Answer:
Step-by-step explanation:
1.To arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Therefore, there are 720 ways to arrange all 6 tables in a line.
2.To choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:
C(6,4) = 6! / (4! x 2!) = (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1) = 15
Therefore, there are 15 ways to choose 4 out of the 6 tables.
There are 720 ways to arrange all 6 tables in a line.
And, there are 15 ways to choose 4 out of the 6 tables.
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom.
Now, After arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Hence, there are 720 ways to arrange all 6 tables in a line.
And, For choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:
⁶C₄ = 6! / (4! x 2!)
= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)
= 15
Thus, there are 15 ways to choose 4 out of the 6 tables.
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PLEASE HELP FASTTT LIKW IN LESS THAN 30 MINUTES PLSS IM GIVING BRAINLIEST
Answer:
Each student will have passed 17 tests; It will take 3 weeks.
Step-by-step explanation:
The explanation is in the picture.
the radius of a circle is 24 cm and an arc length on that same circle is 148.8 cm. what's the radian measure of th central angle which intercepts the arc
The radian measure of the central angle which intercepts the arc is 6.2 radians.
We can use the formula relating the arc length to the angle and radius of the circle:
arc length = radius x central angle in radians
Plugging in the given values, we get:
148.8 = 24 x central angle in radians
Solving for the central angle, we have:
central angle in radians = 148.8/24
central angle in radians = 6.2 radians
Therefore, the radian measure of the central angle which intercepts the arc is 6.2 radians.
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Simplify 9/12x1/12=?
Answer: Exact Form:
1/16
Decimal Form:
0.0625
Step-by-step explanation:
the average temperature for a random sample of 56 covid patients was 101.2 with a known population standard deviation of 6. test at a 10% alpha level if the true average temperature of covid patients exceeds 100. what type of error could have occurred? and what are the chances of that happening?
We reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100, with a type I error rate of 10% and a p-value of 0.0068 indicating a low probability of obtaining the observed sample mean if the null hypothesis were true.
To test if the true average temperature of COVID patients exceeds 100, we can use a one-sample z-test.
The null and alternative hypotheses are
Null hypothesis: The true average temperature of COVID patients is less than or equal to 100.
Alternative hypothesis: The true average temperature of COVID patients exceeds 100.
We can calculate the test statistic as
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean, μ is the hypothesized population mean (100 in this case), σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get
z = (101.2 - 100) / (6 / sqrt(56))
z = 2.47
We can find that the p-value is 0.0068. This means that if the true average temperature of COVID patients is actually 100, there is only a 0.68% chance of getting a sample mean of 101.2 or higher.
Since the alpha level is 10%, and the p-value is less than 10%, we reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100.
The type of error that could have occurred is a type I error, which is rejecting the null hypothesis when it is actually true. The probability of a type I error is equal to the chosen alpha level, which is 10% in this case.
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what is the correct order of the numbers from least to greatest 1\2, 0.6,6%,6\5
Thus, the correct order of the numbers from least to greatest: 6% < 1/2 < 0.6 < 6/5
Explain about the ascending order:In an ascending list, the item that is smallest, first, or oldest will be at the top:
The order of a number or amount is from smallest to largest. The list will be arranged with lower values at the top.The alphabetical order of the sort is A to Z for letters and words.With data that includes both numbers and letters or words, like address lines, the sort is probably alphanumeric, which means that 0–9 is sorted first, then A–Z, and so on.Given number-
1\2, 0.6,6%,6\5
convert all numbers in its fraction form:
1\2 = 0.5
0.6 = 0.6
6% = 0.06
6\5 = 1.2
Order from least to greatest: 0.06, 0.5, 0.6 1.2
Or,
Thus, the correct order of the numbers from least to greatest 6% < 1/2 < 0.6 < 6/5
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Use the binomial theorem to expand (2x^2+5y)^5
The expanded form of (2x² + 5y)⁵ using the binomial theorem is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.
Expand the expression using binomial theorem?Given the expression in the question:
(2x² + 5y)⁵
To expand (2x² + 5y)⁵ using the binomial theorem, we need to apply the following formula:
(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + C(n, 2)a⁽ⁿ⁻²⁾ b² + ... + C(n, r)[tex]a^{(n-r)}[/tex] [tex]b^r[/tex] + ... + C(n, n)a⁰ bⁿ
Where C(n, r) is the binomial coefficient, which represents the number of ways to choose r items from a set of n distinct items.
(2x² + 5y)⁵
Here: a = 2x² and b = 5y, so we have:
Plug into the above formula
(2x² + 5y)⁵ = C(5, 0)(2x²)⁵ (5y)⁰ + C(5, 1)(2x²)⁴ (5y)¹ + C(5, 2)(2x²)³ (5y)² + C(5, 3)(2x²)² (5y)³ + C(5, 4)(2x²)¹ (5y)⁴ + C(5, 5)(2x²)⁰ (5y)⁵
Simplifying each term using the binomial coefficient formula C(n, r) = n! / (r! (n-r)!):
(2x² + 5y)⁵ = 1(32x¹⁰)1(1) + 5(16x⁸)1(5y)¹ + 10(8x⁶)2(25y²) + 10(4x⁴)3(125y³) + 5(2x²)4(625y⁴) + 1(1)5(3125y⁵)
Simplifying the coefficients and the exponents of x and y:
(2x² + 5y)⁵ = 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵
Therefore, the expanded form is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.
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Find the perimeter and area of a regular octagon that has a radius of 10m.
PLEASE HELP!!!!! Select all the correct answers.
If you graph the system of inequalities given below, which points would lie in the solution set? Select all the correct answers.
x-y>-4
2x-y<5
2y + x>1
(-2,3)
(-1,3)
(0, 0)
(2,-2)
(3,5)
Answer:
To determine which points lie in the solution set of the system of inequalities x-y>-4, 2x-y<5, and 2y + x>1, we can graph the inequalities on a coordinate plane and look for the region that satisfies all three inequalities.
To graph the inequality x-y>-4, we can first graph the line x-y=-4 by plotting the points on the line:
x y
0 -4
-4 0
Then, we can shade the region above the line, since all points above the line will satisfy the inequality x-y>-4:
|
-4 | x
| /
| /
| /
|/
-8 +------
-4 0
To graph the inequality 2x-y<5, we can first graph the line 2x-y=5 by plotting the points on the line:
x y
0 5
2.5 0
Then, we can shade the region below the line, since all points below the line will satisfy the inequality 2x-y<5:
|
5 | x
| / |
| / |
| / |
|/ |
0 +----|--
0 2.5
To graph the inequality 2y + x>1, we can first graph the line 2y + x = 1 by plotting the points on the line:
x y
0 0.5
1 0
Then, we can shade the region above the line, since all points above the line will satisfy the inequality 2y + x>1:
|
2 | x
| |
1|-----
| /
| /
| /
|/
0 +------
0 1
The solution set of the system of inequalities is the region that satisfies all three inequalities, which is the shaded region in the graph below:
|
5 |
|
| x
2| |
| |
| |
| /|
| / |
0+------+------
-4 0 2.5
So the points that lie in the solution set are:
(-2,3), (-1,3), (2,-2)
Therefore, the correct answers are:
(-2,3), (-1,3), and (2,-2)
This table shows statistics about the US population in 2010. A table titled U S Population by age group (2010). Column 1 labeled age group: under 18, 18 to 24, 25 to 44, 45 to 64, 65 and older. Column 2 labeled percent of population: 24, 9.9, 26.6, 26.4, 13. Column 3 labeled total number: 74,181,467, 30,672,088, 82,134,554, 81,489,445, 40,267,984. What percent of the population was under the age of 18? nearly 10 percent nearly 25 percent nearly 50 percent nearly 75 percent
According to the table, the "Under 18" age group constitutes 24% of the total population, which is nearly 25 percent. Therefore, the answer is "nearly 25 percent".
The percentage of the population under the age of 18 can be calculated by dividing the total number of people in that age group by the total population, then multiplying by 100 to obtain a percentage.
From the table, we see that the total number of people under 18 is 74,181,467.
The total population is the sum of the total numbers in all age groups, which is 74,181,467 + 30,672,088 + 82,134,554 + 81,489,445 + 40,267,984 = 308,745,538.
Dividing the total number of people under 18 by the total population and multiplying by 100 gives
(74,181,467 / 308,745,538) × 100 ≈ 24%.
Therefore, nearly 25% of the population was under the age of 18 in 2010.
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the base of a pyramid is a rectangle with a length of 7.5 cm and a width of 2 cm. what is the height if the volume is 50 cm^3
The solution to the given problem of volume comes out to be the pyramid is 10 cm tall.
What does volume actually mean?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are the symbols for cubic measures.
Here,
The formula: gives the volume of a pyramid.
=> V = base_area * height * (1/3)
The area of the base (base_area) of a pyramid whose base is a rectangle with dimensions of 7.5 cm in length and 2 cm in width can be computed as follows:
base_area equals length * width,
=> 7.5 cm * 2 cm =15 cm².
Additionally, we are informed that the pyramid's (V) volume is 50 cm3.
=> (1/3) * 15 * height = 50
=> height = (3 * V)/base_area.
When V and base_area's values are entered, we obtain:
=> height = (15/15) / (3*50) = 10 cm
Consequently, the pyramid is 10 cm tall.
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How much money in commission does a real
estate agent who works on a 2.5% commission
rate earn from a $260,000 sale?
A. $6,500
C. $65.000
B. $10,400
D. $1,040,000
It seems like the answer could be $6,500, but I prefer to wait for a professional tbh☹.
Determine the absolute value of the complex number colon open vertical bar 6 straight i close vertical bar
Answer:
√37 ≈ 6.083
Step-by-step explanation:
You want the modulus of the complex number 6 -i.
ModulusThe modulus of a number is written using absolute value bars:
|6 -i|
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts:
|6 -i| = √(6² +(-1)²)
|6 -i| = √37 ≈ 6.083
Solve the quadratic equation 9x2 − 16 = 0
The resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.
What is a quadratic equation?Any equation in algebra that can be written in standard form where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
An algebraic equation of the second degree in x is a quadratic equation.
The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
So, we have the quadratic equation:
9x² − 16 = 0
Now, solve as follows:
a = 9
b = 0
c = -16
Now,
c = -0 ± √0² - 4-9(-16)/2*9
x = ±4/3
Therefore, the resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.
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a measure of relative fit for a simple regression line is called the r² or _ of _.
A measure of relative fit for a simple regression line is called the r² or coefficient of determination.
What is a regression line?A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.
The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.
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Jerome is a photographer. He earns $125 per hour
(d) Part D
Create a graph of the data from the table.
The graph of the data from the table is added as an attachment
Creating a graph of the data from the table.From the question, we have the following parameters that can be used in our computation:
Jerome is a photographer. He earns $125 per hour
This means that the equation of the function is
f(x) = 125x
Where x is the number of hours he works
Using the above as a guide, we have the following table of values
x f(x)
1 125
2 250
3 375
4 500
5 625
6 750
Next, we plot the graph from the table of values and the function f(x) = 125x
The graph of the function is added as an attachment
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Pam has $35.00. Peaches cost $0.85 each. She buys (x) peaches. Which shows how much $ she has left?
Answer:
35.00 - (0.85x) = remaining amount
Step-by-step explanation:
To find out how much money she has left, we need to subtract this amount from her starting amount of $35.00:
35.00 - 0.85x
Therefore, the expression that shows how much money Pam has left after buying (x) peaches is:
35.00 - 0.85x
The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = 1 and x =
8. Use the line segment to determine the average rate of
change of the function f(x) on the interval 1 ≤ x ≤ 8.
The average rate of change of the function f(x) on the interval 1 ≤ x ≤ 8 is given as follows:
5.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
The parameters for the function are given as follows:
For an input of 1, the output is of -10.For an input of 8, the output is of 25.Hence the average rate of change for the function is given as follows:
r = (25 - (-10))/(8 - 1) = 35/7 = 5.
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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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The box plots show a random sample of wait times for two more rides at the theme park. 4) Compare the wait times in the box plots. > The median wait time for Thrill Tower is 5 minutes shorter than the median wait time for River Rapids. The IQR for both rides is ? minutes. Wait Times for Rides Thrill Tower 6 8 River Rapids 12 10 Time (min) 14 16
The IQR for both runs is 8 minutes.
What is the interquartile range?If there are outliers or extreme values in the data set, we summarize the typical value using the median instead of the mean. When there are outliers in a data set, the variation is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.
Based on the given box pairs, we can make the following comparisons:
The average wait time at Thrill Tower is about 5 minutes shorter than the average wait time at River Rapids. That's because the centerline of Thrill Tower is about 5 units below the centerline of River Rapids. The IQR (interquartile range) for both times is not directly in the box. However, we can estimate this by finding the distance between the first quartile (Q1) and the third quartile (Q3) of each run. From the box plot of Thrill Tower, we can see that Q1 is around 6 and Q3 is around 14. Therefore, the IQR for Thrill Tower is:
Thrill Tower IQR = Q3 - Q1 = 14 - 6 = 8 minutes
From the box plot for River Rapids, we can see that Q1 is about 8 and Q3 is about 16. Therefore, the IQR for River Rapids is:
River Rapids IQR = Q3 - Q1 = 16 - 8 = 8 minutes
Therefore, the IQR for both runs is 8 minutes.
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Answer: HERE IS THE ANSWER BELOW :)
PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer: A and D as for angle 24 deg, we are using the sin=opp/hyp and for angle 66 we are using cos=adj/hyp.
To find angle 66, you just subtract all 180 by the angles we know. 180-24-90.
abag contains 8 green balls and 5 red balls. the following events occur in sequence: i aball is randomly drawn and its color is recorded. then, it is returned to the bag. ii 3 balls of the opposite color recorded in step (i) are added to the bag. (for example, if a red ball was drawn in step (i), 3 green balls would be added to the bag) iii a ball is randomly drawn from the bag. what is the probability that the second ball drawn is red?
A bag contains 8 green balls and 5 red balls. Then the probability that the moment ball is drawn is ruddy is 23.1%.To fathom this issue, able to utilize the law of adding up to likelihood and consider:
A ruddy ball is drawn in step (i)The likelihood of drawing a ruddy ball in step (i) is 5/13, as there are 5 ruddy balls out of 13 adding up to balls within the pack.
After step (ii), there will be 5 ruddy balls (unique) + 3 green balls (inverse color) = 8 ruddy balls within the pack. So, the likelihood of drawing a ruddy ball in step (iii) given that a ruddy ball was drawn in step (i) is 8/11.
Presently, we will apply the law of adding up to likelihood to discover the general likelihood of drawing a ruddy ball in step (iii):
P(Red ball in step iii) = P(Green ball in step i) x P(Red ball in step iii | Green ball in step i)
P(Red ball in step i) x P(Red ball in step iii | Ruddy ball in step i)
= (8/13) x (3/11) + (5/13) x (8/11)
= 0.231 or roughly 23.1%.
thus, the likelihood that the moment ball is drawn is ruddy is 23.1%
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There are 30 students in Mr.McRoberts' Grade 8 class. One-third of the students are girls. Three-quarters of the boys play basketball. The number of boys in the class who play basketball is:
PLEASE! :(
Answer: 15.
Step-by-step explanation: If one-third of the students are girls, then two-thirds of the students are boys:
number of boys = (2/3) * 30 = 20
Three-quarters of the boys play basketball, so the number of boys in the class who play basketball is:
number of boys who play basketball = (3/4) * 20 = 15
Therefore, the number of boys in the class who play basketball is 15.
The owner purchases 5 buckets, 10 brushes, 48 towels, and 1 case of air fresheners for the car wash. The total cost of the purchases is $144.08. Each bucket costs $2.89, each brush costs $7.91, and each towel costs $0.36. What is the cost, in dollars, of the case of air fresheners?
The cost of the case of air fresheners is $33.25.
What is the cost of the case of air fresheners?Let the cost of the case of air fresheners be represented by the variable a.
Then, the cost of 5 buckets is 5 times $2.89, or 5 x 2.89 = $14.45.
The cost of 10 brushes is 10 times $7.91, or 10 x 7.91 = $79.10.
The cost of 48 towels is 48 times $0.36, or 48 x 0.36 = $17.28.
The total cost of the purchases, including the case of air fresheners, is $144.08.
Therefore, we can write the equation:
14.45 + 79.10 + 17.28 + a = 144.08
Simplifying the left side of the equation, we get:
110.83 + a = 144.08
Subtracting 110.83 from both sides of the equation, we get:
a = 33.25
Therefore, the cost of the case of air fresheners is $33.25.
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Show: The diagonals bisect each other, and the diagonals are congruent.
From the attached picture, it is proven that the diagonals of rectangle MNOP are congruent.
Proof that the diagonals are congruentTo show that the diagonals of rectangle MNOP bisect each other, we need to show that they intersect at their midpoint. Let's label the diagonals as AC and BD, where AC is the diagonal that goes from vertex M to vertex O, and BD is the diagonal that goes from vertex N to vertex P.
First, let's find the midpoint of AC. The midpoint of a line segment is the point that is exactly halfway between the two endpoints. The endpoints of AC are M and O, so we can find the midpoint by averaging their x-coordinates and y-coordinates:
midpoint of AC = ((Mx + Ox)/2, (My + Oy)/2)
Similarly, we can find the midpoint of BD:
midpoint of BD = ((Nx + Px)/2, (Ny + Py)/2)
Now we need to show that these midpoints are the same point. That is, we need to show that:
((Mx + Ox)/2, (My + Oy)/2) = ((Nx + Px)/2, (Ny + Py)/2)
To do this, we can set the x-coordinates equal to each other and the y-coordinates equal to each other:
(Mx + Ox)/2 = (Nx + Px)/2
(My + Oy)/2 = (Ny + Py)/2
Now we can solve for the values of x and y. First, we'll solve for x:
Mx + Ox = Nx + Px
2Mx + 2Ox = 2Nx + 2Px
Mx + Ox - Nx - Px = 0
(Mx - Nx) + (Ox - Px) = 0
Similarly, we can solve for y:
My + Oy = Ny + Py
2My + 2Oy = 2Ny + 2Py
My + Oy - Ny - Py = 0
(My - Ny) + (Oy - Py) = 0
Now we can see that the x-coordinate and y-coordinate of the midpoint of AC are equal to the x-coordinate and y-coordinate of the midpoint of BD, respectively. Therefore, the diagonals of rectangle MNOP bisect each other.
To show that the diagonals are congruent, we can use the Pythagorean theorem. Let's label the length of AC as a and the length of BD as b. Then we have:
a^2 = OM^2 + ON^2 (by the Pythagorean theorem in triangle OMN)
b^2 = PN^2 + PO^2 (by the Pythagorean theorem in triangle PON)
But we know that OM = ON and PO = PN, since MNOP is a rectangle. Therefore, we can simplify these expressions:
a^2 = 2OM^2
b^2 = 2PO^2
Since OM = PO (they are opposite sides of a rectangle), we can substitute to get:
a^2 = 2OM^2 = 2PO^2 = b^2
Therefore, a = b, and the diagonals of rectangle MNOP are congruent.
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pls hlp thx ur great
Answer:
x = - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
14 = [tex]\frac{8}{3}[/tex] (x + 6) ← multiply both sides by 3 to clear the fraction
42 = 8(x + 6) ← distribute parenthesis
42 = 8x + 48 ( subtract 48 from both sides )
- 6 = 8x ( divide both sides by 8 )
[tex]\frac{-6}{8}[/tex] = x , that is
x = - [tex]\frac{3}{4}[/tex]
which of the following probability distribution types has a mean, median, and mode that are all equal? constant symmetric positively skewed negatively skewed
Answer: B symmetric
Step-by-step explanation:
Since every value in a constant-distribution has the same chance of happening, the distribution is symmetric. The mean and median are both identical to this value because there is only one value, which also makes it the mode.
The mode may or may not be equal to the mean and median for a symmetric distribution, but they are always equal. The mean is often higher than the median and the mode may be lower than the median in a positively skewed distribution. The mode may be higher than the median and the mean is often lower in a negatively skewed distribution.
A constant-probability distribution is a form of probability distribution in which the likelihood of each possible result is the same. In other words, there is an equal chance of each outcome.
Therefore , The Constant-distribution is a sort of probability distribution where the mean, median, and mode are all equal.
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An account is opened with an intial deposit of $7,500 and earns 3. 4% interest compounded semi-annually. Round all answers to the nearest dollar
The accumulated amount 54675 ([tex]2.7^{t}\\[/tex]) in dollars of an account with an initial deposit of $7,500 and earns 3. 4% compound interest semi-annually.
A compound interest is calculated by the formula,
[tex]A = P [ 1 + ( r/n )]^{nt}[/tex]
where, A is the accumulated amount at the end of the period ,
P is the initial amount of deposit,
r is the rate of interest earned on the initial deposit in the period
t is the time periods elapsed
and n is the number of times interest is applied per time period
Here the account has an initial deposit , P = $7500 and earns 3.4% rate of interest, say r, compounded semi- annually, that is n= 2 ( as rate of interest is applied twice a year or twice per time period) in time period, say t.
Therefore by the formula of compound interest we get,
Accumulated amount, A = [tex]7500[ 1 + 3.4/2]^{2t}[/tex]
⇒ A = [tex]7500[ 1 + 1.7]^{2t}[/tex] in dollars
⇒ A = [tex]7500(2.7)^{2t}[/tex] in dollars
⇒ A = 7500 (2.7)² ([tex]2.7^{t}[/tex] ) in dollars
⇒ A = 54675 ([tex]2.7^{t}\\[/tex]) in dollars
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Suppose that we are testing H0: µ = µ0 versus H1: µ > µ0. Calculate the P -value for the following observed values of the test statistic (round all answers to 4 decimal places.
(a)z0 = 2.35,
(b)z0 = 1.53,
(c)z0 = 2.00,
(d)z0 = 1.85,
(e)z0 = -0.15.
For a hypothesis testing, [tex]H_0 : µ = µ_0[/tex] ; [tex]H_1 : µ > µ_0.[/tex] the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.
We are testing the null hypothesis versus alternative hypothesis. Both are defined as [tex]H_0 : µ = µ_0[/tex]
[tex]H_1 : µ > µ_0.[/tex].
We have to calculate the P-value for the following observed values test statistic one by one.
a)z = 2.35
The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)
= 1 - P( z≤ 2.35)
Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387
= 0.990613
b) z₀ = 1.53
The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)
= 1 - P( z≤ 1.53)
Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008
=0.936992
c) z₀ = 2.00
The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)
= 1 - P( z≤ 2.00)
Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275
=0.97725
d) z₀ = 1.85
The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)
= 1 - P( z≤ 1.85)
Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157
=0.967843
e) z₀ = -0. 15
The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)
= P( z≤ 0.15 )
Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.
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Pamela has $50,000 in a savings account. The interest rate is 3% per year and is not
compounded. How much will she have in total in 1 year?
Answer:
$51,500 in her savings account.
Step-by-step explanation:
If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.
So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.
PLEASE HELP!!!!!!!!
The box plots below show attendance at a local movie theater and high school basketball games:
Two box plots shown. The top one is labeled Movies. Minimum at 60, Q1 at 65, median at 95, Q3 at 125, maximum at 150. The bottom box plot is labeled Basketball games. Minimum at 90, Q1 at 95, median at 125, Q3 at 145, maximum at 150. Which of the following best describes how to measure the spread of the data?
a. The IQR is a better measure of spread for movies than it is for basketball games.
b. The standard deviation is a better measure of spread for movies than it is for basketball games.
c. The IQR is the best measurement of spread for games and movies.
d. The standard deviation is the best measurement of spread for games and movies.
a) 'The IQR is a better measure of spread for movies than it is for basketball games' best describes how to measure the spread of the data
According to the information provided, the box plots for movies and basketball games indicate that both have the same range of attendance data, with a minimum of 60 and a maximum of 150. However, when comparing the interquartile ranges (IQRs) of the two box plots, it can be seen that the IQR for movies is smaller than the IQR for basketball games.
The IQR represents the middle 50% of the data, and the smaller IQR for movies suggests that the attendance data for movies is more closely clustered around the median than the attendance data for basketball games. Therefore, the IQR is a better measure of spread for movies than it is for basketball games, as it gives a more accurate representation of the variability of the data for movies.
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