Answer:
12/40=0.3
0.3 car parts per minute
9 / 0.3 = 30 minutes
30 minutes for 9 parts
Hope this helps
Step-by-step explanation:
Jose required 30 minutes to assemble 9 parts.
Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.
In mathematics it deals with numbers of operations according to the statements.
Here,
40 minute = 12 parts
40/12 = 1 part
Time to assemble 9 parts: = 40/12 x 9
= 10/3 x 9
= 30
Thus, Jose required 30 minutes to assemble 9 parts.
Learn more about arithmetic here:
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A restaurant borrows from a local bank for months. The local bank charges simple interest at an annual rate of for this loan. Assume each month is of a year. Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Complete Question:
A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.
Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Answer:
a) Interest that will be owed after 4 months , I = $131.48
b) Amount owed by the restaurant after 4 months = $16231.48
Step-by-step explanation:
Note that the question instructs not to round any intermediate computations except the final answer.
Annual rate = 2.45%
Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]
R = 0.20416666666%
Time, T = 4 months
Interest, [tex]I = \frac{PRT}{100}[/tex]
[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]
b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)
Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)
Amount owed by the restaurant after 4 months = 16100 + 131.48
Amount owed by the restaurant after 4 months = $16231.48
A lake has a large population of fish. On average, there are 2,400 fish in the lake, but this number can vary by as much as 155. What is the maximum number of fish in the lake? What is the minimum number of fish in the lake?
Answer:
Minimum population of fish in lake = 2400 - 155 = 2245
Maximum population of fish in lake = 2400 + 155 = 2555
Step-by-step explanation:
population of fish in lake = 2400
Variation of fish = 155
it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.
For example
for increase
population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc
but it cannot be beyond 2400 + 155.
It cannot be 2400 + 156
similarly for decrease
population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc
but it cannot be less that 2400 - 155.
It cannot be 2400 - 156
Hence population can fish in lake can be between 2400 - 155 and 2400 + 155
minimum population of fish in lake = 2400 - 155 = 2245
maximum population of fish in lake = 2400 + 155 = 2555
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
Which of the following is not an undefined term?
point, ray, line, plane
Answer:
Step-by-step explanation:
Ray
Answer:
ray
Step-by-step explanation:
ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray
hope this helps
What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?
Answer:
Step-by-step explanation:
Answer:
its b on edge
Step-by-step explanation:
Use Green's Theorem to evaluate ?C F·dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) =< x + 4y3, 4x2 + y>
C consists of the arc of the curve y = sin x from (0, 0) to (p, 0) and the line segment from (p, 0) to (0, 0).
Answer:
Step-by-step explanation:
given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then
[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.
In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that
[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]
We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get
[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]
A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows
[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]
This gives use the integral
[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]
Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]
So
[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head
Answer:
See below in bold.
Step-by-step explanation:
We can write the equation as
y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation
y has coordinates (0, 32) at the top of the parabola so
32 = a(0 - 28)(0 + 28)
32 = a * (-28*28)
32 = -784 a
a = 32 / -784
a = -0.04082
So the equation is y = -0.04082(x - 28)(x + 28)
y = -0.04082x^2 + 32
The second part is found by first finding the value of x corresponding to y = 22
22 = -0.04082x^2 + 32
-0.04082x^2 = -10
x^2 = 245
x = 15.7 inches.
This is the distance from the centre of the door:
The distance from the edge = 28 - 15.7
= 12,3 inches.
What is the answer? x^2-y^2=55
Answer:
To solve for x we can write:
x² - y² = 55
x² = y² + 55
x = ±√(y² + 55)
To solve for y:
x² - y² = 55
y² = x² - 55
y = ±√(x² - 55)
The area of the sector of a circle with a radius of 8 centimeters is 125.6 square centimeters. The estimated value of is 3.14.
The measure of the angle of the sector is
Answer:
225º or 3.926991 radians
Step-by-step explanation:
The area of the complete circle would be π×radius²: 3.14×8²=200.96
The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.
[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).
There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.
We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.
Answer:
225º
Step-by-step explanation:
Find the product of
3/5 × 7/11
Answer:
21/55
Step-by-step explanation:
Simply multiply the top 2 together:
3 x 7 = 21
And the bottom 2 together:
5 x 11 = 55
21/55 is your answer!
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?
0.1
1/2
1
10
Please answer this correctly
Answer:
101-120=4
Step-by-step explanation:
All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups
111111105113Therefore, the answer to the blank is 4. If possible, please mark brainliest.
Answer:
There are 4 numbers between 101 and 120.
Step-by-step explanation:
101-120: 105, 111, 111, 113 (4 numbers)
-12.48 -(-2.99)-5.62
Answer:
[tex]-15.11[/tex]
Step-by-step explanation:
[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]
Answer:
-15.11
Step-by-step explanation:
-12.48+2.99-5.62=
-9.49 - 5.62= - (9.49+5.62)=-15.11
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.45 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. (Round your answers to four decimal places.)
Required:
Find the probability that the subsystem operates longer than 1000 hours.
Answer:
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Eight components:
This means that [tex]n = 8[/tex]
Probability of 0.45 of failing in less than 1,000 hours.
So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]
Find the probability that the subsystem operates longer than 1000 hours.
We need at least four of the components operating. So
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]
[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]
[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]
[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]
[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
What transformations to the linear parent function, f(x) = x, give the function
g(x) = 4x - 2? Select all that apply.
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
O c. Horizontally stretch by a factor of 4.
O D. Shift left 2 units.
Answer:
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
Step-by-step explanation:
Given the function
f(x)=x
If we stretch y vertically by a factor of m, we have: y=m·f (x)
Therefore:
Vertically stretching f(x) by a factor of 4, we have: 4x.
Next, if we take down f(x) by k units we have: y= f(x)-k
Therefore: Taking down 4x by 2 units, we obtain:
g(x)=4x-2
Therefore, Options A and B applies.
What is the relative change from 6546 to 4392
Answer:
The relative change from 6546 and 4392 is 49.04
Step-by-step explanation:
How many units of insulin are in 0.75 ML a regular U – 100 insulin
Answer:
0.75 ML of insulin contains 75 units of insulin
Step-by-step explanation:
U - 100 insulin hold 100 units of insulin per ml
This means that:
1 ML = 100 units
∴ 0.75 ML = 100 × 0.75 = 75 units
Therefore 0.75 ML of insulin contains 75 units of insulin
Overweight participants who lose money when they don’t meet a specific exercise goal meet the goal more often, on average, than those who win money when they meet the goal, even if the final result is the same financially. In particular, participants who lost money met the goal for an average of 45.0 days (out of 100) while those winning money or receiving other incentives met the goal for an average of 33.7 days. The incentive does make a difference. In this exercise, we ask how big the effect is between the two types of incentives. Find a 90% confidence interval for the difference in mean number of days meeting the goal, between people who lose money when they don't meet the goal and those who win money or receive other similar incentives when they do meet the goal. The standard error for the difference in means from a bootstrap distribution is 4.14.
Answer:
The 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two means is:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
It is provided that:
[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]
The critical value of z for 90% confidence level is,
z = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
[tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]
Thus, the 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
Which of the following statements are equivalent to the statement "Every integer has an additive inverse" NOTE: (The additive inverse of a number x is the number that, when added to x, yields zero. Example: the additive inverse of 5 is -5, since 5+-5 = 0) Integers are{ ... -3, -2,-1,0, 1, 2, 3, ...} All integers have additive inverses. A. There exists a number x such that x is the additive inverse of all integers.B. All integers have additive inverses.C. If x is an integer, then x has an additive inverse.D. Given an integer x, there exists a y such that y is the additive inverse of x.E. If x has an additive inverse, then x is an integer.
Answer:
B, C and D
Step-by-step explanation:
Given:
Statement: "Every integer has an additive inverse"
To find: statement that is equivalent to the given statement
Solution:
For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.
Here, 0 is the additive identity.
Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
Help meeeee and thank u so much god bless u haha
Answer:
[See Below]
Step-by-step explanation:
For Point Slope Form:Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]
'm' is the slope
(x1, y1) is a coordinate point.
Slope:Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-1,5) and (3,-3).
[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]
The slope of the line is -2.
I will use (-1,5) as the point:
[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]
For Slope Intercept:Slope intercept is: [tex]y=mx+b[/tex]
'm' - Slope
'b' - y-intercept
We can use the point slope equation to convert it into slope intercept form:
[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]
For Standard Form:Standard form is [tex]Ax+By=C[/tex]
Using out slope intercept form equation:
[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]
is 614 divisible by both 2 and 6?
Answer:
No
Step-by-step explanation:
It is not divisible by 6, for if you divide by 6, you will get a non natural number,
It is obviously divisible by 2.
So, No.
Answer:
no
Step-by-step explanation:
only by 2
614/2 = 307
614/6 = 102.33
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
Which graph shows a function whose domain and range exclude exactly one value?
Answer:
C (the third graph)
Step-by-step explanation:
This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.
Answer:
see below
Step-by-step explanation:
This graph has an asymptote at y = 0 and x=0
This excludes these values
The domain excludes x =0
The range excludes y=0
divide and simplify x^2+7x+12 over x+3 divided by x-1 over x+4
Answer:
[tex]\dfrac{x^2+8x+16}{x-1}[/tex]
Step-by-step explanation:
In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...
[tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]
If
f(x) = 13x + 1, then
f-1(x) =
Answer:
(x-1)/13
Step-by-step explanation:
y = 13x+1
To find the inverse, exchange x and y
x = 13y+1
Solve for y
Subtract 1 from each side
x-1 =13y+1-1
x-1 = 13y
Divide each side by 13
(x-1)/13 = y
The inverse is (x-1)/13
Answer:
f(x) = 13x + 1
To find the inverse let f(x) = y
y = 13x + 1
x = 13y + 1
13y = x - 1
y = (x-1)/13
The inverse is x-1/13.
HELP ME Answer it from the forst one to the last one with the rght answer please.This is Urgent so do it Faster if u now the answers
Step-by-step explanation:
2) 63
3) 7000
4) 10
These are some answers
How many solutions does 6-3x=4-x-3-2x have?
Answer:
no solutions
Step-by-step explanation:
6-3x=4-x-3-2x
Combine like terms
6-3x =1 -3x
Add 3x to each side
6 -3x+3x = 1-3x+3x
6 =1
This is not true so there are no solutions
Answer:
No solutions.
Step-by-step explanation:
6 - 3x = 4 - x - 3 - 2x
Add or subtract like terms if possible.
6 - 3x = -3x + 1
Add -1 and 3x on both sides.
6 - 1 = -3x + 3x
5 = 0
There are no solutions.
According to Brad, consumers claim to prefer the brand-name products better than the generics, but they can't even tell which is which. To test his theory, Brad gives each of 199 consumers two potato chips - one generic, and one brand-name - then asks them which one is the brand-name chip. 92 of the subjects correctly identified the brand-name chip.
Required:
a. At the 0.01 level of significance, is this significantly greater than the 50% that could be expected simply by chance?
b. Find the test statistic value.
Answer:
a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
b. Test statistic z=-1.001
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]
The significance level is 0.01.
The sample has a size n=199.
The sample proportion is p=0.462.
[tex]p=X/n=92/199=0.462[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]
As the P-value (0.16) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that:
Complete question is;
In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.
Answer:
P(has diabetes | positive) = 0.442
Step-by-step explanation:
Probability of having diabetes and being positive is;
P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)
We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.
Thus;
P(positive & has diabetes) = 0.08 × 0.95 = 0.076
P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)
P(negative & has diabetes) = 0.004
P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)
We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease
Thus;
P(positive & no diabetes) = 0.92 × 0.1 = 0.092
P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)
P(negative &no diabetes) = 0.828
Probability that a person selected having diabetes actually has the disease is;
P(has diabetes | positive) =P(positive & has diabetes) / P(positive)
P(positive) = 0.08 + P(positive & no diabetes)
P(positive) = 0.08 + 0.092 = 0.172
P(has diabetes | positive) = 0.076/0.172 = 0.442
Using formula:
[tex]P(\text{diabetes diagnosis})\\[/tex]:
[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]
[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]
[tex]\text{P(have been diagnosed with diabetes)}[/tex]:
[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]
[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]
Learn more about the probability:
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