The time taken by car to pass the truck is 1.125 hours
Solution:
A truck enters a highway driving 60 miles per hour a car
The car enters the highway at the same place 9 minutes later and drive 68 miles per hour in the same direction from the time the car enters the highway
Let us first convert 9 minutes to hours
[tex]1 \text{ minute } = \frac{1}{60} \text{ hour }[/tex]
[tex]9 \text{ minute } = \frac{9}{60} = \frac{3}{20} \text{ hours }[/tex]
Let the truck covers 'x' m distance in time 't' hour the car will take [t -(3/20)] hour to cover the same distance 'x'
We know that,
[tex]Distance = Speed \times Time[/tex]
For truck : [tex]x = 60t[/tex] ----------- eqn 1
For car: [tex]x = 68 \times (t - \frac{3}{20})[/tex] ------------ eqn 2
From equations (i) and (ii)
[tex]60t = 68 \times(t-\frac{3}{20})\\\\60t = 68t-10.2\\\\68t - 60t = 10.2\\\\8t = 10.2\\\\t = 1.275[/tex]
Thus the time taken by car to pass the truck is:[tex]t - \frac{3}{20} = 1.275 - \frac{3}{20} = 1.275 - 0.15 = 1.125[/tex]
Thus the time taken by car to pass the truck is 1.125 hours
A hockey player is offered two options for a contract: either a base salary of 50,000 and 1000 per goal, or a base salary of 40,000 and 1500 per goal. How may goals must he score in order to make the same money as the first contract?
Final answer:
The hockey player must score 20 goals to make the same money as the first contract.
Explanation:
In order to make the same amount of money as the first contract, the hockey player must calculate the number of goals required. Let's assume the player needs to score 'x' goals.
For the first contract, the total salary would be 50000 + 1000x. For the second contract, the total salary would be 40000 + 1500x.
Equating the two salaries, we get:
50000 + 1000x = 40000 + 1500x
Subtracting 1000x from both sides, we get:
50000 = 40000 + 500x
Subtracting 40000 from both sides, we get:
10000 = 500x
Dividing both sides by 500, we get:
x = 20
So, in order to make the same money as the first contract, the player must score 20 goals.
HALP ME PLZ::: Find the value of k if it is known that the line y=kx+5 goes through point (−6, 14).
Answer:
k = -3/2
Step-by-step explanation:
Write the equation of the line.
Replace x and y with the x- and y-coordinates, respectively, of the point.
Solve for k.
y = kx + 5
Replace x with -6. Replace y with 14.
14 = k(-6) + 5
Solve for k.
14 = -6k + 5
9 = -6k
k = -9/6
k = -3/2
Answer:
-7/6
Step-by-step explanation:
You know that x = -6 and y = 14 so you can plug them into your equation like this:
12= k(-6) + 5
Then solve for k
12-5 = 7
k = -7/6
lim (8-3x+12x^2)
x 2
3(m+7)=6(m+2) what is m equal to?
Answer:
see attached picture please
STEPS:
1. Start my distributing through the parentheses on each side
of the equation to get 3m + 21 = 6m + 12.
2. Now move your m's to the right and numbers to the left
and you get 9 = 3m.
3. Divide both sides by 3 and 3 = m.
Work is attached.
0.7 is 5% of what number
X/3 is equivalent to 1/3X
Answer:
This is true
Step-by-step explanation:
When looking at x itself it is just ONE x. 1x=x, the 1x isn't necessary to have so it is shown as x. So looking at x/3 you could say it is also 1x/3 which would still be the same if it were 1/3x. Both would still be considered one-third OF x.
The answer is "[tex]3x=3x[/tex]"
Equating:
[tex]\to \frac{x}{3} = \frac{1}{3}x\\\\x=?[/tex]
Cross multiplying the given expression:
[tex]\to \frac{x}{3} = \frac{1}{3}x\\\\\to 3x=3x[/tex]
Therefore, the given statement is "True"
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Write as an equation: The sides of a triangle are 7, x and (x + 1). The perimeter is 30.
A. 30 =7+ (x+1)
B. 30 - 7 = 2x
C. 30 = 7 + 2(x + 1)
D.30 = 8+2x
Answer:
d
This is because 7+x+1=30 (this is the equation btw).
You combine the like terms so you get 30=8+2x (7+1 and x+x)
do the equation so you get:
30=8+2x
-8 -8
22=2x
divide both sides by 2
11=x
Answer:
D
Step-by-step explanation:
Perimeter = addition of all sides
30 = 7 + x + x + 1
30 = 8 + 2x
Collecting like terms
30 - 8 = 2x
22 = 2x
Dividing by 2
22/2 = 2x/2
11 = x
Find The original price of a motorbike if you got a 10% discount and paid a final price of $2160 for it
Answer:
2376
Step-by-step explanation:
2160×1.10
i believe it is this
Final answer:
The original price of the motorbike is calculated by dividing the final price of $2160 by 0.9, which represents the 90% price paid after a 10% discount. The original price of the motorbike was $2400 before the discount was applied.
Explanation:
The question asked us to calculate the original price of a motorbike before a 10% discount was applied and the final price came down to $2160. To do this, we recognize that the final price ($2160) is 90% of the original price because a 10% discount was given. Thus, if we let the original price be 100%, we can find it by dividing the final price by 0.9 (which represents 90%).
Here's the step-by-step calculation:
Express the discount as a decimal: 10% = 0.1.
Determine the percentage of the original price paid: 100% - 10% = 90% = 0.9.
Calculate the original price: Original Price = Final Price / 0.9.
Substitute the known value: Original Price = $2160 / 0.9.
Perform the division to find the original price: Original Price = $2400.
The original price of the motorbike was therefore $2400 before the discount.
Here is a list of incoming and outgoing expenditure for the arena, for one day. Work out the final profit of the arena rounded to the nearest thousand. Incoming / Outgoing Profit / Cost Events £22,765 Staff -£6,711 Security -£3,452 Maintenance -£500 Merchandise £967 The final profit of the arena rounded to the nearest thousand is
Answer:
Final Profit = £11,000
Step-by-step explanation:
Incoming / Outgoing Profit / Cost Events £22,765
Staff £6,711
Security £3,452
Maintenance £500
Merchandise £967
Final Profit = £22,765 - £6,711 - £3,452 - £500 - £967 = £11,135
Simplify the expression.
(6.75) =
The expression (6.75) is already in its simplest form. This is because 6.75 is a decimal number that cannot be reduced further or broken down into a simpler expression.
Explanation:The mathematical expression you've shared, (6.75), is already considered to be in its simplest form. Therefore, simplifying the expression doesn't change it because 6.75 is a decimal number. It can't be reduced further or broken down into a simpler expression. The expression remains as is, which is 6.75. In mathematics, simplifying an expression typically involves combining like terms or reducing fractions, however, this is not applicable in this situation as you've provided a single decimal number.
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This table shows the starting and ending temperature for eight days.
Starting temperature (°F) 130 115 100 85 70 55 40 25
Ending temperature (°F) 20 24 26 30 32 36 40 42
Use the data from the table to create a scatter plot.
Answer:
Using excel, we can form the table to create a scatter plot, as shown in attached figure.
Step-by-step explanation:
Given the starting temperature (°F) as
130 115 100 85 70 55 40 25Given the ending temperature (°F) as
20 24 26 30 32 36 40 42Consider starting temperature (°F) as the x-axis and ending temperature (°F) as y-axis
Using excel, we can form the table to create a scatter plot, as shown in attached figure.
Keywords: data, scatter plot, table
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If y varies directly as x, and y is 20 when xis 4, what is the constant of variation for this relation?
Answer:
The constant of variation for this relation is k = 5
Step-by-step explanation:
Step:1
given 'y' varies directly as x that is [tex]y \alpha x[/tex]
[tex]y = kx[/tex] where k is constant ........(1)
Given y value is 20 and x value is 4
now substitute x = 4 and y=20 in equation (1)
we get solution, 20 = k (4)
dividing '4' on both sides, we get
k = 5
verification:-
y = k x
put k= 5 , y=20 and x= 4
20 = 20
At a football game, a vender sold a combined total of 213 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the
number of sodas and the number of hot dogs sold.
142 sodas and 71 hot dogs are sold
Solution:
Let "a" be the number of sodas sold
Let "b" be the number of hot dogs sold
At a football game, a vender sold a combined total of 213 sodas and hot dogs
Therefore,
number of sodas sold + number of hot dogs sold = 213
a + b = 213 ------------ eqn 1
The number of sodas sold was two times the number of hot dogs sold
Number of sodas sold = two times the number of hot dogs sold
a = 2b ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
2b + b = 213
3b = 213
b = 71
Substitute b = 71 in eqn 2
a = 2(71)
a = 142
Thus 142 sodas and 71 hot dogs are sold
Which of the following statements could be translated to the equation n-5=-2?
If five is subtracted from a number, the result is two.
The difference between a number and five is negative two.
A number less than five equals negative two.
Five less a number is equal to two
Answer: The difference between a number and five is negative 2
Step-by-step explanation:
Answer:
The difference between a number and five is negative 2.
Step-by-step explanation:
~King from 7 deadly sins~
What is -12/11 = -3/?
Answer:
According to my calculations, the missing number is 11/4
Step-by-step explanation:
I don’t need an explanation I just need the answer
Answer:
C
Step-by-step explanation:
Answer:
the answer is the third one
75 of 145 is what......................................................
Answer:
10875
Step-by-step explanation:
of always means you have to multiply
Answer:
51.72
Step-by-step explanation:
Percentage Calculator: 75 is what percent of 145? = 51.72.
Carmen has a deck of cards numbered 1-10. She picks one card and flips a coin. How many outcomes are possible.
Answer:
10
Step-by-step explanation:
Out of the ten cards she has ten chances to pick each one
The total number of possible outcomes will be 20.
What is a random sample?Random sampling is the method of selecting the subset from the set to make a statical inference.
Carmen has a deck of cards numbered 1-10. She picks one card and flips a coin.
Then the total number of samples is calculated as,
Total sample = 10 x 2
Total sample = 20
The samples are given below.
(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (7, H), (8, H), (9, H), (10, H)
(1, T), (2, T), (3, T), (4, T), (5, T), (6, T), (7, T), (8, T), (9, T), (10, T),
The total number of possible outcomes will be 20.
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The value of y varies directly with x, and y = 63 when x = 14. Find y when x = 28. I have been stuck on this for a while...
y = 112
y = 126
y = 4.5
y = 6.2
(the answer choices)
I think it is the second one
What is the equation of the line that is parallel to y = –4x + 3 and has a y-intercept of -1/3
Answer:
12x+3y+1 = 0
Step-by-step explanation:
see see the image for the better explanation.
please ask if something is not clear.
Answer:
Step-by-step explanation:
just deez its d btw
What is the standard deviation of the data set? Round to the nearest tenth if needed.
2, 4, 7, 8, 9
Ο
Ο
2.9
Ο
7
Ο
2.6
Answer:
The standard deviation is 2.6076809621.Step-by-step explanation:
The set of values are 2, 4, 7, 8, 9.
The mean of these values are [tex]\frac{2 + 4 + 7 + 8 + 9}{5} = \frac{30}{5} = 6[/tex].
The mean of the squares of the differences of these numbers and the mean is [tex]\frac{(6 - 2)^{2} + (6 - 4)^{2} + (6 - 7)^{2} + (6 - 8)^{2} + (6 - 9)^{2}}{5} = \frac{(4)^{2} + (2)^{2} + (-1)^{2} + (-2)^{2} + (-3)^{2}}{5} = \frac{34}{5} = 6.8[/tex].
In order to get the value of the standard deviation, we need to square-root the value of 6.8.
Hence, the standard deviation of the data set is [tex]\sqrt{6.8} = 2.607680962081[/tex] ≅2.6076809621.
Answer:
Correct answer is 2.9.
Took the test.
PLEASE HELP ME
Describe the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z”.
Answer:
Reflection in the x-axis followed by a translation 5 units left and 1 unit up
Step-by-step explanation:
The coordinates of X are (-6,2).
When we reflect in the x-axis we get X'=(-6,-2)
When we translate by the rule T(x-5,y+1), we get X"=(-6-5,-2+1)=(-11,-1)
The coordinates of Y are (-4,7).
When we reflect in the x-axis we get Y'=(-4,-7)
When we translate by the rule T(x-5,y+1), we get Y"=(-4-5,-7+1)=(-9,-6)
The coordinates of Z are (-2,2).
When we reflect in the x-axis we get Z'=(-2,-2)
When we translate by the rule T(x-5,y+1), we get Z"=(-2-5,-2+1)=(-7,-1)
Therefore the sequence of transformation is a reflection in the x-axis followed by a translation 5 units left and 1 unit up.
whats the factors of 3x2+4x+1
Solve this equation 2(x + 2)/3 = 6
Answer:
Step-by-step explanation:
2(x + 2)/3 = 6
multiply by : 3
2(x + 2) = 18
2x+4 = 18
2x = 18-4=14
x=14/2
x=7
Which equation requires the use of the division property of equality to be solved? 6 a = 420 a + 6 = 420 StartFraction a Over 6 EndFraction = 420 a minus 6 = 420
Option 1: 6a = 420 requires division property of equality to be solved
Step-by-step explanation:
Solving an equation means to find the value of a variable by isolating the variable on one side of the equation.
We will see all the options one by one.
Option 1:
[tex]6a = 420[/tex]
In this option, 6 is multiplied with the variable so we have to divide the whole equation by 6 to find the value of a.
So we will use "Division property of Equality"
Dividing both sides by 6
[tex]\frac{6a}{6} = \frac{420}{6}\\a=70[/tex]
Hence,
Option 1: 6a = 420 requires division property of equality to be solved
Keywords: Linear equation, variables
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Answer:
6a = 420
Step-by-step explanation:
a scuba diver descended at a rate of 2 1/4 per second. If 0 represents the surface of the water and distances below the surface are negative,which expression represents one way to calculate the location of the diver after 12 1/2 seconds?
To calculate the location of the diver after 12 1/2 seconds, use the formula: location = initial location - (rate of descent * time). The location of the diver after 12 1/2 seconds is -28.
Explanation:To calculate the location of the diver after 12 1/2 seconds, we can use the formula: location = initial location - (rate of descent * time). Since the diver is descending at a rate of 2 1/4 per second, we can plug in the values to calculate their location after 12 1/2 seconds.
Initial location: 0 (surface of the water)
Rate of descent: 2 1/4 per second
Time: 12 1/2 seconds
Using the formula, we have: location = 0 - (2 1/4 * 12 1/2)
Calculating the expression, we find that the location of the diver after 12 1/2 seconds is -28.
Miguel collected aluminum cans for recycling. he collected a total of 150 cans. how many of the cans Miguel collected were not soda cans?
To find the number of non-soda cans collected by Miguel, subtract the number of soda cans from the total number of cans he collected.
Explanation:Miguel collected a total of 150 aluminum cans for recycling. The question asks how many of these cans were not soda cans. To find the answer, we need to subtract the number of soda cans from the total number of cans collected. Let's say x represents the number of soda cans. So, the number of non-soda cans would be 150 - x.
The numbers represented by variables w and y on the number line are integers.
If w < x < y, under which of the following conditions could the expression x > 2 be true? Select TWO that apply.
A
when y = 6 and w = 2
B
when y = 4 and w = –1
C
when y = 2 and w = 0
D
when y = 0 and w = –2
E
when y = –1 and w = –4
Option A) when y=6 and w= 2, Option B) when y=4 and w=-1 are the TWO correct choices.
Step-by-step explanation:
The given inequality is w<x<y and x>2.
step 1: let us assume that x=3, since it is given that x>2.
step 2: substitute the value of x=3 and each options in the inequality
step 3: option A) w=2, y=6. Then w<x<y = 2<3<6 (the condition satisfies).
option B) w= -1, y=4. Then w<x<y = -1<3<4 (the condition satisfies).
option C) w= 0, y=2. then w<x<y ≠ 0<2<2 (does not satisfies).
option D) w= -2, y=0. then w<x<y ≠ -2<2<0 (does not satisfies).
option E) w= -4, y= -1. then w<x<y ≠ -4<2<-1 (does not satisfies).
7 points each plus brainliest! 2/7 divided by 2 3/4
Answer:8/77
Step-by-step explanation:
Answer: 8/77
Step-by-step explanation:
2/7 divided by 11/4 = 2/7 x 4/11
2/7 x 4/11 = 8/77
the function f (x) = 1n ( x ) has been transformed so that there is a vertical asymptote at x= -3 what is the equation of the resulting function g ( x) ?
A: g (x) = 1n (x)-3
B: g (x) = 1n (x) + 3
C: g (x) = 1n ( x-3)
D: g = 1n ( x +3)
Answer:
C
Step-by-step explanation:
The equation of the function g(x) after the transformation is g(x) = kn(x - 3).
What are Vertical Asymptotes?A vertical asymptote of a function is the vertical line x = c such that the function tends to approach to infinity as the value of x approaches c.
Given a function f(x) = = ln (x).
The vertical asymptote of the logarithmic function is x = 0.
If the vertical asymptote of the new function is x = 3, this means that the function is shifted to the right by 3 units.
When f(x) is shifted to right by k units, new function is f(x - k).
So the function g(x) is,
g(x) = f(x - 3) = ln (x - 3).
Hence the correct option is C.
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