Using the given information, the distance from point A to point B is 568ft
How to find distance between two points?You should know that Distance is defined as the numerical or occasionally qualitative measurement of how far apart points are from each other.
The distance between A and B can be measured using the Trigonometric ratio of angles.
The drawing formed a right angled triangle.
Using the tangent function
Tan∅=[tex]\frac{opposite}{adjacent}[/tex]
Tan11⁰=x/126
x=126tan11⁰
Also, in the second angle of depression,
Using the tangent ratio as stated above,
y=126tan78⁰
The distance between A and B is given thus:
AB =126tan78⁰-126tan11⁰
AB =126*4.7046-126*0.1944
AB =592.78-24.4944
AB =568.28553
AB =568ft
In conclusion, the distance from point A to point B is 568ft
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While catching tadpoles, you and your friend decide to have a competition. After m minutes, you have (5m + 7) tadpoles and your friend has (3m+ 18) tadpoles. Select any expressions that could represent the total number of tadpoles that you and your friend can catch.
Answer:
TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)
Step-by-step explanation:
They ask you "elect any expressions that could represent the total number of tadpoles that you and your friend can catch."
then you need the SUM of both.
TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)
Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Keith drove home, there was no traffic and the trip only took 8 hours. If his average rate was 20 miles per hour faster on the trip home, how far away does Keith live from the mountains?
Do not do any rounding.
Keith live 480 miles far way from the mountains.
How far away does Keith live from the mountains?The distance between two locations is represented by the length of the line linking them. If the two points are on the same horizontal or vertical line, subtracting the various coordinates will show how far apart they are.
Consider the provided information.
Keith drove to the mountains last weekend. The trip took 12 hours because of the high traffic on the way there.
Let the distance is D and average rate or speed is x miles.
Distance = speed × time
Substitute the respective values.
D = x * 12
D= 12x
When Keith drove home, there was no traffic and the trip only took
hours. The average rate was 8 miles per hour faster on the trip home,
The average rate or speed during return is x+20 miles.
Substitute the respective values in the above formula.
D = (x+20) ×8
D= 8x+160
Equate both the equations.
8x+160 = 12x
4x= 160
x=160/4
=40
Substitute the value of x in D= 12x
D=12(40)
D= 480
Hence, Keith live 480 miles far way from the mountains.
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Jazzmen's heart rate is 47 beats per minute. If this is her average heart rate, how
many times will her heartbeat in 50 years?
Answer:1235160000 beats
Step-by-step explanation:
There are 525600 minutes in a year
47*525600= 24703200
24703200*50= 1235160000
doreen schmidt is a chemist. she needs to prepare 36 ounces of a 11%
The answer to Question based on Conversion of Units is 1008gm
What is Conversion OF Units?
It is a method to convert units from one version from another.
Solution:
Here in this Question we must know the conversion that 1 ounce is nearly equal to 28gms
Hence if Doreen Schmidt needs to prepare 36 ounces of 11% solution he needs to have exact measurement of chemicals
Hence we can say must have that 36 ounces of chemicals to make that
Hence by unit conversion 36 multiplied by 28 which comes out to be 1008gm of chemical he needs to have
to make 11% solution
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A ship is tied to a dock with a rope
length 10 m. At low tide, the rope is
stretched tight, forming an angle of 45⁰ with the horizontal. At high tide, the stretched rope makes an angle of 30° with the horizontal. How much closer to the dock, horizontally, is the ship at low tide than at high tide?
1 meter and 59 centimeters.
Describe the hypotenuse.The longest side in a right triangle is called the hypotenuse. In other terms, the hypotenuse is the side that faces the right angle.
theorem of Pythagoras
[tex]a^{2} +b^{2} = c^{2}[/tex]
A is a right triangle's side.
B is the right triangle's side.
c = hypotenuse
Think of a right triangle where the height and distance are the legs and the hypotenuse is the rope.
We are aware that:
cos(45°) =x/10
cos(30°) =y/10,
where x represents the distance between the ship and the dock at low tides and y represents the distance during high tides.
We are searching for the y-x distance difference (since it will be farther away during high tides).
Using the previous equations:
x=cos(45°) and y=cos(30°)
Hence:
y - x = 10(cos(30°) - cos(45°))
Hence, the exact value of the distance is 10(cos30° - cos45°)
Using a calculator, this is approximately 1.59 meters.
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Dontrell bought 5 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
Step-by-step explanation:
y = 3.52x
This equation states that the total amount paid, y, is equal to 3.52 multiplied by the number of pounds of potatoes, x.
Writing Equations of lines
Write the equation of each line with the given information
Slope = 7, y-intercept = -3
In a raffle, one ticket will win a $560 prize, one ticket will win a $490 prize, one ticket will win a $270 prize, one ticket will win a $180 prize, and the remaining tickets will win nothing. There are 500 in the raffle. If you have a ticket, what is the expected payoff?
The expected payoff from the raffle is given as follows:
$3.
How to obtain the expected payoff?The payoff is modeled by a discrete distribution, hence the expected payoff is the expected value of the said discrete distribution.
There are 500 tickets in the raffle, hence the probabilities are given as follows:
P(X = 560) = 1/500.P(X = 490) = 1/500.P(X = 270) = 1/500.P(X = 180) = 1/500.P(X = 0) = 496/500.The expected value of a discrete distribution is calculated as the sum of all outcomes multiplied by it's respective probability, hence:
E(X) = 560 x 1/500 + 490 x 1/500 + 270 x 1/500 + 180 x 1/500 + 0 x 496/500 = $3.
(all the outcomes and their probabilities are taken from the distribution built in this problem).
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You have a whole pizza in the refrigerator. On your first trip you eat half of it. On each other trip you eat another half of what is left. After five trips what fractional part of the pizza have you ate?
Answer: You would have eaten 31/32 of the pizza.
Step-by-step explanation:
1/2 + 1/2^2+1/2^3+1/2^4+1/2^5 =
1/2(1-(1/2)^5)/1-1/2 =
1-1/32=
31/32
good question.
What are the measures of 21 and Z2? Explain.
I need help please help me
The measure of [tex]\angle 1[/tex] is [tex]60^{\circ}[/tex] because it is related to one of the angles of the triangle by the alternate interior angles theorem.
The measure of [tex]\angle 2[/tex] is [tex]120^{\circ}[/tex] because it is adjacent to one of the angles in the triangle.
A number is between 58 and 68. It has prime factors of 2, 3, and 5. What is the number?
Answer:
60
Step-by-step explanation:
For the following word problems, first write a system of equations then solve for full marks.
3. The perimeter of a rectangle is 64 cm. Twice the width is 4 cm more than the length.
Find the dimensions of the rectangle.
The length of rectangle is 20cm and width is 12cm.
Let the length is x cm and width is y cm.
then perimeter 2(x+y) =64 cm
=> x+y = 64/2 = 32
=> x + y = 32 .............(1)
and according to question twice the width is 4cm more than length so,
2y = x + 4
=> 2y -x = 4 .............(2)
now we add these two equation to find the value of x and y.
3y = 36
=> y = 12
now put the value of y on any equation to find value of x ,
x +12 = 32
=> x = 32 -12 = 20
so, the length of rectangle is 20cm and width is 12cm.
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Poison Ivy received a total piecework paycheck of $465.47. She receives 89 cents per unit produced. How many units did she produce?
There are 523 units did she produced.
What is paycheck?
Traditionally, an employer would issue a paper document known as a paycheck—also spelled pay cheque, pay check, or pay cheque—to pay an employee for services rendered.
Businesses pay their employees for their work through paychecks. Bi-weekly and semi-monthly delivery schedules are the most typical ones, though this can change depending on the employer's preferences and any applicable state laws and regulations.
Given that:
Piecework pay = $465.47
Price per unit = 89 cents = $0.89
Number of units=$x
Let,
Total piecework pay = Price per unit x number of items sold
$465.47 = 0.89 x x
x = 523
Hence, there are 523 units did she produced.
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Box measures 32 inches long, 6 inches wide and 8 inches high. What is the diagonal length
of the box?
Answer:
[tex]2\sqrt{281}[/tex] inches
Step-by-step explanation:
Using the 3D Pythagorean theorem, the diagonal has length [tex]\sqrt{32^2+6^2+8^2}=2\sqrt{281}[/tex] inches.
The coordinate plane shows the location of teammates during a game of ultimate Frisbee. Each interval on the coordinate plane represents 1 foot
Jonathan
4
Malik
3
Marianne
Ellena
If Marianne throws the Frisbee directly to Malik, how far, in feet (ft), will the Frisbee travel? Round your answer to the nearest tenth.
What is the measure of angle x? (5 points)
A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 45 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 45 degree angle, is labeled as x.
Question 2 options:
1)
45 degrees
2)
90 degrees
3)
135 degrees
4)
140 degrees
Answer:
idek
Step-by-step explanation:
Convert 3 pints into liters. Round your answer to the nearest hundredth
Answer:
1.42 liters is the correct answer
Two basketball players are trying to have the most
points per game for the season. The current leader has
2112 points in 77 games and the second place player
has 2020 in 74 games. Assuming the current leader
plays no more games, how many points per game will
the second place player have to score in each of the
next three games to take the lead in this category?
The second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.
What is PPG Statistics?
The average amount of points scored by a player per game played in a sport, over the length of a run of games, a season, or a career, is known as points per game, or PPG. It is computed by dividing the total points by the number of games. Basketball and ice hockey are two sports where the jargon is frequently utilized.The points per game is an important statistic and it can range between 0 to 40+.First, calculate the PPG earned by the current leader of the season.
The total points earned by the current leader amount to 2112 and he had participated in a total of 77 games.
The following formula can be used to determine the PPG earned by the current leader per game,
PPG = Total Points / Total Games
[tex]\implies PPG=\frac{2112}{77}\\ \implies PPG = 27.42[/tex] -----(1)
Now, calculate the PPG of the player who is ranked in the second place for the season.
The total number of points earned by the second place player is 2020 and he played a total of 74 games.
The second place player earned the following points per game,
PPG = Total Points / Total Games
[tex]\implies PPG=\frac{2020}{74}\\ \implies PPG = 27.29[/tex] ---(2)
The difference in score with the leading team can be found by subtracting (2) from (1),
[tex]\implies 27.42-27.29=0.13[/tex]
So, to be the leading player, the second place player must obtain a lead of 0.14 points per game in the next three games if the current player plays no more games.
In such a situation, the total PPG of the player should be 27.43 and the number of games to be played is 3.
So, the number of points required to take lead can be calculated as,
PPG = Total Points / Total Games
[tex]\implies 27.43=P/3[/tex]
So, the Total Points required, [tex]P=27.43 \times 3 =82.29[/tex]
And, the PPG required by the second place player to score in each of the next three games is calculated as,
[tex]\frac{0.14}{3}=0.0467[/tex]
Therefore, the second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.
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Your friend just returned to the United States from their trip to Nepal and wants to exchange their 10,323 Nepalese rupees for U.S. dollars. How many dollars will they receive if the current exchange rate is 1 U.S. dollar to 124 Nepalese rupees? $103.23 $90.83 $83.25 $14.89
Answer: C) $83.25
Step-by-step explanation: First you multiply 124 by whatever amount equivocates to 10,323 then multiply 1 by that same amount and you get the answer, 124 x 83.25 = 10,323, and 1 x 83.25 = 83.25
If four times my age is
increased by 20, the result is 80.
How old am I?
Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of work hours. How much will they have earned?
The number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Eliza has = 14 + 7x
x is the number of weeks
For Sahana:
y - 8.40 = (16.80-8.40)/(2-1)[x - 1]
y = 8.4x - 8.4 + 8.4
y = 8.4x
14 + 7x = 8.4x
x = 10 hours
Thus, the number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.
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The perimeter of a square is 56. Express the length of a diagonal of the square in simplest radical form.?
The length of the diagonal of a square with a perimeter of 56 is 14√2.
What is a diagonal?A diagonal is the longest line that divides a plane shape into two equal parts.
To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.
Formula:
P = 4a............ Equation 1Where:
P = Perimeter of the squarea = Length of the squareFrom the question,
Given:
P = 56Substitute the value into equation 1 and solve for a
56 = 4aa = 56/4a = 14Finally to find the length of the diagonal of the square, we use the formula below
d = √(2a²)................... Equation 2Where:
d = Lenght of the diagonal of the squarea = Length of the square = 14Substitute into equation 2
d = √(2×14²)d = 14√2Hence, the length of the diagonal is 14√2.
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Answer:
qfewwqeffwqfefewqwqreg
Step-by-step explanation:
If D is the Midpoint of AC and E is the midpoint of BC find the value of X
D is the midpoint of AC, and E is the midpoint of BC, hence the value of x for the given problem will be 9 units.
What is similar triangle?If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.
Here,
Since these are similar triangle,
BE=EC
BC=BE+EC
BC=2BE
6/(3x-15)=1/2
12=3x-15
3x=27
x=9
The value of x for the given problem where D is the Midpoint of AC and E is the midpoint of BC will be 9 units.
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In circle R, RS= 15 and the length of ST =6pi Find angleSRT
Step-by-step explanation:
you can find it by using the arc formula?
You are considering taking out a loan of $8,000.00 that will be paid back over 8 years with quarterly payments of $320.19. If the interest rate is 6.3% compounded quarterly, what would the remaining balance be immediately after the fourteenth payment?
The remaining balance would be $___________. (Round to 2 decimal places.)
Answer:
78.8
Step-by-step explanation:
hi can help with question
The linear regression equation in this problem is given as follows:
y = 4.774x + 39.474.
Then the estimates are given as follows:
a) x = 3 hours: 53.8.
b) x = 4.5 hours: 61.
c) x = 13 hours: 101.5.
d) x = 1.5 hours: 46.6
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the table into a linear regression calculator.
From the table in this problem, the points are given as follows:
(0,39), (1,45), (2,52), (4, 49), (5, 61), (5,72).
Inserting these points into a calculator, the equation is given as follows:
y = 4.774x + 39.474.
Then the estimates are obtained with the numeric values, as follows:
a) x = 3 hours: y = 4.774(3) + 39.474 = 53.8.
b) x = 4.5 hours: y = 4.774(4.5) + 39.474 = 61.
c) x = 13 hours: y = 4.774(13) + 39.474 = 101.5.
d) x = 1.5 hours: y = 4.774(1.5) + 39.474 = 46.6.
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1. A mass of 30kg is suspended from a massless rope on one side of a massless, frictionless pulley. A mass of 10kg is connected to the rope on the other side of the pulley and is sitting on a ramp with an angle of inclination of 30. The system is shown in the following diagram.
a. The coefficient of friction is } 0.10. What is the acceleration of the system?
b. What is the tension in the rope?
a. Acceleration of the system (a) = 6.125 m/s^2
b. The tension in the rope (T) = 110.25
What is the definition of acceleration ?
Acceleration defines that the rate at which velocity changes with time, in terms of both speed and direction.
For 30 kg mass
m . g - T = m . a
30 x 9.8 - T = 30. a ⇒ (1)
For 10 kg mass
T - m base 2 g Sin θ = m base 2 a
T - 10 x 9.8 Sin 30° = 10 x a ⇒ (2)
a. Adding equation (1) and (2)
294 - 49 = 30 a + 10 a
245 = 40 a
a = 245/40
a = 6.125 m/s^2
Therefore, acceleration = 6.125 m/s^2
b. Sub a value in equation (1) we get,
T = 110.25
Therefore , tension in the role = 110.25
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help me solve plsssssss
Answer:
2. C
3. BCEF
4. C
Step-by-step explanation:
2. In a function, the x value cannot have two y values (for example: if the points are (1,2) and (1,3) then that is not a function).
In this question, none of the x values repeat with multiple y values, so it is a function. the answer is C.
It is not D, because not all straight lines are functions. If the straight line is vertical, then there is only one x value and it has infinitely many values for y. So, not all straight lines are necessarily functions.
3. Range is the y values. The points are (3,4), (-2,3), (7,1), (2, 1/2)
Here, the y values are 4, 3, 1, and 1/2
Choices B,C,E,F are the answers.
4. If the domain is x[tex]\geq[/tex]0, then 0 is the lowest we can plug into x.
y=2(0)+6
y=6
So, the answer is C. y[tex]\geq[/tex]6
You were on the right track :)
An employee earns $175 for 15 hours work. Do these quantities (salary and time) vary indirectly or directly?
Based on the information given the constant of variation is 11.67.
What is the rate of change?
The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time
by using this formula
Constant of variation = Amount earned/Time
Where:
Amount earned=$175
Time=15 hours
Let's plug in the formula
Constant of variation=$175/15
Constant of variation=11.66
Constant of variation=11.67 (Approximately)
Hence, the constant of variation is 11.67.
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7 people equally share 1/2 a pan of macaroni and cheese how much of the whole pan each person get
Answer:
1/14
Step-by-step explanation:
If 7 people equally share 1/2 a pan of macaroni and cheese, each person will get 1/2 / 7 = 1/14 of the pan.
To find the fraction of the pan that each person gets in terms of the whole pan, we can multiply the fraction 1/14 by the denominator of the fraction representing the whole pan. If the whole pan is represented by 1 pan, the fraction representing each person's share would be 1/14 * 1 = 1/14 of a pan.
So, each person would get 1/14 of a pan of macaroni and cheese.
Answer: 1/14
Step-by-step explanation:
1/2 / 7 = 1/14≅ 0.07142857