Answer:c is the correct answer
Step-by-step explanation:
A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x
where y is the number of dollars charged and
x is the number of minutes the repair person is on the job.
Therefore, to determine the number of minutes that it would take for the cost of repair to reach $130, we would substitute y =130 into the given model. It becomes
130 = 47.38 + 0.617x
0.617x = 130 - 47.38 = 82.62
x = 82.62/0.617 = 134 minutes
If it takes 6 printing presses 4 hours to print 5000 newspapers, how long should it take 3 presses to print 3000 newspapers?
Answer:
4 hrs 48 min
Step-by-step explanation:
It takes 6 presses 4 * 3/5 = 12/5 hours to print 3000 newspapers.
It takes 3 presses 2 * 12/5 = 24/5 hours = 4h48min to print 3000 newpapers
Which of the following matrices is the solution matrix for the given system of equations? x + 5y = 11 x - y = 5
The solution to the given system of equations, x + 5y = 11 and x - y = 5, is x = 6, y = 1. The solution matrix for this system is therefore [6, 1].
Explanation:To solve the given system of linear equations, x + 5y = 11 and x - y = 5, you can use the elimination or substitution method. Let's use the elimination method:
First, subtract the second equation from the first equation, and you will get: (x+5y)-(x-y) = (11-5) which simplifies to 6y=6.To find the value of 'y', divide both sides by 6, therefore y = 1.Substitute y = 1 into the second equation x - y = 5, you get x - 1 = 5, after simplification, x = 6.The solution of this system of equations is x = 6 and y = 1. For the matrix format of the solution, it would be [6,1] as the solution matrix typically formats solutions in [x, y].
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The solution matrix X is [tex]\(\begin{bmatrix} 3 \\ 2 \end{bmatrix}\)[/tex].
To find the solution matrix for the given system of equations [tex]\(x + 5y = 11\)[/tex] and [tex]\(x - y = 5\)[/tex], we can represent the system in matrix form \(AX = B\), where:
[tex]\[ A = \begin{bmatrix} 1 & 5 \\ 1 & -1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \end{bmatrix}, \quad B = \begin{bmatrix} 11 \\ 5 \end{bmatrix} \][/tex]
The solution matrix X is given by [tex]\(X = A^{-1}B\)[/tex], where [tex]\(A^{-1}\)[/tex] is the inverse of matrix A.
1. Form the matrix equation AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
2. Compute the inverse of matrix A, denoted as [tex]\(A^{-1}\).[/tex]
3. Multiply [tex]\(A^{-1}\)[/tex]by matrix B to obtain the solution matrix X.
By following these steps, you can find that the solution matrix X for the given system is [tex]\(\begin{bmatrix} 3 \\ 2 \end{bmatrix}\).[/tex]
A football player completes a pass 69.4% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes.
The student asked for the calculations of probabilities concerning a football player's passes. The answers are: (a) 21.18%, (b) 90.58%, (c) 8.68%. This involves the use of probability rules and calculations carried out to two decimal places.
Explanation:The subject of this question is probability, particularly in the context of repeated independent trials. The football player has a 69.4% chance of completing a pass, so we can use this information to answer the questions.
The first pass he completes is the second pass: This means that he fails the first pass and succeeds on the second. Both of these are independent events. So, we multiply the probabilities: (1 - 0.694) * 0.694 = 0.2118 or 21.18%.The first pass he completes is the first or second pass: We've already calculated the probability for the second pass. The probability for the first pass is simply his success rate, 0.694 or 69.4%. To find the probability of either event occurring, we add the two probabilities together: 0.2118 + 0.694 = 0.9058 or 90.58%.He does not complete his first two passes: This means he fails both passes. Since these are independent events, we multiply the probabilities: (1 - 0.694) * (1 - 0.694) = 0.0868 or 8.68%.Learn more about Probability here:https://brainly.com/question/22962752
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(a) The probability that the first pass he completes is the second pass is [tex]$\frac{3099}{10000}$[/tex].
(b) The probability that the first pass he completes is the first or second pass is [tex]$\frac{3499}{5000}$[/tex].
(c) The probability that he does not complete his first two passes is [tex]$\frac{9826}{2500}$[/tex].
To solve this problem, we will use the given completion rate of 69.4% and convert it into a fraction to make the calculations easier. The completion rate is equivalent to [tex]$\frac{694}{1000}$[/tex] or [tex]$\frac{347}{500}$[/tex].
(a) To find the probability that the first pass he completes is the second pass, we need to consider two events: he must fail the first pass and then succeed on the second pass. The probability of failing the first pass is [tex]$1[/tex] - [tex]\frac{347}{500}$[/tex], and the probability of succeeding on the second pass is [tex]$\frac{347}{500}$[/tex]. Multiplying these two probabilities gives us the desired probability:
[tex]$$ \left(1 - \frac{347}{500}\right) \times \frac{347}{500} = \frac{153}{500} \times \frac{347}{500} = \frac{3099}{25000}. $$[/tex]
Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:
[tex]$$ \frac{3099}{25000} = \frac{77475}{62500} = \frac{3099}{10000}. $$[/tex]
(b) To find the probability that the first pass he completes is the first or second pass, we need to consider the probability of completing the first pass and the probability of failing the first pass but completing the second pass. We add these two probabilities because they are mutually exclusive events. The probability of completing the first pass is [tex]$\frac{347}{500}$[/tex], and the probability of failing the first pass but completing the second pass is the same as calculated in part (a), [tex]$\frac{3099}{10000}$[/tex]. Adding these probabilities gives us:
[tex]$$ \frac{347}{500} + \frac{3099}{10000} = \frac{694}{1000} + \frac{3099}{10000} = \frac{3499}{5000}. $$[/tex]
(c) To find the probability that he does not complete his first two passes, we need to consider the probability of failing both passes. The probability of failing one pass is [tex]$1[/tex]- [tex]\frac{347}{500}$[/tex], so for two consecutive failures, we square this probability:
[tex]$$ \left(1 - \frac{347}{500}\right)^2 = \left(\frac{153}{500}\right)^2 = \frac{23409}{25000}. $$[/tex]
Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:
[tex]$$ \frac{23409}{25000} = \frac{585025}{62500} = \frac{9826}{2500}. $$[/tex]
These calculations provide the probabilities for each of the specified events.
You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units. You need to cut a slice off the top of the block to decrease the height by 2 units. Th e new block will have a volume of 480 cubic units. a. What are the dimensions of the new block?
Answer:
[tex]Depth = x= 4 units[/tex]
[tex]length = 5x= 5(4)= 20 \ units[/tex]
[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]
Step-by-step explanation:
You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units.
height is decreased by 2 units , so height becomes 2x-2
Volume of a block is length times width time height
[tex]volume = x \cdot 5x \cdot (2x-2)[/tex]
[tex]480 = 10x^3-10x^2[/tex]
divide whole equation by 10
[tex]48= x^3-x^2[/tex]
Subtract 48 from both sides
[tex]x^3-x^2-48=0[/tex]
[tex]\left(x-4\right)\left(x^2+3x+12\right)=0[/tex]
[tex]x-4=0[/tex], x=4
[tex]Depth = x= 4 units[/tex]
[tex]length = 5x= 5(4)= 20 \ units[/tex]
[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]
You want to buy an item with an original price of $75. If there is a 30% discount, how much can you deduct from the original price?
In order to find 30% of 75, we simply calculate 75 x 0.3.
75 x 0.3 amounts to 22.5, which is the amount we deduct.
This leaves a final price of $52.50.
A 30% discount on an item priced at $75 results in a deduction of $22.5.
Explanation:The student's question is about calculating a discount on an item. Here, the discount is a 30% decrease or reduction off the original price of the item, which is $75. To calculate the discount, you multiply the original price by the percentage discount. Remember, since percentage is a proportion, you'll need to convert the percentage to a decimal first by dividing it by 100. Therefore, the formula will be:
Discount = Original Price x Percentage Discount
Substituting in the given values:
Discount = $75 x 30/100 = $22.5
So, with the 30% discount, you can deduct $22.5 from the original price of the item.
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What reason explains why the m∠Q = 115°?
Answer:
What is the figure you are talking about?
Peanuts cost $1.50 per pound. how much does 2 pounds of Peanuts cost?
Answer:
$3.00
Step-by-step explanation:
If you wanna buy 2 pounds, just time it by 2! $1.50*2=$3.00!
If peanuts cost $1.50 per pound, the cost of 2 pounds of peanuts would be equal to $3.0.
Given the following data:
Cost of peanut = $1.50 per pound.Quantity of peanuts = 2 pounds.How to calculate the cost of 2 pounds?In order to determine the cost of 2 pounds of peanuts, we would set up a direct proportion equation as follows:
1 pounds = 1.50 dollars.
2 pounds = X dollars.
Cross-multiplying, we have:
X = 2 × 1.5
X = $3.0
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Maren is painting some doors that are all the same size. She used 3 liters of paint to cover 1 4/5 doors. How many liters of paint are needed for 1 door?
Final answer:
To find out how many liters of paint are needed for one door, when 3 liters were used for 1 4/5 doors, divide the total amount of paint by the number of doors. The calculation is 3 liters divided by 9/5, which results in 1.67 liters of paint for one door.
Explanation:
Maren used 3 liters of paint to cover 1 4/5 doors which implies that the amount of paint needed for 1 door can be found by dividing the total amount of paint by the number of doors painted. To calculate this:
First, convert the mixed number 1 4/5 into an improper fraction. This is 5/5 (which is 1) plus 4/5, which equals 9/5.Next, divide the total liters of paint used (3 liters) by the fraction representing the number of doors (9/5 doors).Since dividing by a fraction is the same as multiplying by its reciprocal, you would multiply 3 liters by 5/9.The calculation will be: 3 L × 5/9 = 15/9 which simplifies to 5/3.Finally, reduce 5/3 to its simplest form 1 2/3 liters or 1.67 liters (to two decimal places).Therefore, 1.67 liters of paint are needed for 1 door.
if u answer i will give u brainliest. :)
Answer:
A
Step-by-step explanation:
Answer:
ima need that brainliest dawg the answer a
Step-by-step explanation:
Can someone help explain this, please?
OP=
4
6
8
Answer:
6
Step-by-step explanation:
jus did it
A chemist has 3 and one half mililiters of ammonia in beaker X 0.2 mililiters of ammonia in beaker Y expressed as a mixed number how many mililiters of ammonia does the chemist have all together
Answer:
Molarity is the concentration of x moles of solute in 1 L of solution. ... have different properties i.e., a low molarity acid and high molarity acid can ... For example, a 0.25 mol/L NaOH solution contains 0.25 mol of sodium hydroxide in every litre of solution ... 15.0 g of NaOH in enough water to make a total of 225 mL of solution
Step-by-step explanation:
the mean of a sample size n=35 is 1860. the standard deviation of the sample is 102 and the population is normally distributed. construct a 99% confidence interval estimate of the mean of the population.
Answer: (1812.967, 1907.033)
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm t_{df,\ \alpha} \dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = Sample mean
n= Sample size.
s = Sample standard deviation
[tex]t_{df,\ \alpha}[/tex] = Critical t-value for degree of freedom(n-1).
As per given , we have
n= 35
[tex]\overline{x}=1860[/tex]
s=102
Significance level : [tex]\alpha=0.01[/tex]
By t- distribution table , for degree of freedom 43 and [tex]\alpha=0.01[/tex] , we have
[tex]t_{df,\ \alpha}=t_{34,\ 0.005} =2.728[/tex]
Substitute all the values in the above formula , we will get
[tex]1860\pm (2.728)\dfrac{102}{\sqrt{35}}[/tex]
[tex]=1860\pm (2.728)(17.2411)[/tex]
[tex]=1860\pm47.034[/tex]
[tex]=(1860-47.033\ 1860+47.033)= (1812.967,\ 1907.033)[/tex]
Hence, the 99% confidence interval estimate of the mean of the population is (1812.967, 1907.033).
Final answer:
To construct a 99% confidence interval for the population mean with a known standard deviation, calculate the standard error, find the appropriate z-score for 99% confidence, and apply the formula Sample mean ± z * SEM. The 99% confidence interval for the given sample data is approximately (1811.26, 1908.74).
Explanation:
A student asked how to construct a 99% confidence interval estimate for the mean of the population given that the mean of a sample of size n=35 is 1860 with a standard deviation of 102, and the population is normally distributed.
To construct a 99% confidence interval, we proceed by calculating the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size:
SEM = σ / √n = 102 / √35 ≈ 17.25
We then find the z-score that corresponds to a 99% confidence level. For a two-tailed test, which is relevant here, this value is approximately 2.576.
The confidence interval is then calculated by:
Sample mean ± z * SEM = 1860 ± 2.576 * 17.25
Lower limit: 1860 - (2.576 * 17.25) ≈ 1811.26
Upper limit: 1860 + (2.576 * 17.25) ≈ 1908.74
Hence, the 99% confidence interval estimate for the population mean is approximately (1811.26, 1908.74).
Given right triangle QRS, what is the value of sin(30°)? StartFraction StartRoot 3 EndRoot Over 3 EndFraction One-half StartFraction StartRoot 3 EndRoot Over 2 EndFraction StartFraction 2 Over 1 EndFraction
Answer:
Option 2: [tex]\sin(30)=\frac{1}{2}[/tex]
Step-by-step explanation:
Given:
From the triangle shown below;
A triangle QRS with angle QRS = 90°, ∠QSR = 30°.
Side QR = 5, SQ = 10 and RS = 5√3
Now, we know from trigonometric ratio that,
[tex]\sin (A) = \frac{Opposite\ side}{Hypotenuse}[/tex]
Here, opposite side of angle QSR is QR and Hypotenuse is the side opposite angle QRS which is SQ. Therefore,
[tex]\sin(\angle QSR)=\dfrac{QR}{SQ}\\\\\\\sin(30)=\dfrac{5}{10}\\\\\\\sin(30)=\dfrac{5}{2\times 5}=\dfrac{1}{2}[/tex]
Therefore, the value of sine of 30° is one-half. So, second option is correct.
Answer:
B
Step-by-step explanation:
VDG~VNQ what is the value of x?
Answer:
x= 8
Step-by-step explanation:
60/48=1.25
15/1.25= 12
12-4=8
Consists of arranging for a market offering to occupy a clear, distinctive, and desirable place relative to competing products in the minds of target consumers.
Answer:
i dont understand
Step-by-step explanation:
Consider the linearization, L(x) of the curve y = x at (36, 6). What are the least and greatest values of x for which this linearization is within 0.1 of the true value of the curve?
Solve the following equation for q. 5q - 4p + 6 = 4q – 8.
Answer:
[tex]q=4p-14[/tex]
Step-by-step explanation:
The first step in solving
[tex]5q-4p+6=4q-8[/tex]
is to bring [tex]4q[/tex] on the right the left side to the right side by subtracting it from both sides:
[tex](5q-4p+6)-4q=(4q-8)-4q\\\\(5q-4q)-4p+6=-8\\q-4p+6=-8[/tex]
and we subtract 6 from both sides and get:
[tex]q-4p=-14[/tex]
finally we add [tex]4p[/tex] to both sides and get:
[tex]q-4p+4p=-14+4p[/tex]
[tex]\boxed{q=4p-14}[/tex]
A commercial jet and a private airplane flu from Denver to Phoenix. It takes the commercial jet 1.1 hours for the flight, and it takes the private plane 1.8 hours. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane
Answer: the speed of the commercial jet is 540 mph
the speed of the private airplane is 330 mph
Step-by-step explanation:
Let x represent the speed of the commercial jet and
Let y represent the speed of the private airplane.
It takes the commercial jet 1.1 hours for the flight from Denver to Phoenix.
Distance = speed × time
Therefore, distance covered by the commercial jet from Denver to Phoenix would be
1.1 × x = 1.1x
it takes the private airplane 1.8 hours to cover the same distance. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. It means that
y = x - 210
Distance covered by the private airplane would be
1.8(x - 210) = 1.8x - 378
Since the distance is the same, then
1.8x - 378 = 1.1x
1.8x - 1.1x = 378
0.7x = 378
x = 378/0.7 = 540
y = x - 210 = 540 - 210
y = 330
To find the speeds of a commercial jet and a private airplane, we can set up and solve an equation using the distance and time information provided in the question.
Explanation:The question is about the speeds of a commercial jet and a private airplane flying from Denver to Phoenix. Let's assume the speed of the private airplane is 'x' miles per hour. According to the question, the commercial jet is 210 miles per hour faster than the private airplane. So, the speed of the commercial jet is 'x + 210' miles per hour.
Now, we have the speeds of both planes. We can use the formula 'speed = distance / time' to calculate the distance. Since the time for the commercial jet is 1.1 hours and the time for the private airplane is 1.8 hours, the distances traveled by the commercial jet and the private airplane are '1.1(x + 210)' and '1.8x' miles, respectively.
Since both planes are traveling the same distance, we can set up the equation '1.1(x + 210) = 1.8x' to find the value of 'x'. Solving this equation will give us the speed of the private airplane. Once we have the speed of the private airplane, we can calculate the speed of the commercial jet by adding 210 to it.
On a number line, Karlie has to divide the space between —5 and —3 into five smaller, equal spaces. On what numbers does Karlie have to place the four marks to create the five spaces?
Answer:
{-4.6, -4.2, -3.8, -3.4}
Step-by-step explanation:
The length of the space Karlie is dividing is -3-(-5) = 2 units. Then the length of each of those equal 5 spaces will be 2/5 units = 0.4 units.
Each mark on the number line is 0.4 units to the right of the previous one. The first (left-most) mark is 0.4 units to the right of -5, so is at -5+0.4 = -4.6.
The marks have to be placed at -4.6, -4.2, -3.8, and -3.4.
Consider the following conditional statement. Rewrite the statement in if-then form, and then write the converse, inverse Converse contrapositive, and biconditional.
Right angles are 90°
If-then:
Converse:
Inverse:
Contrapositve:
Biconditional:
Final answer:
To rewrite a conditional statement in if-then form, use the example given. The converse, inverse, contrapositive, and biconditional can be formed by changing the order and negating the original statement in different ways.
Explanation:
To rewrite the conditional statement 'Right angles are 90°' in if-then form, we can state: 'If an angle is a right angle, then it measures 90°.'
The converse of the conditional statement is: 'If an angle measures 90°, then it is a right angle.'
The inverse of the conditional statement is: 'If an angle is not a right angle, then it does not measure 90°.'
The contrapositive of the conditional statement is: 'If an angle does not measure 90°, then it is not a right angle.'
The biconditional statement is: 'An angle is a right angle if and only if it measures 90°.'
8.) Simplify.
cot^2 0 - cot ^2 0 cos ^2 0
A.) tan^2 0
B.) -1
C.) 3
D.) sin ^2 0
E.) cos^2 0
Answer:
The answer to your question is letter E. cos²α
Step-by-step explanation:
cot²Ф - cot²Фcos²Ф
Remember that cot = [tex]\frac{cos \alpha}{sin \alpha }[/tex] ; substitute in the previous equation
[tex]\frac{cos^{2}\alpha }{sin^{2} \alpha} - \frac{cos^{2}\alpha }{sin^{2}\alpha } cos^{2}\alpha[/tex]
[tex]\frac{cos^{2}\alpha - cos^{4}\alpha }{sin^{2}\alpha }[/tex] Factor cos²α
[tex]\frac{cos^{2}\alpha(1 - cos^{2}\alpha }{sin^{2}\alpha }[/tex]
Remember that sin²α = 1 - cos²α
[tex]\frac{cos^{2}\alpha sin^{2}\alpha}{sin^{2} \alpha}[/tex]
Simplify
cos²α
On a certain airline, customers are assigned a row number when they purchase their ticket, but the four seats within the row are first come, first served during boarding. If Karen and Georgia end up with random seats in the same row on a sold-out flight, what is the probability that they sit next to each other?
Answer:
The probability that they sit next to each other is 50%.
Step-by-step explanation:
Consider the provided information.
It is given that there are four seats within the row are first come, first served during boarding.
There are 4 seats and 2 customers (Karen and Georgia)
The total number of ways in which Karen and Georgia can sit is: [tex]^4C_2[/tex]
Now if they will sit together, then consider Karen and Georgia as a single unit.
Thus, the number of ways in which they can sit together is: [tex]^3C_1[/tex]
The required probability is:
[tex]P=\frac{^3C_1}{^4C_2} \\\\P=\frac{3}{6}\\\\P=\frac{1}{2}[/tex]
Hence, the probability that they sit next to each other is 50%.
Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid?
Answer: 16
Step-by-step explanation:
Answer:
The height of each pyramid is 1/2 h units.
Step-by-step explanation:
did it on edg 2020
Hana babysits for 6 hours a day. How many hours does she work in 45 daysshe is paid 9 an hour, how much money will she earn in 45 days? Explain how you solved this problem .
Answer:$2430
Step-by-step explanation:
6x45=270
270x9=2430
Between 1911 in 1990, the top of the leaning bell tower of Pisa, Italy moved toward the south at an average rate of 1.2 MM/Y. The tower is 55M tall. In radians per second, what is the average regular speed of the towers top about its base?
Answer:
Angular speed of the towers top about its base is [tex]6.91\times 10^{-13}[/tex] rad per sec.
Step-by-step explanation:
Linear velocity of leaning bell tower 'v' = 1.2 mm per year
v = [tex]\frac{1.2\times 10^{-3}}{365\times 24\times 60\times 60}[/tex]
v = 3.8 × [tex]10^{-11}[/tex] meter per second
Height of the tower = 55 meter
From the formula of angular velocity,
v = rω
ω = [tex]\frac{v}{r}[/tex]
ω = [tex]\frac{3.8\times 10^{-11}}{55}[/tex]
ω = [tex]6.91\times 10^{-13}[/tex] rad per second.
Therefore, top of the tower is moving with an angular speed of [tex]6.91\times 10^{-13}[/tex] rad per second.
Which equation represents the graph shown?
y = 2x + 2
y = 2x
y = 2x + 3
y = 2x + 1
PLEASE HELP WILL MARK BRAINLIEST!!!!!! Base the question off this info: An experienced cashier at a grocery store takes 2 seconds to scan each item and 40 seconds to process the customer's payment. ______________________________________________________________ Anna bought 31 items at the grocery store. There was a glitch in the computer system that caused the processing of the payment to take longer than usual. If the total time for Anna's transaction took 2 minutes, how much time did the processing of the payment (p) take?
Answer:the time for processing the payment took 58 seconds.
Step-by-step explanation:
An experienced cashier at a grocery store takes 2 seconds to scan each item and 40 seconds to process the customer's payment. If Anna bought 31 items at the grocery store, the total time for Anna's transaction would be
(31 × 2) + 40 = 62 + 40 = 102 seconds.
The time to to process the Anna's payment took longer due to glitches. If the total time for Anna's transaction took 2 minutes = 120 seconds, then the amount of time it took to process the payment (p) would be
p = 120 - 62 = 58 seconds
If 8 identical blackboards are to be divided among 4 schools,how many divisions are possible? How many, if each school mustreceive at least 1 blackboard?
Response:
if8 boards are to be distributed then the number of ways can be8C4=70
and if every school must get atlest one board then it is possiblein 70-14 ways = 56 ways..
let abcd be the schools
a b c d
0 0 0 8 4C1= 4 (three schools dont get even1 board)
0 0 1 7 4C2= 6 (two schools dont get even 1board)
0 1 1 6 4C3 =4
hence 6+4+4=14.
Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is [tex] {11 \choose 3} = 165 . [/tex] As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is [tex] {7 \choose 3} = 35 [/tex]. Thus, there are only 35 ways to distribute the blackboards in this case.
If 8 identical blackboards are to be divided among 4 schools, there are 70 possible divisions. If each school must receive at least 1 blackboard, there are 56 possible divisions.
Explanation:If 8 identical blackboards are to be divided among 4 schools, the number of ways this can be done is 8C4, which is equal to 70.
If each school must receive at least 1 blackboard, then we need to subtract the cases where one or more schools do not receive a blackboard.
To calculate this, we can subtract the number of ways that three schools do not receive a blackboard (4C1 = 4), the number of ways that two schools do not receive a blackboard (4C2 = 6), and the number of ways that only one school does not receive a blackboard (4C3 = 4).
So, the number of divisions where each school receives at least 1 blackboard is 70 - 4 - 6 - 4 = 56 ways.
Write an equation about the movement of a Ferris wheel.As a Ferris wheel turns , the distance a rider is above the ground varies sinusoidally with time. The highest point on the wheel is 43 feed above the ground. The wheel makes a full circle every 8 seconds and has a diameter of 40 feet. Sketch a graph of your height as a rider as a function of time.a. What is an equation for your graph?b. Use this equation to predict your height above the ground at 4.5 seconds.
Answer:
Step-by-step explanation:
The graph is sketched in the attachment. It's easy to sketch the same graph using the given information. Let's say h is the height. For time t=0 you put a dot on 3 feet since it's the lowest point of the ferris wheel (you get that by substracting the diameter of 40 feet from the highest point given (43 feet).
Second dot is your highest point 43 feet at t=4 sec since it is the half of the circle.
The third dot is your lowest point again at t=8 sec. If you connect the dots like a sine you get the sketched graph.
To find out what is the equation for the graph you need to look at the amplitude which in this case is 20 feet. Then you need to find out the frequency at which the wheel is turning. Since you are given the period (8 sec for a full cycle) you get the frequency:
[tex]f=\frac{1}{T}=\frac{1}{8}[/tex]
Now you need to find out the phase of the wave. Since we want to be at 0 feet at t=0 you need to shift the wave 90° degrees forward or [tex]\frac{\pi}{2}[/tex] in radians.
Finally it's important to shift the whole wave up. You do that by adding the appropriate amount that is in this case the half of the diameter plus the 3 feet to the ground.
The equation you get is:
[tex]h(t)=23+A\sin(2\pi f t-\phi)=23+20\sin(0.25\pi t-\frac{\pi}{2})[/tex]
where A is amplitude, [tex]\phi[/tex] is the phase shift and [tex]f[/tex] is the frequency.
Finally you can get the height at [tex]t=4.5[/tex] sec:
[tex]h(t=4.5)=23+20\sin\left(0.25\pi4.5-\frac{\pi}{2}\right)=41.478\ \text{ft}[/tex]
[tex]-1*f(-8)-4*g(4) =?[/tex]
Answer:
-7
Step-by-step explanation:
From the graph (see attached), we can read off the values of f(-8) and f(4)
when x = -8, y = f(-8) = -5
when x = 4, y = g(4) = 3
hence, substituting the above values into the given equation:
-1 * f(-8) - 4 * g(4)
= -1 * (-5) - 4 * 3
= 5 - 12
= -7