Answer:
a. 4
Step-by-step explanation:
-1(-4) = 4
Answer:
A 4
Step-by-step explanation:
opposite of –4 = 4
Halla x si:
a) 4√5 b) √5 c) 4√3 d) 4 e) 4√2
Answer:
Option A. 4√5
Step-by-step explanation:
To obtain the value of x, we must first obtain the value of y as shown in the attached photo.
The value of y can be obtained by using the pythagoras theory as illustrated below:
In this case y is the longest side i.e the Hypothenus.
y² = 4² + [4√3]²
y² = 4² + [4² × (√3)²]
y² = 4² + [4² × 3]
y² = 16 + [16 × 3]
y² = 16 + 48
y² = 64
Take the square root of both side
y = √64
y = 8
Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.
Note: x is the longest side i.e the Hypothenus in this case.
x² = 4² + 8²
x² = 16 + 64
x² = 80
Take the square root of both side
x = √80
x = √(16 × 5)
x = √16 × √5
x = 4√5
Therefore, the value of x is 4√5.
how many pounds are in 2 tons 1,760 ounces
Answer:
4110
Step-by-step explanation:
One ton is equal to 2000 pounds and one ounce is equal to 0.0625 pounds.
2 tons*2000 lbs per ton = 4000 lbs
1760 ounces*0.0625 lebs per ounce = 110 lbs
4000+110=4110 lbs
The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possible values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Answer:
-3
Step-by-step explanation:
The length of a segment is
sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)
sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)
sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)
Combine like terms
sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)
Square each side
( a-3)^2 + (2a -4) ^2) = 4 *(10)
FOIL the left side
a^2 -6a +9 + 4a^2 -16a +16 = 40
Combine like terms
5a^2 -22a +25 = 40
Subtract 40 from each side
5a^2 -22a -15 =0
Factor
(a - 5) (5 a + 3) = 0
Using the zero product property
a-5 =0 5a +3 = 0
a = 5 5a = -3
a=5 a = -3/5
The product of the terms is
5 * -3/5 = -3
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)
This sequence converges to 0.
Proof: Recall that
[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]
is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].
Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then
[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]
[tex]\implies\dfrac1n<\varepsilon^2[/tex]
[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]
as required.
How would you find the coefficient of the third term in (x+5)^7?
Answer:
The answer is option B
Step-by-step explanation:
To find the coefficient of the third term in
[tex](x + 5)^{7} [/tex]
Rewrite the expansion in the form
[tex](a + x)^{n} [/tex]
where n is the index
So we have
[tex] ({5 + x})^{7} [/tex]
After that we use the formula
[tex]nCr( {a}^{n - r} ) {x}^{r} [/tex]
where r is the term we are looking for
For the third term we are looking for the term containing x²
that's
r + 1 = 3
r = 2
So to find the coefficient of the third term
We have
[tex]7C2[/tex]
Hope this helps you
first of all, the notation is wrong it should be [tex] {}^nC_r \text{ and more usual notation is } {n \choose k} [/tex]
second, the
[tex](r+1)^{\text{th}} \text{ term } T_{r+1} \text{ in the expansion of } (x+a)^n \text{ is } {n \choose r}x^{(n-r)}a^r[/tex]
here [tex] a=5 \text{ and } n=7 \text{ and for } 3^{\text{rd}} \text{ term } T_3, \quad r+1=3 \implies r=2 [/tex]
so the coefficient of third term is, [tex]{7 \choose 2}={7\choose 5}[/tex]
an important property of binomial coefficient you should know:
[tex] {n \choose k}={n \choose {n-k}}[/tex]
and if you interchange [tex] x \text{ and } a[/tex]
only the "order" will get reversed. i.e. the series will start from back.
another thing, the [tex] k^{\text{th}} \text{ term from beginning, is the } (n-k+2)^{\text{th}} \text{ term from behind}[/tex]
which function represents the area of the triangle h(x)=1/2f(x)g(x)
Answer:
h=1/2fg
Step-by-step explanation:
Solve for x, h=1/2fg
It is true for all x; h=1/2fg
h=1/2fg
Both sides are equal
It is true for all x; h=1/2fg
How do i do this equation
-3(-2y-4)-5y-2=
Answer:
Step-by-step explanation: distribute -3 to the parenthesis (-2y-4) to eliminate the parenthesis. you’ll be left with 6y +12 -5y-2. From there you combine like terms. do 6y-5y= 1y or just y and 12-2 = 10. your answer would be 10
The upper-left coordinates on a rectangle are (-1,4), and the upper-right coordinates are (3,4). The rectangle
has a perimeter of 24 units.
Draw the rectangle on the coordinate plane below.
Answer:
Step-by-step explanation:
Note that the perimeter of a rectangle P = 2(Length + Breadth)
The distance between the upper-left coordinates on a rectangle and the upper-right coordinates is the breadth of the rectangle. To get the breadth of the rectangle, we will use tgw formula for calculating the distance between two points as shown.
D = √(y2-y1)²+(x2-x1)²
Given the coordinates (-1,4) and (3,4), the distance between the coordinates where x1 = -1, y1 = 4, x2 = 3 and y2 = 4 will be expressed as.
B = √(4-4)²+(3-(-1))²
B = √0+4²
B = √16
B = 4
Hence the breadth of the rectangle is 4 units.
Substituting the breadth into the formula for calculating the perimeter will give;
P = 2(L+B)
24 = 2(L+4)
L+4 = 24/2
L+4 =12
L = 12-4
L = 8
Hence the length of the rectangle is 8 units.
The diagram of the rectangle on a coordinate is as given in the attachment below.
(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems? (3 Marks) ii. Is a heavy drinker (2 Marks) iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem? (2 Marks) iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker? (2 Marks) v. If a person is found to be a non –drinker, what is the probability that this person has liver problems. (2 Marks)
Answer:
i. Has a liver problems?
= 0.08
ii. Is a heavy drinker ?
= 0.066
iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?
= 0.303
iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?
= 0.25
v. If a person is found to be a non –drinker, what is the probability that this person has liver problems?
= 0.104
Step-by-step explanation:
We have 2 Events in this question
Event A: People with liver problems
Event B : People without liver problems
Event A: People with liver problems
Let us represent people with liver problems as = (L)
a)8% have liver problems. = P(L)
Under liver problems we have:
b) 25% are heavy drinkers = P( L & H)
c) 35% are social drinkers = P( L & S)
d) 40% are non-drinkers. = P( L & N)
Event B( no liver problem)
Let us represent no liver problem as NL
We are not given in the question but Probability of having no liver problem = 100 - Probability of having liver problem
= 100 - 8% = 92 %
P(NL ) = 92%
From the question, For people without liver problems, we have:
a) 5% are heavy drinkers = P(NL & H)
b) 65% are social drinkers = P( NL & S)
c) 30% do not drink at all = P( NL & N)
An adult is chosen at random, what is the probability that this person
i. Has a liver problems?
P(L) = 8% or 0.08
ii. Is a heavy drinker ?
From the question, we have:
Probability of people that have liver problems and are heavy drinkers P(L & H) = 25% = 0.25
Probability of people that have do not have liver problems and are heavy drinkers P(NL & H) = 5% = 0.05
Probability ( Heavy drinker) =
P(L) × P(L & H) + P(NL) × P(NL & H)
= 0.25 × 0.08 + 0.05 × 0.92
= 0.066
iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?
Probability (Heavy drinker and has liver problem) = [P(L) × P(L & H)] ÷ [P(L) × P(L & H)] + [P(NL) × P(NL & H) ]
= [0.25 × 0.08] ÷ [0.25 × 0.08] + [0.05 × 0.92]
= 0.303030303
Approximately = 0.303
iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?
P(L & H) = 25% = 0.25
v. If a person is found to be a non –drinker, what is the probability that this person has liver problems.?
People with liver problems are non-drinkers. = P( L & N) = 40% = 0.4
People without liver problems and do not drink at all = P( NL & N) = 30% = 0.3
Probability (non drinker and has liver problem) = [P( L & N) × P(L & H)] ÷ [P( L & N) × P(L & H)] + [ P( NL & N) × P(NL & H) ]
= [0.4× 0.08] ÷ [0.4 × 0.08] + [0.3 × 0.92]
= 0.1038961039
Approximately ≈ 0.104
This person did something wrong and I do not know what it is :( Please help this is for points!
Answer:
0.4 cm
Step-by-step explanation:
The magnifying glass basically zooms into smaller objects. If the insect appears to be 2cm, then it is actually smaller than this. It cannot be 10 cm.
If the scale factor is 5, then this means that the insect is zoomed in 5 times through the magnifying glass. Use the following ratio:
[tex]\frac{2}{5}[/tex]
This fraction can also be seen as division, so:
[tex]2[/tex]÷[tex]5=0.4[/tex]
The insect is actually 0.4 cm long.
(or 4 millimeters)
:Done
Help me solve this!!!
Answer:
m∠AOD = 140°
Step-by-step explanation:
In the diagram attached,
OA⊥OC and OB⊥OD
m∠AOD = 3.5(m∠BOC)
Since, m∠BOD = 90° [Given: OA⊥OC]
m∠BOC + m∠COD = 90° ---------(1)
Similarly, m∠AOC = 90° [Given : OA⊥OC]
m∠AOB + m∠BOC = 90° --------(2)
Equation (1) - Equation(2)
(m∠BOC + m∠COD) - (m∠AOB + m∠BOC) = 90°- 90°
m∠COD = m∠AOB
m∠AOB + m∠BOC + m∠COD = m∠AOD --------(3)
m∠AOB + m∠BOC + m∠AOB = 3.5(m∠BOC) [Since m∠COD = m∠AOB]
2m∠AOB = 3.5(m∠BOC) - m∠BOC
2m∠AOB = 2.5(m∠BOC)
m∠AOB = 1.25(m∠BOC)
From equation (2),
m∠AOB + m∠BOC = 90°
1.25(m∠BOC) + m∠BOC = 90°
2.25(m∠BOC) = 90°
m∠BOC = 40°
From equation (1),
m∠BOC + m∠COD = 90°
m∠COD + 40° = 90°
m∠COD = 50°
Now by putting these values in equation (3)
m∠AOB + m∠BOC + m∠COD = m∠AOD
m∠COD + m∠BOC + m∠COD = m∠AOD
50° + 40° + 50°= m∠AOD
m∠AOD = 140°
If your starting salary is $40000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn one the first 16 years that you work
Answer:
Total amount in dollars= $64614.00
Step-by-step explanation:
Initial starting salary is $40000.
Rate of increase is 3%
Number of years is 16 years
The salary is compounded yearly.
Amount A after 16 years is given as
A= p (1+r/n)^ (nt)
A=40000(1+0.03/16)^(16*16)
A= 40000(1.001875)^(256)
A=40000(1.61534824)
A= 64613.92959
Total amount in dollars= $64614.00
Answer: the answer is $806275
Step-by-step explanation:
A p e x
Please helppp meee I don’t know the answer
Answer:
First use the protractor then round the number to the nearest 10
Answer:
Round to the nearest tenth
Step-by-step explanation:
what must be added to 2/3 of 5.25 to make it 7.00
Answer:
3.5
Step-by-step explanation:
Well you have to find first 2/3 of 5.25. This means multiplication, which is 3.5. so to find how much to add to this to get 7, we have to subtract 3.5 from 7. 7-3.5=3.5. so we must add 3.5 to get 7. Hope this helps :D
Researchers recorded that a certain bacteria population declined from 120,000 to 200 in 36 hours. At this rate of decay, how many bacteria will there be in 31 hours? Round to the nearest whole number.
Answer: There will 486 bacteria in 31 hours.
Step-by-step explanation:
The population decay in bacteria is exponential.
Exponential function : [tex]y=Ab^x[/tex], where A = initial population, b multiplication decay factor, t= time:
As per given:
Initial population: [tex]A=120,000[/tex]
After 36 hours, population = [tex]120000(b^{36})=200[/tex]
Divide both sides by 120,000 we get
[tex]b^{36}= 0.00167[/tex]
Taking natural log on both sides , we get
[tex]36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372[/tex]
At x= 31,
[tex]y=120000(0.8372)^{31}=120000\times0.00405234\approx486[/tex]
Hence, there will 486 bacteria in 31 hours.
This person made a mistake. what is the mistake and what is the correct answer?!!
Answer: 44
Step-by-step explanation:
If tanA = 3
evaluate
CosA + sinA\
casA - SinA
Answer:
Hi, there!!!
I hope you mean to evaluate cosA+ sonA /cosA - sinA.
so, i hope the answer in pictures will help you.
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
Let pp represent the percentage of all male students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
Enter your answer as a tri-linear inequality using decimals (not percents).
< p
Answer:
Using Anova for a tri linear probability at ∝= 0.005
Step-by-step explanation:
Here simple probability cannot be used because we want to enter your answer as a tri-linear inequality using decimals (not percents).
So we can use ANOVA
Null hypothesis
H0: µA = µB=µC
all the means are equal
Alternative hypothesis
H1: Not all means are equal.
The significance level is set at α-0.005
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom .
The computations are as follows
XA (XA)² XB (XB)² XC (XC)² Total ∑X²
Male 19(361) 4(16) 12(144) 35 521
Female 3(9) 13 (169) 5 (25) 21 203
TotalTj 22 17 17 56 724
T²j (22)(22)
484 289 289 1062
∑X² 370 285 169
Correction Factor = CF = Tj²/n = (56)²/6= 522.67
Total SS ∑∑X²- C. F = 724- 522.67= 201.33
Between SS ∑T²j/r - C.F = 1062/ 2 - 522.877 =8.33
Within SS = Total SS - Between SS
=201.33- 8.33= 193
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 1 8.33 8.33 8.33/ 48.25= 0.1726
Within
Samples 4 193 48.25
The critical region is F >F ₀.₀₀₅ (1,4) = 31.3328
Calculated value of F = 0.1726
Since it is smaller than 5 % reject H0.
However the decimal probability will be
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
There are total 22 people who get an A but only 19 males who get an A
So the probability that a male gets an A is = 19/22= 0.8636
A coin is tossed 4 times. Let E1 be the event "the first toss shows heads" and E2 the event "the second toss shows heads" and so on. That is, Ei is the event that the "i"th toss shows up heads.
A. Are the events e e and f f independent?
B. Find the probability of showing heads on both toss.
Answer:
The events are independent.
The probability of showing heads on both toss is equal to 1/2
Step-by-step explanation:
The sample space for this experiment consists of 2⁴= 16 sample points, as each toss can result in two outcomes we assume that the events are equally likely.
Two events are independent in the sample space if the probability of one event occurs, is not affected by whether the other event has or has not occurred.
In general the k events are defined to be mutually independent if and only if the probability of the intersection of any 2,3,--------, k equals the product of their respective probabilities.
P (A∩B) = P(A). P(B)
P (A∩B) = 1/2. 1/2= 1/4
Head Tail
P(E1)= 1/2 ---------- Coin 1 H,H T,H
1/4 1/4
P(E2)= 1/2 --------------- Coin 2 H, H H,T
1/4 1/4
So the events are independent.
The probability of showing heads on both toss is equal to 1/2
The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.
Or in other words ( 1/4* 1/4) = 2/4 = 1/2
BRAINLIEST ANSWER GIVEN, WHY CAN'T ANYONE HELP ME?! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
15x - y = - 126
or y = 15x + 126
Step-by-step explanation:
will make it simple and short
to find the equation... we need to find slope first.
y2 - y1 -9 - 6
slope = m = --------- = ----------- = 15
x2 - x1 -9 - (-8)
so we know that the equation of the line using point (-8,6) and slope 15 y - 6 = 15( x + 8)
y - 6 = 15x + 120
Writing the equation in the form Ax + By = C
15x - y = -120-6
therefore.... 15x - y = - 126 or simplify it as or y = 15x + 126
Hope this helps
Isreal spends the most time on social media with a total of 11.1.peru has a total of 8.3 how much more time does israel spend on social media
Answer:
2.8
Step-by-step explanation:
11.1-8.3=2.8
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Describe each of the following values as (A) a discrete random variable, (B) a continuous random variable, or (C) not a random variable:
1. Exact weight of quarters now in circulation in the United States
2. Shoe sizes of humans
3. Political party affiliations of adults in the United States
A. 1.C
2.A
3.В
B. 1.B
2.A
3.С
C. 1.A
2.C
3.В
D. 1.A
2.В
3.С
Answer:
(1) B
(2) A
(3) C
Step-by-step explanation:
A random variable is a variable that denotes a set of all the possible outcomes of a random experiment. It is denotes by a single capital letter such as X or Y.
There are two types of random variables.
Discrete random variable: These type of random variable takes finite number of values, such as 0, 1, 2, 3, 4, ... For example, number of girl child in a neighborhood.Continuous random variable: These type of random variables takes infinite number of possible values. For example, the height, weight.(1)
Exact weight of quarters now in circulation in the United States.
The variable weight is a continuous variable.
Thus, the exact weight of quarters now in circulation in the United States is a continuous random variable.
(2)
Shoe sizes of humans.
The shoe size of a person are discrete and finite values.
Thus, the shoe sizes of humans are discrete random variables.
(3)
Political party affiliations of adults in the United States.
This variable is not a quantitative variable.
It is a qualitative variable.
Thus, the political party affiliations of adults in the United States is no random variable.
A tin of tennis balls costs $6.99, and each tin contains 4
tennis balls.
If the tennis balls were sold individually, then
approximately how much would one tennis ball cost?
$
Answer:
About $1.75 per tennis balls
Step-by-step explanation:
A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.
We need to find the unit price, or price per ball.
Divide the cost by the number of tennis balls.
cost / tennis balls
cost = $6.99
tennis balls = 4 tennis balls
$6.99 / 4 tennis balls
Divide 6.99 by 4.
$1.7475 / 1 tennis ball
Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.
$1.75 / 1 tennis ball
It would cost approximately $1.75 for one tennis ball.
9. Find the mean of the following data :
Х
8
10
12
20
16
F
2
3
7
2
5
Answer:
[tex] \boxed{13.15}[/tex]Step-by-step explanation:
( See the attached picture )
Now,
Mean = [tex] \mathsf{\frac{Σfx}{n} }[/tex]
[tex] \mathsf{ = \frac{250}{19} }[/tex]
[tex] \mathsf{ = 13.15}[/tex]
------------------------------------------------------------------------
In the case of repeated data , follow the steps given below to calculate the mean :
Draw a table with 3 columnsWrite down the items ( x ) in ascending or descending order in the first column and the corresponding frequencies in the second column.Find the product of each item and it's frequency ( fx ) and write in the third column.Find the total of f column and fx column.Divide the sum of fx by the sum of f ( total number of items ) , the quotient is the required mean.Hope I helped!
Best regards!
Need Help
*Please Show Work*
Hi there! :)
Answer:
y = -2x + 3
Step-by-step explanation:
We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in values from the table:
[tex]m = \frac{5 - 7}{-1 - (-2)}[/tex]
Simplify:
m = -2 (rate of change)
Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:
7 = -2(-2) + b
7 = 4 + b
7 -4 = b
b = 3
Rewrite:
y = -2x + 3 is the equation for the linear function.
2/5×1 3/12? plz help meh
Answer:
[tex]\boxed{\frac{1}{2} }[/tex]
Step-by-step explanation:
Hey there!
Well given,
[tex]\frac{2}{5} * 1 \frac{3}{12}[/tex]
We need to make 1 3/12 improper,
1*12 = 12
12 + 3 = 15
[tex]\frac{2}{5} * \frac{15}{12}[/tex]
2*15 = 30
5*12 = 60
[tex]\frac{30}{60}[/tex]
Simplified
[tex]\frac{1}{2}[/tex]
Hope this helps :)
The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?
Answer:
255.8
Step-by-step explanation:
first
1/6*1535
=255.8
[tex]f(x) = {x}^{2} + 4x - 5[/tex] ; >-2
Find [tex] \frac{d {f}^{ - 1} }{dx} [/tex] at x=16
Please show solving
The inverse function theorem says
[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(f^{-1}(16))}[/tex]
We have
[tex]f(x)=x^2+4x-5[/tex]
defined on [tex]x>-2[/tex], for which we get
[tex]f^{-1}(x)=-2+\sqrt{x+9}[/tex]
and
[tex]f^{-1}(16)=-2+\sqrt{16+9}=3[/tex]
The derivative of [tex]f(x)[/tex] is
[tex]f'(x)=2x+4[/tex]
So we end up with
[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(3)}=\dfrac1{10}[/tex]
A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?
Answer:
1. elements it contains = (1,3)
2. elements it contains = 35
3. elements it contains = 8
4. elements it contains = 17
Step-by-step explanation:
A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?
NB. Attached is the solution to the problems stated above
a student ran out of time on a multiple choice exam and randomly guess the answers for two problems each problem have four answer choices ABCD and only one correct answer what is the probability that he answered neither of the problems correctly
Answer:
The probability that he answered neither of the problems correctly is 0.0625.
Step-by-step explanation:
We are given that a student ran out of time on a multiple-choice exam and randomly guess the answers for two problems each problem have four answer choices ABCD and only one correct answer.
Let X = Number of problems correctly answered by a student.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r}\times p^{r}\times (1-p)^{n-r};x=0,1,2,3,....[/tex]
where, n = number of trials (samples) taken = 2 problems
r = number of success = neither of the problems are correct
p = probability of success which in our question is probability that
a student answer correctly, i.e; p = [tex]\frac{1}{4}[/tex] = 0.75.
So, X ~ Binom(n = 2, p = 0.75)
Now, the probability that he answered neither of the problems correctly is given by = P(X = 0)
P(X = 0) = [tex]\binom{2}{0}\times 0.75^{0}\times (1-0.75)^{2-0}[/tex]
= [tex]1 \times 1\times 0.25^{2}[/tex]
= 0.0625
