Mr. Parke made snacks in separate gift bags. He gave one each to the 86 seventh grade students going on the field trip. Then he gave 17 bags to the students in Mrs. Mark's class for decorating the trophy cases. Next he gave 11 to the students in Mrs. Green's class for helping during the school play. Mr. Parke had 11 snacks left. How many snacks did he make?

Answer:

\(\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }\)

and the interval of the convergence is (-1, 1)

Step-by-step explanation:

To find a power series for the function, centered at c.

\(g(x) = \dfrac{7x}{x^2 +5x-6} ,\ c = 0\)

If we factorize the denominator, we have:

\(g(x) = \dfrac{7x}{(x +6)(x-1)}\)

\(g(x)= \dfrac{1}{x-1}+\dfrac{6}{x+6}\)

Thus;

\(g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1+\dfrac{x}{6}}\)

\(g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1-(-\dfrac{x}{6})}\)

\(g(x) = - \sum \limits^{\infty}_{n=0} x^n + \sum \limits^{\infty}_{n=0} x^n(\dfrac{-x}{6})^n \ \ if \ \ |x| < 1 \ \ and \ \ |\dfrac{x}{6}< 1\)

\(g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n , \ if |x|<1\)

\(\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }\)

and the interval of the convergence is (-1, 1)

Answer: look at the picture

Step-by-step explanation: Hope this help:D

Answer: y=-6x+11

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

If you simplify,

2/3 = 2/3

2/6 = 1/3

2/4 = 1/2

Now find the LCD,

3 · 2 = 6

Now multiply,

2/3 · 2 = 4/6

1/3 · 2 = 2/6

1/2 · 3 = 3/6

Hence you see,

2/3 is the least.

Answer:

75.0001

Step-by-step explanation:

Used a calculator

Answer:

0.556

Step-by-step explanation:

such easy math

Answer: the graph of the resulting function, |x| + k, is the graph of f (x) shifted k units up

Step-by-step explanation:

just took the test

Given:

The triangles are given.

Required:

Which statement is true.

Answer:

The two triangles given are congruent.

Therefore, from the diagram given , we observed that

Final Answer:

The angles congruent are,

This is the true statement.

Option 3 is correct.

Answer:

A.

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Right angle is a 90-degree angle that is L shape. Perpendicular lines intersecting are two lines that intersect at a right angle. Which means this statement is in fact true. Perpendicular lines always intersective to form four right angles.

Hope this helps.

Answer:

144 people competed in the Chess Tournament

Step-by-step explanation:

So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 \(*\) 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.

After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 \(*\) 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:

512cm³

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This statement describes the process of innovation portfolio management.

A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is another name for a statement. The main point is that there should be no uncertainty. A sentence cannot be both true and untrue in order to be a statement. A mathematical statement is made up of two components. The hypothesis or assumptions come first, followed by the conclusion. When a mathematical sentence makes a mathematically accurate statement, it is true.

Here,

This statement describes the process of innovation portfolio management. Innovation portfolio management involves evaluating and selecting innovation projects in line with an organization's goals and resources, and ensuring that these projects are aligned with the overall strategy of the firm. The aim of innovation portfolio management is to optimize the allocation of resources and maximize the return on investment in innovation.

By selecting and prioritizing innovation projects, companies can ensure that they are working on initiatives that have the greatest potential to drive growth and success, while also balancing risk and resource constraints.

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Answer:

Step-by-step explanation:

Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Answer:R’ (-10,2) S’(-6,8) T’(4,-2)

Step-by-step explanation:

Did it in class

After dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).

Given that, ΔRST with vertices R(-5,1), S(-3,4), and T(2,-1).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given, scale factor is k=2.

So, with using scale factor

R(-5,1)→2(-5, 1)= R'(-10, 2)

S(-3,4)→2(-3,4)=S'(-6, 8)

T(2,-1)→2(2,-1)=T'(4, -2)

Therefore, after dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).

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The value of a is given as follows:

a = 2.

The rate of change is given as follows:

2.4 inches per hour.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The line passes through the points (–1, –5) and (4, 5), hence the slope m is obtained as follows:

m = (5 - (-5))/(4 - (-1))

m = 2.

Hence:

y = 2x + b.

When x = -1, y = -5, hence the intercept b is obtained as follows:

-5 = -2 + b

b = -3.

Hence:

y = 2x - 3.

Then the value of a is obtained as the value of x when y = 1, hence:

2x - 3 = 1

2x = 4

x = 2.

The rate of change in the snowfall is given as follows:

m = (8.1 - 2.3)/2

m = 2.4 inches per hour.

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The answer is \((x+9)+(x-2)\) .

We have given two statements one is " number increased by nine "

Let the number be x .

Mathematically , first statement is represented by

  x + 9

Second statement is " number decreased by two "

Mathematically , second statement is represented by

  x - 2

According to the question

Sum of first and second statement = \((x+9)+(x-2)\)

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9514 1404 393

Answer:

  5/6

Step-by-step explanation:

We assume you want the ratio ...

  (20 hr)/(24 hr) = (4·5)/(4·6) = 5/6 . . . . . factors of 4 and hours cancel

The ratio is 5/6.

Answer:

180°

Step-by-step explanation:

So supplementary agles are angles that add up to 180 degrees thus the measure of each angle is 180 degrees.

The 4x+ 9 and 8x+3 are meant to confuse you. But if you need help figuring out what x is i can help :)

HOPE IT HELPED.

Answer:

18

Step-by-step explanation:

The final velocity of the Ferrari will be 84.53 km/h. with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes.

This is a typical question from Newtonian mechanics. To solve this problem we have to convert all the given data into a standard unit like C.G.S.

Now, we will convert 10 km/h and 50 km/h by using the formula. (km/h × 5/18 = m/s )

10 km/h = 10× 5/18 = 2.78 m/s

50 km/h = 50× 5/18 = 13.89 m/sec/min = 0.23 m/s²

3 min = 3 × 60 = 180 sec. ( 1 min = 60 sec )

Now, we have to use the formula from Newton's law of motion,

v = u + at/2 .

Now we can calculate the final velocity,

v = 2.78 + (0.23 × 180)/2 = 2.78 + 20.7 = 23.48 m/s

Now, we have to calculate the velocity in km/h, which is (23.48 × 5 )/8 = 84.53 km/h. as we know (km/h = m/s ×18/5 ).

Therefore, the final velocity will be 23.48 m/s according to the given inputs and criteria.

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Answer:

60/5 is equal to 12. so 12 x 2= 24, and 5 x 12=60, so 24/60, or just 24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

60×40=2400

2400÷100= 24

if you set it up as a proportion

hope this helps, have a good day

1) Dividing the given formula by W we get:

2) We know that:

Therefore:

Then:

Substituting W=3/4ft and L=18ft in the given formula we get:

Answer:

1)

2)

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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The vertical displacement is of 2 units down, the correct option is B.

Remember that for a function f(x), a vertical displacement of N units is written in general form as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we assume that we start with the parent cosine function:

y = cos(x)

And the transformed function is:

y = -2 - cos(x - π)

So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.

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The blue line passes through the points

(-2.6, 1) and (-1.4, 2.5)

I will label the coordinates as follows for reference:

Step 1: Find the slope of the blue line

The slope between two points is calculated with the formula:

We substitute the values and we get that the slope of the blue line is:

The slope m of the blue line is 1.25.

step 2: With that slope, calculate b (the intercept of the blue line with the y axis).

For this we use the point - slope equation:

Where we will use the sane x1 and x2 as in the previous step, so we get

We compare this with the slope-intercept equation

And we can see that the incercept b is 4.25

step 3: Find the value of c.

to find the value of c, we need to know at which point the blue line crosses the x axis.

Since we already have the equation of the blue line y=1.25x+4.25, and the line crosses the x axis at y=0, we substitute this to find the x value that is equal to c:

The blue line crosses the x axis at (-3.4,0), thus we can conclude that

Step 4: Define the two point where the orange line passes through.

We know from the picture that the orange line passes through (c,0) and (0,-b)

Since we have the values of c = -3.4 and b=4.25, we can say that the orange line passes through (-3.4, 0) and (0, -4.25)

Step 5: Calculate the slope of the orange line.

the orange line passes through (-3.4, 0) and (0, -4.25), so we define: