The probability that a contestant played an electric guitar is 0.8, the probability that a contestant was dressed in sequins is 0.4, and the probability that a contestant played an electric guitar or was dressed in sequins is 0.9.
What is the probability that a randomly chosen contestant played an electric guitar and was dressed in sequins?
By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.
explain probability.Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.
For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.
The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.
The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:
P(A and B) equals P(A) times P(B|A)
where there are two events, A and B.
In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.
P(A) is known to equal 0.8. and P(B) = 0.4.
We also know that P(A or B) = 0.9.
Using the following equation to determine the likelihood of two events occurring together:
P(A or B) = P(A) + P(B) - P(A and B)
we can find P(A and B):
P(A and B)
= 0.8 + 0.4 - 0.9
= 0.3
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I am really stuck on this question please help!!!
Answer:
8 weeks
Step-by-step explanation:
Ok, so the equation given is y=8x+40
If the school needs 104 cabinets in total, we have to find x, the number of weeks to complete this order.
We can input 104 as y as that's the total:
104=8x+40
We have to isolate x, so first, subtract 40 from both sides
64=8x
Next, divide both sides by 8
8=x
So, it will take 8 weeks to fulfill this order.
The perimeter of a triangle is 73 inches. If the second side is 5 inches longer than twice the first side, and the third is 4 inches less than twice the first side how long is each side?
Using the formula for the perimeter of a triangle, x + (2x+5) + (2x-4) = 73. Solving for x, so the first side is 18 inches, the second side is 41 inches, and the third side is 32 inches.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape, such as a polygon or a circle. It is found by adding the lengths of all the sides of the shape.
What is equation?An equation is a mathematical statement that shows the equality of two expressions or values, often with one or more variables that can be solved for.
According to the given information :
Let the first side of the triangle be x.
Then, the second side is 2x + 5, and the third side is 2x - 4, according to the given conditions.
The perimeter of the triangle is the sum of the lengths of its sides, so we can write:
x + (2x + 5) + (2x - 4) = 73
Simplifying the equation:
5x + 1 = 73
5x = 72
x = 14.4
Therefore, the first side of the triangle is 14.4 inches, the second side is 2(14.4) + 5 = 33.8 inches, and the third side is 2(14.4) - 4 = 24.8 inches.
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An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated. (True or False)
The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.
Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.
In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.
This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.
However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.
As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.
As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.
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I went hiking over the weekend. I hiked 1 3/4 miles when I came to a fork
in the trail. I went to the right. I hiked another 2 1/2 miles until I reached
the overlook. How far did I hike to get there?
O 4 1/4
O 4 1/2
O 4 1/3
O 4 1/5
Over the weekend, I went hiking. I had hiked 1 3/4 miles when I came to a trail fork. I turned to the right. I continued hiking for another 2 1/2 km till I arrived at the lookout. I hiked for A) 4 1/4 miles to get there.
In this question, we have been given that the person first hikes for 1 3/4 miles and then for 2 1/2 miles, so we will first convert them into mixed fractions and we will add the fractions.
Total miles hiked to get there = 1 3/4 miles + 2 1/2 miles
= 7 / 4 miles + 5/2 miles
= (7 + 10) / 2 miles
= 17 / 2 miles
= 4 1/4 miles
If the denominators of two fractions are the same (such fractions are said to be similar fractions), they can be added directly. If the denominators are different (such fractions are known as unlike fractions), we must change the denominators and then add the fractions.
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50 POINTS
The average speed of a baseball line drive is 82 miles per hour. Josiah practiced a new technique to improve his hitting speed. His coach recorded the speed of 45 random hits during practice and found that his average speed using the new technique was 83.2 miles per hour, with a standard deviation of 4.6 miles per hour.
Part A: State the correct hypotheses if Josiah is trying to prove the new technique is an improvement over the old technique. (2 points)
Part B: Identify the correct test and check the appropriate conditions. (4 points)
Part C: Carry out the test and determine if there is sufficient evidence at the 0.01 level that Josiah's technique has improved his drive speed.
On solving the provided question, we can say that As a result, we lack sufficient data at the hypothesis 0.01 level to declare that Josiah's new strategy has increased his driving speed.
What is null hypothesis?A null hypothesis is a statistical hypothesis that states that a certain collection of observations has no statistical significance. Hypotheses are examined using sample data to determine their viability. It is also known as "zero" and is represented by the symbol H0. Researchers begin with the assumption that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that there is no such link. Although the null hypothesis may not appear to be significant, it is an important component of research.
Part A: The following are the hypotheses for Josiah's test:
There is no statistically significant change in the average speed of Josiah's hits utilising the old and new techniques. In scientific notation: H0 = 1 - 2 = 0, where 1 represents the population mean speed of hits using the old approach and 2 represents the population mean speed of hits using the new technique.
Alternative hypothesis: There is a substantial difference in the average speed of Josiah's hits when employing the old and new techniques, with the new technique producing a faster average speed. In mathematical terms: Ha: 1 - 2 0.
Part B: We'll use a t-test because we're comparing two means and don't know the population standard deviation. We will assume that the sample sizes are big enough for the Central Limit Theorem to apply, and that the sample means have a normal distribution. We also suppose that the two samples are independent, which means that the speed of one strike is independent of the speed of the other.
Part C: To run the test, we must compute the test statistic and compare it to the critical value with 44 degrees of freedom (n1 + n2 - 2).
The test statistic is calculated as follows:
[tex]t = (x1 - x2 - 0) / (s / \sqrt(n1 + n2 - 2))[/tex]
where x1 represents the sample mean speed using the old approach, x2 represents the sample mean speed using the new technique, s represents the pooled standard deviation, and n1 and n2 represent the sample sizes.
When we plug in the values, we get:
[tex]t = (82 - 83.2 - 0) / (4.6 / \sqrt(45)) = -2.06[/tex]
At the 0.01 significance level, the critical value for a one-tailed t-test with 44 degrees of freedom is -2.681. We cannot reject the null hypothesis since our test statistic (-2.06) is bigger than the crucial threshold.
As a result, we lack sufficient data at the 0.01 level to declare that Josiah's new strategy has increased his driving speed.
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0.305 in word form??
help me please
Answer:
three hundred five thousanths
Step-by-step explanation:
Describe his mistake
Answer:
In (-3)^2, Henry multiplied -3 by 2. That is not correct. (-3)^2 = (-3)(-3) = 9. Additionally, a^3 • a^4 = a^7, and so
[tex] {( - 5ab)}^{3} \times {( - 3 {a}^{2} {b}^{2} )}^{2} [/tex]
[tex] {( - 5)}^{3} {a}^{3} {b}^{3} \times ( { - 3)}^{2} {a}^{4} {b}^{4} [/tex]
[tex]( - 125 \times 9) {a}^{7} {b}^{7} = 1125 {a}^{7} {b}^{7} [/tex]
find the surface area of the trapezoid
The surface area of the trapezoid is calculated to be equal to 731 square feet
How to evaluate for the surface area of the trapezoidarea of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel base. Also the trapezoid have four rectangle sides and two same trapezoid sides.
A = 10ft
B = 13ft
height = 7ft
area of two trapezoid side = 2[1/2 × (10 + 13) ft × 7 ft = 161 ft²
area of rectangle with length 15ft and width 8ft = 8 ft × 15 ft = 120 ft²
area of rectangle with length 15ft and width ft = 15 ft × 105 ft = 105 ft²
area of rectangle with length 15ft and width 13ft = 15 ft × 13 ft = 195 ft²
area of rectangle with length 15ft and width 10ft = 15 ft × 10 ft = 150 ft²
surface area of the trapezoid = 161 ft² + 120 ft² + 105 ft² + 195 ft² + 150 ft² = 731 ft².
Therefore, the surface area of the trapezoid is calculated to be equal to 731 square feet
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see the scatter plot of Wins compared to Free Throw Attempts per Game.
Then use the scatterplot to write your line of best fit and determine the correlation.
I'm confused what's being asked here...but if you're looking for someone to check it then:
The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.
And the correlation is positive
Toshi predicted that he will perform a card trick successfully 95% of the time. He went on to perform the card trick successfully 24 out of 30 times. How did Toshi’s prediction compare with his actual results?
Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.
According to question:Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:
P(success) = 0.95
This is the probability of success for one card trick.
Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:
P(actual success) = 24/30 = 0.8
This is the proportion of successful card tricks that Toshi actually performed.
To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:
P(x) = (n choose x) * pˣ * [tex](1-p)^(n-x)[/tex]
In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:
P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045
This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).
Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.
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When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with
mass 4 kg, the acceleration of the object is 13 m/s². If the same force acts upon another object whose mass is 26 kg, what is this object's acceleration?
According to the given information, we know that:
Force (F) is constant
Mass (m) of the first object is 4 kg, and its acceleration (a) is 13 m/s².
Using Newton's second law of motion, we know that:
F = m*a
Solving for the force (F) acting on the first object:
F = m*a = 4 kg * 13 m/s² = 52 N
What is this object's acceleration?Now, if the same force acts upon an object with a mass of 26 kg, we can use the same equation to find its acceleration (a):
F = m*a
a = F/m
a = 52 N / 26 kg = 2 m/s²
Therefore, the acceleration of the second object is 2 m/s².
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Describe the distribution in terms of magnitude, degree, and direction of skewness.
Skewness measures the magnitude, degree, and direction of asymmetry in a distribution. It is an important tool for describing and understanding the shape of data distributions.
Skewness is a measure of the asymmetry of a distribution. It is a statistical measure that indicates the degree to which a distribution deviates from the symmetry of a normal distribution. Skewness can be either positive or negative, or it can be zero, indicating no skewness.
Magnitude, The magnitude of skewness is determined by the degree of asymmetry in the distribution. The larger the magnitude of skewness, the more asymmetrical the distribution is. A small magnitude indicates a distribution that is close to symmetric.
Degree, The degree of skewness is the extent to which the distribution deviates from symmetry. Positive skewness indicates a distribution with a longer right tail than left, while negative skewness indicates a distribution with a longer left tail than right.
Direction, The direction of skewness is the direction of the longer tail of the distribution. If the tail is to the right, the distribution is positively skewed, and if the tail is to the left, the distribution is negatively skewed.
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(T/F) If the size of a sample is at leastâ 30, then you can useâ z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.
The statement "If the size of a sample is at least 30, then you can use a z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution." is true because when the sample size is at least 30, the Central Limit Theorem applies and the sampling distribution of the sample mean can be approximated by a normal distribution.
If the size of a sample is at least 30, the Central Limit Theorem (CLT) applies, which states that the distribution of sample means is approximately normal, regardless of the underlying distribution of the population, as long as the sample size is sufficiently large.
When the sample size is at least 30, the sampling distribution of the sample mean can be approximated by a normal distribution, and z-scores can be used to calculate probabilities of sample means falling in a given interval.
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Problem 1. What is the best approximation for finding price of individual product? a) Average Cost b) Marginal Cost c) Total Cost d) None of them Problem 2. When do you get profit? a) When cost is greater than revenue b) When cost is equal to revenue c) When Revenue is more than cost d) All of them
Problem 1: The best approximation for finding the price of an individual product is (b) Marginal Cost. This is because marginal cost represents the cost of producing one additional unit of the product. Problem 2: You get profit when (c) Revenue is more than cost. When the revenue generated from selling products is greater than the cost of producing those products, you will have a positive profit.
For problem 1, the best approximation for finding the price of an individual product would be the Marginal Cost. This is because it takes into account the additional cost of producing one more unit of the product, which directly affects the price.
For problem 2, the correct answer would be c) When Revenue is more than cost. This is because profit is calculated by subtracting the cost of producing the product from the revenue earned from selling it. If the revenue is higher than the cost, then there is profit. If the cost is higher than the revenue, then there is a loss. When the cost is equal to the revenue, there is no profit or loss, just a break-even point. Therefore, option d) "All of them" is incorrect.
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If you know a ratio, the inverse trig function gives you an...
Answer: angle
Step-by-step explanation:
How many weeks will it take you to earn $3,437.50, if you work 25 hours
per week and make $12.50 per hour?
Answer:
We can start by calculating the total amount of money earned per week:
$12.50/hour x 25 hours/week = $312.50/week
To find out how many weeks it will take to earn $3,437.50, we can set up a proportion:
Total amount earned / Amount earned per week = Number of weeks
$3,437.50 / $312.50/week = 11 weeks
Therefore, it will take 11 weeks to earn $3,437.50 working 25 hours per week at a rate of $12.50 per hour.
Answer step by step due tmrw
The interior angles measure 160° and the exterior measure 200°
How to find the angles?The sum of the interior angles of a polygon of n sides is:
(n - 2)*180
here n = 18
(18 - 2)*180 = 2880
divide that by the number of sides
2880/18 = 160°
That is the measure of each interior angle, and the exteriors are such that the sum is 360, then:
a + 160 = 360
a = 360 - 160 = 200
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A prism is made from four identical cubes. Show the number of planes of symmetry the prism has.
The number of planes of symmetry the prism has will be 2. Then the correct option is B.
A prism is made from four identical cubes.
Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.
The number of planes of symmetry the prism has will be given as,
The plane divides the shape T into two halves and the plane is perpendicular to the shape T.
The plane divides the shape T and the plane is parallel to the plane of the paper.
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Find the area.
Area =
6 m
10 m
square meters
Answer:
32m
Step-by-step explanation:
area= L×B
L= 10m ×2 =20m
B= 6m×2 =12m
Area= 20m + 12m = 32m
48 students took an arithmetic test. If 36 students passed the test, what percent of students have passed? Show your work using the
scratchpad.
The percentage of the students who passed the test is
If three staff of Chukwudi and Sons Ltd. agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is ₦120,000.00K, How much does the second staff receive?
The second staff member receives ₦40,000.
what is Ratio?In mathematics, a ratio is a comparison of two or more quantities of the same kind or unit. It is expressed as the quotient or fraction of one quantity to another. Ratios are used to compare and express the relationship between different quantities, such as distance, time, weight, or money.
To solve this problem, we need to first determine the total ratio of the ages of the three staff, which is 18 + 20 + 22 = 60.
Next, we need to calculate the share of each staff member by multiplying their age ratio with the total amount of money collected:
The first staff member's share = (18/60) x ₦120,000 = ₦36,000
The second staff member's share = (20/60) x ₦120,000 = ₦40,000
The third staff member's share = (22/60) x ₦120,000 = ₦44,000
Therefore, the second staff member receives ₦40,000.
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GIVEN: Circle with center C and point D.
CONSTRUCT: Equilateral triangle DEF so that points E and F are on circle C.
Circle with center C and point D. Triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.
What is construction?
In the context of geometry, construction refers to the process of creating geometric figures or shapes using only a compass and straightedge (also called a ruler). The goal of construction is to create accurate and precise geometric figures using only these two tools and a given set of instructions.
To construct an equilateral triangle DEF with points E and F on circle C, we will follow the following steps:
Step 1: Draw a circle with center C and point D on it.
Step 2: Draw a line through points C and D. This line will be the base of our equilateral triangle DEF.
Step 3: Construct the perpendicular bisector of line CD. This can be done by drawing two circles with centers at C and D, both with radius greater than half the length of CD. The two circles will intersect at two points, and the line passing through these two points will be the perpendicular bisector of CD.
Step 4: Let G be the intersection point of the perpendicular bisector and circle C that is closest to point D. Draw lines from G to points C and D. These lines will intersect circle C at points E and F, respectively.
Step 5: Check that the length of CE is equal to the length of CF. This can be done using a compass and ruler.
Step 6: Finally, draw lines from points E and F to point D. The resulting triangle DEF will be equilateral.
To prove that triangle DEF is equilateral, we can show that DE = EF = FD. We already know that CE = CF from step 5. Since C is the center of the circle, CE = CF = CD. By construction, angle ECD and angle FCD are both 60 degrees, since they are inscribed angles that intercept the same arc.
Therefore, triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.
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What is the period for the following graph?
A. 180
B. 270
C. 90
D. 360
The period for the following graph is 90 degrees. So correct option is C.
Describe Period?In mathematics, a period is a specific type of repetition in a function or a sequence. A period is the smallest positive value of a constant T for which a function or a sequence f(x + T) = f(x) for all x.
Periods are used to describe the behavior of functions and sequences that exhibit a repeating pattern. The length of the period determines the frequency of the pattern, and it is often used to describe the periodicity of functions in various applications, such as signal processing, harmonic analysis, and Fourier series.
For example, the sine function sin(x) is periodic with a period of 2π. This means that sin(x + 2π) = sin(x) for all x. Similarly, the cosine function cos(x) is also periodic with a period of 2π. Other common examples of periodic functions include the tangent function, cotangent function, and exponential function.
In addition to their applications in mathematics, periods also have practical applications in fields such as physics, engineering, and computer science, where they are used to model periodic phenomena such as waves and oscillations.
Overall, periods are an important concept in mathematics and are used to describe the repeating patterns that are found in many mathematical functions and sequences.
The period for the following graph is 90 degrees.
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Cassie starts college in the fall and has decided to live in an apartment. Her monthly living ex- penses are as follows: Rent with utilities: $800 Hydro: $40 Phone/internet/TV: $129 Groceries: $300 (a) If she attends school for 18 months, what will be her total living expenses?
The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a
mean diameter of 22 mm and a standard deviation of 2. 5 mm. After they are picked and washed, tomatoes with a
diameter of at most 15 mm or at least 30 mm are rejected and not sold. What proportion of such tomatoes are
rejected?
Find the z-table here.
O 0. 0033
O 0. 0201
O 0. 9799
O 0. 9967
The proportion of cherry tomatoes that are rejected based on their diameter is 0.0033. (option a).
To use the CDF, we need to standardize the diameter values using the z-score formula:
z = (x - μ) / σ
where z is the z-score, x is the diameter value, μ is the mean diameter, and σ is the standard deviation.
For tomatoes with a diameter of at most 15 mm, we have:
z = (15 - 22) / 2.5 = -2.8
For tomatoes with a diameter of at least 30 mm, we have:
z = (30 - 22) / 2.5 = 3.2
Next, we use the z-table to find the area under the Normal distribution curve that corresponds to these z-scores. For a z-score of -2.8, the area is 0.0026. For a z-score of 3.2, the area is 0.9993.
Finally, we add these two areas together to get the total proportion of rejected tomatoes:
proportion = 0.0026 + (1 - 0.9993) = 0.0033
Hence the correct option is (a).
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Que tanto mas alto era la calificacion mas alta del examen que la calificacion mas baja
As per the fraction, the lowest score in the examination is 44.
Let's consider the given information. We are told that the highest score and the lowest score in an examination differ by 55 marks. We can represent the highest score as x and the lowest score as y. Therefore, we have:
x - y = 55 ----- equation 1
We are also given that the higher score, which is x, is 9/4 times the lower score, which is y. This can be represented as:
x = (9/4)y
We can use this equation to substitute x in equation 1 and solve for y.
Substituting x in equation 1, we get:
(9/4)y - y = 55
Simplifying the above equation, we get:
(5/4)y = 55
Multiplying both sides by 4/5, we get:
y = 44
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Complete Question:
In an examination, the highest score and the lowest score are different by 55 and the higher one was 9/4 times the lower one. Find the lowest score.
you want to determine what uniform color shirt is the most preferred among 7th grade students. You survey 6 random students in your art class. 4 choose red, so you conlude that red us the preferred color of shirt. is your conclusion valid. explain.
The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.
How to determine if the conclusion is valid.The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.
Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.
Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.
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Vectors u and v are shown in the graph. vector u with initial point at the origin and terminal point at negative 10 comma negative 7 and vector v with initial point at the origin and terminal point at negative 8 comma 4 What is
[tex]proj _{v}u[/tex]
?
Answer:
im sorry i couldnt help myself
Step-by-step explanation:
what is the function showing the total amount of money julia has after x weeks ? use the variable X
The linear function that represent the situation is as follows:
f(x) = 27x + 254
How to represent a function?A function relates input and output values.
Julia has 254 dollars. Each week she saves an additional 27 dollars .
Therefore, the function that models the amount of money Julia has after x week can be represented as follows:
The function is a linear function. A linear function can be represented in the form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
f(x) = 27x + 254
where
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