a small bookshelf is 8/12 yard long. How many books can fit on the shelf if the width of each book is 1/24 yard? Explain

The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:

c.5pi/4

d.7pi/4

To solve this equation, we can start by isolating the cosine term on one side of the equation:

[tex]2cos(x) = -\sqrt{2[/tex]

[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]

The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).

The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].

Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:

[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]

where k is an integer.

Substituting the values from the given choices into this equation, we find that the possible solutions are:

[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]

Therefore, the correct answer is c. and d.

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Answer:

b.3pi/4 

c.5pi/4 

Step-by-step explanation:

The average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3 is

a(x)= -13

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends. Following is the formula for the average rate of change:

a(x) = [f(b) - f(a)]/(b - a)

where,

a(x) = Average Rate of Change

f(a) = Function Value at a

f(b) = Function Value at b

Given,

g (x)=-2x³ +5x² from x=2 to x = 3

Average rate of change is a(x)

g (x)=-2x³ +5x²

Put x=2 in the above equation

g(2)= -2(2)³+5(2)²

= -16+20

=4

g(2)=4

Now, put x=3 in the above equation

g(3)= -2(3)³+5(3)²

= -57+45

= -9

We know that,

Average rate of change a(x)= (g(b)-g(a))/(b-a)

a(x)= g(3)-g(2)/(3-2)

a(x)= (-9-4)/1

a(x)= -13

Therefore, the average rate of change a(x)= -13

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Answer: w ≤ 2200 would represent the situation

Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.

The point that divides a line segment into two equal halves is known as the midway in geometry. A point that divides a line segment into two equal halves is the midpoint of the segment. In other words, the line segment's midpoint is precisely in the middle. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

Given,

VZ = s + 14

WY = s

VZ bisects WY

VZ = 2WY

s + 14 = 2(s)

s + 14 = 2s

2s - s = 14

s = 14

Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.

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According to question.

Given data,

The dilation of ABCD using centre D

And scale factor 1/3

Lebel the dilation IJKL.

With the help of figure,

The dilation of ABCD shown in the figure,

The centre of D shown in the figure,

when EFGH, IJKL are obtained from scaling factor ½,1/3 respectively,

then,

ABCD≈EFGH

and

ABCD≈IJKL

Therefore,

EFGH≈IJKL

(Quadrilaterals similar to the same quadrilateral)

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The gradient of the blue line as shown in the graph is 0.25

The gradient of any line or curve tells us the rate of change of one variable with respect to another.

To calculate the gradient of the blue line, we use the formula below.

Formula:

Where:

From the graph,

Given:

Substitute these values into equation 1

Hence, the gradient of the blue line is 0.25.

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When Haresh weighs 54 pounds on Earth, his weigh on the moon will be 9 pounds.

From the information, person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh only 30 pounds on the moon.

The constant of proportionality will be:

= 180 / 30.

= 6..

Therefore, Haresh weighs 54 pounds on Earth, his weigh on the moon will be:

= 54 / 6

= 9 pounds.

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Answer:

[tex]P = \boxed{\sf 4000}[/tex]

[tex]r=\boxed{\sf 0.03}[/tex]

[tex]n=\boxed{\sf 4}[/tex]

[tex]t=\boxed{\sf 5}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

If you invest $4,000 then the principal amount is $4,000.  As P represents the principal amount:

[tex]\implies P = \boxed{\sf 4000}[/tex]

The interest is 3%.  3% = 3/100 = 0.03.  Therefore:

[tex]\implies r=\boxed{\sf 0.03}[/tex]

"n" represents the number of times interest is applied per year.  

Therefore, if the interest is applied quarterly then:

[tex]\implies n=\boxed{\sf 4}[/tex]

"t" represents the time in years.  Therefore, if you plan to leave the money in the account for 5 years then:

[tex]\implies t=\boxed{\sf 5}[/tex]

-----------------------------------------------------------------------------------------

To calculate the amount in the account after 5 years, substitute the values into the formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.03}{4}\right)^{4 \times 5}[/tex]

[tex]\implies A=4000\left(1+0.0075\right)^{20}[/tex]

[tex]\implies A=4000\left(1.0075\right)^{20}[/tex]

[tex]\implies A=4000(1.16118414...)[/tex]

[tex]\implies A=\$4644.74[/tex]

The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.

From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:

                                       Day                                 Time

First dose                    Monday                               9 am

Second dose              Monday                               9 pm

Third dose                  Tuesday                               9 am

Fourth dose                Tuesday                               9 pm

Fifth dose                   Wednesday                          9 am

Sixth dose                  Wednesday                          9 pm

Seventh dose               Thursday                            9 am

Therese will therefore take the seventh dose at 9 am on Thursday.

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Answer:

7.5 minutes

4/3 km

Step-by-step explanation:

Use a proportion.

2 km is to 3 min as 5 km is to x min

2/3 = 5/x

2x = 3 × 5

2x = 15

x = 7.5

Answer: 7.5 minutes

2 km is to 3 min as x km is to 2 min

2/3 = x/2

3x = 2 × 2

3x = 4

x = 4/3

Answer: 4/3 km

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

Define the variable:

Given information:

First equation

The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:

⇒ 4x + $1.90 = $22.20

⇒ 4x + 1.9 = 22.2

Second equation

The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:

⇒ $22.20 - 4x = $1.90

⇒ 22.2 - 4x = 1.9

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

The distance between the line segments PQ, RS and TV are √53 respectively

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The formula is given as;

d = √(x₂ - x₁)² + (y₂ - y₁)²

In the first line segment;

P = (0,4), Q = (7, 2)

d = √((7-0)² + (2 - 4)²)

d = √53

b)

R = (-7, 6), S = (-5, -1)

d = √((-1 - 6)² + (-5 --7)²)

d = √53

c)

T = (0, -8), V = (2, -1)

d = √((-1 --8)² + (2 - 0)²)

d = √53

The distance between the lines are all √53 units

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Answer:

B

Step-by-step explanation:

g(x) = 12x - 2

g(1/4) = 12(1/4) - 2  ==> plug in 1/4 for x

g(1/4) = 12 * 1/4 - 2

g(1/4) = 12/4 - 2

g(1/4) = 3 - 2

g(1/4) = 1 ==> B

Answer:

Step-by-step explanation:

To evaluate g(1) for the function g(x) = 12x - 2, you can substitute the value 1 for x in the function:

g(1) = 12(1) - 2

g(1) = 12 - 2

g(1) = 10

Therefore, g(1) = 10. B

Answer:

2.5

Step-by-step explanation:

m is the gradient

to find this we do the change in y/change in x

using the first 2 values we have been given:

change in y= 15-10

change in x= 4-2

5/2= 2.5

the gradient in 2.5

a. The hare's distance from the starting line is represented by the expression 7.5t.

b. The tortoise's distance from the starting line is represented by the expression 4.5t+820.

c. The number of meters the tortoise is ahead of the hare is represented by the expression 4.5t+820-7.5t.

In the race, the hare is running at a constant speed of 7.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to run that distance. This is represented by the expression 7.5t, where t is the time in seconds it takes the hare to run.

Similarly, the tortoise is crawling at a constant speed of 4.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to crawl that distance, plus the 820-meter head start they were given. This is represented by the expression 4.5t+820, where t is the time in seconds it takes the tortoise to crawl.

To find the number of meters the tortoise is ahead of the hare, we subtract the hare's distance from the starting line from the tortoise's distance from the starting line, which gives us the expression 4.5t+820-7.5t.

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The interest earned over the 1103 day period is $840

Aaliyah will have $7840 in the account at the end of the 1103 day period.

Simple interest is defined as the amount of money that is paid to an individual following an investment that is made to an account.

The amount of money invested = $7,000.00

The rate of interest= 4%

The time of investment = 1103 = 3 years

Simple interest = P×T×R/100

= 7000×4×3/100

= 84000/100

= $840

The amount of money that is in the account at the end of the 1103 day period = 7000 + 840 = $7,840

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Alison has traveled six miles on her bike.

Distance is defined as the product of speed and time.

To find how far Alison has ridden her bike, we need to first convert 8 1/2 miles to miles as a mixed number.

We can do this by multiplying the fractional part of the mixed number by the denominator of the fraction:

8 1/2 miles = 8 miles + (1/2 x 2) miles = 8 miles + 1 mile = 9 miles

We can now multiply this distance by 2/3 to find how far Alison has ridden her bike:

9 miles x 2/3 = 6 miles

Therefore, she has ridden her bike 6 miles.

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Step-by-step explanation:

correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For

Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, [tex]\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}[/tex].

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

[tex]f(x)=2x+100[/tex]

This can be checked by using the values given in the problem:

[tex]f(30)=2(30)+120=180\\f(50)=2(50)+120=220[/tex]

The base rate of $120 and $2 per person satisfies the given equation and established values.

The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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The population of the island after 10 years will be approximately 2385.

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].

Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.

Given,  an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.

∴ The population be 10 years from now will be,

[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].

We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.

[tex]y_{10} = 1767e^{0.3}[/tex].

[tex]y_{10} = 1767\times1.35[/tex].

[tex]y_{10} = 2385[/tex].

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Answer:

Below

Step-by-step explanation:

358.584 is about 360      8.92 is about 9

360 / 9 = 40 approx   by' doing it in your head '

ACTUAL answer = 358.584/8.92 = 40.2   Pretty darn close !

The mean is 1.2 ,variance is 0.96 and standard deviation of the given data is 96 square root.we can find all these data by using formula of probability.

Probability means possibility.It is a branch that deals with occurrence of random event.The value is given in the probability from 0 to 1.Probability is how likely something is to happen.It is  used in real life for analysis data.we can find probability to favorable outcomes divided by total outcomes.

Standard deviation measures how far apart numbers are in a data set.Variance gives us the actual value to how much the numbers in a data set vary from the mean.The variance is equal to the square standard deviation and standard deviation is the square root of the variance.

NOW we have data

Person(ill)=20% =0.20        n=6

For Exactly two  p(x) =2

now we get  24.58% by using binomial theorem and putting value in the formula.

NOW for at least one p(x)>1  By putting value we get 0.7379.

Now for less than three p(x<30) we get 0.9011

Now to find mean

Mean=person (ill) multiply n

Mean = 0.20 * 6

Mean= 1.2

Variance= 1.2*0.80

             =0.96

IN the last we find standard deviation.it will be 96 square root.

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Answer:

Step-by-step explanation:

a) The percentage of lemon is 25%

b) The percentage of lemon is 20%

c) The percentage of lemon is 20%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

a)

Water : Lemon = 3 : 1

Percent of lemon concentrate:

= 1/4 x 100

= 25%

b)

1 part of lemon = 4 part of water

Percent of lemon.

= 1/5 x 100

= 20%

c)

Cups of lemon = 1

Cups of water = 4

Percent of lemon.

= 1/5 x 100

=  20%

Thus,

The percent of each answer is given above.

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Therefore ,the answer of this integration problem comes out to be  4/9.

To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.

Here,

Given :

=>  [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]

=> substitute x- 8 =u

=>du/dt =d(x-8)/dx = 1

=>du/dt =1

=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]

Substituting x- 8 =u

=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]

=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex]  ]

=> 14( -1/9) + 1/7)

=> 14   ( ( 9 -7 ) / 63 )

=> 14 (2/63)

=> 28/63

=>4/9

Therefore ,the answer of this integration problem comes out to be  4/9.

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The triangle ΔBHK and ΔBDE are congruent with each other. Then the side length ED is equal to the side length HK.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

Replace F with H.

The triangles ΔBHK and ΔBDE are shown.

In triangles ΔBHK and ΔBDE, then we have

BD ≅ BH (Given)

∠HBK = ∠DBE (Common angle)

∠BHK = ∠BDE = 90° (Right angle)

The triangle ΔBHK and ΔBDE are harmonious with one another. Then, at that point, the side length ED is equivalent to the side length HK.

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Answer: see below

Step-by-step explanation:

x=0 -3(0)-6y=0 -6y=0 y=0

x=1 -3(1)-6y=0       -4-6y=0    -6y=4      y=4/6 or 2/3

x=2 -3(2)-6y=0      -6-6y=0      -6y=6    y=-1    

x=3 -3(3)-6y=0         -9-6y=0        -6y=9       y= -9/6   or -3/2

x=-1 -3(-1)-6y=0          3-6y=0           -6y=-3       y=1/2  

x              y

-1               1/2

0              0

1               -2/3

2              -1

3             -1 1/2