The best approximation for the p-value for the test statistic t0 = 2.155 is 0.032.
To find the best approximation for the p-value for the hypothesis test with null hypothesis H0: μ=8 and alternative hypothesis H1: μ>8, with variance unknown and n=10, and a test statistic t0=2.155, we need to use the t-distribution with degrees of freedom (df) equal to n-1 = 10-1 = 9.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. Since this is a one-tailed test with the alternative hypothesis in the form of μ>8, the p-value corresponds to the area in the right tail of the t-distribution.
Using a t-table or calculator with the t-distribution, we can find the probability of obtaining a t-value as large as 2.155 or larger with 9 degrees of freedom. This probability is approximately 0.032. Therefore, the best approximation for the p-value for this hypothesis test is 0.032.
We can interpret this result as follows: if the null hypothesis is true (i.e., if the population mean is 8), the probability of obtaining a sample mean as extreme or more extreme than the observed one (i.e., greater than 8.215) is 0.032. Since this probability is relatively small, we may reject the null hypothesis in favor of the alternative hypothesis at a significance level of 0.05 or smaller.
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Determined the area of a pentagon with a apothem of 10
The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.
How to solve for the ApothemArea = (Perimeter × Apothem) / 2
Central angle = 360° / 5 = 72°
To find the area of a regular pentagon with an apothem of 10 units, we can use the formula:
Area = (Perimeter × Apothem) / 2
Central angle = 360° / 5 = 72°
Now, consider the right triangle formed by half of a side, the apothem, and the radius. The angle between the apothem and the radius (half of the central angle) is:
Angle = 72° / 2 = 36°
In the right triangle, we have:
tan(36°) = (s/2) / 10
Solving for s:
s = 2 * 10 * tan(36°) ≈ 14.142 units (rounded)
Now that we have the length of one side, we can calculate the perimeter of the pentagon:
Perimeter = 5 * s ≈ 5 * 14.142 ≈ 70.710 units (rounded)
Finally, we can find the area of the pentagon using the formula:
Area = (Perimeter × Apothem) / 2
Area = (70.710 × 10) / 2
≈ 353.55 square units (rounded)
The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.
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The signal from a certain satellite takes 0.0054 approximately seconds to reach Earth. Write this number in scientific notation.
The solution is, 5.4 × 10⁻³ is the number in scientific notation.
Given:
The signal from a certain satellite takes approximately 0.0054 seconds to reach earth.
we will write the number in a scientific notation
The scientific notation is the number that is between 1 and 9 multiplied by 10 raised to an exponent
So, the given number will be:
0.0054
=54/10000
=54/10 * 1/1000
=5.4 × 10⁻³
Hence, The solution is, 5.4 × 10⁻³ is the number in scientific notation.
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Approximate the square root to the nearest integer.
√23
The square root of the number 23 is 5 after using the division method the answer is 25.
What is a number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
The number is 23 which is a real number and positive number.
As we know we can find the square root of a positive numbers only, the square root of a negative number cannot exist
The square root of the number 23 = [tex]\sqrt{23}[/tex]
The sign √ is a radical sign.
After using the division method:
[tex]\sqrt{23} = 4.7958[/tex]
After reducing the number up to two decimal places:
[tex]= 4.79[/tex]
Rounding the above number to the whole:
[tex]= 4.79 \thickapprox 5[/tex]
[tex]5\times5 = 25[/tex]
Thus, the square root of the number 23 is 5 after using the division method the answer is 25.
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3 / 1/4 using multiplication
Answer:
12
Step-by-step explanation:
to divide by a fraction use the acronym K.C.F or keep change flip to re-arrange the problem.
[tex]\frac{3}{\frac{1}{4} }[/tex] can be re-written as
[tex]\frac{3}{1} *\frac{4}{1}[/tex]
or 3*4 which equals 12
Question 6
Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car
results in 310 miles on 20 gallons of gas. Which equation below represent the gas milage of the
car? Select ALL answers that apply.
Oy=310-20x
Oy = 15.5x
Oy = 310x + 20
Oy = 31/2x
Answer: Oy = 15.5x
Step-by-step explanation: Gas mileage refers to the quantity of miles driven per unit volume of gasoline, typically expressed as "miles per gallon." In the context of the present inquiry, the vehicle in question exhibited a capacity to traverse a distance of 310 miles subsequent to the utilization of 20 gallons of gasoline. Thus, it is possible to calculate the gas mileage through the division of the quantity of gas consumed by the distance elapsed, resulting in:
The fuel efficiency of a vehicle, represented by the metric of gas mileage, is typically calculated by the ratio of distance traveled in miles to the amount of fuel consumed in gallons. In the present case, the gas mileage is equivalent to the quotient of 310 miles by 20 gallons, resulting in an efficiency rating of 15.5 miles per gallon.
pls hlp thx ur awesome
The value of k is 20.
Describe Equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, division, or exponents. The goal of solving an equation is to determine the value of the variable that makes the equation true. Equations are commonly used in algebra and other mathematical fields to model real-world situations and solve problems. They can be written in various forms, including standard form, slope-intercept form, point-slope form, and general form, among others.
Since the sum of two angles on a straight line is always 180 degrees, we can set up an equation:
First angle + Second angle = 180
112 + 3k + 8 = 180
Simplifying the equation, we get:
3k + 120 = 180
Subtracting 120 from both sides, we get:
3k = 60
Dividing both sides by 3, we get:
k = 20
Therefore, the value of k is 20.
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he life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours
The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.
To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.
First, we need to standardize the distribution using the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
For x = 1,950 hours:
z = (1,950 - 1,975) / 25 = -1
For x = 2,050 hours:
z = (2,050 - 1,975) / 25 = 3
Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:
0.9987 - 0.1587 = 0.84
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9PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED
Answer: sin x= 20/24 x = 34
Step-by-step explanation:
Which operation can we use to solve for x in the equation 12+x=15?
A) Add 12 to both sides of the equation
B) Divide both sides of the equation by 12
C) Multiply both sides of the equation by 12
D) Subtract 12 from both sides of the equation
Answer:
Subtract 12 from both sides of the equation
Step-by-step explanation:
Solve for x:
12+x=15
-12 -12
x = 3
Brainlist please.
Answer:
D) Subtract 12 from both sides of the equation.
To solve for x in the equation 12 + x = 15, we need to isolate the variable x on one side of the equation. We can do this by subtracting 12 from both sides of the equation, which gives:
12 + x - 12 = 15 - 12
x = 3
Therefore, the solution for x is 3.
how many 15 letter arrangements of 5 a's, 5 b's and 5 c's have no a's in the first 5 letters, no b's in the next 5 letters and no c's in the last 5 letters?
The possible number of letter arrangements of 15 letter with 5 a's, 5 b's and 5 c's have no a's in the first 5 letters, no b's in the next 5 letters and no c's in the last 5 letters are equal to 2252.
Total number of letters for arrangement are 15 in count. Arrangment of 5 A's, 5 B's and 5 C's have no A's in the first 5 letters, no B's in the next 5 letters and no C's in the last 5 letters. In other words, we say that the first five letters must be B's or C's, the next five letters must be C's or A's, and the last five letters must be A's or B's. If there are k number of B's in the first five letters, then there must be (5-k) C's in the first five letters, like that there must be k C's and (5 - k ) A's in the next five letters, and k A's and (5-k) B's in the last five letters. That is number of each letter in each group of five letters is determined completely by knowing the number of B's in the first 5 letters. The number of ways to arrange, 15 letters with this restriction is [tex]$\binom{5}{k}^3$[/tex](since there are [tex]$\binom{5}{k}$[/tex]
ways to arrange k B's and 5-k C's that is arrangements ( 1B + 4C , 2B+ 3C , 3B+2C, 4B+ 1C ),similarly for next five arrangements (1A + 4C , 2A+ 3C , 3A+2C, 4A+ 1C ), ( 1B + 4C , 2B+ 3A , 3B+2A, 4B+ 1A ) and ( 5B, 5C, 5A), ( 5C,5B,A). Thus, the final answer for arrangement is [tex]$\sum_{k=0}^{5}\binom{5}{k}^{3}$[/tex]
Solve the above bionomial expression,
[tex]= \binom{5}{0}^{3} + \binom{5}{1}^{3} + \binom{5}{2}^{3} + \binom{5}{4}^{3} + \binom{5}{5}^{3} \\ [/tex]
[tex]= (\frac{ 5!}{5! 0!})^{3} + (\frac{ 5!}{4! 1!})³ + (\frac{5!}{3! 2!})³ + (\frac{5!}{2! 3!})³ + (\frac{5!}{1! 4!})³ + (\frac{5!}{0! 5!})³ \\ [/tex]
= 1 + 5³ + 10³ + 10³ + 5³ + 1
= 2252
Hence, required value is 2252.
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A glass contains 320cm3 of milk. The mass of the milk is 330g. Calculate the density of the milk in kilograms per cubic metre (kg/m3). Give your answer to the nearest integer
The density of the milk is 1031.25 kg/m³.
How to calculate the density of milk?Density refers to the mass of a unit volume of a material substance.
Density (ρ) = mass (m) / volume (V)
Given:
Volume (V) = 320cm³ = 0.00032m³
Mass (m) = 330g = 0.33kg
The Density (ρ) of the milk wll be:
= 0.33kg / 0.00032m³
= 1031.25 kg/m³
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The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Box plot, as the median can be easily ascertained from the substantial amount of data. The answer is option (a).
What is a median?The middle value in a given set of figures or statistics is referred to as the median. The average value for a given collection of integers can be calculated using one of three main methods in mathematics. The mean, the median, and the mode are the three. Central tendency measurements refer to these three factors. The average value of the supplied data is calculated using mean. The midpoint value of the given data is defined by a median. The input data's repeating value is defined by the mode.
A box plot is a very visual way to show a brief summary of one or more sets of data. It is particularly useful for quickly comparing and summing multiple sets of findings from distinct trials. A box plot provides a visual picture of the distribution of results as well as clues regarding data symmetry at a look.
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rational root theorem
The possible rational zeros of the polynomial function are
±1, ±3, ±9, ±1/2, ±3/2, ±9/2
We have,
To find the possible rational zeros of the polynomial function P(x), we can use the Rational Root Theorem.
According to the theorem,
Any rational zero of a polynomial function with integer coefficients must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case,
The constant term is -9, which has factors of ±1, ±3, ±9.
The leading coefficient is 2, which has factors of ±1, ±2.
So the possible rational zeros are:
±1/1, ±3/1, ±9/1, ±1/2, ±3/2, ±9/2
Simplifying the fractions, the possible rational zeros are:
±1, ±3, ±9, ±1/2, ±3/2, ±9/2
Thus,
The possible rational zeros are ±1, ±3, ±9, ±1/2, ±3/2, ±9/2
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A 40-year-old person who wants to retire at age 60 starts a yearly retirement contribution in the amount of $6,000. The retirement account is forecasted to average a 5% annual rate of return, yielding a total balance of $198,395.72 at retirement age. If this person had started with the same yearly contribution at age 30, what would the difference be in the account balances? A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used. a. $200,732.63 b. $200,237.36
c. $398,633.09 d. $389,633.90
Answer: B.
200,237.36
Step-by-step explanation: just got it right on the quiz
Aldo buys one lego set for ten dollars. How many lego set can he buy with loo dollars? what would be the equation?
Answer: 10 lego sets
Step-by-step explanation: The equation is 10X, 10 dollars times the amount of legos he is buying,
An angle measures 56.8° less than the measure of its complementary angle. What is the
measure of each angle?
solve tan^2x = (power reducing formula)
The solutions to the equation [tex]tan^2(x) = (sec^2(x) - 1)[/tex]are:
x = 2nπ or x = (2n+1) π/2, where n is an integer.
The power reducing formula for the tangent function is:
[tex]tan^2(x) = (sec^2(x) - 1)[/tex]
Therefore, we can rewrite the equation as:
[tex](sec^2(x) - 1) = 0[/tex]
Simplifying further, we get:
[tex]sec^2(x) = 1[/tex]
Taking the square root of both sides, we get:
sec(x) = ±1
Recall that secant is the reciprocal of cosine, so we can write:
cos(x) = ±1
The cosine function can only take values between -1 and 1, so the only possible solutions are:
cos(x) = 1, which implies x = 2nπ (where n is an integer)
or
cos(x) = -1, which implies x = (2n+1)π/2 (where n is an integer).
The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.
It is most commonly used for reducing the power of the sine and cosine functions.
The power reducing formula for cosine is:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
The power reducing formula for sine is:
[tex]sin^2(x) = (1 - cos(2x))/2[/tex]
These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]
By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.
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Probably basics
Playing Card problem
Needing help Please:)
It’s due in a little bit so I would deeply appreciate it
The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.
How to solveThe total number of combinations of selecting 5 cards from a deck of 52 cards is 52C5 = 5251504948/120 = 2598960.
The probability of exactly 4 of the 5 cards being Aces is 48*100/2598960 = 0.0018%.
The probability of all 5 of the cards being Spades is 1287*100/2598960 = 0.0495%.
The probability of exactly 4 of the 5 cards being face cards is 49540100/2598960 = 0.7618%.
The probability of exactly 2 Aces and exactly 2 Kings being selected is 1584*100/2598960 = 0.0609%.
The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.
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The circumference of a circle is 7(pie)cm. What is the area, in square centimeters?
Express your answer in terms of TT(pie).
Juan walks mile, Jamal walks 0.78 mile,
Lucia walks mile, and Marisol walks
0.62 mile to school each day. Which lists
the students in the order of the lengths
of their walks to school, from shortest to
longest?
A. Juan, Jamal, Lucia, Marisol
B. Lucia, Juan, Marisol, Jamal
C. Marisol, Juan, Lucia, Jamal
D. Jamal, Marisol, Juan, Lucia
From shortest to longest is: C. Marisol, Juan, Lucia, Jamal.
How to determined the lengths of their walks?By comparing the lengths of the students' walks, it is possible to determine the correct order of the students based on their walks.
Marisol walks 0.62 miles, while Juan walks one mile. So Juan's walk isn't the most limited.
Lucia walks one mile, which is shorter than Jamal's walk of 0.78 miles but longer than Marisol's walk of 0.62 miles. Therefore, neither the shortest nor longest walk is Lucia's.
Therefore, Jamal and Marisol remain choices. The correct order, from shortest to longest, is as follows because Jamal's walk is longer than Marisol's:
C. Marisol, Juan, Lucia, Jamal.
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May you please help me
Line JN = line AE = 22ft
Line DC = Line LM = 17ft
Line KL = line BC = 12 ft
< D = <M = 158°
< K = <B = 135°
What are congruent shape?Two shapes are said to be congruent when they both have the same length size and same angle measurements.
From the given shapes, polygon ABCDE = JKLMN.
Therefore the corresponding angles and lengths is as follows:
Line JN = line AE = 22ft
Line DC = Line LM = 17ft
Line KL = line BC = 12 ft
< D = <M = 158°
< K = <B = 135°
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A two-digit number is less than 6 times the sum of its digits by 1. The difference between the digit is 1. Find the number.
Answer:
the two-digit number is 65.
Step-by-step explanation:
Let's assume that the tens and units digits of the two-digit number are x and y, respectively.
According to the given condition,
10x + y < 6(x + y) - 1 (less than 6 times the sum of its digits by 1)
Simplifying the above equation, we get:
4x - 5y < -1 (dividing both sides by 2)
Also, it is given that the difference between the digits is 1, so we can write:
x - y = 1 (difference between the digits is 1)
Now, we need to solve these two equations to find the values of x and y.
Multiplying the second equation by 4, we get:
4x - 4y = 4
Adding this equation to the first equation, we get:
4x - 5y + 4x - 4y = 3
Simplifying the above equation, we get:
8x - 9y = 3
Now, we can solve these two equations simultaneously to find the values of x and y.
Multiplying the second equation by 8, we get:
8x - 8y = 8
Subtracting this equation from the previous equation, we get:
y = 5
Substituting this value of y in the equation x - y = 1, we get:
x - 5 = 1
x = 6
Therefore, the two-digit number is 65.
what is the probability that a random integer from 91 to 775 is divisible by 14? (all integers in the given range are equally likely to be chosen).
Answer:
There are 775 - 91 + 1 = 685 integers.
In the given range, the smallest multiple of 14 is 98, and the largest multiple of 14 is 770. ((770-98)/14) + 1 = 49 multiples of 14.
So the probability of choosing a multiple of 14 from this range is 49/685.
Why is the central limit therom an important therom in statistics?
The Central Limit Theorem (CLT) is an important theorem in statistics because it serves as the foundation for various statistical techniques and analyses.
The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution, provided that the population has finite mean and variance.
Normality:
The CLT establishes the concept of normality, which is a critical assumption in numerous statistical tests such as the t-test, z-test, and ANOVA. By knowing that the sample means are normally distributed, we can apply these tests to make inferences about population parameters.
Simplification:
Due to the CLT, we can simplify complex statistical problems by using normal distributions instead of dealing with the original population distribution.
Calculations more manageable and allows us to utilize the standard normal distribution table.
Confidence intervals:
The CLT enables us to construct confidence intervals for population parameters such as the mean.
Essential in estimating unknown population parameters based on sample data and understanding the associated uncertainty.
Margin of error:
The theorem helps in determining the margin of error for estimates, allowing us to quantify the accuracy of our estimates and make better decisions based on data.
Large sample sizes:
The CLT is particularly relevant when dealing with large sample sizes, as the distribution of sample means becomes more normal, and we can apply various statistical techniques with greater confidence.
The Central Limit Theorem is important in statistics because it enables us to assume normality, simplify problems, construct confidence intervals, determine the margin of error, and apply various statistical techniques with greater confidence, especially when dealing with large sample sizes.
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please help me find m<1
Angle m1 has a value of 113 degrees.
What is vertically opposite angle?Angles that are vertical (opposite in a vertical direction) Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another.
What is alternate interior angle?Alternate interior angles are made when a transversal joins two coplanar lines. They can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two coplanar lines at two separate points.
According to the statement, it is creating a pair of linear angles whose sum is 180.
m1 + 67° = 180°
m1 = 113°
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Which sequence appear to be converging? Check all that apply
The sequences that appear to be converging are:
2/7, 11/16, 26/37, 47/65, 74/101, 107/144, 146/197...
8/7, 64/49, 512/343, 4096/2401, 37768/16807, 262144/117649...
32.45, 31.80, 31.655, 31.654, 31.653, 31.652,...
What is conveging sequence?converging refers to a sequence or series of numbers approaching a limit as more terms are added. It indicates that the values of the sequence or series are getting closer and closer to a specific value or point without ever reaching it.
What is sequence?a sequence is a list of numbers or objects arranged in a specific order. Each element in the sequence is called a term, and the position of the term in the sequence is called its index.
According to the given information:
The first two sequences are examples of converging sequences. In the first sequence, the numerators and denominators increase by a fixed amount for each term, but the ratio of the terms approaches a limit as the sequence progresses. Similarly, in the second sequence, each term is the previous term multiplied by a fixed factor, and the terms approach a limit as the sequence progresses.
The fifth sequence is also an example of a converging sequence, where the terms are decreasing and getting closer to a specific value as the sequence progresses.
The third sequence is not converging since the terms are increasing without bound, and the fourth sequence is oscillating between two values and not getting closer to any specific value.
The sixth sequence starts with a fixed value and increases by a fixed percentage for each term, so the terms are also increasing without bound and not converging to a specific value.
In summary, converging sequences have terms that approach a specific value as the sequence progresses, while non-converging sequences either increase or oscillate without getting closer to any specific value.
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answer correctly
Spirit
The coordinates of point P are (6.4, 18, -12).
What is the coordinate of point?A coordinate of a point refers to a set of values that specify the position of that point in a particular reference system or coordinate system. Coordinates are used to uniquely identify the location of a point in a geometric space, such as a plane or a three-dimensional space.
According to the given information:
To find the coordinates of point P, we can use the concept of vector comparison. We are given that the ratio of vector AB to vector AP is 6:4.
Let's denote the coordinates of point P as (x, y, z).
Given:
AB vector = (10, 2, -6)
B coordinates = (4, 6, -8)
AB:AP = 6:4
We can calculate the coordinates of point P as follows:
Since AB:AP = 6:4, we can express this as a vector equation:
(10, 2, -6) / (x - 4, y - 6, z + 8) = 6/4
Now we can cross-multiply to get:
10 / (x - 4) = 6/4
2 / (y - 6) = 6/4
-6 / (z + 8) = 6/4
Simplifying further, we have:
10(x - 4) = 6 * 4
2(y - 6) = 6 * 4
-6(z + 8) = 6 * 4
Expanding the equations, we get:
10x - 40 = 24
2y - 12 = 24
-6z - 48 = 24
Solving these equations, we get:
10x = 64
2y = 36
-6z = 72
Dividing by the respective coefficients, we get:
x = 6.4
y = 18
z = -12
So, the coordinates of point P are (6.4, 18, -12).
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ANSWER FAST PLEASE!!
Answer:
P(heads) = 1/2
There are 4 prime numbers less than 10: 2, 3, 5, 7.
P(prime number) = 4/10 = 2/5
1/2 × 2/5 = 1/5
Question 1(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
We may infer from the box plots that Super Fast Food, with its smaller IQR, is better equipped to predict wait times than Burger Quick.answer is option (a).
What is median?When values are sorted in order of magnitude, the median, a measure of central tendency, is the middle value in the collection.
BX charts are a common approach to visually depict a distribution of data, such as wait times at a drive-through restaurant. The bx in a bx plot depicts the interquartile range (IQR), or the middle 50% of the data, with the bttm and tp of the bx standing in for the first quartile (25th percentile) and third quartile (75th percentile), respectively. A line inside the box represents the median, or the value that splits the data into equal halves.
Although the range, which is the difference between the data's highest and minimum values, can also be used as a consistency indicator, its accuracy is lower than that of the IQR due to its sensitivity to extreme values and outliers. In this instance, Burger Quick's range is 30 - 2 = 28 minutes, while Super Fast Food's range is 27 - 3 = 24 minutes. Despite the fact that the range for Super Fast Food is narrower, it is still unreliable as a measure of consistency since it is significantly impacted by the outlier at 27 minutes, which is considerably outside the range of the data.
We may therefore deduce from the box plots that Super Fast Food, due to its smaller IQR, is able to estimate their wait time more reliably than Burger Quick.
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The complete question is,
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
I can’t solve Question 5, can anyone help?