Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = event that the diagnostic test is accurate
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
Now, the probability that the diagnosis is correct is given by;
Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')
= (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.
Find the polynomial for the area.
The area is
Answer: ¹/₂( x² - 10y² + 10xy - xy )
Step-by-step explanation:
From the diagram area of the triangle = ¹/₂ ˣ base ˣ height
where the base = x + 10y and the height = x - y
Therefore putting these into the formula above
Area = ¹/₂ [( x + 10y )( x -y )]
= ¹/₂( x² - xy + 10xy - 10y²)units²
= ¹/₂( x² - 10y² + 10xy - xy )
The probability distribution of a random variable X is given. x 1 2 3 4 P(X = x) 0.4 0.1 0.3 0.2 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation
Mean:
[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]
Variance:
[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]
Standard deviation:
[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]
determine x in the following equation 2x - 4 = 10
Answer:
7
Step-by-step explanation:
10+4 = 14
14/2 = 7
x = 7
What is the quotient of the synthetic division problem below, written in
polynomial form?
5)2 1 -55
O A. -2x+11
O B. -2x+9
O C. 2x+11
O D. 2x+9
Answer:
C. 2x+11
Step-by-step explanation:
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
One number is 4 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 370, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)
Answer:
45, 180, 145
Step-by-step explanation:
Let n represent the first number. Then "one number" is 4n, and the third number is n+100. The sum of the three numbers is ...
n + 4n + (n+100) = 370
6n = 270
n = 45
4n = 180
n+100 = 145
The three numbers are 45, 180, 145.
Evaluate 26 + a if a = 8
Answer:
34
Step-by-step explanation:
= 26 + 8
= 34
do numbers ever stop
Nope, i dont think so
Answer:
no the numbers are infinite
Step-by-step explanation:
rmined that her father’s age is four less than three times her age. If a represents Marcy’s age, which expression represents her fathers age?
Answer:
3x - 4 is the expression that will represent her father's age
PLEASE HELP MEEEEEEEEEEEEEEE
Answer:
x=16.1
Step-by-step explanation:
open the brackets
-4.5= -0.5x-3.55
Take 3.55 to the other side.
-4.5-3.55 = -8.05
5/10x= -805/100
0.5x= - 8.05 = 16.1
the length of a triangle is x and its width is 2x. what is the area if the length and width are each increased by 1?
A. 2x^2+ 3x+ 1
B. 2x^2+ 1
C. 2x^2+ 2x+ 1
D. 2x^2+ 3x+ 2
Answer:
Hey there!
(2x+1)(x+1)
2x^2+1x+2x+1
2x^2+3x+1
The answer would be A.
Let me know if this helps :)
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(2x)
b. y=f)
C. 2y = f(x)
d. = f(x)
9514 1404 393
Answer:
c. 2y = f(x)
Step-by-step explanation:
Each point on the red graph is half the distance from the x-axis as the same point on the black graph. That is, the vertical scale factor is 1/2:
y = (1/2)f(x)
Multiplying this equation by 2 gives one that matches an answer choice:
2y = f(x)
The domain and range for function g are D(−infinity symbol, infinity symbol) and R(−infinity symbol, infinity symbol). Describe the following statement:
the limit as x approaches 3 of the function g of x equals 4
Select one:
a. The value of g at 3 is 4.
b. The value of g at 4 is 3.
c. As x gets closer to 4, the value of g gets closer to 3.
d. As x gets closer to 3, the value of g gets closer to 4.
The answer is d: As x gets closer to 3, the value of g gets closer to 4.
The limit of a function h of x as x approaches the value a, written as [tex]\lim_{x \to a} h(x) = L[/tex] is the value the function h(x) approaches as x tends to the value "a", written as x → a. In this case, L.
Given the domain and range for function g are D(−∞, ∞) and R(−∞, ∞) and that the limit as x approaches 3 of the function g of x equals 4.
This implies that as x gets closer and closer to 3, the value of g gets closer and closer to 4.
Since the value g gets closer to is 3 as x gets closer to 4, we can write that the limit as x approaches 3 of the function g of x equals 4.
we can write this as
[tex]\lim_{x \to 3} g(x) = 4[/tex]
So, as x gets closer to 3, the value of g gets closer to 4.
So, the answer is d: As x gets closer to 3, the value of g gets closer to 4.
Learn more about limits here:
https://brainly.com/question/23144996
What is similar about a line segment and a line? What is different
Answer:
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line. Line segments are only a line that goes from one point to another, and lines go on forever. However, a line segment is also part of a line.
Hope this helps!
Answer:
[see below]
Step-by-step explanation:
A line is a straight path of points that has no start and no end. The line has an arrow on each end.
A line segment is part of a line. They have a start and an end. The line segments have a point on each end. You can use a line segment to make polygons and make calculations about them.
Hope this helps.
reciprocal of dash and dash remains same
Answer:
-1 and 1
Step-by-step explanation:
Reciprocal means "one divided by...".
1/-1 = -1 and 1/1 = 1
Grandma baked 969696 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies than she would have received had all of the cookies been evenly divided among the 888 grandchildren.
Answer:
Answer:
96/8 - c
Step-by-step explanation:
96/8 = 12
The average amount of cookies each grandchild would get is 12. However, Cindy gets c less than the average amount. So, it would be 12 - c.
But, it's asking for the original expression. Therefore, the answer would be 96/8 - c.
sorry to keep asking questions
Answer:
y = [tex]\sqrt[3]{x-5}[/tex]
Step-by-step explanation:
To find the inverse of any function you basically switch x and y.
function = y = x^3 + 5
Now we switch x and y
x = y^3 +5
Solve for y,
x - 5 = y^3
switch sides,
y^3 = x-5
y = [tex]\sqrt[3]{x-5}[/tex]
Answer:
[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=x^3 +5[/tex]
The inverse of a function reverses the original function.
Replace f(x) with y.
[tex]y=x^3 +5[/tex]
Switch variables.
[tex]x=y^3 +5[/tex]
Solve for y to find the inverse.
Subtract 5 from both sides.
[tex]x-5=y^3[/tex]
Take the cube root of both sides.
[tex]\sqrt[3]{x-5} =y[/tex]
The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
a. MP
b. DS
c. MT
d. Conj
e. HS
Answer:
e. HS
Step-by-step explanation:
The argument:
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
is an instance of one of hypothetical syllogism (HS).
Hypothetical syllogism contains conditional statements for its premises.
Let
p = [(P ≡ T) • (H • N)]
q = (T ⊃ ~S)
r = [(H ∨ E) ∨ R]
The this can be interpreted as:
p ⊃ q
q ⊃ r
p ⊃ r
This interprets that:
If p then q
but if q then r
therefore if p then r
Thus, in logic HS is a valid argument form:
p → q
q → r
∴ p → r
Note that ⊃ symbol is used to symbolize implication relationships. This is used in conditional statements which are represented in the if...then... form. For example p ⊃ q means: if p then q. So the type of Hypothetical syllogism used in this is conditional syllogism.
There are three parts of syllogism:
major premise
minor premise
conclusion
An example is:
If ABC is hardworking, then ABC will go to a good college.
Major premise: ABC is hardworking.
Minor premise: Because ABC is hardworking , ABC will score well.
Conclusion: ABC will go to a good college.
Example of Hypothetical syllogism:
If AB is a CD, then EF is a GH
if WX is a YZ, then AB is a CD
therefore if WX is a YZ, then EF is a GH
This can be understood with the help of an example:
If you study the topic, then you will understand the topic.
If you understand the topic, then you will pass the quiz.
Therefore, if you study the topic, then you will pass the quiz.
A random sample of 1400 Internet users was selected from the records of a large Internet provider and asked whether they would use the Internet or the library to obtain information about health issues. Of these, 872 said they would use the Internet
1. The standard error ˆp SE of the proportion pˆ that would use the Internet rather than the library is:_______
a. 0.013.
b. 0.25.
c. 0.485.
d. 0.623.
2. If the Internet provider wanted an estimate of the proportion p that would use the Internet rather than the library, with a margin of error of at most 0.02 in a 99% confidence interval, how large a sample size would be required? (Assume that we don’t have any prior information about p).
a. 33
b. 3909
c. 2401
d. 4161
Answer:
1 [tex]\sigma_{\= x } = 0.0130[/tex]
2 [tex]n = 3908.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_p = 1400[/tex]
The number of those that said the would use internet is [tex]k = 872[/tex]
The margin of error is [tex]E = 0.02[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{k}{n_p}[/tex]
substituting values
[tex]\r p = \frac{ 872}{1400}[/tex]
substituting values
[tex]\r p = 0.623[/tex]
Generally the standard error of [tex]\r p[/tex] is mathematically evaluated as
[tex]\sigma_{\= x } = \sqrt{\frac{\r p (1- \r p)}{n} }[/tex]
substituting values
[tex]\sigma_{\= x } = \sqrt{\frac{0.623 (1- 0.623)}{1400} }[/tex]
[tex]\sigma_{\= x } = 0.0130[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence interval is 95% the we can evaluated the level of confidence as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from normal distribution table (reference math dot armstrong dot edu) , the value is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Give that the population size is very large the sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} ^2 * \r p ( 1 - \r p )}}{E^2} ][/tex]
substituting values
[tex]n = [ \frac{2.58 ^2 * 0.623 ( 1 -0.623 )}{0.02^2} ][/tex]
[tex]n = 3908.5[/tex]
What is the following simplified product? Assume x greater-than-or-equal-to 0 (StartRoot 10 x Superscript 4 Baseline EndRoot minus x StarRoot 5 x squared EndRoot) (2 StartRoot 15 x Superscript 4 Baseline EndRoot + StartRoot 3 x cubed EndRoot) 10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot 11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot 10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot 11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot
Answer:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Step-by-step explanation:
To find:
Simplified product of:
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]
Solution:
First of all, let us have a look at some of the formula:
1. [tex](a+b) (c+d) = ac+bc+ad+bd[/tex]
2. [tex]a^b\times a^c =a^{b+c }[/tex]
3. [tex]\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b[/tex]
4. [tex]\sqrt a \times \sqrt b = \sqrt{a\times b}[/tex]
Now, let us apply the above formula to solve the given expression.
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
The answer is:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Answer:
Its D
Step-by-step explanation:
About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed than other people in the general population. The researcher surveys 200 artists and finds that 26 of them are left-handed.Required:a. Define the parameter of interest and give the null value.b. State the researcher's null and alternative hypotheses.c. What proportion of the sample of artists is left-handed?d. To calculate a p-value for the hypothesis test, what probability should the researcher calculate? Make your answer specific to this situation.
Answer:
Given the information in the question;
a) The parameter of interest is the population of artists who are left-handed and its is 10% = (10/1000 = 0.10
b) The Null hypothesis and alternative hypothesis are;
H₀ : p = 0.10
H₁ : p > 0.10
c) The sample proportion is calculated as:
p = number of left handed artist / sample size
p = 26 / 200
p = 0.13
d) To find the p-value, The researcher should calculate the probability that the sample proportion would be 0.13 or larger for a sample of size 200 if the population proportion is actually 0.10.
Question 6. Which expression is equivalent to 3x(x-6)+5(x-4)?
Answer:
8x- 38
Step-by-step explanation:
3(x-6)+5(x-4)
Distribute
3x- 18+5x -20
Combine like terms
3x+5x -18-20
8x- 38
Answer:
[tex]3(x-6)+5(x-4)[/tex]
[tex]3x-18+5x-20[/tex]
[tex]=(3+5)x-(20x+18)[/tex]
Add:- 3+5= 8, and 20+18= 38
[tex]=8x-38[/tex]
OAmalOHopeO
When x€Q, what is the solution of 3x-2/2=x-1/2 ?
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{2}[/tex] = [tex]\frac{x-1}{2}[/tex]
Cross-multiply:
2(3x-2) = 2(x-1)
Simplify:
6x - 4 = 2x - 2
Subtract 2x from both sides:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = [tex]\frac{1}{2}[/tex]
A circular pizza has a diameter of 12 inches and is cut into 10 congruent slices. What is the area of each slice, to the nearest tenth?
Group of answer choices
14.4 straight pi inches squared
3.6 straight pi inches squared
2.4 straight pi inches squared
12.4 straight pi inches squared
[tex]\\ \sf\longmapsto Area=2\pi r[/tex]
[tex]\\ \sf\longmapsto Area=2(3.14)\times 6[/tex]
[tex]\\ \sf\longmapsto Area=2(18.84)[/tex]
[tex]\\ \sf\longmapsto Area=37.68in^2[/tex]
Now area of each slice
[tex]\\ \sf\longmapsto \dfrac{37.68}{12}[/tex]
[tex]\\ \sf\longmapsto 3.6in^2[/tex]
The area of each slice of the pizza will be 3.6π square inches. The correct option is B.
What is the area of the sector?The circle is defined as the locus of the point traces around a fixed point called the center and is equidistant from the out trace.
It is given that a circular pizza has a diameter of 12 inches and is cut into 10 congruent slices.
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
angle = 2π/10
The area will be calculated as below:-
Area = (2π/10)/2π) πr²
Area = ( π x 6 x 6 ) / 10
Area = 3.6π square inches
Therefore, the area of each slice of the pizza will be 3.6π square inches. The correct option is B.
More about the area of the sector link is given below.
https://brainly.com/question/7512468
#SPJ2
Addition prop of equality
subtraction prop of quality
multiplication prop of equality
Division prop of equality
simplifying
distrib prop
Which equation has the graph shown below? (0, 3) (2,0)
Answer:
6x+4y=12
Step-by-step explanation:
when x-intercept is 0
6(0)+4y=12
0+4y=12
divide by 4 both side
y=3
when y-intercept is 0
6x+4(0)=12
6x+0=12
6x=12
divide by 6 both side
x=2
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen and bedroom)?
Answer:
The area of the house is A. 1,108
Please answer! I am struggling with this question! Please show ALL work! <3 (the answer choices are provided on a separate image)
Answer:
The radius is 18 inches
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
36 pi = 2 * pi *r
Divide each side by pi
36 = 2r
Divide each side by 2
18 =r
Answer:
The answer is option CStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius of the circle
From the question
Circumference = 36π inches
To find the radius substitute the value of the circumference into the above formula and solve for the radius
That's
[tex]36\pi = 2\pi r[/tex]Divide both sides by 2π
We have
[tex] \frac{36\pi}{2\pi} = \frac{2\pi \: r}{2\pi} [/tex]We have the final answer as
r = 18 inchesHope this helps you
Choose the correct ray whose endpoint is B.
Answer:
The second option.
Step-by-step explanation:
The first option consists of a line that extends at both opposite sides to infinity, with no precise end.
The third option is a ray that has an endpoint of A, and extends to infinity towards B.
The fourth option is a line segment. It has two endpoints, B and A.
The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.
The answer is the 2nd option.
Tia uses 3/4 cup of pumpkin to make 1 1/4 pounds of dog treats. How much pumpkin does Tia use to make 1 pound of treats?
Answer:
4/5 cups to make 1 pound of dog treats
Step-by-step explanation:
3/4 cups : 1 1/4 pounds
x cups : 1 pound
Cross multiply
3/4 * 1 = 1 1/4 * x
x = 3/4 / 1 1/4
= 3/4 / 5/4
= 3/4 * 4/5
= 3/5 cups
Which expression corresponds to this graph?
Answer: Choice A
The number line graph is visually showing every number that is 19 or smaller; hence [tex]x \le 19[/tex]
Note the use of a closed or filled in circle at the endpoint (in contrast to an open circle). This indicates we are including the endpoint 19 as part of the solution set, and that's why we go for "or equal to" as part of the inequality sign.