Answer: To compute the t-test statistic for the paired sample data, we need to first calculate the sample mean difference and the sample standard deviation of the differences. Then we can use the formula:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the standard error of the mean difference is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Let's first calculate the sample mean difference:
x 9 6 7 5 12
y 6 8 3 6 7
The differences between each pair of x and y values are:
(9-6), (6-8), (7-3), (5-6), (12-7) = 3, -2, 4, -1, 5
The sample mean difference is the average of these differences:
sample mean difference = (3 - 2 + 4 - 1 + 5) / 5 = 1.8
Next, we need to calculate the sample standard deviation of the differences. To do this, we first calculate the deviations of each difference from the sample mean difference:
(3 - 1.8), (-2 - 1.8), (4 - 1.8), (-1 - 1.8), (5 - 1.8) = 1.2, -3.8, 2.2, -2.8, 3.2
The sample standard deviation of the differences is the square root of the sum of the squared deviations divided by (n-1):
sample standard deviation = sqrt[(1.2^2 + (-3.8)^2 + 2.2^2 + (-2.8)^2 + 3.2^2) / 4] = 3.153
Finally, we can calculate the t-test statistic:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the hypothesized mean difference is 0, and the standard error of the mean difference is:
standard error = sample standard deviation / sqrt(sample size) = 3.153 / sqrt(5) = 1.410
Substituting the values, we get:
t = (1.8 - 0) / 1.410 = 1.277
Rounding the final answer to three decimal places, we get:
t = 1.277
Therefore, the correct option is B. t = 1.292.
ACTIVITY 2: Simplify the following.
The index forms are simplified to;
1. [tex]5^6^\sqrt{2}[/tex]
2.[tex]3^5\sqrt{3}[/tex]
3. [tex]2^2^\sqrt{25}[/tex]
How to simply the index formsIt is important to note the following about the rules of index forms;
Add the exponents when multiplying index forms of like basesSubtract the exponents when dividing index forms of like basesExponents of unlike bases cannot be add or subtracted.From the information given, we have that;
[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]
Add the exponents, we have;
[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]
Then, we have;
[tex]5^6^\sqrt{2}[/tex]
2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]
We have;
[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]
Add the exponents
[tex]3^5\sqrt{3}[/tex]
3. [tex]2^2^\sqrt{25}[/tex]
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What is -2 - 1 3\7 please help
Answer:
Step-by-step explanation:
To solve this expression, we need to first combine the integer part of -2 and -1, which gives us -3. Then, we need to combine the fractional parts of -1 and 3/7.
To do this, we find a common denominator, which is 7, and convert -1 to an equivalent fraction with denominator 7 by multiplying both the numerator and denominator by 7, which gives us -7/7.
Now we can add -7/7 and 3/7 to get -4/7.
Therefore, -2 - 1 3/7 = -3 - 4/7, which can also be written as -3 4/7 or -23/7 in improper fraction form
A triangle has side lengths of (6.1w + 7.8) centimeters, (1.4w + 8.1) centimeters
and (8.7x + 2.5) centimeters. Which expression represents the perimeter, in
centimeters,
of the triangle?
The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.
The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:
(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)
Simplifying and combining like terms, we get:
7.5w + 11.2x + 18.4
Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.
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Virginia earns $69,500 per year at her job as a speech pathologist, and she is paid every two weeks. Her most recent paycheck included the following deductions: FICA $200.20 Federal income tax $180.65 State income tax $72.00 Health insurance $110.00 Retirement savings $250.00 Considering her deductions, what percentage of her gross pay did Virginia take home? 71.65% 62.34% 69.59% 68.55%
She takes 69.5% as gross pay at take home,
Hence option (c) is correct.
Given that,
The amount of earning = $69500
From the given table total deduction = 812.85
Since she pay deductions in every two weeks
Therefore,
The gross earning per year = 69500 - 812.85
= $ 48388
There are 365 days in a year
So earing per day = 69500/365 = 4190.411
So gross earing per day = 48388 /365 = 132.569
SO the gross percentage = (132.5/190.5)x100
= 69.5 %
Hence the required percentage is 69.5%
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Please help with this one as well,,,
The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.
How to draw a whisker plot?A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.
To create a whisker plot, follow these steps:
Collect the data you want to represent and arrange it in order from smallest to largest.Find the median, which is the middle value of the data set. If the data set has an even number of values, the median is the average of the two middle values.Find the lower quartile (Q1), which is the median of the lower half of the data set.Find the upper quartile (Q3), which is the median of the upper half of the data set.Calculate the interquartile range (IQR), which is the difference between Q3 and Q1.Learn more about whisker plots in https://brainly.com/question/2742784
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Can you please help me with this?
The triangles represented in the picture attached are acute, obtuse, acute and right triangles respectively.
Understanding different types of trianglesAcute Triangle is a triangle in which each of the three angles are less than 90°.
In fact all angles in an acute triangle are can be equal and sum to 180°.
Right Triangle is a triangle in which one of the angles is exactly 90°, often denoted as a "square corner".
The side opposite the right angle is called the hypotenuse and it is the longest side.
Obtuse Triangle is a triangle in which one of the angles is greater than 90°.
In other words, one of the angles in an obtuse triangle is "blunt" or greater than a right angle.
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Can someone help me with this please
The measure of x is 36.
We have,
The angle opposite to equal sides is equal.
And,
The sum of the triangle.
27 + 90 + (x + 27)= 180
27 + 90 + x + 27 = 180
x = 180 - 144
x = 36
Thus,
The measure of x is 36.
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Solve for x. Round to the nearest tenth, if necessary.
8.69 is the length of the right angle.
Let's call the length you are trying to find x.
Using trigonometry, we know that:
cos(75) = x/9
Solving for x:
x = 9sin(75)
The sine function (sin) is a mathematical function commonly used in trigonometry. It relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.
Using a calculator to find the cosine of 75 degrees:
x ≈ 8.69
Therefore, the length you are trying to find is approximately 8.69.
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2. If 15% of the first digit equals 21% of the second digit, then what percentage of the second digit equals 25% of the first digit?
Answer:
35%
(I replaced the 1st digit by a and the second digit by b)
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
2,090. because Sarah has long distances and wanted to go home
Write the parametric equations.
x=5t−1,y=1−3t
as a function of x in Cartesian form.
y=
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 12% are pennies and 34% are dimes. There are 3 more nickels than pennies. How much money does the bag contain?
Answer:
i think the bag contains $3.56
Step-by-step explanation:
Question 12: The base and height of the rhombus are given. Apply a formula to find the area of the rhombus
Nevaeh works in a department store selling clothing. She makes a guaranteed salary of $300 per week, but is paid a commission on top of her base salary equal to 20% of her total sales for the week. How much would Nevaeh make in a week in which she made $1975 in sales? How much would Nevaeh make in a week if she made x dollars in sales?
a) When Nevaeh makes $1,975 in sales for the week, her total earnings, based on her base salary and sales commission rate, are $695.
b) When she makes x in sales for the week, her total earnings are represented by the equation, y = 300 + 0.2x.
How the total earnings are computed:The total earnings for the week can be determined using the equation y = 300 + 0.2x, where x represents her total sales for the week while 0.2 represents a 20% sales commission.
The base salary, in this situation, is $300.
Guaranteed (base) salary per week = $300
Sales commission = 20% of sales
Sales for the week = $1,975
a) Total earnings = $695 ($300 + $1,975 x 20%)
Sales for the week = x
b) Total earnings, y = $300 + 0.2x ($300 + 0.2x)
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What is the answer to the equation?
-4(3/2x - 1/2)= -15
A. X= -19/6
B. X= - 29/4
C. X= 13/6
D. X= 17/6
Answer:
D
Step-by-step explanation:
- 4( [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ) = - 15 ← distribute parenthesis by - 4
- 6x + 2 = - 15 ( subtract 2 from both sides )
- 6x = - 17 ( divide both sides by - 6 )
x = [tex]\frac{-17}{6}[/tex] , that is
x = [tex]\frac{17}{6}[/tex]
A radioactive isotope has a half-life of 1,920 years. Let f(t)
be the amount of isotope, in milligrams, that is present after t years. If the sample originally contained 21 milligrams, write an equation modeling this situation.
F(t)=
The equation that models the given situation is: f(t) = 21e^(-0.000361)t
How to solve an exponential decay function?We can model this situation with an exponential decay function.
f(t) = Pe^(rt)
Where:
f(t) = amount of isotope
P = starting amount
r = growth rate
t = time
Let's assume that there is 1 mg of our isotope. Thus,in 1920 years, we will have 1/2 mg. Thus:
(1/2) = (1)e^(1920r)
Take the natural log of both sides to bring the exponent down and to cancel out the e
ln(1/2) = ln(e^(r(1920))
ln(1/2) = r(1920)
ln(1/2)/1920 = r
r = -0000361
Thus, we have:
f(t) = Pe^(-0.000361)t
Plug in 21 for P to get:
f(t) = 21e^(-0.000361)t
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The table shown below lists the U.S. presidents and their ages at inauguration. President Cleveland has two entries because he served two nonconsecutive terms.
Find the mean and the population standard deviation of the ages. Round each result to the nearest tenth.
mean
population standard deviation
The mean age of the U.S. presidents at inauguration is 54.7 years and the population standard deviation is approximately 5.7 years.
To find the mean and population standard deviation of the ages of the U.S. presidents at inauguration, we first need to calculate the sum of the ages and the number of presidents in the data set.
The sum of the ages is:
57 + 61 + 57 + 57 + 58 + 57 + 61 + 54 + 68 + 51 + 49 + 64 + 50 + 48 + 65 + 52 + 56 + 46 + 54 + 49 + 50 + 47 + 55 + 55 + 54 + 42 + 51 + 56 + 55 + 51 + 54 + 51 + 60 + 62 + 43 + 55 + 56 + 61 + 52 + 69 + 64 + 46 + 54 + 47 = 2,405
There are 44 presidents in the data set.
Therefore, the mean age is:
mean = sum of ages / number of presidents = 2,405 / 44 = 54.7
To find the population standard deviation, we first need to calculate the sum of the squared deviations from the mean:
(57 - 54.7)² + (61 - 54.7)² + ... + (47 - 54.7)² = 3,391.5
Then, we divide the sum of squared deviations by the number of presidents and take the square root:
population standard deviation = √(3,391.5 / 44) ≈ 5.7
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h(x) = 2x + 3
Complete the function table.
X. H(x)
-4
0
1
2
3
Answer:
X H(x)=2x+3
-4 -5
0 3
1 5
2 7
3 9
A good rule of thumb is to save 10 percent of what you earn, and have at least three months' worth of living expenses saved up in case of an emergency.
False
True
Answer:
False
Step-by-step explanation:
you have to save at least 20 percent
Bentley invested $670 in an account paying an interest rate of 6 7/8% compounded
quarterly. Camden invested $670 in an account paying an interest rate of 7 3/8%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Bentley's money to triple than for Camden's money to triple?
It will take 15.03 years for Bentley's money to triple.
How longer for Bentley's money to triple than Camden's?For Bentley:
We have
Principal (P) = $670
Interest rate (r) = 6 7/8% = 0.06875 (compounded quarterly)
Time (t) = unknown
Amount after t years (A) = [tex]P(1 + r/4)^{4t}[/tex]
For Camden:
We have
Principal (P) = $670
Interest rate (r) = 7 3/8% = 0.07375 (compounded annually)
Time (t) = unknown
Amount after t years (A) = [tex]P(1 + r)^t[/tex]
We have to find t such that 3P_Bentley = Camden.
[tex]2010 = 2010(1 + r/4)^{4t} / (1 + r)^t[/tex]
Simplifying, we get:
[tex](1 + r/4)^{4t} / (1 + r)^t = 1/3[/tex]
Taking natural logarithm:
4t ln(1 + r/4) - t ln(1 + r) = ln(1/3)
4 ln(1 + r/4) - ln(1 + r) = ln(1/3) / t
t = (4 ln(3.88356) - 4 ln(16)) / ln(3)
Solving for t, we get:
t = 15.034752564
t = 15.03 years.
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Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is 4 : 20 which is 1: 5
Therefore, 4 of the next 20 horses that come to board should you expect to be white horses
Passersby have taken 4 pieces of vanilla cake and 6 pieces of coconut cake from a sample tray. Based on past data, of the next 30 samples taken, how many should you expect to be pieces of vanilla cake?
Answer: The answer is actually 12 pieces of vanilla cake.
Factor the expression. x^2-12x-45
Answer:
(x + 3)(x - 15)
Step-by-step explanation:
To factor the expression x^2 - 12x - 45, we need to find two numbers that multiply to -45 and add to -12. Let's use the method of decomposition to find these two numbers:
x^2 - 12x - 45
We need to find two numbers that multiply to -45 and add to -12. Let's try -15 and 3:
x^2 - 12x - 45 = x^2 - 15x + 3x - 45
Now we can group the first two terms and the last two terms:
x^2 - 15x + 3x - 45 = x(x - 15) + 3(x - 15)
We can see that both terms have a common factor of (x - 15), so we can factor this out:
x(x - 15) + 3(x - 15) = (x + 3)(x - 15)
Therefore, the expression x^2 - 12x - 45 can be factored as (x + 3)(x - 15).
Refer to the attachment ^-^
Hope Helpful ~
A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
The appropriate statistic for testing the null hypothesis is given as D (-2.20/0.07)
How tp get the statisticCoefficient for slope variable (Exercise time) = -2.20
Standard error of coefficient = 0.07
Therefore, the test statistic value to verify whether or not there is an apparent slope on a population regression line can be estimated as follows.
Test statistic = Coefficient for slope variable/Standard error of coefficient = -2.20/0.07
Therefore its correct answer is D (-2.20/0.07)
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Look at the box plot shown below. What is the minimum value of the data set?
A box plot labeled Volunteer Service Hours with the beginning of quartile 1 at 13, the beginning of quartile 2 at 16.5, the beginning of quartile 3 at 20, the beginning of quartile 4 at 23, and the end of quartile 4 at 27.
The minimum value of the data set is 10.5.
Box plots are an effective graphical tool used to display a summary of a dataset. They provide a visual representation of the minimum and maximum values, quartiles, and outliers of the data. They are commonly used in statistics and can provide valuable insights into a dataset.
Now, let's consider the box plot in question. The box plot is labeled "Volunteer Service Hours" and it has four quartiles, each marked by a horizontal line. The first quartile (Q1) is marked at 13, the second quartile (Q2) is marked at 16.5, the third quartile (Q3) is marked at 20, and the fourth quartile (Q4) is marked at 23, with the end of the box extending to 27.
The minimum value of the data set can be found at the lower whisker of the box plot.
The lower whisker represents the minimum value that is not an outlier.
In this box plot, we do not see any outliers, so the minimum value of the dataset is represented by the lower end of the whisker, which is located at 10.5.
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pls answer asap
A traveler has 9 pieces of luggage.
How many ways can the traveler select 3 pieces of luggage for a trip?
Responses
84
84
504
504
60,480
60,480
362,880
Answer:
84
Step-by-step explanation:
Trust me
Answer:
84
Step-by-step explanation:
There are 9 pieces of luggage.
We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left. The third piece can be selected 7 different ways.
9*8*7
504
But order doesn't matter since we are taking 3 pieces.
Divide by (3*2*1)
504/6 = 84
There are 84 different combinations of luggage
Which expression is equivalent to (4.3x + 4)(−1.8x)?
A. −4.14x2 + 0.08x
B. −7.74x2 − 7.2
C. −7.74x2 − 7.2x
D. −7.74x2 + 7.2x
The expression that is equivalent to (4.3x + 4)(−1.8x) is -7.74x² -7.2x (optionC)
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example, 2a+6 is equivalent to 2(a+3) and will surely have thesame value when a value is substituted for a.
Similar (4.3x + 4)(−1.8x) can be simplified by multiplying -1.8x with both 4.3x and 4
= -7.74x²-7.2x
therefore the equivalent of (4.3x + 4)(−1.8x) is -7.74x²-7.2x.
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The probability that Rosie goes to the beach after school is 6 11 If she does go to the beach, then the probability that she does her homework is ) If she does not go to the beach, then the probability that she does her homework is 3 4 Work out the probability that Rosie does her homework. Give your answer as a fraction in its simplest form.
The probability that Rosie does her homework is: 27/44
How to find the conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
Thus, we can solve this probability as:
(6/11 * 1/2) + ((1 - (6/11) * 3/4)
= (3/11) + (5/11 * 3/4)
= (3/11) + 15/44
= 27/44
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find the inverse given T(y)=6.056y+601.39
Answer:
5 (100y -601.39)
3028
Step-by-step explanation:
Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.
someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink
The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below
What is the graph of exponential function?A curve displaying an exponential function is known as an exponential graph. A curve with a horizontal asymptote and a rising or decreasing slope characterizes the graph of an exponential function. i.e., it begins as a horizontal line, grows or drops gradually, and then the growth or decay accelerates.
The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2
The vertical shift = 2
vertical shrink = 1/2
Kindly find the attached graph below
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