Fully Factorise 5k^2+7k​

While there may be other integration techniques that can be used to evaluate some chain rule integrals directly, u-substitution is a powerful and versatile tool that is often used to simplify and evaluate these types of integrals.

The chain rule is a fundamental concept in calculus, and it applies to differentiation as well as integration. The chain rule integration technique involves recognizing the function inside the integral as the composition of two functions, and then using substitution to simplify the integral.

In some cases, it may be possible to use other integration techniques to evaluate chain rule integrals directly, without using substitution. However, in general, the use of substitution (or a related technique, such as integration by parts) is often necessary to evaluate chain rule integrals.

That being said, there are some special cases where the chain rule integrals can be evaluated more directly, such as when the integrand is a polynomial or a rational function, or when it has a simple algebraic form.

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The lower bound of the confidence interval is 0.197 and the upper bound is 0.283. Therefore, we can say with 90% confidence that the true population proportion of people with kids is between 0.197 and 0.283. Both values are rounded to three decimal places.

To construct a 90% confidence interval for the true population proportion of people with kids, we need to use the sample proportion and sample size. The sample proportion is the number of people with kids divided by the total number of people sampled, which is 144/600 = 0.24. The sample size is 600.

Next, we need to calculate the standard error, which is the square root of (sample proportion x (1 - sample proportion) / sample size). Plugging in the values, we get:

SE = √(0.24 x 0.76 / 600) = 0.026

To find the margin of error, we multiply the standard error by the z-score corresponding to a 90% confidence level, which is 1.645. Therefore, the margin of error is:

ME = 1.645 x 0.026 = 0.043

Finally, we can construct the confidence interval by adding and subtracting the margin of error to the sample proportion:

p ± ME = 0.24 ± 0.043

The lower bound of the confidence interval is 0.197 and the upper bound is 0.283. Therefore, we can say with 90% confidence that the true population proportion of people with kids is between 0.197 and 0.283. Both values are rounded to three decimal places.

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Answer:

Try 17

Step-by-step explanation:

The sample mean for the given data set is 3.044 miles.

Let's use the given data to calculate the sample mean. We have the distances in miles that 10 visitors live from the library: 0.5, 0.8, 0.8, 1.5, 1.8, 3.5, 4.8, 6.2, and 8.3.

To find the sample mean, we first add up all the distances:

0.5 + 0.8 + 0.8 + 1.5 + 1.8 + 3.5 + 4.8 + 6.2 + 8.3 = 27.4

Next, we divide the sum by the total number of distances, which is 9 (since we have data for 10 visitors):

27.4 / 9 = 3.044 (rounded to three decimal places)

This means that, on average, the visitors to the library live about 3.044 miles away from the library.

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Answer:

C) Point B is a reflection of point A along the Y-Axis

Step-by-step explanation:

I plotted it on a graph, and it turned out to be an exact mirror reflection.

Hope This Helped!

The area of the triangle ABC is 6 square centimeters.

To find the area of the triangle, we can use Heron's formula, which is based on the lengths of the triangle's sides. Heron's formula states that the area (A) of a triangle with side lengths a, b, and c can be calculated using the following formula:

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths are given as a = 4 cm, b = 5 cm, and c = 3 cm.

Calculating the semi-perimeter:

s = (4 + 5 + 3) / 2 = 6 cm

Using Heron's formula:

A = √(6(6-4)(6-5)(6-3))

= √(621*3)

= √(36)

= 6 cm²

Therefore, the area of triangle ABC is 6 square centimeters.

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Answer:

3r + 4t = 80

Step-by-step explanation:

Roses cost $3 each, tulips cost $4 each

The linear equation for the remaining federal helium reserves, R(t), in billions of cubic feet, in terms of t, the number of years since 2010, can be given as:

R(t) = 15 - 2.2t

In this equation, t represents the number of years since 2010, and R(t) represents the remaining federal helium reserves in billions of cubic feet. The equation shows that the initial reserves of 15 billion cubic feet are being depleted by 2.2 billion cubic feet each year, resulting in a linear decrease in the remaining reserves over time.

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Answer:

B.

Hope this helps!

Hi!

Your answer would be: $159.03.

Reason Being: $1.35 times 118 equals $159.03.

Hope this helps!

Answer:

$91.80

Step-by-step explanation:

To find her total wages, we would multiply 12 x 9 and get 108.

Now we need to find 15% of that.  15% means 15/100 so divide 15 by 100 to get .15.

.15 x 108 = 16.20  This is the amount that we need to subtract from 108.

108 - 16.20 = 91.80

Answer: $91.8

Step-by-step explanation:

12*9=108

108*(1-0.15)=

108*0.85=$91.8

The perimeter be 410 then the maximum area be \($A=\left(\frac{410-3 x}{2}\right) * x$$\).

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

Let the perimeter be p = 410

The perimeter of the fence is:

p = 2(x + y + 5 + y) + x

p = 2x + 2y + 10 + 2y + x

Collect like terms

p = 2x + x + 2y + 2y + 10

p = 3x + 4y + 10

Where, p = 410, then

3x + 4y + 10 = 410

\($$\begin{aligned}& 4 y=410-10-3 x \\& 4 y=400-3 x\end{aligned}$$\)

simplifying the equation, we get

\($y=\frac{400-3 x}{4}$$\)

The area (A) of the fence is:

\($$\begin{aligned}& A=(y+y+5) * x \\& A=(2 y+5) * x\end{aligned}$$\)

Substitute: \($y=\frac{400-3 x}{4}$\)

\($$\begin{aligned}& A=\left(2 * \frac{400-3 x}{4}+5\right) * x \\& A=\left(\frac{400-3 x}{2}+5\right) * x\end{aligned}$$\)

simplifying the equation, we get

\($A=\left(\frac{400-3 x+10}{2}\right) * x$$\)

\($A=\left(\frac{410-3 x}{2}\right) * x$$\)

\($A=\frac{410 x-3 x^2}{2}$$\)

A = 205x - 1.5 x²

Differentiate both sides, we get

A' = 205-3 x

simplifying the equation, we get

205 - 3x = 0

3x = 205

Therefore, the maximum area be \($A=\left(\frac{410-3 x}{2}\right) * x$$\).

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Answer:

I believe the value is equal to 8

The probability that this really contains a letter just after an odd number is one-half. D's likelihood of being in the program but not at the first place is 1/4.

A possibility which deals with the possibility of random occurrences is referred to as probability. All occurrences must have a chance of occuring at least once, or 1.

The possibility or possibility of an incident occurrence is known as probability. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of coin flipping and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.

The size of the sample space is (8, 16, 20, and 24)

If a code is chosen at random,

The probability that it has a letter that immediately follows an odd number (1/8, 1/6, 1/3, 2/5, 2/3)

= 1/2

If a code is chosen at random,

The probability that D is in the code but is not in the first position (1/8, 1/6, 1/3, 2/5, 2/3)

= 1/4

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The value of k such that the graph of f and the graph of g only intersect one is equal to 81 and n =3/2..

we have the following expression:

f(x) = mx²+6x+k        (1)

f(x) = (kx)²-4nx+9      (2)

On comparing we can see that;

(kx)² = mx²

k² = m

Also, 4nx = 6x

n = 3/2

k = 9

then m = 9²  = 81

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 81.

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Type of statistical characteristics of variables found in a sample and describes summarizes and synthesizes collected data is a. Descriptive.

Descriptive statistics are used to describe or summarize the characteristics of a sample or data set, such as a variable's mean, standard deviation, or frequency.

Descriptive statistics can be used to describe a single variable (univariate analysis) or more than one variable (bivariate/multivariate analysis). In the case of more than one variable, descriptive statistics can help summarize relationships between variables using tools such as scatter plots.

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(f)/(g))(x) = (√[(3 + x)(3 - x)]) / (3(x + 2)).

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

To find ((f)/(g))(x), we need to evaluate the function f(x)/g(x) for a given value of x.

We have:

f(x) = √(9 - x^2)

g(x) = 3x + 6

So,

(f/g)(x) = f(x) / g(x) = (√(9 - x^2)) / (3x + 6)

To simplify this expression, we can factor out 3 in the denominator and simplify the square root in the numerator:

(f/g)(x) = (√(9 - x^2)) / (3(x + 2))

= (√[(3^2 - x^2)]) / (3(x + 2))

= (√[(3 + x)(3 - x)]) / (3(x + 2))

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The value of x from the triangle inscribed in the circle which is the unknown angle is 22°

For a given triangle inscribed in a circle, it should be noted that the angle that is inscribed along the diameter of the circle will be regarded as the right angle.

This means that the angle facing the diameter line (C), i.e angle c is 90 degrees. We all know that the sum of angles in a triangle is 180 degrees. Therefore, to find the third unknown angle x, we have:

x  + 68° + 90° = 180°

x + 158° = 180°

x = 180° - 158°

x = 22°

Therefore, we can conclude that the value of x which is the unknown angle is 22°

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This is the reason why Option (B) is the correct option.

The correct interpretation of the given interval is that "We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation."Option (B) is the correct option.Explanation:Confidence intervals tell us about the range of values within which we can expect the true population parameter to lie. Confidence interval is the range within which we believe the population parameter (mean, proportion or standard deviation) lies.A 95% confidence interval implies that if a researcher were to conduct a given study 100 times, 95 of those studies would produce the same interval of estimates.A confidence interval is a range of values, derived from a data sample, within which the true population value is likely to fall with a certain level of confidence. This is the reason why Option (B) is the correct option.

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In a regular polygon, all interior angles have equal measures because the polygon has congruent sides and angles. The sum of all interior angles in a polygon can be found using the formula:

(n-2) * 180°,

where n represents the number of sides of the polygon.

Based on this, we can determine which angles cannot be interior angles in a regular polygon.

24°: This angle can be an interior angle in a regular polygon because it is smaller than the interior angles of any polygon with more than 6 sides.

72°: This angle can be an interior angle in a regular pentagon (5 sides) or any polygon with more sides, as it satisfies the requirement for interior angles.

135°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 8 sides.

164°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 9 sides.

179°: This angle cannot be an interior angle in any regular polygon because it is larger than the maximum measure of interior angles in any polygon.

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Answer:

Choice C

Step-by-step explanation:

The Equation of a circle is (x-h)^2+(y-k)^2=r^2, where h and k are the x and y coordinates respectively of the center of the circle, and r is the radius. Because the center here is (2, -5), we have (x-2)^2+(y- - 5)^2, and the two minuses become (y+5)^2. This eliminates A and B. The radius is 4, so r^2=16, and thus, we get C.

The volume rate of flow per unit width perpendicular to the x-y plane between points (0,0) and (1,1) is `a/2`.

Given information:

Velocity component in x direction, `u = 3ax² - 3ay²`

Velocity component in y direction at `y = 0` is `1 - 0`.

Points between which the volume rate of flow is to be determined are `(0,0)` and `(1,1)`

Formula used: For incompressible flow, volume rate of flow `= (Integral of velocity component normal to the section * dA)

We are given the velocity component in the x direction, and we need to find the velocity component in the y direction using the given information:

Velocity component in y direction at `y = 0`:

v = `∂ψ/∂x`

= 0

=> ψ = f(y) + g(z)

For an incompressible flow, the continuity equation is `∂u/∂x + ∂v/∂y + ∂w/∂z = 0`.

Since the flow is two-dimensional and incompressible, the continuity equation reduces to `∂u/∂x + ∂v/∂y = 0`.

Thus, we have `∂u/∂x = 6ax`.

Using the above equation, we can get the stream function `ψ` such that `u = ∂ψ/∂y` and

`v = -∂ψ/∂x`.

Integrating `∂ψ/∂y = u` w.r.t. `y`, we get:

ψ = `3axy² - ay²y + f(x)`

Differentiating `ψ` w.r.t. `x`, we get:

`v = -∂ψ/∂x

= 3ay² - f'(x)`

Since `v = ∂ψ/∂x` at

`y = 0`, we get:

`1 - 0 = 3a*0² - f'(x)`or

`f'(x) = -1`or

`f(x) = -x + C`

where `C` is a constant of integration. So, the stream function `ψ` is given by:

ψ = `3axy² - ay²y - x + C`

Since `v = ∂ψ/∂x`, we have `v` as:

`v = -6axy + ay²`

At point `(0,0)`, `v = 0`.

So, `C = 0`.

The volume rate of flow `Q` between points `(0,0)` and `(1,1)` is given by:

Q = `(Integral of v * dA)`

= `(Integral of (-6axy + ay²) * dA)`

The limits of the integral are `0` to `1` for both `x` and `y`. Hence, we get:

Q = ∫[0,1] ∫[0,1] `(-6axy + ay²) * dx * dy`

Q = ∫[0,1] `[(3a/2)*y² - y²/3] dy`

Q = `a/2` units/square unit

Therefore, the volume rate of flow per unit width perpendicular to the x-y plane between points (0,0) and (1,1) is `a/2`.

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The given velocity components do not satisfy the continuity equation for incompressible flow. Hence, the problem is incorrect.

The velocity component in x direction, u = 3ax² - 3ay²

The velocity component in y direction, v = ∂ψ/∂x = ∂ψ/∂y = 1-0 (At y=0)

Given that, the fluid is incompressible plane irrotational flow. The continuity equation for incompressible flow is:

(dA/dt) = ∂/∂x(uA) + ∂/∂y(vA)

where, A = Cross-sectional area of the pipe

The cross-sectional area of the pipe perpendicular to x-y plane = A = b*H,

where b = width of the pipe,

H = depth of the pipe

We are to determine the volume rate of flow per unit width perpendicular to the x-y plane between points (0,0) and (1,1).

The volume flow rate is given by: Q = ∫(v.A)dy (Integration limits from 0 to H)

From the above-given stream functions, ψ1 = 12x²y - 4y³andψ2 = xy³

The velocity components are obtained by taking partial derivatives of ψ, u1 = ∂ψ1/∂y = 12x² - 12y²And v1 = -∂ψ1/∂x = 0

Similarly, u2 = ∂ψ2/∂y = 3xy²And v2 = -∂ψ2/∂x = y³

Let's find out the value of constants, a and b:

At x=0, u=0 => 0 = 3a*0 => a = 0

Again at y=0, u = 3ax² - 3ay² = 0 => 3a*0 - 3a*0 = 0 => a = 0

At y=0, v = ∂ψ/∂x = ∂ψ/∂y = 1-0 => 1 = 0 (which is not possible)

Therefore, we can say that the given velocity components do not satisfy the continuity equation for incompressible flow. Hence, the problem is incorrect.

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Answer:

18

Step-by-step explanation:

60% of 45 is 27

So 45-27 = 18

Answer:

$27.

Step-by-step explanation:

To find the percentage of something, simply multiply the value by the percentage ÷ 100:

60% = 60 ÷ 100 = 0.6

0.6 * 45 = 27

So they now cost $27.

Hope this helps!

Answer:

Below.

Step-by-step explanation:

So, first lets graph the line of the equation, I like to put equations into slope intercept form for simplicity.

We have:

3x-y < 4

Subtract x from both sides:

-y < -3x + 4

Multiply by -1(which flips the inequality sign)

y > 3x  - 4

Now to graph this:

We know that the slope is 3.

We know that x hits zero at -4 = (0, -4)

Now we can graph the equation

The image of it is below :D

Hope this helps!

Answer:

10,000,000,000

hopefully this helped :3

Answer:

C.10,000,000,000

Step-by-step explanation:

Answer:

y = -x - 2

Step-by-step explanation:

y-3=-1(x+5)

Expand.

y - 3 = -1x - 5

Add 3 on both parts.

y - 3 + 3 = -1x - 5 + 3

y = -1x - 2

The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

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The speed of the cart begin to decrease at approximately: 3.5 minutes.

A typical time-speed graph shows the time on the x-axis and the speed on the y-axis. When the slope is rising, it means the speed is increasing. When the slope is horizontal, it means the speed is constant. When the slope falls or decline, it means speed is decreasing.

We are given a time-speed graph that shows the speed of a cart over a period of several minutes. Time in minutes is on the x-axis (horizontal axis) while speed in miles per hour is on the y-axis (vertical axis).

From the graph given, the speed of the cart started increasing up to about 3 minutes, since the line slopes upwards. Then, between 3 and 4 minutes, we have a horizontal line which starts to decline at approximately 3.5 minutes.

Therefore, we can conclude that the speed of the cart begin to decrease at approximately: 3.5 minutes.

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for a chis-square goodness of fit test, if the number of categories is 6 and the test statistics is 8.4345, p value will be pchisq(8.4345,5)

To test a hypothesis' validity against actual data, a statistical calculation called a p-value is used. The probability of experiencing the results that were observed is calculated using a p-value, assuming that the null hypothesis is true. The p-value can be calculated by looking up the 8.4345 value in the Chi-Square distribution table with 5 degrees of freedom (6-1=5). The resulting p-value will depend on the significance level you choose.

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Step-by-step explanation:

The domain of a graph is all of the possible x values, and the range is all possible y values.

7. The graph goes on for both the x and y values, so the domain is (-inf, inf) and the range is (-inf, inf).

8. In this case, the domain is also (-inf, inf), but the range is [-2, inf) as there are no y values less than -2.

9. The domain is [-2, 2], as the x values only range from -2 to 2. The range is [-3, 3] as the y values range from -3 to 3.

10. The domain is (-inf, inf) because all x values are possible. The range is [-1, 1], as there are no y values greater than 1 or less than -1.