a company wants to study the effectiveness of a new pain relief medicine. they recruit 100100100 volunteers who suffer chronic pain. they assign each subject a number from 111 to 100100100 and use a random number generator to assign the first 505050 subjects selected to the treatment group. the remaining 505050 subjects are assigned to the control group. what type of experiment design is this?

⇒I will use the trig ratios to find the value x.

[tex]\frac{sin(x)}{11cm}=\frac{sin( 38)}{8} \\[/tex]

⇒Moving on solving I will use the cross multiplication

[tex]8sin(x)=11sin(38)\\sin(x)=\frac{11sin(38)}{8} \\x=sin^{-1} (\frac{11sin(38)}{8} )\\x=57,8[/tex]

∴ x=57,8°

Goodluck!!

The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge.

When applying the z-transform on the sequence h, the ROC concept is applied to the function H(z) (n). The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge. Neither X(z), the input, nor Y(z), the output, are involved in the ROC.

The region (regions) where the z-transform converges is known as the region of convergence (ROC). We can uniquely determine the inverse z-transform thanks to ROC. Let's first think about some examples. The unit sample δ(n)has z-transform 1 , hence ROC exists all the z plane .

The Registrar of Companies assigns the company registration number, or CIN number as it is known in India (ROC). The Ministry of Corporate Affairs oversees the ROC, which is present in several Indian states. It is utilized to locate the essential information for every firm that is registered in India.

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The possible number of ways of selection by using combination formula is 3060.

What is combination?

A grouping of items where the order in which they were chosen is irrelevant is known as combination.

Given that the number of people in the group is 18. Only 4 people will be member of the council.

The formula of combination is [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex] , where r number of objects are selected from n objects.

In the given question the value of n is 18 and the value of r is 2.

Substitute the value of n and r in [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex].

[tex]^{18}C_{4}=\frac{18!}{4!(18-4)!}[/tex]

Solve the above expression:

18^C_4 = 18x17x16x15x14/4x14

18^C_4 = 18x17x16x15/4x3x2x1

3060 18^C_4 = 3060

The number of ways such selection is 3060.

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[tex] = 3 \times 3 \times {10}^{7} \times 10^{8} \\ = 9 \times {10}^{7 + 8} \\ = 9 \times {10}^{15} \\ [/tex]

NOTE YOU CAN WRITE IT IN FULL BUT I CHOSE NOT TO BECAUSE IT'S LARGE .

GOODLUCK

Answer:

y = 0.5x^2 + 1.5x − 5

Step-by-step explanation:

See attached graph

8/13 x 3/1 = 24/13

24 - 13 =11

So, simplified answer is 1 11/13 or 24/13

Hope this helps!

Given:

Point 1 → (-5, 0.6)

Point 2 → (5, -2.4)

Find: the equation of the line and its graph

Solution:

To help us determine the equation of the line passing through the given points, let's use the Two-Point Form formula.

Let's plug into the formula above the coordinates of the two points.

Then, solve.

Multiply -3/10 by the terms inside the parenthesis.

Add 0.6 on both sides of the equation.

Hence, the equation of the line passing through the given points in slope-intercept form is y = -0.3x - 0.9.

In the equation, the slope is -3/10 while the y-intercept is -0.9.

Since the slope is negative, the line must be leaning to the left. Since the y-intercept is -0.9, the line must cross the y-axis or the vertical line at -0.9. Hence, the graph of the equation is:

Answer:

p = 20

Step-by-step explanation:

7 + 3(p - 1) = 64 ( subtract 7 from both sides )

3(p - 1) = 57 ( divide both sides by 3 )

p - 1 = 19 ( add 1 to both sides )

p = 20

Answer:

Below in bold.

Step-by-step explanation:

P(x) = -0.3x² + 75x - 2000

Convert this to vertex form:

p(x) = -0.3(x^2 - 250)^2 - 2000

      = -0.3[(x - 125)^2 - 125^2] - 2000

      = -0.3[(x - 125)^2 - 15625] - 2000

      = -0.3(x - 125)^2 + 4687.5 - 2000

      = -0.3(x - 125)^2 + 2687.5

2687.5 is the maximum value of the profit.

1.  This corresponds to a selling price of $125 for the stands.

2.  Maximum profit is $2687.5.

3.  At the breaking points P(x) = 0:

-0.3(x - 125)^2 + 2687.5 = 0

(x - 125)^2 = 2687.5 / -0.3 = 8958.33

x - 125 = +/- sqrt( 8958.33)

x = 125 +/- sqrt( 8958.33)

x = 30.352, 219.648,

So, the breaking even points are $30.35 and $219.65 to nearest cent.

Answer:

Step-by-step explanation:

Solve each  inequality:

or

The answer is: m < 7 or m ≥ 8

Using the midpoint, the coordinates of point Y in the line segment TY is (-18, -9).

Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.

Therefore, the mid point formula can be represented as follows:

(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

Hence, let's find the coordinates of point B.

(-3, 1.5) = (2 + x₂ / 2 ,  5 + y₂ / 2)

2 + x₂ / 2  = - 3

cross multiply

2 + x₂ = -6

x₂ = -6 -2

x₂ = - 8

1.5 = 5 + y₂ / 2

3 = 5 + y₂

y₂ = 3 - 5

y₂ = -2

Therefore, the coordinates of B is (-8, -2)

Hence, let's find the coordinate of point Y. The coordinates of point B is the mid point of segment TY.

(-8, -2) = (2 + x₂ / 2 ,  5 + y₂ / 2)

(-8, -2) = (2 + x₂ / 2 ,  5 + y₂ / 2)

2 + x₂ / 2 = - 8

-16 = 2 + x₂

x₂ = -18

-2  =  5 + y₂ / 2

-4 = 5 + y₂

-4 - 5 = y₂

y₂ = -9

Therefore, the coordinates of y is (-18, -9)

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Answer: Cost per rides

Step-by-step explanation:

Rainfall anually table data

Then

Option A)

Half of the data are between 6 and 18

TRUE , because there are 8/2 = 4 data in the box plot

Option B)

Data point 27 ,could be an outlier

FALSE, because 27 is a black point. It means it belongs, is not out

Option C)

More points between 6,9 that between 9,18

FALSe,. Area between 6,9. Is smaller than area between 9,18

Option D)

Data are less spread out to the left

TRUE, because box plot is ubicated at left

Option E)

Only one data point is less than 6

TRUE, is data point 3

Part a

The domain is the set of x-values, which is [tex](-\infty, \infty)[/tex].

Part b

The range is the set of y-values, which is [tex](-\infty, \infty)[/tex].

Part c

As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex], and as [tex]x \to -\infty[/tex], [tex]y \to -\infty[/tex].

Part d

The y-intercept is when x=0, which is [tex](0, 1)[/tex].

Part e

The function is increasing when y increases as x increases, which is true for this function.

If Avery is in the business of manufacturing phones. The equation for C, in terms of p, representing total cost, in dollars, of producing pp phones in a given day is: 100p + 300.

Given data:

Labor and materials cost = $100

Numbers of phones = 3

Total cost = $600

Where,

P = Total cost

The equation for C in terms of p is:

100p + 300

Now let determine the total cost

Total cost = $600 + ( 3 × $100)

Total cost = $600 $300

Total cost =$600

Therefore 100p + 300 is the equation.

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Work done in stretching spring from 36 cm to 38 cm is 0.333J.

The work needed to stretch a spring is given by the formula mentioned below:

[tex]W_{s}[/tex] = (1/2) K × [tex]x^{2}[/tex]

Here,  k is spring constant and x is the elongation.

So, x = [tex]x_{f} - x_{i}[/tex]

When spring is stretched from 40 cm to 34 cm

x = 40 - 34  = 6cm = 0.06 m

We need to know the spring constant so that we can calculate work.

3 = (1/2) K × [tex](0.06)^{2}[/tex]

K = 1666.67

Now, when spring is stretched from 36 cm to 38 cm

x = 38 - 36 = 2 cm = 0.02 m

[tex]W_{s}[/tex] = (1/2) × (1666.67) × [tex](0.02)^{2}[/tex]

[tex]W_{s}[/tex] = 0.333J

So, 0.333J work is done in stretching spring from 36 cm to 38 cm.

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The correct option regarding the symmetry of the distribution is given as follows:

The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.

To find the symmetry of the distribution, the mean and the median need to be calculated and compared, if they are equal or which is greater.

A dot plot shows the number of times that each observation appears in the data-set, hence the complete data-set of heart beats per minute is given as follows:

62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.

The mean is the sum of all these observations divided by the number of observations, which is of 20, hence:

Mean = (62 + 3 x 68 + 69 + 2 x 70 + 3 x 72 + 2 x 75 + 76 + 2 x 78 + 3 x 80 + 2 x 89)/20 = 74.55.

The median is the middle value of the data-set, the value which 50% of the observations are less than and 50% are greater than. The cardinality of 20 in this data-set is an even number, hence the median is the mean of the 10th and of the 11th element, as follows:

Median = (72 + 75)/2 = 73.55.

When the mean is greater than the median, as is the case in this problem, the distribution is right skewed, which is the reason for the correct option.

The problem is given by the image at the end of the answer.

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Answer:

Step-by-step explanation:

answer is 16

As per the given three coordinate of the triangle, the area of the triangle is 9.5 square units.

Area of triangle:

In the triangle ABC as with vertices or coordinates are A(x1, y1), B(x2, y2), and C(x3, y3), has the area,

Area(ΔABC) = (1/2){x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)}

As the area is always positive.

Given,

Here we have the triangle VWX,

And their coordinates are V (-9,-7), W(-4,-5), and X(-6,-2).

Now we have to find the area of the triangle.

To find the area of the triangle, let us consider the coordinates (x1,y1) as v(-9,-7), (x2,y2) as W(-4,-5) and (x3,y3) as X(-6,-2).

Now, we have to apply the values on the formula, in order to get the area of the triangle,

=> A = 1/2 |(-9 [-5-(-2)] + (-4)[-2 - (-7)] + (-6)[-7 - (-5)]|

When we expand the terms, then we get,

=> A = 1/2 |(-9)[-3] + (-4)[5] + (-6)[-2]|

Further simplify the expression will gives you the following,

=> A = 1/2 |27 - 20 + 12|

=> A = 1/2 |19|

Therefore, the area of the triangle is 9.5 square units.

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The given  polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)

In the above question, a polynomial function is given

f(x)=x^3 - 2x^2 - 5x + 6

However, we know that, zero of a polynomial means all the x-values that bring a polynomial, p(x), to zero are referred to as its zeros, which means putting any value of x in the function we should get value of f(x) as zero

And, in the question, it is given as

f(0)=6, f(2) = -4, f(-2) = 0, f(3) = 0 , f(-1) = 8 , f(1) =0

We can clearly see that,  f(-2) = 0, f(3) = 0, f(1) =0

=> (x+2), (x-3), (x-1) are the linear factors of the given polynomial

Hence, we can write the given  polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)

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Since a positive number divide or multiplies a negative number

Then the answer will be a negative number

So:

6 / -3 = -2

6 is a positive number and it's being divide by -3 which is a negative number

So the answer is -2

If at least two sides and one angle of two triangles are similar, then the triangles are congruent.

What in mathematics is the congruent?

Use the Third Angles Theorem for  two figures are congruent.

When two of a triangle's angles match up with two of another triangle's angles, the third angle must likewise match up.

If at least two sides and one angle of two triangles are similar, then the triangles are congruent.

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Solution

Given that

Area f small square = 40 inches squared.

Let the side of the large square be L

Since the large square has sides that are 8 times longer than the small square

=> L = 8l

Hence, the area of Large square is;

Hence, the area of the large square is: 256 inches squared.

1) Gathering the data

1/5 inch

7/20 inches long

2) Let's them divide, 7/20 by 1/5 inches

When divide fractions, we multiply the reciprocal of the second fraction

and if possible we can simplify

Answer:

the value of x is 17

Step-by-step explanation:

7x-32+5x-27=9x-8{sum of 2 interior angles of a triangle is equal to the sum of exterior angle}

therefore x=17

Answer:

x = 17°

Step-by-step explanation:

Hello!

Angle KLM is an exterior angle of Triangle JKL. An exterior angle's measure is equal to the sum of the two remote interior angles.

The two remote interior angles are Angle K and Angle J. We can solve for x by setting up an equation: (7x - 32) + (5x - 27) = (9x - 8)

The value of x is 17°.

Answer:

A. k ≥ 8.14

Step-by-step explanation:

Hope this helps! :))

Answer:

The 40 lb bag is cheaper by $4

Step-by-step explanation:

10 x 4 = 40

7 x 4 = 28

If you bought the 10 lb bag 4 times, you'd spend more money than just buying the 40 lb bag once.

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