The sample size is 12 with an error calculation of 5 if 97% of the confidence interval is around a sample mean of 31. 3.
Percent confidence = 97
Sample mean = 31. 3
Standard deviation = 7. 6
Sample size = 40
Error calculation = 5
The formula for a confidence interval using the t-distribution is:
CI = x ± tα/2 * (s/√n)
CI = 31.3 ± 2.423 * (7.6/√40)
CI = 31.3 ± 3.940
CI = (27.36, 35.24)
The population mean with an error of 5,
n = (Zα/2 * σ / E)^2
Assuming a 95% confidence level, the sample size is,
n = (1.96 * 7.6 / 5)^2
n = 11.69
Therefore we can conclude that the sample size is 12 with an error calculation of 5.
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Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesperson can use the equation b=0. 29h+1. 35
where b
is the size of the BMX bike frame in inches and h
is the height of the rider in inches
The slope in the equation b = 0.29h + 1.35 is the measure of the rate at which the bike frame size changes with the height of the rider.
The slope in the equation b = 0.29h + 1.35 refers to the coefficient of the variable h, which represents the height of the rider. The slope is the measure of the rate at which the bike frame size changes with the height of the rider.
In this equation, the slope is 0.29, which means that for every inch increase in the rider's height, the bike frame size increases by 0.29 inches. The slope is a crucial component of the equation as it determines the proportionality of the two variables.
Moreover, the slope is essential in analyzing the relationship between the rider's height and the bike frame size.
It plays a vital role in determining the appropriate size of the BMX bike frame and analyzing the relationship between the two variables.
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Complete Question:
Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use the equation b 0.29h +1.35 where b is the size of the BMX bike frame in inches and h is the height of the rider in inches.
Which sentence explains the slope in the equation?
30 points to help me!
Answer:
Step-by-step explanation:
5+3x/4 = 7/12
[(5*4)+3x]/4 = 7/12
(20+3x)/4 = 7/12
20+3x = 7/12*4
20+3x = 7/3
3x = 7/3 - 20
3x = [7-(20*3)]/3
3x = (7-60)/3
3x = -53/3
x = -53/3/3/1 ( reciprocal )
x = -53/3*1/3
x= -53/9
Will give brainiest
Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
Which of the following is equivalent to the inequality 2x + 13 < 5x - 20?
F. x >-11
G. x<?
H. x>;
J. x < 11
K. x > 11
Answer:
k
Step-by-step explanation:
2x+13<5x−20
Subtract 5x from both sides.
Combine 2x and −5x to get −3x.
Subtract 13 from both sides.
Subtract 13 from −20 to get −33.
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x>11
Jason and Scott plan on biking to the center of town to get ice cream at the convenience store. Since Scott
had to put air in his tires, Jason was able to get 1 mile ahead of Scott before Scott left the house. Both
bikers rode at a speed of 15 miles per hour.
Write an equation in y = mx + b form that represents Jason's trip. Jason =
a.
Write an equation in y = mx + b form that represents Scott's trip.
Will Jason and Scott meet before they both reach the store? Explain.
If you were to graph both lines on the same coordinate plane, predict what your graph would look
like.
Answer:
a. Jason's equation in y = mx + b form is y = 15x + 1.
b. Scott's equation in y = mx + b form is y = 15x.
Since both are moving at the same speed, they will meet at the point where their distances from the starting point are the same. Let d be the distance from Scott's starting point to the store. Then, the distance from Jason's starting point to the store is d + 1. Using the formula distance = rate × time, we can set up an equation:
15t = d
15t - 1 = d + 1
Solving for t in both equations, we get t = d/15 and t = (d+2)/15, respectively. Equating these expressions for t, we get d/15 = (d+2)/15, which simplifies to d = -2. This means that they will not meet before reaching the store, as Jason is already 1 mile ahead of Scott and will stay ahead throughout the trip.
If we were to graph both lines on the same coordinate plane, we would have two parallel lines with a slope of 15, where Jason's line would intersect the y-axis at 1.
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee.
Step-by-step explanation:
Equation
y = -7.37x + 80
substitute 57.89 for y
57.89 = -7.37 + 80 Subtract 80 from both sides
57.89 - 80 = -7.37 + 80 - 80
-22.11 = -7.37x Divide both sides by -7.37
3 = x
3 pound of coffee
Helping in the name of Jesus.
Answer:
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Step-by-step explanation:
Let's first find out how much money Rita spent on coffee:
$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee
Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:
$7.37x = $22.11
Solving for x, we can divide both sides by $7.37:
x = 3
Therefore, Rita bought 3 pounds of coffee.
What is the solution to 3(2k + 3)= 6-(3k -5)
Answer:
[tex]\frac{11}{8}[/tex]
Step-by-step explanation:
3(2k+3)=6-(3k-5)
6k +9=6-3k+5
6k+3k=6+5
8k=11
k=[tex]\frac{11}{8}[/tex]
Answer: I think it is k=2/9
Step-by-step explanation:
Please help, due very soon !!
Enter the values needed to find the
length BC. (Simplify your answer.)
A (-5x, 4y)
B (-2x, -4y)
BC=√([?])² + (3y)²
C (7x, -1y)
Distance Formula
d = √√(x₂ − ×₁)² + (y₂ − y₁)²
The missing value to find the length of BC is 9x.
What is distance formula?The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.
The distance formula is given as:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the values of the coordinates of B and C we have:
distance = √((7x - (-2x))² + (-1y - (-4y))²)
distance = √((9x)² + (3y)²)
distance = √(81x² + 9y²)
distance = 3√(9x² + y²)
Hence, the missing value to find the length of BC is 9x.
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1) Adam wants to buy a home priced at $215,000. The bank requires him to make a 5% down payment and
he will finance the rest for 30 years at 4.5% interest. He has to also pay the closing costs below. Find the
a) the down payment b) the amount of the mortgage c) the closing costs d) the amount financed with
closing costs e) the monthly payment f) the total amount repaid g) the amount paid to interest.
Application Fee
Borrower's Credit check
Points
Appraisal Fee
Title Search
Title Insurance
Attorney Fee
Documentation stamp
Processing fee
$ 25
65
1.5% of Mortgage
350
215
450
400
0.30% of Mortgage
1.25% of Mortgage
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
Answer:
2x=5 > -14
Step-by-step explanation:
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3 3
2x=5 > -14
The perimeter of a rectangular map of the world is 270 cm. It is 90 cm in height. How wide is it?
Answer:
The perimeter of a rectangle is given by:
P = 2(L + W)
where P is the perimeter, L is the length, and W is the width.
In this case, we know that P = 270 cm and L = 90 cm, so we can solve for W as follows:
270 = 2(90 + w)
Divide both sides by 2:
135 = 90 + w
Subtract 90 from both sides:
w = 45
Therefore, the width of the map is 45 cm.
Step-by-step explanation:
About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? . (A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability
The statement that is correct is (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
The binomial distribution can be used to calculate the probability of a certain number of successes in a given number of trials, where each trial has a fixed probability of success.
The probability of a flight being delayed is 0.24, and the probability of a flight not being delayed is 0.76. Therefore, the probability of exactly 10 flights out of 100 being delayed can be calculated using the binomial distribution with n = 100, k = 10, and p = 0.24.
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Given that the number 33,554,432 is equal to 2^25 , explain how you know that 33,554,432 is not a square number
First of all, perfect squares do not end in 2.
The exponent has to be an even number when 2 is the base. For example 2^8 = 64. 8 is an even number. So 64 is a square number.
Which pattern shows a quadratic relationship between the step number and the number of dots? Explain or show how you know.
Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.
We can write quadradic equation as [tex]y=1+x^2[/tex]
Where y is number οf dοts and x is step number.
Then if x=0 and y=1
If x = 1 and y = 2
If x = 2 and y = 5
If x = 3 and y = 10
Hence Patten B fοllοws the quadratic realatiοnship.
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10) A rectangle has a width of 2m+3. The length
is twice as long as the width. What is the length
of the rectangle?
Answer:
4m + 6
Step-by-step explanation:
Since the length is twice as long your equation should look like this
2(2m + 3) = L
which would be 4m + 6 as the length of the rectangle
Need help with math
The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).
What are parallel lines?
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.
If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:
slope = (y2 - y1) / (x2 - x1)
slope = (-5 - 7) / (8 - (-2))
slope = -12 / 10
slope = -6 / 5
So, the equations of the two parallel lines are:
y - 7 = (-6 / 5)(x + 2) --- equation 1
y + 5 = (-6 / 5)(x - 8) --- equation 2
To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).
So, after the rotation, the new coordinates of the two points will be:
(-(-2), -7) = (2, -7) --- for point (-2, 7)
(-(8), -(-5)) = (-8, 5) --- for point (8, -5)
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alexis created the two-way frequency table from information she gathered by asking 88 teenagers about their last online shopping experience. own money parents' money total completed purchase 16 34 50 just looked 22 16 38 total 38 50 88 about what percent of the teenagers purchased something with their parents' money?
The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.
There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:
Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]
Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%
Therefore percent of teenagers who purchased something with their parents' money = 38.64%
Therefore, about 38.64% of the teenagers purchased something with their parents' money.
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What property of real numbers does each statement demonstrate? (3 + 4) + 1 = 3 + (4 + 1)
Answer: Associative property
Step-by-step explanation:
The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!
The net of a triangular prism is shown. a) Work out the length x. b) Work out the area of the shaded face. 3 cm 7 cm 5 cm 8 9 cm Not drawn accurately
The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².
What is area?Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.
The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.
In this figure,
The 5cm flap will be adjacent to the side x. Therefore,
Length of the side x= 5cm
Area of the shaded region= l×b
because the shaded region is a rectangle.
area= 9*x
=9*5= 45 cm²
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Write 2/7 + 1/4 as a sum of two equivalent fractions with the same denominator
2/7 + 1/4 = 15/28 ≅ 0.5357143
Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.
find the length of the cord pt.3
According to the circle theorem, we can find the length of the cord, x = 4 units.
Define circle theorem?Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.
A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.
Here in the given circle,
As per the intersecting chords theorem,
AB × CB= BE × BD
⇒ 6 × 6 = 9× x
⇒ x = 36/9=4
Therefore, the length of the chord, x = 4 units.
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What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
square yards
The surface area of the rectangular prism is 170 square yards.
What is the surface area formula?Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.
To calculate the surface area of the rectangular prism, add the areas of each of its faces.
The front and back faces are 5 yards by 6 yards in size, so each has an area of:
5 yards x 6 yards equals 30 square yards
The top and bottom faces are 5 yards by 5 yards, so each has an area of:
5 yards x 5 yards equals 25 square yards
The two side faces have dimensions of 6 yards by 5 yards, for a total area of:
30 square yards = 6 yards x 5 yards
As a result, the surface area of the rectangular prism is as follows:
Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area
= 30+30+25+25+30+30
= 170 square yards
As a result, the rectangular prism has a surface area of 170 square yards.
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thanks if you answer
Answer:
[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]
Answer:
A- 2
B- 4,100
C- 82
D- 4,182
Which expressions are equivalent to
6
�
−
18
ℎ
6g−18h6, g, minus, 18, h?
Choose 2 answers:
Choose 2 answers:
(Choice A)
(
�
−
3
)
⋅
6
(g−3)⋅6left parenthesis, g, minus, 3, right parenthesis, dot, 6
A
(
�
−
3
)
⋅
6
(g−3)⋅6left parenthesis, g, minus, 3, right parenthesis, dot, 6
(Choice B)
2
⋅
(
3
�
−
18
ℎ
)
2⋅(3g−18h)2, dot, left parenthesis, 3, g, minus, 18, h, right parenthesis
B
2
⋅
(
3
�
−
18
ℎ
)
2⋅(3g−18h)2, dot, left parenthesis, 3, g, minus, 18, h, right parenthesis
(Choice C)
3
(
2
�
−
6
ℎ
)
3(2g−6h)3, left parenthesis, 2, g, minus, 6, h, right parenthesis
C
3
(
2
�
−
6
ℎ
)
3(2g−6h)3, left parenthesis, 2, g, minus, 6, h, right parenthesis
(Choice D)
(
−
�
−
3
ℎ
)
(
−
6
)
(−g−3h)(−6)left parenthesis, minus, g, minus, 3, h, right parenthesis, left parenthesis, minus, 6, right parenthesis
D
(
−
�
−
3
ℎ
)
(
−
6
)
(−g−3h)(−6)left parenthesis, minus, g, minus, 3, h, right parenthesis, left parenthesis, minus, 6, right parenthesis
(Choice E)
−
2
×
(
−
3
�
+
9
ℎ
)
−2×(−3g+9h)minus, 2, times, left parenthesis, minus, 3, g, plus, 9, h, right parenthesis
E
−
2
×
(
−
3
�
+
9
ℎ
)
−2×(−3g+9h)
You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.
The given expression is equivalent to
Option C) [tex]3(2g-6h)[/tex]Option E) [tex]-2\times(-3g+9h)[/tex]What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
What is the distributive property of multiplication over addition?[tex]a(b+c)=a\times b+a\times c[/tex]
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])
The given expression is [tex]6g-18h[/tex]
We know that we can write
[tex]6=2\times3[/tex]
[tex]18=2\times9=3\times6[/tex]
Thus,
[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]
[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]
[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]
All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.
Thus,
The given expression is equivalent to
Option C) [tex]3(2g-6h)[/tex]Option E) [tex]-2\times(-3g+9h)[/tex]Learn more about equivalent expressions here:
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Answer:C & D
Step-by-step explanation:
during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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The distance between new orleans and houston is 353 miles. At 12:20pm, a bus leaves houston for new orleans at a speed of 60mph. 45 minutes late, a motorcycle leaves new orleans for houston at a speed of 72mph. At what time will the bus and the motorcycle pass each other if neither stops or changes speed?
As per the given distance, the bus and the motorcycle will pass each other at 4:50 pm.
Now, let's find the distance the bus travels during that time. We know the speed of the bus is 60 mph, so we can use the formula distance = speed x time. Thus, the distance the bus travels is:
distance = speed x time
distance = 60 x t
Next, let's find the distance the motorcycle travels during the same time. The speed of the motorcycle is 72 mph, so we can use the same formula to find the distance the motorcycle travels:
distance = speed x time
distance = 72 x (t - 3/4)
Here, we subtract 3/4 from the time because the motorcycle leaves 45 minutes later than the bus. Remember, we need to convert 45 minutes to hours by dividing it by 60. Therefore, 45 minutes is equal to 3/4 of an hour.
Now that we have both distances, we can set them equal to each other since the bus and the motorcycle will meet at the same point in time:
60t = 72(t - 3/4)
Let's simplify and solve for "t":
60t = 72t - 54
12t = 54
t = 4.5
Therefore, it will take 4.5 hours for the bus and the motorcycle to meet each other. But, we need to find out what time that will be. We know the bus left at 12:20 pm, so we add 4.5 hours to that time:
12:20 pm + 4.5 hours = 4:50 pm
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Name the shape that will result from connecting the points (-4, 1) , (-4, -4) , (0, 3) , and (0, 6) .
A: Square
B: Rectangle
C: Trapezoid
D: Parallelogram
The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.
What is a trapezoid?A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).
The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.
How to identify a trapezoid?A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:
It has four sidesIt has two parallel sides and two nonparallel sidesIt has two opposite sides that are parallel to one another and two other sides that are not parallelIt has two acute angles and two obtuse anglesIt has diagonals that intersect at a midpointThe formula for the area of a trapezoid is as follows:
Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height
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Laura has done a two-factor factorial completely randomized design. From her experiment, Laura has constructed the following incomplete ANOVA display: Source SS DF MS F A 350.00 2 B 300.00 150 AB 200.00 50 Error 150.00 Total 1000.00 18 a. How many levels of factor B did she use in the experiment? b. How many degrees of freedom are associated with interaction? c. The error mean square is d. The mean square for factor A is e. How many replicates of the experiment were conducted? f. What are your conclusions about interaction and the two main effects? g. An estimate of the standard deviation of the response variable is h. If this experiment had been run in blocks (CRBD) there would have been degrees of freedom for blocks.
a. Two levels of factor B were used in the experiment.
b. The degrees of freedom associated with interaction are 50.
c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.
Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.
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a box contains 75 red marbles, 37 white marbles, and 19 blue marbles if a marble is randomly selected from the box, what's the probability that it is not blue
The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.
If a marble is randomly selected from the box, we have to find the probability that it is not blue.
Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]
The probability that a marble is not blue:-
[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)
[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]
[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]
[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)
[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]
[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]
Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].
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