a circular curve is to be constructed with a 225 ft radius and an interior angle of 55 degrees. the separation between the stakes along the arc is 50 ft. assuming the curve is laid out from point to point, what is the last deflection angle?

Answer:

Step-by-step explanation:

1. The vertex is where the parabola is changing from increasing to decreasing

2. From the picture, we can see that the vertex is at (1,2)

3. The formula for vertex form is f(x)=a(x-h)^2+k

4. Vertex is (1,2) or (h,k)

5. You can see that the parabola opens upside down like a "n" so it has been reflected in the x axis

6. So, your equaltion is f(x)=-(x-1)^2+2

7. In this cause you can see that a=-1, but if not given you would choose a random point on the parabola and plug it in :). Example:(0,1): 1 = a(0-1)^2+2

a=-1.

8. Your answer: f(x)=-(x-1)^2+2

Answer:

Step-by-step explanation:

5 1/2 +2x = 25

25- 5 1/2 = 2x

19 1/2 = 2x

x = 9.75

It took him about 9.75 weeks to lose at least 25 pounds.

Answer:

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

It took Mr. Henry at least 10 weeks to lose 25 pounds.

The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ = 86

sample size, n = 140

standard deviation, σ  = 11

The probability

P(z > 88.4) + P(z < 84.4)

z score for z < 88.4

z = (88.4 - 86) / 11

= 0.21818 p value = 0.41364

z score for z < 84.4

z = (84.4 - 86) / 11

=  -0.14545

p value for z < -0.14545 = 0.44218

The probability required = 0.41364 + 0.44218 = 0.85582

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The number of years to double the investment is 8.824 years.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $3,900

R = 8%

n = 2

A = 2P = 2 x 3,900 = $7,800

Now,

A = P [tex](1 + r/n)^{nt}[/tex]

7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]

78/39 = [tex](1.04)^{2t}[/tex]

2 = [tex](1.04)^{2t}[/tex]

Taking logs on both sides.

log 2 = 2t log(1.04)

0.30 = 2t x 0.017

0.30/0.017 = 2t

17.65 = 2t

Divide both sides by 2.

t = 17.65 / 2

t = 8.824 years.

Thus,

The number of years to double the investment is 8.824 years.

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The hawk is closer to the ground after 8 minutes

It is 130 feet closer

We have the equation as;

Also, x represents the descending time in minutes

Now, let's substitute the value of x as 8 minutes in the equations

If x = 8

For equation (1)

y = - 20(8) + 350

expand the bracket

y = - 160 + 350

y = 190 feet

For equation (2)

y = -10(8) + 400

expand the bracket

y = -80 + 400

y = 320 feet

The hawk is closer after 8 minutes

The distance from the ground(eagle) - The distance from the ground(hawk)

320 - 190

130 feet

Hence, the hawk is closer to the ground

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There is a 136.13 probability that 3 won't increase.

Only 0.65% of seeds will grow into robust plants.

There is a 0.35 probability that a seed won't grow into a robust plant.

In this case, n = 12 and r = 3.

11 seeds will sprout if 1 seed doesn't germinate. Raising 0.65 to the power of 11 and 0.35 to the power of 3 will result in the following: 11 seeds develop, and we use the 11th power; 3 seeds do not grow, so we use the power of 3:

So, the response is:

[tex]{}^{12}C_3[/tex] × [tex]{(chance of successful growth) }^{11}[/tex]x [tex](chance of Unsuccessful growth)^3[/tex]

= [tex]{}^{12}C_3[/tex] × [tex]0.65^{11}[/tex] × [tex]{0.35}^3[/tex]

= 362880 × 0.008750 × 0.042875

= 136.13

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The statement that would be true concerning the graph would be that the graph will have a slope of -0.5.

A slope is defined as the difference between a chosen point on the vertical and horizontal axis.

The slope of a straight line graph has a constant equation that is used to determine its slope. Thus;

y = mx + b

Where m = the measure of the steepness of the straight line graph.

From the equation of the graph that was given;

y = -0.5x + 12. The slope of the graph which is represented by 'm' would be -0.5.

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answer:

(1,3)

step-by-step explanation:

desmos.

The value of x will be equal to 7 for the given slope of 2 for the line.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.

The slope of the line is calculated by the formula,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

2 = ( 3 + 3 ) / ( x - 4)

2(x-4) = 6

2x - 8 = 6

2x = 8 + 6

2x = 14

x = 14 / 2

x = 7

Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.

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The translated absolute value function graphed is defined as follows:

y = |x - 3| + 5.

The absolute value function, of vertex (h,k), is defined by the following piecewise rule, depending on the input of the function:

In this problem, the coordinates of the vertex are given as follows:

Hence the vertex is given by the following point:

(3,5).

Then the equation graphed is defined by the rule presented as follows:

y = |x - 3| + 5.

Which is a translation of 3 units right and 5 units up of the standard absolute value function.

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The probability that both are defective when a customer selects 2 cartridges at random from the shelf will be 0.00766.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The probability of choosing defective cartridge=7/80

So, the probability of choosing 2 defective cartridge=(7/80)²

=0.00765625

=0.00766

When a customer randomly chooses two cartridges from the shelf, the likelihood that both are flawed is 0.00766.

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Answer:

b & d

Step-by-step explanation:

Answer:

The picture is not Clear. Please provide a better view of the question.

Step-by-step explanation:

The leading coefficients and parabolic equations, considering the vertices, are given as follows:

1. a = 7/4, y = 7/4(x - 4)² - 1.

2. a = -2, y = -2(x + 1)² + 2.

The equation of a parabola with vertex given by (h,k) is presented as follows:

y = a(x - h)² + k.

In which a is the leading coeffiicent.

For item 1, the coordinates of the vertex is given as follows:

(4,-1).

Hence:

h = 4, k = -1, and the equation is:

y = a(x - 4)² - 1.

When x = 6, y = 6, hence the leading coefficient is calculated as follows:

6 = a(6 - 4)² - 1

4a = 7

a = 7/4.

Thus the equation is:

y = 7/4(x - 4)² - 1.

For item 2, the vertex is:

(-1,2).

Hence:

y = a(x + 1)² + 2.

When x = 0, y = 0, hence the leading coefficient is calculated as follows:

0 = a(0 + 1)² + 2

a = -2.

Hence the equation is:

y = -2(x + 1)² + 2.

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y is inversely proportional to the square of x, here y in terms of x is 2/5.

From the given problem y is inversely proportional to the square of x.  

A table of values for x and y is shown.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the table:

(a) As we know that, y is inversely proportional to the square of x,

Here k is proportionality constant.

y∝1/x²

y= k/x²

4=k/1²

k=4

So, y in terms of x is y=4/x²

(b) Putting the value of y=25, we get:

25=4/x²

x²=4/25

x=2/5

Therefore, y is inversely proportional to the square of x, here y in terms of x is 2/5.

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Answer:

Assuming the bags sold were for 1 week period.

1.  $659.20 for 1 week and 380 bags of peanuts

2. 890 bags

Step-by-step explanation:

The equation is missing the variable, n (the number of bags sold).  I'll take the liberty to add it after the $0.84/bag term, where it belongs:

    P = 0.84n + 340

The 340 is $340/week.  n must be in units of "bags/week."

1.  How much will Ibram be paid if he sells 380 bags of peanuts?

   P = $0.84n + $340

n = 380 bags (we will assume in 1 week).

   P = $0.84n + $340

   P = $0.84(380) + $340

   P = $659.20

2.  How many bags of peanuts did Ibram sell if he earned $1,087.60?

  P = $0.84n + $340

   P = $1087.60

   $1087.60 = $0.84n + $340

      $1087.60 - $340 = $0.84n

      $0.84n =  $1087.60 - $340

      $0.84n =  $747.60

 n = 890 bags  ( ! - I'm impressed)

Answer:

Rs 80,0000 and Rs 100,000

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

divide the amount by 9 to find the value of one part.

Rs 1,80,000 ÷ 9 = Rs 20,000 , then

4 parts = 4 × Rs 20,000 = Rs 80,000 ← amount son receives

5 parts = 5 × Rs 20,000 = Rs 100,000 ← amount daughter receives

The sum obtained by the son is Rs. 80,000 and the daughter is Rs. 1,00,000.

Mr. Karki divided Rs. 1,80,000 in a ratio of 4:5 between his son and daughter.

Let the common multiple be x

∴ The son obtained Rs. 4x        --------1

And daughter obtained Rs. 5x        --------2

As the total sum is Rs. 1,80,000

∴ 4x + 5x = 180000

9x = 180000

x = 180000/9

∴ x = Rs. 20000

Putting the value of x in 1 and 2 we get,

The sum obtained by son = 4x = 4*20000 = Rs. 80000

And the sum obtained by daughter = 5x = 5*20000 = Rs. 100000

Thus, the son obtained Rs. 80,000 while the daughter obtained Rs. 1,00,000 which is in the ratio of 4:5.

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The statements which are as a result of corresponding parts of congruent triangles being congruent are:

1) EFGH is a rectangle.

The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.

2). EFGH has 4 congruent sides.

The above statement is also false. EFGH has two opposite sides are congruent.

3). Diagonal FH bisect angles EFG and EHG.

The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.

4). Diagonal FH is perpendicular to side Fe.

The above case is not true in general.

5). Angle FEH is congruent to angle FGH.

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Answer:

four tablespoons to make 6 cups of popcorn.

Step-by-step explanation:

1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.

The worth of the book after 10 years is $1061.1

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First edition book worth = $262

Rate of increase per year = 15%

The worth of the book after t years can be given by the expression.

= 262 x [tex]1.15^{t}[/tex]

Now,

The worth of the book when t = 10.

= 262 x [tex]1.15^{10}[/tex]

= 262 x 4.05

= $1061.1

Thus,

The book is worth $1061.1 after 10 years.

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Answer:

Step-by-step explanation:

Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18

The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.

Answer:

(7,5)

Step-by-step explanation:

[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]

the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64  was $ 68.73

We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:

Xw= Cw/Cm * 100%

Where:

Cw: cost of coverage for a woman of 50 years.

Cm: coverage cost for a 30-year-old man.

Xw= 819.73/1192.64 *100%

    = 68.73

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The value for the given expression  [tex]\alpha ^{2} + \beta ^{2}[/tex] will be [tex](\alpha +\beta )^{2}-2\alpha \beta[/tex].

What are Algebraic Identities?

Algebraic identities are algebraic equations that hold true for any value of each of their variables. In factoring polynomials, they are also used.

As we know, [tex](a+b)^{2} = a^{2} +2ab + b^{2}[/tex]  then,

For the given question, [tex](\alpha +\beta )^{2} = \alpha ^{2} +2\alpha \beta + \beta ^{2}[/tex]

Now, subtracting [tex]2\alpha \beta[/tex] on both sides then, we get

or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} +2\alpha \beta + \beta ^{2}-2\alpha \beta[/tex]

or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} + \beta ^{2}\\[/tex]

or, [tex]\alpha ^{2} + \beta ^{2}=(\alpha +\beta )^{2}-2\alpha \beta[/tex]

That's how the value  [tex]-2\alpha \beta[/tex] comes.

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A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat  lowest cost is at (x,y) is (3,2).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given,

Function:

C = x + 1.5y

Subjected to:

30x + 20y ≥ 13/10 ×100 ≥ 130

10x + 4y ≥ 1/5 × 100 ≥ 20

50x + 75y ≥ 3 × 100 ≥ 300

Feasible region:

(0, 13/2), (3,2) (6,0)

C = x + 1.5y

(0, 13/2) ⇒ C = 0+ (1.5)(13/2)

(0.13/2) ⇒ C = 9.75

(3,2) ⇒ C = 3+ (1.5)(2)

(3,2) ⇒ C = 6

(6,0) ⇒ C = 6 + 0

(6,0)⇒ C = 6

A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat  lowest cost is at (x,y) is (3,2).

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I need help too on this one

Answer:

you lowest tempeture in the mesosphere is -96

Step-by-step explanation:

Answer:

87c

Step-by-step explanation: