Mitchel owns a livestock trailer that can hold a maximum of 5,000 pounds. The average weight of each goat is 90 pounds, and the average weight of each calf is 360 pounds. Mitchel would like to know how many goats and calves he can transport in a single trip.

The inequality that represents this situation is graphed here.



A.
Mitchel can transport 42 goats and 2 calves in one trip.
B.
Mitchel can transport 30 goats and 8 calves in one trip.
C.
Mitchel can transport 24 goats and 10 calves in one trip.
D.
Mitchel can transport 50 goats and 4 calves in one trip.

The function of domain is X∈R and the range is \(\[\left\{ {f \in \mathbb{R}:f \le \frac{1}{4}(1 + 4\sqrt 2 )} \right\}\].\)

The given function is  \(\[f\left( x \right) = \sqrt {2 - x - {x^2}} \]\)

Domain: The domain of a function is the set of input or argument values for which the function is real.

Use commutative properties to reorder the terms

\(\[f(x) = \sqrt { - x + 2} - {x^2}\]\)

Separate the function into parts to determine the domain of each part

\(\[f\left( x \right) = \sqrt { - x + 2} \]=-x+2= x^{2}\)

Domain is XR (all real numbers)

The function has no undefined points nor domain constraints. Therefore, the domain is X∈R.

Range: The set of values of the dependent variable for which a function is defined

Range of \(\[\left\{ {f \in \mathbb{R}:f \le \frac{1}{4}(1 + 4\sqrt 2 )} \right\}\]\)

Combine the ranges of all domain intervals to obtain the function range.

Hence, the domain and the range of the function \(\[f\left( x \right) = \sqrt {2 - x - {x^2}} \]\) are

Domain = X∈R

Range \(=\[\left\{ {f \in \mathbb{R}:f \le \frac{1}{4}(1 + 4\sqrt 2 )} \right\}\]\).

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Answer:

Step-by-step explanation:

57-6²÷(2+1)*4=

57-36÷3*4=

57-12*4=

57-48=

9

To solve this inequality, we need to find the values of x that make the expression on the left-hand side greater than or equal to zero.

First, we can look at the factors separately. The factor (x-4)^2 is always non-negative because it is a square. That means it is greater than or equal to zero for all values of x.

The factor (x+3) is positive when x is greater than -3 and negative when x is less than -3.

Now we can use the fact that the product of two non-negative numbers is non-negative. So, for the left-hand side of the inequality to be greater than or equal to zero, we need one of the following:

1. Both factors are non-negative, which means x is greater than or equal to 4 and x is greater than -3.
2. One factor is zero and the other is non-negative. The factor (x-4)^2 can only be zero when x=4, so we need to check if (x+3) is non-negative when x=4. It is not, so x=4 is not a solution.
3. Both factors are zero. This occurs when x=4 and x=-3, but x=-3 is not a solution because (x+3) is negative.

Therefore, the solution to the inequality is x is greater than or equal to 4.

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Answer:

y= -x+2, f(x) = -x+2

Step-by-step explanation:

the slope-intercept form is

y= mx+b where mis the slope and b is the y-intercept

here b=2 because is where the line intersects the y-axis

slope m= rise/run = -1/1 = -1

y= -x+2

in standard form is

f(x) = -x+2

The magnitude of the Pennsylvania earthquake is 4.

An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.

The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.

Using the formula,

log I₁ / I₂ = M₁ - M₂

M₁ = 7.7,     I₁ / I₂ = 4900

log 4900 = 7.7 - M₂

log 4900 ≈ 3.69

On calculating,

M₂ ≈ 4

The magnitude of the Pennsylvania earthquake is 4.

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The system stable with P(1)=1.7 and P(-1)=2.7. The correct answer is b.

To test the stability of a discrete control system with an open loop transfer function, we need to examine the roots of the characteristic equation, which is obtained by setting the denominator of the transfer function equal to zero.

The characteristic equation for the given transfer function G(z) is:

z^2 - 1.2z + 0.2 = 0

We can find the roots of this equation by factoring or using the quadratic formula. In this case, the roots are complex conjugates:

z = 0.6 + 0.4i

z = 0.6 - 0.4i

For a discrete control system, stability is determined by the location of the roots in the complex plane. If the magnitude of all the roots is less than 1, the system is stable. If any root has a magnitude greater than or equal to 1, the system is unstable.

In this case, the magnitude of the roots is less than 1, since:

|0.6 + 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

|0.6 - 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

Therefore, the system is stable.

The correct answer is:

b. Stable with P(1)=1.7 and P(-1)=2.7

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the value of the given function f(g(1)) is 2 , fog is an even function

A function f is even if the equation f(x)=f(x) f (x) = f ( x) holds for every x and x in the domain of f. An even function has a graph that is geometrically symmetric with respect to the y-axis, which means that even after reflection about the y-axis, the graph does not change.

f is even (given)

∴f(−x)=f(x)

g is odd (given)

∴g(−x)=−g(x)

So,

According to question,

fog=f[g(x)]=f(y)             Let [g(x)]=y

and also,

fog=f[g(−x)]        ∵g(x) is odd

       =f[−g(x)]

       =f(−y)

       =f(y)

⇒fog(x)=fog(−x)

∴fog is an even function

f(g(1)) = f(g(1)) = f(3) = 2

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Answer:

it should be y= -4x + 10

Step-by-step explanation:

hope this helps.

Answer:

Step-by-step explanation:

the in this picture is the 3rd one

Answer:16.e+6.18

Step-by-step explanation:

\(m = \frac{y - y1}{x2 - x1} \\ m = \frac{ - 7 - ( - 1)}{ - 8 - 1} \\ m = \frac{ - 7 + 1}{ - 9} \\ m = \frac{ - 6}{ - 9} \\ m = \frac{2}{3} \)

I ALSO PROVIDED THE FORMULA TO USE.

HOPE THIS HELPS

The characteristic of "Mailing Address" would be considered a qualitative variable.

A qualitative variable is a type of variable that is used to assign information that can't be measured by numbers. Qualitative data is used to label the attributes of the individuals, objects, or other items in the study.Types of Qualitative DataThere are many types of qualitative data, for instance:Nominal Data is data that can't be ranked and the measurements have no specific order or sequence.Ordinal Data is data that can be ranked and that has a definite order or sequence.Below are the options given and among them which is qualitative.Size in Square FeetMailing AddressNumber of BathroomsEstimated Market ValueAmong the given options, Mailing Address is considered a qualitative variable. Therefore, the answer is "Mailing Address".

Quantitative data are generally numerical and can be counted or measured, while qualitative data are descriptive and non-numerical. Qualitative data provide a descriptive view of the information that can be used to form ideas or summarize patterns. Qualitative data are frequently used in qualitative studies, but they can also be used in quantitative studies. However, the characteristics of a house that are qualitative variables can be any type of descriptive data that cannot be measured with a numerical value.Mailing Address is a qualitative variable. Because it is a type of data that cannot be counted or measured, it is a qualitative data type. Qualitative data are often used to describe something or to provide more information than can be given by numbers alone. Therefore, the characteristic of "Mailing Address" would be considered a qualitative variable.

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AB = 3

The area of the square ABCD

= (3)^2 square units

= 9 square units.

The answer is 9 square units

The number of cruise passengers must there have been in 2017 is  26.7 million.

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

\(\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}\)

Multiplying both sides by 100;

\(\begin{aligned}&\frac{106.7 x}{100} * 100=28.5 * 100 \\&106.7 x=2850\end{aligned}\)

Dividing both sides by 106.7;

\(\frac{106.7 x}{106.7}=\frac{2850}{106.7}\)

x = 26.7

Therefore, the number of cruise passengers in 2017 must have ranged from 26.7 million.

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Mean of the sampling distribution of xo: Not enough information provided.

Standard deviation of the sampling distribution of xo: 7 points.

In the given scenario, we have a group of 50 students, and we are comparing their blood pressures before and after watching a violent movie. It is mentioned that, on average, blood pressure increases by 5 points after watching something violent with a standard deviation of 7 points.

The mean difference in blood pressure (x1 - x2) is 5 points, and the standard deviation of the differences (the standard deviation of the sampling distribution of xo) is 7 points.

Since n = 50 and od = nd = 5, it appears that "od" and "nd" refer to the standard deviation of the population (before watching the movie) and the standard deviation of the differences (after watching the movie), respectively.

The mean of the sampling distribution of xo (the mean difference in blood pressure) can be calculated as:

Mean of xo = Mean of (x1 - x2) = Mean of x1 - Mean of x2

Given that blood pressure increases by 5 points after watching the violent movie, we can express the mean of xo as:

Mean of xo = Mean of x1 - (Mean of x2 + 5)

However, we are not provided with the specific value of the mean blood pressure before watching the movie. Without that information, we cannot determine the exact value of the mean of xo.

As for the standard deviation of the sampling distribution of xo, it is the standard deviation of the differences, which is given as 7 points.

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For the given figure, we will prove the triangles BGH and BDH are congruent.

So, the proof will be as follows:

Statement Reason

1) m∠F = m∠FEG = m∠FGE Given

2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ

3) FG = GE from (2), the definition of equilateral Δ

4) FG = ED Given

5) m∠ GEH = m∠DEH Given

6) EH = EH Reflexive property

7) ΔGEH ≅ Δ DEH SAS postulate

8) GH = DH from (7) CPCTC

9) m∠GHE = m∠DHE from (7) CPCTC

10) m∠GHB = m∠DHB Definition of supplementary angles

11) HB = HB Reflexive property

12) ΔBGH ≅ ΔBDH SAS postualte

13) ΔAGB is an isosceles Δ Given

14)AG = AB Definition of isosceles Δ

15) ΔBCD is an isosceles Δ Given

16) CB = CD Definition of isosceles Δ

17) CB = AG Given

18) m∠CDB = m∠CBD Definition of isosceles Δ

19) m∠ABG = m∠AGB Definition of isosceles Δ

20) m∠CDB = m∠AGB Given

21) m∠ABG = m∠CBD Transitive property

22) Δ AGB ≅ ΔCBD AAS postualte

\(7 - 4(2w + 1) = 9w - 49 + w \\ 7 - 8w - 4 = 10w - 49 \\ 10w + 8w = 7 - 4 + 49 \\ 18w = 52 \\ w = \frac{52}{18} \\ w= 2.88\)

I hope I helped you^_^

We determine the cumulative weight retained at each sieve and then calculate the cumulative percentage passing by dividing the cumulative weight passing by the total weight of the sample and multiplying by 100.

To calculate the percentage passing for each sieve size in a sieve analysis, we need to determine the cumulative percentage passing at each sieve size.

The sieve analysis provides information about the particle size distribution of an aggregate sample. It involves passing the sample through a series of sieves with different mesh sizes, and measuring the amount of material retained on each sieve.

To calculate the percentage passing, we first need to determine the cumulative weight retained at each sieve size. This is done by subtracting the weight retained on a particular sieve from the weight retained on the previous sieve.

Once we have the cumulative weight retained, we can calculate the cumulative percentage passing by dividing the cumulative weight passing by the total weight of the sample and multiplying by 100.

Here is an example:

Sieve Size (mm) | Weight Retained (g)

4.75 | 50

2.36 | 30

1.18 | 20

0.6 | 15

0.3 | 10

0.15 | 5

To calculate the cumulative percentage passing:

Calculate the cumulative weight retained:

Cumulative weight retained at sieve 4.75 mm = 50 g

Cumulative weight retained at sieve 2.36 mm = 50 g + 30 g = 80 g

Cumulative weight retained at sieve 1.18 mm = 80 g + 20 g = 100 g

Cumulative weight retained at sieve 0.6 mm = 100 g + 15 g = 115 g

Cumulative weight retained at sieve 0.3 mm = 115 g + 10 g = 125 g

Cumulative weight retained at sieve 0.15 mm = 125 g + 5 g = 130 g

Calculate the cumulative percentage passing:

Cumulative percentage passing at sieve 4.75 mm = (Total weight - Cumulative weight retained) / Total weight * 100 = (130 g - 50 g) / 130 g * 100 = 61.54%

Cumulative percentage passing at sieve 2.36 mm = (130 g - 80 g) / 130 g * 100 = 38.46%

Cumulative percentage passing at sieve 1.18 mm = (130 g - 100 g) / 130 g * 100 = 23.08%

Cumulative percentage passing at sieve 0.6 mm = (130 g - 115 g) / 130 g * 100 = 11.54%

Cumulative percentage passing at sieve 0.3 mm = (130 g - 125 g) / 130 g * 100 = 3.85%

Cumulative percentage passing at sieve 0.15 mm = (130 g - 130 g) / 130 g * 100 = 0%

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Answer:

4.5% per year

Answer:

1 : 4 minutes.

Step-by-step explanation:

Given: 15 minutes / 1 hour.

First convert 1 hour to minutes:

1 hour = 60 minutes

Then write the fraction:

15 : 60

Finally, simplify it:

1 : 4 minutes

Answer:

-2

Step-by-step explanation:

just a guess but it's right

Answer:

7/64

Step-by-step explanation:

7/6÷8=7/6*1/8=7/64

Hope this helps :)

The given problem is about a person named Priya who started with $50 in her bank account and deposited $20 each week for 12 weeks. We need to find out after how many weeks she will have $250 in her bank account and also plot the given data on a graph, given that technology is required.Let's solve the given problem step by step:a) We can represent Priya's bank account after n weeks as follows:$50 + $20n

This is because she started with $50 and deposited $20 each week for n weeks.Now, to graph this equation, we can use any graphing calculator or software.

For example, we can use the Desmos Graphing Calculator, which is free and available online.To plot the given data, we need to set the domain as {0, 1, 2, 3, ..., 12} (for 12 weeks), and the range as {50, 70, 90, 110, ..., 290} (according to the equation). Then we can plot the points as follows:

After plotting the points, we can connect them with a straight line to get the graph of the equation.$$$$b)

To mark the point that represents the amount after 3 weeks, we need to find the value of the equation for n = 3, which is:$50 + $20(3) = $110This means that after 3 weeks, Priya will have $110 in her bank account.

We can mark this point on the graph as follows:$$$$$c) To find out after how many weeks Priya will have $250 in her bank account, we need to solve the following equation:$50 + $20n = $250Subtracting $50 from both sides, we get:$20n = $200Dividing both sides by $20, we get:n = 10

This means that after 10 weeks, Priya will have $250 in her bank account. We can mark this point on the graph as follows:$$$$$Therefore,

we can conclude that it will take Priya 10 weeks to have $250 in her bank account, and we can represent this data on a graph using graphing technology.

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[a] Answer: y = 20x + 50

Step-by-step explanation:

    We can write a linear equation to answer this part. Priya starts with $50 and adds $20 every week. Let y be the total amount of money in the bank account and x be the number of weeks passed. We will write a slope-intercept equation, where 20 is the slope and 50 is the y-intercept.

    y = 20x + 50

[b] Answer: (3, 110)

Step-by-step explanation:

    Next, we will use a graphing calculator as asked. Here I am using Desmos Graphing Calculator, it is free to use and online. We can type in our equation above, y = 20x + 50. See attached. Since she will not have negative weeks that she deposits, and she only deposits for 12 weeks, we will add {0 ≤ x ≤ 12} to our equation when we graph.

    Since x is the number of weeks passed, 20(3) + 50 = 110, giving is the point (3, 110).

[c] Answer: 10 weeks

Step-by-step explanation:

    Now, we need to find the point where she has $250 in her bank account. Since y is the total amount of money in her bank account, we can find where y = 250 on the graph.

    This is at (10, 250), or 10 weeks.

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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The average speed of the whole journey is 24 kilometres per hour.

The average speed is the total distance travelled by the object in a particular time interval.

A car travels from X to Y at an average speed of 60km/h and returns to X at a speed of 40km/h.

Therefore, the average speed for the whole journey can be calculated as follows:

The total distance travelled is 120 km.

Hence,

total time = 120 / 60 + 120 / 40

total time = 2 + 3 = 5 hours

Therefore,

average speed = total distance / total time taken

average speed = 120 / 5

average speed = 24 km/hr

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Answer:

x < 4 or x > 6

Step-by-step explanation:

In order to solve for inequalities, we can solve them separately. Given the inequalities:

\(\displaystyle{4x-6 < 10 \ \: \text{or} \ \: 2x-4 > 8}\)

Solve like how you solve for the equation; isolate x-term:

\(\displaystyle{4x-6+6 < 10+6 \ \: \text{or} \ \: 2x-4+4 > 8+4}\\\\\displaystyle{4x < 16 \ \: \text{or} \ \: 2x > 12}\\\\\displaystyle{\dfrac{4x}{4} < \dfrac{16}{4} \ \: \text{or} \ \: \dfrac{2x}{2} > \dfrac{12}{2}}\\\\\displaystyle{x < 4 \ \: \text{or} \ \: x > 6}\)

The variance in time for statistics students is greater than the variance in time for algebra students at 0.05 significance level.

To perform the Two-Variance Test in this problem, we can follow these steps:

State the null and alternative hypotheses:

Null hypothesis (H0): The variance in time for statistics students is equal to or less than the variance in time for algebra students.

Alternative hypothesis (H1): The variance in time for statistics students is greater than the variance in time for algebra students.

Determine the significance level:

The significance level is given as 0.05.

Calculate the test statistic:

We can use the F-statistic to compare the variances of the two populations. The formula for the F-statistic is:

F = (s1^2 / s2^2)

Where s1^2 is the sample variance for statistics students and s2^2 is the sample variance for algebra students.

Find the p-value:

We need to find the p-value associated with the calculated F-statistic. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

Make a decision:

Compare the p-value to the significance level. If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this problem, we are given that the p-value is 0.0376, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis.

At the 0.05 level of significance, we have sufficient evidence to support the claim that the variance in time for statistics students is greater than the variance in time for algebra students.

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As per the given speed, the ball will cross each other at the time of 5 seconds.

Given,

Two balls are thrown upward from the edge of a cliff 432 ft above the ground. The first is thrown with a speed of 48 ft/s and the other is thrown a second later with a speed of 24 ft/s.

Here we need to find if the ball will cross each other.

Let us find the equation for your first ball and it can be identified by using "f" for fast, since it's thrown at twice the speed of the other.

Here we have given the equation is ft/sec, so g = -32.

So, it can be written as,

=> yf = 1/2gt² + v₀ft + y₀f

Apply the values, then we get,

=> yf = -16t² + 48t + 432

Here we know that the second ball, or "slow" ball, is thrown a second later which means all of t values are shifted to the right by 1 second.

So, here we put (t - 1) instead of t

Then we get,

=> ys = 1/2g(t - 1)² + v₀s(t - 1) + y₀s

We know that, the Gravity remains the same.

So, the value of v₀s will be 24, and y₀s will also be 432 ft.

So, the equation is,

=> ys = -16(t - 1)² + 24(t - 1) + 432

When we compare these then we get,

=> -16t² + 48t + 432 = -16(t - 1)² + 24(t - 1) + 432

=> -16t² + 48t = -16(t² - 2t + 1) + 24(t - 1)

=> -16t²+ 48t = -16t² + 32t - 16 + 24t - 24

=> 48t = 56t - 40

=> 8t = 40

=> t = 5

Therefore, it looks like the balls cross each other at t = 5.

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Answer:

50 and 20 that is the answer Thank you