Engineers want to measure the distance from P to Q, but the span from P to Q is across the tip of a lake. So they select a point R on land and fine that the distance from R to Q is 100 feet and from R to P is 120 feet. Angle QPR measures 47 degrees. How far is it from P to Q?

Answer:

354 m

Step-by-step explanation:

to find the height substitute t = 3.5 into the height polynomial

height = - 16(3.5)² + 550 = - 16(12.25) + 550 = - 196 + 550 = 354

The amount will be after 4 years at interest rate of 6%, $624.76

To calculate the total amount you will pay after borrowing $500 for 4 years at an annual interest rate of 6%, you can use the formula for compound interest:

A = P x (1 + r/n)^(nt)

where:

A is the total amount,

P is the principal amount (the initial amount borrowed),

r is the annual interest rate as a decimal,

n is the number of times interest is compounded per year,

t is the number of years the money is borrowed for.

In this case, P = $500, r = 6%, n = 1  and t = 4.

So, the formula becomes:

A = $500 x (1 + 0.06/1)^(1 x 4)

A = $500 x (1.06)⁴

A = $500 x 1.249536

A = $624.76

Therefore, you will pay a total of $624.76 after borrowing $500 for 4 years at an annual interest rate of 6%.

To know more about compound interest check:

https://brainly.com/question/14295570

#SPJ1

Answer: When Mohammed meets Han Fei, she will be 74.6 kilometers away from San Francisco.

Step-by-step explanation:

First, we need to convert Mohammed's speed from miles per hour to kilometers per hour, as Han Fei's speed is given in kilometers per hour.

40 miles per hour = 64.37 kilometers per hour (approximately)

Now, let's determine how long it will take Mohammed to reach the point where he meets Han Fei:

time = distance ÷ speed

time = 240 km ÷ 64.37 km/h

time ≈ 3.73 hours

So, after 3.73 hours, Mohammed will meet Han Fei.

In that time, Han Fei will have traveled:

distance = speed × time

distance = 20 km/h × 3.73 h

distance ≈ 74.6 km

The equations are two parallel lines, then the system of equations has no solutions.

Here we have a system of equations:

-7x + 7y = 1

2x - 2y = -18

Now, if we multiply the second equation by (7/2) we will get:

(7/2)*(2x - 2y) = -18*7/2

7x - 7y = -63

If we multiply this by -1 we will get:

-1*(7x - 7y) = -1*-63

-7x + 7y = 63

Then the system of equations becomes:

-7x + 7y = 1

-7x + 7y = 63

Notice that the left side is equal in both equations but the right side is different, then the system has no solutions.

Learn rmore about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer: B Alex sent the questionnaire only to those who live near her.

Step-by-step explanation:

it is because it were her nieghbors

The cost of 1 kilogram of pears is $5.70.

The cost of 1 kilogram of pears can be found by using the given information and setting up an equation. First, let's repeat the question: "1 kilogram of pears cost as much as 1.5 kilograms of apples. Alex paid $34.20 for 4 kilograms of pears and 3 kilograms for apples. How much did 1 kilogram of pears cost?"

Let's assign variables to the unknowns:

- P = cost of 1 kilogram of pears

- A = cost of 1 kilogram of apples

From the question, we know that:

- 1P = 1.5A - 4P + 3A = 34.20

Now, we can use substitution to solve for P.

1. Substitute 1.5A for P in the second equation: 4(1.5A) + 3A = 34.20

2. Simplify: 6A + 3A = 34.20

3. Combine like terms: 9A = 34.20

4. Solve for A: A = 34.20/9 A = 3.8

5. Substitute 3.8 for A in the first equation: 1P = 1.5(3.8)

6. Solve for P: P = 5.7

Learn more about determine cost at https://brainly.com/question/20534175

#SPJ11

The ratio of the variables makes the equation a circle [tex]x^2\: and \:y^2[/tex]  must be equal,

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced out from the centre. A circle's radius is calculated by measuring it from the centre to the edge.The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.A circle's radius may be measured, making it a basic 2D shape.The inner and exterior parts of the aircraft are separated by the circles.

Equation of a circle

Circle's standard equation is written as

[tex]x^2+y^2+2gx+2fy+C=0[/tex]

Given the equation of the circle

[tex]3x^2 + 6x + 3y^2 + 7y + 4=0[/tex]

Rearrange the equation

[tex]3x^2 + 6x + 3y^2 + 7y + 4=0\\3x^2 + 3y^2+ 6x + 7y + 4=0\\[/tex]

The equation is a circle because the ratio of [tex]x^2\: and \:y^2[/tex]  must be equal,

Learn more about circle

brainly.com/question/29142813

#SPJ4

Answer:

hope this helps.

Step-by-step explanation:

Maileen has 210 Philippine stamps in her collection. This equation can be read as 70 percent of 300, which is equal to 210.

Maileen has a stamp collection of 300 stamps. 70% of the stamps are Philippine stamps. To calculate the number of Philippine stamps Maileen has, we can use the following equation:

(70/100) x 300 = 210

Therefore, Maileen has 210 Philippine stamps in her collection. This equation can be read as 70 percent of 300, which is equal to 210. The equation can be expressed as a fraction, with the numerator being 70, and the denominator being 100. Multiplying the fraction by 300 gives us the answer. In this case, 70 percent of 300 is equal to 210.

Learn more about percent here:

https://brainly.com/question/29172752

#SPJ4

The quantity of liters of both 30% and 10% acid that will make up the 20liters would be= 15 liters and 5 liters respectively.

The quantity of liters of 30% acids ;

= 30+10 = 40

= 30/40×20/1

= 600/40

= 15 liters of 30 % acid will make up 20 liters of 20% acid.

The quantity of liters of 10% acids:

= 10/40× 20/1

= 200/40

= 5 liters of 10% acid will make up 20 liters of 20% acid.

Learn more about percentage here:

https://brainly.com/question/24304697

#SPJ1

Answer:

141 cm^2

Step-by-step explanation:

Given: V = 104 cm3, h = 8 cm

Since V = Bh, where B is the area of the base, and h is the height of a prism, then

B = V/h substitute the given values:

B = 104 cm3/8 cm

B = 13 cm2, which tells us that the long side of the square base equals the square root of 13.

The surface area of a prism = L.A. + 2B, where L.A. is the lateral area of the prism.

L.A. = pH, where p is the perimeter of the base.

Since p = 4(square root of 13) cm, h = 8cm, and B = 13 cm2, we have:

Surface Area = pH + 2B = [4(square root of 13) cm](8 cm) + 2(13 cm2) = 115.38 cm2 + 26 cm2 = 141 cm2

Thus, the surface area of the prism is approximately 141 cm2.

The woods, Sarah’s dog picked up 3 sticks, 2 rocks, and an amount of leaves. An algebraic expression for this is, 3 + 2 + x

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

The total number of items that Sarah's dog picked up in the woods can be represented by the algebraic expression:

3 + 2 + x

where x represents the number of leaves the dog picked up.

The expression 3 + 2 + x represents the sum of the 3 sticks, 2 rocks, and the unknown number of leaves that the dog picked up.

To know more about Expressions check:

brainly.com/question/16804733

#SPJ9

The length and width of the rectangular board is 27 inches and 23 inches respectively

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the mat be = 184 inches²

Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Let the area of the larger rectangle be = ( 2x - 3 ) ( x + 8 )

Let the area of the smaller rectangle be = ( 2x - 7 ) ( x + 4 )

Now , the area of mat = area of the larger rectangle - area of the smaller rectangle

So , 184 = ( 2x - 3 ) ( x + 8 ) - ( 2x - 7 ) ( x + 4 )

On simplifying the equation , we get

2x² - 3x + 16x - 24 - [ 2x² + x - 28 ] = 184

On further simplification , we get

12x + 4 = 184

Subtracting 4 on both sides of the equation , we get

12x = 180

Divide by 12 on both sides of the equation , we get

x = 15

So , the length of the board = ( 2x - 3 ) = 27 inches

And , width of the board = ( x + 8 ) = 23 inches

Hence , the dimensions of the rectangular board is 27 x 23 inches²

To learn more about area of rectangle click :

https://brainly.com/question/15225905

#SPJ9

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

A closed, two-dimensional, flat or planar structure with straight sides is referred to as a polygon. Its sides do not bend in any way. A polygon's sides are also referred to as its edges. A polygon's vertices (or corners) are the places where two sides converge. Polygons and polyhedrons are two names for geometric shapes having three or more sides. The names of a few polygons are listed below. In order to link and develop projects and blockchains that are compatible with Ethereum, Polygon (MATIC), a cryptocurrency and technological platform, was introduced. A fully closed polygon is a flat, two-dimensional form with straight sides. They must have straight sides. Any number of sides can be found in polygons.

To know more about polygon here

https://brainly.com/question/1592456

#SPJ4

Graphically, the feasible solutions represent the points in the x-y plane that are inside the region defined by the three lines, and they can be found by plotting the three lines and shading the region below each line. The feasible solutions are the points in the shaded region that are common to all three.

Let x be the number of cubic yards of mix A used, and y be the number of cubic yards of mix B used. Then the total amount of phosphoric acid, nitrogen, and potash can be expressed as follows:

Phosphoric acid: 20x + 10y >= 460

Nitrogen: 30x + 30y >= 960

Potash: 5x + 10y >= 220

These inequalities represent the minimum monthly requirements for phosphoric acid, nitrogen, and potash. To find the feasible solutions, we need to find the values of x and y that satisfy all three inequalities simultaneously. This can be done graphically by plotting the three inequalities on the same coordinate plane and finding the region that is common to all three.

To plot the inequalities, we can choose convenient values for x and y, substitute them into the inequalities, and find the corresponding values of the right-hand side. For example, if we choose x = 0 and y = 0, then we have:

Phosphoric acid: 20 * 0 + 10 * 0 >= 460

Nitrogen: 30 * 0 + 30 * 0 >= 960

Potash: 5 * 0 + 10 * 0 >= 220

which gives us:

Phosphoric acid: 0 >= 460

Nitrogen: 0 >= 960

Potash: 0 >= 220

These values are all negative, which means that x = 0 and y = 0 do not satisfy the inequalities.

Next, we can choose x = 1 and y = 0, then we have:

Phosphoric acid: 20 * 1 + 10 * 0 >= 460

Nitrogen: 30 * 1 + 30 * 0 >= 960

Potash: 5 * 1 + 10 * 0 >= 220

which gives us:

Phosphoric acid: 20 >= 460

Nitrogen: 30 >= 960

Potash: 5 >= 220

These values are also negative, which means that x = 1 and y = 0 do not satisfy the inequalities either.

We can continue this process until we find values of x and y that satisfy all three inequalities. The feasible solutions are the values of x and y that satisfy all three inequalities, and they are represented by the region in the x-y plane that is common to all three. The feasible solutions can be found by shading the region below each of the lines representing the inequalities, and the set of feasible solutions is the region that is common to all three shaded regions.

To learn more about feasible solutions here:

https://brainly.com/question/30575036

#SPJ4

The exponential function that models this situation is y = 11,000 (0.85)ˣ. The correct answer would be an option (B).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The table below shows the value in dollars of a car at the end of x years.

Number of Years,       xValue, v(x) (dollars)

0                                              11,000

1                                                9,350

2                                               7,948

3                                               6,755

Let the formula for an exponential function would be as

⇒ v(x) = abˣ

Substitute the value of x = 0 and v(x) = 11,000 in the above equation,

⇒ 11,000 = ab⁰

⇒ a = 11,000

Now, substitute the value of x = 1 and v(x) = 9,350, and we get

⇒ 9,350 = ab¹

⇒ 9,350 = (11,000)b

⇒ b = 9,350/11,000

⇒ b = 0.85

Substitute the value of a = 11,000 and b = 0.85 in v(x) = abˣ,

⇒ y = 11,000 (0.85)ˣ

Thus, the exponential function is y = 11,000 (0.85)ˣ.

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ9

Based on the percentage of melons, Sophia's fruit salad will taste more Melony than Joseph's.

The percentage is the quotient of the numerator and denominator.

Like ratios, percentages show the relative size of a value compared to another.

Percentages are expressed as the quotient multiplied by 100.

                          Sophia            Joseph

Cups of melon       5                      8

Cups of apple        2                      5

Ratios                    5:2                   8:5

The sum of ratios 7                     13

Percentages of melon to apple:

                          Sophia              Joseph

                  71.43% (5/7 x 100)  61.54% (8/13 x 100)

Thus, using the percentage of melon to apple, we can conclude that Sophia's fruit salads tastes 71.43% more Melony than Joseph's.

Learn more about percentages at https://brainly.com/question/24877689.

#SPJ1

The length of KJ is 9 unit.

The  length of CB is 10 unit.

The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.

Given:

12. Using Mid segment theorem

Mid segment= 1/2 of Triangle base

Mid segment= 1/2 x 18

Mid segment (KJ) = 9

13. Using Mid segment theorem

Mid segment= 1/2 of Triangle base

x+ 19 = 1/2(x+ 29)

2x + 38 = x+ 29

x = -9

So, length of CB = x + 19 = 10 unit

Learn more about Mid segment theorem here:

https://brainly.com/question/13677972

#SPJ1

Answer:

8252.88

Step-by-step explanation:

This question is a little tricky. you have to use the time a little differently.

Continuously Compounding formula:

P(t)=P(0)e^(rt)

P(0) = initial or starting value

e = constant, on calculator but around 2.718

r = rate

t = The time. usually expressed annually. For example continuously compounding for 6 months, the time would be 0.5. This question is different because we have to treat seconds as "years"

Final Form:

200((e)^(0.04 * 93))

Answer: 8252.88

This statement is False as the probability of intersection of two events is always less than the probability of union.

This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.

The chance of two events A and B occurring together can be calculated using the following formula to see why:

According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.

When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:

Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.

P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:

This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.

For more such questions on probability of the intersection & union

https://brainly.com/question/21333099

#SPJ4

True. The variables x, y, and z have each been assigned an integer value.

Here is a fragment of code that assigns the least of three integer variables to another variable named min:

min = x  # initialize min to the value of x

if y < min:  # check if y is less than min

   [tex]min = y[/tex] # [tex]update min to the value of y if y is less than min[/tex]

if z < min:  # check if z is less than min

   [tex]min = z[/tex] # [tex]update min to the value of z if z is less than min[/tex]

In this code, the variable 'min' is first initialized to the value of 'x'. Then, the code checks if 'y' is less than 'min', and if so, updates the value of 'min' to 'y'. Finally, the code checks if 'z' is less than 'min', and if so, updates the value of 'min' to 'z'. At the end of this code fragment, the variable 'min' will contain the least of the three variables 'x', 'y', and 'z'.

To learn more about integer, refer:-

https://brainly.com/question/15276410

#SPJ4

The two points that lie on the line of the best fit are (3, 7) and (7, 4).

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Given:

The data values of the scatterplot are given in the image below.

The line of the best fit and the calculation are given in the image below.

From the graph;

(3, 7) and (7, 4) are the two points that lie on the line of the best fit.

Therefore, (3, 7) and (7, 4) are the two points.

To learn more about the line of the best fit;

https://brainly.com/question/14279419

#SPJ1

The rate of change in the given graph is 21/4.

The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:

Rate of change = Δy / Δx

To calculate the rate of change of the given graph, we need to identify 2 points first. We take:

(0, 0)

(4, 21)

Rate of change = Δy / Δx

Rate of change = y₂ - y₁

                             x₂ - x₁

Rate of change = 21 - 0

                               4 - 0

Rate of change = 21/4

Learn more about Rate of Change here: brainly.com/question/29518179

#SPJ1

Answer:

13/18

Step-by-step explanation:

Answer:

13/18

Step-by-step explanation:

5/18 + 4/9 .Steps for adding fractions. Find the least common denominator or LCM of the two denominators

The restaurant would make more money by slicing each pizza into sixths. The restaurant would make $36 more than if they sliced each pizza into fourths.

To determine if the restaurant would make more money by slicing each pizza into fourths or sixths, we need to calculate the total amount of money they would make for each option.

Option 1: Slicing each pizza into fourths

Option 2: Slicing each pizza into sixths

Comparing the two options, we can see that the restaurant would make more money by slicing each pizza into sixths. They would make $144 - $108 = $36 more by slicing each pizza into sixths instead of fourths.

Learn more about comparing numbers: https://brainly.com/question/30097421

#SPJ11

The measurement of angle FGH is 27.9° after transformation.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a translation composed with a rotation maps quadrilateral ABCD to quadrilateral EFGH. and m ∠ BCD = 27.9°, we are asked to find measurement of angle FGH,

We know that, any transformation or set of transformation will make similar figures, and similar figures have congruent corresponding angles,

Therefore,

m ∠ BCD = m ∠ FGH

m ∠ BCD = m ∠ FGH = 27.9°

Hence, the measurement of angle FGH is 27.9° after transformation.

Learn more about transformation, click;

https://brainly.com/question/29194193

#SPJ9

The inequality is 25x + 60y + 180 ≤ 2500. x and y are variables.

What is inequality?

In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, whether it is less than or greater than.

Given that a 180-pound person has a load of boxes to deliver. There are types of boxes. The weight of the first type of box is 25 pound and the second type of box is 60 pounds.

Let x represent the number of​ 25-pound boxes, and let y represent the number of​ 60-pound boxes.

The weight of x number of boxes is 25x

The weight of y number of boxes is 60y

The person carrying the box means he is also in the elevator.

The total weight of the boxes and the person is 25x + 60y + 180.

The elevator can hold a maximum weight of​ 2,500 pounds.

The wight of the boxes and the person must be less than or equal to 2500 pounds.

The inequality is

25x + 60y + 180 ≤ 2500

To learn more about symbols of inequality, click on the below link:

https://brainly.com/question/30593940

#SPJ1

The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

Learn more about social security tax here:

https://brainly.com/question/18268724

#SPJ1

Answer:

The room can accommodate 4.5 students.

Step-by-step explanation:

12 square feet = 144 square inches of floor space

24 x 27 = 648 square feet of floor space

648 / 144 = 4.5

The room can accommodate 4.5 students.