drag justifications into the table to explain each step in solvingthe equation


I need help with the last 3 blank spots.

Answer: second option.

Step-by-step explanation:

The formula used for calculate the lateral area of a cylinder is this one:

[tex]LA=2\pi rh[/tex]

Where "r" is the radius and "h" is the height

The formula for calculate the area of a circle (which is the base of a cylinder) is:

[tex]A=\pi r^2[/tex]

Knowing the area of the base, you can solve for the radius:

[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]

Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:

[tex]LA=2\pi (6units)(2units)[/tex]

[tex]LA=24\pi\ units^2[/tex]

For angles between 180° and 360°, only cosine (cos) and cosecant (csc) may yield a positive value. This is because these angles fall in the third and fourth quadrants of the unit circle where only certain functions yield positive results.

In the trigonometric functions, the sign of the function's result can vary depending on the size of the angle. For angles between 180° and 360°, only cosine (cos) and cosecant (csc), which is the reciprocal of sine, may have positive values.

In mathematics circle, these angles are in the third and fourth quadrants. In the third quadrant (180° ≤ θ < 270°), only the function tangent (tan) and its reciprocal cotangent (cot) can be positive. While in the fourth quadrant (270° ≤ θ < 360°), the functions cosine (cos) and its reciprocal secant (sec) can be positive.

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Answer:

Hence correct chcie is C.

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex]

Now it says that function is shifted 4 units to the left and 4 units up.

We need to find about which of the given choice is correct for the given transformation.

When f(x) is shifted "h" units left then we write f(x+h)

So [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex]

When f(x) is shifted "h" units up then we write f(x)+h

So [tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex] will change to

[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]

Answer:

C

Step-by-step explanation:

For a function f(x) = [tex]x^{\frac{1}{3}}[/tex], we have:

Keeping these translation rules in mind, we can clearly say that 4 units shifted left and 4 units up has the equation  [tex]f(x)=(x+4)^{\frac{1}{3}}+4[/tex]

correct answer is C

Answer:

6

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude (in this case, j) is equal to radical(g*f).

Therefore, j=√(g*f), j=√(3*12), j=6

Answer:

[tex]\boxed{6}[/tex]

Step-by-step explanation:

The Geometric Mean Theorem states that the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it creates.

Thus, in your triangle,

j = √(fg)

If f = 12 and g = 3,

j = √(12 × 3) = √ 36 = 6

[tex]\boxed{j = 6}[/tex]

Answer:

5 by 4 face = 20 * 2 = 40

5 by 7 face = 35 * 2 = 70

4 by 7 face = 28 * 2 = 56

Total surface area = 166 square meters

Answer is "b"

Step-by-step explanation:

Answer:

your answer will be A

Answer:

both

Step-by-step explanation:

Depending on how u look at it, one is comprised of 2d figures and the other is of 3d, but the 2d shapes combine to make the faces of any 3d shape, so its basically the same.

I believe it’s b or c... Hope this helps!

The sequence that shows geometric progression are options A), B), C), and E) and this can be determined by finding the geometric ratio.

Check all the options in order to determine which sequence is the geometric sequence.

A) 10, 7.5, 5.625, 4.21875,...

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{7.5}{10}[/tex]

r = 0.75

Ratio between second and third term:

[tex]\rm r =\dfrac{5.625}{7.5}[/tex]

r = 0.75

So, yes this sequence is in geometric progression.

B) 160, 40, 10, 2.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{40}{160}[/tex]

r = 0.25

Ratio between second and third term:

[tex]\rm r =\dfrac{10}{40}[/tex]

r = 0.25

So, yes this sequence is in geometric progression.

C) 20, 70, 245, 857.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{70}{20}[/tex]

r = 3.5

Ratio between third and fourth term:

[tex]\rm r =\dfrac{857.5}{245}[/tex]

r = 3.5

So, yes this sequence is in geometric progression.

D) 13, 16.5, 20, 23.5, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{16.5}{13}[/tex]

r = 1.27

Ratio between third and fourth term:

[tex]\rm r =\dfrac{23.5}{20}[/tex]

r = 1.175

So, no this sequence is not in geometric progression.

E) 5, 5.5, 6.05, 6.655, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{5.5}{5}[/tex]

r = 1.1

Ratio between third and fourth term:

[tex]\rm r =\dfrac{6.655}{6.05}[/tex]

r = 1.1

So, yes this sequence is in geometric progression.

F) 16, 17.1, 18.2, 19.3, …

Check from the geometric ratio whether the above sequence is a geometric sequence or not.

Ratio between first and second term:

[tex]\rm r =\dfrac{17.1}{16}[/tex]

r = 1.07

Ratio between third and fourth term:

[tex]\rm r =\dfrac{19.3}{18.2}[/tex]

r = 1.06

So, no this sequence is not in geometric progression.

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Answer:

1, 2, 3, 5

Step-by-step explanation:

**Cracks knuckles** let's do this.

Area of triangle = 31.25 yd^2

10 x 6.25 = 62.5

62.5 / 2 = 31.25

Area of rectangle A = 50 yd^2

10 (length) x 5 (7.5 - 2.5) (width) = 50

Area of rectangle B = 48.75 yd^2

7.5 x 6.5 = 48.75

Total area of composite = 130 yd^2

31.25 + 50 + 48.75 = 130

Answer:

5,000 meters * 1 kilometer / 1,000 meters = 5 kilometers answer is B

Step-by-step explanation:

Answer:

the answer is 5k

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

If 8 hours are spent the week, and there is only 1/4 used to play piano then you have to know how much 1/4 is of 8.

To get 1/4 of 8 you need to multiply 8 by 1/4.

The answer is 2.

Answer:

B

Step-by-step explanation:

Two times the quantity of a number minus 12.

Represent the number with the variable y.

The quantity of a number minus 12 is then: (y-12).

Two times this quantity is 2(y-12).

So the answer is 2(y-12), which is B.

Answer:

The 3rd person who drove 500 miles in 8 hours drove the fastest.  

Step-by-step explanation:

1st person : 60.5 mph

2nd person : 62.14 mph

3rd person : 62.5 mph

4th person : 43 mph

you simply divide the total miles driven by the amount of time and then you get the miles per hour.

Hope this helps!

Answer: Option A

[tex]P(A|B) = \frac{40}{49}[/tex]

Step-by-step explanation:

In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:

[tex]P(A|B) = \frac{P(A\ and\ B)}{P(B)}[/tex]

Then if [tex]P(A\ and\ B) = \frac{5}{7}[/tex] and [tex]P(B) = \frac{7}{8}[/tex] then:

[tex]P(A|B) = \frac{\frac{5}{7}}{\frac{7}{8}}\\\\P(A|B) = \frac{40}{49}[/tex]

Answer:

Correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].

Step-by-step explanation:

Given that [tex]P(A\cap B)=\frac{5}{7}[/tex], [tex]P(B)=\frac{7}{8}[/tex].

Now using those values , we need to find the value of [tex]P(A|B)[/tex].

So apply the formula of conditional probability:

[tex]P(A\cap B)=P(B) \times P(A|B)[/tex]

Plug the given values into above formula,  we get:

[tex]\frac{5}{7}=\frac{7}{8} \times P(A|B)[/tex]

[tex]\frac{7}{8} \times P(A|B)=\frac{5}{7}[/tex]

[tex]P(A|B)=\frac{\frac{5}{7}}{\frac{7}{8}}[/tex]

[tex]P(A|B)=\frac{5}{7}\cdot\frac{8}{7}[/tex]

[tex]P(A|B)=\frac{40}{49}[/tex]

Hence correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].

The geometric transformation shown in the figure is reflection.

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

here, we have,

Given is a set of lines in the music note.

Three line are drawn separating from a line.

In the first part, when we find the mirror image of the first part, we will get the second part.

Mirror images are found in the transformation of reflection.

So, here, we can say that reflection is the transformation here.

Hence the kind of geometric transformation shown in the line of music is reflection.

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Answer:

Domain = (-∞,∞)

Range: [0,∞)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)=|2x|-sin(x)

From the graph we can see that

- the domain is equal to all real numbers.

- The range goes from [0,∞)

The correct answer is option d, but bear in mind that the range includes zero as well, so it would be Range: [0,∞)

Answer:

Answer is D!!!

Step-by-step explanation:

Answer:

d. [tex]1.82\: or\:4.46[/tex]

Step-by-step explanation:

The given trigonometric equation is;

[tex]\sec \theta=-4.0545[/tex]

Recall that;

[tex]\cos \theta=\frac{1}{\sec \theta}[/tex]

[tex]\implies \cos \theta=\frac{1}{-4.0545}[/tex]

[tex]\implies \cos \theta=-0.2466[/tex]

The cosine function is negative in the second and third quadrant.

[tex]\theta=\pi-\cos^{-1}(0.2466)\: or\:\pi+\cos^{-1}(0.2466)[/tex]

[tex]\theta=1.82\: or\:4.46[/tex]

So I could be completely wrong, or I could be completely right, but quadrilaterals interior angles equal 360 degrees.

So, if you ad up 98, 72, and 65 you end up with 235 degrees.

In order to find the fourth angle, you would just subtract 235 from 360 and get 125 degrees.

BUT, maybe see if someone else answers too, because I am not 100% sure.

Answer:

1. We already have the measure of the hypotenuse and one out of two acute angle, therefore:

sin53° = x/45 => x = sin53° · 45 ≈35.94

2. We already have one out of two legs of the triangle and one acute angle so we know that:

tan27° = 48/x => x = 48/tan27° ≈ 94.21

The value of x in the first right angle triangle is 27.08.

The value of x in the second right angle triangle is 24.46.

In order to determine the value of x in the first triangle, cos would be used.

Cos 53 = opposite / hypotenuse

Cos 53 = x / 45

0.7071 = x /45

x = 45 x 0.6018

x = 27.08

In order to determine the value of x in the second triangle, tan would be used.

Tan 27 = opposite / adjacent

Tan 27 = x / 48

x = 0.5095 x 48  

x = 24.46

Answer:

2√21

Step-by-step explanation:

Diagonal =√(L²+W²+H²)

Diagonal =√(8²+4²+2²)=√(64+16+4)=√84=2√21

ANSWER

A. 150 units^2

EXPLANATION

The surface area of a cube is calculated using the formula:

[tex]SA=6 {l}^{2} [/tex]

where

[tex]l = 5[/tex]

We substitute the length to obtain:

[tex]SA=6 {l}^{2} [/tex]

[tex]SA=6 \times {5}^{2} [/tex]

[tex]SA=150 \: {units}^{2} [/tex]

Answer:

1. Not Independent

2. Independent

3. Not Independent

4. Independent

Step-by-step explanation:

Independent: An event is independent if the outcome of one event doesn't effect the outcome of the other event.

Not independent : An event is Not independent if the outcome of one event effect the outcome of other event.

1. A jar contains twenty coins. Two coins are picked randomly without replacement.

Not Independent because if coins are not replaced the outcome of next event will be effected.

2. A coin is flipped three times.

Independent because when a coin is flipped once its outcome doesn't effect the outcome of the coin flipped again

3. A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.

Not Independent because if balls are not replaced the outcome of next event will be effected.

4. A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.

Independent because when the spinner is spuned once its outcome doesn't effect the outcome of the spinner spun again

The correctcorrect probabilityprobability conditiony for each of the given situation as regards independent or not are;

A) Not Independent

B) Dependent

C) Not Independent

D) Dependent

An independent event is one that doesn't depend on the probability of another one happening while a dependent event is one that depends on the probability of another one happening.

A) A jar contains twenty coins. Two coins are picked randomly without replacement; This is not independent because when we do not replace a selected coin, it affects the outcome of the next choice.

B) A coin is flipped three times; This is dependent because a flip doesn't depend on another flip.

C) A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement; This is not independent because when we do not replace a selected ball, it affects the outcome of the next choice.

D) A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice; This is independent because spinning doesn't affect the outcome of the next spin.

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Answer:

126 cm²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals

The diagonals of a rhombus are perpendicular bisectors of each other, thus

d₁ = 7 + 7 = 14 and d₂ = 9 + 9 = 18, hence

A = 0.5 × 14 × 18 = 126 cm²

The area of the rhombus is equal to 126 cm². The correct option is B.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rhombus in a two-dimensional plane is called the area of the rhombus.

The area (A) of a rhombus is calculated as

A =  × d₁ × d₂ ← diagonals

The diagonals of a rhombus are perpendicular bisectors of each other,

d₁ = 7 + 7 = 14

d₂ = 9 + 9 = 18, hence

The area of the rhombus will be calculated as,

A =  0.5 × d₁ × d₂

A = 0.5 × 14 × 18

A = 126 cm²

Therefore, the area of the rhombus is equal to 126 cm². The correct option is B.

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Answer:

The function is f(n) = 10n - 13 ⇒ answer A

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

# U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

# Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms, n is the position of the

  term in the sequence

* Now lets solve the problem

- The sequence is -3 , 7 , 17 , 27 , .........

∵ 7 - (-3) = 7 + 3 = 10

∵ 17 - 7 = 10

∵ 27 - 17 = 10

∴ The sequence is arithmetic with constant difference 10

∴ f(n) = a + (n - 1)d

∵ a = -3

∵ d = 10

∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it

∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms

∴ f(n) = 10n - 13

* The function is f(n) = 10n - 13

Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).

Looking at the functions provided:

Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

Answer:

P ≈ 56 million

Step-by-step explanation:

Your question is attached in the picture below.

The exponential formula for these cases is

P = Po*e^(kt)

Where,

Po = initial population

k = is a constant used to define the growth rate

t = time transcurred since the time of the initial population

For this exercise,

Po = 50 million

Year 2002

2002 - 1992 = 10

53 million = 50 million *e^(k*10)

(53/50) = e^(k*10)

k*10 = ln(53/50)

k = 0.005827

The equation results

P = 50 million *e^(0.005827*t)

Year 2010

2010-1992 = 18

P = 50 million *e^(0.005827*18)

P = 50 million *(1.11058)

P = 55.53 million

P ≈ 56 million

Answer:

the answer is 56 just got it right

if you need population in 2010

Step-by-step explanation:

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

Explanation:

The base is 10 and the height is 6. So b = 10 and h = 6.

We don't use the 7 at all.

Let's use those b and h values into the formula below

A = b*h/2

A = 10*6/2

A = 60/2

A = 30

Answer:

30 square units

Step-by-step explanation:

Always remember that the equation for the area of a triangle is 1/2 times base times height. With an obtuse triangle, you must always ignore the slant. So, half of the base, which is 10, is equal to 5 and 5 times 6 is 30. Also, remember you can multiply in whichever order and the answer will always be the same because of the commutative property.

YX is corresponding with ED

Hope it helps.

Please mark me brainliest

Answer:

x=0  and x=5

Step-by-step explanation:

x^2 – 5x = 0

Factor out an x

x(x-5) = 0

Using the zero product property

x=0 and x-5 =0

Solving

x=0 x-5+5 = 0+5

x=0  and x=5

Answer:

the number if different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards.

Step-by-step explanation:

this is a valid answer for e2020

Final answer:

In poker, the number of microstates when dealing with five cards from separate decks is 52^5, and the probability of getting 5 queens of hearts is (1/52)^5. The probability of drawing any specific hand is also 1 in 380,204,032. Poker hand values are inversely proportional to their entropy, with rarer hands having greater value.

Explanation:

Calculations Involved in Poker Probabilities

The game of poker involves a combination of skill and luck, with probabilities playing a significant role in the strategy. To answer the student's questions regarding probabilities in poker, we need to delve into some detailed calculations.

In analyzing poker hands and their respective values, we find that the value of a hand is typically inversely proportional to its entropy, meaning a less likely hand equates to a higher value.

Pascal's Wager as applied to gambling is not directly related to poker probabilities, but it is an interesting philosophical approach to decision-making under uncertainty. Rather than calculating monetary risk, it assesses the existential gamble of believing in a deity.

Understanding probabilities like these allows gamblers, politicians, teachers, doctors, and individuals in many other fields to make more informed decisions about probable outcomes.