how many ways can you give 7 (identical) apples to your 4 favourite mathematics lecturers if each of them gets at most two apples
Answers
Thus, we get a total of 210 + 90 + 6 + 60 = 366 number of ways to distribute the 7 apples among the 4 lecturers.
To solve this problem, we can use a combination of techniques from combinatorics and basic arithmetic. Since each lecturer can receive at most two apples, we can break down the problem into several cases:
1. Each lecturer receives 2 apples: In this case, we simply need to distribute the 7 apples among the 4 lecturers in a way that each receives 2. This can be done in (7 choose 2) * (5 choose 2) * (3 choose 2) * (1 choose 2) = 210 ways.
2. Three lecturers receive 2 apples and one receives 1 apple: In this case, we need to choose one of the lecturers to receive 1 apple, and then distribute the remaining 6 apples among the other three in pairs. There are 4 ways to choose the lecturer who receives 1 apple, and then (6 choose 2) * (4 choose 2) * (2 choose 2) = 90 ways to distribute the remaining apples.
3. Two lecturers receive 2 apples each, and two receive 1 apple each: In this case, we need to choose two of the lecturers to receive 2 apples each, and then distribute the remaining 3 apples among the other two in a way that each receives 1. There are (4 choose 2) = 6 ways to choose the two lecturers who receive 2 apples, and then (3 choose 1) * (2 choose 1) = 6 ways to distribute the remaining apples.
4. One lecturer receives 2 apples, and three receive 1 apple each: In this case, we need to choose one of the lecturers to receive 2 apples, and then distribute the remaining 5 apples among the other three in a way that each receives 1. There are 4 ways to choose the lecturer who receives 2 apples, and then (5 choose 1) * (4 choose 1) * (3 choose 1) = 60 ways to distribute the remaining apples.
Adding up the results from each case, we get a total of 210 + 90 + 6 + 60 = 366 ways to distribute the 7 apples among the 4 lecturers.
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Related Questions
Carolina, with the intention of investing money in real estate, acquired a plot of land for R$ 350,000.00. Over four years, the asset underwent changes in its commercial value, as follows variations:
First year: 12% appreciation
Second year: 10% appreciation
Third year: 8% devaluation
Fourth year: 6% appreciation
Having this information as a reference, it is correct to say that at the end of the analyzed period this plot of land
will have the value of:
(A) BRL 329,000.00.
(B) BRL 372,901.76.
(C) BRL 420,000.00.
(D) BRL 420,506.24.
(E) BRL 437,754.24.
Answers
At the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24
What is appreciation and deprecation?Deprecation, also called devaluation, is the decrement in price of an asset. Appreciation is opposite of deprecation. This indicates increment in the price of the considered thing.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
\(\dfrac{a}{100} \times b\)
It is given that:
Initial price of the plot of land = $350,000First year: 12% appreciationSecond year: 10% appreciationThird year: 8% devaluationFourth year: 6% appreciationNow, consider appreciation of an amount A by P%.
Then, we have:
Increased price = Initial price + P% of initial price
Increased price = \(A + \dfrac{A}{100} \times P = A \times \left(1 + \dfrac{P}{100} \right)\)
Similarly, depreciated price by P% of an amount A is:
Decreased price = \(A - \dfrac{A}{100} \times P = A \times \left(1 - \dfrac{P}{100} \right)\)
We've got: A = 350,000
After 1st year, which had 12% appreciation, we get:
\(A_1 =A(1 + 12/100) = A(1.12)\\\)
After 2nd year, 10% appreciation we get:
\(A_2 =A_1(1 + 10/100) = A_1(1.1) = A(1.12)(1.1)\\\)
After 3rd year, which had 8% devaluation effect on the price, we get:
\(A_3 = A_2(1 - 8/100) = A_2(1-0.08) = A_2(0.92) = A(1.12)(1.1)(0.92)\)
After 4th year, which had 6% appreciation effect on the price, we get:\(A_4 = A_3(1 + 6/100) = A_4(1+0.06) = A_3(1.06) = A(1.12)(1.1)(0.92)(1.06)\)
Thus, the final effect on A is:
\(A \rightarrow A(1.12)(1.1)(0.92)(1.06) = A(1.2014464)\\\$350,000 \rightarrow 350000(1.2014464) = 420506.24\: \rm dollars\)
Thus, at the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24
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A water tank at Camp Newton holds 1200 gallons of water at time t = 0. During the time interval Osts 18 hours, water is pumped into the tank at the rate
W(t) = 95Vt sin^2 (t/6) gallons per hour During the same time interval water is removed from the tank at the rate R(t) = 275 sin^2 (1/3) gallons per hour a. Is the amount of water in the tank increasing at time t = 15? Why or why not?
b. To the nearest whole number, how many gallons of water are in the tank at time t = 18? c. At what time t, for 0 st 18, is the amount of water in the tank at an absolute minimum? Show the work that leads to your conclusion d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(C) until the tank becomes empty. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
Answers
(a)The amount of water in the tank is increasing.
(b)Evaluate \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.
(c)Solve part (b) to get the absolute minimum from the critical points.
(d)The equation can be set up as \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.
What is the absolute value of a number?
The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.
To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:
a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.
At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.
Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.
b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:
\(\int\limits^{18}_0(W(t) - R(t)) dt\)
Evaluate this integral to get the number of gallons of water in the tank at t = 18.
c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.
d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.
The equation can be set up as:
\(\int\limits^k_{18}-R(t) dt = 1200\)
Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.
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What is the mean?
2, 5, 4, 8, 4, 10, 2
TYPE ONLY THE NUMERIC ANSWER
Answers
Answer:
5
Step-by-step explanation:
Do you want to answer my most recent question on my profile? Free 50 points and it's just a one-question survey.
A company rents out 16 food booths and 21 game booths at the county fair. The fee for a food booth is $200 plus $10 per day. The fee for a game booth is $50 plus $6 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Answers
Answer: The amount paid for 15 food booths for d days is:
15×(100+5d).
The amount paid for 20 game booths for d days is:
20×(50+7d).
The total amount is:
15(100+5d)+20(50+7d)=1500+75d+1000+140d=1500+1000+140d+75d=2500+215d
Step-by-step explanation:
8 out of 32 is same as??
Please tell me solution with all steps
Answers
Answer:
4
Step-by-step explanation:
32/8
= 4
Pls mark as branlist
Pls, help! will give brainliest if right, and who you got it!
Answers
Answer:
-5/4
Step-by-step explanation:
(-2,5) (2,0)
0 - 5 / 2 - (-2)
-5 / 2- (-2)
-5 / 2 + (+2)
-5/4
-59=-3b-32 love for b
Answers
Answer:
b = 9
Step-by-step explanation:
-3b - 32 = -59
add 59 on both sides.
- 3b - 32 + 59 = 59 - 59
-3b + 27 = 0
subtract 27 on both sides.
-3b = -27
divide both sides by -3.
-3b/-3 = -27/-3
b = 9
Pls mark as brainliest if possible. Cheers
Answer:
b=9
Step-by-step explanation: If Its Correct Answer I Try My Best To Help Yall
Please help me solve for X
I'll give brainlyest
Answers
Answer:
1. x = 8
2. x = 12
3. x = 11
4. x = 6
Step-by-step explanation:
1.
102 + 102 = 204
360 - 204 = 156
156 / 2 = 78
78 = 10x - 2
78 + 2 = 10x
80 = 10x
80 / 10 = x
x = 8
2.
81 = 7x - 3
81 + 3 = 7x
84 = 7x
84 / 7 = x
x = 12
3.
77 = 6x + 11
77 - 11 = 6x
66 = 6x
66 / 6 = x
x = 11
4.
115 + 115 = 230
360 - 230 = 130
130 / 2 = 65
65 = 8x + 17
65 - 17 = 8x
48 = 8x
48 / 8 = x
x = 6
Yednia solved an equation and justified her steps as shown in the table.
2+2x5=−10
Drag and drop the reasons into the boxes to correctly complete the table.
Answers
Given:
Consider the equation
\(2+\dfrac{2x}{5}=-10\)
To find:
The steps and solution for the given equation.
Solution:
We have,
\(2+\dfrac{2x}{5}=-10\)
Step 1: Using subtraction property of equality, subtract 2 from both sides.
\(2+\dfrac{2x}{5}-2=-10-2\)
\(\dfrac{2x}{5}=-12\)
Step 2: Using multiplication property of equality, multiply both sides by 5.
\(\dfrac{2x}{5}\times 5=-12\times 5\)
\(2x=-60\)
Step 3: Using division property of equality, divide both sides by 2.
\(\dfrac{2x}{2}=\dfrac{-60}{2}\)
\(x=-30\)
Therefore, the solution of the given equation is \(x=-30\).
Python formats all floating point numbers to two decimal places when outputting using the print statement O True O False 1 pts >> Question 9 The if statement causes one or more statements to execute only when a Boolean expression is true. O True O False
Answers
Python formats all floating point numbers to two decimal places when outputting using the print statement. (FALSE)
The if statement causes one or more statements to execute only when a Boolean expression is true. ( TRUE)
What are Floating Points?Floating point is a number format that can be used to represent a large or small value.
In writing this number is done by writing it in exponential form, so that the number has a base number, the exponential number and the base number.
The following is writing scientific notation in floating point. example in decimal numbers
261,000,000,000 written 2.61 x 10¹¹
0.000000000261 is written 2.61 x 10^-10
The Floating point representation itself has two parts, namely the mantissa part and the exponent part. The mantissa determines the digits, while the exponent determines the value of how many powers the mantissa is, as follows:
±S * B±E
S = Significant also called mantissa
E = Exponent
B = Base
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use the properties of integrals to verify the inequality without evaluating the integrals. 2≤ ∫1 -1 √1 x^2 dx ≤ 2√2.
Answers
To verify the inequality without evaluating the integrals, we can use the properties of integrals.
First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.
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answer before next week plss
Answers
Answer: Yes, it is a right triangle.
Step-by-step explanation: Use Pythagorean theorem, which is \(a^{2}\) + \(b^{2}\) = \(c^{2}\)
Then plug in 2 of the values.
\(3^{2}\) + \(4^{2}\) = \(c^{2}\)
25 = \(c^{2}\)
c = 5
That makes a right triangle because Pythagorean theorem works only on right triangles.
Can someone please help me ASAP?? It’s due tomorrow!! I will give brainliest If It’s correct.
Answers
Hey there!
Formula: 1/2 * base * height = area
Equation: 1/2 * 6 * 8
Simplifying:
1/2 * 6 * 8
= 1/2 * 6/1 * 8/1
= 1 * 6 * 8 / 2 * 1 * 1
= 6 * 8 / 2 * 1
= 48 / 2
= 24
Therefore, your answer should be:
24 square units
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
the kutta-joukowski theorem, equation (3.140), was derived exactly for the case of the lifting cylinder. in section 3.16 it is stated without proof that equation (3.140) also applies in general to a two-dimensional body of arbitrary shape. although this general result can be proven mathematically, it also can be accepted by making a physical argument as well. make this physical argument by drawing a closed curve around the body where the closed curve is very far away from the body, so far away that in perspective the body becomes a very small speck in the middle of the domain enclosed by the closed curve.
Answers
The Kutta-Joukowski theorem, which is represented by equation (3.140), was originally derived for the case of a lifting cylinder. However, it can also be applied to a two-dimensional body of arbitrary shape, as stated in section 3.16.
A more detailed explanation of the answer.
To make a physical argument for this generalization, we can draw a closed curve around the body.
The key is to draw the curve far enough away from the body such that the body appears as a very small speck in the middle of the domain enclosed by the closed curve.
By doing this, we are essentially treating the body as a point object at the center of the curve. Since the body is now a very small speck in comparison to the large domain, its specific shape becomes insignificant to the overall flow around it.
Therefore, the lifting force calculations derived from the Kutta-Joukowski theorem for the lifting cylinder should also apply to the two-dimensional body of arbitrary shape, as long as the body is small in comparison to the domain enclosed by the closed curve.
This physical argument allows us to accept that equation (3.140) can be applied in general to a two-dimensional body of arbitrary shape without requiring a mathematical proof.
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Which rule explains why these triangles are congruent?
Answers
Answer:
SAS Congruence Rule
A triangle is said to be congruent to each other if two sides and the included angle of one triangle is equal to the sides and included angle of the other triangle.
Answer: SAS (side side angle postulate.)
Step-by-step explanation:
can be used to prove triangles congruent.
sides and the corresponding angle of the other, then the triangles are congruent.
GEOMETRY QUESTIONS PLEASE HELP ASAP, Thank you!!!
Answers
Answer: 6
Step-by-step explanation:
You can find the scale factor by comparing a side that is similar from each
AB is similar to PQ
2.4/2 = 1.2
Your scale factor is 1.2. So each of the sides was multiplied by 1.2
EDx1.2 = x
x= 5(1.2)
x= 6
if x=y+z transpose for z
Answers
Answer:
x = y + z
=> z = y - x
Step-by-step explanation:
Hope u understand
Which term is defined as a fee charged for the use of money?
a interest
b. down payment
C. principal
d. default
Please select the best answer from the choices provided
A
B
C
D
Answers
Which term is defined as a fee charged for the use of money?
\(\sf\purple{a.\:interest}\) ✔
b. down payment
C. principal
d. default
Explanation:
Interest is defined as a fee charge for the use of money.
\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35\:ヅ}}}}}\)
Two vectors are parallel if the absolute value of their dot product is equal to the product of their magnitudes. Which of the following vectors are parallel? Which are perpendicular?
[a = 0.9 1.2] [ b = -2 1.5] [c = 6 -8] [ d = -4.5 -6]
Answers
Vectors a and b are perpendicular to each other. vectors c and d are not perpendicular to each other but parallel. Two vectors are parallel if the absolute value of their dot product is equal to the product of their magnitudes. A vector is perpendicular if the dot product of the two vectors is zero.
(1) Vector a, (0.9, 1.2):
\(|a| = √(0.9² + 1.2²) = √(1.81)\)
= 1.34
\(b) |b| = √((-2)² + 1.5²) = √(6.25)\)
= 2.5
Therefore, to verify if they are parallel or perpendicular, we must calculate the dot product of a and b, which is:
(0.9 * -2) + (1.2 * 1.5)
= -1.8 + 1.8 = 0
So vectors a and b are perpendicular to each other.
(2) Vector c, (6, -8):
\(|c| = √(6² + (-8)²) = √(100)\) = 10
d) \(|d| = √((-4.5)² + (-6)²)\)
= √(45.25 + 36)
= √(81.25)
= 9.03
Therefore, to verify if they are parallel or perpendicular, we must calculate the dot product of c and d, which is:
(6 * -4.5) + (-8 * -6)
= -27 + 48
= 21
Therefore, vectors c and d are not perpendicular to each other but parallel.
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A puppy gained 1/2 ounce in weight every day. At this rate, how long did it take the puppy to gain 16 ounces?
Answers
Answer:
It took 32 days into the puppy was 16 ounces
Step-by-step explanation:
i hope this was helpful
Answer:
32 days to gain 16 ounce
Step-by-step explanation:
I. If y = \(\frac{1}{2}x\)
when y is total weight, x is day
Perform 16 = 1/2x
16 * 2 = x
x = 32
a circle has a circumference of 112pi cm what is its radius?
Answers
The radius of the circle with circumference 112\(\pi\) cm is given by 56 centimeters.
We know that the circumference of a circle with radius r is given by,
C = 2\(\pi\)r
Let the radius of the circle be r cm.
So the circumference of the circle is 2\(\pi\)r cm.
According to the question, the circumference is 112\(\pi\) cm. So,
2\(\pi\)r = 112\(\pi\)
2r = 112
r = 112/2
r = 56
Hence the radius of the circle is 56 centimeters.
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Suppose the commuting time on a particular train is uniformly distributed between 40 and 90 minutes. What is the probability that the commuting time will be between 50 and 60 minutes? Linked below is
Answers
The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.
In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:
f(x) = 1 / (b - a)
where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.
To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.
The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.
Therefore, the probability that the commuting time will be between 50 and 60 minutes is:
P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.
Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.
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the 4 th term of a geometric sequence is 125, and the 10th term is 125/64. find the 14th term. (assume that the terms of the sequence are positive). show your working
Answers
By using the formula of a geometric sequence, the 14th term will be 125/1024
We have, the Fourth term of geometric sequence T_4= 125 and T_10 = 125/64
Let's find the first term and common ratio of the geometric sequence.
Using the formula of the nth term of a geometric sequence, we get,
T_4 = a * r^3 = 125 ....(1)
and,
T_10 = a * r^9 = 125/64 ...(2)
On dividing eq. (2) by eq. (1), we get,
(r^6) = (125/64) / 125 ⇒ 1/64
Taking the sixth root of both sides, we get:
r = (1/64)^(1/6)
r = 1/2
Now that we know the common ratio, we can use the equation for the nth term of a geometric sequence:
T_n = a * r^(n-1)
To find the 14th term, we substitute n=14 and solve:
T_14 = a * (1/2)^(14-1) ⇒ a * (1/2)^13
We don't know the value of a yet, but we can use the fact that the 4th term is 125 to solve for it:
a * r^3 = 125
a * (1/2)^3 = 125
a = 125 * 2^3
a = 1000
Substituting this value for a, we get:
T_14 = 1000 * (1/2)^13
T_14 = 1000 * 1/8192
T_14= 125/1024
Therefore, the 14th term of the geometric sequence is 125/1024.
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Mary drives 33 miles in 3/5 of an hour. After 6 hours of traveling, how far will she drive?
Answers
Answer:
330 miles
Step-by-step explanation:
We can use a ratio to solve
33 miles x miles
------------ = ----------------
3/5 hour 6 hours
Using cross product
33 *6 = 3/5 x
198 = 3/5x
Multiply each side by 5/3
198*5/3 = 5/3 * 3/5x
330 =x
1) Find the value of 1 + 3x when x = 1
Answers
Answer:
4
Step-by-step explanation:
So, since we already know x = 1, we just need to figure out what 3 x 1 is. (Since there's no space between the 3 and the x, 3x would be 3 times x.)
3 x 1 = 3.
So, our "new equation" is:
1 + 3
Add them together to find the answer:
1 + 3 = 4
4 is your answer.
Hope this helps and have a nice day!
ITS BEEN MORE THAN 48 HRS SINCE I HAVE FIRST TIME POSTING THIS MUTILPE TIMES, PLEASE HEP :((((!!!!!!!!!!!!!!!!!!!!!
Find the area of the circle. Give your answer to two decimal places. SHOW YOUR WORK so I can see if the answer makes sense!
Answers
Step-by-step explanation:
Radius of the circle is 20mm.
Use the formula for the area of the circle.
A = r^2 * π
A = 20^2 * π
A = 1256.64 mm^2 (2 d.p.)
Maddox has $12.25 to spend on sports
drinks. Each drink costs $1.75. Use the
guess, check, and revise strategy to solve
the equation 1.75d = $12.25 to find d, the
number of drinks Maddox can buy.
Answers
your answer would be 7, maddox can buy 7 things
Directions: Use the product rule to simplify the following monomials.
24.) (2xy)( -4x²) + (6x)(6x²y)
25.) (2ab²)(4a²b³) - (10a³b)(6b⁴)
ANYONE PLEASE HELP ME I REALLY NEED THE ANSWER RIGHT NOW BECAUSE I HAVE TO PASS THIS TOMORROW MORNING AT MY 1ST CLASS I HOPE Y'ALL CAN HELP ME:(
I'LL MARK YOU AS THE BRAINLIEST!
Answers
Step-by-step explanation:
Multiply everything in the parenthesis.
24. (2xy)( -4x²) + (6x)(6x²y)
---> -8x³y + 36x³y
= 28x³y
25. (2ab²)(4a²b³) - (10a³b)(6b⁴)
---> 8a³b^5 - 60a³b^5
= -52a³b^5
Sorry, i cant turn the 5 into an exponent on my phone lol. but i hope this helps.
Question :
❖ Use the product rule to simplify the following monomials.
Answers :
24. (2xy)( -4x²) + (6x)(6x²y)
\( \tt = (2xy)( -4x²) + (6x)(6x²y) \\ \tt = ( - 8 {x}^{3} y) + 36 {x}^{3} y \\ \tt = 28 {x}^{3} y \: \: \: \: \: \: \\ \\ \\ \)
25. (2ab²)(4a²b³) - (10a³b)(6b⁴)
\( \tt = (2ab²)(4a²b³) - (10a³b)(6b⁴) \\ \tt = 8 {a3}^{2} {b}^{5 } - 60 {a}^{3} {b}^{5 } \: \: \: \: \: \: \\ \tt = - 52 {a}^{3} {b}^{5 } \: \: \: \\ \\ \\ \)
Hope it helps you :DFulton Gardens buys 6,300 flower bulbs. If 70 bulbs can be planted in each flower bed, how many flower beds are needed to plant all the bulbs?
How many flower beds are needed to plant all the bulbs?
btw this is division.
Answers
Answer:
90
Step-by-step explanation:
6300/70=90
factor each:
x^8-13x^4+36=0
Answers
Answer:
Step-by-step explanation:
a = x^4
a^2 - 13a +36 = 0
(a-4)*(a-9)=0
a = 4, a = 9
so
x^4 = 4, x^4 = 9
x = + or - 4th root of 9 and 4