This is equivalent to 3/2 as an improper fraction and 1 & 1/2 as a mixed number.
==========================================================
Explanation:
x = total distance in miles
The train and monorail take 1/3 and 1/2 of the total distance respectively
Add up those fractions to get
1/3 + 1/2 = 2/6 + 3/6 = 5/6
Remember that you can only add fractions when the denominators are the same.
5/6 of the total distance consists of the train and monorail.
That means the walking portion must be 1 - 5/6 = 6/6 - 5/6 = 1/6 of the total distance.
----------------------------
In short, we found that 1/6 of the total distance consists of walking.
(1/6)x = 1/4 mile
x/6 = 1/4
4x = 6*1
4x = 6
x = 6/4
x = 3/2
x = 1.5 miles is the total distance
---------------------------
Check:
1/6 of x = 1/6 of 3/2 = (1/6)*(3/2) = 3/12 = 1/4 mile walking
1/3 of x = (1/3)*(3/2) = 3/6 = 1/2 mile on the train
1/2 of x = (1/2)*(3/2) = 3/4 of a mile on the monorail
1/4 + 1/2 + 3/4 = 1/4 + 2/4 + 3/4 = 6/4 = 3/2 = 1.5 miles total
This confirms our answer.
Can someone please help me solve for Y and X. Question number 5
Using the triangle sum theorem, x = 7 and y = 18.
What is the Triangle Sum Theorem?The theorem that says that all the interior angles of a triangle will be equal to 180 degrees is referred to as the triangle sum theorem.
In the diagram given, since vertical angles are congruent, therefore:
(11x - 9) + (6x - 2) + 72 = 180 [triangle sum theorem]
Solve for x
11x - 9 + 6x - 2 + 72 = 180
17x + 61 = 180
17x = 180 - 61
17x = 119
x = 7
Also,
(5y - 8) + (11x - 9) + 30 = 180 [triangle sum theorem]
5y - 8 + 11x - 9 + 30 = 180
5y + 13 + 11x = 180
Plug in the value of x
5y + 13 + 11(7) = 180
5y + 13 + 77 = 180
5y + 90 = 180
5y = 180 - 90
5y = 90
y = 90/5
y = 18
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Justin is playing tennis. When serving, he stands 12 feet away from the net, which is 3 feet tall. The ball is served from a height of 7.5 feet. Justin thinks the ball travels about 21.4 feet before it hits the ground 8 feet from the net on the opposite side.
a) How far does the ball travel?
b) What assumptions did you make to solve the distance the ball travels?
c) What mathematical practice did you use to solve this problem?
Regarding the situation described, we have that:
a. The ball travels 21.4 feet.
b. The assumption is that the ball was served at an angle of 90º.
c. The Pythagorean Theorem was used to solve this problem.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, it is found that:
The vertical change in the height of the ball was of 7.5 feet, as it was served from a height of 7.5 and hit the ground.The horizontal change in the height of the ball is of 12 + 8 = 20 feet, as he served 12 feet from the net, and the ball hit the ground 8 feet from the net on the opposite side.Assuming that the ball was served at an angle of 90º, the distance traveled by the ball is the hypotenuse of a right triangle of legs 7.5 feet and 20 feet, hence:
d² = 7.5² + 20².
d = sqrt(20² + 7.5²)
d = 21.4 feet. (which is Justin's estimate).
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График функции y=-0,5(10-x) Дополнительная информация -2≤x≤12
Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following. Find f(x) + h(x)
The value of f(x) + h(x) when f(x) = 2x - 1 and h(x) = x² + 1 is x² + 2x.
Addition of linear functions:
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as:
c(x) = a(x) + b(x) = (a+b)(x) – (i)
The addition of the functions strictly restricts to simple linear addition without any pre-defined constraints.
Given, f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1
Using the available formula in (i), we get
f(x) + h(x) = (f + h)(x) = (2x - 1) + (x² + 1) = x² + 2x = x(x + 2), which is a quadratic equation.
Thus, the required value of f(x) + h(x) is x² + 2x.
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construct a 95% confidence interval for the mean number of defects per screen for all screens produced by this manufacturer. a) what is the lower limit on the interval? give your answer to three decimal places. 2.077 incorrect: your answer is incorrect. b) what is the upper limit on the interval? give your answer to three decimal places. 2.203 incorrect: your answer is incorrect.
The 99% confidence interval for the population proportion p is 0.833< p < 0.863.
Given that,
x = 3059
n = 3604
Point estimate = sample proportion = x / n =3059/3604=0.848
[tex]1 - \hat p[/tex] = [tex]1-0.848 =0.152[/tex]
At 99% confidence level the z is ,
[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01
[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005
[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576 ( Using z table )
Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]
= [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]
=0.015
A 99% confidence interval for population proportion p is ,
[tex]\hat p - E < p < \hat p + E[/tex]
0.848-0.015< p <0.848+ 0.015
0.833< p < 0.863
Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.
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Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due?
The total amount due will be equal to $6.24.
This question can be solved by converting the situation into form of an equation. An equation may be defined as an expression which consists of numbers, variables related to each other by arithmetic expressions. The solution of equation often referred to as the variables for which the equation must be solved, are the values of the unknowable variables that satisfy the equality. The cost of video game is given as $12.98, and tax is equal to $0.78, and he paid an amount of $20. let the change left be x.
Total amount = cost of game + tax + change
$20 = $12.98 + $0.78 + x
$20 = $13.76 + x
=> x = $20 - $13.76
=> x = $6.24 which is the due amount.
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Complete Question:
Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due? Next, you decide to pay with a $20.00 bill. How much change will you receive after paying for your video game?
the population of a town increased by 2.59% per year from the beginning of 2000 to the beginning of 2010. the town's population at the beginning of 2000 was 74,500.
the town's population at the beginning of 2000 was 74,500.Then the population in 2010 will be 96206.97
In 2000, the population of a town = 74500
Every year, it increase by 2.59%
To find the equation P(t) which represents the population of this town t years from 2000 to 2010.
Formula
If a be the original population of a town and it increases by r% every year, after t year the population will be
A = P ( 1+r/100)^t
Now,
Taking, P =74500, r = 2.59% we get,
A = 74500( 1+0.0259)^10
A= 74500(1.0259)^10
A= 96206.97
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0.0 mi/hr to 70.0 mi/hr in 10.0 seconds, what would be its final velocity after 5.0 seconds if its starting velocity was 50.0 mi/hr
Based on the calculations, the final velocity of this car is equal to 85.0 mi/hr.
How to calculate the final velocity of this car?In order to determine the final velocity of this car, we would first calculate its acceleration based on the parameters provided. Mathematically, the acceleration of an object can be calculated by using this formula:
a = (V - U)/t
Where:
a represents the acceleration.V represents the final velocity.U represents the initial velocity.t represents the time measured in seconds.Substituting the given parameters into the formula, we have:
a = (70.0 - 0)/10
a = 70.0/10
Acceleration, a = 7.0 mi/hr².
Now, we can determine the final velocity of this car as follows:
V = U + at
V = 50.0 + (7.0)(5)
V = 50.0 + 35.0
Final velocity, V = 85.0 mi/hr.
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Complete Question:
If a car can go from 0.0 mi/hr to 70.0 mi/hr in 10.0 seconds, what would be its final velocity after 5.0 seconds if its starting velocity was 50.0 mi/hr
Which of the following may produce bias? Select all that apply.
The question uses an inaccurate tool.
Some subgroups may be at a disadvantage due to prior experiences.
A medical research study assigns the healthier patients to the group using the new treatment and the sicker patients to the group using the traditional treatment.
Asking school children how they use apps to organize their day.
All students find the question easy.
The things that can lead to bias include:
The question uses an inaccurate tool.
Some subgroups may be at a disadvantage due to prior experiences.
A medical research study assigns the healthier patients to the group using the new treatment and the sicker patients to the group using the traditional treatment.
What is bias?It should be noted that bias simply means anything that leads to a systematic difference between the true parameter.
It should be noted that in a situation where the question uses an inaccurate tool. This will lead to bias and bring about inaccuracy.
Also, using different tools for the patients can lead to bias.
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Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
By the concept of unitary method she can run 320 yards in 2 minutes at the same rate.
What is meant by unitary method?The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach might be helpful for answering questions on ratio and proportion, algebra, and other subjects. "It is a method where we get the value of a single unit from the value of many units and the value of multiple units from the value of a single unit." bra, geometry, etc. Before determining the value of additional or less items, we must first determine the value of one item by dividing it. There are two categories of unitary approaches.
Direct VariationIndirect Variation720 yards = 4.5 minutes
1 minute = 720/4.5
= 160 yards
2 min = 160(2)
= 320 yards
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Does this table show a proportional relationship? If so, what is the constant of proportionality?
A Yes; 1/5
B Yes; 5
C Yes; 10
D The quantities are not proportional.
We can conclude that (A) yes, the table shows the constant of proportionality of 1/5.
What is the constant of proportionality?The ratio connecting two given values in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.So, the constant of proportionality of the given table:
Formula: k = y/x
So, substitute the values in the formula as follows:
8/40 = 1/510/50 = 1/512/60 = 1/514/70 = 1/5So, yes, the table shows the constant of proportionality of 1/5.
Therefore, we can conclude that (A) yes, the table shows the constant of proportionality of 1/5.
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Which is the equation of the perpendicular bisector of a line segment whose midpoint
is (1, -2) and whose slope is - 1/3
asap
Answer: y = 3x - 5
Step-by-step explanation:
3 is the reciprocal of -1/3 and by plugging in (1,-2) in to y=3x+b you get -2 = 3(1) + b which makes b = -5
What is the discriminant of the quadratic equation -x^2+6x-4=0?
Answer:
[tex]x = - 3 + - \sqrt{13} [/tex]
Step-by-step explanation:
formula is x=-b+-sqrt b^2-4ac/2a
Leah runs M miles everyday during the week except for Wednesday or Sunday. A. write an algebraic expression that represents the total number of miles leah runs each week B. there are 52 weeks in a year. write an algebraic expression that represents the total number of miles leah runs in a year
A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.
B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.
Leah runs M miles everyday during the week except for Wednesday or Sunday.
We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.
We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.
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A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7.50, and tickets for children cost $3.50. How many of each type of ticket were purchased?
There are 23 tickets which are purchased for children and 9 tickets are purchased for adults which cost total $148.
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
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how many groups of 10 milliliters are in 1 liter explains
There are 100 groups of 10 milliliters in 1 liter
How to determine the number of groups?From the question, the given parameters are
Volume 1 = 10 milliliters
Volume 2 = 1 liter
The number of groups of the first group in the second is calculated as
Groups = Volume 2/Volume 1
Substitute the known values in the above equation
So, we have the following equation
Groups = 1 liter/10 milliliters
Evaluate the quotient
Groups = 100
Hence, the number of groups is 100
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Write the equation of the line that passes through the points (7,-6)(7,−6) and (3,8)(3,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line is y = -0.35x – 3.55
Given,
The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).
Since the line passes through the points (7,-6) and (3,8),
• (x₁, y₁) = (7,-6) and
• (x₂, y₂) = (3,8).
So, substituting the values of the variables into the equation, we have
m = (y₂ - y₁)/(x₂ - x₁).
m = (8 - (-6))/(3 - 7).
m = (8 + 6)/ -4
m = 14/-4
m = -3.5
The equation of the line passing through the point (x₁, y₁) in point-slope form is given by
y - y₁ = m(x - x₁) where
• m = gradient =- 0.35 and
• (x₁, y₁) = (7, -6)
So, substituting the values of the variables into the equation, we have
y - y₁ = m(x - x₁)
y - (-6) = -0.35(x - 7)
y + 6 =-0.35 (x - 7)
y = (-0.35x + 2.45 – 6)
y = -0.35x – 3.55
So, the equation of the line is y = -0.35x – 3.55
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(04.01 HC)
A person with type A blood can donate red blood cells to people with type A or type AB
blood. About 31% of the US population has type A blood. You are asked to design a
simulation to determine the probability that at least 4 of 10 people will have type A blood.
Part A: Conduct five trials using the following table of random digits: (5 points)
96299 07196 98642 20639 23185 56282
94168
86280
59225
69929 14125 38872
18192 08710 80777 84395 69563
70406 18564 69273 72532 78340 36699
46376 58596 14365 63685 56555 42974 72944 96463 63530 24152
47352 04266 74017 79319 70170 96572 08523 56025 89077 57678
71622 35940 81807
03272 41230 81739
74797
Part B: Based on your simulation, what is the probability that at LEAST 4 of 10 people will
have type A blood? (5 points)
Answer:31%
Step-by-step explanation:
In the figure below, N lies between M and P.
1
Find the location of N so that MN is of MP.
1/2 of MP
Answer:
8
Step-by-step explanation:
See attached image.
X=-3±2√2
Solve for x
answers are in the photo
goodluck
adana is going on vacation with her family in2 hours they travel 90.5 miles. they travel the same speed, write an equation that represents how far they will travel, d, in h hours
If adana is going on vacation with her family in2 hours they travel 90.5 miles. they travel the same speed, The equation that represents how far they will travel, d, in h hours is: r = d / t, D = r × t.
Speed and distanceGiven data;
Travels time : 2 hours in 90.5 miles
Formula for speed is:
r = d / t
Where,
r = Speed
d = Distance
t = Time
Hence,
Speed = 90.5 / 2
Speed =45.25miles per hour
Since they travels d distance in h hour with the same speed let find the distance
D = r × t
Distance = Speed × Time
Distance = 45.25 × h
Distance = 45.25h miles
Therefore r = d / t, D = r × t is the equation that represent the distance they travel.
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2. Find the volume to the nearest cubic millimeter of the 3-D object in the diagram.
200 mm
300 mm
Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.
What is the volume of the square pyramid?Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.
A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.
The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.
32 = 4² × h/3
32 = 16 × h/3
Multiply both sides by 3
96 = 16 × h
Divide both sides by 16
H = 96/16
H = 6
Therefore, the height is 6 feet.
The complete question is:
Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.
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Tea that sells for $2.00 a pound is mixed with a different tea that sells for
$5.00 a pound to produce 40 pounds of a custom blended tea that will
sell for $4.25 a pound. How many pounds of the less expensive tea
should be used in the mixture?
(1) 10
(2) 15
(3) 25
(4) 30
Pls help hellooooo I’ve asked this 5 times and nobody as helped me pls pls pls lsl
Answer:
3 should be the answer to your question
What's the circumference of a circle with a radius of 5 inches
Answer:
31.4
Step-by-step explanation:
C=2πr=2·π·5≈31.41593in
Which expressions simplify to a rational answer?
Select each correct answer.
Options (1), (3), (4), (7) and (8) are rational numbers.
What is the rational number?Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).
1) 1/4 + 1/2 = 1/4 + 2/4
= 3/4
3/4 is the rational number
2) √3 + 4 is an irrational number
3) √4 + 7
2 + 7 = 9
9 is the rational number
4) 2·√9
= 2·3
= 6
6 is the rational number
5) 7·√6 is an irrational number
6) 4·2√3 = 8√3
8√3 is an irrational number
7) 3·7·(1/3) = 7
7 is the rational number
8) 7·√81
=7·9 = 63
63 is the rational number
Therefore, options (1), (3), (4), (7) and (8) are rational numbers.
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PLEASE HELP!
Set up the system of equations for this scenario. Let "b" represent hours babysitting
and "w" represent hours walking dogs.
Answer:
I not to sure but I think it is b+w=h(hours)
Step-by-step explanation:
Evaluate the expression,in simplest form c= 7/10 y=2/15-3y+c
Let's begin by listing out the information given to us:
[tex]undefined[/tex]A store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.
The 2lb candy cost the owner $8 and the 3lb candy cost the owner $4.5
What is the cost of 2lb candyThe total weight of the candy is
[tex]3 + 2 = 5[/tex]
Let's write equation for this.
[tex]3(1.50) + 2x = 2.5(5)\\4.5 + 2x = 12.5\\12.5 - 4.5 = 2x \\8 = 2x\\x = 4[/tex]
The cost of the 2 pound candy is $4 per unit and the store owner spent $8 in the 2lb candy.
The cost of 3 pound candy was $4.5
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I need some help please. Given the functions, complete the sections. a) Find the intercepts with the axes. b) Indicate the basic function that you will use to graph it. c) Identify the transformations that your graph will undergo, starting from its basic function. d) Draw the sketch showing the transformations, taking into account all the previous sections. Highlight f(x) with a pen or marker. e) Determine its domain and range.[tex]f(x) = - \frac{1}{4} \sqrt{8 - 4x} + 1[/tex]
a)
The x-intercept can be found as:
[tex]\begin{gathered} f(x)=0 \\ so\colon \\ -\frac{1}{4}\sqrt[]{8-4x}+1=0 \\ -\frac{1}{4}\sqrt[]{8-4x}=-1 \\ \sqrt[]{8-4x}=4 \\ 8-4x=16 \\ 4x=8-16 \\ 4x=-8 \\ x=-\frac{8}{4} \\ x=-2 \end{gathered}[/tex]Therefore, the x-intercept is: (-2,0)
The y-intercept can be found evaluating the function for x = 0, so:
[tex]\begin{gathered} f(0)=-\frac{1}{4}\sqrt[]{8-4(0)}+1 \\ f(0)=1-\frac{\sqrt[]{2}}{2} \\ f(0)\approx0.29 \end{gathered}[/tex]b) The parent function for this is given by:
[tex]g(x)=\sqrt[]{x}[/tex]c)
1st: A reflection over y-axis:
[tex]\begin{gathered} y=g(-x) \\ y=\sqrt[]{-x} \end{gathered}[/tex]2nd: A horizontal compression:
[tex]\begin{gathered} y=g(-4x) \\ y=\sqrt[]{-4x} \end{gathered}[/tex]3rd: A horizontal translation 8 units to the left:
[tex]\begin{gathered} y=g(x+8) \\ y=\sqrt[]{-4x+8}=\sqrt[]{8-4x} \end{gathered}[/tex]4th: A reflection over y-axis:
[tex]\begin{gathered} y=-g(x) \\ y=-\sqrt[]{8-4x} \end{gathered}[/tex]5th: A vertical compression:
[tex]\begin{gathered} y=\frac{1}{4}g(x) \\ y=-\frac{1}{4}\sqrt[]{8-4x} \end{gathered}[/tex]6th: A vertical translation 1 unit up:
[tex]\begin{gathered} y=g(x)+1 \\ y=-\frac{1}{4}\sqrt[]{8-4x}+1 \end{gathered}[/tex]d)
Where the blue graph is the parent function:
[tex]g(x)=\sqrt[]{x}[/tex]And the red graph is the function after the transformations:
[tex]f(x)=-\frac{1}{4}\sqrt[]{8-4x}+1[/tex]e)
The domain and the range are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\colon x\le2\mright\rbrace \\ R\colon\mleft\lbrace y\in\R\colon y\le1\mright\rbrace \end{gathered}[/tex]picture down below
PLS HURRY FIRST GETS BRAINLIEST
Step-by-step explanation:
come on, this is really simple.
you need to put the given values of x into the places, where x appears in the functional expression.
which expression to be used ? that depends on the given value.
x = -1
is -1 >= 0 (to use the case for x >= 0) ? no, it is not.
-1 < 0, so we need to use the expression for x < 0.
y = -1 - 2 = -3
x = 0
is 0 >= 0 ? yes, it is.
so, we need to use the expression for x >= 0.
y = 3×0 + 1 = 0 + 1 = 1
x = 1
is 1 >= 0 ? yes, it is.
so, we need to use the expression for x >= 0.
y = 3×1 + 1 = 3 + 1 = 4
x = 2
is 2 >= 0 ? yes, it is.
so, we need to use the expression for x >= 0.
y = 3×2 + 1 = 6 + 1 = 7