Which of the following values is closest to the mean for the set of data shown below?
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
A.45.9 B.50 C.58 D.54.3

The correct answer is:

A=4

B=5

hopes this helps you and future people!

Answer:

a = 4 and b = 5

Step-by-step explanation:

The simplest form of square root of eighty can be written as:

[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]

Now as it is a square root function, we will pair up the four 2's in two pairs.

And will take out [tex]2\times2[/tex] outside the square root.

Making the answer = [tex]2\times2\sqrt{5}[/tex]

or [tex]4\sqrt{5}[/tex]

So, a = 4

and b = 5

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

For any triangle, the sum of the measures of the three interior angles is always 180 degrees. An exterior angle is formed by extending one side of the triangle. The sum of the measures of the exterior angle and its corresponding remote interior angles is always 180 degrees. Therefore, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.

Final answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

Explanation:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

For example, if one of the remote interior angles of a triangle measures 40 degrees, then the corresponding exterior angle measures 40 degrees as well. The sum of the measures of the other two interior angles would be 140 degrees, making the exterior angle equal to 40 degrees.

Therefore, the correct option that completes the statement is equal to.

Final answer:

The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.

Explanation:

The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.

Steps to find the nonpermissible value:

Identify the denominator of the expression, which is (Y-3).

Set the denominator equal to zero: Y - 3 = 0.

Solve for y: Y = 3.

Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.

ok so original perimeter = 12 +12 + 17 +17 = 58 mm

if dimensions are multiplied by 12:

12*12 = 144 and 17*12 = 204

 new perimeter = 144 +144 +204 +204 = 696 mm

696 / 58 = 12

so the perimeter increased by a factor of 12, answer is A

Answer:

The perimeter is increased by a factor of 12.

Option (a) is correct .

Step-by-step explanation:

Formula

Perimeter of a rectangle = 2 (Length + Breadth)

As given

A rectangle has a length of 12 millimeters and a width of 17 millimeters.

Perimeter of a rectangle = 2 × (12 + 17)

                                         = 2 × 29

                                         = 58 millimeters ²

As given

when the dimensions are multiplied by 12 .

New Length = 12 × 12

                    = 144 millimeter

New Breadth = 17 × 12

                      = 204 millimeter

Thus

New Perimeter of a rectangle = 2 × (144 + 204)

                                         =  2 × 348

                                         = 696 millimeter²

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]

Therefore the perimeter is increased by a factor of 12.

Option (a) is correct .

Answer: C

c. It decreased the number of combinations by 8.

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.

For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.

Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.

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Jason will take 6 weeks to pay off the home theater system on layaway after making an initial down payment of $25 and weekly payments of $54.

The student's question is about how long it will take Jason to pay for a home theater system using a layaway plan. Jason has made an initial down payment of $25 and will make weekly payments of $54.

To calculate the time it will take to pay off the remaining balance, we subtract the down payment from the total cost: $349 - $25 = $324. Then, we divide the remaining balance by the weekly payment amount: $324 / $54 = 6. This means it will take Jason 6 weeks to pay off the home theater system on layaway.

The correct model for the bank service cost based on the number of checks written during a month is f(x)=0.45x + 12.50.

The question is asking for a model that would represent the cost of a bank service based on the number of checks written during a month. The bank charges $0.45 for each check, which is a variable cost that will change depending on the number of checks, represented by x. Additionally, they also have a monthly fixed service charge of $12.50, which is paid regardless of whether or not a check is written that month.

So, the amount paid every month is $0.45 multiplied by the number of checks, plus $12.50. In function format, that will be represented as $0.45x + $12.50, which is equivalent to the option D i.e f(x)=0.45x + 12.50. So, the correct model for the situation is D.

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Heather's quadratic function must have a double root at x = -6, suggesting a function of the form y = a(x + 6)² here 'a' is a nonzero coefficient. The orientation and width of the parabola depend on the value of 'a'.

Since Heather's quadratic function represents a parabola that touches but does not cross the x-axis at x =
–6, her function must have a double root at x= –6. To achieve this, the quadratic function should be in the form y = a(x + 6), where a is a non-zero coefficient.

The function that Heather could be writing will have a vertex at the point (-6, 0), as the parabola touches the x-axis at this point. Thus, a possible function can be y = (x + 6), if we assume a coefficient of 1 for simplicity. If a is negative, the parabola will open downwards, while a positive a will make the parabola open upwards. However, the exact value of a will depend on other conditions Heather might have, such as the position of the parabola in relation to the y-axis or specific points it must pass through.

Answer:

A)

subtracting; subtracting

Step-by-step explanation:

Answer:

(8,4)

Step-by-step explanation:

yes

The solution of the system is y = -30 and x = 30.

Here we have two equations:

y = -(4/5)*x - 6

y = -30

The second equation can be replaced in the first one, so we get:

-30 = -(4/5)*x - 6

Now we can solve that for x.

-30 + 6 = -(4/5)*x

24*(5/4) = x = 30

So the solution of the system is y = -30 and x = 30.

If you want to learn more about system of equations:

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Answer:

A

Step-by-step explanation:

10/cos30 degree

Charlie needs to apply a force in the opposite direction of the resultant vector sum of his brothers' forces. By converting the forces into Cartesian vectors based on the bearings, we can calculate the components of Charlie's required force to maintain equilibrium.

Step 1: Break down the forces into their x and y components

The force exerted by Noah can be broken down into its x and y components using the following equations:

F_x_Noah = F_Noah × cos(θ_Noah) = 8 N × cos(023°) ≈ 7.13 N

F_y_Noah = F_Noah × sin(θ_Noah) = 8 N ×  sin(023°) ≈ 3.71 N

The force exerted by Jude can be broken down into its x and y components using the following equations:

F_x_Jude = F_Jude ×  cos(θ_Jude) = 5 N × cos(155°) ≈ -4.95 N

F_y_Jude = F_Jude ×  sin(θ_Jude) = 5 N  × sin(155°) ≈ -0.58 N

Step 2: Sum the x and y components of the forces

To find the net force in the x-direction, we sum the x-components of the forces exerted by Noah and Jude:

F_x_net = F_x_Noah + F_x_Jude ≈ 7.13 N - 4.95 N ≈ 2.18 N

To find the net force in the y-direction, we sum the y-components of the forces exerted by Noah and Jude:

F_y_net = F_y_Noah + F_y_Jude ≈ 3.71 N - 0.58 N ≈ 3.13 N

Step 3: Calculate the magnitude of the net force

The magnitude of the net force can be calculated using the Pythagorean theorem:

F_net = √(F_x_net^2 + F_y_net^2) ≈ √(2.18 N^2 + 3.13 N^2) ≈ 3.74 N

Step 4: Find the angle of the net force

The angle of the net force can be calculated using the following equation:

θ_net = atan(F_y_net / F_x_net) ≈ atan(3.13 N / 2.18 N) ≈ 55.6°

Step 5: Calculate the force Charlie needs to exert

In order for Charlie to keep the toy fire truck in equilibrium, he needs to exert a force that is equal in magnitude and opposite in direction to the net force. Therefore, the force Charlie needs to exert is 3.74 N at an angle of 55.6° + 180° = 235.6° (since the net force is acting in the third quadrant).

Hello!

S=R*THETA

so s= is what you are looking for.

givens;

radius=12cm=.12m

theta(RADIANS ONLY)=2pi*2revs=4pi

s=.12*4pi=for an approximate answer of 1.50796m travelled

hope this helps. any questions please ask. thank you

Answer: A) m ≥ 22

Step-by-step explanation:

Hi, to answer this question we simply have to solve the inequality given for m (miles ran per week).

m + 6 ≥ 28  

Subtracting 6 from both sides:

m+6-6 ≥ 28 -6

m ≥ 22

Sean still needs to run 22 miles this week.

So, the correct option is A) m ≥ 22

Feel free to ask for more if needed or if you did not understand something.