Using the binomial distribution, it is found that there is a 0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect, which means that it is a highly likely event.
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:
n = 20, p = 0.05.
The probability that 3 or fewer experienced insomnia as a side effect is given by:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]
0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect.
Since this probability is greater than 95%, this is a highly likely event.
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ABC is an isosceles triangle, with AB = AC. find X
Answer:
67.13°
Step-by-step explanation:
First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule
The hypotenuse of a 90-45-45 triangle is 20√2. What is the short leg and the long leg>
Answer:
Both legs would be 20
Step-by-step explanation:
In the image below, it shows the relationship between the legs and the hypotenuse in every 45 45 90 triangle. If we know that the hypotenuse is 20, then the 2 legs are both 20.
I am slightly confused with the problem since they asked for the "short" leg and the "long" leg. Both legs should be the same length because a 45 45 90 triangle is isosceles, with the two legs being the same length.
Ratio of men to women working for a company is 7to5 there are 75 women working for the company what is total number of employees
Answer:
There is a total of 180 employees.
Step-by-step explanation:
men : women
7 : 5
5 units = 75
1 unit = 15
12 units = 180
which terms could have the greatest common factor of 5m2n2? select two:
m5n5
5m4n3
10m4n
15m2n2
24m3n4
Answer:
5m4n3 and 15m2n2
Step-by-step explanation:
you just have to find the 2 that each are divisible by 5m2n2, which are 5m4n3 and 15m2n2.
Which number produces a rational number when added to 1/2?
Answer:
Another rational number.
Step-by-step explanation:
For example, [tex]\pi[/tex] is incorrect because It is a irrational number
you must add another rational number to 1/2 to make the sum rational.
Rational number are numbers that can be converted into a fraction.
all natural numbers, whole numbers, integers, are rational.
and all rational and irrational numbers are real numbers
What complex number is represented by the polar coordinates (4, -pi/4)
Answer:
[tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
Step-by-step explanation:
A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as |z|).
Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.
Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.
[tex]\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}[/tex]
Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.
[tex]\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
Hence, the complex number that has polar coordinate of (4,-45°) is [tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
solve for x: 5x-4y=24
Answer:
x=4y+24/5
Step-by-step explanation:
add 4y
Divide by 5
From Kansas City to Denver is twice as far as from Kansas City to St. Louis the two distance together total 900 miles what are the two distance?
Answer:
KC to StL = 300
KC to Den = 600
Step-by-step explanation:
KC to StL was the base distance, so we'll call that x.
KC to Denver is twice as long, so we'll call that 2x.
If we add the together is is 900 miles total.
x + 2x = 900 Combine like terms
3x = 900 Divide by 3
x = 300
If x is 300, then 2x is 600.
*
Which of the following are situations that can be modeled with a quadratic function? Select all that apply.
O
0
A tree decays 10% every six weeks.
The height of a diver after jumping from a high dive into the water.
The height of a ball rolled down a hill.
A gym charges $15 perfitness class.
An ant bocid eliminates 50% of bacteria every 24 hours
The height of a rocket after it is Bunched
Answer:
Option 2 and 5 are correct. Look down for my explanation↓:
Step-by-step explanation:
So We need to tell which one of them is quadratic function.
Option 1 is exponential decay so, it is not quadratic.
Option 2 is quadratic because the diver will take the parabolic shape when jumps.
Option 3 is not quadratic. Option 4 is not quadratic it is linear.
Option 4 is again exponential not quadratic.
Option 5 is quadratic because it takes the parabolic shape again.
A medication states that the odds of having an allergic reaction are 2 in 200. What is that probability states as a percent?
Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice.
Answer:
1170$Step-by-step explanation:
Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice.
we can solve with an equation
6 : 540 = 13 : x
x = 540 * 13 : 6
x = 7020 : 6
x = 1170
--------------------------
check
6 : 540 = 13 : 1170
0.01111111111 = 0.01111111111
the answer is good
(a) Solve the following formula for b.
1
A = ab
(b) Evaluate b when A= 18 and a =
6/5
1
(a) The formula A = ab solved for b is b = 3X
6
(b) Evaluate b when A= 18 and a = 5
b = (Type an integer or a simplified fraction.)
Answer:
a. b = 2A/a
b. 30
Step-by-step explanation:
a. to solve for b:
[tex]A = 1/2 ab[/tex]
multiply both sides by 2
[tex]2A = ab[/tex]
divide both sides by a
[tex]2A/a=b[/tex]
so b = 2A/a
b. using the equation b = 2A/a
[tex]b = 2*18/(6/5)\\= 36/(6/5)\\= 30[/tex]
Which statement is true about the end behavior of the graphed function?
Step-by-step explanation:
both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.
Complete the statements below with the process used to achieve steps 1-4.
Select the correct answer from each drop-down menu.
Consider the equation below.
-2(5x+8)=14+6x
The equation was solved using the following steps.
The statements can be completed by using the following :
1) -2 is multiplied with (5x+8)
2) transposing of numeral values and variable values
3) The numerical values are taken one side and added to each other
4) 30 is divided by -16
5) The numerator and denominator are cancelled to the lowest possible value
x= -15/8
Given: -2(5x+8)=14+6x
and steps for solving them have also been given
In the first step, -2 is multiplied with (5x+8) and we get
-10x -16 = 14 +6x
In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14
In step 3,
The numerical values are taken one side and added to each other and we get -16x=30
In step 4, 30 is divided by -16
In step 5, they are cancelled to the lowest possible value and we get
x= -15/8
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Which is the graph of f,(x) = 0.5(4)*
I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.
Select the correct answer. Which number best represents the slope of the graphed line? A linear function on a coordinate plane passes through (minus 6, minus 7), and (4, minus 2) also intercepts the x-axis at 8 units and the y-axis at minus 4 units. A. B. C. D.
The number best represents the slope of the graphed line is 1/2.
We have given the two points,
(-6,-7) and (4,-2) and slope-intercept is 8 units
What is the slope-intercept form of a line?
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
y = y coordinate of the second point
[tex]y_1[/tex] = y coordinate of point one
m = slope
x = x coordinate of the second point
[tex]x_{1}[/tex]= x coordinate of point one
Therefore the
[tex]slope=\frac{y_2-y_1}{x_2-x_!}[/tex]
[tex]=\frac{-2-(-7)}{4-(-6)} \\=\frac{5}{10}\\ =\frac{1}{2}[/tex]
Therefore the correct option is 1/2.
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Evaluate: y(x+x)+3, where x=1 and y=3 A. 3 B. 10 C. 9 D. 5
Answer:
C. 9
Step-by-step explanation:
y(x+x) +3
{x= 1 , y= 3}
Putting values..
3 (1+1) +3
= 3 (2) +3
= 6 + 3
= 9
So, the option C. 9 is the correct answer.
Select the graph for the solution of the open sentence. Click until the correct graph appears.
3|x| > 6
I would really appreciate the help!:)
The solution of the inequality will be x > 2 and x < -2. And the graph is drawn below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The inequality is given below.
3|x| > 6
By solving the equation, we have
|x| > 2
x > 2
x < -2
Then the graph will be drawn.
More about the inequality link is given below.
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The frequency table shows the results of a survey asking people how many
hours they spend online per week. On a piece of paper, draw a histogram to
represent the data. Then determine which answer choice matches the
histogram you drew.
Hours online Frequency
5
8
10
9
7
0-3
4-7
8-11
12-15
16-19
Based on the frequency table given, The option that closely matches the histogram I drew is option C but the last one suppose to be 7 and not 6.
What is the histogram about?Hours online Frequency
5 0-3
8 4-7
10 8-11
9 12-15
7 16-19
Note that in the image attached, you can see how the Hours online were said to be matched with the Frequency.
So since option A and B was not shown to see which matches the option, i can say option c is closest but if look at my own image, you can use it to find the right one.
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Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ
Answer:
LM
Step-by-step explanation:
Perpendicular slope would be - 1 / m = - 1/(-5/6) = 6/5
slope m = rise / run line LM rises 6 for a run of 5
Which absolute value function, when graphed, will be wider than the graph of the parent function, f(x) = |x|?
f(x) = |x| + 3
f(x) = |x − 6|
f(x) = |x|
f(x) = 9|x|
The absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
How to determine the function?The parent function is given as:
f(x) =|x|
A wider function would have the following equation
f(x) = k|x|
Where:
k > 0
From the list of options, we have:
f(x) = 9|x|
Hence, the absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
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Answer:
getting to the point , D.
Step-by-step explanation:
trust
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 12, y = 3
1
y =
?
x
►
Enter
Answer:
1/4
Step-by-step explanation:
Since y/x = 3/12 = 1/4, the answer is 1/4.
Find the solution for x in the equation below.
x² + 72x = 8
[tex]x^2+72x=8\\x^2+72x+1296=1304\\(x+36)^2=1304\\x+36=\sqrt{1304} \vee x+36=-\sqrt{1304} \\x=-36+2\sqrt{326} \vee x=-36-2\sqrt{326}[/tex]
Given the expression: 6x10 − 96x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
The expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, B expression can be simplified by applying identity.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
Part A)
= 6x¹⁰ - 96x²
= 6x²(x⁸ - 16)
Part B)
[tex]\rm =6x^2(\left(x^4\right)^2-4^2)[/tex]
[tex]\rm =6x^2(\left(x^4+4\right)\left(x^4-4\right))[/tex]
[tex]\rm =6x^2\left(x^2+2x+2\right)\left(x^2-2x+2\right)\left(x^2+2\right)\left(x^2-2\right)[/tex]
Thus, the expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, the B expression can be simplified by applying identity.
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(07.01) A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours?
Answer: By 8 hours, there will be 65536 bacteria in the culture.
Step-by-step explanation:
The numerical expression used for this problem is [tex]4^{8}[/tex].
You can find the value of this on a calculator. I hope this helps!! :)
If that is not the answer, then try 32 because 4*8=32.
Classify each of the following variables as quantitative or qualitative. For those which are quantitative, classify them further as continuous or discrete.
a) Weight of adult females
b) Street addresses in Addis Ababa
c) Years of professional experience of employees
d) Number of courses offered to students in AAU in this semester.
Answer:
a) quantitative - continuous
b) qualitative
c) quantitative - discrete
d) quantitative - discrete
Explanation:
A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.
A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.
evaluate 7/8+1/4÷6/7
Step-by-step explanation:
[tex] = \frac{7}{8} + \frac{1}{4} \div \frac{6}{7} [/tex]
[tex] = \frac{7}{8} + \frac{1}{4} \times \frac{7}{6} [/tex]
[tex] = \frac{7}{8} + \frac{7}{24} [/tex]
[tex] = \frac{7 \times 3}{8 \times 3} + \frac{7}{24} [/tex]
[tex] = \frac{21}{24} + \frac{7}{24} [/tex]
[tex] = \frac{28}{24} [/tex]
[tex] = \frac{7}{6} [/tex]
7/8+(1/4÷6/7)
1/4 ÷ 6/7 = 7/24
7/8 + 7/24 = 7/6 = 1 1/6
Compute the length of sides AB, AC.
Which best describes the range of the function #(x) = 2(3)x? O y>0 O y≥0 O y = 2 O y≥2
Answer:
The range of the function f(x) : is y > 0.
The correct option is (A)
Step-by-step explanation:
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
The graph shows f of x equals x squared minus 2, which is an upward opening parabola with a vertex at 0 comma negative 2 and a point at negative 1 comma negative 1 and a point at 1 comma negative 1. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 5 and a point at negative 1 comma 4 and a point at 1 comma 4.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
We will need to shade the region above f(x) and the region below the function g(x)…
How to transform the graph into the solution set?We have:
f(x) = x² - 1
g(x) = -x² + 4
Both of these are already graphed, and we want to transform it into:
y > f(x)
y ≤ g(x)
The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x)…
For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve…
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