An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A
Answer:
[tex]P(x\geq 1) = 0.923[/tex]
Step-by-step explanation:
From the question we are told that:
Percentage of student to get A [tex]P(A)=\%5=0.05[/tex]
Sample size [tex]n=50[/tex]
Generally Number of student to get A is
[tex]N_a=n*P(A)[/tex]
[tex]N_a=50*0.05[/tex]
[tex]N_a=2.5[/tex]
Therefore
Probability that one student gets an A grade is mathematically by
[tex]^nPC_xP^x(1-P)^{n-x}[/tex]
[tex]P(x\geq 1)=1-P(x<1)[/tex]
[tex]P(x\geq 1) =1-P(x=0)[/tex]
[tex]P(x\geq 1) =^50C_0(0.05)^0(0.95)^50[/tex]
[tex]P(x\geq 1) = 0.923[/tex]
Given the functions below,find (f -g) (-1).
f(x) = x2 + 3
g(x) = 4x - 3
Answer:
f(x)=-1,(-1)2+3=-2+3=1g(x)=-1 4(-1)-3=4-3=1(Step-by-step explanation:
(f-g)=1
Write the following comparison as a ratio reduced to lowest terms. 169 inches to 13 feet
Answer:
14.0833333333 feet | 13 feet
Step-by-step explanation:
169 Inches is 14.0833333333 feet on calculator compared to 13 feet
and 1.08333333333 is 14.0833333333 divided by 13
if is not it, then 13/14.0833333333 is 0.92307692307
i guess that is the lowest terms in ratio
The mapping shows a relationship between input and output values.
Answer:
where is the photo
Step-by-step explanation:
Which function of x has a y-intercept of -3?
Answer:
C. y = 2x - 3
Step-by-step explanation:
you look at the number without the x. and the minus three means it's negative. But if it's a plus three then it's positive
6. Donna adds 400 ml (milliliters) of water to 100 ml of coffee. What percentage of Donna's drink is coffee?
9514 1404 393
Answer:
20%
Step-by-step explanation:
100 mL of the drink is coffee
The total amount of drink is 100 mL +400 mL = 500 mL. Then the fraction that is coffee is ...
coffee/total = (100 mL)/(500 mL) = 1/5 = 1/5 × 100% = 20%
20% of Donna's drink is coffee.
circle o has diameter ab and chord ac. calculate the measure of cab id bc = 62⁰
Answer:
sin62 =0.883Step-by-step explanation:
0.883=1/0.836=1.133
The measure of ∠CAB is 31⁰.
Given that,
Circle O has diameter AB and chord AC.
We have to determine,
The measure of ∠CAB if BC is 62⁰.
According to the question,
The measurement of the required angle by using circle properties following all the steps given below.
The measure of the BC is 62 degrees.
If the circle has diameter AB and chord AC,
Then,
By the property of the circle,
[tex]\rm m\angle CAB = \dfrac{1}{2} \times BC \\[/tex]
Substitute the value of the BC in the equation,
[tex]m\angle CAB = \dfrac{1}{2} \times BC \\\\ m\angle CAB = \dfrac{1}{2} \times 62 \\\\ m\angle CAB = 31 \ degree \\\\[/tex]
Hence, The measure of ∠CAB is 31⁰.
For more details refer to the link given below.
https://brainly.com/question/1319201
if ABCD is a cyclic quadrilateral and A,B,C,D are its interior angles , then prove that
tanA/2+tanB/2=cotC/2+cotD/2
answer the question plz
dont spam or else i will report that
9514 1404 393
Explanation:
In a cyclic quadrilateral, opposite angles are supplementary. This means ...
A + C = 180° ⇒ A/2 +C/2 = 90° ⇒ C/2 = 90° -A/2
B + D = 180° ⇒ B/2 +D/2 = 90° ⇒ D/2 = 90° -B/2
It is a trig identity that ...
tan(α) = cot(90° -α)
so we have ...
tan(A/2) = cot(90° -A/2) = cot(C/2)
and
tan(B/2) = cot(90° -B/2) = cot(D/2)
Adding these two equations together gives the desired result:
tan(A/2) +tan(B/2) = cot(C/2) +cot(D/2)
need help asap plz!!!!!
Answer:
Step-by-step explanation:
In the simplest way, the domain of a function is basically all of the possible values of the input variable or x-axis in a graph. While the range of a function would be all of the real possible outputs that the function can create. In a graph this would be all of the possible values for the y-axis. For example, in the following function...
y = 4x + 3
The domain of this function would be any and all values for x, while the range of the function would be any and all values that the function can output for y.
A jacket costs £72 after
a 10% price cut. What
was the original price?
Answer:
£80
Step-by-step explanation:
80-(10%x80)=72. hope this helps
work out the size of angle x.
Answer:
actually I would have solved it but don't know the angle you're talking about
milligrams would you administer?
17. How many milligrams of Rocephin are left in a vial containing
Rocephin 2 grams after 750 milligrams are removed?
Answer:
1250 miligrams.
Step-by-step explanation:
Simple conversion, 2 grams = 2000 miligrams - 750 milligrams = 1250 miligrams.
es urgente
Resuelve cada ecuación. Si tu respuesta es correcta podrás completar con ella la información que esta abajo y aprender también sobre la naturaleza
X - ( x – 10 ) + 50 + (20 - x ) = – 50
Answer:
I hope I've helped /espero haberte ayudado
Khanacademy Unit:Sequences
What does g(2)=?
Answer:
g(2) = -42
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationAlgebra II
SequencesStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \left \{ {{g(1) = 50} \atop {g(n) = 8 - g(n - 1)}} \right.[/tex]
Step 2: Evaluate
Substitute in x [Function g(n)]: g(2) = 8 - g(2 - 1)(Parenthesis) Subtract: g(2) = 8 - g(1)Substitute in function value: g(2) = 8 - 50Subtract: g(2) = -422 times the difference between 49.5 and 37.5
Answer:
24
Step-by-step explanation:
diff is 12
12x2 is 24
PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of
research questions and types of data where one would expect the data to be skewed?
Answer:
Explained below
Step-by-step explanation:
A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.
B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.
Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.
Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.
C) Example of a research question is;
If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.
The math score for ten of Mrs. Moore's students are shown below. How many students made a score of more than 69 but less than 90?
Answer:
8
Step-by-step explanation:
first, 70-79 have 3 students
then 80-89 have 5 students
Tích các nghiệm của phương trình Log(x-1)²=2 là
Answer:
-99
Step-by-step explanation:
Log(x-1)²=2
Log(x-1)²=Log(100)
(x-1)²=100
x-1=10 and x-1=-10
x₁=11 and x₂=-9
x₁ × x₂ = 11 × (-9) = -99
Consider the frequency distribution below, which has single values as classes: Value Frequency 10 11 12 13 14 15 16 17 18 19 20 21 1 3 7 18 10 4 2 7 16 10 6 2 Construct a new frequency distribution for this data with 4 classes.
The original table (attached to this response) shows single values as classes.
To construct a new frequency distribution for this data with 4 classes, follow these steps:
i. Starting from the least value (which is 10) create groups each of 4 values. For example, the first group will contain 10, 11, 12 and 13. Therefore, we have a class of 10 - 13.
The second group will contain 14, 15, 16 and 17. Therefore, we have a class of 14 - 17
The third group will contain 18, 19, 20 and 21. Therefore, we have a class of 18 - 21
ii. Get the frequency of these classes, we add the frequencies of the members of the class.
For example,
Class 10 - 13 will have a frequency of (1 + 3 + 7 + 18) = 29
Class 14 - 17 will have a frequency of (10 + 4 + 2 + 7) = 23
Class 18 - 21 will have a frequency of (16 + 10 + 6 + 2) = 34
The new table has been attached to this response.
What is the volume of sphere with radius 13 ft?
Answer:
[tex]\displaystyle V = \frac{8788 \pi}{3} \ ft^3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Sphere Formula: [tex]\displaystyle V = \frac{4 \pi}{3}r^3[/tex]
r is radiusStep-by-step explanation:
Step 1: Define
Identify variables
r = 13 ft
Step 2: Find Volume
Substitute in variables [Volume of a Sphere Formula]: [tex]\displaystyle V = \frac{4 \pi}{3}(13 \ ft)^3[/tex]Evaluate exponents: [tex]\displaystyle V = \frac{4 \pi}{3}(2197 \ ft^3)[/tex]Multiply: [tex]\displaystyle V = \frac{8788 \pi}{3} \ ft^3[/tex]Answer:
The volume of this sphere is equal to [tex]2929\frac{1}{3} \pi ft^{3}[/tex]
Step-by-step explanation:
In order to solve this question, we need to know the formula for the volume of a sphere which is...
[tex]V = \frac{4}{3}\pi r^{3}[/tex] ("V" is the volume of the sphere, and "r" is the radius of the sphere)
Now we have to substitute the values that we already know into the formula, and we will get that...
[tex]V = \frac{4}{3}\pi r^{3}\\\\V = \frac{4}{3} \pi (13ft)^{3} \\\\V = \frac{4}{3} \pi (2,197ft^{3} )\\\\V = 2,929\frac{1}{3} \pi ft^{3}[/tex]
Therefore, the volume of this sphere is equal to [tex]2929\frac{1}{3} \pi ft^{3}[/tex]
Please help me in this! you get 30 points!
Answer:
y=3x-2
Step-by-step explanation:
You can verify it's not D because the y-intercept is at -2.
You can verify it's not A because that would mean the x-intercept is 2 despite it appearing to be closer to one.
You can verify it's not B because that would mean the x-intercept is 1.5
Please can you help me
Answer:
[tex]x = 24.75[/tex]
Step-by-step explanation:
Required
Find x
To find x, we have:
[tex]\angle PQR + \angle RPQ + \angle QRP = 180[/tex] -- angles in a triangle
Because [tex]\bar {PR}[/tex] is extended to S, then:
[tex]\angle QRS = \angle QRP[/tex]
So, we have:
[tex]2x + 6 + x - 7 + 5x -17 = 180[/tex]
Collect like terms
[tex]2x + x + 5x = 180 + 17 + 7-6[/tex]
[tex]8x = 198[/tex]
Divide by 8
[tex]x = 24.75[/tex]
y+4x=7 find the missing coordinates for a(-3,) and b (5,)
Answer:
-3 1
Step-by-step explanation:
Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.1 minutes and a standard deviation of 2.0 minutes. For a randomly received emergency call, find the following probabilities.
a. between 5 and 10 min
b. less than 5 min
c. more than 10 min
Answer:
a) 0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.
b) 0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.
c) 0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 8.1 minutes and a standard deviation of 2.0 minutes.
This means that [tex]\mu = 8.1, \sigma = 2[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5.
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.1}{2}[/tex]
[tex]Z = 0.95[/tex]
[tex]Z = 0.95[/tex] has a p-value of 0.8289
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.1}{2}[/tex]
[tex]Z = -1.55[/tex]
[tex]Z = -1.55[/tex] has a p-value of 0.0606
0.8289 - 0.0606 = 0.7683
0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which, found from item a, is of 0.0606
0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a, is of 0.8289
1 - 0.8289 = 0.1711
0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.
What the cubic inches…
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
Find the selling price of a $32 item after a 50% markup.
The selling price is $
Answer:
The new price is 48
Step-by-step explanation:
First find the markup
50% of 32
.5 * 32 = 16
Add the markup to the original price
16+32 = 48
The new price is 48
Answer:
$48
Step-by-step explanation:
32 * 0.50 = 16
32 + 16 = 48
Hope this is helpful
What is the line of symmetry for the parabola whose equation is y = -x2 + x + 3?
x = -1
x = -1/2
x = 1/2
Answer:
[tex]x = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = -x^2 + x + 3[/tex]
Required
The line of symmetry
This is calculated using:
[tex]x= -\frac{b}{2a}[/tex]
Where:
[tex]y = ax^2 + bx + c[/tex]
So, by comparison:
[tex]a = -1[/tex] [tex]b = 1[/tex] [tex]c = 3[/tex]
So, we have:
[tex]x = -\frac{1}{2 * -1}[/tex]
[tex]x = -\frac{1}{-2}[/tex]
[tex]x = \frac{1}{2}[/tex]
1/2 is correct, the formula to use is x= - b/2a :)
Write a polynomial that represents the area of the above football field.
Answer:
36x² + 24x + 300 ft²
Step-by-step explanation:
→ Area of rectangle = Length × Width
→ Area of rectangle = (12x + 8) ft × (3x + 15) ft
→ Area of rectangle = 12x(3x + 15) + 8(3x + 15) ft²
→ Area of rectangle = 36x² + 180 + 24x + 120 ft²
→ Area of rectangle = 36x² + 24x + 300 ft²
What is the distance between [(3 + 4i) + (2 - 3i)] and (9 - 2i)?
Answer:
5
Step-by-step explanation:
(3 + 4i) + (2 - 3i) = 3 + 4i + 2 - 3i = 5 + i
distance between (5 + i) and (9 - 2i) is the difference between them. and difference means subtraction.
(9 - 2i) - (5 + i) = 9 - 2i - 5 - i = 4 - 3i
and since we are looking for a distance, we are looking for the absolute value of that subtraction.
after all, we could have done the subtraction also in the other direction
(5 + i) - (9 - 2i) = -4 + 3i
and this must be the same distance.
|(-4 + 3i)| = |(4 - 3i)|
and that is done by calculating the distance of any of these 2 points from (0,0) on the coordinate grid of complex numbers.
|(a +bi)| = sqrt(a² + b²)
in our case here
distance = sqrt(4² + (-3)²) = sqrt(16 + 9) = sqrt(25) = 5
as you can easily see, this is (as expected) the same for the result of the subtraction in the other direction :
sqrt((-4)² + 3²) = sqrt(16+9) = sqrt(25) = 5
The table shows the displacement-time data for a ship relative to a shore.
t(hours) 2.95 3.15 3.75 3.95 3.99 4.00
s(0 (miles) 14.95 17.61 27.23 31.01 31.80 32.00
Estimate the instantaneous velocity of the ship at t = 4 hours.
A.
20.00 mi./h.
B.
20.15 mi./h.
C.
20.25 mi./h.
OD.
20.50 mi./h.
Answer:
Step-by-step explanation:
