Simplify: (4 /5 + 6/ 25 ) X (8/ 9 + −8 /7 )​

The volume of the cylinder is approximately 622 cubic meters.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.

Given that the diameter of the cylinder is 6 m, we can calculate the radius by dividing the diameter by 2:

r = 6 m / 2 = 3 m

Using the value of π as 3.14, we can substitute the values into the volume formula:

V = 3.14 * (3 m)^2 * 22 m

Simplifying the expression:

V = 3.14 * 9 m^2 * 22 m

V = 3.14 * 198 m^3

V ≈ 621.72 m^3

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Answer: 15%

Step-by-step explanation:

From the question, we are informed that a shop makes £2,750 in March while it made £3,162.50 in April. The increase will be:

= £3,162.50 - £2,750

= £412.50

Percentage increase = £412.50/ £2750 × 100

= 15%

Answer:

the domain is 1, 2, 3, 4, 5
the range is  0, 1, 2, 3, 4
the rule will be
X=Y+1

Step-by-step explanation:
domain is all values to x from left to right
range is all values to y from down to up

if X = 2 then Y=1

Answer:

40

Step-by-step explanation:

Any regular polygon has exterior angles  = to 360 / number of sides.

so a 9-gon has 9 sides. The exterior angle = 360 / 9 = 40

Each exterior angle will be 40 degrees.

Try it with simpler n-gons. A triangle has 3 sides. The exterior angle is 360 / 3 = 120

A square has 4 sides. Each exterior angle is 360 / 4 = 90

Part (a)

---------------------

Explanation:

Multiply by 1000 to go from km to meters.

This is because 1000 m = 1 km.

Multiplying by 1000 in scientific notation means we add 3 to the exponent 5. The 3 is because 1000 = 10^3.

So the \(3.84 \times 10^5 \text{ km}\) becomes \(3.84 \times 10^8 \text{ meters}\)

===========================================================

Part (b)

Answer in standard form:  960,000 seconds

Answer in scientific notation: \(9.6\times10^{5} \text{ seconds}\)

---------------------

Work Shown:

\(\text{distance} = \text{rate}*\text{time}\\\\\text{time} = \frac{\text{distance}}{\text{time}}\\\\\text{time} = \frac{3.84 \times 10^8 \text{ meters}}{400 \ \text{ m}/\text{s}}\\\\\text{time} = \frac{3.84 \times 10^8}{4 \times 10^2} \text{ seconds}\\\\\text{time} = \frac{3.84}{4}*\frac{10^{8}}{10^2} \text{ seconds}\\\\\text{time} = 0.96 \times 10^{8-2} \text{ seconds}\\\\\text{time} = 0.96\times 10^{6} \text{ seconds}\\\\\)

\(\text{time} = (9.6\times10^{-1})\times10^{6} \text{ seconds}\\\\\text{time} = 9.6\times(10^{-1}*10^{6}) \text{ seconds}\\\\\text{time} = 9.6\times10^{-1+6} \text{ seconds}\\\\\text{time} = 9.6\times10^{5} \text{ seconds}\\\\\text{time} = 960,000 \text{ seconds}\\\\\)

To go from the scientific notation to standard form, move the decimal point 5 spaces to the right. The 5 is from the exponent.

Answer:

A number cube

Step-by-step explanation:

A coin a 5-sector spinner a number cube a bag of 11 marbles

A number cube is the best to simulate this scenario and predict whether a randomly chosen resident has a library card.

As Coin has only 2 outcomes "Head" and "Tail".

A 5-sector sector spinner has only 5 outcomes we need six outcomes.

A bag of 11 marbles has no differentiated with respect to colors etc.

Hence, A number cube is correct to chosen five out of six residents of Mayville have library cards.

Answer:

c

Step-by-step explanation:

The correct answers are: The test is statistically significant. We have observed something unusual if the null hypothesis is true. The other statements are not necessarily true on the given p-value of 1.5%.

Based on the information provided, we can determine the following:

The test is statistically significant: A p-value of 1.5% indicates that the observed result is unlikely to have occurred by chance, given the null hypothesis.

We have observed something unusual if the null hypothesis is true: A small p-value suggests that the observed data is unlikely to be a result of random chance, which implies that the data is unusual if the null hypothesis is true.

The null hypothesis is not necessarily false: The p-value alone does not provide direct information about the truth or falsehood of the null hypothesis. It only indicates the level of evidence against the null hypothesis.

The alternative hypothesis is not necessarily true: Similarly, the p-value does not provide evidence for the alternative hypothesis being true. It only indicates the strength of evidence against the null hypothesis.

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Answer:

1b 2a 3c

Step-by-step explanation:

Its hegarty right?

Answer:

C D anf F

Step-by-step explanation:

c : by expanding and canceling 4^x .

d : its the expanded form.

f : its just another way of expressing the expression

To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.

The null space will give us the basis vectors of the eigen space

To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.

By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.

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Answer:

19.25

Step-by-step explanation:

C=0.15(50)+11.75

C=7.50+11.75

C=19.25

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

-2.2

Step-by-step explanation:

m = y2 - y1/ x2- x1

m = -5 - 6/ 2 --3

m = -11/5

m = -2.2

\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)

Answer:my brother said 3.

Step-by-step explanation:

9514 1404 393

Answer:

  d.  The triangles are not similar

Step-by-step explanation:

The angle between the given sides is the same, so we need to compare the side ratios. In ΔQRS, we have ...

  QR/RS = 4/15

In ΔVTU, we have ...

  VT/TU = 8/32 = 1/4 ≠ 4/15

The triangles are not similar because corresponding sides are not proportional.

You may determine the greatest potential error, relative error, and percentage error by defining the volome and area of a cube.

The maximum volume mistake is 337.5 cm3.

The volume's relative inaccuracy is 0.1.

The inaccuracy is 10% of the total.

The largest surface area error is 90 cm2.

The surface area relative error is 0.0667.

The volume inaccuracy as a percentage is 6.67%.

Side3 = volume (side x side x side).

The exponent times the base raised to the power minus one makes up the derivative of a power.

In other words, the derivative of a number x raised to the power n is equal to n times xn1.

The volume expression is then obtained by deriving it as follows:

dV/dx=3×side²

So:

dV=3×side²×dx

With a potential measuring error of 0.5 cm, the edge of a cube was discovered to be 15 cm long. This means that side is 15 cm and dx is 0.5 cm. You get: by substituting in the previous expression:

dV = 3 (15 cm) 2 (0.5 cm)

dV=337.5 cm³

The maximum volume mistake is 337.5 cm3.

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Answer:

y = 3x + 2

Step-by-step explanation:

Let's identify two clear points on this line. I can see (0, 2) and (-1, -1)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-1 - 2) / (-1 - 0)

Simplify the parentheses.

= (-3) / (-1)

Simplify the fraction.

-3/-1

= 3

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 3x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (0, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 3(0) + b

To find b, multiply the slope and the input of x(0)

2 = 0 + b

Now, we are left with 0 + b.

2 = b

Plug this into your standard equation.

y = 3x + 2

This is your equation.

Hope this helps!

the rate is 60 minutes per day bo will practice the piano.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

the equation m = 60d

The rate is m/d = 60d/d = 60 minutes per day.

Hence, the rate is 60 minutes per day bo will practices the piano.

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Answer:

Step-by-step explanation:

Let's call the distance across the valley "d". We can use the law of sines to solve for "d". The law of sines states that for any triangle with sides a, b, and c, and angles A, B, and C opposite those sides, the following equation holds:

a/sin(A) = b/sin(B) = c/sin(C)

In this case, we can set up the following equation:

50/sin(57) = 212/sin(180-57-d) = d/sin(57)

Simplifying this equation, we get:

d = (50*sin(57)*212)/sqrt(1-sin(57)^2) = 254.8 meters (rounded to one decimal place)

Therefore, the distance across the valley is approximately 254.8 meters.

Answer: f(-2) = -6

Step-by-step explanation: f(-2) = -2 -4

                                                f(-2) = -6

Answer:

This is a false statement. The distance formula could never yield a negative number as distance cannot be negative.

To transform figure Q onto figure Q', you would need to perform a horizontal translation of 11 units.

A horizontal translation is a transformation in which a figure is moved horizontally along the x-axis, either to the left or to the right. In this case, figure Q is moved 11 units to the right, which brings it into alignment with figure Q'.

Here's how you can verify this:

The coordinates of figure Q are (-9, 3), (-2, 3), (-4, 5), and (-6, 5).

The coordinates of figure Q' are (2, 3), (9, 3), (7, 5), and (5, 5).

If you compare the x-coordinates of the vertices of the two figures, you'll see that figure Q' is 11 units to the right of figure Q. This means that a horizontal translation of 11 units is required to map figure Q onto figure Q'.

The other transformations listed (reflection across the y-axis and horizontal translation of 4 units) would not be sufficient to transform figure Q onto figure Q'.

what do you meant by congruent trapezoids?

Congruent trapezoids are trapezoids that have the same size and shape. In other words, they are identical in every way, except possibly for their orientation or position in space.

To be congruent, two trapezoids must have the same length and height, and their bases must have the same length. In addition, the angles between the sides and the bases must be the same in both trapezoids.

For example, if you have two trapezoids with bases of lengths 5 and 8 and heights of 3, they are congruent if the angles between the bases and the sides are the same in both trapezoids.

Congruent trapezoids can be identified by using the SAS (Side-Angle-Side) Congruence Theorem, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. This theorem can be used to prove that two trapezoids are congruent, as long as you can show that two sides and the included angle are congruent in both trapezoids.

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The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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The total length of two line segments is 80 cm

A line segment is just part of a line. It has two endpoints,

given that

the first line segment is 30cm

the second line segment is 500mm

now we need to convert it into cm from mm

To convert mm to cm, we need to multiply the length in mm by 0.1 cm since 1 mm is equal to 0.1 cm.

500 mm × 0.1 cm = 50cm

now we need to add two line segments

30 cm + 50 cm = 80 cm

The total length of two line segments is 80 cm

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The probability when the value of W = 1 is 0.1 , probability when the value of W = 10 is 0.2 and probability when the value of W = 25 is 0.7  .

In the question ,

the marked price slips are $1, $1, $1, $10 and $25 .

If the winner selects two slips of paper, then the possible outcomes would be ,

total number of slips is = 5 ,

Total number of cases possible = ⁵C₂ = 10

There would be only 1 case in which the winner will win $1

that means when both the slips selected has $1.

So, P(Winning $1) = 1/10 = 0.1

the number of cases to win $10 is {(1,10) , (10,1)}

So , P(Winning $10) is

= 2/10 = 0.2

So , P(Winning $25) is

= 1 - (0.1 \(+\) 0.2)

= 0.7

Therefore , the required probability P(Winning $1) = 0.1 , P(Winning $10) = 0.2 and P(Winning $25) = 0.7

The given question is incomplete , the complete question is

A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)

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Answer: since [B]^-1[B] = I.

Step-by-step explanation:

To find the matrix for T relative to B, we need to find the coordinates of the vectors T(b), T(b^2), and T(b^3) with respect to the basis B.

We have:

T(b) = 6T(b^2) + 1T(b^3) = b, -5b^2

T(b^2) = 1T(b^2) + 0T(b^3) = 7b, -3b^2

T(b^3) = 0T(b^2) - 2T(b^3) = 0, 4b^2

To find the matrix [T], we write the coordinates of T(b), T(b^2), and T(b^3) as columns:

[T] = [b, 7b, 0; -5b^2, -3b^2, 4b^2]

To check this matrix, we can apply it to the basis vectors and see if we get the same coordinates as the vectors T(b), T(b^2), and T(b^3):

[T][b] = [b, 7b, 0][1; 0; 0] = [b; -5b^2]

[T][b^2] = [b, 7b, 0][0; 1; 0] = [7b; -3b^2]

[T][b^3] = [b, 7b, 0][0; 0; 1] = [0; 4b^2]

These are the same as the coordinates we found for T(b), T(b^2), and T(b^3), so our matrix [T] is correct.

To find ITIB, we first need to find the inverse of the matrix [B] whose columns are the basis vectors b, b^2, and b^3. We can do this by row reducing the augmented matrix [B | I]:

[1 0 0 | 1 0 0]

[0 1 0 | 0 1 0]

[0 0 1 | 0 0 1]

So [B] is already in reduced row echelon form, and its inverse is just I:

[B]^-1 = [1 0 0; 0 1 0; 0 0 1]

Therefore,

ITIB = [B]^-1[T][B] = [T]

since [B]^-1[B] = I.

Answer:

Yes god is really good

Step-by-step explanation:

Answer:

Both are answers are not equal