A boat travelled at a constant speed for 5 hours, covering a total distance of 256.28
kilometres. How fast was it going?

A vector Y is orthogonal to vectors U and V, so Y is orthogonal to the vector (U+V).

In the given question,

Suppose that a vector Y is Orthogonal to vectors U And V.

We have to show that Y is orthogonal to the vector U + V.

As to vectors are orthogonal if and only if their dot product is zero.

So Y∙U = 0 and Y∙V = 0.

To prove that Y is orthogonal to the vector(U+V), we have to show that Y∙(U+V) = 0.

As dot product is distributive. Now

Y∙(U+V) = Y∙U + Y∙V

As Y∙U = 0 and Y∙V = 0. So

Y∙(U+V) = 0 + 0

Y∙(U+V) = 0

Hence, Y is orthogonal to the vector (U+V).

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Answer:Tap for more steps... By the Sum Rule, the derivative of x 4 + 3 x 2 x 4 + 3 x 2 with respect to x x is d d x [ x 4] + d d x [ 3 x 2] d d x [ x 4] + d d x [ 3 x 2]. Differentiate using the Power Rule which states that d d x [ x n] d d x [ x n] is n x n − 1 n x n - 1 where n = 4 n = 4.

Step-by-step explanation:

Answer: Please send more, is that all??

Step-by-step explanation:

I need more clarification, what are you trying to answer?

Answer:both a and b are correct

Step-by-step explanation:

All the probabilities are provided for the three situations involving men and women: smoking, developing lung cancer, and developing lung cancer while simultaneously smoking. Then, these are even divided into gender categories.

However, the last query is limited to males who smoke who develop lung cancer. Therefore, I believe that all of the other information is merely a red herring. You just need to search through the other options to locate the answer, which is already there. You should first disregard any possibilities involving ladies because we are only interested in men. The likelihood that males with lung cancer smoke is the next statistic you discover. The solution is 90%.

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

Answer:

(21,0)

Step-by-step explanation:

The function of the parabola is given in vertex form which is \(f(x) = a(x-h)^{2} +k\)

The vertex is equal to (h,k). Looking the function \(f(x)=8(x-21)^{2}\), we see that the h-value is equal to 21 and that the k-value is 0. So the vertex of the function is (21,0).

The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.

Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.

Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.

The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.

The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.

The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.

The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.

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Answer:

A.  1/(x + 8) + 5.

Step-by-step explanation:

Staring with 1/x a shift up of 5 units makes it 1/x + 5.

A shift of 8 to the left makes it 1/(x + 8) + 5

Answer:

  right from the y-axis

Step-by-step explanation:

The ordered pair (3, 4) is understood to be the (x, y) coordinates of the point Paul wants to plot.

__

The x-coordinate (3) is the number of spaces the point lies to the right of the y-axis.

The y-coordinate (4) is the number of spaces the point lies above the x-axis.

__

If Paul is moving 3 spaces from the y-axis, he will be moving to the right to get to where he will plot the point.

The slope of a line can be calculated with the following formula:

In this case, given these points:

You can set up that:

Knowing these values, you can substitute them into the formula and then evaluate, in order to find the slope of the line. This is:

The slope is:

Given Equations

Let it has solution (x,y)

Add both

\(\\ \sf\longmapsto 5x+4x+3y+7y=8+34\)

\(\\ \sf\longmapsto 9x+10y=42\)

It will also have same solution (x,y)

The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

5x + 3y = 8               ...1

4x + 7y = 34            ...2

From equation 1, then we have

5x + 3y = 8

y = 8/3 - (5/3)x

Put in equation 2, then we have

4x + 7[8/3 - (5/3)x] = 34

12x + 56 - 35x = 102

-23x = 46

x = - 2

Then the value of y is calculated as,

y = 8/3 - (5/3)(-2)

y = 8/3 + 10/3

y = 18 / 3

y = 6

Let's check whether (-2, 6) satisfy the equation 9x + 10y = 42 or not. Then we have

9(-2) + 10(6) = 42

- 18 + 60 = 42

42 = 42

The solution of the equations is (-2, 6) which satisfies the equation 9x + 10y = 42.

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the decrease was clearly 110000 - 102300 = 7700.

now, if we take 110,000(origin amount) as the 100%, what is 7700 off of it as a percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 110000 & 100\\ 7700& x \end{array} \implies \cfrac{110000}{7700}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 100 }{ 7 } ~~=~~ \cfrac{ 100 }{ x }\implies 100x=700\implies x=\cfrac{700}{100}\implies x=7\)

Answer:

Answer is B. 76.

Step-by-step explanation:

Let thw unknow angle be y

sin y = p/h

sin y = 32/33

y = sin‐¹(32/33)

y = 75.85888977

so y = 75.9 = 76

The measure of a central angle of a decagon is 36 degrees.

the 1/2 central angle = 18 degrees

Apothem ≈ 16.93

Area of the decagon ≈ 931.15

The figure has ten sides hence a decagon

To find the measure of a central angle of a decagon, we need to use the formula:

Central angle = 360 degrees / number of sides

Substituting the value for a decagon, we get:

Central angle = 360 degrees / 10 sides

Central angle = 36 degrees

To find the 1/2 central angle, we simply divide the central angle by 2:

1/2 central angle = 36 degrees / 2

1/2 central angle = 18 degrees

To find the apothem, we use the formula:

Apothem = (Side length) / (2 x tan(180 / number of sides))

Substituting the given values, we get:

Apothem = (11) / (2 x tan(18 degrees))

Apothem ≈ 16.93

To find the area of the decagon, we first need to find the perimeter using the formula:

Perimeter = (Number of sides) x (Side length)

Perimeter = 10 x 11

Perimeter = 110

Now, we can use the formula for the area:

Area = (1/2) x Apothem x Perimeter

Area = (1/2) x 16.93 x 110

Area ≈ 931.15

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Answer:

option b is your correct answer

hy if it help you then mark me brilliant

.............

The Area of a geometric figure can be calculated based on the appropriate formulas.

For example, the area of a rectangle is based on the size of their sides: width and length

In your example, it seems that the length of the rectangle is 8.5 m and its width (shorter side) is 8 m.

Therefore, the area i calculated via the formula:

Area Rectangle = base x height

Area = 8.5 m x 8 m = 68 square meters

(we are here assuming that the base is the longest side)

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Answer:

Step-by-step explanation:

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

Step-by-step explanation:

To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides. This number divided by 2 is the width.

Answer:

#28: 13

#29: 22

Step-by-step explanation:

The first question

f(5) =3(5) -2

f(5) = 15 -2

f(5) = 13

Second question

P(2,9) = 2(2) + 2(9)

P(2,9) = 4 + 18

P(2,9) = 22

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer:

Car A: 8 minutes

Car B: 6.67 minutes

Step-by-step explanation:

Car A: 60km evrery hour so,

1 km every minute, so he will be in 8km in 8 minutes.

Car B: 72km per hour so,

72/60 = 1.2 = 1.2 km per minute.

8/1.2 = 6.6666666666667 which is about 6.67 to the nearest hundredth.

Answer:

40 min

Step-by-step explanation:

Car A is traveling at 1 km/min (60/60)

Car B is traveling at 1.2 km/min (72/60)

Car B gains .2km on Car A for every minute they drive.

8km/.2 = 40

Step-by-step explanation:

(7x)^2 - 2×7x×1 +1^2 =0

(7x-1)^2 =0

7x-1=0

7x=1

x= 1\7

I think it's D. 48 ft²

because 8 × 6 is 48