\(\sf\large\green{\underbrace{\red{Question*}}}:\)
\(\huge{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red}Factorize}}}} \)
\(4x - 8y + 6\)
\(4 {y}^{2} - 2 {y}^{3} \)

​

The problem involves calculating the subsequent amount of carbon dioxide in a room over time, given the initial concentration, the rate at which air is pumped in and out, and the room's volume.

We can determine the subsequent amount A(t) using a mathematical model that takes into account the flow rate of air and the initial concentration. We can also calculate the concentration of carbon dioxide at a specific time, such as 10 minutes, by using the formula A(t) / V, where A(t) is the amount of carbon dioxide at time t and V is the volume of the room.

To calculate the subsequent amount A(t) of carbon dioxide in the room at time t, we need to consider the inflow and outflow of air. The rate at which air is pumped in and out is 60 m³/min, and the room's volume is 300 m³. The initial concentration of carbon dioxide is 0.2%. We can model the amount of carbon dioxide in the room using the equation A(t) = (A(0) + (0.0006 * 60 * t)) * (1 - t / 10), where A(0) is the initial amount of carbon dioxide.

To find the concentration of carbon dioxide at 10 minutes, we substitute t = 10 into the equation and divide it by the volume of the room: C(10) = A(10) / V. Plugging in the values and calculating, we obtain the concentration of carbon dioxide at 10 minutes.

By using the given information and the mathematical model, we can determine the subsequent amount of carbon dioxide in the room at any given time. By substituting t = 10 into the equation and dividing by the room's volume, we can calculate the concentration of carbon dioxide at 10 minutes.

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Answer:

She would need to make 5 consecutive free successful throws

Step-by-step explanation:

Equations

A basketball player wants to improve his percent of successful throws to 85%.

She currently has made 12 out of 15 free throws, which gives a success percentage of 12/15*100=80%

So, she needs a number of free consecutive free throws to increase that number to the desired target.

The percentage of success can be calculated as:

\(\displaystyle P=\frac{\text{successful throws}}{\text{total throws}}*100\)

Let's assume x is the number of required consecutive successful throws. Since she has already thrown 15 times, out of which has had 12 successful throws, now she will have 15+x total throws and 12+x successes, thus the new percentage is:

\(\displaystyle P=\frac{12+x}{15+x}*100\)

And this percentage must be equal to 85%, thus:

\(\displaystyle \frac{12+x}{15+x}*100=85\)

a) The equation to represent the situation is:

\(\mathbf{\displaystyle \frac{12+x}{15+x}*100=85}\)

b) Let's solve it.

Multiply by 15+x:

\(\displaystyle (12+x)*100=85(15+x)\)

Dividing by 5:

\(\displaystyle (12+x)*20=17(15+x)\)

Operating:

\(\displaystyle 240+20x=255+17x\)

Subtracting 17x and 240:

\(\displaystyle 20x-17x=255-240\)

Simplifying:

\(\displaystyle 3x=15\)

Dividing by 3:

x = 5

She would need to make 5 consecutive free successful throws

The number of throws is an illustration of proportions.

The number of free throws to raise her percent to 85% is 5

(a) The equation

The proportion is given as: 12 out of 15.

Let the number of throws be n.

So, the proportion would be:

\(\mathbf{Proportion = \frac{12 + n}{15 + n}}\)

To make 85% success, then the proportion must equal 85%.

So, we have:

\(\mathbf{\frac{12 + n}{15 + n} = 85\%}\)

(b) The solution to the equation

In (a), we have:

\(\mathbf{\frac{12 + n}{15 + n} = 85\%}\)

Express 85% as decimal

\(\mathbf{\frac{12 + n}{15 + n} = 0.85}\)

Cross multiply

\(\mathbf{12 + n = 0.85(15 + n)}\)

\(\mathbf{12 + n = 12.75 + 0.85n}\)

Collect like terms

\(\mathbf{n -0.85n= 12.75 -12 }\)

\(\mathbf{0.15n= 0.75}\)

Divide both sides by 0.15

\(\mathbf{n= 5}\)

Hence, the number of free throws to raise her percent to 85% is 5

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Answer:

tan360°= 0

I hope this helps you

Answer:

please mark as brainliest

Step-by-step explanation:

tan360°

= cot (90°-360°) = cot -270°

-tan360°

= tan (-360°) = -tan 360°

= cot (90°+360°) = cot 450°

= tan (180°-360°) = tan -180°

The money spent to fill up the tank with gas was $32.90

An equation is an expression that shows the relationship between two or more numbers and variables.

Lou's car had 4.6 gallons of gas in the 14-gallon tank. To fill the tank:

Amount of gas needed = 14 gallon - 4.6 gallon = 9.4 gallons

Lou filled the tank costing 3.50 per gallon, hence:

Total cost = $3.50 * 9.4 gallons = $32.90

The money spent was $32.90

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Answer:

The similarities are

1) Both diagrams consists of an horizontal line l for the upper diagram and k for the lower diagram

2) Both diagrams have a vertical plane Z for the upper diagram and A for the lower diagram

3) Both diagrams have rays, which are C for the upper diagram and G and H for the lower diagram

The differences are

1) The upper diagram has only one plane, while the lower diagram has two planes, seemingly rotated at an angle of about 90° to each other

2) The upper diagram has only one line, l, while the lower diagram has two lines, l and GH

Step-by-step explanation:

Answer:

59049

Step-by-step explanation:

nine times negative 3 8 times

Answer:

a₉ = 59049

Step-by-step explanation:

The nth term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 9 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-27}{9}\) = - 3 , then

a₉ = 9 × \((-3)^{8}\) = 9 × 6561 = 59049

The given line passes through points (0,4) and (-2,0) . So firstly we can find the slope of the line as ,

\(\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\ \)

\(\longrightarrow m =\dfrac{4-0}{0-(-2)}\\ \)

\(\longrightarrow m =\dfrac{4}{2}\\ \)

\(\longrightarrow m = 2 \)

Now we may use point slope form of the line as ,

\(\longrightarrow y - y_1 = m(x-x_1)\\ \)

\(\longrightarrow y - 4 = 2(x-0)\\ \)

\(\longrightarrow y -4 = 2x \\ \)

\(\longrightarrow \underline{\underline{ y = 2x +4}}\)

And we are done!

Answer:

The given line passes through points (0,4) and (-2,0) . So firstly we can find the slope of the line as ,

Now we may use point slope form of the line as ,

And we are done!

Step-by-step explanation:

Answer:

x = 5 ± \(\sqrt{17}\)

Step-by-step explanation:

Given

x² - 10x + 25 = 17 ← left side is a perfect square, thus

(x - 5)² = 17 ( take the square root of both sides )

x - 5 = ± \(\sqrt{17}\) ( add 5 to both sides )

x = 5 ± \(\sqrt{17}\)

Thus

x = 5 - \(\sqrt{17}\)

x = 5 + \(\sqrt{17}\)

Answer:

(D) 1+0.06m

Step-by-step explanation:

Let's say that m=$120

(A)= $127.2

(B)= $127.2

(C)= $127.2

(D)= $8.2

As you can see after I substituted in 120 for (m) and solved, D is the only equation that did not represent her current balance.

I hope this helps!

Answer:

D

Step-by-step explanation:

edge

Answer: 45

Step-by-step explanation: 2 1/4 = 2hr and 15 min

1/3 of 2hr and 15 min = 45

Amount of time spent by Nathan's family watching the video is 3/4 hour or 45 minutes.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Given that,

Nathan’s family spent 2 and 1/4 hours visiting national monument near their home.

They watched a video in the visitor center for 1/3 of that time.

Total time spent by Nathan's family in the monument = 2 + 1/4 hours

                                                                                         = 9/4 hours

Fraction of time spend in watching the video = 1/3

Time spend in watching the video = 1/3 × 9/4

                                                         = 3/4 hour

                                                         = 45 minutes

Hence the time spent is 3/4 hour.

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The 9th term of the given sequence, where each term is obtained by multiplying the previous term by 3, is 39366.

To find the 9th term of the sequence, we need to identify the pattern or rule that governs the sequence. Let's examine the given sequence: 6, 18, 54.

By observing the terms, we can see that each term is obtained by multiplying the previous term by 3. In other words, each term is three times the preceding term.

Using this pattern, we can find the 9th term by successively multiplying the previous term by 3:

6 × 3 = 18 (2nd term)

18 × 3 = 54 (3rd term)

54 × 3 = 162 (4th term)

162 × 3 = 486 (5th term)

486 × 3 = 1458 (6th term)

1458 × 3 = 4374 (7th term)

4374 × 3 = 13122 (8th term)

13122 × 3 = 39366 (9th term)

Therefore, the 9th term of the sequence is 39366.

The sequence follows a pattern where each term is obtained by multiplying the previous term by 3. By identifying this pattern, we can derive the formula for finding any term in the sequence. In this case, to find the 9th term, we multiply the 8th term (13122) by 3, which gives us 39366 as the 9th term.

This pattern is a common example of a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio. In this case, the ratio is 3. By understanding the pattern and applying it repeatedly, we can find any term in the sequence.

By observing the pattern and applying the multiplication rule, we can derive the formula for finding any term in the sequence. In this case, by multiplying the 8th term (13122) by 3, we obtain the 9th term of 39366. Understanding the pattern and the underlying concept of a geometric sequence allows us to extend the sequence and find any desired term.

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Answer:

hello,

answer C

Step-by-step explanation:

area of the rectangle=2b*b=2b²

area of the half cercle= \(\\\dfrac{\pi*(\frac{c}{2})^2}{2} =\dfrac{\pi*c^2}{8} \\\)

Area in blue= 2b²-πc²/8

Answer:

\(\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}\)

Step-by-step explanation:

\(\sqrt{(\frac{5}{4})^7 }\)

Apply rule : \(\sqrt{a} =a^{\frac{1}{2} }\)

\(((\frac{5}{4})^7 )^{\frac{1}{2} }\)

Apply rule : \((a^b)^c=a^{bc}\)

\((\frac{5}{4} )^{7 \times \frac{1}{2} }\)

\((\frac{5}{4} )^{\frac{7}{2}\)

The value of x that maximizes the area of the printed region of the billboard is x = 30 ft.

To determine this, we subtract the margins from the total width and divide it equally on both sides. The remaining width (x) will be maximized when it is distributed evenly on both sides, resulting in a rectangular shape with equal dimensions on the left and right. Therefore, x = (8000 ft - 2 * 5 ft) / 2 = 30 ft.

Using this value of x, we can compute the maximum area of the printed region. The height of the printed region will be the total height of the billboard, which is 8000 ft minus the top and bottom margins, resulting in a height of 8000 ft - 2 * 5 ft = 7990 ft. Thus, the maximum area of the printed region is (30 ft * 7990 ft) = 239,700 square feet.

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You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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The "longest interval between the birth of twins" is 84 days 8 hours, 40 minutes.What is the "longest interval between the birth of twins"?The longest interval between the birth of twins was 84 days 8 hours, 40 minutes.The longest interval between the birth of twins has been recorded at 84 days 8 hours, 40 minutes, and was achieved by Peggy Lynn of Danville, Pennsylvania, who gave birth to Hanna on November 11, 1995, and to Eric on February 3, 1996.

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Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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Answer:

I think it will be rectangle or square

because rectangle and Square have 4 right angles

and each two opposite sides are parallel

a) About two in three years, your return should fall inside the range of -32.3% to 53.7%

b) About one in twenty years, your return should fall outside the range of -96.4% to 117.8%

c) About one in two hundred years, your return should be greater than 87.7%.

a) About two in three years, your return should fall inside the range of (10.7% - 21.5%) to (10.7% + 21.5%) percent

.Lower Range = 10.7% - (21.5% * 2) = -32.3%

Upper Range = 10.7% + (21.5% * 2) = 53.7%

Hence, About two in three years, your return should fall inside the range of -32.3% to 53.7%

b) About one in twenty years, your return should fall outside the range of (10.7% - 43%) to (10.7% + 43%) percent.

Lower Range = 10.7% - (43% * 2.8) = -96.4%

Upper Range = 10.7% + (43% * 2.8) = 117.8%

Hence, About one in twenty years, your return should fall outside the range of -96.4% to 117.8%

c) About one in two hundred years, your return should be greater than 10.7% + (21.5% * 3.29) = 87.7%

Hence, About one in two hundred years, your return should be greater than 87.7%.

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Answer:

D.

Step-by-step explanation:

You can see that the first value(initial) of y is 20 and the difference of the preceding values is 10 but it is decreasing thus -10

Sean's age is 4 years and his brother's age is 11 years.  

Linear Equations in Two Variables: It is an equation written in the form ax+by +c=0. a, b, and c are real values, whereas x and y are variables. We can say that a and b are not equal to zero. Linear equations are solved when the same number is added to both sides, as well as when both sides are multiplied and divided by the same amount. Linear equations with two variables are denoted by x and y.

Let Sean's age be y years.

Let Sean's brother's age be x years.

Sean is three more than twice as old as brother.

∴ y = 2x + 3      -- (1)

Also, the total of their ages is 15.

∴ x+y = 15

⇒ y = 15 -x     -- (2)

Substitute y from equation (2) in equation (1)

⇒ 2x + 3 = 15 - x

⇒ 3x = 12

∴ x = 4

Put x in equation (2)

⇒ y = 15- 4

∴ y = 11

Thus, Sean's age is 4 years and his brother's age is 11 years.

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For the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The given expression is:

3.35x + 115 = 3.25x + 125

Regroup all the terms with variable x on one side of the equation:

3.35x - 3.25x = 125 - 115

0.1x = 10

x = 100

Hence, for the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.

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Answer:

its volume was 450,000 cubic cubits.

Step-by-step explanation:

According to Genesis 6:15, the Ark measured three hundred cubits in length, fifty cubits in width, and thirty cubits in height. Therefore its volume was 450,000 cubic cubits

Adding a new item to the end of an ArrayList with a size of 17000 requires no elements to be shifted if the underlying array has enough capacity to accommodate the new element. Correct option is B.

ArrayList is implemented as an array-based data structure that can dynamically resize itself when the number of elements it contains exceeds its current capacity.

When the capacity of the underlying array is reached, the ArrayList creates a new array with a larger size, copies the existing elements to the new array, and adds the new element to the end. This process is known as resizing. Therefore, correct option is B.

Therefore, if the ArrayList has enough capacity to accommodate the new element, no resizing is needed, and no elements need to be shifted. However, if the ArrayList has reached its capacity limit, then the entire contents of the array must be copied to a new, larger array, which can be a time-consuming process, especially for large arrays.

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Answer:

95 degrees

Step-by-step explanation:

Measure of arc AB is 360 - (101+97+69) = 360 - 267 = 93 degrees.

Measure of arc DAB is 97+93 = 190 degrees, so measure of angle C is 190/2 =  95 degrees.