Write an equation that represents the line.
Use exact numbers. Help quick plz

Choice C, 9, 12, 15, forms a right triangle.

The area of the sector is 16π square inches.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360) x \(\pi r^2\)

where r is the radius of the circle.

In this case, the radius is given as 8 inches.

We are also given that the central angle measures from 60 to 150 degrees. To calculate the area of the sector, we need to find the size of the central angle first.

To do this, we subtract the smaller angle from the larger angle:

150 - 60 = 90 degrees

So, the central angle is 90 degrees.

Now, we can substitute the values into the formula:

Area of sector = (90/360) x \(\pi 8^2\)

Area of sector = (1/4) x π(64)

Area of sector = 16π square inches

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The strawberries that are way more than 2 ounces will be 24 strawberries.

It should be noted that the information stated that 30 of the 54 strawberries she picked the way less than 2 ounces.

Therefore, the strawberries that are way more than 2 ounces will be the difference between the total number picked and 30.

This will be:

= 54 - 30

= 24

Therefore, the strawberries that are way more than 2 ounces will be 24 strawberries.

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To find the margin of error (E) for a confidence level of c = 0.90, sample size (n) of 10, and sample standard deviation (s) of 3.1,

we need to determine the critical value from the t-distribution and then calculate the margin of error using the formula:

E = critical value * (s / sqrt(n))

The critical value is based on the desired confidence level and the degrees of freedom (d.f.) which depend on the sample size.

Since the sample size is 10, the degrees of freedom (d.f.) used in this case would be (n - 1) = (10 - 1) = 9.

To find the critical value corresponding to a 90% confidence level and 9 degrees of freedom, we can use a t-table or a statistical calculator. The critical value is approximately 1.83.

Now, we can calculate the margin of error (E):

E = 1.83 * (3.1 / sqrt(10))

E ≈ 1.83 * (3.1 / 3.162)

E ≈ 1.83 * 0.981

E ≈ 1.794

The value of the degrees of freedom (d.f.) used is 9.

Therefore, the correct answer is D) 1.80 with d.f. = 9.

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Answer:

1/4

Step-by-step explanation:

it came to me in a dream.

1/4 or 25% is the probability that the randomly selected point is in the bullseye.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The area of the bullseye is the area of the inner circle with a radius of 4 cm. Similarly, the area of the entire target is the area of the outer circle with a radius of 8 cm.

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

Therefore, the area of the bullseye is:

A_bullseye = π(4 cm)² = 16π cm²

And the area of the entire target is:

A_target = π(8 cm)² = 64π cm²

So, the probability that the randomly selected point is in the bullseye is the ratio of the area of the bullseye to the area of the target:

P(bullseye) = A_bullseye / A_target

P(bullseye) = (16π cm²) / (64π cm²)

P(bullseye) = 1/4

Therefore, the probability that the randomly selected point is in the bullseye is 1/4 or 25%.

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Interest groups, also known as special interest groups or pressure groups, are organizations that seek to influence public policy by promoting specific causes or by representing the interests of a particular group of people. There are many functions that interest groups serve in a political system including advocacy, information, mobilization, representation and coordination.

Advocacy: Interest groups advocate for the causes or issues that they support by lobbying politicians, running public awareness campaigns, and participating in the policymaking process.

Information: Interest groups provide information and research about the issues they care about to policymakers, the media, and the general public.

Mobilization: Interest groups mobilize their members and supporters to take action on issues, such as contacting politicians or participating in demonstrations.

Representation: Interest groups represent the interests of their members or the groups they serve by advocating for policies that benefit those groups.

Coordination: Interest groups can coordinate the efforts of individuals and organizations that share similar goals or values, helping to build a unified movement around a particular issue.

Overall, interest groups play an important role in a political system by providing a voice for groups of people or causes that may not otherwise be represented in the policymaking process.

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Answer: Approximately 390,244 people per square mile

Work Shown:

Density = population/area

Density = (8 million people)/(20.5 square miles)

Density = 390,243.9024 approximately

This rounds to 390,244 since we're talking about the number of people.

The mass of the lamina is: mass ≈ 0.4444. To find the mass of the lamina, we need to integrate the density function over the given bounds: m = ∫∫ σ(x,y) dA.

We can express the bounds in terms of x and y as follows:

0 ≤ y ≤ 2√x
1 ≤ x ≤ 2

Therefore, the double integral becomes:

m = ∫₁² ∫₀^(2√x) x³ dy dx

Integrating with respect to y first, we get:

m = ∫₁² x³(2√x) dx

m = 2∫₁² x⁵/2 dx

m = 2/7 [x⁷/2]₁²

m = 2/7 (2⁷/2 - 1⁷/2)

m = 2/7 (64 - 1)

m = 2/7 * 63

m = 18

Therefore, the mass of the lamina is 18 units, rounded to four decimal places.
To find the mass of the lamina, we need to integrate the density function over the region bounded by the given curves. The region is defined by y = 2√x, x = 1, and y = 0.

First, let's find the limits of integration. Since x = 1 is an upper bound, and y = 0 is a lower bound:

0 ≤ y ≤ 2√x and 0 ≤ x ≤ 1

Now, we can set up the double integral for mass:

mass = ∫∫_R (σ(x, y) dA) = ∫(x=0 to 1) ∫(y=0 to 2√x) (x^3 dy dx)

Next, integrate with respect to y:

= ∫(x=0 to 1) [x^3 * y] (from y=0 to 2√x) dx

Now substitute the limits of integration for y:

= ∫(x=0 to 1) (x^3 * 2√x - x^3 * 0) dx

Simplify:

= ∫(x=0 to 1) (2x^(7/2)) dx

Now integrate with respect to x:

= [4/9 * x^(9/2)] (from x=0 to 1)

Substitute the limits of integration for x:

= 4/9 * (1^(9/2) - 0)

Finally, the mass of the lamina is:

mass ≈ 0.4444

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Answer: 624 ft^3

work is in the image i attached

Answer:

Step-by-step explanation:

Using a t-distribution table or calculator, we get the t-score and are 98% positive that the interval (32.126, 53.874) includes the genuine population mean amount the medicine would drop a typical patient's systolic blood pressure to.

We must create a confidence interval for the population mean decrease in systolic blood pressure in order to calculate how much the medicine will reduce a typical patient's systolic blood pressure with a 98% confidence level.

CI = x t /2 * (s / n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, t /2 is the t-score for the desired degree of confidence, and is the significance level (1 - confidence level).

With the supplied variables plugged in, we obtain:

CI = 43 t0.01/2 * (11 / 10)

The t-score at a 98% confidence level and 9 degrees of freedom (n-1) are roughly 2.821, according to a t-distribution table or calculator.

We obtain the following number by substituting it:

CI = 43 2.821 * (11 / 10) = (32.126, 53.874)

As a result, we have a 98% confidence that the interval (32.126, 53.874) contains the actual population mean amount that the medication would reduce the systolic blood pressure of an average patient.

The following requirements must be met for the interval to be valid:

1. The sample is a straightforward random sample taken from the population.

2. For the Central Limit Theorem to be applicable, either the population is normally distributed or the sample size is sufficient (n > 30).

3. A fair estimate of the population standard deviation is the sample standard deviation (which is assumed to be unknown).

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Answer:

  (-1, 7)

Step-by-step explanation:

The given point tells you the value of f(-2) is -1, so ...

  -3f(-2) +4 = -3(-1) +4 = 7 . . . . the y-value of the transformed point

The x-value that makes the function argument be -2 is ...

  1/2(x -3) = -2

  x -3 = -4 . . . . . . multiply by 2

  x = -1 . . . . . . . . . add 3

So, the transformed point that corresponds to the given point is ...

  (x', y') = (-1, 7)

_____

If you want to consider the transformations (as the problem suggests), consider this.

  -3f(1/2(x -3)) +4

is a vertical expansion by a factor of -3, then translation upward by 4. It is also a horizontal expansion by a factor of 2, then a shift right by 3.

The combinations of these transformations means ...

  (x, y) ⇒ (2x+3, -3y+4)

  (-2, -1) ⇒ (2(-2) +3, -3(-1) +4) = (-4+3, 3+4) = (-1, 7)

__

  a·f(b(x-c))+d

is a vertical expansion by 'a', an upward shift of 'd', a horizontal compression by 'b' and a right shift of 'c'.  Negative values for 'a' or 'b' represent reflections in the x- or y-axis, respectively.

Here, the compression is by a factor of 1/2, equivalent to expansion by a factor of 1/(1/2) = 2.

Answer:

11.since diagonal are equal of rectangle

QS=RT

4x+6=6x-4

6+4=6x-4x

2x=10

x=10/2

x=5

now

diagonal :4x+6=4*5+6=26

12.

again

QS=RT

9x+12=11x-10

12+10=11x-9x

2x=22

x=11

now

diagonal=9*11+12=99+12=111

Answer: what is

Step-by-step explanation:

Answer:

there is nothing ................

Answer:

A, E

Step-by-step explanation:

The mean of the pizza truck:

(400 + 800 + 1000 + 1000)/4 = 800

The mean of the burger truck:

(800 + 700 + 900 + 800)/4 = 800

A is correct, which voids answer C

The median of the pizza truck:

400, 800, 1000, 1000

              \     /

               900

The median of the burger truck

700, 800, 800, 900

            800

900>800 so E is correct, voiding all other answers

Answer:

The box alone weighs 6 kg

Step-by-step explanation:

Let, weight of Apple be x, Oranges be y, Guavas be z nd box a.

A box of Apple weighs 270kg and 500g i.e270.5kg

a+x =270.5---(1)

A box of oranges weighs 192.5kg

a+y=192.5---(2)

A box of guavas weighs 245

a+z=245---(3)

Fruits together weigh 690 kg

x+y+z=690---(4)

Combining (1),(2),(3), we get

3a+x+y+z=708---(5)

From 4&5

3a+690=708

3a=18

a=6

So the box weighs 6 kg

if the value of x doubles, the value of y will also double, since y is directly proportional to x with a constant of 5. Therefore, the answer is 28. So correct option is A.

In mathematics, an equation is a statement that shows that two expressions are equal to each other. An equation typically consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equals sign (=).

Equations are used to represent mathematical relationships and to solve problems in a variety of fields, including physics, engineering, economics, and finance. They can be linear or non-linear, and they may involve one or more variables.

If the equation is y = 5x, and the value of x doubles, then the new value of x would be 2x. To find the corresponding value of y, we can substitute 2x for x in the equation:

y = 5(2x)

y = 10x

So if the value of x doubles, the value of y will also double, since y is directly proportional to x with a constant of 5. Therefore, the answer is 28.

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Using a system of equations, we have that:

1. The table is completed on the image given at the end of the answer.

2. The equation is: 35w + 25t = 1600.

A system of equations is a set of equations in the context of a problem, and solving these equations, the numeric value of each variable in the context of the problem is found.

The variables in this problem are defined as follows:

A jug of drinking water weighs 35 pounds and a case of paper towels weighs 25 pounds. The truck can carry 1,600 pounds of cargo altogether. Hence the equation is:

35w + 25t = 1600.

When w = 10, the numeric value of t is obtained as follows:

35(10) + 25t = 1600

t = (1600 - 350)/25

t = 50.

When w = 30, the numeric value of t is obtained as follows:

35(30) + 25t = 1600

t = (1600 - 1050)/25

t = 22.

When t = 8, the numeric value of w is obtained as follows:

35w + 25(8) = 1600

w = 1400/35

w = 40.

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The solution to the inequality 13x|20 is all real numbers, as any value of x, no matter how small or large, will make the statement true.

The way to address inequity Using only real values, 13x|20. This means that there is no single solution to this inequality. The inequality is essentially asking what values of x will make the statement true. In this case, any value of x, no matter how small or large, will make the statement true. This is because the absolute value of x is being taken, which means that the value of x is being evaluated regardless of the sign--whether it is positive or negative. For example, if x is -1, then 13x|20 would be 13(-1)|20, which simplifies to -13|20, or 20. This means that no matter what the value of x is, it will always make the statement true. Therefore, the solution to the inequality is all real numbers.

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Answer:

Step-by-step explanation:

Given the equation of a line expressed as y = 3x-1, we are to find y = f(x) for the following values of x in the table.

If y = 3x-1, then f(x) = 3

When x = -1

f(-1) = 3(-1)-1

f(-1) = -3-1

f(-1) = -4

Hence when x = -1, f(x) = -4

When x = 0

f(0) = 3(0)-1

f(0) = 0-1

f(0) = -1

Hence when x = 0, f(x) = -1

When x = 2

f(2) = 3(2)-1

f(2) = 6-1

f(2) = 5

Hence when x = 2, f(x) = 5

Answer:

I think it would be -6 I think u would just do the equation on a calculator

Answer:

Step-by-step explanation:

48/-8 = -6

if you do the math without the negative sign, you would get 6

but, if a positive number gets divided by a negative number than your answer would turn out as a negative. So the answer is -6.

y=360

Step-by-step explanation:

y goes up by 30 everytime and would start at 30 if X =1, so X x 30= y. 12 x 30= 360=y

Answer:

300 or B

Step-by-step explanation: give the other person brainliest

To balance the equation Mgo → Mg + O₂ the coefficient in front of MgO is 2. The smallest possible integers is 2

To balance the equation Mgo → Mg + O₂, we need to ensure that the number of atoms of each element is equal on both sides of the equation.

On the left-hand side (LHS), we have:

1 atom of Mg

1 atom of O

On the right-hand side (RHS), we have:

1 atom of Mg

2 atoms of O

To balance the equation, we need to add coefficients in front of the substances to adjust the number of atoms. In this case, we need to balance the number of oxygen atoms.

To balance the oxygen atoms, we can put a coefficient of 2 in front of MgO:

2MgO → 2Mg + O₂

Now, on the RHS, we have:

2 atoms of Mg

2 atoms of O

Both sides of the equation are now balanced, and the coefficient in front of MgO is 2.

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The question is incomplete the complete question is :

When the following equations are balanced using the smallest

possible integers, what is the number in front of the underlined

substance in each case?

Mgo → Mg + O₂

a) 5

b) 6

c) 4

d) 2

e) 3

The quadratic equation with roots -1 and -4, and a leading coefficient of 4, can be expressed as 4x^2 + 20x + 16 = 0.

To determine the quadratic equation with the given roots and leading coefficient, we need to use the fact that the roots of a quadratic equation are the values of x for which the equation equals zero.

The quadratic equation can be written in the form: ax^2 + bx + c = 0, where a represents the leading coefficient, b represents the coefficient of the linear term, and c represents the constant term.

Given that the leading coefficient is 4 and the roots are -1 and -4, we can start by using the fact that the sum of the roots of a quadratic equation is equal to -b/a. In this case, the sum of the roots is -1 + (-4) = -5.

Since the leading coefficient is 4, we can write the equation as 4x^2 + bx + c = 0. To find the remaining coefficients, we can use the fact that the product of the roots is equal to c/a. In this case, the product of the roots is (-1) * (-4) = 4.

Using the sum and product of the roots, we can set up the following equations:

-5 = -b/4        (from the sum of roots)

4 = c/4            (from the product of roots)

To find the values of b and c, we can solve these equations. From the first equation, we can multiply both sides by 4 to get -20 = -b. Solving for b, we find b = 20.

From the second equation, we can multiply both sides by 4 to get 16 = c. Thus, c = 16.

Substituting the values of a, b, and c into the quadratic equation form, we get:

4x^2 + 20x + 16 = 0.

Therefore, the quadratic equation with roots -1 and -4, and a leading coefficient of 4, is 4x^2 + 20x + 16 = 0.

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Answer:

14

Step-by-step explanation:

If the number of people who are overweight and have high cholesterol is 324, the number of people who are overweight and have low cholesterol is 450, the number of people who are normal weight and have high cholesterol is 368, and the number of people who are normal weight and have low cholesterol is 890, then the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol is 46.8%

To find the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol, follow these steps:

Hence, the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol is 46.8%.

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The time required for the substance to decay to one-half its original amount is approximately 15.909 weeks.

Let's denote the original amount of the substance as Q(0) and the time required for it to decay to one-half as t. According to the given information, we know that Q(0) = 400 mg and Q(t) = Q(0)/2 = 200 mg.

Using the differential equation for radioactive decay, dQ/dt = -rQ, we can integrate it to solve for t. Rearranging the equation, we have dQ/Q = -r dt.

Integrating both sides, we get ∫(1/Q) dQ = -r ∫dt. Integrating gives ln|Q| = -rt + C, where C is the constant of integration.

Applying the initial condition Q(0) = 400 mg, we can solve for C. ln|400| = -r(0) + C, which simplifies to C = ln|400|.

Substituting Q(t) = 200 and C = ln|400| into the equation, we have ln|200| = -rt + ln|400|. Solving for t, we find t ≈ 15.909 weeks (rounded to 3 decimal places). Therefore, it takes approximately 15.909 weeks for the substance to decay to one-half its original amount.

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The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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