In a local survey, 100 citizens indicated their opinions on a revision to a local land use plan. of the 62 favorable responses, there were 40 males. of the 38 unfavorable responses, there were 15 males. if one citizen is randomly selected find the probability a male and has a favorable opinion
Answers
Denote the events like this:
F: Getting a favorable response .
First compute the number of participants: 62+38= 100.
The number of Male with favorable opinion: 40.
We deduce the probability:
[tex]P(F\vert M)=\dfrac{40}{100}=\dfrac{2}{5}[/tex]
The probability that a male and has a favorable opinion is selected is 2/5
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is about Probability.
Given:
Of the 62 favorable responses, there were 40 males and 22 females.
Of the 38 unfavorable responses, there were 15 males and 23 females.
There were total (40+15) males = 55 males
Let P(M) = probability a male is selected
[tex]P(M) = \frac{\texttt{Number of Male Citizens}}{\texttt{Total Number of Citizens}}[/tex]
[tex]P(M) = \boxed{\frac{55}{100}}[/tex]
There were 62 favorable responses
Let P(F) = probability citizens has a favorable opinion is selected
[tex]P(F) = \frac{\texttt{Number of Favorable Opinion Citizens}}{\texttt{Total Number of Citizens}}[/tex]
[tex]P(F) = \boxed{\frac{62}{100}}[/tex]
Let P(M ∪ F) = probability a male or citizens has a favorable opinion is selected
[tex]P(M \cup F) = \frac{\texttt{Number of Favorable Opinion Citizens or Male Citizens}}{\texttt{Total Number of Citizens}}[/tex]
[tex]P(M \cup F) = \frac{40 + 15 + 22}{100}[/tex]
[tex]P(M \cup F) = \boxed{\frac{77}{100}}[/tex]
At last , the probability a male and has a favorable opinion could be calculated as follows:
[tex]P(M \cap F) = P(M) + P(F) - P(M \cup F)[/tex]
[tex]P(M \cap F) = \frac{55}{100} + \frac{62}{100} - \frac{77}{100}[/tex]
[tex]P(M \cap F) = \frac{40}{100}[/tex]
[tex]P(M \cap F) = \large{\boxed {\frac{2}{5}} }[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
Related Questions
Add the sum of the numbers (−5.4) and (+8.2) to the opposite number of (−2 3/4 ).
Answers
Sum of these two numbers are = (−5.4) + (+8.2)
= -5.4 + 8.2
= 2.8
Now we are going to add this to the opposite number of (−2 3/4 ).
(−2 3/4 ) = -11/4 = -2.75
now opposite number of -2.75 is 2.75
Thus,
2.8 + (2.75)
= 2.8 + 2.75
= 5.55
Suppose 6 of 15 students in a grade-school class develop influenza where 20 percent of grade-school students nationwide develope influenza.
Answers
To find the percent of kids that developed influenza in that class do 6÷15 which gives you
.4 and written as a percent would be 40%.
Please message me if you have any questions! Hope this helps!
A ballroom in a hotel has the shape shown in the diagram. The hotel manager needs to determine how much carpet is needed to recarpet this area. All angles are right angles. The area of the ballroom is
Answers
the area of the rectangle :
[tex]3 \times 12 = 36[/tex]
the area of the square:
[tex] {6}^{2} = 36[/tex]
the area of the whole shape:
[tex]36 + 36 = 72[/tex]
hope this helps
Answer:
126 square yards
Step-by-step explanation:
The area of a rectangular barnyard is given by the trinomial 6x2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring. (1 point)
Answers
A=6(6x^2+7x-20)/6
A=[(6^2)(x^2)+7(6x)-120]/6
A=[(6x)^2+7(6x)-120]/6
A=(6x+15)(6x-8)/6
A=(6x+15)(6x-8)/[(3)(2)]
A=(6x/3+15/3)(6x/2-8/2)
A=(2x+5)(3x-4)
A=bh
b=2x+5; h=3x-4
Answer: The possible dimensions of the barnyard are 2x+5 and 3x-4
Answer:
c 2x+5 and 3x-4
Step-by-step explanation:
The set of all points equidistant from the endpoints of a segment What term matches the definition? A) Central Angle Eliminate B) Perpendicular Bisector C) Segment D) Skew Lines
Answers
Hope i helped :)
20 PTS! What are the different shapes of a data set? Explain left and right skew and how this affects the mean of a data set.
Thanks, any help is much appreciated! :)
Answers
When the data is skewed right or left, the pictorial representation of the data will show less data points on the side where it is skewed and more data on the opposite side. The tail will be longer on the right if it is skewed right and vice versa.
In data that is skewed right, the mean will be greater than the median and if the data is skewed left, the mean will be less than the median. Tje mean is not the measure of center when the data is skewed.
A grain of sand has a mass of 2.6 × 10–3 gram. A grain of salt has a mass of 6.5 × 10–2 gram. How many times greater is the mass of the grain of salt than the mass of the grain of sand?
Answers
x-----------> mass a grain of salt
y-----------> mass a grain of sand
r----------> ratio mass a grain of salt than mass a grain of sand
we know that
x=6.5 × 10–2 gram
y=2.6 × 10–3 gram
r=x/y----------> r=[6.5 × 10–2]/[2.6 × 10–3]----------> r=25
the answer is
the mass of the grain of salt is 25 times greater than the mass of the grain of sand
Answer:
the person above me is correct
Step-by-step explanation:
Chi needs to simplify the expression below.
Answers
Consider the graph of the linear equation 2x-5y=10. What is the x-intercept? What is the y-intercept? What is the slope?
Answers
This linear equation is written in standard form, a form in which it's quite easy to find intercepts for one main reason. This reason revolves around zeros. When you see an x intercept, there's always a zero for the y, and when there's a y you see a zero for the x. Therefore, we can do this to get the intercepts.
For x:
2x-5(0) =10
2x = 10
x = (5,0)
For y:
2(0) -5y = 10
-5y=10
y= (0,-2)
Now, to find the slope, we can easily convert it to slope intercept form:
y = mx+b
Where m is the slope and b is he y intercept.
2x-5y=10
-5y=-2x+10
y = 2/5x-2
(notice how we divided both sides by -5)
Therefore, our slope is 2/5. Hope this helps!
For a class gardening project, 1/3 of Mrs. Montoya's students planted marigolds and 1/2 planted tulips. What fraction of the class planted either marigolds or tulips?
Answers
To find the total fraction of the class that selected both marigolds and tulips, we need to add the two fractions together.
1/3 + 1/2 = 2/6 + 3/6
2/6 + 3/6 = 5/6
Hope this helps!
solve this equation 12y=132
Answers
132 / 12 = 11
12×11=132
y = 11
The sum of a number and its square is 2. Find the number(s).
Answers
.. x^2 +x = 2
.. x^2 +x +1/4 = 9/4 . . . . add 1/4 to complete the square
.. x +1/2 = ±3/2 . . . . . . . .square root
.. x = -2, 1
Numbers meeting that requirement are -2 and 1.
The number 'x' that satisfies the condition of the sum of a number and its square equaling 2 are 1 and -2. This is determined by setting up a quadratic equation and solving for 'x'.
Explanation:To solve this problem, let's start by defining the unknown number we are looking for as 'x'. According to the problem, the sum of a number (x) and its square (x²) equals 2. As a mathematical equation, this would be written as x + x² = 2.
Once this equation is set up, we can solve for x. However, the equation is quadratic, which means it may have two solutions. Anyway, the equation can be rearranged into the standard quadratic format as x² + x - 2 = 0. It can be factored into (x - 1)(x + 2) = 0. This gives us two potential solutions for x: x = 1 and x = -2.
To verify if these solutions are valid, we can substitute them back into the original equation: 1 + 1² = 2 is true, and -2 + (-2)² = 2 is also true. Thus, both of these numbers, 1 and -2, are solutions to the original problem.
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Which of the following are equivalent to 85%? 0.085, 0.85, 85/100, 19/20 ? chose all that apply?
Answers
Mark wants a new car that costs $30,000. He only has $500 in his savings account and $300 in his checking account. Which financing option should he choose?
Answers
Answer:
Mark should lease the car with 0% down payment.
Step-by-step explanation:
We know that the new car will cost = $30000.
Mark has only (500+300) = $800 with him.
That means Mark has only 2.66% of the cost of the car which is very less amount.
Thus Mark should have the car by leasing it with 0% down payment because in this way he will be able to buy or own the car with out giving any money for the car or without actually paying for the car and he can also at the same time can have his entire savings amount that he has as savings account and checking accounts.
Thus, he should lease the car with 0% down payment.
Find the absolute maximum and minimum values of f on the set
d. f(x, y) = xy2 + 2, d = {(x, y) | x ≥ 0, y ≥ 0, x2 + y2 ≤ 3}
Answers
[tex]\implies\begin{cases}f_x=y^2=0\\f_y=2xy=0\end{cases}[/tex]
which occurs whenever [tex]y=0[/tex] or [tex]x=0[/tex]. Under either condition, we have [tex]f(x,0)=f(0,y)=2[/tex]. The equations above admit no other critical points on the surface, so we consider the boundaries. We already have [tex]x=0[/tex] and [tex]y=0[/tex] accounted for, so let's look at the circular part.
We can parameterize this by
[tex]\begin{cases}x=\sqrt3\cos t\\y=\sqrt3\sin t\end{cases}[/tex]
with [tex]0\le t\le\dfrac\pi2[/tex]. So now
[tex]f(x,y)=f(x(t),y(t))=F(t)=(\sqrt3\cos t)(\sqrt3\sin t)^2+2[/tex]
[tex]\implies F(t)=3^{3/2}\cos t\sin^2t+2[/tex]
which can be written in terms of cosine alone as
[tex]\implies F(t)=3^{3/2}(\cos t-\cos^3t)+2[/tex]
Now, we get critical points at
[tex]F'(t)=3^{3/2}\sin t(3\cos^2t-1)=0\implies t=0\text{ or }\arccos\dfrac1{\sqrt3}[/tex]
We omit [tex]t=0[/tex], because that gives us [tex]F(0)=2[/tex] again. Meanwhile, when [tex]t=\arccos\dfrac1{\sqrt3}[/tex], we get [tex]F\left(\arccos\dfrac1{\sqrt3}\right)=4[/tex].
Finally, we compute the corresponding critical point in terms of [tex]x,y[/tex]. We have
[tex]\begin{cases}x=\sqrt3\cos\left(\arccos\dfrac1{\sqrt3}\right)=1\\\\y=\sqrt3\sin\left(\arccos\dfrac1{\sqrt3}\right)=\sqrt2\end{cases}[/tex]
So to summarize, minimum values of 2 are obtained anywhere along the borders where [tex]x=0[/tex] or [tex]y=0[/tex], and a maximum value of 4 at [tex](x,y)=(1,\sqrt2)[/tex].
The absolute minimum and maximum values of a function are the least and highest values, the function can take.
The absolute maximum and minimum values of f are 4 and 2, respectively.
The function is given as:
[tex]\mathbf{f(x,y) = xy^2 + 2}[/tex]
First, we determine the partial derivatives of f(x,y)
[tex]\mathbf{f_x(x,y) = y^2}[/tex]
[tex]\mathbf{f_y(x,y) = 2xy}[/tex]
Substitute 0 for y in the first equation.
So, we have:
[tex]\mathbf{x = 0}[/tex]
This means that:
[tex]\mathbf{Critical\ Point = f(0,0) = 0}[/tex]
Next, we calculate the extreme values.
We have:
[tex]\mathbf{x^2 + y^2 \le 3}[/tex]
Express as an equation
[tex]\mathbf{x^2 + y^2 = 3}[/tex]
Make y the subject
[tex]\mathbf{y^2 = 3 - x^2}[/tex]
Take square roots
[tex]\mathbf{y = \sqrt{3 - x^2}}[/tex]
Substitute [tex]\mathbf{y = \sqrt{3 - x^2}}[/tex] in [tex]\mathbf{f(x,y) = xy^2 + 2}[/tex]
So, we have:
[tex]\mathbf{f(x) = x(3 -x^2) + 2}[/tex]
Open brackets
[tex]\mathbf{f(x) = 3x -x^3 + 2}[/tex]
Differentiate
[tex]\mathbf{f(x) = 3 -3x^2 }[/tex]
Set to 0
[tex]\mathbf{3 -3x^2 =0}[/tex]
Collect like terms
[tex]\mathbf{3x^2 =3}[/tex]
Divide through by 3
[tex]\mathbf{x^2 =1}[/tex]
Take square roots of both sides
[tex]\mathbf{x =\±\sqrt1}[/tex]
[tex]\mathbf{x =\±1}[/tex]
The domain is given as:
[tex]\mathbf{x \ge 1}[/tex]
So, the possible value of x is:
[tex]\mathbf{x =1}[/tex]
Substitute 1 for x in [tex]\mathbf{y = \sqrt{3 - x^2}}[/tex]
[tex]\mathbf{y = \sqrt{3 - 1^2}}[/tex]
[tex]\mathbf{y = \sqrt{3 - 1}}[/tex]
[tex]\mathbf{y = \sqrt{2}}[/tex]
So, we have:
[tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex]
This means that, the absolute maximum is at: [tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex], while the absolute minimum is at [tex]\mathbf{(x,y) = (0,0) }[/tex]
Substitute these values in f(x,y)
[tex]\mathbf{(x,y) = (0,0) }[/tex]
[tex]\mathbf{f(0,0) = 0 \times 0^2 + 2 = 2}[/tex]
[tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex]
[tex]\mathbf{f(1,\sqrt 2) = 1 \times (\sqrt 2)^2 + 2 = 4}[/tex]
Hence, the absolute maximum and minimum values of f are 4 and 2, respectively.
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What is the surface area of this right rectangular prism? Enter your answer in the box. in² A rectangular prism with a length of 3 inches, a width of 1 inch, and a height of 2 inches.
Answers
Answer:
Surface Area of Rectangular Prism is 22 [tex]in^2[/tex]
Step-by-step explanation:
Given: Dimensions of Rectangular prism are Length = 3 inches, width = 1 inch and height = 2 inches.
To find: Surface Area of Rectangular Prism
Formula Used for Surface Area of Rectangualr Prism
= 2 × ( Lenght × Width + Width × Height + Height × Length )
⇒ Surface Area = 2 × ( 3 × 1 + 1 × 2 + 2 × 3 )
= 2 × ( 3 + 2 + 6 )
= 2 × ( 11 )
= 22 [tex]in^2[/tex]
Therefore, Surface Area of Rectangular Prism is 22 [tex]in^2[/tex]
Answer:
22 inches
Step-by-step explanation:
VWXY is a rhombus. find the measure
Answers
9. 6m-12+4m+4
10 is the same as above.
I'm not sure about 11.
I don't have access to a calculator. LOL
rhombus, all sides are equal
so
6m - 12 = 4m+4
2m = 16
m = 8
VW = 6(8) - 12
VW = 48 - 12
VW = 36
XY = VW = 36
9)
3n^2 - 0.75 = 90
3n^2 = 90.75
n^2 = 30.25
n = 5.5
so
<YVW = 2(9*5.5 +4) = 2(53.5) = 107 degrees
10)
<VYX = 1/2(360 - 2*107)
<VYX = 1/2 (360 - 214)
<VYX = 1/2 (146)
<VYX = 73 degrees
11)
<XYZ = 1/2 (73) = 36.5 degrees
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem. A cube-shaped container has an edge length of 23 feet. What is the volume of the container? Enter your answer, as a fraction in simplest form, in the box. ft³
Answers
2/3(2/3)(2/3) = (2*2*2)/(3*3*3) = 8/27.
V=s³
s=23 ft
2. When you substitute the value of "s" into the fomula for calculate the volume (V=s³), you obtain:
V=(23 ft)³
V=12167 ft³
3. When you write it as a fraction, you have:
V=(12167/1) ft³
4. Then, the volume of the container is:
V=(12167/1) ft³
Marissa bought 2 1/2 gallons of orange juice to make punch.Marissa pours 1 1/2 cups of punch in each glass.How many fluid ounces is each serving
Answers
:)
What is the area of this trapezoid? 96 in² 132 in² 168 in² 1344 in² Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 3 inches, F E is 8 inches., E C is 3 inches., E B is 12 inches., and A B is 8 inches.
Answers
132 〖in〗^2
Explanation
Although the diagram was not given, I was able to get it in the internet.
The area of a trapezium is found by the use of the following formula:
Area =1/2 h(a+b)
Where h is perpendicular distance between the two parallel lines, while a and b is are the lengths of the parallel lines.
In this question;
h=12 in
a=8 in
b=3+8+3=14 in
Area =1/2×12(8+14)
=6×22
132 〖in〗^2
Answer:
Option B. 132 inch²
Step-by-step explanation:
Since we know the formula to calculate the area of trapezoid is = [tex]\frac{1}{2}(height)(base)[/tex]
where height of the given trapezoid ABCD is side BE and two parallel sides are AB and DC.
It's given in the question
Side BE = 12 inches
AB = 8 inches
DC = (DF + FE + EC) = (3 + 8 + 3) = 14 inches
Now we put these values in the formula
Area of trapezoid ABCD = [tex]\frac{1}{2}(AB+CD).(BE) = \frac{1}{2}(8 + 14).(12)=\frac{1}{2}(22)(12)=(11).(12)=132[/tex]
Therefore answer is Option B. 132 inch²
Mr,angelo sliced two pizzas into equal parts,what fraction greater than 1 names both pizzas
Answers
[tex]Number \ of \ pizzas=2[/tex]
Each pizza is sliced as shown in the figure below, so we can write the new number of pizzas as follows:
[tex]Number \ of \ pizzas=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}[/tex]
But the problem is asking for a fraction greater than 1 to name both pizzas, then:
[tex]Number \ of \ pizzas=\frac{4}{2} \ or \ \frac{2}{1}[/tex]
Find the slope of the line through p and q. p(0, 0), q(10, 8)
Answers
slope = (8 - 0) / (10 - 0)
slope = 0.8
To find the slope of a line passing through points P(0, 0) and Q(10, 8), use the formula (change in y) / (change in x). The slope is calculated as (8 - 0) / (10 - 0), which simplifies to 0.8.
Explanation:The question asks for the slope of the line that passes through two points, P(0, 0) and Q(10, 8). To find the slope, we use the formula:
Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Substituting the coordinates of points P and Q, we get:
m = (8 - 0) / (10 - 0) = 8 / 10 = 0.8
Therefore, the slope of the line through points P and Q is 0.8.
The number of miles that a commuter travels a car per day for one seven day work week is as follows: 19, 28, 17, 39, 22, 44, 56. The number of miles that a commuter travels on a bus per day for one seven day work week is as follows: 32, 26, 25, 40, 39, , 49, 22. Which method of transportation has a higher commuter average? Type either car or bus in the space provided. Use all lower case letters and do not use spaces in your answer.
Answers
19 + 28 +17 +39 + 22 + 44 + 56 = 225
225/7 = 32.14
bus:
32 + 26 +25 + 40 + 39 + 49 + 22 = 233
233/7 = 33.29
the bus has the higher average
What is 0.125 Point rounded to the nearest hundredth
Answers
0.13
0.125 rounded to the nearest hundredth is 0.13.
We have,
To round to the nearest hundredth, we look at the digit in the thousandth place, which is 5.
Since 5 is greater than or equal to 5, we round up the hundredth digit (2) by increasing it by 1.
Therefore,
0.125 rounded to the nearest hundredth is 0.13.
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what is the probability of picking a vowel from the word invite?
Answers
Jan saw 9 full moons in 252 how do I write this in a ratio
Answers
Im sure the 252 means the days.
Emily buys the cage and two bowls for $54 the cage cost $40 each for cost the same amount what is the price of one bowl
Answers
What expression represents "eight more than a number cubed and 2"?
Possible Answers:
Answers
PLEASE HELP WILL GIVE BRAINLIEST!!!!!!! This is the graph of f(x). What is the value of f(2)?
Answers
the question answers are A 2 B 16 C 8 D 4
Please help!:
Charlie built a toy using a rectangular prism and cubes as shown below.
What is the surface area of the toy Charlie built?
A.650 sq cm
B.350 sq cm
C.550 sq cm
D.400 sq cm