Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.
The probability that he got at least 2 questions correct is 0.756
Lets assume, the event of getting a question correct is P
As, each question has 4 answer choices and only one choice is correct,
So, P = [tex] \frac{1}{4} [/tex]
When
the probability of getting 1 success in 1 trial is p, then the probability of getting exactly x successes out of n trials is given by the
formula :
(ⁿCₓ )(P)ˣ (1-P)ⁿ⁻ˣ
Here the total number of questions is 10. So, n= 10
Stan needs to get at least 2 questions correct, that means he can get 2, 3, 4, 5, 6, 7, 8, 9 or 10 questions correct.
Now according to the formula,
P(x=2) = ¹⁰C₂ ([tex] \frac{1}{4} [/tex])² ([tex] 1- \frac{1}{4} [/tex])¹⁰⁻²
= ¹⁰C₂ [tex] (\frac{1}{16})(\frac{3}{4})^8 [/tex]
= 0.281567573
P(x=3) = ¹⁰C₃ ([tex] \frac{1}{4} [/tex])³ [tex] (\frac{3}{4})^7 [/tex]
= (120) ([tex] \frac{1}{4} [/tex])³ [tex] (\frac{3}{4})^7 [/tex]
= 0.250282287
P(x=4) = ¹⁰C₄ ([tex] \frac{1}{4} [/tex])⁴ [tex] (\frac{3}{4})^6 [/tex]
= (210)([tex] \frac{1}{4} [/tex])⁴ [tex] (\frac{3}{4})^6 [/tex]
= 0.145998001
P(x=5) = ¹⁰C₅ ([tex] \frac{1}{4} [/tex])⁵ [tex] (\frac{3}{4})^5 [/tex]
= (252) ([tex] \frac{1}{4} [/tex])⁵ [tex] (\frac{3}{4})^5 [/tex]
= 0.058399200
P(x=6) = ¹⁰C₆ ([tex] \frac{1}{4} [/tex])⁶ [tex] (\frac{3}{4})^4 [/tex]
= (210) ([tex] \frac{1}{4} [/tex])⁶ [tex] (\frac{3}{4})^4 [/tex]
= 0.016222000
P(x=7) = ¹⁰C₇ ([tex] \frac{1}{4} [/tex])⁷ [tex] (\frac{3}{4})^3 [/tex]
= (120) ([tex] \frac{1}{4} [/tex])⁷ [tex] (\frac{3}{4})^3 [/tex]
= 0.003089904
P(x=8) = ¹⁰C₈ ([tex] \frac{1}{4} [/tex])⁸ [tex] (\frac{3}{4})^2 [/tex]
= (45) ([tex] \frac{1}{4} [/tex])⁸ [tex] (\frac{3}{4})^2 [/tex]
= 0.000386238
P(x=9) = ¹⁰C₉ ([tex] \frac{1}{4} [/tex])⁹ [tex] (\frac{3}{4})^1 [/tex]
= (10) ([tex] \frac{1}{4} [/tex])⁹ [tex] (\frac{3}{4})^1 [/tex]
= 0.000028610
P(x=10) = ¹⁰C₁₀ ([tex] \frac{1}{4} [/tex])¹⁰
= 0.000000953
Now we will just add all the probabilities and get:
0.281567573 + 0.250282287+ 0.145998001+ 0.058399200+ 0.016222000+0.003089904+0.000386238+ 0.000028610 +0.000000953
= 0.755974766
= 0.756 (rounding to the nearest thousandth)
So, the probability that he got at least 2 questions correct is 0.756
Answer:
Step-by-step explanation:
C on edge Test
An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:
Hourglass with sand measuring 47 millimeters high
© 2011 Jupiterimages Corporation
Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
A(6.4)
B(62.4)
C(8.5)
D(56.0)
Answer:
62.4
Step-by-step explanation:
The temperature on Saturday was 6 1/2 °C. On Sunday, it became 3 3/4 °C colder. What was the temperature on Sunday?
Answer:
The temperature on Sunday was 2.75 degrees Celsius.
Step-by-step explanation:
The temperature on Saturday was = [tex]6\frac{1}{2}[/tex] or 6.5 degree Celsius
The temperature on Sunday became [tex]3\frac{3}{4}[/tex] or 3.75 degrees colder.
When the temperature falls of it gets colder, this means the new temperature is less than the previous one. The lower the temperature, the more colder it is.
So, in the question, the temperature gets colder by 3.75 degrees, so the temperature must have been = 6.5-3.75 = 2.75 or [tex]2\frac{3}{4}[/tex] degrees Celsius.
Therefore, the temperature on Sunday was 2.75 degrees Celsius.
Add. (−x^3 + 26x^2 − 7x−13) + (6x^4 − x^3 + 8x+27) Express the answer in standard form. Enter your answer in the box.
How many 2 digit numbers can you make using the digits 1,2,3,4 without repeating the digits
The pair of values below is from an inverse variation. Find the missing value.
(4,14), (10,y)
A book is in the shape of a right rectangular prism. It measures 812 inches tall, 7 inches wide, and 212 inches thick.
What is the volume of the book?
a 4712 in³
b 8012 in³
c 14834 in³
d 17912 in³
Please answer ASAP! :)
What is the slant height if the surface area is 243 square centimeters?
8 cm
10 cm
11 cm
9 cm
The answer is 9cm
SA = r + r 2
452.16 m 2 = (3.14)(6 m)(x) + (3.14)(6 m) 2
452.16 m 2 = (3.14)(6 m)(x) + (3.14)(36 m 2)
452.16 m 2 = (18.84 m)x + 113.04 m 2
339.12 m 2 = (18.84 m)x
18 m = x
Answer:
Option D. 9 cm
Step-by-step explanation:
Surface area of the given figure is S = 243 cm² and we have to find the slant height.
We can see this figure comprises of 1 square and 4 triangles.
Let the slant height of the given triangles is L.
So area of one triangle = [tex]\frac{1}{2}(Slant height).(Base)[/tex]
and the area of square = side² = 9² = 81 cm²
Now surface area of total figure = Area of square + 4×(area of a triangle)
[tex]243=9^{2}+\frac{4}{2}(9.L)[/tex]
243 = 81 + 2×9L
18L = 243 - 81 = 162
[tex]L=\frac{162}{18}[/tex]
L = 9 cm
Therefore Option D. 9 cm is the correct answer.
The enrollment at a high school for the year 2007 is approximately 1500. The growth of the school population can be represented by the equation P = 1500(1.04)x where x represents the years after 2007. After how many years will the population of the school be approximately 1900?
Look at some real estate want ads in your newspaper. Enter the price of a two-bedroom home and a three-bedroom home. If you find some abbreviations you do not understand, ask your teacher.
Andy is buying carpet squares for his living room. the length of the room is 20 feet, and the width is 16 feet. each carpet square covers 4 square feet. how many carpet squares will andy need to purchase to cover the room
Answer:
andy needs 80 carpet squares
Step-by-step explanation:
Final answer:
To cover the living room, multiply the room's length by its width to get the area in square feet (320 square feet), then divide by the area that one carpet square can cover (4 square feet), resulting in 80 carpet squares needed.
Explanation:
To calculate the number of carpet squares needed to cover Andy's living room, we start by finding the area of the room. The area is the product of the length and the width, so we multiply the room's dimensions: 20 feet (length) by 16 feet (width). This calculation gives us an area of 320 square feet. Next, we divide the total area by the area that each carpet square can cover. Since each square covers 4 square feet, we divide 320 square feet by 4 square feet per square to determine the number of squares needed:
320 square feet ÷ 4 square feet/square = 80 squares.
Therefore, Andy will need to purchase 80 carpet squares to cover the living room.
distance between 1,3 and -3, -1
Identify the equivalent expressions of 4(2x + x – 3) – 3x + 3 by applying x = 2 and x = 3.
9x-9
9x-1
9x+x-9
9(x-1)
4(3x-3)+3-3x
If f(x) is a linear function, what is the value of n?
Answer:
Option C. 13
Step-by-step explanation:
Since f(x) is a linear function then we can rewrite the function in the form of an equation y = mx + c
where m is the slope of a line.
Since line passes through two points (3, 7), (9, 16)
Therefore m = (16 - 7)/(9 - 3) = 9/6 = 3/2
Now we know a point (16, 26.5) also lie on the line so by putting the values of m, x, and y in the equation.
y = 3x/2 + c
26.5 = 3×16/2 + c
c = 26.5 - 24 = 2.5
So the equation is y = 3x/2 + 5/2
y = 1/2(3x + 5)
If a point (7, n) lies on the line then
n = 1/2(3×7 + 5) = 1/2(21 + 5) = 26/2 = 13
Therefore n = 13 is the answer.
Jason's insurance company pays for 80% of the cost of an ambulance ride, after he pays a $200 deductible. The ambulance ride costs $1200.
How much wold Jason pay for an ambulance ride?
A) 200
B) 240
C) 400
D) 440
Identify the initial amount a and the growth factor b in the exponential function a(x) =680•4.3^
fitness center currently has 320 members. Monthly membership fees are $45. The manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.
Write an equation that can be used to find the revenue of the fitness center in dollars, y, after x price increases of $5.
y = -50x2 + 1,150x + 14,400
y = -50x2 + 3,425x + 14,400
y = -50x2 + 2,975x + 14,400
y = -50x2 + 2,050x + 14,400
Answer:
y= -50x^2+1,150x+14,400
Step-by-step explanation:
fitness center currently has 320 members. Monthly membership fees are $45. The manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.
LEt x be the number of price increases of $5
y is the revenue
Revenue= membership fee * members
for x number of increase in fee by 5 then member ship fee becomes 45+5x
approximately 10 members leave, so members becomes (320-10x)
y = (45+5x) (320-10x)
Multiply it using FOIL method
y=45 * 320 +45*(-10x) + 5x * 320 + 5x * (-10x)
y=14400 - 450x + 1600x - 50x^2
Combine like terms
y= -50x^2+1150x+14400
Paula ran 24 foot with the football and then passed it 15 feet to newt. Newt ran 70 yards for a touchdown. What was the total number of feet the ball traveled?
Rewrite 20/6 as a mixed number.
The improper fraction number 20/6 is converted into a mixed fraction number as 3 ¹/₃.
What is the mixed fraction number?The mixed fraction number is the combination of the whole number and the proper fraction number. In a proper fraction number, the numerator is smaller than the denominator.
The improper fraction is 20/6.
Convert the improper fraction into a fraction number.
⇒ 20 / 6
⇒ 10 / 3
⇒ (9 + 1) / 1
⇒ 9/3 + 1/3
⇒ 3 ¹/₃
The improper fraction number 20/6 is converted into a mixed fraction number as 3 ¹/₃.
More about the mixed fraction number link is given below.
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what are the values of x and y?
Which of the binomials below is a factor of this trinomial?
3x2 + 18x + 24
A. x + 4
B. x - 4
C. x - 3
D. x + 3
Final answer:
The binomial factor of the trinomial 3x^2 + 18x + 24 is 'x + 4', which corresponds to Option A.
Explanation:
The student is asking which binomial is a factor of the trinomial 3x2 + 18x + 24. To find a factor, you can either factor the trinomial directly or use the zero product property, which states that if a product equals zero, then at least one of the factors must be zero. Since we're looking for a binomial factor and not solving for x, we'll factor the trinomial.
Factors of 3x2 are 3x and x, and factors of 24 that add up to 18 (when multiplied by 3 or 1 from the 3x2 term) are 6 and 4. Thus, the trinomial can be factored as (3x + 4)(x + 6). So, the binomial that is a factor of the trinomial is x + 4, which is Option A.
A number divided by three less two is at most two
The required number would be x ≤ 2 which represents the number divided by three less two is at most two.
What is inequality?Inequality is defined as mathematical statements with at least two terms including non-equal variables or integers.
What is algebra?
Algebra is the study of mathematical symbols, whereas logic is the manipulation of those symbols.
The number divided by three less two equals the number specified in the question.
Let the required number would be x
As per the given condition, translate the phrase into an algebraic inequality as:
⇒ x/(3 - 2) ≤ 2
Apply the subtraction operation, and we get
⇒ x/1 ≤ 2
⇒ x ≤ 2
Therefore, the required number would be x ≤ 2.
To learn more about the inequalities click here:
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A shop sells three types of boots (football, rugby and hiking). Sales are usually in the ratio 6 : 2 : 3 last month, 24 pairs of football boots were sold. How many boots altogether were sold last month?
Answer:
Total number of boots sold = 44
Step-by-step explanation:
Ratio of football, rugby and hiking boots sold = 6 : 2 : 3
24 pairs of football boots were sold.
That is
6 n = 24
n = 4.
Number of rugby boots sold = 2 n = 2 x 4 = 8
Number of hiking boots sold = 3 n = 3 x 4 = 12
Total number of boots sold = 6n + 2n + 3n = 11n = 11 x 4 = 44
Total number of boots sold = 44
Help please!!!!!!!!!
Factor completely x^2 + 16.
(x + 4)(x + 4)
(x + 4)(x − 4)
Prime
(x − 4)(x − 4)
12+34+23+9424482+398+42+489+92+12+3+423+1=?
You have two accounts with balances $450 and $35. you want to bring up the balance in the second account but do not want the balance of the first to drop below $215. how much can you transfer from the first to the second account?
a.$35
b.$215
c.$235
d.$450 submit
How many pounds of cashew nuts worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to make a mixture worth $1.00 a pound? Which of the equations could be used to solve for p, the pounds of cashew nuts? 75p + 150(10) = 100(p + 10) 75(p + 10) + 150(10) = 100(p + 10) 75p + 150 = 100(p + 10)
75p + 150(10) = 100(p + 10)
Explanation:Mixture problems such as this can be solved by writing an equation that expresses the total cost of the mixture in terms of the costs of the constituents.
Here, the cost (in cents) of p pounds of cashews will be 75p. The cost (in cents) of the 10 pounds of pecans at $1.50 per pound will be 150(10). The total cost of p+10 pounds of the mixture is desired to be 100(p+10).
The equation of the 1st selection is appropriate. It tells that the prices of the contributing nuts add to give the price of the mixture, just as you want:
75p + 150(10) = 100(p+10)
The correct equation to solve for the pounds of cashew nuts, denoted as p, that must be mixed with pecans to get a mixture worth $1.00 a pound is: 75p + 150(10) = 100(p + 10).
We are trying to determine how many pounds of cashew nuts that are worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to create a mixture worth $1.00 a pound. Let's denote the pounds of cashew nuts needed as p. The respective values of each type of nut are included in calculating the total value of the mix. Therefore, the value of the cashews (at 75 cents per pound) plus the value of the pecans (at $1.50 per pound) should equal the value of the desired mixture (at $1.00 per pound). The correct equation to use would be:
75p + 150(10) = 100(p + 10)
To solve for p, we multiply the cost per pound by the weight for each type of nut, then equate this to the cost per pound of the mixture multiplied by the total weight of the mixture. After solving this equation for p, we will know the required pounds of cashew nuts.
Find the supplement of the complement of a 51 degree angle
What is the absolute value of -4-2i