The distance a car travels is directly proportional to the quantity of gas consumed. To find the constant of proportionality, set up a proportion using the given values. The units for the constant of proportionality will be miles per gallon.
Explanation:In this problem, we are given that the distance a car travels, in miles, is directly proportional to the quantity of gas consumed, in gallons. We are also given that a Lexus travels x miles on y gallons of gas. To find the constant of proportionality, we can set up a proportion using the given values:
x/y = miles/gallons
Using this proportion, we can solve for x and y. The constant of proportionality, which represents the distance a car travels per gallon of gas, will be the value of x when y = 1. The units for the constant of proportionality will be miles per gallon.
A total of $5000 was invested in two accounts. One pays 5% annual interest, and the second pays 7% annual interest. If the first-year interest is $325, how much was invested in each account?
You buy 3.17 pounds of apples, 1.25 pounds of pears, and 2.56 pounds of oranges. What is your total bill rounded to the nearest cent?
Answer:
Total bill = 7 pounds .
Step-by-step explanation:
Given : You buy 3.17 pounds of apples, 1.25 pounds of pears, and 2.56 pounds of oranges.
To find : What is your total bill rounded to the nearest cent.
Solution : We have given
Apple = 3.17 pounds
Peas = 1.25 pounds
Orange = 2.56 pounds.
Total bill = 3.17 + 1.25 +2.56 = 6.98
Total bill = 6 .98 pounds .
We can see number after decimal is greater than 5 so number would be increased b 1.
Total bill = 7 pounds .
Therefore, Total bill = 7 pounds .
Without knowing the price per pound of the fruit, it's impossible to calculate the total bill. However, if you knew the individual prices, like in the example, you could add up these amounts together to find the total cost.
Explanation:The question you're asking appears to be missing some important information. Specifically, we would need to know the price per pound of the apples, pears, and oranges in order to calculate your total bill. However, let's use an analogous example. Suppose you buy 10 apples at 50 cents each, 12 bananas at 20 cents each, and 2 bunches of grapes at 65 cents each. Your total cost would be $5.00 for apples, $2.40 for bananas, and $1.30 for grape. Altogether, this comes to $8.70.
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2 different ways to write 6/9
Find the expressions that are equal..use the equal expressions to write true number sentences ??
Final answer:
To find equal expressions, identify different expressions that have the same value when evaluated. Write true number sentences using these equal expressions.
Explanation:
In order to find equal expressions, we need to identify different expressions that have the same value when evaluated. For example, the expressions 3 + 4 and 7 are equal because both evaluate to 7. We can use these equal expressions to write true number sentences, such as 3 + 4 = 7.
Another example is the expressions 2 * 5 and 10, which are equal because both evaluate to 10. We can write the true number sentence 2 * 5 = 10 using these equal expressions.
It's important to note that we're looking for expressions that are equal in value, not necessarily in form. For example, the expressions x + 2 and 3 + x are equal because they represent the same value for any given value of x. We can write the true number sentence x + 2 = 3 + x using these equal expressions.
Over the course of a year,a tractor-trailer commutes 160,000 miles across America.Assuming a trucker changes his tires every 40,000 miles,and that he starts with a brand new set of tires,how many sets of tires will he use in a year?
Given that a trucker changes his tires every 40,000 miles, if he drives 160,000 miles in a year, he will use a total of 5 sets of tires.
Explanation:The question is asking us to find out how many sets of tires a trucker will use when he drives 160,000 miles in a year, given that he changes his tires every 40,000 miles. To find out, we need to do some simple division.
First, we need to take the total distance traveled, which is 160,000 miles, and divide it by the distance the trucker can travel on a set of tires, which is 40,000 miles. 160,000 miles divided by 40,000 miles equals 4.
So, if the trucker starts the year with a fresh set of tires, he will need to change his tires 4 times throughout the year, meaning he will use a total of 5 sets of tires.
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What is the sum of the angle measures of a 32-gon? A. 5400 B. 5760 C. 6120 D. 5580
Answer:
The sum of measure of angle is 5400
Step-by-step explanation:
Given a 32-gon.
we have to find the sum of the angle measures of a 32-gon
In geometry, 32-gon is a thirty-two-sided polygon i.e polygon of 32 sides
The sum of measure of interior angle of polygon is calculated by the formula
[tex]s=(n-2)180^{\circ}[/tex]
where n is number of sides
[tex]s=(32-2)180=30\times 180=5400[/tex]
Hence, option A is correct.
round to the nearest whole number 5.98
A number p minus 19 algebraic expression
Answer:
Expression p - 19 .
Step-by-step explanation:
Given : A number p minus 19 algebraic expression.
To find : Write expression .
Solution : We have given A number p minus 19 .
A number = p .
According to question :
p is minus 19
We can see the number p is less than 19
So , p - 19 .
Therefore, Expression p - 19 .
"Solve the equation"
Answer:
y = 3 1/13
Step-by-step explanation:
Add 3 and combine like terms:
... (2 3/5)y = 8
Multiply by the reciprocal of the coefficient of y.
... y = 8 · (5/13) = 40/13
... y = 3 1/13
_____
Check
(3/5)(3 1/13) - 3 + 2(3 1/13) = 5
(3/5)(40/13) - 39/13 + 2(40/13) = 5 . . . . express everything with 13 as a denominator
24/13 - 39/13 + 80/13 = 5 . . . . . eliminate parentheses
(24 -39 +80)/13 = 5 . . . . . . . . . . add the fractions
65/13 = 5
5 = 5 . . . . . the answer checks
Find a second-degree polynomial p such that p(2) = 5, p'(2) = 6, and p''(2) = 4.
Over the last 50 years, the average temperature has increas ed by 2.5 degrees worldwide (I made this up). What is the rate of change in worldwide temperatures per year?
dom wants to buy 5 baseballs he has $20 what is the most each baseball can cost?
At a sporting goods store, the price of a bicycle is $650. During a sale, this price is marked down 45%.
What is the sale price of the bicycle
Answer:
the answer is 357.50
Step-by-step explanation:
A useful rule of thumb called the "rule of 70" states that if something grows at a constant rate of z percent per year, it doubles in size approximately every __________ years.
a. z/70
b. 70/z
c. 70 - z
d. 70 × (z/100)
A car rents for $250 per week plus $0.50 per mile.find the rental cost for a two-week trip of 500 miles for a group of three people
The total cost of a two-week car rental for a trip of 500 miles, split three ways, is $250 per person.
Explanation:In this calculation, we'll break down the costs into two parts: the weekly rental cost and the mileage cost. The car rents for $250 per week which, for two weeks, is $250 x 2 = $500. The cost for mileage is $0.50 per mile, hence for 500 miles, it will be $0.50 x 500 = $250. Adding these two gives us the total cost, $500 + $250 = $750 for the trip.
It's also mentioned that there are three people sharing this cost. So, the cost per person would be $750 divided by 3 which gives us $250 per person for the two-week trip of 500 miles.
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The senior class has 412 students. They are assigned to different homerooms. There are 28 students in the smallest homeroom and the remaining 12 homerooms have the same number of students. How many students are in each of the remaining 12 homerooms?
There are 32 students in each of the remaining 12 homerooms.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Total students in a senior class = 412 students.
Total number of students in the smallest homeroom = 28
And, 12 homerooms have the same number of students.
Let number of students in each of 12 homerooms = x
So, Total number of students in each of 12 homerooms = 12x
Then, We can formulate;
12x + 28 = 412
Solve for x as;
12x + 28 = 412
Subtract 28 as;
12x + 28 - 28 = 412 - 28
12x = 384
Divide by 12;
x = 32
Thus, There are 32 students in each of the remaining 12 homerooms.
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I don't know how to solve this
How do you choose the level of accuracy given the limitations of a situation?
Find two fractions with the difference of 1/5 but with neither denominator equal to 5? I know the answer from Google but how is it solved?
A cashier has 30 bills, all of which are $10 or $20 bills. The total value of the money is $460. How many of each type of bill does the cashier have?
Answer:
There are 14 $10 bills and 16 $20 bills.
Step-by-step explanation:
Let
x = number of $10 bills
y = number of $20 bills
The sum of the value of x and y is $460.
10 x + 20 y = 460 [1]
The sum of x and y is equal to the total number of bills.
x + y = 30
y = 30 - x [2]
We replace [2] in [1],
10 x + 20 (30 - x) = 460
10 x + 600 - 20 x = 460
-10 x = -140
x = 14
We can get y if we replace this value of x in [2].
y = 30 - 14 = 16
a line has a slope of -2/3 and passes through the point -3, 8 what is the equation of the line
Answer:
[tex]y=-\frac{2}{3}x+6[/tex]
Step-by-step explanation:
we have been give that
slope, m = -2/3
The line passes through the point (-3,8).
Hence, [tex]x_1=-3,y_1=8[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the known values
[tex]y-8=-\frac{2}{3}(x-(-3))[/tex]
On simplifying, we get
[tex]y-8=-\frac{2}{3}x-2\\\\y=-\frac{2}{3}x+6[/tex]
Thus, equation of line is [tex]y=-\frac{2}{3}x+6[/tex]
Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 7. the hypotheses h0: μ = 75 and ha: μ < 75 are to be tested using a random sample of n = 25 observations. (a) how many standard deviations (of x) below the null value is x = 72.3? (round your answer to two decimal places.) standard deviations (b) if x = 72.3, what is the conclusion using α = 0.01? (round your answers to two decimal places.) test statistic z = critical value z = what can you conclude? reject the null hypothesis. there is sufficient evidence to conclude that the mean drying time is less than 75. do not reject the null hypothesis. there is sufficient evidence to conclude that the mean drying time is less than 75. do not reject the null hypothesis. there is not sufficient evidence to conclude that the mean drying time is less than 75. reject the null hypothesis. there is not sufficient evidence to conclude that the mean drying time is less than 75. (c) what is α for the test procedure that rejects h0 when z ≤ −2.8? (round your answer to four decimal places.) α = (d) for the test procedure of part (c), what is β(70)? (round your answer to four decimal places.) β(70) = (e) if the test procedure of part (c) is used, what n is necessary to ensure that β(70) = 0.01? (round your answer up to the next whole number.) n = specimens (f) if a level 0.01 test is used with n = 100, what is the probability of a type i error when μ = 76? (round your answer to four decimal places.)
A paint drying situation, has the standard deviation 1.93. The detailed solution is given below.
Given :
Standard Deviation, [tex]\sigma = 7[/tex]
Mean, [tex]\mu = 75[/tex]
Sample, n = 25
Solution :
A) We know that,
[tex]z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}[/tex] ---- (1)
Now put the values of [tex]\rm x,\;\mu,\;\sigma \;and \;n[/tex] in equation (1) we get,
[tex]z = \dfrac{72.3-75}{\dfrac{7}{\sqrt{25} }}[/tex]
z = -1.93
Therefore, 72.3 is 1.93 standard deviations below the mean.
B) From the above part we know that z = - 1.93.Therefore p-value is,
P(-1.93) = 0.03
Since [tex]\alpha[/tex] = 0.01 and p-value = 0.03, this means that the p-value is greater than the fail to reject the null hypothesis.
C) The p-value for [tex]z\leq -2.8[/tex]
is 0.00256
Therefore, the [tex]\alpha[/tex] for the test procedure that rejects the null hypothesis when [tex]z\leq -2.8[/tex] is 0.0026.
D) For alternate hypothesis,
[tex]\rm \beta (\mu') = P(X>\mu_0-z_1_-_\alpha \frac{\sigma}{\sqrt{n} }|\mu')[/tex]
[tex]\rm = P(-z_1_-_\alpha +\dfrac{\mu_0-\mu'}{\dfrac{\sigma}{\sqrt{n} }})[/tex]
For [tex]\alpha[/tex] = 0.0026
[tex]\rm \beta (70)=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{25} }})[/tex]
[tex]\rm \beta (70) = 1-P(-2.7949+3.5714)=1-P(0.7765)[/tex]
[tex]\beta (70)=1-0.78128\approx 0.2187[/tex]
E) Now we want n when
[tex]\beta (70) = 0.01[/tex]
[tex]\rm 0.01=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{n} }})[/tex]
[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=0.99[/tex]
[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=P(2.3262)[/tex]
[tex]-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }}=2.3262[/tex]
[tex]\rm \sqrt{n} = 7.1695[/tex]
n = 51.4
Therefore we need n = 52.
F)
[tex]\rm p-value = P(\bar{X}\leq \bar{x})[/tex]
[tex]\rm p-value = P(\bar{X}\leq 72.3)=P(z\leq \dfrac{72.3-76}{\dfrac{7}{5}})[/tex]
[tex]\rm p-value = P(z\leq -2.643)[/tex]
[tex]\rm p-value = 0.00411[/tex]
Since p-value is larger that .01 therefore we fail to reject [tex]\mu[/tex] = 76.
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What are the sine, cosine, and tangent of 5 pi over 4 radians?
Answer:
[tex]\sin\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]
[tex]\cos\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]
[tex]\tan\dfrac{5\pi}{4}=1[/tex]
Step-by-step explanation:
Given : [tex]\theta =\dfrac{5\pi}{4}[/tex]
The angle is on radian.
We need to find the sine, cosine and tangent.
[tex]\sin\theta =\sin(\frac{5\pi}{4}[/tex]
[tex]\sin\theta =\sin(\pi+\frac{\pi}{4}[/tex]
[tex]\sin\theta =-\sin(\frac{\pi}{4}[/tex] [tex]\because \sin(\pi+\theta)=-\sin\theta[/tex]
[tex]\sin\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]
[tex]\cos\theta =\cos(\frac{5\pi}{4}[/tex]
[tex]\cos\theta =\cos(\pi+\frac{\pi}{4}[/tex]
[tex]\cos\theta =-\cos(\frac{\pi}{4}[/tex] [tex]\because \cos(\pi+\theta)=-\cos\theta[/tex]
[tex]\cos\dfrac{5\pi}{4}=-\dfrac{1}{\sqrt{2}}[/tex]
[tex]\tan\theta =\tan(\frac{5\pi}{4}[/tex]
[tex]\tan\theta =\tan(\pi+\frac{\pi}{4}[/tex]
[tex]\tan\theta =\tan(\frac{\pi}{4}[/tex] [tex]\because \tan(\pi+\theta)=\tan\theta[/tex]
[tex]\tan\dfrac{5\pi}{4}=1[/tex]
Ella has three flower beds each has four rows of flowers in it if there are 24 flowers in each row how many flowers are there in all
What is 888 rounded to the nearest ten?
Which graph represents the inequality y<−1+2x?
Answer:
bottom left
Step-by-step explanation:
About 4/5 of all orange juice in the world is produced in Brazil. About what percent of all the orange juice in the world is produced in Brazil?
What inequality represents the graph?
The inequality that represents the graph is y < x.
Explanation:The inequality that represents the graph is y < x. This inequality represents the region below the line that forms the graph. In this case, the line starts at the origin and has a slope of 1, meaning that for every increase of 1 unit on the x-axis, the y-coordinate increases by 1 unit as well.
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Use distributive property
Question 1. 2f+10
Question 2. 20+24g
Question 3. 32b - 20
simplify the expression
Question 4. 24h + 3d - 10hn+ 8d
Question 5. 12s + 4 + 4s - 2
The solutions for the disruptive property are,
2f+10 = 2 (f + 5)
20+24g = 4(5 + 6g)
32b - 20 = 8(4b - 5)
The solution to the expressions is,
E = 24h -10hn +11d
E = 16s + 2
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The solution of the equations by using distributive property,
2f+10 = 2 (f + 5)
20+24g = 4(5 + 6g)
32b - 20 = 8(4b - 5)
Simplify the expression
E = 24h + 3d - 10hn+ 8d
E = 24h -10hn +11d
The solution of the second expression is,
E = 12s + 4 + 4s - 2
E = 16s + 2
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manual travel 2 hours non-stop to Mexico a total of 90 miles. He took a train part of the way, which averaged 60 mph, and then took a bus the remaining distance, which averaged 30mph. How long was Manuel on the train?