Find the sum of the first 10 terms of the following sequence. Round to the nearest
hundredth if necessary.
25,
29,
33.64,..

Sofie will not make a profit if she sells her scarves for $5 or less.

The maximum profit Sofie can make is $200.

A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line.

According to the given problem,

y = (x - 5)(50 - 2x)

⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)

⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)

⇒ y - (x - 5)(-2x + 50) = 0

⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0

⇒ y - ( -2x² + 50x + 10x - 250) = 0

⇒ y - ( - 2x² + 60x - 250 ) = 0

⇒ y + 2x² - 60x + 250 = 0

⇒ 2x² -60x + y + 250 = 0

⇒ ( 2x² - 60x ) + y + 250 = 0

⇒ 2 ( x² - x) + y + 250 = 0

⇒ 2 ( x² - x) + y + 250 = 0

⇒ 2 ( x² - 30x ) + y + 250 = 0

⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0

⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0

⇒ 2( x - 15 )² + y = -2(-225) - 250

⇒ 2( x - 15 )² + y = 450 - 250

⇒ 2( x - 15 )² + y = 200

⇒ y = -2( x - 15 )² + 200

This equation is in the form of y =  a(x - h)² + k where the vertex of the parabola is (h , k).

Therefore the vertex of the parabola is at (15 , 200)

Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.

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Answer:

x³ - 3x² + 5x - 6

Step-by-step explanation:

      1) (2x + y)(4x - 9) = 2x*(4x - 9) + y(4x - 9)

                                 = 2x*4x - 2x*9 + y*4x - y *9

                                = 8x² - 18x + 4xy - 9y

2) (3x + 5y)²

Identity : (a + b)² = a² + 2ab + b²

a = 3x and b = 5y

(3x +5y)² = (3x)² + 2 * 3x *5y + (5y)²

               = 9x² + 30xy + 25y²

3) (x -2)(x² - x + 3) = x*(x² - x + 3) - 2(x² - x + 3)

                             =x*x² - x*x + x*3 -2*x² + 2*x - 2*3

                            = x³ - x² + 3x - 2x² + 2x - 6

                            =x³ - x² - 2x² + 3x + 2x - 6

Combine like terms. Like terms have same variable with same exponent.

                           = x³ - 3x² + 5x - 6

Answer:

d

Step-by-step explanation:

d

Answer:

3.19

Step-by-step explanation:

5.5% of 58 is 3.19

and is you need it,

58 - 3.19 = 54.81

I believe this is right

the sales tax on $58 at a rate of 5.5% is $3.19

How to find the tax on $58 at a rate of 5.5%?

Taxes are a mandatory contribution to the state. So sales must pay taxes, and it is stated that the rate of tax that must be paid is 5.5%

The way to calculate tax from sales is to multiply the tax rate by the income from sales.

the income = $58

the rate of tax = 5.5%

the tax to be paid by sales = the income x the tax

                                             = $58 x 5.5%

                                             = $3.19

so the answer to the question is $3.19

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The chance at least one of the alarms will wake her up is 0.96.

If the probability of one event does not affect the probability of another event, the events are independent.

Given

Probability that Alarm clock 1 is reliable = 60% = 0.60

Probability that Alarm clock 2 is reliable = 90% = 0.90

P of alarm clock 1 not reliable = 0.40

P of alarm clock 2 not reliable = 0.10

Therefore,

The chance at least one of the alarms will wake her up is;

=p1.p2' + p1'. p2 + p1.p2

so, calculating we get,

= 0.96

Hence, the chance at least one of the alarms will wake her up is 0.96.

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The approximate area that Poseidon is searching is given as follows:

64.13 square units.

The area of a triangle is given by half the multiplication of the base length by the height.

The coordinates of the vertices of the triangle in this problem are given as follows:

(-6,1), (4,-5) and (-1,9).

Any of the three sides can be chosen as the base, and we use the equation for the distance between two points to obtain it's length.

Choosing vertices (-6,1) and (4,-5) as the base, it's length is given as follows:

b = sqrt((4 - (-6))² + (-5 - 1)²)

b = 11.66.

The midpoint of the base has the coordinates given as follows:

The height is the distance between the vertices (-1,-2) and (-1,9), hence, as they have the same x-coordinate, the height is given as follows:

h = 9 - (-2)

h = 11.

Then the area is given as follows:

A = 0.5 x 11.66 x 11

A = 64.13 square units.

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6

Hope This Helps!

P2 = 90; 10P2 = 90. Combinations. There are also two types of combinations

Answer:

P(3, 2) = 6

Step-by-step explanation:

A permutation is an ordered combination, i.e. an arrangement in a definite order of a number of objects taken some or all at a time.

[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]

where:

Given P(3, 2):

So we need to calculate the permutations of two numbers taken from three numbers.

The numbers are 1, 2 and 3.  As order matters, the number of ways two numbers from this set can be arranged is:

Therefore, there are 6 ways two numbers from the set of three numbers can be arranged.

To prove this, substitute n = 3 and r = 2 into the permutation formula:

[tex]\begin{aligned}\implies P(3,2)&=\dfrac{3!}{(3-2)!}\\\\&=\dfrac{3!}{1!}\\\\&=\dfrac{3 \times 2 \times 1}{1}\\\\&=\dfrac{6}{1}\\\\&=6 \end{aligned}[/tex]

Therefore, P(3, 2) = 6.

Answer: x=3

Step-by-step explanation:

divide by the common factor 3

3x ÷ 3 = x

9÷3 = 3

hence the reason we get x=3

Answer: 3

Step-by-step explanation:

To solve for x, you need to divide 9 by 3 which equals 3.

Since 3x = (3 ⋅ 3), x = 3.

By applying binomial distribution formula, it can be concluded that the probability less than two have a side effect is 56.86%.

Binomial distribution is the discrete probability distribution of the number of successes or failures in n independent trials, where each trial result has a probability p.

P(x) = C(n,x) · pˣ · qⁿ⁻ˣ where:

C = number of combinations

p = probability of success

q = probability of failure

x = number of times for a specific outcome within n trials

n = number of trials

We have the following information:

p = 12% = 0.12, thus:

q = 1 - p

  = 1 - 0.12

  = 0.88

n = 12

We want to find the probability less than two have the side effect, P(x<2):

P(x<2) = P(0) + P(1)

          = (C(12,0) · 0.12⁰ · 0.88¹²)  +   (C(12,1) · 0.12¹ · 0.88¹¹)

          = (1 · 1 · 0.2157)   +   (12 · 0.12 · 0.2451)

          = 0.2157 + 0.3529

          = 0.5686 ≈ 56.86%

Thus, the probability less than two have the side effect is 56.86%.

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Answer:

Step-by-step explanation:

To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

a = 4 inches

b = 5 inches

c = 7 inches

Using the Pythagorean theorem, we can calculate:

c^2 = a^2 + b^2

7^2 = 4^2 + 5^2

49 = 16 + 25

49 = 41

Since 49 does not equal 41, this means that the triangle is not a right triangle.

Therefore, the answer is no, the triangle is not a right triangle.

The cost of each balloon and each banner is $2 and $1 respectively.

Let

cost of balloon= x

cost of banner= y

6x + 3y = 15

4x + y = 9

Multiply equation (2) by 3

12x + 3y = 27

6x + 3y = 15

12x + 3y = 27

Subtract the equations to eliminate y

12x - 6x = 27 - 15

6x = 12

divide both sides by 6

x = 12/6

x = $2

Substitute into

4x + y = 9

4(2) + y = 9

8 + y = 9

y = 9 - 8

y = $1

Therefore, each balloon cost $2 and each banner cost $1

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If a back-to-school sale offered a laptop for $379 and this sale price reflected a 15% discount, after using the equation the cost of the computer before the reduction in price is, $446.47.

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Let's call the original cost of the laptop "x".

The equation to find the cost after a discount is:

x - x * (discount rate) = sale price

In this case, the discount rate is 15%, or 0.15. Plugging in the given values:

x - x * 0.15 = 379

Expanding the equation:

x - 0.15x = 379

0.85x = 379

Dividing both sides by 0.85:

x = 379 / 0.85

x = 446.47

So, the cost of the laptop before the reduction in price was $446.47.

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The length of the hypotenuse of the isosceles right triangle is 2.8 inches.

An isosceles right triangle is a right triangle with two equal sides. In this case, the two equal sides are each 7 8 inches long.

To find the length of the hypotenuse, we can use the Pythagorean theorem:

a^2 + b^2 = c^2, where c is the length of the hypotenuse

In this case, a = b = 7/8 inches, so:

(7/8)^2 + (7/8)^2 = c^2

(49/64) + (49/64) = c^2

98/64 = c^2

c = sqrt(98/64) inches

To the nearest tenth, c = 2.8 inches, so the length of the hypotenuse of the isosceles right triangle is 2.8 inches.

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The probability that you draw a sphere given that it is blue is given as follows:

5/7.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total outcomes in this problem are the blue shapes, hence the number is given as follows:

6 + 15 = 21 shapes.

The desired outcomes are the blue spheres, hence the number is given as follows:

15.

Hence the probability that you draw a sphere given that it is blue is given as follows:

p = 15/21

p = 5/7. (simplify numerator and denominator by 3).

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The Expected value is the long-term average position of any variable. The anticipated value will be$5.18

The predicted value is the long-run average of all variables. It also shows the loaded normal probabilities for all possible values. Investors use expected value to estimate an investment's return, often in relation to its risk.

Given the data in detail

Pupil Lunch check Bones spent Probability

2$10 20/50.

1$8 8/50.

12$6 72/50.

23$5 115/50.

8$4 32/50.

4$3 12/50

The sum will be

aggregate = 20+ 8 +72 +115 +32 +12

                           50

= 259/50

= $5.18

The anticipated value a pupil would spend on lunch each day will be $5.18

Question

From the following data, calculate the expected  value a pupil can spend on lunch each day?

Students & Amount spent

2$ 10

1$ 8

12$ 6

23$ 5

8$ 4

4$ 3

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

9.3 × 3.5 / 2 = 16.275 ft²

as you can see, yes, really easy.

what was the problem ? do you need any further explanation ?

Answer:

this equation is always true

Step-by-step explanation:

Solve the equation and check your solution: -2(x - 1) = 2 - 2x

-2(x - 1) = 2 - 2x

-2x + 2 = 2 - 2x

-2x + 2x = 2 - 2

0 = 0

(this equation is always true)

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

check

whatever value you give to x the equation is always true, let's take 2 as an example

-2(2-1) = 2 - 2 * 2

-4 + 2 = 2 - 4

-2 = -2

Answer:

[tex]y=4(x-7)^2-196[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]y=4x^2-56x[/tex]

Factor out the coefficient of the term x²:

[tex]y=4(x^2-14x)[/tex]

Add and subtract the square of half the coefficient of the term in x inside the brackets:

[tex]y=4\left(x^2-14x+\left(-\dfrac{14}{2}\right)^2-\left(-\dfrac{14}{2}\right)^2\right)[/tex]

Simplify:

[tex]y=4\left(x^2-14x+\left(-7\right)^2-\left(-7\right)^2\right)[/tex]

[tex]y=4\left(x^2-14x+49-49\right)[/tex]

Factor the perfect square trinomial created by the first three terms inside the brackets:

[tex]y=4\left((x-7)^2-49\right)[/tex]

Distribute:

[tex]y=4(x-7)^2-196[/tex]

The equation is now in vertex form y = a(x - h)² + k, where (h, k) is the vertex of the parabola (turning point).

Compare the equation with the vertex formula to identify the values of h and k:

Therefore, the coordinates of the turning point (vertex) are (7, -196).

Answer:east

Step-by-step explanation:

north: LOW:-8F    HIGH:10F  this have the most change

+18F

south: LOW:-3F     HIGH:2F    this have the third most change

+5F

east: LOW:-2F    HIGH:0F    this have the least change

+2F

west: LOW:-4F    HIGH:3F    this have the second most change

+7F

the east only have +2F so it have the least change

Given all sides are right angles, the height of the sides are equal.

left side = 12

right side = x+5

set equation equal to each other and solve for x.

12 = x +5 =>> 12-5 = x =>> x = 7

x = 7 cm

The distance between the points A and B is 209.4 feet

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12°. Let a represent distance from point A to light house:

tan(12) = 107/a

a = 503.4 feet

They measure the angle of elevation a second time from point B at some later time to be 20°. Hence, if b represent distance from point A to light house:

tan(20) = 107/b

b = 294 feet

Distance from point A to B = 503.4 feet - 294 feet = 209.4

The distance between the points is 209.4 feet

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The value of 9/10  divided by 3/5 is 3/2.

How to multiply two fractions?

When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms.

Firstly , let's find the reciprocal of the divisor

Reciprocal of

3/5 is 5/3

Now, multiply it with the dividend

So,

9/10 ÷ 3/5

= 9/10 × 5/3

=  45/30

After reducing the fraction, the answer is

3/2

Hence , the value of 9/10  divided by 3/5 is 3/2.

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The solution is, For job- A will Des earn the most money per week.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Job A pays £3.80 per hour for 40 hours per week,

Job B pays £4.50 per hour for 32 hours per week.

for, job A - he earns =  £3.80 * 40

                                 = £ 152 pe week

and, for job B - he earns = £4.50 * 32

                                        =£ 144 per week.

Hence, The solution is, For job- A will Des earn the most money per week.

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Answer:

$3.30

Step-by-step explanation:

6 x 1.50 = 9

12.30 - 9 = $3.30

The measures of the angles X, Y, and Z are 5, 50, and 125 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that in ∆XYZ, the measures of angles X, Y, and Z, respectively, are in the ratio 1:10:25.

We have to find the measure of each angle.

Let the measures can be expressed as 1x, 10x, and 25x, respectively, where x is an arbitrary value.

We know that the sum of the angles of a triangle is always 180 degrees, so:

1x + 10x + 25x = 180

36x = 180

Divide both sides by 36

x = 5

Therefore, the measures of the angles X, Y, and Z are 5, 50, and 125 degrees.

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Answer:

a. To find the annual net income, subtract the annual expenses from the annual rental income.

The annual rental income = $750 * 12 months = $9,000

So, the annual net income = $9,000 - $6,890 = $2,110

b. To find the annual yield, divide the annual net income by the investment cost (the down payment) and multiply by 100 to get the answer as a percentage.

The annual yield = ($2,110 / $28,500) * 100 = 7.41%

c. To find the monthly rent required to get a yield of 90%, divide the investment cost by the desired yield and divide by 12 to get the monthly rent.

The investment cost = $28,500

The desired yield = 0.90

So, the monthly rent = ($28,500 / 0.90) / 12 = $2,306.25

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Taylor will get an offer for a free trip as within two hours (10 - 12) even before the end of the midnight show, he got the required views.

from 10: to 10:20

1 : 3

3: 3 in every five minutes i.e. 10:25, 10:30, 10:35 n so on

1: 30 in every four minutes

till 11:32

from 11:32 till 12:00

the views recorded till now doubles every three minutes!!

The number of different sets of three points of this grid can be the three vertices of an isosceles triangle is 36.

An isosceles triangle is one with two equal sides. The two angles that face the two equal sides are also equal. An isosceles triangle, in other words, is a triangle whose two sides are equal in length.

By using the Permutation formula,

Number of isosceles triangle to be formed is,

9!/(7!x2!) = 9x8x7!/7!x2!

= 9x8/2

= 36

So number of isosceles triangle that can be formed of this 3-by-3 grid is 36.

When a square is described as a 3 x 3 Magic square, it has three rows and three columns. An illustration of a 3 by 3 magic square with the magic constant.

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$9.10 in all nickels is how many nickels

9.10 / 0.05

how many 5 cent pieces add up to that

182 nickels

a penny is one cent

just move the decimal place over twice

9.10

910.0

910 pennies

Hope this helps

- Jeron :- )

a. The total of the two sides of the right triangle using Algebraic expression is 3x²+7x-4.

b. The length of the missing side of the triangle is 3x³-4x²-15x+5.

c. If the value of x=2, then the length of the three sides of the triangle is

   a=11, b=11 and c= -17.

d. No, it is not possible to have these side lengths for a right triangle.

Algebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them. These symbols are referred to as variables because they don't have predetermined values. These values are usually represented in algebra by variables, which are symbols like x, y, z, p, or q. These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.

a. Let the sides of the right triangle be a, b and c.

Given, one side of the triangle is 2x² + 2x - 1 and

another side is 5x + x² -3.

So, let a = 2x²+2x-1 and b = 5x+x²-3

Now, the total of the two sides= a+b

          a+b

         =2x²+2x-1 + 5x+x²-3

         = 3x²+7x-4

Therefore, the total of the two sides of the right triangle = 3x²+7x-4.

b. Now the perimeter of the triangle is given= 3x³-x²-8x+1.

Given, a+b+c=3x³-x²-8x+1.

We already have a+b, so by simplifying the equation a+b+c=3x³-x²-8x+1

we can find the length of the third side, c.

a+b+c= 3x³-x²-8x+1

⇒3x²+7x-4 +c= 3x³-x²-8x+1

⇒c= 3x³-x²-3x²-8x-7x+1+4

⇒c= 3x³-4x²-15x+5.

Therefore, length of the missing side is 3x³-4x²-15x+5.

c. We have the three sides of the triangle with us which are:

a = 2x²+2x-1

b = 5x+x²-3

c = 3x³-4x²-15x+5

Now putting the value of x as 2 in the equations as follows:

a= 2(2²) +2(2)-1

 = 8+4-1

 =11

b=5(2) +2²-3

 = 10+4-3

 =11

c=3(2³)- 4(2²) -15(2) +5

 =24-16-30+5

 = -17

Therefore, the length of the three sides of the right triangle

are 11, 11 and -17.

d. The sides of the right triangle are.

a = 11

b = 11

c = -17

We know as per the Pythagorean theorem c² = a² + b².

Accordingly, c²= 289 & a² = 121 and b²= 121, a² + b²= 242

which shows that c² is not equal to a² + b².

As, the sides of the triangle does not follow the Pythagorean theorem, so these are not the sides of a right-angle triangle.

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