Answer: 0.9961
Step-by-step explanation:
Given: Total choices to each question = 4
So, the probability that an answer is correct = [tex]\dfrac{1}{4}=0.25[/tex]
Total questions = 20
i.e. n= 20
Let x be the binomial variable that represents the number of correct answers.
So, the probability that the student has at least 10 correct answers.
[tex]B(x=10;n=20, p=0.25)=\sum\limits_{i=0}^{x}(i;n=20,p=0.25)[/tex]
[tex]=0.9961[/tex] [By using cumulative binomial table]
Hence, the probability that the student has at least 10 correct answers = 0.9961
An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 years is approximated by dh/dt = 1.5t + 4, where t is the time in years and h is the height in centimeters. The seedlings are 12 centimeters tall when planted (t = 0). (a) Find the height after t years.
Answer:
[tex]h(t) = 0.75t^2 + 4t + 12[/tex]
Step-by-step explanation:
The equation given calculates the derivative of the height in relation to the time, that is, the rate of change of the height. To find the equation for the height, we need to integrate this equation:
[tex]dh/dt = 1.5t + 4[/tex]
Multiplying both sides by 'dt', we have:
[tex]dh = (1.5t + 4)dt[/tex]
Using the integral in both sides:
[tex]\int dh = \int (1.5t + 4) dt[/tex]
[tex]h = 0.75t^2 + 4t + h(0)[/tex]
[tex]h = 0.75t^2 + 4t + 12[/tex]
So the height after t years is represented by this equation:
[tex]h(t) = 0.75t^2 + 4t + 12[/tex]
Kadence is twice as likely to randomly pick a blue marble from a bag as she is to pick a red marble. If there are x red marbles and the bag contains
40 marbles, what is the probability that Kadence will pick a blue marble from the bag?
A. 16/40
B. x/10
C. x/20
D. x/40
D
Step-by-step explanation:
Probabilities are used to determine the chances of picking a marble
The probability of picking a blue marble is: x/20
The given parameters are:
[tex]\mathbf{Marbles = 40}[/tex]
[tex]\mathbf{Red = x}[/tex]
The probability of picking a red marble is calculated as:
[tex]\mathbf{Pr = \frac{Red}{Marbles}}[/tex]
Substitute values for Red and Marbles
[tex]\mathbf{Pr = \frac{x}{40}}[/tex]
He is twice as likely to randomly pick a blue marble from a bag as she is to pick a red marble
So, the probability of picking a blue marble is:
[tex]\mathbf{P(Blue) = 2 \times \frac x{40}}[/tex]
This gives
[tex]\mathbf{P(Blue) = \frac x{20}}[/tex]
Hence, the probability of picking a blue marble is: x/20
Read more about probabilities at:
https://brainly.com/question/11234923
the mean of five numbers is 8. when another number is added the mean is 7. find the number added
Answer:
[tex]\large \boxed{\sf \ \ 2 \ \ }[/tex]
Step-by-step explanation:
Hello,
The mean of five numbers is 8 so we can write
[tex]\dfrac{x_1+x_2+x_3+x_4+x_5}{5}=8[/tex]
When another number is added the mean is 7, let s note x the another number we can write
[tex]\dfrac{x_1+x_2+x_3+x_4+x_5+x}{6}=7[/tex]
From the first equation we can say
[tex]x_1+x_2+x_3+x_4+x_5=8*5=40[/tex]
So the second equation becomes
[tex]\dfrac{x_1+x_2+x_3+x_4+x_5+x}{6}=7\\\\<=> \dfrac{40+x}{6}=7\\\\<=>40 + x = 6*7=42\\\\<=> x = 42-40 = 2\\[/tex]
The solution is then 2
Hope this helps
what is math in your visionary state what do you think of when reminded of math I am specifacly asking you
Answer:
answer is.
9382
working
A box contains 6 blue balls, 4 black balls and 5 red balls at the same size . A ball is selected at random from the box and then replaced . A second ball is then selected. Find the probability of obtaining ; (i) two red balls ; (ii) two blue balls or two black balls ; (iii) one black ball and one red balls.
Answer:
(i) 1/21
(ii) 1/10
(iii) Take a look at the explanation: Try this one yourself. I have given you some hints.
Step-by-step explanation:
(i) Two red balls:
To do this, we need to find the total amount of possible choices first. To do this, we multiply 15 by 14. This is our denominator:
15(14) = 210
Now, we need to find the total combinations of red balls. We solve 5 choose 2 for this one.
5 choose 2 = 5(4)/2! = 10
Our numerator is 10. Therefore, our probability is 10/210 = 1/21.
(ii) Two blue balls or two black balls:
To do this, we need to add the probabilities of getting a blue ball with a black ball. (Since there is an "or" sitting there. If there is an "and", we multiply)
So, let's calculate the probability of getting a blue ball first:
Blue:
We use the same denominator as before: 210.
Our numerator is now 6 choose 2, which is:
6 choose 2 = 6(5)/2! = 15.
Now, our fraction is 15/210, BUT, dont simplify, as we will need to add.
Black:
Same steps: denominator is 210, but the numerator is 4 choose 2.
Solving 4 choose 2:
4 choose 2 = 4(3)/2! = 6.
Our numberator is 6.
But, we cant forget to add them!
(15 + 6)/210 is 21/210, which is 1/10.
(iii) I'll let you try this one by yourself. Here is a hint:
Solve for the probability of chooseing a black ball and a red ball. Then, multiply.
Enjoy the process, and I hoped this helped you! (If you have any questions, feel free to ask)
Twenty-eight people in student council are running for the offices of president and vice-president. In how many different ways can those offices be assigned?
378
55
756
Answer: 756
Step-by-step explanation:
The president can be elected in 28 different ways. After a student is elected president, there are 27 students left to elect a vice president from. So there are 28 x 27 = 756 different arrangements.
ANSWER FAST
please help me answer these following question A sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Oregon are: $295, $475, $345, $595, $538, $460. A second sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Washington are $495, $422, $370, $333, $370, $390. Using the Text Editor, answer the following questions: What is the median price of rent for the University of Oregon? What is the median price of rent for the University of Washington? What is the mean price of rent near the University of Oregon? What is the mean price of rent near the University of Washington? Describe the standard deviation for both Universities and explain how you determined this.
Answer:
The mean, median, and standard deviation of the University of Oregon are $451.33, $467.5, and $113.61 respectively.
The mean, median, and standard deviation of the University of Washington are $396.67, $380, and $56.27 respectively.
Step-by-step explanation:
We are given that a sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Oregon is: $295, $475, $345, $595, $538, $460.
A second sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Washington is: $495, $422, $370, $333, $370, $390.
Firstly, we will calculate the mean, median, and standard deviation for the data of the University of Oregon.
Arranging the data in ascending order we get;
X = $295, $345, $460, $475, $538, $595.
The mean of the above data is given by the following formula;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{\$295+ \$345+ \$460+\$475+ \$538+\$595}{6}[/tex]
= [tex]\frac{\$2708}{6}[/tex] = $451.33
So, the mean price of rent near the University of Oregon is $451.33.
For calculating the median, we first have to observe that the number of observations (n) in the data is even or odd.
If n is odd, then the formula for calculating median is given by;Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
If n is even, then the formula for calculating median is given by;Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]
Here, the number of observations is even, i.e. n = 6.
So, Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]
= [tex]\frac{(\frac{6}{2} )^{th} \text{ obs. } + (\frac{6}{2}+1 )^{th} \text{ obs.}}{2}[/tex]
= [tex]\frac{(3 )^{rd} \text{ obs. } + (4 )^{th} \text{ obs.}}{2}[/tex]
= [tex]\frac{\$460 +\$475}{2}[/tex] = $467.5
Hence, the median price of rent for the University of Oregon is $467.5.
Now, the standard deviation is calculated by using the following formula;
Standard deviation, S.D. = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{ (\$295 - \$451.33)^{2} +(\$345 - \$451.33)^{2} +......+(\$595 - \$451.33)^{2} }{6-1} }[/tex]
= $113.61
So, the standard deviation for the University of Oregon is $113.61.
Now, we will calculate the mean, median, and standard deviation for the data of the University of Washington.
Arranging the data in ascending order we get;
X = $333, $370, $370, $390, $422, $495.
The mean of the above data is given by the following formula;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{\$333+ \$370+ \$370+\$390+ \$422+\$495}{6}[/tex]
= [tex]\frac{\$2380}{6}[/tex] = $396.67
So, the mean price of rent near the University of Washington is $396.67.
For calculating the median, we first have to observe that the number of observations (n) in the data is even or odd.
If n is odd, then the formula for calculating median is given by;Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
If n is even, then the formula for calculating median is given by;Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]
Here, the number of observations is even, i.e. n = 6.
So, Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]
= [tex]\frac{(\frac{6}{2} )^{th} \text{ obs. } + (\frac{6}{2}+1 )^{th} \text{ obs.}}{2}[/tex]
= [tex]\frac{(3 )^{rd} \text{ obs. } + (4 )^{th} \text{ obs.}}{2}[/tex]
= [tex]\frac{\$370 +\$390}{2}[/tex] = $380
Hence, the median price of rent for the University of Washington is $380.
Now, the standard deviation is calculated by using the following formula;
Standard deviation, S.D. = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{ (\$333 - \$396.67)^{2} +(\$370 - \$396.67)^{2} +......+(\$495 - \$396.67)^{2} }{6-1} }[/tex]
= $56.27
So, the standard deviation for the University of Washington is $56.27.
some help a homie out in math
Answer:
1. A pentagonal Pyramid
2. Super Easy, tell me to draw one if you need but i am not gonna give in that much effort right now
Please help! Question two
Answer:
4y+6
Step-by-step explanation:
Perimeter is adding up the outside
so.. there are y+y = 2y
y+3 + y+3 = 2y+6
2y+6 + 2y = 4y+6
Hope this helps :)
7y - 12 / 5 minus y - 2/3 is equal to 1
Answer:
y = 61/90
Step-by-step explanation:
7y - 12/5 - y - 2/3 = 1
Combine like terms.
6y -46/15 = 1
Add 46/15 to both sides.
6y = 61/15
Divide both sides by 6.
y = 61/90
If p & q are position vectors of P & Q respectively & R divides PQ externally by the ratio 3:2, which one is the position vector of R? a. 2p-3q b. 3p-2q Please provide an explanation as well
Answer:
b. 3p-2q
Step-by-step explanation:
Let the position vector of P=p
Let the position vector of Q=q
Point R divides segment PQ in ratio 3:2 externally.
[tex]\text{Position Vector of R }=\dfrac{\text{(Position Vector of P)m }-\text{(Position Vector of Q) n}}{m-n}[/tex]
m:n = 3:2
Therefore:
[tex]\text{Position Vector of R }=\dfrac{3p -2q}{3-2}\\=3p-2q[/tex]
Aubreys kitchen countertop is 2/3 meter by 3 4/5 meters she solves 2/3 multiply 3 4/5 to find the area of the countertop in square meters. Enter numers to conplete aubreys calculations for the area
Answer:
[tex]2\frac{8}{15}[/tex] or 2.5333
Step-by-step explanation:
Just multiply the numbers. please mark brainliest
determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use pi key on your calculator.
Answer:
[tex] Volume = 150 yd^3 [/tex]
[tex] Surface Area = 150 yd^2 [/tex]
Step-by-step explanation:
Going by the dimensions of the given three-dimensional figure, we can conclude that the figure is that of a cube. The height, length and width are equal.
Volume of a cube is given as [tex] a^3 [/tex] , while surface area of a cube is given as [tex] 6a^2 [/tex]
Where, a = the side length = 5 yards
[tex] Volume = a^3 = 5^3 [/tex]
[tex] Volume = 150 yd^3 [/tex]
[tex] Surface Area = 6a^2 = 6(5)^2 [/tex]
[tex] Surface Area = 150 yd^2 [/tex]
The length of a rectangle is a centimeters, the width of this rectangle is b centimeters. Write an expression for the perimeter of this rectangle.
Answer:
2a+2b
Step-by-step explanation:
I am pretty sure that if the length is a and width is b, you would add them twice together. I am actually not quite sure.
Hope this helped you
I am sorry if this was wrong, I am still a beginner at this
select the correct answer from the drop-down menu find the surface area of this triangular prism
Answer:
The correct answer is 96
Step-by-step explanation:
leo, Kush and Mai share some money in the ratio 3 : 5 : 8. Kush receives £750 more than Leo. Calculate the total amount of money that they shared?
Answer:
£6000
Step-by-step explanation:
3:5:8
3+5+8=16
5-3 =2
Therefore 2=750
Therefore 1=375
16*375=£6000
Find the area. will mark brainliest
Answer:
240
Step-by-step explanation:
16*8=128
3+3+8=14
14*16=224
224/2=112
112+128=240
240 is the answer
Step-by-step explanation:
area of a rectangle =l*b
8*16=128
area of a triangle =1/2*b*h
1/2*14*16=112
final area=128+112=240
please make me brainliest
La longitud de un rectángulo mide 3m mas que el doble de su ancho del rectángulo, escribe un polinomio que represente el perímetro del rectángulo y simplifica el polígono correspondiente.
Answer:
Step-by-step explanation:
El ancho es x, el largo es x+3
El perímetro es dos veces el largo más dos veces el ancho, es decir: 2(x) + 2(x+3) = 4x+6
El polinomio sería: P(x)=4x+6
Simple and easy question
please help
Answer:
A
Step-by-step explanation:
To find the volume we do 2 * 1.25 * 1.5 (i rewrote the fractions as decimals) which is 3.75 or 3 and 3/4 cubic inches.
Answer:
V = [tex]3 \frac{3}{4}[/tex]
Step-by-step explanation:
Hey there!
Well the volume "v" of a rectangular prism is,
V = l•w•h
Fill in
[tex]V = 2* 1 \frac{1}{4} * 1 \frac{1}{2}[/tex]
V = [tex]3 \frac{3}{4}[/tex]
Hope this helps :)
PLEASE help me with this!! I need help!
Answer:
∠ BDG = 148°
Step-by-step explanation:
The tangent- chord angle BDG is half the measure of its intercepted arc DCG
The 2 arcs in the circle sum to 360°, thus
arc DCG = 360° - arc DG = 360° - 64° = 296° , thus
∠ BDG = 0.5 × 296° = 148°
The length of a rectangle is twice it’s breadth. if the perimeter is 72 meters, find the length and breadth of the rectangle
Perimeter of a rectangle = 2l + 2b
where
l = length
b = breadth
The length is twice it's breadth which is written as
l = 2b
Perimeter = 2(2b) + 2b
72 = 4b + 2b
72= 6b
Divide both sides by 6
b = 12 meters
Since l = 2b
l = 2(12) = 24 meters
The length of the rectangle is 24 meters and it's breadth is 12 meters
Hope this helps
Answer:
If breadth of a rectangle is 19m and perimeter is 80m, find the length of the rectangle.
Step-by-step explanation:
Jenny has a $3,000 balance on her credit card with an 18% interest rate. If she makes no payments on her card and no late fees were charged how long will it take her debt to double?
Answer:
it would take about 4.2 years for her debt to double.
Step-by-step explanation:
With a principal of $3000, and an annual interest rate of 18%, the equation for accumulated debt as a function of time in years, would be given by the expression:
[tex]A(t)=3000\,(1+0.18)^t[/tex]
now, if we want to find when the debt would double, we replace A(t) with $6000, and solve for the time 't' using logarithms to bring down the unknown (t) that resides in the exponent:
[tex]A(t)=3000\,(1+0.18)^t\\6000=3000\,(1.18)^t\\2=(1.18)^t\\log(2)=t\, \, log(1.18)\\t=\frac{log(2)}{log(1.18)} \\t=4.1878\,\,years[/tex]
which we can round to approximately 4.2 years
A fair 6-sided die numbered 1 to 6 is rolled once. Find the probability that the number obtained is either even or a prime number. Define the event ME or MNE. If you can help me, I would be so thankful.
Please answer this question now in two minutes
Answer:
u+43°=u_3°+u+3° (by exterior angle theorem)
u+43°= 2u
or, 2u_u=43°
or, u= 43°
is the value of u.....
50. Write the fraction or mixed number as a
decimal. Then tell whether the decimal is a
terminating decimal or repeating decimal.
23
33
Answer:
0.69, repeatingStep-by-step explanation:
23/33 =0.69repeating
A box contains 5 blue, 4 red, and 3 yellow marbles. Two marbles are randomly drawn and not replaced. What is the probability of drawing a blue then a red marble?
Answer: Probability = 20/132
Step-by-step explanation: There is no replacement in the box, so, once the marble is taken out, there will be one less inside the bag:
Total = 5 + 4 + 3 = 12
Probability of Blue:
P(b) = 5/12
Probability of Red: Since the blue is already out, total will be one less:
P(r) = 4/11
Probability of taken one and then the other:
P(blue,red) = [tex]\frac{5}{12} . \frac{4}{11}[/tex]
P(blue,red) = [tex]\frac{20}{132}[/tex] ≈ 0.15
The probability of drawing a blue and then a red is 20/132.
Answer:
5/33
Step-by-step explanation:
A construction company covered 3\8 of a road which is 10km long with asphalt in the first week and covered 7\18of the road in the second week with asphalt. what length of the road remained to be covered with asphalt?
Answer:
2.36 km
Step-by-step explanation:
First they covered 3/8 of the road, so in figures that is;
= [tex]\frac{3}{8} * 10km[/tex]
=3.75 km
The second week they covered 7/18 of the road which is;
= [tex]\frac{7}{18} * 10km[/tex]
= 3.89 km
If we combine the two distances, we get;
= 3.75 km + 3.89 km
= 7.64 km
Subtract this from the total distance and you get
= 10 km - 7.64 km
= 2.36 km
Which means 2.36 km of the road is left to be covered with asphalt.
Fez rolls 2 fair dice and adds the results from each. Work out the probability of getting a total more than 6
Answer:
7/12 ≈ 0.583
Step-by-step explanation:
See picture below. There are 21 totals higher than 6 out of 36 possible outcomes. The probability is therefore 21/36 = 7/12.
Answer: 21/36 or 7/12. = 58.33%
Step-by-step explanation: 36 possible outcomes
Of those, combinations resulting in numbers greater than 6 are:
# | combinations
7 | 6
8 | 5
9 | 4
10 | 3
11 | 2
12 | 1
The sum of those combinations is 21.
So 21/36 = 0.5833
or 7/12 = 58.33%
Hi can you help me with this please
Answer:
x=13 degrees
Step-by-step explanation:
Supplementary angles: 180 degrees.
180-98=82
Vertical angles: congruent
Corresponding angles: congruent
We have 2 angles of the triangle, so we can find the third. (Angles in a triangle add to 180 degrees)
x=13
[tex]7x^{2} -3=60[/tex]
Answer:
x = -3 , x = 3Step-by-step explanation:
7x² - 3 = 60
7x² - 3 - 60 = 0
7x² - 63 = 0
Simplify the terms
Divide both terms by 7
That's
x² - 9 = 0
Solve the quadratic equation
Use difference of two squares
That's
a² - b² = ( a + b)(a - b)
x² - 9 = 0
(x + 3)(x - 3) = 0
x + 3 = 0 x - 3 = 0
x = - 3 x = 3
Hope this helps you