researchers working on a vaccine for hiv recruited over 16{,}00016,00016, comma, 000 volunteers for a study. each volunteer was randomly assigned to receive monthly injections of either the vaccine or a placebo for a year. the researchers were curious if subjects who received the vaccine would be less likely to contract hiv than subjects who received the placebo. what is the main reason for randomly assigning the subjects?

Answer:

5.6

Step-by-step explanation:

y = 53- 47.4=?

The Probability of cookie is 0.0492

Describe probability.

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two events joining together, are essential to understand in order to properly appreciate this branch of mathematics.

Given That:
chocolate chip cookies = 7

peanut butter cookies = 8

sugar cookies = 4
oatmeal cookies = 7

selecting a sugar cookie from the bag = [tex]\frac{4}{7+8+4+7}=\frac{4}{26}=\frac{2}{13}[/tex]

selecting a oatmeal cookie from the bag = [tex]\frac{8}{7+8+3+7} =\frac{8}{25}[/tex]
Over all probability = [tex]\frac{2}{13} *\frac{8}{25} = \frac{16}{325} =0.0492[/tex]

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Answer:2^(31-1)

Step-by-step explanation:

The inequality 6(4q − 8) > 8(3q + 2) have no solution.

The inequality can be solved as follows:

An inequality is an expression that has <, >, ≤ and ≥ symbols.

Therefore,

6(4q − 8) > 8(3q + 2)

open the bracket on both sides of the inequality

6(4q − 8) > 8(3q + 2)

24q - 48 > 24q + 16

add 48 to both sides of the inequality

24q - 48 > 24q + 16

24q - 48 + 48 > 24q + 16 + 48

24q > 24q + 64

Subtract 24 q from both sides of the inequality

24q > 24q + 64

24q - 24q > 24q - 24q + 64

0 > 64

The inequality cannot be solved

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Answer: 14

Step-by-step explanation:

The formula for slope in this problem is:

[tex]\frac{-5-(-20)}{r-2}=\frac{5}{4}[/tex]

[tex]\frac{15}{r-2} = \frac{5}{4}[/tex] (cross multiply)

60 = 5(r-2)

60 = 5r - 10

70 = 5r

14 = r

Check: (2, -20) (14, -5)

[tex]\frac{-5-(-20)}{14-2}[/tex]

[tex]\frac{15}{12}[/tex]

[tex]\frac{5}{4}[/tex]  

I took a picture because it may be a little difficult to understand if I wrote it in text. Hope this helps.

The next step to bisect the line segment CD is to make an arc above the line as well as an arc below the line.

How to cut a line segment in half is as follows:

• Place the compass at point D.

• Set the compass to be just a little bit longer than half the length of the line segment.

• Draw arcs above and below the line.

• Do the same thing by keeping the compass at C point while maintaining the same compass width.

• Draw the line segment that passes through the points where both arcs crosses each other.

Hence, after keeping compass on point D, the next step will be to draw an arc above and below the line segment.

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Answer:

2

Step-by-step explanation:

2 [tex]\frac{3}{5}[/tex] ÷ 1 [tex]\frac{3}{10}[/tex]

[tex]\frac{13}{5}[/tex] ÷ [tex]\frac{13}{10}[/tex]

[tex]\frac{13}{5}[/tex] x [tex]\frac{10}{13}[/tex] = 2

For a population variance of 484 with a probability of 0.99 the sample size needed if the desired margin of error is 5 or less is 129

Margin of error refers to a statistical measurement that represents the difference between actual and projected outcomes in a random survey sample. In other words, the margin of error enabled the researcher to measure the level of unpredictability in data and research outcomes. Margin of error is given by:

MOE = z x σ/√n

In order to determine the z score, the value is determined by the z table. As the table is set up for one tailed probability and the given confidence level uses a two tailed probability, the p value is determined by (1 + 0.99)/2 = 0.995. As the p value of 0.995 lies in the row containing 2.5 and column containing 0.08, the z = 2.5 + 0.08 = 2.58.

The standard deviation is the square root of the variance, hence σ = √484 = 22

As MOE = z x σ/√n

Substituting the values from the given data,

5 = 2.58 x 22/√n

5√n = 56.76

√n = 11.35

N = 128.8 ≈ 129

Hence, at least a sample size of 129 is required.

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The probability to have women applications between 35% to 45% is 1.

Here we are given that the sample number of applications received was 120.

Also, 40% of total applications are of women.

Hence this is clearly a Binomial Distribution with,

n = 120

p= 0.4

We need to find the probability that the sample applications have women applicants between 35% to 45%. For this, we need to use the method of Normal Approximation

Now,

np = 120 X 0.4

= 48

Since np > 10,

We can use Normal approximation here, with

mean = np = 48

Variance = np(1 - p)

= 48 X 0.6

= 28.8

35% of applicants = 42

45% of applicants = 54

Hence we need to find

P(42<X<54)

P(a<X<b)

= P(X<b) - P(X<a)

Therefore we get

P(X < 54) - P(X<42)

Now subtracting it with its mean and dividing it by its standard deviation we get

P(X < (54 - 48)/5.3666) - P(X < (42- 48)/5.3666)

= P(X < 1.1180) - P(X < -1.1180)

= 0.86650 - 0.13350

= 1

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Number of sugar cubes hold the sugar cube = 768÷1 = 768 unit

Surface area of the prism = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 + 8×8 + 4×4 + 4×8 = 512 sqft  

Divide the base area of figure into three parts

Area of the 1st part = 8×6 = 48 sqft

Area of the 2nd part = 4×4 =  16 sqft

Area of the 3rd part = 4×8 =  32 sqft

Height of the prism is 8 ft

So the total volume of the prism ,

Volume = 8×( 6×8 + 4×4 + 4×8 )

            = 8×( 48 + 16 + 32 )

            = 8×96 = 768 cubic feet

1 feet side  sugar cube solid holds a volume = 1×1×1 = 1 cubic feet

Number of sugar cubes hold the solid prism = volume of prism / volume of sugar cube

Number of sugar cubes hold the sugar cube = 768÷1 = 768 unit.

Surface area of the prism =( lateral surface area) + (top surface area)

Lateral surface area =  8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 = 416 sqft

Top surface area = 8×8 + 4×4 + 4×8 = 96 sqft

Surface area of the prism = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8  + 8×8 + 4×4 + 4×8 = 512 sqft

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Answer:

110

Step-by-step explanation:

2/5=44/x

Cross multiply

2x=44(5)

2x=220

/2.  /2

x=110

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The probability that the selected contestant received a score of 555 on day 222 or day 333 is 5/7.

If it is given that on day 222 the no of contestants received a score of 555 is 2 and no of contestants received a score of 555 on day 222 is 3.

Given:

It is given that no contestant received the same score on two different days. So, we have 7 days in a week which means there are 7 contestants only who could be chosen and have a score of 555.

So, the contestants who received a score of 555 on any day = 7.

Now, the contestant received a score of 555 on day 222 is 2 and on day 333 is 3.

Probability = No of favorable outcomes/Total no. of outcomes

Probability =  (2 + 3)/7 = 5/7

The probability that the selected contestant received a score of 555 on day 222 or day 333 is 5/7.

If it is given that on day 222 the no of contestants received a score of 555 is 2 and no of contestants received a score of 555 on day 222 is 3.

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A line that intersects two or more lines in a plane at different points is called a transversal line.

A line is a geometrical figure that has length and can be extended in both directions.

Line is of two types: Straight and curved.

There are other types of lines also:

1. Parallel lines: Regardless of the length of the lines, two lines that run parallel to one another and are separated by the same distance but do not intersect are known as parallel lines.

2. Perpendicular lines: When two non-parallel lines cross at a place, they are said to be intersecting. The point of intersection is the solitary intersection of two lines.

3. Transversal lines: A straight line called a transversal cuts two or more lines, some of which may or may not be parallel. In the idea of geometry, a transversal line intersects two lines in the same plane at two different locations.

Hence, A line that intersects two or more lines in a plane at different points is called a transversal line.

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Answer:

5 - 1/2x = x - 6

Step-by-step explanation:

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Answer:

[tex]3x \times x = 45 \\ {3x}^{2} = 45 \\ {x}^{2} = \frac{45}{3} \\ {x}^{2} = 15 \\ x = \sqrt{15} \\ x = 3.872983346 \\ x = 3.9[/tex]

Step-by-step explanation:

area of a rectangle is width a length

area of length already given as 45cm²

find the unknown x using a normal equation

By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).

To Prove:- Area of a triangle= 1/2 (base×height)

Diagonals of a rectangle divide it into two parts of equal parts that is area

.

Let  ABCD  be a rectangle.

In ΔABC and ΔADC,

                                         AC=AC

By Alternate Interior Angles:

                                    ∠BAC=∠CAD

                                    ∠BCA=∠CDA

Hence, ΔABC≅ΔACD

                               ∴ar(ΔABC) =ar(ΔACD)

Let ΔABC,

We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.

In rectangle ADBE,

we get,

                     ar(ΔABE)=ar(ΔADB)

Similarly, in rectangle ADCF,

                     ar(ΔADC)=ar(ΔACF)

Now, area of rectangle BCFE, from axiom,

                               =(length)⋅(breadth)

                               =AB⋅BC

                              =AD⋅BC

Also,

ar(BCFE)

                                   =ar(ADBE)+ar(ADCF)

                                   =2⋅ar(ΔADC)+2⋅ar(ΔADB)

                                   =2(ar(ΔADC)+ar(ΔADC)

                                   =2(ar(ΔABC))

From (1) and (2),

                                   2(ar(ΔABC))=AD⋅BC

                                    ar(ΔABC)=1/2AD⋅BC

                                   ar(ΔABC)=1/2(base)⋅(height)

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The complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

From the question, we have the following equation:

f(x) = 3ˣ

From the table of values, we have the following x values

x = -2, -1, 0, 1 and 2

Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ

When x = -2

f(-2) = 3⁻² = 1/9

When x = -1

f(-1) = 3⁻¹ = 1/3

When x = 0

f(-1) = 3⁰ = 1

When x = 1

f(1) = 3¹ = 3

When x = 2

f(2) = 3² = 9

Hence, the complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

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It will take at least 9 days for adaim to reach his goal of 70 miles.

Given that,

The 70-mile mark is Adaim's objective. He can hike 8 miles every day.

To find :  How long will he need to hike the entire 70 miles?

Therefore, your main task will be to find X.

X times 8 equals 70.

Dividing both sides by 8 yields X on its own.

X therefore equals 70/8.

In the event that your teacher prefers a decimal, you would convert that to 8.75 and round to 9 because it is a day.

Therefore, It will take atleast 9 days for adaim to reach his goal of 70 miles.

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Answer:

[tex]r(t)=\dfrac{1}{t}\ln \left(\dfrac{A}{P}\right)[/tex]

Step-by-step explanation:

Given function:  

[tex]A(t)=Pe^{rt}[/tex]

Divide both sides by P:

[tex]\implies \dfrac{A}{P}=e^{rt}[/tex]

Take natural logs of both sides of the equation:

[tex]\implies \ln \left(\dfrac{A}{P}\right)=\ln e^{rt}[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies \ln \left(\dfrac{A}{P}\right)=rt\ln e[/tex]

Apply the natural log law:  ln (e) = 1

[tex]\implies \ln \left(\dfrac{A}{P}\right)=rt[/tex]

Divide both sides by t:

[tex]\implies r=\dfrac{1}{t}\ln \left(\dfrac{A}{P}\right)[/tex]

Answer:

= (5sin(50°)) / sin(70°)

For the given parallelogram of 5-inch side and an 8-inch side  with an angle of 50-degree , the area of the parallelogram is equal to 30.64 square inches and the lengths of its diagonals are 11.85inches and 6.13 inches.

As given in the question,

Side lengths of the parallelogram are :

From the attached diagram we have,

Side AC = 5 inches

Side CD = 8 inches

Angle ACD = 50°

Draw altitude 'h' from vertex A to the base CD at point E.

Length of CE = x inches

In ΔACE,

sin 50° = h / 5

⇒ h = 5 sin 50°

⇒ h = 5 (0.766)

⇒ h = 3.83 inches

cos 50° = x/ 5

⇒ x = 5 cos 50°

⇒ x = 5 ( 0.6428)

⇒ x = 3.214 inches

Length of diagonal BC

BC = √ h² + ( 8 + x )²

     = √(3.83)² + ( 8 + 3.214)²

     = √140.422696

     ≈ 11.85 inches

Length of diagonal AD

AD = √ h² + ( 8 -x )²

     = √(3.83)² + ( 8 - 3.214)²

     =√37.574696

     ≈ 6.13 inches

Area of a parallelogram ABCD

= height × corresponding base

= 3.83 × 8

= 30.64 square inches

Therefore, for the given parallelogram of 5-inch side and an 8-inch side  with an angle of 50-degree , the area of the parallelogram is equal to 30.64 square inches and the lengths of its diagonals are 11.85inch and 6.13 inch.

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Answer:

∴ (x + 2)(x - 1)(x - 2) = x³- x² - 4x + 4

Step-by-step explanation:

(x + 2)(x - 1)(x - 2) = (x² + 2x - x - 2)(x - 2)

                           = (x² + x - 2)(x - 2)

                           = (x³ + x² - 2x - 2x² - 2x + 4)

                           = x³ - x² - 4x + 4

Answer: 3x²(x - 5)²

Step-by-step explanation:

Factoring out 3x² of each term leaves you with 3x²(x² - 10x +25)

We can still factor out (x² - 10x +25) to (x-5)(x-5), which is simply (x-5)².

This will leave you with 3x²(x - 5)².

Option (D) is the correct option and

The position of 0 represents on the surface of the sea.

Given, a turtle is 6 feet below the surface of the sea.

And his position can be recorded as −6 feet.

Now, if his position is recorded as -6 feet, then

according to the cartesian plane

0 represents the origin i.e. the surface of the sea.

Hence, Option (D) is the correct option and

The position of 0 represents on the surface of the sea.

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Answer:

assuming 13 is supposed to be -13, the equation will be y=-5x+2

Step-by-step explanation:

common difference = -5

y=-5x+b

-3=-5(1)+b - plug in the first term of the sequence

b=2

The likelihood that a green marble from jar A will be drawn out of it is 0.105.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.

Here,

For jar A,

Total Marbles=10

Number of green marbles=7

Number of blue of marbles=3

For jar B,

Total Marbles=10

Number of green marbles=3

Number of blue of marbles=7

Probability of choosing jar A=15/100

Probability of choosing jar B=85/100

Probability that a marble is drawn out of it is the marble is green that came from jar a= 15/100*7/10

=105/1000

=0.105

Probability that a marble is drawn out of it is the marble is green that came from jar A is 0.105.

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The inequality x+36>x4+1. The inequality's solution is the value of x.

x+36>4+1

x+36>5

x>5-36

x>-31

-31 value of x is a solution to the inequality.

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In both the steps student has done wrong simplification of the equation.

In step 2, student has done the wrong subtraction of 5 and 12.

Correct subtraction would be 5 - 12 = -7, not -13 so the equation will be (-7/2)(4-6)2.

In step 4, student has wrong multiplication in the  parentheses with 4 and 6.

Correct multiplication would be -6.5(4-6)2 :

-6.5(8-12).

The correct solution of this equation is :

(cube root of 125 − 12 ÷ 2)(4 − 6)2

(5 − 12 ÷ 2)(4 − 6)2,

(5-6)(4 − 6)2, Dividing according to the BODMAS.

-1(-2)2, subtracting

4. multiplying

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Answer:

please put the number of yellow buttons if you can

thank you.