What is the median?
1 ,1 ,2 ,1 ,2

According to combinations formula there are 495 possible committees that can be selected from a group of 12 people.

To calculate this, you can use the formula for combinations

nCr = n!/(r!(n-r)!)

where n is the total number of people (12) and r is the number of people on the committee.
Therefore, the possible number of committees that can be selected is;

= {12!}/{4!8!}
= 12*11*10*9/4*3*2*1

= 11880/24
= 495
Therefore, 495 possible committees can be selected from a group of 12 people if a committee of 4 is to be selected.

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Katie is currently 17 years old.

Let's use substitution to solve for k. We can rearrange the second equation to solve for k:

k = e + 4

Now we can substitute that expression for k into the first equation:

k - 9 = 2(e - 9)

(e + 4) - 9 = 2(e - 9)

Simplifying, we get:

e - 5 = 2e - 18

Subtracting e from both sides, we get:

-5 = e - 18

Adding 18 to both sides, we get:

13 = e

So Elena is currently 13 years old. Now we can use the second equation to find Katie's age:

k = e + 4

k = 13 + 4

k = 17

Therefore, Katie is currently 17 years old.

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Answer:

The answer is B

Step-by-step explanation:

Step-by-step explanation:

\(x-2>4\)

\(x>6\)

And

\(3x+1\leq 28\)

\(3x\leq 27\)

\(x\leq 9\)

So \(x\) ∈ \((6, 9]\)

Please give me a brainliest answer

Answer:

(C)x=11.6, y=23.2

Step-by-step explanation:

Using Theorem of Intersecting Secant and Tangent

\(TQ$ X TP=TR^2\)

\(10(10+x+4)=16^2\\10(14+x)=256\\140+10x=256\\10x=256-140\\10x=116\\$Divide both sides by 10\\x=11.6\)

Next, we apply Theorem of Intersecting Chords

PV X VQ=SV X VR

4 X x= 2 X y

Recall: x=11.6

2y=4 X 11.6

2y=46.4

y=46.4/2=23.2

Therefore: x=11.6, y=23.2

The correct option is C

Answer:

so first we have to find km per hour

so lets divide 452/17=26.5882352941

so it travels 26.6 km per hour so lets mulitply for the 9 hours

26.6*9=239.4

it can travel 239.4 km in 9 hours

Hope This Helps!!!

Answer:

Yes, the graph crosses the x-axis at x = -2.

Step-/by-step explanation:

Substitute x = -2 in the equation.

     \(\sf y =\dfrac{1}{2}x + 1\\\\y =\dfrac{1}{2}*(-2)+1\\\\y = - 1 + 1\\\\y = 0\)

At x-axis, the value of y = 0.

So, the graph crosses the x-axis.

Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing.  I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

y = -(2/3) -(4/3)

y = -(6/3) or -2

The solution is (2,-2)

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

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

Answer:

0.47..................

Step-by-step explanation:

..........

The graph that shows the solution to the system of equations is given by the image presented at the end of the answer.

The system of equations for this problem is defined as follows:

Replacing y = 0.5x on the second equation, the x-coordinate of the solution is given as follows:

x + 2(0.5x) = -8

x + x = -8

2x = -8

x = -4.

The y-coordinate of the solution is given as follows:

y = 0.5(-4)

y = -2.

Hence the graph will show the two lines intersecting at the point (-2,-4).

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Answer:

11 m

Step-by-step explanation:

Answer:

11 m

Step-by-step explanation:

I took the maps testing

I don't know the first one but the second one is The second national bank was chartered in 1816.

Answer:

Step-by-step explanation:

Answer:

it is your test we can't help you sorry

According to the system developed a slice of pizza costs $1.75 and a cookie costs $1.25.

What is a linear equation?

An algebraic equation that can be written in the form ax + b = 0 or ax + by + c = 0, where a, b and c are real numbers and x and y are variables with highest power one.

Let p be the price of a slice of pizza and c be the price of a cookie. Then we can represent the situation with the following system of equations:

2p + 3c = 7.25

1p + 4c = 6.75

To solve this system, we can use the method of substitution. We can solve one equation for one of the variables, and then substitute that expression into the other equation to eliminate that variable. For example, we can solve the second equation for p:

p = 6.75 - 4c

Now we can substitute this expression for p into the first equation:

2(6.75 - 4c) + 3c = 7.25

Simplifying and solving for c, we get:

13.5 - 8c + 3c = 7.25

-5c = -6.25

c = 1.25

Now that we have the price of a cookie, we can substitute this value back into either of the original equations to find the price of a slice of pizza. Using the second equation, we get:

1p + 4(1.25) = 6.75

p + 5 = 6.75

p = 1.75

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(a) Without more information, we cannot determine the initial number of insects. (b) The differential equation satisfied by P(t) is: dP/dt = kP, where k is the growth rate of the insect population.

(c) To find the time it takes for the population to double, we can use the formula:

2P(0) = P(0)e^(kt)

where P(0) is the initial population size. Solving for t, we get:

t = ln(2)/k

(d) Without more information, we cannot determine the time at which the population will equal a certain value.
Hi! To answer your question, I need the specific function P(t). However, I can provide you with a general framework to answer each part of your question once you have the function.

(a) To find the initial number of insects, evaluate P(t) at t=0:
P(0) = [Insert the function with t=0]

(b) To find the differential equation satisfied by P(t), differentiate P(t) with respect to t:
dP(t)/dt = [Insert the derivative of the function]

(c) To find the time at which the population doubles, first determine the initial population, P(0), then solve for t when P(t) is twice that value:
2*P(0) = P(t)
Solve for t: [Insert the solution for t]

(d) To find the time at which the population equals a specific value (let's call it N), set P(t) equal to N and solve for t:
N = P(t)
Solve for t: [Insert the solution for t]

Once you have the specific function P(t), you can follow these steps to find the answers to each part of your question.

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Answer: It should be -(x - 2)

Step-by-step explanation:

the reason is this right here

y - y1 = m(x - x1)

y1 = 4

x1 = 2

m = -1

y - 4 = -(x - 2)

point-slope form: y-y₁ = m (x-x₁)

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

slope-intercept form: y = mx + b

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

We can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).

What are the factors?

what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers divide 12 without leaving a remainder.

The figure given in the question is a quadrilateral with vertices at points A(-4,-1), B(-2,-1), C(-2,-3), and D(-4,-3), as shown in the diagram.

To dilate the figure by a scale factor of 2 with the origin as the center of dilation, we need to multiply the coordinates of each point by 2. When we multiply the x-coordinate of a point by 2, we stretch the figure horizontally by a factor of 2, and when we multiply the y-coordinate of a point by 2, we stretch the figure vertically by a factor of 2.

To find the new coordinates of each point, we apply the transformation:

A' = (2 * x-coordinate of A, 2 * y-coordinate of A) = (2 * (-4), 2 * (-1)) = (-8, -2)

B' = (2 * x-coordinate of B, 2 * y-coordinate of B) = (2 * (-2), 2 * (-1)) = (-4, -2)

C' = (2 * x-coordinate of C, 2 * y-coordinate of C) = (2 * (-2), 2 * (-3)) = (-4, -6)

D' = (2 * x-coordinate of D, 2 * y-coordinate of D) = (2 * (-4), 2 * (-3)) = (-8, -6)

So the new coordinates of the vertices of the dilated figure are A'(-8, -2), B'(-4, -2), C'(-4, -6), and D'(-8, -6), as shown in the diagram below.

To check our answer, we can see that the coordinates of A', B', C', and D' match with those given in option (OA).

Threfore, we can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).

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An integrated explanation of numerous hypotheses, supported by a large number of tests, and accepted by a majority of experts, is known as a theory .

Given,

Definition .

According to definition of theory,

A) It can be an explanation of scientific laws.

B) It is a total explanation of numerous hypothesis, each supported by a large body of results.

C) It is a summary and simplification of many data that previously appeared unrelated.

D) It is an assumption for new data suggesting new relationships among a range of natural phenomena.

Hence the definition given is of theory .

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Answer:

See below

Step-by-step explanation:

It opens upwards ( bowl shaped)   (vertex is on one side and focus on other with focus inside the parabola)

 axis of symmetry is  x = -8

  vertex is  (-8,0)

Answer:

c

Step-by-step explanation:

Answer:

c.

Answer: vw=r

Step-by-step explanation:

Got it right on the test

Answer:

(a) Candy's initial sum as a terms of x is $6x

(b) x = $60

(c) $350

Step-by-step explanation:

The given parameters are;

The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6

The amount Candy later gives Aliyah = $100

The amount Candy later gives Brenda = $50

The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3

(a) Whereby Aliyah has $3x at the start, we have;

Total sum of mony = Y

Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14

Therefore, Y×3/14 = $3x

x = Y×3/14 ÷ 3 = Y/14

Amount of Candy's initial share = Y × 6/14

Therefore Candy's initial sum as a terms of x = $6x

(b) Given that Aliyah's and Candy's initial sum as a function of x are   $3x and $6x, therefore, in the ratio 3:5:6, Brenda's  initial sum as a function of x = $5x

Which gives;

Total amount of money = $14x

With

6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3

Therefore, we have;

14·x × 2/(2 + 3 + 3) = (6·x - 150)

14·x × 2/(8) = (6·x - 150)

14·x × 1/4 = (6·x - 150)

7·x/2 = (6·x - 150)

12·x - 300 = 7·x

12·x - 7·x = 300

5·x = 300

x = $60

(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350

The final amount of money with Brenda = $350.

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Answer:

The y-intercept is where the line crosses the y-axis on the graph also where x=0. In this situation the y-value is however much money the waterpark will make depending on how many adult tickets sold.

There are 1,663,200 different orderings of the letters of millimicron containing the letters cr next to each other in order and the letters next to each other in order.

Total no. of letters = 11

Millimicron, dissecting will give us the following:

Number of m = 2

Number of i = 3

Number of l = 2

Number of c = 1

Number of n =1

Number of r = 1

Number of o = 1

o compute this by using permutation

total no. of ways to arrange = 11! ÷ [ 2! × 3! × 2! × 1! × 1! × 1! × 1!]

= 39,916,800 ÷ 24

= 1,663,200 is the answer

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When the current mortgage rates are high and expected to drop in the near future, the loans that will be gotten is one that has C. variable rate.

It should be noted that a mortgage simply means a loan that's made by a bank to purchase a house.

In this case, the current mortgage rates are high and expected to drop in the near future, the loans that will be gotten is one that has a variable rate. This is because once the mortgage rate decreases, one will pay a lesser amount.

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Answer:

D

Step-by-step explanation:

Recall that the area of a rectangle is given by the formula:

\(A=\ell w\)

Where l is the the length and w is the width.

If we increase our length by 20%, this means that we add 20% or 0.2 of our old length to our old length. So, our new length will be:

\(\ell_{\text{new}}=\ell + 0.2\ell = 1.2\ell\)

Similarly, if we increase our width by 10%, this means that we add 10% or 0.1 of our old width to our old width. So, our new width is:

\(w_{\text{new}}=0.1w+w = 1.1w\)

Therefore, our new area will be:

\(A_{\text{new}}=(\ell_{\text{new}})\left(w_{\text{new}}\right)\)

By substituting:

\(A_{\text{new}}=\left(1.2\ell\right)\left(1.1w\right)\)

Multiply:

\(\displaystyle A_{\text{new}}=1.32\ell w\)

Recall that the old area is given by:

\(\displaystyle A_{\text{old}} = \ell w\)

So, our area increased by a factor of 1.32. In other words, our area increased by 0.32 or 32%.

Therefore, our answer is D.

Answer:

D) 32

Step-by-step explanation:

\(\textsf {The original equation would be :}\)

\(\implies \mathsf {area = length \times width}\)

\(\textsf {Now, length has been increased by 20 percent and} \\\textsf {width has been increased by 10 percent.}\)

\(\textsf {Hence, new length and width will be :}\)

\(\implies \textsf {new length = length + 0.2(length) = 1.2(length)}\)

\(\implies \textsf {new width = width + 0.1(width) = 1.1(width)}\)

\(\textsf {Now the new area will be :}\)

\(\implies \mathsf {area' = 1.2(length) \times 1.1(width)}\)

\(\implies \mathsf {area' = 1.32 \times length \times width}\)

\(\textsf {Now finding the percent change in area, 'a' :}\)

\(\implies \mathsf {a = \frac{1.32 \times length \times width - 1 \times length \times width}{1 \times length \times width}}\)

\(\implies \textsf {a = 0.32 = 32 percent}\)

The correct option is D) 32 .

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

π 36 m^2

Step-by-step explanation:

C = 2π R = 12π m --> R = 6m

A = π R^2 = π 36 m^2

Answer:

Step-by-step explanation:

In the question we are given that circumference of circle is 12π m . And we are asked to find the area of circle in term of π .

Solution : -

For finding area of circle we need to find the radius of circle . In the question circumference of circle is given . So we can find radius of circle using it . We know that ,

\( \qquad \quad \pink{\underline{\pink{\boxed{\frak{Circumference_ {(Circle) }= 2\pi r}}}}}\)

Where ,

But as in the question , it is given that we have to find the area in term of π. So we aren't using π as 3.14 or 22/7 .

Now, Radius :

\( \longrightarrow \qquad \: 12 \cancel{\pi }= 2 \cancel{\pi} r\)

Step 1 : Cancelling π and we get :

\( \longrightarrow \qquad \:12 = 2r\)

Step 2 : Dividing both sides by 2 :

\( \longrightarrow \qquad \: \cancel{\dfrac{12}{2} } = \dfrac{ \cancel{2}r}{ \cancel2} \)

On further calculations we get :

\( \longrightarrow \qquad \: \boxed{ \bf{r = 6 \: m}}\)

Finding Area :

As we have find the radius of circle above so we can find its area easily . We know that ,

\( \qquad \: \qquad \pink{\underline{\pink{ \boxed{{\frak{ Area_{(Circle)} = \: \pi r {}^{2} }}}}}}\)

Now substituting value of radius :

\( \longmapsto \: \qquad \quad\pi (6) {}^{2} \)

\( \longmapsto \: \qquad \quad \pi \times \: 6 \times 6\)

\( \longmapsto \: \qquad \quad \pi \times 36\)

We get :

\( \longmapsto \: \qquad \quad \blue{\underline{\blue{\boxed{\frak{ \bf{36 \pi \: m {}^{2} }}}}}}\)