Evaluate :11/3 + -3/7 + -4/9

When [tex]y\ge0[/tex] (above and on the [tex]x[/tex]-axis), we have [tex]|y|=y[/tex]. The parabola [tex]x=y^2[/tex] intersects with [tex]x=-|y|+12[/tex] in this region when

[tex]y^2 = -y + 12 \implies y^2 + y - 12 = (y-3)(y+4) = 0 \implies y=3[/tex]

On the other hand, when [tex]y<0[/tex] (below the [tex]x[/tex]-axis, we have [tex]|y|=-y[/tex], and so the curves intersect when

[tex]y^2 = -(-y) + 12 \implies y^2 - y - 12 = (y - 4)(y+3) = 0 \implies y=-3[/tex]

The area between the curves is then given by the definite integral,

[tex]\displaystyle \int_{-3}^3 (-|y| + 12) - y^2 \, dy[/tex]

The integrand is symmetric about the [tex]x[/tex]-axis, so the integral is equivalent to

[tex]\displaystyle 2\int_0^3 12 - y - y^2 \, dy = 2 \left(12y - \frac{y^2}2 - \frac{y^3}3\right)\bigg|_0^3 = \boxed{45}[/tex]

The values of b, h and k are (c) b = 2, h = -2 and k = -9

The logarithmic function is given as:

f(x) = log₂(x + 2) - 9

A logarithmic function is represented as:

f(x) = logb(x - h) + k

By comparing both equations, we have

b = 2

h = -2

k = -9

Hence, the values of b, h and k are (c) b = 2, h = -2 and k = -9

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The five number summary and interquartile range for the data-set is given by:

The five number summary is composed by the minimum and maximum value, and the first quartile, median and third quartile. As for each of these data, they are explained below.

In this problem, we have that:

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Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.

Y assume we have an exponential equation of the form:

y = a*b^x + c

In this case, a is what we know as the "initial value" of the exponential.

Notice that when we evaluate in x = 0, we get:

y = a*b^0 + c

y = a + c

So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.

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So, 22, 23 are the two numbers.

There are two distinct but related ideas that are referred to as linear functions: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

Consecutive numbers are preceding and following, hence we need two numbers so that

X+1=Y

or

X- Y = -1

In addition, we are aware of

4x + 3y = 157

Let's increase the top equation by 3 times.

We get

3x - 3y = -3

Then we combine that with the bottom equation.

4x + 3y = 157

      7x= 154

       x = 22

Afterward, we substitute x into the initial equation,

22+1 = 23

So, 22, 23 are the two numbers.

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The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.

According to the statement

We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.

So, For this purpose,

We know that the

A cylinder is a three-dimensional solid, one of the most basic geometric shapes.

In this shape the surface formed by the points at a fixed distance from a  line segment, which is  known as the axis of the cylinder.

As the bases of cylinder are two identical circles which are parallel to the curved surface.

The curved surface when we open will be circle rather than the circle.

So, Due to this reason the answer is a circle.

Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.

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The radius of the circle is 24 hectometers.

Remember that the circumference of a circle of radius R is given by the equation:

[tex]C = 2*\pi*R[/tex]

In this case, we know that the circumference is: C = 150.7968 hm

And π = 3.1416

Replacing that and solving for R, we get:

[tex]R = \frac{C}{2*\pi} = \frac{150.7968hm}{2*3.1416} = 24hm[/tex]

The radius of the circle is 24 hectometers.

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Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The first quartile is the median of 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

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[tex]

\sin^{-1} \left(-\frac{1}{2} \right)=-\sin^{-1} \left(\frac{1}{2} \right)=\boxed{-\frac{\pi}{6}}[/tex]

❄ Hi there,

let us combine the like terms and create an equivalent expression –

[tex]\large\begin{gathered} \sf{9+a-5b-2} \\\sf{9-2+a-5b}\\\sf{7+a-5b} \end{gathered}[/tex]

That's as far as we can go.

❄

The solution to the inequality in discuss involving a rational expression as indicated in the task content is; t (9, infinity).

The inequality given in the task content as evident is; (2t +22)/(2t +2) <= 2.

On this note, the inequality can be solved by cross-multiplication as follows;

2t +22 <= 4t +4

Hence, we have;

-2t <= -18

t >= 9.

Hence, when expressed as an interval notation, we have; t (9, infinity).

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The missing length indicated on the right triangle is 120 units

To start with:

The missing length in the right triangle can be represented with the variable x

Next, we have the following equivalent ratio from the given triangle

64 : x = x : 289 - 64

Express the ratio as a fraction

64/x = x/(289 - 64)

Evaluate the difference on the right-hand side

64/x = x/225

Cross multiply in the above equation

x * x = 64 * 225

This gives

x^2 = 64 * 225

Take the square root of x^2 (do not approximate)

x = 64 * 225

Take the square root of 64 and 225 (do not approximate)

x = 64 * 225

Evaluate the product of 8 and 5

x = 120

Based on the given parameters, the missing length indicated on the right triangle is 120 units

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Answer:

48/80 = 6/10

Step-by-step explanation:

 48 wins

+ 32 lost

= 80 total games

Then the fraction of the games win is:

48/80

= 6/10

Answer:3/5 of the games

Step-by-step explanation: The total number of games played by the team is 48+32 = 80 games. out of hose 80, they won 48 so they won 48/80 games. We can simplify this by dividing both sides by 8 to get 6/10. Which is 60%. Finally we can simplify again by dividing the fraction by 2/2 to get 3/5.

Answer:

2

Step-by-step explanation:

given x=1 and y=7

now, given expression ,

x+y/4

by putting the values of the x and y ,we get

x+y/4

= 1+7/4

= 8/4

= 2 (Ans.)

Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

Answer:

option c

Step-by-step explanation:

option c is a correct answer

There are 27720 strings.

Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 = 531,441 ternary strings of length 12.

There are

C(12,3) = 12! / (9! 3!) = 12 * 11 * 10/ 3 * 2 = 220 possible combinations of positions for the three 0s.

Of the 9 remaining positions, there are

C(9,4) = 9! / (5! 4!)

= 9 * 8 * 7 * 6/ (4 * 3 * 2 * 1)

= 126 possible combinations of positions for the four 2s.

The remaining 5 places are, of course, occupied by the five 1s.

So there that contain exactly three 0s, five 1s, and 4 2s are 220 * 126= 27720 such strings.

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Answer:

2/3

Step-by-step explanation:

Let's solve your equation step-by-step.

9a=(√3)a+2

9a=1.732051a+2

Solve Exponent.

9a=1.732051a+2

log(9a)=log(1.732051a+2)(Take log of both sides)

a*(log(9))=(a+2)*(log(1.732051))

a=(log(1.732051)/log(9))*(a+2)

a=0.25*(a+2)

a=0.25a+0.5(Simplify both sides of the equation)

a−0.25a=0.25a+0.5−0.25a(Subtract 0.25a from both sides)

0.75a=0.5

0.75a/0.75=0.5/0.75

(Divide both sides by 0.75)

a=0.666667

a=2/3

0.666667=2/3

Hope this helps :)

Answer:

2/3

Step-by-step explanation:

9^a = sqrt(3)^a * sqrt(3)^2

9^a = 3^((a/2)+1)

3^(2a) = 3^((a/2)+1)

2a = (a/2)+1

1.5a=1

a=1/(3/2) = 2/3

The average cost of weekly groceries exists at $124.50." The statistical measurement exists they most probably claim exists mean.

The arithmetic mean of a given data exists as the totality of all observations divided by the number of observations.

For instance, a cricketer's scores in five ODI matches exist as follows:

12, 34, 45, 50, 24.

To estimate his average score in a match, we compute the arithmetic mean of data utilizing the mean formula:

Mean = Sum of all observations/Number of observations

Median

The value of the middlemost observation, acquired after organizing the data in ascending or descending order, exists named the median of the data.

For instance, consider the data: 4, 4, 6, 3, 2. Let's organize this data in ascending order: 2, 3, 4, 4, 6. There exist 5 observations.

Therefore, median = middle value i.e. 4.

Mode

The value which occurs most often in the provided data i.e. the observation with the highest frequency exists named a mode of data.

As per the circumstances we have given the average cost of groceries.

The mean exists also the average sum of data divided by the total number of data.

Therefore, the statistical measurement exists as the mean.

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Answer:

Step-by-step explanation:

Comment

Begin by removing the brackets.

6+3(n-4)-8+2n

6 + 3n - 12 - 8 + 2n                 Collect like terms

3n + 2n + 6 - 12 - 8                 Combine

5n - 14

Answer

5n - 14

Answer:

"Unary Association" I believe

Answer:

36

Step-by-step explanation:

Honestly, I'd work this out visually (see image) by drawing a rectangle and dividing it up. But if you need to show the math, here's how to do it:

Let x = the number of students in the homeroom

1/3 x have drama

1/4 (x - 1/3x) have band, and we are told 6 students have band, so

1/4 (x - 1/3 x) = 6

1/4 (2/3 x) = 6    

2/12 x = 6          

1/6 x = 6            

6 × 1/6 x = 6 × 6

1 x = 6 × 6            

x = 36

Answer:

36

Step-by-step explanation:

Let n be the total number of students in Mr. Short's homeroom. Then, working backward, we see that 

6 = 1/4(1 - 1/3)n = 1/4(2/3)n = 1/6n,$

so n = 6 x 6 = 36 students.

Answer:

z = [tex]3\sqrt{13}[/tex]

Step-by-step explanation:

To find the measure of z we can use the Euclidian Theorem:

[tex]z^{2}[/tex] = 9(9+4) do the multiplication

[tex]z^{2}[/tex] = 117 find the root of both sides

z = [tex]3\sqrt{13}[/tex]

The Confidence interval for 95% who believes that the local businesses overcharge = (0.7026, 0.7574)

The range of values we see in our sample and hope to identify the value that most closely represents the population are referred to as a confidence interval.

Sample size n = 1000

73% of town residents believed that local businesses overcharged for their products over 1000 resident.

= (1000/100) x 73

= 730

Sample proportion p = 730/1000

                                    = .73

q = 1-p = 0.23

Std error of proportion = √(pq/n)

                                      = √((.73*0.27)/1000)

                                      = 0.0140

95% Z critical value = 1.96

Margin of error = 1.96*0.0140

                          = 0.0274

Confidence interval = sample proportion ±margin of error

(0.7026, 0.7574)

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Answer:

14×7=98 so multiply the same into 14×8=112

Answer:

112 watermelons

Step-by-step explanation:

7/8 = 7÷7/8÷7 = 1/1.14285714286

1 x 98/ 1.14285714286 x 98

98/112

Answer: 50

Step-by-step explanation:

50% of the class passed the first test, so that 25% that passed both test has to be part of the 50% that passed the first test. 25% that passed both is 50% of the 50% that passed the first test. Hopefully that makes sense.

The first five terms of the given arithmetic sequence are:

54, 45, 36, 27, 18 (First option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) - 9 ............ (1)

Also, f(1) = 54 .............. (2)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

f(1) is the first term of the sequence which is already provided as 54.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) - 9

f(2) = f(1) - 9

Substitute f(1) = 54 from equation (2)

⇒ f(2) = 54 - 9

f(2) = 45

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) - 9

f(3) = f(2) - 9

⇒ f(3) = 45 - 9

f(3) = 36

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) - 9

⇒ f(4) = 36 - 9

f(4) = 27

Likewise, f(5) = f(4) - 9

⇒f(5) = 27 - 9

f(5) = 18

Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:

54, 45, 36, 27, 18

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Answer:

Week 4

Step-by-step explanation:

Victoria has $250 and saves $150 each week, hence have increments $150 each week

250+150 (first week)

= 400

second week = 400 + 150 = 550

third week = 550 + 150 = 700

fourth week = 700 + 150 = $850

Felicia on the other hand has $1,650 and spends $200 each week, hence has decrements of $200 each week.

1650+200 (first week)

= 1450

second week = 1450 - 200 = 1250

third week = 1250 - 200 = 1050

fourth week = 1050 + 200 = $850