -x²) - 2x²/√(16 -x²) = 0

Multiplying by √(16 -x²)/2 gives ...

  16 -x² -x² = 0

  16 = 2x²

  x = √(16/2) = 2√2

The corresponding area of the rectangle is ...

  A = 2(2√2)√(16 -(2√2)²) = 16

The largest rectangle has an area of 16 square inches.

__

Additional comment

As is often the case with rectangle optimization problems, the largest rectangle that can be inscribed in the quarter circle in each quadrant is a square. It has a diagonal of 4 inches, so an area of 4²/2 = 8 square inches.

The attachment shows the cubic curve representing the area of that square as a function of its width. As above, the rectangle area is double this value.

Answer:

[tex]\dfrac{4}{35}[/tex]

Step-by-step explanation:

Dividing a number is the same thing as multiplying by its reciprocal. So:

[tex]\dfrac{4}{7} \div 5 = \dfrac{4}{7} \cdot \dfrac{1}{5}[/tex]

Finally, simplify by multiplying out the numerators and the denominators.

[tex]\dfrac{4}{7} \cdot \dfrac{1}{5} = \dfrac{4 \cdot 1}{7 \cdot 5} = \dfrac{4}{35}[/tex]

Answer:

4/7 divided by 5 is 4/35

Step-by-step explanation:

Step 1: Convert 5 into an improper fraction

    A. 5 = 5/1

Step 2: Divide 4/7 by the reciprocal of 5/1

    B. 4/7 ÷ 1/5 = 4/35

According to the discriminant, the quadratic equation y = 2 · x² - x + 1 has two roots that are complex and conjugate.

Quadratic equations are algebraic expressions of the form a · x² + b · x + c, where a, b, c are real coefficients. In this case, we can infer the nature of its roots by means of a discriminant:

D = b² - 4 · a · c

Whose possible results are listed below:

If we know that a = 2, b = - 1 and c = 1, then the nature of the roots of the polynomial:

D = (- 1)² - 4 · 2 · 1

D = 1 - 8

D = - 7

Then, the quadratic equation has two conjugate complex roots.

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17576000 courses can be given unique catalog numbers.

There are three numbers and three English letters.

Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is  = 10

So the total number to choose three numbers = 10*10*10 = 1000

Each of letters can be chosen from A to Z.

Number of choice for the each letter = 26

So, the outcomes of letter combination = 26*26*26 = 17576

Hence the total possible catalog numbers = 1000*17576 = 17576000

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Answer:  30 in.

Step-by-step explanation:

So when you look at the right triangle closely, you can see that the c is the same length as the 30 in. That's why I think it is 30 in. (May be wrong)

Answer:

y = 2.60 (to 3sf)

Step-by-step explanation:

Since x is directly proportional to y², then x = ky², where k is a constant.

When x = 4, y = 3,

 4 = k(3)²

 4 = 9k

9k = 4

∴[tex]k =\frac{4}{9}[/tex]

∴ When x = 3,

[tex]\frac{4}{9}y^{2} = 3[/tex]

∴y = 2.60 (to 3sf)

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

Karen buys a pack of bottles of water. = 8

Karen sells all 8 bottles of water for rupees =  50p each

=  50p/100 each

= 0.5 rupees

Total rupees for 8 bottles = 8 x 0.5 = 4

The pack costs  = 1.25

Profit % = (Profit / C.P.) × 100

Profit = SP - CP

=  4 - 1.25

= 2.75

then using these values in equation we get :

profit = [tex]\frac{4 - 1.25}{1.25} * 100[/tex]

profit = (2.75/1.25 )x 100

profit = 2.2 x 100 = 220

profit = 220%

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

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The time taken to reach the maximum height is 1.25 seconds.

The maximum height is 32 feet.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

h(t) = -16t² + 40t + 7

Differentiating with respect to t.

h'(t) = -16 x 2t + 40

0 = -32t + 40

32t = 40

t = 40/32

t = 1.25

The maximum height.

h(t) = -16t² + 40t + 7

h(1.25):

= -16 x 1.25 x 1.25 + 40 x 1.25 + 7

= -25 + 50 + 7

= 32 feet

Thus,

The time taken to reach the maximum height is 1.25 seconds.

The maximum height is 32 feet.

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Answer:

6 months.

Step-by-step explanation:

For each solution, the chemist needs 80 liters of 82% solution and 20 liters of 52% solution.

So, a chemist intends to create a 76% acid solution in 100 liters.

He will create it by combining an acid solution that is 52% with an acid solution that is 82%.

Now, calculate as follows:

0.82x + 0.52(100-x) = 0.76(100) (100)

Hence, for each solution, the chemist needs 80 liters of 82% solution and 20 liters of 52% solution.

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Answer:

-6a -13b - 12c + 4

Step-by-step explanation:

-12a + -5b - 12c + 6a - 8b - (-4)

-12a + -5b - 12c + 6a - 8b + 4   [a "- -" = +]

(-12a + 6a) -(5b -8b) - 12c + 4    [Group like terms.]

-6a -13b - 12c + 4

Answer:

  0.591

Step-by-step explanation:

You want the probability that a height falls between 50.5 and 53.7 when the distribution of heights is normal with mean 53.4 and standard deviation 1.2. All measurements are in inches.

The area under the normal distribution curve with mean 53.4 and standard deviation 1.2 can be found using a suitable calculator. The one in the attachment shows the area between 50.5 and 53.7 is about 0.591

P(50.5 < X < 53.7) ≈ 0.591

__

Additional comment

Any spreadsheet and most graphing calculators have the necessary probability functions. Many special-purpose apps also can answer this question. A calculator answer is shown in the second attachment.

The value of x are, x = 9, x = -9.

What is undefined expression?

A mathematical expression that consists of a number of variables and arithmetic operations but has no known solution is referred to as an undefined expression. Any expression that has the symbol ∞ in any part of its expression or that has zero in the denominator is regarded as being undefined.

When the denominator is zero, a rational expression cannot be defined. Set the denominator equal to zero and solve the ensuing equation to get the values that render a rational expression undefined.

So, to find the x - values set denominator equal to zero.

[tex]x^2 - 81 = 0\\x^2 = 81\\x = \sqrt{81}[/tex]

x = ± 9

Therefore, the value of x are, x = 9, x = -9.

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Answer:

f(x) = 4x + 10

Step-by-step explanation:

The given information is in the form f(x) = y.

f(0) = 10 means if x is 0, y is 10. This is the point (0,10)

Likewise, f(6) = 34

means when x is 6, y is 34. That is the point (6,34).

Slope is y-y / x-x

34-10 / 6-0

is 24/6.

The slope is 4.

The y-intercept is where x is 0, that is 10.

y=mx+b is slope-intercept form. Fill in the slope, 4 for m and the y-intercept, 10, for b.

y = 4x + 10

but they also asked to call it f, so for function notation, use f(x) instead of y.

f(x) = 4x + 10

The value of the square root of 60 subtracted from 17 is D. 9.3

It's important to note that a square root simply means the number that you can multiply by itself in order to get the original number.

In this case, the information given regarding the numbers is illustrate below:

= 17 - ✓60

= 17 - 7.7

= 9.3

Therefore, the value is.9.3

The correct option is D.

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Answer: calculate these equations

Step-by-step explanation: if you have times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form. If we substitute what is in the ( ) with a variable like t, then the original equation will become a quadratic equation.