A study concluded that among people with a certain​ virus, 99.2​% of tests conducted were​ (correctly) positive, while for people without the​ virus, 98.1​% of the tests were​ (correctly) negative. If 29​% of patients actually carry the​ virus, what's the probability that a patient testing negative is truly free of the​ virus?

We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal. AB = 8cm ; BC = 6.5 cm.

We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal.

The formula for calculating the area of a circle is [pi r 2], which we should keep in mind. With respect to a rectangle, there is only one such circle.The Pythagorean theorem states that the diagonal of a rectangle with sides lengths a and b is equal to a2 + b2.

The radius is simply a2+b22 since the diagonal has a diameter.Keep this response on hand.

BC = x- 1.5

x * (x-1.5) = 52

x^2 - 1.5x - 52 = 0

Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25

We are searching only positive value

(1.5 + 14.5)/2 = 16 / 2 = 8 cm

AB = 8 cm

BC = 8 - 1.5 = 6.5 cm

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Therefore, 0.4854 to 0.5546 is the 95% confidence range for the percentage of businesses that are anticipated to need greater employee payments for health insurance coverage in 2009.

A. Computation the margin of error

First step is to calculate the Confidence level using this formula

Confidence level= 1 -α

Where,

α=0.95

Let's enter the formula.

Level of confidence = 1-0.95

Level of confidence = 0.05

The following step is to use this formula to get Z.

Zα/2

Let's enter the formula.

Z= 0.05/2

Z=0.025

Finding the Z score of Z=0.025 is the third stage.

Zα/2=1.96

Let's now use this approach to calculating the margin of error.

Margin of error=Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Margin of error=1.96√0.52(1-0.52)/800

Margin of error=1.96√0.52(0.48)/800

Margin of error=1.96√0.2496/800

Margin of error=1.96√0.000312

Margin of error=0.0346

Therefore Margin of error will be 0.0346

B. Calculating the proportion of businesses anticipated to demand greater employee payments for health insurance coverage in 2009 with a 95% confidence interval

computation for the confidence interval's outer limits

p- Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52-1.96√0.52(1-0.52)/800

Confidence interval=0.52-1.96√0.52(0.48)/800

Confidence interval=0.52-1.96√0.2496/800

Confidence interval=-0.52-1.96√0.000312

Confidence interval=0.4854

Computation for the boundaries of confidence interval

Using this formula

p+ Zα/2√p(1-p)/n

Where,

Zα/2=1.96

p=0.52

n=800

Let plug in the formula

Confidence interval=0.52+1.96√0.52(1-0.52)/800

Confidence interval=0.52+1.96√0.52(0.48)/800

Confidence interval=0.52+1.96√0.2496/800

Confidence interval=-0.52+1.96√0.000312

Confidence interval=0.5546

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Yes , a right triangle with the given sides 6 cm 10 cm and 8cm can be formed because the sides satisfies the Pythagoras Theorem .

According to Pythagoras Theorem , the square of the hypotnuse of triangle is equal to the square of the other two sides of triangle ;

The sides of the triangle are given as : 6cm ,10cm and 8cm ;

which means that ,

the hypotnuse is = 10 cm ;

According to Pythagoras Theorem ;

⇒ [tex]10^{2} =8^{2} +6^{2}[/tex] ;

⇒ [tex]100 = 64 + 36[/tex] ;

⇒ [tex]100= 100[/tex] ;

the side satisfies the condition to form  the right triangle .

Therefore , the given sides forms a Right Triangle .

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Answer:

22.6%.

Step-by-step explanation:

To calculate the percent error of a measurement, you can use the following formula:

Percent Error = (|measured value - actual value| / actual value) x 100%

Plugging in the values from the problem:

Percent Error = (|4.1 inches - 5.3 inches| / 5.3 inches) x 100% = (1.2 inches / 5.3 inches) x 100% = 0.226 x 100% = 22.6%

To the nearest tenth of a percent, the percent error is 22.6%.

Answer: [tex]90^{\circ}[/tex]

Step-by-step explanation:

By the converse of the alternate interior angles theorem, we need [tex]\angle CBA \cong \angle BAD[/tex].

The per cent of change for the volume of water inside the aquarium is 93.5.

An aquarium carries 8.6 cubic feet of water.

The aquarium is loaded up further to hold 9.2 cubic feet of water.

We have to find the per cent of change for the volume of water inside the aquarium.

A ratio or value that may be stated as a fraction of 100 is a percentage. If we calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The per cent of change for the volume of water inside the aquarium = Water holds by aquarium/Further filled water × 100

The per cent of change for the volume of water inside the aquarium = (8.6/9.2) × 100

The per cent of change for the volume of water inside the aquarium = 93.5%.

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Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

What is the combination?

In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.

If none of the numbers can be repeated, Joaquin can choose from a total of 22 numbers (0 through 21), and he needs to select three of them for his locker combination. This is a classic example of a combination problem, as the order in which he chooses the numbers does not matter. The number of ways to choose three numbers from a set of 22 without repetition is given by the formula for combinations:

C(22,3) = 22! / (3!(22-3)!) = 222120/(321) = 2310

So, Joaquin can choose from 2310 different locker combinations if none of the numbers can be repeated.

The name "combination lock" is appropriate because it refers to the process of combining numbers in a specific order to open the lock. In this case, the order of the numbers selected does not matter.

If Joaquin could repeat a number, but not use the same number twice in a row, the number of mathematical combinations are possible is given by the formula for permutations:

A(22,3) = 222120 = 9, 612

Hence, Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

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Answer:

0.3

Step-by-step explanation:

Were you asking for 5% of 6? Because then you would just multiply 6 by 0.05 (because percents are always out of 100%, so converted to decimal it is out of 1) and then get 0.3

Answer: The percentage of 6 by 5 (i.e. 6:5) is 120

Step-by-step explanation:

Given: 6 by 5 i.e. 6/5

Solution: (value/ total value)* 100

hence, (6/5)*100

=1.2*100

=120.

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The people who are interviewed constitute a convenience sample.

If the survey company is interviewing anyone who is available in the shopping mall without using any systematic method for selecting the participants, it would be considered a convenience sample.

In a convenience sample, the sample is selected based on ease of access to the participants, and it may not be representative of the entire population. This type of sampling can lead to bias in the sample, as the views of people who happen to be available in the mall at the time may not be representative of the views of the entire population.

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It is solved using the concept of z-table. Correct option is: (E)

The difference from the mean is expressed as a z-score in standard deviation units. It is not clear either one agree or disagree with the null hypothesis. The likelihood that a point as severe as their statistic would be seen that under null hypothesis is known as the p-value.

A z-table, sometimes referred to as the standard normal table, gives the area beneath the curve to the left of a z-score. This region indicates the likelihood that z-values will fall inside a particular area of the standard normal distribution.

Here, we have to calculate the confidence interval for determine the population interval.

Now, P₁ - P₂, this is the difference between the two population proportion.

thus, option (E) is the correct answer.

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The complete question is as follows:

The total area of the two triangles is 28 square inches.

Step 1: Calculate the area of the first triangle.

The first triangle is a right triangle with a base of 4 inches and a height of 3 inches.

Area of a triangle = (1/2) * Base * Height

Area of the first triangle = (1/2) * 4 * 3 = 6 square inches.

Step 2: Calculate the area of the second triangle.

The second triangle is an isosceles triangle with a base of 4 inches and a height of 4 inches.

Area of a triangle = (1/2) * Base * Height

Area of the second triangle = (1/2) * 4 * 4 = 8 square inches.

Step 3: Add the areas of the two triangles.

Total area = 6 + 8 = 14 square inches.

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Answer:

9261

Step-by-step explanation:

[tex](-3-2(-12))^3=(-3+24)^3=21^3=441(21)=9261[/tex]

The right option is Option C: y = 5x + 1

The given line passes through the points (5,0) and (0,1).

The slope of the line is found by:

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

This implies that,

[tex]m = \frac{1-0}{0-5} \\m = \frac{-1}{5}[/tex]

The product of the slope of the two perpendicular lines should be negative one.

Thus,

[tex]m_{1} * m_{2} = -1[/tex]

This implies that,

[tex]\frac{-1}{5} * m_{2} = -1[/tex]

Giving us, m2 = 5

We can use the slope intercept formula,

y = mx + b

where b = 1 is the y-value of the y-intercept.

The equation thus becomes,

y = 5x + 1

Therefore, the right option is Option C: y = 5x + 1

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To create a model to represent (a+b), you could use a mathematical equation such as y = a + b.

Using mathematical concepts and terminology, a mathematical model is an abstract description of a concrete system. To make a forecast or offer insight, mathematical modeling is the act of generating a mathematical representation of a real-world phenomenon.

An equation set and a set of variables that define relationships between the variables make up a mathematical model, which often explains a system. There are numerous types of variables, including texts, boolean values, real or integer numbers, and more.

In this case, the equation y = a + b can be used. This equation represents a linear model where y is the dependent variable and a and b are the independent variables.

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Answer: Ratios are proportional if they represent the same relationship.

Step-by-step explanation:

One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

The cost of a 3.4 mile ride when a taxi charges a base fee of $3.00 and $0.15 for every mile of the ride is $3.51.

Therefore the answer is $3.51

The cost of a 3.4 mile ride can be calculated by multiplying the distance of the ride by the cost per mile and adding the base fee. Here base fee is the fixed charge and $0.15 is the variable charge that depend on distance covered.

To calculate the cost of the ride:

= (3.4 miles * $0.15 per mile) + $3.00 base fee

= $0.51 + $3.00

= $3.51

So, a 3.4 mile ride would cost $3.51.

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Answer:

y^2 + 5y - 750 = 0

y(y + 5) = 750

750 - y(y - 5) = 0

Step-by-step explanation:

Phelan now has 81.48 x 1.08 = 87.79 US dollars, which is 87.79 dollars of the original 250 dollars.

First, we need to find out how many euros Phelan has left after spending 150 euros on his trip.

We are taking the exchange rate of 1 euro = 1.08 USD

He started with 250 US dollars, which he exchanged for 250 / 1.08 = 231.48 euros.

After spending 150 euros, he has 231.48 - 150 = 81.48 euros left.

To convert the euros back to US dollars, we need to multiply the number of euros by the exchange rate (1 US dollar = 1.08 euros)

So, Phelan now has 81.48 x 1.08 = 87.79 US dollars, which is 87.79 dollars of the original 250 dollars.

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Answer:

yes a rational number

Step-by-step explanation:

a rational number has the form

[tex]\frac{a}{b}[/tex] with a and b integers

[tex]\frac{7}{11}[/tex] is in this form and is therefore a rational number

Answer:

it is you just find the total of the 29 mgs

If Last year, Christine had $20,000 to invest. The amount that she invest in each account is First account $16,000 and Second account: $4,000.

Let x represent the amount Christine invested in an account that paid 8% interest

Let y represent  the amount Christine invested in an account that paid 10% interest

x + y = 20,000    

.8x + .010y = 1920

Multiply each sides of this equation by 100 to  remove  the decimal points.

8x + 10y = 192,000

8(20,000-y) + 10y = 192,000

160,000 - 8y + 10y = 192,000

2y = 32,000

y = 32,000/2

y = $16,000

So,

x = 20,000 - 16,000

x = $4000

Therefore the First account is $16,000 and Second account is $4,000.

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A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need.

One possible solution to the problem of food insecurity is to start a food pantry. A food pantry is a place where people can donate non-perishable food items for those in need. These items can include canned goods, boxed goods, and non-perishable items. People can then come to the pantry and take what they need. This helps to ensure that people in the community have access to the food they need.

A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need. People can come to the pantry and take what they need, providing access to food for those in the community.

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Grade 7 maths includes integers, shapes, and symmetry etc. that is incorporated with the earlier study of previous grades.

Grade 7 math covers many topics, including: number sense and operations, geometry, data analysis, probability and statistics, expressions and equations, and problem solving. Number sense and operations involves understanding the properties of integers, rational numbers, and real numbers, and how to use them in operations and equations. Geometry focuses on understanding the properties of shapes and angles, and how to measure, construct, and classify them. Data analysis involves collecting, organizing, and interpreting data, as well as understanding the concept of probability. Expressions and equations involves solving equations and manipulating algebraic expressions. Finally, problem solving involves using the knowledge from all of the topics to solve real-world problems. Grade 7 math builds on the fundamentals learned in earlier grades, and is essential for success in math classes in the future.

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Equating the total costs of the two rental companies, they would cost the same amount after 625 driving miles.

An equation is a mathematical statement that claims that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to depict the equality of the expressions.

                                  Company A    Company B

Fixed rental charge         $75                 $100

Rental charge per mile  $0.07              $0.03

Let the number of miles driven = m

Total cost of Company A's rental = 75 + 0.07m

Total cost of Company B's rental = 100 + 0.03m

For the cost to be the same, 75 + 0.07m = 100 + 0.03m.

Solving for m:

75 + 0.07m = 100 + 0.03m

0.07m - 0.03m = 100 - 75

0.04m = 25

m = 625

Thus, for the two car companies' rental cost to be the same amount, one would rent a car for 625 miles.

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Step-by-step explanation:

what is the question ?

solve for x and y ?

multiply the second equation by 3 and add that result to the first equation. then solve for x. then pick any original equation and solve for y.

-2x - 3y = 8

15x + 3y = 18

-----------------------

13x 0 = 26

x = 26/13 = 2

5×2 + y = 6

10 + y = 6

y = -4

On solving the provided question we can say that so the value of triangle - y + Z = 1+ r = > 1 -r +

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

in triangle

by construction = y0 = r - 1

Pythagoras =  x² + y²

=> (1+r)² = x

=>  x = √(1+r)² - (1-r)²

Pythagoras  = x² + z² = 2²

=> z =√4-4r

so the value of triangle -

=> y + Z = 1+ r

=> 1 -r + 2√1 -r1 =  

=> r = -1 + √5/2

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The complete question is "In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown."

The value of x in the similar triangles is 40.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangles are similar.

That means,

the corresponding sides are in the proportion to each other.

That means,

(x + 8)/x = 12/10

10x + 80 = 12x

2x = 80

x = 40

Therefore, the value of x is 40.

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(a) A system of two equations, x=2 and y=3, is needed to express (2,3) in R2. (b) No, only two equations can express (2,3) in R2. (c) The maximum number of distinct equations that can be added is three. (d) Yes, the general form for the equations is x-2=0, y-3=0, and z=0.

(a) The smallest number of equations you would need is two. The system of linear equations would be:

x + 2y = 6

2x + 4y = 12

(b) Yes, you can add one more equation to the system in (a) so that the new system still has the unique solution (2,3). The equation would be:

3x + 6y = 18

(c) The maximum number of distinct equations you can add to your system in (a) to still maintain the unique solution (2,3) is three. The equations would be:

x + 2y = 6

2x + 4y = 12

3x + 6y = 18

(d) Yes, there is a general form for the equations in (c). The general form is:

ax + by = c, where a, b, and c are constants.

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The probability that a randomly selected participant dreams in black and white or color is 0.01

The probability that a randomly selected participant dreams in black and white or color is the sum of the probabilities of the individual events (dreaming in black and white or dreaming in color) and the probability of the intersection of the two events (dreaming in both black and white and color).

The probability of dreaming in black and white is the number of participants who dream in black and white divided by the total number of participants surveyed:

P(b) = 4/200

The probability of dreaming in color is the number of participants who dream in color divided by the total number of participants surveyed:

P(c) = 10/200

The probability of dreaming in both black and white and color is the number of participants who dream in both black and white and color divided by the total number of participants surveyed:

P(b ∩ c) = 12/200

The probability of dreaming in black and white or color is the sum of the individual probabilities and the intersection probability:

P(b ∪ c) = P(b) + P(c) - P(b ∩ c) = 4/200 + 10/200 - 12/200 = 2/200 = 1/100

The probability that a randomly selected participant dreams in black and white or color is 1/100.

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