Find the length of JN

The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.

The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.

The following is a presentation of the cosine function's generic form;

y =  a + cos(bx - c) + d

amplitude = a

b = cycle speed

Calculation for the model height;

The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Obtain amplitude 'a' as

[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]

The time 'T' is calculated as-

[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]

Now, calculate 'd'

[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]

Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:

h=0.5cos([tex]\pi[/tex]/6t)+9.5

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The complete question is-

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A. h=0.5cos([tex]\pi[/tex]/12t)+9.5

B. h=0.5cos([tex]\pi[/tex]/6t)+9.5

C. h=cos([tex]\pi[/tex]/12t)+9

D. h=cos([tex]\pi[/tex]/6t)+9

Answer: x=11

Step-by-step explanation:

The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.

4x-8 = 3x+3

x=11

Answer:

x = 11

Step-by-step explanation:

these angles are corresponding angles so they are equal to each other.

4x - 8 = 3x + 3 Subtract 2x from both sides

x - 8 = 3   Add 8 to both sides

x = 11

Plug 11 back into the equations find the angle measurements

4(11) -8 = 36 degrees

3(11) + 3 =  36degrees

Answer:

The answer to your question is C. There a specific quantifiable target that we are interested in or trying to predict.

Step-by-step explanation:

I hope this helps and have a good day!

The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

It is given that  the total weight of your backpack and its contents is 13 3/8 pounds.

Also given , we want to carry no more than 15 pounds.

Let the number of bottles we can carry be x.

Each bottles weigh 3/4 pounds.

Total weight of the bottles = 3x/4 pounds.

Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .

Thus the statement equation formed is -

⇒ 107/8 + 3x/4 = 15

⇒ 3x/4 = 13/8

⇒ x = 13/6 = 2.166

∴  x ≈ 2

Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .

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Based on the data set, B. Better measure of center: median. C. Better measure of spread: interquartile range (IQR).

The measure of center should be the median because the mean will be affected by the outliers on the left side.

The IQR will be the best measure of spread because the standard deviation is also affected by the outliers.

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Answer:

Option C more peaked and more widely spread.

Step-by-step explanation:

15 + 35 + 18 + 30 + 25 + 21 + 32 + 16

80 + 78 + 34

192/8 = 24

24 + 22 + 27 + 28

46 + 55 = 101/4 = 25.2

Answer:

  2.0 km

Step-by-step explanation:

The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.

The law of cosines tells us ...

  c² = a² +b² -2ab·cos(C)

Using the given values, we have ...

  c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)

Simplifying the equation, we get ...

  c² = 37.89 -37.8cos(26°) ≈ 3.91559

  c ≈ 1.979 . . . . km

The width of the strait is about 2.0 km.

Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:

(C) 19.

The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:

23 - 4 = 19.

Which means that option C is correct.

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Answer:

[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

Step-by-step explanation:

NOTE :

[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]

………………………………………

f(x) = x² + x +1

     [tex]=x^{2}+2\times \frac{x}{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

We can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.

Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as  the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices

So,  [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]

  [tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]

Thus, we can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

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Answer:4

Step-by-step explanation: 32\8 = 4

Answer:

60 local calls

Step-by-step explanation:

Total price minus the long-distance charges: 54.35 - 8.35 = $46.00

46 minus the fixed per month cost: 46-31 = $15

15 divided by the cost of each local call: 15/0.25 = 60 calls

The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a linear function, that is, a first grade polynomial. By geometry we know that a equation of the line can be known from two distinct points set on Cartesian plane:

Slope

m = [- 4 - (- 2)] / [4 - (- 2)]

m = (- 2) / 6

m = - 1 / 3

Intercept (m = - 1 / 3, (x, y) = (4, - 4)

b = y - m · x

b = - 4 - (- 1 / 3) · 4

b = - 4 + 4 / 3

b = - 8 / 3

Then, we find that the inequality is:

y ≤ (- 1 / 3) · x - 8 / 3

8 / 3 ≤ (- 1 / 3) · x - y

(- 1 / 3) · x - y ≥ 8 / 3

The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

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The rate at which the distance between the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.

Given length of ladder 39 m and the rate at which the wall is increasing is 101, the bottom of the ladder is 36 m from the wall.

Let bottom is x and the length of wall be y.

We have to find the rate at which the distance between the top of the ladder and the ground at that instant.

we have to find dy/dt.

We have to apply pythagoras theorem first.

[tex]x^{2} +y^{2} =39^{2}[/tex]---------------1

[tex]x^{2} +y^{2} =1521[/tex]

put the value of x=36 in the above equation

[tex]36^{2} +y^{2} =1521[/tex]

[tex]y^{2} =225[/tex]

y=15 m

We have to find the derivative of equation 1 with respect to t.

2x*dx/dt+2y*dy/dt=0

Because it is given that bottom is increasing at 101 meters per minute so dx/dt=101

2x*101+2y*dy/dt=0

put the value of y=15

2x*101+2*15*dy/dt=0

2x*101+2*15*dy/dt=0

dy/dt=-3030/2*36

dy/dt=-42.08

Hence the rate at which the rate at which the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.

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Question is wrong so it includes ladder length be 39 meters and the rate of increasing of bottom of ladder from bottom of wall is 101 meters per minute and the bottomis 36 m from the wall.

Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.

The chemist wants to end up with a total volume of 54 liters, so

[tex]a + b + c = 54[/tex]

and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so

[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]

He will also use twice as much of the 60% solution as the 30% solution, so

[tex]c = 2b[/tex]

Substitute this into the first two equations and solve for [tex]a,b[/tex].

[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]

Solve for [tex]b[/tex].

[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]

Solve for [tex]c[/tex].

[tex]c = 2(15) \implies \boxed{c=30}[/tex]

a = 9, b = 15 and c = 30 liters of each solution should be used.

According to the question:

Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.

a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.

and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so

0.20a + 0.30b + 0.60c = 24.3

Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.

Substitute this into the first two equations and solve for a,b

a + 3b = 54

0.20a + 1.50b = 24.3

[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]

a = 9.

9+3b = 54

3b = 45

b = 15.

c = 2(15)

c = 30.

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The sum of the areas of circle C and circle D is 98 units square. Option D

It is important to note that the if the circles overlap each other, then the most have the same radius

Also, the formula for area of a circle is given as;

Area = [tex]\pi r^2[/tex]

For Circle C

The value for π = 3. 142

radius = 7cm

Substitute the values into the formula

We have

Area = π × 7 × 7

Area = 49 π units square

For Circle D

Substitute the values into the formula

Area = [tex]\pi r^2[/tex]

Area = π × 7 × 7

Area = 49 π units square

Sum of the areas of circle C and circle D = area of circle C and area of circle D

Sum of the areas of circle C and D = 49π + 49 π

= 98 units square

The sum of the areas of the circles is 98 units square

Thus, the sum of the areas of circle C and circle D is 98 units square. Option D

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IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.

The relationship that can be proved is ΔACD ΔBCD, because of SAS.

The reason is that m<CDA=M<CDB=90°

CD=CD

AD=BD

Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when  the angle between the two side is equal.

Therefore the correct option is D.

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The cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3

VAT is an acronym for Value Added Tax. This is a tax attach to goods and products.

Given that the price of a new television is $423. This price includes VAT in 17 1/2%.

a) The cost of the television before VAT was added is calculated below.

Let the initial cost = C

(17.5 + 100)/100 x C = 423

117.5/100 x C = 423

1.175C = 423

C = 423/1.175

C = $360

b. By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. If the value of a television was $423 at the start of the year, the value of the television at the end of the third year will be calculated by using the formula

A = P(1 - R%)^3

Substitute all the parameters

A = 423(1 - 12/100)^3

A = 423 x [tex]0.88^{3}[/tex]

A = 288.3 dollars

Therefore, cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3

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The function that could represent the price tag's height relative to the table top is  h(t) = 4sin (22) +4

The question is incomplete because the options are not given and hence the correct option is shown below

Which function could represent the price tag's height relative to the table top, h(t), after it has been rolling for e seconds?

A n(t) = 2008(832) +2

B. h(t) =-2005(522) +2

C h(t) = –2sin(572) +2

D. h(t) = 4sin (22) +4

Given diameter is 4 inches and the time given is  5 seconds and

the number of rotations given is 4

We need to find the function that could represent the price tag's height relative to the table top .

Diameter = 4

So, Radius will be D/2 = 4/2

Radius=2

time given is  5 seconds and

the number of rotations given is 4

So ,   5/4 = 2π/w

Therefore ,

W = 8π / 5

Therefore

h(t) = h(t) = 4sin (22) +4

Hence The function that could represent the price tag's height relative to the table top is  h(t) = 4sin (22) +4

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when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.

How to find large cake pieces ?

Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]

So original large cake weight is

[tex]w=120*3\\\\w=360[/tex]

So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece

[tex]pieces=\frac{360}{2}\\=180[/tex]

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Answer:

(B). 25.25

Step-by-step explanation:

z + 54° + (3z + 1)° + 204° = 360°

4z + 259 = 360

z = 101 ÷ 4

z = 25.25  (B).

The option D is the correct option.

According to the statement

we have to define the sample variance in the words.

So,

The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.

and in the case of the population variance it becomes

The population variance is the average of the squared distances of the measurements on all units in the population from the mean.

This is the method by which we define the sample variance and population variance.

So, The option D is the correct option.

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Answer:

true

-9(z+8)

-9*z +(-9)*8

-9z-72

The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.

Given a fair dice and tossing a fair coin sixteen times.

We have to find the probability that the total number  of heads in all the coin tosses equals 12.

The probability lies between 0 and 1.

Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.

Let X shows the sum of heads while tossing.

P(X=12)=?

We can find the probability using binomial theorem.

=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]

We have to toss sixteen times and out of 16 times we need head 12 times.

=16!/12!4!*0.00024*0.0625

=1820*0.000015

=0.0273

Hence the probability that the total number of heads in all the coin tosses equals 12 is  0.0273.

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The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12

Given the expression;

5.5(x+6 1/2) - (x+9 1/3) - (19-x)

First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction

6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2

So, we have

(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )

Next, we remove the parentheses

11x/2 + 143/4 - x - 28/3 - 19 + x

11x/2 + 143/4 - 28/3 - 19

11x/2 + 317/12 - 19

11x/2 + 89/12

Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.

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Answer:

You subtract 249 minus 5

The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

The formula for finding the equation of a circle is expressed as:

(x-a)² + (y - b)² = r²

where

(a, b) is the centre

r is the radius

Given the following

(a, b) = (0, 0)

r = 12.5/2 = 6.25

Substitute

(x-0)² + (y - 0)² = 6.25²

x²+y²=39.0625

Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

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