The sum of the first 15 terms of the sequences 7, -14, 28, -56, 112,...

The four main principles of randomized experiments are:

True, True, False, True, and True

1. True: Confounding variables can make it harder to draw conclusions from a study because they can obscure the effect of the treatment being studied. Confounding variables are extraneous factors that can affect the outcome of the study and mimic or mask the effect of the treatment being studied.

2. True: In a randomized experiment, the treatment and control groups are designed to be as similar as possible in terms of all relevant factors, except for the treatment itself. This helps to ensure that any observed differences between the groups can be attributed to the treatment being studied, rather than to other factors that might affect the outcome.

3. False: Observational studies are generally considered to be less reliable than randomized experiments because they are subject to a number of biases that can affect the results. For example, observational studies often involve selection bias, in which certain groups are more likely to be included in the study, and measurement bias, in which the measurements used in the study are not accurate or reliable.

4. True: The four main principles of randomized experiments are:  

5. True: In a double-blind study, neither the investigators nor the subjects know who is receiving which treatment. This helps to reduce the potential for bias and increase the reliability of the results, by ensuring that neither the investigators nor the subjects can influence the outcome of the study based on their knowledge of the treatment assignments.

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Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Answer: c = 35 + 45m

Step-by-step explanation: The equation for the total cost, c, of renting an iPad for m months would be:

c = 35 + 45m

Where c represents the total cost and m represents the number of months for which the iPad is rented.

The $35 is the initial renting fee and is a one-time cost, while the $45 is the monthly rental fee that is charged for each month that the iPad is rented. Therefore, the total cost of renting an iPad for m months would be the sum of the initial renting fee and the monthly rental fee multiplied by the number of months the iPad is rented.

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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Answer:

b. g(x)=|x+3|-1

Step-by-step explanation:

If the cost of goods manufactured of $918,700 and cost of goods sold is $955,448. The average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.

Using this formula to determine the average manufacturing cost per unit

Average manufacturing cost per unit= Total cost/Number of units produced

Where:

Total cost=$918,700+$955,448=$1,874,148

Number of units produced=18,374 units

Let plug in the formula

Average manufacturing cost per unit=$918,700+$955,448/18,374

Average manufacturing cost per unit=$1,874,148/18,374

Average manufacturing cost per unit=$102 per unit

Therefore the average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

Answer:

Your answers are 6m-2m+12 and 4(m+3).

Step-by-step explanation:

This is because for 6m-2m+12, you are dealing with like terms. You are subtracting 6m-2m.

4(m+3) on the other hand, you are using the distributive property. You would carry the 4 to the m and to the 3.

Once you've done that with both of those expressions, they will both equal 4m+12.

Expression is a set of numbers, variables, and mathematical operations formed. The expression 4m+12 can be written as 4(m+3).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

In the given expression  4m + 12, there are 2 terms and both of these terms have 4 as the common factor, therefore, we can write the expression as,

\(4m +12\\\\= 4m+(4 \times 3)\\\\ = 4(m + 3)\)

Hence, the expression 4m+12 can be written as 4(m+3).

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Tan(angle) = opposite/ adjacent

tan(42) = 67/x

x =67/tan(42)

X = 74.411

rounded to nearest tenth : x = 74.4

Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

Answer: P = 4s

Step-by-step explanation:

P = 4s where s = the length of each side.  

Since each side of a square is the same length, the side length is multiplied by 4.

The equation of the line is y = 2/3x + 1

The graph represents the given parameter

From the graph, we have the following points that can be used in our computation:

(x, y) = (0, 1) and (3, 3)

The equation of the line is then calculated using the following equation

y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁

Where

(x, y) = (0, 1) and (3, 3)

Substitute the known values in the above equation, so, we have the following representation

y = (3 - 1)/(3 - 0) * (x - 0) + 1

Evaluate

y = 2/3 (x - 0) + 1

So, we have

y = 2/3x + 1

Hence, the line equation is y = 2/3x + 1

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Answer:

I might be able to help what do you need to know

Answer:

The correct answer is 25% increase

Step-by-step explanation:

Hope This Helps!

The ad campaign by TimeRyte claiming that their stopwatches are accurate to a thousandth of a second 98% of the time is fair and honest based on the information provided. The independent research company's findings support this claim.

According to the research, stopwatches assembled with components from the east coast facility are accurate to a thousandth of a second 96% of the time. This implies that the assembly process at the east coast facility may introduce a slight deviation from the claimed accuracy.

Stopwatches assembled with components from the west coast facility, on the other hand, are accurate to a thousandth of a second 99% of the time. This suggests that the assembly process at the west coast facility is more reliable in achieving the claimed accuracy.

Stopwatches assembled with components from both facilities, which accounts for some of the products, are accurate to a thousandth of a second 98% of the time. This suggests that the combined efforts of both facilities maintain the claimed accuracy.

Considering the overall findings and the accuracy percentages provided, it can be concluded that the ad campaign's claim of 98% accuracy to a thousandth of a second is fair and honest, given the performance of the stopwatches across different assembly scenarios.

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Answer:

I think the answer you're looking for is 16807

Answer:

add yeh six plus 99

Step-by-step explanation:

then there is a

The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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Answer: \(7.39466666\)

Step-by-step explanation:

Setting \(x=2.2\) and \(n=3\),

\(e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666\)

Answer:

7.39466667 (8 d.p.)

Step-by-step explanation:

We can approximate the value of eˣ for any x using the following sum formula:

\(\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}\)

To approximate \(e^{2.2}\) with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:

\(e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\)

To calculate the sum, substitute k with each value from 0 to 3 and add the results together:

\(\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}\)

Therefore, the approximate value of \(e^{2.2}\) is:

\(\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}\)

Note: To obtain a more accurate approximate value, increase the value of n.

Answer:

85%

Step-by-step explanation:

Hope it helps!

The amount of Iodine-131 left from 160g after 40 days is 5g.

What is the half-life of a substance?

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life.

In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last.

Given,

half-life of Iodine -131,  = 8 days

Initial amount = 160 g

Number of days t = 40

The final amount of Iodine-131 after 40 days = initial amount * \([(\frac{1}{2} )^\frac{t}{t_{1/2} }]\)

                                                                          = 160 * \([(\frac{1}{2} )^\frac{40}{8} }]\)

                                                                           = 160 * 0.03125 = 5g

Therefore the amount of Iodine-131 left after 40 days is 5g.

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The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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The line can be expressed in slope intercept form in the following manner:

Where "m" is the slope and "b" is the y-intercept. We need at least two known points to find the expression. The expression of the slope is given by:

Applying the known points (0.1, -1.6) and (3, 7.7).

The expression of the line thus far is:

We need to find the value of "b", to do that we need to apply one of the known points:

We now have the whole expression of the line:

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

I think that it is the first one and the third one.....

I hope that it is correct, I tried helping you get it correct

This, is as far as I go. Goodluck with the rest man. Let me know if you need more assistance. :)

Answer:

Option B is correct. the required domain of the function will be expressed as[-5, 3) U (3, ∞)

Step-by-step explanation:

The percentage of Abigail's $2,325.00 monthly retirement income she has saved each month is 20%

What is the total savings for the nine months?

The fact that $627.75 saved for entertainment is only 15% of total savings means that we can determine the total savings in the period of nine months as shown below:

15%=$627.75

divide both sides by 15 to determine 1% of total savings

15%/15=$627.75/15

1%=$41.85

100%=$41.85*100

100% savings=$4,185.00

Now the total savings were saved over the period of 9 months, hence, monthly savings is determined as total savings divided by the number of months savings lasted

monthly savings=$4,185.00 /9

monthly savings=$465.00

monthly savings a percentage of monthly retirement income=$465.00/$2,325.00

monthly savings a percentage of monthly retirement income=20%

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Answer:

\(v=5\)

Explanation:

The equation is asking for multiplication (13 * v), and the opposite of multiplication is division. So if we divide 65 by 13, we find 5.

13 * 5 = 65

Answer:

v = -5

Step-by-step explanation:

1. Pull out like factors :

  -13v - 65  =   -13 • (v + 5)

2. Solve :    -13   =  0

This equation has no solution.

A a non-zero constant never equals zero.

3. Solve  :    v+5 = 0

Subtract  5  from both sides of the equation :

                     v = -5