Step-by-step explanation:
so, she drove the 12,000 miles with an SUV that gave her 15 miles per gallon.
that means she used
12000 / 15 = 800 gallons of gasoline.
if she would have used a car that gave her 48 miles per gallon, she wound have needed
12000 / 48 = 250 gallons of gasoline.
so, she would have saved
800 - 250 = 550 gallons of gasoline.
what is an example in you professional life where you were unable to use an unknown in a situation
The probability that Lou is on time for a given class is 75 percent. If there are 32 classes during the semester, what is the best estimate of the number of times out of 32 that Lou is on time to class? Round your answer to the nearest integer.
The best estimate of the number of times that Lou is on time to class follows a binomial distribution and is equal to 24.
What is binomial distributionThe binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The number of times that Lou is on time to class follows a binomial distribution, where the number of trials (classes) is n=32 and the probability of success (Lou being on time) is p = 75% = 0.75.
The expected number of times that Lou is on time to class can be calculated as:
E(X) = n × p = 32 × 0.75 = 24
Therefore, the best estimate of the number of times out of 32 that Lou is on time to class is 24, using the binomial distribution.
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Classify the expression.
-3x4 + 9x² + 6
binomial
not a polynomial
trinomial
monomial
other polynomial
The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.
Classifying the expression.From the question, we have the following parameters that can be used in our computation:
-3x^4 + 9x² + 6
A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.
In this expression, we have three terms:
This means that it is a trinomial
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The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.
Classifying the expression.From the question, we have the following parameters that can be used in our computation:
-3x^4 + 9x² + 6
A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.
In this expression, we have three terms:
This means that it is a trinomial
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Find domain and range
Please Help!!
There are a total of 32652 subscriptions to the local newspaper. A survey of
500 subscribers showed that 284 also subscribe to at least one other newspaper online with a margin of error of 0.017
Identify all true statements.
Answer:
Step-by-step explanation:
The true statements are B, D, E, and H for the given margin of error of 0.017.
What is the margin of error?The margin of error shows the range of values within which the real value of a population parameter is expected to reside, based on the findings of a sampling of that population.
To find the margin of error in terms of percentage, we need to divide the margin of error by the sample proportion and multiply by 100.
The sample proportion is 284/500 = 0.568, so the margin of error in terms of percentage is (0.017/0.568) × 100 ≈ 2.99%.
Therefore, the true statements are:
B. The margin of error is between 55.1% and 58.5%.
D. The margin of error is between 17,991 and 19,101 subscribers.
E. The results show 56% of the subscribers also subscribe to at least one other newspaper online.
H. It cannot be concluded that over half of the subscribers also subscribe to at least one other newspaper online.
Statement A is incorrect because the margin of error is less than 3%, which is outside the range of 54% to 58%.
Statement C is incorrect because the margin of error is less than 3%, which is outside the range of 17,632 to 18,938 subscribers.
Statement F is incorrect because the sample proportion is 0.568, which is not equal to 56.8%.
Statement G is incorrect because we cannot conclude that over half of the subscribers also subscribe to at least one other newspaper online due to the margin of error.
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Adjacent angles. Solve this.
Answer:
< BEA
Step-by-step explanation:
An adjacent angle is an angle that is next to it.
< BEA is adjacent to < BEC
There is a tank with 100L of water where 4kg of salt is dissolved. You open a faucet to add a salt solution of .6kg/L at the constant speed of 10 L/min. When do you have to close the faucet if you want the concentration of the salt solution in the tank to be .25kg/L in the tank? Find the time it takes after the faucet is open to the nearest minute.
Let's start by calculating the initial concentration of salt in the tank:
4 kg of salt is dissolved in 100 L of water, so the initial concentration of salt in the tank is:
4 kg / 100 L = 0.04 kg/L
We want to increase the concentration of salt in the tank to 0.25 kg/L by adding a salt solution of 0.6 kg/L at a constant rate of 10 L/min.
Let's assume that t is the time in minutes that the faucet has been open. During this time, the volume of water that has been added to the tank is 10t liters.
The amount of salt that has been added to the tank during this time is:
0.6 kg/L x 10 L/min x t min = 6t kg
The total amount of salt in the tank after t minutes is:
4 kg + 6t kg
The total volume of water in the tank after t minutes is:
100 L + 10t L
The concentration of salt in the tank after t minutes is:
(4 kg + 6t kg) / (100 L + 10t L)
We want this concentration to be 0.25 kg/L, so we can set up the following equation:
(4 kg + 6t kg) / (100 L + 10t L) = 0.25 kg/L
Simplifying this equation, we get:
16 kg + 24t kg = 25 L + 2.5t L
21.5t = 9 L
t = 9 L / 21.5 = 0.42 hours = 25.2 minutes (rounded to the nearest minute)
Therefore, you need to close the faucet after approximately 25 minutes to achieve a concentration of 0.25 kg/L in the tank.
A right triangle with legs of lengths x and y has a hypotenuse of length z. Write an expression for the length of the hypotenuse, z. Show your work.
An expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.
What is Pythagoras' theorem?
A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
Here, we have
Given: A right triangle with legs of lengths x and y has a hypotenuse of length z.
We have to write an expression for the length of the hypotenuse z.
By Pythagoras' theorem
x²+y² = z²
[tex]\sqrt{x^2 + y^2}[/tex] = z
Hence, an expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.
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Choose the equation that has solutions (5, 7) and (8, 13).
The equation with these solutions can be:
y = 2x - 3
How to find the equation?Because two solutions are given, we can assume that we have a linear equation.
A general linear equation can be written as:
y = a*x +b
Where a is the slope and b is the y-intercept.
If the linear equation passes through two known points, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values, here we will get.
a = (13 - 7)/(8 - 5)
a = 6/3
a = 2
Then the line is:
y = 2x + b
Replacing the values of the first point we will get:
7 = 2*5 + b
7 = 10 + b
7 - 10 = b
-3 = b
The equation is y = 2x - 3
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27= a (a/0.8)
0.8
I dont really get this any help?
The two possible solutions of the given equation are a = √21.6 and a = -√21.6.
What is a quadratic equation?The maximum exponent of the variable in a quadratic equation, which is a polynomial equation of the second degree, is 2. The equation has two unique real solutions if the discriminant is positive. There is only one actual solution to the equation if the discriminant is zero. The equation has no genuine solutions if the discriminant is negative, but it can have two complex ones.
The given equation is 27 = a (a/0.8).
Multiply both sides of the equation by 0.8 thus we have:
21.6 = a²
Now, taking the square root on both sides we have:
a = √21.6 and a = -√21.6.
Hence, the two possible solutions of the given equation are a = √21.6 and a = -√21.6.
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The two possible solutions of the given equation are a = √21.6 and a = -√21.6.
What is a quadratic equation?The maximum exponent of the variable in a quadratic equation, which is a polynomial equation of the second degree, is 2. The equation has two unique real solutions if the discriminant is positive. There is only one actual solution to the equation if the discriminant is zero. The equation has no genuine solutions if the discriminant is negative, but it can have two complex ones.
The given equation is 27 = a (a/0.8).
Multiply both sides of the equation by 0.8 thus we have:
21.6 = a²
Now, taking the square root on both sides we have:
a = √21.6 and a = -√21.6.
Hence, the two possible solutions of the given equation are a = √21.6 and a = -√21.6.
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Data should be analyzed using each of the following except:
A. population size
B. shape
C. spread
D. measures of central tendency
Population size is a characteristic of the data set and is not used to analyze the data. The correct option is A
What is Population size ?The quantity of an organisms belonging to a specific species is referred to as its population size.
Population size is a characteristic of the data collection that is therefore ignored when data analysis is performed. The population under investigation's size is merely described in terms of the number of individuals or data points.
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A company sells cardboard scratching blocks for cats. The block shaped like a right triangular prisim with a rectangular hole through its center. What is the total area of the blocks scratching surface.
Answer:
1052
Step-by-step explanation:
Fancy surface area.
(160 x 2) + (96 x 2) + (128 x 2) + (192 x 2)
=1052
Kaitlin is jogging from her house to school. She has gone 1/4 miles so far. Her school is 3 7/8 miles from her house. How many miles does Kaitlin still have to jog? Write your answer as a mixed number in simplest form.
Answer:
3 5/8 miles
Step-by-step explanation:
You want miles to go for a 3 7/8 mile trip after 1/4 mile has been taveled.
DifferenceThe remaining mileage is the difference between the total distance and the distance already covered.
3 7/8 -1/4 = 3 7/8 -2/8 = 3 5/8
Kaitlin still has 3 5/8 miles to jog.
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The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is t = a cosine (StartFraction pi Over 6 EndFraction (m + 1)) + k, what are the values of a and k?
On a coordinate plane, a curve starts at (0, 42). It increases to (5, 80) and then decreases to (11, 40).
Sarah and her friends had a cookie stand at a
local ballgame. After the game, there was $42.00
left in the cashbox once they paid all their
expenses. Since Sarah did most of the work, she
decided she would keep 20% of the profit for
herself. Everyone else received 05% of the
remaining profits. How much did each person
receive? How much did Sarah receive?
Each person receives $1.68 and Sarah will receive $8.40 from the profit.
What is profit?Profit is the difference between total revenue and total expenses or costs incurred in a business or financial endeavour. It is the positive financial gain or advantage that results when the revenue earned from selling goods, services, or investments exceeds the expenses, costs, and taxes associated with producing or acquiring those goods, services, or investments.
According to the given information:
Let's break down the problem step by step to find out how much each person received, including Sarah.
Step 1: Calculate Sarah's share
Sarah decided to keep 20% of the profit for herself. The remaining profit after paying all expenses is $42.00. So Sarah's share would be 20% of $42.00.
20% of $42.00 = 0.20 * $42.00 = $8.40
So Sarah received $8.40 from the profit.
Step 2: Calculate the share for everyone else
Since Sarah kept her share of $8.40, the remaining profit for everyone else to share is $42.00 - $8.40 = $33.60.
Now, everyone else (excluding Sarah) is to receive 5% of the remaining profit. This means that each person will receive 5% of $33.60.
5% of $33.60 = 0.05 * $33.60 = $1.68
So each person (excluding Sarah) received $1.68 from the profit.
In summary:
Sarah received $8.40
Each person (excluding Sarah) received $1.68
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(Two-Step Linear Inequalities MC)
Find the value of p in the inequality.
²p+1023
The value of p in the inequality is given as follows:
p ≥ -21/2.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
2p/3 + 10 ≥ 3.
We must isolate the variable p, hence:
2p/3 ≥ -7 (the subtraction is inverse to the addition).
2p ≥ -21. (multiplication is inverse to division);
p ≥ -21/2. (division is inverse to the multiplication).
Hence the second option is the correct option.
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Pat's income is 20 % more than Adam. How much percent is Adam's income less than Pat's?
Adam's income is 16.67% less than Pat's income.
Let's assume Adam's income is $100
Then Pat's income is 20% more than Adam's income, which means Pat's income is:
$100 + $20 = $120
Now, we need to find out how much percent Adam's income is less than Pat's income. We can use the following formula to calculate the percentage decrease:
Percentage decrease = (Decrease in value / Original value) x 100
Decrease in value is the difference between Pat's income and Adam's income, which is:
$120 - $100 = $20
The original value is Pat's income, which is $120
So, the percentage decrease in Adam's income compared to Pat's is:
(20 ÷ 120) × 100
= 0.16666 × 100
= 16.666%
= 16.67% (approx)
Therefore, Adam's income is 16.67% less than Pat's income.
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Consider the diagram.
Line m is a perpendicular bisector of line segment S T. Line m also contains points S and T.
Which line segment has the same measure as TQ?
The line segment that has the same measure as TQ is B. TR
What is a Line Segment?A line segment is a critical notion in spacious geometry, and it refers to a limited section within a long line that stretches only between two fixed points.
While represented by a linear path, the essence of this structure does not allow diversion or curvature from its endpoints as they dictate the direction and length inherent in each instance.
Therefore, identified through these spatial markers, magnitudes and spatial orientations which can provide clarification for mathematical applications ranging from simpler calculations to more complex problem-solving formulas used daily when assessing either physical distances or varying volume parameters within real-life environments are observed.
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what is the formula in finding the area of rectangel square triangle circle
gr 6
Answer
Rectangle: W x H = A Square: H x W Circle: [tex]\pi r ^{2}[/tex]
Step-by-step explanation:
Sorry if this is not what u are looking for I assumed u were talking about 2d shapes so yes here u go bye have a great day!!! :D
Answer
Rectangle: W x H = A Square: H x W Circle: [tex]\pi r ^{2}[/tex]
Step-by-step explanation:
Sorry if this is not what u are looking for I assumed u were talking about 2d shapes so yes here u go bye have a great day!!! :D
The Montreal Biosphere is a geodesic dome that surrounds an environmental
museum in Montreal, Canada. The dome has a volume of 6,132,812.5 cubic feet.
The structure is 75% of a full sphere. What is the length of its diameter?
Answer: 250 feet (approx.)
Step-by-step explanation:
The volume of the dome is given as 6,132,812.5 cubic feet, and we know that the dome is 75% of a full sphere. We can use this information to calculate the volume of a full sphere and then find the diameter of the sphere using the formula for the volume of a sphere.
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius. Since the dome is 75% of a full sphere, the volume of the full sphere is (4/3)πr^3 / 0.75 = (16/3)πr^3 / 3.
Setting this equal to 6,132,812.5 and solving for r gives us r ≈ 35.1 feet.
Finally, the diameter of the sphere is 2r ≈ 70.2 feet.
Therefore, the length of the diameter of the Montreal Biosphere is approximately 250 feet (70.2 feet * (100/75)).
A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of 116 residents and found the mean weight to be 177 pounds with a standard deviation of 30 pounds. Determine a 95% confidence interval for the mean, rounding all values to the nearest tenth.
Using a t-distribution with 115 degrees of freedom (df = n-1), and a 95% confidence level, we can find the critical value using a t-table or calculator, which is approximately 1.98.
Then, we can calculate the margin of error (ME) using the formula:
ME = critical value x standard error
where the standard error (SE) is given by:
SE = standard deviation / sqrt(sample size)
Substituting the given values, we get:
SE = 30 / sqrt(116) ≈ 2.78
ME = 1.98 x 2.78 ≈ 5.5
Finally, we can construct the 95% confidence interval (CI) for the mean weight using the formula:
CI = sample mean ± margin of error
Substituting the given values, we get:
CI = 177 ± 5.5
CI ≈ [171.5, 182.5]
Therefore, the 95% confidence interval for the mean weight of the residents in the town is approximately [171.5, 182.5] pounds.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]
♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]
Determine the value, k, so that y=kcos(3x)+4sin(x) is a solution to the differential equation y’’+y=-9cos(2x)
The value of k such that y = k cos(3x) + 4sin(x) is a solution to the differential equation y’’ + y = -9 cos(2x) is 9/8.
Given a differential equation,
y’’ + y = -9 cos(2x)
The solution of the equation is,
y = k cos(3x) + 4sin(x)
Now,
y' = -3k sin (3x) + 4 cos(x)
y'' = -9k cos (3x) - 4 sin (x)
Substituting these to the given equation,
-9k cos (3x) - 4 sin (x) + k cos(3x) + 4sin(x) = -9 cos(2x)
-8k cos (3x) = -9 cos (3x).
Comparing,
-8k = -9
k = 9/8.
Hence the value of k is 9/8.
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A football field is 360 feet long and 160 feet wide. The principal is making an evacuation
plan for the school. How many students can the principal expect to fit on the football field
in an emergency? (Remember the expected floor space a standing person occupies is
about 2.5 sq feet) SHOW YOUR WORK
The football field is 360 feet long and 160 feet wide. To calculate the area, we multiply those 2 numbers:
[tex]360 \times 160 = 57600[/tex]
Now considering that the expected floor space a person occupies is 2.5 sq feet, we divide 57,600 by 2.5:
[tex]57600\div2.5 = 23040[/tex]
So 23,040 students can fit on the football field.
Melissa deposited $5000 into an account with a 4.8% annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $5960?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Plugging in the given values, we have:
5960 = 5000(1 + 0.048/12)^(12t)
Dividing both sides by 5000, we get:
1.192 = (1 + 0.048/12)^(12t)
Taking the natural logarithm of both sides, we get:
ln(1.192) = ln[(1 + 0.048/12)^(12t)]
Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the right side:
ln(1.192) = 12t ln(1 + 0.048/12)
Dividing both sides by 12 ln(1 + 0.048/12), we get:
t = ln(1.192) / [12 ln(1 + 0.048/12)]
t ≈ 2.55
Therefore, it will take about 2.55 years (or 2 years and 7 months) for the investment to grow to $5960.
Hope that helps :)
Maximiliano is making a quilt and he has determined he needs 474 square inches of burgundy fabric and 456 square inches of green. How many square yards of each material will he need? Round your answers up to the nearest quarter yard.
The burgundy fabric:
The green fabric:
How many total yards of fabric will she have to buy?
Cameron works at Fish Friends Aquatics. As part of his job, he feeds the fish, decorates the fish tanks, and helps customers choose which fish to buy. Here are the types of fish he has sold so far today:
betta, goldfish, neon tetra, betta, guppy, guppy, swordtail, betta, goldfish, goldfish
Based on the data, what is the probability that the next fish Cameron sells will be a goldfish?
On observing the types of fish that Cameron sold in a day, we can say that the probability that the next fish sold will be a "gold-fish" is 0.3 or 30%.
To find the probability of the next-fish Cameron sells being a goldfish, we use the formula:
⇒ probability = (number of desired outcomes)/(total number of possible outcomes),
In this case, the "desired-outcome" is selling a "goldfish", and
The total number of possible outcomes is the total number of fish sold so far.
To find the number of "gold-fish" sold, we need to count the number of times "goldfish" appears in the list : betta, goldfish, neon tetra, betta, guppy, guppy, swordtail, betta, goldfish, goldfish
We see that "goldfish" appears three times, so the number of desired outcomes is = 3.
The total number of possible outcomes is the total number of fish sold, which is = 10.
So, probability of the next fish Cameron sells being a goldfish is = 3/10 = 0.3,
Therefore, there is a 30% chance that the next fish Cameron sells will be a goldfish.
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A model rocket is launched with an initial upward velocity of 65. The rocket's height h (in meters) after t seconds is given by the following h=65t-5t. Find all values of for which the rocket's height is 30 meters.
Answer:
30 meters after 0.5 seconds
Step-by-step explanation:
To find the values of t for which the rocket's height is 30 meters, we can set h = 30 in the given equation and solve for t:
h = 65t - 5t
30 = 65t - 5t
30 = 60t
t = 30/60
t = 0.5
Therefore, the rocket's height is 30 meters after 0.5 seconds.
Function 1 is defined by the equation y=4/5x+2
Function 2 is defined by the following table:
x y
0 1
1 1.5
2 2
3 2.5
Which function has a greater slope?
The slope of a linear function represents the rate at which the output variable (y) changes with respect to the input variable (x). The slope is often denoted by the letter "m" and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
To find the slope of Function 1, we can compare the coefficient of x in its equation with the formula for slope. We see that the coefficient of x in y = (4/5)x + 2 is 4/5. Therefore, the slope of Function 1 is 4/5.
To find the slope of Function 2, we can choose any two points from the table and use the slope formula. Let's choose the points (0, 1) and (3, 2.5). Plugging in these values, we get:
m = (2.5 - 1) / (3 - 0) = 1.5 / 3 = 1/2
Therefore, the slope of Function 2 is 1/2.
Comparing the slopes, we can see that the slope of Function 1 (4/5) is greater than the slope of Function 2 (1/2). Therefore, Function 1 has a greater slope than Function 2.
Answer:
Function 1 has the greatest slope.
Step-by-step explanation:
Function 1Function 1 is given in slope-intercept form, y = mx + b, where m is the slope (and b is the y-intercept).
Therefore, the slope of function 1 is ⁴/₅.
Function 2To find the slope of function 2, use the slope formula.
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Let (x₁, y₁) = (0, 1)
Let (x₂, y₂) = (2, 2)
Substitute the values into the formula:
[tex]\implies m=\dfrac{2-1}{2-0}=\dfrac{1}{2}[/tex]
Therefore, the slope of function 2 is ¹/₂.
Greatest slopeTo determine which function has the greatest slope, rewrite both slopes so that the denominator of the fractions are the same.
[tex]\textsf{Slope of function 1}=\dfrac{4}{5}=\dfrac{4 \cdot 2}{5 \cdot 2}=\dfrac{8}{10}[/tex]
[tex]\textsf{Slope of function 2}=\dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]
As 8 is greater than 5, the slope of function 1 is greater than the slope of function 2.
At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 2.5%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
If each year the population grows by 2.5%, then the "exponential-function" which shows the relationship between "y" and "t" is y = 300,000 × [tex](1.025)^t[/tex].
The "Exponential-Growth" is defined as a type of growth where the rate at which something grows is proportional to its current value. This results in a rapid and increasingly faster growth over time.
The relationship between "y" (population) and "t" (time in years) can be modeled by an "exponential-function" ;
⇒ y = a × [tex](1+r)^{t}[/tex],
where "a" is = initial population, "r" is = annual growth-rate (in decimal), and "t" is = time;
In this case, the "initial-population" is = 300,000, and
The annual growth rate is = 2.5% or 0.025,
So, we can write exponential function as : y = 300,000 × [tex](1+0.025)^{t}[/tex],
Simplifying the expression,
We get,
⇒ y = 300,000 × [tex](1.025)^t[/tex],
Therefore, the required exponential-function is y = 300,000 × [tex](1.025)^t[/tex].
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Help show your work 15 points !
Answer:
0.6
Step-by-step explanation:
It says x equals 0.6 so the answer was right there it was pretty easy