Which equation shows this relationship?

Answer: The answer is Point-by-point graphing

Step-by-step explanation:

Point-by-point graphing is a process where ordered pairs of points that solve an equation are found. The points are plotted on a grid and then connected with a smooth curve.

L = 0.403 is the lower end of the confidence interval

U = 0.487 is the upper end of the confidence interval

The margin of error E is

E = (U-L)/2

E = (0.487-0.403)/2

E = 0.042

Which is half the distance from the lower to upper end

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

The midpoint of the confidence interval is the value of [tex]\hat{p}[/tex] (read out as "p hat")

phat = (U+L)/2

phat = (0.487+0.403)/2

phat = 0.445

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

Answer: The confidence interval (0.403, 0.487) can be rewritten into the form [tex]0.445 \pm 0.042[/tex]

Based on the information given, it should be noted that the 28 years would be considered an example of descriptive statistics.

Therefore, 28 years would be considered an example of descriptive statistics.

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The average age of 28 years in the given class is an example of a statistic, which is a numerical value calculated from a sample of a larger population.

In the context of this question from the subject of mathematics, specifically statistics, the average age of 28 years for students in a class is considered an example of a statistic. A statistic is a value calculated from a sample drawn from a larger population. In this case, the sample consists of students in this particular class, and the population could be all students taking a statistics class in the country or the world. The average (or mean) is a basic type of statistic used to summarise a set of values. It's important to note that the average is just one type of statistic - there are many others, such as median, mode, range, and standard deviation that provide different ways to summarise and represent data.

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The question involves calculating the area between a hyperbola and a line using trigonometric substitution, yet it's more directly related to understanding hyperbola properties and standard integration techniques of hyperbolic functions rather than a straightforward trigonometric substitution problem.

The problem involves finding the area bounded by the hyperbola 25x² - 4y² = 100 and the line x = 3 using trigonometric substitution. This specific problem requires a solid understanding of calculus, particularly integration, and knowledge of hyperbolas and trigonometric identities. To solve this, we first rewrite the hyperbola in its standard form, which is √(25x²/100 - 4y²/100) = 1, simplifying to x²/4 - y²/25 = 1, indicating that a = 2 and b = 5. Using trigonometric substitution, we set x = a sec(θ) and y = b tan(θ) where a and b are the semi-major and semi-minor axes of the hyperbola, respectively. However, the given question simplifies to the computation of an area for a given range of x, particularly up to x = 3, which doesn't directly imply a need for integral computation but rather an understanding of the geometry of hyperbolas.

The straight line x = 3 intersects the hyperbola at specific points, and the area in question could be typically found using trigonometric integrals if it required finding an area under a curve or between two curves. In this context, without further details on the exact method of trigonometric substitution to be used for computing the area directly, we often rely on the integrals involving the hyperbolic trigonometric functions, using limits set by the intersections of the curve and the line. Since a direct solution involving trigonometric substitution for area calculation under these conditions is complex and not standard, it's crucial to review the application within this specific problem's context further.

Answer:

One granola costs $1.40.

One water bottle costs $0.75.

Step-by-step explanation:

This question can be solved by a simple system of equations.

I am going to say that

x is the cost of each granola bar.

y is the cost of each bottle of water.

The first step is building the system:

10 granola bars and twelve bottles of water cost $23.

This means that:

10x + 12y = 23.

5 granola bars and 4 water bottles of water of water cost $10

This means that:

5x + 4y = 10

So we have to solve the following system of equations:

10x + 12y = 23

5x + 4y = 10

I am going to multiply the second equation by -2, and use the addition method. So:

10x + 12y = 23

-10x - 8y = -20

10x - 10x + 12y - 8y = 23 - 20

4y = 3

y = 0.75

y = 0.75 means that each water bottle costs 75 cents.

5x + 4y = 10

5x = 10 - 4y

5x = 10 - 4*0.75

5x = 7

x = 1.4.

x = 1.4 means that each granola costs $1.40.

Answer:one granola costs $1.4

One bottle of water costs $0.75

Step-by-step explanation:

Let x represent the cost of one granola.

Let y represent the cost of one water bottle.

10 granola bars and twelve bottles of water cost $23. It means that

10x + 12y = 23 - - - - - - - - - - - 1

5 granola bars and 4 water bottles of water of water cost $10. It means that

5x + 4y = 10 - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

10x + 12y = 23

10x + 8y = 20

Subtracting, it becomes

4y = 3

y = 3/4 = 0.75

Substituting y = 0.75 into equation 1, it becomes

10x + 12 × 0.75 = 23

10x + 9 = 23

10x = 23 - 9 = 14

x = 14/10 = 1.4

Answer:

y=-3x+7

Step-by-step explanation:

y=mx+b is the formula you are going to end up once completed.

This, by given two points:

(4,-5) (3,-2)

[tex]\frac{-2-5}{3-4}[/tex] = Point-Slope Intercept Form

[tex]\frac{3}{-1}[/tex] = After subtracting both from above

-3 = is your slope, decreasing.

Substitute -3 for y=mx+b

y=-3x+b

Use one of the given points (any) to find what b equals.

(4,-5)

x    y

-5=-3(4)+b

-5= -12+b

7=b

Final Equation:

y=-3x+7

Answer: y = -3x + 7

Step-by-step explanation:

The formula for calculating equation of line that passes through two points is given by :

[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 4

[tex]x_{2}[/tex] = 3

[tex]y_{1}[/tex] = -5

[tex]y_{2}[/tex] = -2

substituting the values into the equation , we have :

[tex]\frac{y-(-5)}{x-4}[/tex] = [tex]\frac{-2-(-5)}{3-4}[/tex]

[tex]\frac{y+5}{x-4}[/tex]    = [tex]\frac{-2+5}{3-4}[/tex]

[tex]\frac{y+5}{x-4}[/tex]    = [tex]\frac{3}{-1}[/tex]

[tex]\frac{y+5}{x-4}[/tex]    = -3

y + 5 = -3( x - 4 )

y + 5 = -3x + 12

y = -3x + 12 - 5

y = -3x + 7

Answer:

(D)

Step-by-step explanation:

[tex](A)[/tex]

Let's have a look at the first sample space, the set

                                      [tex]S = \{b,c\}[/tex]

As we can see, it consists of two elements. Element [tex]b[/tex] implies that a call was made, but the line was busy, and the element [tex]c[/tex] implies that the call was connected. However, this sample space doesn't correspond to the event in which the calls are repeatedly made until a connect is achieved. The element [tex]c[/tex] is suitable, because it is possible that the line wasn't busy at the moment of calling, but the element  [tex]b[/tex] implies that after receiving the busy signal, there were no further attempts to connect to the line.

[tex](B)[/tex]

The second sample space is

                                  [tex]S =\{bbbbbb, \ldots \}[/tex]

It corresponds to the case in which after a few attempts to connect to the line, the person gave up. Therefore, it doesn't correspond to our problem.

[tex](C)[/tex]

The third sample space is

                                  [tex]S = \{ cb, cbb, cbbb, \ldots \}[/tex]

It corresponds to the case in which after one successful attempt, the person tried again for a few more times, and also gave up before connecting again. Therefore, it doesn't correspond to our problem either.

[tex](D)[/tex]

The last sample space is

                              [tex]S = \{ c, bc, bbc, bbbc, \ldots\}[/tex]

The first element corresponds to the case that the line wasn't busy in the first attempt. The second element, [tex]bc[/tex], corresponds to the case in which the line was busy in the first attempt but it wasn't in the second. The third is the one in which the line was busy for three attempts, but wasn't in the fourth, and so on. As we can see, the common thing about all this elements is that the there were no further attempts after a connection was achieved, which corresponds to our case. Therefore, this is the correct sample space.

The correct option is D. S = {c, bc, bbc, bbbc, ...}.

The sample space for this scenario should include all possible outcomes of the calling process until a connection is made.

Since calls are placed repeatedly until the line is no longer busy, the sequence of events will consist of a series of 'b's followed by a 'c'.

The 'c' represents the successful connection, and it must be the last event in the sequence.

Answer:outliers

Step-by-step explanation:

Answer:

The answer is cluster sampling

Step-by-step explanation:

Going back to the basic types of sampling and how they are acconplished, cluster sampling is accomplished by dividing the population into groups (usually geographical) which in the above question is referred to as the geographical area. These groups are called clusters or blocks. The clusters are randomly selected and each element in the selected clusters are used. Therefore the most realistic sampling method that represents the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area is cluster sampling.

Final answer:

Stratified sampling is the most realistic sampling method for geologists to represent the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area.

Explanation:

Stratified sampling is the most realistic sampling method for geologists to represent the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area. This method involves dividing the population into distinct subgroups based on certain characteristics and then randomly selecting samples from each subgroup.

For example, in geology, geologists may stratify the geographical area based on different rock types or layers to ensure a representative sample of the earth's structure. By using stratified sampling, geologists can account for the diverse composition and ages of various layers within the sampled area, leading to more accurate interpretations of the history and structure of the earth.

Stratified sampling allows geologists to focus their analyses on specific layers or formations within the earth's structure, providing a comprehensive understanding of the geological history of a particular area. This method enhances the reliability and validity of the findings obtained from multiple core samples taken within the same geographical region.

Answer:

a) 1

b) 1

Step-by-step explanation:

Data provided in the question:

X = The time in minutes between two successive arrivals

X has an exponential distribution with λ = 1

Now,

a) The expected time between two successive arrivals is minutes i.e

E(X) = [tex]\frac{1}{\lambda}[/tex]

or

E(X) = [tex]\frac{1}{1}[/tex]

or

E(X) = 1

b)  The standard deviation of the time between successive arrivals is minutes

i.e

σₓ = [tex]\sqrt{\frac{1}{\lambda^2}}[/tex]

or

σₓ = [tex]\sqrt{\frac{1}{1^2}}[/tex]

or

σₓ = 1

Answer:

a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

[tex] X \sim Bin(n =20, p=0.8)[/tex]

b) [tex] X \sim Bin(n =20, p=0.8)[/tex]

c) [tex]P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456[/tex]

d) [tex] P(X \geq 15) = P(X=15)+ .....+P(X=20) [/tex]

[tex]P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456[/tex]

[tex]P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218[/tex]

[tex]P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205[/tex]

[tex]P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137[/tex]

[tex]P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058[/tex]

[tex]P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012[/tex]

[tex] P(X\geq 15)=0.804208 [/tex]

e) [tex] E(X) = np = 20*0.8 = 16[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

[tex] X \sim Bin(n =20, p=0.8)[/tex]

Part b

[tex] X \sim Bin(n =20, p=0.8)[/tex]

Part c

For this case we just need to replace into the mass function and we got:

[tex]P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456[/tex]

Part d

For this case we want this probability: [tex] P(X\geq 15) [/tex]

And we can solve this using the complement rule:

[tex] P(X \geq 15) = P(X=15)+ .....+P(X=20) [/tex]

[tex]P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456[/tex]

[tex]P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218[/tex]

[tex]P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205[/tex]

[tex]P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137[/tex]

[tex]P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058[/tex]

[tex]P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012[/tex]

[tex] P(X\geq 15)=0.804208 [/tex]

Part e

The expected value is given by:

[tex] E(X) = np = 20*0.8 = 16[/tex]

Answer:

564 of the cattle are female

Step-by-step explanation:

if 52% of them are male, then 48% are female.

.48*1175=564

Answer:

1227

Step-by-step explanation:

Answer:

D) 1/2

Step-by-step explanation:

A linear function has the following format:

[tex]y = ax + b[/tex]

In which a is the slope, that is, the rate of change of the function and b is the y-intercept, that is, the value of y when x = 0.

We have that:

Point (5,2), which means that when x = 5, y = 2. So

[tex]y = ax + b[/tex]

[tex]5a + b = 2[/tex]

Point (9,4), which means that when x = 9, y = 4. So

[tex]9a + b = 4[/tex]

I am going to write b as a function of a in the second equation, and replace on the first. So

[tex]b = 4 - 9a[/tex]

Then

[tex]5a + b = 2[/tex]

[tex]5a + 4 - 9a = 2[/tex]

[tex]-4a = -2[/tex]

[tex]4a = 2[/tex]

[tex]a = 1/2[/tex]

This means that the slope, which is the rate of change of the function, is 1/2.

So the correct answer is:

D) 1/2

Answer:

15 °

Step-by-step explanation:

The five angles are splitted in the ratio 1:3:5:8:12

The 1st biggest angle is at ratio 12

The 2nd biggest angle is at ratio 8

The 3rd biggest angle is at ratio 5

The 4th biggest angle is at ratio 3.

Time solve for the 4th biggest angle, we will find the sum of the ratios:

Therefore, 1 + 3 + 5 + 8 + 12 = 29

Ratio of 4th biggest angle:

= (3)/(29). * 145

= (3 * 45) / 29

= 3 * 5

= 15 °

Answer:

False. Is the inverse process.

See explanation below.

Step-by-step explanation:

We need to remember two important concepts:

A parameter, is a quantity or value who describe a population desired, for example the population mean [tex]\mu[/tex] or the population standard deviation [tex]\sigma[/tex]

A statistic, is a quantity or value who represent the information of the sample data, for example the sample mean [tex] \bar X[/tex] or the sample deviation [tex] s[/tex]

Based on this we can analyze the statement:

"Inferential statistics involves using population data to make inferences about a sample"

False. Is the inverse process.

If we know the population data then we indeed have parameters and we don't need to do any type of inference in order to estimate these parameters with the statistics.

What we do generally is use the information from the sample in order to obtain statistics representative of the population with the aim to estimate the parameters unknown of the population

Answer:

d) 0.0132

Step-by-step explanation:

In a sample of size n, with proportion p, the standard error of the proportion is:

[tex]SE_{p} = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem, we have that:

[tex]p = 0.26, n = 1100[/tex]

So

[tex]SE_{p} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.26*0.74}{1100}} = 0.0132[/tex]

So the correct answer is:

d) 0.0132

Final answer:

Explaining the calculation of the standard error for a proportion estimate based on a poll of truck drivers encountering aggressive dogs.

Explanation:

Question: In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once. What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once?

Answer:

Calculate the standard error using the formula: SE = sqrt((p*(1-p))/n)

Substitute the values: p = 0.26 (proportion), n = 1100 (sample size)

SE = sqrt((0.26*(1-0.26))/1100) = sqrt((0.26*0.74)/1100) = sqrt(0.1924/1100) = sqrt(0.000175) ≈ 0.0132 (option d)

Answer: 59.91%.

Step-by-step explanation:

We are given , that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

Then, the fraction of the variability in fuel economy is accounted for by the engine size would be [tex]r^2=( - 0.774)^2=0.599076\approx59.91\%[/tex]

[Multiply 100 to convert a decimal into percent]

Hence, the fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

None of the options are correct.

To solve such problems we must know about the fraction of the variability in data values or R-squared.

                                                                           = r²

The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

As it is given that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

the variability in fuel economy = r²

                                                   = (-0.774)²

                                                   = 0.599076

                                                   = 59.91%

Hence, the fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

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Answer:

a) Dimension of AB is DEFINED

b) Dimension of BA is UNDEFINED

Step-by-step explanation:

A matrix is always represented with (mxn) rows and columns. the rows are the elements in the horizontal line while the columns make up the elements in the vertical line. however, there are rules in multiplication of matrix.

To multiply matrix, multiply elements in the rows of the first matrix by the elements in the columns of the second matrix. for example if you're multiplying a 3by2 matrix by a 2by3 matrix, the resulting matrix will be a 3by3 matrix from (mxn) -rows and columns.

from the question, matrix A is a 3by5 (3x5) matrix i.e it has 3rows and 5columns.

matrix B is a 5by2 (5x2) matrix i.e it has 5rows and 2columns.  multiplying AB = (3x5) X (5x2), hence the resultant matrix will be a 3by2 (3x2) and this shows that multiplication or dimension of AB is DEFINED.

As for the multiplication of BA = (5x2) X (3x5), from this multiplication, it is not possible as such we can't determine any resultant matrix, this makes multiplication or dimension of BA to be UNDEFINED.

Final answer:

The total number of possible birth orders with respect to gender in a family with five children is 32.

Explanation:

The appropriate counting technique to answer this question is A. permutations. Permutations are used when the selections come from a single group of items, no item can be selected more than once, and the order of the arrangement matters. In this case, the birth orders with respect to gender can be represented by arranging the genders of the children in different orders.

Since there are 5 children, there are 5 positions to fill. The first position can be filled with either a boy or a girl, so there are 2 options. The second position can also be filled with either a boy or a girl, so there are 2 options again. This goes on for all 5 positions.

Therefore, the total number of possible birth orders with respect to gender is 2 * 2 * 2 * 2 * 2 = 32.

Answer:

P(X > 126) = 0.2119

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 110, \sigma = 20[/tex]

P(X > 126) is the 1 subtracted by the pvalue of Z when X = 126. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{126 - 110}{20}[/tex]

[tez]Z = 0.8[/tex]

[tez]Z = 0.8[/tex] has a pvalue of 0.7881.

P(X > 126) = 1 - 0.7881 = 0.2119

The probability P(X > 126) for a normally distributed random variable X with mean μ = 110 and standard deviation σ = 20 is approximately 21.19%.

This question is about computing the probability that a normally distributed random variable X with a specified mean and standard deviation exceeds a certain value. In our case, mean μ = 110 and standard deviation σ = 20, and we want to find the probability P(X > 126).

To solve this problem, we first need to compute the Z-score, which is a measure of how many standard deviations a given data point is from the mean, using the formula: Z = (X - μ) / σ. To compute P(X > 126), therefore, we first compute Z = (126 - 110) / 20 = 0.8.

Next, we look up the probability associated with Z = 0.8 in a standard normal distribution table. However, standard normal tables usually give the probability P(Z < z). Since we are looking for P(X > 126), or equivalently P(Z > 0.8), we need to subtract the value we get from the table from 1, since the total probability under a normal curve is one. If we look up Z = 0.8 in the table, we get approximately 0.7881. Hence, P(Z > 0.8) = 1 - P(Z ≤ 0.8) = 1 - 0.7881 = 0.2119 or about 21.19%.

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Answer:

{(x, 4f(x)) = (-2,0), (3, 16), (7, 48), (9, -52)}

Step-by-step explanation:

We have the following set of ordered pairs:

(x, f(x))

(-2,0). So f(-2) = 0. That is when x = -2, y = 0.

(3,4). So f(3) = 4. That is, when x = 3, y = 4.

(7,12). So f(7) = 12. That is, when x = 7, y = 12.

(9, -13). So f(9) = -13. That is when x = 9, y = -13.

find the set of ordered pairs (x, 4[f(x)]).

We just need to multiply the values of y by 4. So the set is

{(x, 4f(x)) = (-2,0), (3, 16), (7, 48), (9, -52)}

Answer:

The correct answer is C. 32h = C

Step-by-step explanation:

For finding out the equation that can be used to find the total number of contestants, C, that audition in h hours. we will use these variables:

Number of contestants = C

Number of hours of auditions = h

Number of contestants that can audition per hour = 32

Now, we can affirm that the equation that can be used to find the total number of contestants, C, that audition in h hours is:

C = 32 * h

The correct answer is C. 32h = C

Answer:there are 11 goats and 17 ducks.

Step-by-step explanation:

Let x represent the number of goats in the field.

Let y represent the number of ducks in the field.

A farmer looks over a field and sees 28 heads and 78 feet. some are goats, some are ducks. A goat has one head and a duck also has one head. It means that

x + y = 28

A goat has 4 feets and a duck has two feets. It means that

4x + 2y = 78 - - - - - - - - - - - - - 1

Substituting x = 28 - y into equation 1, it becomes

4(28 - y) + 2y = 78

112 - 4y + 2y = 78

- 4y + 2y = 78 - 112

- 2y = - 34

y = - 34/- 2

y = 17

x = 28 - y = 28 - 17

x = 11

To find the number of goats and ducks in the field, set up a system of equations using the given information. Solve the system of equations using elimination or substitution method. After solving, you will find that there are 11 goats and 17 ducks in the field.

Let's solve this problem by setting up a system of equations. Let's assume that the number of goats is G and the number of ducks is D.

From the given information, we can set up two equations:
1) G + D = 28 (equation 1) - since the total number of heads is 28
2) 4G + 2D = 78 (equation 2) - since each goat has 4 feet and each duck has 2 feet

We can solve these equations using substitution or elimination. Let's solve by elimination method:

Multiplying equation 1 by 2, we get:
2G + 2D = 56 (equation 3)

Subtracting equation 3 from equation 2, we get:
2G = 22
G = 11

Substituting the value of G into equation 1, we get:
11 + D = 28
D = 17

Therefore, there are 11 goats and 17 ducks in the field.

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Answer:

[tex]P(t) = 40e^{0.06931t}[/tex]

Step-by-step explanation:

The population exponential equation is as follows.

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(t) is the population in t years from now, P(0) is the population in the current year and r(decimal) is the growth rate.e = 2.71 is the Euler number.

Find an exponential model for the population (in millions of people) at any time ????, in years after 1980.

There were 40 million people in 1980 (when ????=0).

This means tht P(0) = 40.

So

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]P(t) = 40e^{rt}[/tex]

80 million people in 1990.

1990 is 10 years after 1980. So P(10) = 80. We use this to find the value of r.

So

[tex]P(t) = 40e^{rt}[/tex]

[tex]80 = 40e^{10r}[/tex]

[tex]e^{10r} = 2[/tex]

Applying ln to both sides, since [tex]\ln{e^{a}} = a[/tex]

[tex]\ln{e^{10r}} = \ln{2}[/tex]

[tex]10r = 0.6931[/tex]

[tex]r = \frac{0.6931}{10}[/tex]

[tex]r = 0.06931[/tex]

So the exponential model for the population is:

[tex]P(t) = 40e^{0.06931t}[/tex]

Answer:

A

Step-by-step explanation:

The piano is 0.2 standard deviations below the average piano cost, while the guitar is 0.5 standard deviations above the average guitar cost. The drum set is 1 standard deviation below the average drum set cost. The drums have the lowest cost compared to other instruments of the same type, and the piano has the highest cost.

1.) To find how many standard deviations above or below the average piano cost is the piano, we need to calculate the z-score. The formula for calculating the z-score is

z = (x - mean) / standard deviation

Let's plug in the values for the piano:

z = ($4,000 - $4,500) / $2,500

z = -0.2

So, the piano is 0.2 standard deviations below the average piano cost.

2.) Following the same formula, let's calculate the z-score for the guitar:

z = ($600 - $500) / $200

z = 0.5

Thus, the guitar is 0.5 standard deviations above the average guitar cost.

3.) Using the formula for the z-score again, let's calculate the z-score for the drum set:

z = ($750 - $850) / $100
z = -1

The drum set is 1 standard deviation below the average drum set cost.

4.) The cost of the drums is the lowest when compared to other instruments of the same type.

5.) The cost of the piano is the highest when compared to other instruments of the same type.

The expression in terms of [tex]x[/tex] that represents the number of feet Cody has walked toward Chelsea since they started walking is [tex]x_{Co} = x[/tex].

In this question we assume that both Cody and Chelsea have a uniform motion, in opposite sides and to their encounter. If both travel the same number of feet, the kinematic formulas for each walker are described below:

[tex]x_{Co} = x[/tex] (1)

[tex]x_{Ch} = 270 - x[/tex] (2)

[tex]x_{Co} = x_{Ch}[/tex] (3)

Where:

By (3), (2) and (1) we have the following equation:

[tex]x = 270 - x[/tex]

[tex]2\cdot x = 270[/tex]

[tex]x = 135\,ft[/tex]

The expression in terms of [tex]x[/tex] that represents the number of feet Cody has walked toward Chelsea since they started walking is [tex]x_{Co} = x[/tex]. [tex]\blacksquare[/tex]

To learn more on uniform motion, we kindly invite to check this verified question: https://brainly.com/question/118814

The expression to represent the number of feet Cody has walked toward Chelsea since they started walking is '270 - 2x'. Where 'x' represents the distance Cody has traveled and '2x' reflecting that Chelsea has traveled the same distance. The total is subtracted from 270, the initial distance, to find the remaining distance.

Given that Cody and Chelsea start walking towards each other from a distance of 270 feet and that they are walking at the same speed. If x represents the number of feet Cody has traveled since he started walking, given that Chelsea travels the same distance, the total distance they have both traveled together is represented by 2x. Since they started 270 feet apart, to find out how much more they still have to walk until they meet, you would subtract the total feet they've walked from the original distance. So this can be represented by the expression: 270 - 2x. This expression will give us the remaining distance after Cody has walked 'x' feet towards Chelsea.

https://brainly.com/question/953809

#SPJ3

Answer:

There are 16 possible outcomes, all equally likely. There’s only one way to get four heads and only one way to get no heads. That leaves 14 ways to get two or three heads.

There’s four ways to get three heads. The first coin can be the tail, the second can be the tail, the third can be the tail, or the fourth can be the tail.

There’s also four ways to get one head. The first coin can be the head, the second can be the head, the third can be the head, or the fourth can be the head.

That leaves six ways left to get exactly two heads. So 6/16 or 3/8.

Step-by-step explanation:

Convert pounds to kilograms.

1 pound = 0.4536 kg.

170 pounds x 0.4536 = 77.11 kg.

Multiply weight by grams of protein per kg.

77.11 kg x 1.4 =107.95 grams. Round answer as needed.

Viola should consume approximately 108.18 grams of protein daily based on her weight and the recommended intake for collegiate volleyball players.

To calculate the amount of protein Viola should consume daily, we need to follow these steps:

1. Convert Viola's weight from pounds to kilograms:

170 lbs / 2.2 = 77.27 kg (rounded to 2 decimal places).

2. Determine her protein needs:

77.27 kg * 1.4 g/kg = 108.18 g of protein per day (rounded to 2 decimal places).

Therefore, Viola should consume approximately 108.18 grams of protein daily based on her weight and the recommended intake for collegiate volleyball players.

Answer:

36+24= 60

Step-by-step explanation:

just do 6x6 and add it to 3x8

Answer: 10ft 2in

Step-by-step explanation: