Consider a medical test that is used to detect a disease that 0.6% of the population has. If a person is infected, the test has a 96% chance of detecting the disease. However, in 0.2% of cases, the test will give a false positive result. Suppose that a patient tests positive for the disease, what is the probability of the patient actually being infected? Round your answer to 3 decimal places. P(Patient is infected | Test is positive) = .....

The area of each pizza and cost per inch is $12.82 per square inches and $11.304 per square inches respectively.

Large:

Diameter = 14 inches

Radius, r = 14 / 2

= 7 inches

Area = πr²

= 3.14 × 7²

= 3.14 × 49

= 153.86 square inches

Cost per inch = 153.86 square inches / 12

= 12.8216666666666

Approximately, $12.82 per square inches

Medium:

Diameter = 12 inches

Radius, r = 12/2

= 6 inches

Area = πr²

= 3.14 × 6²

= 3.14 × 36

= 113.04 square inches

Cost per inch = 113.04 square inches / 10

= $11.304 per square inches

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If a = 2b and b is 14% of c, then a is 28% of c.

This means that a is 28% of the total value of c.

Let's break down the given information step by step to determine the relationship between a, b, and c and find the percentage of a in relation to c.

Given:

a = 2b

b = 14% of c

We can substitute the value of b from the second equation into the first equation to express a solely in terms of c:

a = 2(14% of c)

a = 2(0.14c)

a = 0.28c

Now we have expressed a in terms of c.

To find the percentage of a in relation to c, we can calculate the ratio of a to c and multiply by 100 to express it as a percentage:

Percentage of a in relation to c = (a / c) * 100

Percentage of a in relation to c = (0.28c / c) * 100

Percentage of a in relation to c = 0.28 * 100

Percentage of a in relation to c = 28%

Therefore, a is 28% of c.

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Answer:

= 1424.775 in ^3

Step-by-step explanation:

we need 27 ounces of the 11% alcohol solution and 9 ounces of the 23% alcohol solution to obtain 36 ounces of a 14% solution.

Let x be the number of ounces of the 11% alcohol solution, and y be the number of ounces of the 23% alcohol solution. Then we have:

x + y = 36 (total amount of solution)

0.11x + 0.23y = 0.14(36) (total amount of alcohol)

Simplifying the second equation, we get:

0.11x + 0.23y = 5.04

Multiplying the first equation by 0.11 and subtracting from the second equation, we get:

0.12y = 1.08

y = 9

Substituting y = 9 into the first equation, we get:

x + 9 = 36

x = 27

what is numbers?

In mathematics, numbers are abstract concepts used for counting, measuring, and comparing quantities. There are several types of numbers, including natural numbers, integers, rational numbers, irrational numbers, and real numbers. Numbers are used in various mathematical operations, such as addition, subtraction, multiplication, and division, and are a fundamental concept in mathematics.

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Answer:

I belive its C not 100%

Step-by-step explanation:

Responder:

27 de enero

Horas de visita al abuelo antes de que coincida el horario = 1 vez

Horas de visita a Sofía antes de que coincida el horario = 2 veces

Explicación paso a paso:

Para obtener la hora en la que coincidirá su visita, obtenemos la L. C. M de 12 y 8

Abuelos (cada 12 días)

12:12, 24, 36, 48, 60, ...

Sofia (cada 8 días)

8: 8, 16, 24, 32, 40, ....

El mínimo común múltiplo de 12 y 8 es 24.

De ahí que su encuentro vuelva a coincidir a los 24 días.

3 de enero + 24 días = 27 de enero

Horas de visita al abuelo antes de que coincida el horario = 1 vez

Horas de visita a Sofía antes de que coincida el horario = 2 veces

Answer:

12x + 8

Step-by-step explanation:

Distribute -6 to the parentheses:

-6(-2x - 1) + 2

12x + 6 + 2

Add like terms:

12x + 8

So, the simplified expression is 12x + 8

Answer:

8 inches

Step-by-step explanation:

Nacho cheese

v= Pi×radius×2×height

v = 3.14×8×2×4 = 200.96

jalapeño

3.14×4×2=25.12

200.96÷25.12=8

the height is 8

to check your work you can do

(multiply by 8 and see if it equals 200.96)

3.14×4×2×8 = 200.96

since the volume is the same as the volume for nacho cheese we can say that 8 inches for height is correct

The volume that the rest of the items in the box takes up is 212,112 in³.

Volume refers to the space within a three-dimension object.

Volume, which is measured by the object's dimensions (length, width, and height), is also called the capacity of the object.

The product of the object's length, width, and height is known as volume or capacity.

To compute the volume occupied by the remaining items, we first compute the volume occupied by the computer, which is then subtracted from the total capacity of the box.

Width = 9 in

Length = 18 in

Height = 24 in.

Volume of the computer = 3,888 in³ (9 x 18 x 24)

The volume for the rest of the items in the box = 212,112 in³ (216,000 - 3,888).

Thus, Jessenia's other items in the box take up a volume of 212,112 in³.

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Assume that the box has a full capacity of 216,000 in³.

Answer:

sin 61 degrees = x/55

55 * sin 61 degrees = x

x is approximately 48.1 if I did the math right

Step-by-step explanation:

hope it helps! gl

It has proved that the equation \(e^{(x)} * (dy/dx) = y * e^{(x)} * (dy/dx)\) is linear and the equation \((dy/dx) + x^2 * e^{(x)} * y = e^{(x)}\) is not linear.

The equation \(e^{(x)} * (dy/dx) = y * e^{(x)} * (dy/dx)\) is linear because it can be written in the standard form of a linear first-order ordinary differential equation, which is:
dy/dx + P(x) * y = Q(x)

In this case, we can divide both sides of the equation by \(e^{(x)}\) to obtain:
dy/dx = y * (dy/dx)

Now, we can compare this to the standard form and observe that P(x) = 0 and Q(x) = y * (dy/dx).

Since the equation is in the standard form, it is linear.

On the other hand, the equation \((dy/dx) + x^2 * e^{(x)} * y = e^{(x)}\) is not linear.

While it may seem similar to the standard linear form, the presence of the \(x^2 * e^{(x)} * y\) term is what makes it non-linear.

In a linear equation, the term involving y should be of the form P(x) * y, where P(x) is a function of x only.

However, in this case, the term \(x^2 * e^{(x)} * y\) involves both x and y, making the equation non-linear.

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A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Answer:

Years: 25 years .

step-by-step explanation:

Tobias' grandfather had left $2,000 in an account for college. The account earned 6% simple interest and accumulated $3,000 in interest. To determine how many years the money was left in the account, we can use the formula I = Prt, where I is the interest earned, P is the principal (initial amount), r is the interest rate, and t is the time in years. Substituting the given values, we get 3,000 = 2,000 x 0.06 x t. Solving for t gives us 25 years, which means the money was left in the account for 25 years.

Answer:

25 i think

Step-by-step explanation:

I sure It's 25 doing the caculations.

The temperature at the river is 77°F.

Given that the temperature at Grand Canyon is 84°F. We need to find the temperature at given locations, assuming the air is stable and not rising on a given day.

The change in temperature due to the increase in altitude is given by the formula:

T₂ = T₁ - (a × h)

Where,T₁ = Temperature at lower altitude

T₂ = Temperature at higher altitude

a = Lapse rate

h = Altitude

The lapse rate can be taken as 3.5°F per 1,000 ft.

1. At the canyon rim, the altitude is 7,000 ft.

Altitude, h₁ = 7,000 ft

Lapse rate, a = 3.5°F per 1,000 ft

Temperature at canyon rim is:

T₂ = T₁ - (a × h)

T₂ = 84°F - (3.5°F/1,000 ft × 7,000 ft)

T₂ = 84°F - 24.5°F

= 59.5°F

Therefore, the temperature at the canyon rim is 59.5°F.

2. At the river, the altitude is 2,000 ft.

Altitude, h₂ = 2,000 ft

Lapse rate, a = 3.5°F per 1,000 ft

Temperature at the river is:

T₂ = T₁ - (a × h)

T₂ = 84°F - (3.5°F/1,000 ft × 2,000 ft)

T₂ = 84°F - 7°F

= 77°F

Therefore, the temperature at the river is 77°F.

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Answer:

5,000,000

Step-by-step explanation:

10 x 10 x 10 x 10 x 10 x 10 = 1,000,000

1,000,000 x 5 = 5,000,000

Answer:

5 Mg

Step-by-step explanation:

The metric prefix associated with \(10^{6}\) is Mega (M).

This can be written as 5 Mg.

Answer:

Step-by-step explanation:

m<2= 69 degrees

m<1 and m<3 = 21 degrees

Answer:

A quadrilateral is a four-sided closed figure with interior angles that add up to 360 degrees. Some common types of quadrilaterals are:

Parallelogram: A quadrilateral with both pairs of opposite sides parallel21.

Trapezoid: A quadrilateral with at least one pair of opposite sides parallel.

Rhombus: A quadrilateral with all four sides congruent and both pairs of opposite sides parallel.

Rectangle: A quadrilateral with four right angles and both pairs of opposite sides parallel.

Square: A quadrilateral with four right angles and all four sides congruent.

Kite: A quadrilateral with two pairs of congruent and adjacent sides1.

Using these definitions, the names of the quadrilaterals in the activity are:

Quadrilateral MATH with no sides are equal.

Name: Scalene quadrilateral (a quadrilateral with no congruent sides or angles).

Quadrilateral HOPE with both pairs of opposite sides are parallel.

Name: Parallelogram.

Quadrilateral LOVE with four right angles.

Name: Rectangle.

Quadrilateral CARE with all four sides congruent.

Name: Rhombus.

Quadrilateral MADE with all four sides congruent and with four right angles.

Name: Square.

Quadrilateral KITE with two pairs of congruent and adjacent sides.

Name: Kite.

Quadrilateral LIKE with exactly one pair of opposite sides parallel.

Name: Trapezoid.

Step-by-step explanation:

Given both triangles are equal by SAS congruency rule.

Let's call the two triangles Triangle ABC and Triangle DEF, where AB and DE are the hypotenuses.

If the two triangles have the same angles, then they are similar. However, being similar does not necessarily mean that they are congruent.

To prove that the two triangles are congruent, we need to show that they have the same angles and the same side lengths. In this case, we cannot determine whether the two triangles are congruent or not without further information.

But we have given that corresponding sides are equal.

So By SAS congruence rule

both triangles are congruent.

Thus, given both triangles are equal by SAS congruency rule.

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Answer:

\(\sf\longmapsto\sf\boxed {x = 1}\)

Step-by-step explanation:

\(\sf\longmapsto \: 2x + 10 = 12\)

\(\sf\longmapsto \: \: 2x + 10 - 10 = 12 - 10\)

\(\sf\longmapsto \: 2x = 2\)

\(\sf\longmapsto \: \frac{2x}{2} = \frac{2}{2} \)

\(\sf\longmapsto \: x = 1\)

Answer:

\(\boxed {\sf x=1}\)

Step-by-step explanation:

\(\sf 2x+10=12\)

\(\boxed{\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}}\)

\(\boxed{\mathrm{Divide\:both\:sides\:by\:}2}\)

\(\boxed{\sf Hope\: it\:helps!}\)

Answer:

A. segments RS ST RT. I CANT PUT THOSE DASHES KN TOP. THE ANSWER IS A

Answer:

\(82.8571428571\) %

Solution:

\(70*x/100=12\)

\(x/100=12/70\)

\(70x=1200\)

\(x=1200/70\)

\(x=17.1428571429\)

\(100-17.1428571429=82.8571428571\)

Answer: 2 hours and 35 minutes. Aka 2:35

Step-by-step explanation: to find when it starts and ends, subtract 6:35pm by 9:10pm

So 9-6 is 3 and there is a problem when you do 10-35. 35 is bigger which means you have to take away an hour so the 3 becomes a 2 and then you add 60 onto the 10 even though the limit is 60 minutes because it equals an hour. So you now have 2 hours and 70 minutes - 35. Well that is 35 because 35+35 = 70 meaning the movie is 2 hours, 35minutes

So, approximately, the main entrance and the kitchen are 4.47 yards apart by distance equation.

The distance formula is used to calculate the distance between two points in a coordinate plane. The formula is based on the Pythagorean theorem and involves finding the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates of the two points.

In this case, we are given two points: (-9, 8) and (-5, 6). To find the distance between these two points, we can plug the coordinates into the distance formula, which gives us:

distance = √[(x2 - x1)² + (y2 - y1)²]

where x1 and y1 are the coordinates of the first point and x2 and y2 are the coordinates of the second point.

Plugging in the given coordinates, we get:

distance = √[(-5 - (-9))² + (6 - 8)²]

which simplifies to:

distance = √[4² + (-2)²]

The square of 4 is 16, and the square of -2 is also 4 (since the negative sign is squared away), so we can simplify further:

distance = √[16 + 4]

distance = √[20]

Finally, we take the square root of 20 to get the distance:

distance ≈ 4.47 yards.

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Answer:

y = - 2x + 20

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute (7, 6 ) into the partial equation

6 = - 14 + c ⇒ c = 6 + 14 = 20

y = - 2x + 20 ← equation of line

Answer:

y = - 2x + 20

Step-by-step explanation:

I payed attention in my class so I know :)

Answer:

9\(x^{2}\)

Step-by-step explanation:

The area of a parallelogram is equal to the base times the height.

The base is 3x and the height is also 3x so the area will equal

3x × 3x

When you multiply variables you multiply the coefficients and add the exponents so when you multiply 3x and 3x you multiply 3 and 3 and the exponents 1 and 1 so you get 9\(x^{2}\)  

The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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a) The probability that no defective component will be chosen when selecting 5 components at random is approximately 0.7738, or 77.38%.

b) The probability that exactly 2 out of the 5 components will be defective is approximately 0.0874, or 8.74%.

a) To calculate the probability that no defective component will be chosen when selecting 5 components at random, we need to determine the probability of selecting a non-defective component for each selection.

Since 5% of the components are faulty, the probability of selecting a non-defective component in each selection is 1 - 0.05 = 0.95.

The probability of selecting no defective components can be calculated using the multiplication rule for independent events. We multiply the probabilities of each selection being non-defective:

Probability of selecting no defective components = (0.95)⁵

Probability of selecting no defective components = 0.7738

b) To calculate the probability that exactly 2 out of the 5 components will be defective, we need to consider the different combinations of selecting 2 defective components out of 5.

The probability of selecting exactly 2 defective components can be calculated using the binomial probability formula:

Probability = (Number of ways to choose 2 defective components) * (Probability of selecting a defective component)^(Number of defective components) * (Probability of selecting a non-defective component)^(Number of non-defective components)

Probability = (5 choose 2) * (0.05)² * (0.95)³

Probability = (5! / (2! * (5-2)!)) * (0.05)² * (0.95)³

Probability = 0.0874

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