Dara and Jo share £420 in the ratio 25.
Calculate how much Dara and Jo receive each.

Answer:

D + E = 2x⁴ + x³ –  3x²   + x + 1

D - E  = 9x³ +  x²   + x – 3

Step-by-step explanation:

D = x⁴ + 5x³ – x² + x – 1

E = x⁴ – 4x³ – 2x² + 2

D + E :                                                   D - E :

 x⁴ + 5x³ –  x²   + x – 1                          x⁴ + 5x³ –  x²   + x – 1  

+                                                         –                                                                  

 x⁴ – 4x³ – 2x² + 0 + 2                         x⁴ – 4x³ – 2x² + 0 + 2

_________________                      _________________

2x⁴ + x³ –  3x²   + x + 1                          0  +  9x³ +  x²   + x – 3

To find the radian measure of a central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches.

In a circle, the relationship between the central angle (θ) and the arc length (s) is given by the formula s = rθ, where r is the radius of the circle. In this case, the radius (r) is 17 inches, and the arc length (s) is 12 inches.

To find the radian measure of the central angle (θ), we rearrange the formula as follows:

s = rθ  (Divide both sides by r)

θ = s/r

Substituting the given values:

θ = 12/17

Therefore, the radian measure of the central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches is approximately 0.7059 radians.

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The surface area of the part of the plane z = (5/6)x + (4/6)y that lies above the rectangle [1,3] × [1,6] is 10√(77/36).

What is a double integral?

A double integral is a type of integral that extends the concept of a single integral to integrate functions of two variables over a region in a two-dimensional space. It represents the accumulation of a function's values over a two-dimensional region.

To find the surface area of the part of the plane z = 5 6 x 4 y that lies above the rectangle [1, 3] × [1, 6], we can use a double integral over the given region.

Let's define the surface as S, where S is the part of the plane z = 5 6 x 4 y above the rectangle [1, 3] × [1, 6].

The surface area can be calculated using the following double integral:

A = ∬S dA

where dA represents an infinitesimal area element.

To set up the integral, we need to parameterize the surface S in terms of two variables, say u and v.

Let's set u = x and v = y, then we can express the surface equation z = 5 6 x 4 y as z = 5 6 u 4 v.

The limits of integration for u and v will be the boundaries of the rectangle [1, 3] × [1, 6].

Therefore, the integral becomes:

A = ∫[1,3] ∫[1,6] √(1 + (∂z/∂u)² + (∂z/∂v)²) du dv

To find (∂z/∂u) and (∂z/∂v), we differentiate z = 5 6 u 4 v with respect to u and v:

(∂z/∂u) = 5 6 * 4 v = 10 3 v

(∂z/∂v) = 5 6 * u 4 = 5 6 u 4

Now, we substitute these values into the integral:

A = ∫[1,3] ∫[1,6] √(1 + (10/3v)² + (5/6u)²) du dv

Simplifying the integrand:

A = ∫[1,3] ∫[1,6] √(1 + 100/9v² + 25/36u²) du dv

The equation of the plane is given as z = (5/6)x + (4/6)y, which can be rewritten as z = (5/6)x + (2/3)y.

To find the surface area, we need to integrate the square root of the sum of the squares of the partial derivatives of z with respect to u and v, multiplied by the differential element du dv.

Let's proceed with the calculation step by step.

The partial derivative of z with respect to u is:

(∂z/∂u) = 5/6

The partial derivative of z with respect to v is:

(∂z/∂v) = 2/3

Now, we can calculate the integrand:

√(1 + (∂z/∂u)² + (∂z/∂v)²) = √(1 + (5/6)² + (2/3)²) = √(1 + 25/36 + 4/9) = √(36/36 + 25/36 + 16/36) = √(77/36)

The integral for the surface area becomes:

A = ∫[1,3] ∫[1,6] √(77/36) du dv

Since the integrand is constant, we can take it outside the integral:

A = √(77/36) ∫[1,3] ∫[1,6] du dv

Evaluating the inner integral with respect to u over the range [1,3]:

A = √(77/36) ∫[1,3] (u) dv = √(77/36) [u][1,3] v = √(77/36) (3 - 1) [v][1,6] = 2√(77/36) [v]_[1,6]

Now, we evaluate the outer integral with respect to v over the range [1,6]:

A = 2√(77/36) [v]_[1,6] = 2√(77/36) (6 - 1) = 10√(77/36)

Therefore, the surface area of the part of the plane z = (5/6)x + (4/6)y that lies above the rectangle [1,3] × [1,6] is 10√(77/36).

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The lines intersect at two places.

They intersect at approximately (-2,8) and (2,3)

Looking at the choices they would be at (1.8,3.2) and (-2.8,7.8)

The answer is D. Both A and B.

Answer:

inear equations Dear Dr Math: I hope you ... 10-(k+5) = 3(k+2) I would also appreciate any explanation. ... So we have to try to get all the "k's" on one side of the equation, and all the ... Let's look at the right side: 3(k+2) Okay, we could say this as 3 times the sum of k and 2.

Step-by-step explanation:

Answer:

5k-7

Step-by-step explanation:

I just combined like terms

Answer:

Step-by-step explanation:

Using formula

Substitute values

Option A is correct

Form A

H(t) = -8(t – 2)² + 37

Form B

H(t)= -8t² + 32t + 5

a. From form A, the vertex of the parabola is at (2, 37). This means that the maximum height is 37 feet and it's reached after 2 seconds.

b. The initial height corresponds to t = 0 seconds. Replacing t = 0 into form B:

H(0)= -8(0)² + 32(0) + 5 = 5 ft

That is, the initial height was 5 ft

The sample means are distributed along the x-axis for a sampling distribution of a sample mean.

A sample mean is an average of a set of data, that can be used to calculate the central tendency, standard deviation and the variance of a data set.

Now,

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To calculate the utilization, we need to determine the sending rate and the link capacity.

Given:

Segment size = 1,195 bytes

Window size = 9,031 bytes

Link transmission rate = 30 Mbps

End-to-end propagation delay = 20.2 ms

First, we calculate the sending rate:

Sending rate = Segment size / Round Trip Time (RTT)

RTT = 2 * (Propagation Delay)

RTT = 2 * 20.2 ms = 40.4 ms

Sending rate = 1,195 bytes / 40.4 ms

Next, we calculate the link capacity:

Link capacity = Link transmission rate / 8 (to convert from bits to bytes)

Link capacity = 30 Mbps / 8 = 3.75 MBps

The utilization is then given by the ratio of the sending rate to the link capacity:

Utilization = (Sending rate / Link capacity) * 100

Calculating the utilization:

Utilization = (1,195 bytes / 40.4 ms) / (3.75 MBps) * 100

Now, let's calculate the effective delay when network usage is 83.7%.

Given:

Nodal delay when network usage = 0% (no traffic) = 62.9 ms

Effective delay = Nodal delay / (1 - Utilization)

Utilization = 83.7% = 0.837

Effective delay = 62.9 ms / (1 - 0.837)

Now, we can calculate the utilization and effective delay:

Utilization = (1,195 bytes / 40.4 ms) / (3.75 MBps) * 100

Effective delay = 62.9 ms / (1 - 0.837)

Calculating the values:

Utilization ≈ 3.994% (rounded to one decimal place)

Effective delay ≈ 3.884 ms (rounded to three decimal places)

Therefore, the utilization is approximately 3.994% and the effective delay is approximately.

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Answer:

y intercept is -2

Step-by-step explanation:

y intercept is when x is 0.

original equation:

If you want to make it into something solvable, you want to move everything but y to one side.

1. x+4y+8=0

2. 4y+8=-x

3. 4y=-x-8

4. y=-1/4x-2

5. Since this is a linear function, all you have to do to find the y intercept is plug x in with 0. (mentioned above)

6. y=-1/4(0)-2

7.y=-2

8. y int=-2

Answer:

Can you plz attach an image of the graph :O

Step-by-step explanation:

Based on the information provided, it is likely that the distribution of the number of hours students watch television weekly is not perfectly symmetric and might have a slight right-skew.

To determine if the distribution of the number of hours students watch television weekly is symmetric, we can consider the characteristics of the average and the standard deviation.

In a symmetric distribution, the mean (average) and the median are equal, and the data values are distributed evenly on both sides of the mean. Additionally, the standard deviation provides information about the spread of the data.

Given that the average number of hours is 4.73 hours, it suggests that the distribution is not perfectly symmetric. If the distribution were symmetric, we would expect the mean and the median to be very close or equal. However, we cannot conclude definitively without further information about the median.

To determine the shape of the distribution, we can look at the standard deviation of 4.11 hours. A larger standard deviation indicates a wider spread of data points around the mean.

Based on the information provided, it is likely that the distribution of the number of hours students watch television weekly is not perfectly symmetric and might have a slight right-skew. This means that there may be a concentration of data points towards the lower end of the distribution, with a tail extending towards higher values.

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We want to find the value of x, which is the hypotenuse of the triangle on the image.

We will see that the value of x is 5.77 units.

On the figure we can see a right triangle, we want to find the value of x, which is the hypotenuse of this triangle.

To do so, we can use the trigonometric relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Where θ is an internal angle of the triangle, and the adjacent cathetus is the cathetus that forms the angle.

Here we can use θ = 30°, and the adjacent cathetus is the one that has a measure of 5 units,  then the value of x is given by the equation:

cos(30°) = 5/x

Solving that for x we will get:

x = 5/cos(30°) = 5.77

The hypotenuse measures 5.77 units.

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To solve the equation log_s(x-4) + log_3(x-2) = 1, we combined the logarithms and transformed the equation into a quadratic form.
The solutions to the equation are x = 3 + √(1 + s) and x = 3 - √(1 + s), which can be verified by substituting them back into the original equation.

To solve the equation log_s(x-4) + log_3(x-2) = 1, we can combine the logarithms using logarithmic properties.

Using the property log_a(b) + log_a(c) = log_a(b * c), we can rewrite the equation as a single logarithm:

log_s((x-4)(x-2)) = 1

Next, we can rewrite the equation in exponential form. Recall that if log_a(b) = c, then a^c = b. In this case, s is the base of the logarithm:

s^1 = (x-4)(x-2)

Simplifying the equation, we have:

s = (x-4)(x-2)

To find the solutions, we need to solve this quadratic equation. Expanding the right side, we have:

s = x^2 - 6x + 8

Rearranging the equation, we get:

x^2 - 6x + (8-s) = 0

This is a quadratic equation in standard form. We can use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values a = 1, b = -6, and c = 8-s, we have:

x = (6 ± √((-6)^2 - 4(1)(8-s))) / (2(1))

Simplifying further:

x = (6 ± √(36 - 32 + 4s)) / 2

x = (6 ± √(4 + 4s)) / 2

x = (6 ± 2√(1 + s)) / 2

x = 3 ± √(1 + s)

Therefore, the solutions to the equation are x = 3 + √(1 + s) and x = 3 - √(1 + s).

To verify the solutions, substitute them back into the original equation and check if they satisfy the equation.

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Answer:

$10.862005 million

Step-by-step explanation:

150,000*1.036331 monthly

12*10=120

$150,000*1.036331 ^120=$10.862005 million

seams very unrealistic lol

Answer:$10.862005 million

Step-by-step explanation:

150,000*1.036331 monthly

12*10=120

$150,000*1.036331 ^120=$10.862005 million

The correct value of this equation is m = 24

This equation contains a fractional term. We note that the denominator of this equation is the term 4. Therefore, we will multiply the sides by 4:

13 = m/4 + 7

13 . 4 = 4(m/4) + 7 . 4

52 = m + 28

Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:

52 = m + 28

-m = 28 - 58

-m = -24

m = 24

Therefore, the correct value of this equation will be m = 24

Answer:

The distance from the base of the ladder to the base of the house is 10ft

Step-by-step explanation:

From the question, we can gather that the ladder makes a right angle shape with the wall of the house.

The length of this ladder which represents the hypotenuse of the right angled triangle is 26ft while the height of the house to the roof is 24ft

To calculate the distance between the base of the ladder and the base of the house, we shall be employing the use of Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the square of the 2 other sides

We have established that the hypotenuse is the length of the ladder which is 26ft

Let the distance we want to calculate be d

26^2 = 24^2 + d^2

d^2 = 26^2 -24^2

d^2 = 676 - 576

d^2 = 100

d = square root of 100

d = 10ft

Answer:

10

Step-by-step explanation:

24^2 = 576

26^2 = 676

676 - 576 = 100

the square root of 100 is 10 so the answer is 10

Answer:

5

Step-by-step explanation:

Answer:  a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16

The square of any number is always a positive number, so every number has two square roots, one of a positive value, and one of a negative value. For example, both 2 and -2 are square roots of 4.

The linear function which represents the line is y = - 3x + 14.

What is Point slope form?

Point slope form is used to represent a straight line using its slope and a point on the line. It means that the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point-slope form.

Main body:

y - y1 = m (x - x1)

where, (x, y) is a random point on the line and m is the slope of the line.

The given point-slope equation is

y + 1 = - 3 (x - 5)

By further calculation

y + 1 = -3x + 15

y = -3x + 15 - 1

y = -3x + 14

Therefore, the linear function which represents the line is y = - 3x + 14.

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The three types of solutions for systems are:

A consistent system is one where the number of equations is equal to the number of unknowns, and a unique solution can be found. An inconsistent system is one where the number of equations is greater than the number of unknowns and there is no solution.

A dependent system is one where the number of equations is less than the number of unknowns and an infinite number of solutions exist. In a consistent and dependent system, the solution can be found by using methods such as elimination or substitution.

In an inconsistent system, the system has no solution. In dependent system, the solution can be found by using methods such as elimination or substitution, but the solution is not unique it has infinite solutions.

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for a one-to-one function f,

(a) if f(9) = 8, then f⁽⁻¹⁾⁽⁻⁸⁾ = 9, and

(b) if f⁽⁻¹⁾⁽⁻⁶⁾= -5, then f(-5) = -6.

(a) Given that f is a one-to-one function and f(9) = 8, we need to find f^(-1)(8).

The function f⁽⁻¹⁾represents the inverse of f, so finding f⁽⁻¹⁾⁽⁸⁾ means we need to determine the input value that yields an output of 8 when plugged into f.

Since f(9) = 8, we can conclude that f⁽⁻¹⁾⁽⁸⁾ = 9. Therefore, the answer is f^(-1)(8) = 9.

(b) If f⁽⁻¹⁾⁽⁻⁶⁾ = -5, we are asked to find f(-5). Again, f⁽⁻¹⁾ represents the inverse function of f.

In this case, f⁽⁻¹⁾⁽⁻⁶⁾ = -5 indicates that when -6 is plugged into f⁽⁻¹⁾, the output is -5. Since f⁽⁻¹⁾ represents the inverse of f, it implies that f(-5) = -6. Therefore, the answer is f(-5) = -6.

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Answer: He has 47 chairs

Step-by-step explanation:

if he has 7 left over from 8 rows, and 17 from 6 rows of the same length, thats 5 chairs per row that where taken away, 8-6=2, 17-7=10 10/2= 5

5 chairs per row x8 rows +7 extra chairs=47 chairs total

The probability that the sample mean would be less than 127 wpm if 84-speed typists are randomly selected is: 0.033625

What is Mean?

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally. The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organized in ascending order, the Median is the median value of the provided data. While the number in the list that is repeated a maximum of times is the mode.

We have

\(\mu=124\)  

\(\sigma=15\)

n=84

We want to find the probability that the sample mean would be greater than 127 WPM is

\(\begin{aligned}P(\bar{X} > 127) &=P\left(\frac{\bar{X}-\mu}{\sigma / \sqrt{n}} > \frac{127-124}{15 / \sqrt{84}}\right) \\&=P(Z > 1.83)\end{aligned}\)

\(=0.033625\)

The required probability is 0.0336.

Hence, The probability that the sample mean would be less than 127 wpm if 84-speed typists are randomly selected is: 0.033625

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Answer:

\(x=\frac{2}{3}\pm\frac{\sqrt{26}}{3}i\)

Step-by-step explanation:

\(3x^2+10=4x\\\\3x^2-4x+10=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(10)}}{2(3)}\\ \\x=\frac{4\pm\sqrt{16-120}}{6}\\ \\x=\frac{4\pm\sqrt{-104}}{6}\\ \\x=\frac{4\pm2\sqrt{26}i}{6}\\ \\x=\frac{4}{6}\pm\frac{2\sqrt{26}}{6}i\\\\x=\frac{2}{3}\pm\frac{\sqrt{26}}{3}i\)

The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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Step-by-step explanation:

- 8 (3n - 5) \\ - 24n + 40 \\ please \: give \: full \: question \\

Answer:

-24x40

Step-by-step explanation:

-8×3×-8(-5)

-24×-8×(-5)

so the answer is: -24x40

Answer:

16

Step-by-step explanation:

Step 1. Plug the numbers into the equation

Step 2. Solve using PEMDAS

\(\frac{6 ( 6 + 2)}{3}\)

\(\frac{6 ( 8 )}{3}\)

\(\frac{48}{3}\)

16

Answer:

6(a+c)÷b

6(6+2)÷3

6×8÷3

48÷3

16 Ans

Step-by-step explanation 16is the answer

(a) For all x, x squared is greater than 0. True.(b) For every n that belongs to the set of natural numbers, x to the power of n is greater than 0. False.

(a) For all x, x squared is greater than 0. True. This is a true statement because when we square any non-zero real number, the result is always positive. Thus, x squared is indeed greater than 0 for all values of x except when x is equal to 0.

(b) For every n that belongs to the set of natural numbers, x to the power of n is greater than 0. False. This statement is false because when x is negative and n is an odd number, x to the power of n would be negative. For example, (-1)^3 = -1, which is less than 0. Therefore, the statement is not true for all values of x and n.

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