The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.

Answer:

D

Step-by-step explanation:

For the given expression √3, its index form is written as ( 3 )¹/² .

As given in the question,

Given expression is equal to :

√3

Standard form of writing expression in index form is given by:

√  ( square root ) will express the value in index form as 1 / 2 in the exponent.

√x = ( x ) ¹/²

Here x = 3 substitute the value of x in the standard way of index form we have:

Index form of the given expression is written as :

√3

= ( 3 )¹/²

Therefore, for the given expression √3, its index  form is written as ( 3 )¹/² .

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See attached

Triangle DGF is plotted, blue figure.

Find the coordinates of the image using the rule:

The points added to same plot, red figure.

Answer:

D' = (-3, 0)

G' = (0, 3)

F' = (3, -3)

Step-by-step explanation:

Given vertices of the polygon:

To dilate a figure by a given scale factor, multiply the coordinates of the vertices of the figure by the scale factor:

Therefore, the vertices of the image after dilation are:

The equation that describing how x and y are related is y = 2x + 7

From the given table we have to choose two points

The first point = (1, 9)

The second point = (2, 11)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (11-9) / 2 - 1

= 2 / 1

= 2

From the table

At x = 0 the value of y = 7

Therefore the y intercept = 7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Then,

y = 2x + 7

Hence, the equation that describing how x and y are related is y = 2x + 7

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The equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)

The first point = (3, 5)

The second point = (8, 10)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (10-5) / (8-3)
= 5 /5

= 1

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope of the line

Consider the point (3, 5)

Substitute the values in the equation

y-5 = 1(x-3)

Hence, the equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)

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Answer:

y=3x-13

Step-by-step explanation:

Since the parallel equations have equal slope.

The equation of line parallel to y=3x+7 will be y=3x+k.

(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13

Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

Given:

At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.

y varies directly as x :

y = kx

k = constant of proportionality

y = 2.56 and x = 32

y = kx

k = y/x

= 2.56/32

k = 0.08

substitute k we get

y = 0.08x.

so x and y are directly proportional.

Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

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Answer:

g = 204 - 120

Step-by-step explanation:

T - CC = amount of gingersnaps

204 - 120 = 84

Warren and Dirk baked 84 gingersnaps

The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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Answer: 14

Explanation:

(3, -20)    (5, 8)

x1   y1       x2   y2

[tex]\frac{y2 - y1}{x2 -x1}[/tex]

[tex]\frac{8 - -20}{5-3}[/tex]  = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]

The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as  f(x) = (x - 7)^3 + 5.

Let the cubic function be = f(x) = x^3

The transformation required include shifts 7 units right and 5 units up

shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3

moving 5 units up is achieved by adding 5 units to the function hence

f(x) = (x - 7)^3 + 5

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Answer:

Option B

Step-by-step explanation:

3x - 4 > 5

3x > 9

x > 3

-8x - 19 > 21

-8x > 40

x < -5

This means that we can eliminate the first option, since it includes all real numbers. We can also eliminate the last option since it doesn't include any real numbers.

The middle option is the only graph that includes numbers from -∞ to -5, and 3 to ∞

Answer:

  domain: [0, (6+√39)/4] ≈ [0, 3.06125]

Step-by-step explanation:

You want the realistic domain of a height function h = -16t² +48t + 3.

The given polynomial is defined for all values of t. Since it represents height above the ground, and after the ball is thrown, only function values in the first quadrant are of interest: h ≥ 0, t ≥ 0.

The height becomes zero at t = (6+√39)/4 ≈ 3.061 seconds after the ball is hit. Hence the realistic domain is [0, (6+√39)/4], the interval in which the ball is above ground.

__

Additional comment

We can solve this using the "completing the square" method.

  t^2 -3t = 3/16 . . . . . . divide by -16, add 3/16

  (t -3/2)^2 = 3/16 +9/4 . . . . . add 9/4 to complete the square

  t = 3/2 ± √(39/16) = (6 ± √39)/4 . . . . . . take the square root, add 3/2

Only the positive value of the solution is applicable to this problem. That value is ...

  h = 0 at t = (6 +√39)/4 ≈ 3.061249

20 times can you expect to land on yellow if you spin the spinner 100 times.

Given:

A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times.

10 times spinning = landed on yellow 2 times.

divide by 10 on both sides

1 time spinning = landed on yellow 2/10 times

1 time = 1/5 times

multiply by 100 on both sides

1 time * 100 = 1/5*100 landed on yellow

100 times spinning = 20 times landed on yellow.

Therefore 20 times can you expect to land on yellow if you spin the spinner 100 times.

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Answer: 21

Step-by-step explanation:

If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)

So if she makes 30 shots, 21 will go in the basket

(30)(0.70) = 21

The measure of all the angles is given below :

angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°

Given, ΔWXY is an equilateral triangle and ΔWZY is an isosceles triangle.

We have to find the measure of all the angles,

As, ΔWXY is an equilateral triangle

so, ∠WXY = ∠XYW = ∠YWX = 60°

Now, let ∠WZY = ∠WYZ = x and ∠ZWY = y

so, on applying angle sum property, we get

2x + y =180°

so, y = 60°

and 2x = 120°

x = 60°

Hence, angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°

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Answer:

153.9 units squared

Step-by-step explanation:

A = pi*r^2

A = pi* 7^2

A = pi* 49

A = 153.9

Answer:

x=32 degrees

Step-by-step explanation:

Since the triangle is equilateral, each angle is = 60 degrees. This means that 2x-4=60

=) 2x=64

=) x=32

5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)

An expression is combination of variables, numbers and operators.

The given expression is

1/2(13x+5x-6-8x+14)

one by two times of thirteen x plus five times of x minus six minus eight times of x plus fourteen.

In the equation x is the variable

plus, minus and multiply are the operators

1/2(13x+5x-6-8x+14)

1/2(10x+8)

Now apply distributive property

1/2(10x)+1/2(8)

5x+4

Hence 5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)

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The value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.

According to the question,

We have the following expression:

(2x − 12) + (1/2xy-10)

Now, the values of x and y are given to be 8 and 2 respectively.

So, we will put these values of x and y in the given expression:

(2*8-12)+(1/2*8*2-10)

First, we will use multiplication:

(16-12)+(8-10)

4+(-2)

(Note that when two integers are of different signs then the integers are subtracted but the sign in the result is of the larger integer.)

4-2

2

Hence, the value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.

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unable to see the graph

8 hours the driver worked and 240 miles the truck drove.

Assume that the truck traveled y miles per hour. and that the driver worked x hours per day.

The equations describing the provided issue will be

19x + 1.50 y = 512

y = 30x

y = 19 x + 1.50 y = 30 x + 1.50 y

When we enter the second equation into the first one, we get,

19 x + 1.50 (30 x) = 512

19x+ 45x = 512

64x = 512

x = 8

y = 240

The vehicle traveled 240 miles, and the driver put in eight hours' worth of work.

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The probability that exactly two marbles are red, is 0.365.

In the given question we have to find the probability that exactly two marbles are red.

A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.

Total marbles is

10+5+6=21

We draw 5 marbles out at random, without replacement.

Marbles taken out =5

Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].

Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]

[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]

[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]

Simplifying

[tex]^{21}C_{5}[/tex] =7×19×9×17

[tex]^{21}C_{5}[/tex] = 20,349

Probability of exactly two marbles are red is

Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.

Total red marbles are 10. So [tex]^{10}C_{2}[/tex]

The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]

[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]

Simplifying

[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]

[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]

[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]

=5×9×11×5×3

=7,425

So the probability that exactly two marbles are red

P(R)=7,425/20,349

P(R)=0.365

Hence, the probability that exactly two marbles are red, is 0.365.

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The amount of cell taxes on finn’s purchase is $5.94.

Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:

= $29.50 + $42.50

= $72

If the sales tax rate is 8.25%, the amount on tax will be:

= Tax rate × Total cost

= 8.25% × $72

= $5.94

The tax is $5.94.

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the factors of 28 are : 1, 2, 4, 7, 14, and 28.

the prime factors of 28 are : 2, 2, and 7.

The simplified expression is x² + 2x - 15.

We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second  term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.

E = (x + 5)(x - 3)

We will use the distributive property.

E = x*(x - 3) + 5*(x - 3)

E = x*x - x*3 + 5*x - 5*3

E = x² - 3x + 5x - 15

E = x² + 2x - 15

Hence, the expanded and simplified form of the given expression is x² + 2x - 15.

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The measure of each angle of the triangle are 35°, 35°, 110°.

What is an isosceles triangle?

Let's Base angle =x°

Vertex angle = 5° +3x°

The sum of measure of angles of triangle are supplementary.

i.e., Sum of triangle = 180°

So,

x° + x° + 5° + 3x° =180°

5x° + 5° = 180°

5x° = 175°

x° = 175° /5°

 x = 35°

Base angle = 35°

Vertex angle = 5°+ 3x°

                      = 5° + 3×35°

                      = 5° +105°

Vertex angle = 110°

Hence, the measure of each angle of the triangle are 35°, 35°, 110°.

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Answer:

21g-8

Step-by-step explanation:

The product of Goran's score and 21 = 21g, then subtract 8 from that.

Answer:

lo siento no se mucho de este ap