Using the binomial distribution, it is found that the probabilities are given as follows:
a) 0.2036 = 20.36%.
b) 0.0011 = 0.11%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.95, n = 5.
Item a:
The probability is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.95)^{4}.(0.05)^{1} = 0.2036[/tex]
Item b:
The probability is P(X < 3), hence:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} \approx 0[/tex]
[tex]P(X = 1) = C_{5,1}.(0.95)^{1}.(0.05)^{4} \approx 0[/tex]
[tex]P(X = 2) = C_{5,2}.(0.95)^{2}.(0.05)^{3} = 0.0011[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0.0011 = 0.0011.
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Which equations are true for x = -2 and x = 2? Select two options
Ox²-4 = 0
0x²= -4
3x² + 12 = 0
14x² = 16
2(x-2)² = 0
Answer:
x2-4 = 0
x2= 4
x = 2 or x = (-2)
The equations that are true for x = -2 and x = 2 are:
x² - 4 = 0
2(x - 2)² = 0
Options A and D are the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
The values given for x are -2 and 2.
Therefore, we can substitute each value of x into the given equations to determine which are true for those values.
x² - 4 = 0
When x = -2, we have (-2)² - 4 = 0, which is true.
When x = 2, we have (2)² - 4 = 0, which is also true.
x² = -4
When x = -2, we have (-2)² = 4 which is not equal to -4, so this equation is false for x = -2.
When x = 2, we have (2)² = 4 which is not equal to -4, so this equation is false for x = 2.
3x² + 12 = 0
When x = -2, we have 3(-2)² + 12 = 0, which is false.
When x = 2, we have 3(2)² + 12 = 24, which is not equal to 0.
Therefore, this equation is false for x = 2.
14x² = 16
When x = -2, we have 14(-2)² = 56, which is not equal to 16.
Therefore, this equation is false for x = -2.
When x = 2, we have 14(2)² = 56, which is also not equal to 16.
Therefore, this equation is false for x = 2.
2(x-2)² = 0
When x = -2, we have 2(-2-2)² = 0, which is not equal to 0.
Therefore, this equation is false for x = -2.
When x = 2, we have 2(2-2)² = 0, which is equal to 0.
Therefore, this equation is true for x = 2.
Therefore,
The equations that are true for x = -2 and x = 2 are:
x² - 4 = 0
2(x-2)² = 0
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What is the distance between the two end points in the graph below
Step-by-step explanation:
10 that's what my teacher told me
lim(lnx-ln4/x-4) as x approaches 4
Answer:
1/4 = 0.25
Step-by-step explanation:
I assume you mean
lim((ln(x) - ln(4)) / (x - 4))
ln(x) - ln(4) = ln(x/4)
rule of l'hopital
lim f(x)/g(x) = lim f'(x)/g'(x)
if g'(x) <> 0
f(x) = ln(x/4)
g(x) = x - 4
ln(x)' = 1/x
ln(x/4)' = 1/x/4 × 1/4 = 1/x
(x - 4)' = 1
so,
lim f'(x)/g'(x) = 1/x / 1 = 1/x
which is for x approaching 4 : 1/4 = 0.25
Simplify this expression:
12a−8−5a+12
12a - 8 -5a + 12
arranging like terms
12a - 5a - 8 + 12
a ( 12-5) - 8 - 12
a(7) - 4(2 - 3)
a(7) -4(-1)
a(7) + 4
7a + 4
simplifing the expressions
Answer:
12a-5a-8+12
=(12-5)a+4
=7a+4
What is the mean for 14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25
Answer:
Mean: 19.366666666667
Step-by-step explanation:
Mean: Average of the Data set
If you add the numbers below and divide them by the amount of numbers there are, you will get the average of the data set.
14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25
Average= sum/count
Mean= 1162 / 60
Mean= 19.366666666667
Rounded to the nearest tenth: 19.4
Rounded to the nearest hundredth: 19.37
Helppppp meeeee pleaseeee?
Answer:
D
Step-by-step explanation:
A. The domain is not all real numbers since the domain of the inverse is the range of the square root function which is not all real numbers.
B and C. The domain is not x >= -4, that's the range since the domain and range are swapped relative to the original square root function which had a domain x >= 4 and a range x >= 0
D. This is true since the range of the square root function is x >= 0 which is now the range of the inverse.
Tom exercise a total of 150 minutes in two days he exercise 20 minutes less on the first day then on the second day how many minutes did he exercise each day?
Answer:
60 on the first day and 80 on the second
Step-by-step explanation:
the first day was lesser than the second day by 20 minutes.
so the second day was more than the first day by 20 minutes.
Lily pads increase by 25% every 10 days.lf a pond starts with 22 lily pads,how many will there be after 50 days?
We conclude that after 50 days, there will be 67 lily pads.
how many will there be after 50 days?
We know that the number increases by 25% every 10 days.
In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.
We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:
N = 22*(1 + 25%/100)*...*(1 + 25%/100%)
( the factor (1 + 25%/100%) appears five times)
So we can rewrite:
N = 22*(1 + 25%/100%)⁵
N = 22*(1 + 0.25)⁵ = 67.1
Which can be rounded to the nearest whole number, which is 67.
So we conclude that after 50 days, there will be 67 lily pads.
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer: A
Step-by-step explanation:
We can rewrite [tex]8^x[/tex] as follows:
[tex]8^{x}=\left(8^{9} \right)^{x/9}=\left(\frac{1}{8^{9}} \right)^{-x/9}[/tex]
Hence, [tex]A=\frac{1}{8^{9}}=\boxed{8^{-9}}[/tex]
Estimate the solution to the following system of equations by graphing.
9x + 8y=26
3x + 2y=9
Solution of 9x+8y=26 and 3x+2y=9 are given by (C) [tex]\mathbf{x=\frac{10}{3},y=-\frac{1}{2}}[/tex].
We have to plot the graphs of the given two lines or curves, then we have to find the intersection point(s) of the curves or lines. That point is the solution for the system of the equations.
Given equations are,
9x+8y=26 .................(1)
3x+2y=9 ...................(2)
Now multiplying 3 with (2) and then subtracting (1) from that we get,
3(3x+2y)-(9x+8y)=3(9)-26
9x+6y-9x-8y=27-26
-2y=1
y=-1/2, on dividing both sides by -2
Substituting the value of y in (1) we get,
9x+8(-1/2)=26
9x-4=26
9x=26+4
9x=30
x=30/9=10/3
Also if we draw the graphs of the given equations by using graphing calculator we get,
Here in the graph we can see that the lines represented by the given equations intersects each other at point [tex]\left(\frac{10}{3},-\frac{1}{2}\right)[/tex].
Hence the solution is [tex]x=\frac{10}{3},y=-\frac{1}{2}[/tex].
Thus the correct option is (C).
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Need help with this geometry question
Answer: B
Step-by-step explanation:
In triangles ABC and CED, CE=AC and AB=ED, but CD>BC, meaning the angle E is smaller than angle A.
3.
2. The diagram below is divided into equal parts. Which fraction of the parts is
white?
Mark only one oval.
Option 1
Option 3
37
314
I
Option 2
47
Option 4
4/3
Step-by-step explanation:
simply count them.
there are 7 little rectangles building the whole.
from these 7, 4 are gray and 3 are white.
so, 3 of 7 are white.
that means,
3/7 of all the parts are white.
Help solve and get 20 pts! (Math)
O
11
O
12 13
←
14
15
Which number line represents the solutions to -2|x| = -6?
←
16
17
18
←
+ +
-8-7-6-5-4-3 -2 -1 0 1 2 3
+
-8-7-6-5-4-3 -2 -1 0 1
19
+
-8-7-6-5-4-3 -2 -1 0 1 2
2 3
++
20
++ ++
4
567
4 5 6 7
3 4
5 6 7
8
8
+
8
H
-8-7-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
T
Answer:
thats not even understandable
The solution set is {3, -3} and is represented by the number line shown below.
What is number line?It is the representation of numbers in real order.
The difference between the consecutive numbers in a number line is always positive.
We have,
To solve the equation -2|x| = -6,
We can begin by dividing both sides by -2:
|x| = 3
This means that the absolute value of x is equal to 3.
The solutions to this equation are x = 3 and x = -3.
The number line that represents these solutions is:
<--(+)===================(+)--->
-3 3
The open circles indicate that the solutions are not included in the solution set since the absolute value of x cannot be negative.
Therefore,
The solution set is {3, -3} and is represented by the number line shown above.
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Rob bought a pair of jeans at 30% off the original price. If the original price was $55, how much did he pay for the jeans?
Answer:
$38.50
Step-by-step explanation:
(100-30)% of $55
= 70% of $55
= $38.50
Hope this helps :)
"If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c)."
Answer:
The commutative property of addition says that changing the order of addends does not change the sum.
(a+b)+c = a+ (b+c)
( -8 + -7) + 6 = -8 + ( -7 + 6)
-15 + 6 = -8 + -1
-9 = -9
Answer:
Hence, proved (a+b) + c = a + (b+c)."
Step-by-step explanation:
first take left hand side and insert the values of a, b, and c and similarly than take right hand side.
L.H.S
(a+b)+c
(-8+(-7))+6
(-8-7)+6
-15+6
-9
R.H.S
a+(b+c)
-8+(-7+6)
-8+(-1)
-8-1
-9
hence, proved (a+b) + c = a + (b+c)."
A group of students at Brunel university took a test in marketing and they needed to score 50 to pass. The results showed that the final grades have a mean of 62 and a standard deviation of 8. Suppose we approximate the distribution of these grades by normal distribution. Based on this information, you are required to perform the following; a) what percetage(to 3 decimals) of the students scored more than 78? B) what percentage of the students to 3 decimal places scored under 50? And c) what percentage to 3 decimal places of the students scored between 60 and 80?
Answer:
My answer: 15.87%
Step-by-step explanation:
The Final grades follows normal distribution.
It means =70
The Given standard deviation =10
The normal random variable of a standard normal distribution is called a standard score or a z-score. In Every normal condition, random variable X will be transformed into a z score via the following equation:
z=(X)
But when X is a normal random variable, μ is the mean of X.
For That, it is X=60
Z=(60−70)/10=−1
P(X<60)=P(Z<−1)
=0.1587
Hence percent of students failed in test is 15.87%
Solve for B -9/3+ B equals -1
Answer:
-2
Step-by-step explanation:
-9/3=-3
-3+b=-1
b=-1+3
b=-2
line / is parallel to line m. the slope of line / is 4/9. what is the slope of line m?
Answer: 4/9
Step-by-step explanation:
Parallel lines have equivalent slopes.
As line 'l' and line 'm' are parallel to each other ,then the slope of line 'm' is also 4/9.
Parallel lines have the same slope. The slope of line segments is identical because they are all similarly inclined with respect to the positive x-axis. If 'l', and 'm' are the slopes of two parallel lines,
then l = m
Slope-intercept notation for lines may be expressed as y=mx+b.
In this notation, b denotes the location of the line's y-axis intercept, and slope(m) indicates the slope of the line.
The slope of 'l'=4/9
The slope of the two parallel lines is the same.
Therefore, the slope of the parallel line "m" = 4/9.
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only 2/3 of the school districts kindergarten teachers are women. if 59 are men, how many kindergarten teachers in all are employed by the school district
Answer:
177
Step-by-step explanation:
2/3 are women.
that means the remainder, 1/3, are men.
59 = 1/3 of all kindergarten teachers (3/3 = 1 representing the "whole").
so,
59×3 = 177
is the number of all kindergarten teachers employed by the school district.
Which table shows a proportional relationship between x and y
Table second represents the proportional relationship between x and y the answer is the second table.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
As we know,
The proportional relation can be expressed mathematically:
y ∝ x
y = kx
Here k is the constant of proportionality.
k = y/x
From table second:
k = 3/2 = 6/4 = 9/6
Thus, the table second represents the proportional relationship between x and y the answer is the second table.
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8
Diameter;
Radius:
B
(a) Find the perimeter of the square
(b) Find the area of the square Area =
(c) Find the circumference of the circle C = 2πr
(d) Find the area of the circle. Area = πr²
(e) Find the area of the region between the square and the circle
answer: A: 16
B: 16
C: 12.57
D: 12.57
E: 3.43 (do area of square-area of circle 16-12.57
Simplest form of ratio 25g:3kg
Answer:
look at the picture.
Step-by-step explanation:
look at the picture.
Fireside Shop offers chimney caps for $120 less trade discounts of 25/10. The same chimney cap is being offered at Builder's Supply for $111 less trade discounts of 25/5. What is the price difference between the two companies?
The difference in price between the two companies is $81-$79.56 = $1.44
Fire side Shop
Price of Chimney cap =$120
First Discount = 25% of(120)=$30
Price after 1st Discount = $120-$30=$90
Second Discount = 10% of 90=$9
Price after 2nd Discount = $90-$9=$81
Builders' Supply
Price of Chimney Cap= $111
First Discount= 25% of 111 = $27.75
Price after 1st Discount = $111 - $27.75 = $83.75
Second Discount = 5% of $83.75 = $ 4.1875
Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56
Therefore,
a) Builders supply offers the lower price.
b) Difference in price = $81-$79.56 = $1.44
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what of the following points are on the line given by the equation y = 5x
Pls help me answer these questions⬇⬇⬇
Answer:
a) [tex]\frac{450}{100}[/tex] x 45 = 202.5g of sugar is in the can
b)[tex]\frac{4}{100}[/tex] x 80 = 3.2L is left
c)[tex]\frac{2400}{100}[/tex] x 70 = 1480 acres were planted with wheat
a. 202.5g
Since 45% of the energy drink is sugar
⇒ 45% of the total 450 grams will be made up of sugar
∴ sugar = [tex]\frac{45}{100}[/tex] * 450
= 202.5g
Thus, the can contains 202.5g of sugar
b. 3.2L
Since Simon used up 20% of the paint, the paint left in the can will now be 80% of the original 4 liters
∴ paint left = [tex]\frac{80}{100}[/tex] * 4
= 3.2L
Thus, the can has 3.2 liters of paint left.
c. 1680 acres
Here, 30% of the farmer's crop is and the rest is wheat
⇒ 70% is wheat
Total acres of land planted= 2400
∴ Acres planted with wheat = [tex]\frac{70}{100}[/tex] *2400
= 1680 acres
Thus 1680 acres is planted with wheat
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help Which statement describes the pattern shown?
*
1 point
Captionless Image
A. Each figure has 3 fewer squares than the one before it.
B. Each figure has 6 fewer squares than the one before it.
C. Each figure has 3 more squares than the one before it.
D. Each figure has 6 more squares than the one before it.
A pattern is a recurring arrangement of numbers, forms, colours, and so on.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
As per the pattern, Each figure has 3 more squares than the one before it.
Hence, the correct option is C.
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Need help with Math (Quadratic)
Answer:
f(x) = 2(x -3)² +5 or f(x) = 2x² -12x +23
Step-by-step explanation:
The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.
__
vertex formThe vertex form equation for a parabola is ...
f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'
equationFor vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...
f(x) = 2(x -3)² +5 . . . . . vertex form equation
Expanded to standard form, this is ...
f(x) = 2(x² -6x +9) +5
f(x) = 2x² -12x +23 . . . . . standard form equation
Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.) (-5, 10) and (5, -10) a. y = 2x-10 b. C. d. y = 2x y = -2x+ 20 y=-2x A
Answer:
y = -2x
Step-by-step explanation:
It passes through -5, 10 and 5, -10
gradient = Δy/Δx
gradient = -10 - 10 / 5 -- 5
gradient = -20 / 10
gradient = -2
let's use -5, 10 for y = mx + b
10 = -2(-5) + b
10 = 10 + b
b = 10 - 10
b = 0.
the equation of the line is just y = -2x
consider the quadratic function f(x)= x^2 -8x-4 what is the value of the leading coefficient
The leading coefficient of the quadratic equation f(x)= x² – 8x – 4 will be 1.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
Then we have the quadratic equation given below.
f(x)= x² – 8x – 4
f(x)= x² – 8x + 16 – 16 – 4
f(x)= (x – 4)² – 20
Then the leading coefficient will be 1.
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