A line contains the points (-4, 2) and (-4, 6). The line is translated 3 units to the right and 2 units down. What are the new points on the translated line? The new point for (-4, 2) is: () The new point for (-4, 6) is: ()​

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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The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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The equation can be used to determine the ellipse's area, circumference, and other parameters because it is symmetrical.

For this to be a valid probability model, p must be a positive integer between 0 and 1, and p + p2 + p must equal 1. This random experiment must have a probability rea, circumference, and other parameters because it is symmetrical. of each of the three outcomes adding up to 1 in order to be a reliable probability model. This implies that the probabilities p, p2, and p associated with outcomes a, b, and c must all add up to 1. In other words, p + p2 + p = 1 would be the equal. Since p must be a real value between 0 and 1 and satisfy the equation p + p2 + p = 1, this random experiment must be a legitimate probability model.

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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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It would take 17 years for the value of the account to reach $2,550. The solution has been obtained by using the concept of compound interest.

What is compound interest?

The principal as well as the interest that has accrued over the previous period are both used to compute interest. Compound interest factors the principal into the calculation for determining the interest for the subsequent month, in contrast to simple interest, which does not. In mathematics, the symbol for compound interest is typically the letter C.I.

We are given the principal amount as $790 paying an interest rate of 6.9% compounded continuously.

The final balance is $2,550.

We know that formula for continuous compounding interest is

[tex]P(t) = P_{0} e^{rt}[/tex]

So, using this, we get

⇒[tex]2550 = 790 e^{0.069*t}[/tex]

Solving this, we get

t = 17

Hence, it would take 17 years for the value of the account to reach $2,550.

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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.

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 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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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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Answer:

  C. Exponential growth

Step-by-step explanation:

You want to know how to describe the relation that represents a 10% increase per year.

The problem statement tells you the number of guests "increased by approximately 10% each year". The nature of the function depends on what "10%" refers to.

If the amount of increase is constant year after year (10% of the original number of guests), then the relationship is linear.

If the amount of increase is 10% of the previous year's number, so the amount increases each year, then the relationship is exponential.

When the number increases year on year, the number is said to be growing. If the relationship is exponential, it is described as exponential growth.

If the number were decreasing by 10% per year, it would be an exponential decay relationship.

__

Additional comment

Whenever you're dealing with percentages, you always need to understand what is being used as the base amount. (What does 100% represent?)

Usually, a percentage increase or decrease is referring to the current value. Not always.

Sometimes a change from 10% to 6% is referred to as a 4% decrease, and sometimes it is referred to as a 40% decrease. It depends on who is selling what to whom.

Answer: The total volume of concrete that Jimmy will need to create the 4 spheres is 38.25 cubic feet, rounded to the nearest whole number.

Step-by-step explanation:

To find the total volume of concrete needed for the 4 spheres, we need to find the volume of each sphere individually and then add them up. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere.

First, we need to find the radius of the largest sphere, which is 4 feet in diameter. The radius is half the diameter, so it is 2 feet.

The radius of the next sphere is half of the radius of the first sphere, which is 1 foot.

The radius of the next sphere is half of the radius of the second sphere, which is 0.5 feet.

The radius of the last sphere is half of the radius of the third sphere, which is 0.25 feet.

We can now use the formula to find the volume of each sphere and then add them up.

The volume of the first sphere = (4/3)π(2^3) = (4/3)π(8) = 33.49 cubic feet

The volume of the second sphere = (4/3)π(1^3) = (4/3)π(1) = 4.19 cubic feet

The volume of the third sphere = (4/3)π(0.5^3) = (4/3)π(0.125) = 0.52 cubic feet

The volume of the last sphere = (4/3)π(0.25^3) = (4/3)π(0.015625) = 0.05 cubic feet

Total volume of all spheres = 33.49 + 4.19 + 0.52 + 0.05 = 38.25 cubic feet

The total volume of concrete that Jimmy will need to create the 4 spheres is 38.25 cubic feet, rounded to the nearest whole number.

Answer: It would cost $3.35 ?more than the leave cloth.

Step-by-step explanation:so for 2.5 yards the leaves of fabric would cost $16.6 because 6.64×2=$13.28+6.64/2=16.6

Then for the pumpkin which costs $19.95 because you would multiply 7.98 by 2 then add 7.98 divided by 2. So it would cost 19.95-16.6=$3.35

The area, in square units, between the two functions over the interval [−3,3]. is 36 square units

integral is defined to be exactly the limit and summation that we looked at in the last section to find the net area between a function and the

x-axis.

Also note that the notation for the definite integral is very similar to the notation for an indefinite integral.

the fact that a and b were given as an interval the lower limit does not necessarily need to be smaller than the upper limit. Collectively we’ll often call a and b the interval of integration.

[tex]\int\limits^3_3 {f(x)} \, dx -\int\limits^3_3 {g(x)} \, dx\\=\int\limits^3_3 {f(x) - g(x) } \, dx \\= \int\limits^3_3 {(x^{2} -9x-18) - (-9x-9)} \, dx \\=\int\limits^3_3 {x^{2} -9x-18 + 9x+9} \, dx \\\\=\int\limits^3_3 {x^{2} -9} \, dx[/tex]

=[tex]\left \{ {{y=3} \atop {x=-3}} \right. (\frac{x^{3} }{3} -9x)\\= \frac{3^{3} }{3} -9*3 -( \frac{3^{-3} }{3} -9*-3)\\=9-27 +9-27\\= -36[/tex]

The area, in square units, between the two functions over the interval [−3,3]. is 36 square units

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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

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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The change in speed equals 2m/s and Magnitude of acceleration = 2.

What is meant by zero acceleration is the rate of change in speed. Thus, the rate of change in speed is zero while the car is moving at a constant pace. As a result, there is no acceleration. Magnitude is the length of any vector that points in the direction of the vector and is denoted by its unit. As a result, the acceleration's magnitude is equal to the acceleration vector's length and is directed in the same direction. For any vector quantity, this is true.

the sense, or the direction the vector is moving (left/right, up/down); the orientation, or the angle(s) governing the vector's alignment (transversal, longitudinal); and

The "strength" of the function is represented by the magnitude, or the value derived from the scalar quantities.

Change in speed = 5 m/s - 3m/s = 2m/s

As acceleration = rate of change in speed

Magnitude of acceleration = 2

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Answer: I think its X intercept is (-0.75,0) and then y is (0,0.429)

Step-by-step explanation:

Tell me if I'm wrong

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)

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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This statement is called an Income Statement.

December 3 I Income Statement

Revenue

Sales:          $1,027,800

Rental of Equipment to Customers:   $47,000

Total Revenue:        $1,074,800

Cost of Goods Sold:       $537,400

Gross Profit:        $537,400

Expenses

Salaries and Wages:       $15,000

Rent of Facilities:       $70,600

Depreciation of Equipment:     $3,000

Electricity:        $2,900

Supplies:         $1,850

Other Expenses:        $700

Total Expenses:        $93,150

Net Profit:         $444,250

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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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The value of a is 3

The equation of the quadratic function is

f(x) =  3(x+2) (x+1) in factored form and

f(x) = 3x² + 9x+2 in standard form.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

The x-intercepts of the parabola are (-2,0) and (-1,0).

So the factors are (x- (-2)) and (x- (-1))

That is, (x+2) and (x+1)

Now the equation of the parabola,

y = a(x+2) (x+1)

To find a substitute the values -3 and 6 for x and y as these points are on the parabola.

6 = a(-3+2)(-3+1)

6 = a ( -1)(-2)

a = 3

So the equation of the parabola is y = 3(x+2) (x+1)

Therefore the complete statements regarding the parabola is:

The value of a is 3

The equation of the quadratic function is

f(x) =  3(x+2) (x+1) in factored form and

f(x) = 3x² + 9x+2 in standard form.

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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 missing side is 29, because in a triangle, the sum of the angles is 180°.  

A triangle is a three-sided polygon, a two-dimensional shape with three straight sides and three angles. It is one of the most basic shapes in geometry, and can be used to construct more complex shapes and figures such as rectangles and circles. Triangles come in many different varieties, including equilateral, isosceles, and scalene. The angles in a triangle add up to 180°, and the sides of a triangle are always connected.

In this case, 39° + X° = 180°, and X° = 180° - 39° = 141°. Since the angle is given in degrees, the side length can be found using the law of cosines, which states c^2 = a^2 + b^2 - 2ab cos C. In this case, c = 29, a = b = 11, and C = 141°. Plugging this into the equation, we get 29^2 = 11^2 + 11^2 - 2(11)(11)cos(141°). Simplifying and solving for c, we get c = 29. Therefore, the missing side is 29.

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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 translation of 5 units to the left and 3 units down,The new coordinates are therefore (5, 1).

The coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.

By multiplying the value of the horizontal translation by the original x-coordinate, get the new x-coordinate of the translated point (adding a negative number if translating to the left).

Let (A,B)=(3,5) serve as the new origin and (x,y)=(3,4) serve as the provided point.

new coordinates are therefore (X,Y).

x = X+A and y = Y+B

such as 3=X2 and 4=Y+5.

This results in X=5 and Y=1

The new coordinates are therefore (5, 1).

The translation of 5 units to the left and 3 units down,The new coordinates are therefore (5, 1).

Determine the coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down. (3,4) will become

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Answer:  15 (cupcakes)

Step-by-step explanation:

So, as you understand, 3 cupcakes represent 20% of the order.

20% = 20/100 = 1/5

3=1/5

3x5=15

1/5x5=1

Therefore, your one whole order is 15 cupcakes