A group of five individuals with high blood pressure were given a new drug that was designed to lower blood pressure. Systolic blood pressure was measured before and after treatment for each individual. The mean and standard deviation for the before treatment were 168.6 and 9.3, respectively. The mean and standard deviation for the after treatment were 137.2 and 7.4, respectively. The 90% confidence for the mean reduction in systolic blood pressure is nearly:________
Answers
Answer:
The 90% confidence interval for the mean reduction in systolic blood pressure is between 22.66 and 40.14.
Step-by-step explanation:
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
The mean and standard deviation for the before treatment were 168.6 and 9.3, respectively. The mean and standard deviation for the after treatment were 137.2 and 7.4.
This means that
\(\mu = 168.6 - 137.2 = 31.4\)
\(\sigma = \sqrt{9.3^2+7.4^2} = 11.88\)
90% confidence interval:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
\(M = 1.645\frac{11.88}{\sqrt{5}} = 8.74\)
The lower end of the interval is the sample mean subtracted by M. So it is 31.4 - 8.74 = 22.66
The upper end of the interval is the sample mean added to M. So it is 31.4 + 8.74 = 40.14
The 90% confidence interval for the mean reduction in systolic blood pressure is between 22.66 and 40.14.
Related Questions
14. Simon earned 400sh as a for goods sold what Commission 15,000 worth so, 600 could be his varnings for a total sale of 7,000
Answers
His total earnings for a total sale of 7,000 could be 1450sh
How to determine his earnings for a total sale of 7,000.From the question, we have the following parameters that can be used in our computation:
Salary = 400
Commission = 15%
using the above as a guide, we have the following:
Total earnings = 400 + 15% * Total sales
So, we have
Total earnings = 400 + 15% * 7000
Evaluate
Total earnings = 1450
Hence, the total earnings is 1450
Read more about commission at
https://brainly.com/question/26283663
#SPJ1
Question
Simon earned 400sh weekly for goods sold and a commission of 15%
What could be his earnings for a total sale of 7,000.
Share an example of how pascal's triangle is used for binomial expansion. discuss the steps in your binomial expansion example and how it relates to pascal's triangle.
Answers
The final answer is (a+b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴.
Pascal's Triangle is a useful tool in expanding binomial expressions, which is a fundamental concept in algebra. For example, let's expand (a+b)⁴ using Pascal's Triangle.
Step 1: Write out Pascal's Triangle to the 4th row, as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
Step 2: Write out the coefficients in the binomial expression (a+b)⁴:
(a+b)⁴ = 1a⁴ + 4a³b + 6a²b² + 4ab³ + 1b⁴
Step 3: Substitute the coefficients from Pascal's Triangle into the binomial expression:
(a+b)⁴ = 1a⁴ + 4a³b + 6a²b² + 4ab³ + 1b⁴
= 1a⁴ + 4a³b + 6a²b² + 4ab³ + 1b⁴
= 1(a⁴) + 4(a³b) + 6(a²b²) + 4(ab³) + 1(b⁴)
= (1)(a⁴) + (4)(a³)(b) + (6)(a²)(b²) + (4)(a)(b³) + (1)(b⁴)
Step 4: Simplify the expression to get the final answer:
(a+b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴
Notice how the coefficients of each term in the expanded expression (1, 4, 6, 4, 1) correspond to the fourth row of Pascal's Triangle. Pascal's Triangle provides a quick and easy way to determine the coefficients of a binomial expansion for a given power of the binomial expression.
To learn more about Pascal's Triangle refer to:
brainly.com/question/26134164
#SPJ4
I am lost please help thank you all
Answers
Answer:
Step-by-step explanation:
At least 9 means more than 9 and includes 9
x ≥ 9 and [9, +∞)
At most 9 means numbers less than 9
x≤9 and (-∞, 9]
more than 9 means bigger than 9 but not including 9
x > 9 and (9, +∞)
fewer than 9 means less than 9 but not including 9
x<9 and (-∞, 9)
strictly between 7 and 9 means between 7 and 9 but not including
7<x<9 and (7,9) (This is the only one I'm unsure of. Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)
between 7 and 7 inclusive. means it's just =7 There's no boundaries
x=7
no more than 7 means less than 7 and includes 7
x ≤ 7 and (-∞, 7]
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
Answers
A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.
One possible set could be 3 cm, 4 cm, and 5 cm.
To verify if this set forms a right triangle, we can apply the Pythagorean theorem.
Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.
Adding these two values together gives us 25.
Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.
It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.
There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.
These sets are known as Pythagorean triples.
Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.
In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
For similar question on hypotenuse's.
https://brainly.com/question/30390037
#SPJ8
4. Which set of data could be represented by the box-and-whisker plot? (1 point)
O0, 3, 9, 9, 11, 14, 15, 16, 16, 18, 19, 25, 25, 28, 28, 30
O2, 3, 4, 7, 13, 15, 15, 15, 16, 17, 20, 22, 25, 25, 26, 28
O2, 6, 7, 8, 10, 11, 12, 14, 18, 20, 22, 24, 26, 27, 27, 28
O2, 2, 7, 10, 10, 11, 13, 15, 17, 20, 20, 24, 26, 27, 27, 28
Answers
A set of data that could be represented by the box-and-whisker plot include the following: D.
The median of the set of data is equal to 10.
What is a box-and-whisker plot?In Mathematics and Statistics, a box-and-whisker plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set (2, 2, 7, 10, 10, 11, 13, 15, 17, 20, 20, 24, 26, 27, 27, 28), the five-number summary for the given data set include the following:
Minimum (Min) = 2.
First quartile (Q₁) = 16.
Median (Med) = 10.
Third quartile (Q₃) = 25.5.
Maximum (Max) = 28.
In conclusion, we can logically deduce that the median of the data set is 10 and it has no outlier.
Read more on boxplot here: brainly.com/question/29648407
#SPJ1
A car rental company charge $50 a day and 20 cents per mile for renting a car. Let y be the total rental charge (in dollar) for a car for one day and x be the miles driven. The equation for the relationship between x and y is y = 50 + 20x How much will a person pay who rents a car for one day and drives it 100miles
Answers
Answer:$2050.
Step-by-step explanation:
To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:
y = 50 + 20x
y = 50 + 20(100)
y = 50 + 2000
y = 2050
Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.
what is the answer to this question 15-6*b+6=36
Answers
Answer: Im sure the answer is b= -5/2
Step-by-step explanation: Decimal form: b= -2.5
Mixed number form is: b= -2 1/2
Ikr schools just the worst- ;-;
Anywayz i hope this helps :D
If every 2 cm on a scale drawing is equal to 7 feet in real life, which lines on the drawing would be greater than 21 feet in real life? Select all that apply. A) 7 cm B) 5 cm C) 9 cm D) 12 cm
Answers
The correct answers are A) 7cm, C) 9cm and D) 12cm
Define the Conversion of units?The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.
If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.
Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:
⇒ \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)
where y is the length of the line in real life. Solving for y, we get:
⇒ \(y = \frac{7 feet} {2cm} *x\)
⇒ \(y = 3.5 x feet\)
If we put x = 2cm (given) then, y = 7 feet
For y = 21 feet, the value of x = 6cm.
Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.
So, the lines on the drawing that are greater than 21 feet in real life are:
A) 7cm, C) 9cm, D) 12cm
Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm
To know more about conversion, visit:
https://brainly.com/question/13016491
#SPJ1
What is the turning point of the graph of ƒ(x) = |x| +4 ? (0,4) (0, – 4) (4,0) (-4, 0)
Answers
The turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).
What is Turning point of a graph?A stationary point is called a turning point if the derivative changes sign (from positive to negative, or negative to positive ) at that point. There are two types of turning points - local maxima and local minima.
Given in the question is a modulus function -
f(x) = |x| + 4
In order to determine the turning point, we will first have to plot the graph of this function -
f(x) = |x| + 4
Now, we can write f(x) as -
f(x) = { (x + 4) for x ≥ 0 and (- x + 4) for x < 0} }
Alternatively, you can plot the graph of |x| and positive shift it by 4 units. Refer to the graph attached with the answer. From the graph you can see that after the coordinate (0, 4) the slope becomes positive. Slope of a line gives the rate of change of y with respect to x. So (0, 4) represents the turning point.
Therefore, the turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).
To solve more questions on turning point of functions , visit the link below-
brainly.com/question/9982140
#SPJ1
Allen Siegell has a personal injury protection policy that covers each person in, on, around, or under his car for medical expenses up to $50,000. He is involved in an accident and five people in his car are hurt. One person has $3,000 or medical expenses, three people each have $500 worth of medical expenses, and Allen himself has medical expenses totaling $62,000. How much money must the insurance company pay out for these five people?
Answers
The total medical expenses for the five people in the car are $3,000 + $3*$500 + $62,000 = $3,000 + $1,500 + $62,000 = $66,500
What does a math word problem entail?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Since Allen's personal injury protection policy covers each person up to $50,000, the insurance company must pay out $50,000*5 = $250,000 for the five people in the car.
Since the total medical expenses for the five people are $66,500, the insurance company will pay out the total medical expenses for the five people, which is $66,500.
Therefore, the insurance company must pay out $66,500 for these five people.
Learn more about word problem
https://brainly.com/question/21405634
#SPJ1
These triangles
are congruent by
the triangle
congruence
postulate [? ].
A. ASA
B. Neither, they are not congruent
C. AAS
![These trianglesare congruent bythe trianglecongruencepostulate [? ].A. ASAB. Neither, they are not congruentC.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/VYxIojZNVz1y6MOydQga4ffrPLhbaQJk.png)
Answers
Since in the two triangles,
2 angles and the side between them is given and equal, the triangles are congruent using the Criteria ASA.
Option A is the correct answer.
WHAT IS THE VOLUME OF WAX IN THE CANDLE SHAPED LIKE A CYLINDER
A.50.24 cubic inches B,28.3 cubic inches C.25.1 cubic inches
What is the volume of wax in the candle shaped like a cone?
A. 50.24 CUBIC FEET b.28.3 cubic feet C.25.1
Answers
Problem 8
Answer: 28.3 cubic inches------------------------
Work Shown:
V = pi*r^2*h
V = 3.14*(1.5)^2*4
V = 28.26
V = 28.3
Note how the radius r = 1.5 is half of the diameter 3 inches.
=========================================
Problem 9
Answer: 25.1 cubic inches------------------------
Work Shown:
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*2^2*6
V = 25.12
V = 25.1
Answer:
for problem 8 it would be 28.3
Show that the equation 2sinxtanx+3=0 can be expressed as 2cos^(2)x-3cosx-2=0
Answers
The equation 2sin(x)tan(x) + 3 = 0 has been proved to equal 2cos²(x) - 3cos(x) - 2 = 0
How to prove the equationsFrom the question, we have the following equation that can be used in our computation:
2sinxtanx+3=0
Rewrite as
2sin(x)tan(x) + 3 = 0
Express tan(x) as tan(x) = sin(x)/cos(x)
So, we have
2sin²(x)/cos(x) + 3 = 0
Multiply through by cos(x)
2sin²(x) + 3cos(x) = 0
Express sin²(x) as 1 - cos²(x)
So, we have
2(1 - cos²(x)) + 3cos(x) = 0
Expand
2 - 2cos²(x) + 3cos(x) = 0
Multiply through by -1
-2 + 2cos²(x) - 3cos(x) = 0
Rearrange the terms
2cos²(x) - 3cos(x) - 2 = 0
Hence, the equation has been proved
Read more about trigonometry equations at
https://brainly.com/question/24349828
#SPJ1
The ratio of yellow crayons to green crayons is 6 : 5.
If there are 18 yellow crayons, how many green crayons are there?
Answers
Answer:
15 Green crayons
Step-by-step explanation:
Ratio Yellow to green crayons
Thus, 6 → Yellow and 5 → Green
6 5
18 x
We need to divide 18 by 6 which is 3
5 x 3 = 15
Hence, Green Crayons ⇒ 15
[RevyBreeze]
15 green crayons
Step-by-step explanation:
Given:
The ratio of yellow crayons to green crayons is 6:5.To Find:
If there are 18 yellow crayons, how many green crayons are there?Solution:
Let,
yellow crayons = 6x green crayons = 5xIf there 18 yellow crayons so,
6x = 18
x = 18/6 = 3 ...(1)
By putting the value of x from equation (1) :-
➝ 5x => 5 × 3
=> 15
Therefore, there are 15 green crayons.
plz helppppppp ummmmm helpppp
Answers
Because (5/7)x28=20
Estimate the sum. 22.34 + 3.94 + 1.8
Answers
Answer:
28
Step-by-step explanation:
Estimate the sum:
22.34 + 3.94 + 1.8Estimate for each term is:
22.34 = 22, 3.94 = 4, 1.8 = 2Therefore:
22+4+2 = 28 is the estimated numberThe table shows the total distance of four trails. You want to complete a trail in 1 1/2 hours with an absolute deviation of at most 15 minutes. You hike at a rate of 3 miles per hour. Which trails can you hike? Select all that apply
Answers
The required trail is 5 1 / 4. Option A is correct.
Given that,
The table shows the total distance of four trails. You want to complete a trail in 1 1/2 hours with an absolute deviation of at most 15 minutes. You hike at a rate of 3 miles per hour.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
The absolute deviation is 15 minutes = 1 / 4 hour
Interval of time with this deviation = 1 1 / 2 ± 1 / 4 hour
here for +
time = 1 + 1 / 2 + 1 / 4
time = 1 3 /4
for -
time = 1 1/2 - 1/4
time= 1 1 / 4
Now, there is variations of time,
So, the required possible trail could correspond to the time i.e.
Time = 1 3 / 4
Distance = rate * time
= 1 3 / 4 * 3
= 5 1 / 4
Thus, the required trail is 5 1 / 4. Option A is correct.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ1
find the measures of one interior angle and one exterior angle of a regular polygon with 8 sides
one interior angle__________ one exterior angle___________
Answers
Answer:
one interior angle 135
one exterior angle 45
Step-by-step explanation:
Total measure of all angles in a 8 sided regular polygon = (n - 2)* 180
= ( 8 - 2 ) * 180
= 6 * 180
= 1080
Measurement of one interior angle = 1080 / 8 = 135
Interior angle and exterior angle make linear pair.
Measurement of one exterior angle = 180 - 135 = 45
someone please help me answer this!!
Answers
Answer:
5.5 x 10 ^ 0
Step-by-step explanation:
749/d * d/749 = 1
d=?
Answers
Answer:
D=1
Step-by-step explanation:
1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1
Answer:
I honestly don't know but I think its all real numbers but not zero
Step-by-step explanation:
The first quartile of a data set is 32, and the third quartile is 52. Which of
these values in the data set is an outlier?
Answers
Answer: As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier
so...the 83 is outlier
so correct option is D
hope it helps
Step-by-step explanation:
Outline at least 4 methods of solving linear systems.
Answers
The four steps for solving linear systems are;
Graphical methodBy substitution methodBy elimination methodBy augmented matrixSolving linear systemsA variety of ways for solving linear systems exist which include;
Graphical method by seeking the point of intersection.Substitution method involving making a variable the subject of the formula and substituting accordingly.Elimination involves manipulation to get rid of a variable by means of subtraction or addition.Augmented matrices are used to solve linear systems.Read more on solving linear systems;
https://brainly.com/question/384631
Answer:
graphing
algebraic methods
using inverse matrices
transforming an augmented matrix to reduced row echelon form
Cramer’s rule
Step-by-step explanation:
Find the height of the tower using the information given in the illustration.
Answers
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
Heather and her friends want to buy tickets to the Harry Styles concert. Each ticket cost 85$ and parking cost 25$. Write an equation to represent if Heather spends 280$
Answers
answer: 85+85+85+25
when 30 is subtracted from 14 times of a number the result is 20 more than 4 times that number what is the number
Answers
Answer:
number is 5
Step-by-step explanation:
let the number be n, then
30 subtracted from 14 times the number is
14n - 30
the result is 20 more than 4 times the number, that is
4n + 20
the equation is then
14n - 30 = 4n + 20 ( subtract 4n from both sides )
10n - 30 = 20 ( add 30 to both sides )
10n = 50 ( divide both sides by 10 )
n = 5
the number is then 5
What’s 3/8 OF 5 as a mixed number
Answers
Answer:
Step-by-step explanation:
2 3;8
Answer:
1 7/8.
Step-by-step explanation:
5 * 3/8
= 15/8
= 1 7/8.
PLEASE HELP ASAP!!!!!!!!!
Answers
Answer:
I'm sorry but the document says "doesn't exist".
Step-by-step explanation:
I hope this helps! Have a great rest of your day!
Here is Takeshi's work determining a third point on the graph of an exponential function, `h(x)`.
Explain why the work is incorrect.
Answers
Answer:
Step-by-step explanation:
Let h(x) = y
The exponentail function is of the form :
\(y = ab^x\)
We have :
\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)
Given points : (4, 9) and (5, 34.2)
We have:
\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)
Writing the equation with x, y and b:
\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)
a = 0.043
b = 3.8
When x = 6, y will be:
\(y = (0.043)(3.8^6)\\\\y = 128.47\)
This is not the y value in the question y = 59.4
Therefore (6, 59.4) does not lie on the graph h(x)
The parabola below is a graph of the equation y = (x - 1)2 - 3. Which point will
satisfy the inequality y <(x - 1)2 - 3 ?
(1.-3)
O A. (2,5)
O B. (0,5)
O C. (1,0)
OD. (5,-3)
Answers
Answer:
A. (2,5)
Step-by-step explanation:
To save for retirement, starting from her 30th birthday (t = 0), Miss Saver will invest
some money each year in a 30-year deposit in her bank saving account. The first
payment of $1000 will be made at the beginning of the first year. Every subsequent
payment increases by 5%.
She will retire at age 60, and will withdraw $X each year from her bank saving account
from then. The first withdrawal will be made at age 60. After 20 years (i.e. after the
20th withdrawal), she will have taken out all the money she had saved.
Assuming the effective annual interest rate is 2% perpetually, compute the value of X.
Give your answer to the nearest integer.
Answers
Answer:
To calculate the value of X, we first need to calculate the total amount of money Miss Saver will have saved by the time she retires at age 60.
We know that her first payment is $1000, and that every subsequent payment increases by 5%. Using this information, we can calculate the total payments made during the 30 years:
$1000 x (1 + 0.05)^30 = $1000 x 3.3201 = $3320.1
This is the total amount of money Miss Saver will have saved by the time she retires at age 60.
Next, we need to calculate the value of each annual withdrawal over the 20 years of withdrawals.
We know that the effective annual interest rate is 2% perpetually, so we can use the formula for the future value of an annuity:
FV = X * ((1 + r)^n - 1) / r
where X is the annual withdrawal, r is the interest rate (0.02), and n is the number of years (20).
We can use this formula to solve for X:
3320.1 = X * ((1 + 0.02)^20 - 1) / 0.02
X = 3320.1 * 0.02 / (1.02^20 - 1)
X = 3320.1 * 0.02 / 0.1135 = $292.36
Therefore, Miss Saver needs to withdraw $292.36 each year for 20 years to deplete her savings account.
Rounded to the nearest integer, the value of X is $292.