a) The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.
A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.
In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.
If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.
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The complete question is:
A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.
a) What chance of a Type I error was the test designed for, if H0 were true?
b) What judgement would you draw on this test (reject or fail to reject)?
c) What kind of error, if any, was there as a result of this test?
- a gambler offers you to pay even odds if you get 9, 10 or 11 heads in 20 tosses. should you take the bet?
6 (72(x - 2)) = 4(15 - 3x)
What is the solution to the equation above?
00
02
O The equation has no solutions.
O The equation has infinitely many solutions.
The solution to the equation 6(72(x - 2)) = 4(15 - 3x) is x = 77/37.
What is the solution to the given equation?Given the equation in the question
6(72(x - 2)) = 4(15 - 3x)
To solve the equation, remove the parenthesis by applying distributive property.
6( 72 × x - 72 × 2 ) = 4 × 15 - 4 × 3x
6( 72x - 144 ) = 60 - 12x
6( 72x - 144 ) = 60 - 12x
6 × 72x - 6 × 144 = 60 - 12x
432x - 864 = 60 - 12x
Collect like terms
Add -12x to both sides
432x + 12x - 864 = 60 - 12x + 12x
432x + 12x - 864 = 60
Add 864 to both sides
432x + 12x - 864 + 864 = 60 + 864
432x + 12x = 60 + 864
444x = 924
x = 924/444
x = 77/37
Therefore, the value of x is 77/37.
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phone models a particular cell phone company offers models of phones, each in different colors and each available with any one of calling plans. how many combinations are possible?
The number of combinations that are possible for 4 cell phone models of 6 colors with 5 calling plans is 120 .
We have to find the total number of combinations of cell phone models, colors, and calling plans,
So , we multiply the number of choices for each category.
By Using the multiplication principle of counting:
⇒ Total number of combinations = (number of phone models) × (number of colors) × (number of calling plans) ;
⇒ 4 × 6 × 5
⇒ 120
Therefore, there are 120 possible combinations of cell phone models, colors, and calling plans from this particular cell phone company.
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The given question is incomplete , the complete question is
A particular cell phone company offers 4 models of phones, each in 6 different colors and each available with an one of 5 calling plans. How many combinations are possible ?
selecting christmas presents if a person can select presents from presents under a christmas tree, how many different combinations are there?
Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations
When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.
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Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
Answer:
<A=45°,<B=65°,<C=70°
Step-by-step explanation:
<A=3(x+5)=3x+15
<B=5x+15
<C=7x
sum angles in a triangle is 180°
so,<A+<B+<C=180
(3x+15)+(5x+15)+(7x)=180
C.L.T
3x+5x+7x+15+15=180
15x+30=180
15x=180-30
15x=150
divide both sides by 15
x=10
<A=3(x+5)=3(10+5)=3(15)=45°
<B=5(10)+15=50+15=65°
<C=7(10)=70°
How many positive whole numbers less than 2016 have digit sum of 8?
The total number of numbers less than 2016 with a digit sum of 8 is 116 numbers.
How many positive whole numbers less than 2016 are there that have a digit sum of 8?The sum of the digits in the positive whole numbers is to be 8.
So the possibilities are obtained by means of permutation as follows:
Three 0's and an 8; ⁴P₁ = 4
One 1 and one 7, ⁴P₂ = 12
One 2 and one 6; ⁴P₂ = 12
One 3 and one 5; ⁴P₂ = 12
Two 1's and a 6; (⁴P₃/2!) = 12
One 1, one 2, and one 5; ⁴P₃ = 24
Two 2's and a 4; (⁴P₃/2!) = 12
Two 3's and a 2; (⁴P₃/2!) = 12
Two 4's and a 0; (⁴P₃/2!) = 12
Three 1's and a 5; (⁴P₃/3!) = 4
Total = 116 numbers
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A sea horse weighs 42oz. Together, 3 sea monkeys and a sea horse weighs the same as 8 sea monkeys plus 9oz. How much does a sea monkey weigh?
Answer:
a sea monkey weighs 6.6oz
Step-by-step explanation:
For each Diagram, write an unsimplified and simplified equation that represents the relationship between x and y.
I need the unsimplified equations on the left side of the chart from what I know it should be equal to the simplified equation across from it.
For diagram A, the unsimplified equation represents the relationship between x and y is y = x + x/3.
For diagram B, the unsimplified equation represents the relationship between x and y is y = x + 2x/3.
For diagram C, the unsimplified equation represents the relationship between x and y is y = x - x/3.
For diagram D, the unsimplified equation represents the relationship between x and y is y = x - 2x/3.
What is an unsimplified equation?Performing mathematical operations reduces an unsimplified equation to a simplified equation. A simplified equation is used for convenience.
Diagram A:
The value of x contains 3 congruent colored rectangles. The noncolored rectangle is 1. So, the value of the noncolored rectangle will be x/3.
Clearly, y will be the sum of x and x/3, that is, y = x + x/3.
Therefore, the obtained answer is y = x + x/3.
Diagram B:
The value of x contains 3 congruent colored rectangles. The noncolored congruent rectangles are 2. So, the value of the noncolored rectangles will be 2x/3.
Clearly, y will be the sum of x and 2x/3, that is, y = x + 2x/3.
Therefore, the obtained answer is y = x + 2x/3.
Diagram C:
The value of x contains 3 congruent colored rectangles. So, the value of 1 rectangle will be x/3.
Clearly, y will be the difference between x and x/3, that is, y = x - x/3.
Therefore, the obtained answer is y = x - x/3.
Diagram D:
The value of x contains 3 congruent colored rectangles. So, the value of 2 congruent rectangles will be 2x/3.
Clearly, y will be the difference between x and 2x/3, that is, y = x - 2x/3.
Therefore, the obtained answer is y = x - 2x/3.
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In physics lab, you measure three quantities: x, y, and z. Suppose that x=2.5 kg, y=0.8 m, and z=4.9 kg/m. Which of the mathematical combinations might be meaningful?(x/y) - z(x/z) - yx+y+z(xz) + yxyzx - (y/z)xy/z(x-y)/z
In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:
(x/y) - z(x/z) - yx - (yz)In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.
Based on the given quantities' scale, we know that x, y, and z have a relationship where:
z = x/y
Then, the mathematical combinations that might be meaningful are:
- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.
- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.
- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.
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The __________________________________ property of addition states that the way addends are grouped does not affect their sum
The Commutative property Associative property Identity property property of addition states that the way addends are grouped does not affect their sum.
The commutative property of addition states that the sum is unaffected by the order of the addends. 2+3=3+3
Changing the order of the addends has no effect on the sum, according to the associative property of addition.
(2+3)+4=2+(3+4)
Identity of addition property: Any number is equal to the sum of 0 00 and that number. For instance 0+5=5
According to the commutative property of addition, altering the order of addends has no impact on the sum. 2+3 = 3+2
as 3 rules are there only
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a cafe lets you order a deli sandwich your way. there are : e1, six choices for bread; e2, four choices for meat: e3, four choices for cheese; and e4, 12 different garnishes (condiments). what is the number of dffferent sandwich possibilities, if you may choose one bread, 0 or 1 meat, 0 or 1 cheese, and from 0 to 12 condiments? (multiplication principle) (not allowing repetition for bread, meat and cheese) (allowing repetition for condiments)
The number of different sandwich possibilities is 1081.
To calculate this, we must use the multiplication principle. We will begin by calculating the number of possibilities for the bread, meat, and cheese. There are 6 different breads, 4 different meats, and 4 different cheeses. So, there are 6 x 4 x 4 = 96 possible combinations for the bread, meat, and cheese. Next, we must calculate the number of possibilities for the condiments. Since we are allowing repetition for the condiments, we can calculate the possibilities by multiplying 12 (the number of condiments) by itself. So, there are 12 x 12 = 144 possibilities for the condiments. Lastly, we can multiply 96 (the number of bread, meat, and cheese combinations) by 144 (the number of condiment combinations). This yields 1081 different sandwich possibilities.
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Caride Pls this is needed very urgently
1.) Common ailments of senior citizens are arthritis, arteriosclerosis and loss of hearing. A survey of 200 senior citizens found that 70 had arthritis, 60 had arteriosclerosis, 80 had loss of hearing, 35 had arthritis and arteriosclerosis, 33 had arthritis and loss of hearing, 31 had arteriosclerosis and loss of hearing and 15 had all three.
How many of the senior citizens in the survey had; (1). none of these ailments, (f), arthritis but neither of the other two ailments, (iii), exactly one of these ailments, (iv). arteriosclerosis and loss of hearing but not arthritis, (v). arteriosclerosis or loss of hearing but not arthritis, (vi). exactly two of these ailments?
Answer:
i) 84
ii) 7
iii) 47
iv) 16
v) 56
vi) 54
Step-by-step explanation:
The easiest way to understand this problem visually is to create a Venn diagram (See attached diagrams below to help you)
First, note that the total amount of people with each condition beside the relevant circle. Then, since 15 have all 3, write 15 in the center.
We're told 35 had arthritis and arteriosclerosis, and 15 had all 3, so the amount with arthritis and arteriosclerosis only is 25-25=20. So we write 20 in the crosssection between arthritis and arteriosclerosis that doesn't include loss of hearing.
We're told 33 had arthritis and loss of hearing, and 15 had all 3, so the amount with arthritis and loss of hearing but not arteriosclerosis is 33-15=18. So we write 18 in the crosssection between arthritis and loss of hearing that doesn't include arteriosclerosis.
We're told 31 had arteriosclerosis and loss of hearing, and 15 had all 3, so the amount with arteriosclerosis and loss of hearing only is 31-15=16. So we write 16 in the crosssection between arteriosclerosis and loss of hearing that doesn't include arthritis.
(see diagram A to see how this should look)
70 people have arthritis and (18+25+20=63) have arthritis and another condition, so the amount with only arthritis is 70-63=7
60 people have arteriosclerosis and (20+15+16=51) have arteriosclerosis and another condition, so the amount with only arteriosclerosis is 60-51=9
80 people have loss of hearing and (18+15+16=49) have loss of hearing and another condition, so the amount with only loss of hearing is 80-49=31
Marking in these figures completes the diagram (See diagram B to see how it should look)
i)
The total amount of people represented within the diagram (ie, the ones with conditions) is 7+20+9+18+15+16+31=116. If 200 were surveyed, this means the amount without these conditions is 200-116=84
ii)
Above, we found the amount with arthritis only was 7
iii)
7 have only arthrits, 9 have only arteriosclerosis, and 31 have only loss of hearing , so the amount with only one ailment is 7+9+31=47
iv)
Above, we found that 16 had arteriosclerosis and loss of hearing but not arthritis
v)
The amount with arteriosclerosis or loss of hearing but not arthritis is equal to the amount with arteriosclerosis only plus the amount with loss of hearing plus the amount with both arteriosclerosis and loss of hearing: 9+31+16=56
vi)
Above, we found the amount with arthritis and arteriosclerosis only is 20, the amount with arthritis and loss of hearing but not arteriosclerosis is 18, and the amount with amount with arteriosclerosis and loss of hearing only is 16. So the total amount with exactly two conditions is 20+18+16=54
a school cafeteria wants to find out what combinations of food and beverage students are ordering. the results are represented in the two-way table below: food pizza hamburger salad water 11 7 23 beverage slurpee 18 19 5 soda 28 12 14 of the students who ordered salad, what is the probability that a student also ordered water? a.) 42 over 137 b.) 23 over 42 c.) 19 over 42 d.) 23 over 137
The probability that a student ordered a hamburger and a Slurpee is Option D) 23 over 137.
What is probability?Generally, To find the probability that a student ordered a hamburger and a Slurpee, we need to divide the number of students who ordered a hamburger and a Slurpee by the total number of students.
From the table, we can see that 23 students ordered a salad and a water.
There were a total of 38 + 12 + 14 + 18 + 28 + 7 + 23 = 137 students in the cafeteria.
Therefore, the probability that a student ordered a salad and a water is 23/137, or about 0.17.
Therefore, the correct answer is d) 23 over 137.
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In AJKL, if m ZJ is seven less than mZL and mZK is 21 less than twice mZL, find the measure
of each angle?
The measures regarding the angles of the triangle are given as follows:
x = 26.<P = 116º.<Q = 21º.<R = 43º.How to obtain the angle measures?The angle measures are defined as follows:
<P = 5x - 14.<Q = x - 5.<R = 2x - 9.The sum of the measures of the internal angles of a triangle is of 180º, hence the value of x is obtained as follows:
5x - 14 + x - 5 + 2x - 9 = 180
8x = 208
x = 208/8
x = 26.
Then the measures are given as follows:
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There are 15000 average passengers on domestic flights daily. 1/20 of the passengers are tourists and 1/15 of the tourists are travel bloggers. How many tourist passengers on domestic flights are travel bloggers
If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are 15000 * (1/20) = 750 tourists daily.
And if 1/15 of the tourists are travel bloggers, then there would be 750 * (1/15) = 50 travel bloggers daily.
If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are
15000 * (1/20) = 750 tourists daily
So, there would be a total of 50 tourist passengers on domestic flights who are travel bloggers.
It is important to note that these are average numbers and the actual number of tourists and travel bloggers on domestic flights can vary from day to day. However, this calculation provides a general idea of the proportion of tourist passengers who are travel bloggers on domestic flights.
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Which number makes the equation true?
-7 4/5 + ? = -9
Answer:
Step-by-step explanation:
(a) The perimeter of a rectangular garden is 328 m.
If the width of the garden is 67 m, what is its length?
Let L be the length of the rectangular garden.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Substituting the given values, we get:
328 = 2L + 2(67)
Simplifying the equation, we get:
328 = 2L + 134
2L = 328 - 134
2L = 194
L = 194/2
L = 97
Therefore, the length of the rectangular garden is 97 meters.
HELLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
Edit: it's actually translation, sorry about that.
Step-by-step explanation:
Answer: I think it might be translation
Step-by-step explanation:
Translation: A slide of a slide of a shape on a coordinate plane. We can move a shape upward, downward, leftward, or rightward.
Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns.Is the value a parameter or a​ statistic?
A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.
In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.
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Complete Question
Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?
Reynold can make 4 baked zitis in 8 hours. With Donald’s help, they can bake the same amount of food in 4 hours. How long will it take Donald to make 4 baked zitis without help?
Without help, it would take Donald 8 hours to make 4 baked zitis.
What is amount?Amount is the term used to describe a quantity or size of something it will stop to use to refer to a numbers of object items are people with as well as the measure of money time and distance.
This is due to the fact that, as Reynold and Donald work together, they are able to cut the time it takes to make 4 baked zitis in half. Therefore, when working alone, Donald would take twice as long to complete the same task.
For Reynold, in 8 hour he make 4 zitis
Meaning, in 1 hour he make 1/2 zitis
But with the help of Donald he make in 4 hours 4 zitis
both in 1 hour makes 1 zitis
So we have,
Reynold time to make zitis + Donald time to make zitis = both time to make zities
⇒ 1/2 + x = 1
⇒ x = 1 - 1/2
⇒ x = 1/2
So, It take 1/2 hours Donald to make 1 baked zitis without help.
Therefore, It take 8 hours Donald to make 4 baked zitis without help.
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4.21 game of dreidel. a dreidel is a four-sided spinning top with the hebrew letters nun, gimel, hei, and shin, one on each side. each side is equally likely to come up in a single spin of the dreidel. suppose you spin a dreidel three times. calculate the probability of getting
The probability of getting at least one nun in three spins of a dreidel is approximately 0.578
The probability is the ratio of number of favorable outcomes to the total number of outcomes
The probability of getting no nuns in a single spin is 3/4, since there are three non-nun letters (Gimel, Hei, Shin) and four total letters.
The probability of getting no nuns in three spins is then (3/4)^3, since the spins are independent and we can multiply probabilities of independent events.
So the probability of getting at least one nun in three spins is
= 1 - (3/4)^3
= 1 - 0.421875
= 0.578125
Therefore, the probability of getting at least one nun is 0.578
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The given question is incomplete, the complete question is:
A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?
sole the system of equations y=9x+14 and y=6x+35 x= and y=
The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The system of linear equations is given below.
y = 9x + 14 ....1
y = 6x + 35 ....2
From equations 1 and 2, then we have
9x + 14 = 6x + 35
3x = 21
x = 7
The value of 'y' is given as,
y = 6 (7) + 35
y = 42 + 35
y = 77
The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).
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A water sample shows 0.04 grams of some trace element for every cubic centimeter of water. Samir uses a container in the shape of a right cylinder with a radius of 8.1 cm and a height of 17.9 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Samir collected? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the volume of the container, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. Plugging in the given values, we get:
V = π * 8.1^2 * 17.9 = 1146.4 cm^3
Since the sample contains 0.04 g of the trace element per cubic centimeter of water, the amount of trace element in the entire container can be found by multiplying the volume of the container by the concentration of the trace element:
0.04 g/cm^3 * 1146.4 cm^3 = 45.86 g
So Samir has collected approximately 45.9 g of the trace element, rounded to the nearest tenth.
Answer:147.6g
Step-by-step explanation
Parallelogram CALM is multiplied by a scale factor to create Parallelogram
C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the
scale factor for the area of the pre-image to get the image?
The scale factor for the area of the pre-image to get the image is 2.
What is scale factor?Suppose a figure (pre image) is dilated (dilated image) by scale factor of k. So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
L = k × M
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.
So area of first figure = k² × area of second figure
Given that Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. Also, the area of the parallelogram CALM is 121.41 square feet.
Therefore, we can write,
Final Area / Initial Area = (Scale Factor)²
485.64 square feet / 121.41 square feet = (Scale Factor)²
4 = (Scale Factor)²
(Scale Factor) = √4
Scale Factor = 2
Hence, Scale Factor = 2
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The complete question is:
The area of Parallelogram CALM is 121.41 square feet. Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the scale factor for the area of the pre-image to get the image?
Situation
ion below. Then wr
1.
A rectangle is 4 times as long as it is wide. The
perimeter of a rectangle is 50 cm. What are the
dimensions of the rectangle?
Identify what you are looking
for and assign variables..
Write equations to model the
situation described in the
problem.
The dimensions will be as follows;
width is 5cm while the length is 20cm.
Let width = w
Let length = 4w (according to question)
Perimeter = 50cm
Perimeter formula for a rectangle = 2 (l +w)
Substituting in the variables (width and length)
2(w + 4w) = 50
2(5w) = 50
10w = 50
w = 5
Remember that length = 4w
length = 4w
length = 4(5)
length = 20cm
Therefore, the dimensions of the rectangle are 5cm by 20 cm.
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in a train yard there are tank cars, boxcars, and flatcars. how many ways can a train be made up consisting of tank cars, boxcars, and flatcars? (in this case, order is not important.)
There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.
If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:
C(n + k - 1, k - 1)
where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:
C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)
There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:
C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55
Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars
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The double-reciprocal transformation of the Michaelis-Menten equation, also called the Lineweaver- Burk plot, is given by
1/V_0 = K_m /(V_max[S]) + 1/V_max
To determine Km from a double-reciprocal plot, you would:
A) multiply the reciprocal of the x-axis intercept by -1.
B) multiply the reciprocal of the y-axis intercept by -1.
C) take the reciprocal of the x-axis intercept.
D) take the reciprocal of the y-axis intercept.
E) take the x-axis intercept, where V_0 = 1/2 V_max.
To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.
In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.
This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.
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3. There are two candy machines in a restaurant. One is filled with 200 gumballs and the other
is filled with 900 chocolate candies. The gumballs are dispensed 1 at a time and the chocolate
candies are dispensed 8 candies at a time. How many dispenses from each machine will make
the number of candies in the machines equal?
Answer:
100 dispenses
Step-by-step explanation:
To check the answer:
Gumballs: 200 - (1*100) = 100
Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.
Chocolate Candies: 900 - (8*100) = 100
Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.
Answer:
100
Step-by-step explanation:
Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.
GumballsThe number of remaining gumballs after d dispenses is ...
g = 200 -d
ChocolatesThe number of remaining chocolates after d dispenses is ...
c = 900 -8d
Equal numbersThe number remaining in each machine will be equal when ...
g = c
200 -d = 900 -8d . . . . . substitute the above expressions
7d = 700 . . . . . . . . . . add 8d -200
d = 100 . . . . . . . . . divide by 7
100 dispenses from each machine will make the number of candies in the machines equal.
The actual temperature of Noah's oven is 325 degrees, but his oven thermometer is reading 340 degrees. What is the percent error?
Answer:
Est: 4.62%
Step-by-step explanation:
Hassan deposits $325 into an account that pays 4.7% annual interest compounded monthly. Write an equation to represent Hassanʼs account balance A after t years.
Use a system of equations to determine how many years it will take for the account reach $200. Round to the nearest year.
It will take 10 years for the account to reach $200, as determined by solving the equation A = [tex]325(1 + 0.047/12)^(12t)[/tex] for t.
[tex]A = 325(1+0.047/12)^(12t)[/tex]
[tex]200 = 325(1+0.047/12)^(12t)[/tex]
[tex]200/325 = (1+0.047/12)^(12t)[/tex]
[tex]log_((1+0.047/12))(200/325) = 12t[/tex]
[tex]t = log_((1+0.047/12))(200/325) / 12[/tex]
t = 8.75 years
It will take 9 years for the account to reach $200.
Hassan deposited $325 into an account that pays 4.7% annual interest compounded monthly. We can use a system of equations to determine how many years it will take for the account to reach $200. To do this, we first write an equation to represent Hassan's account balance A after t years. This equation is[tex]A = 325(1+0.047/12)^(12t)[/tex]. We then solve for t by taking the logarithm of both sides, which gives us means that it will take 8.75 years for the account to reach $200, which we round up to 9 years.
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