A car uses 3 1/8 gallons of gasoline per hour when driving on the highway, how many gallons will it use after three hours?
Answer:
The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway
Step-by-step explanation:
if a car uses 3 1/8 gollon per one hour
Multiply the gallon usage of the car by the hours the car will travel on the road
3 1/8(gallons) x 3(hours on the road)
9 3/8 or if you change it to simple form it will be equal to 9.375
Triangle rst has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. what is the area of triangle rst? round to the nearest square inch.
The area of the triangle is 94.9 square inches
For given question,
We have been given triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches.
Let x be the third side of ΔRST
⇒ 22 + 13 + x = 50
⇒ x = 50 - 35
⇒ x = 15
Let s = sum of three sides of the triangle / 2
s = (22 + 13 + 15)/2
s = 25
Now using the formula for the area of the triangle,
A = √[s × (s-a) × (s-b) × (s-c)]
Let a = 22 inches, b = 13 inches, c = 15 inches
Substituting the values,
⇒ A = √[25 × (25 - 22) × (25 - 13) × (25 - 15)]
⇒ A = √(25 × 3 × 12 × 10)
⇒ A = √9000
⇒ A = 94.9 square inches
Therefore, the area of the triangle is 94.9 square inches
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The area of triangle rst which have sides 22 inches and 13 inches with perimeter 50 inches is 95 square inches.
We are given that the two sides of the triangle rst are 22 inches and 13 inches respectively. Also perimeter of the triangle rst is 50 inches.
We have to find the area of triangle to the nearest square inches.
Let the third side of the triangle rst be x.
Hence,
22 + 13 + x = 50 inch
35 + x = 50 inch
x = 50 - 35
x = 15 inches
Hence, the third side of the triangle is 15 inches.
We will use the Heron's formula here to find the area of the triangle.
Heron's formula = \(\sqrt{s(s-a)(s-b)(s-c)}\)
Here,
s = Semi- perimeter
a, b, and c are sides of the triangle.
Hence,
\(s=\frac{50}{2} \\\\s=25 inches\)
a = 22 inches
b = 13 inches
c = 15 inches
Hence,
Area of the triangle rst = \(\sqrt{25(25-22)(25-13)(25-15)}\\\\ \sqrt{25(3)(12)(10)} =\sqrt{5*5*3*3*2*2*5*2}=5*3*2\sqrt{5*2}=30\sqrt{10}\)
We know that,
\(\sqrt{10}\) ≈ 3.162277
Hence,
\(\sqrt{10} * 30\) ≈ 94.86831 ≈ 95 square inches.
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g=c+x solve for x please
Explain how to use a number line to find the sum 7 + −2.
Step-by-step explanation:
start at 7 on the number line. move to the left (because the value is negative) 2 jumps. you will land on 5.
Answer: 5
Step-by-step explanation:
Usually you would just do 7+-2 which is also 7-2 which equals 5 but since it's a number line you do this
You would locate 7 on the number line and do the same for -2
Once done, you would take the distance 2 is from 0 and push 7 there(basically moving it to 5) and that would be how you would use a number line to find the sum of 7 + -2
Now if the 2 was positive, this would be different and you would add the distance making it 9 but since it's negative you push it towards 0 which makes it 5
I hope this helps!
At a football game 43% of people attending are supporting the home team while 57% we’re supporting the visiting team if the total number of people at the game was 4,500 how many people were supporting the home team
Answer:
1935
Step-by-step explanation:
Trust Me
1 For 7-8, given two sides of a triangle, find a range of possible lengths for the third side 7. 4 cm, 17 cm 8. 24 ft , 52 ft
The range of possible lengths for the third side is [16.52,17.46] for 1st part and [46.13,57.27] for 2nd.
What is pythagoras theorem?
The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.
Main Body:
To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²
7. 4 cm, 17 cm
4²+17²=c²
16+289=c²
305=c²
To undo the square you have to square root so
√ 305 =17.46
OR
17² = 4²+b²
289 -16 =b²
b = √273 = 16.52
range of possible lengths for the third side is [16.52,17.46]
8. 24 ft , 52 ft
24² =576
52² =2704
2704+576=3280
√3280 =57.27
OR
52² = 24²+b²
b²= 2704-576
b=√2128
b = 46.13
range of possible lengths for the third side is [46.13,57.27]
Hence the range of third side is found out.
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Math Journal Brian says that the expressions 2(x + 2) and 3(x + 1) + 1 are
equivalent because they name the same value when x = 0. Is Brian's reasoning
correct? Explain.
PLEASE HURRY
Step-by-step explanation:
if 2(0+2)=0+4=4 Answer
3(0+1)+1=(0+3)+1=4 Answer
hope it helps
There are 5:12 odds that Jeff’s socks are clean after a day at work on the construction site. What is the probability that Jeff has clean socks after work?What is the probability that Jeff will have dirty (not clean) socks 2 days in a row?What is the probability that Jefff has clean socks all work week (monday-friday)?
Given that there are 5:12 odds that Jeff’s socks are clean after a day at work on the construction site.
This means there are 5 chances that socks are clean and 12 chances that socks are not clean. There are total of 17 chances.
The probability that socks are clean after work is equal to the chances that socks are clean divided by all chances. that is 5/17.
The probability that the socks are not clean is 12/17. The probability that socks are not clean for 2 days in a row will be:
\(\frac{12}{17}\times\frac{12}{17}=\frac{144}{289}\)the probability that Jeff has clean socks all workweek (monday-friday) is given below:
\(\frac{5}{17}\times\frac{5}{17}\times\frac{5}{17}\times\frac{5}{17}\times\frac{5}{17}=\frac{3125}{1419857}\)An electronics store offers an accidental
damage plan for all laptops. The table
shows how the cost of several laptops
changes if the damage plan is included.
Based on the table, which equation can
be used to determine the total cost of a
laptop and damage plan based on the
laptop's cost without the plan?
A y = 0.80x
B y = 1.25x
C y=x+74
D y = x + 160
The equation that satisfies this relationship is: B) y = 1.25x
To determine the equation that can be used to determine the total cost of a laptop and the damage plan based on the laptop's cost without the plan, we can analyze the given data points from the table:
Laptop Cost without Plan ($), x: 296, 456, 619, 779
Laptop Cost with Plan ($), y: 370, 530, 693, 853
By examining the relationship between the two sets of values, we can identify the equation that represents this relationship.
Let's calculate the ratio between the Laptop Cost with Plan (y) and the Laptop Cost without Plan (x) for each data point:
For the first data point (296, 370):
y/x = 370/296 ≈ 1.25
For the second data point (456, 530):
y/x = 530/456 ≈ 1.16
For the third data point (619, 693):
y/x = 693/619 ≈ 1.12
For the fourth data point (779, 853):
y/x = 853/779 ≈ 1.10
From these calculations, we can observe that the ratio between y and x is approximately constant and falls between 1.1 and 1.25 for all data points.
Among the options provided, the equation that satisfies this relationship is:B) y = 1.25x
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2. Identify the intervals for which
function f is increasing.
A (-∞, -0.8) U (0.4, ∞)
B (-0.8, 0.4)
C (-∞, -1) U (-0.5, 0.4)
D(-1,-0.5) U (1, ∞)
The function f is increasing for the interval (-∞, -0.8) U (0.4, ∞).
What is increasing function?For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
Which function is always decreasing?A monotonically declining function (f(x)) constantly moves downward as x moves in the positive direction.
By observing behavior of a function graphically we can clearly see that the function is increasing in the interval (-∞, -0.8) U (0.4, ∞).
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Define and distinguish among positive correlation, negative correlation, and no correlation. How do we determine the strength of a correlation?
Define positive correlation. Choose the correct answer below.
A.
Positive correlation means that both variables tend to increase (or decrease) together.
B.
Positive correlation means that there is a good relationship between the two variables.
C.
Positive correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases.
D.
Positive correlation means that there is no apparent relationship between the two variables.
Positive correlation means that both variables tend to increase (or decrease) together. Thus, Option A is the answer.
Positive correlation refers to a relationship between two variables in which an increase in one variable is associated with an increase in the other variable. Negative correlation, on the other hand, refers to a relationship in which an increase in one variable is associated with a decrease in the other variable. No correlation means that there is no relationship between the two variables.
To determine the strength of a correlation, we can use a statistical measure called the correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, a correlation coefficient of -1 indicates a perfect negative correlation, and a correlation coefficient of 0 indicates no correlation.
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What is the range of the points on the graph?
Answer:16
Step-by-step explanation:
Find the indicated part round your answer to the nearest degree
Solution
For this case we can do the following:
tan x = 35/30
And we can solve for x and we got:
\(x=\tan ^{-1}(\frac{35}{30})=49.39\)And rounded to the nearest degree is:
49º
For every 7 push-ups Dulce can do, Sara can do 6. If Ducle did 28 push-ups during gym class, how many push-ups did sara do?
The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.
How to solve ratio?Number of push ups Dulce can do : number of push ups Sara can do
Let
number of push ups Sara does = x
7 : 6 = 28 : x
7/6 = 28/x
cross product
7 × x = 28 × 6
7x = 168
divide both sides by 7
x = 168/7
x = 24
Therefore, Sara does 24 push ups during the gym class.
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Simplify a/2b times bc/a
Answer:
\(\dfrac{c}{2}\)
Step-by-step explanation:
We can simplify the given expression by canceling like terms.
Remember that anything divided by itself is 1.
ex:
\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)
Applying this logic to the given expression:
\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)
↓ simplify multiplication of fractions
\(\dfrac{a \cdot bc}{2b \cdot a}\)
↓ rewrite to align like variables
\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)
↓ separate out variables that are divided by each other
\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)
↓ represent them as 1
\(1 \cdot 1 \cdot \dfrac{c}{2}\)
↓ rewrite without unnecessary 1's
\(\dfrac{c}{2}\)
18 is 25% of what number?
A 36
B) 48
C с
72
D) 84
Answer:
C. 72
Hope it helps :)
What is 60km/h in m/s?
Answer:i believe its 16.6667
Step-by-step explanation:
16 mi c. john started a carpool with his coworkers to save money. he and his three passengers split the cost of the toll. if each person pays about $0.81 , which includes their contribution to the toll lane entry fee, how many miles do they travel on the toll lane?
John and his three passengers travel a total of 20.25 miles on the toll lane.
To solve this problem, we can use the fact that each person pays about $0.81, which includes their contribution to the toll lane entry fee. This means that the total amount of money paid by John and his three passengers is 4 times $0.81, or $3.24.
We can then use this information to find the cost per mile of the toll lane. If they traveled a total of x miles on the toll lane, then the cost per mile would be:
$3.24 / x
We can set this equal to the given cost of 16 cents per mile:
$0.16 = $3.24 / x
Multiplying both sides by x, we get:
x * $0.16 = $3.24
Dividing both sides by $0.16, we get:
x = $3.24 / $0.16
x = 20.25 miles
In summary, to find the distance they traveled on the toll lane, we used the fact that they split the cost of the toll, and that each person paid about $0.81. We then set the cost per mile equal to the given cost of 16 cents per mile, and solved for the distance traveled on the toll lane, which turned out to be 20.25 miles.
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GUYS PLEASE HELPP PLSPLSOLSOAKGDJXG
Answer:
Let S = starting point
Let ST = length of tunnel
SR = 1414 m
RT = 2236 m
Set up:
ST^2 + SR^2 = RT^2
ST^2 + (1414)^2 = (2236)
Solve for RT to find your answer.
Step-by-step explanation:
Find the values of the variables
Answer:
corresponding value of equal matrix is equal
a=10
b= -6
c=3
Step-by-step explanation:
2. Eli has 600 cubes that are 1 cubic inch. Select the smallest length a cube- shaped box can have while being able to hold the 600 cubes. A 7 in. B 8 in. C 9 in. D 10 in.
Answer:
9 in
Step-by-step explanation:
We need to find x in x^3 > 600
For x=8, 8^3 = 512 < 600 (Too Small)
For x=9, 9^3 = 729 > 600 (Just right)
For x=10, 10^3 = 1000 > 600 (Too big)
Therefore, the smallest length of the cube-shaped box is 9 in.
Peter says there are two distances for which he and Maria charge the same amount. To prove Peter is not correct, Maria graphs a line for her delivery charges and a line for Peter’s delivery charges. Each line represents the relationship between the amount (y), in dollars, each person charges for a delivery and the distance (x), in miles, each drives for the delivery. Without showing the graph, explain how Maria’s graph of the two lines proves Peter is not correct.
Please help me with this math problem!! :) I will mark brainliest!! :)
Answer:
x = 36
Step-by-step explanation:
180 - 48 = 132
This is because angle AC- and ACB form a straight angle (180 degrees).
132 + 12 = 144
180 - 144 = 36
The three interior sides of a triangle always add up to 180 degrees.
Hope this helps!
h(t)= (t+3)^2 + 5
What is the average rate of change of h over the interval -5 < t < -1?
Answer:
The average rate of change for the given function in the interval (-5, -1) is 0 (zero)
Step-by-step explanation:
The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:
the average rte of change of h(t) in the interval (-5, -1) is:
\(\frac{h(-1)-h(-5)}{-1+5}\)
so we find:
\(h(-1)=(-1+3)^2+5=2^2+5=4+5=9\\and\\h(-5)=(-5+3)^2+5=(-2)^2+5=4+5=9\)
then the average rate of change becomes:
\(\frac{h(-1)-h(-5)}{-1+5}=\frac{9-9}{4} =\frac{0}{4} =0\)
The function h is defined by the following rule.
h(x) = 5x - 1
complete the function table
x h(x)
-5
-4
1
2
3
sorry for the bad formatting i couldn't copy and paste the table
We can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.
What is a function?In mathematics, a function is a rule or mapping that assigns a unique output value for every input value in a specified set
According to question:To complete the function table mathematically, we need to use the given rule for the function h(x) = 5x - 1 and substitute the given values of x to find the corresponding values of h(x).
For example, when x = -5, we can find the corresponding value of h(x) as follows:
h(-5) = 5(-5) - 1
= -26
Similarly, we can substitute x = -4, 1, 2, and 3 into the rule for h(x) to find the corresponding values of h(x) for each input value of x. This gives us the completed function table:
x h(x)
-5 -26
-4 -21
1 4
2 9
3 14
Therefore, we can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.
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convert the following decimals to an equivalent fraction: 0.666= [answer1] 0.1875 = [answer2] 0.240 = [answer3] 1.75 = [answer4] 0.3125 = [answer5] 0.60 = [answer6] 0.56 = [answer7] 1.50 = [answer8]
Answer 1: 0.666 can be expressed as the fraction 2/3.
Answer 2: 0.1875 can be expressed as the fraction 3/16.
Answer 3: 0.240 can be expressed as the fraction 6/25.
Answer 4: 1.75 can be expressed as the fraction 7/4.
Answer 5: 0.3125 can be expressed as the fraction 5/16.
Answer 6: 0.60 can be expressed as the fraction 3/5.
Answer 7: 0.56 can be expressed as the fraction 14/25.
Answer 8: 1.50 can be expressed as the fraction 3/2.
In decimal to fraction conversion, the first step is to identify the place value of the last digit.
For example, in 0.666, the last digit is in the thousandths place.
To convert it to a fraction, we write the digits as the numerator and the place value as the denominator. So, 0.666 becomes 666/1000, which simplifies to 2/3.
Similarly, in 0.1875, the last digit is in the ten thousandths place. So, we write it as 1875/10000, which simplifies to 3/16.
This process is repeated for each decimal, identifying the place value and expressing it as a fraction.
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Please do it with step by step explanation it will help me so much thanks!
Carolyn is searching online for tickets to a concert. Two weeks ago, the cost was $30. Now the cost is $39.
a. What is the percent increase?
b. What would be the percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price?
Answer:
A) The percent increase is by 30%.
B) for the original price = 15%.
B2.0) for the existing price (39) = approximately 11.54%.
Step-by-step explanation:
A) First, we divide 30 by 100. The result is the amount that 1% would be(0.3). If you multiply it by 30(which will become 30%) it will be 9. And from 30-39 is 9.
B) First we divide 30 by 100. The result is the amount that 1% would be(0.39). then if you multiply it by 11.54(which will become 11.54%) it will be 4.50(approximately because it actually is 4.5006 and there is no amount that ends up in 4.50). But if you are asking what percentage from the original cost(30) it would be 15% of it(because 0.3 * 15 = 4.50).
Is this correct? I need help
Sara says, "If you subtract 11 from my number and multiply the difference by -5 , the result is -125 ." What is 's number?
Answer:
36
Step-by-step explanation:
x is the number
(x-11)(-5) = -125
x - 11 = 25
x = 25 + 11
x= 36
write the sequence of natural numbers which leaves the remainder 3 on didvidng by 10
The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...
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