Answer:
Step-by-step explanation:
grew graph B for graph A
A family has two cars. During one particular week, the first car consumed 35 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a
combined total of 1575 miles, and the sum of their fuel efficiencies was 60 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Note that the ALEKS graphing calculator can be used to make.computations easier.
First car: miles per gallon
Second car: miles per gallon
Solving a system of equations we will see that the efficiency of the first car is 25 miles per gallon, and the one of the second car is 35 miles per gallon.
How to find the fuel efficiencies?Let's define the variables:
x = fuel efficiency of the first car.
y = fuel efficiency of the second car.
We know that the sum is equal to 60 miles per galon, thus:
x + y = 60
We also know that the he first car consumed 35 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a combined total of 1575 miles, this can be written as:
35x + 20y = 1575
Then we have a system of equations:
x + y = 60
35x + 20y = 1575
We can isolate x on the first equation to get:
x = 60 - y
And substitute that in the other equation:
35*(60 - y) + 20y = 1575
2100 - 15y = 1575
2100 - 1575 = 15y
525/15 = y
35 = y
And x = 60 - y = 60 - 35 = 25
These are the efficiencies.
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Write the equation of each line given the y-intercept and x-
The equation of each line given the y-intercept and x-intercept
5 and -4 is 4y- 20 = 5x.
The line has an x-intercept at x = -4 and y intercept at y = 5 this means that the line passes through the points(,0) and(,5).
Now we find the pitch m of the line passing through the points(,0) and(,5)(x-intercept).
The pitch of the line is
m = y2- y1/ x2- x1
= 5- 0/ 0-(- 4)
= 5/ 4
Point- pitch Formula y = m(x-x1)
where m is the pitch and( x, y) is the given point.
Now substituting the values
y- 0 = (5/4)( x-(- 4))
y = (5/4)( x 4)
4y- 20 = 5x
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The complete question :
Find the equation of the line that has an y intercept and x-intercept at
5 and -4.
3 pens cost £2.25
5 folders cost £5.80
Chris wants to buy 30 pens and 30 folders
he only has £60
does he have enough to buy 30 pens and 30 folders? yes or no
Yes, Chris has enough money to buy 30 folders and 30 pens.
How to know if he has enough to buy the pens and folders?The cost of the stationaries Chris bought are as follows:
3 pens cost £2.255 folders cost £5.80Chris wants to buy 30 pens and 30 folders and he has only £60.
Let's check If he has has enough money to buy the products.
Therefore,
3 pens cost £2.25
1 pen = ?
cost of 1 pen = 2.25 / 3 = 0.75 dollars
5 folders cost £5.80
1 folder = ?
cost of 1 folder = 5.80 / 5 = 1.16 dollars
Hence,
30(0.75) + 30(1.16) = 22.5 + 34.8 = 57.3 dollars
Therefore, he has enough money to buy 30 folders and 30 pens
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Which pair of ratios does not form a true proportion? A)6:16 and 21:56 B) 2 to 10 and 15 to 75 C) 9/11 = 27/15 D) y=5x
The ratios 6:16 and 21:56, 9/11 = 27/15, and y=5x do not form a true proportion. Hence, options A, C, and, D are the correct options.
A true proportion is when both the ratios presented are equal. This can be verified by putting them in their respective fractional form. For example, let's take the ratios in the second option -
= 2/10 and 15/75
Here, we can see that 2*5 = 10 and 15*5 = 75
Hence these can be written as
= 2/2*5 and 15/15*5
Hence, these fractions are the same and as a result, the ratios form a true proportion.
As for the other ratios in question -
A) 6/16 is not equal to 21/56
C) 9/11 is not equal to 27/15
D) y= 5x are not proper ratios and are not equal
Thus, options A, C, and, D are the correct options.
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order reads: klotrix 0.35 meq/lb po dissolved in 6 oz of orange juice at 8 am; available: klotrix 8 meq/ml. how many ml of klotrix will you add to the orange juice for a 20.5 kg patient? round your answer to the nearest tenth.
We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.
We know that , 1 kg=2.20462 pounds
Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb
Additionally we have, 1 lb = 0.35 mEq
Therefore, 45.195 lb= 0.35 mEq × 45.195 = 15.818 mEq.
Also, 8mEq=1 mL
By using unitary method,
1 mEq=1/8 mL
Converting 15.818 mEq to mL, we get
15.818mEq = 15.818 ÷ 8 = 1.9 mL
Thus, 15.818mEq = 1.9 mL
Rounding off the answer we get,
The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL
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describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north.
The description of the route of the limousine is
First, the limousine drives 18 blocks right and 8 blocks down and then it drives 17 blocks left and 2 blocks up
How to describe the route of the limousine in words?From the question, we have the following parameters that can be used in our computation:
T<18, -8> o T<-17, 2>
The above parameters represent the transformation and the positions of the limousine
T<18, -8> represents a movement 18 units right and 8 units downT<-17, 2> represents a movement 17 units left and 2 units upThe above statement represents the direction in words
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inequality notation of 3 − 5x > −2
Answer:x<1
Step-by-step explanation:
move constant -5x>-2-3
Add alike numbers (-2 and -3)
-5x>-5
Divide both sides by -5
Then flip the inequality sign
x<1
Answer:
Step-by-step explanation:
Add 3 to the -2
-5x > 1
Divide by -5 the sign switches because of the negative
x < - 1/5 or X < -0.2
over the past few decades, public health officials in massachusetts have been examining young-teen smoking. the long-run average smoking prevalence in the state has been 26%. officials have been hopeful that their ad campaigns on billboards and tvs have been effective at lowering smoking rates for this age group. researchers surveyed a group of 273 randomly selected teens living in massachusetts (between 12 and 15 years old). sixty-three said they smoked. is there good evidence that smoking rates for young teens have decreased?
There is good evidence that smoking rates for young teens in Massachusetts have decreased.
To answer this question, we need to calculate the proportion of teens in the sample who said they smoked (63/273). This gives us a sample proportion of 0.23, which is lower than the long-run average smoking prevalence in the state (26%). This suggests that there is good evidence that smoking rates for young teens have decreased.
We can also calculate a confidence interval to further assess the evidence. A 95% confidence interval for the true proportion of teens in Massachusetts who smoke would be (0.17, 0.29). This confidence interval does not contain the long-run average smoking prevalence of 26%, which suggests that there is a statistically significant decrease in smoking rates for young teens in Massachusetts.
Overall, there is good evidence that smoking rates for young teens in Massachusetts have decreased.
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Frannie put 1/5 of her music collection on an MP3 player. While on vacation she listened to 1/6 of the music on the player. How much of Frannie’s music collection did she listen to while on vacation? Choose the correct values to describe how to solve the problem.
Draw a rectangular array with 5 rows and A) 5 B) 6 C) 9 rows.
Shade A) 4 B) 1 C) 3 rows gray.
Shade A) 2 B) 1 C) 4 columns black.
Please help me with this I will mark brainliest!!!
Frannie listened to 1/30 of her music collection while on vacation.
We have been given that Frannie put 1/5 of her music collection on an mp3 player. while on vacation, she listened to 1/6 of the music on the player.
To find the amount of music collection listened to by Frannie, while on vacation, we need to find 1/5 of 1/6.
The amount of music collection listened to by Frannie on the vacation: =1/5*1/6
=1/30
Therefore, Frannie listened to 1/30 of her music collection while on vacation.
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A home improvement store sells lumber by the foot. It costs $24 to buy 8 feet of lumber.
Fill in the table.
Answer:
The price per foot is $3
Step-by-step explanation:
The order for the answers on the chart are 3, 4, 72, 40.
Which expression is equivalent to 1/4(3x+4y) + 3(1/4x+ 2/3y)
The expression is equivalent is 6x/4 + 24y/12
What are algebraic expressions?
Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.
These expressions also consisting of mathematical operations, such as;
AdditionParenthesesDivisionSubtractionMultiplicationFloor division, etcGiven the expression;
1/4(3x+4y) + 3(1/4x+ 2/3y)
expand the bracket
3x/4 + 4y/4 + 3/4x + 3/3y
collect like terms
3x/4 + 3/4x + 4y/4 + 3/3y
add like terms
3x + 3x/4 + 12y + 12y /12
add the numerators
6x/4 + 24y/12
Hence, the expression is 6x/4 + 24y/12
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the length of a rectangular platform i 2 feet longer than three time it width. The area of the platform i 56 quare feet. Write a polynomial that repreent the area of the platform
This polynomial represents the area of the platform.A = w(w + 2)^2. the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width
A = w(w + 2)^2
A = Area of the platform
w = width of the platform
Since the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width, we can represent this statement mathematically as:
A = w(w + 2)^2
This polynomial represents the area of the platform.
A = w(w + 2)^2
A = w^2 + 2w^2
A = 3w^2
A = 56
3w^2 = 56
w^2 = 56/3
w = √56/3
A = w(w + 2)^2, area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width.
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When the line of slope of 3 passes through two points, the value of y is -8.
What is slope?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.
Here,
m=3
m=(y2-y1)/(x2-x1)
3=(y+5)/(-3+(2))
-3=y+5
y=-8
The value of y is -8 when the line of slope of 3 is passing through 2 points as given.
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Write an equation in point slope form for the line that passes through (-4, 3) and whose slope is 3.
An equation in point slope form for the line that passes through (-4, 3) and whose slope is 3 is equal to y - 3 = 3(x + 4).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represents the data points.m represents the slope.Next, we would determine the linear equation representing the line which passes through the points (-4, 3) and has a slope of 3 by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 3(x - (-4))
y - 3 = 3(x + 4)
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Complete the conversion.
64 c = pt
Answer:
64c = 32pt
Step-by-step explanation:
There are 2 cups in 1 pt. 64 divided by 2 is 32pt.
Also, just imagine the cups as double the number of the pints
Ex. 32 + 32 = 64
Help me with simplified expressions of a side length of a triangle, please!
Answer:
2w³ +w
Step-by-step explanation:
Given expressions for the sides of a triangle, (-10w³+w) and (4w³-3w), and for the perimeter, (-4w³-w), you want an expression for the third side.
PerimeterThe perimeter is the sum of the side lengths. This relation can be used to find the length of the third side:
Perimeter = side 1 + side 2 + side 3
-4w³ -w = (-10w³ +w) +(4w³ -3w) +side 3
-4w³ -w = -6w³ -2w + side 3 . . . . . . collect terms
side 3 = (-4w³ -w) -(-6w³ -2w) . . . . . . . subtract (-6w³ -2w)
side 3 = 2w³ +w . . . . . . . . . . . . . . . . collect terms
4. Describe the graph of the line x = 12.
O vertical line
Oline with slope of 12
crosses the y-axis
O horizontal line
Answer:
The graph of the line x = 12 is a vertical line.
A vertical line is a line with a constant x-value, in this case x = 12, so all the points on the line will have an x-coordinate of 12, regardless of their y-coordinate. All the point on the line will have the same x-coordinate and it will be parallel to the y-axis.
It does not have a slope, does not cross the y-axis, it is not horizontal.
Solve for p and q so that x=-1.
px+6=3(x+q)
By comparative methods, the values of variables p and q such that p · x + 6 = 3 · (x + q) are 3 and 2, respectively.
How to determine the value of two coefficients within a linear equation
In this question we find the case of a linear equation with three variables (p, q, x). Theoretically, it cannot be solved because the number of variables is greater than number of equations. Nonetheless, we can infer the values of p and q by means of comparative methods and equality properties.
First, write the linear equation:
p · x + 6 = 3 · (x + q)
Second, expand the expression by algebra properties:
p · x + 6 = 3 · x + 3 · q
Third, compare terms on each side of equality:
p = 3
6 = 3 · q
q = 2
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1. Jackie gets paid $45 for 2 hours of work. How many
nickels per minute does she get paid? (PLEASE PUT IN ASPECT RATIO FORM)
Answer:15 nickels per minute (I believe)
Step-by-step explanation:
First, we want to know how much she got paid in total dollar amount, we'll break it up into nickels later. We know Jackie was paid $45 per hour, but we want to figure out how much per minute she makes. There are 60 minutes in an hour, so divide 45 by 60 ( 45/60 in a calculator).
The answer for 45/60 would then be 0.75. This means Jackie gets paid 75 cents a minute. Since a nickel is worth 5 cents, we just need to divide 75 by 5. Then, we get 15.
Now we know Jackie gets paid 15 nickels per minute. I assume this would be put in aspect ratio form by saying "Jackie gets paid 15 nickels per every one minute of work." but that may depend on how your teacher wants you to word your answer. I hope this helps :)
Identify the dependent and independent variables for each relation
The faster you drive your car, the longer it will take to come to a complete stop
The Spanish classes are having a fiesta lunch. Each student that attends is to bring a Spanish side dish or dessert. The more students that attend, the more food there will be
Answer: The dependent variable is the time it takes to come to a complete stop. The independent variable is the speed at which you drive your car.
The dependent variable is the amount of food there will be. The independent variable is the number of students who attend the fiesta lunch.
Step-by-step explanation:
Xander's hedgehog weighs 0.62 pound.
Express his hedgehog's weight in grams.
Round your answer to the nearest gram.
equation=
ordered pair=(3,-4)
Slope(m)=
y-intercept=2
The equation of the line, given the ordered pair and the y - intercept, is y = -2 x + 2
The slope ( m ) is - 2
How to find the equation ?The equation for a linear model takes the form :
y = mx + b
m = slope
b = y - intercept
As we have the ordered pair, and the y - intercept, we can find the slope:
y = mx + b
- 4 = 3 x slope + 2
3 x slope = - 4 - 2
Slope = - 6 / 3
Slope = - 2
The equation is therefore:
y = -2 x + 2
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Plss help 20 points!
Average price is the mean price of an asset or security observed over some period of time.
Define average price in gas?
Weighted Average Gas Price means the total payment made by the Buyer to the Seller for Seller's Gas delivered in a month divided by the total MMBtu of Seller's Gas delivered for that month.In basic mathematics, average price is a representative measure of a range of prices. It is calculated by taking the sum of the values and dividing it by the number of prices being examined.Get the miles traveled from the trip odometer, or subtract the original odometer reading from the new one.Divide the miles traveled by the amount of gallons it took to refill the tank. The result will be your car's average miles per gallon yield for that driving period.To learn more about average refers to:
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Solve and reduce to lowest terms: 5 x 2/7
The multiplication of the numbers given to the reduced form is 10/7.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
The given expression is 5 × 2/7
One of the number is a whole number and the other is a fraction.
We can write 5 as 5/1 in terms of fraction and then multiply the numerators and the denominator.
(5/1) × (2/7) = (5×2) / (1 × 7) = 10/7, which is in the lowest form.
Hence the solution of the multiplication is 10/7.
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I do not understand please 5(x-3)-x=
Answer:4x-15
Step-by-step explanation:
Answer:
4x-15 <---
Step-by-step explanation)
1) Distribute the X to both the x and the -3
2) You'll end up with, 5x-15-x=...
3) And, now look at the like terms. The like terms in this case are 5x and the -x.
4) 5x-x =4x
5) And, now put them together, and you'll get 4x-15!
HOPE IT HELPS! <3
Two bags each contain five letter tiles. The sample space is shown below. Jennifer selects one tile from each bag without looking. What is the probability that Jennifer selects two vowels
The probability that Jennifer selects two vowels is 24%.
How to calculate the probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
Here, the probability that Jennifer selects two vowels is:
= 3/5 × 2/5.
= 6 / 25
= 24%.
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1
2. Jim is 8 years old, and his Uncle Bill is 5 times older
2
than he his. What is his Uncl Bill's age?
Answer:
Uncle Bill is 40 years old.
Step-by-step explanation:
Jim is 8 years old, and Uncle Bill is 5 TIMES older, meaning he is 5x8. Which would be 40 years old.
the length of a rectangular field is twice its breadth. Meghna jogged around it 5 times and covered a distance of 3 km. what is the length of the field?
The length of the rectangular field is 200 meters.
Given, we have length of the field equal to twice its breadth. Let the breadth of the field be "b". Therefore, length will be "2 x b". Now, Meghna jogged around the field 5 times which means she covered the perimeter of the field 5 times. We know that the perimeter of a rectangular field is [tex]2(l+b)[/tex] where l is the length of the rectangle and b is the breadth.
After jogging around the field 5 times, she covered a distance of 3 km. Converting kilo meters into meters: 3km ⇒ 3 x 1000 = 3000 meters. Now, We can equate the perimeter of the rectangle with the given information like this :
⇒[tex]2(l+b) * 5 = 3000m[/tex]
We already know that length = 2b, therefore putting in the equation gives us :
⇒ 2(2b+b) x 5 = 3000m
⇒2(3b) x 5 = 3000m
⇒10(3b) = 3000m
⇒30b = 3000m
Dividing both sides of the equation with 30,
⇒b = 100 m
Since, length = 2b, Therefore Length ⇒ 2 x 100m = 200m
∴ The length of the field is 200m
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Evaluate the expression.
(13×6)×5
=
To the nearest hundredth, find the value of x.
Answer:
Step-by-step explanation: