1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages ​

A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.

To determine which type of function best fits the data, we can analyze the difference in the y values (Estimated Population) as x increases.

Differences between consecutive y values:

58,207 - 49,372 = 8,835

66,998 - 58,207 = 8,791

75,798 - 66,998 = 8,800

The differences between consecutive y values are relatively constant as x increases. This suggests that a linear function would be more appropriate than an exponential function

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Answer:

15h-6k+12m

Step-by-step explanation:

The perimeter of the triangle is the sum of all of its side lengths

P=a+b+c

If a=5h-4k

b=10h+7m

c=5m-2k

Then the formula would be

P=(5h-4k)+(10h+7m)+(5m-2k)

P=15h-6k+12m

Hope this helps!

Answer:

Four units left and one unit up

Step-by-step explanation:

Since we're subtracting from x, the figure is going to go toward the left side of the coordinate plane, and since we're adding to y, the figure is going to go up.

As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.

A tri object's volume is a measurement of how much space it takes up. The usual measurement tool is a cubic unit, such as a cubic metre (m3) or cubic foot (ft3). The formula used to determine a solid item's volume depends on the shape of the object. For instance, the volume of a cube is determined by multiplying the length of a single of its sides by six, whereas the capacity of a cylinder is determined by dividing the area of its base by the diameter. Engineering, mathematics, and architecture are just a few of the disciplines where the idea of volume is crucial.

given

The formula used to calculate a shipping box's volume is based on the box's dimensions.

The box's volume can be expressed as follows if its side length is s:

[tex]V = s^3[/tex]

As a result, the right response is s(23), which can be written as [tex]8s^3[/tex] as to calculate a shipping box's volume is based on the box's dimensions.

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Answer:

  A.  P

Step-by-step explanation:

You want to identify the point that represents a striking deviation in the given box plot.

The interquartile range for this box plot is the difference between the upper and lower quartiles:

  29 -26 = 3

The "fence" that is 1.5 times the IQR below the lower quartile is ...

  26 -3·1.5 = 21.5

Point P lies beyond this fence, so is considered an outlier in the data set.

Point P represents a striking deviation, choice A.

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Answer:

Step-by-step explanation: 0+0=0

Answer:

0

Step-by-step explanation:

0+0= nothing that why.

If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.

Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.

Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.

48700 = 4.87×10ⁿ = 4.87×10⁴

Thus, the n represents the exponent of power 10 to which the number is reduced.

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Based on the information, we identified that the scale used in the construction is approximately 1:35.2.

To find the scale used in the construction of the Crazy Horse Monument, we need to divide the height of the actual monument by the height of the model. Let's use the following formula to calculate the scale:

The height of the actual monument is 563 feet and the height of the scale model is 16 feet. Substituting these values in the formula, we get:

Simplifying the fraction, we get:

Therefore, the scale used in the construction of the Crazy Horse Monument is approximately 1:35.2.

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If cos(x) = -5/6, and x lies in quadrant"II", then exact values are:

sin(2x) = (-5√11)/(18);

cos(2x) = 7/18;

tan (2x) = -5√11/7.

We know that, Cos(x) = -5/6 and "x" is in quadrant II, so, we can use the Pythagorean identity to find sin(x):

sin(x) = √(1 - cos²(x)) = √(1 - (-5/6)²) = √(1 - 25/36) = √(11/36) = √11/6

Using the double angle trigonometry identities for sine and cosine, we find sin(2x) and cos(2x):

Substituting the value of Sin(x) and Cos(x),

We get,

sin(2x) = 2sin(x)cos(x) = 2(√11/6)(-5/6) = (-5√11)/(18);

cos(2x) = cos²(x) - sin²(x) = (-5/6)² - (11/6) = 25/36 - 11/36 = 14/36 = 7/18;

Finally, we find tan(2x) by using the identity:

tan(2x) = sin(2x)/cos(2x) = (-5√11/18) / (7/18) = -5√11/7.

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The volume of each cup shown above are as follows;

Volume of small cup = 50.24 in³.

Volume of medium cup = 127.56 in³.

Volume of large cup = 226.08 in³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the parameters, we have:

Volume of small cylinder, V = 3.14 × 2² × 4

Volume of small cylinder, V = 50.24 in³.

Volume of medium cylinder, V = 3.14 × 2.5² × 6.5

Volume of medium cylinder, V = 127.56 in³.

Volume of large cylinder, V = 3.14 × (6/2)² × 8

Volume of large cylinder, V = 226.08 in³.

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The missing parameters of the regular polygons are listed below:

Case 1: θ = 45°, a = 10.864 cm

Case 2: θ = 72°, s = 5.812 cm

In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:

Central angle

θ = 360 / n

Relationship between apothema and side length

a = s / [2 · tan (180 / n)]

Where:

Now we proceed to find missing parameters:

Case 1: s = 9 cm, n = 8

θ = 360 / 8

θ = 45°

a = (9 cm) / [2 · tan (180 / 8)]

a = 10.864 cm

Case 2: a = 8 cm, n = 5

θ = 360 / 5

θ = 72°

s = 2 · a · tan (180 / n)

s = 2 · (8 cm) · tan (180 / 5)

s = 5.812 cm

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The scale factor between a square of dimensions 7 by 7 and a scaled copy of dimensions 21/2 by 21/2 is 3/2 or 1.5.

We know that the dimensions of the square on the left are 7 by 7, and the dimensions of the square on the right are 21/2 by 21/2.

To find the scale factor, we can divide the dimensions of the square on the right by the dimensions of the square on the left

scale factor = (21/2) / 7

We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 7

scale factor = (21/2) / 7 = (21/2) * (1/7) = 3/2

Therefore, the scale factor is 3/2, or 1.5.

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Answer:

x =  7, y = 3, z = -4

Step-by-step explanation:

After 4 years, the investment of $700 at 4% compounded daily results in a future value of $821.45.

The future value represents the present value or investment compounded at an interest rate periodically for a certain number of years.

The future value can be determined using the FV formula or an online finance calculator.

N (# of periods) = 1,460 days (4 years x 365)

I/Y (Interest per year) = 4%

PV (Present Value) = $700

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $821.45

Total Interest = $121.45

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The difference between the adjustable-rate mortgage (ARM) and the  fixed-rate mortgage is $176,494.80.

First, find the total amount paid on the adjustable-rate mortgage would be :
= ( 5 years x 12 months x 2, 506.43 payment ) + ( 10 x 12 x 3, 059. 46 ) + ( 5 x 12 x 3, 646.76) + ( 5 x 12 x 3, 630.65 )

=  $ 1, 172, 971. 20

Then we can find the total payment for the fixed - rate mortgage :

= Monthly payment x Number of years

= 2, 767. 99 x 30 years x 12 months

= $ 996, 476. 40

The difference is:

= 1, 172, 971.20 - 996, 476. 40

= $ 176,494. 80.

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Answer:

To find the perimeter of a regular pentagon, you need to know the length of one side and the number of sides. In a regular pentagon, all sides have the same length and the shape has 5 sides.

Let's say the length of one side of the regular pentagon is 's'.

The formula for the perimeter of a regular pentagon is:

Perimeter = 5s

This is because a regular pentagon has 5 sides of equal length, so you can simply add the length of each side together 5 times.

Therefore, the perimeter of a regular pentagon with a side length 's' is 5s.

Step-by-step explanation:

Answer: 27.33

Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze

Answer: y = -|x + 1| + 1

Step-by-step explanation:

This is a "V" shaped graph, so we know it uses the absolute value function. This is the parent function:

    y = |x|

This represents the possible transformations:

➜ a is amplitude

➜ h is horizontal shift

➜ k is vertical shift

    f(x) = a | x - h | + k

Next, we see it is shifted one unit upwards.

    y = |x| + 1

Then, we see it is also shifted one unit left.

➜ Note that this shift is -h units, so we will use positive for moving left.

    y = |x + 1| + 1

Lastly, we see this graph is flipped and has a negative slope, or amplitude.

    y = -|x + 1| + 1

The integral for this problem has the result given as follows:

[tex]\int_2^5 -8f(x) dx = 168[/tex]

The integral over the largest region for this problem is given as follows:

[tex]\int_2^9 f(x) dx = -14[/tex]

The integral can be divided into two smaller regions, as follows:

[tex]\int_2^9 f(x) dx = \int_2^5 f(x) dx + \int_5^9 f(x) dx[/tex]

Hence the integral from x = 5 to x = 9 is given as follows:

[tex]-14 = \int_2^5 f(x) dx + 7[/tex]

[tex]\int_2^5 f(x) dx = -21[/tex]

Multiplying -21 by -8, the result of the integral is given as follows:

[tex]\int_2^5 -8f(x) dx = 168[/tex]

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the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.

b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.

The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.

Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)

P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19

Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

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If local supermarket offers a pack of 12 sodas for $3.48 on sale, and the local discount warehouse offers the soda in a 36-can case for $11.52, In terms of price per soda, the supermarket pack is the better value.

To determine which is the better value between the supermarket pack of 12 sodas for $3.48 and the discount warehouse 36-can case for $11.52, we need to calculate the price per soda for each option.

For the supermarket pack, the price per soda can be found by dividing the total cost by the number of sodas in the pack:

Price per soda = $3.48 / 12 = $0.29

For the discount warehouse case, the price per soda can be found by dividing the total cost by the number of sodas in the case:

Price per soda = $11.52 / 36 = $0.32

From these calculations, we can see that the price per soda is lower for the supermarket pack at $0.29 compared to $0.32 for the discount warehouse case. Therefore, in terms of price per soda, the supermarket pack is the better value.

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The ratio of the two arc lengths is equal to a / b. (Correct choice: B)

In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:

s = θ · r

Where:

s - Arc length

θ - Angle, in radians.

r - Radius

And the ratio of the length JK to the length MN is:

JK / MN = (θ · a) / (θ · b)

JK / MN = a / b

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The vertices that produces the circuit of lowest cost is A and D. So, the correct answer is A) and D).

To apply the repeated nearest neighbor algorithm, we need to start at a vertex and repeatedly choose the nearest neighbor until all vertices have been visited. Then, we return to the starting vertex to complete the circuit.

Starting at vertex A, we can follow the path A-DE-BE-C-AD-BC-E-A. The total cost of this circuit is 3 + 1 + 13 + 7 + 6 + 5 + 3 = 38. Starting at vertex B, we can follow the path B-E-DE-BC-AD-C-A-B. The total cost of this circuit is 1 + 3 + 7 + 6 + 5 + 15 + 10 = 47.

Starting at vertex C, we can follow the path C-BC-AD-DE-E-B-CA-C. The total cost of this circuit is 5 + 6 + 1 + 13 + 3 + 15 = 43. Starting at vertex D, we can follow the path D-AD-BC-C-E-DE-BD-DA. The total cost of this circuit is 6 + 5 + 7 + 3 + 10 + 11 = 42.

Starting at vertex E, we can follow the path E-DE-BE-C-BC-AD-CA-E. The total cost of this circuit is 1 + 13 + 7 + 5 + 6 + 15 = 47. Therefore, the circuits with the lowest cost are those starting at vertex A and vertex D, both with a total cost of 38 and 42 respectively. So, the correct option is A) and D).

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Using the continuously compounded interest formula, the amount of debt owed after 5 years is $ 8988.18

The continuous compounding interest formula is given by P = Peⁿˣ where

Since Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously? To determine that, we use the continuously compounded interest formula.

Given that

Substituting the values of the variables into the equation, we have that

P = Peⁿˣ

P = $7000e⁰°⁵ ˣ ⁵

P = $7000e⁰°²⁵

P = $7000(1.28)

P = $ 8988.18

So, the amount of debt owed is $ 8988.18

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Answer: 189 m^2

Step-by-step explanation:

Area = (Diagonal 1 x Diagonal 2) ÷ 2

Time taken by final lesson is 48 minutes and time consumption will not be affected if first lesson takes less time to finish.

Given that;

The time to finish five lessons = 4 hours

Then one lesson takes = 4/5 hours to finish

(a) Since  each lesson takes equal amount of time

Therefore,

The time taken by final lesson in minutes = (4/5)x60

                                                                      = 48 minutes

(b) Since each lesson has own capacity of time so the time consumption for other lesson is not affected if first lesson takes less time.

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Answer:

(x-3)(x+4)

Step-by-step explanation:

This way is how it s done in Greece. If u don't understand don't read the explanation Δ=β2-4αγ=81-32=49

χ1,2=-1+-7^2=3

=-4

Based on the data in the table, if Colin draws a marble 336 times, he predicts a yellow marble will be drawn roughly 63 times,  but probably not exactly 63 times.

Based on the data in the table, if Colin draws a marble 216 times, he predicts a white marble will be drawn roughly 2 times that a purple marble will be drawn.

If Colin draws a marble x times, he predicts a yellow marble will be drawn roughly 63 times.

The number of times = 63 / 3/16)

The number of times = 336 times.

If Colin draws a marble 216 times,

Number of times he can draw a white marble = 216 * 1/4

Number of times he can draw a white marble = 54 times

Number of times he can draw a purple marble = 216 * 1/6

Number of times he can draw a purple marble = 36 times

The number of times a white marble can be drawn more than a purple marble = 54/36 or 1.5 times more

The number of times a white marble can be drawn more than a purple marble is approximately two times.

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The proof that angles D and E are congruent is added below

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

∠CDB and ∠CEB are inscribed in a circle A.

The general rule is that angles that are inscribed in the same arc are congruent.

So, we have the following two column proof

Statements                                     Reasons

∠CDB = ∠CEB                                Given

Segments BD = CE                         CPCTC

Segments BE = CD                         CPCTC

Arcs BE = CD                                   Corresponding arcs

∠D = ∠E                                           Corresponding angles

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