Factor completely.
Y^2-12y+32
A. (y+4)(y+8)
B. (y-4)(y-8)
C. (y+18)(y + 2)
D. (y-18)(y-2)
Answer:
B
Step-by-step explanation:
y² - 12y + 32
consider the product of factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)
the factors are - 4 and - 8 , since
- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then
y² - 12y + 32 = (y - 4)(y - 8)
Answer:
B. (y-4)(y-8)
Step-by-step explanation:
Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.
1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.
They are: -8 and -4.
2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.
y² - 8y - 4y +32
y(y - 8) - 4(y - 8)
(y - 4)(y -8)
The answer for this math problem because I don’t really understand it
Answer:
See below
Step-by-step explanation:
Start by subtracting 5.2 from both sides of the equation
so "subtraction property of equality " I suppose ......
then the next step would be divide both sides by 2.5
which would be division property of equality
Answer: Subtraction Property of Equality
Step-by-step explanation:
- the subtraction property of equality is the rule that when you subtract the same number to or from both sides of an equation and get an equivalent equation
__________________________________________________________
- for this equation you would subtract 5.2 from the left-side of the equation and subtract it from 35.2 on the right side of the equation
- this is to isolate n
- basically 2.5n = 30 since n is a variable and that number multiplied by 2.5 will equal 30
- so the new equation would be 2.5n = 30
- so then: [tex]\frac{n}{2.5}[/tex] = [tex]\frac{30}{2.5}[/tex] so n = 12
hope this helps :)
Use a graphing calculator to find the value of the correlation coefficient r and determine if there is a strong correlation among the data.
(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)
Using a calculator, the correlation coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Using a calculator, we insert the points (x,y) to find the coefficient. In this problem, the points are given as follows:
(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)
The coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.
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A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders and randomly assigns each second grader to participate in the reading intervention program or not participate in the program. The researcher knows that the standard deviation of the reading comprehension scores among all second graders is σ = 25.24.
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8. Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.
Of the plots that follow, which best represents a plot of these results?
The brackets or error bars shown at the top of each bar extend _______ above and below each of the group means. For group 1, the error bar extends _______units above and below the mean for group 1.
The brackets or error bars shown at the top of each bar extend one standard error above and below each of the group means. For group 1, the error bar extends 3.9 units above and below the mean for group 1.
A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8.
Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.
Error bar, are the line through a point on a graph,axes, which emphasizes the uncertainty or variation of the corresponding coordinate of the point.
We have the data,
σ = 25.24, n₁ = 52 M₁ = 36.8.
n₂ = 56 M₂ = 52.4.
Error bar = M2-M1/n2-n1
= (52.4-36.8)/(56-52)
= 3.9
Thus, the required value that will be put in black space is 3.9
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3x9= 2x+5
Step Two: 3x = 2x + 14
Which choice justifies this step?
Answer: Addition property of equality
Step-by-step explanation:
Assuming you meant 3x-9=2x+5, it would be the addition property of equality since you are adding 9 to both sides.
What is the range of the function f(x)=1/2√x?
A. all real numbers
B. all real numbers greater than but not equal to 0
C. all real numbers less than or equal to 0
D. all real numbers greater than or equal to 0
Answer:
D. all real numbers greater than or equal to 0
Step-by-step explanation:
The range is the set of y-values.
You are one of 16 finalists on a game show.
One finalist is randomly selected to answer
a trivia question for a prize. What is the
probability that you will be selected?
Write your answer as a percent.
If one finalist is randomly selected for a prize then the probability that person will be selected is 6.25%.
Given A person is one of 16 finalists and one finalist is randomly selected for a prize.
Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability is number of events possible/total outcomes.
The value of probability lies between 0 and 1. It cannot be negative because there might be chances of something and sometimes not so the value be 0.
Total finalists=16
Probability=1/16
When we convert it in percentage it will be 1*100/16
=6.25%
Hence the probability that person will be selected is 6.25%.
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Work out the height of this
triangle with base, b = 4.9mm
and area, A = 108.29mm².
Answer: 44.2
Step-by-step explanation:
108.29*2/4.9=44.2
Two rules for creating a pattern are given below. Each rule begins with a number called the input and creates a number called the output.
Rule 1: Divide the input by 2 to get the output.
Rule 2: Subtract by 10 to get the output.
Which input and output table works for both rules?
The input and output table that works for both rules is input = 20 and output = 10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the output and x represent the input.
From the first rule:
y = x/2
From the second rule:
y = x - 10
To work for both rules:
x/2 = x - 10
x = 2x - 20
x = 20
y = 20 - 10 = 10
The input and output table that works for both rules is input = 20 and output = 10.
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Two trains leave a station at the same time. One train is heading south at a rate that is 1.5 times faster than the other train, which is heading north. After 5 hours, the trains are 750 miles apart.
1) At what speed, in mph, are the two trains getting farther away from each other?
2) What is the speed, in mph, of the faster train?
3) Suppose the trains simultaneously leave stations that are 450 miles apart and travel toward each other. In how many hours will the trains meet?
Answer:
1) 150 mph
2) 90 mph
3) 3 mph
Explanation:
1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150
2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.
3) We know that both trains combined travel 150 mph. 450/150=3.
Based on the data given, the speeds and time taken are as follows:
The combined speed of the two trains is 150 mphThe speed of faster train 150 x 3/5 = 90 mphThe time taken by the trains to cover 450 miles = 3 hoursWhat is speed?Speed is the ratio of distance covered and time taken.
Speed = distance/time1)The distance covered by the two trains in 5 hours = 750 miles.
The trains move at a constant speed and their combined speed will be:
Combined speed = 750/5
Combined speed = 150 mph
2) The train heading south has a speed 1.5 times faster than the other train heading north.
Ratio of speeds = 3 : 2
Speed of faster train 150 x 3/5 = 90 mph
3) The combined speed of the trains = 150 mph
Distance to be covered = 450 miles
Time taken = 450/150
Time taken = 3 hours
In conclusion, the speed of the two trains are determined from the distance travelled and time taken.
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Can someone please help me
Answer:
Vertex form: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]
Standard Form: [tex]y=0.50x^2-2x-1[/tex]
Step-by-step explanation:
Well the vertex form of an equation is given in the form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you: [tex]y=a(x-2)^2-3[/tex]. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in
Plug in (0, -1) as (x, y)
[tex]-1 = a(0-2)^2-3[/tex]
calculate inside the parenthesis
[tex]-1 = a(-2)^2-3[/tex]
square the -2
[tex]-1 = 4a-3[/tex]
Add 3 to both 3 to both sides
[tex]2 = 4a[/tex]
divide both sides by 4
[tex]a=\frac{1}{2}[/tex]
This gives you the equation: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]
To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to: [tex](a+b)^2=a^2+2ab+b^2[/tex].
Original equation:
[tex]y=\frac{1}{2}(x-2)^2-3[/tex]
expand square binomial:
[tex]y=\frac{1}{2}(x^2-4x+4)^2-3[/tex]
Distribute the 1/2
[tex]y=0.50x^2-2x+2-3[/tex]
Combine like terms:
[tex]y=0.50x^2-2x-1[/tex]
Solve: 4x−1>7 or 5x−1<−6
Answer and Explanation:
First, solve for x in both inequalities:
4x − 1 > 7 5x − 1 < −6
4x > 8 5x < −5
x > 2 x < −1
Because this is an OR problem, determine if there is any overlap. (See the attached image for details.) There is not, so the answer is no solution or Ø.
Anil is a married teacher in a college. He has monthly salary of Rs 45,000
dearness allowance Rs 4,000. His life insurance premium paid by his college is
Rs 15,000. Dashain allowance is equals to one month's basic salary. Anil has contributed
in Employee Provident Fund 10% of basic salary. The college also contributed same amount.
Tax rate for first 450000 1% , next 100000 10% and 25% above that
The amount paid in tax based on the information is Rs 13500.
How to compute the tax?From the information given, the monthly salary is 45000. Therefore, the yearly salary will be:
= 45000 × 12
= 540000
Also, it's stated that the tax rate for first 450000 is 1% and next 100000 is 10%. Therefore, the amount that will be paid in tax will be:
= (450000 × 1%) + (90000 × 10%)
= 4500 + 9000
= 13500
Therefore, the amount paid in tax will be Rs 13500.
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Figure B is a scaled copy of Figure A.
Figure B
Figure A
What is the scale factor from Figure A to Figure B?
Answer:
The scale factor would be 1/2.
Step-by-step explanation:
2 of the sides both are 4 units.
If you go to figure B, it got smaller.
So in this case, you would divide.
On figure B, 2 of the sides are 2 units.
If you did it in reverse, you would get 2 because 2 times 2 is 4.
But we divide, so 4/2 is 2, so the scale factor would be:
1/2
Hope this helped!
And brainliest pls :)
Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.
The center of mass is mathematically given as
[tex]\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]
What is the center of mass.?Determine the center of mass in one dimension:
Represent the masses at the respective distances.
[tex]\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end[/tex]
We calculate the total mass of the system.
[tex]\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}[/tex]
Step 03: Calculate the moment of the system.
[tex]\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}[/tex]
we calculate the center of mass.
[tex]\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]
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LC)A polygon is shown:
A polygon MNOPQR is shown. The top vertex on the left is labeled M, and rest of the vertices are labeled clockwise starting from the top left vertex labeled, M. The side MN is parallel to side QR. The side MR is parallel to side PQ. The side MN is labeled as 5 units. The side QR is labeled as 7 units. The side MR is labeled as 3 units, and the side NO is labeled as 2 units.
The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)
The area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
How to determine the area of the rectangleFrom the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ
With a perpendicular line drawn from point O on the side RQ, which intersects with line RQ at point S.
We can then divide the polygon into two different rectangles
MNSR with A₁ as its area
OPQS with A₂ as its area
For rectangle MNSR, line MN is 5 units and line MR is 3 units
The formula for area of a rectangle is given as;
A₁ = (length)×(width)
Substitute the values
A₁ = 5 × 3
A₁ = 15 square units
For rectangle MNSR, line MN= line RS and line MR = line NS,
We have RS= 5 units and NS= 3 units
So, line SQ= RQ- RS = 7-5 = 2 units
Also, OS= NS - NO = 3- 2 = 1 unit
Let's substitute the values
A₂ = 2 × 1
A₂ = 2 square units
Therefore, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
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How to solve the inequality of ...
Answer:
x<3−√11 /2 or x > 3 +√11/2
Step-by-step explanation:
Solve the inequality for x by finding a, b, and c of the quadratic then applying the quadratic formula.
The radius of a circle is 17 inches. What is the circumference? Round your
answer to the nearest tenth.
OA. 106.8 inches
OB. 907.9 inches
OC. 53.4 inches
OD. 289 inches
Answer: A
Step-by-step explanation:
[tex]C=2\pi r=2(\pi)(17) \approx 106.8[/tex]
Consider the limaçon with equation r = 3 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop?
If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.
Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.
Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.
formula of polar graph is similar to r= a+ b cos (θ).
Case 1. If a<b or b/a>1
then the curve is a limacon with inner loop.
Case 2. If a>b or b/a<1
Then the limacon does not have an inner loop.
Here given that [tex]r=3+4cos[/tex] (θ)
It is observed that , a<b or b/a>1
Therefore the curve is limacon with an inner loop.
Hence because b/a>1 the curve is a limacon with an inner loop.
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Answer:
The answer is B
Step-by-step explanation:
QUESTION IS DOWN BELOW
Using proportions, the ratios are given as follows:
a) 9:196.
b) 27:2744.
c) 3:14.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the standard ratio of 3:14 units, we have that:
The area is given in units squared, hence the ratio will be of [tex]\left(\frac{3}{14}\right)^2 = \frac{9}{196}[/tex].The volume is given in cubic units, hence the ratio will be of [tex]\left(\frac{3}{14}\right)^3 = \frac{27}{2744}[/tex]. The width is also given in units, hence the ratio is also of 3:14.More can be learned about proportions at https://brainly.com/question/24372153
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each value to the correct expression.
8
5
0
27
15
22
Using PEDMAS, the value of each expressions are:
a. 1 + 5 × 2 + (1 + 3)² = 27
b. 0.25 × 4³ - 1 = 15
c. 4 + 8(1/4 + 2) = 22
How to Apply PEDMAS in Evaluating an Expression?PEDMAS implies that you solve a problem first following the order, parentheses, exponent, division, multiplication, addition, and subtraction.
Let's evaluate the expressions using PEDMAS:
a. 1 + 5 × 2 + (1 + 3)²
1 + 5 × 2 + (4)²
1 + 5 × 2 + 16
1 + 10 + 16
= 27
b. 0.25 × 4³ - 1
0.25 × 64 - 1
16 - 1
= 15
c. 4 + 8(1/4 + 2)
4 + 8(9/4)
4 + 18
= 22.
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What is the value of x in the equation three-fourths (one-fourth x 8) minus (one-half x 2) = startfraction 3 over 8 endfraction (4 minus x) minus one-fourth?
The value of x in the equation is x=-44.
The given equation is [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex].
An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.
Firstly, apply the distributive property as a(b+c)=ab+ac and get
[tex]\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end[/tex]
Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as
[tex]\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2[/tex]
Further, simplify the above expression by taking L.C.M as
[tex]\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end[/tex]
Then, multiply both sides with 4 and get
[tex]\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end[/tex]
Furthermore, cross multiply both sides and get
[tex]x=-44[/tex]
Hence, the value of x in the equation which is given [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex] is x=-44.
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A baker is making 41/8 batches of cookies. If each batch requires 3/4 of a stick of butter, how much butter will he need for all 41/8?
Answer: 123/32 or 3 27/32 sticks
Step-by-step explanation:
41/8*3/4 =
41*3/8*4 =
123/32 =
3 27/32
To solve the division problem, multiply
by the reciprocal of the divisor.
1/9 divided by 3=1/9X1/? Solve the question mark.
Answer:
?=3
Step-by-step explanation:
3=3/1
Flip 3/1 and you get
1/3
Determine the slope of a line that is perpendicular to the equation 3x + 6y =18
Rewriting the equation of the given line in slope-intercept form,
[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]
This means the slope of the given line is -1/2.
As perpendicular lines have slopes that are negative reciprocals, the answer is 2.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Determine the slope of the line perpendicular to 3x+6y=18
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form
[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x
[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].
[tex]\cline{1-2}[/tex]
Now, perpendicular lines' slopes are opposite inverses of each other.
The opposite inverse of -1/2 is
= 2
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=2}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]
The following shape is only based on squares, semicircles and quarter circles. Find the Area and Perimeter of the shaded part. Answers in terms of pi.
The perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have shown a square in which a one-fourth circle is shown and making an ellipse.
The perimeter of the circle = 2πr = 2π(8) = 16π cm
The perimeter of the one-fourth is circle = (16π)/4 = 4π cm
The perimeter of 2 one-fourth circle = 2(4π) = 8π cm
The area of the one-fourth circle = (1/4)πr² = (1/4)π(8)² = 16π square cm
The area of the right-angle triangle = (1/2)(8)(8) = 32 square cm
The area of the shaded region = 2(16π - 32) = 36.53 square cm
or
= 32(π - 2)cm²
Thus, the perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.
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A recent survey found that 4% of the population of the United States is unemployed. If Charlotte, North Carolina, has 26,440 unemployed, what is the population of Charlotte?
The population of Charlotte is 661,000.
What is the population of Charlotte?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
The population of Charlotte = number of unemployed people / percentage of unemployed
26,440 / 0.04 = 661,000
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A certain medical test is known to detect 73% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:
P(At least 8 have the disease) ≈ 0.4378P(At most 4 have the disease) ≈ 0.0342How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
X = B(n,p)
The probability that out of n trials, there'd be x successes is given by
P(X=x) = [tex]^nC_xp^x(1-p)^{n-x}[/tex]
Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.
Let we say
Success= Probability of a diseased person tagged as diseased by the clinic
Failure = Probability of a diseased person tagged as not diseased by the clinic.
Then,
P(Success) = p = 72% = 0.72 (of a single person)
P(Failure) = q = 1-p = 0.28
Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)
Calculating the needed probabilities, we get:
a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)
P(X≥8) = [tex]^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0[/tex]
P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378
b) P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)
P (X ≤ 4) =
[tex]^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\[/tex]
[tex]+^{10}C_4(0.73)^4(0.27)^6[/tex]
P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719
P (X ≤ 4) = 0.0342
Thus,
The probabilities of considered events are:
P(At leased 8 have disease) = 0.4378 approxP(At most 4 have the disease) = 0.0342 approxLearn more about binomial distribution here:
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The diagonal of the square is 10 cm. The length of the sides in cm is:
A. 5
B. 5sqrt2
C. 10sqrt2
D. 20
E. 100
*sqrt = square root I can't put the icon in
The length of a square with diagonal of 10 cm is 5√2 cm.
How to find the length of a square?Each angle in a square is 90 degrees.
Therefore, the diagonal form a right triangle with the length of the square.
The length of the square are equal.
Hence, using Pythagoras theorem,
let
x = length of square
x² + x² = 10²
2x² = 100
x² = 50
x = √50
x = 5√2
Therefore, the length of a square with diagonal of 10 cm is 5√2 cm.
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Please give an answer and solution.
Using proportions, it is found that 78 students would prefer long jump.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Out of 300 students, 26% would prefer long jump, hence the amount is given by:
n = 0.26 x 300 = 78 students.
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