Answer:
x = -1223, y = -629, and z = -31.
Step-by-step explanation:
This question can be solved using multiple ways. I will use the Gauss Jordan Method.
Step 1: Convert the system into the augmented matrix form:
• 1 -2 1 | 4
• 3 -5 -17 | 3
• 2 -6 43 | -5
Step 2: Multiply row 1 with -3 and add it in row 2:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 2 -6 43 | -5
Step 3: Multiply row 1 with -2 and add it in row 3:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 -2 41 | -13
Step 4: Multiply row 2 with 2 and add it in row 3:
0 2 -40 -18
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 0 1 | -31
Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• x - 2y + z = 4
• y - 20z = -9
• z = -31
Step 6: Since we have calculated z = -31, put this value in equation 2:
• y - 20(-31) = -9
• y = -9 - 620
• y = -629.
Step 8: Put z = -31 and y = -629 in equation 1:
• x - 2(-629) - 31 = 4
• x + 1258 - 31 = 4
• x = 35 - 1258.
• x = -1223
So final answer is x = -1223, y = -629, and z = -31!!!
Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a basic
tile that costs $1.50 per square foot, but he also wants to use an accent tile that costs $9.00 per square foot. How many
square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot?
Provide your answer below:
square feet basic tiles,
square feet accent tiles???
Hurrryyyy please
Answer:
800 basic 200 accent tiles
Step-by-step explanation:
The required square feet of basic tile and accent tile is 800 and 200 square feet respectively.
As the data available, 1,000 square feet of tile. He will do most of the floor with a basic tile that costs $1.50 per square foot, but he also wants to use an accent tile that costs $9.00 per square foot.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Here,
Let the number of basic tiles be x and the number of accent tiles be y,
According to the question,
x + y = 1000
x = 1000 - y - - - - - -- - - - - - - (1)
1.5x + 9y = 3000 - - - - - - -- - - (2)
Put the value of x in equation 2
1.5 (1000 - y ) + 9y = 3000
1500 - 1.5y + 9y = 3000
7.5y = 1500
y = 1500 / 7.5
y = 200
Now, put y in equation 1
x = 800
Thus, the required square feet of basic tile and accent tile is 800 and 200 square feet respectively.
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Find the values of x and y in the diagram
Answer:
x=15
y=5
Step-by-step explanation:
The small looking triangle has 3 angles that are congruent to each other. We know this because they all share that same single marker. That means each of those angles ate 60 degrees. That triangle is known as both a equilateral and equilangular. All that means is all of it's 3 sides are congruent and all of it's 3 angles are congruent.
So that angle that measures 8x forms a linear pair with the angle right next to it in the other triangle. All that means is that is supplementary to and adjacent to that angle that measures 60 degrees.
So we have 8x+60=180.
We need to solve this equation for x:
8x+60=180
Subtract 60 on both sides:
8x. =120
Divide both sides by 8
x. =120/8
x. =15
Now to find y.
The bigger looking triangle is an isosceles. We know this because its two base angles are congruent (they have the same double marker). This means 5y+1=26.
Solving:
5y+1=26
Subtracting 1 on both sides:
5y. =25
Dividing 5 on both sides:
y. =5
The values of [tex]x[/tex] and [tex]y[/tex] are required.
[tex]x=15,y=5[/tex]
In the figure
[tex]\angle BAD=\angle BDA[/tex]
This means the sides opposite to the angles will also be equal.
So, [tex]AB=BD=26[/tex]
In [tex]\Delta BDC[/tex] all angles are equal, so it is an equilateral triangle.
So, all angles are [tex]60^{\circ}[/tex]
[tex]\angle ABD+\angle DBC=180\\\Rightarrow 8x+60=180\\\Rightarrow x=\dfrac{180-60}{8}\\\Rightarrow x=15[/tex]
All sides are equal in [tex]\Delta BDC[/tex]
[tex]26=5y+1\\\Rightarrow y=\dfrac{26-1}{5}\\\Rightarrow y=5[/tex]
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Which of the following could lead to a misleading graph?
The x- and y-axes start at zero,
The intervals on the y-axis are inconsistent
The intervals on the y-axis and the intervals on the x-axis are different
Differing heights are used on a bar graph.
Answer:
The intervals on the y-axis are inconsistent.
Step-by-step explanation:
The x- and y-axes start at 0 - this is what graphs normally start with - it is out of the norm to not start at 0.
The intervals on the y-axis are inconsistent - this can cause a problem - we humans tend to judge a graph on height, so changing some of the intervals can mess up a human's actions based on the graph,for example people might think more positively or negatively of a brand or company, and even a totally different view.
The intervals on the y and x-axis are different - they can be different for particular reasons, for example a company might want to put time intervals in months on the x-axis and revenue in dollars on the y-axis - sometimes it is just necessary.
Differing heights are used on a bar graph - this allows us to compare data - without it we would not be able to do much with it.
Misleading graphs can occur due to various reasons such as inconsistent intervals on the axes or the axes not starting at zero. Using different heights on a bar graph can also lead to misleading data representation.
Explanation:Misleading graphs can occur when certain elements are not accurately represented. Three situations that could lead to a misleading graph are:
The x- and y-axes start at zero: When the axes of a graph do not start at zero, it can distort the visual representation of data and lead to misinterpretation.The intervals on the y-axis are inconsistent: Inconsistent intervals on the y-axis can exaggerate or downplay differences between data points, distorting the true picture of the dataAdditionally, using differing heights on a bar graph can also lead to a misleading representation of data.
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Leo has b boxes of pencils. Each box contains 6 pencils. He has a total of 42 pencils.
Answer:
7 boxes
Step-by-step explanation:
Simply divide 42 by 6 to get your answer.
I am joyous to assist you anytime.
find the missing side, round to the nearest tenth place
Answer:
8.87
Step-by-step explanation:
The square means "right angle"
[tex] \sin(\alpha ) = \frac{x}{13} \\ \\ \sin(43) = \frac{ x }{13} \\ \\ x = \sin(43) \times 13 \\ x = 8.86597868081 \\ x = 8.87[/tex]
In reducing ones speed from 70mph to 50 mph how much of a percentage decrease in stopping distance is realized
Answer:
28.57142857% decrease
Step-by-step explanation:
To find the percentage decrease in speed, take the original speed minus the new speed over the original speed. Then multiply by 100%
original speed = 70 new speed =50
percent decrease = (70-50)/70 *100%
= 20/70 *100%
=28.57142857%
HELPPPPPPPPPPP?????????
Answer:
14.21 units
Step-by-step explanation:
We can use distance formula to solve this easily.
Distance Formula is [tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Where
D is the distance
x_1, y_1 is the first points, respectively (let it be -6,-6)
x_2,y_2 is the second pints, respectively (let it be 3,5)
Substituting the values into the formula, we can get the value of D:
[tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\D=\sqrt{(5--6)^2+(3--6)^2}\\D=\sqrt{11^2+9^2}\\ D=\sqrt{202} \\D=14.21[/tex]
This is the distance, the first answer choice is right.
What is the x-intercept of the line shown below? Enter your
answer as a coordinate pair.
Answer:
(0,3)
Step-by-step explanation:
The x-intercept is the point in the graph where x=0. On the graph you can see that when x=0, y=3. Therefore our coordinate is (0,3)
Our coordinate pair in the graph is (0,3)
The x-intercept of a line occurs where the line intersects the x-axis, meaning the y-coordinate is zero. In the provided graph, when x equals zero, the corresponding y-value is three. Thus, the coordinate pair (0,3) represents the point where the line intersects the x-axis. This result indicates that when x equals zero, the line crosses the y-axis at a height of three units.
To find the x-intercept, one sets y equal to zero and solves for x. In this case, when y equals zero, there is no such point on the line, so the x-intercept does not exist. Therefore, the coordinate (0,3) accurately identifies the x-intercept of the given line, demonstrating the point where it intersects the x-axis on the graph.
What is the solution to log^2(9x) -log^2 3=3
Answer: [tex]\bold{B)\quad x = \dfrac{8}{3}}[/tex]
Step-by-step explanation:
[tex]log_2(9x)-log_2(3)=3\\\\\\log_2\bigg(\dfrac{9x}{3}\bigg)=3\qquad\qquad \rightarrow \text{used rule for condensing logs}\\\\\\log_2(3x)=3\qquad\qquad \rightarrow \text{simplified}\\\\\\3x=2^3\qquad\qquad \rightarrow \text{used rule for eliminating log}\\\\\\3x=8\qquad\qquad \rightarrow \text{simplified}\\\\\\\large\boxed{x=\dfrac{8}{3}}[/tex]
325,25 1.58 which digit is in the thousands place
Answer:
The 5 all the way to the left
325,251.58
Step-by-step explanation:
The 8 is in the hundredths place
The 5 is in the tenths place
The 1 is in the ones place
The 5 is in the tens place
The 2 is in the hundreds place
The 5 is in the thousands place
The 2 is in the ten-thousands place
The 3 is in the hundred-thousands place
Hope This Helped :}
Neither of the given numbers (325,25 and 1.58) have a thousands place. This would typically be represented by the digit to the left of the hundreds place.
Explanation:The student has asked about the thousands place in a pair of numbers. Looking at the numbers provided (325,25 and 1.58), neither of these numbers actually have a thousand place digit. In a number, the thousands place digit is the digit to the left of the hundreds place. For example, in the number 6528, which is from an arithmetic operation given in the reference information (6527.23 + 2 = 6528.23), the 6 represents 6 thousands, or 6000.
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If f(x) = 5x + 40, what is f(x) when x = -5?
0
-9
0
-8
O7
O 15
Replace x in the equation with -5 and solve.
5(-5) +40 = -25 + 40 = 15
The value of f(x) when x = -5 is f(-5) = 15 by substitution.
Given that a function is defined as:
f(x) = 5x + 40
It is required to find the value of f(x) when the value of x = -5.
Substitute the value of x = -5 in the expression for f(x).
So,
f(-5) = 5(-5) + 40
= -25 + 40
= 15
So, the value of f(x) when x = -5 is 15.
Hence f(x) = 15 when x = -5.
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How many distinguishable 3-letter word of the how many distinguishable five letter combinations are possible of the letters of the word toy
Answer:
that is really confusing.
Step-by-step explanation:
Which inequality statement best represents the graph below?
What is the completely factored form of 2x^3+4x^2-x
Answer:
I think it's:
x(2x^2+4x-1)
In 1993, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic model y =0.2313x2 +2.600x + 35.17
approximates this cap in millions of dollars for the years 1993-2013, where x = 0 represents 1993, X = 1 represents 1994, and so on. Complete parts a and b.
a. Approximate the sports league salary cap in 2009.
me
nts
ontents
The approximate sports league salary cap in 2009 is $ million
(Round to the nearest tenth as needed.)
b. According to the model, in what year did the salary cap reach 65 million dollars?
Cuccess
According to the model in the salary cap reached 65 million dollars.
(Round down to the nearest year)
ts for a
Answer:
a. The approximated salary cap in 2009 is $136.0 millions
b. The salary cap reached 65 million dollars in 2000
Step-by-step explanation:
* Lets explain how to solve the problem
- The quadratic model of the salary cap in million is
y = 0.2313 x² + 2.600 x + 35.17
- The approximation of this cap in millions of dollars for the years
1993-2013 where x = 0 represents 1993, x = 1 represents 1994,
and so on
a. Lets calculate the approximated sports league salary cap in 2009
∵ x at 2009 = 2009 - 1993 = 16
∵ y = 0.2313 x² + 2.600 x + 35.17
∴ y = 0.2313 (16)² + 2.600 (16) + 35.17
∴ y = 135.98 ≅ 136.0 millions
* The approximated salary cap in 2009 is $136.0 millions
b. Lets calculate in what year did the salary cap reach 65 million dollars
∵ y = 65
∵ y = 0.2313 x² + 2.600 x + 35.17
∴ 65 = 0.2313 x² + 2.600 x + 35.17
- Subtract 65 from both sides
∴ 0.2313 x² + 2.600 x - 29.83 = 0
- Use the calculator to find the value of x by solving the quadratic
equation
∴ x = 7.05 and x = -18.29 (we will reject this value)
∴ x ≅ 7 years
∴ The salary cap reached 65 million dollars in (1993 + 7) = 2000
* The salary cap reached 65 million dollars in 2000
Final answer:
To approximate the sports league salary cap in 2009, plug in 2009 for x in the given quadratic model equation. The salary cap in 2009 is approximately $942.9 million. If we set the salary cap to $65 million and solve for x using the quadratic model, we find that the cap reached $65 million in the year 2004.
Explanation:
To approximate the sports league salary cap in 2009, plug in 2009 for x in the quadratic model given. The equation becomes:
y = 0.2313(2009)^2 + 2.600(2009) + 35.17
Simplifying the equation gives:
y ≈ 942.85
Therefore, the approximate sports league salary cap in 2009 is $942.9 million (rounded to the nearest tenth).
To determine the year when the salary cap reached $65 million, set y = 65 in the quadratic model and solve for x:
65 = 0.2313x^2 + 2.600x + 35.17
By rearranging the equation and solving for x using the quadratic formula, we find that:
x ≈ 4.56
Rounding down to the nearest year, we can conclude that the salary cap reached $65 million in the year 2004.
What is the smallest positive x-intercept of the graph
Answer:
smallest positive x intercept =Π/2
The sentences based on the graph of the function:
This is the graph of a function.
The y-intercept of the graph is the function value y = 0.
The smallest positive x-intercept of the graph is located at 2.5.
The greatest value of y is y = 7.
For x between 2 and 3, the function value y = 0.
A function is a relation between two sets, where each element in the first set is paired with exactly one element in the second set. In other words, for every input, there is only one output. The graph above shows that for every input value of x, there is only one output value of y. Therefore, the graph represents a function.
The y-intercept of a graph is the point where the graph crosses the y-axis. The y-intercept of the graph above is (0, 0), which means that the function value at x = 0 is y = 0.
The x-intercept of a graph is the point where the graph crosses the x-axis. The smallest positive x-intercept of the graph above is (2.5, 0), which means that the smallest positive input value for which the function value is 0 is 2.5.
The greatest value of y is the highest point on the graph. The highest point on the graph above is (3, 7), which means that the greatest value of y is 7.
For the interval 2 < x < 3, the function value is 0. This means that for all input values in this interval, the output value is 0.
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The following question may be like this:
• This is the graph of a function.
• The y-intercept of the graph is the function value y =
• The smallest positive x-intercept of the graph is located at 25
• The greatest value of y is y =
What is the simplified expression
Answer:
7y - 4x
Step-by-step explanation:
Given
- 3(2x - y) + 2y + 2(x + y) ← distribute both parenthesis
= - 6x + 3y + 2y + 2x + 2y ← collect like terms
= - 4x + 7y
= 7y - 4x
How many hours is from 10:30 to 2:50
Answer:
4 hours and 20 minutes
Step-by-step explanation:
Answer:
4 1/3 hours
Step-by-step explanation:
10:30 to 11:30 1 hour
11:30 to 12:30 1 hour
12:30 to 1:30 1 hour
1:30 to 2:30 1 hour
2:30 to 2:50 20 minutes 20 minutes/60 minutes = 1/3 hour
1+1+1+1 +1/3 = 4 1/3 hours
Can someone please explain this question? I have a pic
Step-by-step explanation:
recall in a linear equation expressed in the form
y = mx + b,
m represents the slope or the rate of change in the value of y for a unit change in the value of x
b represents the y-intercept (i.e the value of y when x = 0)
If you compare these definitions to what was given in the question, the rate of change in snowfall is given as 1/2 inches per hour. This is equivalent to the m value in our general equation above. Hence we can say that the rate of change in snowfall is equal to the slope of the graph.
The question also states that before the snow even started to fall (i.e when x=0 hours), there was already 8 inches on the ground. This is equivalent to the value of b in our general equation above. Hence we can say that the y-intercept is representative of the 8 inches that was already on the ground when the snow started falling.
AB¯¯¯¯¯¯¯¯ is the diameter of circle T. Point A is located at (-9,-1) and point B is located at (-1,-5). What are the coordinates of the center of this circle?
Answer:
The coordinates of the center of this circle are (-5 , -3)
Step-by-step explanation:
* Lets explain how to solve the problem
- The mid-point of the segment whose endpoints are (x1 , y1) , (x2 , y2)
is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
- AB is the diameter of circle T
∵ The diameter must passing through the center of the circle
∵ The center of the circle is the mid-point of all diameters of the circle
∵ The center of the circle is point T
∴ T is the mid point of the diameter AB
- Lets calculate the coordinates of point T by using the rule above
∵ A = (-9 , -1) and B = (-1 , -5)
∵ T is the mid-point of AB
- Let A = (x1 , y1) , B = (x2 , y2) and T = (x , y)
∴ x1 = -9 , x2 = -1 and y1 = -1 , y2 = -5
∴ [tex]x=\frac{-9+-1}{2}=\frac{-10}{2}=-5[/tex]
∴ [tex]y=\frac{-1+-5}{2}=\frac{-6}{2}=-3[/tex]
∴ The coordinates of point T are (-5 , -3)
* The coordinates of the center of this circle are (-5 , -3)
Answer:
(-5,-3)
Step-by-step explanation:
I got it correct on founders edtell
help!!!!!!!!!!! If one factor of x2 + 2x – 24 is (x+6), what is the other factor?
(x+8)
(x–8)
(x+4)
(x−4)
Answer:
the other factor is (X-4)
Step-by-step explanation:
this is a perfect square trinomial so the two factors should interact the next way:
x2 + 2x – 24
(X+6) * (X-4) the two numbers added give you the middle . . number (2)
and multiplied give you the final number (24) so:
1) +6-4 = 2
and
2) +6 * - 4 = -24
A new sweater costs $15.99. If the sweater is on sale for 1/4 off
its price, about how much
would you save?
the sweater costs $15.99 regularly, however today is on sale, 1/4 off the regular price, how much is 1/4 of 15.99? well just their product, 15.99 * (1/4) = 3.9975.
that means that just for today, the sweater costs 15.99 - 3.9975.
so, today you're not really paying $15.99 for the sweater, you're paying 3.9975 less, so you're saving 3.9975. That's $3.9975 that you won't be spending on it, thus saving it.
Answer:
4 dollars off
Step-by-step explanation:
The cost of the sweater is 15.99
You get 1/4 off
Multiply the cost by the discount
15.99 * 1/4
The questions asks about how much so you can round 15.99 to 16
16*1/4 = 4
You will get about 4 dollars off
Solve by completing the square. x2+6x−6=0
For this case we must solve the following equation by completing squares:
[tex]x ^ 2 + 6x-6 = 0[/tex]
We add 6 to both sides of the equation:
[tex]x ^ 2 + 6x = 6[/tex]
We divide the middle term by 2, and square it:
[tex](\frac {6} {2}) ^ 2[/tex]
And we add it to both sides of the equation:
[tex]x ^ 2 + 6x + (\frac {6} {2}) ^ 2 = 6 + (\frac {6} {2}) ^ 2\\x ^ 2 + 6x + (3) ^ 2 = 6 + 9[/tex]
We rewrite the left part of the equation:
[tex](x + 3) ^ 2 = 15[/tex]
We apply root to both sides:
[tex]x + 3 = \pm \sqrt {15}[/tex]
We have two solutions:
[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]
Answer:
[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]
Answer:
[tex]x=-3\±\sqrt{15}[/tex]
Step-by-step explanation:
We have the following equation
[tex]x^2+6x-6=0[/tex]
To use the method of completing squares you must take the coefficient of x and divide it by 2 and square the result.
[tex](\frac{6}{2})^2=9[/tex]
Now add 9 on both sides of equality
[tex](x^2+6x+ 9)-6=9[/tex]
Factor the term in parentheses
[tex](x+3)^2-6=9[/tex]
Add 6 on both sides of the equation
[tex](x+3)^2-6+6=9+6[/tex]
[tex](x+3)^2=15[/tex]
Take square root on both sides of the equation
[tex]\sqrt{(x+3)^2}=\±\sqrt{15}[/tex]
[tex]x+3=\±\sqrt{15}[/tex]
Subtract 3 from both sides of the equation.
[tex]x+3-3=-3\±\sqrt{15}[/tex]
[tex]x=-3\±\sqrt{15}[/tex]
If N || P and P bisects M then _____ (13)
If N || P and P bisects M then, line N must be perpendicular to line M (N ⊥ M) (option A).
How to determine the relationship between line N and line P?
From the given diagram we are told that line N is parallel to line P and line P is perpendicular to line M.
So line P bisect line M and it is also perpendicular to line M, we can deduce the following;
line N is perpendicular to line M
So based on the information given to us, we can only deduce the relationship between M, N and P.
Hence N must be parallel to P, then line P must be perpendicualr to line M and line N and line M must be perpendicular to each other.
Write an equation;
If a number is decreased by five and then the result is multiplied by two the result is 26
The equation of the word problem is ( x - 5 ) × 2 = 26 and the value of the unknown number is 18.
What is the equation?Given that;
A number is decreased by five and then the result is multiplied by two.
The result is 26.
Let x represent the unknown know number.
Number is decreased by five: x - 5Then the result is multiplied by two: ( x - 5 ) × 2The result is 26: ( x - 5 ) × 2 = 26Hence,
The equation is ( x - 5 ) × 2 = 26
We can go further and solve for the value of the unknown number.
( x - 5 ) × 2 = 26
2x - 10 = 26
2x = 26 + 10
2x = 36
x = 36 ÷ 2
x = 18
The equation of the word problem is ( x - 5 ) × 2 = 26 and the value of the unknown number is 18.
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Final answer:
The equation based on the given statement is 2(x - 5) = 26. By following the order of operations and solving for the unknown number x, we find that x = 18.
Explanation:
To write an equation for the statement "If a number is decreased by five and then the result is multiplied by two, the result is 26," we start by letting x represent the unknown number. First, we decrease x by five, which is represented mathematically as x - 5. Following this, we then multiply the result by two, which gives us 2(x - 5). The statement concludes by saying that this expression is equal to 26, giving us the final equation:
2(x - 5) = 26
To solve for x, we can follow these steps:
Distribute the 2 across the parentheses: 2*x - 2*5 = 26, which simplifies to 2x - 10 = 26.Add 10 to both sides of the equation to isolate the term with x on one side: 2x - 10 + 10 = 26 + 10, simplifying to 2x = 36.Divide both sides of the equation by 2 to solve x: 2x / 2 = 36 / 2, which simplifies to x = 18.Therefore, the number we are looking for is 18.
a certain stock starts the day at $27 3/8 per share. if it drops $2 1/2 during the day what is it’s closing value
let's firstly convert the mixed fractions to improper fractions and then simply get their difference, our denominators will be 8 and 2, so our LCD will be 8.
[tex]\bf \stackrel{mixed}{27\frac{3}{8}}\implies \cfrac{27\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{219}{8}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{219}{8}-\cfrac{5}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)219~~-~~(4)5}{8}}\implies \cfrac{219-20}{8}\implies \cfrac{199}{8}\implies 24\frac{7}{8}[/tex]
Find the following when : a=-2,b=3c=-1/3 7b-2/-a+1
Answer: [tex]\bold{\dfrac{19}{3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{7b-2}{-a+1}\\\\\\=\dfrac{7(3)-2}{-(-2)+1}\\\\\\=\dfrac{21-2}{2+1}\\\\\\=\dfrac{19}{3}[/tex]
Emily just hires a new employee to work in your bakeshop. In one hour the employee burned 650 chocolate chip cookies. if this represented 13% of the day’s production, how many cookies did you plan on producing that day?
Answer:
5000
Step-by-step explanation:
650 is 13% of the day's production.
650 = 0.13 × n
n = 5000
Derive the equation of the parabola with a focus at (-2,4) and a directrix of y=6 . Put the equation in standard form
Answer:
[tex]y = - \frac{1}{4} {(x + 2)}^{2} + 5[/tex]
Step-by-step explanation:
The vertex of this parabola is the midpoint of the focus (-2,4) and where the directrix intersects the axis of symmetry of the parabola (-2,6)
This parabola must open downwards due to the position of the directrix and has equation of the form:
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
This implies that:
[tex]h = - 2[/tex]
and
[tex]k = \frac{4 + 6}{2} = 5[/tex]
The value of p is the distance from the vertex to the focus:
[tex]p = |6 - 5| = 1[/tex]
We substitute all the values into the formula to get:
[tex](x - - 2)^{2} = - 4(1){(y - 5)}[/tex]
[tex] {(x + 2)}^{2} = - 4(y - 5)[/tex]
Or
[tex]y = - \frac{1}{4} {(x - 5)}^{2} + 5[/tex]
if there is a 10% chance of sun tomorrow and 20% chance of wind and no sun what is the probability that it is windy given that it is not sunny? round your answer to the nearest percent
Answer:
=22%
Step-by-step explanation:
Since we have given two conditions simultaneously that is windy and not sunny. So we will use the concept of conditional probability.
The probability of sunny day= P(sunny)=10%
P(sunny)=10%=0.1
The probability of windy and not sunny=P(windy|not sun)=20%
P(windy|not sun)=20% = 0.2
Now divide the both probabilities:
P(windy|not sun)/P(sunny)
=0.2/[1-0.1]
{Hence there are 10% chances of sun tomorrow than there are (1 - 0.1) chances of no sun}
If we subtract 1 from 0.1 than it becomes:
=0.2/0.9
=2/9
=0.2222222222
=22%
Hence the probability that it is windy = 22% ....
The probability that it is windy given that it is not sunny is approximately 22% when rounded to the nearest percent.
To find the probability that it is windy given that it is not sunny, you apply the concept of conditional probability. There's a 10% chance of sun, hence, there is a 90% chance of no sun (100% - 10%). Among this 90%, there is a 20% chance that it's windy without sun. To find the probability of windiness given no sun, you would take the chance of wind and no sun (20%) and divide it by the probability of no sun (90%).
The calculation would be as follows:
(20% chance of wind and no sun) / (90% chance of no sun) = (0.20) / (0.90)
= approximately 0.222
When expressed as a percentage and rounded to the nearest percent, this is approximately 22%.