the picture is attached

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

From the question, we have the following function that can be used in our computation:

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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Answer:

y = 5x + 25

Step-by-step explanation:

She starts out with 25 dollar.  That does not get increased each day, but what does get increased every day is $5

Answer:

\(\frac{1}{16}\)

Step-by-step explanation:

Given;

\(\frac{1}{4}\div \:4\)

Solve;

\(\mathrm{Convert\:element\:to\:fraction}:\quad \:4=\frac{4}{1}\)

\(=\frac{1}{4}\div \frac{4}{1}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

\(\frac{1}{4}\times \frac{1}{4}\)

\(\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)

\(=\frac{1\times \:1}{4\times \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:1\times \:1=1\)

\(=\frac{1}{4\times \:4}\)

\(\mathrm{Multiply\:the\:numbers:}\:4\times \:4=16\)

\(=\frac{1}{16}\)

Number line given below:

~Learn with Lenvy~

Answer:

Incorrect statement

Step-by-step explanation:

Its wrong because when we add 2x on both sides we get

2x+7=2x+20

Then, subtract 2x

7=20

This statement is incorrect and therfore wrong

Answer: you cant

Step-by-step explanation:

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Answer:

32.

Step-by-step explanation:

The first 32 have buttons but NO zips.

Then 35 have NEITHER buttons OR zips.

Then 32 have ZIPs, but no buttons.

The question only asks for zips. The other bag is unaccounted for.

Answer:

12 over 15 and 1 over 15 i think

Step-by-step explanation:

1365 batting orders  are possible for the game.

Given,

In the question:

In a cricket match, you have a squad of 15 players and you need to select 11 for a game.

To find the how many batting orders are possible for the game?

Let's Know:

What are combination?

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

ⁿCr = n! / ((n – r)! r!

n = the number of items.

r = how many items are taken at a time.

Substitute the values in above formula :

15! / 11! (15 - 11)!

= 15! / 11! 4!

= 15 × 14 × 13 × 12 / 4 × 3 × 2

= 1365 orders

Hence, 1365 batting orders  are possible for the game.

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Answer:

make a stem and leaf plot as it says

Step-by-step explanation:

answer it yourself

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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Answer:

51.256km/hr

Step-by-step explanation:

average speed is equal to the distance over time

Time = 5hr

distance = 256.28 km

speed = 256.28/5

speed =51.256km/hr

Answer:

1300

Step-by-step explanation:

453 trees left + 773 new ones = 1226    approx 1300

9514 1404 393

Answer:

  B.  1/2

Step-by-step explanation:

Maybe you want  the solution to ...

  \(9^x-1=2\)

You can use logarithms, or your knowledge of powers of 3 to solve this.

  \(9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}\)

Using logarithms, the solution looks like ...

  \(x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}\)

The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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Answer:

\(\sf 13m+16p\)

Step-by-step explanation:

\(\sf 9m+p+12p+4m+3p\)

\(\sf combine \:like \:terms\)

\(\sf \:9m+4m=13m\)

\(\sf p+12p+3p=16p\)

\(\sf 13m+16p\)

Answer:

16p + 13m

Step-by-step explanation:

9m + p + 12p + 4m + 3p = 16p + 13m because if you add -

12p + p + 3p = 16p because p = 1p

9m + 4m = 13m

Thus the answer is 16p + 13m ( Also I took the quiz )

Answer:

The greatest number of identical arrangements is 6 units of 9 roses and 7 tulips each.

Step-by-step explanation:

Tulips represent the limiting quantity. In this case, the easiest and most effective approach is determining the ratio of roses to tulips to get how many roses must be left along with a minimum quantity of tulips in a unit. That is:

\(x = \frac{54\,roses}{42\,tulips}\)

\(x = \frac{27\,roses}{21\,tulips}\)

\(x = \frac{9\,roses}{7\,tulips}\)

The greatest number of identical arrangements is 6 units of 9 roses and 7 tulips each.

Answer:

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

First, you simplify both sides of the inequality by combining like terms

\(-8x + 2x -16 < -5x + 7x\)

\(-6x - 16 < 2x\)

Then, you add 6x to both sides in order to isolate x (bring all the Xs to one side)

\(-6x - 16 + 6x < 2x + 6x\)

\(-16 < 8x\)

Lastly, you divide by 8 in order to cancel out 8x solve for x. Since 8 is not a negative number, you DO NOT flip the sign.

\(\frac{-16}{8} < \frac{8x}{8}\)

\(-2 < x\)

The width of the rectangle is 9 inches, and its length is 3 times the width, or 27 inches.

A right triangle's connection between its sides is described by the Pythagorean Theorem, a fundamental idea in geometry. It says that the square of the length of the longest side of a right triangle is equal to the sum of the squares of the lengths of the two shorter sides (the legs) (the hypotenuse).

Let us suppose width = x.

The length of the rectangle = 3x.

The perimeter of the rectangle is given as:

P = 2(l + w)

Substituting the values:

72 = 2(3x) + 2(x)

72 = 6x + 2x

72 = 8x

x = 9

Hence, the width of the rectangle is 9 inches, and its length is 3 times the width, or 27 inches.

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A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

(a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

The Continuous Compounding formula for the principal P , rate of interest r , and time t is

A = P×\(e^{rt}\)

In the question ,

it is given that

Part(a)  

the amount deposited (P) = $5200

rate percent (r) = 3.7% = 3.7/100 = 0.037

time = 9 years

Amount = 5200×\(e^{0.037\times9}\)

= 7254.76

the future value after 9 years is $7254.76   .

Part(b)

the effective rate is calculated using the formula

effective rate = \(e^{r}\) - 1

effective rate = \(e^{0.037}\) - 1

= 1.03769 - 1

= 0.03769

= 3.769%

Part(c)

the time to reach $10000 is calculated using the formula

10000 = 5200\(e^{0.037\times t}\)

\(e^{0.037\times t}\) = 10000/5200

\(e^{0.037\times t}\) = 100/52

taking ㏑both the sides , we get

0.037×t×㏑(e) = ㏑(100/52)

0.037t = 0.65392

t = 0.65392/0.037

t = 1.76735

t ≈ 1.77 years

Therefore , (a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

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Answer:

1.847

Step-by-step explanation:

divide 2.45 and 1.75 dats ur ans

Answer:

The equation of the tangent line

\(y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )\)

Step-by-step explanation:

Step(i):-

Given function y = x cot (x) ....(i)

Differentiating equation (i) with respective to 'x' , we get

\(\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)\)

Step(ii):-

The slope of the tangent line

\(\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x\)

\((\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}\)

We will use trigonometry formulas

\(Cosec(\frac{\pi }{4} ) = \sqrt{2}\)

\(sec(\frac{\pi }{4} ) = \sqrt{2}\)

\(Cot(\frac{\pi }{4} ) = 1\)

Now the slope of the tangent

\(\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1\)

\(\frac{dy}{dx} =-\frac{\pi }{2} +1\)

Step(iii):-

Given

Substitute \(x=\frac{\pi }{4}\) in y = x cot (x)

               \(y = \frac{\pi }{4} cot (\frac{\pi }{4} )\)

              \(y = \frac{\pi }{4}\)

The point of the tangent line  \((x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )\)

The equation of the tangent line

\(y - y_{1} = m ( x - x_{1} )\)

\(y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )\)

Answer: The distance left after 20 days is 1350 miles

Step-by-step explanation:

To calculate the distance, we use the formula:

\(s=\frac{d}{t}\)

where,

s = speed of the bicycle = 90 miles/day

t = time taken = 20 days

d = distance travelled = ? miles

Putting values in above equation, we get:

\(d=(90miles/day\times 20days)=1800 miles\)

Total distance to the destination = 3150 miles

Distance travalled in 20 days = 1800 miles

Distance left after 20 days = [3150 - 1800] = 1350 miles

Hence, the distance left after 20 days is 1350 miles

Answer:*

Step-by-step explanation:

Answer:

\( \huge{ \boxed{ \bold{ \tt{ - 2x + 1}}}}\)

Distribute 2 through the parentheses

\( \dashrightarrow{ \sf{5 - 2x - 4}}\)

Now , subtract 4 from 5

\( \dashrightarrow{ \boxed{\sf{ - 2x + 1}}}\)

Therefore , Option A is the best choice.

Hope I helped!

Have a wonderful time! ツ

~TheAnimeGirl

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = \((1-p)^{k-1}\)×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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