if the speed of x meters per second is equivalent to the speed of y kilometers per hour, what is y in terms of x ? (1 kilometer

The total capital raised from selling 10 investment units at $100,000 per unit with a preferred return of 7% and a 70%/30% split would be $1,000,000.

To calculate the total capital raised, we need to consider the number of units sold, the price per unit, and the preferred return.

Given that 10 investment units were sold at $100,000 per unit, the total value of the units sold would be 10 units * $100,000 = $1,000,000.

The preferred return of 7% indicates that the investors will receive a fixed return of 7% on their investment before any profit sharing occurs. However, for the purpose of calculating the total capital raised, we do not deduct the preferred return from the total value of the units sold.

The 70%/30% split suggests that after the preferred return is paid, the remaining profits will be split between the owner and the investors in a 70%/30% ratio. This split does not affect the calculation of the total capital raised.

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The sample mean of 43.4 is greater than the hypothesized population mean of 38, which supports the researcher's claim that the mean age of the residents is more than 38 years.

The sample mean is calculated by adding up all the ages and dividing by the sample size, which gives us:

x = (40 + 42 + 44 + ... + 50)/30 = 43.4

The sample standard deviation is calculated using the formula:

s = √[Σ(xi - x)²/(n-1)]

where xi is the age of each resident in the sample. We will not calculate s here, but assume that it has been calculated and is known.

Next, we will calculate the test statistic using the formula:

t = (x - μ)/(s/√n)

where μ is the hypothesized population mean (38 in this case) and n is the sample size (30). Plugging in the values, we get:

t = (43.4 - 38)/(s/√30)

The critical value from the t-distribution can be found using a t-table or a calculator, with degrees of freedom equal to n - 1 = 29. For a one-tailed test at α = 0.10, the critical value is 1.310.

If the calculated test statistic is greater than the critical value, we reject the null hypothesis and accept the alternative hypothesis. If the calculated test statistic is less than or equal to the critical value, we fail to reject the null hypothesis.

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Answer:

The length of the hypotenuse is 30 feet

Step-by-step explanation:

Here, we are to calculate the length of the hypotenuse of an iscosceles right triangle.

For the triangle to be isosceles, it means that the opposite and the adjacent are equal in length.

Now, to calculate the value of the hypotenuse, we make use of the Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Mathematically;

let’s say the hypotenuse is length h feet

h^2 = {15√(2)}^2 + {15√(2)}^2

h^2 = (225 * 2) + (225 * 2)

h^2 = 450 + 450

h^2 = 900

h = √(900)

h = 30 feet

Answer:

30 feet

Step-by-step explanation:

Answer:

10400MM

1.04 litre

Step-by-step explanation:

volume = length x width x height

13 x 8 x 10 = 1040 cm^3

1cm = 10 mm

1040 x 10 = 10400MM

1cm = 0.001 litres

1040 x 0.001 = 1.04 l

Answer:

A and D are the correct answers

Answer:

First, second and fourth are correct;

The third might be correct since fractions and ratios can often represent the same information in different ways and in some cases even in the same way, but this may not always be true.

Answer:

A 5

Step-by-step explanation:

60 mins = 1 hour

60 divided by 4 is 15

60 divided by 3 is 20

15 times 3 is 45

20 times 2 is 40

45 - 40 is 5

The length of the marsh, AC, is approximately 345.7 meters.

From the given information, we can see that the surveyor has formed a right triangle ABC, where AB is the distance walked by the surveyor and AC is the length of the marsh.

Using the Pythagorean theorem, we can find the length of AC:

AC² = AB² - BC²

AC² = (410m)² - (220m)²

AC² = 168,100m² - 48,400m²

AC² = 119,700m²

AC ≈ √119,700m²

AC ≈ 345.7m (rounded to one decimal place)

Therefore, the length of the marsh, AC, is approximately 345.7 meters.

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The solution is, the value of DE = 6.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Let's consider some theorem:

1- The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to equal to half of it

2. A straight line through the mid point of one side of a triangle parallel to a second side bisects the third side.

Having noted that, let's see that;

∆ ABC is similar to ∆ BAC

Therefore, from the above theorem and the information given,

(DE / AC) = ( BE / BC)

From the question, BC is 10

Therefore,

(DE/12) = (5 / 10)

Cross multiplying:

10*DE = 12*5

10DE = 60

DE = 60/10

DE = 6

Hence, The solution is, the value of DE = 6.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

B

Step-by-step explanation:

Angles in a triangle add up to 180

Take 45 + 90 then subtract the answer from 180

multiply the length and with by the scale factor:

24 x 4/3 = 32 feet

20 x 4/3 = 26 2/3 feet

Area is length x width:

32 x 26 2/3 = 853 1/3 square feet.

The process of minimizing or maximizing an objective function f(x) parameterized by x is referred to as optimization. In terms of deep learning or machine learning

Finding the values of the parameters of a function (linear regression, logistic regression, etc.) that is used to lower a cost function is done using the optimization process known as gradient descent. The ratio of the vertical change to the horizontal change between any two points on a line is known as the slope (Slope = y/x). It is used to specify the direction of the line as well as its steepness.

When making the modifications to the parameters, we use batch gradient descent, which involves adding up all of the examples from each iteration. Based on the batch size, Mini-batch Gradient Descent adds up over fewer samples. Each example's parameters are updated using stochastic gradient descent (SGD).

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Answer:

The Correct answer is

57°

Answer:

You solve them by using the order of operations in math, which calls for parentheses, exponents, multiplication, division, addition, and subtraction. Follow these steps in order in mathematical equations, and you'll be a math professional in no time. :)

Hope this helps.

Answer:

In summary, to solve multi-step equations, the following procedures are to be followed:

Eliminate any grouping symbols such as parentheses, braces, and brackets by employing the distributive property of multiplication over addition.

Simplify both sides of the equation by combining like terms.

Isolate a variable on any side of the equation depending on your preference.

A variable is isolated, performing the two opposite operations, such as addition and subtraction. Addition and subtraction are the opposite operations of multiplication and division.

example:

12x + 3 = 4x + 15

Solution

This is a typical multi-step equation where variables are on both sides. This equation has no grouping symbol and like terms to combine on opposite sides. Now, to solve this equation, first decide where to keep the variable. Since 12x on the left side is greater than 4x on the right side, therefore we keep our variable to the LHS of the equation.

This implies that, we subtract by 4x from both sides of the equation

12x – 4x + 3 = 4x – 4x + 15

6x + 3 = 15

Also subtract both sides by 3.

6x + 3 – 3 = 15 – 3

6x = 12

The last step now is to isolate x by dividing both sides by 6.

6x/6 = 12/6

x = 2

The y intercept is where the graph crosses the vertical y axis. In this case, it's at the point (0,-1). Focus on the y coordinate and we see y = -1. The y intercept is b = -1.

The slope is m = 2 because we start at a point like the y intercept, and do the following steps

and arrive at the point (1,1) which is also on the graph. We can follow these steps again to go from (1,1) to (2,3) and so on.

Alternatively, you can pick two points on the graph such as (1,1) and (2,3) to use the slope formula

m = (y2 - y1)/(x2 - x1)

m = (3-1)/(2-1)

m = 2/1

m = 2

Either way, the slope is 2.

Answer:

m=2 b=1 aka B

Step-by-step explanation:

trust me i know

Answer:

28 points per game

42 miles per gallon

$2.99 per bag

Step-by-step explanation:

140 points in 5 games. To find the amount of points in one game, we divide the total points by the total games: 140/5=28

504 miles with 12 gallons. To find the amount of miles with one gallon, we divide the total miles by the total gallons: 504/12=42

$8.97 for 3 bags. To find the amount of dollars for one bag, we divide the total amount of dollars by the total bags: 8.97/3=2.99

Answer:

A. x=35

Step-by-step explanation:

Two perpendicular lines create a 90 degree angle. Because of this the 2 angles must add up to 90.

(2x-12) + 32 = 90

2x-12 = 58

2x = 70

x=35

The angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

The given values are:

AD = 150 mm

AB = 40 mm

CD = 80 mm

The crank AB rotates at 120 r.p.m. clockwise.

BC and AD are of equal length.

To find:

The angular velocity of link CD when angle BAD = 60°.

From the given data, we have to first find the value of angle BCD.

Angle BCD can be calculated as follows:

AB = 40 mm

BC = AD

= 150 mm

In ΔABC,

By using Cosine rule;

AC² = AB² + BC² - 2 × AB × BC × Cos ∠ABC∴ AC² = (40)² + (150)² - 2 × 40 × 150 × Cos 180°

∴ AC = 160.6 mm

In ΔBCD,

By using Cosine rule;

BD² = BC² + CD² - 2 × BC × CD × Cos ∠BCD

∴ BD² = (150)² + (80)² - 2 × 150 × 80 × Cos ∠BCD

In ΔABD,By using Cosine rule;

BD² = AB² + AD² - 2 × AB × AD × Cos ∠BAD

∴ BD² = (40)² + (150)² - 2 × 40 × 150 × Cos 60°

∴ BD = 184.06 mm

In ΔABD,By using Sine rule;

AB / Sin ∠BAD = BD / Sin ∠ABD

∴ Sin ∠ABD = BD × Sin ∠BAD / AB

∴ ∠ABD = Sin⁻¹ [BD × Sin ∠BAD / AB]

∴ ∠ABD = Sin⁻¹ [184.06 × Sin 60° / 40]

∴ ∠ABD = 87.2°∠ACD = ∠ABD - ∠ACB

∴ ∠ACD = 87.2° - 180°

∴ ∠ACD = - 92.8°∠BCD

= 180° - ∠ACD

∴ ∠BCD = 180° - (- 92.8°)

∴ ∠BCD = 272.8°

As we know that for four-bar mechanism, we have a formula for finding the angular velocity of link CD.

ωCD / Sin ∠BCD = ωAB / Sin ∠BADωCD / Sin 272.8°

= ωAB / Sin 60°

Substituting the values, ωCD / Sin 272.8° = ωAB / Sin 60°ωCD

= ωAB × Sin 272.8° / Sin 60°

But, ωAB = 2 × π × N / 60

= 2 × π × 120 / 60

= 4 × π rad/s

∴ ωCD = 4 × π × Sin 272.8° / Sin 60°ωCD

= 21.16 rad/s

Therefore, the angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

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Answer:

Part B--solution is (36, 45)

Step-by-step explanation:

\(12 = \frac{1}{3} x\)

\(x = 36\)

\(y - 36 = 9\)

\(y = 45\)

So the solution is (36, 45).

Answer:

24,024 different ways

Step-by-step explanation:

There are 9 boys and 13 girls competing for the medals. The number of ways to choose 3 boys out of 9 is C(9,3) = 84. The number of ways to choose 3 girls out of 13 is C(13,3) = 286. The total number of ways to choose 6 medals is the product of these two numbers: 84 * 286 = 24024.

The required rate of return for DAK Corporation is 12.34%.

What is the required rate?

The minimal profit (return) an investor will seek or expect in exchange for taking on the risk of investing in a stock or other type of security is known as the required rate of return (RRR). RRR can also be used to determine a project's potential profitability in relation to its funding costs.

Here, we have

Given Information

Beta =   1.25

The yield on 30-year T bonds (rf)=     5.65%

Return on S&P (rM) =    11%

Required Return for DAK = rf + Beta*(rM - rf)

= 5.65% + 1.25*(11% - 5.65%)

=  12.34%

Hence,  the required rate of return for DAK Corporation is 12.34%.

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Answer: 2: v = -26 | 3: k = 7 | 4: x = 3/14 |

Step-by-step explanation:

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

2: 4 + v/8 = 3/4

First we have to leave the variable "v" alone and we do the opposite on the other side.

So we do 4 + v/8 = 3/4 ----> v/8 = 3/4 - 4

---> v/8 = -3 1/4

next we do 8 * v/8 = -3 1/4 * 8

We get v = -26

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

3: 2/3 + 3/4k = 71/12

Subtract 2/3 from both sides

= 3/4k = 63/12

Reduce 63/12 to 21/4

= 3/4k = 21/4

Multiply each side by 4/3, the reciprocall of 3/4

then we get k = 21/3

Which means k = 7

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

4: 1/2 + 7/10x = 13/20

Subtact 1/2 from both sides

= 7/10x = 3/20

Multiply each side by 10/7, the reciprocal of 7/10

x = 3 * 10/20 * 7

= x = 30/140

= x = 3/14

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer:

the bin 60-69 contain the most data values

Answer:

third option is the right one

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

6(7)+5=42+5=47

mark me brainliest if it helped

Answer:

x² + x = 342

Step-by-step explanation:

Let x be the 1st integer

x + 1 be the 2nd integer

x(x+1) = 342

Simplify

x² + x = 342

or in standard form:

x² + x - 342 = 0

Answer:

D. x2 − x − 342 = 0

Step-by-step explanation:

the value of greater integers can be 19 or -18.

(Edge 2023)

The value of x is 4.47 units

In the given figure, there are two right angle triangle, to find the value of x we have to solve each triangle using the Pythagorean theorem.

Consider the bottom triangle

Base of the triangle = 6 units

The hypotenuse of the triangle = 9 units

Apply the Pythagorean theorem

The third side of the triangle = \(\sqrt{9^2-6^2}\)

= \(\sqrt{81-36}\)

= \(\sqrt{45}\) units

Similarly consider the top triangle

The base of the triangle = 5 units

The hypotenuse of the triangle = \(\sqrt{45}\) units

The third side of the triangle = \(\sqrt{\sqrt{45}^2- 5^2}\)

= \(\sqrt{45-25}\)

= \(\sqrt{20}\)

= 4.47 units

Hence, the value of x is 4.47 units

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The first four nonzero terms of the Taylor series for f(x) = 5xex, centered at a = 0, are 5x, \(5x^2\), \(5x^3^/^2, 5x^4^/^6.\)

The Taylor series expansion allows us to express a function as an infinite sum of terms, providing an approximation of the function near a specific point. In this case, we are given the function f(x) = 5xex and the center a = 0.

To find the first four nonzero terms of the Taylor series, we need to compute the derivatives of f(x) at x = 0.

Starting with the first derivative, we differentiate f(x) with respect to x, which gives us f'(x) = 5(1+x)ex.

Next, we evaluate the second derivative by differentiating f'(x) with respect to x. This yields f''(x) = 5(2+x)ex.

Continuing this process, we find the third derivative f'''(x) = 5(3+x)ex and the fourth derivative f''''(x) = 5(4+x)ex.

The terms of the Taylor series are obtained by evaluating each derivative at x = 0 and dividing it by the corresponding factorial term. The first four nonzero terms of the series for f(x) centered at a = 0 are 5x, \(5x^2\), \(5x^3^/^2\), and \(5x^4^/^6\).

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