Solution :
It is given that :
P (positive | Has disease) = 0.7
P (positive | No disease) = 0.08
P (has disease) = 0.18
P (No disease) = 1 - 0.18
= 0.82
Now if test administered to the individual is positive, the probability that the person actually have the disease is
P (Has disease | positive) [tex]$=\frac{P(\text{positive}| \text{has positive}) \times P(\text{Has disease})}{P(\text{positive})}$[/tex] ......(1)
The P(positive) is,
[tex]$P(\text{positive}) = P(\text{positive} \cap \text{Has disease})+P(\text{positive} \cap \text{No disease})$[/tex]
= P(positive | has disease) x P(Has disease) + P(positive | no disease) x P(No disease)
= 0.7 (0.19) + 0.04 (0.81)
= 0.1654
Now substituting the values in the equation (1), we get
P (Has disease | positive) [tex]$=\frac{P(\text{positive}| \text{has positive}) \times P(\text{Has disease})}{P(\text{positive})}$[/tex]
[tex]$=\frac{0.7(0.19)}{0.1654}$[/tex]
= 0.8041
What is the area?
Write your answer as a fraction or as a whole or mixed number.
Answer:
1247/90 km² or 13 77/90 km²---------------------------
Given is the parallelogram.
Area of a parallelogram:
A = bhSubstitute the values and find the area:
A = 3 2/9 × 4 3/10 = Convert to fraction 29/9 × 43/10 = Multiply 29*43/90 = 1247/90 = Fraction 13 77/90 Mixed numberbrainly has it out for me
Answer:
answer is 341
pls mark me as brainlliest
What’s the denominator of x-3+5
The expression denominator is 1.
What is denominator?
In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.
Here the given is x-3+5
Now simplifying them
=> x-3+5 = x+2.
We know that the whole number or Integer always has 1 as Denominator. Then,
=> [tex]\frac{x-2}{1}[/tex]
Hence the denominator of the given is 1.
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8. Bonnie worked for 40 hours each week for 30
weeks. How many hours did she work
altogether? /
Answer:
1,200 40×30=. h. h= hours
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent the circle are x² + (y - 3)² = 36 and x² + (y + 8)² = 36.
What is Circle?A circle is a two dimensional figure which consist of all the points which are at equal distance from a fixed point called center of the circle.
Standard equation of a circle is,
(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Given that,
Diameter = 12
Radius = Half of diameter = 6
Center lies on the y axis.
So the coordinates of center (h, k) will be of the form (0, k).
So the equation will be of the form,
(x - 0)² + (y - k)² = 6² or x² + (y - k)² = 36
The equations of this form in options are,
x² + (y - 3)² = 36 and
x² + (y + 8)² = 36
Hence the equations are x² + (y - 3)² = 36 and x² + (y + 8)² = 36.
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Olivia's class collected 3,591 bottle caps in 57 days. The same number of battle caps were collected each day. How many bottle caps did the class collect per day?
Answer: 63 bottle caps
Step-by-step explanation:
3591 caps collected
57 days
3591/57=63
Caps collected per day 63 caps
What is the sum of a °+c °?
Answer:
300 degrees.
Step-by-step explanation:
a = 180 degrees
c = 180 - 60 = 120 degrees
Use the diagonals to determine whether a parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a rectangle, rhombus, or square. Give all the names that apply.
The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square
How to solve for the shapeIn order to get the shape using the vertices that we have, we would have to find the length of the diagonals
We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)
The length of the diagonal PQ is given as:
PQ = [tex]\sqrt{(0-4)^2+(4-0)^2}[/tex]
= [tex]\sqrt{32}[/tex]
Next we have to solve for the length of the diagonal RS
RS = [tex]\sqrt{(4-(-4))^2+(0-(-4))^2[/tex]
RS = [tex]\sqrt{32}[/tex]
Since PQ = RS we would have to conclude that the shape is a square.
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2 variables x and y vary inversly and x=12 when y=4 what is the value of y when x=3
The value of y given the inverse proportional relationship between the variables is 16.
What is the inverse proportion?When two variables vary inversely, as one of the variable increases, the other variable decreases.
The equation that represents inverse proportion : x = k / y
where b = constant of proportionality
k = xy
k = 12 x 4 = 48
y = k / x
48 / 3 = 16
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please choose the correct answer and explain why it’s correct. i will mark you brainliest!
Answer: C
Step-by-step explanation:
This is simple algebra! First, try to find the slope which would be -3.
Let's say x is hours and y is degrees. We will find the slope by finding the change in x and y.
change in y 45 - 54 = -9
change in x 5 - 2 = 3
The slope is -3. Therefore the temperature decreases by 3 degrees every hour.
Hope that helps! :-)
If 3/4 cup of chai tea latte concentrate is 60 calories, how many calories is 1/2 cup of chai tea latte concentrate?
If 3/4 cup of chai tea latte concentrate is 60 calories, we can use proportion to find out how many calories 1/2 cup of chai tea latte concentrate is.
What does a math ratio mean?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could athe ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
We know that:
(3/4 cup) = 60 calories
To find out the number of calories in 1/2 cup, we can set up a proportion using the information we have:
(1/2 cup) / x = (3/4 cup) / 60
we can cross-multiply to get:
x = (1/2 cup) * (60 / (3/4 cup))
then we can simplify
x= (1/2)*(4/3)*60
x= 80/3
Therefore, 1/2 cup of chai tea latte concentrate is 80/3 calories.
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The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = y minus 1 equals StartFraction one-fourth EndFraction left-parenthesis x minus 12 right-parenthesis.(x – 12). What is the standard form of the equation for this line?
x – 4y = 8
x – 4y = 2
4x – y = 8
4x – y = 2
The standard form of the equation for the line which is as described is; x - 4y = 8.
Which equation represents the standard form equation of the line?It follows from the task content that the equation of the line in discuss in point-slope form as given in the question is;
( y - 1 ) = 1/4 ( x - 12 )
Therefore, the equation above can be written so that we have that;
4 ( y - 1 ) = ( x - 12 )
4y - 4 = x - 12
4y - x = -12 + 4
x - 4y = 12 - 4
x - 4y = 8
Therefore, the standard form equation of the line as required is; x - 4y = 8.
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Which of the following expense items should be included when determining whether a taxpayer who wishes to file as head of household paid more than half the cost of keeping up their home?
Education.
Medical expenses.
Real estate taxes.
Rental value of the home owned by the taxpayer.
Answer:
The Answer is (D)
Step-by-step explanation:
When determining when a taxpayer wants to file as head, then the answer will become clearer when checking for their position on the house
Which system of equations cannot be readily solved by the substitution method?
Answer: C
Step-by-step explanation:
4x - 12y = -10
-3x + 10y = 10
In order to solve this using substitution method, you will have to
divide one equation by the coefficient of x or y
e.g. divide 4x-12y = -10 by 4 to get x-3y = -5/2
x = 3y-5/2
and substitute x for 3y-5/2 which is pretty complicated.
Not sure what you mean by "readily solved", though.
Can some one solve the inequality for me I have a d in class
-5x -1>9
Answer:
Step-by-step explanation:
-5x-1>9
add 1 to both sides
-5x>10
divide by negative 5
x<-2
the sign flips since you divided by a negative
and your answer is x<-2
The bill for dinner was $41.76 . You left $8.24 for the tip. What percentage of the original bill was the tip? Round your answer to the nearest whole percent.
Answer: 20%
Step-by-step explanation:
Im SOO sorry if i got it wrong but you make a porportion, it would look like this. 8.24/41.76 = x/100, were assuming x is the percent, we then do cross multiplication which would then look like. 41.76x=824. After this we want to seperate the variable so divide 41.76 on both sides.
what is the equation of the line that has a slope of 1/2 and goes though the point (4,-1)
The equation of line that has a slope of 1/2 and goes through (4,-1) is y=-3.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
y = mx + c
where m denotes the line's slope and c is the y-intercept.
In the question, we have been given the slope and the (x,y) through which it passes.
Substituting these in y = mx + c, we get
-1= 0.5(4)+c
-1= 2+c
-3=c
c=-3.
Hence, the equation of line is y=-3.
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can you graph the line with the slope -2 that passes through the point (3,-1) ?
Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.
The definition of slope.A line's slope determines how steep it is. A gradient-based equation is referred to as having a gradient overflow. By dividing average horizontal difference (run) between 2 places by both the vertically change (rise) between those same two points, the slope is determined. The equation of a horizontal path is expressed as y = mx + b and is known as the hill form of an equation. The y-intercept of the line is located where the grade is m, b = b, and (0, b). In the case of the equations y = 3x - 7, the slope y y-intercept are (0, 7). The y-intercept is situated where the slope of the line is m and b is
Here,
Given :
that m=2, the point (x1,y1)=(— 3, —1)
Equation for the necessary straight line:
=>(y — y1)=m(x — x1)
=>y+1=2(x+3)
X=0 on the y-axis indicates that nothing is being measured.
=>y=2+3
The y-intercept value is 5.
Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.
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A metalworker has a metal alloy that is 30% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 51% copper alloy?
Robert is purchasing shirts for his weekend soccer team. The shirts he wants to buy are normally $12 each but are on sale for $9 off. His team has a total of 9 players. How much will he spend to buy the shirts?
Answer:
Robert will spend $27 on shirts for the team.
Step-by-step explanation:
Given InformationThe shirts typically retail for $12The shirts are now on sale for $9 off ($3 per shirt)There are 9 players on the teamCross-multiplyIf one shirt is now $3, then 9 shirts are $X.[tex]\frac{1 shirt}{9shirts} = \frac{3 dollars}{X dollars}[/tex]3 X 9 = $27.Therefore, Robert will spend $27 on shirts for the team.
Please let me know if this helped!!!
how do i solve this..
Answer:
1. 26
2. x = 1.5
Step-by-step explanation:
1. C(0.7) means to plug in 0.7 into the equation
here, C(x) = 30x + 5. replace x with 0.7 to get
C(0.7) = 30*0.7 + 5= 26
2. C(x) = 30x + 5 = 50
30x+5 = 50
subtract 5 from both sides to isolate x and its coefficient
30x = 45
divide both sides by 30 to find x
x = 1.5
a. Calculate WTW: What do you get? Why should we expect this result? b. Enter the following vectors into MATLAB: 6 = ; Compute the norm of b and the norm of Wb. What do you notice? Also compute the dot products (a, b) and (Wa; Wb): One of the fundamental properties of orthogonal matrices is that they preserve norms of vectors and the standard inner product (You can define orthogonal matrices as the ones with this property; in fact:) c. The columns of W are linearly independent because the vectors are orthogonal, so W should clearly be invertible: Use inv(W) to compute the inverse of W, and then compare it to WT What do you observe?
We were informed that an is a matrix with numerous elements in this query. A is an order matrix, and we also have an order matrix.
3 by 3, resulting in a determinant of b that is -5. We were successful in locating a matrix c that is equal to minus three times of a b cube times a.
We must determine the determinant because an is equivalent to a transport and an is equal to an identity matrix. If I take into account the period of a transposition, what is the determinant of a so-called determinant of this identity, which is equal to 1 accurate and we are aware of this characteristic.
This will be the result of those who are in a situation where a transposition is crucial. This is the first result is that the cube's time has the same determinant as a matrix's time.
Because a 3 by 3 matrix and lambda are real numbers, we can leverage this property. Using this property, it will be -3 q in this case. Once more, I'll be able to obtain a transposition b times c times a determinant. Splitting it is a possibility. The times of the b cube determinant are determined by minus 3 c. We know that the determinants of a transpose and the determinant of a that is 1 are, so what we are obtaining is just minus 27.
We shall obtain the b cube's determinant from this location. This is only multiplied by 1 minus 27. There won't be an entire cube. The determinant of c is equal to 3125, which is the product of -27 and -125.
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A container can hold a maximum of 17.75 pounds. There are two objects in the container. The first object weighs 6.53 pounds and the second object weighs 10.1 pounds. How many more pounds can the container hold? Wrote your answer as a decimal
The maximum weight of objects which the container can hold as required is; 1.12 pounds.
What is the maximum weight of objects which the container can hold?As evident in the task content;
The maximum which the container can is able to hold is; 17.75 pounds.
However, there are two objects in the can in which case one weighs 6.53 pounds and the other weighs 10.1 pounds.
On this note, the total weight which the can can hold more is given as;
= 17.75 - 6.53 - 10.1
= 1.12 pounds.
Ultimately, the maximum weight which the container can hold more is; 1.12 pound.
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Using the rule of 72, approximately how many years will it take a $1000.00
investment to double its value at an interest rate of 3.60%, compounded
annually?
Approximately 20 years will it take a $1000.00 investment to double its value at an interest rate of 3.60%, compounded annually.
What is rule of 72?The rules of 72, 70, and 69.3 are ways for calculating the doubling time of an investment in finance. To determine the roughly necessary number of periods for doubling, the rule number is divided by the interest percentage each period. For modest rates of return, the Rule of 72 is fairly accurate. The Rule of 72's estimates are compared to the actual number of years it takes for an investment to double in the graph below. Although it provides an estimate, the Rule of 72 becomes less accurate as rates of return rise.An investor or advisor can easily determine using the Rule of 72 how long it will take an investment to double based on its fixed annual rate of return. You may determine roughly how long it will take for your portfolio to double in size by dividing 72 by the fixed rate of return.Approximately 20 years will it take a $1000.00 investment to double its value at an interest rate of 3.60%, compounded annually.
The complete question is,
Approximately how many years will it take a $1000.00 investment to double its value at an
interest rate of 3.60%, compounded annually?
A. 5
B. 7.2
C. 20
D. 50
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Two groups are hiking on a glacier. Group B starts 1 mile ahead of Group A and walks 2 miles per hour.
To catch up to Group B, Group A walks 3 miles per hour.
Q
* 2: hours since the start of the hike
v: miles from the start of the trail
) Which equation shows Group A's
distance from the start?
U = x + 1
3=2+3
Group A
3 miles
per hour
Group B
U = 3х
v=30+1
The equation that shows Group A's distance from the start, given their speed and the number of hours is C. y = 3 x.
How to find the equation for the distance ?When trying to find the distance that a person or object has travelled in a given time, the general formula is;
= Speed x Time
The speed is given as 3 miles per hour for Group A.
The time is given as x for either group
This means that the distance that Group A has gone since the hike up the glacier started is :
Distance from the start = Speed x Time
y = 3 miles per hour × x
y = 3x
In conclusion, given the speed that Group A is using, this means that their distance from the start can be modelled by the equation, y = 3 x.
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Answer:
Step-by-step explanation:
Write a ratio to represent the scale used in the drawing.
The ratio of these two figures would be for every 1cm in image A, in image B there are 2cm. So the ratio would be 1:2
What is ratio?The ratio is a mathematical term that refers to the quantified relationship between two magnitudes that reflects a proportion, that is, the ratio is the way of representing the proportion between two magnitudes. In this case, the ratio refers to the length of each side of these triangles and their relationship to each other.
According to the above, the ratio could be 1:2 because the larger triangle has lengths that are twice the lengths of the sides of the smaller triangle. For example, the left side of the small triangle is 6 cm, while the left side of the large triangle is 12 cm.
It's a proportionality relationship twice as big. Therefore, the ratio would be 1:2.
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Help pls its due in 30 minutes
Select the correct answer. A line t runs downward to the right through two parallel horizontal lines a and b, forming 8 angles numbered from 1 to 8. In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true? A. m∠1 = m∠7 B. m∠3 = m∠6 C. m∠5 + m∠8 = 90° D. m∠6 + m∠7 = 180°
Since in the diagram, transversal t cuts parallel lines a and b, an equation which is necessarily true include the following: B. m∠3 = m∠6.
What is the Alternate Interior Angles Theorem?In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Based on the diagram representing (showing) the two parallel horizontal lines a and b, we can reasonably infer and logically conclude that angle 3 (m∠3) and angle 6 (m∠6) forms a pair of alternate interior angles because line a is parallel to line b and transversal (t) cuts parallel lines a and b.
Similarly, angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line a is parallel to line b.
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Solve for x
I need 20 characters so I’m just typing this
Answer:
x = 4
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation to find the value of x based on this information:
6x + 6 + 17x + 2 = 100
Add like terms.23x + 8 = 100
Subtract 8 from both sides23x = 92
Divide both sides by 23x = 4
Given: AC ⊥ BD and DB bisects ∠ABC.
Prove: △ABD ~ △CBD.
By ASA (Angle side angle) theorem, triangle △ABD≅ triangle △CBD.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now
As BD is common for both triangles ABD and CBD.
and
∠ADB=∠CDB=90°
also as DB bisects ∠ABC
∠ABD=∠CBD
Hence,
By Angle Side Angle theorem, triangle △ABD≅ triangle △CBD
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