Use a polynomial Identity to expand this squared binomial
(x + 6)2

1. Maximum height of the Function H(t) = -12cos( πt/45 ) + 18   is  30 units.

2. For the given sinusoidal function the values of the following are as follow :

amplitude = 6ft, period = π/3 , Maximum = 9ft,

Equation of the midline y = 6, Minimum = 3 ft.

Function with height 'H' is given by:

H(t) = -12cos( πt/45 ) + 18

Here 't' represents the time in seconds.

As we know that range of cosine trigonometric function is ,

-1 ≤ cosα ≤ 1

This implies cos function lies between  -1 and 1.

Replace cos( πt/45 ) by 1 or -1

For cos( πt/45 ) = 1

H(t) = -12(1) + 18

      = 6 units

For cos( πt/45 ) = -1

H(t) = -12(-1) + 18

      = 30 units

Maximum height is equals to 30 units.

Therefore, function H(t) = -12cos( πt/45 ) + 18  representing maximum height is equal to 30 units.

2. In general sinusoidal function is given by :

   y = Asin(Bx + C) + D

A is amplitude

A = High tide - low tide

   = 9 - 3 /2

   = 3ft

Time = 12:30 p.m.  - 6: 39 a.m.

        = 6 : 09 minutes

         = 6hours(approximately)

period B = 2π /T

              = 2π/6

              = π/3

Vertical shift = 9 - 3

                     = 6

Equation of the midline is

y = c

⇒ y = 6

Function is y = 3sin (π/3)x + 6

Maximum sin (π/3)x = 1

y = 9

Minimum sin (π/3)x = -1

⇒ y = 3

Therefore, the values of the following for the given function is :

amplitude = 6ft, period =  π/3 , Maximum = 9ft,

Equation of the midline y = 6, Minimum = 3 ft.

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Part A = The possible outcomes of each roll are the integers 1 to 6, with an equal chance of 1/6 for each number to appear.

Part B = Confidence Interval ≈ (0.201, 0.379)

Part C = The confidence interval does support Isaiah's suspicions that the die may not be fair, as it suggests a higher probability of landing on 5 compared to a fair die.

Explanation =

Part A: Simulation to Test Die Rolls :-

To simulate the rolling of a fair die, we can use a random number generator to mimic the outcomes.

Here's a step-by-step description of the simulation:

1) Representation: Let's represent each die roll as an integer from 1 to 6, with 1 representing a roll showing one dot, 2 for two dots, and so on, up to 6 for six dots.

2) Possible Outcomes: The possible outcomes of each roll are the integers 1 to 6, with an equal chance of 1/6 for each number to appear. For this simulation, we will specifically track how many times the die lands on the number 5.

3) Simulation Procedure:

a. Initialize a counter to zero, which will track the number of times the die lands on 5.

b. Repeat the following steps 100 times (representing 100 die rolls):

i. Generate a random number between 1 and 6, representing the result of the die roll.

ii. If the generated number is 5, increment the counter by 1.

4) Interpretation: After the simulation is completed, the value of the counter will represent the number of times the die landed on the number 5 out of the 100 rolls.

Part B: Constructing the 95% Confidence Interval :-

To construct the 95% confidence interval for the true proportion of rolls that will land on the number 5, we can use the formula for a confidence interval for proportions:

Confidence Interval = \(\pi \pm Z \times \sqrt{\frac{\pi(1-\pi)}{n}\)

Where,

π is the observed proportion of successes (rolling a 5) in the sample (total of 29/100).

Z is the critical value for a 95% confidence level (approximately 1.96 for a large sample size).

n is the sample size (100 rolls in this case).

Now, let's calculate the confidence interval:

π = \(\frac{29}{100}\)

π = 0.29

Z = 1.96

n = 100

Confidence interval = \(0.29 \pm 1.96 \times \sqrt{\frac{0.29(1-0.29)}{100}\)

= \(0.29 \pm 1.96 \times \sqrt{\frac{0.29 \times 0.71 }{100}\)

= \(0.29 \pm 1.96 \times \sqrt{\frac{0.2059}{100}\)

= \(0.29 \pm 1.96 \times 0.04537\)

Therefore,

Confidence Interval ≈ (0.201, 0.379)

Part C: Interpretation of the Confidence Interval :-

The 95% confidence interval for the true proportion of rolls landing on the number 5 is approximately (0.201, 0.379).

This means that based on the data from the simulation, we are 95% confident that the true proportion of rolls resulting in a 5 lies between 20.1% and 37.9%.

Isaiah's suspicion is that the die landed on the number 5 more often than usual. Since the lower bound of the confidence interval is 20.1%, which is above 0 (no rolls with a 5), it suggests that the true proportion of rolls resulting in a 5 could be higher than expected.

Therefore, the confidence interval does support Isaiah's suspicions that the die may not be fair, as it suggests a higher probability of landing on 5 compared to a fair die.

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Answer: 25

Step-by-step explanation: I just entered the equation into my calculator like so.

A negative number times a negative number equals a positive number.

I hope this helps, have a nice day.

Answer: this one is the hardest one i had all year

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

\(\frac{AB}{DE}\) = \(\frac{BC}{EF}\) ( substitute values )

\(\frac{x}{24}\) = \(\frac{9}{27}\) = \(\frac{1}{3}\) ( cross- multiply )

3x = 24 ( divide both sides by 3 )

x = 8

Answer:

2.75 hours, or 2 hours and 45 minutes

Step-by-step explanation:

Subtract the cost of materials from the bill, 134-46=88.

Then, for every hour, he charges 32, so divide the difference by 32, 88/32.

Answer:

10

Step-by-step explanation:

-7x+3y=30

3y=7x+30

y=7/3x + 10

if x = 0

y = 10

Answer:

its 5

Step-by-step explanation:

think about it,  if you pick 4 socks, it cold be all four different colors but if its 5 then there has to be at least one pair of matching socks so the answer is 5

The equivalent expression of a + 5 is -(-a - 5)

The expression is given as:

a + 5

Multiply by 1

1 * (a + 5)

Express 1 as -1 * -1

-1 * -1 * (a + 5)

Open the bracket

-1 * (-a - 5)

This gives

-(-a - 5)

Hence, the equivalent expression of a + 5 is -(-a - 5)

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The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.

The numeric value of an expression is found replacing each letter by it's attributed value.

In this problem, the expression is:

-a² - 2bc - |c|

The attributed values are:

a = -3, b = -5 and c = 2

Hence the numeric value will be given by:

-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.

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Answer:

Not enough info.

Step-by-step explanation:

We do not have enough information as we are only given the measure of 2 sides in triangle ABC and one side in triangle XYZ. The side XY is congruent to AB as they correspond to each other.

So the perimeter could be 12.5, 17 or 17.5.

Answer:

Not enough information

Step-by-step explanation:

With the information given, we can only find two sides.

It could be represented by: 5+7+x = P, This is an equation with many solutions, and so, we don't have enough information.

Answer:

First you make 3/10=0.3 the 1/3=0.33 then 0.3+0.33=0.63

Answer:

The correct option is;

A(-12, -19) and B(20, 45) matches with point C(6, 52) such that ∠ABC = 90°

Step-by-step explanation:

Given slope AB =

A point is perpendicular to two points

Where A(3, 3), B(12, 6) C(6, 52) we have;

Slope AB = (3 - 6)/(3 - 12) = -3/(-9) = 1/3

Slope BC = -3

y - 12 = -3(x - 6)

y = -3x + 18 + 12 = -3x + 30

A(-10, 5) and B(12, 16)

Slope AB = (5 - 16)/(-10 - 12) = -11/(-22) = -1/2

Slope BC = 2

y - 16 = 2(x - 12)

y = 2x - 24 + 16 = 2x - 8

A(-8, 3) and B(12, 8)

Slope AB = (3 - 8)/(-8 - 12) = -5/(-20) = -1/4

Slope BC = -4

y - 8 = -4(x - 12)

y = -4x + 48 + 8 = -4x + 56

A(12, -14) and B(-16, 21)

Slope AB = (-14 - 21)/(12 + 16) = -35/(28)

Slope BC = 28/35

y - 21 = 28/35(x + 16)

y = 28/35x + 28/35*16 + 21 = -4x + 56

A(-12, -19) and B(20, 45)

Slope AB = (-19 - 45)/(-12 - 20) = 2

Slope BC = -1/2

y - 45 = -1/2(x - 20)

y = -1/2x + 10 + 45 = -1/2x + 55

Which corresponds with the point C(6, 52)

A(30, 20) and B(-20, -15)

Slope AB = (20 + 15)/(30 + 20) = 35/50 = 7/10

Slope BC = -10/7

y + 15 = -10/7(x + 20)

y = -10/7x - 10/7*20 - 15 = -10/7x - 305/7

Answer:

A(3, 3) and B(12, 6)  =  C(16, -6)

A(-10, 5) and B(12, 16) = C(18, 4)

A(-12, -19) and B(20, 45) =  C(6, 52)

A(12, -14) and B(-16, 21) =C(-11, 25)

Step-by-step explanation:

that it is important for likert-type scale response choices to be balanced at the ends of the response continuum. This means that there should be an equal number of positive and negative response options to avoid any bias or skew in the results.

An explanation for this is that if there are too many positive or negative response options, respondents may feel pressured to choose a certain option even if it doesn't accurately reflect their true opinion. This can result in inaccurate data and can skew the results of the survey or study.

balancing the response choices on a likert-type scale is crucial for obtaining accurate and unbiased data. By having an equal number of positive and negative options, respondents are more likely to provide honest and accurate responses.

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The measure of the smallest angle of the quadrilateral is  60° .

In the question ,

it is given that ,

the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .

So , the measure of the largest angle is = 9x

and the measure of the smallest angle is = 4x .

we know that the sum of the measure of all the angles of the quadrilateral is 360° .

that means ,

4x + 5x + 6x + 9x = 360°

24x = 360

dividing both sides by 24 ,

x = 360/24

x = 15 .

the smallest angle is = 4(15) = 60°

Therefore ,  The measure of the smallest angle of the quadrilateral is  60° .

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In order to calculate the diameter of the soap bubble, we need to use the Laplace equation and solve for the radius of the bubble.The diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

We will then double the radius to get the diameter of the bubble.Here's the solution:

Given that:

Radius of the soap bubble =

r = 0.065 mm

= 6.5 x 10⁻⁵ m

Surface tension of soap in air =

σ = 0.019 N/m

Pressure outside the bubble =

P₂ = 75.0 kPa

= 75,000 Pa

Ambient temperature =

T = 300 K

Atmospheric pressure =

P₁ = 1 atm = 101,325 Pa

Laplace's equation states that the pressure inside the bubble is given by:

Pinside = Poutside + (2σ/r)

where σ is the surface tension and r is the radius of the bubble.

Rearranging the above equation to solve for the radius of the bubble:

2σ/r = Pinside - Poutside

r = 2σ/(Pinside - Poutside)

Substituting the given values into the above equation:

r = [2 x 0.019] / [Pinside - 101325]

After the soap bubble rises up, the pressure outside the bubble becomes 75 kPa.

Therefore:

Pinside - 101325 = 75000

Pinside = 176325 Pa

Substituting this value of Pinside into the above equation:

r = [2 x 0.019] / [176325 - 101325]

= 4.02 x 10⁻⁷ m

The diameter of the soap bubble is twice the radius:

D = 2r = 2 x 4.02 x 10⁻⁷ m

= 8.04 x 10⁻⁷ m

Converting the diameter to mm:

D = 8.04 x 10⁻⁷ m x 1000 mm/m

= 8.04 x 10⁻⁴ mm (answer)

Therefore, the diameter of the soap bubble is 8.04 x 10⁻⁴ mm.

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i am not sure

but I think it is a

The length of AE is given as follows:

AE = 7 units.

The midsegment of a triangle states that the segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.

The midsegment of the triangle in this problem is given by the following segment:

BD.

The length of BD is given as follows:

BD = 2 - (-1.5)

BD = 3.5 units.

Hence the length of AE is obtained as follows:

AE = 2BD

AE = 2 x 3.5

AE = 7 units.

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The path that the Bettle walks is given in the Image attached. The two points at which they can meet are marked accordingly. These are the intersections of the circle - Points C and D.

An arc is a trajectory produced in geometry when the distance from a given point has a set numerical value.

The following actions must be done to identify points C and D:

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Full Question:

Bertie Beetle walks so that he is always exactly 1.3 cm from Crumb A. Adam Ant walks so that he is always exactly 3.5 cm from Crumb B. There are only two points at which they can meet - mark the points with crosses.

Answer:

The percentage increase from 8000 to 10000 is 25%.

The percent of increase from 8000 to 10000 is given as 25%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100. The percent of increase or decrease can be found by taking the ratio of the increased or decreased value to the initial value.

The given numbers are 8000 and 10000.

The percent increase can be obtained as follows,

The increased value ÷ Initial number × 100

⇒ (10000 - 8000) ÷ 8000 × 100

⇒ 2000 ÷ 8000 × 100

⇒ 25%

Hence, the percent increase is obtained as 25%.

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x is -7. The solution set for an equation is the set of all values of the variable that make the equation true.

To find the solution set for the equation -3x - 4 = 17, we can use the following steps:

Isolate the variable on one side of the equation. To do this, we can add 4 to both sides of the equation:

-3x - 4 + 4 = 17 + 4

-3x = 21

Divide both sides of the equation by the coefficient of the variable. To do this, we can divide both sides of the equation by -3:

(-3x)/(-3) = 21/(-3)

x = -7

The solution set for the equation -3x - 4 = 17 is therefore x = {-7}. This means that the value of x that satisfies the equation is -7.

It is important to note that a solution set is the set of all values of the variable that make the equation true. In this case, there is only one value of x that satisfies the equation, so the solution set is a singleton set.

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Answer:

3/20 (fraction form) OR 0.15 (decimal form)

Step-by-step explanation:

First, you multiply 3/4*1/5 which would be 3*1/4*5, which is 3/20.

Answer:

60 cm^2

Step-by-step explanation:

I did it hope it helps

Answer: 60 cm²

Step-by-step explanation:

OUTLINE:

1. Find the area of triangles

2. Find the area of rectangles

SOLVE:

#1 Area of Triangles

Formula: a=(1/2)bh

a=area

b=base

h=height

b=6 cm

h=4 cm

a=(1/2)bh

a=(1/2)(6)(4)

a=12 cm²

There are 2 triangles ⇒ 12×2=24 cm²

#2 Area of Rectangles

Formula: a=bh

b=base

h=height

b=6 cm

h=2 cm

a=bh=6×2=12 cm²

There are 3 rectangles ⇒ 12×3=36 cm²

Find the total surface area: 36+24=60 cm²

Hope this helps!! :)

Please let me know if you have any questions

ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.

What is congruent ?

In geometry, congruent refers to the condition where two or more figures have the same size and shape. Congruent figures have the same dimensions, angles, and proportions. Two figures are congruent if they can be superimposed exactly on each.

1) If, C.) Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.

2) If, D.) Angle A is congruent to angle D then ∆ABC and ∆DEF are congruent by the SAS criterion.

3) ∆ABC and ∆DEF are congruent if B.) AB=DE

ASA criterion: If in two triangles, two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.

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The list of all the positive common divisors of 48 and 60 is:1, 2, 3, 4, 6, 12.

To find all the common divisors of 48 and 60, we need to first list the divisors of both numbers. So let's list out the divisors of both 48 and 60.

Divisors of 48:1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Divisors of 60:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Now, we can identify the common divisors by comparing the two lists. The common divisors of 48 and 60 are:1, 2, 3, 4, 6, 12

In division, we divide a number by any other number to get another number as a result. So, the number which is getting divided here is called the dividend. The number which divides a given number is the divisor.

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The sample range, denoted as r, is defined as the difference between the maximum value and the minimum value in a sample. It must always be true that the sample range is greater than or equal to zero.

The sample range is a measure of the dispersion or spread of a set of data points in a sample. It is calculated as the difference between the maximum value and the minimum value in the sample.

By definition, the maximum value in the sample cannot be smaller than the minimum value. This means that the difference between these two values will always be greater than or equal to zero. Therefore, the sample range will always be greater than or equal to zero.

A sample range of zero indicates that all the values in the sample are the same, resulting in no variation or spread. On the other hand, a positive sample range indicates that there is variation in the data, with the extent of the variation increasing as the range becomes larger.

In conclusion, it is always true that the sample range (r) is greater than or equal to zero, as the minimum value cannot exceed the maximum value in the sample.

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La probabilidad de obtener en el dado blanco un número menor que tres y en el rojo un valor mayor a tres es:

p = 1/6.

Tiramos dos dados, uno blanco y uno rojo, y queremos obtener la probabilidad de obtener un número menor a 3 en el dado blanco y un numero mayor a 3 en el dado rojo.

Primero, el dado blanco tiene los posibles valores {1, 2, 3, 4, 5, 6}, los valores menores que 3 son {1, 2}

Entonces 2 de 6 resultados son menores que 3, es decir, la probabilidad es:

P = 2/6 = 1/3.

Para el dado rojo los posibles valores son los mismos, y los valores mayores que 3 son {4, 5, 6}, entonces 3 de 6 resultados son mayores que 3, es decir, la probabilidad es:

Q = 3/6 = 1/2.

La probabilidad conjunta es el producto de la dos probabilidades individuales:

p = P*Q = (1/3)*(1/2) = 1/6.

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Answer: $164

Step-by-step explanation:

25*7=175

175+12.5

226.50-187.50

5*25=125+39

Jones family payed $164

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

  2048

Step-by-step explanation:

You want the value of a10 = 4(2^(10 -1)).

If you don't have powers of 2 memorized, you can put this expression into your calculator or spreadsheet to get it evaluated. You will need parentheses around the exponent.

  4(2^(10-1)) = 4(2^9) = 4(512) = 2048

The value of the expression is 2048.

__

Additional comment

This looks like an instance of the equation for the n-th term of a geometric sequence:

  an = a1·r^(n -1)

where a1 = 4, r = 2, and n = 10.

This is why we have assumed that the "-1" is part of the exponent, and that you simply want the value of the right-side expression.

If this equation means something else, then it needs to be written differently. For example, if a10 means 'a' to the 10th power, it needs to be written as a^10, and we need to be told we're solving for 'a'.

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