Alex has a pet snake that eats 1 mouse every week. How many mice will the snake eat if Alex has the snake for 4 years?

Answer: UR QUESTION HERE

Step-by-step explanation:

The time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

The Linear equation for a scatter plot y = mx+b has two variables i.e., a Dependent Variable [Y] and an Independent variable [X] .

A student who spends more time on his work and do it nicely will automatically get good exam grade . On the other side, a student who did'nt dedicate much time to the homework and carelessly does it , will obviously score a low exam grade.We can see that the exam grade is dependent on the time spent on the homework which naturally makes exam grade a response variable and time spent on home a independent thus an explanatory variable.

Hence, the time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

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Answer:

The z-score is -2

Step-by-step explanation:

Here, we are asked to calculate the z-score of the height.

Mathematically, we can calculate z-score by using the formula below;

z-score = (x-mean)/SD

According to this question, mean = 44cm and SD = 3cm with x here = 38cm

Plugging these values into the z-score equation, we have

z-score = (38-44)/3 = -6/3 = -2

Answer:

5p-6q or 5p+ (-6q)

If you are looking to create one equation, then combine like terms.

2p+3p and -5q + (-q or 1)

5p and -6q

5p-6q or 5p+ (-6q)

Answer:

256

1.  2^3=8       2^6=64      2^5=32

2.  8/64=0.125

3. 32/0.125=256

Answer:

Step-by-step explanation:

The length of an arc can be obtained using the formula: \(2\pi r(\frac{\theta}{360})\)

Using this formula we can substitute in the variables as needed.

We know that:

\(\pi = 3.14r = 4\theta = 115\)°

So plugging them in we get the following:

\(2\pi r(\frac{\theta}{360})\) = \(2*3.14 *4(\frac{115}{360})=8.02\)

So the length of the arc \(DC\) \(= 8.02\)

Answer:

6 miles on the first day and 14 miles on the second day

Step-by-step explanation:

Answer:

\(in \: day \: one \: she \: ran \: 8 \: mile s.\\ in \: day \: two \: she \: ran \: 12 \: miles.\)

Step-by-step explanation:

\(let \: the \: number \: of \: miles \: for \: the \: first \: day \: be : x \\ let \: the \: number \: of \: miles \: for \: the \: second \: day \: be : x + 4 \\ therefore \: in \: two \: days \: she \: ran \: 20 \: miles = x + (x + 4) \\ now......thats \: the \: required \: equation....... \\ if \: x + (x + 4) = 20 \: then : \\ 2x + 4 = 20 \\ 2x = 20 - 4 \\ 2x = 16 \\ x = 8. \\ so \: in \: day \: one \: she \: ran \: 8 \: mile \\ in \: day \: two \: she \: ran \: (8 \: + 4) \: miles = 12 \: miles\)

its so funny how you reacted to the other helper

♨Rage♨

Answer:

Step-by-step explanation:

what two numbers can you multiply that will equal to 30 when you multiply but 13 when you add them?

10+3=13     10*3=30  

so we can use 10 and 3

since the first symbol (x^2+13x) is positive than the bigger number you got earlier (10) will be positive

(x+10)

since the second symbol (13x+30) is positive than our next symbol will be positive as well

(x+3)

combine them so now they are (x+10)(x+3)

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The experimental probability of rolling the number one on the number cube is approximately 0.2047.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials.

In this case, the event is rolling the number one on the number cube and it occurs 44 times out of 215 trials.

So, the experimental probability of rolling the number one is -

Experimental probability = Number of times event occurred / Total number of trials

Substituting the values into the equation, we get -

Experimental probability = 44 / 215

Experimental probability ≈ 0.2047

Therefore, the probability value is obtained to be approximately 0.2047.

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The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

The relation S={(a,b)∈R×R:a²+b²=1} is not an equivalence relation on the set of real numbers R.

To show that S is not an equivalence relation, we need to demonstrate that it fails to satisfy one or more of the properties of an equivalence relation: reflexivity, symmetry, and transitivity.

Reflexivity: For a relation to be reflexive, every element of the set should be related to itself. However, in the case of S, there are no real numbers (a, b) that satisfy the equation a² + b² = 1 for both a and b being the same number. Therefore, S is not reflexive.

Symmetry: For a relation to be symmetric, if (a, b) is related to (c, d), then (c, d) must also be related to (a, b). However, in S, if (a, b) satisfies a² + b² = 1, it does not necessarily mean that (b, a) also satisfies the equation. Thus, S is not symmetric.

Transitivity: For a relation to be transitive, if (a, b) is related to (c, d), and (c, d) is related to (e, f), then (a, b) must also be related to (e, f). However, in S, it is not true that if (a, b) and (c, d) satisfy a² + b² = 1 and c² + d² = 1 respectively, then (a, b) and (e, f) satisfy a² + b² = 1. Hence, S is not transitive.

Since S fails to satisfy the properties of reflexivity, symmetry, and transitivity, it is not an equivalence relation on the set of real numbers R.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

$5.25 = 525 cents

525/7=75

each bottle is 75 cents or $0.75

Answer:

Question 11.1

At 7 : 00 pm in Sydney, it will be 10 : 00 pm in Berlin.

Question 11.2

Place | Time

Sydney | 5 : 00 pm

Berlin | 8 : 00 pm

It would be a good time for Mark and Hans to cha,t when it's 5 : 00 pm in Sydney and 8 : 00 pm in Berlin.

hope that helps ...

The coordinates to plot is (0, 18) with a slope 4

The standard equation of a line in slope intercept form is expressed as y = mx +b

where:

m is the slope

b is the y-intercept

Given the equation y = 9x

Hence the coordinates to plot is (0, 18)

Plot the graph of graph of the equation with slope of 4 and point (0,18) as shown

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(x - (a+48))² + (y - (b+19))² = 24.5² This is the equation for all possible positions (x,y) on the boundary of the cell tower's service coverage.

To write an equation for all possible positions (x,y) on the boundary of the cell tower's service coverage, we first need to determine the coordinates of the center of the coverage.

We know that the cell tower is located 48 miles east and 19 miles north of the center of the small town, so we can add these distances to the coordinates of the town's center. If we let (a,b) be the coordinates of the town's center, then the coordinates of the cell tower would be (a+48,b+19).

Next, we know that the cell tower services everything within a radius of 24.5 miles from it. This means that any point (x,y) on the boundary of the coverage circle would be exactly 24.5 miles away from the cell tower. We can use the distance formula to write an equation for this:

√[(x - (a+48))² + (y - (b+19))²] = 24.5

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Answer:

\( ( \frac{x}{6} + \frac{y}{2 \sqrt{a} } )( \frac{x}{6} - \frac{y}{2 \sqrt{a} }\)

Step-by-step explanation:

⠀

⠀

\( \sf \large\frac{ {x}^{2} }{36} - \frac{ {y}^{2} }{4a} \)

⠀

⠀

⠀

⠀

Using (a² - b²) identity

(a² - b²) = (a + b)(a - b)

⠀

⠀

\( \sf \large {( \frac{x}{6}) }^{2} - {( \frac{y}{2 \sqrt{a} }) }^{2} \\ \\ \boxed{ \large {\tt( \frac{x}{6} + \frac{y}{2 \sqrt{a} } )( \frac{x}{6} - \frac{y}{2 \sqrt{a} } )}}\)

The integral of (x^2 + 4x) cos x dx is given by (-x^2 - 2x + 4) sin x + (2x + 4) cos x + C.

The integral of the given function involves both the product rule and the integration by parts method. The final result consists of two terms: one involving the sine function and the other involving the cosine function. The coefficients of x in each term are determined by applying the integration by parts method. The constant of integration, denoted by C, represents the arbitrary constant that is added when integrating.

To obtain the detailed explanation of the answer, let's break it down step by step:

Using the integration by parts method, we choose u = x^2 + 4x as the first function and dv = cos x dx as the second function. Taking the derivatives and antiderivatives, we find du = (2x + 4) dx and v = sin x.

Applying the integration by parts formula ∫u dv = uv - ∫v du, we have:

∫(x^2 + 4x) cos x dx = (x^2 + 4x)(sin x) - ∫(sin x)(2x + 4) dx.

Expanding the first term on the right side, we get (x^2 + 4x) sin x. For the second term, we distribute the sin x into (2x + 4) and integrate term by term:

∫(sin x)(2x + 4) dx = 2∫x sin x dx + 4∫sin x dx.

Integrating each term separately, we find:

2∫x sin x dx = -2x cos x + 2∫cos x dx = -2x cos x + 2sin x + C1,

and 4∫sin x dx = -4cos x + C2.

Combining all the terms, we have:

(x^2 + 4x) sin x - 2x cos x + 2sin x - 4cos x + C.

Simplifying further, we obtain the final result:

(-x^2 - 2x + 4) sin x + (2x + 4) cos x + C.

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Thus, the curl of the vector field F = (x2 − y2) i + 4xy j is (2x − 2y) k.

The curl of a vector field is a measure of how much the field rotates around a point. To compute the curl of the given vector field F = (x2 − y2) i + 4xy j, we need to calculate the cross product of the gradient operator (del) and F.

Using the formula for the curl, we have:
curl F = (∂Fz/∂y − ∂Fy/∂z) i + (∂Fx/∂z − ∂Fz/∂x) j + (∂Fy/∂x − ∂Fx/∂y) k

Where Fx, Fy, and Fz are the components of F in the x, y, and z directions, respectively.

In this case, F has no z-component, so we can simplify the formula to:
curl F = (∂Fy/∂x − ∂Fx/∂y) k

Now, let's calculate the partial derivatives:
∂Fx/∂y = 0 - (-2y) = 2y
∂Fy/∂x = 2x - 0 = 2x

Therefore, the curl of F is:
curl F = (2x − 2y) k

This means that the field rotates around the z-axis with a magnitude proportional to the difference between x and y. The curl is zero when x equals y, which corresponds to a point of no rotation.

In summary, the curl of the vector field F = (x2 − y2) i + 4xy j is (2x − 2y) k.

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer:

x ^2 − 2 y ^2 −8 x y

Step-by-step explanation:

To find the point on the curve r(t)=(2cost, 2sint, e^t) we need to evaluate the x, y, and z coordinates at a specific value of t. Let's choose t=0 for simplicity.

So, plugging in t=0 we have:

r(0) = (2cos(0), 2sin(0), e^0)
r(0) = (2, 0, 1)

Therefore, the point on the curve at t=0 is (2, 0, 1).

To find the point on the curve r(t) = (2cos(t), 2sin(t), e^t) for a specific value of t, you can plug in the value of t into the parameterized equation:

1. Replace t with the specific value you're interested in (e.g., t = a).
2. Compute 2cos(a) for the x-coordinate.
3. Compute 2sin(a) for the y-coordinate.
4. Compute e^a for the z-coordinate.

The point on the curve will be (2cos(a), 2sin(a), e^a).

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Answer:

1/169

Step-by-step explanation:

52 cards in a deck, 13 are diamonds

P(diamond) = number of diamonds/ total

                    = 13/52 = 1/13

Replace the card

52 cards in a deck, 13 are diamonds

P(diamond) = number of diamonds/ total

                    = 13/52 = 1/13

P (diamond, replace, diamond) = 1/13 * 1/13 = 1/169

The first seven terms of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 105, 225.

Sequence is an ordered arrangement of elements, usually numbers or objects, which follows a specific pattern. It is a mathematical concept that is used in a variety of areas, such as computer science, data analysis, and number theory. A sequence can be finite, like the first 10 numbers in the counting sequence, or it can be infinite, such as the set of natural numbers. It is important to understand the concept of a sequence in order to be able to use it in various areas.

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers, starting from 0 and 1.

The Fibonacci sequence is named after mathematician Leonardo Fibonacci, who introduced the sequence in his book Liber Abaci in 1202.

The sequence is also known as the Golden ratio, because the ratio of successive numbers in the sequence converges on the Golden ratio of 1.618. The first seven terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, and the fourth and sixth terms of the sequence are 105 and 225 respectively.

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Answer:

Height After 8 weeks: 14 inches

Height after w weeks: y=0.5w+10

Step-by-step explanation:

The equation of the sunflower is y=0.5x+10.

Height after 8 weeks: y=0.5(8)+10

y=4+10

y=14

Height After 8 weeks: 14 inches

Height after w weeks: y=0.5w+10

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The population of the small city in the year 2020 using the given growth rate is; 51600 people

We are given that;

Population of the small city in the year 2010 = 36000

Population in the year 2015 = 43800

Now, we are told that the growth rate occurs at the same rate per year. Thus;

Population change from 2010 to 2015 = 43800 - 36000 = 7800

Thus, the population increases by 7800/5 = 1560 people each year.

General form of exponential function is; y = bˣ

where b is rate of growth while x is number of years

But here we will use sequence to get;

y(10) = 1560 * 10 = 15600

Thus;

Population in 2020 = 36000 + 15600 = 51600 people

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