The amount of gas Karen has and the amount Karen needed to put into her boat obtained using basic arithmetic operations are;
Yes, Karen had enough gas available for both daysKaren needed to put a total of 69 quarts of gas into her boatWhat are basic arithmetic operations?Basic arithmetic operations include addition, subtraction, division and multiplication operations.
The amount of gas Karen has can be found using basic arithmetic operations as follows;
On Monday, Karen needed to put 5 gallons 3 quarts of gas into her boat. Since 1 gallon is equal to 4 quarts, this is equivalent to (5 × 4 + 3) = 23 quarts of gas
On Saturday, she needed to put twice as much gas into her boat as she did on Monday. So on Saturday she needed to put (2 × 23) = 46 quarts of gas into her boat.
In total, Karen needed to put (23 + 43) = 69 quarts of gas into her boat over both days.Since, Karen had 18 gallon jug of gas available and 1 gallon is equal to 4 quarts, this mean she had (18 × 4) = 72 quarts of gas available.
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The volume of air in a person's lungs can be modeled with a periodic function,
V (t) = 500 cos ( ² (t – 0.25)) + 1500, where V represents the volume of air, in
mL, in a person's lungs and time t is measured in seconds.
What is the midline and what does it represent in this
context?.
The midline is 1500. The midline in this context represents the average volume of air in a person's lungs over a period of time.
What is the midline and what does it represent in this context?The midline of a periodic function is the horizontal line that passes through the middle of the function's range.
For a function of the form V(t) = A cos(B(t - C)) + D, the midline is given by the equation y = D, which represents the average value of the function over a period.
In this case, the function is V(t) = 500 cos(²(t - 0.25)) + 1500, so the midline is given by the equation:
y = 1500
This represents the average volume of air in a person's lungs over a period of time.
Since the cosine function oscillates between -1 and 1, the actual volume of air in the person's lungs will oscillate around the midline, between 1500 - 500 = 1000 mL and 1500 + 500 = 2000 mL.
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Find the equation of L
[tex]y=\frac{7}{2.4} x-6[/tex] ; if estimated then : [tex]y=\frac{7}{2.5} x-6[/tex]
Explination:
Y-intercept is -6, (0,-6)
The rise over run it [tex]\frac{7}{2.4} x[/tex]. The denominator is 2.4 because it nearly 2.5.
Jeriel is going to invest in an account paying an interest rate of 6.5% compounded continuously. How much would Jeriel need to invest, to the nearest cent, for the value of the account to reach $137,000 in 5 years?
Jeriel would need to invest approximately $98,986.25 for the value of the account to reach $137,000 in 5 years, assuming continuous compounding.
How much would Jeriel need to invest for the account to reach the accrued amount?The formula accrued amount compounded continuously is expressed as;
A = P × e^(rt)
Where A is accrued amount, P is principal, r is interest rate and t is time.
In this case, we are given that the final amount to be $137,000, the interest rate is 6.5% and the time is 5 years.
We want to solve for Principal P.
First, convert R as a percent to r as a decimal
r = R/100
r = 6.5/100
r = 0.065 per year
Plug these values into the above formula and solve for P.
A = P × e^(rt)
P = A / e^(rt)
P = 137,000.00 / e^(0.065 × 5)
p = $98,986.25
Therefore, the value of the principal P is $98,986.25.
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DUCK is a rectangle. Solve:
X=
UDK=
For the rectangle, the value x will be 14 and angle UDK will be 35°.
What exactly is a rectangle?
A rectangle is a four-sided polygon with four right angles (90-degree angles). It has opposite sides that are equal in length and parallel to each other. The rectangle is a special case of a parallelogram, where the opposite sides are also parallel. The two sides that are equal in length are called the "width" or "short side", while the other two sides are called the "length" or "long side". The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding the lengths of all four sides.
Now,
As we know all angles of a triangle are 90°.
then 5x-15+2x+7=90
7x=98
x=14
and in triangle UDK
sum of all angles = 180°
∠UDK+90+5x-15=180
∠UDK=180-145
∠UDK=35°
Hence,
the value x will be 14 and angle UDK will be 35°.
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what did one dog say to the other dog
Answer: I like "Hot Dogs"?
Step-by-step explanation:
Eric owns and operates the Hot Ham food truck. The expression 3. 25b+2h3. 25b+2h3, point, 25, b, plus, 2, h gives the cost of bbb burgers and hhh hot dogs. What is the cost of 444 burgers and 666 hot dogs?
\$
As per the expression, the cost of 444 burgers and 666 hot dogs from Eric's Hot Ham food truck would be $2773.
In this case, Eric's expression is 3.25b + 2h, where b represents the number of burgers and h represents the number of hot dogs. The expression tells us how much it costs to buy a certain number of burgers and hot dogs from Eric's truck.
To find the cost of 444 burgers and 666 hot dogs, we can substitute b = 444 and h = 666 into the expression. So the cost would be:
3.25(444) + 2(666)
Now we just need to simplify this expression by using the order of operations.
First, we multiply 3.25 by 444 to get 1441. Then, we multiply 2 by 666 to get 1332.
Next, we add these two values together:
1441 + 1332 = 2773
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: 2 points Which of the following is NOT an example of a human activity that directly threatens the biodiversity of species? o the picking of flowers o the overexploitation of resources o the introduction of invasive species o the destruction of habitats o the burning of fossils fuels Previous
The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.
The burning of fossil fuels is not an example of a human activity that directly threatens the biodiversity of species. While burning fossil fuels can contribute to climate change, which can have indirect impacts on biodiversity, such as changing habitats or altering migration patterns, it is not a direct threat to individual species or their populations.
On the other hand, the picking of flowers, overexploitation of resources, introduction of invasive species, and destruction of habitats are all examples of human activities that directly threaten the biodiversity of species. For example, overexploitation of resources such as fishing can lead to the depletion of fish populations, while the introduction of invasive species can outcompete and displace native species. The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.
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To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtain [Cr^3+]=0.03933 M. Calculate the %Cr in the complex.
the %Cr in the complex is 26.294%.
To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtained [Cr3+]=0.03933 M. Calculate the %Cr in the complex.
To determine the % Cr in the chromium-complex synthesized by Legna, we can use the following formula:% Cr = (mass of Cr/mass of sample) x 100We have the mass of the sample, which is 1.0240 g. We need to find the mass of Cr in the sample. To do this, we need to find the number of moles of Cr in the solution, and then use the molar mass of Cr to convert this to mass.
The concentration of Cr3+ in the solution is given as 0.03933 M. We know that the complex is made up of Cr and some other ligands, and the concentration of Cr3+ is not the same as the concentration of Cr in the complex. To find the concentration of Cr in the complex, we need to use the formula:[Cr] = [Cr3+] x (1/x), where x is the number of moles of Cr3+ in the complex.
Let's assume that there is one mole of Cr3+ in the complex, then x = 1. If there are n moles of Cr3+ in the complex, then x = n. We can find x by using the formula:x = (mass of sample/Mr of Cr3+) x [Cr3+]/volume of solutionWe know that the mass of the sample is 1.0240 g, and the volume of the solution is 100.0 mL = 0.1000 L. The molar mass of Cr3+ is 52.00 g/mol. Substituting these values into the formula, we get:x = (1.0240/52.00) x 0.03933/0.1000x = 0.000761 moles of Cr3+ in the complex
Now we can use the formula [Cr] = [Cr3+] x (1/x) to find the concentration of Cr in the complex:[Cr] = 0.03933/0.000761[Cr] = 51.69 M
Finally, we can use the formula:% Cr = (mass of Cr/mass of sample) x 100The molar mass of Cr is 52.00 g/mol. The mass of Cr in the complex is 51.69 x 52.00 = 2689.88 g/mol. Substituting this value and the mass of the sample (1.0240 g) into the formula, we get:% Cr = (2689.88/1.0240) x 100% Cr = 262944.53% Cr = 26.294%
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help pls its too much
Answer:
24.13
Step-by-step explanation:
Given that x = (5,-5) and y = (8,-3), find x•y
If x = (5,-5) and y = (8,-3), x•y is: 55.
How to find the vectors?The dot product (also called scalar product or inner product) of two vectors x = (x1, x2) and y = (y1, y2) is given by:
x•y = x1y1 + x2y2
Using the coordinates of the given vectors:
x = (5, -5)
y = (8, -3)
x•y = (5)(8) + (-5)(-3) = 40 + 15 = 55
Therefore, x•y = 55.
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i need some help please
Answer: 4
Step-by-step explanation:
Given when y = 2, x = -2
Therefore 2 = -2 + ?
? = 2 + 2
? = 4
help
I need this asap
Answer: natural number=11
integer= -4
irrational= pi, 0.1010010001.....,root 5
rational= 0.1212...., -3/5,0.3,2 1/4
Step-by-step explanation:
a laptop has a listed price of 882.99 before tax. if the sales tax rate is 6.25% , find the total cost of the laptop with sales tax included. round your answer to the nearest cent, as necessary.
The total cost of the laptop with the sales tax included is 938.18.
The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:
Total Cost = Original Price + (Original Price * Sales Tax Rate)
In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:
Total Cost = 882.99 + (882.99 * 0.0625)
Total Cost = 882.99 + 55.19
Total Cost = 938.18
Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.
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you randomly select 15 cards from a deck of 52 cards. what is the probability that it contains exactly one queen given that it contains exactly two aces?
The probability that the 15 cards contain exactly one queen given that they contain exactly two aces is approximately 0.060 or 6.0%.
We can use conditional probability. Let A be the event that the 15 cards contain exactly two aces, and B be the event that they contain exactly one queen. Then we want to find the conditional probability P(B|A).
First, let's find the probability of A. There are C(4,2) ways to choose the two aces out of four, and C(48,13) ways to choose the other 13 cards out of the remaining 48 cards. So the total number of ways to choose 15 cards with exactly two aces is:
C(4,2) × C(48,13) ≈ 4.57 × 10^12
Next, let's find the probability of both A and B. There are C(4,2) ways to choose the two aces out of four, C(4,1) ways to choose one queen out of four, and C(47,12) ways to choose the other 12 cards out of the remaining 47 cards. So the total number of ways to choose 15 cards with exactly one queen and exactly two aces is:
C(4,2) × C(4,1) × C(47,12) ≈ 2.76 × 10^11
Finally, we can use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
P(B|A) = (C(4,2) × C(4,1) × C(47,12)) / (C(4,2) × C(48,13))
P(B|A) ≈ 0.060
Therefore, the probability is approximately 0.060 or 6.0%.
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A researcher found a study relating the distance a driver can see, y, to the age of the driver, When researchers looked at the association of x and y, they found that the coefficient of determination was =0.542. Select two conclusions that the researcher can make from this data. a.) The correlation coefficient, t, is-0 458. b.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. O c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see O d.) The correlation coefficient, t.is -0736. e.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. 1.) The correlation coeficient 0 271 A data set was grapned using a scatterpion 30 25 20 15 10 5 0 0 5 10 15 20 25 30 The correlation coefficient, r, is 0.813 Which of the following statements explains how the correlation is http/phoenix.sophia.org/tutorials/cautions-about-correlation-2/download ndf The correlation coefficient, r, is 0.813. Which of the following statements explains how the correlation is affected? O a.) It is affected by inappropriate grouping. O b.) It is not affected. c.) It is affected by an influential point. d.) It is affected by non-linearity. SUBMIT MY ANSWER Which of the following statements is TRUE? O a.) Low correlation implies causation b.) A high correlation means that the response variable is caused by the explanatory variable. O c.) High correlation does not always establish causation O d.) To imply causation, the correlation must be 1. SUBMIT MY ANSWER Javascriptvo do)
1)From the data:
Two conclusions that the researcher can make are:
b.) About 54% of the variation in the distance that the driver can see is explained by a linear relationship with the driver's age.
d.) The correlation coefficient, t, is -0.736. (This can be found by taking the square root of the coefficient of determination and considering the negative correlation)
2)"It is not affected" is the correct statement,that is option b
3)The "High correlation does not always establish causation" is the TRUE statement, that is option c .
What is Correlation?
Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.
A positive correlation indicates that as one variable increases, the other variable also increases.
A negative correlation indicates that as one variable increases, the other variable decreases. In other words, it shows the relationship between two variables and helps to understand if they are related or independent.
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how many feet are in 300.0 inches? type in your numerical answer only, do not include units. do not use scientific notation.
There are 25 feet in 300.0 inches.
What is conversion?Conversion is a numerical quantity that enables you to convert one unit to another. There are various units for measurements such as length, weight, mass, and so on.
The conversion factor between inches and feet is important to understand when performing this type of calculation. As I mentioned earlier, there are 12 inches in one foot, which can be expressed as:
1 foot = 12 inches
This means that to convert a measurement in inches to feet, we need to divide the number of inches by 12.
300.0/12 = 25
Therefore, 300.0 inches is equivalent to 25 feet.
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19. INVESTMENTS Kent invested $5000 in a retirement plan. He allocated x dollars of the money to a bond account
that earns 4% interest per year and the rest to a traditional account that earns 5% interest per year.
a. Write an expression that represents the amount of money invested in the traditional account.
b. Write a polynomial model in simplest form for the total amount of money T Kent has invested after one year.
(Hint: Each account has A + IA dollars, where A is the original amount in the account and I is its interest rate:)
c. If Kent put $500 in the bond account, how much money does he have in his retirement plan after one year?
Part a: Expression for conventional account: $(5000-x) at 5%pa.
Part b: polynomial model: T = 5250 - 0.01x
Part c: Sum of investments in retirement account: T= $5245.
Explain about the bond account?When they need to raise money, governments and businesses issue bonds.
a. Create an expression to show how much money is invested in the conventional account.
Back $(5000-x) at 5%pa
b. Construct a polynomial model in its simplest form to represent the entire sum of investments made by T. Kent after a year (possibility: thus every account has A + iA dollars, in Which a is the account's initial balance and I is the interest rate).
The bond will increase to after a year to : x + 0.04x
= x(1+0.04)
= 1.04x ...eq 1
So, after the time of one year this traditional account growth will be-
(5000-x) + 0.05(5000-x)
= 5000 - x + 0.05*5000 - 0.05x
= 5000 - x + 250 - 0.05x
= 5250 - 1.05x ..eq 2
From eq 1 and eq 2
T = 1.04x + 5250 - 1.05x
T = 5250 - 0.01x
c. If Kent invested $500 in bonds, how much will he have in the retirement account in a year?
x=500
T= 5250 - 0.01*500
T= 5250 - 5
T= $5245
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Find explicit formulas for sequences of the form a1, a2, a3, ... with the initial terms given
0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7
This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
Notice that the sequence alternates between positive and negative terms and that the denominators of each term increase by 1 while the numerators increase by 1 or -1. To find the explicit formula, we can write it in terms of its general form:
a1 = 0
a2 = -1/2
a3 = 2/3
a4 = -3/4
a5 = 4/5
a6 = -5/6
a7 = 6/7
We can see that the numerator of each term is equal to its index number, n, if n is even and equal to -n if n is odd. The denominator of each term is equal to n+1 for all terms.
Using this observation, we can write the explicit formula for the sequence as:
an = (-1)^(n+1) * n / (n+1)
where (-1)^(n+1) is equal to -1 if n is odd and 1 if n is even. This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
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suppose we decided to calculate a 95% confidence interval for this same data instead of a 99% confidence interval. how would this change the width of the interval?
If a 95% confidence interval is used instead of a 99% confidence interval, the width of the interval would decrease.
The reason behind this is that a 95% confidence interval is narrower than a 99% confidence interval, as it does not cover as much area as a 99% confidence interval. What is a confidence interval? The concept of a confidence interval (CI) is used in statistics to provide a range of values that may contain an unknown population parameter.
The term "confidence" implies that if the same population parameter were estimated from numerous samples and the confidence intervals calculated for each, the proportion of such intervals that contain the parameter would match the specified confidence level.
The width of the interval is based on the confidence level, sample size, and the data variability. When the confidence level increases, the width of the interval increases because the amount of uncertainty increases. In comparison, when the confidence level decreases, the interval width decreases because there is less uncertainty.
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The expected value of the number of points for one roll is:_____.a. 0 b. 1 c. 3 d. 6
Answer:
2023- answer is A-0
Step-by-step explanation:
suppose that iq scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17 . using the empirical rule, what percentage of iq scores are less than 79 ? please do not round your answer.
Suppose that IQ scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17. Using the empirical rule, 15.87 percentage of IQ scores are less than 79.
The empirical rule says that for a normal distribution, almost all of the data will fall within three standard deviations of the mean.
Specifically:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Almost all (99.7%) of the data falls within three standard deviations of the mean.
Given that the mean of IQ scores is 96 and the standard deviation is 17.
Hence the Z score can be calculated as
z=(x−μ)/σ=(79−96)/17=−1
From the standard normal distribution table, the percentage of the data that is less than z = -1 is 15.87%.
Hence the percentage of IQ scores that are less than 79 is approximately 15.87%.
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Korey and I have been working with a financial planner named Stephen for years. He's been so good to us in explaining things like retirement, high yield savings, life insurance and college planning. This last time that we met with Stephen he explained to us that our money for the kids college savings account could be modeled with an equation to help my math brain see the big picture.
Currently, our savings account for the kids college is modeled by A of x equals 20000 times 1.05 raised to the x minus 1 power .
He explained that with inflation that we really needed to have a steady increase in our savings to be able to pay for both kids college funds. Stephen suggested that we look at how much money we would have if we didn't deposit any more money in our savings account and just relied on the interest to build based on this equation. He gave us a random number of 5% for the interest rate as shown in the model above and x is the number of years.
A) Is this sequence arithmetic, geometric, or neither?
B) Break apart the equation -Tell me what each of those terms represent above in the A(x) equation.
C) How much money would we have if we only did interest on this account in 11 years when Kolton starts college?
SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!
Answer:
A) This sequence is geometric.
B) In the equation A(x) = 20000(1.05)^(x-1):
A(x) represents the amount of money in the savings account after x years.
20000 represents the initial amount of money in the savings account.
1.05 represents the interest rate, which is compounded annually.
(x-1) represents the number of compounding periods, which is one less than the number of years because the initial amount is not compounded.
C) To find out how much money we would have in the savings account in 11 years when Kolton starts college, we can substitute x = 11 into the equation and simplify:
A(11) = 20000(1.05)^(11-1)
A(11) = 20000(1.05)^10
A(11) ≈ 35,123.58
Therefore, if we only relied on the interest to build our savings for 11 years, we would have approximately $35,123.58 in the savings account when Kolton starts college. However, this amount may not be enough to cover the total cost of college, so it is important to continue making regular deposits to the savings account.
PLEASE HELP WITH EXPLANATION PLEASE PLEASE PLEASE NO SCAMMING FOR THE COINS OR I WILL REPORT YOU
The correct solutions for the given equation is given by table in option 3.
Explain about the solution of linear equation?A straight line is produced when a linear equation, which is a two-variable equation, is graphed. The intersection of corresponding values which satisfy the equation results in the line.
The variables x and y are most frequently used in linear equations, hence the associated values can be shown as (x,y) on the coordinate plane, pairs. A collection of two maybe more linear equations is known as a system of linear equations.
The given equation is-
y = x - 6
Put the value of 'x' from the options and check for 'y', if its correct.
The option are the solution of the equation.
option 1:
y = x - 6
x = --5
y = -5 - 6 = -11 (incorrect)
option 2:
y = x - 6
Put x = -8
y = -8 - 6 = -14 (incorrect)
option 3:
y = x - 6
Put x = -7
y = -7 - 6 = -13 (correct)
Thus, the correct solutions for the given linear equation is given by table in option 3.
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If g(x) = -3x - 4, find g(4) + 8
Answer:
Step-by-step explanation:
To find g(4), we substitute x = 4 into the expression for g(x):
g(4) = -3(4) - 4 = -12 - 4 = -16
To find g(4) + 8, we add 8 to the value we just found for g(4):
g(4) + 8 = -16 + 8 = -8
Therefore, g(4) + 8 = -8.
Select ALL the set of numbers that are possible values for x in the inequality, x<-3
The set of numbers that are possible values for x in the inequality x < -3 is: {-9, -7, -5}. (Option 2)
To find the possible values of x that satisfy the inequality x < -3, we need to look for numbers that are less than -3. Among the given sets of numbers, only {-9, -7, -5} contains numbers that are less than -3, so this is the set of possible values for x.
{-33, -22, -11} are all greater than -3, so they are not possible values for x in the given inequality.
{5, 7, 9} and {-5, 0, 5} are also greater than -3, so they are not possible values for x in the given inequality.
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Complete Question:
Select all the sets of numbers that are possible values for x in the inequality, x<-3.
{5,7,9}{-9, -7, -5}{-33, -22, -11}{-5,0,5}The path of a firework is described by the function:
h(t) = -4.9(t-5)² + 124 where h(t) is the height of the firework, in meters, and t is the time in
seconds, since the launch.
What is the vertex of the function, and what does it mean in context?
A. (5, 4.9); At 5 seconds, the firework is 4.9 meters above the ground.
B. (124, 5); At 124 seconds, the firework is 5 meters above the ground.
C. (4.9, 124); At 4.9 seconds, the firework is 124 meters above the ground.
D. (5, 124); At 5 seconds, the firework is 124 meters above the ground.
Answer:
D
Step-by-step explanation:
Because this binary function opens down, and it has an extreme point, at t=5, and you plug it in and you get 124 as the maximum.
a bag contains 2 black marbles, 8 white marbles, and 27 red marbles someone offers to play this game: you randomly select one marble from the bag if it is black, you win $3. if it is white, you win $2. if it is red, you lose $1. what is your expected value if you play this game?
The expected value of the game is -$0.054, which means that if you play this game many times, you can expect to lose around 5 cents per game on average.
We need to calculate the expected value of a game where you randomly select a marble from a bag containing 2 black marbles, 8 white marbles, and 27 red marbles.
If the marble is black, you win $3.
If the marble is white, you win $2.
If the marble is red, you lose $1.
The expected value of a game is the sum of the products of each outcome and its probability.
To find the expected value of this game,
we need to first calculate the probabilities of each outcome.
P(bag contains a black marble) = 2/37P(bag contains a white marble)
= 8/37
P(bag contains a red marble)
= 27/37
Probability of winning $3
= P(black marble)
= 2/37
Probability of winning $2
= P(white marble)
= 8/37
Probability of losing $1
= P(red marble) = 27/37
Expected value
= (Probability of winning $3 × $3) + (Probability of winning $2 × $2) + (Probability of losing $1 × $-1)
Expected value = (2/37 × 3) + (8/37 × 2) + (27/37 × -1)
Expected value = -0.054$
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A one-to-one function is given. Write an expression for the inverse function. f(x)=√x+7 Select one: O af¹¹(x)=x²-7 Ob. f¹(x)=(x-7)³ O c.f¹(x) = (x + 7)³ O d. f¹(x)=x³ +7
The correct option B. The expression for the inverse is f¹(x) = (x - 7)².
A one-to-one function is given. We have to write an expression for the inverse function.
Given function: f(x)=√x+7
The inverse of a function is found by switching the x and y coordinates and solving for y.
So, the expression for the inverse function will be:
f¹(x) = y = √x + 7 ... (1)
Replace x with y and simplify to isolate y from the radical.
y = √x + 7
=> y - 7 = √x
=> (y - 7)² = x
Hence, the inverse of the given function is given byf¹(x) = (x - 7)².
So, the correct option is B) f¹(x)=(x-7)².
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There are 6 cups of oatmeal in a container. Stella eats ¼ cup of oatmeal every day for breakfast. In how many days will Stella finish all the oatmeal in the container?
It will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.
The container has 6 cups of oatmeal and Stella eats 1/4 cup every day for breakfast.
To find the number of days it will take Stella to finish all the oatmeal, we can use the formula:
Number of days = Total amount of oatmeal ÷ Amount of oatmeal consumed per dayTotal amount of oatmeal in the container = 6 cups
Amount of oatmeal consumed by Stella per day = 1/4 cup
Number of days = 6 cups ÷ 1/4 cup = 24 daysTherefore, it will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.
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Write an equation to describe the relationship between t, the number of tickets, and c
, the total cost of tickets
The relationship between t, the number of tickets, and c, the total cost of tickets is: c = 55t
Relation between two variables, i.e, total cost and number of tickets:
The statistical relationship between two variables is called their correlation. The correlation can be positive, which means that the two variables move in the same direction, or negative, which means that when the value of one variable increases, the value of the other variable decreases.
Based n the Question:
Since there is no processing fee and the ticket price remains the same, we know that the fee will be proportional to the number of tickets purchased. The general form of the equation expressing the proportional relationship between the cost (c) and the number of tickets (t) is:
c = kt
where k is the constant of proportionality (the cost per ticket).
We can find k by using any of the data points given in the table. Using the first point, we have :
110 = k·2
Dividing the equation by 2:
110/2 = k = 55
Then using this value for k, the desired equation can be written:
c = 55t
Complete Question:
Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),
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