Answer:
The required equation is given by,
2 + [tex]\frac {13x}{4}[/tex] = [tex]\frac {1}{2} + \frac {11y}{2}[/tex]
Step-by-step explanation:
Let, each jar of Liam's paint contains x quarts of paint.
Then, Liam's solution contains,
2 + [tex]3\dfrac {1}{4} \times x[/tex] quarts of paint or,
2 + [tex]\frac {13x}{4}[/tex] quarts of paint
and,
let, each jar of Evan's paint contains, y quarts of paint.
Then, Evan's solution contains,
[tex]\frac {1}{2} + 5 \dfrac {1}{2} \times y[/tex] quarts of paint or,
[tex]\frac {1}{2} + \frac {11y}{2}[/tex] quarts of paint
now, according to the question,
the required equation is given by,
2 + [tex]\frac {13x}{4}[/tex] = [tex]\frac {1}{2} + \frac {11y}{2}[/tex]
To find an equation that represents the volume of paint mixed by Liam and Evan, we assume that 1 jar equals 1 quart. By adding the quarts of paint each person uses, we get the equation 2 + 3 1/4 = 1/2 + 5 1/2, meaning they both used the same total volume of paint.
Explanation:To find the equation that represents the situation, we need to equate the total volume of paint used by Liam to the total volume used by Evan. We know that Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint. Evan, on the other hand, uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. Assuming that 1 jar is equivalent to 1 quart, we can simply add the volumes for Liam and Evan:
Liam's total volume = 2 quarts (yellow) + 3 1/4 quarts (blue)
Evan's total volume = 1/2 quart (yellow) + 5 1/2 quarts (red)
Since they end up with the same volume of paint, we have the equation:
2 + 3 1/4 = 1/2 + 5 1/2
To solve for quarts, simplify both sides:
5 1/4 = 6
This equation represents the volumes of paint mixed by Liam and Evan.
math please help! thanks
Answer:
B
Step-by-step explanation:
For a function to be true, there cannot be any same x value for two different y value. Therefore, B, there is the same x value for 4 but with 2 different ys, 4 and 1.
Answer:
B.
Step-by-step explanation:
It is B because it contains a one-to-many relation.
4 maps to 4 and also 4 maps to 1.
Nuri joins a game for a car. The rule is that Nuri picks one key from the box either A, B, or C. A box has two keys but only one can be used. B box has three keys but only one can be used. C box has two keys but none of them can be used.
What is the probability that Nuri can win the car?
Answer:0.277
Step-by-step explanation:
Given there are three boxes i.e. A , B and C
Probability of selecting any box is [tex]P_1=\frac{1}{3}[/tex]
Box A contains 2 keys out of which is 1 is correct so Probability of selecting the right key is [tex]P_2=\frac{1}{2}[/tex]
Box B contains 3 keys out of which is 1 is correct so Probability of selecting the right key is [tex]P_3=\frac{1}{3}[/tex]
Box C contains 2 keys out of which is 1 is correct but we cannot use it so Probability of selecting the right key is [tex]P_4=0[/tex]
Probability of selecting the right key is [tex]P=P_1\times P_2+P_1\times P_2+P_1\times P_3[/tex]
[tex]P=\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times \frac{1}{3}+\frac{1}{3}\times 0[/tex]
[tex]P=\frac{5}{18}[/tex]
[tex]P=0.277[/tex]
The fractional reserve banking system depends upon the _________________ of the public.
Answer:
The fractional reserve banking system depends upon the confidence and trust of the public.
Step-by-step explanation:
The fractional reserve banking means that bank uses the deposits of customers to lend money to the borrowers.
I honestly need help on this...I tried to work it out but I just don’t know where to start...
Answer:
Step-by-step explanation:
1) The sum of angles on a straight line is 180 degrees. Therefore
75 + a + 70 = 180
145 + a = 180
a = 180 - 145 = 35 degrees
2) Sum of the angles in a triangle is 180 degrees. Therefore,
a + b + 95 = 180
35 + b + 95 = 180
130 + b = 180
b = 180 - 130 = 50 degrees
3) c + 95 = 180 degrees (sum of angles on a straight line).
c = 180 - 95 = 85 degrees
4) 70 + c + d = 180 degrees
70 + 85 + d = 180
155 + d = 180
d = 180 - 155 = 25 degrees
5) e = 75 degrees
6) f + e + 75 = 180 degrees
f + 75 + 75 = 180
f + 150 = 180
f = 180 - 150 = 30 degrees
Use the next of a rectangular prism to answer the question
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Work out the area of the square :
6 x 6 = 36
As there are 2, multiply by 2:
36 x 2 = 72
Work out the area of the rectangle:
12 x 6 = 72
As there are 4, multiply by 4:
72 x 4 = 288
Add these values:
288 + 72 = 360
Thus, your answer is E. 360 in^2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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Four friends went out for dinner. The bill, including tax, totaled $64.00. If they want to leave a 15% tip and want to share the bill and tip equally, what should each person pay?
Answer:
$18.40
Step-by-step explanation:
64*1.15=73.60
73.60/4=18.40
a basketball coach is ordering new basketballs for the upcoming season. Let X be the number ball she can buy. Balls cost $65 and she will buy at least one shopping is a flat fee of $25 she has a budget of $545 that she can spend. Which inequality and solution set best model this situation?
A. 545>25x+65
B. 545>65x+25
C. 545(65+25)x
D. The solution set is all positive integers less than or equal to 6
E. Solution set is all positive integers less than or equal to 8
F. The solution set is all positive integers less than or equal to 19
Select each correct answer
Answer:
B & E.
Step-by-step explanation:
$25 is the y value, because she has to pay the fee no matter what.
Integers can be less than or equal to 8 because 65(8) + 25 is equal to 545, which does not exceed the budget.
Hope this helps!
A collection of numerical information, such as the scores on a test, is referred to as simple random sampling.True / False.
Answer:
False. See explanation below.
Step-by-step explanation:
False
A simple random sample "is a subset of a statistical population in which each member of the subset has an equal probability of being chosen"
In other words that means in order to apply a random sampling we need to ensure that we have the same probability of inclusion for every possible element of the population of interest.
And for this case a collection of any numerical information is not referred as random sampling since we don't know if these scores are representative of the population of interest.
And we don't know if this information is obtained using any sampling frame or sampling methodology.
Industries pollute because Select one: a. manufacturing consumes energy and produces waste. b. they want to cut costs and increase profits. c. proper waste disposal is too costly. d. All of these are correct.
Answer:
d
Step-by-step explanation:
Industries Pollute because of following reasons
Lack of Policies and Unplanned industrial growthApplication of obsolete technologiesInefficient Waste disposalAs the cost of disposal is high so industries dump their waste in the nearby water bodies which causes water pollution. As industries want to maximize their profit so they neglect the disposal part to increase it.
Proper disposal includes the treatment of waste material to reduce its hazardous nature.
question : The diagram shows a plan for creating a zoo’s elephant exhibit. The elephant pen will be surrounded on two sides by a walkway with a viewing area in one corner. The sides, shown as dotted lines, will be fenced. How much fencing separates the elephant area from the walkways
answer choices :
(A) 180 feet
(B) 250 feet
(C) 540 feet
(D) 750 feet
Answer:
C
Step-by-step explanation:
We need to find the length of the red dotted line.
It is divided into 3 parts: the top, the middle slant, and the bottom
The top
Goes from y = 50 to y = 120, the length is:
120 - 50 = 70 units
The bottom
Goes from x = 60 to x = 120, the length is:
120 - 60 = 60 units
The middle slant
This is hypotenuse of the right triangle shown.
We will use Pythagorean Theorem to solve for this length, let it be x.
The theorem is:
Leg^2 + Another Leg^2 = x^2
One leg goes from x = 20 to x = 60, the length is 60 - 20 = 40
Another leg goes from y = 20 to y = 50, the lenth is 50 - 20 = 30
So, we have:
[tex]30^2+40^2=x^2\\2500=x^2\\x=\sqrt{2500}\\x=50[/tex]
THe slant length is 50 units
TOtal fencing is: 70 + 60 + 50 = 180 units
1 unit is 3 feet, so
180 units * 3 = 540 feet
C is the correct answer
Marge bought a computer for $699 on the installment plan. The terms of the plan were a down payment of $100, then payments of $58 a month for 12 months. How much was her total cost?
Answer:
$796
Step-by-step explanation:
We have been given that Marge bought a computer for $699 on the installment plan. The terms of the plan were a down payment of $100, then payments of $58 a month for 12 months.
First of all, we will find the amount paid in 12 months by multiplying $58 by 12 as:
[tex]\text{Amount paid in 12 months}=\$58\times 12[/tex]
[tex]\text{Amount paid in 12 months}=\$696[/tex]
Since Marge paid $100 as down payment, so her total cost would be down payment plus amount paid in 12 months.
[tex]\text{Marge's total cost}=\$100+\$696[/tex]
[tex]\text{Marge's total cost}=\$796[/tex]
Therefore, Marge's total cost was $796.
Sometimes a trigonometric equation is written in quadratic form. This means that you can solve the equation the same way you would solve a standard quadratic equation. For example, the equation: sin2 2.5x − 4 sin 2.5x − 5 = 0 can be considered to be like the form x 2 − 4x − 5 = 0. Use this fact to solve this trigonometric equation on the interval 0 ≤ x < 2π.
Answer:
108 degrees
Step-by-step explanation:
To solve this adequately, we simply make a substitution. We can say let sin2.5x = x
Hence we can thus have the quadratic equation form which we can solve.
x ^2 − 4x − 5 = 0.
Solving this yields the following:
x^2 +x - 5x -5 = 0
x( x + 1) -5(x + 1) = 0
(x - 5) (x + 1) = 0
x = 5 or -1
Recall the substitution:
sin2.5x = x
We cannot use the value -5 as the value of the sine function cannot be in this range. We thus ignore it and pick the -1 answer only.
Sin2.5x = -1
2.5x = arcsin(-1) = 270
2.5x = 270
x = 270/2.5 = 108 degrees
Which of the following is the slope of the line?
Help ASAP PLZ
Answer: the second option is the correct answer
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the information on the graph y2 = - 1
y1 = - 2
x2 = 4
x1 = 0
Slope = ( - 2 - - 1)/(4 - 0) = - 1/4
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
To find the slope of a line we need two points through which it is passing.
From the figure, we can see that the line passes through (0,-2) and (4,-1).
Slope of a line passing through two points [tex](x_{1},y_{1})\ and\ (x_{2},y_{2})[/tex] is given by the formula:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here x1=0 y1=-2 x2=4 y2=-1
Slope = [tex]\frac{-1-(-2)}{4-0}=\frac{1}{4}[/tex]
Hence the slope of the line is [tex]\frac{1}{4}[/tex]
Nour and Rana are shopping for a Christmas tree. They are deciding between 2 different types of trees (real and fake) and 4 colors for the ornaments (white, silver, gold, and purple). They each created a display to represent the sample space of randomly picking a type of tree and a color for the ornaments.
There are no actual questions provided for this post. However, based on the details given, the question will probably asked about the following:
a) list the sample space
b) the probability of having a type of tree with certain color
I will explain to you how to answer such questions. Though it may defer a bit from the actual question, you could use guidance to provide the basis for your answer.
Answer and Step-by-step explanation:
List of sample space must incorporate each sample on two different events given that both events are independent to each other.
In this case we have two events:
i) type of tree - real or fake
ii) color of ornaments - white (W), silver (S), gold (G) or purple (P)
Each sample must have one choices of each events. In this case the sample space are:
(real,W), (real,S), (real,G),(real,P)
(fake,W), (fake,S), (fake,G), (fake,P)
To find probability of any choices, we need to know the probability of each samples. Assuming the selection is random and both events are independent to each other, we can have each sample for each event having different probability.
Event: type of tree
Number of choice: 2
Hence, Pr(real) = Pr(fake) = 1/2
Event: ornament color
Number of choices: 4
Hence, Pr(W) = Pr(S) = Pr(G) = Pr(P) = 1/4
To find the probability of any sample space, we can base our probability using individual probability as above.
For example, if the choice is fake tree with red ornaments
Pr(fake & R) = Pr(fake) x Pr(R)
= 1/2 x 1/4
= 1/8
Answer: Guys the answer is both
Math question any help appreciated ! Find x.
==================================
Explanation:
Mark point D as the center of the circle. Segment EG is the diameter, so angle EDG is 180 degrees. By the central angle theorem, arc EFG is also 180 degrees.
The minor arc from E to F (follow the shortest path along the circle) is 56 degrees. From F to G, along the shortest path, we have y degrees.
(minor arc EF)+(minor arc FG) = arc EFG
56+y = 180
56+y-56 = 180-56
y = 180-56
y = 124
Minor arc FG is 124 degrees.
This is equivalent to saying that central angle FDG is 124 degrees.
-----------------
The inscribed angle for minor arc FG is the angle FEG, which is half that of the minor arc measure.
inscribed angle = (1/2)*(arc measure)
angle FEG = (1/2)*(minor arc FG)
x = (1/2)*(124)
x = 62
Good evening ,
Answer:
x = 62°
Step-by-step explanation:
x equals to half the measure of the central angle FOG
x = (1/2)×(m∠FOG)
m∠FOG = 180 - m∠EOF
= 180 - 56
= 124
then x = 124/2 = 62.
:)
2,250 watts to horsepower (Round answer to the nearest thousandth.
Answer: 3.017hp
Step-by-step explanation: 745.7watts = 1hp
2250watts will be (2250/745.7)hp
i.e 3.017watts
3.017 horsepower will be the value of the 2,250 watts of horsepower
Standardization and kinds of horsepower vary widely. Mechanical horsepower meaning around 745.7 watts, and the metric horsepower, which is roughly 735.5 watts, are two commonly used classifications today. The horsepower is denoted by hp.
The value of 1 horsepower will be:
745.7 watts = 1 horsepower
Calculating the value of 2250 watts with respect to the horsepower
= (2250/745.7)
= 3.017 horsepower
Therefore, the value is 3.017 horsepower
Learn more about horsepower, here:
https://brainly.com/question/13259300
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Mrs Gonzalez has three children whose names are Javier Juan and Rosa. Their mean age is 11 .The median age is 10 .Rosa is 15 years old .What is the age of the youngest child?
Answer:
8
Step-by-step explanation:
Since there are 3 (an odd number) ages, the median is the middle one. So, we know two of the ages are 10 and 15. In order for the mean of the three ages to be 11, their total must be 33. The total of the two known ages is 25, so the remaining one must be ...
33 -25 = 8
The youngest child is 8.
A line is parallel to y = 4x + 1 and intersects the point (-2, -5) What is the equation of this parallel line?
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y= 4x + 1
Comparing with the slope intercept form, slope = 4
If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (-2, - 5) is 4
To determine the intercept, we would substitute m = 4, x = - 2 and y = -5 into y = mx + c. It becomes
- 5 = 4 × - 2 + c = - 8 + c
c = - 5 + 8 = 3
The equation becomes
y = 4x + 3
Answer:
Step-by-step explanation:
any eq. of line parallel to y=4x+1 is
y=4x+a
it passes through (-2,-5)
so -5=4(-2)+a
a=-5+8
a=3
reqd. eq. is y=4x+3
Water flows straight down from an open faucet. The cross-sectional area of the faucet is 1.9 × 10-4m2 and the speed of the water is 0.75 m/s as it leaves the faucet. Ignoring air resistance, find the cross-sectional area of the water stream at a point 0.10 m below the faucet.
Answer:
[tex]8\times10^5m^2[/tex]
Step-by-step explanation:
To find the cross-section area at a point below the faucet
we can use following equations
[tex]v_1^2=v_2^2+2ay[/tex]
and equation of continuity
[tex]A_1v_1=A_2v_2[/tex]
v_1= velocity at the out let
v_2= velocity at the inlet (faucet)= 0.75 m/s
y = distance below the faucet = 0.10 m
A_1= cross-sectional area of the water stream at a point 0.10 m below the faucet.
A_2= area of faucet= 1.9 × 10-4m2
from above two equation we can write
[tex]A_1= \frac{A_2v_2}{\sqrt{v_2^2+2ay} }[/tex]
now putting the values we get
[tex]A_1= \frac{1.9\times10^{-4}\times0.75}{\sqrt{0.75^2+2\times9.80\times0.10} }[/tex]
A_1= 0.00008= [tex]8\times10^5[/tex]
How is volume calculated given mass and density? (1 point) Question 8 options: 1) Sum of mass and density 2) Mass divided by density 3) Mass multiplied by density 4) Difference of mass and density
Answer:
Option 2. Mass divided by density
Step-by-step explanation:
we know that
The formula to calculate the density is equal to
[tex]D=\frac{m}{V}[/tex]
where
D is the density
m is the mass
V is the volume
Solve for V (that means isolate the variable V)
Multiply both sides for V
[tex]DV=m[/tex]
Divide by D both sides
[tex]V=\frac{m}{D}[/tex]
so
Mass divided by density
Distributive property you want to buy three books that are on sale at 20% off. The original prices of the books are $2.50, $4.95, andb$6.00. How much will you save?
Answer:
The saving amount on selling of three books together after discount of 20% is $2.69
Step-by-step explanation:
Given as :
The original price of first book = $2.50
The original price of second book = $4.95
The original price of third book = $6.00
The total percentage discount on the book = d = 20%
Let The saving money after purchased of book = $x
And Let the selling price of the book = s.p = $y
Now, According to question
The total market price of three books = m.p = $2.50 + $4.95 + $6.00
I.e m.p = $13.45
Now, from discount formula
Discount % = [tex]\dfrac{market price - selling price}{market price}[/tex]
Or, d% = [tex]\dfrac{m.p - s.p}{m.p}[/tex]
Or, 20% = [tex]\dfrac{13.45 - y}{13.45}[/tex]
Or, [tex]\dfrac{20}{100}[/tex] = [tex]\dfrac{13.45 - y}{13.45}[/tex]
Or, 20 × 13.45 = (13.45 - y) × 100
Or, 269 = 1345 - 100 y
Or, 100 y = 1345 - 269
Or, 100 y = 1076
∴ y = [tex]\dfrac{1076}{100}[/tex]
i.e y = $10.76
So, The selling price of three books = y = $10.76
∴ The saving amount on selling of three books together after discount of 20% = x = Total market price - Selling price
i.e x = m.p - y
or, x = $13.45 - $10.76
or, x = $2.69
Hence ,The saving amount on selling of three books together after discount of 20% is $2.69 Answer
Stella Blue gets in a serious car accident 2 months after buying a new policy and only paying $700 in premiums. Her insurer had to pay $500,000; this is an example of what type insurance contract characteristic?
Answer:
Aleatory
Step-by-step explanation:
This is an example of Aleatory type of insurance contact.
Definition:
A contract preoccupied with an unclear occurrence that delivers for imbalanced transfer of worth between the parties. Insurance plans are discretionary investments and, after sustaining a reported loss, a person must pay premiums for many years. Most insurance policies are aleatory contacts.
It takes 2 minutes to print out 3 photos. Write an equation relating the number of photos N to the number of minutes M. At this rate, how long will it take to print 10 photos? 14 photos?
Answer:
Part a) [tex]M=6\frac{2}{3}\ min[/tex]
Part b) [tex]M=9\frac{1}{3}\ min[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, M, and N, represent a proportional variation if it can be expressed in the form [tex]k=\frac{N}{M}[/tex] or [tex]N=kM[/tex]
In this problem, the relationship between the number of photos N to the number of minutes M represent a proportional variation
we have that
For M=2, N=3
Find the the constant of proportionality k
[tex]k=\frac{N}{M}[/tex]
substitute the value of N and M
[tex]k=\frac{3}{2}[/tex]
so
[tex]N=\frac{3}{2}M[/tex]
Part a) How long will it take to print 10 photos?
For N=10
substitute in the linear equation
[tex]10=\frac{3}{2}M[/tex]
solve for M
[tex]M=\frac{10*2}{3}[/tex]
[tex]M=\frac{20}{3}\ min[/tex]
Convert to mixed number
[tex]M=\frac{20}{3}\ min=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ min[/tex]
Part b) How long will it take to print 14 photos?
For N=14
substitute in the linear equation
[tex]14=\frac{3}{2}M[/tex]
solve for M
[tex]M=\frac{14*2}{3}[/tex]
[tex]M=\frac{28}{3}\ min[/tex]
Convert to mixed number
[tex]M=\frac{28}{3}\ min=\frac{27}{3}+\frac{1}{3}=9\frac{1}{3}\ min[/tex]
need help please ty (:
Find x.
===================================
Work Shown:
Through the inscribed angle theorem, we can say that 2 times the inscribed angle gets us the arc that the inscribed angle cuts off.
2*(inscribed angle) = arc measure
2*(2x+2) = 76
4x+4 = 76
4x+4-4 = 76-4 ... subtract 4 from both sides
4x = 72
4x/4 = 72/4 ... divide both sides by 4
x = 18
Answer:
Step-by-step explanation:
2 × inscribed angle = 76
2 × (2x + 2) = 76
Open bracket
4x + 4 = 76
Collect like terms
4x = 76 - 4
4x = 72
Divide both sides by 4
4x/4 = 72/4
X = 18
Therefore X is Equal to 18.
Jamie bought a soda for $3. He also bought some corn dogs for $4 each. Jamie did not spend more than $27 on the corn dogs and the soda. Which inequality can be used to find h, the number of corn dogs that Jamie could have bought?
Answer:
The number of corn dogs bought is 3.
Step-by-step explanation:
It is given that, cost of soda is $3 and cost of corn dogs is $4 each.
Let the number of soda bought be "x" and corn dogs be "y".
Thus the total amount spent is given by,
[tex]A = 3x + 4y[/tex]
The total amount is less than or equal to $27, which means;
[tex]3x+4y\leq 27[/tex]
The above inequality can be used to find the number of corn dogs bought.
[tex]y\leq \frac{27-3x}{4}[/tex]
Now, number of items bought are greater than zero and integers, thus x and y are greater than zero integers.
Inserting x from 0 to 9, we get only two only 2 answers,
(x,y) = (5,3) and (9,0)
But it is said that number of corn dogs is not zero, some are bought, thus correct solution is (5,3).
Thus the number of corn dogs bought is 3.
Answer:
The Answer is (A)
Step-by-step explanation:
Sonia bought 30 t shirts at a clothing store. 20% of the t shirts were blue and 1/2 of the t shirts were black. How many of the t shirts were neither black or blue?
9 T-Shirts
Step-by-step explanation: There are 30 t shirts. 20% of the t shirts were blue and 1/2 of the t shirts were black. 20% is equivalent/ the same as 20/100 and simplified, 1/5. 1/2 black + 1/5 blue = 70/100 black and blue. This leaves 30/100(30%) remaining t shirts (neither black or blue). This leaves us to find 30% of 30 (shirts). 30% of 30 equals 9. 30/100 = 9/30.Final answer:
To find the number of t-shirts that were neither black nor blue, subtract the number of black and blue t-shirts from the total. In this case, there were 9 t-shirts that were neither black nor blue.
Explanation:
To find the number of t-shirts that were neither black nor blue, we need to subtract the number of black and blue t-shirts from the total number of t-shirts.
20% of the t-shirts were blue, which means there were 30 x 0.20 = 6 blue t-shirts.
1/2 of the t-shirts were black, which means there were 30 x (1/2) = 15 black t-shirts.
Now, to find the number of t-shirts that were neither black nor blue, we subtract the number of black and blue t-shirts from the total number of t-shirts:
Total number of t-shirts - (Number of black t-shirts + Number of blue t-shirts) = 30 - (15 + 6) = 30 - 21 = 9.
Therefore, there were 9 t-shirts that were neither black nor blue.
James and Lucas competed in climbing a mountain and coming back. James climbed at an average rate of 3 mph and ran back at 4 mph. Lucas climbed at an average rate of 2 mph and ran back at 5 mph. If the path from the bottom to the top of the mountain was 2 miles, how much time did each take to finish and who was faster?
Answer:Lucas is faster
Step-by-step explanation:
Distance = speed × time
Time = distance × speed
the path from the bottom to the top of the mountain was 2 miles.
James climbed at an average rate of 3 mph. This means that the time it took James to climb to the top of the mountain would be
2/3 hours
James ran back at 4 mph. This means that the time it took James run back to the bottom of the mountain would be
2/4 = 1/2 hours
Total time that James spent would be
2/3 + 1/2 = 7/6 = 1.7 hours.
Lucas climbed at an average rate of 2 mph. This means that the time it took Lucas to climb to the top of the mountain would be
2/2 = 1 hour
Lucas ran back at 5 mph. This means that the time it took Lucas to run back to the bottom of the mountain would be
2/5 hours
Total time that James spent would be
1 + 2/5 = 1.4hours.
Answer:
James is faster
Step-by-step explanation:
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Step-by-step explanation:
Keep in mind that Distance = Speed * Time
First lets starts off with James,
Climbing rate of James = 3 mph
Running back rate of James = 4 mph
Total time taken by James = 3/4 x 2/4 = 14/12 = 7/6
Lets convert that into min to make it easier,
7/6 x 60 = 70 min
Now, lets look at lucas,
Climbing rate of Lucas = 2/2 = 1 hour(s) or 60 minutes
Climbing back rate of Lucas = 2/5 of an hour
Now lets convert this one into minutes,
2/5 x 60 = 24 minutes
Total time taken by Lucas = 24 + 60 = 84 minutes
so that means
James = 70 minutes
Lucas = 84 minutes
Therefore James was faster
Hope this helped and please correct me if I got something wrong :)
Using the diagram, find the value of x.
←—→–————↗———→
10x
7x-7
←—→–—↙——————→
A. -9
B. 2
C. 8
D. 11
If you could elaborate on what this is, I would be gladly to assist you, but there is uncertainty going on here. I apologise.
Rosita earns money by walking dogs after school and on weekends.She walks Madeline every other day,buddy every fourth day,and ernie every third day.Today she walked all three dogs. What day did she walk all three dogs?
On 12th day Rosita will walk all three dogs
Solution:
Given that Rosita earns money by walking dogs after school and on weekends
She walks Madeline every other day,buddy every fourth day,and ernie every third day
Today she walked all three dogs
To find: the day when she walked all three dogs
From given question,
Madeline is walked every other day means every two days: 2
Buddy is walked every fourth day: 4
Ernie is walked every third day: 3
To find the day when she walked all three dogs, we have to find the least common multiple (LCM) of 2, 4, 3
L.C.M of 2, 4, 3:
List all prime factors for each number
Prime Factorization of 2 shows:
2 is prime => [tex]2^1[/tex]
Prime Factorization of 3 shows:
3 is prime => [tex]3^1[/tex]
Prime Factorization of 4 is:
[tex]2 \times 2 = 2^2[/tex]
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 3
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 = 12
Thus on 12th day Rosita will walk all three dogs
There are 6 showings of a film about Van Gogh at the art museum. A total of 459 people saw the film. The same number of people were at the showing. About how many people were at the showing ? Circle the numbers the quotient is between
Final answer:
About 76 or 77 people were at each showing of the Van Gogh film at the art museum.
Explanation:
The student's question asks about dividing the total attendance at a film showing into equal parts to find out how many people were at each showing. To solve this, we would take the total number of attendees, which is 459, and divide it by the number of showings, which is 6. This division is necessary to distribute the total equally among all showings.
Performing the division: 459 ÷ 6 = 76.5. Since you cannot have half a person attending, it suggests that the number of attendees per showing must either be rounded to 76 or 77, if we are dealing with whole numbers. However, since the exact division gives us 76.5, this suggests that the division of attendees was not perfectly even among all showings or requires rounding for an approximate answer.
Therefore, about 76 or 77 people were at each showing of the Van Gogh film at the art museum.