What is (0.2 + -5) x (4.1) ?

The perimeter of ΔAEB is 18.5 feet.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

As,  side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.

Since, AE/AD = EB/ BF

AE/2 = 7.2/8.4

AE = 6.5 feet

So, the perimeter of ΔAEB is

= AE + EB + BE

=6.5+4.2+7.8

=18.5 ft.  

Hence, the perimeter  is 18.5 feet.

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Answer: 29.5

Step-by-step explanation:

Answer:

80 degrees

Step-by-step explanation:

The 132-deg angle is an exterior angle of the left triangle.

The 52-deg angle is a remote interior angle to the exterior angle above.

Angle VZY is also a remote interior angle to the exterior angle above.

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

We use the theorem above to find the measure of angle VZY.

52 + m<VZY = 132

m<VZY = 80

Angles WZX and VZY are vertical angles, so they are congruent.

m<WZX = m<VZY = 80

Answer: 80 degrees

Answer:

m∠WZX = 80°

Step-by-step explanation:

Angle V is a flat angle, so it measures 180°.

Find ∠YVZ (blue angle): 180° - 132° = 48°

Triangle VYZ is 180° (all triangles are 180°).

Find ∠YZV (red angle): 180° - 52° - 48° = 80°

Since you know ∠YZV, you can find ∠WZX (green angle).

∠YZV and ∠WZX are opposite angles, so they are congruent.

Therefore, ∠WZX = 80°

Hope this helps :)

Given:

\(OA=3\) units

\(OA'=9\) units

To find:

The scale factor of the dilation.

Solution:

From the given figure it is clear that the center of dilation is point O. Point A' is the image of point A. So,

\(\text{Scale factor}=\dfrac{OA'}{OA}\)

Putting the given values, we get

\(\text{Scale factor}=\dfrac{9}{3}\)

\(\text{Scale factor}=3\)

Therefore, the scale factor of the dilation is 3.

The limit of 1/n does not diverge.The difference of limit of 1/n is explained below.

It converges to 0 as n approaches infinity. The difference between a series and a limit is that a series is the sum of the terms in a sequence, while a limit is a value that a sequence approaches as its terms become increasingly large. In other words, the limit of a sequence is the "endpoint" of the sequence, while the series is the sum of all the terms in the sequence. In the case of 1/n, the series does not converge because the terms gradually increase with no endpoint. However, the limit of 1/n does converge because the terms become progressively smaller and approach 0 as n approaches infinity. Therefore, the limit of 1/n does converge, while the series of 1/n does not.

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Answer:

2.5h + 4 = 12 is your equation

2.5h = 12 - 4

2.5h = 8

h = 8 / 2.5

h = 3.2 hrs

Step-by-step explanation:

Answer:

2.5h + 4 = 12 is your equation

2.5h = 12 - 4

2.5h = 8

h = 8 / 2.5

h = 3.2 hrs

Answer:

The answer is D.

Step-by-step explanation:

Find the boundary line, and then just shade the area.

y < 1/2x + 2

Answer:

d

Step-by-step explanation:

2023

The portobello mushroom was growing faster.

Given that, Andrew has two mushrooms, he recorded their height, enoki mushroom was 3.9 centimeters tall, after 5 days, it was 4.8 centimeters tall.

Also, the height of the portobello mushroom is given by equation,

y = 0.2x + 4.1, where y is the height of the portobello mushroom in centimeters and x is the number of days since he brought it,

So,

Considering the portobello mushroom height, after 5 days,

y = 0.2(5) + 4.1 = 5.1 cm

And the enoki mushroom was 4.8 cm tall on its 5th day,

Since, the height of portobello mushroom is more than enoki mushroom on 5th day.

Hence, the portobello mushroom was growing faster.

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The set of real numbers includes both rational and irrational numbers.


1. Real numbers: Real numbers include all rational and irrational numbers. They can be represented on a number line and are not limited to whole numbers or integers.

2. Rational numbers: Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers. They can be written in the form a/b, where a and b are integers and b is not equal to 0. For example, 3/4, -2/5, and 0.6 are all rational numbers.

3. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. They cannot be written in the form a/b. Examples of irrational numbers include √2, π (pi), and e.

Therefore, the set of real numbers includes both rational and irrational numbers.

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Answer:

The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Step-by-step explanation:

Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).

To find the values in the domain where f(x) = 0, we look at the ordered pairs given.

We look for the pair in which f(x) = 0.

So f(x) = 0 in (-2.5, 0)

f(x) = 0 in (-0.75, 0)

and f(x) = 0 in (1, 0)

The corresponding values of x  in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Answer:

C. \(x=1\)

Step-by-step explanation:

When x is 1, y is 0.

Answer:

Domain is all real numbers if they want specifics ig you could say

{-4,-3, 0, 2, 3}

Step-by-step explanation:

Answer:

{-4,-3,-2,-1, 0, 1, 2, 3} <--assuming we are only using whole numbers

{-4,-3,0,2,3}  <-- If your only using the points given

Step-by-step explanation:

Domain is the x values

Range is the y values

3 is the farthest/biggest x value

-4 is the least/smallest x value

Therefore the domain is {-4,3}

But since the instructions say "write the numbers in the domain," assuming we are using only whole numbers, the answer is {-4,-3,-2,-1, 0, 1, 2, 3}.

BUT

{-4,-3,0,2,3} is the answer if you only are allowed to use the x values of the given points.

Answer:

X=1/7

Step-by-step explanation:

a. The probability that a randomly selected American worker does not take a single nap during a month is approximately 0.0183, or 1.83%.

b. The probability that the total number of naps for two randomly selected American workers during a month is zero is approximately 0.0336, or 3.36%.

In the first step, the probability of a randomly selected American worker not taking a single nap during a month is calculated. Since the mean number of naps per month is four, the probability of not taking a nap can be found by using the Poisson distribution with a mean of four.

The formula for the Poisson distribution is P(x; μ) = (e−μ * μx) / x!, where x is the number of naps and μ is the mean. Plugging in x = 0 and μ = 4 into the formula, we get P(0; 4) = \((e^(^-^4^) * 4^0) / 0!\) ≈ 0.0183.

In the second step, the probability of the total number of naps for two randomly selected American workers being zero is calculated. This can be done by finding the probability of each worker not taking a nap and then multiplying those probabilities together. Since the probability of a worker not taking a nap is 0.0183, the probability of both workers not taking a nap is 0.0183 * 0.0183 ≈ 0.0336.

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The length of the rectangular building is 80 meters, since the perimeter is 110 meters and the width is 1/4 of the length.

First, let's determine the width of the rectangular building. Since the length is four times the width, we can set up a proportion. Let x equal the width of the building. Then 4x will equal the length.

4x/x = 110/x

Simplifying this equation gives us:

4 = 110/x

Multiplying both sides by x gives us:

x = 110/4

The width of the building is 27.5 meters.

To find the length, we use the fact that the length is four times the width. So we multiply the width by 4:

Length = \(27.5 * 4 = 110\) meters

Therefore, the length of the rectangular building is 80 meters.

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Answer:

\(\displaystyle{\sin \theta = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{a^2-b^2}{2ab}}\)

Step-by-step explanation:

We are given that:

\(\displaystyle{\tan \theta = \dfrac{2ab}{a^2-b^2}}\)

To find other trigonometric ratios, first, we have to know that there are total 6 trigonometric ratios:

\(\displaystyle{\sin \theta = \sf \dfrac{opposite}{hypotenuse} = \dfrac{y}{r}}\\\\\displaystyle{\cos \theta = \sf \dfrac{adjacent}{hypotenuse} = \dfrac{x}{r}}\\\\\displaystyle{\tan \theta = \sf \dfrac{opposite}{adjacent} = \dfrac{y}{x}}\\\\\displaystyle{\csc \theta = \sf \dfrac{hypotenuse}{opposite} = \dfrac{r}{y}}\\\\\displaystyle{\sec \theta = \sf \dfrac{hypotenuse}{adjacent} = \dfrac{r}{x}}\\\\\displaystyle{\cot \theta = \sf \dfrac{adjacent}{opposite} = \dfrac{x}{y}}\)

Since we are given tangent relation, we know that \(\displaystyle{y = 2ab}\) and \(\displaystyle{x = a^2-b^2}\), all we have to do is to find hypotenuse or radius (r) which you can find by applying Pythagoras Theorem.

\(\displaystyle{r=\sqrt{x^2+y^2}}\)

Therefore:

\(\displaystyle{r=\sqrt{(a^2-b^2)^2+(2ab)^2}}\\\\\displaystyle{r=\sqrt{a^4-2a^2b^2+b^4+4a^2b^2}}\\\\\displaystyle{r=\sqrt{a^4+2a^2b^2+b^4}}\\\\\displaystyle{r=\sqrt{(a^2+b^2)^2}}\\\\\displaystyle{r=a^2+b^2}\)

Now we can find other trigonometric ratios by simply substituting the given information below:

Hence:

\(\displaystyle{\sin \theta = \dfrac{y}{r} = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{x}{r} = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{r}{y} = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{r}{x} = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{x}{y} = \dfrac{a^2-b^2}{2ab}}\)

will be other trigonometric ratios.

Answer:

-20x

Step-by-step explanation:

remove parentheses: -4*5x

multiply the numbers: -4*5x

answer: -20x

The matrix A has two distinct eigenvalues: λ1 = 4 with a multiplicity of 2 and λ2 = 0 with a multiplicity of 2. The eigenspace corresponding to λ1 is spanned by the vectors [1 0 0 0] and [0 1 0 0], while the eigenspace corresponding to λ2 is spanned by the vectors [0 0 1 0] and [0 0 0 1].

To find the eigenvalues and eigenvectors of a matrix, we solve the equation (A - λI)X = 0, where A is the matrix, λ is the eigenvalue, I is the identity matrix, and X is the eigenvector.

In this case, let's subtract λI from the matrix A:

A - λI = [2-λ 2 0 0]

[2 2-λ 0 0]

[0 0 -λ 0]

[0 0 0 -λ]

To find the eigenvalues, we set the determinant of (A - λI) equal to zero:

det(A - λI) = (2-λ)(2-λ)(-λ)(-λ) = 0

Solving this equation, we find two distinct eigenvalues: λ1 = 4 and λ2 = 0, each with a multiplicity of 2.

To find the eigenvectors corresponding to each eigenvalue, we substitute the eigenvalues back into the equation (A - λI)X = 0 and solve for X.

For λ1 = 4:

(A - 4I)X = 0

[2-4 2 0 0] [x1] [0]

[2 2-4 0 0] [x2] = [0]

[0 0 -4 0] [x3] [0]

[0 0 0 -4] [x4] [0]

Simplifying this system of equations, we get:

[-2 2 0 0] [x1] [0]

[2 -2 0 0] [x2] = [0]

[0 0 -4 0] [x3] [0]

[0 0 0 -4] [x4] [0]

Solving each equation, we find that x1 = x2 and x3 = x4. Therefore, we can express the eigenvectors as:

X1 = [x1 x1 0 0] = x1 [1 1 0 0]

X2 = [x3 x3 0 0] = x3 [0 0 1 1]

Hence, the eigenspace corresponding to λ1 = 4 is spanned by the vectors [1 1 0 0] and [0 0 1 1].

For λ2 = 0:

(A - 0I)X = 0

[2-0 2 0 0] [x1] [0]

[2 2-0 0 0] [x2] = [0]

[0 0 -0 0] [x3] [0]

[0 0 0 -0] [x4] [0]

Simplifying this system of equations, we get:

[2 2 0 0] [x1] [0]

[2 2 0 0] [x2] = [0]

[0 0 0]

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Answer:

Step-by-step explanation:

Yes, you can perform row echelon form on a calculator. Most scientific or graphing calculators have a built-in matrix function that can perform row operations and row echelon form.

To do row echelon form on a calculator, you typically input the matrix, perform row operations to simplify the matrix, and then the calculator outputs the row echelon form of the matrix. The row echelon form of a matrix has the following properties:

The first non-zero element in each row is called a leading 1, and is to the right of the leading 1 in the previous row.

Each leading 1 is the only non-zero element in its column.

All elements above and below a leading 1 are 0.

By using the row echelon form of a matrix, you can quickly determine the solutions to a system of linear equations represented by the matrix. This makes it a valuable tool for solving linear algebra problems.

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Answer:

2/1

Step-by-step explanation:

(a) The inequality ∣x∣² ≤ ∣x∣ᵠn²¹/q is proven for q ≥ 2. (b) The inequality E∣X∣ᵠ ≤ 4σn²¹/q is proven for q > 1. (c) Using the bound, E[max₁≤i≤n ∣Xᵢ∣] ≤ 4eσlog(n) is derived.

(a) The inequality ∣x∣² ≤ ∣x∣ᵠn²¹/q is proven by using Hölder's inequality. It shows that for any vector x in Rᵈ and q ≥ 2, the ℓ²-norm of x is bounded by the ℓᵠ-norm of x scaled by n²¹/q. This inequality cannot be improved.

(b) By applying Jensen's inequality and using the fact that Xᵢ is sub-Gaussian with variance proxy σ² and E(Xᵢ) = 0, it is proven that E∣X∣ᵠ ≤ 4σn²¹/q holds for q > 1.

(c) From the bound E∣X∣ᵠ ≤ 4σn²¹/q, it follows that E[max₁≤i≤n ∣Xᵢ∣] ≤ 4eσlog(n) by setting q = log(n) and using the fact that n > 1. This shows that the expectation of the maximum absolute value of the entries of X is bounded by 4eσlog(n).

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We can see that there are 6 sections and three of them are yellow. So, the theoretical probability of the spinner landing on the yellow section is:

3 ( yellow sections)/ 6 (Total number of sections)

3/6 = 1/2 (Simplifying)

The answer is 1/2.

The second is a Uniform distribution with a minimum value of 50 and a maximum value of 100, where all values have equal frequencies.

Frequency distribution is a statistical representation of the number of occurrences of each value in a set of data. Let's consider the given set of values and describe two types of distributions for it.

Distribution Type 1: Normal Distribution with mean = 75 and standard deviation = 25.

This distribution follows a bell-shaped curve that is symmetric around the mean value of 75. The standard deviation of 25 indicates that the data is spread out with a moderate amount of variability. The highest frequency occurs at the mean value of 75, and as we move away from the mean in either direction, the frequency gradually decreases. The distribution provides information about how the values are distributed around the mean.

Distribution Type 2: Uniform Distribution U[50, 100].

This distribution is characterized by a rectangular shape, where all values have the same frequency. In this case, the minimum value is 50, and the maximum value is 100, resulting in a range of 50. The frequencies are uniform throughout the distribution, meaning that each value has the same frequency. In this case, since there are seven values in the set, each value has a frequency of 1/7.

To summarize, the given set of values can be represented by two different distributions. The first is a Normal distribution with a mean of 75 and a standard deviation of 25, which shows the overall pattern and spread of the data.

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The plot that represents the data in the table is:A dot plot line labeled Ice Cream Flavors and titled Ice Cream. Four tick marks labeled Chocolate, Pistachio, Strawberry, and Vanilla. There is 1 dot above Chocolate, 3 above Pistachio, 2 above Strawberry, and 4 above Vanilla.

This plot accurately represents the number of friends who like each type of ice cream, with the corresponding number of dots above each flavor. In the given table, we have four different types of ice cream (Chocolate, Pistachio, Strawberry, and Vanilla) and the corresponding number of friends who like each flavor.

The plot that represents this data is a dot plot. A dot plot is a type of graph where dots are used to represent the frequency or count of a specific value. In this case, we are using dots to represent the number of friends who like each type of ice cream.

The dot plot has a horizontal line labeled "Ice Cream Flavors" and titled "Ice Cream". This line represents the x-axis. Above the line, there are four tick marks labeled with the names of the ice cream flavors (Chocolate, Pistachio, Strawberry, and Vanilla). These tick marks represent the different categories or values being plotted.

For each flavor, the plot shows the corresponding number of dots above it. The dots represent the count or frequency of friends who like that particular flavor. According to the table, there is 1 dot above Chocolate, 3 dots above Pistachio, 2 dots above Strawberry, and 4 dots above Vanilla.

By visualizing the dots above each flavor on the dot plot, we can easily compare the frequencies and see the distribution of ice cream preferences among the student's friends.

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Answer:

volume of a cylinder = 536.9 cm³

Step-by-step explanation:

volume of a cylinder, V = πr²h

where π = 3.14

h = 19 cm

r = ?

given is diameter = 6 cm

as we know, r = d/2 = 6/2 = 3 cm

by substituting the values in the formula,

V = 3.14 * 3² * 19

= 536.94 cm³

by rounding off to the nearest tenth place,

volume of a cylinder = 536.9 cm³

Answer:

v = 537.2 cm3

Step-by-step explanation:

volume:

\(v=\pi r^{2} h\)

\(r=d/2=6/2=3cm\)

\(h=19cm\)

\(v=\pi (3)^{2} (19)=171\pi\)

\(v=537.21\)

Rounded nearest tenth:

\(v=537.2cm^{3}\)

Hope this helps

Answer:

Step-by-step explanation:

To find:

Given:

\(\sf{7p+4=-p+9+2p+3p}\)

Isolate the term of p, from one side of the equation.

Combine like terms.

\(\rightarrow \sf{7p+4=-p+2p+3p+9}\)

Add the numbers from left to right.

-p+2p+3p=4p

7p+4=4p+9

Then, you subtract by 4 from both sides.

\(\sf{7p+4-4=4p+9-4}\)

Solve.

7p=4p+5

Subtract by 4p from both sides.

7p-4p=4p+5-4p

Solve.

\(\boxed{\sf{3p=5}}\)

Divide by 3 from both sides.

3p/3=5/3

Solve.

p=5/3

Divide is another option.

5/3=1.6666

So, the final answer is 3p=5.

I hope this helps, let me know if you have any questions.

Because the lines drawn are straight.

Explanation:

When the straight lines join together, the original point from where the first line started, becomes a right angle (90°)

Let's check each option:

a.

b.

c.

d.

Hence, the correct answers are options A and C.

Answer:

1/81

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

Parenthesis first, (6+3=9)^2 (9)^2 = 81-4 = 77

The parametric equations of the line of intersection between the planes x - y + z = 0 and x + 2y + 3z = 6 are x = 2t + 6, y = t, and z = -t - 6.



To find the parametric equations of the line of intersection between two planes, we need to determine a point on the line and find its direction vector.

First, we solve the system of equations formed by the two planes: x - y + z = 0 and x + 2y + 3z = 6. By eliminating x, we get -3y - 2z = -6.Setting y = t and z = s as parameters, we can express the point on the line as (x, y, z) = (2t + 6, t, s).Now, substituting these values into the first equation, we obtain 2t + 6 - t + s = 0, which simplifies to t + s = -6.

Therefore, the parametric equations for the line of intersection are:

x = 2t + 6

y = t

z = -t - 6, where t and s are parameters.

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