Find the dot product of vectors u and v, where |u| = 12, |v| = 7, and the angle between is θ = 55°.

Therefore, for every 100 meters climbed, the price increases by $12.

To determine the increase in price for every 100 meters climbed, we need to find the rate of change of the fee with respect to the distance climbed.

The fee for climbing d meters is given by the function F = 110 + 0.12d. To find the rate of change, we need to take the derivative of this function with respect to d.

dF/dd = 0.12

The derivative, dF/dd, represents the rate of change of the fee with respect to the distance climbed. In this case, it is a constant value of 0.12, which means that for every 1 meter climbed, the fee increases by $0.12.

To find the increase in price for every 100 meters climbed, we can multiply the rate of change by 100:

Increase in price = 0.12 * 100 = $12

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Answer:

See the three examples, below:

Step-by-step explanation:

One way of approaching this would be to separate 48:

48 times 6 is equivalent to (40 + 8) times 6, or 240 + 48, or 288.

That's just one of many examples.

48 times 6 could also be expressed as 48 times (2 + 4) = 96 + 192 = 288.

And so on.

Next time please share more of the instructions.  Thank you.

The result of the expression 48 times 6 is 288

Given the expression :

Using the distributive property:

Multiplying the sum by 6 :

(40 + 8) * 6

240 + 48 = 288

Therefore, the value of 48 times 6 is 288.

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b. r(t) = (cos(t), sin(t)), for 0 <= t <= pi. c. Sphere of radius 1 centered at the origin: r(u, v) = (cos(u) * sin(v), sin(u) * sin(v), cos(v)), for 0 <= u <= 2pi and 0 <= v <= pi.

b) Here are the parameterizations for a line segment connecting two points of your choice and half of a circle centered at the origin:

Line segment from (0, 0) to (1, 2): r(t) = (1 - t) * (0, 0) + t * (1, 2) = (t, 2t), for 0 <= t <= 1.

Half of a circle of radius 1 centered at the origin: r(t) = (cos(t), sin(t)), for 0 <= t <= pi.

c) Here are the parameterizations for a plane and a sphere:

Plane passing through (1, 0, 0), (0, 1, 0), and (0, 0, 1): r(u, v) = u * (1, 0, 0) + v * (0, 1, 0) + (1 - u - v) * (0, 0, 1), for 0 <= u <= 1 and 0 <= v <= 1.

Sphere of radius 1 centered at the origin: r(u, v) = (cos(u) * sin(v), sin(u) * sin(v), cos(v)), for 0 <= u <= 2pi and 0 <= v <= pi.

Note that for the plane parameterization, we used the fact that a plane passing through three non-collinear points can be parameterized by a linear combination of the points, with the coefficients summing to 1. For the sphere parameterization, we used spherical coordinates to express the position of each point on the sphere in terms of two angles, u and v.

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Answer:

$45.30

Step-by-step explanation:

Divide $73.50 by 5 = $15.10

Multiply $15.10 by 3 = $45.30

Answer:

44.1

Step-by-step explanation:

73.50/5=14.7

14.7x3=44.1

yes your answer are correct

Answer:

400+4n ≥ 750; The club will need to raise an average of $87.50 or more per month.

The medicine bottle has 120 doses of 100 miligram each.

As per the known fact, 1000 miligram is 1 gram. So, the amount of medicine in the bottle in milligrams = 12×1000

Performing multiplication on Right Hand Side of the equation

Amount of medicine in bottle = 12000 milligrams.

Now, number of dose of 100 miligram medicine = 1

Amount of dose of 12000 miligram medicine = (1/100)×12000

Performing division and multiplication on Right Hand Side of the equation

Amount of doses in 12000 miligram medicine = 120

Thus, there are 120 doses in a medicine.

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The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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All five brothers have a total of $100 combined.

Let's assume Peter's total amount of money is P dollars. We are given that 25% of Peter's money is equal to $5,

so we can set up the equation:

0.25P = 5

To solve for P,

we divide both sides of the equation by 0.25:

P = 5 / 0.25 = 20

Now that we know Peter has $20,

we can find out how much money all five brothers have combined. Since Peter and his four brothers combined their money, the total amount would be:

Total = Peter's money + 4 brothers' money

Total = $20 + 4 x (Peter's money)

Total = $20 + 4 x $20

Total = $20 + $80

Total = $100

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Answer:28/40 and if you need to simply it would be 7/10

Step-by-step explanation:

Answer:

10.8

Step-by-step explanation:

√(5-(-5))² + (8 -4)²

√10² + 4²

√100+16

√116 = 10.8

\(\\ \sf\longmapsto CD=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\\ \sf\longmapsto CD=\sqrt{(5+5)^2+(8-4)^2}\)

\(\\ \sf\longmapsto CD=\sqrt{(10)^2+(4)^2}\)

\(\\ \sf\longmapsto CD=\sqrt{100+16}\)

\(\\ \sf\longmapsto CD=\sqrt{116}\)

\(\\ \sf\longmapsto CD=10.4\)

If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .

In the question ,

it is given that ,

the number of residents in the local apartment complex is = 71

the mean electric bill for the 71 residents = $62 ;

we know that the sample mean is itself called as the best point estimate ;

So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of  local apartment complex which is given as $62 .

Therefore , the best point estimate is $62 .

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Answer:

the smallest number by which 350 by answer is 15

a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.

The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).

Substituting these values into the formula, we have:

Sn = (200/2)(1 + 200)

  = 100(201)

  = 20,100

Therefore, the sum of the first 200 natural numbers is 20,100.

(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.

For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.

Let's represent the initial drop distance as h (30 ft).

The total distance traveled after the 6th rebound is given by the sum of a geometric series:

Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6

Using the formula for the sum of a geometric series, we can simplify this expression:

Distance = h * (1 - (3/4)^7) / (1 - 3/4)

Simplifying further:

Distance = h * (1 - (3/4)^7) / (1/4)

        = 4h * (1 - (3/4)^7)

        = 4 * 30 * (1 - (3/4)^7)

Calculating the value:

Distance ≈ 4 * 30 * (1 - 0.1335)

        ≈ 4 * 30 * 0.8665

        ≈ 104 ft

Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

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Answer:

65

Step-by-step explanation:

55 + 65 + 57 = 177

there are more factors, but I found this one the quickest.

hope this helps!

Answer:

finsish the question

Answer:

a=11, b=10, c=32, and d=14.

Step-by-step explanation:

Answer:

67 units

Step-by-step explanation:

Perimeter  of a shape is the sum of all sides.

Perimeter = a + b + c + d

                = x +7  + 2x + 2 + 8x + x +10

                = x + 2x + 8x + x  +7 + 2 + 10

Combine like terms,

                 = 12x + 19

Now, substitute x = 4 in the above expression,

                  = 12*4 + 19

                  = 48 + 19

                  = 67

Answer:

Answer is B because 24 divided by 3 is 8

Step-by-step explanation:

Nillllll

The value of the angle y in the quadrilateral is 90° .

There are four sides, four vertices, and four angles in a closed quadrilateral.

We know that from the properties of parallel line x = 70° as the angles are alternate angles.

Again the interior angle adjacent to the 70° angle is equal to

180° - 70° = 110°

Given another interior angle is 90°.

We know sum of all the four angles of a quadrilateral is 360°.

Therefore

70 + 90 + 110 + y = 360°

Hence we will find the value of y.

y = 360° - 270°

or, y = 90°

Therefore the value of y is 90° .

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Answer:

The value of the expression when i is 1 is equals to 5.

Step-by-step explanation:

We are given the following expression:

\(2 + 3^{i}\)

Evaluate the expression when i is 1.

We replace i by 1. When we elevate a number to the 1, the result is the number we elevate. So

\(2 + 3^{i} = 2 + 3^{1} = 2 + 3 = 5\)

The value of the expression when i is 1 is equals to 5.

Answer:

3,000 is the numerical increase and 15% is the percentage increase.

Step-by-step explanation:

It's quite easy to see that 3,000 more people were added to 20,000, since 23,000 - 20,000 = 3,000. To find the percentage, simply take 20,000 and divide it by the additional increase number, which is in this case 3,000. 20,000/3,000 = 0.15. Converting decimals to percentages, we take the digits behind the decimal and add the percent sign since 100 is equal to 1 or the whole. So 0.15 = 15%, which is the percent increase.

Answer:

actual amount of increase is 3000

% increase is 15%

Step-by-step explanation:

The actual amount of increase is

23,000-20,000= 3,000

To find the percent increase, take the actual amount of increase and divide by the original amount

3,000/20000=.15

Change to percent

15%

Answer:

x=3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

8 - 5 = 3

(Checking v)

3 + 5 = 8

The planets' sizes and masses are critical to our understanding of the solar system's formation and evolution.

The solar system consists of eight planets, all with varying sizes and masses. Jupiter, the most massive planet, has a mass of approximately 1,898,000,000,000,000,000,000,000,000 kg.

In contrast, Mercury, the smallest planet in the solar system, has a mass of about 330,000,000,000,000,000,000,000 kg. The mass of a planet is a fundamental property that helps us understand how it interacts with its surroundings.

A planet's mass affects the strength of its gravitational pull, which, in turn, influences the orbits of other planets, moons, and other celestial bodies within its gravitational field.

Besides Mercury and Jupiter, the other six planets in the solar system are Earth, Venus, Mars, Saturn, Uranus, and Neptune.

Although Earth is relatively small compared to Jupiter, it has a much greater mass than Mercury, tipping the scale at roughly \(6 * 10^24 kg.\)

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The length of AB is 10 units. Option D is the correct option.

What are the coordinates of a point?

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given that the coordinates of A are (3,4) and the coordinates of B are (-3,-4).

The distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²]

Here x₁ = 3, y₁ = 4, x₂ = -3, y₂ = - 4.

The distance between points is

√[(-3 - 3)² + (-4 - 4)²]

= √[6² + 8²]

=√100

= 10 units

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Answer:

145°

Step-by-step explanation:

because opposite angles r equal

The distribution has a 90th percentile for the value of 86.45 of x.

Let the normal distribution be X.

Hence according to the problem,

X ~ N(80, 25)

where,

the mean = μ = 80

the variance = σ² = 5² = 25

To find the 90th percentile we need to find a variable whose CDF is equal to 90% or 0.9

Let the variable be x.

Then

P(X < x) = 0.9

Now to find this we will first transform this to the standard normal form Z.

Any distribution can be brought to the standard normal form by,

Z = (X - μ)/σ

where

μ is the mean of the distribution

σ is the standard deviation of the distribution

Here,

μ = 80

σ = 5

Hence we get,

Φ[(x - 80)/5] = 0.9

From the standard normal table we get that for Φ(1.29) the p-value is approximately 0.9

hence we get

Φ[(x - 80)/5] = Φ(1.29)

or, (x - 80)/5 = 1.29

or, x - 80 = 6.45

or, x = 86.45

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Answer: $30

Step-by-step explanation:

Answer:

$30

Step-by-step explanation:

10% of 600 = 60

5% of 600 = 30