0.77 m = how many cm

The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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The solution to this system of equations is dependent.

Dependent matrix is a matrix where one or more rows can be expressed as a linear combination of the other rows. This means that the rows are not linearly independent, and there is redundancy in the information they provide.

A dependent matrix has less than full rank, which means that the rank of the matrix is less than the number of rows or columns. In a dependent matrix, one or more variables can be expressed in terms of the other variables, and the system of equations represented by the matrix has infinitely many solutions.

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Answer:

l= 10 , w=7

Step-by-step explanation:

If the length of a rectangle is 11 m less than 3 times the width, then we can come up with this equivalency:

l = 3w - 11

where l stands for length and w stands for width. Now we plug in the equivalency into the equation for the area of a rectangle:

A = lw

A = (3w - 11)w

70 = (3w - 11)w

70 = 3w2 - 11w

Then solve for w by completing the square. Now, in order to complete the square for this, we need to find a completion that fits 3w2 - 11w +  ?  and completes the base factoring of (√(3)w -  ? )2. The only one that fits the second question mark so that it can work out to the first is (11√3)/6, and when we work it into the first question mark, the first question mark becomes 121/12. Essentially, what we have for completing the square is:

70 + 121/12 = 3w2 - 11w + 121/12

80.08333 = (√(3)w - (11√3)/6)(√(3)w - (11√3)/6)

80.08333 = (√(3)w - (11√3)/6)2

8.94893 = √(3)w - (11√3)/6

Solving for w, we get:

12.124 = √(3)w

w = 7

Since we know that the length is 11 m less than 3 times the width, we can plug w into the first equation to find l:

l = 3w - 11

l = 3(7) - 11

l = 21 - 11

l = 10

And if we want to check, lw = (10)(7) = 70.

To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

Consider an example where vertex is (2,1) and y-intercept is (0,-3).

The equation of parabola needs to be deduced using these points.

The equation of a parabola in vertex form is -

y=a(x-h)^2+k

Here, a is a constant and (h ,k) are the coordinates of the vertex.

So, (h,k)=(2,1)

⇒y=a(x−2)^2+1

To obtain the value of a, substitute (0,−3) into the equation -

-3=4a+1

4a=-4

a=-1

⇒y=-1(x−2)^2+1

Now, distribute and simplify -

y=-1(x−2)^2+1

y=-(x^2-4x+4)+1

y=-x^2+4x-4+1

y=-x^2+4x-3

On, graphing this equation a parabola is obtained.

Therefore, to write an equation of parabola vertex form is used.

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a) The area of each of the walls is 60 feet².

b) The combined area of the four walls is 240 feet².

c) The total cost Mason will spend on paint is $34.375.

The area refers to the space occupied by two-dimensional objects.

We can compute the area by multiplying the length by the width.

Areas are stated in square units.

Length of each wall = 6 ⅖ feet

Width of each wall = 9 ⅜ feet

The area of each wall = 60 feet² (6 ⅖ feet x 9 ⅜ feet).

The combined area of the walls = 240 feet² (60 ft² x 4).

The number of cans of paint required for each wall = 2¾ cans.

The cost per can of paint =  3⅛ dollars or $3.125.

The total cost of paint = $34.375 (4 x 2¾ x $3⅛).

Thus, Mason will spend $34.375 for the four walls with a combined area of 240 ft².

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The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

0.52

Step-by-step explanation:

Answer:

0.521

Step-by-step explanation:

Answer:

The answer is 49 inches

Step-by-step explanation:

Divide 294 by 6 to get the answer.

Hope that helps!

Answer:

49 inches

We know that for every 6 feet in real life, there will be 1 inch in the picture.

So, that means if we divide 294 by 6, we can find how many inches wide the picture is.

294 ÷ 6 = 49

Since there are 49 sixes in 294, the picture is 49 inches wide.

Consider that 1 km = 1000 m, then, you have:

7 km = 7(1000 m) = 7000 m

Hence, Kay swam 7000 meters

Answer:

0.7 km = 700 meters

Step-by-step explanation:

1 km = 1000m, so 0.7 km is 7/10 of a km, or 700 m.

The standard deviation of f$ ar{x},f$ is usually called the "sample standard deviation".

This is a commonly used statistical measure that represents the amount of variation or dispersion within a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The sample standard deviation is often used to compare the variability of different sets of data and to determine the significance of differences between them. Financial contracts known as derivatives are those entered into by two or more parties and whose value is derived from an underlying asset,

collection of assets, or benchmark. A derivative may be traded over-the-counter or on an exchange. Derivative prices are based on changes in the underlying asset.

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Answer:-1

Step-by-step explanation:

Answer:

$610.70

Step-by-step explanation:

$558.99 + 9.25 percent of $558.99

Answer:

Line A

Step-by-step explanation:

Answer:

During the fifth or sixth grade, students are usually asked to divide a mixed number and a whole number. The process is very similar to dividing fractions, but the main difference is that you have to multiply the fraction first before dividing it. This is a simple process. Then, you have to invert the second fraction.

Answer:

7% of 33= 2.1

2% of 640= 12.8

15% of 470=70.5

7/9 of 51= 119/3

.52 of 62= 32.24

Answer:

1) 2.31

2) 12.8

3) 72

4) 44.625

5) 32.24

Step-by-step explanation:

7% of a number is simply 0.07*the number.

7/8 is just .875*the number

Hope it helps <3

Answer: 6

Step-by-step explanation:

By the geometric mean theorem,

\(\frac{BD}{3}=\frac{27}{BD}\\\\(BD)^{2}=81\\\\BD=9\\\\\implies x=9-3=6\)

Answer:

x = 6

Step-by-step explanation:

BD is the height of the triangle.

We can find the height of this triangle using one of the Euclidian Theorem:

h^2 = AD*DC rewrite the equation using the given information

(x + 3)^2 = 3*27 multiply

(x + 3)^2 = 81 find the root of both sides

x + 3 = 9 subtract 3 from both sides

x = 6

Construct a 95% confidence interval for the expected difference in average test scores between the small class (Classroom A) and the regular class (Classroom B),

a. You can follow these steps:
1. Refer to column (4) of Table 13.2 and find the results for the regressors.
2. Calculate the standard error of the difference in average test scores using the formula:
  SE(difference) = sqrt[SE(Classroom A)^2 + SE(Classroom B)^2]
  where SE(Classroom A) and SE(Classroom B) are the standard errors for each class.
3. Calculate the margin of error (ME) by multiplying the critical value (z*) corresponding to a 95% confidence level by the standard error (SE).
4. Finally, construct the confidence interval by subtracting the margin of error from the difference in average test scores and adding it to the difference in average test scores.

b. To construct a 95% confidence interval for the expected difference in average test scores between the small class with a teacher with 5 years of experience (Classroom A) and the regular class with a teacher with 10 years of experience (Classroom B), you can follow similar steps as in part a. However, this time you need to account for the difference in teacher experience as a regressor.

c. To construct a 95% confidence interval for the expected difference in average test scores between the small class with a teacher with 5 years of experience (Classroom A) and the regular class with a teacher with 10 years of experience (Classroom B), you can follow similar steps as in part a. However, this time you need to consider both the class type and teacher experience as regressors.

d. The intercept is missing from column (4) because it represents the expected average test score when all the regressor variables are equal to zero. In this case, the intercept is not relevant to the question being asked, so it is not included in the table.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

there is no picture but the y intercept can be either positive or negative. it is the point where the x is 0 and the y is a number. it lies on the y axis.

Step-by-step explanation:

Answer:

Y intercept is is where the line crosses the y-axis (touches the y-axis).

Step-by-step explanation:

For the given question there are always 425 skiers on the chair lift at any given time.

The chair lift unloads 1700 skiers per hour at the top of the slope. The ride from the bottom to the top takes 15 minutes. We have to determine the number of skiers who are riding on the lift at any given time.

There are a few steps that we can take to solve this problem:

Step 1:Calculate how long the trip is from top to bottom:

The trip from bottom to top takes 15 minutes.

Therefore, the trip from top to bottom would take the same amount of time.

Step 2:Calculate how many trips the lift makes in an hour:

We have to convert 1 hour to minutes.1 hour = 60 minutes

Therefore, 1 hour = 60/15 = 4 trips from top to bottom

Step 3:Calculate how many skiers are riding on the lift at any given time.

The chair lift unloads 1700 skiers per hour at the top of the slope.

So, every 15 minutes, 425 skiers are unloaded at the top.

Since the lift takes 15 minutes to make one trip, there are always 425 skiers on the lift at any given time.

There are always 425 skiers on the chair lift at any given time.

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Answer:

1 4/7

Step-by-step explanation:

To determine the seiching periods in a rectangular basin, we need to consider the dimensions of the basin, specifically the length (L), width (W), and water depth (h).

Please provide the values for the length, width, and depth of the basin, and will be able to assist with the calculations.

The seiching periods depend on these dimensions and can be calculated using the following formula:

Seiching period = 2 × sqrt(L × W / (g × h))

Where:

sqrt represents the square root function

L is the length of the basin

W is the width of the basin

g is the acceleration due to gravity (approximately 9.8 m/s^2)

h is the water depth

By substituting the values of L, W, and h into the formula, you can calculate the seiching periods for the specific rectangular basin of interest.

Please provide the values for the length, width, and depth of the basin, and will be able to assist with the calculations.

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If xn>0 for all nN, and lim (xn)=0, then lim(√(xn))=0

We know that the limit of a sequence is unique. Since lim(xn) = 0, we have that for every ε > 0, there exists an N ∈ ℕ such that for all n ≥ N, we have |xn - 0| < ε, which implies xn < ε. Now, consider the sequence √(xn). Since xn > 0 for all n ∈ ℕ, we can take the square root of both sides of the inequality xn < ε. This gives us:
√(xn) < √(ε).
Since ε > 0 can be arbitrarily small, it's clear that lim(√(xn)) = 0, as for every ε > 0, there exists an N such that for all n ≥ N, we have √(xn) < √(ε).

Given the conditions that xn > 0 for all n ∈ N and lim(xn) = 0, we have shown that lim(√(xn)) = 0.

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The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.

The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`

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Answer:

22/9

Step-by-step explanation:

The rate at which the y-coordinate of the jogger is changing is \({-\frac{3}{4}}\) times the rate at which the x-coordinate of the jogger is changing.

Given information:

Radius of the circular track = 75 ft

Coordinates of the jogger: (45, 60)

We know that the coordinates of a point in the Cartesian plane can be represented as (x, y), where x represents the horizontal displacement and y represents the vertical displacement.

Let us now consider a jogger who runs around a circular track of radius 75 ft, with the center of the track being the origin. Therefore, the horizontal and vertical displacements of the jogger will be its coordinates, respectively.

Let us now consider a right-angled triangle with the hypotenuse representing the radius of the circular track, and the vertical and horizontal sides representing the y and x coordinates of the jogger, respectively. Since the radius of the circular track is constant, we can use the Pythagorean theorem to relate x and y.

Since we know that the radius of the track is 75 ft, we can say that:

\(\[x^2 + y^2 = 75^2\]\)

Differentiating with respect to time t, we get:

\(\[\frac{d}{dt}(x^2 + y^2)\)

= \(\frac{d}{dt}(75^2)\]\\\2x \cdot \frac{dx}{dt} + 2y \cdot \frac{dy}{dt} = 0\]\)

Now, since we are given that the jogger's coordinates are (45, 60), we can substitute these values to obtain:

\(\[2(45) \cdot \frac{dx}{dt} + 2(60) \cdot \frac{dy}{dt} = 0\]\)

On solving, we obtain:

\(\[\frac{dy}{dt} = -\frac{3}{4}\cdot \frac{dx}{dt}\]\)

Hence, the rate at which the y-coordinate of the jogger is changing is \({-\frac{3}{4}}\) times the rate at which the x-coordinate of the jogger is changing.

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a) The value of y₁(t) can be found by evaluating t₃ at t = 2, which gives y₁(t) = 8.

(b) The value of y₂(t) can be found by evaluating cos(t) at t = π/3, which gives y₂(t) = cos(π/3) = 1/2.

(c) The value of y₃(t) can be found by evaluating -1 - 3t₅ at t = 2, which gives y₃(t) = -1 - 3(2)^5 = -193.

The sampling property of impulses states that when an impulse function δ(t - a) is multiplied with a function f(t), the value of f(t) at t = a is obtained. Using this property, we can compute the given integrals involving impulse functions.

(a) For y₁(t), we have y₁(t) = ∫(t³ * δ(t - 2)) dt. Since δ(t - 2) is non-zero only when t = 2, we evaluate t³ at t = 2, giving y1(t) = 2³ = 8.

(b) For y₂(t), we have y₂(t) = ∫(cos(t) * δ(t - π/3)) dt. Since δ(t - π/3) is non-zero only when t = π/3, we evaluate cos(t) at t = π/3, giving y₂(t) = cos(π/3) = 1/2.

(c) For y₃(t), we have y₃(t) = ∫((-1 - 3t⁵) * δ(t - 2)) dt. Since δ(t - 2) is non-zero only when t = 2, we evaluate (-1 - 3t⁵) at t = 2, giving y₃(t) = -1 - 3(2)⁵ = -193.

Therefore, the values of y₁(t), y₂(t), and y₃(t) are 8, 1/2, and -193, respectively.

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The angle in the capital letter "L" measures 90°, making it a right angle.

A right angle is one that is exactly 90 degrees, or half of a straight angle. There is usually a quarter turn in it. The fundamental geometric forms, rectangle, and square, each have four angles that measure 90 degrees.

When two lines cross, and there is a 90-degree angle between them, the lines are said to be perpendicular. A few examples of 90-degree angles in real life include the angle between the hands of a clock at 3 o'clock, the angles between two neighboring sides of a rectangular door or window, etc.

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