Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3

Population size is a characteristic of the data set and is not used to analyze the data. The correct option is A

The quantity of an organisms belonging to a specific species is referred to as its population size.

Population size is a characteristic of the data collection that is therefore ignored when data analysis is performed. The population under investigation's size is merely described in terms of the number of individuals or data points.

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The slope of a linear function represents the rate at which the output variable (y) changes with respect to the input variable (x). The slope is often denoted by the letter "m" and can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

To find the slope of Function 1, we can compare the coefficient of x in its equation with the formula for slope. We see that the coefficient of x in y = (4/5)x + 2 is 4/5. Therefore, the slope of Function 1 is 4/5.

To find the slope of Function 2, we can choose any two points from the table and use the slope formula. Let's choose the points (0, 1) and (3, 2.5). Plugging in these values, we get:

m = (2.5 - 1) / (3 - 0) = 1.5 / 3 = 1/2

Therefore, the slope of Function 2 is 1/2.

Comparing the slopes, we can see that the slope of Function 1 (4/5) is greater than the slope of Function 2 (1/2). Therefore, Function 1 has a greater slope than Function 2.

Answer:

Function 1 has the greatest slope.

Step-by-step explanation:

Function 1 is given in slope-intercept form, y = mx + b, where m is the slope (and b is the y-intercept).

Therefore, the slope of function 1 is ⁴/₅.

To find the slope of function 2, use the slope formula.

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Let (x₁, y₁) = (0, 1)

Let (x₂, y₂) = (2, 2)

Substitute the values into the formula:

[tex]\implies m=\dfrac{2-1}{2-0}=\dfrac{1}{2}[/tex]

Therefore, the slope of function 2 is ¹/₂.

To determine which function has the greatest slope, rewrite both slopes so that the denominator of the fractions are the same.

[tex]\textsf{Slope of function 1}=\dfrac{4}{5}=\dfrac{4 \cdot 2}{5 \cdot 2}=\dfrac{8}{10}[/tex]

[tex]\textsf{Slope of function 2}=\dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]

As 8 is greater than 5, the slope of function 1 is greater than the slope of function 2.

Answer: 250 feet (approx.)

Step-by-step explanation:

The volume of the dome is given as 6,132,812.5 cubic feet, and we know that the dome is 75% of a full sphere. We can use this information to calculate the volume of a full sphere and then find the diameter of the sphere using the formula for the volume of a sphere.

The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius. Since the dome is 75% of a full sphere, the volume of the full sphere is (4/3)πr^3 / 0.75 = (16/3)πr^3 / 3.

Setting this equal to 6,132,812.5 and solving for r gives us r ≈ 35.1 feet.

Finally, the diameter of the sphere is 2r ≈ 70.2 feet.

Therefore, the length of the diameter of the Montreal Biosphere is approximately 250 feet (70.2 feet * (100/75)).

Let's start by calculating the initial concentration of salt in the tank:

4 kg of salt is dissolved in 100 L of water, so the initial concentration of salt in the tank is:

4 kg / 100 L = 0.04 kg/L

We want to increase the concentration of salt in the tank to 0.25 kg/L by adding a salt solution of 0.6 kg/L at a constant rate of 10 L/min.

Let's assume that t is the time in minutes that the faucet has been open. During this time, the volume of water that has been added to the tank is 10t liters.

The amount of salt that has been added to the tank during this time is:

0.6 kg/L x 10 L/min x t min = 6t kg

The total amount of salt in the tank after t minutes is:

4 kg + 6t kg

The total volume of water in the tank after t minutes is:

100 L + 10t L

The concentration of salt in the tank after t minutes is:

(4 kg + 6t kg) / (100 L + 10t L)

We want this concentration to be 0.25 kg/L, so we can set up the following equation:

(4 kg + 6t kg) / (100 L + 10t L) = 0.25 kg/L

Simplifying this equation, we get:

16 kg + 24t kg = 25 L + 2.5t L

21.5t = 9 L

t = 9 L / 21.5 = 0.42 hours = 25.2 minutes (rounded to the nearest minute)

Therefore, you need to close the faucet after approximately 25 minutes to achieve a concentration of 0.25 kg/L in the tank.

Each person receives $1.68 and Sarah will receive $8.40 from the profit.

Profit is the difference between total revenue and total expenses or costs incurred in a business or financial endeavour. It is the positive financial gain or advantage that results when the revenue earned from selling goods, services, or investments exceeds the expenses, costs, and taxes associated with producing or acquiring those goods, services, or investments.

According to the given information:

Let's break down the problem step by step to find out how much each person received, including Sarah.

Step 1: Calculate Sarah's share

Sarah decided to keep 20% of the profit for herself. The remaining profit after paying all expenses is $42.00. So Sarah's share would be 20% of $42.00.

20% of $42.00 = 0.20 * $42.00 = $8.40

So Sarah received $8.40 from the profit.

Step 2: Calculate the share for everyone else

Since Sarah kept her share of $8.40, the remaining profit for everyone else to share is $42.00 - $8.40 = $33.60.

Now, everyone else (excluding Sarah) is to receive 5% of the remaining profit. This means that each person will receive 5% of $33.60.

5% of $33.60 = 0.05 * $33.60 = $1.68

So each person (excluding Sarah) received $1.68 from the profit.

In summary:

Sarah received $8.40

Each person (excluding Sarah) received $1.68

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The value of p in the inequality is given as follows:

p ≥ -21/2.

The inequality in the context of this problem is defined as follows:

2p/3 + 10 ≥ 3.

We must isolate the variable p, hence:

2p/3 ≥ -7 (the subtraction is inverse to the addition).

2p ≥ -21. (multiplication is inverse to division);

p ≥ -21/2. (division is inverse to the multiplication).

Hence the second option is the correct option.

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Answer:

1052

Step-by-step explanation:

Fancy surface area.

(160 x 2) + (96 x 2) + (128 x 2) + (192 x 2)

=1052

If each year the population grows by 2.5%, then the "exponential-function" which shows the relationship between "y" and "t" is y = 300,000 × [tex](1.025)^t[/tex].

The "Exponential-Growth" is defined as a type of growth where the rate at which something grows is proportional to its current value. This results in a rapid and increasingly faster growth over time.

The relationship between "y" (population) and "t" (time in years) can be modeled by an "exponential-function" ;

⇒ y = a × [tex](1+r)^{t}[/tex],

where "a" is = initial population, "r" is = annual growth-rate (in decimal), and "t" is = time;

In this case, the "initial-population" is = 300,000, and

The annual growth rate is = 2.5% or 0.025,

So, we can write exponential function as : y = 300,000 × [tex](1+0.025)^{t}[/tex],

Simplifying the expression,

We get,

⇒ y = 300,000 × [tex](1.025)^t[/tex],

Therefore, the required exponential-function is y = 300,000 × [tex](1.025)^t[/tex].

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The value of k such that y = k cos(3x) + 4sin(x) is a solution to the differential equation y’’ + y = -9 cos(2x) is 9/8.

Given a differential equation,

y’’ + y = -9 cos(2x)

The solution of the equation is,

y = k cos(3x) + 4sin(x)

Now,

y' = -3k sin (3x) + 4 cos(x)

y'' = -9k cos (3x) - 4 sin (x)

Substituting these to the given equation,

-9k cos (3x) - 4 sin (x) + k cos(3x) + 4sin(x) = -9 cos(2x)

-8k cos (3x) = -9 cos (3x).

Comparing,

-8k = -9

k = 9/8.

Hence the value of k is 9/8.

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Answer:

30 meters after 0.5 seconds

Step-by-step explanation:

To find the values of t for which the rocket's height is 30 meters, we can set h = 30 in the given equation and solve for t:

h = 65t - 5t

30 = 65t - 5t

30 = 60t

t = 30/60

t = 0.5

Therefore, the rocket's height is 30 meters after 0.5 seconds.

An expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.

What is Pythagoras' theorem?

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, we have

Given: A right triangle with legs of lengths x and y has a hypotenuse of length z.

We have to write an expression for the length of the hypotenuse z.

By Pythagoras' theorem

x²+y² = z²

[tex]\sqrt{x^2 + y^2}[/tex] = z

Hence, an expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.

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Answer:

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

Plugging in the given values, we have:

5960 = 5000(1 + 0.048/12)^(12t)

Dividing both sides by 5000, we get:

1.192 = (1 + 0.048/12)^(12t)

Taking the natural logarithm of both sides, we get:

ln(1.192) = ln[(1 + 0.048/12)^(12t)]

Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the right side:

ln(1.192) = 12t ln(1 + 0.048/12)

Dividing both sides by 12 ln(1 + 0.048/12), we get:

t = ln(1.192) / [12 ln(1 + 0.048/12)]

t ≈ 2.55

Therefore, it will take about 2.55 years (or 2 years and 7 months) for the investment to grow to $5960.

Hope that helps :)

Answer:

< BEA

Step-by-step explanation:

An adjacent angle is an angle that is next to it.

< BEA is adjacent to < BEC

Answer:

Step-by-step explanation:

The true statements are B, D, E, and H for the given margin of error of 0.017.

The margin of error shows the range of values within which the real value of a population parameter is expected to reside, based on the findings of a sampling of that population.

To find the margin of error in terms of percentage, we need to divide the margin of error by the sample proportion and multiply by 100.

The sample proportion is 284/500 = 0.568, so the margin of error in terms of percentage is (0.017/0.568) × 100 ≈ 2.99%.

Therefore, the true statements are:

B. The margin of error is between 55.1% and 58.5%.

D. The margin of error is between 17,991 and 19,101 subscribers.

E. The results show 56% of the subscribers also subscribe to at least one other newspaper online.

H. It cannot be concluded that over half of the subscribers also subscribe to at least one other newspaper online.

Statement A is incorrect because the margin of error is less than 3%, which is outside the range of 54% to 58%.

Statement C is incorrect because the margin of error is less than 3%, which is outside the range of 17,632 to 18,938 subscribers.

Statement F is incorrect because the sample proportion is 0.568, which is not equal to 56.8%.

Statement G is incorrect because we cannot conclude that over half of the subscribers also subscribe to at least one other newspaper online due to the margin of error.

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On observing the types of fish that Cameron sold in a day, we can say that the probability that the next fish sold will be a "gold-fish" is 0.3 or 30%.

To find the probability of the next-fish Cameron sells being a goldfish, we use the formula:

⇒ probability = (number of desired outcomes)/(total number of possible outcomes),

In this case, the "desired-outcome" is selling a "goldfish", and

The total number of possible outcomes is the total number of fish sold so far.

To find the number of "gold-fish" sold, we need to count the number of times "goldfish" appears in the list : betta, goldfish, neon tetra, betta, guppy, guppy, swordtail, betta, goldfish, goldfish

We see that "goldfish" appears three times, so the number of desired outcomes is = 3.

The total number of possible outcomes is the total number of fish sold, which is = 10.

So, probability of the next fish Cameron sells being a goldfish is = 3/10 = 0.3,

Therefore, there is a 30% chance that the next fish Cameron sells will be a goldfish.

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The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.

From the question, we have the following parameters that can be used in our computation:

-3x^4 + 9x² + 6

A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.

In this expression, we have three terms:

This means that it is a trinomial

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The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.

From the question, we have the following parameters that can be used in our computation:

-3x^4 + 9x² + 6

A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.

In this expression, we have three terms:

This means that it is a trinomial

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The football field is 360 feet long and 160 feet wide. To calculate the area, we multiply those 2 numbers:

[tex]360 \times 160 = 57600[/tex]

Now considering that the expected floor space a person occupies is 2.5 sq feet, we divide 57,600 by 2.5:

[tex]57600\div2.5 = 23040[/tex]

So 23,040 students can fit on the football field.

Answer:

  3 5/8 miles

Step-by-step explanation:

You want miles to go for a 3 7/8 mile trip after 1/4 mile has been taveled.

The remaining mileage is the difference between the total distance and the distance already covered.

  3 7/8 -1/4 = 3 7/8 -2/8 = 3 5/8

Kaitlin still has 3 5/8 miles to jog.

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The line segment that has the same measure as TQ is B. TR

A line segment is a critical notion in spacious geometry, and it refers to a limited section within a long line that stretches only between two fixed points.

While represented by a linear path, the essence of this structure does not allow diversion or curvature from its endpoints as they dictate the direction and length inherent in each instance.

Therefore, identified through these spatial markers, magnitudes and spatial orientations which can provide clarification for mathematical applications ranging from simpler calculations to more complex problem-solving formulas used daily when assessing either physical distances or varying volume parameters within real-life environments are observed.

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The equation with these solutions can be:

y = 2x - 3

Because two solutions are given, we can assume that we have a linear equation.

A general linear equation can be written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the linear equation passes through two known points, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values, here we will get.

a = (13 - 7)/(8 - 5)

a = 6/3

a = 2

Then the line is:

y = 2x + b

Replacing the values of the first point we will get:

7 = 2*5 + b

7 = 10 + b

7 - 10  = b

-3 = b

The equation is y = 2x - 3

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The calculated value of the perimeter of △JKL is 88 units

Assuming that segments that appear to be tangent are tangent, we have

7y - 9 = 2y + 11

8x - 35 = 5x - 8

When the expressions are evaluated, we have

y = 4

x = 9

So, we have the following side lengths

OK = 2(4) + 11

OK = 19

Also, we have

JM = 5(4) - 8

JM = 12

Lastly, we have

LO = 32 - 19

LO = 13

The perimeter of △JKL is then calculated as

Perimeter = 2 * (OK + JM + LO)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (19 + 12 + 13)

Evaluate

Perimeter = 88

Hence, the perimeter is 88 units

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The two possible solutions of the given equation are  a = √21.6 and a = -√21.6.

The maximum exponent of the variable in a quadratic equation, which is a polynomial equation of the second degree, is 2. The equation has two unique real solutions if the discriminant is positive. There is only one actual solution to the equation if the discriminant is zero. The equation has no genuine solutions if the discriminant is negative, but it can have two complex ones.

The given equation is 27 = a (a/0.8).

Multiply both sides of the equation by 0.8 thus we have:

21.6 = a²

Now, taking the square root on both sides we have:

a = √21.6 and a = -√21.6.

Hence, the two possible solutions of the given equation are  a = √21.6 and a = -√21.6.

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The two possible solutions of the given equation are  a = √21.6 and a = -√21.6.

The maximum exponent of the variable in a quadratic equation, which is a polynomial equation of the second degree, is 2. The equation has two unique real solutions if the discriminant is positive. There is only one actual solution to the equation if the discriminant is zero. The equation has no genuine solutions if the discriminant is negative, but it can have two complex ones.

The given equation is 27 = a (a/0.8).

Multiply both sides of the equation by 0.8 thus we have:

21.6 = a²

Now, taking the square root on both sides we have:

a = √21.6 and a = -√21.6.

Hence, the two possible solutions of the given equation are  a = √21.6 and a = -√21.6.

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Answer

Rectangle: W x H = A Square: H x W Circle: [tex]\pi r ^{2}[/tex]

Step-by-step explanation:

Sorry if this is not what u are looking for I assumed u were talking about 2d shapes so yes here u go bye have a great day!!! :D

Answer

Rectangle: W x H = A Square: H x W Circle: [tex]\pi r ^{2}[/tex]

Step-by-step explanation:

Sorry if this is not what u are looking for I assumed u were talking about 2d shapes so yes here u go bye have a great day!!! :D

Using a t-distribution with 115 degrees of freedom (df = n-1), and a 95% confidence level, we can find the critical value using a t-table or calculator, which is approximately 1.98.

Then, we can calculate the margin of error (ME) using the formula:

ME = critical value x standard error

where the standard error (SE) is given by:

SE = standard deviation / sqrt(sample size)

Substituting the given values, we get:

SE = 30 / sqrt(116) ≈ 2.78

ME = 1.98 x 2.78 ≈ 5.5

Finally, we can construct the 95% confidence interval (CI) for the mean weight using the formula:

CI = sample mean ± margin of error

Substituting the given values, we get:

CI = 177 ± 5.5

CI ≈ [171.5, 182.5]

Therefore, the 95% confidence interval for the mean weight of the residents in the town is approximately [171.5, 182.5] pounds.

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[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

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Answer:

0.6

Step-by-step explanation:

It says x equals 0.6 so the answer was right there it was pretty easy