f(x) = x2 + 2x + 1, find f(x + h) and simplify.

Answer:

2.94117647 m/s

Step-by-step explanation:

hope this helped <3

Answer:

option e

Step-by-step explanation:

It should be arranged in table form

Row ------> Classes

Column  -----> Courses

                     Sophomores           Juniors          Seniors

Biology                 110                        60                 20

Chemistry              50                        140               85

Physics                    17                         70                107

Step-by-step explanation:

let x be the number of adults and y number of childrens

so we have. x+y=100 people

and. 12*x+8*y=1056 dollars

x=100-y

replace 100-y to the second equation

12*(100-y)+8y=1056

1200-12y+8y=1056

1200-4y=1055

1200-1056=4y

144=4y

y=144/4=36

so x=100-y=100-36=64

so in this group were 64 adults and 36 childrens

In this group were 64 adults and 36 children.

In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

let x be the number of adults and y number of children

so we have. x + y = 100 people

and. 12 × x + 8 × y = 1056 dollars

x=100 - y

replace 100 - y to the second equation

12 × (100 - y) + 8y = 1056

1200 - 12y + 8y = 1056

1200 - 4y = 1055

1200 - 1056 = 4y

144 = 4y

y = 144/4 = 36

so x = 100 - y = 100 - 36 = 64

Hence, in this group were 64 adults and 36 children.

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Answer:

\(x < 5\)

Step-by-step explanation:

Given

\(Savings = \$595\)

Rate of Lifting Ticket = $35 per ticket

Expected Amount = More than $420

Required

Determine the number of tickets she can buy

If the cost of lifting 1 ticket is 35, then the cost of x tickets is 35x.

Her spendings is then calculated as:

Total = Savings - Cost of lifting tickets

\(Total = 595 - 35x\)

From the question, we understand that she wants to have more than 420 left.

This is represented as:

\(595 - 35x > 420\)

Collect Like Terms

\(- 35x > 420 - 595\)

\(- 35x > -175\)

Divide through by -35

\(x < \frac{-175}{-35}\)

\(x < 5\)

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Answer:

Length is approximately 7.073 m

Step-by-step explanation:

One of the formulas we can use for surface area of a triangular prism is:

SA = bh + L(s1 + s2 + s3), where

So far, we know that the surface area is 297 and the height is 8.7.

Step 1:  We see that the line indicating the height splits the larger triangle into two right triangles, Thus, we can find the base of one of the right triangles using the Pythagorean theorem and multiply this by 2 to find the measure of the entire base.

The Pythagorean theorem is:

a^2 + b^2 = c^2, where

We have the measure of one leg (8.7 m) and the hypotenuse (10 m) and we must solve for leg:

a^2 + 8.7^2 = 10^2

a^2 + 75.69 = 100

a^2 = 24.31

a = √24.31 m

Multiplying this by 2 gives us that the measure of the entire base is 2√24.31 m.

Step 2:  Now we can plug in 297 for sa, 2√24.31 for b, 8.7 for h, and 10, 10, and 2√24.31 for s1, s2, and s3 respectively.  This will allow us to solve for L, the length of the triangular prism:

\(297 = (2\sqrt{24.31})(8.7)+L(10+10+2\sqrt{24.31})\\ 297=(17.4\sqrt{24.31})+L(20+2\sqrt{24.31} \\297-(17.4\sqrt{24.31})=L(20+2\sqrt{24.31})\\ (297-(17.4\sqrt{24.31}))/(20+2\sqrt{24.31})=L\\ 7.073063761=L\\ 7.073=L\)

Thus, the length of the missing side is approximately 7.073 m

Optional Step 3:  We can check that we've found the correct length of the missing side by plugging in 7.073 for L in the surface area formula and checking that we get 297 (or at least something very close to it):

297 = (2√24.31)(8.7) + 7.073(10 + 10 + 2√24.31)

297 = (17.4√24.31) + 7.073(20 + 2√24.31)

297 = (17.4√24.31) + 141.46 + 14.146√24.31

297 > 296.998096

You get approximately the same answer since we rounded the length to the nearest thousandth.  If you were to plug in a more exact answer like ((297 - (17.4√24.31)) / (20 + 2√24.31) for L, you'd get exactly 297 as I plugged this in for L on my TI-84 and got 297 exactly.

The rectangle with the best measurements for a tree house is Rectangle C.

To determine which rectangle uses the best measurements for a tree house, we need to consider the aspect ratio and size of each rectangle.

Rectangle A:

Dimensions: 2.62' x 12.5'

Aspect ratio: 2.62/12.5 ≈ 0.2096

Size: 2.62' x 12.5' = 32.75 square feet

Rectangle B:

Dimensions: 3 m x 2 m

Aspect ratio: 3/2 = 1.5

Size: 3 m x 2 m = 6 square meters (64.58 square feet)

Rectangle C:

Dimensions: 84" x 120"

Aspect ratio: 84/120 = 0.7

Size: 84" x 120" = 7,680 square inches (53.33 square feet)

Comparing the rectangles, we can conclude that the rectangle with the best measurements for a tree house is Rectangle C.

It has a larger size compared to Rectangle A and a better aspect ratio (closer to a square shape) compared to Rectangle B.

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Step-by-step explanation:

For a RIGHT triangle , TanΦ = opposite leg/adjacent leg = height/12

tan 30 = height /12

12 tan 30 = height

12 (sin 30 / (cos 30)  = height

12  *  1/2 / (sqrt(3) /2) = height

6 * 2 / sqrt (3) = 12 /sqrt 3  = 4 sqrt 3

Answer: 6 units

Step-by-step explanation:

To find the height of the right triangle with an angle that measures 30 degrees adjacent to a base of 12, you can use the formula h = (b x sin(theta)), where h is the height, b is the base, and theta is the angle in radians.

First, convert the angle of 30 degrees to radians by multiplying it by pi/180:

theta = 30 degrees x pi/180 = pi/6 radians

Then, substitute the values into the formula:

h = 12 x sin(pi/6) = 12 x 1/2 = 6

Therefore, the height of the right triangle is 6 units.

Answer:

59049+0

59048.1+0.9

59048.01+0.99

...

Step-by-step explanation:

There's infinite.

\(\huge\text{Hey there!}\)

\(\mathsf{3^{10}}\)

\(\mathsf{= 3\times 3\times3\times 3 \times 3\times 3\times3\times3\times3\times3 }\)

\(\mathsf{3\times3 = \bf 9}\)

\(= 9\times9\times 9\times 9\times9\)

\(\mathsf{9\times9 = \bf 81}\)

\(\mathsf{= 81\times81\times 9}\)

\(\mathsf{81 \times 81 = \bf 6,561}\)

\(\mathsf{= 6,561\times9}\)

  \(\mathsf{\bf = 59, 049}\)

\(\boxed{\boxed{\large\text{Answer: \huge \bf 59,049}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The reward-to-variability ratio of the best feasible is 0.4221 that is option a.

The proportion of stocks invested in the optimal risky portfolio can be calculated with the use of following formula:

Portfolio Invested in the Stock = [(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 - (Expected Return of the Bond - Risk Free Rate)*Covariance between Bond and Stock]/[(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 + (Expected Return of the Bond - Risk Free Rate)*(Standard Deviation of Stock)^2 - (Expected Return of Stock - Risk Free Rate + Expected Return of Bond - Risk Free Rate)]*Covariance between Bond and Stock

Portfolio Invested in Bond = 1 - Portfolio Invested in the Stock

Here, Risk Free Rate = 4 and Covariance = 32*24*.1250 = 96

Using these values and other information provided in the question, we get,

Portfolio Invested in the Stock = [(10 - 4)*(24)^2 - (7 - 4)*96]/(10 - 4)*(24)^2 + (7 - 4)*(32)^2 - [(10 - 4 + 7 - 4)]*96 = .5593

Portfolio Invested in Bond = 1-.5593 = .4407

Step 2: Calculate Expected Return and Standard Deviation of the Optimal Risky Portfolio

Expected Return = Portfolio Invested in Stock*Expected Return of Stock Portfolio Invested in Bond*Expected Return of Bond = .5593*10% + .4407*7% = 8.68%

Standard Deviation = [(Portfolio Invested in Stock)^2*(Standard Deviation of Stock)^2 + (Portfolio Invested in Bond)^2*(Standard Deviation of Bond)^2 + 2*(Portfolio Invested in Stock)*(Portfolio Invested in Bond)]^(1/2) = [(.5593)^2*(32)^2 + (.4407)^2*(24)^2 + 2*(.5593)*(.4407)*(96)]^(1/2) = 21.90%

Step 3: Calculate Reward-to-Volatility Ratio

The reward-to-volatility ratio can be calculated with the use of following formula:

Reward-to-Volatility Ratio = (Expected Return of the Portfolio - Risk Free Rate)/Standard Deviation of Portfolio = (8.68 - 4)/21.90 = .4221

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Approximately, Brianne percentage rate of contribution is 0.5%.

Brianne's annual contribution to her union dues is $200. Her salary is $38,500.

Approximately, her percentage rate of contribution can be calculated as follows:

percentage rate of contribution = union dues / salary × 100

union dues = 200 dollars

salary = 38500

percentage rate of contribution = 200 / 38500 × 100

percentage rate of contribution = 20000 / 38500

percentage rate of contribution =  0.51948051948

Therefore,

percentage rate of contribution ≈ 0.5%

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As per the regression model, the estimated project cost in $1000 for 20000 Square feet located in the sixth floor is $101,000

The term regression in statistics is known as the statistical measure that defines co-relationship or association of two variables.

Here we have given that the cost engineer of a project management group has developed a simple regression model for costing each floor of a height rise project. And the model has an intercept of 100K and the slope or gradient is shown to be an increase of $278 per added square feet plus $20000 per added floor.

And we need to find the estimated project cost in $1000 for 20000 Square feet located in the sixth floor .

While we looking into the given question, we have identified that the value of the following are given in the question,

=> Intercept = 100K or 100000

=> Slope = $278/feet  and $20000/floor

Then the simple regression model for the situation is written as,

=> y = 278x + 100000

Or

=> y = 20000x + 100000

Then the cost of  $1000 for 20000 Square feet located in the sixth floor is calculated by using the given equation is illustrated as follows,

=> y = 20000(1000) + 100000

=> y = 101000

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The total amount that will be in the account 40.00 years from today, considering the annual deposits of $6,460.00 for 21.00 years and an annual interest rate of 14.00%, will be approximately $6,120,433.84.

Derek plans to deposit $6,460.00 per year for 21.00 years into an account with an annual interest rate of 14.00%. The first deposit will be made next year.

To calculate the total amount in the account 40.00 years from today, we need to consider the annual deposits, the interest earned, and the compounding effect over the years.

The annual deposit is $6,460.00, and the duration of deposits is 21.00 years.

Therefore, the total amount of deposits made over the 21.00 years will be 21.00 × $6,460.00 = $135,660.00.

To calculate the future value of the deposits and the interest earned, we can use the compound interest formula:

Future Value = Principal × \((1 + interest\, rate)^{number\, of\, periods}\)

In this case, the principal is $135,660.00, the interest rate is 14.00%, and the number of periods is 40.00 years.

Future Value = $135,660.00 × \((1 + 0.14)^{40}\)

Future Value = $135,660.00 × \((1.14)^{40}\)

Future Value = $135,660.00 × 45.094

Future Value = $6,120,433.84

Therefore, the total amount that will be in the account 40.00 years from today, considering the annual deposits of $6,460.00 for 21.00 years and an annual interest rate of 14.00%, will be approximately $6,120,433.84.

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Total cups of trail mix which Orly makes if she uses 8 cups of raisins will be 48 cups.

To answer the question, we need to form an equation. An equation is a set of variables which are constrained through a situation or case. To form an equation, first, we have to determine the known quantities and label the unknown quantity as a variable.

In this case, given information that Orly uses 2 cups of raisins to make 12 cups of trail mix.

So, if 2 cups of raisins ⇔ 12 cups of trail mix;

Then, if we multiply by 4, it will be:

2 x 4 cups of raisins ⇔ 12 x 4 cups of trail mix

8 cups of raisins ⇔ 48 cups of trail mix

Thus, the number of cups of trail mix which Orly could make if she uses 8 cups of raisins will be 48 cups.

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what graph? I don't see one

This is the graph for this question

Answer:

14

Step-by-step explanation:

5x = 70

x = 14

Answer:

The answer is option 1.

Step-by-step explanation:

Given that total angles in a quadrilateral is 360°. So in order to find x, you have to substract the remaining angles from 360° :

\(5x + 110 + 110 + 70 = 360\)

\(5x + 290 = 360\)

\(5x = 360 - 290\)

\(5x = 70\)

\(x = 70 \div 5\)

\(x = 14\)

Using it's concept, it is found that there is a 0.713 = 71.3% probability that Rachel takes no more than three sweets from the bag.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

So:

\(p = \frac{3}{10} + \frac{7}{10} \times \frac{3}{9} + \frac{7}{10} \times \frac{6}{9} \times \frac{3}{8} = 0.713\)

0.713 = 71.3% probability that Rachel takes no more than three sweets from the bag.

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Answer:

6,16,25,27,33,39,45 are the composite numbers.

Answer:

Step-by-step explanation:

si...  yono  em usho de cmopu preo sloo estoy usand una jjssjsjsj jsjsj  c

Answer:

-11, -9 and -7

or

7, 9 and 11

Step-by-step explanation:

Let the middle number be x

Then the number before that is x - 2

The number after that is x + 2

This is because they are consecutive odd integers and odd integers are separated from the next or previous by 2

Product of first and last = (x - 2)(x+2)

(x - 2)(x + 2) = x² - 4 through the relationship (x - a)(x + a) = x² -a²

77 over 81 times the square of the middle = \(\dfrac{77}{81}x^2\)

Setting the two expressions equal to each other we get

\(x^2 - 4 = \dfrac{77}{81}x^2\\\\\)

Subtract \(\dfrac{77}{81}x^2\) from both sides:
\(x^2 - 4 -\dfrac{77}{81}x^2= 0\)

Add 4 to both sides:
\(x^2 - \dfrac{77}{81}x^2 = 4\\\\\)

\(x^2(1 - \dfrac{77}{81})= 4\\\\\)

\(1 - \dfrac{77}{81} = \dfrac{81}{81} - \dfrac{77}{81}= \dfrac{4}{81}\)

Therefore
\(x^2(1 - \dfrac{77}{81})= 4\\\\\\\rightarrow x^2 \cdot \dfrac{4}{81} = 4\\\\\\\)

Multiply both sides by 81:
\(81\cdot \dfrac{4}{81}x^2=4\cdot \:81\)

\(4x^2=324\)

\(x^2=81\)

\(x=\pm \sqrt{81}\\\\x=\sqrt{81},\:x=-\sqrt{81}\)

\(x=9,\:x=-9\)

This would be the middle integer

If x = -9, first integer = -9-2 = -11 and last integer = -9 + 2 = -7

If x = 9, first integer = 9-2 = 7  and last integer = 9 + 2 = -11

So the integers can be
-11, -9 and -7

or

7, 9 and 11

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

x = 2, y = - 25

Step-by-step explanation:

(1)

note that 36 = 6² , then

\(6^{x}\) = 6²

Since bases on both sides are equal then equate the exponents

x = 2

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

(2)

Using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\)

note that 25 = 5² , then

\(25^{11+3y}\) = \((5^2)^{11+3y}\) = \(5^{22+6y}\)

Then

\(5^{5y-3}\) = \(5^{22+6y}\)

Since bases on both sides are equal then equate the exponents

22 + 6y = 5y - 3 ( subtract 5y from both sides )

22 + y = - 3 ( subtract 22 from both sides )

y = - 25

Answer:

2 rocks

Step-by-step explanation:

2 crates + 2 rocks = 1 crate + 4 rocks

2 crates + 2 rocks = 2 crates + 8 rocks

Hence, 1 crate = (8-4)÷2

= 2 rocks

It can be expected that the spinner will land on a multiple of 3 approximately 12.6 times when spun 42 times. Since we cannot have a fraction of a spin, we can expect it to land on a multiple of 3 about 12 times.

To determine how many times the spinner can be expected to land on a multiple of 3 when spun 42 times, we need to consider the probability of landing on a multiple of 3 on each spin.

Out of the 20 equal sections on the spinner, the numbers that are multiples of 3 are 3, 6, 9, 12, 15, and 18. There are six multiples of 3 in total.

The probability of landing on a multiple of 3 in one spin is given by the ratio of the favorable outcomes (multiples of 3) to the total outcomes (20 sections).

Probability of landing on a multiple of 3 = (Number of favorable outcomes) / (Total number of outcomes)

= 6 / 20

= 0.3

Therefore, the probability of landing on a multiple of 3 in one spin is 0.3 or 30%.

To find the expected number of times the spinner will land on a multiple of 3 in 42 spins, we multiply the probability of each spin by the total number of spins:

Expected number of times = (Probability of landing on a multiple of 3) * (Number of spins)

= 0.3 * 42

= 12.6

Therefore, it can be expected that the spinner will land on a multiple of 3 approximately 12.6 times when spun 42 times. Since we cannot have a fraction of a spin, we can expect it to land on a multiple of 3 about 12 times.

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We need 1.75 litres of water to make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water

To make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water, we need to calculate how much water is needed.

We can do this by using the following formula:

Water = Diluted Squash - Squash First, we need to find out how much squash is in 2 litres of diluted squash.

Since the ratio is 1:7, we can divide 2 litres by the total number of parts (1 + 7 = 8) to find out how much squash is in 2 litres of diluted squash: Squash = 2 litres / 8 = 0.25 litres

Now we can use the formula to find out how much water is needed:

Water = 2 litres - 0.25 litres = 1.75 litres

Therefore, we need 1.75 litres of water to make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water.

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Answer:

true

true

True

true

False

Step-by-step explanation:

Answer:

B.(x − 5)(x − 3)(x + 2)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

11

Step-by-step explanation:

First number is 5,the second is five times the first so 5×5=25 and the third is 14 less than the second so 25-14=11

The third number is 11.

According to the question,

Sum of the three numbers = 41

Let the first number be x

Then,

Second number will be 5x

Third number will be (5x - 14)

The equation formed will be

x + 5x + (5x-14) = 41

On solving,

x + 5x + 5x - 14 = 41

x + 5x + 5x = 41 +14

11x = 55

x = 55/11

x = 5

Thus,

First number will be 5

Second number will be 5x = 25

And Third number will be 5x - 14 = 25 - 14 = 11

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