Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
In probability theory, "AND" means multiplication and "OR" means "addition".
We can find the 2 probabilities separately and multiply them (as there is "AND")
So,
Probability number rolled greater than 4 = number of numbers that are greater than 4/total number of numbers
There are 2 numbers greater than 4 in a die (5 & 6) and total 6 numbers, so
P(number greater than 4) = 2/6
Now,
Probability that tails come up in coin toss = 1/2 (there are 1 tail and 1 head in a coin)
Hence,
P(number greater than 4 and tails in coin) = 2/6 * 1/2 = 1/6
To find the probability of rolling a number greater than 4 on a die and getting tails on a coin toss, you multiply the individual probabilities: (1/3) for the die roll and (1/2) for the coin toss, resulting in a combined probability of 1/6.
Explanation:The question is asking to find the probability of a specific combined event involving the roll of a number cube (a six-sided die) and the flip of a coin. To solve this problem, we need to calculate the probability that the number cube shows a number greater than 4 (which can be either a 5 or 6) and that the coin toss results in tails.
First, we find the probability of rolling a number greater than 4 on a six-sided die. There are 2 favorable outcomes (5 or 6) out of 6 possible outcomes, so the probability of this event is 2/6, which simplifies to 1/3.
Next, we calculate the probability of getting tails on a coin flip. Since a coin has two sides, and only one side is tails, the probability is 1/2.
To find the combined probability of both events happening together, we multiply the probabilities of the individual events:
Combined Probability = Probability (Number > 4) × Probability (Tails) = (1/3) × (1/2)
Therefore, the combined probability is:
(1/3) × (1/2) = 1/6
Which models selecting a combination of 3 objects taken from a group of 8 items?
Answer:
see attached
Step-by-step explanation:
nCk models k objects taken from a group of n.
nCk = n!/(k!·(n-k)!)
Fill in n=8 and k=3 to get ...
8C3 = 8!/(3!·5!)
Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.
[tex] {2}x^{2} + 8 {y}^{2} = 16 \\ \\ 1. \: {2x}^{2} = - 8 {y}^{2} + 16 \\ 2. \: {x}^{2} = - 4y^{2} + 8 \\ 3. \: x = \sqrt{ - 4y^{2} + 8} \\ x = - \sqrt{ - 4y^{2} + 8 } \\ \\ answer \\ x = \sqrt{ - 4y^{2} + 8 } \\ x = - \sqrt{ - 4y^{2} + 8} [/tex]
Answer:
Step-by-step explanation:
2x² + 8y² = 16
divide both sides of equation by the constant
2x²/16 + 8y²/16 = 16/16
x²/8 + y²/2 = 1
x² has a larger denominator than y², so the ellipse is horizontal.
General equation for a horizontal ellipse:
(x-h)²/a² + (y-k)²/b² = 1
with
a² ≥ b²
center (h,k)
vertices (h±a, k)
co-vertices (h, k±b)
foci (h±c, k), c² = a²-b²
Plug in your equation, x²/8 + y²/2 = 1.
(x-0)²/(2√2)² + (y-0)²/(√2)² = 1
h = k = 0
a = 2√2
b = √2
c² = a²-b² = 6
c = √6
center (0,0)
vertices (0±2√2,0) = (-2√2, 0) and (2√2, 0)
co-vertices (0, 0±√2) = (0, -√2) and (0, √2)
foci (0±√6, 0) = (-√6, 0) and (√6, 0)
Noah scored 20 points in a game Maya score was 30 points the mean score for Noah Maya and Claire was 40 points what was Claire score explain or show your reasoning
Answer:
70 points
Step-by-step explanation:
Let n represent Noah's score, m as Maya's score, and c as Claire's score.
n=20
m=30
c=?
Let's try make an equation for this problem. The mean score for the three of them is 40, so the following equation is possible:
n+m+c/3=40
Now replace the variable with their values and continue to simplify.
20+30+c/3=40
Multiply both sides by 3.
20+30+c=120
Add 20 and 30 together.
50+c=120
Subtract 50 from 120 to find c.
c=70
Claire's score is 70 points.
Final answer:
To find Claire's score, calculate the total points based on the mean score and then subtract the scores of Noah and Maya. This calculation reveals that Claire's score was 70 points.
Explanation:
The question asks for the score of Claire based on the mean score of Noah, Maya, and Claire combined. Noah scored 20 points, Maya scored 30 points, and the mean score for all three players was 40 points.
To find Claire's score, we first calculate the total points scored by all three. The mean score is the total points divided by the number of scores, which in this case is 3. Therefore, we multiply the mean score (40 points) by 3 to get the total points.
Mean score × number of players = Total points
40 × 3 = 120 points
Next, we subtract Noah's and Maya's scores from the total to find Claire's score.
Total points - Noah's score - Maya's score = Claire's score
120 points - 20 points - 30 points = 70 points
Therefore, Claire's score was 70 points.
Which ordered pair is on the graph of the function y = 8x - 1 ? A (2, 15) B (8, –1) C (8, 1) D (15, 2)
Answer:
A(2,15)
Step-by-step explanation:
Plug it in on the desmos calculator!!! Put the equation first and then add the points and see which one touches the line.
The ordered pair which is on the graph of the given function is (2, 15).
What is a function?It gives the relationship between each element of a set to another non-empty set.It is one of the most important part of the calculus.It is a rule, that gives unique output for the any input we provide.
Given: Function
y = 8x - 1
Now, among the given ordered pair (x, y), the pair that satisfies the given function is the point on the graph.
Option (A): (2, 15)
⇒ y = 8x - 1
⇒ 15 = 8(2) - 1
⇒ 15 = 16 - 1
⇒ 15 = 15
Hence, this ordered pair is on the graph of the given function.
This option is correct.
Option (B): (8, -1)
⇒ y = 8x - 1
⇒ -1 = 8(8) - 1
⇒ -1 = 64 - 1
⇒ -1 ≠ 63
Hence, this ordered pair is not on the graph of the given function.
This option is incorrect.
Option (C): (8, 1)
⇒ y = 8x - 1
⇒ 1 = 8(8) - 1
⇒ 1 = 64 - 1
⇒ 1 ≠ 63
Hence, this ordered pair is not on the graph of the given function.
This option is incorrect.
Option (D): (15, 2)
⇒ y = 8x - 1
⇒ 2 = 8(15) - 1
⇒ 2 = 120 - 1
⇒ 2 ≠ 119
Hence, this ordered pair is not on the graph of the given function.
This option is incorrect.
Therefore, (2, 15) is the only ordered pair on the graph of the given function.
Hence, Option (A) is correct.
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Willie and Emily each purchase one raffle ticket. If a total of seven raffle tickets are sold, what is the probability that Willie wins the grand prize and Emily wins the second prize?
1/42
First, find the probability of Willie winning the grand prize. He has 1 ticket out of the 7 total tickets, so the probability is 1/7.
Now, find the probability of Emily winning the second prize. After the grand prize winner has been announced, there are only 6 tickets left. Emily has 1, so the probability is 1/6.
Finally, multiply the two probabilities together to find the probability that they will both happen together. To multiply fractions, multiply the numerators together and multiply the denominators together. This leaves us with (1 * 1) / (7 * 6), which is easy to simplify to 1/42, which is the final probability.
Answer:
1/42
Step-by-step explanation:
Veata is buying a new video game for $45. She has $150 in her checking account and $5 in her wallet. Which is the most reasonable way for Veata to pay for the game?
2 bill of 20 and 3 of 1
Answer:
Debit card
Step-by-step explanation:
A line passes through the point (-8,9) and has a slope of 3/4.
Help pls
Answer:
I have no idea what you're asking for but I got y= -3/4x+3 as the equation for the line.
ANSWER
[tex]y = \frac{3}{4}x + 15[/tex]
EXPLANATION
The given line passes through the point
(-8,9) and has a slope be of
[tex]m = \frac{3}{4} [/tex]
We obtain the equation of this line using
[tex]y-y_1=m(x-x_1)[/tex]
We plug in the values into the formula to get,
[tex]y - 9 = \frac{3}{4} (x - - 8)[/tex]
[tex]y = \frac{3}{4} (x + 8) + 9[/tex]
Expand the parenthesis to get:
[tex]y = \frac{3}{4}x + 6 + 9[/tex]
[tex]y = \frac{3}{4}x + 15[/tex]
A punch recipe calls for of a pint of fruit juice for each pint of soda. The ratio of soda to fruit juice in the punch is____ to _____
Answer:
Step-by-step explanation:
If the ratio is soda to juice, set up the proportion like this:
[tex]\frac{s}{j}[/tex]
and everything related to soda goes on top and everything related to fruit juice goes on the bottom. You just want the ratio, so it is best stated as follows:
[tex]\frac{soda}{juice}[/tex]
just to be clear on what s and j mean!
You could use this proportion to solve problems with one unknown.
Find the circumference and the area of a circle with diameter 6 cm Use the value 3.14 for pie , and do not round your answers. Be sure to include the correct units in your answers.
The circumference of the circle is 18.84 cm and the area is 28.26 cm².
Explanation:To find the circumference of a circle, we use the formula C = πd, where d is the diameter. In this case, the diameter is 6 cm, so the circumference is:
C = 3.14 × 6 = 18.84 cm
To find the area of a circle, we use the formula A = πr², where r is the radius. Since the radius is half the diameter, the radius in this case is 6/2 = 3 cm. So the area is:
A = 3.14 × 3² = 28.26 cm²
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Which expression could be used to determine the cost of a 50$ video game after a 20 percent discount?
Answer:
50x.2 is the correct expression. :)
Step-by-step explanation:
50x.2 =10
So you would get a $10 discount off of a $50 video game.
Hope this helps! If you don't mind, please mark as brainliest! Thx :)
Answer:
0.80($50)
Step-by-step explanation:
1.00 times the $50 cost is the initial price of the video.
(1.00 - 0.20) times $50 is the discounted price.
0.80($50) is the desired expression.
Next time, please be sure to share the answer choices. Thanks.
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 6)2
Answer:
Translate 6 units to the right.
Step-by-step explanation:
The y = x^2 function is a quadratic function with vertex at (0,0). It can be transformed to have a vertex of (6,0) like the function y = (x-6)^2 by shifting it 6 units to the right. It is now the graph of y = (x-6)^2.
The equation y = (x - 6)² represents a transformation of the graph y = x², specifically a horizontal shift 6 units to the right on the 2-dimensional (x-y) plane.
Explanation:To transform the graph of y = x² to the graph of the equation y = (x – 6)², you must understand that these both take the form of a quadratic equation, producing a parabola when graphed. The difference between these two equations is indicated by the term '– 6' in the x of the second equation which corresponds to a horizontal shift in the graph.
In the equation y = (x – 6)², this specifically means that the graph of y = x² is shifted 6 units to the right. This shift doesn't change the shape of the graph, it only moves the location in the 2-dimensional (x-y) plane. So, when you plot data pairs for both y = x² and y = (x – 6)², the second graph would be identical to the first, just moved 6 units to the right.
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The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. what is the expected number of students who had scores greater than 60?
Answer:
23 students expected to have scores greater than 60.
Step-by-step explanation:
60 is 2 standard deviations above the mean. This translates into a z-score of +2. According to a table of z-scores, the area under the standard normal curve to the left of z = 2 is 0.9772; that to the right of z = 2 is 1.0000 - 0.9772, or 0.0228. This 0.0228 represents the probability that a given score is greater than 60.
This fraction (0.0228) of 1000 students comes out to 23 (rounded up from 22.75).
Final answer:
To find the expected number of students who had scores greater than 60 on a standardized test, we can calculate the probability using the properties of the normal distribution. The expected number is approximately 23 students.
Explanation:
To find the expected number of students who had scores greater than 60, we can use the properties of the normal distribution. We know that the mean score is 50 and the standard deviation is 5. We want to find the probability of getting a score greater than 60. First, we need to calculate the z-score for a score of 60 using the formula:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (60 - 50) / 5 = 2
Next, we use a z-table or calculator to find the area to the right of z = 2. This represents the probability of getting a score greater than 60. A z-table or calculator will give us a value of approximately 0.0228.
Finally, we multiply this probability by the total number of students (1000) to find the expected number of students who had scores greater than 60:
Expected number = probability * total number of students = 0.0228 * 1000 = 22.8
Therefore, we can expect approximately 23 students to have scores greater than 60.
Assume that there are 2 trials.
X = 2 where X represents the number of successes.
Which probability matches the probability histogram?
Round the answer to one decimal place.
A. P(success) = 0.2
B. P(success) = 0.4
C. P(success) = 0.6
D. P(success) = 0.8
Step-by-step explanation:
According to the graph, the probability of 2 successes is 0.36, which rounds to 0.4.
The number of success is X = 2, the P(success) = 0.4 according to the given histogram.
What is probability?It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.
Number of successes is represented by X (given)
X = 2
The number of successes are plotted on the X - axis of the histogram
So according to the graph , P(success at X = 2) = 0.36
Rounding off the probability to 0.4
Hence, the P(success at X = 2) = 0.4 according to the histogram.
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The functions f(x) and g(x) in the graph below are most likely which two equations?
Answer:
It's C.
Step-by-step explanation:
The red curve pass through the point (0, 1) and also y = 2 when x = 1 , so this is y = 2^x. The inverse is the reflection of f(x) in x = y so the blue curve is y = log2 x.
The two equation shown in the graph are y = e^x and y = lnx.
What is a function?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable).
The red line shown in the graph represents y = e^x
The graph of y = e^x will never have a negative value of y, as the value of x increases the value of y will keep on increasing till ∞ . The value of y at x = 0 is 1, so the graph will cross the y-axis at (0,1).
The blue line shown in the graph represents y = lnx
The value of y will be negative when the value of x lies between 0 and 1 after that the value of y will keep on increasing and the point (1,0) satisfies the equation so it will cross the X - axis at (1,0)
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Identify the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in. HELP PLEASE!!
Answer:
[tex]\boxed{\text{L = 90 in}^{2};\text{ S = 115 in}^{2}}[/tex]
Step-by-step explanation:
Data:
s = 5 in
l = 9 in
1. Lateral surface area
The general formula for the lateral surface area L of a regular pyramid is
L =½pl
where p represents the perimeter of the base and l the slant height.
The base is a square, so
p = 4 × 5 = 20 in
L = ½pl = ½ × 20 × 9 = [tex]\boxed{\text{90 in}^{2}}[/tex]
2. Total surface area
Total surface area = lateral surface area + area of base
S = L + B
B = b² = 5² = 25 in²
S = 90 + 25 = [tex]\boxed{\text{115 in}^{2}}[/tex]
50 POINTS!!! Which of the following expressions are equivalent to 2/x^8-y^8
Answer:
it's A&B
Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{\bold{A.} } \ \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}} \\\\\\ \large \boxed{\mathrm{\bold{B.} } \ \frac{2}{(x^4)^2 -(y^4)^2 } }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2}{x^8-y^8 }[/tex]
Factor the denominator.
[tex]\displaystyle \frac{2}{(x^4)^2 -(y^4)^2 }[/tex]
[tex]\displaystyle \frac{2}{(x^4-y^4)^2 }[/tex]
[tex]\displaystyle \frac{2}{(x^4-y^4)(x^4 +y^4) }[/tex]
Split the fraction into two fractions.
[tex]\displaystyle \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}[/tex]
Please answer I’ll rate brainlyest
Answer:
The third choice is correct
Step-by-step explanation:
The given expression is
[tex]2^n-1[/tex]
when n=7, we substitute into the formula to obtain;
[tex]2^7-1[/tex]
Note that;
[tex]2^7=2\times 2\times 2\times 2\times 2\times 2\times 2=128[/tex]
[tex]2^7-1=128-1=127[/tex]
The third choice is correct
The graph of this function is "M" shaped? f(x)=−3x4−7x3+6x2+5 Question 28 options: True False
the answer of this question is 8 bro..........................................................
please help me with this geometry question
image attached
Answer:
32
Step-by-step explanation:
Since AP and BP are tangents from the same point, they are equal. So 2x+12=4x-8. So solving for x, we get 2x=20. So x=10. Plugging that in, we get 20+12=32. So the answer is 32.
A writer earns 8% of total sales dollars as a commission. If 2000 copies of his book are sold at $14.95 each, how much commission does he earn? $119.60 $1.20 $2,392 $160
Answer:
C $2392
Step-by-step explanation:
The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?
Show all work
Answer:
possible values of 4th term is 80 & - 80
Step-by-step explanation:
The general term of a geometric series is given by
[tex]a(n)=ar^{n-1}[/tex]
Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term
Given, 5th term is 40, we can write:[tex]ar^{5-1}=40\\ar^4=40[/tex]
Given, 7th term is 10, we can write:[tex]ar^{7-1}=10\\ar^6=10[/tex]
We can solve for a in the first equation as:
[tex]ar^4=40\\a=\frac{40}{r^4}[/tex]
Now we can plug this into a of the 2nd equation:
[tex]ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}[/tex]
Let's solve for a:
[tex]a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640[/tex]
Now, using the general formula of a term, we know that 4th term is:
4th term = ar^3
Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:
[tex]ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80[/tex]
possible values of 4th term is 80 & - 80
What are the values of a, b, and c in the quadratic equation 0 = 5x 4x2 2? a = 5, b = 4, c = 2 a = 5, b = 4, c = 2 a = 4, b = 5, c = 2 a = 4, b = 5, c = 2
Answer:
d. 4,-5,-2
Step-by-step explanation:
The values of {a}, {b} and {c} in the quadratic equation are a = 4, b = 5, c = 2 respectively.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c.
Given is the quadratic equation as follows -
5x + 4x² + 2 = 0
The given quadratic equation is -
5x + 4x² + 2 = 0
4x² + 5x + 2 = 0
A quadratic equation is of the form -
ax² + bx + c
So, on comparing, we get -
a = 4, b = 5, c = 2
Therefore, the values of {a}, {b} and {c} in the quadratic equation are a = 4, b = 5, c = 2 respectively.
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What is the solution to the equation below?
3log4x=log432+log42
X=-8
X=-4
X=4
X=8
Answer:
[tex]\large\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]3\log_4x=\log_432+\log_42\qquad\text{use}\ \log_ab^c=c\log_ab\ \text{and}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_4x^3=\log_4(32\cdot2)\\\\\log_4x^3=\log_464\iff x^3=64\to x=\sqrt[3]{64}\\\\x=4[/tex]
Answer: 4
Step-by-step explanation: Its on EDG
Classify each of the angel (example. right, acute, etc). Then identify each angle as interior or exterior
interior is the angle
Answer:
1 = 139 degrees
Step-by-step explanation:
You can use the corresponding angles theorem
What is the difference between 4Σn=1, 2n+1 and 4Σi=1, (2i+1)?
a. 0
b. 3
c. 4
d. 7
Answer:
0
Step-by-step explanation:
Each expression is a way to write the sum ...
3 + 5 + 7 + 9
That sum in each case is 24, so the difference is 24-24 = 0.
Answer:
it is not 0 !!!
Step-by-step explanation:
got it wrong bc of top answer
Please help with this....
Answer:
i think its 20
Step-by-step explanation:
Answer:
x = 12.8 cm
Step-by-step explanation:
Using the sine ratio in the right triangle to solve for x
sin70° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{x}[/tex]
Multiply both sides by x
x × sin70° = 12 ( divide both sides by sin70° )
x = [tex]\frac{12}{sin70}[/tex] ≈ 12.8
A box contains 17 nickels, 11 dimes and 19 pennies. if a coin is picked at random from the box, what is the average value of the draw in dollars?
Answer: its not possible
Step-by-step explanation: there are 17 nickels, 11 dimes and 19 pennies, NO dollars
The longest river in the UK is the river Severn which has a length of 24 cm on a map. If the map is drawn at a scale of 1:1,500,000, then how many kilometers is the river actually?
Answer:
360 km
Step-by-step explanation:
The length on the ground will be ...
(24·10^-2 m)·(1.5·10^6) = 36·10^4 m = 360·10^3 m = 360 km
Answer:
The length of river is 360km
Explanation:
Length on the map of Severn river = 24cm
Scale on the map = x:y axis
=1:1500000
Where y is the length
Hence 1 cm= 15 km
Therefore
Length of the river
=24[tex]\times[/tex]15
=360 km
Hence the length of river is 360 km
Which of the following is not a characteristic of the normal probability distribution? Select one: a. Symmetry b. The total area under the curve is always equal to 1. c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean d. The mean is equal to the median, which is also equal to the mode
Answer:
c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean
Step-by-step explanation:
In a normal distribution, the shape is bell-shaped; this means it is symmetric.
The area under a normal distribution will always be equal to 1.
The mean, median and mode in a normal distribution are equal.
However, the data assumes values within 1 standard deviation above or below the mean 68% of the time, not 99.72% of the time. This is the characteristic that doesn't fit.
The statement which is not a characteristic of the normal distribution is:
c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.The area under the normal curve is always equal to 1.The mean, the mode and median are equal.The Empirical Rule states that 68% of the measures are within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3, thus, statement c is false.For more on the normal distribution, you can check https://brainly.com/question/13011828
A. 22.59
B. 14.34
C. 20.48
D. 10.70
Answer:
B. 14.34
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between the side opposite the angle of interest and the hypotenuse:
Sin = Opposite/Hypotenuse
For the given triangle, this means ...
sin(35°) = b/25
b = 25·sin(35°)
b ≈ 14.34