-x + 3y = -27 3x - 3y = 39

The area between y = x² - 1 and the x-axis, for x in the interval (0, 3) is [3] Jo¹ (1 - x²) dx + 13 (x² - 1) dx.

We must find the area bounded by the curve y = x² - 1, x-axis, and x = 0 and x = 3.

Since the function is below the x-axis, we must consider its absolute value and take the integral in the interval (0, 3).

Thus, the area bounded by the curve is given by= ∫₀³ ∣x² - 1∣ dx When x ∈ [0, 1], x² ≤ 1, so ∣x² - 1∣ = 1 - x².

Thus, the integral becomes:

∫₀¹ (1 - x²) dx = [x - (x³ / 3)] [0, 1] = 2/3

Similarly, when x ∈ [1, 3], x² - 1 ≥ 0, so ∣x² - 1∣ = x² - 1.

Thus, the integral becomes:

∫₁³ (x² - 1) dx = [(x³ / 3) - x] [1, 3] = 8/3.

Therefore, the total area bounded by the curve is equal to= 2/3 + 8/3 = 10/3

Hence, the area between y = x² - 1 and the x-axis, for x in the interval (0, 3) is [3] Jo¹ (1 - x²) dx + 13 (x² - 1) dx.

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Answer:

This equation has 4 solutions, its real solutions are x = -1 and 3

Step-by-step explanation:

Correct for Plato Users

The equation has 4 solutions and its real solutions are 3, -1.

The given polynomial equation is 6(x - 3)(x² + 4)(x + 1) = 0.

A real solution in algebra is simply a solution to an equation that is a real number.

Now, 6(x - 3)(x² + 4)(x + 1) = 0

⇒(x - 3)(x² + 4)(x + 1) = 0

⇒(x - 3)=0, (x² + 4)=0 and (x + 1) = 0

⇒x=3, -1 and ±√-4.

Therefore, the equation has 4 solutions and its real solutions are 3, -1.

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Answer:

5

Step-by-step explanation:

im pretty sure its 8.94

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Answer:

5\(\sqrt{2}\)

Step-by-step explanation:

prime factorising 50 inside root,

\(\sqrt{50}\)=\(\sqrt{5*5*2}\)

      5*5 is a perfect square

    So root of 5*5(or 25) is 5.

Hence 5 comes outside and 2 remains in bracket.

=5\(\sqrt{2}\)

Answer: \(32y^2 -1\)

Step-by-step explanation:

\(f(4y)=2(4y)^2 -1=2(16y^2)-1=32y^2 -1\)

The probability of the intersection of events A and B (P(A and B)) is 0.16 or 16%.

To find the probability of the intersection of events A and B (P(A and B)), we can use the formula:

P(A and B) = P(A) * P(B|A)

Given that P(A) = 0.2 and P(B|A) = 0.8, we can substitute these values into the formula:

P(A and B) = 0.2 * 0.8

Calculating this expression gives us:

P(A and B) = 0.16

Therefore, the probability of the intersection of events A and B (P(A and B)) is 0.16 or 16%.

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The equation representing the total amount Emma earns at the event is y = $10x.

If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:

y = kx

where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:

y = $10 * x

Therefore, the equation representing the total amount Emma earns at the event is y = $10x.

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The equation representing the total amount Emma earns at the event is y = $10x.

If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:

y = kx

where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:

y = $10 * x

Therefore, the equation representing the total amount Emma earns at the event is y = $10x.

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Answer:

Step-by-step explanation:

Theres no picture

Answer:

Can you show the picture real quick use ctrl shift s to screen shot or window  F11

Step-by-step explanation:

Answer:

The answer is 72 inches in 24 hours.

Step-by-step explanation:

If 3 inches tall per hour, and you need to find the amount of rain in 24 hours, you just need to multiply the number of inches per hour by the number of hours required (24 hours):

3×24=72 inches

Answer:

Express the ratio 6 inches of rain in 24 hours as a unit rate. *

Step-by-step explanation:

Answer:

The volume of the rectangular prism can be calculated by multiplying its length, width, and height: 8 x 4.12 x 3.12 = 128.064 cubic inches.

Answer:

V=342,784in

Step-by-step explanation:

V=1/3(L×W×H)

where v=volume of rectangular prism,L=length.W=width or breadth,H=height

V=1/3×8×412×312

V=342,784in

The mean of the function f(x) = (1/10)e^(-x/10) for x ≥ 0 is 0. Thus, the correct answer is A) 0.10.

To find the mean of the function f(x) = (1/10)e^(-x/10) for x ≥ 0, we need to calculate the definite integral of xf(x) over the range of x ≥ 0 and divide it by the integral of f(x) over the same range.

The integral of xf(x) is given by ∫(x/10)e^(-x/10) dx, and the integral of f(x) is ∫(1/10)e^(-x/10) dx.

To evaluate these integrals, we can use integration by parts. Let's use the formula ∫u dv = uv - ∫v du, where u = x/10 and dv = e^(-x/10) dx.

Differentiating u with respect to x, we have du = (1/10) dx.

Integrating dv, we have v = -e^(-x/10).

Applying the integration by parts formula, we get:

∫(x/10)e^(-x/10) dx = -(x/10)e^(-x/10) + ∫(1/10)e^(-x/10) dx.

Simplifying further, we have:

∫(x/10)e^(-x/10) dx = -(x/10)e^(-x/10) - e^(-x/10) + C,

where C is the constant of integration.

Now, to find the mean, we need to evaluate the definite integral of xf(x) and divide it by the definite integral of f(x). The range is x ≥ 0.

Let's evaluate the definite integrals:

∫[0, ∞] (x/10)e^(-x/10) dx = lim(b→∞) [-(x/10)e^(-x/10) - e^(-x/10)] [0, b]

= -[b/10)e^(-b/10) - e^(-b/10)] + (0/10)e^(-0/10) - e^(-0/10)

= 0.

∫[0, ∞] (1/10)e^(-x/10) dx = lim(b→∞) [-e^(-x/10)] [0, b]

= -e^(-b/10) + e^(-0/10)

= 1.

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Answer:

Cumulative Frequency:

The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.

The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.

Step-by-step explanation:

3. You have the following fraction:

In terms of units fraction it is better to express the previous fraction as a sum of units fractions, as follow:

Consider that in the right side of the previous expression you have homogeneous fractions. It means that you can add it by adding the numerators and putting the same denominator.

Hence, the answer is:

1/8 + 1/8 + 1/8

Answer:

153* for both

Step-by-step explanation:

This makes a circle, which is 360*. One angle is given, and it is 27*. If the angle on the opposite side is the same, the total degrees so far would be 54.

Say b and c were equal. Then, the remaining 306* would be split even among them. 306/2 is 153.

Therefore, 153* is the correct answer.

Hope I helped!!!

If the population variances are exactly equal, the sample F test statistic will be zero is false.

The F-test statistic compares the variances of two populations based on sample data.

If the population variances are exactly equal, the sample F-test statistic will not be zero.

Instead, it will be close to 1, indicating that the variances are similar.

The F-test statistic is calculated by dividing the sample variances, and if the population variances are equal, the division will result in a value close to 1.

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a) With V=0 at infinity, what is the electric potential at corner A  is -5.07 μC and corner B is = +2.48 μC.

b) The amount of work is required to move a charge from B to A along a diagonal of the rectangle is -2.59 μC.

c) Yes, this work increase the electric potential energy of the three-charge system inside the rectangle but not on a diagonal and outside the rectangle.

The electric potential at a point in a rectangle can be calculated using the electric potential equation. In the given figure, we have a rectangle with sides of length 4.34 cm and 18.5 cm, with charges q1 = -5.07 μC and q2 = +2.48 μC.

=> -5.07 + 2.48 = -2.59

To find the electric potential at corner A and corner B, we must first calculate the electric field from the two charges.

If V=0 at infinity, then the electric potential at corner A and corner B can be calculated using the electric potential equation given by V = ∫E⋅dr.

The amount of work required to move the same charge q3 from point B to point A along a path that is inside the rectangle but not on a diagonal and outside the rectangle will be different.

This is because the path of the charge will determine the electric field and electric potential at each point.

If the path is longer and passes through areas of higher electric potential, then more work will be required to move the charge

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A total of 2 triangles can be formed after the given modifications to "a"

Firstly, Between the red and the black marks, make another separate blue mark. After that, Now, spin the strip and use the new length for "a", to try to make a triangle (or triangles). We'll see that by doing this, two triangles can be formed.

We know the triangle's area = \(\frac{1}{2}\)× base × height.

Here from the given data, we can say the height is b sinA and the base is a.

∴ Area =  \(\frac{1}{2}\)× a × b sin A

So, the total area of two triangles is, the area

=  \(\frac{1}{2}\) × a × b sin A +  \(\frac{1}{2}\) × a × b sin A= ab sin A

Hence, we can say two triangles are formed given the modifications to "a", in Activity 1 . and the total area is ab sin A.

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The complete question is, "Determine the number of triangles that can be formed given the modifications to "a" in Activity 1 ab sin A (Hint: Make a blue mark between the black and the red marks. Then rotate the strip to try to form triangle(s) using this new length for 'a' .)"

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Answer:

Step-by-step explanation:

The volume is the product of three dimensions, so the ratio of volumes is the cube of the scale factor:

The exponential regression equation for this set of data is y = \(14.129e^{(0.495x)\) and the number of bacteria present after 10 hours is approximately 24684.

The exponential regression equation for this set of data can use a calculator or spreadsheet software.

The equation will have the form y = abˣ a is the initial number of bacteria and b is the growth rate.
Using the given data can create a table of values for the equation:
x                y                   ln(y)
---------------------------------------
0              16                2.773
1               66               4.189
2             311                5.739
3            791                6.672
4          1553                7.349
5          2571               7.853

A regression tool can find that the equation is approximately y = \(14.129e^{(0.495x)\) rounded to three decimal places.

The initial amount of bacteria is approximately a = 14.129 and the growth rate is approximately b = 1.649.
The number of bacteria present after 10 hours can plug x = 10 into the equation:
y = \(14.129e^{(0.495\times 10)\)

= 24683.522
Rounding to the nearest whole number get that the number of bacteria present after 10 hours is approximately 24684.

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Answer:

88

Step-by-step explanation:

9 × 8 + \(2^{4}\)

=> PEMDAS

so first exponent 2^{4} = 16

next multiplication

9*8 = 72

=> 72 + 16

=> 88

Answer:65 i think

Step-by-step explanation:

Answer:

X = 68°

Step-by-step explanation:

First every angle equal 180°

Take 47° + 65°= 112°

180°- 112°= 68°

The sequence of transformations that results in the same transformation as translating figure X down 5 and reflecting it over the y-axis is reflecting figure X over the y-axis and then translating the reflected figure down 5.

The sequence of transformations that results in the same transformation as translating figure X down 5 and reflecting it over the y-axis is:

Reflect figure X over the y-axis.

Translate the reflected figure down 5.

To see why this sequence of transformations works, consider the effect of each transformation on the coordinates of the points in figure X.

Reflecting figure X over the y-axis negates the x-coordinate of each point. So if a point in figure X has coordinates (x, y), the corresponding point in the reflected figure has coordinates (-x, y).

Translating the reflected figure down 5 simply subtracts 5 from the y-coordinate of each point. So if a point in the reflected figure has coordinates (-x, y), the corresponding point in the final transformed figure has coordinates (-x, y-5).

Thus, the sequence of transformations that results in the same transformation as translating figure X down 5 and reflecting it over the y-axis is reflecting figure X over the y-axis and then translating the reflected figure down 5.

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The bearing is the angle measured clockwise from the north direction to a specified direction. To find the bearing of Town Y from Town B, we use the given information that Town B is located south 38 degrees east from Town Y. By subtracting this angle from 180 degrees, we find that the bearing is 142 degrees.

To determine the bearing, we need to find the angle between the north direction and the direction from Town B to Town Y.

Since Town B is located south of Town Y, the bearing will be a southern direction. The bearing angle can be calculated as 180 degrees minus the given angle, which is 38 degrees.

Therefore, the bearing of Town Y from Town B is 180 - 38 = 142 degrees.

In conclusion, the main answer is that the bearing of Town Y from Town B is 142 degrees.

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Step-by-step explanation:

8x+12x+16x=180

36x=180

x=5

16x=5×16=90

Answer: 5 degrees

Step-by-step explanation: im just built different

If a patient is given a β1 receptor agonist, it would be expected to activate β1 adrenergic receptors, which are primarily located in the heart.

This could lead to an increase in heart rate and contractility, as well as increased cardiac output. β1 receptor agonists are commonly used to treat conditions such as heart failure, shock, and certain types of arrhythmia. However, they can also have side effects such as tachycardia (abnormally fast heart rate), palpitations, and increased blood pressure. It is important to note that the specific effects of a β1 receptor agonist can vary depending on the dose and the individual's physiological response.

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The corresponding parts are:

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

To do this, we simply make use any of the following congruent theorems:

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

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