Sloan the sloth crawls at $100$ meters per hour when crawling uphill, $120$ meters per hour when crawling across flat ground, and $150$ meters per hour when crawling downhill. One day, Sloan crawls across the forest floor from a tree stump to a spring, and then takes the same route in reverse to return to the tree stump. What was Sloan's average speed during the entire round trip?

Answer:

a

Step-by-step explanation:

Answer:

(0, 4)

Step-by-step explanation:

Hi there!

We are given the following systems of equations:

x=8-2y

y-x=4

And we want to solve it by substitution

When we solve an equation by substitution, we solve for one of the variables in one of the expressions, which should be an expression containing the other variable, then we substitute that expression as the variable we solved for into the other expression  to find the value of that variable, then use the value of the solved variable to find the value of the other variable.

In this case, we already have x solved in the first equation; x is equal to 8-2y.

We can substitute that as x in y-x=4 to solve for y.

y-(8-2y)=4

Subtract

y-8+2y=4
Combine like terms

3y-8=4

Add 8 to both sides
3y=12

Divide both sides by 3

y=4

Substitute 4 as y into x=8-2y to solve for x.

x=8-2(4)

x=8-8

x=0

The solution is x=0, y=4, or as a point,  (0, 4)

Hope this helps!

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In order to solve this problem, we'll use the Combinations Formula. This is because the order in which the coins are flipped is unimportant; all that matters is the total number of heads and tails. We'll begin by counting the number of ways to get exactly 4 tails and exactly 8 tails, then the number of ways to get 5 tails and 6 tails, and finally the number of ways to get 7 tails. We will then add all of these numbers together to get the final answer.

When you toss a coin, there are only two possibilities: heads or tails.

Let's call the number of times you get tails "t." We want to find the number of ways to toss the coin 11 times so that

4 <= t <= 8.

Here's how we can do it:

First, we'll find the number of ways to get exactly 4 tails. We know that we're flipping the coin 11 times, so there are 11 choose 4 ways to choose which 4 of those tosses will be tails. The other 7 tosses will be heads. Using the Combinations Formula, this gives us:

11 choose 4 = 330

Next, we'll find the number of ways to get exactly 8 tails. This is similar to the previous step, except that we're choosing 8 of the 11 tosses to be tails. The other 3 tosses will be heads. Using the Combinations Formula, this gives us:

11 choose 8 = 330

Again, using the Combinations Formula, we can find the number of ways to get exactly 5 tails and 6 tails:

11 choose 5 = 462

11 choose 6 = 462

Finally, we need to find the number of ways to get exactly 7 tails. This is a little trickier, but we can do it by splitting the problem into two cases: when the first toss is a tail and when the first toss is a head.

Case 1: The first toss is a tail. Then we need to get 6 tails in the remaining 10 tosses. There are 10 choose 6 ways to choose which 6 of the remaining 10 tosses will be tails. Using the Combinations Formula, this gives us:

10 choose 6 = 210

Case 2: The first toss is a head. Then we need to get 7 tails in the remaining 10 tosses. There are 10 choose 7 ways to choose which 7 of the remaining 10 tosses will be tails.

Using the Combinations Formula, this gives us:

10 choose 7 = 120

Adding up all of these numbers, we get:

330 + 330 + 462 + 462 + 210 + 120 = 1914

So there are 1914 ways to toss a coin 11 times so that the number of tails is between 4 and 8 inclusive.

Thus, the required answer is 1914.

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Answer:

B

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.

Marks obtained are 33 and 45 when two students took an exam. one of them achieved 9 marks more than the other and his marks were 56% of the sum of both of their marks.

Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3 . Variables can be written straight after a regular integer in algebraic expressions that use them, with no symbol needed in between. An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x²+ 2xy + c.

Given,

Two students took an exam. one of them achieved 9 marks more than the other and his marks were 56% of the sum of both of their marks.

Let the marks be x and x+9

Algebraic equation,

x+ 9 = 56/100(x+x+9)

x + 9 = 14/25 (2x +9)

25(x+ 9) = 14(2x+9)

25x + 225 = 28x +126

28x - 25x = 225 - 126

3x = 99

x = 33

Marks obtained are 33 and 45.

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Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

Lets take two points from this line, (4,9) and (2,6).

Method 1: Count the slope

We can use \(\frac{rise}{run}\) to count the slope.

Counting the slope, we get \(\frac{3}{2}\).

Method 2: Slope formula

We can use the formula \(\frac{y2-y1}{x2-x1}\) to calculate the formula.

Lets plug in the coordinates and solve.

\(\frac{6-9}{2-4}\)

\(\frac{-3}{-2} = \frac{3}{2}\)

Answer:

A. 2x+8

Step-by-step explanation:

you take the two and multiply it to the X and the eight and that would give you 2X2 + 64

Answer:

25 advance

20 same day

Step-by-step explanation:

1700=40x+35y

*40 45=x+y

1700=40x+35y

- 1800=40x+40y

-100= -5y

y=20 tickets

45-20=25

25*40 + 35*20= 1700

1000. + 700 = 1700

Normal curve A normal curve is a bell-shaped curve that represents the probability distribution of a random variable. It's symmetrical and centered around the mean. It's commonly used in statistics because many real-world phenomena follow this pattern.

Here is an example of a normal curve:b) Critical values and rejection regions for hypothesis tests using z-table or t-table:1. Right-tail test,\(n=20, σ=4.7, α=0.05\)First, we need to find the critical value for a right-tail test with \(α=0.05\)and 19 degrees of freedom (n-1) using the t-table. The critical value is 1.7291. Because it's a right-tail test, we only need to shade the rejection region in the right tail of the curve.

The critical value is \(±1.7109\). Because it's a two-tail test, we need to shade the rejection regions in both tails of the curve. The rejection regions are to the left of -1.7109 and to the right of 1.7109. Here is a graphical representation of the test

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Answer:

x=5.657 y=5.657

Step-by-step explanation:

The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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Answer: See attached.

Step-by-step explanation:

     First, we will find the unit rate by dividing.

30 rings / $12 = 2.5 rings per dollar

     Then, we can fill out the other values using this unit rate.

2 dollars * 2.5 rings per dollar = 5 rings

45 tosses / 2.5 rings per dollar = 18 rings

       Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.

Answer:

Does this seem right to you?

Answer:

Parent function:
\(x^2+y^2=r^2\)
General equation:
\((x-h)^2+(x-k)^2=r^2\)
Transformations:
Its a circle with a center of (100,60) and a radius of 15

The square root of 0.36

= \(\sqrt{0.36}\)  = 0.6

ans: 0.36

Happy to help!

The p-value for a right-tailed test is 0.0096.so the melodic kortholt company should consider changing its current health plan.the standard error for the proportion (SE = sqrt(0.64*(1-0.64)/25) = 0.144).

1. Calculate the proportion of employees dissatisfied (16/25 = 0.64).

2. Calculate the standard error for the proportion (SE = sqrt(0.64*(1-0.64)/25) = 0.144).

3. Calculate the z-score for the test (z = (0.64 - 0.5)/SE = 1.39).

4. Calculate the p-value (p-value = 1 - cdf(z) = 0.0096).

The p-value is an indication of how likely it is that the proportion of employees dissatisfied is significantly different from the expected proportion (in this case, half). The p-value of 0.0096 means that there is only a 0.96% chance that the observed proportion of employees dissatisfied is due to chance alone, and so the melodic kortholt company should consider changing its current health plan.

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Answer:

A

Step-by-step explanation:

because y=one over four and one over four is a fuction

Answer:

x = 50

Step-by-step explanation:

       3x  = 2x + 50

Subtract 2x from both sides,

  3x - 2x = 2x -2x + 50

          x  = 50

The coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2 are x(t) = 2t - (1/3) and y(t) = -10t^2/3 + (10t/3) - (5/9).

To find the coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2, we need to use the vector form of the line and substitute in the given values of t.

First, let's recall the vector form of the line which is r(t) = a + tb where r(t) is the position vector of a point on the line, a is a point on the line, t is a scalar parameter, and b is the direction vector of the line. In this case, we are given the direction vector as (3,-5) and a point on the line as (2,0). So, the vector form of the line is r(t) = (2,0) + t(3,-5).

Now, we need to find the coordinate functions by replacing t with the given values in the parametrization r(t) = 6t - 1, 9t^2.

For the x-coordinate function, we have:

x(t) = 2 + 3t
x(t) = 2 + 3((6t - 1)/9)
x(t) = 2 + 2t - (1/3)

So, the x-coordinate function is x(t) = 2t - (1/3).

For the y-coordinate function, we have:

y(t) = 0 - 5t
y(t) = 0 - 5((6t - 1)/9)^2
y(t) = 0 - 10t^2/3 + (10t/3) - (5/9)

So, the y-coordinate function is y(t) = -10t^2/3 + (10t/3) - (5/9).

Therefore, the coordinate functions of the line parametrized by r(t) = 6t - 1, 9t^2 are x(t) = 2t - (1/3) and y(t) = -10t^2/3 + (10t/3) - (5/9).

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There are 167 integers from 1 to 1000 that are multiples of 6 or multiples of 8.

We can use the inclusion-exclusion principle to count the number of integers from 1 to 1000 that are multiples of 6 or multiples of 8.

First, we count the integers that are multiples of 6. Because we know that 6 is a multiple of both 2 and 3, we can say that an integer is a multiple of 6 if and only if it is a multiple of both 2 and 3. There are 166 multiples of three from one to one thousand, and half of them are even, so there are 83 multiples of six from one to one thousand.

The number of integers that are multiples of 8 is then determined. From 1 to 1000, there are 125 multiples of 8.

We did, however, count the multiples of 24 (which are multiples of both 6 and 8). To compensate, we deduct the number of multiples of 24, which is 41.

As a result, the sum of all integers from 1 to 1000 that are multiples of 6 or multiples of 8 is:

83 + 125 - 41 = 167

So, from 1 to 1000, there are 167 integers that are multiples of 6 or multiples of 8.

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Answer:

x = 3

y = 5

Step-by-step explanation:

we can add these equations together

4x - 2y +2x + 2y = 18

6x = 18

x = 3

to find y

6 + 2y = 16

2y = 10

y = 5

The solution of the equation 2x - 1 = 7 is x = 4.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign .

Therefore, let's solve the equation as follows:

2x - 1 = 7

add 1 to both sides of the equations

2x - 1 = 7'

2x - 1 + 1 = 7 + 1

2x = 8

divide both sides of the equation by 2

2x / 2 = 8 / 2

x = 4

Therefore, the solution of the equation is x = 4.

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The value which is a solution of the given one-variable equation is; Choice D; x = 4.

It follows from the task content that the value which is a solution of the given equation is to be determined.

Since the given equation is;

2x - 1 = 7

The equation can be solved as follows;

2x - 1 = 7

Add 1 to both sides of the equation;

2x = 7 + 1

2x = 8

Divide both sides of the equation by 2;

x = 8/2

x = 4.

Therefore, the required solution of the equation is; Choice D; x = 4.

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Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Step-by-step explanation:

A shaded right rectangular pyramid is shown. where is the shade rectangular pyramid....how do I know the answer when you did post the full

question

Answer:

0.5 kg/week

Step-by-step explanation:

rate of change = (change in weight)/(change in time)

rate of change = (8.4 kg - 2.4 kg)/(18 weeks - 6 weeks)

rate of change = 6 kg / 12 weeks

rate of change = 0.5 kg/week

Answer:

yes, no, yes, no

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes, No, Yes, No. Hope this helps!

Differential equations (DEs) are mathematical tools used to model and analyze real-world phenomena. DEs describe the relationships between variables and their rates of change. When applied to real-world data, DEs help in understanding and predicting how systems evolve over time.

DEs are utilized in various ways when working with real-world data. Here are some key aspects:

1. Modeling: DEs are used to create mathematical models that represent the behavior of a system. By identifying the relevant variables and their relationships, DEs capture the dynamics and interactions within the system. Real-world data, such as measurements or observations, can be used to inform the parameters and initial conditions of the DE model.

2. Parameter Estimation: DE models often have parameters that need to be estimated based on real-world data. Statistical techniques, such as regression analysis or optimization methods, can be employed to determine the values of these parameters that best fit the observed data.

3. Simulation and Prediction: Once a DE model is established and parameters are estimated, numerical methods can be used to solve the equations and simulate the system's behavior over time. By comparing the simulated results to real-world data, the accuracy and validity of the model can be evaluated. DE models can also be used for prediction, allowing for forecasts or projections of future behavior based on the established mathematical relationships.

4. Sensitivity Analysis: DE models enable sensitivity analysis to understand the impact of different factors on the system's behavior. By varying the parameters or initial conditions within certain ranges, it is possible to assess how changes in these variables affect the model's output. This analysis provides insights into the robustness and stability of the system.

Overall, DEs provide a powerful framework for analyzing and interpreting real-world data. By formulating mathematical equations that capture the underlying dynamics, DEs enable us to gain a deeper understanding of complex systems and make predictions or informed decisions based on the mathematical insights derived from the data.

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Answer:

13.25

Step-by-step explanation:

Answer:

13.25

Step-by-step explanation:

I did the ixl

The translations performed are

From the question, we have the following function that can be used in our computation:

f(x) = ln(x)

g(x) = -ln(x + 1) - 3

First, we have the transformation to be:

From f(x) = ln(x) to f(x) = -ln(x)

This means a reflection across the x-axis

Next, we have

From f(x) = -ln(x) to f(x) = -ln(x + 3)

This means the function is translated left by 3 units

Next, we have:

From f(x) = -ln(x + 3) to f(x) = -ln(x + 3) - 3

This means the function is translated down by 3 units

Hence, the translation is 3 units left and 3 units down

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