The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
To purchase 13700 worth of restaurant equipment for her business.
Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.
The total amount Maria ended up paying for the equipment will be
Total amount = 371.16 × 3 × 12 + 1500
Total amount = $14,861.76
The interest of Maria on the loan will be
Interset = [(14861.76 – 13700) / 13700] x 100
Interset = 8.48%
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At a certain time of day, the angle of elevation of the sun is 80degree. Find the height of a tree whose shadow is 44 feet long.
The height of the tree is 249.5 feet
How to determine the height of the tree?The given parameters are:
Elevation angle = 80 degreesShadow length (L) = 44 feetLet the height of the tree be x.
So, we have:
tan(80) = x/44
Multiply both sides by 44
x = 44 * tan(80)
Evaluate
x = 249.5
Hence, the height of the tree is 249.5 feet
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An empty rectangular tank was 25 cm long, 23 cm wide and 18 cm high. Ravi filled 5 identical bottles with water to the brim. Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle? height of water, = = 1/2 X 18 3 23 cm Co 25 cm 3 full. 18 cm 2 An empty rectangular tank was 25 cm long , 23 cm wide and 18 cm high . Ravi filled 5 identical bottles with water to the brim . Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle ? height of water , = = 1/2 X 18 3 23 cm Co 25 cm 3 full . 18 cm
Which relation is a function??????
Answer:
A
Step-by-step explanation:
there cannot be 2 different points on the same x coordinate
A hostel has food for 60 days if after 15 days 500 more students joined th hostel and the food lasted for 40days only. How many students were there in hostel
Answer:
625
Step-by-step explanation:
here we are in an inverse proportion situation :
As the number of days increases
when the number of students decreases and vice versa.
__________________
Say n is the original number of students.
___________________________________________
After 15 days, the rest of food is enough for n students for 45 days,
or enough for n+500 students for 25 days.
Then
45n = 25×(n + 500)
Then
45n = 25n + 25×500
Then
45n - 25n = 25×500
Then
20n = 12500
Then
n = 12500÷20
= 625
and thus , there were 625 students in the hostel.
B is the set of odd numbers greater than 5 and less than 21
Answer:
List method: {7,9,11,13,15,17,19}
Set method: {X:N where N is odd, N>5 and N<21}
The odd numbers greater than 5 and less than 21 are {7, 9,11,13,15,17,19}.
What are odd numbers?Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly.
Odd numbers are opposite to even numbers this means that even numbers are numbers that can be divided by 2.
When we say numbers greater than 5 and less than 21 this means 5< x < 21
The odd numbers greater than 5 and less than 21 are ;
{7, 9,11,13,15,17,19}. These odd numbers are greater than 5 and less than 21.
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Help please!! I’m stuck with these questions. :)
Answer:
20 elements.
Step-by-step explanation:
Lets say
n(U) = 114
n(A) = 57
n(B) = 79
n(A n B)= 42
Now,
n(A U B) = n(A) + n(B) - n(A n B)
= 57 + 79 - 42
= 94
Now,
n(A U B) compliment = n(U) - n(A U B)
= 114 - 94
= 20
Can someone answer this
The order of the graphs from largest to lowest correlation coefficients is:
Graph D, Graph A, graph C, graph B.
Which graph has the largest correlation coefficient?The correlation coefficient between two variables is a coefficient that tells us "how much" these variables relate.
So, in the case for linear correlation, as "more linear" the data appears to be, a large correlation is between the two variables.
With that in mind, we conclude that the order of the graphs (going for larger correlation coefficient to smaller correlation coefficient) is:
Graph D, Graph A, graph C, graph B.
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Convert the following angle from degrees to radians. Express your answer in simplest
form.
495°
Answer:
11/4 Pi
Step-by-step explanation:
because 1.= 70/180. (180.=Pi)
so 495 x 70/180
=11/4 Pi
ASAP!!!!!!!!!!!!
PLEASE GIVE A STEP BY STEP EXPLANATION!!!
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The two transformations for fx and gx would be to shift by 6 units and also go up by 18.
What is a transformation?This is the term that is used in mathematics to describe the manipulation of a line or a shape.
a. The possible transformations that can be gotten here would be to shift to the left by 6 units from what we have in the graph and also shift to the top by 18.
b. How to solve for K in the transformationg of x = f(x - k) then
g(x)= f(x) + k
C. The value of k should be based on the way it changes based on the given points.
Vertically, g(x)=f(x) +18
Horizontally , g(x)=f(x-6)
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A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.
(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)
Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Researching the problem on the internet, the coordinates are as follows:
Rock (3,2).Treasure (x,y).Tree (16,21).The treasure is buried between a rock and a tree in a 5:9 ratio, hence the expression is:
[tex]Ts - R = \frac{5}{14}(Tr - R)[/tex]
Hence, for the x-coordinate:
[tex]x - 3 = \frac{5}{14}(16 - 3)[/tex]
x - 3 = 5 x 13/14
x = 7.6.
For the y-coordinate:
[tex]y - 2 = \frac{5}{14}(21 - 2)[/tex]
y - 2 = 5 x 19/14
y = 8.8.
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Answer: the answer is b
Step-by-step explanation:
NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
[tex]\boxed {1)log_{b}(75) = 4.317}[/tex]
[tex]\boxed {2)ln(20) = 2.9957}[/tex]
Step-by-step explanation:
[tex]\textsf {Question l :}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(3) = 1.099}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5) = 1.609}[/tex]
[tex]\textsf {Identities applied :}[/tex]
[tex]\boxed {log(ab) = loga + logb}[/tex]
[tex]\boxed {log(a)^{x} = xloga}[/tex]
[tex]\textsf {We can rewrite the problem as :}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(75)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(25 \times 3)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5^{2} \times 3)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5)^{2} + log_{b}(3)}[/tex]
[tex]\longrightarrow \mathsf {2log_{b}(5) + log_{b}(3)}[/tex]
[tex]\textsf {Now, substitute the values :}[/tex]
[tex]\longrightarrow \mathsf {2(1.609) + (1.099)}[/tex]
[tex]\longrightarrow \mathsf {3.218 + 1.099}[/tex]
[tex]\longrightarrow \mathsf {4.317}[/tex]
[tex]\boxed {log_{b}(75) = 4.317}[/tex]
[tex]\textsf {Question ll :}[/tex]
[tex]\longrightarrow \mathsf {ln(4) = 1.3863}[/tex]
[tex]\longrightarrow \mathsf {ln(5) = 1.6094}[/tex]
[tex]\textsf {Rewriting the problem :}[/tex]
[tex]\longrightarrow \mathsf {ln(20)}[/tex]
[tex]\longrightarrow \mathsf {ln(4 \times 5)}[/tex]
[tex]\longrightarrow \mathsf {ln(4) + ln(5)}[/tex]
[tex]\longrightarrow \mathsf {1.3863 + 1.6094}[/tex]
[tex]\longrightarrow \mathsf {2.9957}[/tex]
[tex]\boxed {ln(20) = 2.9957}[/tex]
Answer:
[tex]\sf \log_b(75)=4.317[/tex]
[tex]\sf \ln (20)=2.9957[/tex]
Step-by-step explanation:
Question 1
Given:
[tex]\sf \log_b(3)=1.099[/tex]
[tex]\sf \log_b(5)=1.609[/tex]
To evaluate [tex]\sf \log_b(75)[/tex], replace 75 with (5 × 5 × 3):
[tex]\implies \sf \log_b(5 \cdot 5 \cdot 3)[/tex]
[tex]\textsf{Apply the Product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_b5+\log_b5+\log_b3[/tex]
Substitute the given values to solve:
[tex]\implies \sf 1.609 + 1.609 + 1.099=4.317[/tex]
Question 2
Given:
[tex]\sf \ln(4)=1.3863[/tex]
[tex]\sf \ln(5)=1.6094[/tex]
To evaluate ln(20) replace 20 with (4 × 5):
[tex]\implies \sf \ln (4 \cdot 5)[/tex]
[tex]\textsf{Apply the Product log law}: \quad \ln xy=\ln x + \ln y[/tex]
[tex]\implies \sf \ln (4)+\ln (5)[/tex]
Substitute the given values to solve:
[tex]\implies \sf 1.3863+1.6094=2.9957[/tex]
A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising, it sells 250 units. For each additional $4000 spent, an additional 25 units are sold. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.
The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250
How to illustrate the equation?From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.
The formula for y will be:
y = (25/4000)x + 250
y = 0.00625x + 250
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The length of a golden rectangle is 35 cm. Find the width to the nearest centimeter.
17cm
25cm
22cm
29cm
16cm
Answer:
22 cm
Step-by-step explanation:
First we need to know that The golden number
= (1+√(5))÷2
= 1.61803398875 (in decimal)
………………………………………………
We get the length of a golden rectangle
by multiplying its width by the golden number itself.
Then
The width = 35÷ 1.61803398875
=21.631189606245
What is the vertex of the quadratic function given in the table?
Answer:
The vertex is (-3,-2)
The vertex is basically the very top or very lowest, so you will notice how values around (-3,-2) are relatively the same in the y coordinate, but -2 is the "highest/lowest" so that's how you know it's a vertex.
If you try picturing the points in your head, you will see it make a U and at the bottom of the U is the vertex.
The age of trees in a forest is known to be approximately normal with an average age of 40 years and a standard
deviation of 10 years. What is the standardized score for a tree that is 34 years old?
A. 1.90
B.-0.60
C. -1.90
D. 0.60
Answer:
B -o.60
Step-by-step explanation:
34 - 40 = -6. -6 divide by 10 = -3/5 or - 0.6. So answer is B
. It costs C(x) = [tex]\sqrt{x}[/tex] dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)
The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.
What is a Marginal Production Cost?A marginal production cost is a derivative of a cost function. From the information given, the total cost is:
C(x) = [tex]\mathbf{\sqrt{x}}[/tex]The marginal production cost can be expressed as:
[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]
[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]
However, when the cost is 25, the marginal production is:
[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]
C' (25) = $0.1
Also, when the cost is 100, the marginal production is:
[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]
C' (100) = $0.05
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If a line has a slope of 4 and goes through the point open parentheses short dash 1 comma 1 close parentheses, then the equation for the line in slope-intercept form is ______________.
a.)
y equals short dash 4 x minus 3
b.)
y equals 4 x plus 3
c.)
y equals 4 x plus 5
d.)
y equals short dash 4 x minus 5
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y =4x+5. Thus, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given the slope of the line is 4 and it goes through (-1,1), therefore, the equation of the line will be,
y = mx + c
y = 4x + c
Substitute the value of points,
1 = 4(-1) + c
1 = -4 + c
5 = c
Hence, the equation of the line will be y =4x+5. Thus, the correct option is C.
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Suppose that an examination consists of 10 questions with the choice A, B, C, and D. Assume that a student has no knowledge of the subject matter. Then what is the probability that: Guessing at most two correct answers? Guessing at least seven correct answers? Which type of probability distribution it has? Why? average five smokers pass a crain traat B. C. Suppose that an examination consists of 10 questions with the choice A , B , C , and D. Assume that a student has no knowledge of the subject matter . Then what is the probability that : Guessing at most two correct answers ? Guessing at least seven correct answers ? Which type of probability distribution it has ? Why ?
The probability of getting two correct answers will be 0.0625.
How to calculate the probability?The probability of getting two correct answers will be:
Probability of getting the correct answer will be:
= 1/4 = 0.25
The probability of getting two correct answers will be:
= 0.25 × 0.25
= 0.0625
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Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12? O X= -2. x = 1 O x= -2 x = 4 O x = 2. x = 4 O x = 2, x = 4
The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3
What is function?
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
According to the question,
The given function is
[tex]f(x) = -5|x + 1| + 3[/tex]
Here f(x) = -12
Substitute f(x) and solve for x
[tex]- 12 = -5|x + 1| + 3[/tex]
By subtracting 3 on both sides
[tex]- 12 - 3 = -5|x + 1| + 3 - 3[/tex]
[tex]- 15 = -5|x + 1|[/tex]
By dividing -5 on both sides
[tex]3 = |x + 1|[/tex]
We get absolute values for the function.
[tex]x + 1 = 3 , x + 1 = -3[/tex]
By subtracting 1 on both sides
[tex]x + 1 - 1 = 3 - 1 = 2\\\\x + 1 - 1 = - 3 - 1 = -4\\\\x = 2 , x = - 4[/tex]
Therefore, the values of x are 2 and - 4 of the given function f (x) =-5|x+1| +3
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P, Q and R are points in the same
horizontal plane. The bearing of
Q from P is 150° and the bearing
of R from Q is 060°.
If |PQ| = 5m and QR = 3m,
Find the bearing of R from P.
correct to the nearest degree./
Answer: 119°
Step-by-step explanation:
From the positive y-axis, all angles are measured clockwise
PR = PQ + QR = 5[150°] + 3[60°]
X = 5*sin150 + 3*sin60 = 5.1
Y = 5*Cos150 + 3*Cos60 = -2.83
TanA = X/Y
A = -61° = 61° East of South = 119° Clockwise
Therefore, the bearing of R from P is 119°
Find the greatest number which divides 6168, 2447, and 3118 leaving the same remainder in each case.
Answer:
Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.
x + 4 = x2? Assume x greater-than 0
Answer:
The value comes out to be
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
Step-by-step explanation:
The quadratic equation is an equation containing a single variable of degree [tex]2[/tex]. Its general form is [tex]ax^{2} +bx + c=0[/tex].
The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
The equation we are given is :[tex]x+4=x^{2} \\x^{2} -x-4=0\\[/tex]
We know the formula as :
[tex]x=[-b[/tex]±[tex]\sqrt{b^{2}-4ac}][/tex] ×[tex]\frac{1}{2a}[/tex]
[tex]x=[-(-1)[/tex]±[tex]\sqrt{(-1)^{2} -4(1)(-4)}][/tex]×[tex]\frac{1}{2(1)}[/tex]
[tex]x=\frac{1}{2}[/tex] ±[tex]\frac{\sqrt{17} }{2} }[/tex]
Since [tex]x[/tex]≥[tex]0[/tex]
Other negative option is neglected
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
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Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
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5
сл
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is
units. The point (-15,
) lies on this circle.
Part 1: Finding radius
The radius of a circle is defined as the distance from the center to a point on the circle's circumference.
Using the distance formula,
[tex]r=\sqrt{(-7-8)^{2}+(-1-7)^{2}}=\boxed{17}[/tex]
Part 2: Finding the point with x-coordinate -15
Let the y coordinate of the point be y. Then, we have the point (-15, y). Substituting into the distance formula,
[tex]\sqrt{(-15-(-7))^{2}+(-1-y)^{2}}=17\\\\64+(-1-y)^{2}=289\\\\(-1-y)^{2}=225\\\\-1-y =\om 15\\\\y=\boxed{-16, 14}[/tex]
Select all the correct answers. Function g is a transformation of the parent exponential function. Which statements are true about function g? A Linear graph function where red line g intercepts y-axis at (0, 4) and passes through (minus 10, 3) and (3, 10) Function g is positive over the interval . The domain of function g is . Function g has a y-intercept of . Function g decreasing over the interval . Function g is 4 units above function f. The range of function g is .
The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
The parent function i.e. exponential function is defined by:
y=f(x)=aˣ
From the graph given below,
1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function
2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).
3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).
4. From the graph it is clear that Function g increases over the interval (-∞, 0) .
5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.
6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).
Therefore The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
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if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
[tex]60200cm^{2}[/tex]
Step-by-step explanation:
(I am assuming that the units for the measurements in this question are all centimeters)
Surface area = 2 * (Area of Base) + (Perimeter of base)*(Height)
First, we'd need to solve for the area of the base by finding the area of the triangle and subtracting it from the area of the rectangle. The area of the rectangle is [tex]100 * 150 = 15000[/tex]. The area of the triangle is [tex]\frac{1}{2} * 120 * 90 = 5400[/tex]. (We can do this because it is a right triangle with leg lengths in the pattern of a 3-4-5 triangle.) Now, subtracting the area of the triangle from the rectangle, we get [tex]15000 - 54000 = 9600[/tex]. This is the area of the base.
Next, the perimeter of the base is [tex]100 + 150 + 90 + 120 = 460[/tex]. Multiplying this by the height, we get [tex]460 * 110 = 50600[/tex].
Finally, we add 9600 and 50900 to get [tex]9600 + 50900 = 60200[/tex].
An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the box as a function of the length of a side of the base, x.
The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
[tex]= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}[/tex]
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
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There are 192 pencils in 8 Super Saver packs. If there are the same number of pencils in each Super Saver pack, how many pencils are in 5 packs?
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Positive test.Event B: Has the disease.The percentages associated with a positive test is:
93.9% of 3.8%(has the disease).4.1% of 100 - 3.8 = 96.2%(does not have the disease).Hence:
[tex]P(A) = 0.939(0.038) + 0.041(0.962) = 0.075124[/tex]
The probability of both a positive test and having the disease is given by:
[tex]P(A \cap B) = 0.939(0.038) = 0.035682[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035682}{0.075124} = 0.4750[/tex]
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The angles of a quadrilateral have measures m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =
(6x + 15)◦, m∠D = (6x −5)◦. Find the value of x. If a diagonal bisects ∠B and ∠D, what
type of quadrilateral is ABCD?
The value of x is 15° and the type of quadrilateral is a rhombus.
Quadrilateral
A quadrilateral is a polygon that has four sides.The sum of all angles of a quadrilateral is 360°.
Here, we are given,
m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =(6x + 15)◦, m∠D = (6x −5)◦
So, we will have
7x+4x+5+6x+15+6x-5=360°
23x+15°=360°
23x=345°
x=345°/23°
x=15°
Hence, the angles of the quadrilateral are:
m∠A = (7x)◦=105°,
m∠B = (4x + 5)◦ =65°
m∠C =105°
m∠D = (6x −5)◦ =85°
Since the diagonal bisects ∠B and ∠D, we get that the quadrilateral is a rhombus.
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