Thus, the area of triangular region BCE is √(1/2) / 2.
The area of triangular region BCE can be found using the formula for the area of a triangle: (1/2) * base * height. In this case, the base of triangle BCE is equal to the side length of square ABCD, which is 1. To find the height, observe that triangle BEC is a right triangle with right angle at vertex B.
Since the length of line segment BE is equal to the length of line segment DE, and CE has a length of 1, we can deduce that triangle BED is an isosceles right triangle. Therefore, the angle BEC is 45 degrees, and the angle BED is also 45 degrees.
Using the Pythagorean theorem on triangle BED, we have:
[tex]BE^2 + DE^2 = CE^2[/tex]
Since BE = DE, we can rewrite the equation as:
[tex]2(BE^2) = 1[/tex]
[tex]BE^2 = 1/2[/tex]
[tex]BE = √(1/2)[/tex]
Now that we know the length of BE, we can use it as the height of triangle BCE. Therefore, the area of triangle BCE is:
Area = (1/2) * base * height
[tex]Area = (1/2) * 1 * √(1/2)[/tex]
[tex]Area = √(1/2) / 2[/tex]
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latrell's pool table is 3 feet wide and 7 feet long. latrell wants to replace the felt on the pool table. the felt costs $5.00 per square foot. how much would it cost in total to replace the felt on the pool table?
Latrell would need to pay 105 to replace the felt on his pool table.
Latrell has a pool table that is 3 feet wide and 7 feet long.
The pool table's felt needs to be replaced, and the cost of the felt per square foot is $5.00.
Let's find out how much it would cost Latrell to replace the pool table's felt.
What is the surface area of the pool table.
To determine the surface area of the pool table,
we need to multiply the length by the width, as shown below:
Surface area = length × width
Surface area = 7 ft × 3 ft
Surface area = 21 square feet
Now that we know the surface area of the pool table, we can determine the cost of the felt.
Latrell will need 21 square feet of felt, and it costs $5.00 per square foot.
We can use the following formula to determine the total cost of the felt:
Total cost of felt = cost per square foot × surface area.
Total cost of felt = $5.00 × 21 square feet.
Total cost of felt = $105
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Determine the area and perimeter of the figure below. Note that each square is 1 unit in length.
Answer:
area = 127[tex]units^{2}[/tex]
perimeter = 46 units
Step-by-step explanation:
count them
the australian sheep dog is a breed renowned for its intelligence and work ethic. it is estimated that 45% of adult australian sheep dogs weigh 65 pounds or more. a sample of 12 adult dogs is studied. what is the mean number of dogs who weigh 65 lb or more?
5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.
We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:
p = 0.45
Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.
The formula for X's mean or expected value is:
E(X) = np
When we change the values of n and p, we obtain:
E(X) = 12(0.45) = 5.4
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what did one dog say to the other dog
Answer: I like "Hot Dogs"?
Step-by-step explanation:
Cameron packed two pairs of shorts and three shirts for a trip. What are some combinations of shirts and shorts. How many days will he have a different outfit to wear?
As per the combination method, Cameron can wear a different outfit for 6 days.
If we want to find the number of different combinations of shirts that Cameron can wear with a pair of shorts, we need to calculate the value of 3C1 (which means choosing 1 shirt out of 3). Using the formula above, we get:
³C₁ = 3! / (1! x (3-1)!) = 3
So there are 3 possible combinations of shirts that Cameron can wear with a pair of shorts.
Since Cameron has 2 pairs of shorts, he can wear each combination twice (once with each pair of shorts). Therefore, the total number of different outfits he can wear is:
3 (number of shirt combinations) x 2 (number of pairs of shorts) = 6
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Find the height of a triangle whose area is 24cm squared and has a base of 3cm
Answer:
4cm
Step-by-step explanation:
Area of a triangle=[tex]\frac{1}{2}[/tex]×b×h
[tex]\frac{1}{2}[/tex]×3cm×h=[tex]24cm^{2}[/tex]
L.C.M=2
6cmh=[tex]24cm^{2}[/tex]
h=[tex]24cm^{2}[/tex]÷6cm
h=4cm
Answer:
Step-by-step explanation:
area = [tex]\frac{1}{2} base[/tex]×height
24 = [tex]\frac{1}{2}[/tex](3)×height
24 = 1.5×height
[tex]\frac{24}{1.5}[/tex] = [tex]\frac{1,5}{1,5}[/tex]height
16 = height
Down below are the coordinates after dilation but it says its wrong
Answer:
For the original triangle:
A is at (-3, 6), B is at (1, 2), C is at (-5, 1).
For the new triangle:
A' will be at (-3 - 3, -(6 + 2)) = (-6, -8)
B' will be at (1 - 3, -(2 + 2)) = (-2, -4)
C' will be at (-5 - 3, -(1 + 2)) = (-8, -3)
which variables are basic and which variables are nonbasic in this tableau? what basic variables are associated with rows 1, 2, and 3 of this tableau? what are the values of all the variables associated with this basic feasible solution?
In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.
In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.
The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.
The values of all the variables associated with this basic feasible solution are:
x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.
Note that these values correspond to the entries in the tableau in the "BV" column.
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The missing tableau is in the image attached below
PLEASE HELPPP
Answer:
Step-by-step explanation:
You didnt attatch anything
Edwin drives his car at a speed of 70km per hour how much distance will he cover in 3 hour and 30 minutes
The total distance covered by Edwin in duration of 3 hours and 30 minutes at a speed of 70km per hour is equal to 245 kilometers.
Use the formula,
distance = speed x time
To find the distance Edwin covers in 3 hours and 30 minutes.
First, convert 3 hours and 30 minutes to hours.
1 hour is equal to 60 minutes, so,
This implies,
3 hours and 30 minutes
= 3 + 30/60
= 3.5 hours
Now apply the formula we have,
distance = speed x time
⇒ distance = 70 km/h x 3.5 h
⇒ distance = 245 kilometers
Therefore, distance covered by Edwin will be 245 kilometers in 3 hours and 30 minutes, if he drives at a speed of 70 km/h.
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the volume of the right cone below is 392\piπ units^3 3 . Find the value of xx.
The value of x is approximately 8.15.
To find the value of x, we need to use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the
radius of the base and h is the height of the cone. We know that the volume of the cone below is 392π, so we can set
up the equation:
[tex]392π = (1/3)πx^2h[/tex]
Simplifying, we can divide both sides by π and multiply by 3 to get:
[tex]1176 = x^2h[/tex]
Using the Pythagorean theorem, we can relate the height, radius, and slant height of the cone:
[tex]h^2 + r^2 = x^2[/tex]
Since the cone is a right cone, we know that the radius is half of the diameter, which is equal to x/2. Substituting this in,
we get:
[tex]h^2 + (x/2)^2 = x^2[/tex]
Simplifying:
[tex]h^2 = x^2 - (x/2)^2
h^2 = 3x^2/4[/tex]
Now we can substitute this expression for [tex]h^2[/tex] into our equation for the volume:
[tex]1176 = x^2(3x^2/4)[/tex]
Simplifying again:
[tex]1176 = 3x^4/4[/tex]
[tex]1568 = 3x^4[/tex]
[tex]x^4 = 1568/3[/tex]
Taking the fourth root of both sides:
[tex]x = (1568/3)^(1/4)[/tex]
x ≈ 8.15
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Answer: 14
Step-by-step explanation:
kim rolls a dice and flips a coin calculate the probability that he gets a 2 and a head
The probability of Kim getting a 2 and a head is 1/12.
What is probability?A subfield of mathematics known as probability studies random occurrences and the possibility that they will occur. It is a technique of putting a number on the degree of ambiguity surrounding a situation or result. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express probability. The probability of an occurrence is determined by dividing the number of possible outcomes by the number of ways the event may occur. Several disciplines, including science, engineering, economics, and statistics, employ probability.
For a fair dice, the probability of getting a 2 on the dice is 1/6.
The probability of getting a head on the coin is 1/2.
Thus,
P(getting a 2 and a head) = P(getting a 2) × P(getting a head)
= (1/6) × (1/2)
= 1/12
Hence, the probability of Kim getting a 2 and a head is 1/12.
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the measures of two acute angles of a right triangle differ by 22 degrees. find the measure of each angle.
Answer:
In a right triangle, one of the angles measures 90 degrees, and the other two angles are acute angles that add up to 90 degrees. Let's call the measures of the two acute angles x and y.
We know that x and y differ by 22 degrees. So we can set up an equation:
x - y = 22
We also know that x + y = 90, since the two acute angles add up to 90 degrees.
Now we can solve this system of equations for x and y. One way to do this is to add the two equations together, which eliminates y:
x - y + x + y = 22 + 90
2x = 112
x = 56
Now we can substitute x = 56 into one of the equations to find y:
x + y = 90
56 + y = 90
y = 34
Therefore, the measures of the two acute angles of the right triangle are 56 degrees and 34 degrees.
If a, b, and c are different positive integers and a2+b3+c4=55, Then what is the greatest value for a*b*c=?
Answer:
Step-by-step explanation:
Given a^2 + b^3 + c^4 = 55, we need to find the greatest value for a * b * c.
To solve this problem, we can use the AM-GM inequality, which states that the arithmetic mean of a set of non-negative numbers is always greater than or equal to their geometric mean.
Using this inequality, we have:
(a^2 + b^3 + c^4) / 3 >= (a*b*c)^(2/3)
55/3 >= (a*b*c)^(2/3)
(55/3)^(3/2) >= a*b*c
The maximum value of a, b, and c occurs when they are as close together as possible. We can use the fact that a, b, and c are distinct positive integers to determine that the closest they can be is 1, 2, and 3.
So the greatest value for a * b * c is (1*2*3) = 6, and we have:
(55/3)^(3/2) >= 6
Approximately: 23.1 >= 6
Therefore, the greatest value for a * b * c is 6.
The greatest value for abc is 3,240.
What is the greatest value for abc?We want to find the greatest value of the product abc, given that a, b, and c are different positive integers and a + b + c = 55.
To maximize the value of abc, we want to maximize each individual factor, a, b, and c. We can do this by setting a to be as small as possible and c to be as large as possible, while ensuring that a, b, and c are still different positive integers.
Since a, b, and c are different positive integers, the smallest value for a is 1.
To maximize c, we set b = a + 1 and c = 55 - a - b.
Substituting b and c in terms of a, we get:
c = 55 - a - (a + 1) = 54 - 2a
Now we can express the product abc in terms of a:
abc = a x b x c = a (a + 1)(54 - 2a)
Expanding this expression, we get:
abc = -2a³ + 53a²+ 54a
To find the maximum value of abc, we can take the derivative of this expression with respect to a and set it equal to zero:
d(abc)/da = -6a² + 106a + 54 = 0
Solving for a, we get:
a = 8.93 (rounded to two decimal places)
Since a must be a positive integer, we round up to a = 9.
Using this value of a, we can find the corresponding values of b and c:
b = a + 1 = 10
c = 55 - a - b = 55 - 9 - 10 = 36
Therefore, the greatest value of abc is:
abc = 9 x 10 x 36 = 3,240
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The complete question is below:
If a, b, and c are different positive integers and a₂+ b₃ + c₄ = 55, Then what is the greatest value for abc= ?
The hypotenuse of a right triangular plot of land has a ratio of 16:65 with the shorter leg. The longer leg is
exactly 189 feet long. Find the perimeter of the plot of land.
Using Pythagorean theorem, the perimeter of the plot of land is 1783/16 feet.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental mathematical concept that outlines the relationship between a right triangle's three sides. It states that the square of the hypotenuse's (triangle's longest side) length equals the sum of the squares of the other two sides (the legs).
The Pythagorean theorem can be expressed numerically as follows:
a² + b² = c²
Let x= length of the shorter leg. Then, using the given ratio, the length of the hypotenuse can be expressed as 16x/65.
By the Pythagorean theorem, we have:
x² + 189² = (16x/65)²
Simplifying this equation, we get:
4225x² + 189² * 65² = 16² * x²
Solving for x, we get:
x = 315/4
Therefore, the perimeter is
189 + 315/4 + √(189² + (16/65)² * 315²/16)
Simplifying this expression, we get:
189 + 315/4 + 243/4 = 207/4 + √(2134441/256)
207/4 + 1463/16 = 1783/16
Therefore, the perimeter of the plot of land will be 1783/16 feet.
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What are the integer solutions to the inequality below?
−
1
≤
x
≤
3
Answer:
i don't know i haven't done integers in a long time
Step-by-step explanation:
Triangle TUV has coordinates T(0, 3) , U(−3, 0) , and V(−4, 4) . The triangle is reflected across the y-axis.Write the coordinate notation for a reflection across the y-axis.
Answer:
t(0,3) reflected on your axis is t(-0,3)
Ben Weatherstaff has a flower garden that is 9 m wide and 13 m long. He wants to increase the area to 221m² by increasing the width and the length the same amount. What will be the length (greater dimension) of the new flower garden?
A: 4m
B: 26m
C: 13m
D: 17m
Using area of the rectangle, we can find that the new flower garden will be 13m in length (greater dimension).
What do you mean by area?The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. Multiplying the length by the width yields the area of a rectangle (breadth).
As a result, the following formula can be used to determine the area of a rectangle whose length and breadth are "l" and "w," respectively. The rectangle's area is L × W. A rectangle's area is therefore equal to length * width.
Now here the dimensions of the rectangle are, l = 13m and b, = 9m.
Area of the rectangle is 13 × 9 = 117m².
Now the area of the rectangle is increased to 221m².
So, when we increase the length from 13 m to 17m and the breadth from 9m to 13m, we get area = 17 × 13 = 221m².
Therefore, length of the new garden will be 17m long.
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Here are a few pairs of positive numbers whose sum is 50.
a. Find the product of each pair of numbers.
b. Find a pair of numbers that have a sum of 50
and will produce the largest possible product.
First
Number
1
2
10
Second
Number
49
48
40
c. Explain how you determined which pair of numbers have the largest
product.
tor ic
Product
Answer:
a. The product of each pair of numbers is:
1 x 49 = 49
2 x 48 = 96
10 x 40 = 400
b. The pair of numbers that will produce the largest possible product is when the two numbers are equal to half of the sum, which is 25. So the pair of numbers is 25 and 25, and the product is 25 x 25 = 625.
c. We can determine the pair of numbers that have the largest product by using the following reasoning: For any two numbers whose sum is fixed, their product is maximized when the two numbers are as close together as possible. This is because the product of two numbers that are far apart is always smaller than the product of two numbers that are closer together and have the same sum. In this case, the sum is 50, so the two numbers that are closest together and add up to 50 are 25 and 25, which give the largest possible product.
Quadratic function in standard form having zeros of 3 and 1/2
The standard form of a quadratic function is:
`f(x) = ax^2 + bx + c`
If the zeros of the function are 3 and 1/2, then the factors of the function are:
`(x - 3)` and `(x - 1/2)`
To find the quadratic function using these factors, you can first multiply them together:
`(x - 3)(x - 1/2) = x^2 - 7/2x + 3/2`
Now we have:
`f(x) = x^2 - 7/2x + 3/2`
This is the quadratic function in standard form that has zeros of 3 and 1/2.
Fill in the table using this function rule.
y = -2x+3
X. Y
-4. ?
-2. ?
0. ?
2. ?
Answer: (-4,11)(-2,7)(0,3)(2,-1)
Step-by-step explanation:
Put the function into desmos and create a table.
10. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
Flying to Kampala with a tail wind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and I child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
Let's assume that each van and each bus can carry "x" number of students.
What is the equations based information?Let's assume there are "x" students in each van and each bus. Therefore, the total number of students in High School A's senior class is 8x + 8x = 16x. We know that the total number of students in High School A's senior class is 240, so we can set up an equation:
16x = 240
Solving for x, we get:
x = 15
So, each van and each bus had 15 students in it for High School A's senior class.
Similarly, for High School B, the total number of students is 4x + 1x = 5x. We know that the total number of students in High School B's senior class is 54, so we can set up an equation:
5x = 54
Solving for x, we get:
x = 10.8
Since the number of students must be a whole number, we can round up to 11. Therefore, each van and each bus had 11 students in it for High School B's senior class.
Therefore, the total number of students in High School A's senior class is 1x + 6x = 7x. We know that the total number of students in High School A's senior class is 372, so we can set up an equation:
7x = 372
Solving for x, we get:
x = 53
Therefore, each van and each bus can carry 53 students for High School A's senior class.
Similarly, for High School B, the total number of students is 4x + 12x = 16x. We know that the total number of students in High School B's senior class is 780, so we can set up an equation:
16x = 780
Solving for x, we get:
x = 48.75
Since the number of students must be a whole number, we can round up to 49. Therefore, each van and each bus can carry 49 students for High School B's senior class.
Let's assume that the price of one senior citizen ticket is "s" and the price of one child ticket is "c". Therefore, we can set up two equations based on the given information:
[tex]3s + 9c = 75[/tex]
[tex]8s + 5c = 67[/tex]
We can solve these equations simultaneously to find the values of "s" and "c". One way to do this is to multiply the first equation by 8 and the second equation by 3, so that we can eliminate "c" and solve for "s":
[tex]24s + 72c = 600[/tex]
[tex]24s + 15c = 201[/tex]
Subtracting the second equation from the first, we get:
57c = 399
Solving for "c", we get:
c = 7
Substituting this value into one of the original equations, we can solve for "s":
[tex]3s + 9(7) = 75[/tex]
[tex]3s + 63 = 75[/tex]
[tex]3s = 12[/tex]
[tex]s = 4[/tex]
Therefore, one senior citizen ticket costs $4 and one child ticket costs $7.
Let's assume that the speed of the boat in still water is "b" and the speed of the current is "c".
Therefore, we can set up two equations based on the given information:
[tex]336 = (b + c) * 12[/tex]
[tex]336 = (b - c) * 14[/tex]
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Find the value of x.
xº
108°
32°
suppose that for a particular distribution of scores, the mean is 6 with a standard deviation of 3. what is the z score for a raw score of 12?
The z-score for a raw score of 12 in a distribution with a mean of 6 and a standard deviation of 3 is 2.
The z-score is a measure of how many standard deviations a raw score is above or below the mean of a distribution. It is calculated by subtracting the mean from the raw score and then dividing the result by the standard deviation.
In this case, we have a mean of 6 and a standard deviation of 3. To find the z-score for a raw score of 12, we can use the formula:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the values we have, we get:
z = (12 - 6) / 3 = 2
Therefore, the z-score for a raw score of 12 in this distribution is 2. This means that the raw score of 12 is 2 standard deviations above the mean of 6. The z-score can be used to compare scores from different distributions, and to calculate probabilities and percentiles.
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in general, the first step in conducting exploratory research is to group of answer choices assemble a focus group. perform an experience survey. conduct a literature search. perform an analysis of selected cases. narrow a group of hypotheses to one specific hypothesis for investigation.
The first step in conducting exploratory research is to conduct a literature search. (Option 3)
Exploratory research is a type of research design used when the researcher has little or no knowledge about the research problem. The purpose of exploratory research is to gain a better understanding of the problem, identify potential research questions, and develop a hypothesis or research design.
The first step in exploratory research is to conduct a literature search, which involves reviewing existing research and publications related to the research problem. This helps the researcher to identify key concepts and theories related to the problem, as well as to identify any gaps or limitations in the existing research.
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Complete Question:
in general, the first step in conducting exploratory research is to___.
group of answer choices
assemble a focus group. perform an experience survey. conduct a literature search. perform an analysis of selected cases. narrow a group of hypotheses to one specific hypothesis for investigation.a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404.0 404.0 gram setting. it is believed that the machine is underfilling the bags. a 41 41 bag sample had a mean of 396.0 396.0 grams. a level of significance of 0.05 0.05 will be used. determine the decision rule. assume the standard deviation is known to be 25.0 25.0 . enter the decision rule.
The decision rule is as follows: If Z < -1.96, reject the null hypothesis. If not, fail to reject the null hypothesis.
The decision rule in statistics is a statement that instructs on the null hypothesis’s rejection or acceptance. It is a predetermined criterion used to test a hypothesis. When the calculated test statistic falls outside the critical region, the null hypothesis is rejected. A chocolate chip producer wants to know if the 404.0 gramme setting on their bag-filling machine is correct.
It is suspected that the machine is underfilling the bags. The chocolate chip manufacturer uses a 41 bag sample with an average weight of 396.0 grams to determine whether the machine works correctly at 404.0 gram setting.
With a significance level of 0.05, the decision rule is as follows:
If Z < -1.96, reject the null hypothesis. If not, fail to reject the null hypothesis.
Z can be calculated as follows:
z = (x - μ) / (σ / √n)
where:
x = sample mean = 396.0
μ = population mean = 404.0
σ = standard deviation = 25.0
n = sample size = 41
Substitute the values in the equation:
z = (396.0 - 404.0) / (25.0 / √41)z = -2.67Z < -1.96
Thus, reject the null hypothesis that the machine is filling bags correctly at 404.0 gram setting.
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ming Math th grade > Assessment Language arts Analytics S.11 Solve two-step equations: word problems D2Y Science 18c+ 4 = 42 4c+18 42 Painted Pots lets customers choose and paint their own pottery. The store has teap multiple sizes. Rebecca chose to paint the largest teapot offered, which cost $18. She a painted 4 small teacups to go with her teapot. Rebecca spent a total of $42 on pottery. Which equation can you use to find c, the cost of each teacup? Learn with an example ✓ OF Watch a video > Social studies 4(c + 18) 42 = Recommendations 18(c + 4) = 42
The equation representing the cost of each teacup is given as follows:
4c + 18 = 42.
Hence the cost is of: $6.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The meaning of the slope and of the intercept for this problem are given as follows:
Slope -> cost per teacup.Intercept: fixed cost.Hence the function is given as follows:
C = xc + 18.
(as the cost of the pot is of $18).
4 teacups push the price up to $42, hence the equation is given as follows:
4c + 18 = 42
4c = 24
c = 6.
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The length of a rectangular porch is (x + 7) feet. The area of the porch is (x² + 9x + 14) square feet. Factor the expression for the area in order to find an expression for the width of the porch.
We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
area of a rectangle
Area = length x width
To do this, we can factor the expression for the area, which gives us:
x² + 9x + 14 = (x + 2)(x + 7)
Area = length x width
(x + 2)(x + 7) = (x + 7) x width
x + 2 = width
Therefore, the expression for the width of the porch is x + 2 feet.
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Enlarge shape A by scale factor 1. 5 with centre of enlargement (0, 0)
To enlarge Shape A by a scale factor of 1.5 with the center of enlargement (0, 0), we have to multiply every length by 1.5.
Enlargement of Shape A
Enlargement of a shape is when it is either stretched or shrunk in one or both directions. The original shape is called the pre-image, while the new shape is called the image. What is the centre of enlargement?
The center of an enlargement is the point about which all of the points of the pre-image are scaled to obtain the image. When the scale factor is greater than 1, the image of the pre-image is an enlargement. When the scale factor is between 0 and 1, the image of the pre-image is a reduction.In an enlargement, each point on the pre-image is mapped onto a corresponding point on the image along a straight line which goes through the centre of enlargement.
The new shape has a larger size than the original shape. To expand shape A by a scale factor of 1.5, you need to multiply each length by 1.5. You have to create new points. It's easy to use a scale ruler to make sure each length is multiplied by 1.5.
A Centre of enlargement is a point in the coordinate plane that enlarges or shrinks a figure by some scale factor. In the problem, the center of enlargement is (0, 0).
Thus, we have to extend every length of Shape A by 1.5, and our scale factor is 1.5. We get Shape B by doing so. Now, we can conclude that to enlarge Shape A by a scale factor of 1.5 with the center of enlargement (0, 0), we have to multiply every length by 1.5.
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claire invests £200000 in a saving account foe 4 years .the account pays compound interest at a rate of 1.6% per annum
calculate the total amount of interest claire will get at the end of four years
Answer:
We can use the compound interest formula to find the total amount of interest Claire will get at the end of four years:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money in the account at the end of the four years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = £200000
r = 0.016 (1.6% expressed as a decimal)
n = 1 (compounded annually)
t = 4
So, the formula becomes:
A = £200000(1 + 0.016/1)^(1*4)
= £200000(1.016)^4
= £219,463.18
To find the total amount of interest Claire will get, we need to subtract the principal amount from the total amount of money in the account at the end of four years:
Total interest = £219,463.18 - £200,000
= £19,463.18
Therefore, Claire will get £19,463.18 in total interest at the end of four years.