Answer:
It's prime:)
Step-by-step explanation:
Which set of ordered pairs represents y as a function of x?
{(5, 4), (2, 3), (1, 1), (2, 4)}
{(-9, 2), (0, 6), (1, -2), (0, 6)}
{(3, 2), (-4, -2), (3, 1), (-4, 1)}
{(-1, 0), (4, 3), (-7, -3), (-1, -8)}
What is the absolute value of -5.75 ?
Given D = 5, E = 10 and F = 4, evaluate
D*E/F
...?
What is the probability of getting 3 tails when tossing a coin 4 times?
The probability of getting 3 tails, when tossing a coin 4 times is 25%
To find the probability of getting 3 tails when tossing a coin 4 times, we can use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
- P(X = k) is the probability of getting exactly k successes (in this case, 3 tails).
- n is the number of trials (coin tosses).
- k is the number of successes we are interested in (in this case, 3 tails).
- p is the probability of success on each trial (in this case, the probability of getting tails).
- [tex]\( (1 - p) \)[/tex] is the probability of failure on each trial (in this case, the probability of getting heads).
Since the coin is fair, the probability of getting tails p is [tex]\( \frac{1}{2} \)[/tex], and the probability of getting heads [tex](\( 1 - p \))[/tex] is also [tex]\( \frac{1}{2} \)[/tex].
Substituting these values into the formula:
[tex]\[ P(X = 3) = \binom{4}{3} \times \left(\frac{1}{2}\right)^3 \times \left(1 - \frac{1}{2}\right)^{4 - 3} \][/tex]
[tex]\[ P(X = 3) = \binom{4}{3} \times \left(\frac{1}{2}\right)^3 \times \left(\frac{1}{2}\right)^1 \][/tex]
[tex]\[ P(X = 3) = 4 \times \left(\frac{1}{8}\right) \times \left(\frac{1}{2}\right) \][/tex]
[tex]\[ P(X = 3) = \frac{4}{16} \][/tex]
[tex]\[ P(X = 3) = \frac{1}{4} \][/tex]
To express the probability as a percentage, we multiply by 100:
[tex]\[ P(X = 3) = \frac{1}{4} \times 100\% = 25\% \][/tex]
Therefore, the probability of getting 3 tails when tossing a coin 4 times is 25%.
Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval: f(x) = cot(x), (0,pi)
To show that f(x) = cot(x) is strictly monotonic on the interval (0,pi), we need to show that the derivative of f(x) is either strictly positive or strictly negative on that interval.
Explanation:To show that f(x) = cot(x) is strictly monotonic on the interval (0,pi), we need to show that the derivative of f(x) is either strictly positive or strictly negative on that interval.
The derivative of f(x) can be found using the chain rule as follows:
Find the derivative of cot(x): d(cot(x))/dx = -csc^2(x)Since f(x) = cot(x), the derivative of f(x) is -csc^2(x).Now, let's consider the interval (0,pi). The function f(x) = cot(x) is defined on this interval, and its derivative -csc^2(x) is strictly negative for all x in (0,pi). Therefore, f(x) is strictly decreasing on the interval (0,pi), which means it is strictly monotonic.
Since f(x) is strictly monotonic on the interval (0,pi), it has an inverse function on that interval. The inverse function of f(x) is denoted as f^{-1}(x).
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p² 13p=-30 menentukan nilai p
A "bit" is 1/8 of a dollar. How many bits are in a dollar.
There are 8 bits in a dollar.
We have,
If a "bit" is defined as 1/8 of a dollar, we can calculate the number of bits in a dollar by dividing the dollar amount by the value of a bit.
1 dollar / (1/8) bit = 1 dollar * (8/1) bit
Simplifying the equation:
1 dollar * 8 bits = 8 bits
Therefore,
There are 8 bits in a dollar.
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Assuming x > 0, which of these expressions is equivalent to 11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third? ?
5 x times the square root of 104 x
20 times the square root of 290 x to the sixth
20 x times the square root of 290 x
104 x times the square root of 5 x
I do not understand how to do this problem please help!
6. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.
The first month they made 1200 and the second month they made 1500...
graph a line using the slope-intercept form:
Manipulate the equation into slope-intercept form, y = mx + b.
Identify and plot the y-intercept of the line. Remember, the y-intercept is b. Don't forget: The sign goes with the number.
Identify and use the slope of the line to find a second point. Remember, the slope is m. Don't forget: Starting at the y-intercept, the numerator tells you the rise (count up if positive and down if negative), the denominator tells you the run (count right.)
Draw a straight line through the two points to complete the graph.
Linear Functions:
A linear function is a function that is defined by a linear equation.
To write a linear function with function notation, first write it in slope-intercept form, and then replace y with f(x).
The graph of a linear function is all points (x, f(x)), where x is in the domain of the function.
what are the 12 numbers of pi
Sandra rode her bike 5 times as many miles as Barbara. If b, the distance Barbara rode, equals 3.4 miles, what is the correct expression and distance Sandra rode?
a) b+5; when b=3.4, the distance Sandra rode is 17 miles.
b) 5b; when b=3.4, the distance Sandra rode is 17 miles.
c) 5b; when b=3.4, the distance Sandra rode is 8.4 miles.
d) b+5; when b=3.4, the distance Sandra rode is 8.4 miles.
Answer:
Option b is correct
5b; when b = 3.4 miles , the distance Sandra rode is 17 miles
Step-by-step explanation:
Here, b represents the distance Barbara rode.
As per the statement:
Sandra rode her bike 5 times as many miles as Barbara.
⇒[tex]\text{Distance Sandra rode} = 5b[/tex] miles ....[1]
It is also given that:
the distance Barbara rode, equals 3.4 miles
⇒[tex]b = 3.4[/tex] miles
Substitute in [1] we have;
[tex]\text{Distance Sandra rode} = 5(3.4)=17[/tex] miles
Therefore, the correct expression and distance Sandra rode is
5b ; when b = 3.4 miles , the distance Sandra rode is 17 miles
2. Construct a line that is perpendicular to line m and that passes through point P.
(Apologies since this is extremely late; hopefully this helps future people who need help with this question.)
Answer:
The image below would be the correct construction :)
A computer virus is eating disk space. during the first day it eats 1/2 of the disk. during the second day, it eats 1/3 the remaining disk space. the third day it eats 1/4 of what still remains and the fourth day it eats 1/5 of what is left. what fraction of the original disk space remains intact?
the lines below are parallel. if the slope of the green line is -3, what is the slope of the red line
why do bees have sticky hair
Answer:
From the honey, and pollen
Step-by-step explanation:
What is the factor of 40?
in which area of the brain does mathematical processing occur?
Mathematical processing involves various cognitive processes and can engage multiple areas of the brain. However, certain brain regions are commonly associated with mathematical processing such as Parietal Cortex
In which area of the brain does mathematical processing occur?Parietal Cortex: The parietal cortex, specifically the intraparietal sulcus, plays a crucial role in numerical processing, spatial processing, and quantity representation.
Frontal Cortex: The frontal cortex, particularly the dorsolateral prefrontal cortex, is involved in problem-solving, logical reasoning, and working memory, which are essential for mathematical processing.
Angular Gyrus: The angular gyrus, located in the parietal lobe, is involved in mathematical thinking, number processing, and mathematical reasoning.
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What is 5 3/20 as a decimal?
integrate (sqrt((x-1)/x^5)) using substitution (no trig substitution) ...?
You roll 2 dice. You can use a tree diagram to calculate the probability that the sum of the dice is an even number. true or false? ...?
Answer correctly for brainliest and also get a thanks ! Don't answer if you don't know it please !
HELP PLEASE?! I'm very bad at math and I need help with this question please.
What is the value of y in the equation 6 + y = −3?
A.) −9
B.) −3
C.) 3
D.) 9
Round 0.978 to the nearest tenth
There are $3.90 worth of nickles and quarters in a piggy bank. There are 6 more quarters than nickels.
How many of each coin are in the piggy bank?
Enter your answers in the boxes.
_____ nickels and ____ quarters
For this case, the first thing we must do is define variables.
We have then:
x: number of nickles
y: number of quarters
We now write the system of equations.
We have then:
[tex] 0.05x + 0.25y = 3.90
y = x + 6
[/tex]
Solving the system of equations graphically we have:
[tex] x = 8
y = 14
[/tex]
Answer:
8 nickels and 14 quarters
Note: see attached image for the graphic solution.
Answer: There are 8 nickels and 14 quarters.
Explanation:
Since we have given that
there are $3.90 worth of nickles and quarters in a piggy bank.
Let the number of nickles be x
Let the number of quarters be x+6
As we know that
[tex]1\ nickle=0.05\ dollars\\\\and\\\\\ 1\ quarter=0.25\ dollars[/tex]
According to question,
[tex]0.05x+0.25(x+6)=3.90\\\\0.05x+0.25x+1.5=3.90\\\\0.3x=3.90-1.5\\\\0.3x=2.4\\\\x=\frac{2.4}{0.3}=8\\\\and \\\\x+6=8+6=14[/tex]
Hence, there are 8 nickels and 14 quarters.
(This is my little sister's homework, she needs help!)
Katrina is 69.75 inches tall. Her best friend, Allison, is 64.85 inches in height. How many inches taller is Katrina than Allison?
A) 4.10
B) 4.90
C) 5.10
D) 5.90
Answer: B) 4.90
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Katrina: 69.75 inches tall Allison: 64.85 inches tall.Since Katrina is taller than Allison, to calculate the how many inches taller is Katrina than Allison, we have to subtract Allison’s height to Katrina’s height:
Mathematically speaking:
69.75 -64.85 = 4.9 inches.
A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.
A. Self interest
B. Correlation and casualty
C. Loaded questions
D. Nonresponse
Im stuck between self interest or Nonresponse
Nonresponse. The others might occur, but with this degree of nonresponse inferences to the entire population cannot be made.
Which lines are parallel if m4 = m5? Justify your answer.
Answer:
r and s are parellel
Step-by-step explanation:
The correct answer is that lines 4 and 5 are parallel if [tex]\( m_4 = m_5 \).[/tex]
To justify this answer, we must understand the concept of slope in the context of lines in a plane. The slope of a line, denoted by m is a measure of its steepness and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. Mathematically, if two points on a line have coordinates [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \),[/tex] then the slope m is given by: [tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex] For two lines to be parallel, they must have the same slope. This is because parallel lines have the same steepness and never intersect. Therefore, if the slope of line 4, [tex]\( m_4 \)[/tex], is equal to the slope of line 5, [tex]\( m_5 \)[/tex], then lines 4 and 5 are parallel. In mathematical notation, if [tex]\( m_4 = m_5 \),[/tex] then line 4 and line 5 are parallel, which can be written as: [tex]\[ m_4 = m_5 \Rightarrow \text{Line 4} \parallel \text{Line 5} \][/tex] This conclusion is based on the fundamental properties of slopes and parallel lines in Euclidean geometry. If the slopes of two lines are equal, it means that they rise and run at the same rate, and thus, they will maintain a constant distance from each other, never intersecting, which is the definition of parallel lines.
Which power has a value of 1?
Choose all the correct answers.
1^4
2^3
3^2
4^1
5^0
if you were to place $2,500 in a savings account that pays 5% interest compounded continuously, how much money will you have after 10 years? assume you make no other deposits or withdrawals.
Write the area as a product and as a sum.
The area of the square as a product is a multiplication of the two sides.
What is the area of the square?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
The square is a quadrilateral having all the sides to be equal and all the angles at 90 degrees. The area of the square will be calculated as,
Area = side x side
Therefore, the area of the square as a product is a multiplication of the two sides.
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