Answer:
A) F or G = {5, 6, 7, 8, 9, 10, 11, 12}; B) P(F or G) = 8/12 = 0.667
Step-by-step explanation:
The outcomes in event F are 5, 6, 7, 8 and 9. The outcomes in event G are 9, 10, 11 and 12. This means that the event F or G, containing all elements of both events, will be
{5, 6, 7, 8, 9, 10, 11, 12}. Note that we do not count 9 twice; it only appears in the sample space once. There are 8 elements out of 12 total in the sample space; this means the probability is 8/12 = 0.667.
Using the addition rule, we begin with P(F). There are 5 elements in this event; this makes P(F) = 5/12.
For P(G), there are 4 elements in G; this makes P(G) = 4/12.
To add them, we add P(F) and P(G) but then must take out the element counted twice; this gives us
5/12+4/12-1/12 = 9/12-1/12 = 8/12 = 0.667.
We have that
F&G={5, 6, 7, 8, 9, 10, 11, 12}[tex]P(FG)=0.667[/tex][tex]P(F or G)=5/12+4/12-(1/12)\\\\ P(F or G)=5/12+1/4[/tex]From the question we are told
S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, F={5, 6, 7, 8, 9}G={9, 10, 11, 12}
a)
Generally
The P(F or G) by counting the number of outcomes in F or G is
F&G={5, 6, 7, 8, 9, 10, 11, 12}
b)
P(F or G) using the general addition rule
[tex]P(FG)=\frac{N_f}{N_g}\\\\P(FG)=\frac{8}{12}[/tex]
[tex]P(FG)=0.667[/tex]
c)
Generally Using addition Rue to attain P(F or G) we have
For P(F or G)
[tex]P(F or G)=PF+PG-P(F+G)[/tex]
[tex]P(F or G)=5/12+4/12-(1/12)\\\\ P(F or G)=5/12+1/4\\\\ P(F or G)=\frac{8}{12}[/tex]
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hey this text is just for min word requirement the problem is in the picture
Answer:
(-2, 0)
Step-by-step explanation:
Because both equations are to find Y, set them equal to each other to solve:
3x+6 = x+2
Subtract x from both sides:
2x + 6 = 2
Subtract 6 from both sides:
2x = -4
Divide both sides by 2:
x = -4 /2
x = -2
Now you have a value for x, replace X with -2 in one of the equations and solve for y:
y = 3x +6 = 3(-2) +6 = -6 +6 = 0
X = -2 and Y = 0
(-2,0)
Find the value of x and y.
A) x=109, y=108
B) x=108, y=109
C) x=108, y=108
D) x=109, y=109
Answer:
B
Step-by-step explanation:
Since a quadrilateral has an angle sum of 360 degrees you just add the three angle measures together and subtract them from 360 leaving you with 108.
The angle which is outside is supplementary which means it adds to 180 degrees. All you have to do here is subtract 71 from 180 which gives you 109.
It’s B) x=108,y=109
Es la respuesta
A bag contains 4 red, 3 green and 2 blue marbles. What is the probability of selecting a green marble and then a blue marble assuming you replace the first marble?
1st of all, this makes my brain hurt
2nd of all, which one was the first marble?
Please help with this!!!!
Answer: 7
Step-by-step explanation:
[tex]\dfrac{\overline{CD}+\overline{A F}}{2}=\overline{BE}\\\\\\\dfrac{(18)+(6x-12)}{2}=2x+10\\\\\\(18)+(6x-12)=2(2x+10)\\\\\\6x +6 = 4x +20\\\\2x+6=20\\\\2x=14\\\\\large \boxed{x=7}[/tex]
Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and i exponential form by filing in the boxes for exponents)
the answer is 90 because 360/90=4 270/90=3
Given the system of equations, what is the solution?
x + 2y = 7
x - 2y = -1
{(-8, -12)}
{(3, 2)}
{(-4, 6)}
Answer:
[tex]\large\boxed{x=3\ and\ y=2\to(3,\ 2)}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}x+2y=7\\x-2y=-1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=6\qquad\text{ivide both sides by 2}\\.\qquad x=3\\\\\text{Put the value of x to the first equation:}\\\\3+2y=7\qquad\text{subtract 3 from both sides}\\\\2y=4\qquad\text{divide both side by 2}\\\\y=2[/tex]
The solution to the given system of linear equations is (3, 2), which is found by eliminating y and solving for x, then substituting back to find y.
Given the system of equations:
x + 2y = 7
x - 2y = -1
To find the solution to the system, we can add the two equations to eliminate y:
(x + 2y) + (x - 2y) = 7 + (-1)
2x = 6
x = 3
Substituting x = 3 into the first equation:
3 + 2y = 7
2y = 4
y = 2
So, the solution to the system of equations is (3, 2). None of the other provided options, {(-8, -12)} or {(-4, 6)}, match this solution.
A study looked at n=238 adolescents, all free of severe illness.23 Subjects wore a wrist actigraph, which allowed the researchers to estimate sleep patterns. Those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.8 millimeters of mercury (mm Hg) higher than that of other adolescents. The standard deviation of this difference is 1.4 mm Hg. Based on these results, test whether this difference is significant at the 0.01 level.
Answer:
Step-by-step explanation:
Since n < 30, we will find the t-score and compare that to the t-score of a significance level of 1%.
Since they are asking if the difference is significant, we will have a two tailed test, with degree of freedom being 22, so our critical values are
t < -2.704 and t > 2.704
Our t-value for this situation is
t = ([µ + 5.8] - µ)/(1.4/√23)
It's µ + 5.8 because the problem told us that their levels are 5.8 mm higher than the average, so it's the average, plus 5.8
Simplify the equation...
t = 5.8/(1.4/√23)
t = 19.868
19.868 > 2.704, the evidence supports that there is significant difference between the sample and the population
There is a significant difference between the sample and the population.
What is standard deviation?A standard deviation (or σ) indicates how dispersed the data is in relation to the mean.
What is t-distribution?The t-distribution indicates the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.
What is t-score?A t-score is the number of standard deviations away from the mean of the t-distribution.
How to find whether the difference is significant at the 0.01 level?Here n < 30.So, we will find the t-score and compare that to the t-score of a significance level of 1%.Here the degree of freedom is 22 and so the critical values are:
t < -2.704 and t > 2.704
In the problem, it is given that those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.8 millimeters of mercury (mm Hg) higher than that of other adolescents∴ The t-value for this situation is
t = ([µ + 5.8] - µ)/(1.4/√23)
⇒ t = 5.8/(1.4/√23)
⇒t = 19.868
Now, 19.868 > 2.704So, we can say that there is significant difference between the sample and the population.
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Find the measure of Arc AB.
Answer:
The measure of arc AB is [tex]88\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<ACB=\frac{1}{2}(arc\ AB)[/tex]
we have
[tex]m<ACB=44\°[/tex]
substitute
[tex]44\°=\frac{1}{2}(arc\ AB)[/tex]
[tex]88\°=arc\ AB[/tex]
rewrite
[tex]arc\ AB=88\°[/tex]
The measure of arc AB is 88°
The inscribed angle measures half that of the arc comprising
so
[tex]m < ACB=(1)/(2)(arc\ AB)[/tex]
we have
[tex]m < ACB=44°[/tex]
substitute
[tex]44\°=(1)/(2)(arc\ AB)[/tex]
[tex]88\°=arc\ AB[/tex]
rewrite
[tex]arc\ AB=88\°[/tex]
Find the length and width of a rectangle whose area is 56 units squared and whose length is 10 units less than it's width
Answer:
l = 4, w = 14
Step-by-step explanation:
[tex]A_r = 56 = l * w[/tex]
l - length;
w - width;
l = w - 10;
We substitute the 'l' using the previous formula =>
[tex][tex]A_r = (w -10) \cdot w = w^2 - 10w = 56 =>\\w^2 - 10w - 56 = 0\\[/tex]
By the quadratic formula we solve for 'w':(we will use the positive value, because we're talking about lengths of planes in a Euclidean space)
[tex]w = \frac{10 + \sqrt{100+224} }{2} = \frac{10+18}{2} = \frac{28}{2} = 14[/tex]
l = w - 10 = 14 -10 = 4
The value 5pi/2 is a solution for the equation 2sin^2x -sin x -1=0
Answer:
5π/2 it is not a solution for the equation 2sin²x - sinx - 1 = 0
Step-by-step explanation:
∵ 2sin²x - sin x - 1 = 0
* Lets factorize it as a quadratic equation
∴ ( 2sinx + 1)(sinx - 1) = 0
∴ 2sinx + 1 = 0 ⇒ 2sinx = -1 ⇒ sinx = -1/2
* ∵ The value of sinx is -ve
∴ x is in the 3rd or 4th quadrant ⇒ According to ASTC Rule
- ASTC Rule: 1st all +ve , 2nd sin only +ve ,
3rd tan only +ve , 4th cos only +ve
* Let sinα = 1/2 where α is an acute angle
∴ α = π/6
∵ x is in 3rd or 4th quadrant
∴ x = π + α = π + π/6 = 7π/6 or
∴ x = 2π - π/6 = 11π/6
OR
∴ sinx - 1 = 0 ⇒ sinx = 1
∴ x = π/2
∴ ALL values of x are π/2 , 7π/2 , 11π/2 if 0 ≤ x ≤ 2π
∴ 5π/2 it is not a solution for the given equation
Answer:
5pi/2 is a solution for the equation 2sin²x -sin x -1=0
Step-by-step explanation:
We need to check 5pi/2 is a solution for the equation 2sin²x -sin x -1=0.
Substituting 5pi/2 in equation
[tex]2sin^2x-sin x-1=2sin^2\left (\frac{5\pi}{2} \right )-sin\left (\frac{5\pi}{2} \right )-1\\\\=2sin^2\left (2\pi +\frac{\pi}{2} \right )-sin\left (2\pi +\frac{\pi}{2} \right )-1\\\\=2sin^2\left (\frac{\pi}{2} \right )-sin\left (\frac{\pi}{2} \right )-1\\\\=2\times 1-1-1=0[/tex]
So 5pi/2 is a solution for the equation 2sin²x -sin x -1=0.
Your estimate that the length of a board is 24 feet. The actual length of the board is 22 feet. Find the percent error.
Answer:
9.09%
Step-by-step explanation:
You over estimated by 2 feet. Find out how much 2 feet of 22 is by dividing 2 by 22...
2/22 = 0.090909090909
To convert a decimal to a percent, multiply the decimal by 100%
0.0909090909(100%) = 9.0909090909% or 9.09%
Final answer:
The percent error in the student's estimate of the board's length is approximately 9.09%. The exercise demonstrates the value of precise calculations over rough estimates, although some thoughtful guesses can be quite close.
Explanation:
To find the percent error of the student's estimate, we'll use the following formula:
Percent Error = |(Actual Value - Estimated Value) / Actual Value| × 100%
The actual length of the board is 22 feet, and the estimated length is 24 feet. So we can calculate the percent error as follows:
|(22 - 24) / 22| × 100% = |(-2) / 22| × 100% = (2 / 22) × 100% ≈ 9.09%
The percent error in the student's estimate is approximately 9.09%. This calculation underscores the importance of making careful calculations rather than relying on rough guesstimates, which can lead to significant errors in certain situations. However, it can also show that even guesses made with some thought, like the example of 10 feet versus an actual of 12 feet, can sometimes be surprisingly close.
What is the degree measure of the angle formed by the hands of a clock when the time is 12:00
Answer:
0 degrees
Step-by-step explanation:
when it is hour 12 and 0 minutes, the hour and minute hand will be on top of each other, so therefore it does not form an angle
Need help picture below is ez like crazy i just need help on it AND 22 POINT FOR IT DO YOUR BEST
A. Explain the error and redo the problem showing the correct answer. *
B. Are both of the boys correct? If not who is correct and explain your answer. *
Answer:
I know a is because he added 0.2 instead of still decreasing since its subtraction in negatives
and b : since -0.2 - -0.3 is -0.5 so neither are correct
2 cars started to move at the same time, at the same direction but one was moving twice as fast as the other. 6 hours later, the 2 cars were 204 miles apart. Find the speed for each car.
Answer:
The speeds are 34 mph for the slower car and 68 mph for the faster car.
Step-by-step explanation:
speed = distance/time
Using s for speed, d for distance, and t for time, we have the equation for speed:
s = d/t
Solve for distance, d, by multiplying both sides by t.
d = st
Now we use the given information.
Speed of slower car: s
Speed of faster car: 2s
Distance traveled by faster car: d
Distance traveled by slower car: d - 204
time traveled by faster car = time traveled by slower car = 6
Distance equation for faster car:
d = st
d = 2s * 6
d = 12s <---- equation 1
Distance equation for slower car:
d = st
d - 204 = s * 6
d - 204 = 6s
d = 6s + 204 <----- equation 2
Now, using equations 1 and 2, we have a system of two equations in two unknowns.
d = 12s
d = 6s + 204
Since the first equation is already solved for d, we can use the substitution method. Substitute 12s for d in the second equation:
12s = 6s + 204
6s = 204
s = 34
The speed of the slower car is 34 mph.
The speed of the faster car is
2s = 2(34) = 68
The speed of the faster care is 68 mph.
Two cars started moving simultaneously where one was twice as fast as the other. After setting x as the speed of the slower car, the equations showed the slower car traveled at 34 mph and the faster car at 68 mph, based on being 204 miles apart after 6 hours.
Two cars started moving at the same time and direction where one car's speed was twice as fast as the other. After 6 hours, they were 204 miles apart. To solve for the speed of each car, let's set up an equation where the speed of the slower car is x miles per hour and the faster car is 2x miles per hour.
The distance covered by each car after 6 hours would then be:
Slower car: 6x milesFaster car: 6(2x) = 12x milesSince the cars are 204 miles apart after 6 hours, the equation can be set up as:
12x - 6x = 204
So the distance difference is:
6x = 204
Divide both sides by 6 to find the speed of the slower car:
x = 34
Therefore, the slower car travels at 34 mph and the faster car travels at 68 mph (twice the speed of the slow car).
(4Q) If c < d and x > 1, which of the following must be true?
Use the rule to change the base
[tex]\log_a(b) = \dfrac{\log_c(b)}{\log_c(a)}[/tex]
To express both logarithms in terms of the natural logarithm (for example, any common base would be fine:
[tex]\log_c(x) = \dfrac{\ln(x)}{\ln(c)},\quad \log_d(x) = \dfrac{\ln(x)}{\ln(d)}[/tex]
Since the natural logarithm is an increasing function, we have
[tex]c<d\implies \ln(c)>\ln(d)[/tex]
which implies
[tex]\dfrac{\ln(x)}{\ln(c)}=\log_c(x)<\log_d(x)=\dfrac{\ln(x)}{\ln(d)}[/tex]
Can you help me and please explain...
Explanation:
For each exponent inside the radical, you will divide it over the root index. The root index is the small number to the left and above the radical symbol. So the root index is 6 in this case.
Divide each exponent over 6
3/6 = 1/2 is the final exponent for x
18/6 = 3 is the final exponent for y
which is how we get to x^(1/2)*y^3
--------------------
note: x^(1/2) is the same as the square root of x
[tex]x^{1/2} = \sqrt{x}[/tex]
The more general rule is
[tex]x^{m/n} = \sqrt[n]{x^m}[/tex]
If g(x)=3/4x+2,find g(-12)
Answer:
g(-12) = -7
Step-by-step explanation:
Answer: g(-12)=-7
Step-by-step explanation:
g(x)= 3/4x+2
g(-12)= 3/4(-12)+2
g(-12)=-9+2
g(-12)=-7
(25 Points) What is the area of a triangle that has a base of 3 feet and a height of 6 feet?9 ft?or4.5ft?
Let's start with the formula for the area of a triangle
[tex] \frac{1}{2} bh[/tex]
And for the first one, insert the numbers
[tex] \frac{1}{2} 3 \times 6[/tex]
To make this easier, 3×6=18, 1/2 of 18 is 9, so the answer is 9 square feet. There's all you need to complete the rest, good luck .
If a dice is rolled one time, find the probability of getting a number less than 5
Total Outcomes = {1,2,3,4,5,5}
Less than 5 = {1,2,3,4}
P(less than 5) = 4/6 = 2/3
what is the value of x?
Answer:
2
Step-by-step explanation:
The rule for secants from an external point is that the product of the near and far distance to the intersection with the circle is a constant.
EA·EB = EC·ED
(x+12)·(x+1) = (x+4)·(x+5)
x^2 +13x +12 = x^2 +9x +20 . . . . . . eliminate parentheses
4x = 8 . . . . . . . . . . . . subtract x^2+9x+12 from both sides
x = 2 . . . . . . . . . . . . . divide by 4
The value of x is 2.
Find approximate solution for the equation in the interval -π
tan x= 2 csc x
Answer:
Option a.
-1.144 , 1.144
Step-by-step explanation:
Since we are dealing with trascendental equations, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.
Please, see attached image
We graph both equations and find the intersection between them in the interval from -pi to pi
This will give the solution to the equation
tan(x) = 2* csc(x)
The answer is
x = -1.144
x = 1.144
The question requires solving a trigonometric equation tan x = 2 csc x by using trigonometric identities to express it in terms of sine and cosine and then finding the approximate solutions within the interval -π to π.
Explanation:The student is asking for an approximate solution for a trigonometric equation within a specified interval. The equation given is tan x = 2 csc x. To solve this trigonometric equation, you need to use trigonometric identities to express both sides of the equation in terms of a single trigonometric function and then find the values of x that satisfy the equation within the given interval.
To start with, we can use the identity csc x = 1/sin x and then rewrite the equation as tan x = 2/sin x. Since tan x = sin x/cos x, we can now express the equation purely in terms of sine and cosine:
sin x/cos x = 2/sin x
Multiplying both sides by sin x cos x, we obtain sin2 x = 2 cos x. From here, we can use numerical methods or graphing techniques to find an approximate solution for x within the interval -π to π.
Princess peach has a cell phone plan that charges $50 a month and $0.12 for every minute that she uses the phone beyond what her plan allows. One month she was billed $63.32
she was 111 minutes over what her plan allowed.
Write the sum using summation notation, assuming the suggested pattern continues. 2 - 6 + 18 - 54 + ... summation of two times negative three to the power of n from n equals zero to infinity summation of two times three to the power of n from n equals zero to infinity summation of two times three to the power of the quantity n plus one from n equals zero to infinity summation of two times negative three to the power of the quantity n minus one from n equals zero to infinity
Answer:
It's the first choice.
Step-by-step explanation:
The common ratio is -6/2 = 18/-6 = -3.
2*(-3)^0 = 2*1 = 2.
2*(-3)^1 = -6
2*(-3)^2 = 18
2*(-3)^3 = -54.
So in summation notation is
∞
∑ 2(-3)^n
n=0
The sum using summation notation is given by:
Summation of two times negative three to the power of n from n equals zero to infinity.
i.e. numerically it is given by:
[tex]\sum_{n=0}^{\infty} 2(-3)^n[/tex]
Step-by-step explanation:The alternating series is given by:
[tex]2-6+18-54+........[/tex]
The series could also be written in the form:
[tex]=2+(2\times (-3))+(2\times (-3)\times (-3))+(2\times (-3)\times (-3)\times (-3))+....\\\\i.e.\\\\=2\times (-3)^0+2\times (-3)^1+2\times (-3)^2+2\times (-3)^3+.....\\\\i.e.\\\\=\sum_{n=0}^{\infty} 2(-3)^n[/tex]
For the function F(x)= [tex]\frac{1}{x+1}[/tex], which of these could be a value of F(x) when x is close to -1?
A. -1
B. -10,000
C. 0.01
D. -0.01
Answer:
C
Step-by-step explanation:
Answer:
it is B
Step-by-step explanation:
14.3 rounded to the nearest one
Answer:
14
Step-by-step explanation:
To round 14.3 to the nearest one, we round down because the digit to the right of the decimal point is less than 5. Therefore, the answer is 14.
Explanation:To round 14.3 to the nearest one, we look at the digit to the right of the decimal point, which is 3. Since 3 is less than 5, we round down. Therefore, 14.3 rounded to the nearest one is 14.
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DESCRIBE HOW TO USE THE SCALE FACTOR TO DILATE A POLYGON ON THE COORDINATE PLANE.
Answer:
Multiply the original points by the fraction or ratio of the dilution needed
Step-by-step explanation:
I'm less confident in this answer, but Scale factor is the ration between two geometric figures, like 1:2 is for every one unit on one figure is two on the other, so to dilute a figure, you multiply the points by 1/2 to make a smaller figure, or by 2 to get a bigger one. Plot the given answers and you have diluted :) Hope this helps!
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y=csc (x) -9
Answer:
The answer is vertical translation down 9 units ⇒ answer (d)
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) - k
* Lets study the problem
- The basic function is y = csc(x)
∵ y = csc(x) - 9
- That means the function translated vertically 9 units down
* Vertical translation 9 units down
* Look to the graph
-The red graph is y = csc(x)
- The green graph is y = csc(x) - 9
A certain four-cylinder combination lock has 55 numbers on it. to open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a four-number lock combination has been affected. repetitions are allowed, and any of the 55 numbers can be used at each step to form the combination. (a) how many different lock combinations are there
Answer:
9,150,625.
Step-by-step explanation:
Any one of the 55 numbers can be combined with any one of the 55 in the other cylinders.
So the number of different combinations are 55^4
= 9,150,625.
The total number of different combinations that can be made with a four-cylinder combination lock that has 55 numbers on each cylinder is 9,150,625. This is calculated using the multiplication principle of counting.
Explanation:This question involves the principle of counting or combinatorics in mathematics. Specifically, it relates to the multiplication principle, which says that if event A can occur in m ways, and after it happens, event B can occur in n independent ways, then the total number of ways in which both events can occur is calculated as m times n.
In the case of the four-cylinder combination lock with 55 possible numbers for each cylinder, there are 55 ways to choose a number for the first cylinder. Since repetitions are allowed and each choice is independent, there are also 55 ways to choose a number for the second cylinder, 55 ways for the third cylinder, and 55 ways for the fourth cylinder. Using the multiplication principle, we can find the total number of possible lock combinations by calculating 55 * 55 * 55 * 55 = 9,150,625 possible combinations.
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Please help me out!!!!!
(132°-x)+(6x-12°) = 180°(Co-interior Angles)
132°-12°-x+6x = 180°
120° + 5x = 180°
5x = 180° - 120°
5x = 60°
x = 12°
(132°-x)+(6y+18°) = 180°(Co-interior Angles)
132°-x+6y+18°=180°
132°-12°+18°+6y=180°
138°+6y=180°
6y=180°-138°
6y=42°
y = 7°
HOPE THIS WILL HELP YOU
Jenna brought in $25,000 to her startup firm at the beginning of the year. During the year, she withdrew $2,500 for her personal expenses. The business earned $10,000 at the end of the accounting period after paying off all its expenses. What is the value of Jenna’s capital account at the end of the accounting year?
A. $25,000
B. $22,500
C. $35,000
D. $32,500
➷ 25,000 - 2500 = 22500
22500 + 10,000 = 32,500
The correct answer would be option D. $32,500
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
Step-by-step explanation:
I would have to go with D. The 25,000 is what you start with minus the 2,500 she withdrew which would leave her at 22,500. She then receives 10,000 for the business leaving her with 32,500