In Mr. Clayton's mathematics class, 7/12 of the students received A's and 1/4 received B's. What fraction of the students received either A's or B's?

a) The limiting value of the temperature of the coffee is 25°C.

b) The limiting value of the rate of cooling is equals to 0.

c) The value of constant k in the

differential equation is -0.05.

d) The temperature of the coffee at time t = 10 is 66.33°C.

Newton's Law of Cooling: The rate at which an object's temperature changes is proportional to the difference in temperature between the object and its surroundings. For an object that has a temperature very close to that of its surroundings, the rate of heating or cooling becomes very small. We have the temperature of the coffee, T(t), satisfies the differential equation,

dT/dt= k(T − T (room)),

where T(room) = 25 is the room temperature, and k is some constant.

A) Limiting value of the temperature

= 25°C

B)limiting value of dT/dt = k[(limit temp) - (room temp)] = k(25 - 25)= 0

C) dT/dt = k(T - 25)

=> -2 = k (65 - 25)

=> -2 = 40k

=> k = -0.05

D) T' = -0.05 x (95-25) = - 3.5

h = 2, ∆T = -3.5x 2 = -7

T = 95- 7 = 88

Then T' = -0.05 x (88-25) = - 3.15

=> T = 88 - 2 x 3.15 = 81.7

=> 81.7 after 4 minutes

Then T' = -0.05x (81.7-25) = -2.835

T = 81.7 - 2x 2.835 = 76.03 after 6 mins

Then T' = -0.05 x (76.03-25) = -2.5515

T = 76.03 - 2 x 2.5515 = 70.92700 after 8 mins

Then T' = -0.05 x (70.927-25) = -2.29635

T = 70.927 - 2 x 2.29635

= 66.3343 after 10 minutes

so temperature = 66.33 after 10 mins by Euler's method.

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Complete question:

Suppose you have just poured a cup of freshly brewed coffee with a temperature of 90∘C in a room where the temperature is 25∘C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation

dT/dt= k(T−Troom), where T(room) = 25 is the room temperature, and k is some constant.

Suppose it is known that the coffee cools at a rate of 2∘C per minute when its temperature is 65∘C.

A. What is the limiting value of the temperature of the coffee?

B.What is the limiting value of the rate of cooling?

C. Find the constant k in the differential equation.

D. Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes_ Answer (in Celsius): T(10)

This means that when all 8 parts are arranged in a single row, probability there are 28 different conceivable configurations. Finley can have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces.

Finley features eight game pieces, each of which is entirely either all red or all black and simply differs in colour. This indicates that there are 28 distinct configurations that may be made using the 8 pieces arranged in a single row. Finley could have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces. This is due to the fact that the 8 pieces can be arranged in a variety of ways, and each arrangement will be deemed distinct as long as it contains at least one red and one black piece. For instance, the configuration could be as follows if there are 4 red and 4 black pieces: If there are four red pieces and four black pieces, for instance, the arrangement might be either black-red-black-red-black-red-red or red-black-red-black-red-black. No matter the configuration, there are a total of 28 arrangements.

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The part of the quadratic equation that says it's shifting to the right is -3.

What is a quadratic equation?

Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a ≠ 0 is a quadratic equation.

f(x) = ax² bx + c = 0

The given equation g(x) = (x − 3)² is the equation of a parabola.

The general equation of a parabola is given by y = a(x – h)²+ k.

The graph of y=x² is shifted to h units to the right and k units up to produce the graph of y=a(x-h)²+k.

The above equation is similar to the equation given in the question.

Comparing,

a = 1

h = 3

So the given quadratic equation states that a parabola of the form g(x) = x² is shifted to the right by 3 units to give the resulting equation

g(x) = (x − 3)²

Therefore the part of the quadratic equation that says it's shifting to the right is -3.

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let me know if answers are correct coz it has been a year that I learnt it and now I'm not doing those exercises so...

Step-by-step explanation:

c) 24 degree
d) 80 degree
e) 93 degree
f) 26 degree
g) ist es gegeben, dass Alpha das Zentrum ist? Wenn ja, ist der Winkel 150
h) Hier gilt das gleiche

Answer:

Senior ticket = $10

Child's ticket = $8

Step-by-step explanation:

s = senior ticket

c = child's ticket

We need to write 2 equations, and we have 2 unknowns, s and c.

12s + 12c = 216

12() + 12c = 216

(70 - 5c) + 12c = 216

4 (70 - 5c) + 12c = 216

280 - 20c + 12c = 216

280 - 8c = 216  Add 8c to each side

280 - 8c + 8c = 216 + 8c

280 = 216 + 8c   Subtract 216 from each side.

280 - 216 = 216 - 216 + 8c

280 - 216 = 8c

64 = 8c   Divide each side by 8

64/8 = 8c/8

64/8 = c

8 = c

Now plug c into the first equation and solve for s.

3s + 5c = 70

3s + 5(8) = 70

3s + 40 = 70    Subtract 40 from each side.

3s + 40 - 40 = 70 - 40

3s = 70 - 40

3s = 30  Divide each side by 3

3s/3 = 30/3

s = 30/3

s = 10

So a senior ticket costs $10 and a child's ticket costs $8.

The probability that an individual student likes between 5.5 and 8.5 songs from Eminem is approximately 0.6826 or 68.26%.

We need to find the z-score corresponding to 5.5 and 8.5 and then use the standard normal distribution table to find the area under the curve between these z-scores.

Z-score for 5.5 is (5.5 - 7.0) / 1.5 = -1

Z-score for 8.5 is (8.5 - 7.0) / 1.5 = 1

The probability of a z-score being between -1 and 1 is equal to the area under the standard normal curve between these two z-scores.

According to the standard normal distribution table, this area is approximately 0.6826.

Therefore, The probability that an individual student likes between 5.5 and 8.5 songs from Eminem is approximately 0.6826 or 68.26%.

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Answer:

a

Step-by-step explanation:

because as time increases by 1 hr, the number of arrangements increases simultaneously by 3. so I can conclude that a=3hrs

Answer:1.25/

Step-by-step explanation:

The eigenvalue λ is equal to -tan(θ)(4cos(4θ)) / sin(4θ). The exact value of the eigenvalue depends on the specific value of θ, as both tan(θ) and cos(4θ) vary with θ.

To find the eigenvalue, we need to multiply the operator by the eigenfunction and see what we get:

(-tan(θ)d/dθ)(sin(4θ)) = -tan(θ)(d/dθ)(sin(4θ)) = -tan(θ)(4cos(4θ))

Since sin(4θ) is an eigenfunction, we expect that the result of the operator multiplied by the eigenfunction should be proportional to the eigenfunction. In other words, there should be a scalar factor multiplying the eigenfunction. This scalar factor is the eigenvalue.

So, we can write:

(-tan(θ)d/dθ)(sin(4θ)) = λsin(4θ)

where λ is the eigenvalue. Equating the right-hand sides of the two equations, we find:

-tan(θ)(4cos(4θ)) = λsin(4θ)

Dividing both sides by sin(4θ), we get:

-tan(θ)(4cos(4θ)) / sin(4θ) = λ

So, the eigenvalue λ is equal to -tan(θ)(4cos(4θ)) / sin(4θ). The exact value of the eigenvalue depends on the specific value of θ, as both tan(θ) and cos(4θ) vary with θ.

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Since probability each student helper must receive at least one of each type of doughnut, there are 120 ways to divide the 8 chocolate donuts and 7 jelly donuts among the three students.

If each student helper desires at least one doughnut of each flavor, there are 120 ways to divide 8 chocolate donuts and 7 jelly donuts among the three students who are helping. This is so because there are exactly as many ways to distribute donuts as there are different methods to distribute each type of doughnut. For instance, there are eight ways to divide the eight chocolate donuts among the three helpers—eight options for the first assistant, seven for the second, and six for the third—and seven ways to divide the eight jelly donuts (7 choices for the first helper, 6 for the second, and 5 for the third). The sum of these two figures (8 x 7 = 56) results in the number of combinations (56). (56). The total number of options must be multiplied by 2 to accommodate for the requirement that each helper receive at least one donut of each flavor: 56 x 2 = 120. If each student helper desires at least one doughnut of each flavor, there are 120 ways to divide 8 chocolate donuts and 7 jelly donuts among the three student volunteers.

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Answer:

The solid formed by rotating the above rectangle around the horizontal axis shown is best described as a cylinder with radius 3cm and height 6cm. The volume of this solid is 108 cubic centimeters, which can be calculated as follows: V = πr2h, where r is the radius and h is the height. In this case, r = 3cm and h = 6cm, so the volume is π x (3 cm)2 x 6 cm = 108 cubic centimeters.

Answer:

Look at the y axis

Step-by-step explanation:

Each division is 2 units, so look and mark 8,2 carefully
If it confuses you, take 16, 4 as well because I dunno how flexible are your drawing tools
Hope this helps :)

Edit: Sorry but I have just realized what had happened, I took the time variable for the y axis. (Sorry, I am used to using the time variable on the y axis

The required fill-in-the-blank below as:

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given

2.) RS≅RS | Reflexive Property

3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

Two triangles are said to be congruent if their corresponding sides and angles are equal.

The given in question as:

RS ⊥ ST

RS ⊥ SQ

∠STR = ∠SQR

To prove:

△RST ≅ △RSQ

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given

2.) RS≅RS | Reflexive Property

According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

Hence, △RST ≅ △RSQ

Thus, the required fill-in-the-blank above is in the solution.

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Answer:

C.

Step-by-step explanation:

The rule for dilation around the origin with a scale factor of k is (x,y) -> (kx,ky).

Dilation is a transformation in geometry that changes the size of a figure while preserving its shape. A dilation centered at the origin involves scaling the figure down by a factor, causing it to become smaller.

In this case, the origin acts as the center of dilation, with the original figure being mapped to a smaller, similar figure.

To perform a dilation, each point of the original figure is multiplied by the same scale factor, resulting in a smaller, proportional figure.

The scale factor determines how much the figure will be reduced. It is important to note that dilations centered at the origin preserve the orientation of the figure, meaning it will look the same as the original, but just smaller.

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0, no solutions

that is the answer

The maximum value of the expression ax² + 10x + c is 7, which means that the parabola represented by this equation opens upwards and its vertex is at the highest point.

The vertex of a parabola represented by the equation ax² + 10x + c is given by (-b/2a, f(-b/2a)), where b is the coefficient of x, a is the coefficient of x² and f(x) is the function.

Therefore the vertex of this parabola is (-10/2a, 7 - c)

Since the vertex is the highest point, the y-coordinate of the vertex is the maximum value of the expression.

7 - c = 7

therefore c = 0

We also know that the x-coordinate of the vertex is -10/2a, this means that the x-coordinate of the vertex is -5/a

There are many possible combinations of a and c that work for this question, some possible combinations are:

   a=1, c=0

   a=2, c=0

   a=-2, c=0

Another way to find a and c is by expanding the equation:

ax² + 10x + c = a(x²+ 10/a x) + c = a(x²+ 10/a x + (100-100a)/(4a²)) + c = a(x+5/a)² + c -25/a + 7

So, when a=1, c=0 and a=2, c=0 will give you the maximum value of 7, where it's a parabola that opens upwards and it's vertex is at the highest point.

The integer numbers for each card describing the motions are given as follows:

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

Regarding the movements, the integers can be classified as positive or negative, as follows:

Considering the movements described for each card in the problem, the equations are built in the answer given at the beginning of the answer.

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Total number of historical fiction books are 153.

Given is that of the total number of books in a library, 50% are non fiction, 30% are historical fiction, and the rest are science fiction. There are 102 science fiction books in the library.

Assume that the total number of books in the library are {x}. Then, we can write -

(50 + 30)% of {x} = {x} - 102

80% of {x} = {x} - 102

(80/100){x} = {x} - 102

8x/10 = x - 102

x - 4x/5 = 102

(5x - 4x)/5 = 102

x = 102 x 5

x = 510

Number of historical fiction books will be -

30% of 510

(30/100) x 510

3/10 x 510

3 x 51

153

Therefore, total number of historical fiction books are 153.

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The scatter plot for the correlation of weight and intelligence scores for 250 students would likely be very close to the origin, meaning that the majority of the points would be clustered around the point (0,0), with a very small range of points scattered further away.

This would indicate that there is no correlation between the two variables, which is reflected in the computed correlation coefficient of .00.

A scatter plot is a type of plot that displays data points on a two-dimensional graph. The data points are represented as dots or circles on the graph and show the relationship between two variables. The location of each data point is determined by the value of the two variables for that point. Scatter plots can be used to identify patterns in data, such as clusters, linear relationships, or nonlinear relationships. They can also be used to identify outliers or unusual data points.

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Answer:

Step-by-step explanation:

[tex]2x+\frac{1}{3} x^{2} =9[/tex]

Move all terms to l.h.s.

[tex]\frac{1}{3} x^{2} +2x-9=0[/tex]

Multiply everything by 3

[tex]x^{2} +6x-27=0[/tex]

Factorize

[tex](x+ 9)(x-3 )=0[/tex]

therefore

[tex]x+9=0[/tex]  or [tex]x-3 =0[/tex]

x= -9  or x =3

Since x is a positive answer the answer must be

x=3

if we flip a coin, we would expect the probability of its landing heads to be the same as its landing tails is referred to as the law of large numbers.

The law of large numbers is a probability and statistics, which defines that as a sample size grows, its mean gets closer to the average of the whole population.

This is due to the sample being more representative of the population as the sample becomes larger.

This is the theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

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We need to roll a die at least 3 times and a coin should be tossed at least 2 times.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given this, Becca repeatedly tosses a fair coin until she gets a head.

The probability of getting a head P(H) is = 1/2.

The probability of getting a number 3 or higher is,

P(3) + P(4) + P(5) + P(6).

= 1/6 + 1/6 + 1/6 + 1/6.

= 4/6.

= 2/3.

So, to get a number 3 or higher we need at least 3 rolls, and to get a head we need at least 2 tosses.

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The scale factors of 9/7 and 0.25 would result in an expansion.

Scale factor is a numerical value used to represent the proportional change between two similar objects. This value is often used to compare the size of objects in different measurements, such as inches to millimeters or feet to meters. Furthermore, the scale factor can be used to find the area, volume, or surface area of an object, as the measurements are proportional to the scale factor. This is especially useful when objects are enlarged or reduced, as it allows for the accurate calculation of the changed measurements.

Expansion occurs when the scale factor is greater than zero. In this case, the scale factors of 9/7 and 0.25 would result in an expansion. The scale factors of -3 and -3/4 would result in a contraction.

When an object is scaled, the size of the object changes in one or more directions. If the scale factor is greater than one, the object will expand. Conversely, if the scale factor is less than one, the object will contract. The scale factor can either be multiplied by the length of the object or by the area of the object to determine the change in size. For example, if the scale factor is two, the length of the object would double and the area of the object would quadruple.

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Answer:

D (-2, -9)

Step-by-step explanation:

Parallel slopes are equal.  From C to A it is down 3 and right 5.  To go from B to D go down 3 and right 5.  

B go down 3 -6 - 3 = -9

B go right 5 -7 + 5 = -2

The new dimension of the matrix t. a is 5 columns and 3 rows.

To generate the transpose of the matrix a and save it into t.a, you can use the following code:t.a <- t(a)The new dimension of the matrix t.a is 5 columns and 3 rows.

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Answer:

a function is said to be positive if all the values of y are above the x-axis and it is said to be negative if all the values of y are below the x-axis.

The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.

The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.

The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima.  M(t) = 2t + 1

   d/dt M(t) = d/dt 2t + 1

                  = 2

d/dt m'(t) = 0

2 not equal to 0

The function does not have a critical point. Therefore, the maxima do not exist for the function.

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The sample space for this experiment is the set of all possible outcomes of drawing 2 marbles from the box, where order matters. There are 3 choices for the first marble, and 3 choices for the second marble, so the sample space is {RR, RG, RB, GR, GG, GB, BR, BG, BB}. There are 9 possible outcomes in this sample space.

To determine the sample space for this experiment, we first list all the possible outcomes for the first marble that we could draw. There are 3 marbles in the box (red, green, and blue), so there are 3 choices for the first marble. We can represent these choices as R, G, and B.

Next, we list all the possible outcomes for the second marble that we could draw. Since the box is being replaced with the first marble before the second draw, there are still 3 marbles in the box (red, green, and blue), so there are still 3 choices for the second marble. We can represent these choices as R, G, and B.

Finally, we list all possible combinations of the first and second marble, which forms the sample space. Since order matters, we list all the possible combinations of R, G, and B as pairs. In this case, there are 3 choices for the first marble and 3 choices for the second marble, which gives us 3 * 3 = 9 possible outcomes in the sample space: {RR, RG, RB, GR, GG, GB, BR, BG, BB}.

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