What is the slope of the line containing the points (-4,-6) and (3,-4)

Answer:

h(t)=-36.25cos(0.2618t)+34.25

Step-by-step explanation:

We can start by drawing a sketch of what the whaterwheel's height over time looks like. (See attached picture.)

We can see on the graph that at t=0, the bucket will be located at its lowest point. So in this case we can make use of a cosine function. Cosine functions look like this:

\(y=Acos(\omega t + \phi)+b\)

where:

A=amplitude

\(\omega\) = angular speed

\(\phi\)=phase shift

b= vertical shift.

So let's find each of the necessary data:

The amplitude is the distance between the highest point of the trajectory and the middle point of the sine wave, so:

\(A=\frac{highest-lowest}{2}\)

\(A=\frac{70.5ft-(-2ft)}{2}\)

A=36.25 ft

since the trajectory starts at its lowest point when t=0 we will make the amplitude a negative amplitude, so:

A=-36.25ft

Next, we can find the angular speed:

\(\omega = \frac{2\pi}{T}\)

Where T is the period (the time it takes the wheel to make one whole turn) so:

\(\omega=\frac{2\pi}{24}\)

\(\omega=0.2618 rad/s\)

the phase shift in this case is zero since the graph starts at the lowest point.

the vertical shift is the distance between the x-axis and the middle point of the graph. So we find the midpoint between the lowest and the highest point of the graph:

\(b=\frac{highest+lowest}{2}\)

\(b=\frac{70.5ft-2ft}{2}\)

b=34.25ft

so we can now input all this data into the formula to get:

\(h(t)=-36.25cos(0.2618 t)+34.25\)

Answer:

Step-by-step explanation:

Irrational number

It is a radical.

Answer:

an=87+(n-1)(-3.6)

Step-by-step explanation:

hope this helps

Answer:

an=87+(n-1)(-3.6)

The value of cos 2θ will be;

⇒ cos 2θ = 7/25

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The sides of triangle are 3 , 5, 4

Now,

Since, In a triangle;

cos 2θ = 2cos²θ - 1   .....(i)

And, cos θ = Base / Hypotenuse

Substitute all the values, we get;

cos θ = Base / Hypotenuse

cos θ = 4 / 5

Substitute above value in equation (i), we get;

cos 2θ = 2cos²θ - 1  

cos 2θ = 2(4/5)² - 1  

cos 2θ = 32/25 - 1

cos 2θ = 7/25

Thus, The value of cos 2θ will be;

⇒ cos 2θ = 7/25

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Answer:

1) -20.5

-8

4.5

13

2) 9

4

-1

-6

3) 2

4

6

8

Step-by-step explanation:

plug in the x values, then use pemdas

Answer:

246

Step-by-step explanation:

482 - 200 = 282

282 - 30 = 252

252 - 2 = 250

250 - 4 = 246

Or

482 - 236 = 246

Hope this helps. :)

Have a good day!

Answer:

x=-4

Step-by-step explanation:

46 = -7x + 18

subtract 18 from each side to get:

28 = -7x

divide each side by -7 to get:

x = -4

The amount that one family paid is 25 pound

Here two families had dinner and bill was 100 pound

They used the coupon on which they got 50% off

To find the percentage we have to use percentage formula:

\(=\frac{Value}{Total \ Value} *100\)

\(=\frac{50}{100} *100\)

\(= 50 \ Pounds\)

The remaining bill was 50 pound

Now this amount is divided between the 2 families

\(=\frac{50}{2}\)

\(= 25 \ pound\)

So one family has to pay 25 pounds

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False. the statement "If a variable x does not depend on a variable y, both coefficients are equal to zero" is false.

The coefficient of determination (R-squared) and the coefficient of correlation (Pearson's correlation coefficient) are related but distinct measures.

The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable (y) that can be explained by the independent variable(s) (x). It ranges from 0 to 1, where a value of 0 indicates that the independent variable(s) do not explain any of the variance in the dependent variable, and a value of 1 indicates that the independent variable(s) completely explain the variance in the dependent variable.

On the other hand, the coefficient of correlation, denoted as r, measures the strength and direction of the linear relationship between two variables (x and y). It also ranges from -1 to 1, where a value of -1 indicates a perfect negative linear relationship, a value of 0 indicates no linear relationship, and a value of 1 indicates a perfect positive linear relationship.

If a variable x does not depend on variable y, it means there is no linear relationship between the two variables. In this case, the coefficient of correlation (r) would be 0, indicating no linear relationship. However, the coefficient of determination (R²) could still be non-zero if there are other independent variables that explain the variance in the dependent variable y.

Therefore, the statement "If a variable x does not depend on a variable y, both coefficients are equal to zero" is false.

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d) there must be at least 30 trials.

The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

I dont have an explanation, sorry

Given information:Position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds.

To determine the position at the following times. a. t = 3.30 s, b. t = 3.30 s + Δt xf and c. Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 3.30 s. a. To find the position when t = 3.30 s, substitute t = 3.30 s in x = 3t².x = 3t² = 3(3.30)² = 32.67 metersTherefore, the position at t = 3.30 s is 32.67 meters.

b. To find the position when t = 3.30 s + Δt, substitute t = 3.30 s + Δt in x = 3t².x = 3t² = 3(3.30 s + Δt)² = 3(10.89 + 6.6Δt + Δt²) = 32.67 + 19.8Δt + 3Δt²Therefore, the position when t = 3.30 s + Δt is 32.67 + 19.8Δt + 3Δt².c. Velocity is given by Δx/Δt.Δx/Δt = [x(t + Δt) - x(t)]/ΔtBy substituting the given values, we have;Δx/Δt = [x(3.30 + Δt) - x(3.30)]/Δt= [3(3.30 + Δt)² - 3(3.30)²]/Δt= 19.8 + 6ΔtTaking the limit of Δx/Δt as Δt → 0, we have;Δx/Δt = 19.8 + 6(0)Δt = 19.8Therefore, the velocity at t = 3.30 s is 19.8 m/s.

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A professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6.

First, let's define some variables to represent the probabilities of making a hole for a professional golfer and an amateur golfer:

Let p be the probability that a professional golfer makes a hole with the new club.

Let q be the probability that an amateur golfer makes a hole with the new club.

According to the company's claims, we know that:

p = 1.2q (since the professional golfer makes a hole 120% of the time, which is 1.2 times the probability of the amateur golfer making a hole)

Next, we need to determine the probability of each golfer making a hole during one round of golf, which consists of 18 holes. Let's assume that each hole is independent of the others, meaning that the outcome of one hole does not affect the outcome of another. In that case, the probability of making at least one hole in a round can be calculated using the complement rule:

The probability that a professional golfer makes at least one hole in a round is 1 minus the probability that the golfer misses every hole: \(1 - (1-p)^{18} .\)

The probability that an amateur golfer makes at least one hole in a round is\(1 - (1-q)^{18} .\)

Now, let's use these probabilities to calculate the expected number of holes each golfer will make in 5 rounds of golf:

The expected number of holes made by a professional golfer in 5 rounds is 5 times the expected number of holes made in one round, which is \((1 - (1-p)^{18} )\times18.\)

The expected number of holes made by an amateur golfer in 5 rounds is 5 times the expected number of holes made in one round, which is \((1 - (1-q)^{18} )\times18.\)

We can simplify these expressions using the relationship between p and q:

The expected number of holes made by a professional golfer in 5 rounds is \(518(1 - (1-1.2q)^{18} ).\)

The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-q)^{18} ).\)

We can now evaluate these expressions using the values of p and q:

\(p = 1.2q, so q = p/1.2\)

Substituting this into the expressions above, we get:

The expected number of holes made by a professional golfer in 5 rounds is\(518(1 - (1-1.2(p/1.2))^{18} ) = 518(1 - (1-p)^{18} ).\)

The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-p/1.2)^{18} ).\)

Finally, we can evaluate these expressions using the given probabilities:

The expected number of holes made by a professional golfer in 5 rounds is\(518(1 - (1-1.2q)^{18} ) = 518(1 - (1-1.2(0.1))^{18} ) = 40.7.\)

The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-q)^{18} ) = 518(1 - (1-0.1/1.2)^{18} ) = 1.6.\)

So according to these calculations, we would expect a professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6

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Ion has a total of $4,378.05 in his savings account at the end of 3 years.

To solve this problem, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the total amount of money in the account at the end of the time period

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, we have:

P = $120

r = 0.029 (2.9% expressed as a decimal)

n = 12 (compounded monthly)

t = 3 (years)

We also need to calculate the total number of deposits made during the 3-year period. Since a deposit of $120 is made at the end of every month, and there are 12 months in a year, the total number of deposits made is:

12 deposits/year × 3 years = 36 deposits

Now we can plug in the values into the formula:

A = \(120(1 + 0.029/12)^(12 × 3) + 120[(1 + 0.029/12)^(12 × 3) - 1]/(0.029/12)\)

A = $4,378.05

Therefore, Ion has a total of $4,378.05 in his savings account at the end of 3 years.

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6t+31=41

6t=10

t=10/6

t=5/3

Answer:

4 + 6

Step-by-step explanation:

when you subtract, you 'add the opposite'

so the subtraction sign becomes an addition sign and the opposite of -6 is 6

4-(-6) is the same as 4+6

The function S maps subsets of X to bit strings of length 3. For each element in X, if it belongs to the subset Y, the corresponding bit in the string is set to 0; otherwise, it is set to 1. The value of S(X) will provide the bit string representation of all elements in X.

Given the set X={a, b, c}, the function S maps subsets of X to bit strings of length 3. Let's determine the value of S(X).

For element a, since a∈X, the corresponding bit s1 is set to 0.

For element b, since b∈X, the corresponding bit s2 is set to 0.

For element c, since c∈X, the corresponding bit s3 is set to 0.

Therefore, the value of S(X) is 0, 0, 0; representing that all elements a, b, and c are present in the set X.

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The power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

To find the minimum radius of convergence R of power series solutions about the ordinary point x0 = 1 for the given differential equation, we need to use the Cauchy-Hadamard formula. The formula states that the radius of convergence R is given by:

R = 1/lim sup(|an|)^(1/n)

where an is the nth coefficient of the power series solution.

First, we need to find the power series solution of the differential equation about x0 = 1. We can assume that the solution is in the form of a power series:

y(x) = ∑ an (x-1)^n

We can differentiate this power series to find the derivatives needed to substitute into the differential equation. After substituting and simplifying, we get:

∑ (n+2)(n+1)an (x-1)^n + ∑ (n+1)an (x-1)^n + 4∑ an (x-1)^n = 0

Next, we need to find the coefficients an. We can do this by equating the coefficients of each power of (x-1) to zero. The first few coefficients are:

a0 = y(1)

a1 = y'(1)

a2 = y''(1)/2!

Substituting these coefficients into the formula for R, we get:

R = 1/lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n))

Taking the limit as n approaches infinity, we get:

lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n)) = 1

Therefore, the minimum radius of convergence R is:

R = 1/1 = 1

So the power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

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Answer: the X intercept mean this here

Ms.

Padilla is charged $0.04/min.

Ms. Padilla pays $16 for months she makes 0 min of calls

Step-by-step explanation:

Answer:

8.5

Step-by-step explanation:

Hope it helps!

Answer:

21.50 + 0.25r = 22.25

Step-by-step explanation:

Thats ur equationnn

The formula that can be used to describe the sequence is:\(a(n) = (-1)^(n+1) * 3^(n) * 4.\)

The given sequence is -81, 108, -144, 192.

The formula that can be used to describe the sequence is:  \(a(n) = (-1)^(n+1) * 3^(n) * 4\), where n is the nth term in the sequence.

This formula is a geometric sequence formula that can be used to describe the given sequence.

The formula represents the nth term of the sequence as a function of the position of the term in the sequence.

Here, n represents the position of the term in the sequence

.For the given sequence, the first term is -81, which corresponds to the first position in the sequence (n = 1).

The second term is 108, which corresponds to the second position in the sequence (n = 2).

The third term is -144, which corresponds to the third position in the sequence (n = 3).

The fourth term is 192, which corresponds to the fourth position in the sequence (n = 4).

Therefore, the formula that can be used to describe the sequence is: \(a(n) = (-1)^(n+1) * 3^(n) * 4.\)

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The counterexample proves that the converse of the theorem is not always true, and we have to be careful when making statements about limit points and convergence of sequences.

A sequence is a set of numbers that are generated one after the other in a specific pattern.

The theorem states that if a sequence converges, it will have exactly one limit point. In other words, if a sequence is getting closer and closer to a certain number, there will be only one number that it approaches. This is a fundamental idea in mathematics, and it is important to understand why it is true.

To prove this theorem, let's consider a sequence (a_n) that converges to a limit L. If there were two different limit points, say L1 and L2, then there would be a contradiction. This is because by definition, the sequence (a_n) would be getting closer and closer to L1 and L2 at the same time, which is not possible. Hence, it must be true that the sequence (a_n) has exactly one limit point, L.

The converse of this theorem is not always true. In other words, just because a sequence has exactly one limit point, it doesn't necessarily mean that it converges to that limit. To see why this is the case, let's consider the following sequence:

(2, 3, 4, 5, 6, ...)

In this sequence, the limit point is 6. However, the sequence does not converge to 6 because it is not getting closer and closer to 6 as it goes on. Instead, it is increasing by 1 with each term, and therefore it does not converge.

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Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

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Answer:

A. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).

Step-by-step explanation:

I will solve the problem by applying the perfect square trinomial. In this way we obtain the canonical form. Another way would be to derive the function, but I don't know if you're familiar with it.

First: let us take out the common factor: , since we remember that the canonical form is characterized as follows:

Then, it remains:

Then: the coefficient of the variable  We divided it between , And we square it (they will be one positive and one negative). In our case:

Let's accommodate terms to make it easier:

Can be written as :

Now, what is underlined is our perfect square trinomial, let us recall its form:

Applying the same principle we are left:

Applying distributive property we get:

Therefore it will have its vertex in:  

The axis of symmetry is a straight line that makes the function to be projected being , for this you need some reference point, for the parabola you need the coordinate in  of the vertex.

For which the axis of symmetry is .

I love you so much !

a. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 8.25).

Step-by-step explanation:

The axis of symmetry is x = − b/2a

= -(-3) / 2(-1)

= 3/(-2)

= -1.5

the vertex => x = -1.5

y= -(-1.5)²-3(-1.5)+6 =

-2.25 +4.5+6= 8.25

Answer: SSS

Step-by-step explanation:

SSS or Side-Side-Side postulate means that the 2 triangles have all 3 of their sides to be congruent.

Side AB is congruent to side DE

Side BC is congruent to side EF

Side AC is congruent to side DF

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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