16. Find the equation of a parabola with a focus at (3,1) and a directrix at y = 3.
A) y = 1∕4(x – 3)^2 + 3
B) y = –1∕4 (x – 3)^2 + 3
C) y = –1∕4 (x – 3)^2 + 2
D) y = 1∕4(x – 3)^2 + 2

Answer:

867.44 ft²

Step-by-step explanation:

The area of the shaded region is A = 196π + 252.

We have the dimensions of the unshaded region are 14ft x 18ft.

We have to find the area of shaded region.

The area of a rectangle is -

A(R) = Length x Breadth = L x B

and the area of Circle is -

A(C) = [tex]\pi r^{2}[/tex]

According to the question -

Dimensions of the unshaded region -

L = 18ft

B = 14ft

Area of the shaded region (A) = Total Area - Area of Rectangle

Total Area = Area of 2 semicircles of radius (7 + 7) 14ft + Area of rectangle of length 18ft and breadth 28ft.

Total Area = ( [tex]2\times \frac{1}{2}\times \pi \times14 \times 14[/tex] ) + ( 18 x 28)

Total Area = 196π + 504

Area of the shaded region (A) = 196π + 504 - 252 = 196π + 252

Hence, the area of the shaded region is A = 196π + 252.

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Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

The geometric sequence with the first term a, a common ratio r has the nth term given as

Tₙ = arⁿ⁻¹

where Tₙ is the nth term

From the given sequence

a = 0.2

r = -0.06/0.2

= -0.3

Hence the nth term

= 0.2 * -0.3ⁿ⁻¹

The right option is E

Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

Answer:

x=−3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  7*x-8-(8*x-5)=0

Pull out like factors :  -x - 3  =   -1 • (x + 3)

Solve  :    -x-3 = 0  

Add  3  to both sides of the equation :    -x = 3

Multiply both sides of the equation by (-1) :  x = -3

Answer:

56x^2−99x+40

Step-by-step explanation:

 Evaluate (8x−5)(7x−8)

Apply the distributive property by multiplying each term of 8x−5 by each term of 7x−8.

56x^2−64x−35x+40

Combine −64x and −35x to get −99x.

56x^2−99x+40

Answer:

[tex]2 \times 10 {}^{ - 7} [/tex]

Step-by-step explanation:

[tex] \frac{4 \times 10 {}^{ - 4} }{20 \times 10 {}^{2} } = \frac{0.0004}{2000} = 2 \times 10 {}^{ - 7} [/tex]

Hope this helps ;) ❤❤❤

Answer:

54 units^2

Step-by-step explanation:

The formula to find the area of a right triangle is bh/2.

Plug the values in.

9*12/2

Multiply.

108/2

Divide.

52

The area is 54 units squared.

Answer: 54u²

Step-by-step explanation:

The area of a triangle is 1/2bh

1/2bh

1/2(12)(9)

(6)(9)

54

Hope it helps <3

Answer:

3.87

Step-by-step explanation:

The computation is shown below:

Data provided in the question

mean distance = [tex]\bar x[/tex] = 188 meters

Standard deviaton = [tex]\sigma = 14[/tex]

Hits drivers = 15

The distance = 174 meters

H_0: μ≤174;

H_a: μ>174

Based  on the above information, the test statistic z-score is

[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]

= 3.87

Hence, the test statistic is 3.87

Note:

We take the μ≤174 instead of μ=174;

Answer:  114°

Step-by-step explanation:

[tex]\overrightarrow{u}=\bigg<3, 2, -1\bigg>\\\\\overrightarrow{v}=\bigg<1,-4,2\bigg>\\\\\\u\cdot v=3(1)+2(-4)+\ -1(2)\quad =-7\\\\|u|=\sqrt{3^2+2^2+(-1)^2}\quad =\sqrt{14}\\\\|v|=\sqrt{1^2+(-4)^2+2^2}\quad =\sqrt{21}\\\\\\\cos\theta=\dfrac{u\cdot v}{|u|\ |v|}\\\\\\\cos\theta=\dfrac{-7}{\sqrt{14}\cdot \sqrt{21}}\\\\\\\cos\theta=\dfrac{-1}{\sqrt6}\\\\\\\large\boxed{\theta=114^o}[/tex]

Answer:

$125,800

Step-by-step explanation:

Amount (A) = ?

Principal (P) = $85,000

Rate (r) = 6%

Time (t) = 8 years

Simple interest formula;

A = P(1 + rt)

A = $85,000(1 + 0.48)

A = $125,800

Answer:

Probability of orange hat = 0.0833

Step-by-step explanation:

We have to find the probability of getting an orange hat while we randomly choose from 444 pieces of clothing and 333 colors.

So we have to get hat from the clothing and we have to get orange color from the colors. All shirts , pants , socks and hats are in equal numbers and are 111 each. Also purple, blue and orange are 111 each in number.

The probability of getting hats =

                                                   = 0.25

The probability of getting orange =  = 0.333

Final probability = 0.25 0.333

                          = 0.0833

Answer: 1/12

Step-by-step explanation:

I just had khan academy

Answer:

A). 55

Step-by-step explanation:

Number of Variegated Fritillaries for each year is

2009 = 7

2010= 95

2011= 63

The sum total of the samples= 7+95+63

The sum total of the samples= 165

Number of years= 3

The average= total/number of years

The average= 165/3

The average= 55

Answer: A

Step-by-step explanation: I have a massive brain (•-*•)

Answer:

Option (D)

Step-by-step explanation:

Endpoints of the sides of any polygon are called as vertices. Any polygon is named by its vertices either in a consecutive order either clockwise or counterclockwise.

In the picture attached,

Vertices of the triangle or endpoints of the sides of the polygon are A, T and X.

Therefore, we can name this triangle as ΔATX, ΔTXA, ΔXAT or ΔXTA, ΔAXT, ΔTAX.

Option (D) will be the answer.

Answer:

d

Hope this help :)

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Answer:

Option (3)

Step-by-step explanation:

[tex](x-i\sqrt{3})[/tex] is a factor of a polynomial given in the options, that means a polynomial having factor as [tex](x-i\sqrt{3})[/tex] will be 0 for the value of x = [tex]i\sqrt{3}[/tex].

Option (1),

3x⁴ + 26x² - 9

= [tex]3(i\sqrt{3})^{4}+26(i\sqrt{3})^2-9[/tex] [For x = [tex]i\sqrt{3}[/tex]]

= 3(9i⁴) + 26(3i²) - 9

= 27 - 78 - 9 [Since i² = -1]

= -60

Option (2),

4x⁴- 11x² + 3

= [tex]4(i\sqrt{3})^4-11(i\sqrt{3})^2+3[/tex]

= 4(9i⁴) - 33i² + 3

= 36 + 33 + 3

= 72

Option (3),

4x⁴ + 11x² - 3

= [tex]4(i\sqrt{3})^4+11(i\sqrt{3})^2-3[/tex]

=  4(9i⁴) + 33i² - 3

= 36 - 33 - 3

= 0

Option (4),

[tex]3x^{4}-26x^{2}-9[/tex]

= [tex]3(i\sqrt{3})^4-26(i\sqrt{3})^{2}-9[/tex]

= 3(9i⁴) - 26(3i²) - 9

= 27 + 78 - 9

= 96

Therefore, [tex](x-i\sqrt{3})[/tex] is a factor of option (3).

The value of x in terms of b is x = [tex]\frac{-3}{b}[/tex]. Therefore the value of x when b = 3 is x = [tex]\frac{-3}{3}[/tex] = -1.

We can find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:

-2(bx - 5) = 16

-2bx + 10 = 16

- 10

-2bx = 6

÷ -2

bx = -3

÷ b

x = -3/b, which is the answer to the first part.

To get the second answer, we just substitute b = 3 into this equation and we get:

x = -3/b = -3/3 = -1

I hope this helps!

The value of x in terms of b is x = -3/b. Therefore, the value of x when b = 3 is x = -1.

An equation is an expression that shows the relationship between two or more numbers and variables.

We need to find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:

-2(bx - 5) = 16

-2bx + 10 = 16

-2bx = 6

bx = -3

x = -3/b,

Now we just substitute b = 3 into this equation and we get:

x = -3/b = -3/3 = -1

The value of x in terms of b is x = -3/b.

Therefore, the value of x when b = 3 is x = -1.

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Answer:

x = 69°

Step-by-step explanation:

In the picture attached,

Length of the ladder = 15 ft

This ladder reaches the height of a building = 14 ft

We have to find the measure of angle formed between the base of the ladder and the ground.

By applying Sine rule in the right triangle formed,

sin(x)° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

sin(x)° = [tex]\frac{14}{15}[/tex]

x = [tex]\text{sin}^{-1}(\frac{14}{15})[/tex]

x = 68.96°

x ≈ 69°

Answer: Option D, composition.

Step-by-step explanation:

In a function f(x) = y

x is the input, and the set of the possible values of x is called the domain.

y is the output, and the possible values of y is called the range.

Now, if we have two functions:

f(x) = y

g(x) = y.

we can define the composition of functions as: using the output of one function as the input of the other function, we can write this as:

f( g(x)) or fog(x)

In words, first we evaluate the function g in the point x, and the output of that is used as the input for the function f.

Then, the correct option here is D, composition.

Answer:

First answer.

Step-by-step explanation:

Multiply everything by 10, to get rid of the decimals.

Answer:

6[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]

y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]

y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]

Answer:

see answers below

Step-by-step explanation:

A 'This statement is always true'

B 'This statement is sometimes true'

C 'This statement is never true'

a) When you add two negative numbers the answer is negative. _A_

e.g. -4 + -1 = -5

b) When you subtract a positive number from a negative

number the answer is negative. _A_

e.g.  -5 - (+4) = -9

c) When you subtract a negative number from a positive

number the answer is negative. _C_

e.g. 5- (-2) = 8   always positive, => never negative

d) When you subtract a negative number from a negative

number the answer is negative. _B_​

-2 - (-4) = +2

-2 - (-1)  = -1

Answer:

The confidence interval is  [tex]25.16 < \mu < 26.85[/tex]

Step-by-step explanation:

From  the question we are given a data set

     25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is  

       [tex]\= x = \frac{\sum x_i}{n}[/tex]

where is the sample size with values  n =  10

         [tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]

          [tex]\= x = 26[/tex]

The standard deviation is evaluated as

             [tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]

substituting values

     [tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]

                  [tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]

     [tex]\sigma = 1.625[/tex]

The  confidence level is given as 90% hence the level of significance is calculated as

    [tex]\alpha = 100 -90[/tex]

    [tex]\alpha =10[/tex]%

   [tex]\alpha = 0.10[/tex]

Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as

      [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The reason  we are obtaining  the critical values of [tex]\frac{\alpha }{2}[/tex] instead of  [tex]\alpha[/tex] is because  we are considering two tails of the area under the normal curve

  The margin of error is evaluated as

            [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

           [tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]

           [tex]MOE = 0.845[/tex]

The  90%, two sided confidence interval is mathematically evaluated as

           [tex]\= x - MOE < \mu < \= x + MOE[/tex]

           [tex]26 - 0.845 < \mu < 26 + 0.845[/tex]

           [tex]25.16 < \mu < 26.85[/tex]

Given that the lower and the upper limit is greater than  25 then we can assure the manufactures  that the battery life exceeds 25 hours

Answer:

z-value of rachel = 1.875

z-value of rob = -2

z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.

Step-by-step explanation:

Let's denote the salary of Rob and Rachel per year by X. So, X = $50,000

We are told that;

For Rachel's industry;

Mean salary;μ1 = $35,000

Standard deviation;σ1 = $8,000

For Rob's industry;

Mean salary;μ2 = $60,000

Standard deviation;σ2 = $5,000

Formula for z - value is;

z = (X - μ)/σ

Thus;

z-value for rob is;

z2 = (X - μ2)/σ2

z2 = (50000 - 60000)/5000

z2 = -2

z-value for rachel is;

z1 = (X - μ1)/σ1

z1 = (50000 - 35000)/8000

z1 = 1.875

z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.

Answer:

y > -x/6 + 1

Step-by-step explanation:

Hope this can help

The graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The inequality : [tex]y > -(\frac{1}{6} )x+1.[/tex]  

now first we take out points to plot graph for that we will assume inequality to equation

i.e  

[tex]y = -(\frac{1}{6} )x+1[/tex]

x          y  

0          1

6          0

Now , as inequality have > sign

i.e according to the graph of inequality rules:

The boundary line is dashed for > and < and If the symbol ≥ or > is used, shade above the line.

Therefore,

Graph will be option "A" only .

Hence, the graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex]  is option "A" .

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Answer:

Thickness of rectangle prism is 20 inches.

Step-by-step explanation:

Given:

Surface area of rectangular prism, A =  992 sq inches.

Height, h = 12 inches

Width, w = 8 inches

To find:

Thickness / length of prism, [tex]l[/tex] = ?

Solution:

First of all, let us learn the formula for surface area of a rectangular prism.

Formula for surface area of a prism is given as:

[tex]A=2(wl+hl+hw)[/tex]

As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.

Putting all the given values in the formula to find the value of [tex]l[/tex]:

[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]

So, the answer is Thickness of rectangle prism is 20 inches.

Answer:

34.38

Step-by-step explanation:

45 minutes is 45/60 or .75 of an hour

The up front cost  plus the hours times the hourly cost

The cost is 25 + .75 * 12.50

25 +9.375

34.375

Rounding to the nearest cent

34.38

Question:

Which of the following values cannot be probabilities? 3 / 5,  2,  5 / 3,  1.39, −0.57,  1,  0,  0.04 Select all the values that cannot be probabilities.

A. 0

B. 2

C. 3 / 5

D. − 0.57

E. 0.04

F. 1.39

G. 5 / 3

H. 1

Answer:

B, D, F, G

Step-by-step explanation:

The probability, P(A), of an event A occurring is given by;

0 ≤ P(A) ≤ 1

This means that the probability of an event happening is always between 0 and 1 (both inclusive).

Therefore;

=> 3 / 5 is a valid probability value as;

0 ≤ 3/5 ≤ 1

=> 2 is NOT a valid probability value as 2 is not within the range 0 and 1

=> 5 / 3 is NOT a valid probability value as 5 / 3 = 1.6667 is not withing the range 0 and 1

=> 1.39 is NOT a valid probability value

=> -0.57 is NOT valid. Probability values are not and cannot be negative.

=> 1 is a valid probability value. This just means that the probability that an event will occur is 100% likely.

=> 0 is a valid probability value. This just means that the probability that an event will occur is 0% likely.

=> 0.04 is valid as;

0 ≤ 0.04 ≤ 1

Answer:

(-1,-2)

Step-by-step explanation:

[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]

so the only one is (-1,-2)

Answer:

61 and -87

Step-by-step explanation:

If the numbers are x and x - 148, we can write the following equation:

x + x - 148 = -26

2x - 148 = -26

2x = 122

x = 61 so x - 148 = 61 - 148 = -87

Answer:

Graph C.  See explanations below.

Step-by-step explanation:

Looking for graph corresponding to   d <= (w^2)/5

Take the third graph, which has a solid line (to correspond to the inequality <=, or less than or equal to).

For a dog's weight of 10 lb, the corresponding dose is 20 mg = 10^2/5

for 20 lb, dose = 80 mg (=20^2/5)

...

For 40 lb, dose = 320 mg (=40^2/5).

So this is the correct graph.

The fourth (d) is similar. But the dotted line eliminates the equality in

d <= w^2/5

so not correct.

Answer:

The elevation of the airplane decreases by 9 km.

Step-by-step explanation:

We use the distance-rate-time formula: d = rt.

Here, the rate is r = 0.15 km/min and the time is t = 60 min. Simply plug these into the formula:

d = rt

d = 0.15 * 60 = 9 km

So, the change in elevation in the last 60 minutes is 9 km. However, note that the rate is negative (-0.15 km/min), which means that the elevation actually is decreasing.

Thus, the answer is: the elevation of the airplane decreases by 9 km.

~ an aesthetics lover

Answer:

The elevation of the airplane _decrease_ by __9____ km

Step-by-step explanation:

Take the rate and multiply by the time to get the distance traveled

-.15 km per minute * 60 minutes

- 9 km

The plane will go down 9 km in that 60 minutes