In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were correctly positive, while for people without HIV, 98.5% of tests conducted were correctly negative. A clinic serving an at-risk population offers free HIV testing, believing that 15% of the patients may actually carry HIV. What's the probability that a patient testing negative is truly free of HIV?

If we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)

In this question, we have been given a formula V=πh^(r-h/3)

We need to make r the subject formula

This means we need to rewrite formula for r.

V = πh^(r-h/3)

h^(r-h/3) = V/ π

r - h/3 = log_h(V/π)

r = log_h(V/π) + (h/3)

Therefore, if we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)

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Answer:

6 x 10^18

Step-by-step explanation:

3  x 2 = 6

10^9 * 10^9 = 10^(9+9) = 10^18

Answer:

It costs 32.75 for five pounds. and the expression would be p7.25-3.50

Step-by-step explanation:

5*7.25 = 36. 25. 36.25-3.50=32.75

c=p7.25-3.50 would be the expression. :)

Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Given,

Two planes intersected by a third plane are parallel.

Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.

A line is formed by the intersection of two planes. The planes are parallel if they do not intersect. Due to the endless nature of planes, they cannot meet at a single place. Stack a hardcover book on your desk and open the two hard covers at any random angle. The coverings' planes are not parallel to one another but are individually perpendicular to the desk top (or necessarily perpendicular to each other).

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Answer:

t = (x - μ) / SE. where x is the sample mean, μ is the hypothesized population mean in the null hypothesis, and SE is the standard error. P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic.

Step-by-step explanation:

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The mean in hypothesis testing is the parent population from which the samples are drawn.

In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population parameter. The analyst's methodology is determined by the nature of the data and the purpose of the analysis. Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis.

Hypothesis testing is a type of statistical inference that employs sample data to draw conclusions about a population parameter or probability distribution. First, an educated guess is made about the parameter or distribution.

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The angles of the given figure are:

∠1 = 128°

∠2 = 52°

∠3 = 47°

∠4 = ∠5  = 81°

What are corresponding angles?

The angle is supplementary(∠5)

52° + ∠5 + 47° = 180°

∠5 + 99° = 180°°

∠5  = 180° - 99°

∠5  = 81°

Then the  ∠1 and 52° are supplementary (Interior adjacent angles)

∠1 + 52° = 180°

∠1 = 180° - 52°

∠1 = 128°

Now,  ∠2

∠2 +  ∠5  + 47° = 180°

∠2 + 81° + 47° = 180°

∠2 = 180° - 128°

∠2 = 52°

Based on interior opposite angles are equal. Then

∠5 =  ∠4 and ∠3 = 47°

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Answer: 2z+2

Step-by-step explanation:

The height of the two trees will be same after 13 years and the height of the trees will be 24 feet.

According to the question,

We have the following information:

One tree, a ficus, was 6 feet tall when it. was planted and has grown 1.5 feet per year. The other tree, an oak, was grown from an acorn on the ground and has grown 2 feet per year.

So, for first tree, we have:

6, 7.5, 9, ...

Now, this is an arithmetic progression.

So, for the second tree, we have:

0,2,4, ...

Now, this is again an arithmetic progression.

Formula to find nth term of an A.P.:

an = a+(n-1)d where a is the first term and d is the common difference

6+(n-1)1.5 = 0+(n-1)2

6+1.5n-1.5 = 0+2n-2

4.5 = 2n-1.5n-2

6.5 = 0.5n

n = 13 years

Now, we have the height of the trees after 13 years:

an = 0+(13-1)2

an = 12*2

an = 24 feet

Hence, the height of the two trees will be same after 13 years and the height of the trees will be 24 feet.

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When a transversal crosses a pair of parallel lines same side interior angle pair are supplementary.

What is parallel lines?
Two lines in same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both lateral and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks. Different shapes' sides run parallel to one another. The single arrow lines in the rectangle below are parallel to one another, and the double arrow lines also are parallel to one another.

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The missing terms of the arithmetic sequence -13, - 6,  1 , 8 , 15,  22.

an = a1, a2, a3, a4, a5, a6

formula for nth term is :

an = a + (n - 1)d

where

an = last term

a = a1 = first term

n = number of terms

d = difference between two terms

here

a2 = a + d

- 6 = a + d    ....(1)

a5 = a + 4d

15 = a + 4d      .......(2)

on solving equation we get :

- 6 = a   +    d    ....(1)

15 =  a    +    4d      .......(2)

(-)    (-)      (-)

- 21 =  - 3d

d = 21/3

d = 7

using the value of d in equation the value of a is :

- 6 = a + d  

-6  = a + 7

a = -6 -7 = -13

then

a1 = a = -13

a2 = a + d  = -13 + 7 = -6

a3 = a + 2d  = -13 +2 x 7 = 1

a4 = a + 3d =  -13 + 3 x 7 = 8

a5 = a + 4d =  -13 +4 x 7 = 15

a6 = a + 5d = -13 +5 x 7 = 22

The missing terms of the arithmetic sequence -13, - 6,  1 , 8 , 15,  22.

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Answer:

  3 -n/2 ≤ 5

Step-by-step explanation:

You want a math expression that means "half a number less than 3 is at most 5."

We can let "n" represent "a number." Then "half a number" is (1/2)n or n/2.

That amount "less than 3" means it is subtracted from 3:

  3 -n/2 . . . . . . half a number less than 3

The wording "is at most" means "is less than or equal to." In symbols, the words mean ...

  3 -n/2 ≤ 5

__

Additional comment

Often 'x' is used to represent an unknown quantity. We like 'n' for "a number" because it is mnemonic, and because the numbers of interest are often integers or natural numbers from the set represented by ℕ.

English expressions of math relations are often ambiguous. In this case, we're not completely sure that the intention is not "half (a number less than 3)", which would be (3 -n)/2. Usually, we fall back on the Order of Operations, which requires that multiplication be done before addition. That is "half a number" must be computed before "less than 3" is evaluated, hence 3 -n/2.

Answer: p = -2/3, sum = 0

Step-by-step explanation:

Additive inverse has the name numerical value as the given number but has the opposite sign so when they are added together they equal zero. The sum of any number and its additive inverse equal 0.

EX: 1 and -1      

1+ (-1) = 0

EX: -4.5 and 4.5

-4.5 + 4.5 = 0

The geometric relationship sum of ∠A+∠B = 90° as they are complementary.

What is are complementary?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

They are referred to as complementary angles when the sum of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.

It is given that angle A and angle B are complementary.

Hence, The geometric relationship sum of ∠A+∠B = 90°

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Answer:

11.0 cm

Step-by-step explanation:

Answer:

11.8 cm

Step-by-step explanation:

2.5 + 5 + 2.5√3 = 7.5 + 2.5√3 = 11.8 cm

The gas bill exceeded $87 from last month to this month.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, The Haddad expected the automatic withdrawal of their gas bill to

be more than last month's bill of $215.85 but did not know by how much.

Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.

∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.

Haddads' present balance is $555.82,

∴ The gas bill is $(858.69 - 555.82) = $302.87.

So the gas bill s exceeded by $(302.87 - 215.85) = $87.

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Answer:

x=7y+x

Step-by-step explanation:

Isolate x on one side

x-7y=8

 +7y.  +7y

x=7y+8

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The velocity experimented by the car is equal to - 1 feet per second.

Herein we have the graph of the position of the car (y), in feet, versus time (t), in seconds. The graph shows a linear equation, that is, the position is described by a polynomial of the form:

y = m · t + b

Then, the functions for the velocity and acceleration are shown below:

Velocity

dy / dt = m

The slope represents the velocity of the car.

Acceleration

d²y / dt² = 0

Then, the velocity of the car is found by means of the secant line formula:

dy / dt = (0 ft - 10 ft) / (10 s - 0 s)

dy / dt = - 1 ft / s

The velocity of the car is - 1 feet per second.

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Answer:23000

Step-by-step explanation:

The principal amount​ is ₹20000.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Let the money at beginning of the year 2005, a person invests in a bank be x.

At the beginning of 2010, the accumulated interest was ₹10000.

Now, x(1+r/100)⁵=x+10000 ------(I)

Let x(1+r/100)⁵=A

At the beginning of 2015, the accumulated interest became ₹25000.

So, x(1+r/100)¹⁰=x+25000 ------(II)

From the equation (I),

x(A-1)=10000 ------(III)

From equation (II), we get

x×A²=x+25000

x(A²-1)=25000 ------(IV)

From equation (III) and (IV), we get

10000(A+1)=25000

A=1.5

Put A=1.5 in equation (III), we get

0.5x=10000

x=10000/0.5

x=₹20000

Therefore, the principal amount​ is ₹20000.

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Answer:

3000/17281 mm

Step-by-step explanation:

We can model this as a cylinder with a volume of 66 mm³, a radius of 11 mm, and an unknown height [tex]h[/tex] mm.

Using the formula for the volume of a cylinder,

[tex]V=\pi r^2 h \\ \\ 66=11^2 \pi h \\ \\ h=\frac{66}{121\pi} \\ \\ h=\frac{6}{11\pi} \\ \\ h \approx \frac{6}{11(3.142)} \\ \\ h \approx 3000/17281[/tex]

Answer:

0.17 (2d.p)

Step-by-step explanation:

volume of cylinder= πr^2Xh

22/2=11 which is radius

11^2=121

121X3.142=380.182

380.182Xh=66

h=66/380.182=0.1736010648

The area of the circle is 25.12 unit² and the circumference is 17.75 units.

The space a circle takes up on a two-dimensional plane is known as the area of the circle. The region included by the circle's radius or perimeter is another way to define the circle's area.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant π.

The given points of radius are

(x₁, y₁) = (2, 3)

(x₂, y₂) = (4, 1)

The formula for the distance between the specified points is

r = [tex]\sqrt{(y_{2}-y_{1})^{2} + (x_{2}-x_{1})^{2} }[/tex]

r = [tex]\sqrt{(1-3)^{2} + (4-2)^{2} }[/tex]

r =  [tex]\sqrt{4+4}[/tex]

r = 2[tex]\sqrt{2}[/tex] units

The area of the given circle will be given by the formula A = πr²

A = 3.14 × (2√2)²

= 3.14 × 8

= 25.12 unit²

The circumference of the given circle will be given as

C = 2πr

C = 2 × 3.14 ×2√2

C = 12.56√2

C = 12.56 × 1.414

C = 17.75 unit

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1) Saleena worked for 20 hours in total.

2) She earned $220 during the week.

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Given,

Saleena has a part time job.

a) On Monday

Start time = 4: 30 pm

End time = 9:00 pm

Hours worked = 4 : 30 hours

b) On Tuesday

Start time = 3: 00 pm

End time = 9 : 00 pm

Hours worked = 6 hours

c) On Thursday

Start time = 4: 30 pm

End time = 9: 00 pm

Hours worked = 4 hours 30 minutes

d) On Saturday

Start time = 10:30 pm

End time = 3 : 30 pm

Hours worked = 5 hours

Total hours worked = 4:30 + 6 + 4: 30 + 5

1) Saleena worked for 20 hours in total.

2) She earns $11/h

Saleena worked for 20 hours in total.

Multiplying by $11 for per hour

20 × 11

220

2) She earned $220 during the week.

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Moloch have $133,737.75 after 2 years at the interest of 1.02% per month.

Interest accrued on both the principal sum of money and the interest already earned.

The formula for compound interest is A= p(1+r/100)ⁿ

Where A is amount, p is principal, r is rate and n is time.

Given that,

The amount Moloch placed in account = $104,828

The rate of interest = 1.02% per month

time = 2 years,

To find total amount Moloch has after 2 year,

Use formula

Amount = [tex]p(1+r/100)^{nt}[/tex]

             = 104,828 (1+1.02/100)²ˣ¹²

              = 104,828 (1+0.0102)²⁴

              = 104,828 (1.0102)²⁴

               = 104,828×1.27578

               = 133,737.75

After 2 years, Moloch have $133,737.75 in account.

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Answer:

XY - YT = 2

Step-by-step explanation:

substitute the given values into the expression

XY - YT

= (12 × [tex]\frac{1}{3}[/tex] ) - ([tex]\frac{1}{3}[/tex] × 6 )

= 4 - 2

= 2

Answer:

yes, The result is the same

Step-by-step explanation:

-3(5)=-15

5(-3)=-15

Answer:

They are same (equal)

Step-by-step explanation:

-3 multiplied with 5 is equal to -15.

5 multiplied with -3 is also equal to -15

so these two expressions are same when multiplied because the products are equal to one another.

The ratio 5 to 2 is written in other notations as

Mathematicians use the term "ratio" to compare two or more numbers.

It serves as a comparison tool to show how big or small an amount is in relation to another.

In a ratio, division is used to compare two amounts.

The ratio 5 is to 2 can be represented as a fraction to 5 / 2

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The independent variable in this situation is C. area of the prism.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they are dependent, by some law or rule, on the values of other variables.

The term "independent variable" means exactly what it sounds like. It is a variable that is independent of the other variables you are attempting to measure. For example, age could be an independent variable.

In this case, the area doesn't change in relation to others. It's independent.

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A) Y = [tex]-2^{x}+4[/tex] is the equation which have real zero(s) corresponding to the x-intercept(s) of the graph below

What does a mathematical coordinate mean?

a set of numbers used to represent the horizontal and vertical divisions of the positions of two reference axes in a coordinate plane. often shown as the combination of x-values and y-values (x,y).

What is the Slope Intercept Form Equation?

The slope intercept equation can be used to find the general equation of a straight line using its slope and the point of its y-axis junction. The equation in slope intercept form is Y = mx + b.

You must enter y=0 for the x intercept.

in equation A we can see that at x=2 , y=0

so hence answer is option A) Y =[tex]-2^{x}+4\\[/tex]

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