Can someone help me with the questions in the picture?

Answer:

26 m and 20 m

Step-by-step explanation:

Let the length of the room be l, the breadth be b and perimeter be P.

Given:

Since P = 2(l + b), P/2 = l +b, we have following equations:

Substituting l in first equation:

Then the length is:

Frequency tables are used to show the number of occurrence of each data in a dataset.

The complete frequency table is as follows:

\(\begin{array}{cc}{Trick}&{Years}\\52&0&53&1&54&2&55&1&56&2\end{array}\right]\)

The given data are:

54, 56, 53, 54, 56, 55

To complete the frequency table, we simply count each data element and the number of occurrence (i.e. the frequency).

So, we have:

52 has a frequency of 0

53 has a frequency of 1

54 has a frequency of 2

55 has a frequency of 1

56 has a frequency of 2

So, the complete frequency table is:

\(\begin{array}{cc}{Trick}&{Years}\\52&0&53&1&54&2&55&1&56&2\end{array}\right]\)

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Answer:

12

Step-by-step explanation:

Ratio of adults to children = 3 : 11

Let

x = number of adults at the party

32 + x = number of children at the party

Ratio of adults to children = x : (32 + x

Equate both ratios

3 : 11 = x : 32 + x

3/11 = x : (32 + x)

Cross product

3 * (32 + x) = 11 * x

96 + 3x = 11x

96 = 11x - 3x

96 = 8x

x = 96/8

x = 12

x = number of adults at the party = 12

The formula to find the tangent line to a curve at a given point is y = f'(x) (x - x₀) + f(x₀).

The derivative of the function, f'(x) is calculated at the given point, x₀. Then, the equation of the tangent line is found by substituting the x₀ and f'(x) values into the formula.

To find the tangent line to a curve at a given point, the formula for the slope of the tangent line must be used. The slope of a tangent line is equal to the derivative of the function at that point. The resulting equation is a line with a slope equal to the derivative of the function at the given point, and a y-intercept equal to the value of the function at the given point. For example, if you want to find the tangent line to the function f(x) = 4x² + 3 at the point (2, 19), the derivative of the function at that point is f'(x) = 8x = 8(2) = 16. Then, the equation of the tangent line is y = 16(x - 2) + 19.

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Answer:

x = 120

z = 21

Step-by-step explanation:

x and 60 are supplementary, so added together they make 180.

x + 60 = 180

subtract 60 from both sides

x = 180 - 60

x = 120

next, x and 4z+36 are equal, so you can make this equation:

x = 4z + 36

substitute x for 120 as established earlier.

120 = 4z + 36

subtract 36 from both sides

120 - 36 = 4z

84 = 4z

divide both sides by 4

84/4 = z

21 = z

Answer:

b

Step-by-step explanation:

2m is term because it is what you are looking for

In the expression 4(2m-n), (2m-n). is a term and  In expression 4(2m-n), 2m is also a term. The correct options are B and B for both.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or the number of variables multiplied but never added or subtracted.

Variables in certain words have a number in front of them. A term is defined as a single number or single variable or number and variable multiplying with each other in a mathematics expression.

The first expression is 4(2m-n), then in the expression 2m - n will be the term of the expression.

The second expression is 4(2m-n), then in the expression 2m is the term of the expression.

Therefore, the expression 4(2m-n), (2m-n). is a term and  In expression 4(2m-n), 2m is also a term.

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Answer:

constant temperature is -56.5°C (-69.7°F), and this is also the lowest assumed temperature in respect to ISA.

The percentage of students who scored between 340 and 458 on the exam is 47.1%, rounded to 3 significant figures.

To solve this problem, we need to standardize the values of 340 and 458 using the given mean and standard deviation. We can then use the standard normal distribution table or a calculator to find the area under the standard normal curve between the standardized values.

The standardized value for 340 is:

z = (340 - 458) / 59 = -1.998

The standardized value for 458 is:

z = (458 - 458) / 59 = 0

Using a standard normal distribution table or a calculator, we can find that the area under the standard normal curve between -1.998 and 0 is approximately 0.471. This means that about 47.1% of the students scored between 340 and 458 on the exam.

Therefore, the percentage of students who scored between 340 and 458 on the exam is 47.1%, rounded to 3 significant figures.

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The characteristic of an experiment where the binomial probability distribution is applicable is that exactly two outcomes are possible on each trial.

What is the binomial probability distribution?

The binomial probability distribution is a probability model that is used to evaluate the probability of having an exact number of successes in a particular number of independent trials that have two possible outcomes (success and failure).

The characteristics of an experiment where the binomial probability distribution is applicable are as follows: It is an experiment that comprises a set of trials with a fixed number of independent trials.

It has only two outcomes, namely success and failure. The trials are independent of each other.

The probability of success is constant for each trial of the experiment.

The binomial distribution has a discrete set of outcomes. Each of these outcomes is measured by a single random variable that takes on only one of two possible values. Exactly two outcomes are possible on each trial. The experiment is a random variable that can be counted by counting the number of successes (X) in n trials.

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Answer:

The answer is 98 square cm

Step-by-step explanation:

14/2=7

14*7=98

The percentage change from 92 to 108 is 13.4% approx

What is Percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term per cent refers to one hundred percent.

Solution:

Percentage = Change / Original * 100

Change = 108 - 92 = 16

Original/Initial Value = 92

Percentage Change = 16/92 * 100 = 17.39% = 17.4% (approx)

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Answer:

uh 36

Step-by-step explanation:

did you really need this answer or did u just felt like giving away points

The radius of convergence R of the Taylor series is 2

The term convergence in math is defined as the process of a sequence or other function converging to a limit in a metric space.

Here we have know that the expression is written as,

=> f(x)=ln x, c=2.

By using the Taylor series formula we can write the expression like the following,

=> f(x) = ln(2) + ∑ (-1)ⁿ⁺¹ / n (2ⁿ)

Then the above power series will converge if and only if:

\(= > \lim_{n \to \infty} |\frac{-1}{(1+\frac{1}{n} )\times2}\times(x-2) | < 1\)

When we simplify this one then we get,

=> |x-2/2| < 1

Then the value of x lies between 0 to 4.

And the Radius of convergent is 2.

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Answer:

x = 100

Step-by-step explanation:

You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.

Answer:

30.25 seconds

Step-by-step explanation:

If you want to find the time at which the wrench hits the ground, you must recognize that the height of the wrench is 0 feet. If h represents the height, then 0 can be plugged in for h. The equation is now 0=16x+484. You then must subtract 484 from both sides, giving you -484=16x. You then divide both sides by 16 to give you x by itself. -484/16=-30.25. Because this is dealing with time and negative time does not exist, the negative sign on the 30.25 can be neglected.

Answer: 9500000

Step-by-step explanation: 95 × 100000 = 9500000

*Multiply the value by 100000*

a) Marginal PDF of X and marginal pdf of Y:fX(x) = 0.5x for 0 < x < 2.

b)The conditional PDF of Y given X = x is fY|X(y|x) = 1 / x for 0 < y < x < 2.

c)The conditional PDF of X given Y = y is fX|Y(x|y) = 1 / (2 - y) for 0 < y < x < 2.

d) E(X) = 4/3and E(Y)= 2/3

e) Var(X)= = 2/9 and Kar(K)= 2/9, Cov(X, Y) = 10/9

f)The correlation coefficient of X and Y is 5.

To find the marginal PDF of X, the joint PDF over the range of Y:

fX(x) = ∫[0 to 2] f(x, y) dy

Since the joint PDF f(x, y) = 1/2 for 0 < y < x < 2, the integral as follows:

fX(x) = ∫[0 to x] (1/2) dy

= (1/2) ×[y] evaluated from 0 to x

= (1/2) × (x - 0)

= 1/2 × x

= 0.5x, for 0 < x < 2

The conditional PDF of Y given X = x can be found using the joint PDF and the marginal PDF of X. The conditional PDF is given by:

fY|X(y|x) = f(x, y) / fX(x)

Given that f(x, y) = 1/2 for 0 < y < x < 2 and fX(x) = 0.5x for 0 < x < 2, substitute these values:

fY|X(y|x) = (1/2) / (0.5x)

= 1 / x, for 0 < y < x < 2

Similar to part (b), the conditional PDF of X given Y = y can be found using the joint PDF and the marginal PDF of Y. The conditional PDF is given by:

fX|Y(x|y) = f(x, y) / fY(y)

Given that f(x, y) = 1/2 for 0 < y < x < 2 and the marginal PDF of Y, fY(y) = ∫[y to 2] (1/2) dx, the integral:

fX|Y(x|y) = (1/2) / ∫[y to 2] (1/2) dx

= (1/2) / [(1/2) ×(2 - y)]

= 1 / (2 - y), for 0 < y < x < 2

E(X) = ∫[0 to 2] x × fX(x) dx

= ∫[0 to 2] x × (0.5x) dx

= 0.5 ∫[0 to 2] x² dx

= 0.5 × (1/3) × [x³] evaluated from 0 to 2

= 0.5 × (1/3) × (2³ - 0³)

= 0.5 × (1/3) × 8

= 4/3

E(Y) = ∫[0 to 2] y × fY(y) dy

= ∫[0 to 2] y × ∫[y to 2] (1/2) dx dy

= ∫[0 to 2] y × (1/2) × (2 - y) dy

= (1/2) × ∫[0 to 2] (2y - y²) dy

= (1/2) ×[(y²) - (1/3)y³] evaluated from 0 to 2

= (1/2) × [(2²) - (1/3)(2³) - 0]

= (1/2) × [4 - (8/3)]

= (1/2)× (12/3 - 8/3)

= (1/2) × (4/3)

= 2/3

e) Variances and Covariance:

Var(X) = E(X²) - [E(X)]²

Var(Y) = E(Y²) - [E(Y)]²

Var(X) = ∫[0 to 2] x² ×fX(x) dx - [E(X)]²

= ∫[0 to 2] x² × (0.5x) dx - (4/3)²

= 0.5 × ∫[0 to 2] x³ dx - (4/3)²

= 0.5 × (1/4) ×[x³] evaluated from 0 to 2 - (16/9)

= 0.5 × (1/4) × (2³ - 0³) - (16/9)

= 0.5 × (1/4) × 16 - (16/9)

= 2 - (16/9)

= 2/9

Var(Y) = ∫[0 to 2] y² × fY(y) dy - [E(Y)]²

= ∫[0 to 2] y² × ∫[y to 2] (1/2) dx dy - (2/3)²

= (1/2) × ∫[0 to 2] y² × (2 - y) dy - (2/3)²

= (1/2) ×[(2/3)y³ - (1/4)y²] evaluated from 0 to 2 - (4/9)

= (1/2) × [(2/3)(2³) - (1/4)(2²) - 0] - (4/9)

= (1/2) × [(16/3) - (16/4)] - (4/9)

= (1/2) ×[(16/3) - (12/3)] - (4/9)

= (1/2) × (4/3) - (4/9)

= 2/3 - 4/9

= 6/9 - 4/9

= 2/9

Cov(X, Y) = E(XY) - E(X)E(Y)

= ∫∫[0 to 2] xy × f(x, y) dy dx - (4/3)(2/3)

= ∫∫[0 to 2] xy × (1/2) dy dx - (8/9)

= (1/2) × ∫∫[0 to 2] xy dy dx - (8/9)

= (1/2) × [(1/2)x × ∫[0 to x] y² dy] evaluated from 0 to 2 - (8/9)

= (1/2) × [(1/2)x × (1/3)y³] evaluated from 0 to x, evaluated from 0 to 2 - (8/9)

= (1/2) × [(1/2)x × (1/3)x³ - 0] evaluated from 0 to 2 - (8/9)

= (1/2) × [(1/2)(2) × (1/3)(2³) - 0] - (8/9)

= (1/2) × [1/2 ×8 - 0] - (8/9)

= (1/2) × [4 - 0] - (8/9)

= (1/2) × 4 - (8/9)

= 2 - (8/9)

= 18/9 - 8/9

= 10/9

f) Correlation coefficient:

The correlation coefficient (ρ) of X and Y is given by:

ρ = Cov(X, Y) / sqrt(Var(X) × Var(Y))

Using the values

ρ = (10/9) / sqrt((2/9) × (2/9))

= (10/9) / (2/9)

= 10/2

= 5

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The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

Object b

Step-by-step explanation:

So you see that when you look at the graph it shows two point and you would think A is bigger because its higher. So when looking closely it look that object B is a lot farther that object A making it greater than object A because A is a lot higher but time is shorter than abject B.

This might be wrong so sorry I tried.

:)

Answer:

A

Step-by-step explanation:

You could do a calculation.

A: d/t = 10 / 2 = 5 m/s

B: d/2 = 4/3 = 1.33 m/s

A has the greater unit rate.

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

the expression has 3 terms

Step-by-step explanation:

Hope it helps

Step-by-step explanation:

the smallest :13

the largest :75

Answer:

smallest :13

largest :75

Answer:

48.0 m

Step-by-step explanation:

12.0*4 = 48.0m

The first four terms and the stated term, with an as the first term, are given the arithmetic sequence: 11 + 9n, a6.

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The graph represents this system of inequalities:

F. y ≤ −x + 4

G. y ≤ 3x − 1

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line of f(x) which passes through the points (0, 4) and (4, 0) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (4 - 0)/(0 - 4)(x - 4)

y - 0 = -1(x - 4)

y = -x + 4

Therefore, an inequality representing the line of f(x) is y ≤ -x + 4

For the line of g(x), we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-1) = (5 - (-1))/(2 - 0)(x - 0)

y + 1 = 3(x - 0)

y = 3x - 1

Therefore, an inequality which represents the line of g(x) is y ≤ 3x - 1.

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Complete Question:

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line. The graph represents which system of inequalities?

y ≤ −3x − 1

y ≤ −x − 4

y > −3x + 1

y ≤ −x − 4

y < 3x − 1

y ≤ −x + 4

y ≤ 3x − 1

y ≥ −x + 4