00 Σ() 3)". =1 5n+ 1 (1 point) Consider the series Evaluate the the following limit. If it is infinite, 2n3 + 3 type "infinity" or "inf". If it does not exist, type "DNE". lim vanl = n-00 Answer: L = = What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive" Answer: Divergent Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent". Answer: Divergent

Answer:

C.

Step-by-step explanation:

The pattern is the amount of sides each shape has.

Triangle - 3

Rectangle - 4

Pentagon - 5

Logically, the next shape would be a hexagon, a shape with 6 sides.

Answer: 6 inches and a width of 4 inches

Step-by-step explanation:

Answer:

The length is 6 and the width is 3

Step-by-step explanation:

Original length: 0.5

0.5 x 12 (scale factor) = 6

0.25 x 12 (scale factor) = 3

The height of the flagpole with a 60-foot shadow with maintaining the given ratio will be 37.5 feet.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

A 10-foot flagpole casts a 16 foot

The ratio of the flagpole's actual height to the length of the shadow

⇒ 10/16

Let's say the height of flagpoles whose shadow is 60 feet.

The ratio of the flagpole's actual height to the length of the shadow,

⇒ x/60

Both ratios must be the same.

Therefore, x/60 = 10/16

x = 600/16 = 37.5 foot.

Hence "The height of the flagpole with a 60-foot shadow with maintaining the given ratio will be 37.5 feet".

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If the chi-square test's expected frequencies rule is broken, either the row or the column is combined to provide a higher frequency that can be used to run the independence test.

Generally speaking, if more than 20% of the anticipated frequencies have a value of less than 5, Chi-Square should not be used (it does not matter what the observed frequencies are).

Both the chi-square test and Fisher's exact test are inappropriate if the sampled values' independence is broken. This presumption will be broken if the same subject results in more than one observation in the contingency table.

There are distinct assumptions for each non-parametric test as well. The data in the cells should represent frequencies or counts of cases rather than percentages or other data transformations, according to the Chi-presumptions. square's The variables' levels are mutually exclusive.

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The theorem that applies to the similar triangles is AA theorem.

Similar triangles are triangle with same shapes but may be different sizes.

Similar triangle have corresponding sides as a ratio of each other.

The triangles above have two of their angles equal, therefore, the triangles are similar.

They are similar by AA theorem.

AA theorem of similarity states that If two of angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.

30 ≅ 30

95 ≅ 95

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To prove that I₁ ...In = I₁ · ... · In, we need to show that both sets contain the same elements.

First, we will show that I₁ ...In ⊆ I₁ · ... · In. Let x ∈ I₁ ...In. This means that x can be written as a product of elements, where each element is in one of the ideals I₁,...,In. Since I₁,...,In are R-ideals, this product is also in each of the ideals I₁,...,In. Therefore, x ∈ I₁ · ... · In.

Next, we will show that I₁ · ... · In⊆ I₁ ...In. Let x ∈ I₁ · ... · In. Then x can be written as a product of elements, where each element is in one of the ideals I₁,...,In. By assumption, each ideal I_i has a complement in the form of another ideal J_i such that I_i + J_i = R. Since the product of elements in I_i can be multiplied with elements in J_j without restriction, we can replace each element in the product with an element in its complement. Specifically, let x_i ∈ I_i and y_i ∈ J_i such that x = x₁y₁...x_ny_n. Then each x_i ∈ I_i and y_i ∈ J_i, and since I_i + J_i = R for all i, we can write 1 as a sum of products of elements in the complements J_i. Specifically, 1 = ∑j_1∈J₁...∑j_n∈J_n p(j₁, ... , j_n) where p(j₁, ... , j_n) is a product of elements of the form y_i or y_i y_j where j ≠ i. Multiplying x by this expression, we get:

x = x(∑j_1∈J₁...∑j_n∈J_n p(j₁, ... , j_n)) = ∑j_1∈J₁...∑j_n∈J_n (x₁j₁...x_nj_n)y₁...y_n

Each term in this sum is in I₁...In since each term contains an element from I_i and an element from J_i for each i. Therefore, x ∈ I₁...In.

Combining the two inclusions, we have shown that I₁...In = I₁ · ... · In.

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The image of the given point (2, -1, -3) is (-4, 1, -3). and , the required pre-image of the given point (-1, 5, 2) is (1, 2).

Let T(x,y) = (-x + y + z, -x - 3y + 2z, z)

Here is the solution to the given problem.

Image of the given point (2, -1, -3):T(2, -1, -3) = (-2 + 1 - 3, -2 - 3 + 6, -3)= (-4, 1, -3)

Therefore, the image of the given point (2, -1, -3) is (-4, 1, -3).

Pre-image of the given point (-1, 5, 2):

We have T(x,y) = (-x + y + z, -x - 3y + 2z, z)

Now, we can equate T(x,y) = (-1, 5, 2)as (-x + y + z, -x - 3y + 2z, z) = (-1, 5, 2)

Comparing the first element, we have,-x + y + z = -1y = x + z - 1

Comparing the second element, we have,-x - 3y + 2z = 5-x - 3(x + z - 1) + 2z = 5-4x - z = 8z = 4x - 3

Now, comparing the third element, we have z = 2

We get z = 2 from the third element above.So, x = 1, from the first element

y = 2 from the relation obtained earlier

Therefore, pre-image of the given point (-1, 5, 2) is (1, 2).

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Answer:

Step-by-step explanation:

b

Answer:

\(-15\)

Step-by-step explanation:

\(11-(-2)\\11+2\\13\)

Line KL has a range of 13.

Line JK has the same range covered as line KL.

\(-2-13\)

\(-15\)

J is located at -15.

Answer:

33.1 years

Step-by-step explanation:

Let x be the number of years it takes for the population to reach 49000.

Starting with a population of 19000 and growing at 4.5% per year, the population after t years can be represented by the exponential function:

P(x) = 19000(1 + 0.045)^x

We want to find the value of x that makes P(x) = 49000.

=> 49000 = 19000(1 + 0.045)^x

Dividing both sides by 19000, we get:

=> 2.57895 = 1.045^x

Taking the logarithm of both sides with base 10, we get:

=> log(2.57895) = x log(1.045)

=> x = log(2.57895) / log(1.045)

=> x ≈ 33.1

Therefore, it will take approximately 33.1 years for the population to reach 49000.

Answer: 21.5 cause i got the answer wrong and they gave me the correct answer

Answer:

a. 0.81

b. 0.81

Step-by-step explanation:

Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.

So if he makes 90% of his free throws, then:

a. The probability that he will make both free throws is (90/100)^2 = 0.81.

b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.

The answers to the questions rounded to 4 decimal places are:

a. 0.81

b. 0.81

Answer:

A)3.375

Step-by-step explanation:

0.75 * 4.5 = 3.375

Answer: A)3.375

Few years late

Rahul ate more tangerines...

Answer:

In reality, the 5's go on forever, but we have to round off somewhere.

========================================================

Explanation:

Break up the triangles as your teacher recommends. See the diagram below as to what I mean.

The smaller triangle has A = 8 as the horizontal side, and B = x as the vertical side

The larger triangle has C = 10+8 = 18 as the horizontal aside, and D = 8 as the vertical side.

We can form the proportion A/C = B/D.

A/C connects the horizontal sides (small/large) while B/D has the vertical sides tied together. The order of division is the same small over large. You could do large over small, but make sure you keep both sides consistent.

-----------------

Let's solve for x

A/C = B/D

8/18 = x/8

8*8 = 18*x .... cross multiply

64 = 18x

18x = 64

x = 64/18 .... divide both sides by 18

x = 32/9  exactly in fraction form

x = 3.556 approximately in decimal form

-------------------

Another proportion you can solve is A/B = C/D and you should get the same x value. It's the same as A/C = B/D because the B and C swap places. There are many other approaches you could take using different proportions.

The probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

To find the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur, we need to determine the individual probabilities of each event and then multiply them together since the events are independent.

Event A: The coin lands on heads

A fair coin has two equally likely outcomes, heads or tails. Since we are interested in the probability of heads, there is only one favorable outcome out of two possible outcomes.

P(A) = 1/2

Event B: The die is 5 or greater

A fair six-sided die has six equally likely outcomes, numbers 1 through 6. Out of these six outcomes, there are two favorable outcomes (5 and 6) for Event B.

P(B) = 2/6 = 1/3

To find the probability of both events occurring (A and B), we multiply the individual probabilities:

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6

Therefore, the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

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The coordinate pairs of vertices  D₅ (△JKL) of  are J'(-15,-10), K'(5,20) and L'(20,10).

What does a math definition of a coordinate plane mean?

A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is a single number line that runs horizontally. The y-axis is the name given to the vertical number line that is the other number line.

                              A place known as the origin is where the two axes collide. To graph points, lines, and other things, we can utilize the coordinate plane.

We know that, D₅ (△JKL) means triangle JKL dilated by scale factor 5 with origin as center of dilation.

If a figure is dilated by factor k and origin is the center of dilation, then

    ( x, y )    ⇒ ( kx , ky )

 From the given problem, the rule of dilation is

       ( x , y ) ⇒ ( 5x , 5y )

Now

    J( -3 , -2 ) ⇒ J'( 5(-3), 5(-2)) = J'( -15 , -10 )

  K( 1,4 ) ⇒ K'(5(1) , 5(4)) = K'( 5,20 )

   L( 4,2 ) ⇒ L'(5(4), 5(2)) = L'( 20,10 )

Therefore, the coordinate pairs of vertices  D₅ (△JKL) of  are J'(-15,-10), K'(5,20) and L'(20,10).

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Answer:

r = 3ft

Step-by-step explanation:

example of a cone-shaped hole is a funnel

V = 1/3 • π • r² • height

21π = 1/3 • π • r²• height

(21)3  = (1/3 • r² • 7)3

63/7 = (r² • 7)/7

√9 = √r²

r = 3

Answer:

Vertex form

y = -4(x + 3)^2 + 10

Standard form;

y = -4x^2-24x - 26

Step-by-step explanation:

Mathematically, we have the vertex form as

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

(h,k) represents the vertex

We have h as -3 and k as 10

y = a(x+3)^2 + 10

To get a, we substitute any of the points

Let us use (-1,-6)

-6 = a(-1+3)^2 + 10

-6-10 = 4a

4a = -16

a = -16/4

a = -4

So we have the equation as;

y = -4(x+3)^2 + 10

For the standard form;

We expand the vertex form;

y = -4(x + 3)(x + 3) + 10

y = -4(x^2 + 6x + 9) + 10

y = -4x^2 - 24x -36 + 10

y = -4x^2 -24x -26

Answer:

y = -4x + 12

Step-by-step explanation:

For a line to be parallel, it needs to have the same slope.

Point intercept form: y - y₁ = m (x - x₁)

Where y and x are just kept as y and x, y₁ and x₁ are the parts of a coordinate, and m = slope.

So, in order for the line to be parallel, it needs to have the same slope as the first equation. The slope of the line (which is the "m" in y = mx + b) is..

4x + y = 7

y = -4x + 7

So, m, or the slope, is -4.

Plug this, along with the coordinate the problem gives you into point-intercept form.

y - y₁ = m (x - x₁)

y - 8 = -4 (x - 1)

Simplify.

y - 8 = -4x + 4

Add 8 to both sides.

y = -4x + 12

\(2y = 3x + 6\\y = \frac{3}{2}x + \frac{6}{2} = \frac{3}{2}x + 3\)

Answer:

Carmela made $9 per hour

270÷30=9

Hope this helps !

Answer:

true

Step-by-step explanation:

Answer:

(4, 2 ) and (2, 4 )

Step-by-step explanation:

xy = 8 → (1)

y = - x + 6 → (2)

substitute y = - x + 6 into (1)

x(- x + 6) = 8

- x² + 6x = 8 ( subtract 8 from both sides )

- x² + 6x - 8 = 0 ( multiply through by - 1 )

x² - 6x + 8 = 0 ← in standard form

(x - 4)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 2 = 0 ⇒ x = 2

substitute these values into (2) for corresponding values of y

x = 4 : y = - 4 + 6 = 2 ⇒ (4, 2 )

x = 2 : y = - 2 + 6 = 4 ⇒ (2, 4 )

Here, we have a right triangle with a missing side length.

To determine the length of the missing side, apply pythagorean theorem

Where:

c is the longest side (hypotenuse) = 20

a = 16

Substitute values into the equation and solve for the missing side.

We have:

Subtract 256 from both sides:

Take the square root of both sides:

Therefore, the missing length is 12 units

ANSWER:

x = 12

Step-by-step explanation:

The answer is in the picture above

The partial fraction expansion of the given bilateral z-transform expression is to be found. It can be expressed as ???????? (z) = K1 z / (z - ???? ) + K2 z / (z - ???? ). The steps to determine the values of K1 and K2 will be explained.

To find the partial fraction expansion of the given expression, we first factorize the denominator as (z - ???? )(z - ???? ), where ???? and ???? are the roots of the denominator. In this case, the roots are 1/2 and -1/2.

Next, we express the expression as a sum of two fractions, with each fraction having a distinct root in the denominator. The partial fraction expansion can be written as:

???????? (z) = K1 z / (z - 1/2) + K2 z / (z + 1/2)

To determine the values of K1 and K2, we can multiply both sides of the equation by the common denominator (z - 1/2)(z + 1/2) and equate the numerators. This gives us:

z 2 (z 2 - 1/4) = K1 z(z + 1/2) + K2 z(z - 1/2)

Expanding and collecting like terms, we get:

z 2 (z 2 - 1/4) = (K1 + K2)z 2 + (K1/2 - K2/2)z

By comparing the coefficients of like powers of z on both sides, we can determine the values of K1 and K2. Equating the coefficients, we have:

K1 + K2 = 1

K1/2 - K2/2 = -1/4

Solving these equations simultaneously, we can find the values of K1 and K2, which will complete the partial fraction expansion.

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Answer:

the answer would be(0, -1) happy to help you ahmed

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

hope this helps

Answer:

43.7378554573

Step-by-step explanation:

use pythagoream thereom :D

Answer:

m∠RST= m RT= 60°

⭒⭒⭒⭒⭒⭒⭒⭒⭒⭒⭒⭒

✎--------------

hope it helps...

have a great day!!