Answer:
a) 23.67 miles per gallon
b) 34 miles per gallon
c) The silver car could travel a greater distance.
Step-by-step explanation:
a)
Conversion of the mixed numbers to fractions:
[tex]1\frac{1}{2}=\frac{1\ast2+1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex][tex]35\frac{1}{2}=\frac{35\ast2+1}{2}=\frac{70+1}{2}=\frac{71}{2}[/tex]Gas mileage:
3/2 gallons - 71/2 miles
1 gallons - x miles
Simplifying the top line by 2.
3 gallons - 71 miles
1 gallon - x miles
3x = 71
x = 71/3
x = 23.67 miles per gallon
b)
Conversion of the mixed number to fraction:
[tex]27\frac{1}{5}=\frac{27\ast5+1}{5}=\frac{135+1}{5}=\frac{136}{5}[/tex]Mileage:
4/5 gallons - 136/5 miles
1 gallon - x miles
Simplifying the top line by 5
4 gallons - 136 miles
1 gallon - x miles
4x = 136
x = 136/4
x = 34 miles per gallon
c)
Blue car: 23.67 miles per gallon
Silver car: 34 miles per gallon
Silver car could travel a greater distance.
!!PLEASE HELP IMMEDIATELY!!
Solve the inequality
-1/3x - 12 > 21 or -6x + 10 < -2
x < ? or x > ?
solve for both
Answer:
x < 2 or x > -11
Step-by-step explanation:
b. 1. add 12 to both sides to get -1/3x > 33
2. multiply by -3/1 to both sides to get x > -11
a. 1) subtract 10 to both sides
2) divide by -6 to both sides
A committee must be formed with 5 teachers and 4 students. If there are 6 teachers to choose from, and 15 students, how many different ways could the committee be made?
There are 6 teachers and 15 students to choose from
To form a committee of 5 teachers and 4 students
The combination rule will be applied
From 6 teachers, The number of ways 5 teachers can be selected is
[tex]^6C_5[/tex]From 15 students, the number of ways 4 students can be selected is
[tex]^{15}C_{4^{}}[/tex]Therefore, the total number of ways a committee of 5 teachers and 4 students can be formed from 6 teachers and 15 students is
[tex]^6C_5\times^{15}C_{4^{}}[/tex]Simplifying this gives
[tex]^6C_5\times^{15}C_{4^{}}=\frac{6!}{(6-5)!\times5!}\times\frac{15!}{(15-4)!\times4!}[/tex]This further gives
[tex]\begin{gathered} ^6C_5\times^{15}C_{4^{}}=\frac{6!}{1!\times5!}\times\frac{15!}{11!\times4!} \\ ^6C_5\times^{15}C_{4^{}}=\frac{6\times5!}{1\times5!}\times\frac{15\times14\times13\times12\times11!}{11!\times4\times3\times2\times1} \end{gathered}[/tex]Cancel out common factors
[tex]\begin{gathered} ^6C_5\times^{15}C_{4^{}}=6\times\frac{15\times14\times13\times12}{4\times3\times2\times1} \\ ^6C_5\times^{15}C_{4^{}}=6\times\frac{32760}{24} \\ ^6C_5\times^{15}C_{4^{}}=6\times1365 \\ ^6C_5\times^{15}C_{4^{}}=8190 \end{gathered}[/tex]Therefore, the number of ways the committee can be formed is 8190 ways
Pls someone help me! Giving brainless
Answer:
ANSWER=5
Step-by-step explanation:
GIVEN=8+(-3)
(+)×(-)=(-)
SO 8-3=5
PLEASE MARK ME AS BRILLINT
Divide. −3.52−2.2 What is the quotient
The quotient of - 3.32 / - 2.2 is 8 ÷5.
What is the quotient?Given fraction:
-3.32 / -2.2
First step is to re-write the given fraction which is - 3.52 / - 2.2
3.52 / 2.2
Second step is to convert the decimal to fraction
352 ÷ 100 / 22 ÷10
Third step is to reduce the fraction
reducing 352/100
=(2^5 × 11)/(2^2 × 5^2)
= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]
= (2^3 × 11)/5²
= 88/25
Reducing 22/10
Divide the numerator and denominator by the greatest common divisor
= 22 ÷ 2 / 10 ÷ 2
= 11 /5
Now let determine or find the quotient
88 ÷ 25 × 11 ÷ 5
= 8 ÷ 5
Therefore we can conclude that 8 ÷ 5 is the quotient.
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A hoverboard manufacturer has just announced the Glide 5 hoverboard. The accounting department has determined that the cost to manufacturer the Glide 5 hoverboard is y = 42.96x + 32976. The revenue equation is y = 88.76x. What is the break even point for the - Glide 5 hoverboard? The break even point for the Glide 5 hoverboard is
The break-even point for the glide 5 hoverboard is 36670.4.
What is the break-even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in production where the revenue from a product equals the cost of manufacture.Given that:
Cost function: - y = 25.42x + 23452Revenue function: - y = 70.52xWe know that at break-even:
Cost price = Revenue priceNow,
70.52x = 25.42x + 23452By subtracting "25.42x" from both sides, we get:
70.52x - 25.42x = 25.42x + 23452 - 25.42x45.1x = 23452x = 23452/45.1Then,
y = 70.5270.52*52036670.4Therefore, the break-even point for the glide 5 hoverboard is 36670.4.
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What is the value of 12x if x = −5?
−60 −17 −125 −47
Answer:
-60
Step-by-step explanation:
Graph the solution of the linear inequality and answer the questions on the bottom
The inequality is given
[tex]-2y\leq6x+18[/tex]To draw the graph of the inequality which is less than equal to
shron spent 1 1/4 hours reading her book report and 2 2/5 hours doing her other homework. how much longer did sharon spent doing her homework than reading her book report
sharon spent 23/20 hour doing her homework than reading.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Sharon spent reading the book = [tex]1 \frac{1}{4}[/tex] = 5/4 hours
= 25/20 hours
Sharon spend doing homework = [tex]2 \frac{2}{5}[/tex] = 12/5 hours
= 48/20 hours
So, the difference between both activities
= 48/20- 25/20
= 23/20
Hence, sharon spent 23/20 hour doing her homework than reading.
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8 Solve: 2 3= 4x + 2 - O- O 1 2 AP 4 ( ) 1 4. O 1 2
We will have the following:
[tex]3=4x+2\Rightarrow1=4x[/tex][tex]\Rightarrow x=\frac{1}{4}[/tex][Third option]
Sports Authority marks up New Balance sneakers $30 and sells them for $109. Markup is on cost. What are the cost and percent markup?
If Sports Authority marks up New Balance sneakers for $30 and sells them for $109, then the cost will be $79 while the percent markup will be 37.97%.
What is the cost and percent markup?The original cost of the product can be obtained by subtracting the markup price from the selling price as seen below.
Cost = selling price - markup
Cost = $109 - $30
Cost = $79
Thus, we arrive at the result that the cost of the product by Sports Authority is $79.
Next, we calculate the percent markup with the formula below:
Percent markup = Markup/cost × 100
Percent markup = 30/79 × 100
= 37.97%
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Samuel's family members are choosing numbers to see in what order they will choose gifts. The numbers 1 through 10 are written on pieces of paper. All numbers are equally likely to be chosen. What is the probability that the first person chooses a number less than 3? O A. 10 3 B. 10 2 C. 2 10 O D. 3 10
Answer:
[tex]\text{Probability}=\frac{2}{10}[/tex]Step-by-step explanation:
Probability is represented by the following expression:
[tex]=\frac{\text{Number of ways it can occur}}{Total\text{ number of outcomes}}[/tex]Then, since there are 2 numbers less than 3:
[tex]\text{Probability}=\frac{2}{10}[/tex]ifvx varies directly as y and x =36 when y=6 find x when y=9
Answer:
54
Step-by-step explanation:
Hello!
A direct variation can be expressed as [tex]y = ax[/tex], where a is multiplied.
As you can see, x is 6 times greater than y, proving that when y is 6, x is 36 (6*6 = 36).
Therefore, we can say that if y is 9, we can multiply the value by 6 to find the x-value:
x = 6 * 9x = 54So the value of x is 54.
on a trip of 2,300 miles, a missionary went 9 times as far by plane as by car. How for did the missionary travel by plane
Let the trip by car be c and the trip by plane be p.
The missionary travelled 9 times as far by plane as he did by car. This means if his trip by car is modelled by c, then the trip by plane would be 9c.
Hence, knowing that the entire trip of 2300 miles is by plane and by car;
[tex]\begin{gathered} c+p=2300 \\ \text{When p=9c, then} \\ c+9c=2300 \\ 10c=2300 \\ \text{Divide both sides by 10} \\ c=230 \\ \text{Therefore, his trip by plane would be derived as;} \\ c+p=2300 \\ 230+p=2300 \\ \text{Subtract 230from both sides} \\ p=2070 \end{gathered}[/tex]Question 10 of 11 Step 1 of 1CorrectThcorrectOne group (A) contains 390 people. Three fifths of the people in group A will be selected to win $100 fuel cards. There is another group (B) in a nearby town that willreceive the same number of fuel cards, but there are 553 people in that group. What will be the ratio of nonwinners in group Ato nonwinners in group B after theselections are made? Express your ratio as a fraction or with a colon.AnswerkeypadRestore Your Guth2019 Hawkes Learning
Given : Two groups
Group A: contains 390 people.
Three fifths of the people in group A will be selected to win $100 fuel cards.
So, the number of people who will win = 3/5 * 390 = 234
Group B : contains 553 people
the group will receive the same number of fuel cards
so, the group will receive 234 cards
The non-winners of group A = 390 - 234 = 156
The non-winners of group B = 553 - 234 = 319
The ratio between them = 156 : 319
Drag the curve to the correct location on the graph. A small museum opened in 2004 with 80 pieces of art in its collection. In 2005, the number of pieces of art in the collection was 1.2 times the initial number of pieces of art. Then, in 2006, the number of pieces of art in the collection was 1.2 times the size of the previous year's collection. The directors of the museum plan to continue acquiring pieces of art at the same rate. Complete the graph of this relationship. 1207 ces of Art f(x) 3001 240 180 120
The most appropriate choice for geometric series will be given by
The equation is [tex]y = 80 (1.2)^x[/tex] and it is a geometric function.
What is geometric series ?
The series in which the ratio between consecutive terms of the series are same is called geometric series
For example, 2, 4, 8, 16, ... is a geometric series in which ratio between two consecutive terms is 2.
Number of pieces of art in 2004 = 80
Number of pieces of art in 2005 = [tex]80 \times 1.2[/tex]
Number of pieces of art in 2006 = [tex]80\times (1.2)^2[/tex]
Number of pieces of art after x years from 2004 = [tex]80 \times (1.2)^x[/tex]
The equation is [tex]y = 80 (1.2)^x[/tex]
This is a geometric function
The graph has been attached here.
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Write standard form for the equation of the line: y = 1/2x - 5*
Explanation
the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers
so, we need to write in this form
[tex]Ax+By=C[/tex]Step 1
subtrac 1/2x in both sides
[tex]\begin{gathered} y=\frac{1}{2}x-5 \\ \\ y-\frac{1}{2}x=\frac{1}{2}x-5-\frac{1}{2}x \\ \\ y-\frac{1}{2}x=-5 \\ \text{reorder} \\ -\frac{1}{2}x+y=-5 \end{gathered}[/tex]I hope this helps you
I dont know the steps to solve this expression, help.
5
1) Let's solve that expression step by step
[tex]\frac{35}{2^3-1}[/tex]2) As we have an exponent, let's firstly solve this
[tex]\frac{35}{8^{}-1}[/tex]Now proceeding with the subtraction, and then divide it:
[tex]\frac{35}{7}=5[/tex]3) Hence, the answer is 5
Suzanne is designing a garden for the Gateway Botanical Center. She used a scale of 1 : 600 to make the drawing below. 5 cm 15 cm What is the actual area of the garden, in square meters? (1m = 100 cm)
The given scale is 1:600.
The dimensions of the drawing are 5 by 15.
We just have to multiply each dimension by 600.
[tex]\begin{gathered} 5\times600=3000 \\ 15\times600=9000 \end{gathered}[/tex]So, the dimensions of the actual area are 3,000 cm and 9,000 cm. But, we know that 1 meter equals 100 centimeters, let's transform.
[tex]\begin{gathered} 3000cm\cdot\frac{1m}{100\operatorname{cm}}=30m \\ 9000\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}}=90m \end{gathered}[/tex]Then, we multiply the dimensions to find the area.
[tex]A=30m\times90m=2700m^2[/tex]Hence, the actual area is 2,700 square meters.Please find the square root. Round your answer to the nearest tenth. [tex] \sqrt{58 } = [/tex]
Determine the square root of 58.
[tex]\begin{gathered} \sqrt[]{58}=7.615 \\ \approx7.6 \end{gathered}[/tex]So answer is 7.6.
csc 0 (sin2 0 + cos2 0 tan 0)=sin 0 + cos 0= 1
Okay, here we have this:
Considering the provided expression, we are going to prove the identity, so we obtain the following:
[tex]\frac{csc\theta(sin^2\theta+cos^2\theta tan\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{\frac{1}{sin\vartheta}(sin^2\theta+cos^2\theta\frac{sin\theta}{cos\theta})}{sin\theta+cos\theta}=1[/tex][tex]\frac{\frac{1}{sin\vartheta}(sin^2\theta+cos\text{ }\theta sin\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{(\frac{sin^2\theta}{sin\theta}+\frac{cos\text{ }\theta sin\theta}{sin\theta})}{sin\theta+cos\theta}=1[/tex][tex]\frac{(sin\text{ }\theta+cos\text{ }\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{1}{1}=1[/tex][tex]1=1[/tex]We need to know how to Convert the fraction into its decimal representation on level seven using step by step instructions. We especially need to know how to solve 1/7 in level seven
We want to convert our fractions in a way the denominators are potencys of 10. Let's start with the first one.
[tex]\frac{32}{40}[/tex]If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{32\times25}{40\times25}=\frac{800}{1000}=0.8[/tex]Now, with the next fraction
[tex]\frac{12}{48}[/tex]Dividing both numerator and denominator by 12, we have
[tex]\frac{12}{48}=\frac{1}{4}[/tex]Again, If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{1}{4}=\frac{25}{100}=0.25[/tex]For the next fraction, it is enough to multiply both numerator and denominator by 4
[tex]\frac{3}{25}=\frac{12}{100}=0.12[/tex]For the next one, we can again multiply both the numerator and denominator by 25
[tex]\frac{18}{40}=\frac{450}{1000}=0.45[/tex]f(x) varies inversely with x and f(x)=−10 when x = 20. What is the inverse variation equation? Responses f(x)=−2x f ( x ) = − 2 x f(x)=−5x f ( x ) = − 5 x f(x)=−200x f ( x ) = − 200 x f(x)=−0.5x f ( x ) = − 0.5 x
The equation representing the constant of proportionality is k = xf(x) and the constant of proportionality k = -200
What is proportionality?In mathematics, proportionality indicates that two quantities or variables are related in a linear manner. If one quantity doubles in size, so do the other; if one of the variables diminishes to 1/10 of its former value, so does the other.
Likewise, if the variables are inversely proportional to one another, as one quantity increases, the other quantity decreases by the same proportion or quantity.
We can proceed to substitute the values into the equation above.
k = xf(x)
k = 20 * (-10)
k = -200
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Graph the line... running through: (1,3) with m=3
First, you have to locate the point (1,3)
Next, from that point, you have to locate the next one. To do that, you need the slope, which in this case is 3. So, from (1,3) you have to move 1 unit to the right and 3 units up, reaching the point (2, 6). Finally, you draw the line that passes through these two points
What are the rotations that will carry this equilateral triangle onto itself?A. 90° counterclockwise rotation about its center PB. 270° counterclockwise rotation about its center PC. 120° counterclockwise rotation about its center PD. 240° clockwise rotation about its center PE. 225 clockwise rotation about its center PF. 200 counterclockwise rotation about its center Prights reserved
Given -
Equilateral Triangle
To Find -
The number of rotations that will carry this equilateral triangle onto itself =?
Step-by-Step Explanation -
We know that in an equilateral triangle each question is of 60°
So,
Since it is a three-sided symmetry So, a rotation of 120° will carry this equilateral triangle onto itself.
Final Answer:
C. 120° counterclockwise rotation about its center P
If 12 gallons of gas cost $26.68, howmuch will 15 gallons cost? (proportion)
It is expected that the cost of gas will increase as the number of gallons increases and decrease as the number of gallons decrease. This is a direct proportion
As such, if
12 gallons of gas cost $26.68
15 gallons will cost 15/12 * $26.68
= $33.35
15 gallons of gas will cost $33.35
subtract 7 1/4 - 4 3/4 simplify the answer and write as a mixed number .122 1/21/43 1/2
Answer
The simplified fraction is 2 1/2
Step-by-step explanation:
[tex]\begin{gathered} \text{Substract 7}\frac{1}{4}\text{ - 4}\frac{3}{4} \\ \text{Step 1: convert the mixed fraction into an improper fraction} \\ 7\frac{1}{4}\text{ = }\frac{(7\text{ x 4) + 1}}{4} \\ 7\frac{1}{4}\text{ = }\frac{29}{4} \\ \\ 4\frac{3}{4}\text{ = }\frac{(4\cdot4)+3}{4} \\ 4\frac{3}{4}\text{ = }\frac{19}{4} \\ We\text{ have} \\ \frac{29}{4}\text{ - }\frac{19}{4} \\ \text{ Find the common denominator} \\ \text{The common denominator is 4} \\ \frac{29\text{ - 19}}{4} \\ =\text{ }\frac{10}{4} \\ =\text{ }\frac{5}{2} \\ =\text{ 2}\frac{1}{2} \\ \text{Hence, the answer is 2}\frac{1}{2} \end{gathered}[/tex]AABC was dilated from point A to get AADE. Find the length of AD given a scale factor of 2.D0 3O 1005O 26EB6x-8X+2
Answer:
[tex]AD\text{ = 10}[/tex]Explanation;
Here, we want to get the length of AD
From the information given:
[tex]AD\text{ = 2AB}[/tex]Thus, mathematically:
[tex]\begin{gathered} 6x-8\text{ = 2\lparen x+2\rparen} \\ 6x-8\text{ = 2x + 4} \\ 6x-2x\text{ = 4+8} \\ 4x\text{ = 12} \\ x\text{ = }\frac{12}{4} \\ x\text{ = 3} \end{gathered}[/tex]Now, we can get AD
We simply substitute for the value of x
We have that as:
[tex]\begin{gathered} AD\text{ = 6x-8} \\ AD\text{ = 6\lparen3\rparen -8} \\ AD\text{ = 10} \end{gathered}[/tex]#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?I’m
Answer:
2 hours
Explanation:
[tex]\text{Speed}=\frac{Dis\tan ce}{Time}[/tex]The first bicyclist rides at a speed of 8 mph. Therefore:
[tex]\begin{gathered} 8=\frac{d}{t} \\ \implies d=8t \end{gathered}[/tex]One hour later, the second bicyclist leaves and rides at a speed of 12 mph.
Therefore, the time of the second bicyclist = (t-1) hours.
Therefore:
[tex]\begin{gathered} 12=\frac{d}{t-1} \\ \implies d=12(t-1) \end{gathered}[/tex]Since the second bicyclist will catch up to the first bicyclist, the distance traveled will be the same.
So:
[tex]\begin{gathered} 8t=12(t-1) \\ 8t=12t-12 \\ 8t-12t=-12 \\ -4t=-12 \\ \frac{-4t}{-4}=\frac{-12}{-4} \\ t=3\text{ hours} \end{gathered}[/tex]Therefore, the second bicyclist will have traveled for:
(t-1) = (3-1) =2 hours.
Find the real solutions of the equation by graphing. 4x^3-8x^2+4x=0
x = 0,1 are the real solutions of the equation .
What are real solutions in math?
Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.4x³ - 8x² + 4x = 0
x( 4x² - 8x + 4 ) = 0
x( 4x² - 4x - 4x + 4 ) = 0
x ( 4x ( x - 1) -4 ( x - 1 )) = 0
x ( ( 4x - 4 ) ( x - 1 ) ) = 0
x = 0
4x - 4 = 0 ⇒ x = 1
x - 1 = 0 ⇒ x = 1
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12. Suppose you buy 20 gallons of gasoline in a city that collects excisetax of .16 per gallon. If you pay $1.25 per gallon, what percent of theprice is city excise tax?a.b.c.13.4%13.2%12.8%
We can calculate the percent of the price that is excise tax by dividing the amount of tax per gallon by the final price of the gallon.
If the tax is 0.16 per gallon and the final price is 1.25 per gallon, the percentage can be calculated as:
[tex]p=\frac{0.16}{1.25}\cdot100\text{ \%}=0.128\cdot100\text{ \%}=12.8\text{ \%}[/tex]The percentage that is city excise tax is 12.8% of the final price of the gasoline.
