The advertising director for a television show has 7 ads to use on the program. If she selects 1 of them for the opening of the show,1 for the middle of the show,and 1 for the ending of the show,how many possible ways can this be accomplished
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Decide the formula to use
Since it can be seen from the question that order is important, we use the Permutation approach which is given by the formula:
\(^nP_r=\frac{n!}{\left(n-r\right)!}\)STEP 2: Find the number of possible ways
\(\begin{gathered} n=7,r=1\left(opening\right)+1\left(middle\right)+1\left(ending\right)=3 \\ we\text{ have;} \\ ^7P_3=\frac{7!}{\left(7-3\right)!}=\frac{7!}{4!}=\frac{7\times6\times5\times4!}{4!}=7\times6\times5=210 \end{gathered}\)Hence, there are 210 possible ways
Related Questions
simplify √([2m5z6]/[ xy])
Answers
The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:
Simplify the numerator:
√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)
= √2m√5z√6
Simplify the denominator:
√(xy) = √(x) * √(y)
Combine the numerator and denominator:
√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)
Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
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dont know how to solve this
Answers
Answer: Neither of them are correct.
Explanation4/x = x/8 and x is about 5.7
If the function y=sin(x) is transformed to y = sin(2x), how does the graph change?
It is stretched vertically.
It is compressed vertically.
It is stretched horizontally.
It is compressed horizontally..
Answers
Step-by-step explanation:
The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.
The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.
To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:
For y = sin(x):
x = 0, y = 0
x = π/2, y = 1
x = π, y = 0
x = 3π/2, y = -1
x = 2π, y = 0
For y = sin(2x):
x = 0, y = 0
x = π/2, y = 0
x = π, y = 0
x = 3π/2, y = 0
x = 2π, y = 0
As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).
Therefore, the correct statement is: It is compressed horizontally.
Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels, how much butter does she need? Round your answer to the nearest hundredth.
Answers
The required butter she needed is given as 1.67 cups of butter.
As given in the question, Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels,
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
here,
Let the nutter need be x cups,
now,
Taking the ratio o butter to kernels
[1 / 2] / 3 = x / 10
x = 10 / 6
x = 1.67
Thus, As of the given proportion, she requires 1.67 cups of butter.
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I am not divisible by 2,3,5 or 7. My two digits are not the same, but they are both squares. What two numbers could I be?
I NEED HELP FASTTT
Answers
Answer:
19 is suitable no in which 1 is square of itself and 9 is of 3
The only square single digits are 1, 4 and 9
Possible two digit numbers are:
14 - divisible by 2
19
41
49 - divisible by 7
91 - divisible by 7
94 - divisible by 2
Humanity would achieve in life expectancy of 110 years in approximately
Answers
Humanity would achieve a life expectancy of 110 years in approximately 60 years.
To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.
In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.
110 years - 80 years = 30 years
Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:
30 years / 5.3 years per decade ≈ 5.66 decades
Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.
To calculate the number of years, we multiply the number of decades by 10:
6 decades * 10 years per decade = 60 years
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how many ping pong balls do you need if you want to arrange them in the shape of an equilateral triangle with 23 rows
Answers
You would need a total of 276 ping pong balls
Step by step explanation:
To determine the number of ping pong balls needed to form an equilateral triangle with 23 rows, we can calculate the total number of balls in the triangle. In an equilateral triangle, each row has one more ball than the previous row. The formula for the sum of the first n natural numbers is given by:
Sum = (n * (n + 1)) / 2
In this case, we want to find the sum of the first 23 natural numbers. Substituting n = 23 into the formula, we get:
Sum = (23 * (23 + 1)) / 2 = 276
Therefore, you would need 276 ping pong balls to arrange them in the shape of an equilateral triangle with 23 rows.
What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a
vertex of the triangular bases?
A
a parallelogram that is not a rectangle
O a rectangle
O a triangle that must have the same dimensions as the bases
O a triangle that may not have the same dimensions as the bases
Answers
Answer:
a triangle that may not have the same dimensions as the bases
Step-by-step explanation:
The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.
A 16" × 16" square tray can hold at most 9 bagels placed side by side, as shown below. At most how many bagels can a 32" × 32" square tray hold if bagels are placed side by side?\
Answers
Answer:
At most it can hold 18 bagels
Step-by-step explanation:
So we can make this an equation
16 · 16 square tray = 9 bagels on top of it
We just doubled both sides of it
giving us 32 · 32 square tray = 18 bagels can be held.
Devon’s bike has wheels that are 26 inches in diameter. After the front wheel picks up
a tack, Devon rolls another 100 feet (1200 inches) and stops. How far above the ground in inches is the tack?
Answers
To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.
First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:
C = π × 26
C ≈ 81.64 inches
This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.
Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:
1200 / 81.64 ≈ 14.68 revolutions
Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.
Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.
Therefore, the tack is located 13 inches above the ground.
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Which shows the use of the associative property?
A. 7n + 1/5 = 1/5 + 7n
B. 7 + (1/5 + n) = (7 + 1/5) + n
C. 7(n + 1/5) = 7n + 5/7
D. (7 + 1/5) +n = 7 1/5 + n
Edugenity 2021
Common Core math
Answers
Answer:
B shows the associative property
Calculus application
1. Supposed that a ball is dropped from the upper observation deck of the Horizons 101 Tower 1., located
178 m above the ground. (a) What is the velocity of the ball after 5 sec? (b) How fast is the ball traveling
when it hits the ground?
Answers
Answer:
49m/s
59.07 m/s
Step-by-step explanation:
Given that :
Distance (s) = 178 m
Acceleration due to gravity (a) = g(downward) = 9.8m/s²
Velocity (V) after 5 seconds ;
The initial velocity (u) = 0
Using the relation :
v = u + at
Where ; t = Time = 5 seconds ; a = 9.8m/s²
v = 0 + 9.8(5)
v = 0 + 49
V = 49 m/s
Hence, velocity after 5 seconds = 49m/s
b) How fast is the ball traveling when it hits the ground?
V² = u² + 2as
Where s = height = 178m
V² = 0 + 2(9.8)(178)
V² = 0 + 3488.8
V² = 3488.8
V = √3488.8
V = 59.07 m/s
Franklin can jog approximately 2,000 meters in 4 minutes. Express this rate as a unit
rate.
I need it in step by step
Answers
You always get a unit rate from dividing. You always have two ways to do it, and get two unit rates, but one of them is more helpful.
2000 meters/4 minutes = 500 meters per minute
4 minutes/2000 meters = 0.002 minute per meter
(By the way ... Franklin is "jogging" a 3:13.12 mile. The world record is 3:43.13 .)
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.
Answers
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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Determine the y-interceptfor the following equation:7.2y + 4.5x = 72Y intercept:
Answers
The given expression is
\(7.2y+4.5x=72\)To find the y-intercept, we have to solve the equation for y.
\(\begin{gathered} 7.2y=72-4.5x \\ y=\frac{72-4.5x}{7.2} \\ y=10-0.625x \end{gathered}\)Remember that the y-intercept is the independent term.
Therefore, the y-intercept is 10, or the point (0, 10).The store bought a pair of shoes for $50 and sold them for $80. What percentage was the markup?
Answers
Answer: They resold them for $30 more than the original price.
Answer: 37.5%
Step-by-step explanation:
$80 - $50 = $30,
$30/$80 = 0.375 > 37.5%
A college class had 22 men and 14 women. Which other class has the same ratio of men to women?
Answers
Answer:
C-A class with 32 and 24 woman
Step-by-step explanation:
A college class had 22 men and 14 women. Which other class has the same ratio of men to women?
Original-22-14=8 (8)
A-40-18=22 (22)22 does not equal 8.
B-33-21=12 (12)12 does not equal 8.
C-32-24=8 (8)8 does equal 8.
D-11-6=5 (5)5 does not equal 8.
C has the same ratio because as you see men-woman=8 is the answer for both. Hence C is your answer.
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Albert is traveling 70 mph in his car. After 4 hours, how far will he have traveled?
A.
285 miles
B.
290 miles
C.
270 miles
D.
280 miles
Answers
Answer:
D.280 miles
Step-by-step explanation:
Albert is travelling 70mph (70 miles per hour).
So this can be worked out by:
70 x 4 hours= 280 miles
Answer:
D. 280
Step-by-step explanation:
if he is traveling 70 mph that means every hour he goes 70 miles so in 4 hours he will travel 280 miles
70 mph x 4 hours = 280 miles
Find the distance between the points (a, 0) and (0, b). StartRoot (a minus b) squared EndRoot StartRoot a squared + b squared EndRoot StartRoot (a + b) squared EndRoot StartRoot a squared minus b squared EndRoot
Answers
Answer:
\(\sqrt{a^2+b^2}\)
Step-by-step explanation:
Calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (a, 0) and (x₂, y₂ ) = (0, b)
d = \(\sqrt{(0-a)^2+(b-0)^2}\)
= \(\sqrt{(-a)^2+b^2}\)
= \(\sqrt{a^2+b^2}\)
Answer:
b
Step-by-step explanation:
uwu
what is the answer to x+2y=2 and
3x+4y=-4
Answers
Answer:
x = − 8 and y = 5 or (-8, 5)
Step-by-step explanation:
What is 4+1 lets see how smart u sre
Answers
Answer:
its legit 5
Step-by-step explanation:
Answer:
Very tricky question..
4 + 1 is 5 because you have written 4+1 not 4 1
so 5 is correct answer
Step-by-step explanation:
hope it helps
For the following, find the arc length:
(Use pi=3.14 and round your final answer to the hundredths.)
X=
Answers
\(\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47\)
Hi can someone please help me solve the following system of inequalities and state the coordinates in the solution setz
Answers
The graph of the system of the inequalities is attached.
To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.
Let's begin with the equation y = -x - 4:
Choose a range of x-values to plot.
For simplicity, let's use x-values from -10 to 10.
Substitute different x-values into the equation to find corresponding y-values.
For example:
When x = -10, y = -(-10) - 4 = 10 - 4 = 6.
When x = 0, y = -(0) - 4 = -4.
When x = 10, y = -(10) - 4 = -10 - 4 = -14.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = -x - 4.
Next, let's graph the equation y = (3/5)x + 4:
Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.
Substitute different x-values into the equation to find corresponding y-values. For example:
When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.
When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.
When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = (3/5)x + 4.
Now, let's shade the regions based on the inequalities:
For y < -x - 4, we need to shade the region below the line y = -x - 4.
For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.
Hence, the region where the shaded regions overlap represents the solution to both inequalities.
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how do you write the inequality -
"sixteen is less than a number"
Answers
Answer:
16<a number
Step-by-step explanation:
This is the less than symbol: <
16 is less than ( < ) a number
Lets put "a number" as x
16<x
Answer:
16 < n
Step-by-step explanation:
< - Less than. They way I remember is that the symbol is like an L.
n - Stands for number. You can use any letter I just chose that one.
A lawn service recommends covering 36,000 square feet with 6 pounds of fertilizer. Which graph has a slope that best represents the average amount of square feet covered per pound of fertilizer.
Answers
Answer:
Fertilizer recommendations for lawns are usually given in pounds of nitrogen to be applied per 1,000 square feet. Home gardeners sometimes have difficulty converting these recommendations to the amounts needed for their selected grade of nitrogen fertilizer and their lawn size. This fact sheet provides conversion tables and examples showing you how to calculate the amount of fertilizer needed for your lawn.
Step 1
To determine the pounds of fertilizer to apply, first determine the percentage of nitrogen in your fertilizer. This can be found on the fertilizer bag. Nitrogen is always the first number in the three-number series listed on the fertilizer bag.
Step 2
Now determine the number of pounds of fertilizer to apply based on the percentage of nitrogen in your fertilizer and your fertilizer recommendation. Table 1 lists the number of pounds of material needed when nitrogen content ranges from 1 to 46%.
Justin is buying tickets to a concert online from Ticketmaster. He buys 3 tickets that all have the same price.
There is also a service charge, since he is buying it from Ticketmaster, for $5 per ticket. The total cost of his
order was $138.
Answers
Answer:
I don't know if your asking for the price for each ticket, but if you are, it's $41 each.
Step-by-step explanation:
5 x 3 = 15(price of the service charge)
138 - 15 = 123(price with out service tax)
123/3 = 41
Hope this was helpful
Tom and Blair live the same
distance from their school.
Marcia lives 2 blocks from the
school, but 7 blocks from Blair.
She lives 1 block closer to the
school than she does to Tom.
They all live on the same street
as the school. How far apart do
Tom and Blair live?
Answers
Answer:
Step-by-step explanation:
We can think of this problem like a triangle that Tom, Blair, and Marcia live in.
This triangle is a right triangle.
the opposite is 3, the hypotenuse is 7, and the adjacent side is unknown.
Solving for the adjacent side will give us the distance that Tom and Blair live from each other
a^2 +b^2 = c^2
3^2 + b^2= 7^2
Now we solve for B
7^2 =49
3^3=9
9+b^2=49
Now we subtract
49-9=40
9+40=49
The square root of 40 is 6.3246
Now we check our work
3^2 +6.32^2=7^2
9+ 40 =49
The answer is, tom and Blair live approximately 6.3246 blocks from each other
Hope this helps!
Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
Answers
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
Johnny and his father go fishing at 5:00 AM. After motoring 6 km upstream, Johnny writes a letter to his friend, puts the letter in a bottle and drops it into the river. the bottle floats in the current and reaches at 7 : 40 AM the point where Johnny and his father began the trip. If the speed of the boat in still water is 9 km/h, what is the speed of the river current?
Answers
Answer:
4.5
Step-by-step explanation:
Probably too late for your RSM homework, but here is the solution:
6/(9-x) [Time they motored upstream] +6/x [Time it took the bottle to get back to the starting point] = 8/3 [Total Time]
Simplify to 54/(x(9-x))=8/3
Cross multiply: 162=(8x)(9-x)
Simplify -x^2+9x=20.25
Multiply both sides by negative one and move 20.25 to the other side. x^2-9x+20.25=0
Solve and get 4.5 :D!
what is the inverse of r(t)=5^t
Answers
Answer:
t(r) = log(r)/log(5) = log₅(r)
Step-by-step explanation:
You want the inverse of r(t)=5^t.
Solve for tAn exponential function is solved using logarithms.
\(r = 5^t\qquad\text{given}\\\\\log(r)=t\cdot\log(5)\qquad\text{take logarithms}\\\\\boxed{t(r)=\dfrac{\log(r)}{\log(5)}}\qquad\text{divide by the coefficient of t}\)
The change of base formula can be used to simplify this a bit.
\(\boxed{t(r)=\log_5(r)}\)
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Additional comment
The latter form of the inverse function can be found directly at the first step by taking logarithms base 5.
The notation here is slightly different from the usual "inverse function" notation, where we designate the inverse of f(x) using f⁻¹(x). The notation we have used recognizes that the function r(t) generates ordered pairs (t, r), and the inverse function t(r) generates ordered pairs (r, t).
You are welcome to make use of whatever inverse function notation will satisfy your grader.