graph the line through (1,1) with slope 3/2​

The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.

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:

In this problem, the events are:

The percentages associated with a positive test is:

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 value of x is 15° and the type of quadrilateral is a rhombus.

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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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.

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

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].

Answer:

B -o.60

Step-by-step explanation:

34 - 40 = -6.  -6 divide by 10 = -3/5 or - 0.6. So answer is B

The largest angle of the triangle is equal to 80 degrees.

Concept: Angle sum property of a triangle i.e., the sum of all angles of a triangle is equal to 180 degree

Given :  Degree measures of the angles in a triangle are in the ratio 2:3:4

Let one part of each angle of the triangle be x, so the different angles of triangle are 2x,3x,4x (taking the ratios given in the question  and multiplying by each of them by x)

2x +3x +4x = 180x

180x = 20

The angles of a triangle are 40,60,80

The largest angle of the triangle is equal to 80 degrees.

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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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The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.

A marginal production cost is a derivative of a cost function. From the information given, the total cost is:

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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Answer:

11/4 Pi

Step-by-step explanation:

because 1.= 70/180.       (180.=Pi)

so 495 x 70/180

=11/4 Pi

The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3

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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The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250

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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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}.

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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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°

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.

Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).

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:

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:

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]

Answer:

A

Step-by-step explanation:

there cannot be 2 different points on the same x coordinate

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]

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).

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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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.

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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Given:

Formula:

AB × AD = AC × AE

Here if applied:

EA × EB = EC × ED

2 × 12 = 3 × (3 + y)

24 = 9 + 3y

3y = 15

y = 5

Answer:

y = 5

Step-by-step explanation:

Secant: a straight line that intersects a circle at two points.

Segment: part of a line that connects two points.

The given diagram shows two secant segments EB and ED drawn to the circle from one exterior point E.  Therefore, using the Intersecting Secants Theorem,  the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

⇒ EB · EA = ED · EC

⇒ (2 + 10) · 2 = (3 + y) · 3

⇒ (12)2 = 3(3 + y)

⇒ 24 = 9 + 3y

⇒ 15 = 3y

⇒ y = 5        

The probability of getting two correct answers will be 0.0625.

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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The two transformations for fx and gx would be to shift by 6 units and also go up by 18.

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.

g 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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The height of the tree is 249.5 feet

The given parameters are:

Let 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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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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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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The order of the graphs from largest to lowest correlation coefficients is:

Graph D, Graph A, graph C, graph B.

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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