On a snow day, Moussa created two snowmen in his backyard. Snowman A was built to a height of 59 inches and Snowman B was built to a height of 39 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 9 inches per hour and Snowman B's height decreased by 4 inches per hour. Let � A represent the height of Snowman A � t hours after sunrise and let � B represent the height of Snowman B � t hours after sunrise. Write an equation for each situation, in terms of � , t, and determine the number of hours after sunrise when both snowmen have an equal height.

Answer: I hope this helped!

Step-by-step explanation:

.

The new position of Rhombus ABCD after the translation can be described as follows: point A is now at (-1,-8), point B is at (2,-3), point C is at (7,0), and point D is at (4,-5).

To translate Rhombus ABCD using the rule (x, y) = (x+2, y-6), we add 2 to the x-coordinate and subtract 6 from the y-coordinate for each vertex.

Thus, the new vertices for the translated rhombus are:

A' = (-3+2, -2-6) = (-1, -8)

B' = (0+2, 3-6) = (2, -3)

C' = (5+2, 6-6) = (7, 0)

D' = (2+2, 1-6) = (4, -5)

Therefore, the coordinates for the translated Rhombus ABCD are A'(-1,-8), B'(2,-3), C'(7,0), and D'(4,-5).

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Answer:

n > 10

Step-by-step explanation:

2n > 20

2n/2 > 20/2

n > 10

Answer:

120 km/h.

Step-by-step explanation:

480 km / 4h

Divide top and bottom by 4 to get the desired km/h.

We have 120 km/h.

Hope this helps!

From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm

To construct triangle ABC, we can follow these steps:

To measure the length of BC in triangle ABC, we can use the law of sines.

The law of sines states that in any triangle ABC:

a / sin(A) = b / sin(B) = c / sin(C)

Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.

In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:

angle ACB = 180 - angle BAC - angle ABC

= 180 - 96 - 35 = 49 degrees

Now, we can apply the law of sines to find the length of BC:

BC / sin(35) = 6 / sin(96)

BC = 6 × sin(35) / sin(96)

Using a calculator, we can evaluate this expression to get:

BC ≈ 4.22 cm

Therefore, the length of BC in triangle ABC is approximately 4.22 cm.

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The smallest number of batteries in the package for the probability to exceed 1% is a) 17. This can be calculated using the binomial distribution with parameters n=17 and b)p=0.2927 and number of batteries is c)4. (Where p is the probability from part a).

a) The probability that a battery does not reach the significant milestone after 8 hours of usage is 0.2927.

This can be calculated using the cumulative normal distribution function. The parameters are μ=7.36, σ=0.29, and x=8.

b) The probability that at least 10 batteries will last more than 7.5 hours is 0.7012.

This can be calculated using the binomial distribution with parameters n=12 and p=0.2927 (where p is the probability from part a).

c) The number of batteries should be in package is μ*4.2/7.5 = 4.

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The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

Recall from the task content; the given functions are;

f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ

Therefore, for intersection; f (θ) and g(θ):

2 cos²θ = −1 − 4cos θ − 2cos²θ

4cos²θ + 4cosθ + 1 = 0

let cos θ = y;

4y² + 4y + 1 = 0

y = -1/2

Therefore; -1/2 = cos θ

θ = cos-¹ (-1/2)

θ = 2π/3, 4π/3.

Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

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Answer:

35 passengers produce the maximum revenue for the bus company.

Step-by-step explanation:

Define the variables:

If there are 30 or fewer passengers, each passenger will be charged $80. Therefore, the equation for the total revenue for 30 or fewer passengers is:

[tex]y = 80x,\quad x \leq 30[/tex]

If there are more than 30 passengers, each passenger will be charged $80 minus $2 for every passenger over 30. Therefore, the equation for the total revenue for more than 30 passengers is:

[tex]y = [80 - 2(x - 30)]x, \quad x > 30[/tex]

This simplifies to:

[tex]y = [80 - 2x + 60]x, \quad x > 30[/tex]

[tex]y = [140 - 2x]x, \quad x > 30[/tex]

[tex]y = 140x - 2x^2, \quad x > 30[/tex]

To maximize revenue, we need to find the value of x that maximizes the above equation.

Since this is a quadratic function, the maximum value occurs at the vertex of the parabola.

The x-value of the vertex of a parabola in the form y = ax² + bx + c is when x = - b/2a. Therefore, the x-value of the vertex is:

[tex]\implies x_{\sf vertex}=\dfrac{-140}{2(-2)}=\dfrac{-140}{-4}=35[/tex]

Therefore, the number of passengers that produce the maximum revenue for the bus company is 35.

She should navigate at angle 76.86° to go to Island C.

The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

cosA = (b²  +  c² - a²)/2bc

where a, b and c are the lengths and A, B and C are the angles for the islands respectively

Using the formula:

cosA = (b²  +  c² - a²)/2bc

cosA = (13²  +  11² - 15²)/(2*13*11)

cosA = 5/22

A = arc cos(5/22)

A = 76.86°

Thus, θ = 76.86

Therefore, she should navigate at angle 76.86° to go to Island C.

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Completing the proof that if A has strictly positive diagonal entries, then all of its eigenvalues have a positive real part.

For any square matrix A, a diagonal element is any element that is on the main diagonal, i.e., (i,i) for 1<=i<=n. If A has strictly diagonal dominance, then for each row i of A, the absolute value of the diagonal element of that row is more than the sum of the absolute values of the non-diagonal elements of that row.If A is invertible, then det(A) is nonzero. If all the diagonal entries are positive, then det(A) is also positive, which implies that all the eigenvalues of A have the same sign (either all are positive or all are negative).As a result, suppose all of A's diagonal entries are positive. Then all of A's eigenvalues are positive since they all have the same sign as det(A).

And if all of A's eigenvalues are positive, then all of their real parts are positive as well, hence completing the proof that if A has strictly positive diagonal entries, then all of its eigenvalues have a positive real part.

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Answer:

Step-by-step explanation:

You want to make 5.4 in three different ways.

You can add, subtract, multiply, or divide numbers to obtain a result of 5.4:

  2.9 +2.5 = 10.0 -4.6 = 2.0×2.7 = 10.8÷2 = 5.4

  √29.16 = ∛157.464 = 5.4

  [tex]\displaystyle\sum_{n=1}^\infty{10.8(3^{-n})}=5.4[/tex]

The formula for the nth term of the series will be (11+n)*(n+1).

A series in mathematics is essentially the process of adding an infinite number of quantities, one after the other, to a specified starting quantity. A significant component of calculus and its extension, mathematical analysis, is the study of series. The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, whereas a sequence is an ordered group of elements in which repeats of any kind are permitted. One of the typical instances of a series or a sequence is an arithmetic progression.

In this the pattern of the series is

24=12*2

39=13*3

54=14*4

hence The formula for the nth term of the series will be (11+n)*(n+1).

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Answer:

A ,B ,C

Step-by-step explanation:

2+2+2+2 equals 8

4x2 equals 8 and

1x8 equals 8

Answer:

A) 2 + 2 + 2 + 2

B) 4 × 2

C) 1 × 8

Hope this helps!

Step-by-step explanation:

A = 4 + 4 = 8

B = 8

C = 8

D = 16

E = 16

The probability of the given event is 11/13.

A card is drawn randomly from a deck of 52 cards.

The probability that the card drawn is neither an ace nor a king is a question that can be answered with probability.

We know that there are 4 aces and 4 kings in a deck of 52 cards.

The probability of drawing an ace or a king is P(Ace or King) = 4/52 + 4/52 = 8/52 = 2/13

There are four of each card rank in a deck of 52 cards, and there are a total of 52 cards. A player must choose one of the 52 cards at random.

The probability of drawing an ace or a king is P(Ace or King) = 4/52 + 4/52 = 8/52 = 2/13

The probability of at drawing neither an ace nor a king is:

P(Not Ace and Not King) = 1 - P(Ace or King) = 1 - 2/13 = 11/13

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The number of different selections possible if at least 3 balls must be blue is 35


1. Calculate the total number of possible selections (6 red + 7 blue = 13 total): 13C4 = 715
2. Calculate the number of possible selections that have fewer than 3 blue balls: 6C4 = 15
3. Subtract the number of possible selections with fewer than 3 blue balls from the total number of possible selections: 715 - 15 = 700
4. Divide the answer by the number of selections with exactly 3 blue balls: 700/7 = 100
5. Multiply the result by the number of selections with exactly 4 blue balls: 100 * 7 = 700
6. Finally, subtract the number of selections with 4 blue balls from the total number of possible selections: 715 - 700 = 35

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As per the confidence interval, the true proportion of people in the population who prefer Candidate A lies somewhere between 0.622 and 0.698, based on the results of the survey of 1050 voters.

To calculate the margin of error, we will use the following formula:

Margin of error = z x standard error

Where z is the critical value from the standard normal distribution corresponding to our desired confidence level (95%), and the standard error is given by:

Standard error = √[(sample proportion x (1 - sample proportion)) / sample size]

Using a z-table, we find that the critical value for a 95% confidence interval is 1.96

Plugging in the values we have, we get:

Standard error = √[(0.66 x 0.34) / 1050] = 0.0193

Margin of error = 1.96 x 0.0193 = 0.0378

Therefore, the 95% confidence interval for the proportion of people who prefer Candidate A is:

0.66 ± 0.0378

Rounded to the nearest thousandth, the lower bound of the confidence interval is 0.622 and the upper bound is 0.698.

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The two options are as follows: a. 20, 24, 21, 19, 18.

This sample is a possible bootstrap sample.

A bootstrap sample is created by taking samples from the original sample with replacement. Therefore, we can include the original data multiple times.

Here, 20, 24, 19, 23, 18 is the original sample.

Sample a includes 20, 24, 19, 23, and 18 which are part of the original data, and 21 which is not part of the original data. Since we can include the original data multiple times in bootstrap samples, a is possible.b. 20, 20, 20, 20, 20This sample is not a possible bootstrap sample.

In the original sample, we have five unique data points: 20, 24, 19, 23, and 18. Sample b includes only one unique data point, 20, repeated five times. We cannot create a bootstrap sample with the same data point repeated multiple times. Hence A is correct.

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The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.

Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.

Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".

The formula for Spearman's rank correlation coefficient:

Rs = 1 - {6Σd₂}/{n(n₂-1)}

Where, Σd₂ = the sum of the squared differences between ranks.

n = sample size

Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.

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The real part of the particular solution to the differential equation is [tex](1/30)Re(e^(3it))(sin(3t) - cos(3t))[/tex]

The real part of the particular solution to the differential equation:

[tex]\frac{d^2y}{dt^2} +3\frac{dy}{dt} +7y = e^(3it)[/tex]

First, we assume a particular solution of the form:

[tex]y(t) = Bcos(3t) + Csin(3t)[/tex]

where B and C are real fractions.

Taking the first and second derivatives of y(t), we get:

[tex]\frac{dy}{dt} = -3Bsin(3t) + 3Ccos(3t)[/tex]

[tex]\frac{d^2y}{dt2} = -9Bcos(3t) - 9Csin(3t)[/tex]

Substituting these into the differential equation, we get:

[tex](-9Bcos(3t) - 9Csin(3t)) + 3(-3Bsin(3t) + 3Ccos(3t)) + 7(Bcos(3t) + Csin(3t)) = e^(3it)[/tex]

Simplifying and collecting terms, we get:

[tex](-9B + 21C)*cos(3t) + (-9C - 9B)*sin(3t) = e^(3it)[/tex]

Comparing the coefficients of cos(3t) and sin(3t), we get:

[tex]-9B + 21C = Re(e^(3it))[/tex]

[tex]-9C - 9B = 0[/tex]

Solving for B and C, we get:

[tex]B = -C[/tex]

[tex]C = (1/30)*Re(e^(3it))[/tex]

Therefore, the particular solution is:

[tex]y(t) = -Ccos(3t) + Csin(3t) = (1/30)Re(e^(3it))(sin(3t) - cos(3t))[/tex]

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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In order to solve this problem, we need to begin by examining the graph of Amir's altitude relative to sea level. We can see that the graph starts at an altitude of 700 meters and ends at an altitude of 400 meters.

We can also see that the slope of the graph is negative, which means that the altitude is decreasing over time. This means that it will take Amir some amount of time to reach sea level (which is 0 meters).

To calculate how long it took Amir to reach sea level, we can use the following equation:

Time = (Altitude Final - Altitude Initial) / (Rate of Change)

In this equation, the Rate of Change is the slope of the graph, which can be determined by examining the graph.

Plugging in our values, we get:

Time = (400 - 700) / (-6) = 100 / (-6) = -16.67 minutes

Therefore, it took Amir 16.67 minutes to reach sea level.

Answer:

Cos2a - cot2a/sin2a - tan2a

Step-by-step explanation:

Answer:

Step-by-step explanation:

When we divide two exponential expressions with the same base, we can subtract their exponents. Using this property, we can simplify the given expression as:

2^(x+2) /2^(x-1) = 2^x * 2^2 / 2^x * 2^(-1)

= 2^(x-1+2)

= 2^(x+1)

Therefore, the simplified expression is 2^(x+1).

The Objective Function in the linear programming problem given in the above-stated scenario is:

B. S = 3x + 5y

Linear programming is a statistical technique used to find a maximum or minimum value of an equation in order to find a solution to a problem. It is used to calculate how much to produce to maximize profits, how to allocate resources, and determine which investments to make.

Linear programming problems include an objective function, which is the equation to be maximized or minimized, and constraints that must be followed. Linear programming problems can be solved graphically or algebraically. In order to solve a linear programming problem, we first need to identify the objective function and constraints.

Objective Function in the linear programming problem:

The score of the student is to be maximized in the given time frame by answering the maximum number of questions of both types.

Therefore, the objective function is: S = 3x + 5y

Answer: B. S = 3x + 5y

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Answer: y = -192

Step-by-step explanation:

The equation given is:

-24 = y/8

To solve for y, we need to isolate the variable y on one side of the equation. We can do this by multiplying both sides by 8:

-24 x 8 = y

Simplifying the left side:

-192 = y

Therefore, the solution is y = -192.

False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).

Probability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.

This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.

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Answer: 105:210

Step-by-step explanation:

1:2 = ?:210

? = 210/2 = 105

1:2 = 105:210