Answer: i believe the answer is 26
Step by step explanation
Total no. of observation = (12+13) = 25
Median = Average of 18/2 observation + (18/2+1)
=1/2 (12th observation + 13 observation)
1/2 × (25 +27) = 1/2 × 52
=26
A man spent one-fourth of his salary on food and one-half of the remainder on clothing. If his salary is 120000, how much did he spend on clothing
Answer:
salary=120000
1/4×120000=30000= money spent
remainder=120000- 30000
= 90000
money spent on clothing =1/2×90000
=45000
Explanation: If his salary is $120,000 and 1/4 is used on food he has a remaining of $80,000. He uses 1/2 on clothing so he has a remainder of $40,000 so now we know that he used $40,000 on clothing
Answer: $40,000
Hope this helps you! :D
Given y = [tex]\frac{2x-5}{x^{2} -2}[/tex], find the value of [tex]\frac{dy}{dx}[/tex] at x = 2.
▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]
▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
» [tex] \tt{For \: \: y,}[/tex]
[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]
[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]
[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]
[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]
» [tex] \tt{At \: \: x = 2,}[/tex]
[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]
[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]
[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]
[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]
The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
What is the Y-intercept of a Linear equation?A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.
Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:
Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2
To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b
3 = 1(2) + b
3 = 2 + b
Subtract 2 from both sides
3 - 2 = 2 + b - 2
1 = b
b = 1
Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
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3 bells ring at interval of 12,15 and 18 minutes.Respectively they all ring together at 6am,at what time will they ring together? again?
The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.
We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore
The lcm of 12,15, 1812 - 15 - 18 | 2 6 - 15 - 9 | 2 3 - 15 - 9 | 3 1 - 5 - 3 | 3 1 - 5 - 1 | 5 1 - 1 - 1 |L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min
The least common multiple of 12, 15, and 18 is 180.
Convert the minutes to hours, for this we apply the rule of 3:
x = 180 * 1 / 60 = 3 hrAs the bells all together ring at 6 am, so we add
6 a.m + 3 = 9Answer: The bells are rung together again at 9 in the morning.
Calculate angles in a triangle
HELP
Answer:
angle a = [tex]\boxed{154}^{\circ}[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠a + 13° + 13° = 180°
⇒ ∠a + 26° = 180°
⇒ ∠a = 180° - 26°
⇒ ∠a = 154°
Answer:
Angle a equals= 154°
Step-by-step explanation:
you have two angles which add up to 26°
remember that triangle always adds up to 180°
so you calculate 180-26 and you get 154
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
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What is the area of the given triangle?
24 square units
12 square units
48 square units
17.2 square units
Answer: 12 square units
Step-by-step explanation: first you must count hom many units there are between points A and B, which is 4, and then count the points between B and C, which is 6.
Now that we have the units we do 6 x 4 = 24, however, you may be asking why we do not do 24 then, well if you were to be doing 6 x 4, you would be getting the area of a rectangle, and half of a rectangle is a triangle, so we have to do 24/2 which equals 12.
What is the answer of the fractions 9 and 1/6 multiplied by 1 and 1/11? Then, that answer simplified into simplest form?
The simplest form is 10.
We can find simplest as form:
Given, fractions are [tex]9\frac{1}{6}[/tex] and [tex]1\frac{1}{11}[/tex]
[tex]9\frac{1}{6}\times 1\frac{1}{11}[/tex]
[tex]\frac{55}{6}\times \frac{12}{11}[/tex]
[tex]=\frac{55\times 12}{6\times 11}[/tex]
=10
Hence, simplest form of given fraction is 10.
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how do you solve this question?
The answers to the questions are as follows:
The value of the empty box in the diagram is 10The probability that the number is in AnB = 1/5How to solve the Venn diagramWe have E = {1, 3,5, 7, 9, 11, 13, 15, 17, 19}
A= { 3, 7, 9, 11, 15}
B = {5, 7, 11, 13}
We have A n B = numbers that are contained in both of the sets
= 7, 11
a.) We have to count the total number in the dataset. That is the total number of odd numbers that are less than 20.
Hence total numbers in the set = 10
b. The probability that the number is in set AnB
= 7, 11
= 2/10
= 1/5
We can conclude that the probability that the number is in A intersect B = 1/5
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What is the solution to the equation 1/x =x+3/2x^2?
Ox=-3
Ox= -3 and x = 0
O x = 0 and x = 3
O x = 3
The solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C
How to determine the equationIn solving for the values of 'x' we need to:
Simplify the expression, that is, make a quadratic equationSolve the quadratic equation formed by either fractorisation or completing the square methodsGiven the expression;
1/x =x+3/2x^2
Cross multiply
x ( x+ 3) = 2x² ( 1)
Expand the bracket
x² + 3x = 2x²
collect like terms and equate all the variables to zero, we have ;
2x² - x² - 3x = 0
We then subtract the like terms, we getv
x²- 3x = 0
Now, let's find the common factor
Factor out 'x':
x ( x - 3 ) = 0
Equate each of the factors to zero and find the value of 'x' for each
So,
x = 0
And
x - 3 = 0
x = 3
Thus, the solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C
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For Exercises 11-15, sketch the locus of points in a plane that satisfy the
given conditions.
14. equidistant from both points
A and B and points C and D
B C
A
O
D
15. equidistant from the sides of
LJKL and on OC
L
A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.
Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.
A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).
An equidistant locus is one that is at the same distance to a reference point or a line.
In question 14, the required locus should be at the same distance to points A, B, C, and D.
In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.
The required construction is herewith attached to this answer.
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Suppose we are given the following information.
Line 1 passes through (0, 6) and (6, 4).
Line 2 passes through (-1, -7) and (1, -1).
Are these lines parallel, perpendicular, or neither?
Group of answer choices
Since the product of the slope is -1, hence the lines are perpendicular
Parallel and Perpendicular linesTwo lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1
Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;
Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3
Similarly for the coordinate points (-1, -7) and (1, -1).
Slope = -1+7/1+1
Slope of line 2 = 6/2
Slope = 3
Take the product of the slopes
Slope = -1/3 * 3
slope = -1
Since the product of the slope is -1, hence the lines are perpendicular
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The average of 15,19,23,41,and Z is 20. What is the value of x
The value of x from the given data is 2
Calculating the average of numbersMean is the ratio of sum of numbers to the total samples. Given the following data
15,19,23,41, and Z
The mean is calculated as
Mean = 15+19+23+41+z/5
Since the mean the of the data is given as 20. Substitute
20 = 15+19+23+41+z/5
Cross multiply
20*5 = 15+19+23+41+z
100 = 15+19+23+41+z
100 = 98 + z
z = 100- 98
z = 2
Hence the value of x from the given data is 2
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suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth
In quadrant I, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]
please i need help FAST
A single card is drawn from a standard 52-card deck. find the conditional probability that the card is a club, given that it is a ten______
The probability of getting a Club given that the card is a Ten is 0.25.
According to the statement
we have given that the there is a deck of the 52 cards and we have to find the conditional probability that the card is a club and the given card is a 10 number card.
So, For this purpose we know that the
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
And according to this,
The probability P is
P(Club) = 13/52 = 1/4
P(Ten) = 4/52 = 1/13
P(Club and Ten) = (1/4)(1/13) = 1/52
And we know that the
P(Club|Ten) = P(Club and Ten)/P(Ten)
And then substitute the values and it become
= (1/52)/(1/13) = (1/52)(13/1)
= 13/52 = 1/4
= 0.25
So, The probability of getting a Club given that the card is a Ten is 0.25.
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Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x 5)(x − 1).
Plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.
What is a parabola?A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.To plot the value(s) on the number line where the given function is equal to zero:
The equation is written as: y = (x+5)(x-1)
This is further written as:
(x+5)(x-1) = 0 and x+5 = 0x- 1 = 0Giving x = -5 and x = 1.The highest point occurs when x = 0, which is (5)(-1) = -5
Therefore, plot a parabola that cuts the x-axis cut at x = -5 and 1, and a turning point at y = -5.
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The correct question is given below:
Use the drawing tool(s) to form the correct answers on the provided number line. plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).
Which if the following rational functions is graphed below?
A.F(x)=1/x+4
B.F(x)=1/4x
C.F(x)=1/x-4
D.F(x)=4/x
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Take note that there is a vertical asymptote at x = -4. This means that our function has the form:
▪ [tex]\longrightarrow \sf{F (x)=\dfrac{A}{x + 4} }[/tex]
[tex]\leadsto[/tex] By comparing it with the given options, the correct option is A.
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{A. \: \: F(x)= \dfrac{1}{x + 4} }[/tex]
Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).
The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point (-6,8) is -6x+8y=100.
Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]
and point at which the tangent meets the circle is (-6,8).
A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.
Linear equation looks like y=mx+c.
Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:
xz+ty=[tex]a^{2}[/tex].
We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at (-6,8).
It will be as under:
x(-6)+y(8)=100
-6x+8y=100
Hence the equation of tangent to the circle at the point (-6,8) is -6x+8y=100.
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1
Select the correct answer.
Which expression is equivalent to x+y+x+y+ 3(y+5)?
OA. 2x+5y+5
OB. 2x+y+30
OC. 2x+ 5y + 15
OD. 2x+3y + 10
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
I need to know how to solve it
The solution to the system of equations is x = 1, y = 10 and z = 4
How to solve the system of equations?The system of equations is given as:
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
Multiply the second equation by 2
So, we have
4x - 2y + 6z = 8
Add this equation to the first equation
3x + 4x + 2y - 2y + 4z + 6z = 11 + 8
Evaluate the like terms
7x + 10z = 19
Multiply the second equation by 3
So, we have
6x - 3y + 9z = 12
Subtract this equation from the third equation
6x - 5x - 3y + 3y + 9z - 5z = 12 + 1
Evaluate the like terms
x + 4z = 13
Make x the subject
x = 13 - 4z
Substitute x = 13 - 4z in 7x + 10z = 19
7(13 - 4z) + 10z = 19
Expand
91 - 28z + 10z = 19
Evaluate the like terms
-18z = -72
Divide
z = 4
Substitute z = 4 in x = 13 - 4z
x = 13 - 4 * 4
Evaluate
x = 1
We have:
2x -y +3z = 4
This gives
2(1) - y + 3 * 4 = 4
Evaluate
2 - y + 12 = 4
This gives
y = 10
Hence, the solution to the system of equations is x = 1, y = 10 and z = 4
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Which function represents the following graph?
X
The last one because the other ones only go to the positive side and not the negative too since the cube root
A rectangular prism with a volume of 3x^3+16x^2+5x cubic units has a base area of x^2+5xsquare units. Find the height of the rectangular prism.
The height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.
Volume of rectangular prismVolume of the prism = 3x³ + 16x² + 5x cubic unitsBase area = x² + 5x square unitsVolume of a rectangular prism = Base area × height
Height = Volume of a rectangular prism ÷ Base area
3x³ + 16x² + 5x cubic units = (x² + 5x) square units × h
h = (3x³ + 16x² + 5x) cubic units ÷ (x² + 5x) square units
h = (3x³ + 16x² + 5x) / (x² + 5x) units
Therefore, the height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.
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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=10
There is a maximum value of 7/6 located at (x, y) = (5/6, 7).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 10.
Rearranging the constraint, we get:
6x + y = 10,
or, y = 10 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(10 - 6x) = 10x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 10 - 12x ... (i)
Equating to 0, we get:
10 - 12x = 0,
or, 12x = 10,
or, x = 5/6.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.
The value of y, when x = 5/6 is,
y = 12 - 6x,
or, y = 12 - 6*(5/6) = 7.
The value of f(x, y) when (x, y) = (5/6, 7) is,
f(x, y) = xy,
or, f(x, y) = (5/6)*7 = 7/6.
Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).
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-6(4x + 5) = -24x - 30 associative property of addition commutative property of multiplication distributive property inverse property of addition
Answer:
distributive property
Step-by-step explanation:
The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.
Why are the events not mutually exclusive
The events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)
Why are the events not mutually exclusive?The probability values are given as:
P(A) = 0.3
P(B) = 0.6
P(A or B) = 0.8
For mutually exclusive events, we have:
P(A or B) = P(A) + P(B)
Substitute the known values in the above equation
P(A or B) = 0.3 + 0.6
Evaluate the sum
P(A or B) = 0.9
From the given parameters, we have
P(A or B) = 0.8
Hence, the events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)
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Answer:
D
Step-by-step explanation:
edge 2023
The sum of P(A) and P(B) is not equal to P(A or B).
Which of the following scatter plots does not have a zero correlation?
The first scatter plot is the only one that does not have a zero correlation.
When does a scatter plot has zero correlation?When the scatter plot has the format of a line, it does not have zero correlation.When the scatter plot has a format different than that of a line, it does have zero correlation.In this problem, the last three graphs do not have the format of a line, that is, they have zero correlation, and the first scatter plot is the only one that does not have a zero correlation, as the points are in the format of a line.
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An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
Which equation represents this ellipse?
Answer:
In standard form x^2/64 + y^2/100 = 1
Step-by-step explanation:
The major axis is the y axis because 10 has a larger value than 8.
8x8 = 64
10 x10 = 100
What is the equation for the line of best fit on the scatter plot below?
Answer:
The correct answer is the third option: y = 4x - 20
Step-by-step explanation:
To solve this problem, we should first find two points that are located along our line of best fit. We can see that the points (25,80) and (15, 40) are both located along the line. Next, we can calculate the slope using these two points.
slope = rise/run = Δy/Δx = (80-40)/(25-15) = 40/10 = 4
Therefore, the slope of the line of best fit is 4.
To find the y intercept, we can use our equation for slope and plug in one of our points.
y = mx + b
y = 4x + b
40 = 4(15) + b
40 = 60 + b
b = -20
Therefore, the y intercept is -20.
If we put both our slope and y intercept into one equation, we get:
y = mx + b
y = 4x - 20
The correct answer is the third option.
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I need help with this please and thank you.
Answer: I believe the answer would be as follows:
8.431 grams
5.46 seconds
980 meters
900 miles
Step-by-step explanation:
it would first be which has the largest number after the decimal point, so if there’s three it goes first (0.12*3*). Then you would pick the one that is the smallest form of measurement, which would be meters in this case.
Hope this helped!
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]
It has to be the last line in the second picture since it intersects the x axis at approximately x=-1.333[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{Last \: option \: (D.)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Write the equation in slope-intercept form. Then solve y.
▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]
▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]
Identify the x-intercept,
[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]
[tex]\small\longrightarrow \sf{3x=-4}[/tex]
[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]
[tex]\small\longrightarrow \sf{x = -1.33}[/tex]
The graph has the next properties:
[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]
[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]
[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]
