3/5 = 0.6 or 3/5 as a fraction in its simplest form. 7/8 = 0.875 or 7/8 as a fraction in its simplest form. 2/3 = 0.666... or 2/3 as a fraction in its simplest form. 5/6 = 0.833... or 5/6 as a fraction in its simplest form. 1/4 = 0.25 or 1/4 as a fraction in its simplest form
To rename a fraction as a whole number or mixed number, we divide the numerator by the denominator. If the result is a whole number, then the fraction is renamed as that whole number. If the result is a mixed number, we take the integer part as the whole number and the fractional part as the numerator of the proper fraction. For example, 7/8 can be renamed as a mixed number by dividing 7 by 8, which gives 0.875. The integer part is 0, so we take the fractional part 0.875 as the numerator of the proper fraction. We can simplify it to 7/8. Similarly, we can rename the other fractions in the same way.
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Complete question:
Rename each fraction as a whole number or mixed number
3/5
7/8
2/3
5/6
1/4
write 1 and 1/3 as an improper fraction
Answer:
4/3
Step-by-step explanation:
to change a mixed number to an improper fraction, you have to multiply the denominator by the whole number and add the numerator to the product. This is your numerator. The denominator stays the same.
Thus,
Numerator = 3 x 1 +1 = 4
Denominator = 3
Fraction = 4/3
Hope this helps.
The improper fraction of 1(1/3) is 4/3.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
1 and 1/3
An improper fraction means the numerator is greater than the denominator.
So,
1 and 1/3
= 1(1/3)
= (3 x 1 + 1) / 3
= 4/3
4 > 3 so it is an improper fraction.
Thus,
The improper fraction of 1(1/3) is 4/3.
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a woman has 7 keys, one of which will open a door. she tries the keys at random discarding those that do not work. what is the probability that she will open the door on her 3rd try?
She will likely succeed in opening the door on her third attempt is 3/7 of the time.
The area of mathematics known as probability deals with the outcomes of random events. Probability refers to a result's chance or potential. It clarifies the likelihood that a specific occurrence will take place. We frequently say things like, "He will probably pass the test," "There is very little chance of receiving a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for every instance of chance, uncertainty, likely, etc. in these statements.
In essence, probability is the ability to anticipate an outcome based on the variety and quantity of potential possibilities or the analysis of historical data.
overall keys = 7
choosing 1 opens the door since p(1)=1/7
trying to throw out = 2/7
The likelihood that she will succeed in doing so on her third attempt is:
P= 1/7 + 2/7.
P= 3/7
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A bag has 4 red balls ,3 green balls and 5 blue balls. What is the probability of getting a red ball randomly
1-100%. You'll never know until you try it yourself.
Now imagine that a small gas station is willing to accept the following prices for selling gallons of gas: They are willing to sell 1 gallon if the price is at or above $3 They are willing to sell 2 gallons if the price is at or above $3.50 They are willing to sell 3 gallons if the price is at or above $4 They are willing to sell 4 gallons if the price is at or above $4.50 What is the gas station's producer surplus if the market price is equal to $4 per gallon? (Assume that if they are willing to sell a gallon of gas, there are buyers available to buy it at the market price) o $0.5
o $1 o $1.50 o $2 $2.50
The gas station's producer surplus is $1.50.
How much is the gas station's producer surplus?The gas station's producer surplus is the difference between the market price and the minimum price at which the gas station is willing to sell the corresponding number of gallons. In this case, the market price is $4 per gallon.
For the first gallon, the gas station is willing to sell it if the price is at or above $3. Since the market price is higher at $4, the producer surplus for the first gallon is $1.
For the second gallon, the gas station is willing to sell it if the price is at or above $3.50. Again, the market price is higher at $4, resulting in a producer surplus of $0.50 for the second gallon.
For the third gallon, the gas station is willing to sell it if the price is at or above $4. Since the market price matches this threshold, there is no producer surplus for the third gallon.
For the fourth gallon, the gas station is willing to sell it if the price is at or above $4.50, which is higher than the market price. Therefore, there is no producer surplus for the fourth gallon.
Adding up the producer surplus for each gallon, we have $1 + $0.50 + $0 + $0 = $1.50 as the total producer surplus for the gas station.
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Goran ran three times last week. Here are the distances he ran (in kilometers).9.94,6.65,10 What is the total distance Goran ran on these three days?
Answer:
26.59 kilometers
Step-by-step explanation:
Can someone help me find the domain of this??
RIGHT ANSWERS ONLY PLS
NO LINKS!
Answer:
D, assuming that the function continues past the line shown
Step-by-step explanation:
There is no reason that the X is ending on either side. There should be arrows on both ends of the graphed function though.
Four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. which student found the correct mean? ashrita’s work: startfraction 26 31 39 30 16 16 18 38 over 8 endfraction = startfraction 214 over 8 endfraction = 26.75 collette’s work: startfraction 26 38 over 2 endfraction = startfraction 64 over 2 endfraction = 32 daniel’s work: startfraction 26 31 39 30 18 38 over 7 endfraction = startfraction 198 over 7 endfraction = 28.29 lora’s work: startfraction 30 16 over 2 endfraction = startfraction 46 over 2 endfraction = 23
In calculating the mean of this data set Ashrita did the best job.
The Mean of the data set is the most commonly used measures of central tendency.
It means the average value of the data set.
one doesn't have to arrange the data in order for finding it.
What is the meaning of mean?The data set value takes is to add them all together and divide that by the number of the data.
It can be written as
\(,(x_1 + x_2 + x_3 + ..... + x_n) / n\)
Where \(x_1 , x_2 , x_3 , ..... ,x_n\)are the values in the data set
Therefore we can conclude that Ashrita did the best job in calculating the mean of this data set.
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any point on the perpendicular bisector of a segment is
It is correct to say that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.
Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. What is a perpendicular bisector? A perpendicular bisector is a line that intersects a line segment and forms a 90-degree angle. It divides the line segment into two equal halves.Each point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. This means that the distance from any point on the line to one endpoint of the segment is the same as the distance to the other endpoint of the segment.
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From the mbsa scan performed in task 3, how many users have non-expiring passwords?
Based on the explanation using the combination method, the correct answer to the question is D. All four users have non-expiring passwords.
The MBSA scan likely provided a list of users along with their corresponding password expiration settings. The term "non-expiring passwords" refers to passwords that do not have an expiration date, meaning they remain valid indefinitely.
Now, let's analyze each option given in the question and determine the correct answer using the combination method:
A. 3 of 4:
If three out of the four users have non-expiring passwords, it means that only one user has an expiring password. However, this does not match our definition of non-expiring passwords. Therefore, Option A is incorrect.
B. 1 of 4:
If only one user out of the four has a non-expiring password, it means that the other three users have expiring passwords. This option does not satisfy the condition of non-expiring passwords for the majority of users. Hence, Option B is also incorrect.
C. 2 of 4:
If two users out of the four have non-expiring passwords, it means that the remaining two users have expiring passwords. This option suggests that half of the users have non-expiring passwords, which does not correspond to our definition of non-expiring passwords for the majority of users. Thus, Option C is incorrect.
D. 4 of 4:
If all four users have non-expiring passwords, it means that every user's password is set to never expire. This option aligns with our definition of non-expiring passwords for the majority of users. Therefore, Option D is the correct answer.
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Complete Question:
From the MBSA scan performed in Task 3, how many users have non-expiring passwords?
A. 3 of 4
B. 1 of 4
C. 2 of 4
D. 4 of 4
1. Draw the following curve in R^2 and write a vector function which describes the curve. Include the domain for t, and indicate the direction of motion on the drawing: (a) The line segment from (2, 3) to (-1,5) (b) The part of y=4 – x^2 from (0,4) to (-2,0) (c) The part of the circle x^2 + y^2 = 9 from (3,0) to (0, -3), moving counter-clockwise
The Vector functions are :
a) r(t) = (1-t) <2, 3> + t <-1, 5>
b)r(t) = (1-t) <0, 4> + t <-2, 0>
c) x = 3 cos(t), y = 3 sin(t)
(a) The line segment from (2, 3) to (-1,5):
To draw the line segment from (2, 3) to (-1, 5), we first plot the two points on the Cartesian plane:
(2, 3)
*
/
/
/
(-1, 5) *
The direction of motion along this line segment is from (2, 3) to (-1, 5), so we can write a vector function that starts at (2, 3) and ends at (-1, 5) by using the position vector:
r(t) = (1-t) <2, 3> + t <-1, 5>
where t ranges from 0 to 1. This vector function starts at (2, 3) when t = 0 and ends at (-1, 5) when t = 1.
(b) The part of y=4 – x^2 from (0,4) to (-2,0):
To draw the part of y = 4 - x^2 from (0, 4) to (-2, 0), we first plot the two points on the Cartesian plane:
(0, 4) *
/ \
/ \
/ \
(-2, 0) * / \
*--------*
The direction of motion along this curve is from (0, 4) to (-2, 0), so we can write a vector function that starts at (0, 4) and ends at (-2, 0) by using the position vector:
r(t) = (1-t) <0, 4> + t <-2, 0>
where t ranges from 0 to 1. This vector function starts at (0, 4) when t = 0 and ends at (-2, 0) when t = 1.
(c) The part of the circle x^2 + y^2 = 9 from (3, 0) to (0, -3), moving counter-clockwise:
To draw the part of the circle x^2 + y^2 = 9 from (3, 0) to (0, -3), moving counter-clockwise, we first plot the two points on the Cartesian plane:
markdown
* (3, 0)
/ | \
/ | \
*----*----*
(0, -3)
We know that the equation of the circle is x^2 + y^2 = 9, so we can parameterize this curve by writing x and y in terms of cos(t) and sin(t):
x = 3 cos(t)
y = 3 sin(t)
where t ranges from π/2 to π. This vector function starts at (3, 0) when t = π/2 and ends at (0, -3) when t = π. Since we want to move counter-clockwise along the circle, we start at the point (3, 0) and move towards (0, -3) as t increases.
In mathematics, we use vector functions to describe curves in two- or three-dimensional space. Vector functions are functions that map a parameter t to a vector in space, allowing us to describe the position and movement of an object over time.
In this problem, we are asked to draw three different curves in the plane and write vector functions that describe each curve.
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Question 8 of 15:
Select the best answer for the question.
8. What is dy/dx if y = (x² + 2)³(x³ + 3)²?
O A. 3(x² + 2)²(x3 + 3)² + 2(x² + 2)²(x³ + 3)
O B. 6(x2 + 2)2(x³ + 3)
O C. 6x(x² + 2)2(x³ +3)² + 6x²(x² + 2)³(x³ + 3)
O D. 2x(x³ + 3)² + 3x²(x² + 2)³
The best answer for dy/dx is option C. dy/dx = 6x(x² + 2)²(x³ + 3)² + 2(x² + 2)³(x³ + 3)(3x²)
To find dy/dx, we need to differentiate the given function y = (x² + 2)³(x³ + 3)² with respect to x.
Using the chain rule, the derivative can be found as follows:
dy/dx = d/dx[(x² + 2)³(x³ + 3)²]
= [(x² + 2)³]'(x³ + 3)² + (x² + 2)³[(x³ + 3)²]'
Now, let's find the derivatives of each term separately:
[(x² + 2)³]' = 3(x² + 2)²(2x) (using the power rule and chain rule)
[(x³ + 3)²]' = 2(x³ + 3)(3x²) (using the power rule and chain rule)
Plugging these derivatives back into the expression for dy/dx:
dy/dx = 3(x² + 2)²(2x)(x³ + 3)² + (x² + 2)³(2(x³ + 3)(3x²))
= 6x(x² + 2)²(x³ + 3)² + 2(x² + 2)³(x³ + 3)(3x²)
Therefore, the best answer for dy/dx is option C:
dy/dx = 6x(x² + 2)²(x³ + 3)² + 2(x² + 2)³(x³ + 3)(3x²)
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Need to generate a recursive formula to the story problem given below. Give the recursive equation at the top of your answer (do not forget your base case(s)) and then show your thought process after. Question: How many n-letter "words" can be created from an unlimited supply of a’s, b’s, and c’s, if each word MUST contain an even number of a’s?
The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,
To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.
If the first letter is not 'a', we have the freedom to ch
oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.
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Find the derivative of the function using the definition of derivative. f(x) = 5x4
The derivative of the function \(f(x) = 5x^4\) using the definition of derivative is \(f'(x) = 20x^3.\)
To find the derivative of the function \(f(x) = 5x^4\) using the definition of derivative, we can follow these steps:
Step 1: Start with the definition of derivative, which is given by:
\(f'(x) = \lim_{(h- > 0)} [(f(x + h) - f(x)) / h]\)
Step 2: Substitute the given function f(x) = 5x^4 into the definition:
\(f'(x) = \lim_{(h- > 0)} [(5(x + h)^4 - 5x^4) / h]\)
Step 3: Expand the expression (x + h)^4:
\(f'(x) = \lim_{(h- > 0)} [(5(x^4 + 4x^3h + 6x^2h^2 + 4xh^3 + h^4) - 5x^4) / h]\)
Step 4: Simplify the expression by distributing the 5:
\(f'(x) = \lim_{(h- > 0)} [(5x^4 + 20x^3h + 30x^2h^2 + 20xh^3 + 5h^4 - 5x^4) / h]\)]
Step 5: Cancel out the common terms 5x^4:
\(f'(x) = \lim_{(h- > 0)} [(20x^3h + 30x^2h^2 + 20xh^3 + 5h^4) / h]\)]
Step 6: Divide each term by h:
\(f'(x) = \lim_{(h- > 0)} [20x^3 + 30x^2h + 20xh^2 + 5h^3]\)
Step 7: Take the limit as h approaches 0:
\(f'(x) = 20x^3\)
Therefore, the derivative of the function f(x) = 5x^4 using the definition of derivative is \(f'(x) = 20x^3.\)
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Jennifer and Jasmine are selling fruit for a school fundraiser. Customers can buy small boxes of grapefruit and large boxes of grapefruit. Jennifer sold 8 small boxes of grapefruit and 14 large boxes of grapefruit for a total of $254. Jasmine sold 1 small box of grapefruit and 14 large boxes of grapefruit for a total of $191. How much does one small box of grapefruit cost?
Answer:
$9Step-by-step explanation:
Small box = sLarge box = lEquations:
8s + 14l = 254s + 14l = 191Subtract the second equation from the first:
8s - s = 254 - 1917s = 63s = 9Create equations
\(\\ \tt\Rrightarrow 8x+14y=254--(1)\)
\(\\ \tt\Rrightarrow x+14y=191--(2)\)
Substract eq(2) from eq(1)
\(\\ \tt\Rrightarrow 7x=63\)
\(\\ \tt\Rrightarrow x=\dfrac{63}{7}\)
\(\\ \tt\Rrightarrow x=9\)
Jacob takes 7 classes, each 50.00 minutes long, every day of the 5 day school week. How many hours per week does he spend in class
7×50×5 = 1750 minutes
1750minutes/60minutes = 29.161 hours
A line passes through (-2, 7) and (3, 2).
Find the slope-intercept form of the equation of the line.
Then fill in the value of the slope, m , and the value of the y-intercept, b, below.
m=
b=
\(\huge{ \mathfrak{ \underline{ Answer \: \: ✓ }}}\)
Slope of the line :
\( \large\boxed{ \mathrm{ \frac{y_2 - y_1 }{x_2 - x_1} }}\)
\( \dfrac{7 - 2}{ - 2 - 3} \)\( \dfrac{ 5}{ - 5} \)\( - 1\)therefore, m = slope = -1
The equation of the line will be :
y = mx + by = (-1 × x) + by = -x + bNow, let's plug the value of x and y from coordinates of second point,
\(y = - x + b\)\(2 = - 3 + b\)\(b = 5\)Hence, the required values are :
\( \boxed{m = - 1}\)\( \boxed{ \: \: \: b = 5 \: \: \: }\)_____________________________
\(\mathrm{ ☠ \: TeeNForeveR \:☠ }\)
The slope of line passing through (-2, 7) and (3, 2). is -1 and the value of the y-intercept b is 5.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
A line passes through (-2, 7) and (3, 2). We need to find the slope.
x₁=-2, x₂=3, y₁=7, y₂=2
substitute the values in formula of slope
m=2-7/3-(-2)
m=-5/5=-1
The slope intercept form of line is y=-x+b
To find b put the values of (-2,7)
7=-(-2)+b
7=2+b
7-2=b
5=b
y intercept is 5
Hence the slope of line passing through (-2, 7) and (3, 2). is -1 and the value of the y-intercept b is 5.
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"What set of reflections would carry hexagon ABCDEF onto itself?. . Hexagon ABCDEF on the coordinate plane with pointA at negative 1, 1, pointB at negative 3, 1, pointC at negative 4, 2, pointD at negative 3, 3, pointE at negative 1, 3, and pointF at 0, 2. . .x-axis, y=x, x-axis, y=x .. y=x, x-axis, y=x, y-axis .. y-axis, x-axis, y-axis .. x-axis, y-axis, y-axis ."
A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".
What is a combination of reflections?
Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.
Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.
One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.
This would take the hexagon from its original position to itself.
Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.
This would also take the hexagon from its original position to itself.
Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".
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As the error bound of the proportion (EBP) increases, what is the effect on the sample size?
There is an inverse relationship between the EBP and the required sample size. As the EBP increases, the required sample size decreases, and vice versa.
As the error bound of the proportion (EBP) increases, the required sample size decreases.
The EBP is a measure of the maximum error that is allowed in estimating a population proportion using a sample proportion. It is calculated as the difference between the sample proportion and the true population proportion, divided by the sample proportion. For example, an EBP of 0.02 means that the estimated proportion could differ from the true population proportion by up to 2%.
When the EBP is large, it means that the allowable margin of error is also large, so we do not need as large a sample size to achieve the desired level of precision in our estimate. In other words, if we are willing to tolerate a larger error in our estimate, we can use a smaller sample size to achieve the same level of accuracy.
Conversely, when the EBP is small, it means that the allowable margin of error is also small, so we need a larger sample size to achieve the desired level of precision in our estimate. This is because a smaller margin of error requires a more precise estimate, which in turn requires a larger sample size to reduce the effect of random sampling variability.
Therefore, there is an inverse relationship between the EBP and the required sample size. As the EBP increases, the required sample size decreases, and vice versa.
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One circle has a circumference of 123 cm. Another circle has a circumference of 32 cm. What is the ratio of the radius of the
smaller circle to the radius of the larger circle?
3:8
8:3
1:3
3:1
Answer:
1:3
Step-by-step explanation:
First find the measure of radius for both circles:
Circle 1:
2 x pi x r = 123
r = 123 divided by 6.28 = 19.58
Circle 2:
2 x pi x r = 32
r = 32 divided by 6.28 = 5.09
So, Ratio:
5.09 : 19.58
Approximately 1:3 ( 6:18)
Answer: 1:3
Step-by-step explanation:
Cir. of the bigger circle = 123 cm
r = C / 2π
r = 123 / 2π = 19.58
Cir of smaller circle = 32 cm
r = 32 / 2π = 5.09
Ratio = 5.09 : 19.58
= 1:3
Brigid has a 25-foot ladder she will use to paint the side of her house. What angle does the ladder need to make with house so she can reach 18 feet up the side of her house
The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.
To determine the angle the ladder needs to make with the house, we can use the tangent function.
First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.
Opposite side = 18 feet
Adjacent side = 25 feet
We can then use the tangent function to find the angle:
tan(angle) = opposite / adjacent
Solving for the angle, we get:
angle = arctan(18/25) = approximately 54.7 degrees
Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.
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I’ll give the Brainliest to who answers these questions with reasonable explanations.
1. A bag has 16 marbles in it: 6 red, 4 blue, 3 yellow, and 3 green. A marble is drawn and put back, and then another marble is drawn. What is the probability that a blue marble was drawn followed by a yellow marble?
2. A bag has 16 marbles in it: 6 red, 4 blue, 3 yellow, and 3 green. A marble is drawn and not put back, and then another marble is drawn. What is the probability that a blue marble was drawn followed by a yellow marble?
Thank you.
Answer:
1. 0.0469 (4.d.p)
2. 0.05
Step-by-step explanation:
1. First we'll find the probability of drawing a blue marble.
P = (No. favourable events)/(Total events)
In this case it's:
P = (No. blue marbles)/(Total Marbles)
Therefore P(Blue) = 4/16 = 0.25
Now we find the probability of drawing a yellow marble:
The total number will be the same because the blue marble will have been put back.
P(Yellow) = 3/16 = 0.1875
Now, since we are calculating the probability of both happening we multiply together the two individual probabilities to get the combined probability of both:
0.25 x 0.1875 = 0.0469 (4.d.p)
2. The probability of drawing a blue marble is still the same so we can keep that: P(Blue) = 0.25
But this time, the marble is not replaced. This means that the total number of marbles has changed when drawing the yellow marble:
P(Yellow) = 3/15 = 0.2
Now we multiply them together again to find the combined probability of both happening:
0.25 x 0.2 = 0.05
Hope this helped!
*UNIT RATE AND PROPORTIONS*
the price for 4 pound of ribs is $28.00
*QUESTIONS* *what is the unit rate?* *how much would 6pounds cost?*
*how many pounds can be bought for $70* NEED HELP ASAP‼️‼️
Answer:
six pounds of ribs will cost you $42
Step-by-step explanation:
and 10 lb will cost $70 so that's how much pounds will get you to $70 worth of ribs
find the nth term in the following sequesnce: 1, 3, 9, 27
Answer:81
Step-by-step explanation: it is skip by 3x so 21 x3 = 81
:)
PLEASE HELP Review the equation, then complete the following. f(x)=1/x-4, g(x)=4x+1/x Use composition to prove whether or not the functions are inverses of each other. Express the domain of the compositions using interval notation.
Answer:A. Yes, they are inverse of each other.
B. Domain and range of the compositions is .
Step-by-step explanation:
A. We have, and .
Now, 'when two functions f and g are inverses of each other, they satisfy the property '.
So, we have,
Thus, we get for the given function f and g, .
Hence, they are inverse of each other.
B. Now, as we have,
That is, the composition of the functions is equal to the identity function.
Thus, the domain and range are the set of all real numbers respectively.
So, in the interval notation, we have,
Domain and range of the compositions is .
The economy is initially in long-run equilibrium. The AD curve shifts to the right and the price level rises. Assuming that the economy is self-regulating, the SRAS curve will shift to the left and the price level will rise even further. If the price level now remains constant, what have we witnessed
We witnessed that the economy has moved from its initial short-run equilibrium to a new long-run equilibrium, where the price level has stabilized despite the changes in aggregate demand and short-run supply.
Suppose the price level remains constant despite the initial shift of the AD (Aggregate Demand) curve to the right, followed by the leftward shift of the SRAS (Short-Run Aggregate Supply) curve. In that case, it suggests that the economy has experienced a change toward long-run equilibrium.
The initial shift of the AD curve to the right causes an increase in both output and the price level. However, the subsequent leftward shift of the SRAS curve indicates that in the short run, the price level has led to higher costs for businesses, potentially due to factors such as increased wages or input prices.
As a result, with a leftward shift in the SRAS curve, the output level decreases, and the price level rises further. However, if the price level remains constant after this adjustment, it suggests that the economy has reached a new equilibrium point where aggregate demand and short-run aggregate supply are once again balanced.
In short, witnessing a constant price level after the initial shifts in the AD and SRAS curves implies that the economy has moved from its initial short-run equilibrium to a new long-run equilibrium, where the price level has stabilized despite the changes in aggregate demand and short-run supply.
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Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
Answer:
5
Step-by-step explanation:
the probability of getting a 6 every time you roll the die once is just 1/6. multiply that by 30 and we get our answer, which is 5 times.
Jimrgrant or Anyone solve this PLZZZZZZ
Answer:
it is B and D
Step-by-step explanation:
mark brainliest or 5 stars and heart
correct me if im wrong
Answer:
B and A
Step-by-step explanation:
Calculate distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
(1) with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 8)
d = \(\sqrt{6-0)^2+(8-0)^2}\)
= √(6² + 8²)
= √ (36 + 64)
= √ 100
= 10 → B
(2)
Using (x₁, y₁ ) = (- 5, 3) and (x₂, y₂ ) = (3, 15)
d = √ (3 + 5)² + (15 - 3)²
= √ 8² + 12²
= √ 64 + 144
= √ 208
≈ 14.4 ( to the nearest tenth ) → A
What is the area of the wreck site?
Answer:
where is the photo?
Step-by-step explanation:
Where is the photo, I need you to give me more details so i can officially answer your question, thank you :)
Maths question, will mark Brainliest! Find the area of a circle with a radius of 4.
Answer:
8\(\pi\)
Step-by-step explanation:
area=\(\pi\)\(r^{2}\)
\(\pi\)\(4^{2}\)
16\(\pi\)
since it is a semicircle, cut that number in half.
Answer:
25.12units squared
Step-by-step explanation:
A = \(\frac{\pi r^2}{2}\) or \(\frac{3.14r^2}{2}\)
r = 4
3.14 x 4^2 = 50.24
50.24/2 = 25.12
If y = 4 find slope, X-intercept and y-intercept.
Answer:
An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero