Which inequality is represented by this graph?
A: y/2 >4-x
B:y>4-x/2
C:y<4-x/2
y/2<4-x
Answers
An inequality that is represented by this graph include the following: C. y ≤ (4 - x)/2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 3)/(2 + 2)
Slope (m) = -2/4
Slope (m) = -1/2.
At data point (2, 1) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -1/2(x - 2)
y = -x/2 + 1 + 1
y = -x/2 + 2
y ≤ (4 - x)/2 (since the solid line is shaded below)
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Related Questions
2. Calculate the mean absolute deviation of the following data set: (36, 54, 49, 39, 41, 48, 50)
45.3
8.7
5.7
07
Answers
To calculate the mean absolute deviation, we first need to calculate the mean of the data set:
Mean = (36 + 54 + 49 + 39 + 41 + 48 + 50) / 7 = 45
Next, we calculate the absolute deviation of each data point from the mean:
|36 - 45| = 9
|54 - 45| = 9
|49 - 45| = 4
|39 - 45| = 6
|41 - 45| = 4
|48 - 45| = 3
|50 - 45| = 5
To calculate the mean absolute deviation, we take the average of these absolute deviations:
Mean Absolute Deviation = (9 + 9 + 4 + 6 + 4 + 3 + 5) / 7 = 5.7
Therefore, the answer is option (c) 5.7.
Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 5 km from the nearest point B on a straight shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 13 km apart. (a) In general, if it takes 1. 4 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area?(b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. What would a large value of the ratio W/L mean in terms of the bird's flight? What would a small value mean? Determine the ratio W/L corresponding to the minimum expenditure of energy. (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? What should the value of W/L be for the bird to fly to B and then along the shore to D?(d) If the ornithologists observe that birds of a certain species reach the shore at a point 4 km from B, how many times more energy does it take a bird to fly over water than land?
Answers
The bird should fly to a point on the shoreline that is 4km from B to minimize total energy expenditure. A large W/L ratio means it's more efficient to fly over land, while a small ratio means it's more efficient to fly over water. The minimum ratio is 2.834. The W/L ratio should be 1 for the bird to fly directly to D, and 0 for the bird to fly to B and then along the shore to D. It takes a bird 1.4 times more energy to fly over water than land.
To minimize the total energy expended in returning to its nesting area, the bird should fly to the point on the shoreline that is 4 km from B. This can be found using the principle of least action, which states that the bird will choose the path that minimizes the integral of the energy expended along the path.
A large value of the ratio W/L would mean that it takes significantly more energy to fly over water than over land. A small value of the ratio would mean that there is not much difference in energy expenditure between flying over water and over land. The ratio W/L corresponding to the minimum expenditure of energy can be found using the same principle of least action as in part (a).
we are asked to determine the ratio W/L corresponding to the minimum expenditure of energy. Let x be the distance from B to C, and let y be the distance from C to D along the shoreline. Then the total energy expended in returning to its nesting area is given by
E(x, y) = L(13 - x - y) + W(√(25 - x²)) + W(√(y² + (13 - x)²))
To minimize E(x, y), we take partial derivatives with respect to x and y and set them equal to zero
dE/dx = L + Wx/√(25 - x²) - Wy/√(y² + (13 - x)²) = 0
dE/dy = L - Wy/√(y² + (13 - x)²) = 0
Solving for x and y, we get
x = 5√((W/L)/(1.4(W/L) - 1))
y = 13 - x - 5√((W/L)/(1.4(W/L) - 1))
The ratio W/L corresponding to the minimum expenditure of energy is obtained by substituting these values into the expression for E(x, y) and simplifying
W/L = 2.5(1.4 + √(1.96 + 4/25))/(4.9 - √(1.96 + 4/25))
W/L ≈ 2.834
Therefore, the ratio W/L corresponding to the minimum expenditure of energy is approximately 2.834.
To fly directly to its nesting area D, the value of W/L should be equal to 1. To fly to B and then along the shore to D, the value of W/L should be equal to 0.
If birds of a certain species reach the shore at a point 4 km from B, it takes 1.4 times more energy for the bird to fly over water than over land. This can be found by comparing the energy required to fly directly from the island to the point on the shoreline that is 4 km from B (which is entirely over water) to the energy required to fly along the shoreline from that point to D (which is entirely over land).
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Find the length of a side of a square if its area is: 40 inches
Answers
Answer:
Side = 6.3245 inches
Step-by-step explanation:
Area of square = side²
40 in² = side²
√(40 in²) = √(side²)
6.3245 in = side
Write two different quadratic functions that go through the points (5,3) and (8,0). (PLEASE ANSWER CORRECTLY)
Answers
Answer:
[tex]y=x^{2} -14x+48[/tex] (when a=1)
[tex]y=2x^{2} -27x+88[/tex] (when a=2)
The general form of the quadratic functions you asked is :
[tex]y=a(x-5)(x-8)-x+8\\(a\neq 0)[/tex]
Here,
-x+8 is a line that passes two given points.
When you put x=5, you get y=3,
which is a coordinate of one of the given points.
When you put x=8, you get y=0,
which is a coordinate of the other one.
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This is the way I got the form above :
Since what we're looking for is a quadratic function, (let's call it "f(x)")
the equation
f(x)=-x+8
can have at most 2 different real solutions.
You can note that the real solution of the equation above
represents the x coordinate of the intersection point of two graphs:
y=f(x) and y=-x+8.
Again, the equation can have at most 2 different solutions.
And we have 2 different real solutions already given -
(It's a requirement ; we want y=f(x) to contain (5,3) and (8,0))
- which are x=5, x=8.
So these are the only two solutions of the equation.
Since the coefficient of a highest order term
hasn't been decided, we can introduce an unknown 'a' for it.
(i.e. Let 'a' be the coefficient of a highest order term.)
To sum up, an equation
f(x)=-x+8
f(x)+x-8=0
has two different real solutions x=5, x=8,
thus it can be written like this;
a(x-5)(x-8)=0
where a is not zero.
Therefore
f(x)+x-8 = a(x-5)(x-8)
(Because two italic-texted equations have the same meaning)
∴ [tex]f(x)=a(x-5)(x-8)-x+8[/tex][tex]\QED[/tex].
Anybody know how to do this?
Answers
The point which is a solution to the system y = x + 7 and y = 11 - x is: 2. (2, 9).
The value of b in the second equation must be: 1. 10.
The x-coordinate of the solution to the system is: 4. x = -2.
The y-coordinate of the solution is: 4. y = 4.
The point (2, 5) would not be a solution to this equation: 4. 2x + 4y = 12
How to determine the solution to the system of equations?In this scenario and exercise, you are required to determine the solution to the given system of equations as follows;
y = x + 7
y = 11 - x
By using the substitution method, we have the following:
x + 7 = 11 - x
2x = 4
x = 4/2 = 2.
y = x + 7 = 2 + 7 = 9.
Question 2:Next, we would determine the value of b as follows;
x = 1
y = 3x + 5 = 3(1) + 5 = 8
y = -2x + b
b = y + 2x = 8 + 2(1) = 10.
Question 3:For the x-coordinate of the solution to the system, we have:
y = 4x + 7
x + y = -3
-3 - x = 4x + 7
5x = -10
x = -10/5 = -2.
Question 4:For the y-coordinate of the solution, we have:
x + 3 = -2x + 6
3x = 3
x = 1
y = x + 3 = 1 + 3 = 4
Question 5:2x + 4y = 12
2(2) + 4(5) = 12
4 + 20 = 12
24 = 12 (False).
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Ixl please help please
Answers
The ordering of the topics from broader to narrowest are given as follows:
The influence of popular media on elections.The influence of television programs on elections.The influence of televised debates on elections.What are broad and narrow topics?Broad topics are topics that affect a larger amount of the population than narrower topics affect.
In the context of this problem, we have that the television is a subset of the popular media, hence the popular media is broader than the television.
Televised debates are one program on the television, that is, it is a subset of the television, hence television programs are broader than television debated.
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What is the area of this figure
Thanks for any answer or help :)
Answers
Answer:
72
Step-by-step explanation:
3x6=18
8x7=56
18+56=72
Hope this helps :)
it takes carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. how many minutes will it take carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?
Answers
It will take Carlos 33 minutes to cycle from home to work along the same route at an average distance rate of 6 miles per hour.
To find out how many minutes it will take Carlos to cycle from home to work, we'll need to determine the distance of the route first, and then calculate the time it takes to cover that distance at the average cycling speed.
To solve this problem, we can use the formula:
time = distance/speed
1. Find the distance: Since Carlos drives from home to work in 9 minutes at an average rate of 22 miles per hour, we can calculate the distance using the formula: distance = rate × time.
First, convert the time from minutes to hours: 9 minutes ÷ 60 minutes/hour = 0.15 hours.
Now, calculate the distance: distance = 22 miles/hour × 0.15 hours = 3.3 miles.
2. Calculate the cycling time: Now that we know the distance is 3.3 miles, we can find out how long it will take Carlos to cycle at an average rate of 6 miles per hour.
Use the formula: time = distance ÷ rate.
time = 3.3 miles ÷ 6 miles/hour = 0.55 hours.
Now, convert the time back to minutes: 0.55 hours × 60 minutes/hour = 33 minutes.
So, it will take Carlos 33 minutes to cycle from home to work along the same route at an average rate of 6 miles per hour.
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(5 points) how many ways are there to distribute seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear?
Answers
There are 77,910 ways to distribute the seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear.
How to use the principle of inclusion-exclusion to solve this problem?We can use the principle of inclusion-exclusion to solve this problem. Let A be the set of all possible ways to distribute the apples and pears without any restrictions, and let B, C, and D be the sets of ways to distribute the apples and pears such that person 1, person 2, and person 3, respectively, does not receive a pear.
We can compute |A|, the total number of ways to distribute the apples and pears, as follows:
|A| = (7 + 6) choose 3 = 78 choose 3 = 82,251
To compute |B|, we can first choose 6 pears to give to persons 2 and 3 (since person 1 cannot receive a pear). This can be done in (6 choose 2) = 15 ways. Then, we can distribute the remaining 7 apples and 1 pear to the three people in any way, which can be done in (8 choose 1) * (6 choose 2) = 84 ways. Therefore, |B| = 15 * 84 = 1,260.
Similarly, |C| = |B| and |D| = |B|, since the problem is symmetric with respect to the three people.
To compute |B intersection C|, we can choose 6 pears to give to person 3 (since persons 1 and 2 cannot receive a pear). This can be done in (6 choose 1) = 6 ways. Then, we can distribute the remaining 7 apples and 2 pears to persons 1 and 2 in any way, which can be done in (9 choose 2) = 36 ways. Therefore, |B intersection C| = 6 * 36 = 216.
Similarly, |B intersection D| = |C intersection D| = |B intersection C|, since the problem is symmetric with respect to the three people.
To compute |B intersection C intersection D|, we can simply distribute the 7 apples and 3 pears among the three people in any way, which can be done in (13 choose 3) = 286 ways.
Therefore, by the principle of inclusion-exclusion, the number of ways to distribute the apples and pears such that each person has at least one pear is:
|A intersection complement(B union C union D)| = |A| - |B union C union D| = |A| - (|B| + |C| + |D| - |B intersection C| - |B intersection D| - |C intersection D| + |B intersection C intersection D|) = 82,251 - (3 * 1,260 - 3 * 216 + 286) = 77,910.
Therefore, there are 77,910 ways to distribute the seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear.
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You have the chance to purchase a car for $6,250.
You must put 10% down and finance the balance at 6% for 36 months. Sales tax is 8.25 %.
You have no trade in.
What are the monthly payments?
Answers
The monthly payments after the down payment are $186.58 per month.
What are the monthly payments?We will first calculate amount of the down payment which is:
= 10% * 6,250.
= $625.
So, the financed amount for the purchase will be:
= $6,250 - $625
= $5,625.
We will now calculate the amount of sales tax where tax rate is 8.25%, this give us:
= $6,250 * 8.25%
= $515.63.
The total amount financed including sales tax is:
= $5,625 + $515.63
= $6,140.63.
To calculate the monthly payments, we can use the formula M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
M = $6,140.63* [ 0.005(1 + 0.005)^36 ] / [ (1 + 0.005)^36 – 1 ]
M = $6,140.63* 0.03042193745
M = $186.58
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What value of X makes the equation 33x=11 true
Answers
Answer:
x = 1/3
Step-by-step explanation:
To solve this equation for x, divide each side by 33.
33x/33 = 11/33
x = 1/3
Answer:
x=3
Step-by-step explanation:
The value of x that makes the equation true is 3.
What is an equation?
An equation is a statement that equates to two expressions.
The given equation is:
Divide both sides by 11
So, the required value of x=3.
Questions from Page 45 in Dale Seymour Publications' Developing Skills in Algebra Book B (adding all of this info in case someone needs to keyword it at some point)
4.] The side of one square is five times that of another square. The difference in the areas of the two squares is 96. Find the sum of the areas of the two squares.
6.] The second side of a triangle is four more than the first side, and the third side is five more than the second. If the product of the first and third sides is added to the product of the second and third sides, the result is 124 more than twice the square of the first side. Find the perimeter of the triangle.
7.] A concrete walk 5 m wide is built around a grass court. The length of the court is 12 m more than its width. The area of the walk is 560 m^2. Find the dimensions of the grass court.
Answers
The sum of the areas of the two squares = 104
The perimeter of the triangle is 27.67
How to solve for the area1. We have 5x)² - x² = 96
next wer have to solve for x
25x² - x² = 96
x = 2
x² = 2² = 4
5x)² = 10² = 100
sum of the areas = 4 + 100 = 104
2. b = a + 4
c = b + 5
ac + bc = 2a^2 + 124
substitute b and c from the relationships:
When we simplify we have 18a = 88
a = 44/9
b = a + 4 = 44/9 + 4 = 80/9
c = b + 5 = 80/9 + 5 = 125/9
perimeter = a + b + c:
= 44/9 + 80/9 + 125/9
= 249/9 = 27.67
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find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ).
Answers
To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first visualize the graph of the limaçon.
The equation r = 1 2 + cos(θ) represents a curve that resembles a snail shell or a heart shape with a loop inside another loop. To find the area inside the larger loop and outside the smaller loop, we need to set up the integral using the polar coordinates.
The formula for the area enclosed by a polar curve is given by:
A = 1/2 ∫(θ2-θ1) (r2-r1)² dθ, where r2 is the outer curve, r1 is the inner curve, and θ1 and θ2 are the angles where the curves intersect.
In this case, the inner curve is r = 1 - cos(θ), and the outer curve is r = 1/2 + cos(θ). The curves intersect when cos(θ) = 1/2 or θ = π/3 and θ = 5π/3.
So, we need to split the integral into two parts, one for θ = π/3 to θ = 5π/3, and another for θ = 5π/3 to θ = π/3.
This is because the outer curve becomes the inner curve and vice versa when we cross the angle θ = 5π/3. For the area inside the larger loop and outside the smaller loop, we need to subtract the area enclosed by the inner curve from the area enclosed by the outer curve.
Using the formula above and plugging in the values, we get:
A = 1/2 ∫(5π/3-π/3) [(1/2 + cos(θ))² - (1-cos(θ))²] dθ
Simplifying this integral, we get:
A = 1/2 ∫(5π/3-π/3) [5/4 + 2cos(θ)] dθ
A = 5/8 [θ + sin(θ)](5π/3-π/3)
A = 5/8 [4π/3 + sin(4π/3) - (π/3 + sin(π/3))]
A = 5/8 [4π/3 - √3/2]
A = 5π/6 - (5/16)√3
Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is 5π/6 - (5/16)√3.
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To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 + 2cos(θ), use the formula for finding the area enclosed by a polar curve.
Explanation:122π/3∫0(12+cosθ)2dθ, r=(1/2)+cos\u0026#952, , 1, 2, cos, , FindThe general formula is A = (1/2)∫(r^2)dθ, where r is the equation of the curve. In this case, we need to find the area between two curves: the larger loop given by r = 1 + 2cos(θ) and the smaller loop given by r = 1. To find the limits of integration, we need to find the values of θ where the two curves intersect. After finding the values of θ where the curves intersect, we can integrate the difference between the two equations r = 1 + 2cos(θ) and r = 1 with respect to θ.
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A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
Answers
What is the volume of the solid figure?
A rectangular prism on top of another longer rectangular prism. The top prism measures 5 inches by 5 inches by 5 inches. The bottom prism measures 20 inches by 5 inches by 5 inches.
Answers
Answer:
The volume of the solid figure is 625 cubic inches.
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying its length, width, and height.
For the top prism, the volume is:
5 inches x 5 inches x 5 inches = 125 cubic inches
For the bottom prism, the volume is:
20 inches x 5 inches x 5 inches = 500 cubic inches
To find the total volume of the solid figure, we need to add the volumes of the two prisms together:
Total volume = 125 cubic inches + 500 cubic inches = 625 cubic inches
Therefore, the volume of the solid figure is 625 cubic inches.
Regenerate response
A student says the histogram is skewed right with an outlier and intervals of 5. Is the student correct? If not explain
Answers
The student is not correct because there are intervals of 4 and the histogram is relatively symmetric.
Why is the student wrong ?The histogram is not skewed right, but instead appears to be faintly symmetrical; the frequency of points commence from a count of 0, proceeding to pulsate up to 4 and then progressively meander downward from there to 3.
No apparent outlier can be seen in the provided histogram data; this refers to any data point that disagreeably differs from the remainder of datasets. In this occurrence, no numbers stand out significantly deviantly from the rest.
The intervals used in the histogram are not five units wide, but four units wide instead.
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The two figures are similar. What is the value of x?
Answers
Answer:
Step-by-step explanation:
Create a proportion between the sides of both triangles:
4 corresponds to 8 and 2x+2 corresponds to 12:
So, the proportion will be [tex]\frac{4}{8}=\frac{2x+2}{12}[/tex].
Continue by simplifying the rest:
[tex]\frac{1}{2}=\frac{2x+2}{12}[/tex]
Multiply by 12 on both sides (the 12 will cancel out with itself on the right side):
[tex]12*\frac{1}{2}=2x+2[/tex]
[tex]2x+2=6[/tex]
So, using basic algebra skills, we get that x = 2.
Check:
Is [tex]\frac{4}{8}=\frac{6}{12}[/tex] ?
Yes, it is!
A first number plus twice a second number is 8. . Twice the first number plus the second totals 34
Answers
Answer:
20-6Step-by-step explanation:
You want two numbers such that ...
first plus twice the second is 8twice the first plus the second is 34.SetupLet x and y represent the first and second numbers, respectively. Then the given relations can be written as the equations ...
x +2y = 8
2x +y = 34
SolutionSolving the first equation for x gives ...
x = 8 -2y
Using that in the second equation, we have ...
2(8 -2y) +y = 34
16 -3y = 34 . . . . . . eliminate parentheses
-18 = 3y . . . . . . . . add 3y-34
-6 = y . . . . . . . . divide by 3
x = 8 -2(-6) = 8 +12 = 20
The first number is 20, and the second number is -6.
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write a funtion whose graph has two vertical asymptotes located at x = -5 and x = 2
Answers
The denominator, (x+5)(x-2) + 1, ensures that the function is never zero and avoids any potential holes in the graph. The numerator, (x+5)(x-2), is zero precisely when x=-5 or x=2, which leads to the vertical asymptote
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
One possible function whose graph has two vertical asymptotes located at x = -5 and x = 2 is:
f(x) = (x+5)(x-2) / ((x+5)(x-2) + 1)
The denominator, (x+5)(x-2) + 1, ensures that the function is never zero and avoids any potential holes in the graph. The numerator, (x+5)(x-2), is zero precisely when x=-5 or x=2, which leads to the vertical asymptotes.
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In the diagram below, the dimensions of the large rectangle are (3x-1) by (3x+7) units. The Demi sound of the cut-out rectangle are x by 2x+5 units. Write a simplified expression for the area of the shaded region, in square units.
Answers
The expression that represents the area of shaded region is expressed as:
How to Write the Expression for the Area of the Shaded Region?The area of the shaded region = area of larger rectangle - area of smaller rectangle.
Area of a rectangle = length * width
Area of shaded region = [(3x + 7)(3x - 1)] - [(2x + 5)(x)]
Area of shaded region = (9x² + 18x - 7) - (2x² + 5x)
Open the bracket:
9x² + 18x - 7 - 2x² - 5x
Combine like terms:
9x² - 2x² + 18x - 5x - 7
Area of shaded region = 7x² + 13x - 7
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in the standard normal distribution, what is the proportion of values between negative infinity and 1 z-score?
Answers
Thus, the proportion of values between negative infinity and 1 z-score in the standard normal distribution is about 84.13%.
In the standard normal distribution, the proportion of values between negative infinity and 1 z-score can be determined using the cumulative distribution function (CDF) of the normal distribution.
The standard normal distribution, also known as the Z-distribution, has a mean (µ) of 0 and a standard deviation (σ) of 1. The proportion of values between negative infinity and any z-score corresponds to the area under the curve of the standard normal distribution up to that z-score.To find the proportion of values between negative infinity and 1 z-score, you can consult a Z-table or use a statistical calculator or software that provides the CDF for the standard normal distribution. The CDF value for a z-score of 1 is approximately 0.8413.Therefore, the proportion of values between negative infinity and 1 z-score in the standard normal distribution is about 84.13%. This means that 84.13% of the data points lie to the left of a z-score of 1 in a standard normal distribution.Know more about the cumulative distribution function (CDF)
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construct a 90 confidence interval for the population standard deviation o if a sample of size 10 has standard deviation s=16
Answers
The standard deviation of the random variable X is 2.73861279.
What is standard deviations?Standard deviations is a measure of the spread of a data set around the mean. It is calculated by taking the square root of the variance of the data set and is used to measure the variability of a data set from the mean. Standard deviations are used to measure the probability of a certain outcome occurring and can be used to compare different data sets to see how much variability there is in the data.
Standard deviation is a measure of dispersion of data points around the mean of the data set. It is a measure of the variability of the data set. It is calculated by taking the square root of the variance of the data set.
Variance is the average of the squared differences of each data point from the mean. It is calculated by taking the sum of the squares of the differences of each data point from the mean and dividing by the number of data points minus one.
In this case, the mean of the data set is 3, because the probabilities of -2 and 5 are equal.
The variance of the data set is calculated as follows:
Variance = (0.3*(3-(-2))2 + 0.2*(3-3)2 + 0.5*(3-5)2) / (3-1)
Variance = (0.3*25 + 0 + 0.5*4) / 2
Variance = 7.5
The standard deviation of the data set is calculated by taking the square root of the variance, which is equal to 2.73861279.
Therefore, the standard deviation of the random variable X is 2.73861279.
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a sticker shaped like a rectangle has an area of 56 square centimeters. it has a width of 7 centimeters.how long is the sticker?enter your answer in the box.
Answers
The length of the rectangle shaped sticker of stated dimensions is 8 centimetres.
Rectangle is the four shaped structure with two parallel sides. The area of rectangle is given by the formula -
Area of rectangle = length of the rectangle × breadth of the rectangle
Keep the values in formula to find the value of length of rectangle
56 = length × 7
Rewriting the equation in terms of length to find its value
Length = 56/7
Performing division on Right Hand Side of the equation
Length = 8 cm
Hence, the length of rectangle is 8 centimetres.
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Two restaurants sell meals for different
prices, as shown below.
Ruby wants to buy 2 meals. What is the
difference between the prices she would
pay at the two restaurants?
Give your answer in pounds (£).
Restaurant A
£19.50 each
Buy one meal,
get another meal
half price
Restaurant B
£18 each
Buy two meals,
get 15% off the
cost of both
Answers
Answer:
Step-by-step explanation:
To calculate the price at Restaurant A, we need to find the cost of one meal at full price and the cost of the other meal at half price. One meal at full price would be £19.50, and the other meal at half price would be £19.50/2 = £9.75. So the total cost at Restaurant A would be:
£19.50 + £9.75 = £29.25
To calculate the price at Restaurant B, we need to find the cost of two meals with a 15% discount. The cost of two meals at full price would be £18 x 2 = £36. Then we can calculate the discount:
15% of £36 = £5.40
So the total cost at Restaurant B would be:
£36 - £5.40 = £30.60
The difference between the prices at the two restaurants is:
£29.25 - £30.60 = -£1.35
So Ruby would pay £1.35 less if she bought the meals at Restaurant B.
Answer: Hence the correct answer is difference between price=£1.35
Step-by-step explanation:
Ruby wants to buy two meals at Restaurant A ,price of meal=£19.5 each and get another meal at half price, Price of two meal= 19.5+9.75=£29.25.
At Restaurarant B, Price of meal=£18 each and get 15% Off the cost of both.
The price of two meal= 36-36 x 15/100= £30.6.
Differece between the price =30.6-29.25=£1.35,
Hence the correct answer is difference between price=£1.35
I hoped this helped you!<3!
solve for x: 4(x−3) = 96
Answers
4(x−3) = 96
x=27
-12 + 12 + 4x = 96 + 12
Combine like terms: -12 + 12 = 0 0 + 4x = 96 + 12
4x = 96 + 12
Combine like terms: 96 + 12 = 108
4x = 108
Divide each side by '4'.
x = 27
Find the GCF:
-60 + 60n2 + 50n3
Answers
Step-by-step explanation:
You can factor out a '10' from each of the terms
10 ( -6 + 6n^2 + 5 n^3 )
If you meant - 60 n + 60 n^2 + 50 n^3
you can factor out a 10 n
10n ( -6 + 6n + 5n^2)
The graph of f(x) = x³ with three reference points
is shown. Which of the following represents
points from f(x) to a point on
g(x) = 2(x-4)³-3? Select three that apply.
A. (5,3)
B. (5,-1)
C. (3,-5)
D. (4,-3)
☐ E. (2,-5)
Answers
Based on the graph of f(x) = x³ with three reference points, the points from f(x) to a point on g(x) = 2(x - 4)³ - 3 include the following:
B. (5, -1)
C. (3, -5)
D. (4, -3)
What is a translation?In Mathematics and Geometry, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
At the ordered pair (5, -1), the function g(x) = 2(x - 4)³ - 3 would be tested with given points as follows;
g(x) = 2(x - 4)³ - 3
-1 = 2(5 - 4)³ - 3
-1 = 2(1) - 3
-1 = -1 (True).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Please find it quickly
Answers
The area of the shade region as shown in the figure below is 50 yd².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the shaded region, we use the formula below.
Formula:
Area of the shaded region = Area of the rectangle-area of the triangleA = LW-bh/2Where:
A = Area of the shaded portionL = Length of the rectangleW = Width of the rectangleb = Base of the triangleh = Height of the triangleFrom the diagram,
Given:
L = 9 ydW = 6 ydb = 4 ydh = 2 ydSubstitute these values into equation 1
A = (9×6)-(4×2/2)A = 54-4A = 50 yd²Hence, the area is 50 yd².
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Which of the equations below could be used as a line of
best fit to approximate the data in the scatterplot?
Hint: Try to imagine a line that fits the data well.
Approximately what would its y-intercept be?
Approximately what would its slope be?
scatterplot
Answers
The equations below could be used as a line of best fit to approximate the data in the scatterplot will be; y = 0.48x + 11
To determine the equation of the line of best fit, we first need to plot the data points on a scatterplot. Here is a scatterplot of the given data:
The method of least squares, which involves finding the line that minimizes the sum of the squared distances between the line and each data point.
Using this method, we can find that the equation of the line of best fit for this data ;
y = 0.48x + 11
This means that for every increase of 1 unit in x, we can expect an increase of 0.48 units in y. The y-intercept of 11 means that when x is 0, we would expect y to be approximately 11.
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you guys. please. help
Rectangle QUAD has coordinates Q(0,0), U(0,4), A(6,4), and D(6,0). Q'U'A'D' is the image of QUAD after a dilation with center (0,0) and scale factor 5. What are the coordinates of point U'?
Answers
The coordinates of point U' are (0, 20).
We have,
To perform a dilation with center (0,0) and scale factor 5, each coordinate of the original points needs to be multiplied by 5.
And,
The new coordinates of U' will be (0, 4) x 5 = (0, 20).
When performing a dilation with center (0,0) and scale factor 5, each coordinate of the original point is multiplied by 5 to get the corresponding coordinate of the dilated point.
So, the new coordinates of point U' will be (0, 4) * 5 = (0, 20).
Therefore,
The coordinates of point U' are (0, 20).
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