The shortest distance is 5.83 miles as we calculate this by distance formula.
A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:
PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
The school is located 5 miles west of your home the co ordinate is (-5,0)
The playground is 3 miles south of the school so co - ordinate is (0,-3)
shortest distance = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
√([tex]5^{2} +3^{2}[/tex]) = √34
=5.830 miles
And this Question also can be do by right angle triangle method
know more about co-ordinate system click here ;
https://brainly.com/question/8503793
#SPJ4
During a 36 - year period, lightning killed 2,457 people in the United States. Assuming that rate holds true today and is constant throughout the year. Find the probability that tomorrow: (a) No one in the United States will be struck and killed by lightning.
The probability that no one in the United States will be struck and killed by lightning tomorrow is approximately 0.835, or 83.5%.
To find the probability that no one in the United States will be struck and killed by lightning tomorrow, we can use the Poisson distribution, which models the number of rare events occurring in a fixed period of time, given the average rate of occurrence.
The Poisson distribution has the following probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!
where:
X is the random variable representing the number of events (in this case, the number of people struck and killed by lightning)
λ is the average rate of events per unit of time (in this case, the average number of people struck and killed by lightning per day)
We can use the data given in the problem to estimate the value of λ:
λ = (2457 deaths) / (36 years * 365 days/year) ≈ 0.18 deaths/day
Now we can use the Poisson distribution to find the probability that no one in the United States will be struck and killed by lightning tomorrow:
P(X = 0) = (e^(-0.18) * 0.18^0) / 0! ≈ 0.835
This means that there is a high likelihood that no one will be killed by lightning tomorrow, given the historical average rate of lightning deaths.
To learn more about probability click on,
https://brainly.com/question/30666048
#SPJ4
Solve for X and Y using substitution
y=5x-7
-3x-2y=-12
Answer:
So the solution to the system of equations is (x,y) = (3,-2).
Step-by-step explanation:
To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.
Starting with the second equation:
4x - 3(-2) = 18
Expanding the -3(-2) using the distributive property:
4x + 6 = 18
Subtracting 6 from both sides:
4x = 12
Dividing both sides by 4:
x = 3
Now that we have x = 3, we can substitute that back into the first equation to find y:
y = -2
So the solution to the system of equations is (x,y) = (3,-2).
Graph the line that represents this equation:
3x - 4y = 8
Drawing Tools
Select
Point
Line
X
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10-
4
8
2
S
A
2
2
Delete
++
Answer:
Step-by-step explanation:
place the following scores in a frequency distribution table. based on the frequencies, what is the shape of the distribution? 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15
The frequency table is:-
Data Frequency
10 1
11 2
12 2
13 4
14 6
15 5
What is a frequency table?The frequency table determines the frequency of the data. In other words, it tells us how many times the same data is repeated.
The given data set is, 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15
The frequency table can be written as:-
Data Frequency
10 1
11 2
12 2
13 4
14 6
15 5
The distribution's shape for the next data set you provided is left- or negatively skewed. This is due to the fact that as a number's value increases, so does its frequency.
To know more about the frequency table follow
https://brainly.com/question/16148316
#SPJ1
A pet toy company performed an experiment to see how
many toys dogs might play with. Each of the 60 dogs
involved was put in a room with its owner and 4 different
toys.
The researchers recorded how many toys each of the 60
dogs used.
Fill in the blanks to complete the probability
distribution.
Do not round your answers.
Toys used
Frequency
Probability .05
0
3
1 2
2
0.25
3
3 4
21 12
9
0.35 0.2 0.15
The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To fill in the blanks, we need to use the given information to complete the probability distribution table.
We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
To learn more about probability, Visit
https://brainly.com/question/13604758
#SPJ1
Shape ABCD is a rectangle.
C is the point with coordinates (0,-8)
The equation of the straight line through A and B is 2y + x = 4.
Find the equations of the lines
DC, AD and BC.
Answer:
c
Step-by-step explanation:
trust me
The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For a month in which the executive's cellular phone bill was $95.40, how many minutes did the executive use the phone?
Answer: 151 minutes
Step-by-step explanation:
95.40 - 35 =
60.40
60.40/.40 = 151
Draw one candy
from the bag.
Pink=10
Purple= 6
Blue= 4
If you replace the candy each time,
predict how many times a purple
candy will be chosen out of 80 draws.
[?] times
Answer:
24 times out of 80 draws
Step-by-step explanation:
The probability of choosing a purple candy is 6 out of 20 candies, or 6/20, which simplifies to 3/10 or 0.3.
If you make 80 draws and replace the candy each time, the number of purple candies selected can be estimated using the expected value formula:
Expected value = number of trials * probability of success
In this case, the expected value is 80 * 0.3 = 24.
So, it can be estimated that a purple candy will be chosen 24 times out of 80 draws.
The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 14 mph and the Mystic travels at 21 mph. How far apart will they be in 3 hours?
They will be 74 km apart after 2 hours.
What is the relative speed of two moving objects?
For two objects, the relative speed between them equals the change in distance between them divided by the change in time. If two bodies are going in opposite directions, their relative speed is equal to the sum of their individual speeds. If they are moving in the same direction, their relative speed is equal to the difference in their individual speeds.
Given here, the Serenity travels at 17 mph and the Mystic travels at 20 mph in the opposite direction .
therefore, the relative speed is sum of their speeds = 17 + 20 = 37 mph
After 2 hours the distance between them would be = 37 × 2 = 74 mph
Hence, they will be 74 km apart after 2 hours.
Learn more about relative speed here:
brainly.com/question/14362959
#SPJ1
what is the probability of drawing a black card in a standard deck of 52 cards? (enter your probability as a fraction.)
The probability of drawing a black card in a standard deck of 52 cards is 1/2.
Probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1. There are total 52 cards out of which 26 are black cards and 26 are red cards.
There are 26 black cards (13 spades and 13 clubs) in a standard deck of 52 cards.
Therefore, the probability of drawing a black card from a standard deck of 52 cards is 26/52.
Probability = 26/52 = 1/2
So, the probability of drawing a black card is 1/2.
Learn more about probability here: brainly.com/question/13604758
#SPJ4
There are 423 athletes at the vollyball tournament another 9 teams were added with 6 athletes on each team
There are a total of 477 athletes after the 9 new teams with 6 athletes on each team were added.
If there were 423 athletes at the volleyball tournament and 9 teams with 6 athletes each were added, we can calculate the total number of athletes as follows:
Number of athletes at the tournament: 423
Number of athletes in each new team: 6
Number of new teams: 9
The total number of new athletes is the product of the number of new teams and the number of athletes in each new team:
Total number of new athletes = 9 x 6 = 54
To find the total number of athletes after the new teams were added, we add the number of athletes at the tournament to the total number of new athletes:
Total number of athletes = 423 + 54 = 477
To learn more about team click on,
https://brainly.com/question/29315948
#SPJ4
Complete question is:
There are 423 athletes at the volleyball tournament another 9 teams were added with 6 athletes on each team. How many total atheletes are present?
The lines intersect at
1 point.
different. The
parallel.
Do You Understand?
1. Essential Question How are slopes and
y-intercepts related to the number of solutions
of a system of linear equations?
The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.
What is linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
The number of solutions for a system of linear equations depends on the relationship between the slopes and y-intercepts of the lines represented by the equations. If the lines are intersecting, then there is exactly one solution where the lines cross. If the lines are parallel, then there are no solutions, as the lines will never intersect.
If the lines are coincident, then there are infinitely many solutions, as the lines represent the same line.
Therefore, The slopes and y-intercepts can be used to determine the type of relationship between the lines, and therefore the number of solutions.
To learn more about Linear equation from given link.
https://brainly.com/question/29739212
#SPJ1
What is the answer? How do I solve this?
You solve it using your brain.
Davis will plant seeds in row that are 3 feet apart. In each row he will plant seeds about 4 to 6 inches apart. Estimate the number of corn seeds Davis can plant in section 1
Davis can plant a total of about 1555 corn seeds in the section one.
Davis wants to plant in a row that are 3 ft apart each row, plant are about 4 to 6 inches apart from each other.
We have to find out that how many plant can be planted. Section 1 has 12 columns 18 rows.
Each block formed by a row and column will have an area of 9 square feet. Each row will have a total of 86.4 seeds of corn seeds in it.
The total number of columns in the section 1 are 54. So, multiplying the number by 54 will get the total number of counts,
Total corn seeds = 86.4 x 54.3
= 1555 corns seeds.
So, a total of 1555 corn seeds can be planted.
To know more about Area calculation, visit,
https://brainly.com/question/2607596
#SPJ4
Ashley created 3 music playlists using a total of 48 rock and pop songs. Each playlist has 9 rock songs. Each playlist also has the same number of pop songs. Which equation could be used to determine the number of pop songs, x
, Ashley has in each playlist?
Responses
1. x(3+9)=48
2. 3(x+9)=48
3. 3x+9=48
4. 9x+3=48
Answer:
2. 3(x + 9) = 48
Step-by-step explanation:
We are given
There are a total of 3 playlistsThere are a total of 48 rock and pop songsEach playlist has 9 rock songsEach playlist has x pop songsIf each playlist has 9 rock songs and x pop songs, then each playlist has 9 + x songs.
If there are three playlists, there are three playlists which each have x + 9 songs. In other words, 3(x+9). This represents the total number of songs, which is 48. Therefore the answer is 3(x+9)=48.
Hope this helps!
Solve for n !
[tex] \large{ \gray{ \frak{3x+5= 4(n - 5) \frac{6}{3} }}}[/tex]
Thank You!
Answer:
n = (3/8)x+(45/8)
Step-by-step explanation:
3x+5 = 4(n-5)*(6/3)
Is this written correctly?
3x+5 = 4(n-5)*(6/3)
3x+5 = 8(n-5) [Simplify: {4*(6/3) = 8)]
3x+5 = 8n-40 [Expand the parentheses]
8n-40 = 3x+5 [Rearrange]
8n = 3x+5 + 40 [Rearrange]
8n = 3x+45 [Simplify]
n = (3x+45)/8 [Divide both sides by 8]
n = (3/8)x+(45/8) [Rearrange]
The figure shows the size of a pool. 6 ft 4 ft 16 ft What is the volume of the pool? A. 60 ft³ B. 224 ft3³ 12 ft O C. 1728 ft³ D. 3136 ft³ 8 ft 14 ft h
The volume of the pool is 768 cubic feet.
What is the Volume?
In mathematics, volume refers to the amount of space occupied by a three-dimensional object. It is a measure of the total amount of space enclosed within the boundaries of an object. The volume of an object is usually measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³).
To find the volume of the pool, we need to multiply its length, width, and depth. Looking at the figure, we see that the length of the pool is 16 ft, the width is 6 ft, and the depth is 8 ft.
So, the volume of the pool is:
V = length x width x depth = 16 ft x 6 ft x 8 ft = 768 cubic feet
Hence, the volume of the pool is 768 cubic feet.
To learn more about Volume, Visit
https://brainly.com/question/463363
#SPJ1
The length of a shadow of a building is 98 ft when the sun is 66° above the horizon. Find the height of the building. Round your answer to the nearest tenth.
000
000
66°
98
If the length of a shadow of a building is 98 ft when the sun is 66° above the horizon then the height of the building is, 267.7 ft.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
We can use the tangent function to solve for the height of the building.
tan(66°) = height of building / 98 ft
Solving for the height of the building,
we get:
height of building = 98 ft x tan(66°)
Using a calculator, the value of tan(66°) is approximately 2.73.
So,
height of building = 98 ft x 2.73
height of building = 267.74 ft
Rounding to the nearest tenth, the height of the building is approximately 267.7 ft.
To know more about angle check:
https://brainly.com/question/28451077
#SPJ1
explain the differences between the 3rd angle projection and the 1st angle projection in terms of the orthographic projection.
In third-angle projection, the view of a component is drawn next to where the view was taken. In first-angle projection, the view is drawn on the other end of the component, at the opposite end from where the view was taken.
First angle Protuberance is a system of creating a 2D delineation of a 3D object. It's substantially used in Europe and Asia and has not been officially used in Australia for numerous times. In Australia, third angle protuberance is the favored system of orthographic protuberance. Note the symbol for first angle orthographic protuberance
Third Angle Projection the Object is placed in the Third Quadrant. This means that the Vertical Aeroplane is in front of the object and the Vertical Aeroplane is above the object. These changes in the position of the views are the only difference between protuberance styles.
To know more about First angle projection, visit: brainly.com/question/13255256
#SPJ4
What if the well was 40 feet deep, the frog climbs 6 feet per hour, and it slips back only 1 foot while resting for an hour?
If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.
However, the frog slips back 1 foot while resting for an hour, so the frog would only have covered 5 feet of the well after each hour of climbing. The frog would need to climb for a total of
40/5 = 8 hours
to reach the top of the well. Additionally, the frog would need to take 8 hours of rest to make up for the slipping back.
So the total time it would take the frog to get out of the well would be 8 hours + 8 hours = 16 hours.
If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.
Learn more about feet :
https://brainly.com/question/20111809
#SPJ4
The Jacob family plans to attend a concert. An adult ticket (a) is $7.50 each and a child's ticket (c) is $5.00 each. Mr. Jacob purchased a total of 11 tickets for a total of $65. How many of each kind of ticket was purchased?
Explain how to do please
Answer: Therefore, we purchased 4 adult tickets and 7 child's tickets.
Step-by-step explanation:
Through the information provided, we set up a system equation:
a + c = 11
7.50a + 5.00c = 65
By the first equation, we convert it into a form, then we get a = 11 - c. Then we plug in the a = 11 - c to the second equation:
7.50(11 - c) + 5.00c = 65
82.5 - 7.50c + 5.00c = 65
82.5 - 2.50c = 65
- 2.50c = 65 - 82.5
- 2.50c = - 17.5
c = - 17.5/- 2.50
c = 7
And we plug c = 7 back into the first equation, which is a + c = 11.
a + c = 11
a + 7 = 11
a = 11 - 7
a = 4
Therefore, we purchased 4 adult tickets and 7 child's ticket.
Find the roots of the equation
x² − 2(a² + b²)x + (a²-b²)² = 0
Answer:
We can solve the above mathematical problem with the following approach.
We know that (a²-b²) = (a + b) (a - b).
So the given equation can be written as:
Jerome hiked three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles
per hour?
2 mile per hour
I
b. 1 miles per hour
C.
mile per hour
d. 1 miles per hour
Answer as a mixed number = 1 1/8 mph
Answer as a decimal = 1.125 mph
Work Shown:
(3/4) of a mile : (2/3) of an hour
12*(3/4) of a mile : 12*(2/3) of an hour
9 miles : 8 hours
9/8 miles : 8/8 hours
1.125 miles : 1 hour
His speed is 1.125 miles per hour. This converts to the mixed number 1 1/8
helppppppppppppppppppppppppppp
Answer: x = 6 (look at the image for the solution)
Step-by-step explanation:
Answer: the answer is 35
Step-by-step explanation:
find the pythageoran theorem of the thing and then solve
help asap pls. question in pic
the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
One side of rectangle is 200m
When the measure of the other side is 50 m
the area will be 50*200 = 1000m².
The expression of area A(x) = 200x,
hence the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
Learn more about rectangular by following the link below.
brainly.com/question/25292087
#SPJ1
There are 3 female teachers and 31 male teachers at Eddie's high school. What is the ratio of the number of female teachers to the number of male teachers?
Answer:
3:31
Step-by-step explanation:
please help me with my homework!!
10. The value of a book is $58 and decreases at a rate of 10% per year; 8 years.
Answer:
$24.96
Step-by-step explanation:
The question was incomplete. If you are asking how much is the book worth after 8 years, here's how to do it
Original cost = $58
Since the rate of decrease = 10%, the cost of the book after 1 year is 90% of the original price
90% = 90/100 = 0.9
Therefore after 1 year, the book cost is 58(0.9)
After another year(effectively 2 years) the above cost will drop by another 10% to 90% of the first year value: 58(0.9)(0.9) = 58(0.9)²
So the value of the book after a period of n years is modeled by the function
V = 58 (0.9)ⁿ
After 8 years the value is
58 (0.9)⁸ = 58 x 0.43046721
V = $24.96 rounded to the nearest cent
HELP PLEASE
The blood platelet count of a group of women have bell-shaped distribution with a mean of 245.5 and a standard deviation of 68.2 (all units are 1000 cells/ L) Using the empirical rule, fill in the blanks below (Round to the nearest hundredth):
a. Approximately 95% of healthy women in this group
b. Approximately 99.7% of healthy women in this have blood platelet counts between
group have blood platelet counts between
and(1000 cells/ ML). and (1000 cells/ ML).
Answer:
a) Approximately 95% of healthy women in this group have blood platelet counts between 109.1 and 381.9 (1000 cells/μL).
b) Approximately 99.7% of healthy women in this group have blood platelet counts between 40.9 and 450.1 (1000 cells/μL).
Step-by-step explanation:
Empirical RuleThe Empirical Rule (also known is the "68-95-99.7" rule) states that nearly all of the data within a normal distribution will fall within three standard deviations of the mean.
Approximately 68% of the data will fall within one standard deviation of the mean.Approximately 95% of the data will fall within two standard deviations of the mean.Approximately 99.7% of the data will fall within three standard deviations of the mean.Given the blood platelet count of a group of women has a bell-shaped distribution with:
Mean μ = 245.5 (1000 cells/μL)Standard deviation σ = 68.2 (1000 cells/μL)To determine the lower and upper bounds for blood platelet counts for 95% of the women, subtract and add two standard deviations to the mean:
[tex]\begin{aligned}\text{Lower bound}&= \mu - 2\sigma \\&= 245.5 - 2(68.2)\\&=245.5-136.4\\&=109.1\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 2\sigma \\&= 245.5 + 2(68.2)\\&=245.5+136.4\\&=381.9\end{aligned}[/tex]
Therefore, approximately 95% of healthy women in this group have blood platelet counts between 109.1 and 381.9 (1000 cells/μL).
To determine the lower and upper bounds for blood platelet counts for 99.7% of the women, subtract and add three standard deviations to the mean:
[tex]\begin{aligned}\text{Lower bound}&= \mu - 3\sigma \\&= 245.5 - 3(68.2)\\&=245.5-204.6\\&=40.9\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 3\sigma \\&= 245.5 + 3(68.2)\\&=245.5+204.6\\&=450.1\end{aligned}[/tex]
Therefore, approximately 99.7% of healthy women in this group have blood platelet counts between 40.9 and 450.1 (1000 cells/μL).
2 Gallons of Juice for $4.50. How much per Gallon?
Answer: 2.25 per gallon
Step-by-step explanation:
4.50 divided by 2 = 2.25
surface area of a rectangular prism with sides of 5,4,3,3.7
Surface area of a rectangular prism is 444 square unit.
A rectangular prism is a three-dimensional shape with six faces (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular. As an outcome, there really are three sets of exactly equal faces here. A rectangular prism is also recognized as a cuboid due to its shape.
The sides of a rectangular prism is 5, 4, 3, 3.7.
This can be calculated by multiplying each of the side lengths together and then multiplying that result by two.
Surface area of a rectangular prism = 2 × (5 × 4 × 3 × 3.7)
Surface area of a rectangular prism = 2 × 222
Surface area of a rectangular prism = 444 square unit
To learn more about rectangular prism link is here
brainly.com/question/21308574
#SPJ4
