1) The distance left in the race is 554.93km
2) The total amount earned is $2,178.91
How many kilometers remain in the race?We know that the total race is of 1000km, to find the distance missing, we need to take that total distance and subtract the amounts that the cyclist already traveled.
Then we will get:
distance left = 1000km - 145.8km - 136.65km - 162.62 km
distance left = 554.93km
That is the distance left in the race.
2) We know that each piece costs $19.99, and 109 pieces are sold, then the amount earned is the product between these two numbers.
Earnings = 109*$19.99 = $2,178.91
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Deation 15 of 25
mat is the point-slope equation of a line with alope -3 that contains the point
A.y-4--3(x-8)
By+4=3(x-8)
ay+4=3(x+8)
Dy-4=3(x*8)
Answer:
y = -3x + 20.
Step-by-step explanation:
The correct point-slope equation of a line with slope -3 that contains the point (8,-4) is:
y - (-4) = -3(x - 8)
Expanding the right-hand side:
y + 4 = -3x + 24
Subtracting 4 from both sides:
y = -3x + 20
Therefore, the answer is not given in any of the options provided. The correct equation is y = -3x + 20.
Allen opens a retirement savings account with an initial deposit of $5,000. he makes annual contributions to the account, and at the end of 5 years the account has grown to $8,650. which best describes allen’s investment?
a. allen invests in a retirement savings account that earns 5.5% interest compounded annually.
b. allen invests in a retirement savings account that earns 3% simple interest.
c. allen invests a retirement savings account that earns 2.75% interest compounded annually.
d. allen invests in a retirement savings account that earns 5.5% simple interest.
The answer would be
A = $8,650
P = $5,000
t = 5 years
Find out the compound interest?To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money after t years
P = the principal (initial deposit)
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the number of years
We know that Allen opened a retirement savings account with an initial deposit of $5,000 and made annual contributions. After 5 years, the account grew to $8,650. We don't know the annual interest rate or how the interest is compounded, so we can use the formula to find out.
Let's assume that Allen made no additional contributions to the account after the initial deposit. Then:
A = $8,650
P = $5,000
t = 5 years
We can rearrange the formula to solve for r:
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Fill in the blank: as the number of trials gets ____________, the experimental probability of an event approaches the theoretical probability of the event.
As the number of trials gets larger, the experimental probability of an event approaches the theoretical probability of the event.
The Law of Large Numbers, a key idea in probability theory, holds that as trials or experiments are conducted, the experimental probability of an occurrence tends to converge toward the theoretical or predicted probability of that event.
In other words, the experimental results improve in accuracy and reliability as the sample size grows when forecasting the actual course of an event. This is because a bigger sample size reduces the significance of random changes or data errors and increases the likelihood that the experimental results will accurately reflect the true underlying probability of the event.
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Express the volume of the part of the ball p < 5 that lies between the cones т/4 and
т/3.
The volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3 is 0.
To express the volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3, we first need to determine the limits of integration in spherical coordinates.
Since the ball has radius 5, we know that the limits on ρ are 0 and 5.
For the limits on φ, we know that the region of interest lies between the cones φ = π/4 and φ = π/3, which correspond to angles of 45 degrees and 60 degrees, respectively.
Therefore, the limits on φ are π/4 and π/3.
For the limits on θ, we know that the region of interest extends all the way around the ball, so the limits on θ are 0 and 2π.
Using these limits, we can express the volume of the region of interest as:
V = ∫∫∫E ρ sin φ dρ dθ dφ
where,
E is the region of interest defined by the limits on ρ, θ, and φ that we just determined.
Substituting the limits and the volume element in spherical coordinates,
Integrating with respect to θ, we have:
V = 0
Therefore, the volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3 is 0.
This result suggests that there may be an error in the problem statement or that the region of interest is not well-defined.
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A person completes 68 km in 50 minutes via Jeep. Starting 20 minutes, he travels by x km/hr and
next 25 minutes by 2x km/hr and rest time by 3x km/hr. What is the value of x ?
The value of x is 48 km/hr.
How to solve for X
Total distance = 68 km
Total time = 50 minutes
First part:
Duration = 20 minutes
Speed = x km/hr
Second part:
Duration = 25 minutes
Speed = 2x km/hr
Third part:
Duration = 50 - (20 + 25) = 5 minutes
Speed = 3x km/hr
We can calculate the distance traveled in each part using the formula:
distance = speed × time
For the first part:
distance1 = x × (20/60) = (1/3)x (because 20 minutes = 1/3 hour)
For the second part:
distance2 = 2x × (25/60) = (5/6)x (because 25 minutes = 5/12 hour)
For the third part:
distance3 = 3x × (5/60) = (1/4)x (because 5 minutes = 1/12 hour)
Now, we know that the total distance is 68 km, so:
distance1 + distance2 + distance3 = 68
(1/3)x + (5/6)x + (1/4)x = 68
To solve for x, we'll first find a common denominator for the fractions, which is 12:
(4/12)x + (10/12)x + (3/12)x = 68
Now, add the fractions:
(4+10+3)/12 * x = 68
17/12 * x = 68
To isolate x, we'll multiply both sides by the reciprocal of the fraction (12/17):
x = 68 * (12/17)
x = 4 * 12
x = 48
So, the value of x is 48 km/hr.
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write an expanded form of the expression
y(0.5+8)
Answer:
8.5y
Step-by-step explanation:
you add what's in the parentheses, 0.5+8, it's 8.5
You then do 8.5*y, and you get
8.5y
On the Employee Sales Summary sheet, the function used to add together the last employee's sales for the three months is ___________________.
Group of answer choices
=SUM(E16)
=E16+E16+E16
=SUM('Employee Sales October:Employee Sales December'!E16)
=SUM('Employee Sales January:Employee Sales March'!E5)
The function used to add together the last employee's sales for the three months on the Employee Sales Summary sheet is: =SUM('Employee Sales January:Employee Sales March'!E5)
SUM(E16): This function adds up the values in cells E16 from the current sheet. If the last employee's sales for the three months are stored in cells E16, E17, and E18, then this function would correctly calculate the total.
E16+E16+E16: This expression adds up the value in cell E16 three times. If the last employee's sales for the three months are stored in cells E16, E17, and E18, then this expression would not calculate the total correctly.
SUM('Employee Sales October:Employee Sales December'!E16): This function adds up the values in cell E16 from all sheets between Employee Sales October and Employee Sales December (inclusive). If the last employee's sales for the three months are stored in cells E16, E17, and E18 on different sheets, then this function could be used to calculate the total.
SUM('Employee Sales January:Employee Sales March'!E5): This function adds up the values in cell E5 from all sheets between Employee Sales January and Employee Sales March (inclusive).
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Full Question: On the Employee Sales Summary sheet, the function used to add together the last employee's sales for the three months is ___________________.
Group of answer choices
=SUM(E16)=E16+E16+E16=SUM('Employee Sales October:Employee Sales December'!E16)=SUM('Employee Sales January:Employee Sales March'!E5)HELP DUE TOMORROW!!!
The equation of the attached graph is
y = 1 cos (1x) + 0 How to write the equation of the graphThe equation is written by the general formula
y = A cos (Bx + C) + D
where:
A = amplitude.
B = 2π/T
where T = period
C = phase shift.
D = vertical shift.
A = amplitude
A = (maximum - minimum) / 2
Using the graph,
maximum = 1
minimum = -1
A = [1 - (-1)] / 2 = 2/2 = 1
B = 2π/T
where T = 2π
B = 2π/(2π) = 1
C = phase shift = 0
D = vertical shift
D = 1 - 1 = 0
substituting results to
y = 1 cos (1x + 0) + 0
this is written as
y = 1 cos (1x) + 0
y = cos (x)
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Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0. 76, 4. 34). What was the sample mean difference from these 24 pairs of siblings?
–0. 76 inches
0 inches
1. 79 inches
4. 34 inches
The sample mean difference from these 24 pairs of siblings is 1.79 inches.
To find the sample mean difference from these 24 pairs of siblings, you can use the given 95% confidence interval for the mean difference in heights, which is (-0.76, 4.34).
The sample mean difference is the midpoint of the confidence interval. To calculate this, add the lower bound (-0.76) and the upper bound (4.34) of the confidence interval, and then divide by 2:
(-0.76 + 4.34) / 2 = 3.58 / 2 = 1.79 inches
So, the sample mean difference from these 24 pairs of siblings is 1.79 inches.
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x Which statement about prime and composite numbers is true?
x
A The product of any two prime numbers is a prime number.
* B The product of any two prime numbers is a composite number.
* C All prime numbers are odd numbers.
√x
D All even numbers are composite numbers.
Taussig Corp. S bonds currently sell for $960. They have a 6. 35% annual coupon rate and a 20-year maturity, but they can be called in 5 years at $1,067. 50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds?
The rate of return should an investor expect to earn if he or she purchases these bonds is equal to 4.184%.
Annual coupon rate = 6.35%
Maturity time = 20 years
To calculate the rate of return an investor should expect to earn if they purchase the Taussig Corp. S bonds,
Consider the cash flows from the bond and the purchase price.
Determine the cash flows from the bond,
The bond has a 6.35% annual coupon rate,
which means it pays $63.50 per year 6.35% of $1,000 face value.
The bond has a 20-year maturity, so there will be 20 coupon payments of $63.50 each.
If the bond is not called, the investor will receive the face value of $1,000 at maturity.
Calculate the purchase price of the bond,
The bonds are currently selling for $960.
Calculate the yield to maturity (YTM) on the bond,
Assume the yield curve is horizontal, so the yield to maturity will be the same as the coupon rate.
Calculate the rate of return using the following formula,
Rate of Return = [tex](Total Cash Flows / Purchase Price)^{(1 / Holding Period)}[/tex] - 1
Let us calculate the rate of return step by step,
Total Cash Flows,
Coupon payments,
$63.50 × 20 years = $1,270
Face value at maturity = $1,000
Total Cash Flows = $1,270 + $1,000
= $2,270
Rate of Return = [tex]($2,270 / $960)^{(1 / 20)}[/tex] - 1
Using a financial calculator , Attached calculation.
solve for the rate of return:
Rate of Return ≈ 4.184%
Therefore, an investor should expect to earn approximately a 4.18% rate of return if they purchase these bonds.
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A resale store is having a sale on DVDs and CDs. DVDs cost $7 and CDs cost $4. On one day, the store made $211 from DVD and CD sales and sold a total of 40 items. Write a system of equations, then solve to find how many DVDs and CDs were sold
Answer:
17 DVDs and 23 CDs
Step-by-step explanation:
x is the number of DVDs
y is the number of CDs
7x + 4y = $211
x + y = 40 ----(x4)----> 4x + 4y = 160
3x = 51
x = 17
x + y = 40
17 + y = 40
y = 23
In conclusion, 17 DVDs and 23 CDs were sold.
In her math class, carla used unit cubes to build a right rectangular prism with a volume of 24 cubic units. The height of the prism was two units. Which figure could be bottom layer of the prism
Carla's right rectangular prism could have either a 3x4 or a 2x6 rectangle as the bottom layer, with a height of 2 units, to achieve the given volume of 24 cubic units.
Carla built a right rectangular prism using unit cubes, with a volume of 24 cubic units and a height of 2 units. To determine the possible figure for the bottom layer of the prism, we need to understand the relationship between the volume, height, and the base area.
The volume of a rectangular prism can be calculated using the formula: Volume = Base Area × Height. In Carla's case, the volume is 24 cubic units, and the height is 2 units. By rearranging the formula, we can find the base area: Base Area = Volume ÷ Height. Substituting the given values, Base Area = 24 ÷ 2, which equals 12 square units.
Now, we need to find a possible figure for the bottom layer with an area of 12 square units. Since the bottom layer is made of unit cubes, it must have whole-number dimensions. There are two possible rectangular figures that meet this requirement: 1) a 3x4 rectangle, and 2) a 2x6 rectangle. Both of these figures have an area of 12 square units (3x4 = 12 and 2x6 = 12) and can be formed using unit cubes.
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1) You want your savings account to have a total of $23,000 in it within 5 years. If you invest your money in an account that pays 6.8% interest compounded continuously, how much money must you have in your account now? 2) You buy a brand new Audi R8 for $148,700 before taxes. If the car depreciates at a rate of 8%, how much will it be worth in 5 years?
After 5 years with 8% depreciation, the Audi R8's value will be around $81,249.36.
To determine how much money you must have in your account now, you can use the formula A = Pe^(rt), where A is the final amount, P is the principal (the initial amount invested), e is the constant 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years. We will calculate using this formula.Plugging in the given values, we get:
A = $23,000
r = 0.068 (6.8% expressed as a decimal)
t = 5 years
So, $23,000 = P*e^(0.068*5)
Solving for P, we get:
P = $16,376.59
Therefore, you must have $16,376.59 in your account now to reach your goal of $23,000 in 5 years with 6.8% continuous compounding interest. To determine how much the Audi R8 will be worth in 5 years, you can use the formula A = P(1 - r)^t, where A is the final amount, P is the initial amount, r is the annual depreciation rate expressed as a decimal, and t is the time in years. Plugging in the given values, we get:
P = $148,700
r = 0.08 (8% expressed as a decimal)
t = 5 years
So, A = $148,700*(1 - 0.08)^5
Simplifying, we get:
A = $81,249.36
Therefore, the Audi R8 will be worth approximately $81,249.36 in 5 years with 8% depreciation.
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Color the circles, so it would be certain you get an orange one.
Answer:
1 orange
Step-by-step explanation:
you just color 1 circle.
pa help, pleaseeee. sana mahanap to ng matalino, pumuputok utak ko, pahelp naman po please
How many terms are to be considered in the series with first term - 3 and common ratio r = -4 for the sum to exceed 1507
,Based on the information, we need to consider 5 terms in the series for the sum to exceed 1507.
How to explain the seriesSubstituting the given values, we get:
1507 < -3(1 - (-4)^n)/(1 - (-4))
Simplifying this inequality, we get:
-4^n < 502
Taking the logarithm of both sides, we get:
n*log(4) > log(502)
n > log(502)/log(4)
n > 4.29
n = 5
Therefore, we need to consider 5 terms in the series for the sum to exceed 1507.
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The regular price of a sofa, in dollars, is represented by p. the sale price of the sofa is 30% off the regular price. select all true statements. a. the sale price of the sofa can be represented by p-0.3p.
The sale price of the sofa can be represented by the equation p - 0.3p. This equation correctly represents the sale price after a 30% discount has been applied to the regular price.
The question is about the regular price of a sofa represented by p, and its sale price which is 30% off the regular price. You'd like to know if the statement "the sale price of the sofa can be represented by p-0.3p" is true.
Step 1: Understand the problem
The regular price of the sofa is represented by p. The sale price is 30% off the regular price.
Step 2: Represent the sale price
To find the sale price, we need to subtract the discount (30% of p) from the regular price (p).
Step 3: Calculate the discount
The discount can be calculated as 30% of p, which is 0.3 * p (or 0.3p).
Step 4: Determine the sale price
Now, subtract the discount from the regular price: p - 0.3p.
Step 5: Confirm the statement
The statement "the sale price of the sofa can be represented by p-0.3p" is indeed true.
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Pleas help im stuck on this question and im too afraid to get it wrong
Step-by-step explanation:
g(x) is just f(x) shifted UP three units ...so
g(x) = f(x) +3
PLEASE HELP FAST!!!!
On Monday a group of students took a test and the average ( arithmetic mean ) score was exactly 80. 4. A student who was absent on Monday took the same test on Tuesday and scored 90. The average age test score was then exactly 81. How many students took the test on Monday?
A) 14
B) 15
C) 16
D) 17
E) 18
With steps please
The number of students who took the test on Monday is found to be 15, hence the correct option is B.
Let us assume that the number of student taking test on Monday is n. The total score for Monday's test is n times the average score of 80.4,
Monday's total score = 80.4n
When the student who missed the test on Monday took the test on Tuesday and scored 90, the total score became,
Total score = 80.4n + 90
The new average score of 81 can be expressed as,
81 = Total score / (n+1)
Substituting the value of the total score, we get,
81 = (80.4n + 90)/(n+1)
Multiplying both sides by n+1, we get,
81(n+1) = 80.4n + 90
Expanding the brackets,
81n + 81 = 80.4n + 90
Simplifying,
0.6n = 9
n = 15, so, the number of students who took the test on Monday is 15.
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WILL MARK YOU BRAINLIEST QUESTION IN THE PHOTO
The measure of arc DF is given as follows:
mDF = 58º.
How to obtain the arc measure?We have two secants in this problem, and point E is the intersection of the two secants, hence the angle measure of 52º is half the difference between the angle measure of the largest arc of 162º by the angle measure of the smallest arc.
Then the measure of arc DF is obtained as follows:
52 = 0.5(162 - mDF)
52 = 81 - 0.5mDF
0.5mDF = 29
mDF = 58º.
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In a recent study on worldâ happiness, participants were asked to evaluate their current lives on a scale from 0 toâ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5. 7 with a standard deviation of 2. 3.
â(a) What response represents the 90th âpercentile?
â(b) What response represents the 62nd âpercentile?
â(c) What response represents the first âquartile?
The z-score for the 90th percentile is approximately 1.28, for the 62nd percentile is approximately 0.31, and for the first quartile (25th percentile) is approximately -0.67.
To calculate the percentiles for this dataset, we need to use the z-score formula. Unfortunately, I cannot directly provide you the responses for the 90th, 62nd, and first quartile percentiles without more information.
However, I can help you understand the process of finding these percentiles:
1. Determine the z-score corresponding to the desired percentile using a z-score table or calculator. For example, the z-score for the 90th percentile is approximately 1.28, for the 62nd percentile is approximately 0.31, and for the first quartile (25th percentile) is approximately -0.67.
2. Use the following formula to find the response corresponding to the z-score:
Response = Mean + (Z-score × Standard Deviation)
For example, to find the 90th percentile:
Response = 5.7 + (1.28 × 2.3)
Calculate this for each percentile using their respective z-scores, and you will find the responses you are looking for.
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Solve the separable differential equation for u. du dt e2u+9t Use the initial condition u(0) = 4. = U =
The solution to the differential equation with the given initial condition is:
[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
How to solve the separable differential equation?To solve equation, we can separate the variables and write:
[tex]1/e^{(2u)} du = e^{(9t)} dt[/tex]
Integrating both sides, we get:
[tex]\int 1/e^{(2u)} du = \int e^{(9t)} dt[/tex]
Integrating the left side requires the substitution v = 2u, dv/du = 2, and du = dv/2, which gives:
[tex]\int 1/e^{(2u)} du = \int 1/2 * 1/e^v dv = -1/2 * e^{(-2u)}[/tex]
Integrating the right side gives:
[tex]\int e^{(9t)} dt = 1/9 * e^{(9t)}[/tex]
Substituting these integrals back into the original equation, we get:
[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} + C[/tex]
where C is the constant of integration.
We can solve for the constant of integration using the initial condition u(0) = 4:
[tex]-1/2 * e^{(-24)} = 1/9 * e^{(90)} + C[/tex]
[tex]-1/2 * e^{(-8)} = 1/9 + C[/tex]
[tex]C = -1/2 * e^{(-8)} - 1/9[/tex]
Therefore, the solution to the differential equation [tex]du/dt = e^{(2u+9t)}[/tex] with initial condition u(0) = 4 is:
[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} - 1/2 * e^{(-8)} - 1/9[/tex]
Solving for u, we get:
[tex]e^{(-2u)} = -2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9[/tex]
Taking the natural logarithm of both sides, we get:
[tex]-2u = ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
Dividing by -2, we get:
[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
Therefore, the solution to the differential equation with the given initial condition is:
[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]
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Algebra 1. please help!!
Answer: f(t) = 2.4t - 500
Step-by-step explanation:
So first of all, we need how much she actually profits from each taco. She charges $3.25 per taco, but we cannot forget that it is not free to make a taco in the first place. It costs her $0.85 to make a taco. This means we have to subtract the 85 cents from the 3 dollars 25 cents, which means it ends up being $2.40, or as the answer choices have it, 2.4.
So now we know what the number of tacos is being multiplied by: 2.4.
2.4t is now the profit per taco multiplied by the number of tacos.
But we're not quite done yet.
She has a fixed expense of $500 a month, which means this has to be subtracted from her taco profits to find her true profit.
Putting all of this together, we get f(t)=2.4t - 500.
(t)= (profit per taco)(amount of tacos sold) - (fixed expenses)
Help with problem in photo! Find the perimeter!
The perimeter of the shape is 53.7 units
What is perimeter ?Perimeter is a math concept that measures the total length around the outside of a shape.
A theorem of circle geometry states that the tangent from a point on a circle are equal.
Therefore the base sides is calculated as
9.9 + 3.2
= 13.1
since the perimeter is the addition of all the sides then;
P = 13.1 + 21.9 + 18.7
P = 53.7
therefore the perimeter of the triangle is 53.7
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A rectangular prism has a volume of 27 in³ If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
___in³
fill in the blank
ty
A movie theater has a seating capacity of 349. The theater charges $5. 00 for children, $7. 00 for students, and $12. 00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2540, How many children, students, and adults attended?
194 children, 58 students, and 97 adults attended the movie.
Let's use algebra to solve this problem.
Let's assume the number of children who attended the movie is C, the number of students is S, and the number of adults is A.
From the problem, we know that:
The seating capacity of the theater is 349:
C + S + A = 349
The theater charges $5 for children, $7 for students, and $12 for adults:
5C + 7S + 12A = $2540
There are half as many adults as there are children:
A = 1/2C
Now we can substitute A = 1/2C from the third equation into the first and second equations:
C + S + 1/2C = 349
3/2C + S = 349
5C + 7S + 12(1/2C) = $2540
5C + 7S + 6C = $2540
11C + 7S = $2540
Now we have two equations with two variables, C and S.
We can solve for S in the first equation:
3/2C + S = 349
S = 349 - 3/2C
Now we can substitute S = 349 - 3/2C into the second equation:
11C + 7S = $2540
11C + 7(349 - 3/2C) = $2540
11C + 2443 - 10.5C = $2540
0.5C = 97
C = 194
Therefore, 194 children attended the movie of total sales.
We can use A = 1/2C from the third equation to find the number of adults:
A = 1/2C
A = 1/2(194)
A = 97
Therefore, 97 adults attended the movie.
We can use C + S + A = 349 to find the number of students:
C + S + A = 349
194 + S + 97 = 349
S = 58
Therefore, 58 students attended the movie.
In summary, 194 children, 58 students, and 97 adults attended the movie.
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Answer Immeditely Please
Answer:
6
Step-by-step explanation:
Write out the base fine numerals in order from 1 base five to 100 base five
Here are the base five numerals from 1 to 100
1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100.
With the base five, every number can only take on the values of 0, 1, 2, 3, or 4.
After the number 4, we carry over to the following place value and start again with 0. So, for instance, the number after 4 in base five is 10, because we've carried over to the next place value and started with 0 again.
In this way, we can count all the way up to 100 in base five, using these 25 unique numerals.
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Tiffany was cutting out some fabric for her friend she cut a piece that was 6 cm wide in an area of 30 cm to the power of two how long was the piece
The length of the fabric piece is 5 cm.
We are given the width and area of the fabric piece and need to find its length. Here are the steps:
1. The terms involved in this problem are width, length, and area.
2. The formula to calculate the area of a rectangle is Area = Width × Length.
3. We are given the width (6 cm) and area (30 cm²) of the fabric piece.
4. To find the length, we'll rearrange the formula: Length = Area ÷ Width.
5. Plug in the given values: Length = (30 cm²) ÷ (6 cm).
6. Perform the calculation: Length = 5 cm.
So, the length of the fabric piece is 5 cm.
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