Answer:
(c) 4
Step-by-step explanation:
You want the scale factor that dilates point A(1, 1) to point A'(4, 4).
DilationDilation about the origin multiplies each coordinate value by the scale factor. That factor is ...
k = A'/A = (4, 4)/(1, 1) = 4
The dilation scale factor is 4.
__
Additional comment
You will notice the same scale factor can be computed from any corresponding pair of points:
k = A'/A = B'/B = C'/C = D'/D = 4
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5. the academy of orthopedic surgeons states that 80% of women wear shoes that are too small for their feet. a researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. how large of a sample is necessary? round to the nearest whole number. (10 points
To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.
Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)
Plugging in the values:
n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67
Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.
To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:
n = (Z^2 * p * q) / E^2
where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.
In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03
Now, we can plug these values into the formula:
n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65
Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.
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a jar contains eight marbles. one of them is blue. if five marbles are independently drawn from the jar, what is closest to the probability that the blue marble is drawn twice? group of answer choices 0.001 0.015 0.105 0.196 not enough information given
The answer is closest to 0.196. This means that if we repeat the experiment many times, we would expect to draw the blue marble twice in approximately 19.6% of the trials.
We can solve this problem using the hypergeometric probability distribution. The hypergeometric distribution is used when we have a finite population and we want to calculate the probability of drawing a certain number of objects of a specific type without replacement.
In this case, the population consists of 8 marbles, one of which is blue. We want to calculate the probability of drawing the blue marble twice when we draw 5 marbles without replacement. The number of ways to choose 5 marbles out of 8 is given by the binomial coefficient:
C(8,5) = 56
The number of ways to choose the blue marble twice and the other three marbles from the remaining 7 is:
C(1,2) * C(7,3) = 35
Therefore, the probability of drawing the blue marble twice is:
P = 35/56 = 0.625.
The closest answer choice to this probability is 0.196. Therefore, the answer is closest to 0.196. This means that if we repeat the experiment many times, we would expect to draw the blue marble twice in approximately 19.6% of the trials.
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2 kilos de platanos y 3 kilos de pera cuestan 7.80€ 5 kilos de platanos y 4 kilos de pera cuestan 13.20 € ¿Como esta el kilo de platanos y el kilo de peras
Realizando los cálculos, encontramos que el kilo de plátanos tiene un precio de 1.20€ y el kilo de peras tiene un precio de 1.80€.
Para resolver este problema, podemos plantear un sistema de ecuaciones utilizando el método de sustitución. Denotemos por "x" el precio del kilo de plátanos y por "y" el precio del kilo de peras.
A partir de la primera información, tenemos la ecuación 2x + 3y = 7.80€.
De la segunda información, obtenemos la ecuación 5x + 4y = 13.20€.
Podemos resolver este sistema de ecuaciones utilizando el método de sustitución. Despejamos "x" de la primera ecuación: x = (7.80€ - 3y)/2.
Sustituyendo este valor de "x" en la segunda ecuación, tenemos:
5((7.80€ - 3y)/2) + 4y = 13.20€.
Simplificando y resolviendo la ecuación resultante, encontramos el valor de "y" (precio del kilo de peras). Después, sustituimos este valor en la primera ecuación para obtener el valor de "x" (precio del kilo de plátanos).
Realizando los cálculos, encontramos que el kilo de plátanos tiene un precio de 1.20€ y el kilo de peras tiene un precio de 1.80€.
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Olivia had 50 beads 10 of them were red, 20 of them were blue and the rest were green. What percent of the beads were blue?
The percent of the beads that were blue is 40%. To determine the percent of beads that were blue, we need to first find the total number of blue beads and then divide that by the total number of beads.
The total number of blue beads is 20, which we can determine from the problem statement. The total number of beads is 50, which we can calculate by adding the number of red, blue, and green beads together:
10 + 20 + x = 50
where x represents the number of green beads
Solving for x, we get:
x = 20
Therefore, there were 20 green beads, and the total number of beads is 10 + 20 + 20 = 50.
Now we can calculate the percent of beads that were blue:
20/50 x 100% = 40%
Therefore, 40% of the beads were blue.
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aiden read that blue jays can mimic the calls of other birds like hawks and crows. he wanted to listen to the sounds blue jays make, so he put out some treats to attract them to his yard. here are the treats the blue jays have eaten so far today:peanut, acorn, peanut, corn kernel, acorn, peanut, acorn, peanut, corn kernel, peanutbased on the data, what is the probability that the next treat eaten by a blue jay will be a peanut?
Answer:
The answer is 5/10
Step-by-step explanation:
Just trust me! I got it right!
To calculate the probability of the next treat eaten by a blue jay being a peanut, we need to determine the ratio of peanuts to the total number of treats observed.
Based on the data provided, we can count the number of peanuts eaten by the blue jays. In this case, out of the 10 treats listed, 5 of them are peanuts.
To calculate the probability, we divide the number of peanuts by the total number of treats observed. Therefore, the probability that the next treat eaten by a blue jay will be a peanut is 5/10 or 0.5 (50%).
Since the blue jays have eaten an equal number of peanuts and non-peanut treats so far, the probability suggests that the next treat they consume is equally likely to be a peanut or a different type of treat.
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does listening to mozart lead to higher scores on an iq test? an experiment involved listening to mozart while performing abstract reasoning skills on an iq test. these results were compared to the completion of similar tasks with a silent background. the mean iq scores were 1.2 points higher after listening to mozart than with the silent background. the p-value for the test was calculated to be 0.0004. can we conclude that listening to mozart will lead to much higher scores on iq test?
We cannot conclude that listening to Mozart will lead to much higher scores on an IQ test based on the given information.
While the mean IQ scores were 1.2 points higher after listening to Mozart, the statistical significance of this difference depends on the chosen level of significance (alpha level) and the sample size. The p-value of 0.0004 indicates that if there is no difference in IQ scores between the Mozart and silent background conditions in the population, there is only a 0.04% chance of observing a sample mean difference of 1.2 points or larger. However, we would need to know the alpha level and sample size used in the study to determine if this is statistically significant at a practical level. Additionally, this experiment only shows a correlation between listening to Mozart and higher IQ scores, and cannot prove causation.
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Select all of the following that you can use to fully
describe a rotation.
Centre
Line of reflection
Scale factor
Direction
(clockwise/anticlockwise)
Angle
Vector
The features needed to describe a rotation are Center, Direction and Angle
How to determine all features needed to describe a rotation.From the question, we have the following parameters that can be used in our computation:
The key features
From the key features, the terms that describe rotation are:
Center: This represents the center which the rotation is doneThe direction: This represents whether the rotation is clockwise or counterclockwiseThe angle of rotationRead more about rotation at
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a store has 80 modems in its inventory, 30 coming from source a and the remainder from source b. of the modems from source a, 20% are defective. of the modems from source b, 8% are defective. calculate the probability that exactly two or exactly three out of a random sample of five modems from the store's inventory are defective.
The probability that exactly two or exactly three out of a random sample of five modems from the store's inventory are defective is 0.256.
To solve this problem, we can use the binomial distribution formula. Let X be the number of defective modems in a sample of 5 randomly selected modems. Then, we need to find P(2 <= X <= 3), which is the probability of having exactly 2 or exactly 3 defective modems in the sample.
To calculate the probability of a defective modem from source a, we can use the fact that 20% of the modems from this source are defective. So, the probability of selecting a defective modem from source a is 0.2. Similarly, the probability of selecting a defective modem from source b is 0.08.
Now, we can use the binomial distribution formula:
P(2 <= X <= 3) = P(X = 2) + P(X = 3)
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the sample size (5), k is the number of defective modems, and p is the probability of a defective modem.
P(X = 2) = (5 choose 2) * 0.2^2 * 0.8^3 = 0.2048
P(X = 3) = (5 choose 3) * 0.2^3 * 0.8^2 = 0.0512
Therefore, P(2 <= X <= 3) = 0.2048 + 0.0512 = 0.256.
In other words, the probability that exactly two or exactly three out of a random sample of five modems from the store's inventory are defective is 0.256.
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What will the following statement do if x equals 17 and answer = 20? answer = x > 100 ? 0 : 1; A) Assign 1 to x. B) Assign 1 to answer. C) Assign 0 to x.
The statement "answer = x > 100 ? 0 : 1;" is a ternary operator in programming, which means it evaluates a condition and returns one of two values depending on whether the condition is true or false. The answer is: B) Assign 1 to answer.
In this case, the condition is "x > 100", which means "Is x greater than 100?"
If x equals 17 and answer equals 20, the condition is false because 17 is not greater than 100. Therefore, the statement will return the value after the question mark, which is 1.
So the answer is: B) Assign 1 to answer.
The given statement is using the ternary conditional operator, which has the following format: condition ? value_if_true : value_if_false.
In this case, the statement is:
answer = x > 100 ? 0 : 1;
Given that x = 17 and answer = 20, let's evaluate the statement step-by-step:
1. Check the condition: x > 100
Since x = 17, the condition is false (17 is not greater than 100).
2. Since the condition is false, we choose the value after the colon (:), which is 1.
3. Finally, assign the chosen value to answer: answer = 1
So the correct option is B) Assign 1 to answer.
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or a birthday party caterer counted the number of juice cups on the table. the cups contained different flavored juices and different shaped straws. what is the probability that a randomly selected cup contains a star-shaped straw given that the cup contains orange juice?
The probability of selecting a star-shaped straw from a cup that contains orange juice is 1/3.
The probability that a randomly selected cup contains a star-shaped straw given that the cup contains orange juice is obtained by dividing the number of cups containing orange juice and star-shaped straws by the total number of cups containing orange juice.
P(probability) = (Number of cups containing orange juice and star-shaped straws) / (Number of cups containing orange juice)
We are not given any information about the number of cups, thus we can assume that it is an equal amount. Hence, the number of cups containing orange juice would be equal to the number of cups containing different flavored juices. Therefore, Number of cups containing orange juice = Number of cups containing different flavored juices
The number of cups containing orange juice and star-shaped straws is not given, so we can assume that it is 3 since there are three flavors of juice. The number of cups containing orange juice and star-shaped straws = 3
Thus, the probability that a randomly selected cup contains a star-shaped straw given that the cup contains orange juice is: Probability = (3/9) = 1/3
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Ángel participa en una rifa de un automóvil comprando 4 boletos si se han vendido en total 4800 boletos ¿Cual es la probabilidad que tiene Ángel de ganar el automóvil?
Ocean water freezes at a temperature of 2° below zero
What integer represents the freezing point of ocean water?
answer fast pls
Answer:
the answer is -2
MARK IT AS A BRAINLIEST PLS, THANKS!
Help with question above I thought it was the last one but it said it was incorrect
The perimeter of the garden is:
90 + 30√3 feet
How to the perimeter of the garden?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The perimeter of the garden is the sum of all the three sides of the garden.
Check the attached for the sketch of the garden.
Thus, we can say:
sin 60 = (30√3)/y
(√3)/2 = (30√3)/y
1/2 = 30/y
y = 2 * 30
y = 60 feet
tan 30 = x/(30√3)
1/√3 = x/(30√3)
(√3) x = 30√3
x = 30 feet
perimeter = x + y + 30√3
perimeter = 30 + 60 + 30√3
perimeter = 90 + 30√3 feet
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HELP! NEED ANSWER ASAP
The Area of the figure below is composed of a rectangle and semicircles that will be 56.1 unit sq.
The semicircles can be composed into a circle with a radius 3,
The area of a circle is πr² where r is the radius.
πr²= 3 x 3 /2 π
A ≈ = 99/7
A = 14.1
The area of the rectangle = Length x width
= 7 x 6
= 42
Total area of a figure = 14.1 + 42 = 56.1
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write an exponential function in the form y=abx that goes through points 0,20 and 2,320
The final Exponential function is: y = 20(4)^x
To write an exponential function in the form y = ab^x that goes through two points, we need to first determine the values of a and b.
Given points (0, 20) and (2, 320), we can use the first point to determine the value of a:
y = ab^x
20 = ab^0 (when x = 0, y = 20)
20 = a(1)
a = 20
Now we can use the second point to determine the value of b:
y = ab^x
320 = 20b^2 (when x = 2, y = 320)
16 = b^2
b = 4 or -4
Since b cannot be negative in this case (as it is an exponential growth function), we can use b = 4.
Therefore, the exponential function that goes through the points (0, 20) and (2, 320) is:
y = 20(4)^x
We can check this by plugging in the x-values of the two given points:
y = 20(4)^0 = 20 (when x = 0, y = 20, as expected)
y = 20(4)^2 = 320 (when x = 2, y = 320, as expected)
So the final exponential function is: y = 20(4)^x
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A concrete foundation for a building has the shape of a rectangular prism. The foundation is 20 yards long, 13 yards wide, and 2 yards high. If concrete costs 5$ per cubic yard, how much did the concrete cost for the foundation?
Answer:
$2,600
Step-by-step explanation:
To find the cost of the concrete foundation of a building in the shape of a rectangular prism, multiply its volume (in cubic yards) by the cost per cubic yard.
The volume of a rectangular prism is the product of its width, length and height.
[tex]\boxed{V=w \cdot l \cdot h}[/tex]
Given values:
w = 13 yardsl = 20 yardsh = 2 yardsTherefore, the volume of the concrete foundation is:
[tex]\begin{aligned}V&=13 \cdot 20 \cdot 2\\&=260 \cdot 2\\&=520\; \sf yd^3\end{aligned}[/tex]
Given the concrete costs $5 per cubic yard, multiply the volume by the cost to calculate the total cost of the concrete for the foundation is:
[tex]\begin{aligned}\textsf{Total cost}&=\sf Volume \cdot cost\\&=\sf 520 \; yd^3 \cdot \$5/yd^3\\&=\sf 520 \cdot \$5\\&= \sf \$2600\end{aligned}[/tex]
Therefore, the total cost of the concrete for the foundation is $2,600.
Martina wants to rent a boat and spend at most $51. The boat costs 58 per hour, and Martina has a discount coupon for $7 off. What are the possible Lumbers
of hours Martina could rent the boat?
User for the number of hours
Exh
y = -3x + 22
5x + 2y = 44
Linear equation method
The solution is x = 0 and y = 22.
Equation 1: y = -3x + 22
Substitute y in Equation 2:
5x + 2(-3x + 22) = 44
Simplify and solve for x:
5x - 6x + 44 = 44
-x + 44 = 44
-x = 0
x = 0
Substitute x = 0 back into Equation 1 to find Y:
Y = -3(0) + 22
Y = 0 + 22
Y = 22
So the solution is x = 0 and y = 22.
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which of the following shows the correct simplification of the quadratic formula used to solve 8x^2-2x=1
HELLO
8x² - 2x = 1
8x² - 2x - 1 = 0
x = (-b±√(b² - 4ac)) / 2a
= (-(-2)±√((-2)² - 4*8*(-1))) / (2*8)
= (2±6)/16
x₁ = (2+6)/16 = 1/2
x₂ = (2-6)/16 = -1/4
Mrs holland wants to paint her garage wall. The wall measures 6 2/3 by 3 1/7. Each paint of can covers 5m
each can of paint costs 7. 50
how much will it cost mrs holland to paint her garage wall
To determine how many cans of paint Mrs. Holland needs to paint her garage wall, we need to find the area of the wall. The wall measures 6 2/3 by 3 1/7, which can be converted to an improper fraction to make calculations easier.
6 2/3 = (6x3 + 2)/3 = 20/3
3 1/7 = (3x7 + 1)/7 = 22/7
So the wall measures 20/3 meters by 22/7 meters. To find the area, we can multiply these two values:
(20/3) x (22/7) = 440/21 square meters
Each can of paint covers 5 square meters, so we need to divide the area of the wall by 5 to determine how many cans of paint we need:
(440/21) ÷ 5 ≈ 4.19 cans
Since we can't buy a fraction of a can of paint, we need to round up to 5 cans.
So, it will cost Mrs. Holland 5 cans x $7.50 per can = $37.50 to paint her garage wall.
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Part B
The artist will use concrete to create the form of the sculpture. How much concrete will the artist need to make up each of the three parts that make up the sculpture?
Use the text tool to write the volume of each of the three parts on the diagram. Round each volume to the nearest whole cubic meter.
Once you have the dimensions for each part, let me know, and I can assist you with the volume calculations and rounding to the nearest whole cubic meter. I can guide you through the process of calculating the volume of each part of the sculpture.
To calculate the volume of each part, we need to know the dimensions or specific shape of each part. If you provide the dimensions or shape information, I can help you calculate the volumes.
In general, to calculate the volume of a three-dimensional shape like a rectangular prism or cylinder, you multiply the length, width, and height (or base area and height) of the shape. Make sure to use consistent units of measurement (such as meters) for accurate results.
If you can provide the specific shapes and dimensions of the three parts of the sculpture, I can assist you in calculating their volumes. Once we have the dimensions, we can use the appropriate volume formulas and round the results to the nearest whole cubic meter, as instructed.
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Note the full question is Part B
The artist will use concrete to create the form of the sculpture. How much concrete will the artist need to make up each of the three parts that make up the sculpture?
Use the text tool to write the volume of each of the three parts on the diagram. Round each volume to the nearest whole cubic meter.
To determine the amount of concrete needed for each part of the sculpture, calculate the volume of each part based on their geometrical shape's formula and round to the nearest whole cubic meter.
Explanation:To calculate the amount of concrete the artist will need for the sculpture, we need to know the volume of each of the three parts comprising the sculpture. Volumes of geometric forms are generally calculated using the formulas:
Sphere: 4/3*π*r³ Cylinder: π*r²*hCube/Box: length*width*height
By substituting the given dimensions of each part into the appropriate formula, we can calculate the volume. Finally, each volume should be rounded to the nearest whole cubic meter. Therefore, the artist needs to have the exact volume of concrete in cubic meters for each part of the sculpture.
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the dice faces are as follows: blue: 2,3,3,3,6,6 green: 0,1,1,4,4,4 the two dice are rolled and the sum of the results is calculated. what is the probability of the sum equaling 5?
Step-by-step explanation:
There are 36 possible rolls
NONE will result in a '5' total
0/36
there is nothing on the blue die that added to from the green die = 5
quick answer please I've tried figuring this out for hours
Answer:
Step-by-step explanation:
the number of trials and the population proportion are respectively represented by what symbols?
The number of trials is typically represented by the letter "n" in statistics. This refers to the number of independent and identical observations that are taken during an experiment or study. The population proportion, on the other hand, is often represented by the letter "p".
This refers to the proportion or percentage of individuals in a population that exhibit a certain characteristic or behavior. For example, if we were studying the proportion of people who prefer chocolate ice cream, "p" would represent the percentage of people in the population who prefer chocolate ice cream.
It's important to note that the number of trials and the population proportion are both key factors in statistical analysis, as they can help researchers draw conclusions about the population as a whole based on a smaller sample size.
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Pat starts with two identical square pieces of paper. On the first one, she draws straight lines that divide the paper into a 3 by 3 grid of squares. The total length of the lines she draws is 18 cm.
On the second piece of paper, Pat draws straight lines that divide the paper into a 6 by 6 grid of squares.
What is the total length of the lines that Pat draws on the second piece of paper?
Answer:
36 cm
Step-by-step explanation:
the total length of the lines that pat draws on the second piece of paper is 36 cm.
A rectangular dog run has a width of 2 √7 yards and a length of 10 √7 yards.
here is the rest of the problem:
The owner has 2 dogs that need to be separated so she is going to put a diagonal fence connected on each corner.
a. What would the length and width be in decimals? Round to one decimal place.
b. How long is the diagonal fence? Write your answer in radical and decimal form.
c. The old fence doesn’t match the new fence so she wants to replace it. How many yards of fencing does she need? Write your answer in radical and decimal form.
In radical form, the perimeter is 2√(7) yards, and in decimal form, it's approximately 57.8 yards (rounded to one decimal place).
a. To find the length and width in decimal form, simply multiply the given values by √7.
Width = 2√7 yards ≈ 5.3 yards (rounded to one decimal place).
Length = 10√7 yards ≈ 23.6 yards (rounded to one decimal place).
b. To find the length of the diagonal fence, you can use the Pythagorean theorem since it forms a right triangle with the width and length of the dog run.
Diagonal (d) = √[tex](Width^2 + Length^2)[/tex]
d = √([tex](5.3 yards)^2[/tex] + [tex](23.6 yards)^2)[/tex]
d ≈ √(28.09 + 556.96)
d ≈ √585.05 yards
In decimal form, the diagonal fence is approximately 24.2 yards (rounded to one decimal place).
c. To find how many yards of fencing the owner needs to replace the old fence, add the four sides of the rectangular dog run:
Perimeter = 2(Width + Length)
Perimeter = 2(5.3 yards + 23.6 yards)
Perimeter = 2(28.9 yards)
Perimeter ≈ 57.8 yards (rounded to one decimal place).
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in order for us to use this sample of 30 heart-attack patients to make inferences about the whole population of heart-attack patients, what assumption must we make regarding the sample and how it was obtained? what risk do we run in performing any inference about the population of interest if this assumption is not met?
If this assumption is not met, the risk we run in making inferences about the population is that our conclusions may be biased or inaccurate, leading to misleading or incorrect results when applied to the entire population of heart-attack patients. This could have negative implications for treatments or public health policies based on these inferences.
In order for us to use this sample of 30 heart-attack patients to make inferences about the whole population of heart-attack patients, we must assume that the sample is representative of the population. This means that the 30 patients were chosen randomly from the population of heart-attack patients and that the sample accurately reflects the characteristics of the population. Additionally, we must assume that the sample size is large enough to provide reliable results.
If this assumption is not met, then we run the risk of making incorrect inferences about the population of interest. For example, if the sample is biased and not representative of the population, the inferences we draw may not be applicable to the larger population. Similarly, if the sample size is too small, our inferences may be unreliable and subject to sampling error.
In order to avoid these risks, it is important to carefully consider the sampling method and sample size when conducting research. By ensuring that the sample is representative and the size is appropriate, we can have more confidence in our inferences about the larger population. Answer more than 100 words.
To make inferences about the whole population of heart-attack patients using a sample of 30, we must assume that the sample is representative of the entire population. This means that the sample should be random, unbiased, and large enough to capture the diversity in the population.
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pls help me with this
Answer:
x-intercept coordinates: (9, 0)
y-intercept coordinates: (0, 21)
Step-by-step explanation:
Put the equation in slope-intercept form, y = mx + b
3y = -7x + 63 divide both sides by 3
y = -7/3x + 21
y-intercept = b = 21
y-intercept coordinates: (0, 21)
Find x intercept by setting y = 0 and solving for x:
0 = -7/3x + 21
7/3x = 21
x = 21(3/7) = 9
x-intercept coordinates: (9, 0)
Simplify: 3x3+2y3+6x3+5y Responses 9x6+7y4 9 x to the 6th power plus 7 y to the 4th power 9x6+2y3+5y 9 x to the 6th power plus 2 y cubed plus 5 y 5xy3+6x3+5y 5 x y cubed plus 6 x cubed plus 5 y 9x3+2y3+5y 9 x cubed plus 2 y cubed plus 5 y
To simplify the expression 3x^3 + 2y^3 + 6x^3 + 5y, we can combine like terms to get 9x^3 + 2y^3 + 5y.
The given expression has two terms with x cubed and two terms with y cubed. We can combine the coefficients of the x cubed terms and the coefficients of the y cubed terms to get:
3x^3 + 6x^3 = 9x^3
2y^3 = 2y^3
Therefore, the simplified expression so far is 9x^3 + 2y^3.
The last term in the given expression is 5y, which is not like the first two terms. Therefore, the expression cannot be simplified any further by combining like terms. The final simplified expression is 9x^3 + 2y^3 + 5y.
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Which value of x makes the following equation true? 2 ( x − 4 ) + 48 = − 3 x A. − 7 1 5 B. 8 C. − 8 D. − 7
The value of x that makes the equation true is -8. The correct option is C.
To find the value of x that makes the equation true, follow these steps:
1. Write down the given equation: 2(x - 4) + 48 = -3x
2. Distribute the 2 to both terms inside the parentheses: 2x - 8 + 48 = -3x
3. Simplify the equation by combining like terms: 2x + 40 = -3x
4. Add 3x to both sides of the equation to isolate x terms on one side: 2x + 3x + 40 = -3x + 3x
5. Simplify further: 5x + 40 = 0
6. Subtract 40 from both sides to isolate the x term: 5x + 40 - 40 = 0 - 40
7. Simplify: 5x = -40
8. Divide both sides by 5 to solve for x: 5x / 5 = -40 / 5
9. Simplify: x = -8
The value of x that makes the equation true is -8 (Option C).
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