Answer:
The probability that no more than 6 students belong to a ethnic minority is 0.9815.
Step-by-step explanation:
The question is incomplete:
In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?
We can model this with a random variable, with sample size n=10 and probability of success p=0.33.
The probability that k answers are guessed right in the sample is:
[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{10}{k}\cdot0.33^k\cdot0.67^{10-k}[/tex]
We have to calculate the probability that 6 or less students belong to a ethnic minority. This can be calculated as:
[tex]P(x\leq6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)\\\\\\[/tex]
[tex]P(x=0)=\dbinom{10}{0}\cdot0.33^{0}\cdot0.67^{10}=1\cdot1\cdot0.0182=0.0182\\\\\\P(x=1)=\dbinom{10}{1}\cdot0.33^{1}\cdot0.67^{9}=10\cdot0.33\cdot0.0272=0.0898\\\\\\P(x=2)=\dbinom{10}{2}\cdot0.33^{2}\cdot0.67^{8}=45\cdot0.1089\cdot0.0406=0.1990\\\\\\P(x=3)=\dbinom{10}{3}\cdot0.33^{3}\cdot0.67^{7}=120\cdot0.0359\cdot0.0606=0.2614\\\\\\[/tex]
[tex]P(x=4)=\dbinom{10}{4}\cdot0.33^{4}\cdot0.67^{6}=210\cdot0.0119\cdot0.0905=0.2253\\\\\\P(x=5)=\dbinom{10}{5}\cdot0.33^{5}\cdot0.67^{5}=252\cdot0.0039\cdot0.135=0.1332\\\\\\P(x=6)=\dbinom{10}{6}\cdot0.33^{6}\cdot0.67^{4}=210\cdot0.0013\cdot0.2015=0.0547\\\\\\\\\\\\[/tex]
[tex]P(x\leq6)=0.0182+0.0898+0.1990+0.2614+0.2253+0.1332+0.0547\\\\\\P(x\leq6)=0.9815[/tex]
The probability that 6 or less students belong to a ethnic minority is 0.9815.
When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. How y’all is a person if he casts a 1.5 foot shadow at the same time?
Answer:
6 ft
Step-by-step explanation:
The building height of 100 ft is 4 times the shadow length of 25 ft. At the same ratio, the person's height is 4 times the 1.5 ft shadow length, so is ...
4 × (1.5 ft) = 6.0 ft
The person is 6 ft tall.
Arthur drops a ball from a height of 81 feet above the ground. it’s height, , is given by the equation h=16ft^2+81, where t is the time in seconds. for which interval of the time is the height of the ball less than 17 feet
Answer:
The height of the ball is less than 17 feet for t > 2 seconds.
Step-by-step explanation:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -16t^{2} + 81[/tex]
For which interval of the time is the height of the ball less than 17 feet
This is t for which:
[tex]h(t) < 17[/tex]
So
[tex]-16t^{2} + 81 < 17[/tex]
[tex]16t^{2} < -64[/tex]
Multiplying by -1
[tex]16t^{2} > 64[/tex]
[tex]t^{2} > \frac{64}{16}[/tex]
[tex]t^{2} > 4[/tex]
[tex]t > \sqrt{4}[/tex]
[tex]t > 2[/tex]
The height of the ball is less than 17 feet for t > 2 seconds.
6x^2-2x=20 use ac method
Answer:
Cannot be factored
Step-by-step explanation:
the table shows the time it took a group of students to complete a puzzle
Answer:
Where is the table because I dont see it up here?
15. A zoo is building a glass cylindrical tank
for the small sharks. The tank is 10 feet
high and has a diameter of 16 feet. How
much water is needed to fill the tank?
(The volume of a right circular cylinder is
V = Tr?h, where r is the radius, h is the
height, and a = 3.14.)
Answer:
2009.6
Step-by-step explanation:
As we know, volume of a right cylinder is πr²h.
here, diameter is mentioned, which gives that the radius is half of the diameter.
r= 1/2*16=8 feet
height= 10 feet
π=3.14
volume= 3.14*8²*10
= 3.14*64*10
=3.14*640
= 2009.6
so, that much water is needed to fill the tank
Answer:
2,010.6192982
Step-by-step explanation:
what is the answer for 8=22x+1
Answer:
x = 22/7Step-by-step explanation:
22x + 1 = 8
Send 1 to the right side of the equation
22x = 8 - 1
22x = 7
Divide both sides by 22
x = 7/22
Hope this helps you
This table represents a quadratic function.
where is the table that represents the quadratic function
Please answer this correctly
Answer:
7/8
Step-by-step explanation:
The numbers that are not 3 are 1, 2, 4, 5, 6, 7, and 8.
7 out of 8 numbers.
P(not 3) = 7/8
Answer:
7/8
Step-by-step explanation:
There are a total of 8 cards, and one of the cards is 3.
Their cards that are not 3 are 1,2,4,5,6,7,8. Therefore, there is a total of 7 cards that are not 3.
Now, let’s find the probability of drawing a card that is not 3.
P(not 3)= numbers that are not 3 / total numbers
There are 7 numbers that are not 3 and 8 total number cards.
P(not 3)= 7/8
The double cone is intersected by a vertical plane passing through the point where the tips of the cones meet. What is the shape of the cross section formed? HELP PLEASE ITS FOR PLATO
Answer:
B.
Step-by-step explanation:
The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that gets to a point at the middle of the height.
Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.
Answer:
B.
Step-by-step explanation:
answer: B. one triangle tip on top and invert above it with the top touching
Scott has verified that the window is a rectangle. Side AB is half of the length of side AC. If the perimeter of the window is 120 ft., what are the lengths of side AB and side AC?
Answer:
AB = 20 ft
AC = 40 ft
Step-by-step explanation:
==>Given:
Rectangular window ABCD, where,
side AB = ½ of side AC
Perimeter = 120ft
==>Required:
Length of side AB and side AC
==>Solution:
Let AB = x
If x = ½ of AC
AC = 2x
Perimeter = 2(AB + AC)
Thus,
120 = 2(x+2x)
120 = 2(3x)
120 = 6x
Divide both sides by 6 to solve for x
120/6 = x
20 = x
AB = x = 20 ft
AC = 2x = 2(20) = 40ft
please help pleaseeeeeeeee
━━━━━━━☆☆━━━━━━━
▹ Answer
#3. 1.89/100
▹ Step-by-Step Explanation
1.89 → hundreths place so..
1.89/100 is the correct answer
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an equation to show the profit she will make on sneakers and sandals. P = [answer0]
Answer:
The equation that shows the profit: P = 2x + 3y
Step-by-step explanation:
The number of sneaker = x
The number of sandals = y
Cost of sneaker = 8 dollars.
Cost of sandals = 14 dollars.
Selling price of sneaker = $10
Selling price of sandals = $17
Total revenue = $10x + $17y
Total cost = $8x + $14y
Profit (P) = Total revenue - Total cost.
Profit = ($10x + $17y) – ($8x + $14y)
P = 10x +17y – 8x – 14y
P = 2x + 3y
A regression line is the line that best fits the data, but this does not mean that the fit is good. In other words, there can still be a lot of variability about the regression line. Which combination describes a regression line that is a good fit for the data?
a. Larger-sq and small Se
b. Larger-sq and large Se
c. Small r-sq and small Se
d. Smallr-sq and large Se
Answer:
The following combination describes a regression line that is a good fit for the data
a. Larger R-sq and small Se
Step-by-step explanation:
In regression analysis, we measure the goodness of fit in terms of two parameters.
1. R² ( R-squared or also called the coefficient of determination)
2. SE ( Standard Error)
1. R-squared
The R-squared indicates the relative measure of the percentage of the variance with respect to the dependent variable.
R-squared is measured in percentage so it doesn't have any unit.
The greater the R-squared percentage, the better is the goodness of fit.
2. Standard Error
The SE basically indicates that on average how far the data points are from the regression line.
The unit of the standard error is the same as the dependent variable.
The lower the SE, the better is the goodness of fit.
Therefore, the correct option is (a)
a. Larger R-sq and small Se
The measure of angle 1 is (10 x + 8) degrees and the measure of angle 3 is (12 x minus 10) degrees. 2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4. What is the measure of angle 2 in degrees?
Answer:
Measure of angle 2 = 82°
Step-by-step explanation:
m∠1 = (10 x + 8)°
m∠3 = (12 x - 10)°
2 lines are said to intersect to form 4 angles. And the labelling of the angles was done starting from top left, clockwise: the angles are 1, 2, 3, 4.
Find attached the diagram obtained from the given information.
Vertical angles are angles opposite each other when two lines intersect. As such, they are equal to each other.
Considering our diagram
m∠1 = m∠3
m∠2 = m∠4
Sum of all four angles firmed = 360° (sum of angles at a point)
m∠1 +m∠2 + m∠3 + m∠4 = 360°
m∠1 = m∠3
(10 x + 8)°= (12 x - 10)°
10x-12x = -10-8
-2x = -18
x= 9°
Also m∠2 = m∠4, let each equal to y
(10 x + 8)°+ y + (12 x - 10)° + y = 360
10x + 12x - 10 +8 +2y = 360
Insert value of x
22(9) -2 + 2y = 360
2y = 360-196
2y = 164
y = 82°
m∠2 = m∠4 = y = 82°
Measure of angle 2 = 82°
Answer:
2 = 82°
Step-by-step explanation:
match each function on the left to all points on the right ! Please help!
Answer:
f(x)=2x-2 with =( -1, 4)
f(x)=2(x^2) -2 with (-1,0)
f(x)=2√(x-2) with (2,0)
Step-by-step explanation:
f(x)=2x-2
(2,0)
0=2(2)-2=2 0=2
(-1,-4)
4=2(-1)-2=-4 -4 = -4 f(x)=2(x^2) -2
(2,0)
0=2(2^2)-2=6 0=6
(-1,0)
0=2(-1^2)-2=0 0=0 f(x)=2√(x-2) (2,0)
0=2√(2-2)=0 0=0
The function f ´( x ), which would be read `` f -prime of x '', means the derivative of f ( x ) with respect to x .
What is f(x) ?A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The output value, also known as the dependent variable, is denoted by the letter y, or f(x).
f(x)=2x-2\s(2,0)
0=2(2)
-2=2 0=2
(-1,-4)
4=2(-1)-2=-4 -4 = -4 f(x)=2(x^2) -2\s(2,0) (2,0)
0=2(2^2)
-2=6 0=6\s(-1,0)
0=2(-1^2)
-2=0 0=0 f(x)=2 √(x-2) (2,0) (2,0)
0=2√(2-2)=0 0=0
The phrase "f (x)" denotes a formula with x serving as its input variable. Not "multiply f and x," though! Never try to "multiply" the function name with its parenthesized input and avoid embarrassing yourself by pronouncing (or thinking of) "f (x)" as being "f times x".
Will give brainliest answer
Answer:
9π or 28.3 units²
Step-by-step explanation:
A = πr²
A = π(3)²
A = 9π
or
A= 28.3 units²
Hope this helps. :)
What is the area of the sector shown in the diagram below?
A.
50 cm2
B.
11.1 cm2
C.
2.5 cm2
D.
39.3 cm2
Answer:
B
Step-by-step explanation:
Each letter of the alphabet is assigned a numerical value according to its position in the alphabet. Encode the message SEND âHELP, using theâ one-to-one function defined by f(x) = x^3 - 1. Give the inverse function that the decoder would need when the message is received.Write the encoded message. Use space to separate the numbers?
The inverse function is:_________.
f -1 (x) = ?
Answer:
f⁻¹(x) = ∛(x+1)Step-by-step explanation:
Given the encoded message defined by the function f(x) = x³-1, the inverse function that the decoder would need when the message is received can be expressed as thus:
let the inverse of the function be represented as y such that y = x³-1.
Making x the subject of the formula from the equation above;
x³ = y+1
Taking the cube root of both sides:
∛x³ = ∛(y+1)
x = ∛(y+1)
replacing y with x:
y = ∛(x+1)
f⁻¹(x) = ∛(x+1)
The encoded message is the inverse function ∛(x+1)
Consider a one-player game with zero cost (i.e., the player pays nothing to play the
game). The player can win $1.00, $5.00, $10.00, or nothing at all. The probability of winnin
g $1.00 is 40%, $5.00 is 20%, and $10.00 is 5%.
What is the probability of winning nothing at all?
A. 30%
B. 35%
OC. 40%
D.25%
Answer:
B. 35%
Step-by-step explanation:
P(winning $1.00)=40%
P(winning $5.00)=20%
P(winning $10.00)=5%
In a probability distribution, the sum of the probability must always be equal to 1.
Therefore:
P(winning $0.00)=1-(40%+20%+5%)
=1-(0.4+0.2+0.05)
=1-0.65
=0.35
The probability of winning nothing at all is 35%.
Use the properties of logarithms to prove log81000= log210.
Answer:
Step-by-step explanation:
Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
[tex]log_81000\\[/tex]= log₈ 10³= log_ 2^3 (10³)= log₂10Human body temperatures have a mean of 98.20degrees°F and a standard deviation of 0.62degrees°F. Sally's temperature can be described by zequals=minus−1.5. What is her temperature? Round your answer to the nearest hundredth.
Answer:
Her temperature is 97.27ºF.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 98.2, \sigma = 0.62[/tex]
Z = -1.5. What is her temperature?
Her temperature is X when Z = -1.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.5 = \frac{X - 98.2}{0.62}[/tex]
[tex]X - 98.2 = -1.5*0.62[/tex]
[tex]X = 97.27[/tex]
Her temperature is 97.27ºF.
Find the first four terms of the sequence defined by a(n subscript)= 1/n (separated by a comma).
Answer:
1,1/2,1/3,1/4
Step-by-step explanation:
an = 1/n
n is the term number
a1 = 1/1 =1
a2 = 1/2
a3= 1/3
a4 = 1/4
The first 4 terms are 1,1/2,1/3,1/4
E = { x l x is a perfect square <36}
Answer:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
Step-by-step explanation:
For this problem we have the following set:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
The graph of F(x) shown below resembles the graph of G(x) = K, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x)=?
G(X) = 1x1
O A. F(X) = 3M+3
O B. F(X) --
O C. F(x) = -3M-3
O D. F(X) = 3W-3
Step-by-step explanation:
O D. F(X) = 3W-3 the answer is D
The function that represents the situation is F(x) = -x² - 3.
The correct option is A.
What is transformation on the graphs?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.
here, we have,
Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The value of k can find the direction of shift:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Given that ,
the parent function is g(x) = x².
To find the transformed function F(x):
The function's diagram is in the opposite direction.
That means the function is -x².
And the function is shifted 3 units down vertically.
From the definition the required function is,
F(x) = -x² - 3.
Therefore, F(x) = -x² - 3.
To learn more about the transformation on the graphs;
brainly.com/question/19040905
#SPJ7
complete question:
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
A.
F(x) = –x2 – 3
B.
F(x) = x2 – 3
C.
F(x) = –(x + 3)2
D.
F(x) = –(x – 3)2
If a couple plans to have 9 children, what is the probability that there will be at least one boy? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one boy in 9 children?
Answer:
It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.
Step-by-step explanation:
I listed all of the possible combinations below
GGGGGGGGG BGGGGGGGG
BBGGGGGGG BBBGGGGGG
BBBBGGGGG BBBBBGGGG
BBBBBBGGG BBBBBBBGG
BBBBBBBBG BBBBBBBBB
Total number of combinations with at least one boy is 9/10
This is a very high percentage, which means the couple is very likely to have at least one boy.
Pls help me :(((( Thank you
Step-by-step explanation:
[tex] \frac{2}{ \sqrt{9} } [/tex]
[tex] \frac{2 \times \sqrt{9} }{ \sqrt{9} \times \sqrt{9} } [/tex]
[tex] \frac{2 \sqrt{9} }{9} [/tex]
Answer:
[tex]\frac{2\sqrt{9} }{9}[/tex]
Step-by-step explanation:
[tex]\frac{2}{\sqrt{9} } \\[/tex]
[tex]\frac{2}{\sqrt{9} } * \frac{\sqrt{9} }{\sqrt{9} }[/tex]
[tex]\frac{\sqrt{9} }{\sqrt{9} }[/tex] is equal to 1, so it doesn't change the value, just helps us simplify.
[tex]\frac{2\sqrt{9} }{9}[/tex]
There are no common factors between 2 and root 9, so we are done
A trade discount of 20% amounts to $25.98.
What was the list price?
What was the net price?
Step-by-step explanation:
Net $103.92 [$25.98 ÷ 20%]
List. $129.90 [ $103.92 + $25.98]
For the functions f(x)=−9x^2+9 and g(x)=8x^2+9x, find (f+g)(x) and (f+g)(−1)
Answer:
f(x) = - 9x² + 9
g(x) = 8x² + 9x
To find (f+g)(x) add g(x) to f(x)
That's
(f+g)(x) = -9x² + 9 + 8x² + 9x
Group like terms
(f+g)(x) = - 9x² + 8x² + 9x + 9
(f+g)(x) = - x² + 9x + 9To find (f + g)(- 1) substitute - 1 into (f+g)(x)
That's
(f + g)(- 1) = -(-1)² + 9(-1) + 9
= - 1 - 9 + 9
= - 1Hope this helps you
HELP WITH THIS QUESTION(I know the answer I just need to double check)
Answer:
-5, -3, -1 , 1 , 3
Step-by-step explanation:
Which of the following sets contains all factors of 12?
Answer:
Step-by-step explanation:
Factors of 12
2, 3 , 6 , 4, 1, 12