Phillip wants to find the width, QP, of his driveway. He walks along the edge of the driveway 45 ft and
marks point R. Then he walks 13 ft further and marks point N. He turns 90° and walks until his location,
point R, and point P are collinear. He marks point M at this location, as shown.
(a) Can Phillip conclude that ΔPQR and ΔMNR are similar? Why or why not?
(b) Suppose MN = 15 ft. Calculate the width of the driveway, QP. Show all your work and round
answer to nearest tenth.

The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.

Number theory is the study of integers and functions of arithmetic.

The number of hours in 3 days = 72 hours

Number theory indicates that the multiples of the periods of hooting are;

The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72

The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72

The multiples of 12 are; 12, 24, 36, 48, 60, 72

The common multiples of 3 and 8 are 24, 48, 72

The common multiples of 8 and 12 are 24, 48, 72

The number of times in 72 hours when at least 2 owls are hooting are therefore;

The times when only one owl is hooting are

8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting

3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69   = 21 times when only the first owl hoots

The times when non of the owls hoot  are;

72 - 24 - 6 = 42 times

Learn more on number theory here: https://brainly.com/question/4301692

#SPJ1

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi* r^2 *h[/tex]

Part A

The total length of the assembled rocket will be the length of the cone and the cylinder.

The total length of the assembled rocket  = 25 + 3 = 28cm

Part B

The volume of the rocket is the combined volume of the cone and cylinder.

=  4/3 × 3.14 × 16 × 28

= 1875.62 cubic cm

To convert cm into pounds

1875.62 cubic cm = 4.135 pound

Part C

If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.

Then 1875.62 cubic cm × 0.006

= 11.253

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

Read more about volume here:

https://brainly.com/question/27710307

#SPJ1

Answer:

48

Step-by-step explanation:

total cost will be the answer

Answer:

x=144

Step-by-step explanation:

since they are similar their sides have a common ratio

24/x=42/7

7x=42*24

7x=1008

x=144

Answer:

3

Step-by-step explanation:

The missing height of the triangle is h = 66 inches

Given data ,

Let's denote the missing height of the triangle as "h" inches.

The formula for the area of a triangle is given by:

Area = (1/2) * base * height

Given that the area of the triangle is 6,460 inches squared and the base is either 136 inches or 196 inches, we can set up two equations to solve for "h".

For the base of 136 inches:

Area = (1/2) * 136 * h

6460 = 68h

h = 6460 / 68

h ≈ 95 inches

For the base of 196 inches:

Area = (1/2) * 196 * h

6460 = 98h

h = 6460 / 98

h ≈ 66 inches

Hence , the height of the triangle is h = 66 inches or 95 inches

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

Answer:
y=2x3 - 3

Step-by-step explanation:

Here's the photo for the solution if needed.

The linear model for the given equation would be the model that has the points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).

To find the linear model that has the given equation, come up with values of x and then use the equation to solve for y. The linear model that has the points that you solve for, would be the right one.

Assuming values of x of -1, 0, 1, 2, 3

The y values would be:

x = - 1 :

y = - 2 x ( - 1 ) - 3

y = - 1

x = 0

y = - 3

x = 1

y = - 5

x = 2

y = - 7

x = 3
y = - 9

The linear model has points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).

Find out more on linear models at https://brainly.com/question/28860456

#SPJ1

Answer:  Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.

For vertex (15,15):

3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15

3x + 2y = 90 --> 3(15) + 2y = 90 -->

Step-by-step explanation: A. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we can use a system of inequalities to represent the constraints:

Let "x" be the number of bags of trail mix that Oki makes and "y" be the number of bags that Stephen makes. Then we have:

3x + 4y ≤ 120 (constraint on the number of cups of nuts)

3x + 2y ≤ 90 (constraint on the number of cups of dried fruit)

x ≥ 0 (non-negative constraint for Oki's bags)

y ≥ 0 (non-negative constraint for Stephen's bags)

B. To graph the feasible region, we can start by graphing the two constraint equations as lines:

3x + 4y = 120 (line A)

3x + 2y = 90 (line B)

We can find the x and y intercepts for each line:

For line A:

When x = 0, 4y = 120, y = 30 (y-intercept)

When y = 0, 3x = 120, x = 40 (x-intercept)

For line B:

When x = 0, 2y = 90, y = 45 (y-intercept)

When y = 0, 3x = 90, x = 30 (x-intercept)

Next, we can shade the region that satisfies all of the constraints. This region is below line A and to the left of line B, and is bounded by the x and y axes.

We can find the vertices of the feasible region by finding the intersection points of the two lines and the axes. These vertices are (0,0), (0,30), (15,15), and (30,0).

C. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we need to evaluate the objective function at each vertex of the feasible region, and choose the vertex that maximizes the objective function.

The objective function is the total number of bags of trail mix:

z = x + y

Evaluating at the vertices:

Vertex (0,0): z = 0 + 0 = 0

Vertex (0,30): z = 0 + 30 = 30

Vertex (15,15): z = 15 + 15 = 30

Vertex (30,0): z = 30 + 0 = 30

The maximum value of the objective function occurs at vertices (0,30) and (15,15), where z = 30 bags of trail mix.

To determine how many of each type of recipe to make, we can substitute each vertex into the two constraint equations to find the corresponding values of x and y.

For vertex (0,30):

3x + 4y = 120 --> 3x + 4(30) = 120 --> 3x = -90 --> x = -30

3x + 2y = 90 --> 3(-30) + 2(30) = 90 --> y = 15

Therefore, Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.

For vertex (15,15):

3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15

3x + 2y = 90 --> 3(15) + 2y = 90 -->

The graph of the table is attached accordingly. It examines the relationship betwen Hours and Height of the tides.

The graph shows that there is very wide variations between the height of the tides.

The relationship cannot said to be inverse or positive

Note, the following are three advantages of graphs: It makes data more attractive and understandable. It aids in the concise summarization of facts. It allows for more accurate data comparison.

Learn more about graphs:
https://brainly.com/question/17267403?
#SPJ1

The equation is solved to give 16z² - z - 4 = 0

Note that algebraic expressions  are defined as expressions that are composed of terms, variables, coefficients, constants and also factors.

The expressions are also identified with mathematical operations, such as;

From the information given, we have that;

√z= -4z - 2

Find the square of both sides, we get;

z = 16z² - 4

collect the like terms

16z² - z - 4

Equate to zero

16z² - z - 4 = 0

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

x = -5±-55i/5 is the solution and the best method to solve is by using the general formula.

Given the quadratic equation below;

2x^2+5x+10=0

The best method to solve the equation is by using the completing the square method as shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

From the equation;

a = 2

b = 5

c = 10

Substitute into the formula to have:
x = -5±√5²-4(2)(10)/2(2)
x = -5±√25-80/4

x = -5±√-55/5

x = -5±-55i/5

Hence the solution to the given system of equation is x = -5±-55i/5

Learn more on quadratic equation formula here: https://brainly.com/question/1214333

#SPJ1

The person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

The above problem is asking how much farther a person will travel in one revolution of the Adventure Land ferris wheel compared to one revolution of the Kiddie Land ferris wheel.

The Adventure Land ferris wheel has a diameter of 30 meters, and the Kiddie Land ferris wheel has a diameter of 10 meters.

This means that the circumference of the Adventure Land ferris wheel (the distance traveled in one revolution) is

3.14×30= 94.2 meters

The circumference of the Kiddie Land ferris wheel is

3.14 ×10= 31.4 meters

Here, 94.2-31.4 =62.8 meters

Therefore, the person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

To learn more about the circumference visit:

https://brainly.com/question/4268218.

#SPJ1

The rectangular coordinate from the given polar coordinate is (2.73, -0.73)

To find the rectangular coordinate from the polar coordinates, we can rewrite this as;

x = r cosθ

y = r sinθ

x = r cosθ

Let's substitute the values into it;

x = (2√2)* cos(-π/12)

x =(2√2)cos(-15)

x = √3 + 1

x = 2.73

y = r sin θ

y = (2√2)sin(-π/12)

y = (2√2) * sin (-15)

y = -√3 + 1

y = -0.73

Learn more on polar and rectangular coordinates here;

https://brainly.com/question/2142816

#SPJ1

Answer:

t = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

calculate the gradient (slope) of AB using the slope formula and equate to the slope of the perpendicular line.

given line with slope 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex]

calculate [tex]m_{AB}[/tex] using slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (2, - 3 ) and (x₂, y₂ ) = B (- 2, t )

[tex]m_{AB}[/tex] = [tex]\frac{t-(-3)}{-2-2}[/tex] = [tex]\frac{t+3}{-4}[/tex]

equating corresponding slopes

[tex]\frac{t+3}{-4}[/tex] = - [tex]\frac{4}{5}[/tex] ( multiply both sides by - 4 to clear the fraction )

t + 3 = - [tex]\frac{4}{5}[/tex] × - 4 = [tex]\frac{16}{5}[/tex] ( subtract 3 from both sides )

t = [tex]\frac{16}{5}[/tex] - 3 = [tex]\frac{16}{5}[/tex] - [tex]\frac{15}{5}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

8 and -5

Step-by-step explanation:

8 - 5 = 3

(-5) (8)=-40

Answer:

-8,+5

Step-by-step explanation:

-8+5 = 3

-8×+5 = -40

Answer:

-35.7 as a mixed number is -35 and 7/10.

Answer:

Your answer should be [tex]-35 \frac{7}{10}[/tex]

Step-by-step explanation:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.

Answer:

your answer

Step-by-step explanation:

analogous colors

The solution of the equation 39=2x+1 is 19

The given equation is 39=2x+1

We have to find the solution of the equation

2x+1=39

Let us find the value of x

Subtract 1 from both sides

2x=38

Divide both sides by 2

x=19

Hence, the solution of the equation 39=2x+1 is 19

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The box plot that represents the data is the second box plot.

To find the box plot, look for the measure that is different in both box plots and you will find it to be the value of Q1.

Therefore find the value of Q1 in the data by Ellen by first arranging the riders in order :

0, 0, 2, 2, 3, 4, 6, 8, 8, 9, 11, 14, 16

Q1 would be at the 25 th percentile :

= 25 / 100 x 13

= 3.25 position

Q1 is therefore 2 which makes the correct box plot the second one which shows the Q1 value as 2.

Find out more on box plots at https://brainly.com/question/24335827

#SPJ1

The required, there were 644 premium seats and 646 regular seats sold.

Let x be the number of premium seats sold and y be the number of regular seats sold. Then we have two equations:

x + y = 1290 (total seats sold)

30x + 20y = 32240 (total revenue)

We can use the first equation to solve for y in terms of x:

y = 1290 - x

Substituting this into the second equation, we get:

30x + 20(1290 - x) = 32240

Simplifying and solving for x, we get:

x=644

So 644 premium seats were sold. Substituting this into the first equation, we get:

644+ y = 1290

y = 646

So 646 regular seats were sold.

Learn more about simultaneous equations here:

https://brainly.com/question/31067094

#SPJ1

Answer:

The probability of getting a sum of 5 or 8 when 2 dice are rolled once is 1/4.

Step-by-step explanation:

Your welcome ;)

Answer:

∠ GJK = 102°

Step-by-step explanation:

(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so

2x + 92 + 3x + 63 = 180

5x + 155 = 180 ( subtract 155 from both sides )

5x = 25 ( divide both sides by 5 )

x = 5

Then

∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°

The correct equation is 45(x+3)=60x. Option A

We are told in the word problem that the contractor got 45 expensive wood and 60 cheap wood for the same total price and that  the 45 expensive wood cost $3.00 more than the 60 cheap wood.

If x =price of the 60 cheap wood then we have that 45(x + 3) + 60x = total cost of the wood.

45x + 135 + 60x = total cost of the wood

105x + 135 = total cost of the wood

45(x + 3) + 60x = 105x + 135

Simplifying;

45(x + 3) = 60x

Learn more about equation:https://brainly.com/question/29538993

#SPJ1

Alan paid  an amount $850 to the bank each month to repay his debt.

The total amount that Alan paid back to the bank is equal to the initial amount that he owed minus the remaining amount after 0.5 year(s):

Total amount paid = Initial amount - Remaining amount

= $11750 - $6650

= $5100

We know that Alan paid this amount back over a period of 0.5 year(s), which is equivalent to 6 months.

Let x be the fixed amount that Alan paid back to the bank each month. Therefore, we can set up the following equation:

Total amount paid = Monthly payment × Number of months

$5100 = x × 6

x = $5100 / 6

= $850

Therefore, Alan paid  an amount $850 to the bank each month to repay his debt.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Johnson's pizza had a 120-degree angle when he ate it. The solution is choice C.

When a pizza is cut into 12 equal pieces, each piece has a central angle of:

360 degrees / 12 pieces = 30 degrees/piece

If Johnson ate 4 adjacent pieces, then he ate a total central angle of:

4 pieces * 30 degrees/piece = 120 degrees

Therefore, the measure of the angle of the pizza that Johnson ate is 120 degrees. The answer is option C).

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

Answer:45.06

Step-by-step explanation:

no explanation

The height of the low tide at 7 AM was 45.06 feet.

Given that, the high tide at midnight was 15.42 feet.

A nearing hurricane tripled the tide height. At low tide it went down by 1.2 feet at 7 AM.

We need to find the height of the low tide at 7 AM,

So,

When the hurricane is near the height of the tide is triples so the height is 15.42 × 3 = 46.26 feet

Now, at low tide it went down by 1.2 feet at 7 AM.

so, the height will be = 45.26 feet - 1.2 feet = 45.06 feet

Hence, the height of the low tide at 7 AM was 45.06 feet.

Learn more about high and low tides, click;

https://brainly.com/question/14683300

#SPJ1

The fraction of the game board that is orange is 1/6

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

Sections = 6

Orange = 1

using the above as a guide, we have the following:

Fraction = Orange /Total Number of sections

So, we have

Fraction = 1/6

Other forms of the fraction are

Fraction = 2/12 and 3/18

Hence, the fraction is 2/6

Read more about proportions at

https://brainly.com/question/870035

#SPJ1

There are 60 seconds in 1 minute, so 4 minutes would be:

4 minutes * 60 seconds/minute = 240 seconds

Therefore, it takes 240 seconds to complete the administrative task.