Evaluate the following expression.

25
1/25
-25
-1/25

If Martin's mass is initially m kilograms, his mass after gaining 7 kilograms would be:

m + 7 kilograms.

In the question, it's given that Martin's initial mass is m kilograms. This means that he weighs m kilograms at some point in time.

If Martin gains 7 kilograms, we need to add 7 to his initial mass to get his new mass. The formula for this is:

Martin's new mass = Martin's initial mass + the mass he gained

Martin's new mass = m + 7

So if Martin's initial mass is m kilograms, his mass after gaining 7 kilograms would be m + 7 kilograms. This means that he would weigh m + 7 kilograms at this point in time.

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The key features include random assignment of participants into two groups (drug A and placebo), administration of the drug or placebo without participants knowing which one they received, and comparison of outcomes (number of pain episodes) between the groups at the end of the treatment period.

This is a randomized controlled trial (RCT). An RCT is a type of research study where participants are randomly assigned to receive either the treatment (drug) or a placebo, and then the outcomes of both groups are compared. In this case, the study was conducted by the National Institutes of Health to investigate whether drug A can reduce the pain associated with sickle-cell disease. 150 sickle-cell sufferers were randomly assigned to receive the drug and another 150 were given placebos. The researchers took great care to ensure that the participants did not know whether they were receiving the drug or the placebo. At the end of the treatment period, the number of episodes of pain reported by each subject was counted. This study is important in helping researchers and healthcare professionals understand the effectiveness of the drug in reducing the pain associated with sickle-cell disease.

This study is a double-blind randomized controlled trial (RCT).

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Answer:

range = 6

Step-by-step explanation:

the range is the difference between the maximum and minimum values in the data set.

maximum = 8 and minimum = 2 , then

range = 8 - 2 = 6

The area of the resulting image after the dilation is 187.5π square units.To find the area of the resulting image after the dilation, we need to calculate the area of the dilated circle.

The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.

Given that the radius of circle w is the square root of 30, we can calculate its area as follows:

Area of circle w = π * (√30)^2 = π * 30 = 30π

Now, we need to apply the dilation with a scale factor of 2.5 to find the area of the resulting image.

The scale factor affects both the radius and the area. When a circle is dilated by a scale factor of k, the new radius becomes k times the original radius. In this case, the new radius is 2.5 * √30.

Area of resulting image = π * (2.5 * √30)^2 = π * (2.5^2 * 30) = π * (6.25 * 30) = 187.5.

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The length of segment BD is given as follows:

BD = 6.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

BD.

The bases for this problem are given as follows:

3 and 12.

Hence the length of segment BD is obtained as follows:

(BD)² = 3 x 12

(BD)² = 36

BD = 6 -> taking the square root.

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On the drawing, there are 18.75 inches between each door.

The blueprint scale states that 2 inches on the blueprint represents 8 meters in actual distance. We need to determine how many inches on the blueprint correspond to a distance of 75 meters.

We can set up a proportion to solve this problem. Let x be the distance between the doors on the blueprint, in inches. Then:

2 inches / 8 meters = x inches / 75 meters

Cross-multiplying, we get:

2 inches × 75 meters = 8 meters × x inches

150 inches = 8x

Dividing both sides by 8, we get:

x = 18.75 inches

Therefore, the distance between the doors on the blueprint is 18.75 inches. This means that, according to the blueprint's scale, the blueprint representation of the actual distance between the doors is 18.75 inches.

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The radius of given circle would be 18 cm.

Given that a right △ABC is inscribed in circle k(O, r) and m ∠C = 90°, AC = 18 cm, m ∠B = 30°.

We are asked to find the radius of the circle.

Draw a diagram that represent the given scenario. [check the attached diagram]

AB is diameter of circle O and it a hypotenuse of triangle ABC.

We will use sine of the angle to find side AB.

Sin x = AC/AB

Sin 30° = 18 / AB

AB = 36

So, the radius = 18 cm.

Therefore, the radius of given circle would be 18 cm.

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The complete question is =

A right △ABC is inscribed in circle k(O, r). Find the radius of this circle if:

m∠C = 90°, AC = 18 cm, m∠B = 30°.

Answer:

If a researcher cannot gain access to a target population, snowball sampling procedures can assist in locating subjects. In regard to sampling procedures, if a researcher wants to be able to generalize results to the total population of interest, then a purposeful sampling technique is the best approach.

Answer:

Non-probability sampling

Step-by-step explanation:

Non-probability sampling is a method of selecting units from a population using a subjective  method.

The language paradigm that is based on the mathematical concept of a function is the functional programming paradigm.

In functional programming functions are treated as first-class citizens means that they can be passed as arguments to other functions returned as values from functions and assigned to variables.

This is similar to mathematical functions are used in algebra and calculus.

Functional programming emphasizes on the use of pure functions are functions that produce output only based on their input and do not have any side effects.

This helps in writing code that is easier to reason about and test.

Functional programming languages such as Haskell Lisp and OCaml are based on this paradigm and provide built-in support for functions as first-class citizens.

Object-oriented programming (OOP) is based on the concept of objects encapsulate data and behavior.

Imperative programming is based on a sequence of statements that change the state of the program declarative programming focuses on what the program should achieve rather than how to achieve it.

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The experimental probability that Kyle's next toss will be a hit is 11/18 or approximately 0.61.

The experimental probability of Kyle's next toss being a hit can be calculated by dividing the number of hits by the total number of tosses. In this case, the total number of tosses is the sum of hits and misses, which is 22 + 14 = 36. Therefore, the experimental probability of Kyle's next toss being a hit is 11/18 or approximately 0.61.
To find the experimental probability of Kyle's next toss being a hit, you need to consider the number of hits and total tosses so far.
Hits: 22
Misses: 14
Total tosses: 22 hits + 14 misses = 36 tosses
Now, calculate the experimental probability by dividing the number of hits by the total number of tosses:
Experimental probability = Hits / Total tosses = 22 / 36
Simplify the fraction:
Experimental probability = 11/18
So, the experimental probability that Kyle's next toss will be a hit is 11/18.

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Answer:

11/18

Step-by-step explanation:

A survey was conducted to determine the number of family and non-family members living in their house. The results showed that out of 100 households surveyed, an average of 3.5 family members and 1.2 non-family members were living in each household.

Explanation:

The survey was conducted by randomly selecting 100 households in a particular area and asking them how many family and non-family members were living in their house. The results were then tabulated to determine the average number of family and non-family members per household.

The results showed that on average, each household had 3.5 family members and 1.2 non-family members living in their house. This information can be useful for various purposes, such as city planning, resource allocation, and understanding social dynamics within a community.

It's important to note that the results of this survey may not be representative of all households in the area, as the sample size is relatively small. Additionally, the definition of "family member" may vary from household to household, which could impact the results. Nevertheless, this survey provides some insight into the demographics of households in the area and can be used as a starting point for further research.

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Answer: How Much Does the Farmer Get From the Sale of 10 Baskets?

Step-by-step explanation:  If the greatest common divisor of 78 artichokes and 90 courgettes is 6, then the farmer can form at most 6 baskets with the same number of artichokes and courgettes. Therefore, the answer is $6.

If each artichoke is sold for €0.70 and each courgette is sold for €0.40, then the revenue from one basket is (0.70 * 6) + (0.40 * 6) = €6.60. The revenue from 10 baskets is 10 * €6.60 = €66.

Converting this to USD at the current exchange rate of 1 EUR = 1.18 USD, the revenue from 10 baskets is approximately $78.

{Hope This Helps! :)}

Answer: 5.56%

Step-by-step explanation:

Compound interest formula:

A = P(1 + r/n)^nt

A = final amount

P = principle amount (original amount of money)

r = interest rate

n = number of times interest in compounded per year

t = time

Step 1:

Fill in the formula

A = 700 (she ends up with this amount of money)

P = 530 (she started with this)

r = ?

n = 365 (it is compounded 365 times per year, or once a day)

t = 5 (she left the money in the account for 5 years)

700 = 530(1 + r/365)^365(5)

Step 2:

Solve the equation for r. You will get 0.055644...

Convert this to a percent and you get the final answer of 5.56%

The total amount Elizabeth paid can be expressed as 1.27x, where x is the subtotal on the bill.

    To calculate the total amount, first, we need to add the tax to the subtotal, which gives us 1.06x. Then, we need to add the tip to the entire amount, which is 21% of the sum of the subtotal and the tax. This can be expressed as 0.21(1.06x) = 0.22386x. Finally, we add the tip to the subtotal and the tax, which gives us 1.06x + 0.22386x = 1.28386x. This is the same as multiplying the subtotal by 1.27, which gives us the expression 1.27x. Therefore, the total amount Elizabeth paid is 1.27 times the subtotal on the bill.

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The sample mean is approximately normally distributed when a random sample of size n is taken from a population, provided that n is at least 30. This is known as the Central Limit Theorem. It states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

If a random sample of size n is taken from a population, then the sample mean is approximately normally distributed, if the sample size n is at least 30. However, this assumption is valid only when the population is normally distributed, and the population distribution is known. Additionally, it is assumed that the random sample is unbiased, meaning that every member of the population has an equal chance of being selected. If the population is not normally distributed, the sample size may need to be larger than 30 to approximate normality. Stratified sampling can also be used to ensure representation of different subgroups within the population, but it does not affect the assumption of normality or unbiasedness. Overall, ensuring that these assumptions are met can increase the accuracy of statistical inference based on the sample mean.
An unbiased random sample ensures that each member of the population has an equal chance of being selected, and stratified sampling involves dividing the population into homogeneous subgroups and selecting samples from each subgroup. This method can provide more accurate and representative results when analyzing population characteristics.

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To find the average mark of the boy, we need to add up all of his scores and divide by the total number of subjects.

Average mark = (89% + 60% + 80% + 96% + 89%) / 5

= 414% / 5

= 82.8%

Therefore, the boy's average mark is 82.8%. It's worth noting that this calculation assumes that all subjects have equal weight, which may not always be the case in real-life scenarios. If different subjects have different weightings, the calculation of the average mark would need to take this into account.

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The interest on $5.255 at 12% for 30 days using ordinary interest can be calculated using the formula:I = PRT,Where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.

Here, P = $5.255, R = 12% = 0.12 (as a decimal), and T = 30/365 = 0.08219 (in years, as the time is given in days).

So,

I = 5.255 x 0.12 x 0.08219 = $0.0518

Rounding to two decimal places, the interest on $5.255 at 12% for 30 days using ordinary interest is $5.26. Therefore, the correct answer is option (c).

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The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

[tex]S = 4\pi r^2,[/tex]

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

[tex]V = (4/3)\pi r^3.[/tex]

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

[tex]dV/dt = d/dt [(4/3)\pi r^3].[/tex]

Using the power rule of differentiation, we get:

[tex]dV/dt = (4/3)\pi * 3r^2 * (dr/dt).[/tex]

Simplifying further, we have:

[tex]dV/dt = 4\pi r^2 * (dr/dt).[/tex]

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

[tex]100\pi = 4\pi r^2.[/tex]

Dividing both sides by 4π, we get:

[tex]r^2 = 25.[/tex]

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

[tex]dV/dt = 4\pi(5^2) * (0.3).[/tex]

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

-4,096

Step-by-step explanation:

If you multiply:

4x4x4x4x4x4= 4,096

Then, just make that negative:

-4,069

Hope this helps :3

The solution to the given absolute value problems is:

1) x > 0 and x < 0

2) x > 0 and x < 0

3) y = |x| + 2

The absolute value which is also referred to as modulus | x | of a real number x is the non-negative value of x without any regard given  to its sign. For example, the absolute value of 4 is 4, and the absolute value of −4 is also 4. The absolute value of a number may be referred to as its distance from zero along real number line.

1) |x - 5| if x > 5

Using the concept of absolute value functions, we have:

For (x - 5) if x > 5: x > 0

For -(x - 5) if x > 5: x < 0

Thus, the solution is: x > 0 and x < 0

2) |x - 5| if x > 5

Using the concept of absolute value functions, we have:

For (x - 5) if x > 5: x > 0

For -(x - 5) if x > 5: x < 0

Thus, the solution is: x > 0 and x < 0

3) When we translate a function by two units upwards, then it means that we add 2 to the function.

Thus, we have:

y = |x| + 2

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A line plot for the weight of each piece of fruit, in pounds is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the weight of each piece of fruit, in pounds on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the data set is skewed.

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The domain and the range of the given function will be same and all the real numbers.

Given is a function f(x)= -√√x we need to see the range and the domain of the function,

Since the function is a root function, so the range and the domain will be all real numbers and hence equal.

Hence the domain and the range of the given function will be same and all the real numbers.

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The correct statement is: The range and domain of the graph are the same.

The function f(x) = -√-x is a valid function for all real numbers.

When x is negative, -x is positive and √-x is an imaginary number, which is then multiplied by -1 to make the function real.

Therefore, the range of the graph is all real numbers.

Thus, The range and domain of the graph are the same.

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Answer:To find f(g(x)), we first substitute g(x) into the expression for f(x), then simplify:

f(g(x)) = f(√x-1)

= 3(√x-1) + 2   (substitute √x-1 for x in the expression for f(x))

= 3√x - 3 + 2

= 3√x - 1

Therefore, f(g(x)) = 3√x - 1.

Step-by-step explanation:

(a) The probability that both John and Jane watch the show is 0.07.

(b) The probability that Jane watches the show, given that John does, is 0.11

(c) No. John and Jane do not watch the show independently of each other.

(a) The probability that both John and Jane watch the show is given by the product of their individual probabilities:

P(John and Jane watch) = P(John watches) x P(Jane watches)

     = 0.7 x 0.1

     = 0.07.

(b) The probability that Jane watches the show, given that John does, is given by Bayes' theorem:

P(Jane watches | John watches) = P(John watches | Jane watches) x P(Jane watches) / P(John watches)

From the information given, we know that:

To find P(John watches), we can use the law of total probability:

P(John watches) = P(John watches | Jane watches) * P(Jane watches) + P(John watches | not Jane watches) * P(not Jane watches)

           = (0.8 x 0.1) + (0.7 x 0.9)

           = 0.71

Therefore,

P(Jane watches | John watches) = 0.8 x 0.1 / 0.71 = 0.1127

(c) John and Jane do not watch the show independently of each other, since the probability that John watches the show changes depending on whether or not Jane watches it. In other words, the events "John watches the show" and "Jane watches the show" are dependent events.

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Figure L is a translation of Figure J.

Option B is the correct answer.

We have,

Translation refers to the movement of an object in a certain direction without changing its shape, size, or orientation.

In other words,

The object is shifted or moved from one location to another in a straight line while maintaining its properties such as length, angles, and size.

Now,

Translation will give the same shape and size.

So,

Figure J has the same shape and size as Figure L.

Thus,

Figure L is a translation of Figure J.

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The perimeter of parallelogram ABCD is given as follows:

360 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

On a parallelogram, the opposite sides are congruent, hence the equations relating x and y are given as follows:

The solutions to the system are given as follows:

x = 4 and y = 15.

Hence the side lengths are:

The perimeter is of:

P = 2 x (76 + 104)

P = 360 units.

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Using the tables we can evaluate the given functions to get:

Here we have two tables for the functions f(x) and g(x), first we want to find the sum:

(f + g)(3) = f(3) + g(3)

Using the table we can see that:

f(3) = 8

g(3) = 1

Then:

(f + g)(3) = 8 + 1 = 9

For the second one we have:

(f times g)(-1) = f(-1)×g(-1)

Where:

f(-1)= -2

g(-1) = 4

Then we will get (f times  g)(-1) = -2*4 = -8

Now we have the compositions:

f(g(2))

and g(2) = 3, then:

f(g(2)) = f(3) = 8

Finally:

g(f(0))

Where f(0) = 0

Then:

g(f(0)) = g(0) = 2

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Answer:

He makes 12 shortcakes.