Answer:
P(red and blue) = 1/12
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of independent events:
If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each event happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
P (red and blue).
Probability of choosing a red marble, then a blue marble. The marbles are replaced, so the trials are independent.
Probability of a red marble:
3 out of 3 + 5 + 4 = 12. So
[tex]P(A) = \frac{3}{12} = \frac{1}{4}[/tex]
Probability of a blue marble:
4 out of 12, so:
[tex]P(B) = \frac{4}{12} = \frac{1}{3}[/tex]
P (red and blue).
[tex]P(A \cap B) = P(A)P(B) = \frac{1}{4} \times \frac{1}{3} = \frac{1}{4*3} = \frac{1}{12}[/tex]
So
P(red and blue) = 1/12
PLEASE HELP! Don’t know how to solve this or where to start. I tried multiplying and dividing but still got the wrong answer. How do I solve this problem?
Answer:
306 square meters.
Step-by-step explanation:
Divide the shape into 2 rectangles.
Lets do the one that is sticking to the top first.
The area is 6 * 15, which is 90.
Lets do the second rectangle. The area is:
27 * 8, which is 216.
Add them all up (90 + 216), which is 306.
Answer:
306m²
Step-by-step explanation:
Split the shape into two rectangles with the accureate lengths
The top-most of the two rectangles with length 6m and width 15m:
6 x 15 = 90 m² (area of rectangle A)
The bottom rectangle:
27(full length) x 8m(full width) = 216m²
Add the two areas together for the full shape
216 + 90 = 306m²
A rectangular field 50 meters in width and 120 meters in length is divided into two fields by a diagonal line. What is the length of fence (in meters) required to enclosed one of these fields?
A-130
B-170
C-180
D-200
E-300
Answer:
E. 300
Step-by-step explanation:
A rectangle split in half diagonally yields 2 right triangles.
((For this problem, you are probably supposed to use the pythagorean theorem to find the diagonal length, and then calculate perimeter (length of fence around triangular field). In other words:
(sqrt( (50m)^2 + (120m)^2 )) + 50m + 120m)
))
By definition, the hypotenuse (diagonal) is the longest side.
This means that it must be longer than 120m.
If you add the 2 sides (50m + 120m), you get 170m.
Since the third side has to be longer than 120m, the answer _must_ be over 290m (170m + 120m).
300m is the only answer that fits.
please help please help
Answer:
1. number line or 3
2. D
3. E and K
4. B
5. A
Brainliest please~
. Which equation represents y = −x2 + 4x − 1 in vertex form?
Answer:
Rewrite in vertex form and use this form to find the vertex
(
h
,
k
)
.
(
2
,
3
)
Step-by-step explanation:
True or False: The points T, Z, W and U coplanar in the following image
Answer:
False
Step-by-step explanation:
Points T & W are coplanar. Point Z is on both planes, so it depends on how you see it. HOWEVER, Point U is on another plane (plane Q to be exact), so points T, Z, W, and U are NOT coplanar.
Hope it helps (●'◡'●)
Which of the following is the result of the equation below after completing the square and factoring? x^2-4x+2=10
A. (x-2)^2=14
B. (x-2)^2=12
C. (x+2)^2=14
D. (x+2)^2=8
9514 1404 393
Answer:
B. (x-2)^2=12
Step-by-step explanation:
The constant that completes the square is the square of half the coefficient of the x-term. That value is (-4/2)^2 = 4.
There is already a constant of 2 on the left side of the equal sign, so we need to add 2 to both sides to bring that constant value up to 4.
x^2 -4x +2 = 10 . . . . . . . given
x^2 -4x +2 +2 = 10 +2 . . . . complete the square (add 2 to both sides)
(x -2)^2 = 12 . . . . . . . . . write as a square
What is the confidence interval estimate of the population mean percentage change in the price per share of stock during the first quarter? Do not round intermediate calculations. Enter negative values as negative numbers, if any.
Answer:
(-0.1059 ; - 0.0337)
Step-by-step explanation:
The data table is attached in the picture below:
These is a matched pair design ; which requires taking the difference of the two values for each sample :
The mean and standard deviation of the difference will be used to construct the confidence interval :
The mean of difference, dbar = Σx/n = - 0.0698
The standard deviation of difference, Sd ;
Sd = [√Σ(d - dbar)²/(n-1)] = 0.1054
n = sample size = 25
The confidence interval :
dbar ± [TCritical * Sd/√n]
Tcritical at 90% ; df = n -1 = 25 -1
Tcritical(90% , 24) = 1.1711
C.I = - 0.0698 ± (1.711 * 0.1054/√25)
C.I = - 0.0698 ± 0.0361
C.I = (-0.1059 ; - 0.0337)
A jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint. Each time you draw out an item, you record the outcome and put the item back in the jar before making another draw. What is the probability that you get exactly the following sequence: candy—mintmcandy, in that order?
(a) 0.0300.
(b) 0.0530.
(c) 0.1607.
(d) 1.2143.
Answer:
The correct answer is B.
Step-by-step explanation:
Since a jar contains 4 pieces of gum, 7 pieces of candy, and 3 pieces of mint, and each time you draw out an item, you record the outcome and put the item back in the jar before making another draw, to determine what is the probability that you get exactly the sequence candy-mint-candy, in that order, the following calculation should be performed:
4 + 7 + 3 = 14
7/14 x 3/14 x 7/14 = X
0.5 x 0.2142 x 0.5 = X
0.053 = X
Therefore, the probability that the chosen sequence will be obtained is 0.0530, or 5.3%.
For what value of the variable : is the value of 9-y twice as much as the value of y?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]y = 3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{"The value of 9-y twice as much as the value of y" can be written as:}}\\\\9-y = 2y[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'y'...}}\\\\9-y=2y\\------------\\\rightarrow 9 -y + y = 2y + y\\\\\rightarrow 9 = 3y\\\\\rightarrow \frac{9=3y}{3}\\\\\rightarrow 3 = y\\\\\rightarrow \boxed{y = 3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
You are given the following information about x and y.
x y Independent Dependent Variable Variable 15 5 12 7 10 9 7 11
The least squares estimate of b 0 equals ______.
a. 16.41176
b. â1.3
c. 21.4
d. â7.647
Answer:
[tex]b_0 = 16.471[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccc}x & {15} & {12} & {10} & {7} \ \\ y & {5} & {7} & {9} & {11} \ \end{array}[/tex]
Required
The least square estimate [tex]b_0[/tex]
Calculate the mean of x
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{15+12+10+7}{4} =\frac{44}{4} = 11[/tex]
Calculate the mean of y
[tex]\bar y = \frac{\sum y}{n}[/tex]
[tex]\bar y = \frac{5+7+9+11}{4} =\frac{32}{4} = 8[/tex]
Calculate [tex]\sum(x - \bar x) * (y - \bar y)[/tex]
[tex]\sum(x - \bar x) = (15 - 11) * (5 - 8)+ (12 - 11) * (7 - 8) + (10 - 11) * (9 - 8)+ (7 - 11) * (11 - 8)[/tex]
[tex]\sum(x - \bar x) = -26[/tex]
Calculate [tex]\sum(x - \bar x)^2[/tex]
[tex]\sum(x - \bar x)^2 = (15 - 11)^2 + (12 - 11)^2 + (10 - 11)^2 + (7 - 11)^2[/tex]
[tex]\sum(x - \bar x)^2 = 34[/tex]
So:
[tex]b = \frac{\sum(x - \bar x) * (y - \bar y)}{\sum(x - \bar x)^2}[/tex]
[tex]b = \frac{-26}{34}[/tex]
[tex]b_0 = y - bx[/tex]
[tex]b_0 = 5 - \frac{-26}{34}*15[/tex]
[tex]b_0 = 5 + \frac{26*15}{34}[/tex]
[tex]b_0 = 5 + \frac{390}{34}[/tex]
Take LCM
[tex]b_0 = \frac{34*5+ 390}{34}[/tex]
[tex]b_0 = \frac{560}{34}[/tex]
[tex]b_0 = 16.471[/tex]
g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19
Answer:
[tex]241^{257}\ mod\ 12 =1[/tex]
[tex]7 * 20 = 140[/tex]
[tex]\frac{1}{700}[/tex]
Step-by-step explanation:
Solving (a): 241^257 mod 12
To do this, we simply calculate [tex]241\ mod\ 12[/tex]
Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]
The highest number less than or equal to 241 that is divisible by 12 is 240; So:
[tex]241\ mod\ 12 = 241- 240[/tex]
[tex]241\ mod\ 12 =1[/tex]
Hence:
[tex]241^{257}\ mod\ 12 =1[/tex]
Solving (b): 7 * 20
[tex]7 * 20 = 140[/tex]
Solving (c): Multiplicative inverse of 7 in 719
The position of 7 in 719 is 700
So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number
Suppose 58% of the population has a retirement account. If a random sample of size 570 is selected, what is the probability that the proportion of persons with a retirement account will be less than 57%
Answer:
The probability that the proportion of persons with a retirement account will be less than 57%=31.561%
Step-by-step explanation:
We are given that
n=570
p=58%=0.58
We have to find the probability that the proportion of persons with a retirement account will be less than 57%.
q=1-p=1-0.58=0.42
By takin normal approximation to binomial then sampling distribution of sample proportion follow normal distribution.
Therefore,[tex]\hat{p}\sim N(\mu,\sigma^2)[/tex]
[tex]\mu_{\hat{p}}=p=0.58[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{0.58\times 0.42}{570}}[/tex]
[tex]\sigma_{\hat{p}}=0.02067[/tex]
Now,
[tex]P(\hat{p}<0.57)=P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.57-0.58}{0.02067})[/tex]
[tex]P(\hat{p}<0.57)=P(Z<-0.483)[/tex]
[tex]P(\hat{p}<0.57)=0.31561\times 100[/tex]
[tex]P(\hat{p}<0.57)[/tex]=31.561%
Hence, the probability that the proportion of persons with a retirement account will be less than 57%=31.561%
95, 86, 78, 71, 65, 60 _____
Answer:
hello there here is your answer
51 is your next term.
Step-by-step explanation:
you are subtracting 9 from each number
95-9= 86
86-9=78
78-9=65
65-9=60
60-9=51
so on and so on
Hope this help
have a good day
bye
Step-by-step explanation:
[tex]here \: is \: your \: solution: - \\ \\ given \: number \: = 95.86.78.71.65.60 \\ \\ = > 95 - 9 = 86 \\ \\ = > 86 - 8 = 78 \\ \\ = > 78 - 7 = 71 \\ \\ = > 71 - 6 = 65 \\ \\ = > 65 - 5 = 60 \\ \\ \: now \: follow \: the \: sequence \: \\ \\ subtract \: 4 \: from \: 60 \\ \\ = > 60 - 4 = 56 \\ \\ = > \: \: 56 \: \:( ANSWER✓✓✓)[/tex]
simple equation:
6m=12
Step-by-step explanation:
Divide both sides of the equation by the same term6m/6 =12/6
Cancel terms that are in both the numerator and denominatorDivide the numbersm=2
Answer:
m=2
Step-by-step explanation:
Divide 6 on both sides
6m / 6 = 12/6
m= 12/6 = 2
So, m=2
Verification:
LHS = 6m m=2
6 * 2 = 12
RHS = 12
Both the LHS and RHS are same, so our answer is correct
An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?
A. 8
B. 9
C. 10
D.11
Answer:
option B
Step-by-step explanation:
Sum of interior angles of a polygon with n sides:
[tex]= (n - 2 )\times 180[/tex]
[tex]Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180[/tex]
[tex]Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ[/tex]
[tex][ \ because \ straight \ line \ angle = 180^\circ \ ][/tex]
That is ,
[tex]Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9[/tex]
OR
Sum of exterior angles of a regular polygon = 360
Given 1 exterior angle of the regular polygon is 40
Therefore ,
[tex]n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9[/tex]
Answer:
9
Step-by-step explanation:
Explain how to divide a decimal by a decimal
Answer:
To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.
Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
Then divide the new dividend by the new divisor
Step-by-step explanation:
see in the example
We know that 1 1 − r = [infinity] n = 0 rn has interval of convergence (−1, 1). This means the series converges for |r| < 1. Therefore, the series f(x) = 1 2 + x = [infinity] n = 0 (−1)n xn 2n + 1 will converge when − x 2 < 1. Thus, what is the interval of convergence for f(x)? (Enter your answer using interval notation.)
Answer: hello your question is poorly written attached below is the complete question
answer :
I = ( -2, 2 )
Step-by-step explanation:
Determine the internal convergence for f(x)
given that f(x) converges at |-x/2 | < 1
I ( internal convergence for f(x) ) = ( -2, 2 )
Attached below is the detailed solution
A traveling salesman figures it costs 19 cents for every mile he drives his car. How much does it cost him (in dollars) a week to drive his car if he travels 340 miles a week?
Answer:
$64.60
Step-by-step explanation:
$0.19 x 340 = $64.6, which simplifies to $64.60.
Answer:
$64.60
Step-by-step explanation:
Just multiply 340 by 19, then convert into American Currency.
Please I need help!!!!!!!!
Answer:
10 is the correct answer
Answer:
Go with the third option 10!
i hope this helped!
1. Using the factorisation method, simplify the following √32
Answer:
[tex]4 \sqrt{2} [/tex]
[tex] \sqrt{32} = \sqrt{16 \times 2} = 4 \sqrt{2} [/tex]
Find the value of x in each case:
Answer:
36
Step-by-step explanation:
2x is an exterior angle
Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).
Put symbolically
<LEG = <EGF + <EFG
<EFG = 180 - 4x In this case you need to find the supplemtnt
<LEG = x + 180 - 4x
2x = 180 - 3x Add 3x to both sides
5x = 180 Divide by 5
x = 36
The volume V of a rectangular solid can be expressed as a formula in terms of the length L, width w, and height h. Solve this formula for w.
WE
(Simplify your answer.)
Please help :)
Answer:
[tex] W = \frac {V}{LH} [/tex]
Step-by-step explanation:
Let the length of the rectangle be LLet the width of the rectangle be WLet the height of the rectangle be HMathematically, the volume of a rectangular solid is given by the formula;
V = L * W * H
V = LWH
Making W the subject of formula, we have;
[tex] W = \frac {V}{LH} [/tex]
According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0746 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 318 independent returns from this year, what is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Answer:
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.
This means that [tex]p = 0.0746[/tex]
Random sample of 318 independent returns
This means that [tex]n = 318[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]
What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?
Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]
[tex]Z = -0.26[/tex]
[tex]Z = -0.26[/tex] has a p-value of 0.3974.
1 - 0.3974 = 0.6026
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Tracy leaves the beach at 3:00 p.m. and drives along the highway at 55 mph. One hour later, Quinn leaves the same beach and drives along the same highway in the same direction at 65 mph. How many hours will it take Quinn to catch up to Tracy?
10 hours
6.5 hours
8.5 hours
15 hours
Answer:
8.5 hours
Step-by-step explanation:
55 x 9.5 (add extra hour) = 552.5 miles
65 x 8.5 (actual time spent) = 552.5 miles
The time taken for Quinn to catch up to Tracy during the journey is 8.5 hours.
Time of motion of Tracy and QuinnThe time of motion of tracy and quinn is determined by using the following equation as shown below;
For tracy, d = 55(t + 1)
For Quinn, d = 65t
where;
55(t + 1) = 65t
55t + 55 = 65t
55 = 10t
t = 55/10
t = 5.5 hours
3 hour from noon + 5.5 hours = 8.5 hours
Learn more about time of motion here: https://brainly.com/question/2364404
#SPJ2
Jeremy bought 3 pairs of pants that cost
The same amount of money. He had a
$10 off coupon for the pants. Using the
coupon, Jeremy spent $35. Write an
equation that can be used to find the cost
of the pants before the coupon was
applied
(use p as your variable)
Help fasttt
Answer:
3p - 10 =35
Step-by-step explanation
You want to cancel out everything, besides the p, on the left side.
then add the ten to 35 to cancel it out
divide 3 by 45 to cancel it out
p equals 15
The answer is 15
The endpoints of a line are (10, 4) and (-2, 8). Find the slope of
the line.
A teacher has a 2-gallon (52 cup) container of juice. She gives each student z cup of juice. Which equation represents the amount of juice that remains, y, after x students are served?
Answer:
[tex]y = 32 - \frac{1}{2}x[/tex]
Step-by-step explanation:
Given
[tex]Cups = 32[/tex] ---- not 52
[tex]Students = x[/tex]
[tex]Remainder = y[/tex]
[tex]Each = \frac{1}{2}[/tex] --- not z
Required
The equation for y
The remainder y is calculated as:
[tex]y = Cups - Students * Each\\[/tex]
[tex]y = 32 - \frac{1}{2}x[/tex]
Which functions have a range of {y e R | -
Answer:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.
Step-by-step explanation:
idontknow
Verify that the equation is an identity.
Step-by-step explanation:
We need to prove that ,
cot x / csc x - csc x / cot x = - tan x sec x .
LHS :-
> cot x / csc x - csc x / cot x
> cos x / sin x ÷ csc x - sin x × csc x / cos x
> cosx - 1/ cos x
> cos² x - 1 / cos x
> - sin²x / cosx
> -sin x / cos x × sin x
> -tan x sin x
= RHS
Hence Proved !
Which graph shows the solution to this system of linear inequalities?
y<-1/3x+2
y<_2x-3
Answer:
C
Step-by-step explanation:
Since all the graphs have the same line, you’re just looking for the correct shaded region. Since for both equations you want the shaded region to be less than the line, answer c solves the inequality.