Answer:
46+46 = 92
180-92 = 88
x = 88
Step-by-step explanation:
Which operation would help solve for t?
T-13=35
Answer:
t = 48
Step-by-step explanation:
Hector plays a video game that awards gems based on how long he plays. He made this graph to study how his playing time relates to number of gems:
A graph plots t=playing time in hours on the horizontal axis, from 0 to 7, in increments of 1, versus g=total gems on the vertical axis, from 0 to 48, in increments of 8, on a coordinate plane. Points are plotted as follows: (2, 16), (4, 32), and (6, 48).
A graph plots t=playing time in hours on the horizontal axis, from 0 to 7, in increments of 1, versus g=total gems on the vertical axis, from 0 to 48, in increments of 8, on a coordinate plane. Points are plotted as follows: (2, 16), (4, 32), and (6, 48).
How many total gems will Hector get if he plays for
10.5
10.510, point, 5 hours?
gems
The number of gems that Hector will get if he plays for 10.5 hours is given as follows:
84 gems.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
From the table, the constant is given as follows:
k = 48/6 = 32/4 = 16/2 = 8.
Hence the equation giving the number of gems after playing for x hours is given as follows:
y = 8x.
After 10.5 hours, the number of gems is then given as follows:
y = 8 x 10.5
y = 84 gems.
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Answer:
84
Step-by-step explanation:
A recipe call for 2 eggs for every 3 cups of sugar used. A total of 9 cups of sugar are used. How many eggs do I need?
Answer:
6
Step-by-step explanation:
Answer:
Step-by-step explanation:
(help) Write an expression for the quotient of 371 and y .
Answer: 371 / y
Step-by-step explanation: 371 is the dividend and y is the divisor
I just need the function the justification for both answers please help
We are given a table of x and y values and we are asked to find a possible function that represents it.
We notice that the function has a symmetry around the y axis, since the relationship shows:
when x = 1 , y = 2
when x = -1, y = 2
and also
when x = 3 , y = 10
when x = - 3, y = 10
(same value of y for opposite values of x)
In fact, this function could be well represented by a quadratic function of thr form:
f(x) = x^2 + 1
since
f(1) = 1^2 + 1 = 2
f(-1) = (-1)^2 + 1 = 2
f(3) = 3^2 + 1 = 10
f(-3) = (-3)^2 + 1 = 10
The second function that comes expressed as points on the plane, and given by the following 5 points:
(-9,0), (-4, 5), (0, 9), (4, 5), and (9,0)
is again a function that shows a symmetry around the y-axis, so it is an even function again, and loos like the vertex of it is located at the point (0.9)
notice as well, that as we move away from the y-axis in the x values, the values for y decrease (are less and less than 9, as the x value lies further away from the y-axis.
Then we suspect that the function representing this, is an absolute value function with vertex at the point (0, 9) on the y-axis.
Notice that the "slope" of this function is (to the right of the y axis) given by:
slope = (y2 - y1) / (x2 - x1) = (0 - 5) / (9 - 4) = -5 / 5 = -1
and on the left of the y-axis, the slope is "1".
Then, we use the following absolute value function:
f(x) = - |x| + 9
we now chek the given pairs :
f(-9) = - |-9| + 9 = 0 correct!
f(-4) = - |-4| + 9 = - 4 + 9 = 5 correct!
f(0) = - |0| + 9 = 9 correct!
f(4) = - |4| + 9 = -4 + 9 = 5 correct!
f(9) = - |9| + 9 = -9 + 9 = 0 correct!
Then the function we suggest for this second case is:
f(x) = - |x| + 9
Question 7 of 25
If F(x) = 2x-5 and G(X) = x2 + 1, what is G(F(x))?
O A. 4x2 + 26
O B. 2x2 + 2x-5
O C. 4x2 - 20x + 26
O D. 2x3-5
Answer: C
Step-by-step explanation:
G(F(x)) means F(x) is being plugged into every x in G(x). Since we are given the G(x) and F(x) functions, we can directly plug 2x-5 into x²+1.
G(F(x))=G(2x-5)
G(F(x))=(2x-5)²+1 [use FOIL method to expand (2x-5)²]
G(F(x))=(4x²-10x-10x+25)+1 [combine like terms]
G(F(x))=4x²-20x+26
Now that we have found G(F(x))=4x²-20x+26, we know that the answer is C.
Help&EXPLAIN
Don’t use for points or I’ll take it back and report
Answer:
132
Step-by-step explanation:
a straight line is 180% , so if the other triangle has a 48% we would subtract 180% by 48%.
Answer:
132
Step-by-step explanation:
Since those two angles are linear, they would form to make 180 degrees. So 180-48 is 132.
Which is more, 1 kilometer or 1,359 meters?
Answer:
1359 meters
Step-by-step explanation:
thenks and mark me brainliestt :))
Answer:
1359 meters
Step-by-step explanation:
1 kilometer=1000 meters
2x + 3 = 5 x = plz answer thank you
x=1
explaination:
2x+3=5x
Subtract 5x from both sides.
2x+3−5x=0
Combine 2x and −5x to get −3x.
−3x+3=0
Subtract 3 from both sides. Anything subtracted from zero gives its negation.
−3x=−3
Divide both sides by −3.
x=
−3
−3
Divide −3 by −3 to get 1.
x=1
the difference between three times a number M and 11 is 10
Answer:
m = 7
Step-by-step explanation:
3m - 11 = 10
3m = 10 + 11
3m = 21
m = 21/3
m = 7
A car travels a distance of 112km at an average Speed of 70km/h. It then Travells Further for 60km at an average Speed of 50 km/hr. Calculate for the entire Journey of the total time taken.
The total time taken for the entire journey is 2.8 hours.
To calculate the total time taken for the entire journey, we can use the formula:
Time = Distance / Speed
For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:
Time1 = 112 km / 70 km/h = 1.6 hours
For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:
Time2 = 60 km / 50 km/h = 1.2 hours
To find the total time for the entire journey, we sum up the times for both parts:
Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours
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why is this equavilant
Answer:
Distribution property
Step-by-step explanation:
a fridge costs €336 after a price increase of 40%. what was the original price
the original cost is "x", which is the 100% of the original price, and we also know that €336 is its price increased by 40%, namely 100% + 40% = 140%, so
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 336& 140 \end{array} \implies \cfrac{x}{336}~~=~~\cfrac{100}{140} \\\\\\ \cfrac{x}{336}=\cfrac{5}{7}\implies 7x=1680\implies x=\cfrac{1680}{7}\implies x=240\)
6. Journalise the following transactions
1. Bricks for Rs 60,000 and timber for Rs 35,000 purchased for
the construction of building. The payment was made by cheque.
2. Placed in fixed deposit account at bank by transfer from current
account Rs 13,000.
3. Appointed Mr. S.N. Rao as Accountant at Rs 300 p.m. and
Received Rs 1000 as security Deposit at 5% p.a. interest.
4. Sold goods to shruti for Rs 80,000 at 15% trade discount and
4% cash discount. Received 75% amount immediately through a
cheque.
5. Purchased goods from Richa for Rs 60,000 at 10% trade
discount and 5% cash discount. 60% amount paid by cheque
immediately.
6.
On 18th jan,Sold goods to shilpa at the list price of Rs 50,000
20% trade discount and 4% cash discount if the payment is made
within 7 days. 75% payment is received by cheque on Jan 23rd.
7. On 25th jan, sold goods to garima for Rs 1,00,000 allowed her
20% trade discount and 5% cash discount if the payment is made
within 15 days. She paid 1/4th of the amount by cheque on Feb 5th
and 60% of the remainder on 15th in cash.
8. Purchased land for Rs 2,00,000 and paid 1% as brokerage and
Rs 15,000 as registration charges on it. Entire payment is made by
cheque.
9. Goods worth Rs 25,000 and cash Rs 40,000 were taken away
by the proprietor for his personal use.
10. Sold goods costing Rs 1,20,000 to charu at a profit of 33% 3 %
on cost less 15% trade discount.
9
11. Paid rent of building Rs 60,000 by cheque. Half the building is
used by the proprietor for residential purpose.
12. Sold goods costing Rs 20,000 to sunil at a profit of 20% on
sales less 20% trade discount .
13. Purchased goods for Rs 1000 from nanda and supplied it to
helen for Rs 1300. Helen returned goods worth Rs 390, which in
turn were returned to nanda.
14. Received invoice at 10% trade discount from rohit and sons
and supplied these goods to madan, listed at Rs 3000.
1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)
2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)
3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)
4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)
5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)
6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)
7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)
8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)
9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)
10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)
11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)
12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)
13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)
14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)
Here are the journal entries for the given transactions:
1. Bricks and timber purchased for construction:
Debit: Bricks (Asset) - Rs 60,000
Debit: Timber (Asset) - Rs 35,000
Credit: Bank (Liability) - Rs 95,000
2. Transfer to fixed deposit account:
Debit: Fixed Deposit (Asset) - Rs 13,000
Credit: Current Account (Asset) - Rs 13,000
3. Appointment of Mr. S.N. Rao as Accountant:
Debit: Salary Expense (Expense) - Rs 300
Debit: Security Deposit (Asset) - Rs 1,000
Credit: Accountant (Liability) - Rs 300
4. Goods sold to Shruti:
Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000
Credit: Sales (Income) - Rs 80,000
5. Goods purchased from Richa:
Debit: Purchases (Expense) - Rs 60,000
Credit: Accounts Payable - Richa (Liability) - Rs 60,000
6. Goods sold to Shilpa:
Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000
Credit: Sales (Income) - Rs 50,000
7. Goods sold to Garima:
Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000
Credit: Sales (Income) - Rs 1,00,000
8.Purchase of land:
Debit: Land (Asset) - Rs 2,00,000
Debit: Brokerage Expense (Expense) - Rs 2,000
Debit: Registration Charges (Expense) - Rs 15,000
Credit: Bank (Liability) - Rs 2,17,000
9. Goods and cash taken away by proprietor:
Debit: Proprietor's Drawings (Equity) - Rs 65,000
Credit: Goods (Asset) - Rs 25,000
Credit: Cash (Asset) - Rs 40,000
10. Goods sold to Charu:
Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000
Credit: Sales (Income) - Rs 1,20,000
Credit: Cost of Goods Sold (Expense) - Rs 80,000
Credit: Profit on Sales (Income) - Rs 40,000
11. Rent paid for the building:
Debit: Rent Expense (Expense) - Rs 60,000
Credit: Bank (Liability) - Rs 60,000
12. Goods sold to Sunil:
Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000
Credit: Sales (Income) - Rs 24,000
Credit: Cost of Goods Sold (Expense) - Rs 20,000
Credit: Profit on Sales (Income) - Rs 4,000
13. Goods purchased from Nanda and supplied to Helen:
Debit: Purchases (Expense) - Rs 1,000
Debit: Accounts Payable - Nanda (Liability) - Rs 1,000
Credit: Accounts Receivable - Helen (Asset) - Rs 1,300
Credit: Sales (Income) - Rs 1,300
14. Goods received from Rohit and Sons and supplied to Madan:
Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)
Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700
Debit: Accounts Receivable - Madan (Asset) - Rs 3,000
Credit: Sales (Income) - Rs 3,000
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What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.
In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.
Order-Preserving Function:
A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.
Increasing Function:
If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).
Isomorphism:
A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:
a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).
b. f is onto (surjective): Every element in Q has a pre-image in P.
When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.
Automorphism:
An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.
These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.
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Distribute the negative sign: -(x - 6y)
Answer:
-x + 6y.
Step-by-step explanation:
-(x - 6y)
= -1*x -1*-6y
= -x + 6y
A used-car costs $5,000. You figure you can get 4 years out of it. You drive 10,000 miles per year. Your car insurance costs $1,200 per year. You figure you'll spend $400 per year on maintenance. Gas costs $3 per gallon, and the car gets 25 miles per gallon. What will your average cost (all costs included) per mile be over the 4 years?
Answer:
26,800
Step-by-step explanation:
Im not sure but thats what I got
Answer:
$0.405
I just took the test.
!!!!!MAJOR HELP!!!!!
!!!!!I will give Brainy!!!!!
The function Y equals 5X is graft in coordinate plane. Which point will not be on the line?
A.(0,5)
B.(3,15)
C.(4,4,22)
D,(5,25)
If no idea then look at image
Answer: its b or c try one then the other
Step-by-step explanation:
If a student thinks of a number from 1 to 75, what is the probability that the number will be 20, 30, or 40?If a student thinks of a number from 1 to 75, what is the probability that the number will be 20, 30, or 40?
Answer:
the probability is 3/75.
Please gimme the variables to define the sytem and 2 system of equations
Answer:
\(8.5x+4y=99.5,\ x+y=17\)
Step-by-step explanation:
\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)
TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
The statements supported by the data in the table are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
To determine which statements are supported by the data in the table, let's analyze the given information:
The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean, we need to find the average number of cars sold each month at each dealership.
For Admiral Autos:
(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13
For Countywide Cars:
(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13
Since both dealerships have an average of 13 cars sold per month, the statement is supported.
The median number of cars sold in a month is the same at both dealerships.
To find the median, we arrange the numbers in ascending order and select the middle value.
For Admiral Autos: 4, 10, 15, 17, 19
Median = 15
For Countywide Cars: 9, 10, 14, 15, 17
Median = 14
Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.
The total number of cars sold is the same at both dealerships.
To find the total number of cars sold, we sum up the values for each dealership.
For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65
For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65
Since both dealerships sold a total of 65 cars, the statement is supported.
The range of the number of cars sold is the same for both dealerships.
The range is determined by subtracting the lowest value from the highest value.
For Admiral Autos: 19 - 4 = 15
For Countywide Cars: 17 - 9 = 8
Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.
The data for Admiral Autos shows greater variability.
To determine the variability, we can look at the range or consider the differences between each data point and the mean.
As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.
Based on the analysis, the statements supported by the data are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
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Solve using a proportion.
Answer:
i cant see it
Step-by-step explanation:
Given vector u=<3,-4> find magnitude and degree
The sum of magnitude of u + v is 15.99.
What is magnitude?The magnitude or size of a mathematical object is described as a property which determines whether the object is larger or smaller than other objects of the same kind.
Given that, magnitude of u = 5
Magnitude of v = 11
The angle between them i= 40°
we represent u and v in vector form,
u = 5 ( cos 40° i + sin 40° j ) = 3.83 i + 3.21 j
v = 11 ( cos 40° i + sin 40° j ) = 8.42 i + 7.07 j
The sum of two vectors is given by
u + v = 3.83 i + 3.21 j + 8.42 i + 7.07 j
u + v = 12.25 i + 10.28 j
Magnitude of u + v = √(12.25²+10.28²)
Magnitude of u + v
Magnitude of u + v = √( 150.063 + 105.678)
Magnitude of u + v = 15.99
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complete question:
Given the magnitudes of vectors u and v and the angle θ between them, find sum of . Give the magnitude to the nearest tenth when necessary and give the direction by specifying the angle that the resultant makes with u to the nearest degree. ∣ u∣ = 5, ∣ v∣ = 11, θ = 40°
please help 30 points
The price of admission at a movie theater is $6 for an adult and $4 for a child. In one day, the movie theater sold 80 tickets and made $420. How many adults and how many children bought tickets to the movie theater that day?
x + y = 80,
6x + 4y = 420
Which is a solution of the system of equations, and what does it represent?
(20, 60); 20 adult tickets and 60 child tickets
(30, 50); 30 adult tickets and 50 child tickets
(40, 40); 40 adult tickets and 40 child tickets
(50, 30); 50 adult tickets and 30
Last option: (50, 30); 50 adult tickets and 30 child tickets
What is Linear Equation?A linear equation is an equation in which the highest power of the variable is always 1.
We have the system of equations:
x + y = 80
6x + 4y = 420
We will use elimination method to solve it:
Multiply the first equation by -6 and then add the equations:
- 6x - 6y = -480
6x + 4y = 420
We get:
-2y = -60
After dividing both sides by -2 we get:
y = 30
then plugging 30 in place of y into the original first equation we get:
x+30=80
Then subtracting 30 from both sides we get:
x = 50
The solution to the system is (50, 30)
Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.
Thus, x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.
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Answer:
( 50, 30)
Step-by-step explanation:
A quarterback completes 44% of his passes. Show all work.
a. Construct a probability distribution table (out to n = 6) for the number of passes attempted before the quarterback has a completion?
b. What is the probability that the quarterback throws 3 incomplete passes before he has a completion?
c. How many passes can the quarterback expect to throw before he completes a pass?
d. Determine the probability that it takes more than 5 attempts before he completes a pass.
e. If he throws 8 passes on the opening drive, what is the probability that he made at least half of them?
a.The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. the probability is 0.1399.
c. the quarterback can expect to throw about 2.27 passes before completing one.
d. the probability is 0.1865.
e. the probability is 0.7349.
what is probability?The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.
a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:
P(X=k) = \((1-p)^{k-1}\)×p
where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.
The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:
P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰
= 0.56²×0.44
= 0.1399
Therefore, the probability is 0.1399.
c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:
E(X) = 1/p
where p is the probability of completion on each attempt.
In this case, p = 0.44, so the expected number of passes is:
E(X) = 1/0.44
= 2.27
Therefore, the quarterback can expect to throw about 2.27 passes before completing one.
d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:
P(X > 5) = 1 - P(X <= 5)
= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]
= 0.1865
Therefore, the probability is 0.1865.
e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:
P(X ≥ 4) = 1 - P(X < 4)
where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.
Using the binomial probability distribution table or calculator, we can find:
P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]
= 0.7349
Therefore, the probability is 0.7349.
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How much would you have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would
earn?
Round to 2 decimal places and do not include the $
symbol.
Answer:
To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:
PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)
where:
- PV is the present value of the annuity due (the amount you would have to deposit today)
- PMT is the monthly payment ($75)
- r is the annual interest rate (3.5%)
- n is the number of times interest is compounded per year (12 for monthly compounding)
- t is the number of years (10)
PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**
Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.
What is 3-3×6+2 please?
Answer:
-13Step-by-step explanation:
What is 3-3×6+2 please?
remember PEMDAS
3 - 3 × 6 + 2 = (solve multiplication)
3 - 18 + 2 = (solve addition)
3 - 16 = (solve subtraction)
-13 (result)
At the movie theatre, child admission is 6.20 and adult admission is $9.90. On Tuesday, four times as many adult tickets as child tickets were sold, for a total
sales of $1419.80. How many child tickets were sold that day?
Answer:
31
Step-by-step explanation:
For every 4 adult tickets sold, only 1 child ticket was sold. So the cost of 4 adult tickets and 1 child ticket is:
4 x 9.9 + 1 x 6.2 = 45.80
Divide the total sales by 45.80: 1419.80 ÷ 45.80 = 31
So there were 31 lots of "4 adult tickets and 1 child ticket" sold.
Therefore, there were 31 x 4 = 124 adult tickets sold
and 31 x 1 = 31 child tickets sold
Which function does this graph represent?
A downward open parabola rises from (negative 2 point 4, negative 4) to (negative 1, 2) and declines through (0 point 4, negative 4) on the x y coordinate plane.
A.
f(x) = 3(x + 1)2 + 2
B.
f(x) = -3(x + 1)2 + 2
C.
f(x) = -3(x + 1)2 − 2
D.
f(x) = 3(x − 1)2 + 2
The function that corresponds to the parabola Graph is f(x) = -3(x + 1)² + 2, which is option B.
The graph represents a downward open parabola that rises from (-2.4,-4) to (-1,2) and then declines through (0.4,-4) on the x-y coordinate plane.
To determine the function that corresponds to this graph, we need to consider the key features of a parabolic function, including its vertex and axis of symmetry.
The vertex of a parabola in the form f(x) = a(x-h)² + k is (h,k), and the axis of symmetry is x = h
From the graph, we can see that the vertex of the parabola is at (-1,2), which means that h = -1 and k = 2.
We also know that the parabola opens downward, which means that a < 0.
Therefore, we can eliminate options A and D since they both have a positive value of "a."
Next, we can test options B and C.
Option B has the form f(x) = -3(x + 1)² + 2, which means that the vertex is at (-1,2) and the parabola opens downward due to the negative coefficient of (x+1)².
To confirm if option B is correct, we can check if the point (0.4,-4) lies on the parabola:
f(0.4) = -3(0.4+1)² + 2 = -3(1.4)² + 2 = -5.88
Since the y-coordinate of the point (0.4,-4) is -4, which is equal to -5.88, we can see that the point lies on the parabola.
Therefore, the function that corresponds to the graph is f(x) = -3(x + 1)² + 2, which is option B.
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