a person tosses a coin 15 times. in how many ways can he get 3 heads?

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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when possible, the best way to establish that an observed association is the result of a cause and effect relation is by means of well designed experiment.

In an experiment, a researcher manipulates one or more variables, while holding all other variables constant. By noting how the manipulated variables affect a response variable, the researcher can test whether a causal relationship exists between the manipulated variables and the response variable. Characteristics of a Good Experimental Design:

Provides unbiased estimates of the factor effects and associated uncertainties Enables the experimenter to detect important differences Includes the plan for analysis and reporting of the results Gives results that are easy to interpret Permits conclusions that have wide validity Shows the direction of better results Is as simple as possible Basic Principles of  experimental design:

The basic principles of experimental design are

(i) Randomization

(ii) Replication

(iii) Local Control

Randomization:

Randomization is the cornerstone underlying the use of statistical methods in experimental designs.  Randomization is the random process of assigning treatments to the experimental units. The random process implies that every possible allotment of treatments has the same probability.

Replication:

By replication, we mean that repetition of the basic experiments. For example, If we need to compare the grain yield of two varieties of wheat then each variety is applied to more than one experimental units.

Local Control

it has been observed that all extraneous source of variation is not removed by randomization and replication, i.e. unable to control the extraneous source of variation. Thus we need to a refinement in the experimental technique.

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Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

26

Step-by-step explanation:m a t h w a y

Answer:

26

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Answer:

d.

Step-by-step explanation:

As the number is +5, start your pencil at point -3 and move it just 5 times to the right until you reach point +2 on the number line.

So, (-3) + 5 using number line:

(Refer to the number line given below)

Therefore, as the number is +5, start your pencil at point -3 and move it just 5 times to the right until you reach point +2 on the number line.

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The lower bound of the 95% confidence interval is given as follows:

7.981 mm.

The level of confidence of the statement is of 95%.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.

The parameters for this problem are given as follows:

\(\overline{x} = 8.1, s = 0.6, n = 100\)

Hence the lower bound of the interval is given as follows:

8.1 - 1.9842 x 0.6/10 = 7.981 mm.

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Answer:

x - 11

Step-by-step explanation:

"A number" is the same thing as a variable.

Answer:

x-11

Step-by-step explanation:

Minimum score required for the scholarship = 605

To find the minimum score required for the scholarship, we need to find the score that corresponds to the top 6% of scores.

First, we need to find the z-score that corresponds to the top 6%. We can use the standard normal distribution table or calculator to find this.

Using the calculator, we can input:

normalcdf(0.94,9999)

This gives us the area under the curve to the right of z=0.94, which is the z-score that corresponds to the top 6%.

We get: 0.1664

This means that the top 6% of scores correspond to z-scores greater than 0.94.

Now we can use the z-score formula:

z = (x - μ) / σ

where x is the score we want to find, μ is the mean (489), and σ is the standard deviation (112).

Rearranging this formula, we get:

x = z * σ + μ

Substituting in the values we have:

x = 0.94 * 112 + 489

x = 605.08

Rounding this to the nearest whole number, we get:

Minimum score required for the scholarship = 605

To find the minimum score required for the scholarship, we will use the given information about the SAT writing scores being normally distributed with a mean (µ) of 489 and a standard deviation (σ) of 112. We need to find the score that corresponds to the top 6%.

Step 1: Convert the percentage to a decimal. Top 6% = 0.06.

Step 2: Find the Z-score that corresponds to the top 6%. This means we want to find the Z-score that has 1 - 0.06 = 0.94 area to the left. Using a Z-table, you can find that the Z-score is approximately 1.555.

Step 3: Use the Z-score formula to find the minimum score (X):

Z = (X - µ) / σ

1.555 = (X - 489) / 112

Step 4: Solve for X:

1.555 * 112 = X - 489

174.16 = X - 489

X = 663.16

Round to the nearest whole number: X = 663.

So, the minimum score required for the scholarship is 663.

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Answer:

x = - 3/28

Step-by-step explanation:

Report if wrong

-Stylez-

Answer:

x= -3/28

Step-by-step explanation:

Multiply both sides of the equation by 42

-28x+18=21

-28x=21-18

-28x=3

x= -3/28

The missing terms of the sequence are 15.75 and 7.875, and the sequence is geometric.

What is sequence?

In mathematics, a sequence is an ordered list of numbers or objects in a specific pattern or order. Each individual element in the sequence is called a term or member of the sequence.

To determine the missing terms of the sequence and determine its pattern (whether arithmetic, geometric, or neither), let's examine the given sequence: 252, 126, 63, 63/2, __, __.

First, let's check if the sequence has a common difference between consecutive terms to determine if it is an arithmetic sequence. We'll calculate the differences between consecutive terms:

Difference between the 2nd and 1st terms: 126 - 252 = -126

Difference between the 3rd and 2nd terms: 63 - 126 = -63

Difference between the 4th and 3rd terms: (63/2) - 63 = -63/2

The differences are not constant, so the sequence is not arithmetic.

Next, let's check if the sequence has a common ratio between consecutive terms to determine if it is a geometric sequence. We'll calculate the ratios between consecutive terms:

Ratio between the 2nd and 1st terms: 126/252 = 1/2

Ratio between the 3rd and 2nd terms: 63/126 = 1/2

Ratio between the 4th and 3rd terms: (63/2) / 63 = 1/2

The ratios are constant (1/2), so the sequence is geometric.

Since the sequence is geometric with a common ratio of 1/2, we can use this ratio to find the missing terms.

To find the next term, we multiply the previous term by the common ratio:

(63/2) * (1/2) = 63/4 = 15.75

To find the term after that, we multiply the previous term by the common ratio again:

(63/4) * (1/2) = 63/8 = 7.875

Therefore, the missing terms of the sequence are 15.75 and 7.875.

In summary, the missing terms of the sequence are 15.75 and 7.875, and the sequence is geometric.

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Answer:

The price of per ounce of strawberries is $ 0.25.

Step-by-step explanation:

Pounds to ounce conversion:

As we know that,

 One pound = 16 Ounce

Since, Jill bought a pound of strawberries for $4

It means that,

Price of 16 Ounces of strawberries = $ 4

So taht,  Price of one ounce of strawberries

Hence, the price of per ounce of strawberries is $ 0.25.

Answer:

0.25

Step-by-step explanation:

16 ounces = 1 pound

4.00 / 16 = 0.25

No, it is not correct to conclude that the sample means cannot be treated as being from a normal distribution solely based on a small sample size of n = 15.

The Central Limit Theorem states that the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution, as the sample size increases. Therefore, even with a small sample size, the sample means can still be considered to follow a normal distribution under certain conditions.

The Central Limit Theorem assures that, as the sample size increases, the distribution of sample means becomes approximately normal, regardless of the shape of the population distribution. Although a sample size of n = 15 may be considered small, it is not sufficient to conclude that the sample means cannot be treated as following a normal distribution.

The applicability of the Central Limit Theorem depends on certain conditions, such as the independence of observations, a sufficiently large sample size, and the absence of extreme outliers. If these conditions are satisfied, the sample means can be treated as approximately normally distributed, even with a small sample size.

Therefore, it is not appropriate to conclude that the sample means cannot be treated as being from a normal distribution based solely on a small sample size of n = 15. Further analysis and consideration of the Central Limit Theorem should be conducted to determine the distributional properties of the sample means.

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Answer: 435.24, 294.44 and 573.73.

Step-by-step explanation:

Helping dmitri sort his accounts from lowest to highest absolute value of account value will be for us to choose the smallest number first till the highest. Thus will be:

= -435.24, 294.44 and 573.73.

Answer:

87.5% increase

Step-by-step explanation:

75 - 40 = 35

Find what percentage 35 is of 40, and you can do so by dividing.

35 ÷ 40 = 0.875

0.875 = 87.5%

The conclusion of the hypothesis is that we fail to reject the null hypothesis and conclude that the means are different.

Let us first define the hypothesis;

Null Hypothesis; H₀: μ_a = μ_b

Alternative Hypothesis; Hₐ: μ_a ≠ μ_b

From the given significance value, we can say that we will reject H₀ if the calculated test statistic is greater than 2.797 or t is less than 2.797.

The pooled variance from the attached table with the aid of a statistics calculator gives;

Pooled variance = 0.5938

The test statistic from online calculator is; t = -3.299 or 3.299

This test statistic falls falls within the rejection region and so we reject the null hypothesis and conclude that there is a difference in the average errors of the two processes.

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The constant of proportionality in the equation Y = 5x + 0 is 5, so option B is correct.

When the corresponding elements of two numerical sequences, frequently experimental data, have a fixed ratio, this is referred to as the coefficient of proportionality, and the two sequences are said to be proportional or directly proportional.

Given:

Y = 5x + 0

Simplify the above equation,

Y = 5x

Here, the value of Y will increase with the multiple of 5 of the value of x,

Therefore, the constant of proportionality in the equation Y = 5x + 0 is 5.

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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(a) Derivative, function, f(x), √x, sin(x), product rule, differentiate, term, apply, sin(x)/2√x, √x cos(x)

(b) Derivative, function, f(x), (1+sin(x))/(x+cos(x)), quotient rule, differentiate, numerator, denominator, apply, cos(x) - (1-sin(x))², (x+cos(x))²

(c) Derivative, function, y, x² sin(x) tan(x), product rule, differentiate, term, apply, 2x sin(x) tan(x), x² cos(x) tan(x), x² sin(x) sec²(x)

(a) To find the derivative of f(x) = √x sin(x), we can use the product rule. Let's differentiate each term separately and apply the product rule:

f(x) = √x sin(x)

f'(x) = (√x)' sin(x) + √x (sin(x))'

= (1/2√x) sin(x) + √x cos(x)

= sin(x)/2√x + √x cos(x)

(b) To find the derivative of f(x) = (1+sin(x))/(x+cos(x)), we can use the quotient rule. Let's differentiate the numerator and denominator separately and apply the quotient rule:

f(x) = (1+sin(x))/(x+cos(x))

f'(x) = [(1+sin(x))' (x+cos(x)) - (1+sin(x))(x+cos(x))'] / (x+cos(x))²

= [0 + cos(x) - (1+sin(x))(1 - sin(x))] / (x+cos(x))²

= (cos(x) - (1-sin(x))²) / (x+cos(x))²

(c) To find the derivative of y = x² sin(x) tan(x), we can use the product and chain rules. Let's differentiate each term separately and apply the product rule:

y = x² sin(x) tan(x)

y' = (x²)' sin(x) tan(x) + x² (sin(x))' tan(x) + x² sin(x) (tan(x))'

= 2x sin(x) tan(x) + x² cos(x) tan(x) + x² sin(x) sec²(x)

= 2x sin(x) tan(x) + x^2 cos(x) tan(x) + x^2 sin(x) sec^2(x)

These are the derivatives of the given functions.

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The requried, “There are 4 4/5 groups of 5/8in 3.” statement is correct.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Here,
As mentioned in the question we are asked to verify the statment “There are 4 4/5 groups of 5/8in 3.”

Which says that,
4 4/5 = 3 / [5/8]
4 + 4/5 = 3 (8/5)
24 /5 = 24/5

Thus, the requried, “There are 4 4/5 groups of 5/8in 3.” statement is correct.

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Answer:

\(\Large \boxed{x_1=\frac{9+\sqrt{51} }{3} \ \ ; \ \ x_2=\frac{9-\sqrt{51} }{3} }\)

Step-by-step explanation:

\(\displaystyle \Large \boldsymbol{} 3x(x+6)=-10 \\\\3x^2+18x=-10 \\\\3x^2+18x+10=0 \\\\D=324-120=204 \\\\ x_{1;2}=\frac{18\pm2\sqrt{51} }{6} =\frac{9\pm\sqrt{51} }{3}\)

Answer:

Step-by-step explanation:

The perpendicular lines have opposite reciprocal slopes.

The given line has a slope of:

The perpendicular slope is:

And its y-intercept is:

The line is:

Convert this into standard form and compare with answer choices:

Correct choice is A

Answer:

3h³ - h² - 10h

Step-by-step explanation:

(5h​³​​−8h)+(−2h​​³−h​²-2h)

= 5h³ - 8h - 2h³ - h² - 2h

= 3h³ - h² - 10h

So, the answer is  3h³ - h² - 10h

Answer:

--------------------------

Simplify the expression in below steps:

The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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First put it in decreasing power according to x.

x^4-5x+8+x^2

=x^4+x^2-5x+8

Now this question is asking what is the highest degree of x you see in this function.

4 of course.

Therefore the answer to his question is degree of 4.

Done!

The perimeter of the nonagon attached is

124.5

The formula for the perimeter of a nonagon (a polygon with nine sides):

Perimeter = 9 * side length

side length = 2 * apothem * tan(π/9)

= 2 * 19 * tan(π/9)

= 13.831

The perimeter

Perimeter = 9 * side length

Perimeter = 9 * 13.81

Perimeter = 124.5

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Answer:

16 and 56

Step-by-step explanation:

gcf of 24 and 48 is 24

gcf of 14 and 32 is 2

gcf of 16 and 28 is 4

Let's find one by one

#1

24 and 48

No

#2

14 and 32

No

#3

GCF is 4

No

#4

16 and 56

Yes

Answer:

2712.96 yd

Step-by-step explanation:

v (volume) = π\(r^{2}\)h

v = 3.14 x \(12^{2}\) x 6

v = 3.14 x 144 x 6

v = 2712.96