What is the value of the 3rd term of the expansion (3y-2)^7?A. 35a^4b^3B. -10206y^5C. 21a^5b^2D. 20412y^5
Answers
Solution
Using the Binomial Theorem
\((A+B)=\sum ^n_{k\mathop=0}{{{{n\choose k}}}}A^{n-k}B^k\)The r-th term of a binomial expansion is given as;
\(T_r={{{{{{{n\choose r-1}}}}}}}A^{n+1-r}B^{r-1}\)so when r = 3
\(\begin{gathered} T_3={{{{{{{n\choose 2}}}}}}}A^{n-2}B^2 \\ \text{ If }n=7,A=3y\text{ and }B=-2 \\ \Rightarrow T_3={{{{{{{{7\choose 2}}}}}}}}\times(3y)^{7-2}(-2)^2 \\ \Rightarrow T_3=21\times(3y)^5\times4 \\ \Rightarrow T_3=21\times3^5\times y^5\times4 \\ \Rightarrow T_3=20412y^5 \end{gathered}\)Hence the correct option is D
Related Questions
Hello! Help please! Can you show steps?
Answers
Answer:
$283. 81
Step-by-step explanation:
Start with P = 200.00 dollars.
If the interest is compounded continuously, then after t = 7 years the at the rate r = 5% = .05, the total amount of money in the account will be A.
\(A= P e^{r*t}\)
\(A = 200*e^{.05*7}\)
A = 283.8135097
A ≈ $283. 81
if a tree is 105 metres tall in real life what would be the height of the diagram of the tree if the scale was 1: 1000
Answers
Answer:
1.05
Step-by-step explanation:
it is 105 divided by 1000
Answer:
0.105 metres
Step-by-step explanation:
105 divided by 1000
POINTS, AND BRAINLIEST
Answers
The identification of parts A,B andC is illustrated below with their various reasons given.
What is an equilateral triangle?An equilateral triangle is the triangle that has all its sides equal in length and each angle is made up of angle 60°.
Part A = The similar triangle are RGE and PBE
Part B = The triangles selected are similar because it was formed by an interception of the parallel lines of the rectangle GCPR.
Part C= All the sides of the equilateral triangle are the same therefore the distance from B to E and from P to E is the same with BP which is 225ft.
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please help. will give brainliest
Answers
Answer:
B. The probability that the student received a grade better than C is 0.45Step-by-step explanation:
Total number of students:
15 + 30 + 35 + 16 + 4 = 100StatementsA.
p(<D) = 4/100 = 0.040.04 ≠ 0.2IncorrectB.
p(>C) = (30 + 15)/100 = 45/100 = 0.450.45 = 0.45CorrectC.
p(not A or B) = (100 - 15 - 30)/100 = 55/100 = 0.550.55 ≠ 0.45IncorrectD.
p(B or C) = (30 + 35)/100 = 65/100 = 0.650.65 ≠ 0.35IncorrectIn the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F. The highest monthly average temperature occurs in July at 78 °F. Write and graph a sinusoidal curve equation to model the average monthly temperature in Michigan. Assume the period is 12 months and that January is at the origin of the graph of this function. (6 points)
ANSWER ATTACHED
Answers
sinusoidal curve equation 29 sin (\(\pi\)/9 x)-49
What is Equation of a sinusoidal curve ?Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.
In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.
The highest monthly average temperature occurs in July at 78 °F
Assume the period is 12 months and January is at the origin of the graph of this function.
sinusoidal curve equation that models the data y
Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.
So, using the property of sinusoidal curve equation we have
=29 sin (\(\pi\)/9 x)-49
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Julio spent $40 and now has no money left. He had _before his purchase
Answers
Answer:
$40
Step-by-step explanation:
If he spent $40 and has none left that means he currently has $0.
If you subtract $40 - b = $0
b = $40
Q1 Combining Functions
An accident at an oil drilling platform on top of the ocean is causing a circular-shaped oil slick to grow on the surface of the water. The area of the oil slick is given by A(r)=πr ^2, where r is the radius of the oil slick in feet. The radius is increasing according to the function r(t)=1.5t, where t is measured in minutes.
Q1.1 Part a)
If it has been 60 minutes since the accident started, what is the area of the oil slick? (Round your answer to 2 decimal places, and include correct units.)
Q1.2 Part b)
Find the function, (A∘r)(t), and then explain what this function means in the context of the question.
Q1.3 Part c)
How long after the accident started will the area of the oil slick be 20,000 square feet? (Round your answer to 1 decimal place and include correct units.)
Q2 Combining Functions
The cost (in dollars) to heat a home during a Summer day in Tucson is a function of the day's high temperature, and it is approximately given by C(H)=0.07H+0.42, where H is the day's high temperature. Suppose that the predicted high temperatures for the next 7 days are given in the table below. (graph at the bottom)
Q2.1 Part a)
Express the high temperature as a linear function of the day. (Make sure to use the given variables.)
Q2.2 Part b)
Use the linear function from Part a) to create a function that represents the daily cost to heat a home in Tucson as a function of the day. (Make sure to use the given variables.)
Q2.3 Part c)
Pick one ordered pair on the graph of the new function from Part b), and then explain what it tells you in the given context of the question.
Answers
The volume of the slick would be 25 cubic feet after 60 mins/
How to solve thisConsider the volume of the slick is roughly given as:
V(r) = 0.08\(\pi r^2\)
r is the radius of the slick in feet
And r(t) = 0.5t
V(r(t)) = V(0.5t)
= 0.08\(\pi\)(0.5t)^2
= 0.02\(\pi t^2\)
Recall the volume is 225ft^3
225 = 0.02\(\pi t^2\)
Make t subject formula
t = 60 mins.
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Find the volume of the cone that sits on top of the cylinder
Answers
Answer:
Vc = (π/3)✓17 ≈ 4.12 ft³
Step-by-step explanation:
h = ✓(4²+1²)
h = ✓17
V = πr²h/3
V = π(1)²✓17/3
V = (π/3)✓17 ≈ 4.12
Find the next three terms of the following geometric sequence:
Leave your answers in surd form.
2√√3
2
6
Answers
Answer: here I hope this helps
Step-by-step explanation: To determine if the sequence is geometric, we find the ratio of the consecutive terms shown.
Find the ratio of the consecutive terms. 4,8428,168216,3216232,6432264,128642128,…
The sequence is geometric. The common ratio is r=2.
Find the ratio of the consecutive terms. −2,6−2−36,−126−2−12,36−12−336,−7236−2−72,216−72−3216,…
The sequence is not geometric. There is no common ratio.
27,9,3,1,13,19,…
Find the ratio of the consecutive terms. 927133913131313113191313
The sequence is geometric. The common ratio is r=13.
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.3 years with a standard deviation of 1.1 years.
Step 1 of 2: If a sampling distribution is created using samples of the ages at which 35 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.
give thanks for more! your welcome!
Step-by-step explanation:
Can someone help me with this?
Answers
Bag A contains 7x counters.
Bag B contains 2x counters.
Five counters are taken from bag A and put in bag B.
Write an expression, in terms of x, for the number of counters now in bag B.
Answers
In 2017, a website reported that only 10% of surplus food is being recovered in the food-service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume this is the true population proportion and that you plan to take a sample survey of 575 companies in the food service and restaurant sector to further investigate their behavior.1. What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion? (Round your answer to four decimal places.)?
2. What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion? (Round your answer to four decimal places.)?
Answers
Answer:
1. 0.9836 = 98.36% probability that your survey will provide a sample proportion within ±0.03 of the population proportion
2. 0.7698 = 76.98% probability that your survey will provide a sample proportion within ±0.015 of the population proportion.
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
In this question, we have that:
\(p = 0.1, n = 575\)
So
\(\mu = 0.1, s = \sqrt{\frac{0.1*0.9}{575}} = 0.0125\)
1. What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion?
This is the pvalue of Z when X = 0.1 + 0.03 = 0.13 subtracted by the pvalue of Z when X = 0.1 - 0.03 = 0.07. So
X = 0.13
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.13 - 0.1}{0.0125}\)
\(Z = 2.40\)
\(Z = 2.40\) has a pvalue of 0.9918
X = 0.07
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.07 - 0.1}{0.0125}\)
\(Z = -2.40\)
\(Z = -2.40\) has a pvalue of 0.0082
0.9918 - 0.0082 = 0.9836
0.9836 = 98.36% probability that your survey will provide a sample proportion within ±0.03 of the population proportion.
2. What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion?
This is the pvalue of Z when X = 0.1 + 0.015 = 0.115 subtracted by the pvalue of Z when X = 0.1 - 0.015 = 0.085. So
X = 0.115
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.115 - 0.1}{0.0125}\)
\(Z = 1.2\)
\(Z = 1.2\) has a pvalue of 0.8849
X = 0.085
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.085 - 0.1}{0.0125}\)
\(Z = -1.2\)
\(Z = -1.2\) has a pvalue of 0.1151
0.8849 - 0.1151 = 0.7698
0.7698 = 76.98% probability that your survey will provide a sample proportion within ±0.015 of the population proportion.
Write the exact value of the side length of a square with an area of1.100 square units.2.95 square units.3. 36 square units.4.30 square units.
Answers
We have that the first one is 10, the second one between 9 and 10, the thid one is 6 and the last one is between 5 and 6.
A roll of breakfast sausage weighing 4/5:of a pound is cut into 3 patties of the same size. What is the weight of each patty?
NO LINKS!!!
Answers
Solution:
Note that:
4x/5 ÷ 3 = 1 pattySolve for x to find the weight of each patty.
4/5 ÷ 3 = Weight of 1 patty=> 4/5 x 1/3 = 1 patty=> 4/15 = 1 pattyThe weight of a patty is 4/15 of a pound.
Answer:
4/15
Step-by-step explanation:
Hope this helps! Sorry if I am wrong.
on sale, boxes of cereal cost $11 for 4 boxes, $24.75 for 9 boxes, and $33 for 12 boxes. Predict the cost of twelve boxes.
Answers
Answer:
omg this is so eaasy like u need tia tammera
Step-by-step explanation:
Answer:
$33(the answer is $33)
Is the given value a solution of the inequality?
2 + s ≥ 10; s = 7
14 – r < 9; r = 6
j – 11 ≥ 20; j = 32
t + 6 > 40; t = 35
show work pls
Answers
Answer:
35
Step-by-step explanation:
There are 39 calories in 12 fluid ounces of a tea drink. Based on this information, how many calories are in 36 ounces of the tea drink?
Answers
Answer:
Let '?' be the calories in 36 ounces.
39 12
? 36
When the above numbers are cross-multiplied you get the equation:
12x = 1404
? = 1404/12
? = 117
Therefore, there are 117 calories in 36 ounces of tea drink.
Parker spent $12.75 having her bike fixed on Monday. The next day she spent $3.99 on a new water bottle for his bike. The same day he made $20.48 mowing yards. Which of the following describes the result of these two days?
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The measure of angle D of the given Kite is: 127°
How to find the angle of the Kite?From the diagram, the figure represents a kite.
Properties of a kite are:
- Two pairs of adjacent sides are equal.
- Two diagonals intersect each other at right angles.
- The longer diagonal bisects the shorter diagonal.
- The angles opposite to the main diagonal are equal.
Thus:
The angle B = the angle D
The sum of all angles of a quadrilateral = 360
Given: ∠A = 36 and ∠C = 70
Thus:
2∠D = 360 - (36 + 70)
2∠D = 254
∠D = 127°
So, the measure of angle D = 127°
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f(x)=−x+2, find f(-6)
Answers
Answer: -4
Step-by-step explanation:
f(x) = -x+2
-6+2
=-4
Please answer number 5 find the surface area
Answers
Ill edit this later to answer the question, but what is the question???
Consider the curve given by the equation x2 − y2 = 2x + y + xy − 4. Find the equation
of the tangent line to the curve at the point (1, 1).
Answers
The equation of the tangent line at (1,1) is given as follows:
y - 1 = -0.25(x - 1).
How to obtain the equation of the tangent line?The curve for this problem is given as follows:
x² - y² = 2x + y + xy - 4.
Applying implicit differentiation, we obtain the slope of the tangent line, as follows:
2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y
(dy/dx)(1 + x + 2y) = 2x - 2 - y
m = (2x - 2 - y)/(1 + x + 2y).
At x = 1 and y = 1, the slope is given as follows:
m = (2 - 2 - 1)/(1 + 1 + 2)
m = -0.25.
Hence the point-slope equation is given as follows:
y - 1 = -0.25(x - 1).
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What is 4x + 2 < 5x?
Answers
Step-by-step explanation:
4x +2 <5x4x <5x-24x-5x<-2-x<-2x<2Asp please
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 28 fU/sec. The function s(1) = - 16? + 281 + 5 gives the height of the ball, in feet, t seconds after it has been thrown. Determine
the time at which the ball reaches its maximum height and find the maximum height.
The ball reaches its maximum height of [ ft [ sec(s) after the bal is thrown.
(Type integers or decimals.)
Answers
The ball reaches a maximum height of 35.375 ft.
The height of the ball can be expressed as:s(t) = -16t^2 + 28t + 5
To find the time at which the ball reaches its maximum height, we can take the derivative of the height function with respect to time:
s'(t) = -32t + 28
And then set the derivative equal to zero and solve for t:
-32t + 28 = 0
32t = 28
t = 28/32 = 7/8 sec
So, the ball reaches its maximum height 7/8 seconds after it was thrown.
Next, we can plug this value of t back into the height function to find the maximum height:
s(7/8) = -16 * (7/8)^2 + 28 * (7/8) + 5 = 9.375 + 21 + 5 = 35.375 ft
Therefore, The ball reaches a maximum height of 35.375 ft.
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Question 6 of 10
What is the solution to the system of equations graphed below?
y = -2x + 4
y=x-5
Answers
Answer:
the solution to the system of equations is (x, y) = (3, -2).
Step-by-step explanation:
y = -2x + 4 (Equation 1)
y = x - 5 (Equation 2)
To solve for x, we can equate the right sides of the equations:
-2x + 4 = x - 5
Now, we can solve for x:
-2x - x = -5 - 4
-3x = -9
x = (-9) / (-3)
x = 3
Substituting the value of x back into Equation 2, we can solve for y:
y = 3 - 5
y = -2
During her first month, a salesperson sold $24,000 worth of merchandise.
During the second month, she sold 25% more than in her first month.
During the third month, she sold $42,000 worth of merchandise.
What was the percent increase in sales from the second month to the third?
Answers
Answer:She receives a monthly salary of $2,500 for which she must sell $20,000 wo
Step-by-step explanation:
simplify 14+ 18/2 * 18-7
Answers
Answer:
the solution is 169
Step-by-step explanation:
Answer:
169
Step-by-step explanation:
14 +18/2 x 18-7
14+9 x 18-7
14+162-7
169
What is the length of the diagonal of a non -regulation tennis court with length 20 feet and width 15 feet
Answers
Answer:
25 feet
Step-by-step explanation:
using the sides 20 and 15, use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the 2 side lengths and the diagonal.
\(a^{2} +b^{2} =c^{2} \\20^{2} +15^{2} =c^{2} \\400+225=c^{2} \\625=c^{2} \\25=c\)
What is the common difference in this sequence?{48, 32, 16, 0, ...