What is the maximum value of the transformed function, y = -3cos (2x - 8) + 5
A. 3 units
B. 5 units
C. 8 units
D. 11 units

Answer: 63 Stickers

Step-by-step explanation:

Given information:

Ratio = Slade : Corbett = 5 : 2

Corbett has 27 fewer stickers

Set variables:

Let x be the number of stickers Corbett has

Let x + 27 be the number of stickers Slade has

Set proportional equation:

[tex]\frac{2}{5}~ =~\frac{x}{x~+~27}[/tex]

Cross multiply the system

[tex]2~(x~+~27)~=~5~*~x[/tex]

Simplify by distributive property

[tex]2~*~x~+~2~*~27~=~5x[/tex]

[tex]2x~+~54~=~5x[/tex]

Subtract 2x on both sides

[tex]2x~+~54~-~2x~=~5x~-~2x[/tex]

[tex]54~=~3x[/tex]

Divide 3 on both sides

[tex]54~/~3~=~3x~/~3[/tex]

[tex]{x=18}[/tex]

Add Corbett's and Slade's amounts together

Corbett = x = 18 stickers

Slade = x + 27 = 18 + 27 = 45 stickers

Total = 18 + 45 = [tex]\Large\boxed{63~Stickers}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

63 stickers

Step-by-step explanation:

Define the variables:

Given ratio:

Slade : Corbett = 5 : 2

Substitute the defined variables:

[tex]\implies \sf x : x - 27 = 5 : 2[/tex]

[tex]\implies \sf \dfrac{x}{x-27}=\dfrac{5}{2}[/tex]

Cross multiply:

[tex]\implies \sf 2x=5(x-27)[/tex]

Expand:

[tex]\implies \sf 2x=5x-135[/tex]

Subtract 5x from both sides:

[tex]\implies \sf -3x=-135[/tex]

Multiply both sides by -1:

[tex]\implies \sf 3x=135[/tex]

Divide both sides by 3:

[tex]\implies \sf x=45[/tex]

Therefore, Slade had 45 stickers.

Substitute the found value of x into the expression for the number of stickers Corbett had:

[tex]\implies \sf 45-27=18[/tex]

Therefore, Corbett had 18 stickers.

Total number of stickers = 45 + 18 = 63

Answer:

A dealer bought digital watches at Rs 5500  per piece and fixed the price of each watch to make 20  profit. How much should a customer pay for it with 13  VAT? A trader purchased a laptop for Rs 45000   and marked its price to make 24  profit.

Step-by-step explanation:

The two ratios in the tables shown which have a common denominator you could use to compare is; 3/12 and 4/12

Machael's ratio:

lemons to water = 1:4

Equivalent ratio

= 3 : 12

= 4 : 16

Sondra's ratio:

lemons to water = 2 : 6

Equivalent ratio

= 4 : 12

= 6 : 18

Therefore, the two ratios in the tables shown which have a common denominator you could use to compare is; StartFraction 3 Over 12 EndFraction and StartFraction 4 Over 12 EndFraction

Complete question

Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables. Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?

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Answer:

Multiply both sides of the first equation by 2.

Multiply both sides of the second equation by 3.

Step-by-step explanation:

The y terms are

-3y

2y

The LCM of 2 and 3 is 6.

We need the y terms to add to zero.

Multiply both sides of the first equation by 2 to get -6y.

Multiply both sides of the second equation by 3 to get 6y.

Then -6y + 6y = 0 eliminating the y terms after adding the equations.

There is two of them each getting $16.32

So take the $16.32 × 2=$32.64

The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.

According to thr question.

We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.  

Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.

Now,

The total number of ways of selecting 6 numbers from 48

[tex]= ^{48} C_{6}[/tex]

[tex]= \frac{48!}{6!\times 42!}[/tex]

[tex]= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}[/tex]

= 8835488640/6!

And, the total number of ways of selecting 6 incorrect numbers from 42

= [tex]^{42} C_{6}[/tex]

[tex]= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}[/tex]

= 3776965920/6!

Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by

[tex]= \frac{^{42C_{6} } }{^{48} C_{6} }[/tex]

[tex]= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }[/tex]

= 3776965920/8835488640

= 0.427

≈ 0.43

Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.

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Step-by-step explanation:

I answered this already yesterday.

the composite figure is actually the combination of 2 figures :

1. a 7cm × 6cm × 2cm box (purple)

2. a 8cm × 7cm × 6cm triangular shaped half-box (pink) with 10cm length of the rectangular "roof".

2 sides are completely blocking each other, so they are not part of the combined surface area.

let's start with the purple box. its contribution to the surface area is :

top and bottom 7×2 rectangles

front and back 6×2 rectangles

no left (blocked by the half-box)

right 6×7 rectangle

so, we get

2 × 7×2 = 2×14 = 28 cm²

2 × 6×2 = 2×12 = 24 cm²

6×7 = 42 cm²

in total that is : 94 cm²

the half-box contributes to the surface area :

top 10×7 rectangle

bottom 8×7 rectangle

front and back 8×6/2 triangles

no left (due to the triangular shape)

no right (blocked by the box)

so, we get

10×7 = 70 cm²

8×7 = 56 cm²

2 × 8×6/2 = 2×24 = 48 cm²

in total that is : 174 cm²

and so, the total surface area of the composite figure is

174 + 94 = 268 cm²

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-2)})\implies y+5=6(x+2)[/tex]

He worked 43 hours to earn Rs. 23250

His basic pay is Rs. 18000 for a basic 36 hours a week. His salary is

Rs. 23250. This proves that he has worked extra time. So the amount earned in the extra hours equals Rs. 23250 - Rs. 18000 = Rs.5250.

Amount per hour earned in basic pay = 18000/36 = Rs.500 a hour.

∴ Amount per hour earned in extra hours = 1.5 x 500 = 750  per hour.

So number of hours he worked in extra time =  Rs.5250/750 = 7 hours.

Thus total number of hours = 36 + 7 = 43 hours.

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The first scatter plot does not have a zero correlation.

Option(a) is correct.

A statistic called correlation gauges how much two variables change in connection to one another.

Correlation quantifies correlation but cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.

A scatterplot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.

Zero means there is no correlation between the two variables under comparison.

A 0 correlation indicates that there is no relationship between the two variables according to the correlation statistic. This merely indicates that there isn't a linear relationship, not that there isn't any link at all. The first scatter plot does not represent a linear relationship, thus, it has zero correlation.

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The value of x is 11 1/2 OR 11.5

From the question, we are to determine the value of x

In the given diagram, we have two isosceles triangles

Since base angles of isosceles triangles are equal,

Then, each of the base angles of the isosceles triangle is 68°

Then, we can write that

m ∠2 + 68° + 68° = 180° (Sum of angles in a triangle)

From the given information,

m ∠2 = 4x - 2

Then,

4x -2 + 68° + 68° = 180°

4x = 180 - 68 - 68 +2

4x = 46

x = 46/4

x = 11 1/2 OR 11.5

Hence, the value of x is 11 1/2 OR 11.5

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The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.

In a quadratic equation ax² + bx + c = 0

when (b² - 4ac) exists a perfect square only then we can factorize the equation.

In the given equation x² - 8x - 12 we have to determine the value of

b² - 4ac

From the equation, we get b = -8 and c = -12

b²- 4ac = (-8)² - 4(1)(-12)

= 64 + 48 = 112

Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.

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The answer of your question is option (B)

The expression which is equivalent to the required expression (p - q)(x) is; Choice C; (x²-1)-5(x - 1).

It follows from the task content that the premise functions as given in the task content are;

p(x) = x² - 1

g(x)= 5(x-1).

Consequently, the required expression for the function operations; (p - q)(x) is simply;

p(x) - q(x) and is equivalent to;

(x² - 1) - 5(x - 1)

Therefore, the expression which is equivalent to the required expression (p - q)(x) is Choice C; (x²-1)-5(x - 1).

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find the following what?

Answer:

11 units.

Step-by-step explanation:

[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]

So, we need to find

[tex]\sum^{\infty}_{n=1} n(5/6)^n

[/tex]

Let this sum be S.

Then,

[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]

Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10

The given parameters are:

f(x) = 3x^2 + kx - 7

Divisor = x - 4

Remainder = 81

To solve for k, we use the remainder theorem

Set the divisor to 0

x -4 = 0

Add 4 to both sides of the above equation

x - 4 + 4 = 0 + 4

This gives

x = 4

Substitute x = 4 in the function f(x) = 3x^2 + kx - 7

f(4) = 3(4)^2 + k * 4 - 7

Evaluate the exponents

f(4) = 3 * 16 + k * 4 - 7

Evaluate the products

f(4) = 48 + 4k - 7

So, we have:

f(4) = 41 + 4k

The remainder is 81.

So, we have

41 + 4k = 81

Subtract 41 from both sides

4k = 40

Divide both sides of the above equation by 4

4k/4 = 40/4

Evaluate the division

k = 10

Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem

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A situation where peace is being enforced refers to a peacekeeping mission.

Peacekeeping missions refer to actions by regional and global international bodies to maintain the peace in an area.

For instance, if there has been conflict in an area, a peacekeeping force will work to prevent further violence between the parties in conflict.

An example of such missions include the United Nations Peacekeeping mission to the Democratic Republic of Congo and the African Union Peacekeeping mission to Somalia.

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Answer:

20 cookies

Step-by-step explanation:

8 in 1.5 minutes

so we want to find how many in 3.75 minutes since 3 + 45/60 = 3.75

so then its 1.5*2 = 3 so 8*2 = 16 to get that 16 cookies in 3 minutes

then we still have .75 left so then divide 8/2 to get 4 cookies in 0.75 minutes

16+4 = 20

you can also just find how many in 0.25 minutes (15 seconds) you get 6/8

multiply that by 3.75/0.25 = 15 you get 15*(8/6) = 20

Answer: 8 Oranges

Step-by-step explanation:

Given information

3 Oranges = $1.23

Total cost = $3.28

Determine the unit price of an orange

Unit price = Cost ÷ Number of Oranges

Unit price = 1.23 ÷ 3

Unit price = $0.41 / orange

Determine the number of oranges bought

Number of orange × Unit price = Total cost

N × (0.41) = (3.28)

Divide 0.41 on both sides

N = 3.28 ÷ 0.41

[tex]\Large\boxed{Number~of~oranges=8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]y = x + 8[/tex]

Step-by-step explanation:

The equation of a line is:

[tex]y = mx + c[/tex]

Where m is the gradient (or as you call it, the slope), and c is the y-intercept. We already know what the slope is, therefore we need to find the y-intercept. You have been given the coordinates (-6, 2), but to find the y-intercept, X must be equal to 0. Since the gradient is 1, we know that for every value we add to X, we must add the same to y. To get from -6 to 0, we must add 6, so we must do the same 2, leaving our y-intercept coordinates as (0, 8), and our y-intercept as 8. Plugging in our values, we are left with the following equation:

[tex]y = x + 8[/tex]

The number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

The equation is given as:

a+b+c+d+e+f = 2006

In the above equation, we have:

Result = 2006

Variables = 6

This means that

n = 2006

r = 6

The number of solutions is then calculated as:

(n + r - 1)Cr

This gives

(2006 + 6 - 1)C6

Evaluate the sum and difference

2011C6

Apply the combination formula:

2011C6 = 2011!/((2011-6)! * 6!)

Evaluate the difference

2011C6 = 2011!/(2005! * 6!)

Expand the expression

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006 * 2005!/(2005! * 6!)

Cancel out the common factors

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/6!

Expand the denominator

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/720

Evaluate the quotient

2011C6 = 9.12 * 10^16

Hence, the number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

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Answer:

210 = 6!/1!•1!•1!•1!•1!•1!

Step-by-step explanation:

We can use the stars and bars method to solve this problem. Imagine we have 2006 stars and we want to distribute them among 6 bins (a, b, c, d, e, and f). We can represent the stars as follows:

... * (a stars)

| * * * ... * (b stars)

| | * * * ... * (c stars)

| | | * * * ... * (d stars)

| | | | * * * ... * (e stars)

| | | | | * * * ... * (f stars)

The bars divide the stars into 6 bins, and the number of stars in each bin represents the value of the corresponding variable (a, b, c, d, e, or f).

To ensure that each variable is a positive integer, we can add 1 to each variable and distribute the remaining stars. For example, if we add 1 to a, b, c, d, e, and f, the equation becomes:

(a+1) + (b+1) + (c+1) + (d+1) + (e+1) + (f+1) = 2012

Now we have 6 stars and 5 bars, and we can use the stars and bars formula to find the number of solutions:

Number of solutions = (6+5-1) choose (5-1) = 10 choose 4 = 210

Therefore, the equation a+b+c+d+e+f=2006 has 210 positive integer solutions.

Expressing the answer in the form x!/x!•x!, we have:

210 = 6!/1!•1!•1!•1!•1!•1!

The stars and bars formula is a combinatorial formula that allows us to count the number of ways to distribute identical objects into distinct groups.

Suppose we have n identical objects and k distinct groups. We can represent the objects as stars and the groups as bars. For example, if we have 7 objects and 3 groups, we can represent them as:

| | |

The bars divide the 7 stars into 3 groups, and the number of stars in each group represents the number of objects in that group.

The stars and bars formula tells us that the number of ways to distribute n identical objects into k distinct groups is:

(n+k-1) choose (k-1)

where "choose" is the binomial coefficient. This formula can be derived using a technique called "balls in urns" or by using generating functions.

In the example above, we have n = 7 objects and k = 3 groups, so the number of ways to distribute the objects is:

(7+3-1) choose (3-1) = 9 choose 2 = 36/2 = 18

Therefore, there are 18 ways to distribute 7 identical objects into 3 distinct groups.

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The height from the ground to the base of the window is 16 inches.

The ladder and the wall of the window form a right angled triangle. A right angled triangle is a three-sided polygon. The square of the longest side of a right angled triangle is equal to the sum of the squares of the other two sides.

In order to determine the length from the ground to the window, the law of similar triangles would be used. The similar triangles are triangle WXY and triangle VXZ. It is expected that the length of the sides are proportional to each other.

XY / XZ = WY / VZ

(8 / 24) = WY / 48

WY = (8 X 48) / 24 = 16 inches

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The probability that the sample mean will be between  89.17 and 101.05 is: 0.940091407

A sample mean is a data set's average. A data set's central tendency, standard deviation, and variance may all be calculated using the sample mean.

The sample mean may be used to calculate population averages, among other things.

The information given are as follows:
μ = 94,

σ = 18

Where Χ = Sample Mean

hence P (89.17 < X< 101.05) =

P [[tex]\frac{89.17 -94}{18/\sqrt{36} } \leq \frac{X -mu}{sd/\sqrt{xn} } \leq \frac{101.5-94}{18/\sqrt{36} }[/tex]]

= P [ -1.61 ≤ Z ≤ 2.5]

= P (Z ≤ -1.61) - P (Z ≤ 2.5)

= NORMSIDST (-1.61) - NORMSDIST (2.5)

= 0.053698928 - 0.993790335

= -0.940091407

Since probability cannot be negative,

The probability that the sample mean will be  between 89.17 and 101.05 is: 0.940091407

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30 full cylindrical containers are required to completely fill the fish tank.

To find what is the least number of full cylindrical containers needed to completely fill the fish tank:

We know the volume of the cylinder is given by: [tex]V=\pi r^{2} h[/tex]

The volume of a cylinder:

[tex]V=\pi (\frac{6}{2} )^{2} (8)\\V=75\pi inches^{3}[/tex]

The volume of cube V = 24 × 24 × 12 = 6912 cubic inches

A number of full cylindrical containers are needed to completely fill the fish tank:

Therefore, 30 full cylindrical containers are required to completely fill the fish tank.

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The measure of the angle between the vectors

[tex]$\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex].

What is the measure of the angle between the vectors?

Given:

[tex]$\mathrm{u}=\langle -3,2\rangle$[/tex] and [tex]$v=\langle 2,1\rangle$[/tex]

Computing the angle between the vectors, we get

[tex]$\quad \cos (\theta)=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$[/tex]

To estimate the lengths of the vectors, we get

Computing the Euclidean Length of a vector,

[tex]$\left|\left(x_{1}, \ldots, x_{n}\right)\right|=\sqrt{\sum_{i=1}^{n}\left|x_{i}\right|^{2}}$[/tex]

Let, [tex]$\mathrm{u} &=\langle -3,2\rangle \\[/tex] and [tex]$\mathrm{v} &=\langle 2,1\rangle \\[/tex]

If [tex]$\mathrm{u} &=\langle -3,2\rangle \\[/tex]

[tex]$|u| &=\sqrt{-3^{2}+(2)^{2}} \\[/tex]

[tex]$&=\sqrt{5}i \\[/tex] and

[tex]$\mathrm{v} &=\langle 2,1\rangle \\[/tex]

[tex]$|v| &=\sqrt{2^{2}+(1)^{2}} \\[/tex]

[tex]$&=\sqrt{5}[/tex]

Finally, the angle is given by:

Computing the angle between the vectors, we get

[tex]$ $\cos (\theta)=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$[/tex]

[tex]$&\cos (\Phi)=-\sqrt{13 } i/ \sqrt{5 } \\[/tex]

simplifying the above equation, we get

[tex]$&\Phi=\arccos (\cos (\Phi))[/tex]

[tex]$=\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex]

Therefore, the measure of the angle between the vectors

[tex]$\arccos[ (-\sqrt{13 } i )/ (\sqrt{5 }) ]\\\sqrt{5 }[/tex].

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