The probability that at least 8 patients show improvement is; 0.94
How to use Binomial Probability Distribution?The formula for Binomial Probability Distribution is;
P(X = r) = nCr * p^(r) * (1 - p)^(n - r)
where;
n = number of trials
r = number of specific events you wish to obtain
p is probability of success
From the question, we have;
n = 12
r = 8
p = 81% = 0.81
The probability that at least 8 patients show improvement is expressed as;
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
Using online binomial probability calculator gives us;
P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977
P(X ≥ 8) = 0.94
Read more about Binomial Probability Distribution at; https://brainly.com/question/15246027
#SPJ1
the chairs in a hall are about to be arranged in a row. if i put 6 chairs in a row there will be 4 left if i put 7 chairs in a row there will be 3 short how many chairs are there
Step-by-step explanation:
THERE WILL BE
6+4+3+7= 23
I need help to this it would be awesome if you could help.
In the given diagram, the value of JI is 6
Solving equations
From the question, we are to determine JI
From the given diagram, we can write that
JI + IH = x + 22
Also,
JI = 2x + 28
and
IH = 5
Then, we can write that
2x + 28 + 5 = x + 22
Collect like terms
2x - x = 22 -28 -5
x = -11
Now, substitute the value of x into the equation
JI = 2x + 28
JI = 2(-11) + 28
JI = -22 +28
JI = 6
Hence, the value of JI is 6
Learn more on Solving equations here: https://brainly.com/question/3926291
#SPJ1
Assume that the average healthy body temperature is 98.249 degrees and the standard deviation is 0.733 degrees. How many standard deviations below the mean would I be if my body temp is 97.2 degrees,
The standard deviation is 1.43 below the mean
How to determine the number of standard deviation?The given parameters are:
Mean = 98.249
Standard deviation = 0.733
x = 97.2
To calculate the number of standard deviation below the mean, we use
[tex]x = \bar x - n\sigma[/tex]
So, we have:
[tex]97.2 = 98.249 - n * 0.7333[/tex]
Evaluate the like terms
[tex]-1.049 =- n * 0.7333[/tex]
Divide both sides by -0.733
n =1.43
Hence, the standard deviation is 1.43 below the mean
Read more about standard deviation at:
https://brainly.com/question/15858152
#SPJ1
Solve for x.
x-2.13 = 5.3
Answer:
x = 7.43
Step-by-step explanation:
X - 2.13 = 5.3
add -2.13 to both sides
x -2.13+2.13 = 5.3 + 2.13
-2.13 + 2.13 cancel out and 5.3 +2.13 equals 7.43
therefore x =7.43
check your work by substituting 7.43 for x
7.43 - 2.13 = 5.3
Assume that Hogan Surgical Instruments Co. has $2,500,000 in assets. If it goes with a low-liquidity plan for the assets, it can earn a return of 18 percent, but with a high-liquidity plan, the return will be 14 percent. If the firm goes with a short-term financing plan, the financing costs on the $2,500,000 will be 10 percent, and with a long-term financing plan, the financing costs on the $2,500,000 will be 12 percent.
The the anticipated return after financing cost with the most aggressive asset financing mix is $200000.
Most aggressive
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $450,000 + (-$250,000)
Anticipated return = $200,000
Most conservative
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Long-term financing = –$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $350,000 + (-$300,000)
Anticipated return = $50,000
Moderate approach
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Long-term financing =–$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $450,000 + (-$300,000)
Anticipated return = $150,000
Moderate approach
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $350,000 + (-$250,000)
Anticipated return = $100,000
Learn more about returns on:
https://brainly.com/question/20813118
#SPJ1
Complete question:
a. Compute the anticipated return after financing cost with the most aggressive asset financing mix.
b. Compute the anticipated return after financing cost with the most conservative asset financing mix.
c. Compute the anticipated return after financing cost with the two moderate approaches to the asset financing mix.
Help again please. 10 points for help!! Thanks
Answer: 23 inches by 7 inches
Step-by-step explanation:
161 = 7 x 23 (or 1 x 161 but that doesn't help...)
And to check:
7 x 3 + 2 = 23
Answer:
23inches by 7inches
Step-by-step explanation:
7 ×3+2=23
write the explicit formula for this geometric sequence.
81,27,9,3, …
Find the common ratio, r.
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.
The geometric sequence 81, 27, 9, 3, … has common ratio:
r = 27/81 = 1/3
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Using the following table, construct and interpret a 90% confidence interval for the population standard deviation of the carbon in metric tons.
Nation
Brazil
Germany
Mexico
Emissions
Canada
361
844
398
Great Britain 577
631
The 90 percent confidence interval for the data is given as 396.02, 727.98
First we have to find the meanThe formula is fx/n
= Mean, μ = 562.2
sum up the data and divide by 5
sd =
Σ(xi - μ)2/N
= (361 - 562.2)² + ... + (631 - 562.2)²/5
= 151806.8/5
= 30361.36
sd = √30361.36
= 174.24511470914
1 - confidence level
= 1 - 0.90
= 0.1
df = 4
Using excel
T.INV.2T(0.1, 4) = ±2.13
562 +- 2.13 x 174.245/√5
562- 165.98, 562+ 165.98
= 396.02, 727.98
Hence the confidence interval can be calculated to be 396.02, 727.98
Read more on confidence interval here:
https://brainly.com/question/14825274
#SPJ1
find the slope of this line.
Answer:
4/5
Step-by-step explanation:
SImply use slope formula. We see the graph has defined points at (5, 4), and (-5, -4).
m=(Y2-Y1)/(X2-X1)
(4-(-4))/(5-(-5))=8/10
Simplify 8/10
=4/5
Which is the graph of the function f(x)= - squared x
Answer:
top left graph
Step-by-step explanation:
The function is not defined for negative x.
Eliminate top middle and top rightAlso, the range should not include positive numbers.
Eliminate bottom left.So, the answer is the top left graph.
Which of the following are equations for the line shown below? Check all that
apply.
(-4,3)
(4,-5)
A. y=-x-1
B. y+ 5=-(x-4)
C. y-3 = -(x+4)
D. y=-x-9
Answer: A, B, C
Step-by-step explanation:
[tex]m=\frac{-5-3}{4-(-4)}=-1[/tex]
Substituting into point-slope form, we get [tex]y-3=-(x+4)[/tex] and [tex]y+5=-(x-4)[/tex]. Rearranging this into slope-intercept form,
[tex]y-3=-(x+4)\\\\y-3=-x-4\\\\y=-x+1[/tex]
If f(x) = 4x, which statements are true of g(x)? Select two options.
The two statements that are true for g(x ) are:
g(x) = [tex]4^{x}[/tex] - 1
g(x) is translated both vertically and horizontally.
What is a function?A function is a relation showing the relationship between two or more variables.
A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.
Analysis:
If we use the values of x as 0,1,2,3
for x = 0
g(0) = [tex]4^{0}[/tex] -1 = 1 -1 = 0
for x = 1
g(1) = [tex]4^{1}[/tex] -1 = 4 - 1 = 3
for x = 2
g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15
for x = 3
g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63
Therefore g(x) = [tex]4^{x}[/tex] - 1
Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.
Learn more about functions: brainly.com/question/25638609
#SPJ1
I need help with my work
(In c) * 1/c = 0.0604 is the change in the function.
According to the statement
y = (In x)^2 on interval [1,4]
By mean value theorem
we use this formula to find a change f '(c)= [f(b) - f(a)] / (b - a)
Let it f(y) = (In x)^2
Now, f(4) = (In 4)^2
f(4) = (0.602)^2
f(4) = 0.3624
and
f(1) = (In 1)^2
f(1) = (0)^2
f(1) = 0
Now, f'(c) = 2 (In c) * 1/c
Substitute all these values in a formula
2 (In c) * 1/c = 0.3624 - 0 / 4 - 1
2 (In c) * 1/c = 0.3624/3
2 (In c) * 1/c = 0.1208
(In c) * 1/c = 0.0604
So, (In c) * 1/c = 0.0604 is the change in the function.
Learn more about FUNCTION here https://brainly.com/question/2456547
#SPJ1
The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice?
The number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is: 32 pints of 95% juice, and 48 pints of 45% juice.
Number of pints neededLet x be the amount of 95% juice.
Let the amount of 65% juice be 80-x
Hence:
.95x+.45(80-x)=.65(80)
.5x+36=52
Collect like term
5x=16
Divide both side by 5x
x=16/5
x=32
Therefore the number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is: 32 pints of 95% juice, and 48 pints of 45% juice.
Learn more about Number of pints needed here:https://brainly.com/question/25435604
#SPJ1
Practise the Skill
A container holds 4 yellow balls, 3 blue balls and 1 red ball.
Luke chooses a ball at random.
What is the probability that Luke will pick a blue ball?
Give your answer as a fraction in its lowest terms.
The probability that Luke will pick a blue ball is 3/8.
We have,
To find the probability of Luke picking a blue ball, we need to determine the total number of balls in the container and the number of blue balls.
Total number of balls
= 4 (yellow balls) + 3 (blue balls) + 1 (red ball)
= 8 balls
Number of blue balls = 3
Now, the probability (P) of picking a blue ball is given by:
P = Number of favorable outcomes (picking a blue ball) / Total number of possible outcomes
P = 3 (number of blue balls) / 8 (total number of balls)
Now, we can simplify the fraction to its lowest terms:
P = 3/8
Thus,
The probability that Luke will pick a blue ball is 3/8.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ7
If the average work week was 43 hours in 2009 and 42 hours and 30 minutes in 2010, by what percentage did the average number of hours worked per week drop from 2009 to 2010?
The average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%
How to determine the percentage change?The average work weeks are given as:
Year 2009 = 43 hours
Year 2010 = 42 hours 30 minutes
Rewrite as:
Year 2010 = 42.5 hours
The percentage change is then calculated as:
Percentage change= (Final - Initial)/Initial * 100%
So, we have:
Percentage change= (42.5 - 43)/43* 100%
Evaluate
Percentage change= -1.16%
Hence, the average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%
Read more about percentage change at:
https://brainly.com/question/11360390
#SPJ1
Nicky opened a savings account with a single deposit of R1 000 on 1 April 2011. She
then makes 18 inonthly deposits of R700 at the end of every month. Her first payment
is made on 30 April 2011 and her last payment on 30 September 2012. The account
earns interest at 15% per annum compounded monthly.
Determine the amount that should be in her savings account inmediately after her last
deposit is made (that is on 30 September 2012).
The amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
What is the future value?The future value refers to the compounded value (at an interest rate) of the present value, including the periodic cash investments, over a period.
The future value can be determined using either the future value formula, future value table, or an online finance calculator, as below.
Data and Caluclations:N (# of periods) = 18 months
I/Y (Interest per year) = 15%
PV (Present Value) = R1,000
PMT (Periodic Payment) = R 700
Results
FV = R15,282.91 (R12,600 + R1,000 + R1,682.91)
Sum of all periodic payments = R12,600 (R700 x 18)
Total Interest = R1,682.91
Thus, the amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
Learn more about determining future values at https://brainly.com/question/24703884
#SPJ1
Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 95%, sample size 10.
Using the t-distribution, the critical value needed is: t = 2.2622.
How to find the critical value for the t-distribution?The critical value is found using a calculator, with two parameters:
The confidence level.The number of degrees of freedom, which is one less than the sample size.For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.
More can be learned about the t-distribution at https://brainly.com/question/16162795
#SPJ1
guillermo has sold 95,47,114, and 72 appliances in the last fourth months,respectively.how many appliances will he need to sell this month to maintain an average of 80 sales per month?
The number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.
What is an average?An average refers to a central value obtained after adding together several amounts and then dividing this total by the number of variables added.
An average is a central value in a dataset.
Data and Calculations:Average sales per month = 80 units
Number of months involved = 5 months
Total for five months based on the average = 400 units
Total units sold in four months = 328 (95 + 47 + 114 + 72)
Sales units required to meet the average target = 72 (400 - 328)
Thus, the number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.
Learn more about average at https://brainly.com/question/20118982
#SPJ1
A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1027. Find the substance's half-life, in days. Round your answer to the nearest tenth
The substance's half - life is 7 days
How to determine the half-life
The formula for finding the half - life is given as;
Half - life = [tex]\frac{0. 693}{k}[/tex]
The k value given is 0.1027
Half - life = [tex]\frac{0. 693}{0.1027}[/tex]
Half - life = 6. 75
Half - life = 7 days in the nearest tenth
Thus, the substance's half - life is 7 days
Learn more about half - life here:
https://brainly.com/question/15575933
#SPJ1
1. The mean urine sodium concentrationof18caseswas120mmol/L with standard deviation of 15 mmo/L. assume the urine sodium is normally distributed, what is the 95%confidence interval within which the mean of the total population of such cases is expected lie
Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:
(112.5, 127.5).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.
The parameters for this problem are:
[tex]\overline{x} = 120, s = 15, n = 18[/tex].
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]
More can be learned about the t-distribution at https://brainly.com/question/25890103
#SPJ1
10 8 12 10 14 ? sequence
Answer:
The Sequence
Step-by-step explanation:
the Sequence is a decrease by 2 and a increase of 4. So subtract 2 by 10 to get 8 then add 4 to get 12 and so on.
“The length of a rectangle is two feet greater than twice it’s width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct
The width of the rectangle is 3.5 feet
Solving for the missing sides of a rectangle
The width of the rectangle = w
The length of the rectangle = l
The perimeter = p
Length of the rectangle is two feet greater than twice it’s width
l = 2w + 2
p = 2(l + w)
p = 2(2w + 2 + w)
p = 2(3w + 2)
p = 6w + 4
The perimeter of the rectangle is 25 ft
25 = 6w + 4
This can be rewritten as:
6w + 4 = 25
6w = 25 - 4
6w = 21
w = 21/6
w = 3.5
Therefore, the width of the rectangle is 3.5 feet
Learn more on missing sides of a rectangle here: https://brainly.com/question/383764
#SPJ1
A concert manager counted 525 ticket receipts the day after a concert. The price for a student ticket was $10.50, and the price for an adult ticket was $18.00. The register confirms that $8,325.00 was taken in. How many student tickets and adult tickets were sold?
Answer:
150 student tickets and 375 adult tickets
Step-by-step explanation:
Let x = # of student tickets sold, and y = # of adult tickets sold.
Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.
x + y = 525
10.50x + 18y = 8325
18x + 18y = 9450
10.50x + 18y = 8325
7.5x = 1125
x = 150
150 + y = 525
y = 375
find the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years
The interest obtained after 4 years from a loan of $7500 is = $750
Calculation of generated interestThe principal amount of the loan = $7500
The rate at which the interest is paid is = 2.5%
The time that it will take to pay the interest = 4 years
Using the formula for Simple interest;
SI= P×T×R/100
SI = 7500×4 × 2.5/100
SI= 75000/100
SI=$750
Therefore, the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years is = $750
Learn more about simple interest here:
https://brainly.com/question/20690803
#SPJ1
Determine the number of solutions for the equation shown below.
4x+6= 4x+6
Ο Α. 0
OB. Infinitely many
* O C. 1
OD. 2
Michael starts a new paper company. The function fff models the company's net worth (in thousands of dollars) as a function of time (in months) after Michael starts it.
Considering the function for the net worth of the function, it is found that it will not be in debt for the first time after 6 months in month 14, at point (14,0), which is plotted on the graph.
When a company is in debt?A company is said to be in debt if it's net worth is negative. On a graph, it is represented by the curve being below the x-axis.
From month 2 until the end of month 13, the company is in debt, hence it will not be in debt for the first time after 6 months in month 14, at point (14,0), which is plotted on the graph.
More can be learned about functions at https://brainly.com/question/25537936
#SPJ1
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
11.65 seconds
50.00 seconds
171.65 seconds
210.00 seconds
The time it will take the roller coaster to reach the ground is 171.65 seconds
Function and valuesGiven the roller coaster’s height given by the following parameters
h = –0.025t² + 4t + 50
On the ground level, the height will be zero. Substitute h = 0 and determine the value of t
–0.025t² + 4t + 50 = 0
0.025t² - 4t - 50 = 0
Factorize
On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds
Learn more on functions here: https://brainly.com/question/10439235
#SPJ1
Simplify the following
Answer:
29/12
Step-by-step explanation:
hello :
2/3 +5/6 +11/12 = (2×4)/(3×4) + (5×2)/(6×2) + 11/12
2/3 +5/6 +11/12 = 8/12 +10/12 +11/12 = (8+10+11)/12
2/3 +5/6 +11/12 = 29/12
Answer:
[tex]2\frac{5}{12}[/tex]
Step-by-step explanation:
To add fractions, we have to make sure that they have the same denominators. To do that, we have to find their lowest common multiple (LCM).
The LCM of 3, 6, and 12 is 12.
Then we have to multiply the numerator and denominator of each fraction by a number so that the denominator becomes the LCM (12).
[tex]\frac{2}{3} + \frac{5}{6} + \frac{11}{12}[/tex]
⇒ [tex]\frac{2 \times 4}{3 \times 4} + \frac{5 \times 2}{6 \times 2} + \frac{11 \times 1}{12 \times 1}[/tex]
⇒ [tex]\frac{8}{12} + \frac{10}{12} + \frac{11}{12 }[/tex]
⇒ [tex]\frac{8+10+11}{12}[/tex]
⇒ [tex]\frac{29}{12}[/tex]
⇒ [tex]\bf 2\frac{5}{12}[/tex]
Identify a horizontal or vertical stretch or compression of the function f(x) = x
by observing the equation of the function g(x) = 6x.
The base graph vertically stretched by a factor of 6.
The base graph horizontally stretched by a factor of 6.
The base graph vertically compressed by a factor of 6.
The base graph horizontally compressed by a factor of 6.
Answer: The base graph vertically stretched by a factor of 6.
Step-by-step explanation:
See attached image.