Each year, a school committee sells donated cakes to raise money for a trip. The table shows the number of cakes sold each year for 5 years
Which measure of center best summarizes the number of cakes sold each year, and what is the value of the chosen measure?
Move a word and a value to the lines to complete the sentences.

The best measure of center for this data is the ____.

which has a value of ______.

mean

median

mode

21

22

23

The planet's a) size has virtually no effect on its structure.

The size of a planet does not affect its internal structure significantly because the same physical laws govern the formation and evolution of all planets. However, the size of a planet does have some impact on its atmosphere, gravity, and surface features.

For example, smaller planets may have weaker gravity, which makes it easier for gases to escape their atmosphere. Conversely, larger planets may have stronger gravity, which can compress their atmosphere and create more extreme weather patterns.

Overall, a planet's structure is primarily determined by its mass, composition, and magnetic field, rather than its size.

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Answer:

it will take about 14.3 years

The function rule of a table calculator, you need to examine the given input-output pairs in the table and look for patterns or relationships between the inputs and outputs.

The step-by-step process to determine the function rule:

Identify the pattern: Look for any consistent relationship between the input and output values. Consider how the output changes as the input changes.

Determine the type of relationship: Based on the pattern, determine the type of relationship between the input and output. It could be linear, quadratic, exponential, or some other mathematical relationship.

Write the general function rule: Once you determine the type of relationship, write a general function rule that expresses the output (y) in terms of the input (x) using appropriate mathematical operations and constants.

Test the function rule: Check if the function rule you derived matches the given input-output pairs in the table. Plug in the input values into the function rule and verify if the corresponding outputs match the given outputs in the table.

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Answer:

Step-by-step explanation:

what i do not undersante

49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

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To simplify, we multiply each single one in the first bracket with both in the second bracket :

\((3x+1)(3x-5) = 9x^{2} -15x + 3x - 5\)

Answer:

Distribute or Die part 2: Attack of the PEMDAS!

The equation that models this scenario is: \(c(x) = -2x^2 + 16x + 168\).

Given:

Average number of students per session = 14

Fee per session = $12

For every $2 increase in the fee.

Let x be the number of $2 fee increases.

So, the fee for each session is $12 + ($2 x) as there is a $2 increase for each x.

and, the average reduces by 1 for each $2 increase then the average number of students per session is 14 - x.

Now, the revenue generated

\({\text} Revenue (c(x)) =\) \({\text} Fee per session * Average number of students per session\)

Substituting the values of fee per session = 12 + 2x and Average= 14- x into above formula as:

\(c(x) = (12 + (2 x)) * (14 - x)\)

Expanding and simplifying the equation:

\(c(x) = (12 + 2x) * (14 - x)\)

\(c(x) = 168 - 12x + 28x - 2x^2\)

\(c(x) = -2x^2 + 16x + 168\)

Therefore, the equation is: \(c(x) = -2x^2 + 16x + 168\)

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Th question attached here seems to be incomplete, the complete question is:

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1. Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.

c(x) =_x^2 +_x+_

Answer:

Step-by-step explanation:

its correct [hope this helped]

Step-by-step explanation:

For crossing chords in a circle, the products of the segments are equal

6 * 4  =   x   *   14 -x

24 = -x^2 + 14x

-x^2 + 14x - 24 = 0      Use quadratic Formula ( or factoring ) to find:

x = 2   or  12      ( drawing is not to scale)

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer: rotation can be expressed as the composition of two reflections. A composition of reflections over two parallel lines is equivalent to a translation. Example: Given a || b, and pre-image ΔABC, where parallel lines are vertical. The composition of reflections over two intersecting lines is equivalent to a rotation. A composition of transformations is a combination of two or more transformations, each performed on the previous image. A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines). i hope this helps.

Step-by-step explanation:

Answer:

\(x-8y=-24\)

Step-by-step explanation:

Standard form of a linear equation:  \(Ax+By=C\)

(where A, B and C are integers, and A shouldn't be negative)

Given equation:

\(y=\dfrac{1}{8}x+3\)

Multiply both sides by 8:

\(\implies 8 \cdot y=8 \cdot \dfrac{1}{8}x+8 \cdot 3\)

\(\implies 8y=x+24\)

Subtract 8y from both sides:

\(\implies 8y-8y=x+24-8y\)

\(\implies 0=x+24-8y\)

Subtract 24 from both sides:

\(\implies 0-24=x+24-8y-24\)

\(\implies -24=x-8y\)

In standard form:

\(\implies x-8y=-24\)

Answer: 11

if u put 1 and 1 together

u get 11

Answer:

2

Step-by-step explanation:

1 +1=2

because 1 means you only have one thing then add one more thing that gives you two things

The likelihood that a shooter will hit the target at least 13 times is 27.92%.

For such a binomial distribution, the probability density function equals the amount of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of achievements is five (i.e., x = 13), as we are keen in the development that the objective will be hit exactly five times.

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit the target at most 13 times.

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Answer:

reeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{4x - 12}}}}}\)

Choice A is correct.

Step-by-step explanation:

\( \sf{8 - 4( - x + 5)}\)

Distribute -4 through the parentheses

\( \longrightarrow{ \sf{8 + 4x - 20}}\)

The negative and positive integers are always subtracted but posses the sign of the bigger integer

\( \longrightarrow{ \sf{4x - 12}}\)

Hope I helped!

Best regards! :D

Answer:

6.9

Step-by-step explanation:

6 4/5 in decimal form is 6.8.
6.9 is higher than 6.8 but lower than 7.

The area, in square units, between the two functions over the interval [−3,3]. is 36 square units

integral is defined to be exactly the limit and summation that we looked at in the last section to find the net area between a function and the

x-axis.

Also note that the notation for the definite integral is very similar to the notation for an indefinite integral.

the fact that a and b were given as an interval the lower limit does not necessarily need to be smaller than the upper limit. Collectively we’ll often call a and b the interval of integration.

\(\int\limits^3_3 {f(x)} \, dx -\int\limits^3_3 {g(x)} \, dx\\=\int\limits^3_3 {f(x) - g(x) } \, dx \\= \int\limits^3_3 {(x^{2} -9x-18) - (-9x-9)} \, dx \\=\int\limits^3_3 {x^{2} -9x-18 + 9x+9} \, dx \\\\=\int\limits^3_3 {x^{2} -9} \, dx\)

=\(\left \{ {{y=3} \atop {x=-3}} \right. (\frac{x^{3} }{3} -9x)\\= \frac{3^{3} }{3} -9*3 -( \frac{3^{-3} }{3} -9*-3)\\=9-27 +9-27\\= -36\)

The area, in square units, between the two functions over the interval [−3,3]. is 36 square units

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Answer:

1/3

Step-by-step explanation:

total is 1.

Left = 1 - 2/3

       = 1/3

The binomial vector B for the given space curve is i + j + k, and the torsion τ is 0.

To find the binomial vector B, we need to calculate the cross product of the tangent vector T and the normal vector N. Given T = \((1/\sqrt{(t^2+1)} )i + t/\sqrt{((t^2+1)} )j\) and N = (-t/√(t^2+1))i + (1/√(t^2+1))j, we can calculate their cross product:

T × N = \((1/\sqrt{(t^2+1)} )i + (t/\sqrt{(t^2+1)} )j * (-t/\sqrt{(t^2+1)} )i + (1/\sqrt{(t^2+1)} )j\) .

Using the cross product formula, the resulting binomial vector B is:

B = (1/√(t^2+1))(-t/√(t^2+1))i × i + (1/√(t^2+1))(t/√(t^2+1))j × j + ((1/√(t^2+1))i × j - (t/√(t^2+1))j × (-t/√(t^2+1))i)k.

Simplifying the above expression, we get B = i + j + k.

Next, to find the torsion τ, we can use the formula:

τ = (d(B × T))/dt / |r'(t)|^2.

Since B = i + j + k and T = (1/\(\sqrt{(t^{2+1)}}\))i + (t/√(t^2+1))j, the cross product B × T is zero, resulting in a zero torsion: τ = 0.

In summary, the binomial vector B for the given space curve is i + j + k, and the torsion τ is 0.

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A: (a) A = [0 1; -1 0]. This matrix has only real entries and when we square it, we get A² = [-1 0; 0 -1], which is equal to -I.

(b) B = [0 1; 0 0]. This matrix is not 0, but when we square it, we get B² = [0 0; 0 0], which is equal to 0.

(c) C = [0 1; -1 0] and D = [1 0; 0 -1]. When we multiply these two matrices, we get CD = [-1 0; 0 1] and DC = [0 -1; 1 0], which are opposite matrices.

(d) E = [1 1; 1 1] and F = [-1 1; 1 -1]. When we multiply these two matrices, we get EF = [0 0; 0 0], which is equal to 0, although no entries of E or F are zero.

Here is explanation -

(a) A = [[0, -1], [1, 0]] is a 2x2 matrix with real entries that satisfies A^2 = -I. To see this, we can simply calculate the square of the matrix A:

A^2 = [[0, -1], [1, 0]] * [[0, -1], [1, 0]]

= [[00 + -11, 0*-1 + -10], [10 + 01, 1-1 + 0*0]]

= [[-1, 0], [0, -1]]

As we can see, A^2 = -I, where I is the 2x2 identity matrix.

(b) B = [[0, 1], [0, 0]] is a 2x2 matrix with real entries that satisfies B^2 = 0, although B ≠ 0. To see this, we can calculate the square of the matrix B:

B^2 = [[0, 1], [0, 0]] * [[0, 1], [0, 0]]

= [[00 + 10, 01 + 10], [00 + 00, 01 + 00]]

= [[0, 0], [0, 0]]

As we can see, B^2 = 0, although B ≠ 0.

(c) C = [[0, 1], [-1, 0]] and D = [[0, -1], [1, 0]] are 2x2 matrices with real entries that satisfy CD = -DC. To see this, we can calculate the product of matrices C and D:

CD = [[0, 1], [-1, 0]] * [[0, -1], [1, 0]]

= [[00 + 10, 0*-1 + 11], [-10 + 01, -1-1 + 0*0]]

= [[0, 1], [1, 1]]

DC = [[0, -1], [1, 0]] * [[0, 1], [-1, 0]]

= [[00 - 11, 01 + -10], [10 - 0-1, 11 + 00]]

= [[-1, 0], [1, 1]]

As we can see, CD ≠ -DC, so C and D do not satisfy the condition CD = -DC, not allowing the case CD = 0.

(d) E = [[1, 1], [0, 1]] and F = [[1, 0], [1, 1]] are 2x2 matrices with real entries that satisfy EF = 0, although no entries of E or F are zero. To see this, we can calculate the product of matrices E and F:

EF = [[1, 1], [0, 1]] * [[1, 0], [1, 1]]

= [[11 + 10, 11 + 11], [01 + 10, 01 + 11]]

= [[1, 2], [0, 1]]

As we can see, EF = 0, although no entries of E or F are zero.

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a) The average velocity of a) is -14 ft/s.

b) The average velocity of b) is 100 ft/s.

c) The average velocity of c) is 180 ft/s.

d) The average velocity of d) is 840 ft/s.

e) The instantaneous velocity when t = 2 is -24 ft/s.

(a) If the height of the ball thrown in the air is given by y = 40t -16t2,

   the average velocity can be calculated for the time period beginning  

   when t = 2 and lasting 0.5 second using the given formula:

   Average velocity = [y(2 + 0.5) - y(2)] / 0.5= [y(2.5) - y(2)] / 0.5

   Now, substituting t = 2.5 and t = 2, we get,

   Average velocity = [40(2.5) - 16(2.5)2] - [40(2) - 16(2)2] / 0.5

 = [25 - 32] / 0.5

 = -14 ft/s

 Therefore, the average velocity is -14 ft/s.

(b) If the height of the ball thrown in the air is given by y = 40t -16t2,

the average velocity can be calculated for the time period beginning

when t = 2 and lasting 0.1 second using the given formula:

Average velocity = [y(2 + 0.1) - y(2)] / 0.1= [y(2.1) - y(2)] / 0.1

Now, substituting t = 2.1 and t = 2, we get,

Average velocity = [40(2.1) - 16(2.1)2] - [40(2) - 16(2)2] / 0.1

= [42 - 32] / 0.1

= 100 ft/s

Therefore, the average velocity is 100 ft/s.

(c) If the height of the ball thrown in the air is given by y = 40t -16t2,

the average velocity can be calculated for the time period beginning

when t = 2 and lasting 0.05 second using the given formula:

Average velocity = [y(2 + 0.05) - y(2)] / 0.05= [y(2.05) - y(2)] / 0.05

Now, substituting t = 2.05 and t = 2, we get,

Average velocity = [40(2.05) - 16(2.05)2] - [40(2) - 16(2)2] / 0.05

= [41 - 32] / 0.05

= 180 ft/s

Therefore, the average velocity is 180 ft/s.

(d) If the height of the ball thrown in the air is given by y = 40t -16t2,

the average velocity can be calculated for the time period beginning

when t = 2 and lasting 0.01 second using the given formula:

Average velocity = [y(2 + 0.01) - y(2)] / 0.01

= [y(2.01) - y(2)] / 0.01

Now, substituting t = 2.01 and t = 2, we get,

Average velocity = [40(2.01) - 16(2.01)2] - [40(2) - 16(2)2] / 0.01

= [40.4 - 32] / 0.01

= 840 ft/s

Therefore, the average velocity is 840 ft/s.

(e) The instantaneous velocity can be estimated when t = 2 by finding the derivative of the function y = 40t -16t2 with respect to time t.

The derivative of y is given by:

y' = 40 - 32tAt t = 2,

y' = 40 - 32(2) = -24 ft/s

Therefore, the instantaneous velocity when t = 2 is -24 ft/s.

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Step-by-step explanation:

3x-3(20)=12

3x=72

x=24.

24 stickers on each sheet

Answer:

x=10

Step-by-step explanation:

Answer:

I can't give an exact answer but...

Step-by-step explanation:

Try adding all three equations together and make them equal to 180. Then see what X.

So 3x + 11 + 7x - 5 + 9x - 16 = 180

Answer:

-3

Step-by-step explanation:

The k value represents when the function moves up or down.

Since there are no vertical compressions or shifts, we can just focus on how much the graph went down. The function g(x) went down 3 units.

Therefore, k would equal -3.

Answer:

$ 3,018.93

Step-by-step explanation:

This question is asking us to find the Principal.

Hence, the formula for compound interest that is compounded continuously is :

A = Pe^rt

P = Principal/Initial amount

A = Amount after investment = $7500

r = Interest rate = 7% = 0.07

t = time in years = 13 years

Hence,

7500 = Pe^0.07 × 13

P = 7500/e^0.07 × 13

P = 7500/e^0.97

P = $3018.9316803

Approximately P (The amount that should be invested ) = $3,018.93

E The relative frequency of a direction for the goalie is not the same as the relative frequency adjusted for the shooter's direction.

A is incorrect because the marginal relative frequencies for the shooter and the goalie are not equal.

B is incorrect because this does not indicate an association between the shooter's choice of direction and the goalie's choice of direction.

C is incorrect because this does not indicate an association between the shooter's choice of direction and the goalie's choice of direction.

D is incorrect because for the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.

E is correct because it indicates that there is an association between the shooter's choice of direction and the goalie's choice of direction. This is because the relative frequency of a direction for the goalie is not equal to the relative frequency conditioned on the shooter's direction.

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Answer:

\( \huge{ \fbox{ \sf{x = 5}}}\)

Step-by-step explanation:

\( \star{ \sf \: - 8 = 12 - 4x}\)

\( \text{Step \: 1 \: : Swap \: the \: sides \: of \: the \: equation}: \)

\( \mapsto{ \sf{12 - 4x = - 8}}\)

\( \text{Step \: 2 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \mapsto{ \sf{ - 4x = - 8 - 12}}\)

\( \text{Step \: 3 \: : Calculate}\)

\( \text{ \underline{Remember ! }} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}\)

\( \mapsto{ \sf{ - 4x = - 20}}\)

\( \text{Step \: 4 \: : Divide \: \: both \: sides \: by \: 4}\)

\( \mapsto{ \sf{ \frac{ - 4x}{ - 4} = \frac{ - 20}{ - 4}}} \)

\( \text{Step \: 5 \: : Calculate}\)

\( \mapsto{ \sf{x = 5}}\)

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.