Solve the equation by factoring y= x^2-8x+16=7

The portfolio weight of Stock A is 0.625 for the given situation.

The percentage of a portfolio's investments that are assigned to each asset or security is shown by the portfolio weights. Investors can meet their chosen risk and return objectives by varying the weights of various assets in their portfolios. Portfolio weights are a key component of asset allocation and portfolio optimization methodologies since they are used to determine the expected return and risk of a portfolio.

Let w be the weight (proportion) of Stock A in the portfolio.

The weight of Stock B would be (1-w).

Given that, the portfolio has an expected return of 10.2 percent.

0.102 = w(0.117) + (1-w)(0.083)

w = (0.102 - 0.083)/(0.117 - 0.083) ≈ 0.625

Hence, the portfolio weight of Stock A is 0.625 for the given situation.

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The probability that when a couple has three​ children, there are exactly 0 girls is 12.5%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Calculation of the probability:

Here we assume b for boy, g for girl

Now, the probability conditions are;

g - g - g

g - g - b

g - b - g

g - b - b

b - g - g

b - g - b

b - b - g

b - b - b

Thus, There are 8 outcomes, one of which (b - b - b) with exactly 0 girls.

So, We get;

⇒ 1 ÷ 8

= 0.125

= 12.5%

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Dan's average speed score for the season is -1.

What is the arithmetic operations?

Arithmetic operations are mathematical operations that involve manipulating numbers to perform calculations. The four basic arithmetic operations are addition, subtraction, multiplication, and division.

To find Dan's average speed score for the season, we need to add up all his scores and divide by the total number of scores. We can do this as follows:

-1 + (-3) + 1 + (-1) + (-2) + 0 = -6

Dan's total score for the season is -6. To find his average score, we need to divide this total by the number of scores, which is 6 in this case:

-6 / 6 = -1

Hence, Dan's average speed score for the season is -1.

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Sketch of  ABC and drawn image after the translation (x,y) (x+4, y + 2) is mentioned below.

In mathematics, translation refers to the process of moving a geometric shape or object from one location to another without changing its size, shape, or orientation. This movement is typically described in terms of the distance and direction of the translation.

For example, a point on a coordinate plane can be translated by adding or subtracting a constant value to its x and y coordinates. Similarly, a line segment or polygon can be translated by moving each of its vertices by the same distance and in the same direction.

Mathematical translations can be represented using transformation matrices or vectors. A translation matrix is a square matrix that describes the movement of a point or object in a specific direction and distance. A translation vector is a one-dimensional vector that describes the direction and distance of the translation.

To sketch the triangle ABC, we first plot the three given points on a coordinate plane:

We connect the three points to form triangle ABC:

    |

 6  |        C(0,5)

    |              /\

 3  |           /    \

    |          /        \

    |        /            \

    |      /                 \

    |    /__________\

    |A(-3,3)       B(1,-1)

    |

    |

    |

    |

    |

    |

        -3     -1    1     3

To find the image of the triangle under the translation (x,y) → (x+4, y+2), we add 4 to the x-coordinates and 2 to the y-coordinates of each point. This gives us the following new coordinates:

A(-3,3) → A'(-3+4, 3+2) = A'(1,5)

B(1,-1) → B'(1+4, -1+2) = B'(5,1)

C(0,5) → C'(0+4, 5+2) = C'(4,7)

We can now plot these new points and connect them to form the image of triangle ABC under the given translation:

    |

 9  |       C'(4,7)

    |             / \

 7  |          /     \

    |         /         \

 5  |      /             \

    |      /                 \

    |    /__________\

 3  |A'(1,5)       B'(5,1)

    |        

    |        

    |        

 1  |        

    |

    |

        -3     -1    1     3     5

This is the final image of triangle ABC after the translation.

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The vertices of the translated figure are A'(1, 5), B'(5, 1), and C'(4, 7).

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To translate the figure by (x+4, y+2), we add 4 to the x-coordinate and 2 to the y-coordinate of each vertex.

So the new coordinates of A' would be -

x-coordinate: -3 + 4 = 1

y-coordinate: 3 + 2 = 5

Therefore, A' has coordinates (1, 5).

The new coordinates of B' would be -

x-coordinate: 1 + 4 = 5

y-coordinate: -1 + 2 = 1

Therefore, B' has coordinates (5, 1).

The new coordinates of C' would be -

x-coordinate: 0 + 4 = 4

y-coordinate: 5 + 2 = 7

Therefore, C' has coordinates (4, 7).

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The probability that exactly three plants don't grow is given as follows:

0.0054 = 0.54%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

The probability that exactly three don't grow is P(X = 3), hence:

P(X = 3) = C(8,3) x (0.05)^3 x (0.95)^5 = 0.0054.

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Answer:

The given polynomial already has two terms that can be factored out:

9x^2y^6 - 25x^4y^8 = (3xy^3)^2 - (5x^2y^4)^2

Now we have a difference of squares:

= (3xy^3 - 5x^2y^4)(3xy^3 + 5x^2y^4)

Therefore, 9x^2y^6 - 25x^4y^8 can be rewritten as the product of (3xy^3 - 5x^2y^4) and (3xy^3 + 5x^2y^4).

Answer: The answer would be   (3xy^3-5x^2y^4)(3xy^3+5^2y^4)

(C)

Step-by-step explanation: Cant explain how to but for a quick answer it is C, and you can check the image for proof.

The answer of the question based on distance and width of the canyon is width of the trapezoid is approximately 67.43 feet.

A trapezoid is  quadrilateral ( four-sided polygon) that has two parallel sides and two non-parallel sides. The parallel sides are referred to as  bases of the trapezoid, while the non-parallel sides are called  legs. The distance between  two parallel sides is called  height or altitude of trapezoid.

The figure in the provided link is a trapezoid with parallel sides AB and CD, and non-parallel sides BC and AD.

Since AB and CD are parallel, we know that the length of the altitude is the same as the distance between them.

Let's call the width of the trapezoid "x". Then, we can use the following equation using the Pythagorean Theorem:

(AC)^2 = (BC)^2 + (AB - CD + 2x)^2

where AC is the diagonal connecting points A and C.

Substituting the given values, we get:

(AC)^2 = (35)^2 + (35 - 80 + 2x)^2

(AC)^2 = 1225 + (2x - 45)^2

(AC)^2 = 1225 + 4x^2 - 180x + 2025

(AC)^2 = 4x^2 - 180x + 3250

Now, we can use the distance formula to find the length of AC:

AC = sqrt[(A - C)^2 + (B - D)^2]

AC = sqrt[(35 + 35)^2 + 80^2]

AC = sqrt[4900 + 6400]

AC = sqrt(11300)

AC = 106.23 feet (rounded to two decimal places)

Substituting the value in  equation above, we will get:

(106.23)^2 = 4x^2 - 180x + 3250

11299.77 = 4x^2 - 180x + 3250

4x^2 - 180x + 8049.77 = 0

Solving the quadratic equation using quadratic formula, we will get:

x = [180 ± sqrt(180^2 - 4(4)(8049.77))] / (2(4))

x = [180 ± sqrt(129322.08)] / 8

x = [180 ± 359.44] / 8

We take the positive root, since x represents a length, and we get:

x = (180 + 359.44) / 8

x = 67.43 feet (rounded to two decimal places)

Therefore, the width of the trapezoid is approximately 67.43 feet.

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Answer:

5a + 3b = 13

7a + 6b = 20

And solve for the values of "a" and "b" using algebraic methods like substitution or elimination.

Step-by-step explanation:

Solving for a and b in the system of equations:

5a + 3b = 13

7a + 6b = 20

We can multiply the first equation by 2 to get:

10a + 6b = 26

Then, we can subtract the second equation from this to eliminate b:

(10a + 6b) - (7a + 6b) = 26 - 20

3a = 6

Solving for a, we get:

a = 2

Substituting this value into the first equation, we can solve for b:

5a + 3b = 13

5(2) + 3b = 13

10 + 3b = 13

3b = 3

b = 1

Therefore, the solution to the system of equations is:

a = 2

b = 1.

Answer:

2,118.01

Step-by-step explanation:

The distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.

While travelling from one location to another and back again just multiplying the distance between the two places will give you the total distance travelled when travelling from one spot to another and returning to the beginning position.

The distance from frank's house to john's house = 4/10.

The distance back to Frank's house = 4/10.

Total distance = 4/10 + 4/10

Total distance = 8/10

The distance is thus,

1 - 8/10

Take the LCM:

(10 - 8) / 10

2/10 = 1/5

Hence, the distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.

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Answer:

Let's start by defining some variables to represent the width and length of the pool:

Let w be the width of the pool (in feet).

Let l be the length of the pool (in feet).

We know from the problem statement that the length of the pool is 5 feet more than 3 times its width:

l = 3w + 5

We also know that the deck surrounding the pool is 2 feet wide. This means that the overall width of the pool and the deck combined is:

w_total = w + 2 + 2 = w + 4

Similarly, the overall length of the pool and the deck combined is:

l_total = l + 2 + 2 = l + 4

We are given that the area of the deck is 196 square feet. The area of the deck can be calculated by subtracting the area of the pool from the area of the pool and deck combined:

Area of deck = Area of pool and deck - Area of pool

196 = w_total * l_total - w * l

We can substitute the expressions for w_total and l_total in terms of w and l:

196 = (w + 4) * (l + 4) - w * l

Simplifying this expression gives:

196 = wl + 4w + 4l + 16

We can substitute the expression for l in terms of w:

196 = w(3w + 5) + 4w + 4(3w + 5) + 16

Simplifying this expression gives:

196 = 13w + 36

Solving for w, we get:

w = 14

Therefore, the width of the pool is 14 feet.

By performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

Subtraction in mathematics is the process of subtracting one integer from another. In other words, the result of subtracting two from five is three. After addition, subtraction is usually the second operation you learn in math class.

So, to find the weight of apples, perform subtraction as follows:

= 6.7 - 2.5

= 4.2 kilograms

Therefore, by performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.

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The solutions to the inequality s < 30 are 20%, 17%, 29 and one-half percent (which is equivalent to 29.5%), and 1.5%.

The disparity that best illustrates the phrase "the possibility of snow is less than 30%" is:

s < 30

This implies that the inequality can be solved for any value of s that is less than 30.

We must compare the numbers to 30 and see if they are less than it in order to identify which ones are the answers to the inequality.

The answer is yes because 20% = 0.2 is less than 30%.

It is not a solution because 35% = 0.35 is not less than 30%.

The answer is yes because 17% = 0.17 is less than 30%.

It is not a solution because 30% = 0.3 is not less than 30%.

That is a solution since 29 and a half percent = 0.295 is less than 30%.

The answer is yes because 1.5% = 0.015 is less than 30%.

As a result, the answers to the inequality s 30 are 20%, 17%, 29 and a half percent (or 29.5%), and 1.5 percent.

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Answer:

a no

b. no

c.no

d. yes

Step-by-step explanation:

Answer:

[tex]\mathrm{225\:in\:\right)^3}[/tex]

Step-by-step explanation:

Given:

base = b = 10 in

height = h = 9 in

length = l = 5 in

[tex]\mathrm{Use\:formula}\:\mathrm{V= \dfrac{1}{2}\times\:b\times\:h\times\:l:}[/tex]

[tex]\mathrm{V= \dfrac{1}{2}\times\:10\times\:9\times\:5}[/tex]

[tex]\mathrm{= 225\:in\:\right)^3}[/tex]

Final answer is rounded to 3 decimal places.

Answer:

13

Step-by-step explanation:

1. 20/2 = n - 3

2. 10 = n - 3

3. 10 + 3 = n

4. 13 = n

The percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, a flower shop received a shipment of 250 red roses, they will use 200 out of this for decorating for the grand opening of the Historical Museum,

We need to find the percentage of the red roses used there,

So, the percentage of the red roses used in decoration =

200 / 250 x 100

= 0.8 x 100

= 80%

Hence. the percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%

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(-x+18)(x+4)

-x(x+4) + 18 (x+4)

-(x^2+4x) + 18(x+4)

-x^2-4x+18x+72

−x^2+14x+72

I hope this helps! :)

Answer:

26

Step-by-step explanation:

10(2) -2(-3)=20+6=26

Answer:

Step-by-step explanation:

[tex]\tt 10a-2b[/tex]

[tex]\tt a=2[/tex]

[tex]\tt b=-3[/tex]

______

Simplify: 10×2 = 20

Simplify: 2×-3= -6

Simplify:-

_____________________

Hope this helps! :)

Step-by-step explanation:

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, the circumference of the circular track is 0.4 mile, which is equal to 2112 feet (0.4 x 5280 = 2112).

Therefore, we can write the equation:

2112 = 2πr

Solving for r, we get:

r = 2112 / (2π)

r ≈ 336.31 feet (rounded to the nearest hundredth)

Therefore, the radius of the track, in feet, is approximately 336.31 feet. The closest option to this answer is 336.31 feet.

Answer:

334.31

Step-by-step explanation:

please give brainliest

The measurements of the diagonal distance across the middle school gym is given by the following persons and is rounded to the nearest hundredths

The calculation of Arturo = 31.75 yards

The calculation of Bonnie = 32.98 yards

The calculation of Courtney = 31.42 yards

The calculation of Dawson = 31 yards

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the measurements of the diagonal distance across the middle school gym be represented as A

Now , the measured values are

a)

The measurement of Arturo = 6√28 yards

The measurement of Arturo = 6 x 5.2915

On rounding , we get

The measurement of Arturo = 31.75 yards

b)

The measurement of Bonnie = 8√17 yards

The measurement of Bonnie = 8 x 4.123

On rounding , we get

The measurement of Bonnie = 32.98 yards

c)

The measurement of Courtney = 10π yards

The measurement of Courtney = 10 x 3.142

On rounding , we get

The measurement of Courtney = 31.42 yards

d)

The measurement of Dawson = 3.1√100 yards

The measurement of Dawson = 3.1 x 10

On rounding , we get

The measurement of Dawson = 31 yards

Hence , the measurements are rounded

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The equation of the circle x² + y² - 8x - 6y + 16 = 0 in standard form is (x - 4)² + (y - 3)² = 3².

Given the equation of the circle ;

x² + y² - 8x - 6y + 16 = 0

To write the equation of a circle in standard form, we need to express it as:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

To do this, we need to complete the square for both x and y terms in the given equation.

Starting with the x terms:

x² - 8x = x² - 8x + 16 - 16

= (x - 4)² - 16

Similarly, for the y terms:

y² - 6y = y² - 6y + 9 - 9

= (y - 3)² - 9

Substituting these results into the original equation, we get:

x² + y² - 8x - 6y + 16 = 0

(x - 4)² - 16 + (y - 3)² - 9 + 16 = 0

Simplifying, we get:

(x - 4)² + (y - 3)² - 9 = 0

(x - 4)² + (y - 3)² = 9

So the equation of the circle in standard form is:

(x - 4)² + (y - 3)² = 3²

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Answer: 8

Step-by-step explanation:

Since 1 batch uses 1/8 of a bag of flour, I would use equivalent fractions to find how many 8ths are in 3/4.  3/4=?/8

4 times 2 equals 8, so I would multiply 3 by 2 also.  3/4=6/8.  If 1 batch takes 1/8, then 6 batches would use 6/8 or 3/4 of a bag of flour.

Answer:

If Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Then she can go six times to the movies.

Step-by-step explanation:

Two or more expressions with an Equal sign is called as Equation.

Given,

Robin was given a $40 monthly allowance.

She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert.

The amount spent on movies

40-12.5

$27.5

A movie ticket costs $5.

We need to find how many times can she go to the movies.

To find this we need to divide $27.5 by 5

$27.5/5=5.5

Robin can go 6 times to the movies.

Using linear equations, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.

Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. In the elimination procedure, any coefficient is first made equal, then deleted. After elimination, the equations are solved to provide the other equation.

Given that, the car wash charges $5.25 to use its facilities, plus an additional $0.69 for each minute.

C = 5.25 + 0.69x

For 8 minutes:

C = 5.25 + 0.69(8)

C = $10.77

Hence, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.

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( 2,-9) points lie on the same line.

Line point intercept is defined.

Quantifying soil cover, including vegetation, litter, rocks, and biotic crusts, quickly and accurately can be done using the line-point intercept approach.

                                  These metrics deal with the erosion caused by wind and water, water infiltration, and the site's capacity to withstand damage and recover from it.

k = -5 - 3/1 - (-1)  = -8/2 = -4

the formula of the line is  

                                    y - 3 = -4(x+ 1)

 when x  = -3 , y = 11 ≠ 12 the points aren't on line.

 when x = -5, y = 19 ≠ 1

  when x = 4, y = -7 ≠ 15

   when x = 2, y = -9 ≠ 7

    when x = 0, y = -1 ≠ -2

  ( 2,-9) are on the same line.

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Answer:

65

Step-by-step explanation:

All 4 sides of a polygon equals 360 degrees. We are given the equation of 2 sides to find the degree.

12x + 19 + 8x + 1 = 180

(We put it equal to 180 instead of 360 since we are only given 2 sides)

Subtract 19 from both sides

12x + 8x + 1 = 161

Subtract 1 from both sides

12x + 8x = 160

Add 12x + 8x

20x = 160

Divide 20x by 160

x = 8

Plug in x value to (8x + 1)

(8(8) + 1)

= 65