Answer:
a. 0.008 = 0.8% probability that the person will answer all three questions correctly.
b. 0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. 0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. 0.512 = 51.2% probability that the person will answer no questions correctly.
e. The expected value of the person’s score for the three questions is -0.2.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the person answers it correctly, or they do not. The probability of a person answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has five possible answers.
Person has no idea which option is correct, so the probability of answering correctly is:
[tex]p = \frac{1}{5} = 0.2[/tex]
Three questions:
This means that [tex]n = 3[/tex]
a. What is the probability that the person will answer all three questions correctly?
This is [tex]P(X = 3)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008[/tex]
0.008 = 0.8% probability that the person will answer all three questions correctly.
b. What is the probability that the person will answer exactly two questions correctly?
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096[/tex]
0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. What is the probability that the person will answer exactly one question correctly?
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.2)^{1}.(0.8)^{2} = 0.384[/tex]
0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. What is the probability that the person will answer no questions correctly?
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512[/tex]
0.512 = 51.2% probability that the person will answer no questions correctly.
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
The expected number of correct answer is:
[tex]E(X) = np = 3*0.2 = 0.6[/tex]
And the expected number of wrong answers is 3 - 0.6 = 2.4. So, the expected score is:
[tex]S(x) = 0.6 - \frac{2.4}{3} = 0.6 - 0.8 = -0.2[/tex]
The expected value of the person’s score for the three questions is -0.2.
A chain weighs 10 pounds per foot. How many ounces will 3 inches weigh?
Answer:
40 ounces
Step-by-step explanation:
One foot = 12 inches
3 inches is 1/4 of a foot
Divide 10 pounds by 4 to get 2.5 pounds
Convert to ounces
2x + y = 3
x - 2y = -1
If equation two is multiplied by -2 and then the equations are added, the result is
3y = 5
5y = 5
-3y = 3
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Answer:
5y = 5
Step-by-step explanation:
-2(x -2y) +(2x +y) = -2(-1) +(3) . . . . -2 times [eq2] + [eq1]
-2x +4y +2x +y = 2 +3 . . . . eliminate parentheses
5y = 5 . . . . . . . . collect terms
Abigail loves collecting stamps. A particular pack of stamps costs a lot of money, so she sells half of her collection in order to afford it. She buys the pack of 15 stamps and now has 145 total . How many did she have before she sold half of the collection?
Answer:
260
Step-by-step explanation:
145-15=130
130 x 2 = 260
Only answer if you're very good at Math.
What is the minimum value of the function g(x) = x^2 - 6x - 12?
A: -21
B: 3-√21
C: 3
D:3+ √21
Answer:
A: -21
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic function:
[tex]g(x) = x^2 - 6x - 12[/tex]
So [tex]a = 1, b = -6, c = -12[/tex].
Minimum value:
This is the y-value of the vertex. So
[tex]\Delta = b^2-4ac = (-6)^2 - 4(1)(-12) = 36+48 = 84[/tex]
[tex]y_{v} = -\frac{\Delta}{4a} = -\frac{84}{4} = -21[/tex]
The minimum value is -21, and the correct answer is given by option A.
Which is the equation of the line that is parallel to the given line and has an X -intercept of -3
Answer:
Answer:Uh oh! It looks like your question is missing some crucial information.
Step-by-step explanation:
You didn't include the"given line"
Solve for z
3z-5+2z=25-5z
Answer:
z=3
Step-by-step explanation:
1. collect like terms
5z-5=25-5z
2. Move the variable to the left hand side and change its sign
5z-5+5z=25
3. Collect like terms
10z=25+5
4. Divide both sides of the equation by 10
z=3
The solution to the equation is z = 3.
To solve for z in the equation 3z - 5 + 2z = 25 - 5z, we can simplify and combine like terms on both sides:
3z + 2z + 5z = 25 + 5
Combining the terms on the left side gives:
10z = 30
Next, we isolate the variable z by dividing both sides of the equation by 10:
(10z)/10 = 30/10
This simplifies to:
z = 3
Therefore, the solution to the equation is z = 3.
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Write the equation of the trigonometric graph.
Answer(s):
[tex]\displaystyle y = 3sin\: (1\frac{1}{2}x + \frac{\pi}{2}) - 2 \\ y = 3cos\: 1\frac{1}{2}x - 2[/tex]
Explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{3}} \hookrightarrow \frac{-\frac{\pi}{2}}{1\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}\pi} \hookrightarrow \frac{2}{1\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 3[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}\pi} \hookrightarrow \frac{2}{1\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 3[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\: 1\frac{1}{2}x - 2,[/tex] in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{pi}{3}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle \frac{\pi}{3}\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{3}} = \frac{-\frac{\pi}{2}}{1\frac{1}{2}}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\: (1\frac{1}{2}x + \frac{\pi}{2}) - 2.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, 1],[/tex] from there to [tex]\displaystyle [1\frac{1}{3}\pi, 1],[/tex] they are obviously [tex]\displaystyle 1\frac{1}{3}\pi\:unit[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 1\frac{1}{3}\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -2,[/tex] in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts horisontally, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Find the value of the expression (4x – 12)+(1/3xy – 5) when x = 6 and y=2
Answer:
11
Step-by-step explanation:
GIVEN
x = 6
y = 2
STEPS
(4x - 12) + (1/3xy - 5 )
(4(6) - 12 ) + ( 1/3(6x2) - 5)
(24 - 12) + ( 1/3(12) - 5)
12 + (4 - 5)
12 + (-1)
(12 - 1)
11
please help now
Your pump empties the water from a swimming pool in 4 hours. When your friend's pump is used together with your pump, the pool is emptied in 48 minutes. How long (in hours) does it take your friend's pump to empty the pool when working alone?
Answer:
Time taken for pump B to empty pool = 1 hour.
Step-by-step explanation:
Given:
Time taken for pump A to empty pool = 4 hour
Time taken together = 48 minutes = 48 / 60 = 4/5 hour
Find:
Time taken for pump B to empty pool
Computation:
Assume;
Time taken for pump B to empty pool = a
1/4 + 1/a = 1 / (4/5)
1/4 + 1/a = 5/4
1/a = 5/4 - 1/4
1/a = (5 - 1) / 4
1/a = 1
a = 1
Time taken for pump B to empty pool = 1 hour.
In the figure below, which term best describes point A?
S
A
R
A. Incenter
B. Orthocenter
C. Centroid
D. Circumcenter
GEOMETRY PLEASE HELP!!!!!!!
If the triangle shown in the diagram is dilated by a scale factor of 1 / 2
What will be the area of the resulting triangle?
A) 1.5 units²
B) 3 units²
C) 6 units²
D) 12 units²
Answer:
1.5 units^2
A
Step-by-step explanation:
AB (the base) = 4 - 1 = 3
AC (the height) = 5 - 1 = 4
Area = 1/2 * b * h
Area = 1/2 * 4 * 3
Area = 6 units^2
Now when you dilate it by a factor or 1/2, it means that each dimension is multiplied by 1/2.
So AB becomes 1.5
AC becomes 2
The area of the new triangle = 1/2 * 1.5 * 2 = 1.5
Be careful with this. Be sure that you understand that it is the sides making up the triangle that get cut in 1/2 and not just the area.
(x+3)(x−1)
Cual seria su resultado
Answer:
x² -1x + 3x -3
= x² +2x -3
hope it helps
Multiply the following using the vertical multiplication method: 3x^2-5x+1
x x^2+2x+4
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Answer:
3x^4 +x^3 +3x^2 -18x +4
Step-by-step explanation:
The multiplication is done the same way as "long multiplication" with numbers. Each partial product is placed in the column corresponding to its "place value" (the degree of the variable). The only difference from numerical multiplication is that the sums of the partial products have no carry into any column with a different "place value".
what is the slope of the line that passes through these two points?
Answer:
slope of the line is 0
Step-by-step explanation:
given points are:
(-3 , 2)=(x1 , y1)
(4 , 2)=(x2 , y2)
slope =y2 - y1/x2 - x1
=2-2/4-(-3)
=0/4+3
=0/7
=0
61 1/20 as a decimal
Answer:
61.05
Step-by-step explanation:
1/20 = 5/100 = 0.05
61+0.05 = 61.05
I’ll mark brainliest
Answer:
[tex]\text{A. }y=1.30x+1.50[/tex]
Step-by-step explanation:
The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.
What is the unit rate for the following point?
(7, 1 3/4)
Answer:
Step-by-step explanation:
7
this zigzag crystal vase has a height of 10 inches. The cross sections parallel to the base are always rectangles that are 6 inches by 3 inches long.
If we assume the crystal itself has no thickness, what would be the volume of the vase? NO LINKS!!!
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Answer:
180 in³
Step-by-step explanation:
V = Bh
V = (6 in × 3 in)(10 in) = 180 in³
The volume is the product of the cross section area (6 in × 3 in) = 18 in² and the height perpendicular to that cross section, 10 in.
Use the substitution method or the elimination method to solve the following system.
2x−20y
=
10
−7x+70y
=
−35
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Answer:
x -10y = 5 . . . . . infinite number of solutions
Step-by-step explanation:
We can put each equation into standard form by dividing it by its x-coefficient.
x -10y = 5 . . . . first equation
x -10y = 5 . . . . second equation
Subtracting the second equation from the first eliminates the x-variable to give ...
(x -10y) -(x -10y) = (5) -(5)
0 = 0 . . . . . . . true for all values of x or y
The system has an infinite number of solutions. Each is a solution to ...
x -10y = 5.
What is the expression in radical form?
(20) 5/2
Enter your answer, in simplest form, in the box.
How do i do this math equasion?
Answer:
f(t) = -16t² + 36
Step-by-step explanation:
f(t) = a(t - h)² + k
This is vertex form where (h, k) is the (x, y) coordinate of the vertex
The vertex is give as (0, 36)
f(t) = a(t - 0)^2 + 36
f(t) =at² + 36
use point (1, 20) to find "a"
20 = a(1²) + 36
20 = a + 36
-16 = a
f(t) = -16t² + 36
Marcia sells lemonade for $2 per cup and candy for $1.50 per candy bar. She earns $425 selling lemonade and candy bars. If Marcia sold 90 bars of candy, which equation could be used to figure out how many cups of lemonade she sold?
Answer:
145 cups of lemonade; 2x+1.50y=425, where y=90
Step-by-step explanation:
Let us first set up an equation, where x represents number of cups of lemonande, and y represents number of candy bars. We know that every cup of lemonade costs $2, every candy bar sold costs $1.50, and that Marcia sold a total of $425. We now have equation:
[tex]2x+1.50y=425[/tex]
However, we actually know how many candy bars Marcia sold. Therefore, our y value is 90. Let's rewrite the equation:
[tex]2x+1.50*90=425\\2x+135=425\\2x=290\\x=145[/tex]
Therefore, Marcia sold 145 cups of lemonade.
I hope this helps! Let me know if you have any questions :)
Do the following lengths form a right triangle?
Answer:
Yes, they do
Step-by-step explanation:
Because
6+8=14>9
6+9=15>8
8+9=17>6
Determine the value of x
Answer:
the answer is "C" because I did it on Khan academyThe value of x in the triangle is 17.51
Option C is the correct answer.
We have,
From the figure,
We can use the tangent function.
This means,
Tan = perpendicular / Base
i.e
tan 35 = x / 25
0.700 = x / 25
x = 0.700 x 25
x = 17.5
Thus,
The value of x in the triangle is 17.51.
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Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of the cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.
a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]
[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]
⇒ 198x - 12x² = 0
[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]
By solving for x:
x = 0 or x = [tex]\dfrac{33}{2}[/tex]
Again:
V = 99x² - 4x³
[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]
At x = [tex]\dfrac{33}{2}[/tex]
[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]
[tex]\implies 198 - 12 \times 33[/tex]
= -198
Thus, at maximum value;
[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]
Recall y = 99 - 4x
when at maximum x = [tex]\dfrac{33}{2}[/tex]
[tex]y = 99 - 4(\dfrac{33}{2})[/tex]
y = 33
Finally; the volume V = x² y is;
[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]
[tex]V =272.25 \times 33[/tex]
V = 8984.25 inches³
If f(x)= 10 sin(x) – 3 then f (30%) = ?
A) - square root 3/2 -3
B.) 2
C.) -5/2
D.) 4/3 - square root 3/2
Answer:
The value of f(30) is equal to 2.
Step-by-step explanation:
The given expression is :
[tex]f(x)= 10 \sin(x) - 3[/tex]
We need to find the value of f(30)
Put x = 30 in above expression.
So,
[tex]f(x)= 10 \sin(30) - 3\\\\=10\times \dfrac{1}{2}-3\\\\=5-3\\\\=2[/tex]
Hence, the value of f(30) is equal to 2.
The length of a rectangle is 4 meters more than the width of the rectangle. The perimeter of the rectangle is 40 meters. What are the length and the width of the rectangle? *
Answer:
Length = 12 m, Width = 8 m
Step-by-step explanation:
Let the width of the rectangle is b.
Length, l = 4+b
The perimeter of the rectangle = 40 m
We know that,
Perimeter of rectangle = 2(l+b)
2(4+b+b) = 40
4+2b = 20
Subtract 2 from boths sides,
2b = 16
b = 8
Width = 8 m
Length = 4+8 = 12 m
Hence, the length and the width of the rectangle is 12 m and 8 m respectively.
Let f(x)=x2+10x+37 .
What is the vertex form off(x)?
What is the minimum value off(x)?
Enter your answers in the boxes.
Vertex form: f(x)=
Minimum value of f(x):
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
Find the area of the circle. Round your answer to the nearest tenth.
Answer:
254.47 mm
Step-by-step explanation:
Political party affiliation is believed to be a very strong indicator of how voters will vote in Presidential Elections. You are interested in determining if voter party loyalty has changed since 1992. During the 1992 election, the proportion of self-proclaimed Republicans who voted for George H. W. Bush was 0.924. During the 2012 election, in a survey of 277 Republican voters, 213 indicated that they had voted for Mitt Romney. The 90% confidence interval for this proportion is ( 0.7273 , 0.8106 ). What is the best conclusion you can make from this information that is listed below
Answer:
The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
The 90% confidence interval for the proportion of Republican voters that had voted for Mitt Romney is (0.7273, 0.8106). The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.
