Answer:
There are 436937109262510348800 ways to selected 12 countries.
Step-by-step explanation:
Let [tex]x_1, x_2, x_3, x_4,x_5[/tex] the countries selected from the block of 45. For [tex]x_1[/tex] there are 45 options of countries to select. For [tex]x_2[/tex] there are 44 options of countries to select because there can be no repeated countries. With the same reasoning, for [tex]x_3[/tex] there are 43 options, for [tex]x_4[/tex] there are 42 options and for [tex]x_5[/tex] there are 41 options.
Let [tex]x_6, x_7, x_8, x_9[/tex] the countries selected from the block of 57 countries. For [tex]x_6[/tex] there are 57 options of countries to select. For [tex]x_7[/tex] there are 56 options of countries to select because there can be no repeated countries. With the same reasoning, for [tex]x_8[/tex] there are 55 options and for [tex]x_9[/tex] there are 54 options.
Let [tex]x_{10}, x_{11}, x_{12}[/tex] the countries selected from the block of 69 remain countries. For [tex]x_{10}[/tex] there are 69 options of countries to select. For [tex]x_{11}[/tex] there are 68 options of countries to select because there can be no repeated countries and for [tex]x_{12}[/tex] there are 67 options.
For find the total of options o ways to select 12 countries we multiply the above options.
[tex]45*44*43*42*41*57*56*55*54*69*68*67= 436937109262510348800[/tex]
Final answer:
The number of ways to select 12 countries from the United Nations to serve on a council is determined by calculating the combinations for each block of countries and then multiplying these values together.
Explanation:
The student question deals with determining the number of ways to select 12 countries from the United Nations to serve on a council, given specific blocks of countries to choose from. To calculate this, we use the principles of combinations, as the order of selection does not matter. The number of ways to select 5 countries from the first block of 45 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial. Applying this to the first block:
C(45, 5) = 45! / (5! * (45-5)!) = 1,221,759 ways
Similarly, for the second block of 57 countries, from which 4 must be chosen:
C(57, 4) = 57! / (4! * (57-4)!) = 496,674 ways
For the remaining 3 countries from the last block of 69:
C(69, 3) = 69! / (3! * (69-3)!) = 54,834 ways
To find the total number of combinations, we multiply the number of ways for each block, as each selection is independent of the others:
Total ways = C(45, 5) * C(57, 4) * C(69, 3) = 1,221,759 * 496,674 * 54,834
After calculating this product, we obtain the total number of ways to select 12 countries from the United Nations for the council.
You receive a bonus at work for $5,000. You decide to invest in a bank account for 5 years. The bank gives you a 2.45% interest rate. Determine the amount of money that will be in the account if the interest is compounded
Answer:
5000(1+0.0245) raise to 5
$5643.26
Step-by-step explanation:
The amount of money that will received after 5 years is $5643.256
Compound Interest
The compound interest of a primary money P with rate of interest r for time t is the total money that include interest and primary as well and can be calculated with the formula
[tex]A=P(1+\frac{r}{100})^t[/tex]
SolutionHere we have given
Primary money = P = $5000
Rate of interest = r = 2.45 %
Time = 5 year
Substitute these values into above formula and we get
[tex]A=5000(1+\frac{2.45}{100})^5[/tex]
[tex]A=5000(1.0245)^5[/tex]
A = $5643.256
Therefore the total amount that will received after 5 year is $5643.256
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Upper A 55 ft wire is used to brace a utility pole. If the wire is attached 6 ft from the top of the 40 ft pole, how far from the base of the pole will the wire be attached to the ground
Two samples, each with n = 16 scores, produce an estimated standard error of 4 points and a t statistic of t = 2.00. What is the sample mean difference?
Final answer:
To find the sample mean difference, multiply the t statistic by the standard error. With a t statistic of 2.00 and a standard error of 4 points for samples with n = 16 scores, the sample mean difference is 8 points.
Explanation:
The student asks how to calculate the sample mean difference given the standard error and the t statistic for two samples each with n = 16 scores. This information is used to conduct a hypothesis test to compare two population means, using the t distribution when the population standard deviations are unknown and the sample sizes are small.
The formula to find the sample mean difference when given the t statistic and the standard error is:
sample mean difference = t statistic × standard error
Plugging the given values:
sample mean difference = 2.00 × 4 = 8
Therefore, the estimated sample mean difference is 8 points.
Donald is counting chairs in the auditorium there are 6 sections with 40 chairs each on each of 2 sides how many vhairs were on one side of the auditorium?
The answer is 240 chairs.
Julie rides her bike from the sports complex to the school. Then she rides from the school to the mall, and then on to the library. Kyle rides his bike from his house to the mall, and then to the library.
The person that traveled the most distance is Julie.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the figure,
Julie:
Total distance covered.
= sports complex to school + school to mall + mall + library
= 2/3 + 2/5 + 1(1/3)
= 2/3 + 2/5 + 4/3
= (10 + 6 + 20)/15
= 36/15
= 12/5
= 2(2/5) miles
= 2.4 miles
Kyle:
Total distance covered.
= house to mall + mall to library
= 4/5 + 1(1/3)
= 4/5 + 4/3
= (12 + 20)/15
= 32/15
= 2(2/15) miles
= 2.13 miles
Thus,
Julie has traveled more distance than Kyle.
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a fish tank in the shape of a rectangular prism measures 100 x 60 x 40/The water level reached the midpost of the base (50cm mark) when the tank was tilted to rest on a 60cm edge. What would be the depth of the water, if the tank is returned to its horizontal position (resting on a 60x100 base)?
Answer:
Step-by-step explanation:
volume of water
[tex]=\frac{1}{2}*50*40*60=60000 ~cm^3[/tex]
when the base is 100×60
let h be depth of water.
100×60×h=60000
h=60000/6000=10 cm.
What is the product? 2y/y-3 x 4y -12/2y+8
Answer:
4y/(y+4)
Step-by-step explanation:
2y/(y-3) x [(4y -12) /(2y+8)]
To determine this, at first we have to break the parentheses. Since there is no matching values, we have to multiply the numerators and denominators.
[2y x (4y - 12)] / (y-3) x (2y + 8)
or, [(2y*4y) - (2y*12)]/[(y*2y) + (y*8) - (3*2y) - (3*8)]
(using algebraic equation)
or, (8y^2 - 24y)/(2y^2 + 8y - 6y - 24)
or, (8y^2 - 24y)/(2y^2 + 2y - 24)
or, 8y(y - 3)/2(y^2 + y - 12) (taking common)
or, 4y(y - 3)/(y^2 + 4y - 3y - 12)
or, 4y(y - 3)/[y(y + 4) - 3 (y + 4)] (Using factorization or Middle-Term factor)
or, 4y (y - 3)/(y + 4)(y - 3)
or, 4y/(y + 4) [as (y-3)/(y-3) = 1, we have dropped the part]
The answer is = 4y/(y+4)
A rain storm came through Clifton park and it was accumulating 2/3 inches of rain/hour. How many inches of rain would fall in 6 hours if it continued at this rate?
4 inches of rain would fall in 6 hours
Solution:Given that, A rain storm came through Clifton park
And it was accumulating [tex]\frac{2}{3}[/tex] inches of rain/hour
So amount of rain accumulated in 1 hour = [tex]\frac{2}{3}[/tex]
Thus amount of rain accumulated in six hours is calculated by multiplying the amount of water accumulating per hour and 6
Amount of water accumulated in 6 hours = Amount of water accumulated in 1 hour [tex]\times[/tex] 6
[tex]\text { Amount of water accumaulated in 6 hours }=\frac{2}{3} \times 6=4[/tex]
Another way:
Let "n" be the amount of rain accumulated in 6 hours
1 hour ⇒ [tex]\frac{2}{3}[/tex] rain accumulated
6 hours ⇒ "n"
By cross multiplication, we get
[tex]6 \times \frac{2}{3} = 1 \times n\\\\n = \frac{2}{3} \times 6 = 4[/tex]
Hence, 4 inches of rain would fall in 6 hours.
If the rain fell at a constant rate of 2/3 inch per hour, then 4 inches of rain would fall in a total of 6 hours. This calculation is made by multiplying the rate of rainfall by the total time.
Explanation:The question asks how many inches of rain would fall in Clifton park in 6 hours if the rate was consistently 2/3 inch per hour. Given the constant rate of rainfall, we can calculate the total inches of rain that fell in 6 hours by multiplying the rate (2/3 inches/hour) by the total time in hours (6 hours).
So, doing the multiplication:
(2/3 inch/hour) * (6 hours) = 4 inches of rain.
This means that if the rain continued to fall at the same rate, we would expect 4 inches of rain to accumulate in Clifton park over 6 hours.
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Consider slicing the cube with a plane. What are all the different-shaped slices we can get? One slice, for example, could be a rectangular. What other shaped slices cane we get. Sketch both the shape of the slice and show how it is a slice of the cube?
Answer: Triangle, Square, Rectangle, Trapezium
Step-by-step explanation:
Cutting the cube from above, in a way that the slice is diagonal, making the slice touches two points that's almost at the edges diagonally facing each other of the cube will give a Trapezium (A)
Cutting the cube from above, in a way that the slice cuts exactly through the edges diagonally facing each other will give a Triangle (B)
Cutting the cube from above perpendicularly to the length, the two new faces made from the cube are squares (C)
Cutting the cube from above perpendicularly too will give two rectangles from the above face (D)
An apple orchard contains 50 trees per hectare. The avergae yield per tree is 600 apples. If the trees are spaced more closely, when being planted, the yield per tree drops by 10 apples for each extra tree. Find the number of trees that should be planted per hectare in order to maximize the total yield.
Answer:
55 trees per hectare.
Step-by-step explanation:
An apple orchard contains 50 trees per hector. The average yield per tree is 600 apples.
If the trees are spaced more closely, when being planted, the yield per tree drops by 10 apples for each extra tree.
Let x extra tree is planted and then the average yield per tree reduces by 10x.
Therefore, yield as a function of x can be written as
Y(x) = (50 + x)(600 - 10x) = 30000 + 100x - 10x²
Therefore, condition for maximum yield is [tex]\frac{dY(x)}{dx} = 0[/tex]
So, 100 - 20x = 0
⇒ x = 5
So, when the number of trees that should be planted per hectare is (50 + 5) = 55, then only the yield will be maximum. (Answer)
Simplify
(4x−3+2x2)+(2x+1)
a.8x2−2
b.2x2+2x+4
c.2x2+6x−2
d.2x2−6x−2
Aa. 8x2 - 2
i
Step-by-step explanation:
4x2 = 8
8-3 = 5
5 + 4 =
Answer:
c. 2x2+6x−2
Step-by-step explanation:
Which is the graph of y = ⌊x⌋ – 2?
Answer:
The third graph from left to right
Step-by-step explanation:
The function [tex]f(x)=\left [ x \right ][/tex] is called Greatest Integer Function of x is such that it returns the largest integer less than or equal to x
Some examples of points are (0,0),(0.5,0),(1,1),(1.9,1),(-0.7,-1)
Since our function is
[tex]f(x)=\left [ x \right ]-2[/tex]
We must subtract 2 to the points above like
(0,-2),(0.5,-2),(1,-1),(1.9,-1),(-0.7,-3)
The only graph that complies with such requirements is the third one
The sum of three numbers is 97. The third number is 3 times the second. The second number is 8 more than the first. What are the numbers? A) First number: B) Second number: C) Third number:
Answer:
A) First number: 13
B) Second number: 21
C) Third number: 63
Step-by-step explanation:
Let x, y and z be 1st, 2nd and 3rd numbers respectively.
We have been given that sum of three numbers is 97. We can represent this information in an equation as:
[tex]x+y+z=97...(1)[/tex]
The 3rd number is 3 times the second. We can represent this information in an equation as:
[tex]z=3y...(2)[/tex]
The second number is 8 more than the first. We can represent this information in an equation as:
[tex]y=x+8...(3)[/tex]
Substituting equation (3) in equation (2), we will get:
[tex]z=3(x+8)[/tex]
Substituting [tex]z=3(x+8)[/tex] and [tex]y=x+8[/tex] in equation (1), we will get:
[tex]x+x+8+3(x+8)=97[/tex]
[tex]x+x+8+3x+24=97[/tex]
[tex]5x+32=97[/tex]
[tex]5x+32-32=97-32[/tex]
[tex]5x=65[/tex]
[tex]\frac{5x}{5}=\frac{65}{5}[/tex]
[tex]x=13[/tex]
Therefore, the first number is 13.
Now, we will substitute [tex]x=13[/tex] in equation (3) as:
[tex]y=21[/tex]
Therefore, the second number is 21.
Now, we will substitute [tex]y=21[/tex] in equation (2) as:
[tex]z=3(21)[/tex]
[tex]z=63[/tex]
Therefore, the third number is 63.
This is my last problem on this sample work. Dx Please help! There are no multiple choice options so this is a free for all. Thank you!!
Answer:
[tex]\left\{\begin{array}{l}y\ge 2x+4\\ \\y<-x+2\end{array}\right.[/tex]
Step-by-step explanation:
1. The solid line passes trough the points (0,4) and (-2,0). The equation of this line is:
[tex]\dfrac{x-0}{-2-0}=\dfrac{y-4}{0-4}\\ \\y-4=2x\\ \\y=2x+4[/tex]
The origin doesn't belong to the shaded region, so its coordinates do not satisfy the inequality. Thus,
[tex]y\ge 2x+4[/tex]
2. The dotted line passes trough the points (0,2) and (2,0). The equation of this line is:
[tex]\dfrac{x-0}{2-0}=\dfrac{y-2}{0-2}\\ \\y-2=-x\\ \\y=-x+2[/tex]
The origin belongs to the shaded region, so its coordinates satisfy the inequality. Thus,
[tex]y< -x+2[/tex]
Hence, the system of two inequalities is
What is the domain of the function f(x)=[tex]\sqrt{x}[/tex]?
Step-by-step explanation:
The domain of f(x) is all values of x for which f(x) is defined.
For f(x) to be defined, the expression under the radical must be non-negative.
Therefore, the domain is x ≥ 0, or in interval notation, [0, ∞).
Arica can run 1/6 of a kilometer in a minute her school is 3/4 A kilometer away from her home At this speed how long will it take Erica to run from home to school
Erica will take 4.5 minutes to run from home to school
Solution:Given that , Arica can run [tex]\frac{1}{6}[/tex] of a kilometer in a minute
Her school is [tex]\frac{3}{4}[/tex] th of a kilometer away from her home
We have to find at this speed how long will it take Erica to run from home to school
The relation between speed distance and time is given as:
[tex]\text { Distance }=\text { speed } \times \text { time }[/tex]
Plugging in values, we get
[tex]\frac{3}{4}=\frac{1}{6} \times \text { time taken }[/tex]
[tex]\begin{array}{l}{\text { Time taken to reach school }=\frac{3}{4} \times 6} \\\\ {\text { Time taken to reach home }=\frac{3}{2} \times 3} \\\\ {\text { Time taken to reach home }=\frac{9}{2}=4.5}\end{array}[/tex]
Hence, she takes 4.5 minutes to reach school from her home
If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as V=5000(1−t40)20≤t≤40. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
Answer:
V'(t) = [tex]-250(1 - \frac{1}{40}t)[/tex]
If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.
Step-by-step explanation:
Given:
V = [tex]5000(1 - \frac{1}{40}t )^2[/tex] , where 0≤t≤40.
Here we have to find the derivative with respect to "t"
We have to use the chain rule to find the derivative.
V'(t) = [tex]2(5000)(1 - \frac{1}{40} t)d/dt (1 - \frac{1}{40}t )[/tex]
V'(t) = [tex]2(5000)(1 - \frac{1}{40} t)(-\frac{1}{40} )[/tex]
When we simplify the above, we get
V'(t) = [tex]-250(1 - \frac{1}{40}t)[/tex]
If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.
In a department of biology, there are five professors and five students. If seven members of the department are randomly selected to form a committee for admission, and if the number of professors must be one more than students, how many combinations are possible?
Answer: There are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.
Step-by-step explanation:
Since we have given that
Number of professors = 5
Number of students = 5
We need to find the number of ways of 7 members in such that number of professors must be one more than students.
So, if we select 3 students, then there will be 4 professors.
So, Number of ways would be
[tex]^5C_3\times ^5C_4\\\\=10\times 5\\\\=50[/tex]
Hence, there are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.
Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate.) sin(5θ) − sin(3θ) = cos(4θ)
Answer:
Solutions of the equation are 22.5°, 30°.
Step-by-step explanation:
The given equation is sin(5θ) - sin(3θ) = cos(4θ)
We take left side of the equation
sin(5θ) - sin(3θ) = [tex]2cos(\frac{5\theta+3\theta}{2})sin(\frac{5\theta-3\theta}{2})[/tex]
= [tex]2cos(4\theta)sin(\theta)[/tex] [From sum-product identity]
Now we can write the equation as
2cos(4θ)sin(θ) = cos(4θ)
2cos(4θ)sinθ - cos(4θ) = 0
cos(4θ)[2sinθ - 1] = 0
cos(4θ) = 0
4θ = 90°
θ = [tex]\frac{90}{4}[/tex]
θ = 22.5°
and (2sinθ - 1) = 0
sinθ = [tex]\frac{1}{2}[/tex]
θ = 30°
Therefore, solutions of the equation are 22.5°, 30°
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Answer:
y = 6
Step-by-step explanation:
Its going by 6's
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?(A) 648
(B) 1,800
(C) 2,700
(D) 10,800
(E) 64,800
Answer: B
Step-by-step explanation:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. Since the machines are identical and running at the same constant rate, it means each of them as the same rate. The rate of each machine can produce would be determined by dividing the combined unit rate by 6. It becomes
270/6 = 45 bottles per minutes
The rate for 10 machines running at the same constant rate would be
10 × 45 = 450 bottles per minutes.
If the 10 machines produce 450 bottles per minutes, then,
In 4 minutes, the 10 machines will produce 4 × 450 = 1800 bottles
Bill Casler bought a $1000, 9-month certificate of deposit (CD) that would earn 8% annual simple interest. Three months before the CD was due to mature, Bill needed his CD money, so a friend agreed to lend him money and receive the value of the CD when it matured.
(a) What is the value of the CD when it matures?
value = ? $
(b) If their agreement allowed the friend to earn a 10% annual simple interest return on his loan to Bill, how much did Bill receive from his friend? (Round your answer to the nearest cent.) value = ?
The value of Bill Casler's CD (certificate of deposit) when it matures is $1060 and Bill receives $1036.36 from his friend.
Explanation:First, we'll calculate the value of the CD (certificate of deposit) when it matures. To do this, we can use the formula for simple interest, which is PRT (Principal, Rate, Time). Here, P = $1000, R = 8% (or 0.08) and T = 9/12 years (converted to years).
So, the interest earned = 1000 * 0.08 * (9/12) = $60. The value of the CD when it matures would thus be the principal plus the interest earned, which is $1000 + $60 = $1060.
Now, for the second part of the question, we need to find out how much Bill received from his friend. The friend wants to earn a 10% annual simple interest return on his loan to Bill, so we'll equate the maturity value to the formula for simple interest. Here, P represents the amount loaned and we need to solve for P. Thus 1060 = P + P*0.10*(3/12).
Solving for P, we get P = $1036.36. So, Bill received $1036.36 from his friend.
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To find the value of the CD when it matures, use the simple interest formula. Add the interest earned to the principal to find the value. To find how much Bill received from his friend, set up an equation with the interest earned by the friend as 10% of the loan amount.
Explanation:To find the value of the CD when it matures, we can use the formula for simple interest which is I = PRT, where I is the interest, P is the principal, R is the interest rate, and T is the time in years. In this case, P = $1000, R = 8%, and T = 9/12 years. Plugging the values into the formula, we get:
I = $1000 imes 0.08 imes (9/12)
I = $60
So, the interest earned is $60. To find the value of the CD when it matures, we simply add the interest to the principal:
Value = $1000 + $60
Value = $1060
For the second question, we need to find how much Bill received from his friend. Since the friend will earn a 10% annual simple interest return on his loan to Bill, we know that the interest earned by the friend is 10% of the amount he lent. Let's call this amount X. So, the interest earned by the friend is 10% of X. To find X, we can set up an equation:
10% of X = $1060
0.10X = $1060
X = $1060 / 0.10
X = $10,600
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Which are the solutions of x2 = –13x – 4? 0, 13 0, –13 StartFraction 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction 13 + StartRoot 153 EndRoot Over 2 EndFraction StartFraction negative 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction negative 13 + StartRoot 153 EndRoot Over 2 EndFraction
Answer:
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}[/tex]
Step-by-step explanation:
The given expression is
[tex]x^{2}=-13x-4[/tex]
To solve this quadratic equation, we first need to place all terms in one side of the equation sign
[tex]x^{2} +13x+4=0[/tex]
Now, to find all solutions of this expression, we have to use the quadratic formula
[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
Where [tex]a=1[/tex], [tex]b=13[/tex] and [tex]c=4[/tex]
Replacing these values in the formula, we have
[tex]x_{1,2}=\frac{-13\±\sqrt{(13)^{2}-4(1)(4)}}{2(1)}\\x_{1,2}=\frac{-13\±\sqrt{169-16}}{2}=\frac{-13\±\sqrt{153}}{2}[/tex]
So, the solutions are
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}[/tex]
If we approximate each solution, it would be
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\approx -0.32\\\\x_{2}=\frac{-13-\sqrt{153}}{2} \approx -12.68[/tex]
Answer:
D on Edge
Step-by-step explanation:
Write the ratios for sin A and cos A
Answer: The correct option is C
Step-by-step explanation:
Looking at the right angle triangle ABC, three sides are known and the angles are unknown. To find sin A, we will take A to be our reference angle, we will have the following
Hypotenuse = AB = 26
Opposite side = BC = 24
Adjacent side = AC = 10
Applying trigonometric ratio
SinA = opposite/hypotenuse
SineA = 24/26
To find cos A, A remains our reference angle, we will have the following
Hypotenuse = AB = 26
Opposite side = BC = 24
Adjacent side = AC = 10
Applying trigonometric ratio
CosA = adjacent/hypotenuse
CosA = 10/26
The correct option is C
The vertical line passing through the vertex of a parabola is called the
Answer:
Axis of symmetry.
Step-by-step explanation:
We have been given an incomplete statement. We are supposed to complete the given statement.
Given statement: The vertical line passing through the vertex of a parabola is called the ________.
We know that a parabola is symmetric about axis of symmetry . The line passing through the vertex of parabola divides the parabola into two mirror images.
Therefore, the vertical line passing through the vertex of a parabola is called the the axis of symmetry.
Which of the following sums does not equal the others?
the sum from i equals 1 to 3 of i squared
the sum from i equals 1 to 2 of i cubed
the sum from i equals 1 to 4 of the quantity i plus 1
the sum from i equals 4 to 5 of the quantity 2 times i minus 2
Sum of Option 2 does not equal to others
Step-by-step explanation:
We have to find each sum to check which is a outlier.
so,
Option 1:
∑i^2 where i = 1 to 3
[tex]Sum = 1^2+2^2+3^2\\=1+4+9\\=14[/tex]
Option 2:
∑i^3 where i = 1 to 2
So,
[tex]Sum = 1^3+2^3\\= 1 +8\\=9[/tex]
Option 3:
∑(i+1) where i = 1 to 4
[tex]Sum = (1+1) + (2+1) +(3+1) +(4+1)\\=2+3+4+5\\=14[/tex]
Option 4:
∑(2i-2) where i = 4 to 5
[tex]Sum = [2(4)-2]+[2(5)-2]\\=(8-2)+(10-2)\\=6+8\\=14[/tex]
Hence,
Sum of Option 2 does not equal to others
Keywords: Sum, Formulas
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The sum from i equals 1 to 2 of i cubed does not equal the others.
Explanation:To determine which sum does not equal the others, we need to evaluate each sum.
The sum from i equals 1 to 3 of i squared: 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14The sum from i equals 1 to 2 of i cubed: 1^3 + 2^3 = 1 + 8 = 9The sum from i equals 1 to 4 of the quantity i plus 1: (1+1) + (2+1) + (3+1) + (4+1) = 2 + 3 + 4 + 5 = 14The sum from i equals 4 to 5 of the quantity 2 times i minus 2: (2*4-2) + (2*5-2) = 6 + 8 = 14From the evaluations, we can see that the sum from i equals 1 to 2 of i cubed does not equal the others.
when 2x^3-3x^2+kx-1 is divided by x-1 the remainder is 2 find k?
Answer:
k = 4
Step-by-step explanation:
The remainder theorem tells you that the remainder from division of f(x) by (x-1) is f(1). Evaluating the expression for x=1 gives ...
2(1³) -3(1²) +k(1) -1 = 2 -3 +k -1 = k -2
We want this to be equal to 2, so ...
k -2 = 2
k = 4
Applying the Remainder Theorem to the given polynomial, we can substitute x = 1 into the polynomial equation and solve for k, which gives us k = 4.
Explanation:The question asks to find the value of k when given polynomial 2x^3 - 3x^2 + kx - 1 is divided by x - 1 and the remainder is 2. We utilize the Remainder Theorem for this, which states that when a polynomial f(x) is divided by x-c, the remainder is equal to f(c).
So, by substituting x = 1 in the given polynomial as per the Remainder Theorem, we have: 2(1)^3 - 3(1)^2 + k(1) - 1 = 2. Simplifying this equation leads us to: 2 - 3 + k -1 = 2, which can further be simplified to k - 2 = 2. Thereby, solving for k gives us k = 4.
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A solid lies between planes perpendicular to the y-axis at yequals0 and yequals2. The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola x equals StartRoot 6 EndRoot y squared. Find the volume of the solid.
Answer:
The volume of the solid is [tex]\frac{48\pi}{5}[/tex]
Step-by-step explanation:
Consider the provided information.
The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola [tex]x=\sqrt6y^2[/tex]
Therefore, diameter is [tex]d=\sqrt6y^2[/tex]
Radius will be [tex]r=\frac{\sqrt6y^2}{2}[/tex]
We can calculate the area of circular disk as: πr²
Substitute the respective values we get:
[tex]A=\pi(\frac{\sqrt6y^2}{2})^2[/tex]
[tex]A=\pi(\frac{6y^4}{4})=\frac{3\pi y^4}{2}[/tex]
Thus the volume of the solid is:
[tex]V=\int\limits^2_0 {\frac{3\pi y^4}{2}} \, dy[/tex]
[tex]V=[{\frac{3\pi y^5}{2\times 5}}]^2_0[/tex]
[tex]V=\frac{48\pi}{5}[/tex]
Hence, the volume of the solid is [tex]\frac{48\pi}{5}[/tex]
The volume of solid represent the how much space an object occupied. In the given problem volume can be determine by taking the integration of Area of solid.
The volume of solid is [tex]\frac{48\pi }{5}[/tex].
Given:
The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola is [tex]x=\sqrt{6}y^2[/tex].
The diameter of the solid is [tex]d=\sqrt{6}y^2[/tex].
Calculate the radius of the solid.
[tex]r=\frac{d}{2}\\r=\frac{\sqrt{6}y^2}{2}[/tex]
Write the expression for area of circular disk.
[tex]A=\pi r^2\\A=\pi (\frac{\sqrt{6}y^2}{2})^2\\A=\frac{3\pi y^4}{2}[/tex]
Calculate the volume of solid.
[tex]V=\int\limits^2_0 {\frac{3\pi y^4 }{2} } \, dy\\V=[\frac{3\pi y^5}{2\times 5}]_{0}^{2}\\V=\frac{48\pi }{5}[/tex]
Thus, the volume of solid is [tex]\frac{48\pi }{5}[/tex] .
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A random sample of n 1n1equals=139139 individuals results in x 1x1equals=3737 successes. An independent sample of n 2n2equals=147147 individuals results in x 2x2equals=5858 successes. Does this represent sufficient evidence to conclude that p 1 less than p 2p1
Answer:
[tex]z=-2.32[/tex]
[tex]p_v =P(Z<-2.32)= 0.010[/tex]
If we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.
Step-by-step explanation:
1) Data given and notation
[tex]X_{1}=37[/tex] represent the number of people with characteristic 1
[tex]X_{2}=58[/tex] represent the number of people with characteristic 2
[tex]n_{1}=139[/tex] sample 1 selected
[tex]n_{2}=147[/tex] sample 2 selected
[tex]p_{1}=\frac{37}{139}=0.266[/tex] represent the proportion of people with characteristic 1
[tex]p_{2}=\frac{58}{147}=0.395[/tex] represent the proportion of people with characteristic 2
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the value for the test (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the proportion 1 is less than the proportion 2, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]
We need to apply a z test to compare proportions, and the statistic is given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{37+58}{139+147}=0.332[/tex]
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
[tex]z=\frac{0.266-0.395}{\sqrt{0.332(1-0.332)(\frac{1}{139}+\frac{1}{147})}}=-2.32[/tex]
4) Statistical decision
For this case we don't have a significance level provided [tex]\alpha[/tex] we can assuem it 0.05, and we can calculate the p value for this test.
Since is a one left tailed test the p value would be:
[tex]p_v =P(Z<-2.32)= 0.010[/tex]
So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significant lower than the proportion 2 at 5% of significance.
A garden is shaped like a square root with area 4w2. What is the length of each side of the garden
Answer: 2w
Step-by-step explanation: if the garden is shaped like a square, then all the sides are equal,
length = breadth, and the Area of a square or rectangle is the length multiplied by the breadth
and to find the length and breadth, we find the square root of the area
The area is 4w2
We know that 4 is the perfect square of 2, making 2 the square root of 4
And w2 is the square of w
This is elementary algebra, a x a = a2
b x b = b2, w x w = w2
So adding both together, the square root of 4w2 = 2w
The length of each side of the square-shaped garden with area 4w2 is 2w.
Explanation:The student has given the area of a square-shaped garden as 4w2. Since the area of a square is calculated by squaring the length of one of its sides (side2), to find the length of each side, we need to find the square root of the area. The square root of 4w2 is 2w, because (2w)2 equals 4w2. Therefore, the length of each side of the garden is 2w.