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?.

The graph of the quadratic function x² + 3x - 108 is given by the image shown at the end of the answer.

Three features have to be considered to obtain the graph of a quadratic function.

The function for this problem is defined as follows:

a = 1, b = 3, c = -108.

Hence the coefficients of the function are given by:

a = 1, b = 3, c = -108.

Inserting these points into a calculator, the x-intercepts of the function are:

Hence the function crosses the x-axis at x = -12 and at x = 9, and it is a concave up parabola, as the coefficient a is positive.

The y-intercept of the function is given as follows:

f(0) = 0² + 3(0) - 108 = -108.

Hence the graph crosses the y-axis at y = -108.

The axis of symmetry of the function is:

x = -b/2a = -3/2 = -1.5.

The y-coordinate of the vertex is:

f(-1.5) = (-1.5)² + 3(-1.5) - 108 = -110.25.

Which is the turning point of the graph.

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The point we get after 180 degree clockwise rotation is E' (-3,-1)

When rotating 180° clockwise about the origin the coordinates of the image will be the same x and y numbers but the opposite sign of the pre-image.

Using the above as an example, pre-image E is located at (3,1) so the rotated image would be E' (-3,-1).

Pre-image D is located at (-1,3) so the rotated image would be D' (1,-3).

Pre-image F is located at (2,-2) so the rotated image would be F' (-2,2).

Hence we get the required point.

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Answer:

Step-by-step explanation:

Proportional relationship equation:

Use the given point (3, 1) to find the value of k:

Answer:

k = 1/3

Step-by-step explanation:

Now we have to,

→ find the constant of proportionality.

Formula we use,

→ y = kx

The constant of proportionality is,

→ y = kx

→ 1 = k × 3

→ 3k = 1

→ [ k = 1/3 ]

Hence, required answer is 1/3.

The non-real solutions according to the equation is (1 + √5 i)/3 and (1 - √5 i)/3.

A polynomial can be factored, and its roots can be discovered using the factor theorem. The polynomial residual theorem is indeed a special instance of this one.

A polynomial f(x) has a factor (x-a), as was noted in the beginning, if and only if f(a) = 0.

As per the given equation in the question,

3x⁵ + 25x⁴ + 26x³ - 86x² + 76x - 48

The function can be written as:

f(x) = g(x).h(x)  (i)

The real solutions from the graph is,

x₁ = -6, x₂ = -4 and x₃ = 1.

So,

g(x) = (x + 6) × (x + 4) × (x - 1)

g(x) = (x² + 10x + 24) × (x - 1)

g(x) = x³ + 9x² + 14x - 24.

Now, substitute the values in (i)

3x⁵ + 25x⁴ + 26x³ - 86x² + 76x - 48 = (x³ + 9x² + 14x - 24) × (ax² + bx + c)

Therefore,

ax⁵ = 3⁵

a = 3.

-24c = -48  

c = 2.

-24(bx) + 14(cx) = 76x

-24b + 28 = 76

b = -2.

The equation for non-real solution:

h(x) = 3x² - 2x + 2.

Δ = b² - 4ac = (-2)² - 4(3)(2) = -20

x₁ = (2 + √20)/6 = (1 + √5 i)/3

x₂ = (2 - √20)/6 =  (1 - √5 i)/3

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Answer:

-31

Step-by-step explanation:

-31 add 7 on a calculator equals -24

Answer:

Step-by-step explanation:

Ok: Hi

1. First Isolate the x on the left side of equation. Remember that if a variable or number goes over the equal sign, it becomes opposite!

x+7=-24

x=-24-7

x=-31

2. Always double check equations!

-31+7=-24 TRUE

Answer x=-31 or choice B

Answer:

Step-by-step explanation:

V = 64

a = ∛V = ∛ 64 = 8

Sum = 12·a = 12·8 = 48

Answer:

16(x+5)

Step-by-step explanation:

16x+80

=8(2x+10)

=16(x+5)

The algebraic factor of the given expression 16x + 80 will be 16(x + 5).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given expression,

⇒ 16x+80

Take 8 as common

⇒ 8(2x + 10)

Take 2 as common

⇒ 8 × 2 (x + 5)

⇒ 16 (x + 5)

Hence "The algebraic factor of the given expression 16x + 80 will be 16(x + 5)".

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To reach the break-even point, the publisher should sell 40,000 books.

A break-even point (BEP) is the point where revenues = total cost. Hence, at this point, the company does not gain profit or loss.

On the other hand, total cost is calculated as:

Total cost = fixed cost + variable cost

Where variable cost depends on the number of units produced.

Therefore,

Total cost = fixed cost + number of unit produced x cost per unit

Parameters given in the problem:

fixed cost = h. 400,000

unit cost = h. 35

selling price = h.45 per unit

Let p be the number of books sold. Then,

Revenues = 45 x p

Total cost = 400,000 + 35 x p

At break-even point:

Revenues = total cost

45 x p = 400,000 + 35 x p

10 p = 400,000

p = 40,000

Hence, the break-even point is 40,000 books

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Answer:

1. 95=8x+55  8x=40  x=5  Reason: Since m and n are parallel, and a line traverse through it, they are corresponding angles, meaning that their angle is the same.

2. 200-2x=130  200-130=2x  2x=70  x=35  Reason: The two angles are the same because the "130-degree" angle's corresponding angle is the vertical angle of the "200-2x" angle.

3. Yes, we can use the corresponding angle theorem to prove that m and n are parallel.

4. No, there's not enough information to determine because both given angles are on line m, we need an angle on line n as well.

5. No, the same explanation as 4^^^ Vertical angles do not necessarily prove that two lines are parallel.

6. Yes, we can use the corresponding angles theorem, and then use the vertical angles theorem.

Good luck, and comment on anything you don't understand. I suggest you watch some help videos.

The situation can be represented in a linear equation using a slope-intercept form as y = 2x - 58

A linear equation is an algebraic equation of the form y = mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Data;

We can find the slope of the line using

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the equation

m = 116 - 102 / 87 - 80

m = 2

We can find the y-intercept using any point.

y = mx + c

102 = 2(80) + c

102 = 160 + c

c = -58

The equation in slope-intercept form will be y = 2x - 58

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The cost of materials for the least expensive such container is 245.31 dollars .

Suppose the width of container is x (m),

length of the base of container is 2x (m)

the base area of container is (length × width)sq. m i.e 2x² meter².

Since the volume of container is 10 m³.

the height of container = area of container/ volume of container

height of container= 10/2x² m = 5/x² m

The cost of making such container is cost of base = 2x²*10 = 20x².

cost of sides of container = (2×2x × 5/x² + 2× x × 5/x²)×6 = 180/x

The overall cost is hence the sum of the base and the sides: f(x) = 20x² + 180/x

The get the minimum,

df(x)/dx = 20×(2x - 9/x²) = 0

so 2x = 9/x^2 => 2x = 2.0800 ==> x = 1.651 m

f(x) = 245.31 dollars

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The value of 1.735 to nearest hundred is 1.74.

What is nearest hundredth form?

The second digit following the decimal point is the nearest hundredth.

The last digit of the fractional part of 1.735 should be eliminated if it is less than 5 in order to complete the calculation. and If the fractional part of 1.735 has a last digit that is 5 or more and a second digit that is less than 9, we will add 1 to the second digit of a fractional part and remove the third digit. If the fractional part of 1.735 has a last digit that is 5 or greater, a second digit that is 9, and a first digit that is 9, then you can add 1 to the integer part to make the fractional part 00.

Hence, The hundredth form is 1.74.

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She put decimals incorrectly. The correct product of the decimal numbers is 7.8 and 0.3 will be 2.34.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

Janelle composed 23.4 for the result of 7.8 x 0.3. Utilize number sense to choose if Janelle put the decimal point perfectly located in the item.

Then the multiplication of the numbers 7.8 and 0.3 will be given by putting a cross sign between them. Then we have

⇒ 7.8 x 0.3

⇒ 2.34

She put decimals incorrectly. The correct product of the decimal numbers is 7.8 and 0.3 will be 2.34.

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Answer:

Step-by-step explanation:

let's go back to making 1 loaf.  

1 cup water                                  1*x1

1/4 cup white sugar                 1/4*x2

3/4 teaspoon dry yeast          3/4*x3

1/4 teaspoon salt                     1/4*x4

1/8 cup vegetable oil              1/8*x5

2.5 cup flour                           5/2*x6

now just multiply by 13   :)

13*x1        cups water                 13

13/4*x2  cups white sugar        3.25

39/4*x3 Tspoon dry yeast       9.75

13/4*x4  Tspoon salt                3.25

13/8*x5  cups veggie oil         1.625

65/2*x6 cups flour                  32.5

Answer:

13.12%

Step-by-step explanation:

Answer:

$48,000

Step-by-step explanation:

The sum of the interior angles of a 17-sided polygon is 2700 °.

Given:

sum of the interior angles of a 17-sided polygon.

we know that:

sum of interior angles = n-2 * 180

n = 17

= (17-2)*180

= 15*180

= 2700 °

Therefore the sum of the interior angles of a 17-sided polygon is 2700 °.

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Answer:

2067.5

Step-by-step explanation:

divide each number and when you get to the end add a zero for the decimal.

In statistics, a confidence interval defines the possibility that a population parameter will fall between a set of values for a certain proportion of the time. Analysts commonly incorporate confidence zones that encompass 95% or 99% of the expected data. Thus, if a point estimate of 10.00 is derived using a statistical model with a 95% confidence interval of 9.50 - 10.50, there is a 95% chance that the real value falls within that range.

What is the need for Confidence Intervals?

Confidence intervals are one technique to illustrate how "accurate" an estimate is; the higher the 90% confidence interval for a certain estimate, the more the precaution advised when employing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limitations.

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Answer: 6 zeros

Step-by-step explanation: 30 x 10^5

using P.E.M.D.A.S

you do exponents first

10^5 = 100000

then 100000 x 30 = 3000000

and there is 6 zeros

Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

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Answer:

x = 59/10 aka 5 9/10 or 5.9

Step-by-step explanation:

Answer:

X= 59/10

Step-by-step explanation:

First, we can turn 6 1/2 into a improper fraction (when the numerator is greater than the denominator)

So,

[tex]6\frac{1}{2}[/tex]  

Turns into

[tex]\frac{13}{2}[/tex]

Now we have:

[tex]X+\frac{3}{5} =\frac{13}{2} \\\\[/tex]

Next, we subtract 3/5 from both sides of the equation which equals:

[tex]X =\frac{13}{2}-\frac{3}{5} \\\\[/tex]

Simplify we get:

[tex]X= \frac{59}{10}[/tex]

or X = 5.9

The correct function represented in the table given is y=2x+3.

Given table:

x            y

0           3

1            5

2           7

3           9

Take any two points suppose take (0,3) and (1,5)

slope m = 5 - 3 / 1 - 0

= 2/1

m = 2.

(0,3) passes through y = mx + c

3 = m*0 + c

m value substitute

3 = 2*0 + c

3 = 0+c

c = 3.

y = mx+c

y=2x+3.

Therefore the correct function represented in the table given is y=2x+3.

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Answer:

This can go both ways but out of 124 black women and only 10 selected you have a chance at least one experienced IPV

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are sorta on the right track, but .... ∠3+81°+∠4 =180°

along with 88°+∠1=180°

∠1-92°

I know why  you put 88° for ∠2 but , it's only 88° from a line parallel to that top line,  not the hypotenuse of the triangle.  But good idea, just not able to apply that here.  

you've nicely marked the two parallel lines so we know that ∠3 will math the other 64° angle ,  now you can solve for ∠2

∠1=92° and ∠3=64°  so ∠2 must equal 180-92-64=24°

∠2=24°

now solve for ∠4

180-64-81=∠4

∠4=35°

finally we can get ∠5

180-35-64=∠5

∠5=81°

and , we should have also seen that ∠5 would be the same as the 81° angle above it by ∠3 and ∠4  since those lines are parallel.

Hope that helps :)

The given expression 81x[tex]^2-[/tex] 36 is a multiply of conjugates.

In the given question we have to find expression is a result of multiplying conjugates together, squaring binomials, or neither.

The given expression is 81x[tex]^2-[/tex]36.

If we simplify the expression, then it is written as;

81x[tex]^2-[/tex] 36=(9x)^2-(6)^2

We write it as

81x[tex]^2-[/tex] 36=(9x-6)(9x+6)

It is a multiply of conjugates.

Hence, the given expression 81x[tex]^2-[/tex] 36 is a multiply of conjugates.

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