Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS.
Figures are not drawn to scale.

One mile is equal to 5,280 feet. Therefore, to convert the altitude of Denver from miles to feet, we can multiply by 5,280:

1 mile × 5,280 feet/mile = 5,280 feet

So, Denver's altitude of 1 mile is equal to 5,280 feet.

Answer:

We can use the proportion:

48 pages / x = 80% / 100%

where x is the required length of the paper in pages.

First, we can simplify the right-hand side of the equation:

80% / 100% = 0.8

Next, we can solve for x by cross-multiplying:

48 pages / 0.8 = x

x = 60 pages

Therefore, the required length of the paper is 60 pages

The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The integration equation is given below.

[tex]\begin{aligned} \rm I = \int _1^2 \sqrt{x^2 - 4} \ dx \end{aligned}[/tex]

We know that the formula is given as,

∫√(x² - a²) dx = (x/2)√(x² - a²) + (a² / 2) log [x + √(x² - a²)]

Then by the integration, we can write it as,

[tex]\begin{aligned} \rm I &= \int _1^2 \sqrt{x^2 - 4} \ dx \\\rm I &= \int _1^2 \sqrt{x^2 - 2^2} \dx\\\rm I &= \left [ \dfrac{x}{2}\sqrt{x^2-2^2} + \dfrac{2^2}{2} \log (x + \sqrt{x^2 - 2^2}) \right ]^2_1\\\end{aligned}[/tex]

Simplify the equation further, then we have

I = [(1/2) i√3 + 2 log (1 + 3i)]

The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].

More about the integration link is given below.

https://brainly.com/question/18651211

#SPJ9

(x^2 - 7x - 18)/(x + 2) = x - 9 can be simplified by multiplying both sides of the equation of x + 2. The new equation is x^2 - 7x - 18 = x^2 - 7x - 18. Therefore the equation's solution is all real numbers.

Answer:

84

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve for 150% of 56, we can multiply 56 by 150%.

Therefore, 150% of 56 is 84.

Answer:

The record high temperature of 118°F is 63°F higher than the mean temperature of 55°F. The record low temperature of -40°F is 95°F lower than the mean temperature of 55°F. The record high temperature of 118°F is closer to the mean temperature than the record low temperature of -40°F by 32°F.

The account with compound interest of 7.2 % quarterly after 5 years is given by A = $ 1,428.75

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The initial principal amount = $ 1000

The rate of interest r = 7.2 %

The number of times interest is applied n = 4 ( quarterly )

The number of years b = 5 years

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

A = 1000 ( 1 + 0.072/4 )⁴ˣ⁵

On simplifying the equation , we get

A = 1000 ( 1 + 0.018 )²⁰

On further simplification , we get

A = 1000 ( 1.018 )²⁰

A = $ 1,428.75

Hence , the amount after 5 years is $ 1,428.75

To learn more about compound interest click :

https://brainly.com/question/21270833

#SPJ9

Stoichiometry formula is founded on the basis that law of conservation of mass where the total mass of the reactants = total mass of the products.

This is referred to as the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers.

The stoichiometry of a balanced chemical equation identifies the maximum amount of product that can be obtained. The stoichiometry of a reaction describes the relative amounts of reactants and products in a balanced chemical equation.

Read more about Stoichiometry here https://brainly.com/question/14935523

#SPJ1

The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

Answer:

205

Step-by-step explanation:

3hrs is 180 min

5/12 hours is just 25 min

180+25=205

Answer:

205 minutes

Step-by-step explanation:

*60 minutes = 1 hour

3 x 60 = 180

5/12 x 60 = 5/12 x 60/1 = 300/12 = 25

180 + 25 = 205 minutes

Answer: D (210.00)

Step-by-step explanation:

According to the formula of compound INTEREST this is correct

Therefore, after answering the given query, we can state that the as we can multiply it as 7 multiply by 7 = 7*7 = 49.

Multiplication is one of the four matrix multiplication, along with arithmetic, addition, and subtraction. Multiplication in mathematics is the process of repeatedly combining subgroups of the same size. Multiplication is calculated using the formula multiplicand multiplier gives product. multiplicand: Starting number, to be more exact (factor). as a separator, use number two (factor). The result is what remains after splitting both the multiplicand and the multiplier. There are numerous additions necessary when adding numbers. similar to 5 x 4 = 5 x 5 x 5 x 5 = 20. What I did was multiply 5 by 4. Because to this, multiplication is frequently referred to as "doubling."

The standard form for seven squared is 49.

as we can multiply it as 7 multiply by 7 = 7*7 = 49.

To know more about multiply visit:

https://brainly.com/question/23536361

#SPJ1

Answer:

Step-by-step explanation: n The graph is of an absolute value function. Step-by-step explanation: For x ≥ 0, the graph is given by. ⇒ x + 2y = 6. ⇒. ⇒ ........ (1).

Missing: 50 ‎32 ‎2₁

Hope that helps:)

The probability that he teleports at least once per day is [tex]\frac{5}{9}[/tex].

the Marvin must select one of the three transportation alternatives at random.

The likelihood of selecting any one of the three alternatives is the same since the selection is random.

The likelihood of successful teleportation on the first try is:

[tex]P_t=\frac{1}{3}[/tex]

Consequently, the likelihood that you do not teleport is

q=1-p

q=1-[tex]\frac{1}{3}[/tex]

q=[tex]\frac{2}{3}[/tex]

The likelihood that the Marvin won't teleport when leaving for work and returning from work is as follows:

P=[tex]\frac{2}{3}[/tex]×[tex]\frac{2}{3}[/tex]

P=[tex]\frac{4}{9}[/tex]

As a result, the probability that someone will teleport at least once is:

P=1-[tex]\frac{4}{9}[/tex]

P=[tex]\frac{5}{9}[/tex]

Learn more about probability

brainly.com/question/30034780

#SPJ4

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Area = length x breadth

To find the surface area of the postal box, we first find the area of each sides of the box and add them together.

Top and bottom area = L x B = 12 x 8 = 96inches² x 2 = 192inches²

Front and back areas = L x B = 12 x 2 = 24inches² x 2 = 48inches²

Area of the sides = L x B = 8 x 2 = 16inches² x 2 = 32inches²

Total surface area will be 192 + 48 + 32 = 272inches²

To learn more visit https://brainly.com/question/287426

#SPJ1

An exponential decay function that shows the relationship between y and t is y = 16,000 (0.74)^t.

An exponential decay function is one of the two types of exponential functions, including an exponential growth function.

Exponential functions are depicted as y = abˣ, where "a" is a constant, b is the base and x is the variable exponent.

The purchase value of a car = $16,000

Annual decreasing rate in value = 26%

Decayed value after 1 year = 0.74 (1 - 26%)

Let the number of years after the purchase = t

Let the resale value of the car after t years = y

Resale value after t years, y = 16,000 x (1.074)^t

Learn more about exponential functions at https://brainly.com/question/2456547.

#SPJ1

Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

Learn more about linear equation here

https://brainly.com/question/11897796

#SPJ4

Answer:

Step-by-step explanation:

Let x be the number of $1.78 paperback books and y be the number of $2.51 hardcover books that were sold. The total number of books is x + y = 30 and the total amount of money earned is $62.16. The cost of the paperback books is x * $1.78 and the cost of the hardcover books is y * $2.51.

So, we have the following system of equations:

x + y = 30 (the total number of books is 30)

x * $1.78 + y * $2.51 = $62.16 (the total amount of money earned is $62.16)

This system of equations can be used to determine the number of $1.78 paperback books and the number of $2.51 hardcover books that were sold at the yard sale.

Answer: a = 2 because 1 + 1 = 2

Step-by-step explanation:

Step-by-step explanation:

We can find the other point using the axis of symmetry.

The axis of symmetry for a parabola passes through the x coordinate of the vertex.

So our axis of symmetry is x=4, which is a vertical line.

For any point on a parabola curve except the vertex, there will two points that share the same y value. The two x coordinates of those points midpoints should be the axis of symmetry.

So,

If we know (0,-6) and the vertex is 4, let's find the other point

[tex]( \frac{0 + b}{2} = 4[/tex]

[tex]b = 8[/tex]

So our other point is

(8,-6).

So the answer to #1 is we found point (8,-6) by using the axis of symmetry. By reflecting the point (0,-6) about the vertical line x=4, we end up getting the point (8,-6)

To find q, q(x) has the same vertex, so it is (4,10).

We know the axis of symmetry is x=4, we also know the y intercept is 18 so we have point (0,18)

Using the axis of symmetry we will get (8,18).

So the graphs above are the graphs of p and q

The graph facing upwards is q

The graph facing downwards is p.

For #2, you can say we know the vertex is (4,10) and using the y intercept and axis of symmetry we found the other point on the curve.

I don't fully see the table but if the other coordinates have a higher y value, the vertex is a minimum.

Else, of the other coordinates have a lower y value, the vertex is a maximum.

The answer is 1.6!!!

How old are?

The radius of the circle is 21.92 feet

From the question, we have the following parameters that can be used in our computation:

A square lawn has an area of 1922 square feet

This means that

Area = 1922

Take the square root of both sides to determine the side length

side length = 43.84

This represents the circle diameter

So, we divide by 2

radius = 21.92

Hence, the radius is 21.92

Read more about radius at

https://brainly.com/question/24375372

#SPJ1

The value of x and y in the right triangle are as follows:

x = 15√3 units

y = 30 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right angle triangle is 180 degrees.

The side x and y can be found using trigonometric ratios,

tan 60° = opposite / adjacent

tan 60° = x / 15

cross multiply

x = 15 tan 60°

x = 15 × √3

x = 15√3 units

Let's find y as follows:

cos 60° = adjacent / hypotenuse

cos 60° = 15 / y

cross multiply

y = 15 / cos 60

y = 15 ÷ 1 / 2

y = 15(2)

y = 30 units

learn more on right triangle here: https://brainly.com/question/6322314

#SPJ1

Step-by-step explanation:

so, for x = 0, y = 30.5

that means the first answer is out.

for x = 1, y = 21.35

so, only

y = 30.5(0.7)^x

can be right.

all other functions have an y-value of way over 30.5 (because the factor of 30.5 is larger than 1).

and to verify :

30.5 × 0.7¹ = 30.5 × 0.7 = 21.35

correct.

-9(k-5+2k-8) and -27k+117 are equivalent expressions since the solution of -9(k-5+2k-8) = -27k+117.

Equivalent expressions are algebraic expressions that produce the same answer when being simplified. They are said to be a similar expression for whatsoever process used to solve the expression, either by substitution of values or applying mathematical property, they tend to produce equivalent expressions at the end. The equality sign is used between two algebraic expressions that are said to be equivalent.

Given that:

= -9(k-5+2k-8)  

Open brackets

= -9k + 45 - 18k + 72

= -27k + 117

Therefore, we can say  -9(k-5+2k-8) and -27k+117 equivalent expressions are equivalent expressions.

Learn more about equivalent expressions here:

https://brainly.com/question/24734894

#SPJ1

The required number maximum number of copies can be afforded c < 13.33.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have $4.00 and you need to make copies of a flyer at a store that charges $0.30 per copy.

Here,

Let the number of copies be c,

According to the question,

0.30c < 4

c < 4/ 0.30

c < 13.33

Learn more about inequality here:

brainly.com/question/14098842

#SPJ9

The height of the cylindrical tub of ice cream is 6.75 inches.

A cylinder is a 3 dimensional shape which has a curved side and two circular surfaces. The total surface area can be determined by the expression;

total surface area of a cylinder = 2πr^2 + 2πrh

where r is the radius of it circular surface, and h is its height.

Considering the given question, we have;

total surface area of a cylinder = 2πr^2 + 2πrh

But total surface area = 183.69 square inches

r = D/2

  = 6/ 2

r = 3 inches

Thus,

183.69 = 2*3.14*3^2 + 2*3.14*3*h

           = 56.52 + 18.84h

183.69 - 56.52 = 18.84h

127.17 = 18.84h

h = 127.17/ 18.84

  = 6.75

The height of the cylindrical tub of ice cream is 6.75 inches.

Learn more about surface area of cylinder at https://brainly.com/question/27440983

#SPJ1

Answer: The answer is (C) 6.75

Step-by-step explanation:

The formula for Surface Area is: SA = 2πr^2 + 2πrh

Let's do the first part: 2πr^2

So you need to find the radius, which is half the diameter. 6 is the diameter so half that, and you get 3.

Now, times 3 by itself

3 * 3 = 9

And then times 9 by 2

9 * 2 = 18

And times 18 by pi, 3.14

18 * 3.14 = 56.52

Now that we have our first value, lets move on to the second part of the formula: 2πrh

So we need the diameter, and the question gives us the value of the diameter.

6 is the diameter

so times 6 by pi, 3.14

6 * 3.14 = 18.84h  (leave h there because we don't know the height)

Now do this:

183.69 =  56.52 + 18.84h

You cannot add 56.52 and 18.84h because they are not like terms

So take away 56.52 from both sides

56.52 - 56.52 = 0

183.69 - 56.52 = 127.17

Now divide 127.17 by 18.84h

127.17/18.84  = 6.75 inches

Here is proof that my answer is correct. I have a photo of my results and it shows that 6.75 inches is correct. Here is the photo:

Have a an amazing day

The manager would expect 1000 defective players in the shipment.

A store receives a shipment of 5,000 mp3 players out of which 300 were found to be defective.

The clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players.

The results are given AS:

2,806 623 232 3,955 3,799 657 2,140 262 844 561

This means that out of the 10 samples 2 were found to be defective and 8 were in the working condition.

( Since the number 232 and 262 represent the defective mp3 players as they are the numbers which are less than or equal to 300 )

Hence, the Probability that the mp3 players were defective is:

P( defective)=2/10=1/5

Hence, out of 5000 mp3 players the number of players that clerk predict to be defective are:

P( defective)×5000

= 1/5 × 5000

= 1000.

Read more about defective samples at; https://brainly.com/question/30486439

#SPJ1