Final answer:
The question asks for the average speed of the second car given that two cars travel in opposite directions and the total distance between them after 4 hours. By calculating the distance one car traveled at 20 mph after 4 hours, it's possible to determine that the other car must have traveled at an average speed of 60 mph to cover the remaining distance.
Explanation:
The student's question is a problem involving distance, speed, and time, which are fundamental concepts in mathematics. To find the average speed of the other car, we can use the formula distance = speed times time. Since the two cars travel in opposite directions, their distances add up to the total separation distance after a certain time.
In this case, one car travels at 20 mph, so in 4 hours it covers 20 mph times 4 h = 80 miles. The total distance between them after 4 hours is 320 miles. Therefore, the distance covered by the second car is 320 miles - 80 miles = 240 miles. To find the average speed of the second car, we divide the distance it covered by the time it traveled which is 240 miles / 4 h = 60 mph. Hence, the average speed of the other car is 60 mph.
The scale of a map is 1 in. :500 mile. City A is 650 miles from City B. How far is it's distance on the map?
Show that (2-√x)^2 divided by √x can be written as 4x^(-1/2)-4+x^1/2
An expression to convert 50 miles per hour to miles per minute is shown.
What value can be entered in the box to correctly make this conversion?
Answer:
x = 60
Step-by-step explanation:
We have to convert 50 miles per hour to miles per minute.
1 hour = 60 minutes
Comparing with the given expression, we get
x = 60
Which is the best simplification of (24 x 32) / (2 x 3)?
To simplify (24 x 32) / (2 x 3), perform the multiplication operations first. Then perform the division operation. This results in the simplification of the given expression to 128.
Explanation:To simplify the expression (24 x 32) / (2 x 3), we'll first carry out the multiplication operations because of the BIDMAS or PEMDAS rule that gives the order of operations in maths. B or P stands for brackets, I or E stands for Indices or Exponents, D/M for Division/Multiplication and A/S for Addition/Subtraction. According to this rule, Division or Multiplication is performed from left to right. Therefore, we first multiply 24 x 32 which gives 768, and secondly multiply 2 x 3 which gives 6. Thus, the expression now becomes 768 / 6. This division gives us the final answer of 128.
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In which number is the digit 4 one hundred times larger than the value of 4 in the number 41?
A) 435
B) 540
C) 4,350
D) 9,400
What is the integer of the square root of 70?
Ivan can type 54 words in 3 minutes. At this rate, how many words can he type in 10 minutes?
The product of a number and 7 is at most the difference of the number and 5. write an inequality and solve for the variable
Earl runs 75 meters in 30 seconds. How many meters does Earl run per second?
divide distance by time
75 /30 = 2.5 meters per second
one week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091. find the cost of a trumpet, a clarinet would, and a violin.
One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1240. the next week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1027. the following week, they sold 5 trumpets, 7 clarinets, and 2 violins for $2091.
Let x be the cost of trumpets
y be the cost of clarinets
z be the cost of violins
Now we frame equations
2x +3y + 5z = 1240 ---> equation 1
3x + 1y + 4z = 1027---> equation 2
5x + 7y + 2z = 2091 ---> equation 3
Now we solve for x,y and z using elimination method
Multiply the second equation by -3 and with first equation
2x +3y + 5z = 1240
-9x - 3y -12z = -3081
--------------------------------
-7x - 7z = -1841 ( divide both sides by -7)
x + y = 263 ----------> equation 4
Multiply the second equation by -7 and add it with third equation
-21x - 7y - 28z = -7189
5x + 7y + 2z = 2091
------------------------------------
-16x - 26z = -5098 (divide the whole equation by -2)
8x + 13z = 2549 --------> equation 5
Now use equation 4 and 5 to eliminate x. Multiply equation 4 by 8
-8x - 8z = -2104
8x + 13z = 2549
------------------------------
5z = 445
z = 89
We know x + z = 263, replace z with 89
x + 89 = 263 ( subtract 89 on both sides)
x = 174
2x +3y + 5z = 1240 ---> equation 1 ( substitute the values of x and z)
2(174) + 3y + 5(89) = 1240
348 + 3y + 445 = 1240
793 + 3y = 1240 ( subtract 793 on both sides)
3y = 447 ( divide by 3 on both sides)
y = 149
The cost of trumpets = $174
The cost of clarinets = $149
The cost of violins = $89
Using a system of equations, it is found that:
The cost of a trumpet is of $174.The cost of a clarinet is of $149.The cost of a violin is of $89.------------------
For the system of equations, i will say that:
The cost of a trumpet is x.The cost of a clarinet is y.The cost of a violin is z.------------------
2 trumpets, 3 clarinets, and 5 violins for $1240, thus:
[tex]2x + 3y + 5z = 1240[/tex]
3 trumpets, 1 clarinet, and 4 violins for $1027, thus:
[tex]3x + y + 4z = 1027[/tex]
5 trumpets, 7 clarinets, and 2 violins for $2091, thus:
[tex]5x + 7y + 2z = 2091[/tex]
------------------
From the second equation:
[tex]y = 1027 - 3x - 4z[/tex]
Replacing into the other two:
[tex]2x + 3y + 5z = 1240[/tex]
[tex]2x + 3(1027 - 3x - 4z) + 5z = 1240[/tex]
[tex]-7x - 7z = -1841[/tex]
Simplifying by 7:
[tex]x + z = 263 \rightarrow z = 263 - x[/tex]
Also:
[tex]5x + 7y + 2z = 2091[/tex]
[tex]5x + 7(1027 - 3x - 4z) + 2z = 2091[/tex]
[tex]-16x - 26z = -5098[/tex]
[tex]16x + 26z = 5098[/tex]
------------------
Solving for x:
[tex]16x + 26z = 5098[/tex]
[tex]16x + 26(263 - x) = 5098[/tex]
[tex]10x = 1740[/tex]
[tex]x = \frac{1740}{10}[/tex]
[tex]x = 174[/tex]
The cost of a trumpet is of $174.
------------------
Solving for z:
[tex]z = 263 - x = 263 - 174 = 89[/tex]
The cost of a violin is of $89.
------------------
Solving for y:
[tex]y = 1027 - 3x - 4z = 1027 - 3(174) - 4(89) = 149[/tex]
The cost of a clarinet is of $149.
A similar problem is given at https://brainly.com/question/22826010
Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university, however, she must pay in euros. How many euros can Varia expect to pay per month to the university? (Round to the nearest whole euro.)
A flower store has 42 carnations and 21 pansies. It puts the same number of flowers in each of 7 bouquets.
How many flowers are in each bouquet?
Suppose you are building a rectangular pen for your goats. You use 400 feet of fencing for the pen.
Sammie bought just enough fencing to border either a rectangular plot or a square plot, as shown. The perimeters of the plots are the same.How many meters of fencing did she buy?
The fencing purchased by Sammie corresponds to the perimeter of either a square or rectangular plot. The perimeters of both these shapes are equal. Therefore, the amount of fencing purchased is equivalent to the perimeter calculated using either of these shapes' formulas.
Explanation:This question is about the concept of perimeter in mathematics. Perimeter is the distance around the border of a shape. In this case, the shapes in question are a square and a rectangle. Because the question states that Sammie has enough fencing for either shape and that the perimeters are the same, we can infer that she bought a length of fencing equivalent to the perimeter of either shape.
Let's take a look at how we calculate perimeter:
For a square, the perimeter (P) is calculated by multiplying the length of one side (s) by 4. So, P = 4s.For a rectangle, the perimeter is calculated by adding twice the width (w) and twice the length (l) of the rectangle. So, P = 2l + 2w.In this scenario, even without specific numerical information, because the perimeters for both shapes are equal, it means that the fencing purchased would correspond to the same value obtained using either of these formulas.
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Write the domain of the function given in the graph in set builder notation.
a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}
I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.
I need major help!!!!
What is the area of a circle with a diameter of 13.2 cm?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer in the box.
Which explanation can be used to derive the formula for the circumference of a circle?
A. Find the length of the diameter and double this amount. Subtract it from the length of the circumference. Set an equation to show the difference equaling the ratio between a circumference and radius. Then rearrange the equation to solve for the circumference.
B. Find the length of the radius. Then find the circumference. Use the square of the radius to set up an equation showing the relationship that the square of the radius equals the π times circumference. Then rearrange the equation to equal the circumference.
C. Find the length of the radius and the area of the circle. Divide the area by the radius to get a quotient of π . Write an equation showing the area of a circle equals this quotient times the radius. Then substitute the area for 3 times the circumference and rearrange the equation to equal the circumference.
D. Find the length of the diameter and the length of the circumference of the circle. Divide the length of the circumference by the length of the diameter. Set up an equation showing the ratio of the circumference to the diameter equal to π . Then rearrange the equation by solving it for the circumference. Substitute 2 times the radius for the diameter.
A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle.
Let s be the side length of the polygon,
let r be the hypotenuse of the right triangle,
let h be the height of the triangle, and
let n be the number of sides of the regular polygon.
polygon area = n(1/2*sh)
Which statement is true?
As h increases, the area of the regular polygon approaches the area of the circle.
As s increases, the area of the regular polygon approaches the area of the circle.
As n increases, the area of the regular polygon approaches the area of the circle.
As r increases, the area of the regular polygon approaches the area of the circle. (has picture)
What is the area of a circle whose radius is 5 ft?
5π ft²
10π ft²
20π ft²
25π ft²
The circumference of a circle is 5π cm.
What is the area of the circle?
25π cm²
10π cm²
6.25π cm²
2.5π cm²
I cant seem to figure out this question? someone please help me please
h is measured in miles so you need to convert 1135ft to miles
1 mile = 5280 feet
so 1135/5280 = 0.21496 miles
D = sqrt(2(3960)(0.21496) + 0.21496^2)
D = sqrt(1702.4832 + 0.046207801)
D = sqrt(1702.529408
D = 41.2617 miles round answer as needed
Diego says that the product of 0.51 * 2.427 will have have five decimal places. is Diego correct? Explain
A scientist measures a substance to be 0.6 grams. Calculate the percent of error in the measurement. Show all work for full credit.
Calculate f (-3) f (x)=-2x+3
Lois and Clark own a company that sells wagons. The amount they pay each of their sales employees (in dollars) is given by the expression 12h+30w where h is the number of hours worked and w is the number of wagons sold. What is the amount paid to an employee that works 6 hours and sells 3 wagons?
Let f(x) = x2 and g(x) = x − 3. Evaluate (g ∘ f)(−2).
Answer:
The value of (g ∘ f)(-2) is 1
Step-by-step explanation:
Given two functions
[tex]f(x)=x^2, g(x)=x-3[/tex]
we have to evaluate (g ∘ f)(-2).
As, (g ∘ f)(-2)=g(f(x))
[tex]g(f(x))=g(x^2)[/tex]
As g(x)=x-3
[tex]g(x^2)=x^2-3[/tex]
Therefore,
[tex](g o f)(x)=x^2-3[/tex]
To find the value of (g ∘ f)(-2), we have to substitute x=-2
[tex](g o f)(-2)=(-2)^2-3=4-3=1[/tex]
Hence, the value of (g ∘ f)(-2) is 1
You see a used car you wish to buy. The dealer quotes you a price of $11,550. You have a blue book quotation of $8,400 for the same model and year. How much markup on cost is the dealer using?
Answer:
37.5%
Step-by-step explanation:
We have been given that the dealer quotes you price of a car $11,550. You have a blue book quotation of $8,400 for the same model and year.
First of all, we will subtract the blue book quotation price from the price quoted by dealer to get the amount of markup.
[tex]\text{Mark-up}=\$11,550-\$8,400[/tex]
[tex]\text{Mark-up}=\$3,150[/tex]
Now, we will find $3,150 is what percent of $8,400.
[tex]\text{Mark-up percent}=\frac{\$3150}{\$8400}\times 100[/tex]
[tex]\text{Mark-up percent}=0.375\times 100[/tex]
[tex]\text{Mark-up percent}=37.5\%[/tex]
Therefore, the dealer is using 37.5% of markup on the cost.
Diana received $35 worth in Starbucks gift cards for Christmas her favorite drink caramel macchiato costs about $4:00 help diana keep track of the balance left in her gift cards each time she buys a drink how many caramel macchiato will she be able to buy with her gift cards?
Diana can buy a total of 8 caramel macchiatos with her $35 Starbucks gift cards, and she will have a remaining balance of $3.
To help Diana keep track of the balance on her Starbucks gift cards after purchasing her favorite drink, the caramel macchiato, we need to perform a series of simple subtractions. She starts with a $35 balance, and each caramel macchiato costs $4.00.
After buying the first caramel macchiato, the new balance is $35 - $4.00 = $31.
After the second purchase, $31 - $4.00 = $27.
This process continues until the balance is less than the cost of a caramel macchiato.
To find out how many drinks she can purchase in total, we divide the initial balance by the cost of one caramel macchiato:
$35 / $4.00 = 8.75
Since she cannot buy a fraction of a drink, Diana can buy a total of 8 caramel macchiatos with her gift cards and will have a remaining balance of $3, which is not enough for another drink.
Last year shantell bought a car for $24,000 the current value of the car is $21,000 find the percent decrease in the value of the car
On the first of three tests sally scored 75 points. on the third test her score was one point more than the second test her average on the three test was 82 what were her scores on the second and third test
At 12 noon in anchorage Alaska Janice noticed that the temperature outside was 12
f. The temperature dropped at a steady rate of 2 F per hour.
What the simplified form of x- 1 +4+7x-3
What is 23% of 256? please help
Are you smart enough to answer this??