Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division
Which of the following equations is of a parabola with a vertex at (0, 3)?
y = (x - 3) 2
y = (x + 3) 2
y = x 2 - 3
y = x 2 + 3
Answer:
Option D.
Step-by-step explanation:
We have to find the equation of the parabola which has vertex at ( 0,3 )
If we write the equation of a parabola in the vertex from then we will write
y = ( x - h )² + (k)²
In this equation ( h, k) will be the vertex.
(a) y = (x-3)² + 0
so ( 3,0) will be the vertex
(b) y = ( x+3)² + 0
or y = [x - (-3)]² + 0
then ( -3,0) will be the vertex
(c) y = (x² - 3)
y = ( x-0 )² + (-3)
then ( 0, -3) is the vertex.
(d) y = x² + 3
y = ( x-0 )² + 3
Then ( 0, 3 ) will be the vertex of this parabola.
Option D. is the answer.
The stock price for a corporation increased by 0.11%. Write 0.11% as a decimal and as a fraction in simplest form
the pmf for the r.v. x is as shown
The following formula relates three quantities force mass and acccelerations
F=ma
Here is the five-number summary for a group of 100 runners in a 5-kilometer race. the variable is the time to complete the race. five-number summary: minimum: 15 minutes q1: 27 minutes median: 31 minutes q3: 32 minutes maximum: 50 minutes are there any outliers in the runners’ finish times by the 1.5 * iqr definition?
The interquartile range (IQR) is 5 minutes. Any values below 19.5 minutes or above 39.5 minutes would be considered outliers. In this data set, both the minimum time of 15 minutes and the maximum time of 50 minutes are outliers.
Explanation:
The question is whether there are any outliers in the finish times of a group of runners based on the IQR definition. To determine this, we first calculate the interquartile range (IQR), which is the range of the middle 50 percent of the data. Q1 = 32 min - 2 For this data set, we calculate the IQR by subtracting the first quartile (Q1) from the third quartile (Q3). Here, IQR = Q3 - 7 min = 5 min.
Next, we multiply the IQR by 1.5, which is our test for outliers. This gives 1.5 * IQR = 1.5 * 5 min = 7.5 min.
An outlier is defined as a data point that is below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. So, any time less than 27 min - 7.5 min = 19.5 min or greater than 32 min + 7.5 min = 39.5 min would be considered an outlier.
Given the five-number summary: min=15 min, Q1=27 min, median=31 min, Q3=32 min, max=50 min, we can clearly see that the minimum time of 15 min is an outlier because it's less than 19.5 min. Also, the maximum time of 50 min is an outlier because it's greater than 39.5 min.
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The minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the given data set.
To determine if there are any outliers using the 1.5 * IQR (interquartile range) definition, we need to calculate the IQR first. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
Given:
- Q1 = 27 minutes
- Q3 = 32 minutes
We can calculate the IQR as follows:
[tex]\[ IQR = Q3 - Q1 = 32 - 27 = 5 \text{ minutes} \][/tex]
Now, we can use the 1.5 * IQR rule to find the lower and upper bounds for potential outliers:
Lower Bound: Q1 - 1.5 * IQR
Upper Bound: Q3 + 1.5 * IQR
[tex]\[ \text{Lower Bound} = 27 - 1.5 \times 5 = 27 - 7.5 = 19.5 \text{ minutes} \]\[ \text{Upper Bound} = 32 + 1.5 \times 5 = 32 + 7.5 = 39.5 \text{ minutes} \][/tex]
Any finish times below 19.5 minutes or above 39.5 minutes would be considered potential outliers according to the 1.5 * IQR rule.
Since the minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the data set.
5c - 6 = 4 - 3c I got c = 5 and I have a problem that says c = 5 for this and the equations solution was
2c - 6 = 4
2c = 10
C = 5
Which step do I change and how. Also what is the new solution for c =
pls I help I need answers and work shown
0.30 as a fraction is 30/100 = 3/10
0.30 as a percent = 0.30 * 100 = 30%
answer is D. 3/10 and 30%
.30 is .3
do .30 divided by 1 and you get 3/10
Percentage= move the decimal 2 places to the right and you get 30%
So your answer is D.
You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324(pi) cubic inches. What is the least possible height of the container?
9 inches
Step-by-step explanation:The volume of a cylinder is given by ...
... V = πr²h
The least height will be the height that makes the volume exactly that which is necessary.
... 324π in³ = π·(6 in)²·h . . . . . . fill in the given information
... (324π in³)/(36π in²) = h = 9 in . . . . . divide by the coefficient of h
The least possible container height is 9 inches.
solve 5.3×0.5 and show work
Marcus walked 5 km due east and then he turned around and walk 5 km to West how many kilometers is Marcus now from his starting point
what is the graph of the equation 2x -y =2?
Answer:
Refer the attached graph.
Step-by-step explanation:
Given : Equation [tex]2x-y=2[/tex]
To find : What is the graph of the equation ?
Solution :
To plot the graph of the equation we have to determine the x and y-intercept of the equation as [tex]2x-y=2[/tex] is a linear equation.
For x-intercept, put y=0
[tex]2x-0=2[/tex]
[tex]x=\frac{2}{2}[/tex]
[tex]x=1[/tex]
Point is (1,0).
For y-intercept, put x=0
[tex]2(0)-y=2[/tex]
[tex]-y=2[/tex]
[tex]y=-2[/tex]
Point is (0,-2).
So, The graph passing through (1,0) and (0,-2) with linear line.
Refer the attached figure below.
The graph of the equation 2x - y = 2 will be a straight line passing through the points (0, -2), (1, 0), and (-1, -4).
We have,
To graph the equation 2x - y = 2, we can start by rearranging it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
Rearranging the equation:
2x - y = 2
y = -2x + 2
y = 2x - 2
Now we have the equation in slope-intercept form, where the slope (m) is 2 and the y-intercept (b) is -2.
To graph this equation, you can plot the y-intercept at (0, -2), and then use the slope to find additional points.
The slope of 2 means that for every 1 unit increase in x, y will increase by 2.
So, from the y-intercept (0, -2), you can move 1 unit to the right and 2 units up to get another point (1, 0).
Similarly, you can move 1 unit to the left and 2 units down to get another point (-1, -4).
Now you can plot these points and draw a straight line through them to represent the graph of the equation.
Thus,
The graph of the equation 2x - y = 2 will be a straight line passing through the points (0, -2), (1, 0), and (-1, -4).
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Express the area of each square below as a monomial
14g5h9
Kate have 110 bows. 10 bows fit in a bag. how many bags can she fill
By dividing the total number of bows (110) by the number of bows that fit in one bag (10), we find that Kate can fill 11 bags with her bows.
Explanation:To find out how many bags Kate can fill with her bows, we need to divide the total number of bows by the number of bows that fit in one bag. In this case, Kate has 110 bows and 10 bows fit in one bag.
So, we divide 110 by 10: 110 / 10 = 11
Therefore, Kate can fill 11 bags with her 110 bows.
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Kate can fill 11 bags with her 110 bows.
Given:
Kate has 110 bows
No. of bows fit in the bag = 10
No. of bags she can fill:
110 bows ÷ 10 bows per bag
= [tex]\frac{110}{10}[/tex]
= 11 bags.
So, Kate can fill 11 bags with her 110 bows.
which
of the following is the least?
A.0.105
B.0.501
c.o.015
D.0.15
(a/20)+(4/15)=(9/15)
Rational numbers are _____ natural numbers.
always
sometimes
never
one positive integer is 5 less than another. the product of the two integers is 36. what are the integers?
1st number = x
2nd number = x-5
x*(x-5) = 36
x^2-5x =36
x^2 -5x-36 = 0
factor the polynomial:
(x-9) (x+4)
9-9 = 0, -4 +4 = 0
so x = 9 or -4
the question states a positive number
so x = 9
the 2 numbers are 9 and 4
write 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form
The standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]
In order to write 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones in standard form, let us write each of the expressions in figures
4 hundred-thousand = 400,000
13 thousand = 13,000
11 hundreds = 11 x 100
11 hundreds = 1100
4 ones = 4 x 1
4 ones = 4
The next step is to sum up all the figures together
400000 + 13000 + 1100 + 4 = 414,104
Convert 414104 to standard form
[tex]414104 = 4.14104 \times10^5[/tex]
Therefore, the standard form of the expression 4 hundred-thousand, 13 thousand, 11 hundreds, 4 ones is [tex]4.14104 \times10^5[/tex]
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You want to replace the countertops in a kitchen. One counter measures 24 inches by 6 feet. The other is 30 inches by 4 feet. If the new countertop costs $42.00 per square foot, what will be the cost of the new top?
Answer:
The cost of the new top $924.
Step-by-step explanation:
You want to replace the counter-tops in a kitchen.
The dimensions of the first counter is 24 inches by 6 feet.
i.e [tex]24 \text{ inch} \times 6 \text{ feet}[/tex]
or [tex]2\text{ feet} \times 6 \text{ feet}[/tex]
As 1 feet =12 inches
Hence the area of the counter is [tex]2\times 6=12\text{ feet}^2[/tex]
The dimensions of the second counter is 30 inches by 4 feet.
i.e [tex]30 \text{ inch} \times 4 \text{ feet}[/tex]
or [tex]2.5\text{ feet} \times 4 \text{ feet}[/tex]
Hence the area of the counter is [tex]2.5\times 4=10\text{ feet}^2[/tex]
Hence, the total area will be [tex]12+10=22 \text{ feet}^2[/tex]
The unit cost of the counter-top is [tex]\$42.00\text{ feet}^2[/tex]
So the net cost will be,
[tex]=42\times 22=\$924[/tex]
Find the equation in standard form of the line with slope
[tex] \frac{7}{2} [/tex] that passes through the point (5,7)
Please explain as well
Between two tenths of a mile will the second relay exchange occur? Explain.
2/10
There is one tenth in a mile. I have the same question. But I am just guessing.
complete the steps to solve the inequality 0.2 (x+20)-3>-7-6.2x
0.2x+4-3>-7-6.2x
0.2x+1>-7-6.2x
0.2x+0.6x>-8
0.8x>-8
the correct answer is: x>-1.25
There are 60 minutes in 1 hour. What fraction of an hour is 4 minutes? Write your answer in lowest terms.
The fraction of an hour is 4 minutes in lowest terms is 1/15.
What fraction of an hour is 4 minutes in lowest terms?To find the fraction of an hour that 4 minutes represents, we need to compare the number of minutes to the total number of minutes in an hour, which is 60.
We can set up a fraction where the numerator represents the number of minutes we want to find the fraction for (4 minutes) and the denominator represents the total number of minutes in an hour (60 minutes).
So, the fraction can be written as 4/60.
To simplify the fraction to its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 60 is 4.
Dividing both the numerator and denominator by 4, we get:
4/60 = (4 ÷ 4) / (60 ÷ 4) = 1/15.
Therefore, 4 minutes in lowest terms is equal to 1/15th of an hour.
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What is the explicit formula for the geometric sequence with the recursive formula?
Answer:
Option A. [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex]
Step-by-step explanation:
Recursive formula of the geometric sequence is given as [tex]a_{1}=(-7)[/tex]
and [tex]a_{n}=\frac{1}{3}(a_{n-1})[/tex]
From these formulas it is clear that first term of the sequence a1 = -7
and common ratio of the sequence = [tex]\frac{1}{3}[/tex]
Since explicit formula of any geometric sequence is represented by
[tex]a_{n}=a_{1}(r)^{n-1}[/tex]
Therefore, [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex] will be the explicit formula of the given geometric sequence.
A picture frame has a total perimeter P of 5 meters. The height of the frame is
2/3 times its width.
The height of the frame is 1.5 meters.
The Width of the frame is 1 meter.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
Given that,
P = 5 meters
w = 2/3h = 0.67h
We have to determine the height of the frame.
The perimeter of the frame = 2h + 2W
We know all the other values So we can plug in values to solve for h:
5 = 2h + 2(.67h)
5 = 2h+ 1.33h
5 = 3.33h
5/3.33 = h
h = 1.5
So the height of the frame is 1.5 meters
We need to find the width and we know that W = 0.67h
W = 0.67(1.5)
W = 1
So the Width of the frame is 1 meter.
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if f(x)=x/2-2 and g(x)=2x^2+x-3, find (f+g)(x)
Answer:
B. [tex]2x^2+\frac{3x}{2}-5[/tex]
Step-by-step explanation:
Given functions,
[tex]f(x)=\frac{x}{2}-2[/tex]
[tex]g(x)=2x^2+x-3[/tex]
Since, (f+g)(x) = f(x) + g(x)
[tex]=\frac{x}{2}-2+2x^2+x-3[/tex]
[tex]=2x^2+\frac{x+2x}{2}-5[/tex] ( combine like terms )
[tex]=2x^2+\frac{3x}{2}-5[/tex]
Option 'B' is correct.
Find the point p where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -4.
The point of intersection between the given line and plane is (1/6, -5/3, 5/2). This is determined by substituting the parametric line equations into the plane equation, simplifying to find the value of the parameter t, and substituting that value back into the line equations.
Explanation:The given line and plane equations are, x = 1 + t, y = 2t, z = -3t and x + y - z = -4 respectively. To find where the line intersects the plane, we need to substitute the parametric line equations into the plane equation.
Step by Step Solution
Step 1: Substitute x, y, and z from the line equation into the plane equation, giving you (1+t) + 2t - (-3t) = -4.
Step 2: Simplify the equation to find the value of t. You get 6t + 1 = -4, so t = -5/6.
Step 3: Substitute t = -5/6 into the line equations to find x = 1/6, y = -5/3, and z = 5/2.
So, the point P where the line intersects the plane is (1/6, -5/3, 5/2).
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33x-8(3x+9)>-9 what is the answer
if I drop a book from the same height as a feather which will land first?