===================================================
Explanation:
"given that the first die rolled is a 2" means we know 100% that the first die shows a 2. Either we can see the die or a friend is telling us the status. Since we know the first die is a 2, this means we can effectively ignore it. Everything will hinge on the second die. If the second die shows an odd number, something like 1, then 2+1 = 3 is the result which is also odd.
The general rule is odd+even = odd and even+even = even.
Therefore, the two dice must together be even for the sum to be even.
Of the six possible ways to roll a die {1,2,3,4,5,6}, there are 3 even values {2,4,6} so the chances of rolling an even number on the second die is 3/6 = 1/2. Again we dont need to consider the first die at all since everything practically hinges on this second die.
Answer:
50%
Step-by-step explanation:
For the total to be even, when the first number is even, the second number also has to be even.
2, 4, and 6 are even, out of 6 numbers. That is 3 numbers out of 6, which gives us that the probability is 1 out of 2, or 50%.
Please help with multiple choice question
The function f(x) = 2x + 5 represents Ken’s earnings working x hours as a waiter. On
3 separate days, he works 2, 8, and 14 hours, representing the domain of the function.
What is the range of f(x)?
a. {4, 16, 28}
b. {–1, 11, 23}
c. {14, 26, 38}
d. {9, 21, 33}
Answer:
D: {9, 21, 33}
Step-by-step explanation:
Ken worked 2, 8 and 14 hours on 3 separate days.
For working 2 hours, his earnings were f(2) = 2(2) + 5, or 9;
For working 8 hours, his earnings were f(28) = 2(8) + 5, or 21; and
For working 14 hours, his earnings were f(14) = 2(14) + 5, or 33
Thus, the range of this function for the days given is {9, 21, 33} (Answer D)
Joe spends 18.75% of his working day washing cars. He spends 1.5 hours washing cars. How many total hours does he work per day?
Answer:
8 hours
Step-by-step explanation:
Joe spends 18.75% of his working day washing cars.
Joe spends 1.5 hours washing car.
Therefore 18.75% is equal to 1.5 hour.
18.75% = 1.5 hour
1% = 1.5 ÷ 18.75 = 0.08 hour
100% = 0.08 x 100 = 8 hours
What percentage of the data values represented on a box plot falls between the minimum value and the lower quartile?
Answer:
first 25%
Step-by-step explanation:
A quartile is a quarter, so the first 25% falls between the minimum and lower quartile
Answer:
A. 25%
Step-by-step explanation:
Because it asks you where one section to another section (on a box plot there are four areas containing 25% within each one.)
If you park 3 levels below the lobby floor of a hotel and take the elevator to the 15th floor, how many floors apart are you from your vehicle? Floors
I think 18 because 3+15=18
Answer:
I think it's 12
Step-by-step explanation:
15-3=12
Rico's backpack weighed 3.6 pounds. Then he added his school books which weighed an additional 24.76 pounds. How much did Rico's backpack weigh with his school books?
Answer:
The answer should be 28.36
Step-by-step explanation:
You add them together
Hope this helps!
Answer:
28.36
Step-by-step explanation:
3.6 + 24.7 = 28.36
Convert 17π/8 to degrees.
Answer:
382.5°
Step-by-step explanation:
Multiply
17π 180°
------ by the conversion factor ------------
8 π
obtaining:
(17)(180)°
------------- = 382.5°
8
scientists are studying the temperature on a distant planet. they find that the surface temperature at one location is 45 Celsius. they also find that the temperature decreases by 7 Celsius for each kilometer you go up from the surface.
let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). write an equation relating T to H, and then graph your equation using the axes.
Final Answer:
The equation[tex]\(T = 45 - 7H\)[/tex] represents the relationship between temperature (T) and height above the surface (H) on the distant planet, where the surface temperature is 45 Celsius, decreasing by 7 Celsius for each kilometer of height. Graphing this equation reveals a linear line with a negative slope, portraying the systematic decrease in temperature as one moves higher above the planet's surface.
Explanation:
The equation [tex]\(T = 45 - 7H\)[/tex] is derived from the given information about the distant planet's temperature. The surface temperature is 45 Celsius, and for each kilometer above the surface (represented by H), the temperature decreases by 7 Celsius.
The equation reflects this linear relationship. The term 45 is the starting temperature at the surface, and the term -7H represents the decrease for each kilometer above.
For example, let's substitute H = 1 into the equation to find the temperature at a height of 1 kilometer:
[tex]\[ T = 45 - 7(1) = 45 - 7 = 38 \][/tex]
This calculation shows that at a height of 1 kilometer, the temperature is 38 Celsius. Similarly, for H = 2:
[tex]\[ T = 45 - 7(2) = 45 - 14 = 31 \][/tex]
This process can be repeated for different values of H to create a set of coordinates (H, T) that form a linear relationship. Graphing these points produces a straight line with a negative slope, illustrating the temperature decrease with increasing height.
In essence, the detailed calculation demonstrates how the equation captures the specified temperature-height relationship on the distant planet. It provides a mathematical representation of the observed data and allows scientists to predict temperatures at various heights above the surface.
Lionel needs money quite frequently and doesn't need much interest at all. Which of these options for saving money is best for him?
A. savings bond
B. money market account
C. certificate of deposit
D. savings account
Answer: Savings account - Apex
Answer:
Option D is the correct answer.
Step-by-step explanation:
The saving bonds are a good way to earn money but they work at fixed rate of interest over a set time period.
Money market accounts give a limited access to account and not more than three checks are written in a month. Its a type of short term savings.
The certificate of deposit or CD's have higher interest rate than savings account. But one cannot withdraw the money before the term maturity otherwise penalty is to be paid.
Savings account are deposit accounts that can be accessed whenever needed. These yield less interest as compared to money market accounts or CD's.
Therefore, the best option for Lionel to choose will be Savings account
Andrew drove from his house to his sister's house in 8 hours at an average of 60 miles per hour. On the way home he drove at an average rate of 64 miles per hour. How long did it take him to drive home?
Answer:
288
Step -by-step explanation:I'm not explaining :D
Answer:
It took him 7.5 hrs to drive home.
Step-by-step explanation:
The distance is the same, going or returning.
Recall that distance = rate times time.
Here, distance from Andrew's to his sister's is (60 mph)(8 hr) = 480 mi
If distance = rate times time, then time = distance / rate.
Here we have time = 480 mi / 64 mph = 7.5 hrs
It took him 7.5 hrs to drive home.
Which set of steps could be used to solve this story problem? Helen read 4 books per week for the first 3 weeks of her summer vacation. She read 2 books per week for the last 4 weeks. She also read 2 magazines each week. How many books did Helen read over summer vacation? A. Multiply 4 by 3. Then multiply 2 by 4. Add the two products. B. Add 3 and 4. Then add 2 and 4. Add the two sums. C. Multiply 3 × 4. Then add 4 to that product. Then subtract 2. D. Add 4 and 4. Then divide that sum by 2 and add 3 to the quotient.
Answer:
A. Multiply 4 by 3. Then multiply 2 by 4. Add the two products.
Step-by-step explanation:
As with many rate problems, ...
quantity = rate · time
The total quantity will be the sum of quantities associated with different rates or time periods:
total quantity = quantity1 + quantity2
= (rate 1)(time 1) + (rate 2)(time 2)
= (4 books/week)(3 weeks) + (2 books/week)(4 weeks)
= 4·3 books + 2·4 books . . . . . . units of (weeks/weeks) cancel
= (4·3 + 2·4) books . . . . . . formula matches selection A
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
B = 49°, a = 16, b = 14
The answer is:
The first triangle is:
[tex]A=59.6\°\\C=71.4\°\\c=17.6units[/tex]
The second triangle is:
[tex]A=120.4\°\\C=10.6\°\\c=3.41units[/tex]
Why?To solve the triangles, we must remember the Law of Sines form.
Law of Sines can be expressed by the following relationship:
[tex]\frac{a}{Sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}[/tex]
Where,
a, b, and c are sides of the triangle
A, B, and C are angles of the triangle.
We are given,
[tex]B=49\°\\a=16\\b=14[/tex]
So, solving the triangles, we have:
- First Triangle:Finding A, we have:
[tex]\frac{a}{Sin(A)}=\frac{b}{Sin(B)}\\\\Sin(A)=a*\frac{Sin(B)}{b}=16*\frac{Sin(49\°)}{14}\\\\Sin^{-1}(Sin(A)=Sin^{-1}(16*\frac{Sin(49\°)}{14})\\\\A=59.6\°[/tex]
Finding C, we have:
Now, if the sum of all the interior angles of a triangle is equal to 180°, we have:
[tex]A+B+C=180\°\\\\C=180-A-B\\\\C=180\°-59.6\°-49\°=71.4\°[/tex]
Finding c, we have:
Then, now that we know C, we need to look for "c":
[tex]\frac{14}{Sin(49\°)}=\frac{c}{Sin(71.4\°)}\\\\c=\frac{14}{Sin(49\°)}*Sin(71.4\°)=17.58=17.6units[/tex]
So, the first triangle is:
[tex]A=59.6\°\\C=71.4\°\\c=17.6units[/tex]
- Second Triangle:Finding A, we have:
[tex]\frac{a}{Sin(A)}=\frac{b}{Sin(B)}\\\\Sin(A)=a*\frac{Sin(B)}{b}=16*\frac{Sin(49\°)}{14}\\\\Sin^{-1}(Sin(A)=Sin^{-1}(16*\frac{Sin(49\°)}{14})\\\\A=59.6\°[/tex]
Now, since that there are two triangles that can be formed, (angle and its suplementary angle) there are two possible values for A, and we have:
[tex]A=180\°-59.6\°=120.4\°[/tex]
Finding C, we have:
Then, if the sum of all the interior angles of a triangle is equal to 180°, we have:
[tex]A+B+C=180\°\\\\C=180\°-A-B\\\\C=180\°-120.4\°-49\°=10.6\°[/tex]
Then, now that we know C, we need to look for "c".
Finding c, we have:
[tex]\frac{14}{Sin(49\°)}=\frac{c}{Sin(10.6)}\\\\c=\frac{14}{Sin(49)\°}*Sin(10.6\°)=3.41units[/tex]
so, The second triangle is:
[tex]A=120.4\°\\C=10.6\°\\c=3.41units[/tex]
Have a nice day!
Write the standard equation of the circle shown.
Answer:
b
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ← r is the radius
The circle shown is centred at the origin and has a radius of 5, thus
x² + y² = 5² ⇒ x² + y² = 25 → b
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The number of unshelled peanuts in a 1 lb container is normally distributed with a mean of 375 peanuts and a standard deviation of 24 peanuts.
Suppose 4000 different 1 lb containers are in a warehouse.
About how many containers contain more than 447 peanuts?
Answer: a) 6
Step-by-step explanation:
The mean is 375 which has a z-score of 0.
The standard deviation is 24 so:
z-score of 1 is: 375 + 24 = 399z-score of 2 is: 399 + 24 = 423z-score of 3 is: 423 + 24 = 477A z-score of 3 is 99.85% from the left (or 1 - 99.85% from the right = 0.15%)
Since we are looking for the "more than" a z-score of 3, it is 0.15% of the total.
4000
× 0.0015
6.0000
1) Find f(x) if it is known that f(5a)=5a−2.
2) Find g(x) if it is known that g(2t)=8t−1.
Answer:
Step-by-step explanation:
One
f(5a) means that wherever you see an x, you put in 5a
x = 5a
f(x) = x/5t * 5t - 2
f(x) = x - 2
===============
Two
g(2t) = 8t - 1
x = 2t
g(x) = 8t/2t*x - 1
g(x) = 4x - 1
1)for the first one you can put a=(1/5)a in the function and it will be:
[tex]f(a) = a - 2[/tex]
so in a function , alphabet is not important and you can rewrite it to this:
[tex]f(x) = x - 2[/tex]
2)the same as the first , we can put t=(1/2)t and conclusion is :
[tex]g(t) = 4t - 1[/tex]
and then change the t to x:
[tex]g(x) = 4x - 1[/tex]
The function, f(t)= 1.2 cos 0.5t, does not have an amplitude and has a period of 4π.
Answer:
False
Step-by-step explanation:
Given in the question a function,
f(t)=1.2cos0.5t
Standard form of cosine function is
f(t)=acos(bt)
Amplitude is given by = |a|
Period of function is given by = 2π/b
So the amplitude is |1.2| = 1.2
the period is 2π/0.5 = 4π
Answer:
False
Step-by-step explanation:
The given function is
[tex]f(t)=1.2\cos 0.5t[/tex]
This function is of the form:
[tex]f(t)=A\cos(Bt)[/tex]
where A=1.2 and B=0.5
The amplitude of this function is given by;
|A|=|1.2|=1.2
The period of this function is given by;
[tex]T=\frac{2\pi}{|B|}[/tex]
[tex]T=\frac{2\pi}{|0.5|}[/tex]
[tex]T=\frac{2\pi}{0.5}=4\pi[/tex]
The correct answer is False
At a fair, each person can spin two wheels of chance. The first wheel has the letters F, A, I, and R. The second wheel has the numbers 1, 2, and 3.
What is the sample space of spinning the two wheels?
Answer:
12 possible outcomes.
Sample space:
[tex]\begin{array}{cccc}(F,1)&(A,1)&(I,1)&(R,1)\\(F,2)&(A,2)&(I,2)&(R,2)\\(F,3&(A,3)&(I,3)&(R,13)\end{array}[/tex]
Step-by-step explanation:
The collection of all possible outcomes of a probability experiment forms a set that is known as the sample space.
1. There are four possible outcomes for the first wheel: F, A, I and R
2. There are three possible outcomes for the second wheel: 1, 2 and 3
So, the sample space is
[tex]\begin{array}{cccc}(F,1)&(A,1)&(I,1)&(R,1)\\(F,2)&(A,2)&(I,2)&(R,2)\\(F,3&(A,3)&(I,3)&(R,13)\end{array}[/tex]
Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1 squared divided by 64 equals 1.
Vertices: (-1, 3), (-1, -13); Foci: (-1, -13), (-1, 3)
Vertices: (3, -1), (-13, -1); Foci: (-13, -1), (3, -1)
Vertices: (-1, 1), (-1, -11); Foci: (-1, -15), (-1, 5)
Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Answer:
Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)
Step-by-step explanation:
Center at (-5,-1) because of the plus 5 added to the x and the plus 1 added to the y.
a(squared)=36 which means a=6 and a=distance from center to vertices so add and subtract 6 from the x coordinate since this is a horizontal hyperbola, which is (1,-1), (-11,-1). From there you dont need to find the focus since there is only one option for this;
Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)
Answer:
Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Step-by-step explanation:
Ok so we have 5x[tex]\frac{5x^{2} }{36}-\frac{y^{2} }{64}=1[/tex]
As you know we have the equation of the hyperbola as (x-h)^2/a^2-(y-k)^2/b^2, so the formula of the foci is [tex](h+-c,k) and for vertices (h+-a,k)[/tex]
then we have to calculate c using pythagoras theorem we have that
a=6 because is the root of 36
b=8 beacause is the root of 64
And then we have that [tex]c^{2}=a^{2}+b^{2}[/tex]
[tex]c=\sqrt{36+64}[/tex]
So the root of 100 is equal to 10
Hence c=10
Using the formula given before and the equation we know that
h=-5
k=-1
And replacing those values on the equation we have that the foci are
(-5-10, -1)=(-15,-1)(-5+10,1)=(5,-1)And the vertices are:
(-5-6, -1)=(-11,-1)(-5+6, 1)= (1,-1)So the correct answer is D
help plsssssssssssssssssssssssssssssss
Answer:
[tex]t\le 4[/tex]
Step-by-step explanation:
Let t hours be the number of hours needed to rent the room. If one hour costs $8.30, then t hours cost $8.30t. The reservation fee is $34, so the total cost is
[tex]\$(34+8.30t).[/tex]
The history club wants to spend $67.20, thus
[tex]34+8.30t\le67.20\\ \\8.30t\le 67.20-34\\ \\8.30t\le 33.20\\ \\t\le \dfrac{33.20}{8.30}=\dfrac{332}{83}=4[/tex]
The maximum possible whole number of hours is 4 hours.
The graph shows the number of paintballs a machine launches, y, in x seconds:
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line. A line is shown connecting points on ordered pair 2, 12 and 4, 24 and 6, 36 and 8, 48.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
A.) 2/12
B.) 12/2
C.) 2/48
D.) 48/2
Answer:
Option B.) 12/2
Step-by-step explanation:
we know that
The rate of a linear equation is equal to the slope m
The slope is equal to
points (2,12) and (4,24)
m=(24-12)/(4-2)
m=12/2
m=6 balls/sec
Can someone please help with this question it’s confusing me
The answer might be 2.66
Answer:
0.5
Step-by-step explanation:
12 is the total amount of bags
(2*1/6+ 2*1/3 + 3*1/2 + 4*2/3 + 1*5/6 ) / 12 =
[1/3 + 2/3 + 3/2 + 8/3 + 5/6]/12 = [(1+2+8)/3 + (3*3+5)/6 ]/12 =
(11/3+14/6)/5 = [(22+14)/6 ]/12 = (36/6) /5 = 6/12=0.5
What is the solution to the system of equations?
x+y+3z=-4
2x-z=-3
-x-y-2z=5
a. (-1, -6, 1)
b. (1, -6, 1)
c. (-1, 6, 1)
d. (-1, -6, -1)
Answer:
a
Step-by-step explanation:
Let's use the elimination method on equations 1 and 3 and see what happens:
x + y + 3z = -4
-x - y - 2z = 5
It looks like both the x terms and the y terms cancel out leaving us with the fact that z = 1.
Let's go back to the second equation now and sub in a 1 for z:
2x - z = -3 implies 2x - 1 = -3 and x = -1.
Pick any equation now to sub in the known values to find y. I chose the first one, just because:
x + y + 3z = -4 implies -1 + y + 3(1) = -4 and
-1 + y + 3 = -4 so
y + 2 = -4 and
y = -6
So the solution set is (-1, -6, 1)
Find the domain and range of f(x)=-2x+|3sinx|
Answer:
Domain: (-∞, ∞); range: (-∞, ∞).
Step-by-step explanation:
In the given function, f(x)= -2x + |3sinx|, the range of the |3sinx| term is [0, 3]. That of the -2x term is (-∞, ∞).
The range of f(x)= -2x+|3sinx| is thus (-∞, ∞); the |3sinx| term has no effect on this.
There are no restrictions on the input to f(x)= -2x+|3sinx|. The domain is thus (-∞, ∞).
during the first years of growth the height of a tree can be modeled with the function h=-t^2 +12t+10 where t is the time in years since being planted and h is the height in inches. Enter the average rate cof change, in inches per year, from year 1 to year 5.
ANSWER
6 inches
EXPLANATION
The given function is
[tex]h(t) = - {t}^{2} + 12t + 10[/tex]
The average rate of change from t=1 to t=5 is given by:
[tex] = \frac{h(5) - h(1)}{5 - 1} [/tex]
[tex]h(5) = - {(5)}^{2} + 12(5) + 10[/tex]
[tex]h(5) = - 25 + 60+ 10[/tex]
[tex]h(5) = 45[/tex]
Also,
[tex]h(1) = - {(1)}^{2} + 12(1) + 10[/tex]
[tex]h(1) = - 1+ 12+ 10[/tex]
[tex]h(1) = 21[/tex]
The average rate of change is now
[tex] = \frac{45 - 21}{4} [/tex]
[tex] = \frac{24}{4} [/tex]
[tex] = 6[/tex]
The number of defective units in a production run of 850 circuit boards are normally distributed with 21 defective units and 3 defective units. Find the probability P(17 < X < 25) with the help of the graphing calculator. Round your answer to the nearest integer.
77%
81%
80%
82%
Answer:
82%
Step-by-step explanation:
We let the random variable X denote the number of defective units in the production run. Therefore, X is normally distributed with a mean of 21 defective units and a standard deviation of 3 defective units.
We are required to find the probability, P(17 < X < 25), that the number of defective units in the production run is between 17 and 25.
This can be carried out easily in stat-crunch;
In stat crunch, click Stat then Calculators and select Normal
In the pop-up window that appears click Between
Input the value of the mean as 21 and that of the standard deviation as 3
Then input the values 17 and 25
click compute
Stat-Crunch returns a probability of approximately 82%
Find the attachment below.
Given the value of cos 50° ? 0.6428, enter the sine of a complementary angle. Use an expression relating trigonometric ratios of complementary angles.
ANSWER
[tex]\sin(40) \degree = 0.6428[/tex]
EXPLANATION
The sine and cosine ratios are complementary.
This means that:
[tex] \cos(x \degree) = \sin(90 - x) \degree[/tex]
We were given that,
cos(50°)=0.6428
We want to find the sine of the complement of this angle.
[tex] \cos(50\degree) = \sin(90 -5 0) \degree[/tex]
[tex]\cos(50\degree) = \sin(40) \degree[/tex]
This implies that,
[tex] \sin(40) \degree = 0.6428[/tex]
Write the equation in standard form for the circle with center (9,
-
4) and radius 9.
Answer:
[tex](x-9)^{2}+(y+4)^{2}=81[/tex]
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex](h,k)=(9,-4)[/tex]
[tex]r=9\ units[/tex]
substitute
[tex](x-9)^{2}+(y+4)^{2}=9^{2}[/tex]
[tex](x-9)^{2}+(y+4)^{2}=81[/tex] ----> equation of the circle in standard form
Use technology or a z-score table to answer the question.
Scores on a standardized military exam are normally distributed with a mean of 57 and a standard deviation of 9. Consider a group of 4000 military students.
Approximately how many students will score less than 66 on the test?
A. 200
B. 634
C. 3366
D. 3800
Answer:
C
Step-by-step explanation:
Finding the z-score:
z = (x - μ) / σ
z = (66 - 57) / 9
z = 1
Using a z-score table or calculator:
P(z < 1) = 0.8413
84.13% of 4000 is:
0.8413 (4000) = 3365.2
Rounding up to the nearest whole number, approximately 3366 students will score less than 66. Answer C.
Using the normal distribution, it is found that approximately 3366 students will score less than 66 on the test.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 57, \sigma = 9[/tex]
The proportion of students that scored less than 66 is the p-value of Z when X = 66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66 - 57}{9}[/tex]
Z = 1
Z = 1 has a p-value of 0.8413.
Out of 4000 students:
0.8413 x 4000 = 3366, which means that option C is correct.
More can be learned about the normal distribution at https://brainly.com/question/24663213
#SPJ2
Suppose a sample mean is distributed normally. if the sample size increases, what happens to the shape of the sampling distribution of the sample mean?
a. distribution becomes wider and flatter.
b. distribution becomes narrower and taller.
c. distribution remains the same.
d. distribution turns upside down and inside ou
Answer:
(b)
Step-by-step explanation:
(b) is correct: the distribution becomes narrower and taller.
Please help me out....
Answer:
x = 6
Step-by-step explanation:
Given that the line segment is an angle bisector then the following ratios are equal
[tex]\frac{42}{78}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex], that is
[tex]\frac{7}{13}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex] ( cross- multiply )
13(6x - 1) = 7(10x +5) ← distribute parenthesis on both sides
78x - 13 = 70x + 35 ( subtract 70x from both sides )
8x - 13 = 35 ( add 13 to both sides )
8x = 48 ( divide both sides by 8 )
x = 6
PLEASE HELP FAST!
A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on the marble selected will be recorded as the outcome.
Consider the following events.
Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
Answer:
A and B: {4, 6}
A or B: {2, 3, 4, 5, 6, 8}
Complement of B: {1, 2, 7, 8}
Step-by-step explanation:
A and B refer to the elements that are in both A and B at the same time
The even numbers from 1 to 8 are {2, 4, 6, 8}
The numbers from 3 to 6 are {3, 4, 5, 6}
Look for the common elements between both sets.
A and B: {4, 6}
A or B is the union of the two sets
Join the elements of both sets
A or B: {2, 3, 4, 5, 6, 8}
The complement of B are all the elements that are not in B.
Write all the elements of the sample space except those of event B
Complement of B: {1, 2, 7, 8}
Event A: 2, 4, 6, 8; Event B: 3, 4, 5, 6.
Explanation:In probability theory, events are outcomes or sets of outcomes from a random experiment. They are subsets of the sample space, representing possible results. Simple events consist of a single outcome, while compound events involve more than one outcome. Probability measures the likelihood of events occurring.
Event A consists of the even numbers 2, 4, 6, and 8.
Event B consists of the numbers 3, 4, 5, and 6.
The outcomes for Event A are 2, 4, 6, and 8.
The outcomes for Event B are 3, 4, 5, and 6.
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