Answer:
The fifth term of the binomial expansion
[tex]T_{5} = 70 x^{8} y^{20}[/tex]
Step-by-step explanation:
Step:1
Given that the binomial expansion
( x² + y⁵ )⁸
we know that
[tex]T_{r+1} = n_{C_{r} } a^{r} x^{n-r}[/tex] ...(i)
Step:2
put r = 4
[tex]T_{4+1} = 8_{c_{4} } (x^{2} )^{4} (y^{5} )^{8-4}[/tex]
[tex]T_{5} = 70 x^{8} y^{20}[/tex]
Final answer:-
The fifth term of the binomial expansion
[tex]T_{5} = 70 x^{8} y^{20}[/tex]
The student council raised $150 during the school dance if they charge $3per ticket and received $24 in other donations what is the amount of tickets they sold?
Help me with this question
Answer:
20[tex]\pi[/tex]
Step-by-step explanation:
Circumference formula: [tex]2\pi r[/tex]
Since the diameter is 20, the radius will be half of the diameter
r=d/2, where d=20
r=20/2=10
C=[tex]2\pi r[/tex]
C=2(10)[tex]\pi[/tex]
C=20[tex]\pi[/tex]
What is the range of 5,4,6,3,4?
Answer:
Range=2
Step-by-step explanation:
Range=Highest number-Lowest number
=5-3=2
Hope it Help
Mark Me Brillainest
What is the probability that a randomly selected subprime mortgage in the state during November 2008 was not current? (Round your answer to two decimal places.)
Complete question is;
The attached chart shows the (approximate) total number of subprime home mortgages in a state in November 2008, broken down into four categories.
What is the probability that a randomly selected subprime mortgage in the state during November 2008 was not current? (Round your answer to two decimal places.)
Answer:
Probability that the one randomly selected was not current = 0.36
Step-by-step explanation:
From the attached image, we can see that the four mortgage categories are mutually exclusive. This means that none of the 4 status depends on any other.
From the image attached;
Total number of subprime mortgages = 196,280
Number of current mortgages = 126,330
Thus;
Probability of a randomly selected subprime mortgage being current = 126330/196280 = 0.64
Then;
Probability that the one randomly selected was not current = 1 - 0.64
Probability that the one randomly selected was not current = 0.36
Round to The nearest hundred 554,695 help
Answer:
554,700
Step-by-step explanation:
HALLPPP DUE TODAY!!!! I RLLY NEED THIS DONE ASAP!! PLS AND THANK YOU!!!!
Find the compound interest
Principal: $750
Interest Rate: 6% or 0.06 Time: 2 years
Answer:92.7
Step-by-step explanation:
Use the compound interst formula: A= P(1+r)^n
750(1+.06)^2=842.7
Now substract the principal to find the compound interest : 842.7-750= 92.7
Hope it helps
Each of two parents has the genotype green/blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a
child. Assume that if the child has at least one green allele, that color will dominate and the child's eye color will be green
a. List the different possible outcomes. Assume that these outcomes are equally likely
b. What is the probability that a child of these parents will have the blue / blue genotype?
c. What is the probability that the child will have green eye color?
Step-by-step explanation:
what is the ability that the children will have green eyes collar
Abigail ordered a 32 oz steak that cost $60.
(cost to weight)
1
In a circle, the coordinates of the endpoints of
a diameter are (4,5) and (10,1). What are the
coordinates of the center of the circle?
Answer: (7,3)
Step-by-step explanation:
Find the midpoint of the diameter to find the center
mid-point formula
[tex](\frac{(x_{1} +x_{2)} }{2} ,\frac{(y_{1} +y_{2} )}{2} )[/tex]
Using points (4,5) and (10,1)
[tex](\frac{4+10}{2} , (\frac{5+1}{2} )\\(\frac{14}{2},\frac{6}{2}) \\\\(7,3)[/tex]
The coordinates of the center of the circle are (7, 3).
Given that, in a circle, the coordinates of the endpoints of a diameter are (4,5) and (10,1).
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]
The center of the circle is midpoint of a diameter
Here, (x, y) = ((4+10)/2, (5+1)/2)
= (14/2, 6/2)
= (7, 3)
Therefore, the coordinates of the center of the circle are (7, 3).
To learn more about the formula of midpoint visit:
https://brainly.com/question/4728902.
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the 11th term of an arithmetic sequence is 57 and the sum of the first and fourth term is 29. determine the first three terms of the sequence, the formular of nth term
Let a (n) denote the n-th term of the sequence. Since the terms form an arithmetic sequence, you have
a (n) = a (n - 1) + d
for some fixed constant d. You can write any term in the sequence as a function of the first term:
a (n) = [a (n - 2) + d] + d = a (n - 2) + 2d
a (n) = [a (n - 3) + d] + 2d = a (n - 3) + 3d
and so on, down to
a (n) = a (1) + (n - 1) d
so given that a (11) = 57 (so that n = 11), you have
a (1) + 10d = 57 … … … [1]
The sum of the first and fourth terms is 29:
a (1) + a (4) = 29
but we can write a (4) in terms of a (1) :
a (1) + [a (1) + 3d] = 29
which gives us another equation in a (1) and d :
2 a (1) + 3d = 29 … … … [2]
Now solve [1] and [2] :
-2 (a (1) + 10d) + (2 a (1) + 3d) = -2 (57) + 29
-17d = -85
d = 5
a (1) + 10d = a (1) + 50 = 57
a (1) = 7
Then the n-th term of the sequence is given by
a (n) = 7 + 5 (n - 1) = 5n + 2
32614 round to nearest 100 place?
Answer:
32600
Step-by-step explanation:
Which answer choice below describes an equation?
A
7 - X
B
x is 10 times greater than y
3
+n
5
D
Six times a number
b
x is 10 times greater then y 3+n 5
A farmer wants to know the effect of using various amounts of fertilizer in relation to the yield of his crops. Be subdivided a portion of his land into 10 separate but essentially equal plots. He divided the land so that all of the plots had equal exposure to sun, rain, and other environmental conditions. He randomly selected 2 of the 10 plots and spread 2 pounds of fertilizer over each of them. Then he randomly selected 2 of the remaining plots and spread 3 pounds of fertilizer over each of them. He continued with the last sets of plots in the same manner, spreading 4, then 5, then 6 pounds of fertilizer over each of them. Below is a computer output for linear regression of amount of fertilizer versus yield for the 10 plots of land.
Predictor Coef SE Coef T P
Constant 10.100 0.7973 12.67 0.000
Fertiz 1.150 0.1879 6.12 0.000
Required:
What is the equation of the least squares regression line from this sample?
Answer:
The equation of line is
[tex]\text{yield}=1.15\times \text{fertilizer}+10.1[/tex]
Step-by-step explanation:
The general equation of line is given as
[tex]y=mx+b[/tex]
where
y is the dependent variable which is yield in this case.
x is the independent variable which is fertilizer in this case
m is the coefficient of the fertilizer whose value is 1.150 from the given values.
b is the constant whole value is 10.100 from the given values.
Thus the equation becomes.
[tex]\text{yield}=1.15\times \text{fertilizer}+10.1[/tex]
Question Progress
Homework Progress
20/32 Marks
a) Write 375 as the product of prime factors.
Give your answer in index form.
b) Work out the Highest Common Factor of 375 and 150.
Answer:
a) 375 = 3 × 3 × 3× 3 × 5
in index form it is 3 × 5³.
prime factor of,
150 = 2 × 3 × 5 × 5.
To find the HCF, multiply all the prime factors common to both numbers: Therefore, HCF = 3 × 5 × 5.
ANS : 75
hope this helps you☺️☺️
Jackie wants to buy a $25,000 car, but she can afford to pay only $400 per month for 5 years. If the interest rate is 8.25% compounded monthly, how much does she need to put down?
Answer:
A down payment of $5,388.50 to get the principle to $19611.50 for a monthly payment of $400 for 60 months at 8.25%
Step-by-step explanation:
I used a payment calculator
I don't know how else to solve the problem. I thought I could find the equation, but I don't think this is it, since P didn't equal 19611.50
A = P[r(1+r)n] / [(1+r)n - 1]
if you have the correct formula follow this process
A = 400 P principle ??? r = i%/12 = 0.0825/12 = 0.006875 n= 5×12 = 60
solve for P then down payment = 25000 - P
P = A / [r(1+r)n] / [(1+r)n - 1]
= A [(1+r)n - 1] / [r(1+r)n]
= 400 [(1 +.006875)60 -1] / [0.006875( 1 +0.006875)60]
Solution set no links please
I believe that the answer is 11/4. I hope this helps!
answer this asap I will give out brainliest test: "Birmingham was like an oven" (p 162) is an example of... *
idiom
personification
simile
metaphor
Answer:
that's confusing.. is there a picture?
what is the area of the donut pictured below? use 3.24 for pi
How much salt is needed to fill a pit (rectangular) that is 8 m deep and 16 m wide and 4 m long? Show work
Answer:
512
16 · 4 = 64
64 · 8 = 512
If you had 2 angles that equal 180 degrees and you was given a angle of
117. What degree is the missing angle? *
Answer:
angle=63°
I hope it's helps you
John gets his first job working at an ice cream shop because he loves ice cream. He gets paid $9 per hour. Create a table to demonstrate how much money John will make from 0 - 6 hours. Let x equal the number of hours worked, and let y equal the amount of money that he will make. Then, create a graph with your results.
Answer:
1hr: $9
2hr: $18
3hr: $27
4hr: $36
5hr: $45
6hr: $54
Step-by-step explanation:
You can use Desmos, the graphing calculator (online tool)
Solve the system of equations.
12x-5y = -20
y =x+4
Answer:
1. 12x-5y = -20 Answer: 2(picture)
2. y =x+4 Answer: 1(picture)
Step-by-step explanation: Hope this help :D
Fencing with the length of 840 m surrounds two identical playing fields with a common side. The fields can be side-by-side and separated by a fence, as shown in the figure. Find the dimensions in the maximum area of each field.
Answer:
x = 140 y = 105 x · y = 14700 m²
Step-by-step explanation:
good question
it looks like 3 sides of length x
and 4 sides of length y
area 1 = area 2
and the length of all the sides sum to 840
3x + 4y = 840 find the maximum area = 2· x · y
This is a calculus problem that I can't remember how solve
if x = 0 y = 210
if y = 0 x = 280 280 / 2 = 140 the mid-point the logical answer
if x = 140 y = 105 x · y = 14700 m² this appears to be the max
if x = 135 y = 108.75 x · y = 14681.25 m² smaller area
if x = 145 y = 101.25 x · y = 14681.25 m² smaller area
I need an eqaution with a quadratic and take the first derivative
y = (840 - 3x) / 4 xy = max area y = max area/x
(max area) / x = (840 - 3x) / 4 solve for x
max area = x(840 - 3x) / 4
max area = [840x/4 - 3x²/4] '
max area = 210x - 3x²/4 take the first derivative
max area = 210 - 6x/4 maximum occurs when slope = 0
0 = 210 - 3x/2
3x/2 = 210
x = 210·2/3
x = 420 / 3
x = 140 y = 105
3(140) + 4(105) = 420 + 420 = 840 checks
can anyone help me with this and explain it will mark brainlyiest.
9514 1404 393
Answer:
x = (8/9)(4 +√7) ≈ 5.9073
Step-by-step explanation:
Maybe you want to know the value of x.
The Pythagorean theorem can be used to find the length of the bottom side of the right triangle. It is ...
bottom = √((5x)² -(3x)²) = √(16x²) = 4x
Then the cosine of the angle at lower left is ...
cos(α) = Adjacent/Hypotenuse
cos(α) = 4x/5x = 4/5
Now, the law of cosines can be used to find x. Using the angle whose cosine we just found, we have ...
(4x)² = (5x)² +8² -2(5x)(8)cos(α)
16x² = 25x² +64 -80x(4/5)
9x² -64x +64 = 0 . . . . . put in standard form
The quadratic formula can be used to find the solutions.
x = (-(-64) ±√((-64)² -4(9)(64)))/(2(9))
x = (64 ±√1792)/18 = (32 ±8√7)/9 ≈ {1.204, 5.907}
In this context, only the larger solution makes sense.
x = (8/9)(4 +√7) ≈ 5.9073
_____
Formulas used
Law of Cosines
For sides a, b, c and angle C opposite side c, ...
[tex]c^2=a^2+b^2-2ab\cdot\cos(C)[/tex]
Quadratic formula
For quadratic ax²+bx+c=0, the solutions are ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Pythagorean theorem
For legs a, b, and hypotenuse c of a right triangle, ...
c² = a² + b²
_____
Alternate solution
As an alternative to using the Law of Cosines, you can define "y" to be the length of the dashed bottom leg of the triangle whose hypotenuse is 4x. Two equations can be written using y and the Pythagorean theorem for the right triangles in which y is all or part of a leg. This set of equations can be solved for x to get the same result as the one shown above.
Can someone help me with this question plz Show work.
Answer:
D. 32.3
Step-by-step explanation:
Length-a
Width-b
A=ab=6.8×4.75=32.3
A blueprint shows an apartment with an area of 15 square inches. If the blueprint's scale is 1 inch : 8 feet, what will the actual square footage of the apartment be?
The actual area of the apartment will be 960 square feet.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
A blueprint shows an apartment with an area of 15 square inches.
If the blueprint's scale is 1 inch : 8 feet.
Then the scale factor will be 8/1 feet per inch.
Then the actual area square footage of the apartment will be
Actual area = 15 x (scale factor)²
Then the actual area of the footage will be
Actual area = 15 x (8/1)²
Actual area = 15 x 64
Actual area = 960 square feet
Thus, the actual area of the apartment will be 960 square feet.
More about the dilation link is given below.
https://brainly.com/question/2856466
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MAX POINTS PLEASE HELp
part a. What are the values of x and y? If your answer is not a whole number, write it as a decimal and round to one decimal place if necessary.
part b:
Here is a triangular prism.
What is the volume of the prism, in cubic centimeters?
cubic centimeters
What is the surface area of the prism, in square centimeters?
cubic centimeters
Answer:
X=35 Y=73
Step-by-step explanation:
use the opposite angle theorem for x. X would equal 35.
we know that x is 35. So 2y+35=180
180-35=2y
y=72.5 or 73
srry I can’t help with question 2. I don’t know how
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Topic: Profit and Loss
Ex: 7a, page no. 92
cost price
12
Q1. A man purchased a dozen pens for Rs 25 each and sold them at Rs 28
each. Find the total profit as well as the profit per cent on the transaction.
Ans. Solution:
Answer:
RS 36
12%
Step-by-step explanation:
Profit = total selling price - cost price
(28 - 25) x 12 = 36
Percentage profit = (profit / cost price) x 100
Cost price = 25 x 12 = 300
(36/300) x 100 = 12%
Please answer someone!!!
Answer:
TrueStep-by-step explanation:
[tex]\sqrt{(xy)^3}[/tex] = [tex]((xy)^{1/2})^3[/tex] =[tex](xy)^{{1/2}*3}[/tex] =[tex](xy)^{3/2}[/tex]The answer is TRUE
True
HELP ME PLEASE EDCITE !!!!
Answer:
I might be in highschool, but I'm sure I can still help.
Step-by-step explanation:
See the 45 degree angles? that means they're equal sides. So 4v2 = 5.65, right? so if you take 180 - 5.65, and then divide by two, you should have the length to each of those sides. They're equal, remember. So, the answer would be 180 - 5.65 = 174.35. 174.35 / 2 = 87.175. In this case, k = 87.175 :)