The middle term of the expansion of (√x + √y)⁸ is; B: 70 * x² * y²
How to solve binomial theorems?We want to expand the expression;
(√x + √y)⁸
Now, according to binomial expansion, we know that;
(x + y)ⁿ = ⁿC₀ xⁿ y⁰ + ⁿC₁ xⁿ ⁻ ¹ y¹ + ⁿC₂ xⁿ ⁻ ² y² + ..... + ⁿCₙ x⁰ yⁿ.
Now, for an 8 power binomial, the coefficient of each term from formula are respectively;
1 8 28 56 70 56 28 8 1
The mid term is the fifth term and so, we have;
(⁸C₄ * (√x)⁽⁸ ⁻ ⁴⁾ * (√y)⁴)
⇒ 70 * x² * y²
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What is the value of 9+n/3when n equals 12
Answer:
13
Step-by-step explanation:
Divide 12 by 3 first because of (PEMDAS) you get 4 tge add that to the 9 the you get 13.
P = parentheses
E = exponent
M = multiplication
D = division
A = addition
S = subtraction
Find the inverse, picture below!
Answer:
[tex]f^{-1}(x) = (x+7)^2[/tex]
Step-by-step explanation:
[tex]y=f(x) = \sqrt x - 7 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~~x= \sqrt y -7\\\\\implies \sqrt y = x+7\\\\\implies y = (x+7)^2\\\\\implies f^{-1}(x) = (x+7)^2[/tex]
There are 35 students on the Step Team to raise a total of 3,500 for uniforms. So far they have raised a total of 1,800. How much more money in dollars, does each member of the Step Team need to raise
Answer:
48.57 USD
Step-by-step explanation:
Just subtract 3500 from 1800 you get 1700
then
1700 divided by 35
Classify the following triangle as acute, obtuse, or right.
A. Obtuse
B. Acute
C. Right
D. None of these
Answer:
Acute Triangle.
Explanation:
The figure shows an equilateral triangle which has all the angles equal.
Acute Triangles are those who has angles less than 90°
Hence, an equilateral triangle is always an acute triangle.
Additional,
A right angle triangle has 90° angle.
An obtuse triangle has greater than 90° angle.
Estimate the solution to the following system of equations by graphing.
3x + 5y = 14
6x - 4y = 9
Answer:
(2.405, 1.537)
Step-by-step explanation:
When you graph these, they intersect at (2.405, 1.537).
You can use desmos as a graphing calculator, it is extremely helpful.
Hope this helps!
There are ten cards numbered from 1 to 10. Take out three cards from them.
i) the probability that the product of the numbers of the three cards is an odd number is
ii) the probability that the sum of the numbers of the three cards is an even number is
Answer:
Step-by-step explanation:
Part A
There are 5 odd numbers from 1 to 10. All three of them must be odd when drawn. I have to assume that there is no replacements.
Probability (odd) = (5 * 4 * 3) / (10 * 9 * 8) = 60 / 720
Probability (odd) = 0.083333
Part B
This is a little harder because 1 even number will turn everything even. So the way to handle this is to assume that there is (1 - probability(odd)) *720 that you have even
So the chances of an even result is 1 - odd/ total or
(1 - 1/12) * 720 = 660/720 = 0.917
Answer
Odd: 0.0833
Even: 0.917
simplify 2 2/3-1.25+5/6
Answer:
2.25or21/4
Step-by-step explanation:
hope it helps
Answer:
2 1/4 or 2.25Step-by-step explanation:
GivenExpression:
2 2/3 - 1.25 + 5/6SolutionSimplify it in below steps:
2 2/3 - 1.25 + 5/6 = 2 + 2/3 - 1 - 0.25 + 5/6 = 1 + 4/6 + 5/6 - 1/4 =1 + 9/6 - 1/4 =1 + 1 + 3/6 - 1/4 = 2 + 2/4 - 1/4 = 2 + 1/4 = 2 1/4 or 2.25Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are complementary, then the sum of their measures is 90°. E and F are complementary.
Using the law of detachment, the conclusion we can draw from the two given statements is: C. m∠E + m∠F = 90°.
What is the Law of Detachment?The law of detachment states that, if two statements are true, a third statement that is true can be derived also.
From the information given, we have:
First statement: If 2 angles are complementary, then their sum equals 90 degrees (If p, then q).
Second statement: Angles E and F are complementary (p).
The third true statement (q) would be:
m∠E + m∠F = 90°. (option C)
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100 points
1942 divded by 2^4
Answer: 121.375
Step-by-step explanation:
[tex]2^4=16[/tex]
[tex]\frac{1942}{2^4}[/tex]
[tex]\frac{1942}{16}=121.375[/tex]
The distance between two cities is 13 kilometers. There are approximately 1.6 kilometers in 1 mile. What is the number of miles between the two cities?
The number of miles between the two cities is 8.13 miles.
What is the number of miles between the two cities?In order to determine the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.
Number of miles = 13 / 1.6 = 8.13 miles
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A line intersects the points (-5, 1) and (-2,7). What is the slope of the line in simplest form? m=[?}
Step-by-step explanation:
To find slope : y2- y1 / x2 - x1
we have ( -5 , 1 ) which is ( x1 , y1 )
and ( -2 , 7 ) is ( x2 , y2 )
so; 7 - 1 / -2 - (-5)
6/3
= 2
Explain a time in your life you underwent metamorphosis
Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time
Step-by-step explanation:
I Hope This Helps!
Statistics
Assume there are 20 advanced English level students, 8 intermediate English
level students and 15 beginner English level students at statistics class. What
is the probability of selecting 10 advanced English level students and 10
non_ advanced English level students?
Answer:
no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44
Answer:
o
Step-by-step explanation:
A rubber bouncy ball is dropped from a
height of 101.00 inches onto a hard flat
floor. After each bounce, the ball returns
to a height that is 19% less than the
previous maximum height. What is the
maximum height reached after the 5th
bounce?
Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:
[tex]a_1 = 101, q = 0.81[/tex]
Then, the height of the nth bounce is given by:
[tex]a_n = 101(0.81)^{n-1}[/tex]
And the height of the 5th bounce is:
[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]
The maximum height reached after the 5th bounce is of 43.48 feet.
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The difference between two numbers is 31. Four times the smaller is equal to eight more than the larger. What are the numbers?
Answer:
13 and 44
Step-by-step explanation:
let x and y be the 2 numbers with y < x , then
x - y = 31 ( add y to both sides )
x = y + 31 ( subtract 31 from both sides )
x - 31 = y → (1)
4y = x + 8 → (2)
substitute y = x - 31 into (2)
4(x - 31) = x + 8
4x - 124 = x + 8 ( subtract x from both sides )
3x - 124 = 8 ( add 124 to both sides )
3x = 132 ( divide both sides by 3 )
x = 44
substitute x = 44 into (1)
44 - 31 = y , then
y = 13
the 2 numbers are 13 and 44
solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8
It looks like the differential equation is
[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]
Factorize the right side by grouping.
[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]
[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]
Now we can separate variables as
[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]
Integrate both sides.
[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]
[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]
[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]
You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.
(a-4)(a-11) please answer this
Write the equation of the circle whose center is (-5, -8) with diameter 12
Answer:
(x + 5)^2 + (y + 8)^2 = 6^2
Step-by-step explanation:
A circle formula: (x - h)^2 + (y - k)^2 = r^2
We are given diameter. To find the radius divide diameter by 2.
d = 12
12/2 = r = 6
H and K are given to be (-5 , -8)
(x - (-5))^2 + (y - (-8))^2 = 6^2
(x + 5)^2 + (y + 8)^2 = 6^2
I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.
Jessica and Callista go the local burger joint. They both want to buy the meal deal. Jessica has 34 of the money needed to buy the meal deal and Callista has half of the money needed to buy the meal deal. If the meal deal was $3 cheaper, then together they would have exactly enough money to buy two of the meal deals.
What is the original price of the meal deal? Show or explain how you got your answer.
The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4
How to write and solve equation?let
x = cost of the meal
Both = 2x - 3
Jessica = 3/4xCallista = 1/2x3/4x + 1/2x = 2x - 3
(3+2)x / 4 = 2x - 3
5/4x = 2x - 3
5/4x - 2x = - 3
(5-8)x/ 4 = -3
-3/4x = -3
x = -3 ÷ -3/4
= -3 × -4/3
= 12/3
x = $4
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If events A and B are independent, what must be true?
P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)
Answer: P(A|B) = P(A)
Step-by-step explanation:
If they are independent, one event being given doesn't impact the probability of the other event.
Answer:b
Step-by-step explanation:
b
The distribution of head circumference for full term newborn female infants is approximately normal with a mean of 33.8 cm and a standard deviation of 1.2 cm.
Determine the approximate percentage of full term newborn female infants with a head circumference between 31 cm and 36 cm. Enter your answer using two decimal places.
Using the normal distribution, it is found that 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 33.8, \sigma = 1.2[/tex]
The proportion of full term newborn female infants with a head circumference between 31 cm and 36 cm is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 31, hence:
X = 36:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 33.8}{1.2}[/tex]
Z = 1.83
Z = 1.83 has a p-value of 0.9664.
X = 31:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 33.8}{1.2}[/tex]
Z = -2.33
Z = -2.33 has a p-value of 0.0099.
0.9664 - 0.0099 = 0.9565.
0.9565 = 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.
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5 more than n is the quotient of n and 4
Answer:
3
Step-by-step explanation:
Determine the composition of
transformations that would map figure ABCD to figure A'B'C'D"
1. The transformation that would map vertex B to B' is
It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".
What is transformation of quadrilateral?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
here, we have,
from the given figure we get,
there is a transformation of ABCD to A'B'C'D".
now,
Reason: choices are translation, reflection, rotation, or dilation, this is translation.
Hence, It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".
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A copy machine makes 36 coples per minute. How many coples does it make in 4 minutes and 45 seconds?
What is the value of the expression 30+(-6)?
A -180
B -5
C 5
D 24
Answer:
24
Step-by-step explanation:
from the question above,
30+(-6) =
when plus is multiplying minus it's minus
+ × - = -
30-6 = 24
this shape is a triangular Pyramid the 3 sides slant height is 14 the base width is 8 and the base height is 6.9
The surface area of a triangular prism with the 3 sides slant height as 14 the base width as 8 and the base height as 6.9 is 155. 705 in²
What is the surface area of a triangular prism?
The surface area of a triangular pyramid is the total area of all it's faces.
The properties of a triangular prism are;
It has a triangular base It is bounded y three lateral triangular faces meeting at one vertex. It has all its faces as trianglesHow to determine the surface area
Surface area = Base Area + 1÷2 (perimeter × base height)
But base area = 1÷2 (base side × height)
Base area = 1÷ 2 (8 × 14) = 0.5 × 112 = 56 in²
Perimeter = sum of all the sides = 14 + 8 + 6.9 = 28. 9 in
Base height = 6. 9in
Surface area = 56 + 1 ÷ 2 ( 28.9× 6. 9) = 56 + 0.5 × 199.41 = 56 + 99. 705 = 155. 705 in²
Surface area = 155. 705 in²
Therefore, the surface area of the triangular prism is 155. 705 in²
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You plan to build a house that is 1 ½ times as long as it is wide. You want the land around the house to be 20 feet wider than the width of the house, and twice as long as the length of the house, as shown at the right.
The total area with land based on the information given is 3x² + 60x.
How to find the area?Let the width = x
Let the length = (1.5 × x) = 1.5x
Area = 1.5x × x = 1.5x²
The area along with land:
Width = x + 20
Length = 3 × x = 3x
The total area with land:
= Length × Width
= 3x(x + 20)
= 3x² + 60x.
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A convenience store was charging $3.83 for a
bag of chips but raised the price 13%. The new price after the increase is $4.33.
Enter an expression to show how the new price
was calculated.
Answer:
See below
Step-by-step explanation:
4.33 = 3.83 * (1.13) .13 is decimal for 13%
A triangle has sides measuring 2 inches and 7 inches.If x represents the length in inches of the third side, which inequality gives the range of possible values for x?
Answer:
I would say A is the answer.
Hurry HELP :The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side lengths equal to 5 inches Which calculation will give the total surface area of the solid figure? (1 point) a 5 ⋅ 6 ⋅ 6 square inches b 6 ⋅ 5 ⋅ 5 square inches c 6 ⋅ 5 ⋅ 5 ⋅ 5 square inches d 5 ⋅ 6 ⋅ 6 ⋅ 6 square inches
The calculation that will give us the total surface area of the solid figure that is made up of square faces is: B. 6 × 5 × 5
What is the Area of a Square?Area of a square = (side length)².
Therefore are six (6) square faces that make up the solid figure.
Area of the 6 square faces = total surface area of the solid figure = 6(5²)
Total surface area of the solid figure = 6 × 5 × 5
Total surface area of the solid figure is: B. 6 × 5 × 5
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