Question 10 of 10
Which set of polar coordinates are plotted in the graph below?

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

16x²

Step-by-step explanation:

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer: 1022.75 kWh.

Step-by-step explanation:

Given: In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh.

i.e. [tex]\mu=1050\ kWh[/tex] and [tex]\sigma=218\ kWh[/tex]

Let X denote energy consumption levels for random single-family homes and x be the energy consumption level for the 45th percentile.

Then, [tex]P(X<x)=0.45[/tex]

From z-table, [tex]P(z<-0.125)=0.45[/tex]

Also, [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]\Rightarrow\ -0.125=\dfrac{x-1050}{218}\\\\\Rightarrow\ x=-0.125\times218+1050=1022.75[/tex]

Hence, the energy consumption level for the 45th percentile is 1022.75 kWh.

Answer:

32

Step-by-step explanation:

8(3 + 4) = 24 + ?

8(3)+8(4)= 24 + ?

24+32= 24 + ?

24-24+32=?

32=?

Answer:

? = 32

Step-by-step explanation:

Let's assume a = 8 , b = 3 , c = 4

[tex] \sf \: So :- \: \: a(b + c) = 8(3 + 4)[/tex]

[tex]8 \times 3 + 8 \times 4[/tex]

[tex]24 + 32[/tex]

Hence, The required value of ? = 32 .

let us build equation for unknown legs

If we keep the length pf one leg as x

the other leg would be x +3

so we can build a relationship using pythagoras theorem

x^2 + (x+3)^2 = 15^2

x^2 + x^2 + 6x + 9 = 225

2x^2 + 6x + 9 = 225

2x^2 + 6x+ 9-225 = 0

2x^2 + 6x - 216 = 0

x^2 + 3x - 108 = 0 dividing whole equation by 2

x^2 + 12x - 9x - 108 = 0

x ( x + 12 ) - 9 (x + 12) = 0

(x -9) ( x +12) = 0

solutions for x are

x = 9 or x = -12

as lengths cannot be negative

one side length is 9cm

and other which is( x + 3)

9 + 3

12cm

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = First Leg² + Second leg²

Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:

15² = x² + (x + 3)²

x² + 6x + 9 + x² = 225

2x² + 6x - 216 = 0

x² + 3x - 108 = 0

x = - 12 or x = 9

Since the length cant the negative hence x= 9, x + 3 = 12

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

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Answer:

4 ft

7.2 ft

20 ft

Step-by-step explanation:

When the balloon is shot, x = 0.

y = -0.05(0)² + 0.8(0) + 4

y = 4

The balloon reaches the highest point at the vertex of the parabola.

x = -b / 2a

x = -0.8 / (2 × -0.05)

x = 8

y = -0.05(8)² + 0.8(8) + 4

y = 7.2

When the balloon lands, y = 0.

0 = -0.05x² + 0.8x + 4

0 = x² − 16x − 80

0 = (x + 4) (x − 20)

x = -4 or 20

Since x > 0, x = 20.

The slingshot launched the ballon from a height of 4 feet. The balloon's maximum height was 72 feet. The balloon landed 20 feet from the slingshot.

To determine the height from which the slingshot launched the balloon, we need to evaluate the function f(0) because when x is zero, it represents the starting point of the balloon's trajectory.

f(x) = -0.05x² + 0.8x + 4

f(0) = -0.05(0)² + 0.8(0) + 4

f(0) = 4

Therefore, the slingshot launched the balloon from a height of 4 feet.

To find the maximum height of the balloon, we can observe that the maximum point of the parabolic function occurs at the vertex.

The x-coordinate of the vertex can be calculated using the formula x = -b / (2a).

In our case, a = -0.05 and b = 0.8.

Let's calculate the x-coordinate of the vertex:

x = -0.8 / (2×(-0.05))

x = -0.8 / (-0.1)

x = 8

Now, substitute this x-coordinate into the function to find the maximum height:

f(x) = -0.05x² + 0.8x + 4

f(8) = -0.05(8)² + 0.8(8) + 4

f(8) = -0.05(64) + 6.4 + 4

f(8) = -3.2 + 6.4 + 4

f(8) = 7.2

Therefore, the balloon reached a maximum height of 7.2 feet.

To determine how far from the slingshot the balloon landed, we need to find the x-intercepts of the quadratic function.

These represent the points where the height is zero, indicating the balloon has landed.

Setting f(x) = 0, we can solve the quadratic equation:

-0.05x² + 0.8x + 4 = 0

x² - 16x - 80= 0

x=-4 or x=20

We take the positive value, so  the balloon landed 20 feet from the slingshot.

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Answer:

a

   $10,151   [tex]< \mu <[/tex]  $11448.12

b

  [tex]n = 158[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  19

    The  sample mean is  [tex]\= x =[/tex]$10,800

     The  standard deviation is  [tex]\sigma =[/tex]$1095  

    The  population mean is  [tex]\mu =[/tex]$225

Given that the confidence level is 99%  the level of significance is mathematically represented as

       [tex]\alpha = 100 -99[/tex]

      [tex]\alpha = 1[/tex]%

=>    [tex]\alpha = 0.01[/tex]

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

        [tex]Z_{\frac{0.01}{2} } = 2.58[/tex]

The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex]  is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Now the margin of error is obtained as

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

substituting values

    [tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]

     [tex]MOE = 648.12[/tex]

The  99% confidence interval for the population mean yearly premium is mathematically represented as

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

substituting values

   [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

    [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

   $10,151   [tex]< \mu <[/tex]  $11448.12

The  largest sample needed is mathematically evaluated as

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

substituting values

       [tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]

      [tex]n = 158[/tex]

Answer:

x = {-3, -2, -1, 0}

Step-by-step explanation:

x ≤ 0

x > -4

then

x {-3, -2, -1, 0}

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} = 0[/tex]

[tex]\alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]

[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]

Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:

[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{1} = -2\cdot k[/tex]

[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{2} = -3\cdot k[/tex]

It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} + \alpha_{3} = 0[/tex]

[tex]3\cdot \alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

The set of vectors A and C are linearly independent.

Answer:

what we have to tell

Step-by-step explanation:

please send the correct information

Answer:

The answer on PLATO is Graph Z.

Step-by-step explanation:

I just had this question and got it right!!!

Hope this Helps!!!

Answer:

c. ax+b=ax+b

Step-by-step explanation:

To know what equation has infinite solutions, you first try to simplify the equations:

a.

[tex]ax=bx+c\\\\(a-b)x=c\\\\x=\frac{c}{a-b}[/tex]

In this case you have that a must be different of b, but there is no restriction to the value of c, then c can be equal to a or b.

b.

[tex]ax+b=ax+c\\\\b=c[/tex]

Here you obtain that b = c. But the statement of the question says that a, b and c are three different numbers.

c.

[tex]ax+b=ax+b\\\\0=0[/tex]

In this case you have that whichever values of a, b and are available solutions of the equation. Furthermore, when you obtain 0=0, there are infinite solutions to the equation.

Then, the answer is:

c. ax+b=ax+b

Answer:

ax + b = ax + b

Step-by-step explanation:

i just answered it

Answer:

Step-by-step explanation:

Assuming the colon between 40 and 8 is a mistype...

PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)

[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]

Hope it helps <3

━━━━━━━☆☆━━━━━━━

▹ Answer

57

▹ Step-by-Step Explanation

You need to follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

40 - 8 + 3² + (15 - 7)* 2

40 - 8 + 9 + (15 - 7) * 2

40 - 8 + 9 + 8 * 2

40 - 8 + 9 + 16

= 57

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Please look at the picture below!

Step-by-step explanation:

Hope this helps!

If you have any question, please feel free to ask any time.

Answer:2/3-4

Step-by-step explanation:

Hi,

The correct answer is √ra = v or v = √ra.

The original equation is a = v^2/r.

Then we multiply r to get ra = v^2

After that we √ra = √v^2

Our final answer is then √ra = v

XD

Answer:

[tex]g(x)=4x^{2} +10[/tex]

Step-by-step explanation:

If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the y-axis, in another words: up or down.

Let:

[tex]a>0,\hspace{10}a\in R[/tex]

For:

If:

[tex]f(x)=4x^{2} +6[/tex]

and is translated vertically upward by 4 units, this means:

[tex]a=4[/tex]

and:

[tex]g(x)=f(x)+a=(4x^{2} +6)+4=4x^{2} +10[/tex]

Therefore:

[tex]g(x)=4x^{2} +10[/tex]

I attached you the graphs, so you can verify the result easily.

Answer:

I hope it will help you...

The value of [tex]x+y[/tex] will be equal to 185 degrees.

From figure it is observed that,

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

        [tex]y=45+60=105[/tex]

We know that, By triangle property  sum of all three angles in a triangle must be equal to 180 degrees.

  So that,             [tex]x+55+45=180[/tex]

                           [tex]x=180-100=80[/tex]

Thus,    [tex]x+y=105+80=185[/tex] degree

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Answer:

A) 64 observations

B) analytic study

Step-by-step explanation:

Given:  

There are 3 number of factors i.e. armature length, spring load, and bobbin depth.

There are 4 levels i.e. low, fair, moderate, and high

There is a single i.e. 1 observation on flow made for each combination of levels.

A)

To find:

Number of observations.

There are 4 levels so these 4 levels are to be considered for each factor.

Number of observations = 4.4.4 = 64

For example if we represent low fair moderate and high as L,F,M,H

and factors armature length, spring load, and bobbin depth as a,s,b

Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]

So resulting data set has 64 observations.  

B)

This is analytic study.

The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.

Answer: C. 3.68

Step-by-step explanation:

Given that;

Sample size n = 18

degree of freedom for numerator k = 2

degree of freedom for denominator = n - k - 1 = (18-2-1) = 15

level of significance = 5% = 5/100 = 0.05

From the table values,

the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68

Therefore option C. 3.68 is the correct answer

Answer:

[tex]z = \frac{x}{y} [/tex]

Step-by-step explanation:

Let x be the price of carton of ice cream

Let y be the number of grams in carton

Let z be price per gram.

[tex]z = \frac{x}{y} [/tex]

Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.

Hope this helps ;) ❤❤❤

Answer:

78

Step-by-step explanation:

The measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.

x = 31 + 47

x = 78

Answer:

41.1 miles

Step-by-step explanation:

84 - 42.9 = 41.1

Answer:

75%.

Step-by-step explanation:

In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.

The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.

Hope this helps!

Answer:

Step-by-step explanation:

We will develop a test to compare the mean of two population

Population 1.

population mean μ₀₁  = 25  ; Sample variance 27 ; and sample size n = 45

Population 2.

population mean μ₀₂  = 23 ; Sample variance 7,56; and sample size n = 36

As our major interest is to investigate if the new machine uses less time for the same production, the test will be a one tail test ( left test)

Test Hypothesis        

Null Hypothesis                   H₀     ⇒         μ₀₂ -  μ₀₁  = 0    

Alternative Hypothesis       Hₐ     ⇒         μ₀₂ -  μ₀₁ < 0

We will use  confidence of 90 %, therefore α = 10 %   α = 0,1

α  = 0,1    

We get    z score of z = 1,28   or   z = - 1,28   ( left tail)

And  compute z(s)  = ( μ₀₂ -  μ₀₁ ) /√ (s₁)²/n₁   + (s₂)²/n₂

z(s) = -  2 / √(729/45) + (57,15/36)

z(s) = - 2 / √16,2  + 1,59

z(s) =  - 2 / 4,2178

z(s) =  - 0,4742

As |z(s)|  < |z(c)|

We are in the acceptance region. If we lok at 90 % as Confidencial Interval α = 0,1 and  α/2 =  0,05 in this case

₀,₉CI (  μ₀₂ -  μ₀₁)  =  [  -2  ± z(0,05)√  (s₁)²/n₁   + (s₂)²/n₂ )

From z Table  z ( 0,05 )   ⇒ z score   z = 1,64

And √  (s₁)²/n₁   + (s₂)²/n₂ ) =  √(729/45) + (57,15/36)  =  4,2178

₀,₉CI (  μ₀₂ -  μ₀₁)  = [ -2  ± 1,64 *4,2178]

₀,₉CI (  μ₀₂ -  μ₀₁)  = (  - 8,917 ;  4,917 )

We can see that 0 is a possible value in the ₀,₉CI (  μ₀₂ -  μ₀₁) so again we cannot reject H₀. Then as we are not quite sure about the strengths of the new machine over the old one  we should not recomend to purchase the new machine

Answer:

2/5

Step-by-step explanation:

(7-5)/(6-1)

Problem 1

Focus: (5, 0)

Directrix:  y = -18

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

Explanation:

The given equation can be written as 4*9(y-(-9)) = (x-5)^2

Then compare this to the form 4p(y-k) = (x-h)^2

We see that p = 9. This is the focal distance. It is the distance from the vertex to the focus along the axis of symmetry. The vertex here is (h,k) = (5,-9)

We'll start at the vertex (5,-9) and move upward 9 units to get to (5,0) which is where the focus is situated. Why did we move up? Because the original equation can be written into the form y = a(x-h)^2 + k, and it turns out that a = 1/36 in this case, which is a positive value. When 'a' is positive, the focus is above the vertex (to allow the parabola to open upward)

The directrix is the horizontal line perpendicular to the axis of symmetry. We will start at (5,-9) and move 9 units down (opposite direction as before) to arrive at y = -18 as the directrix. Note how the point (5,-18) is on this horizontal line.

================================================

Problem 2

Focus:  (13,-3)

Directrix:  x = 3

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

Explanation:

We'll use a similar idea as in problem 1. However, this time the parabola opens to the right (rather than up) because we are squaring the y term this time.

20(x-8) = (y+3)^2 is the same as 4*5(x-8) = (y-(-3))^2

It is in the form 4p(x-h) = (y-k)^2

vertex = (h,k) = (8,-3)

focal length = p = 5

Start at the vertex and move 5 units to the right to arrive at (13,-3). This is the location of the focus.

Go back to the focus and move 5 units to the left to arrive at (3,-3). Then draw a vertical line through this point to generate the directrix line x = 3

Answer:

[tex]\boxed{x = 7}[/tex]

Step-by-step explanation:

75 = 11x-2 (Corresponding angles are equal)

11x -2 = 75

Adding 2 to both sides

11x = 75+2

11x = 77

Dividing both sides by 11

x = 7

Answer:

[tex]\left[\begin{array}{ccc}\\x = 7\\\end{array}\right][/tex]

Step-by-step explanation:

Well to find x we can set up the following equation,

11x - 2 = 75

So we have to single out x.

+2 to both sides

11x = 77

Divide 11 by both sides

x = 7

Thus,

x = 7.

Hope this helps :)

Answer:

Step-by-step explanation:

[tex] \frac{8}{7} = \frac{x}{5} [/tex]

To find x first cross multiply

We have

7x = 8 × 5

7x = 40

Divide both sides by 7

That's

[tex] \frac{7x}{7} = \frac{40}{7} [/tex]

[tex]x = \frac{40}{7} [/tex]

x = 5.7142

We have the final answer as

Hope this helps you

Answer:

[tex]\boxed{\sf x = 5.7}[/tex]

Step-by-step explanation:

[tex]\sf \frac{8}{7} = \frac{x}{5} \\=> 1.142 = \frac{x}{5}\\ Multiplying \ both \ sides \ by \ 5\\1.142 * 5 = x\\5.7 = x\\OR\\x = 5.7[/tex]

Answer:

Spinner: 50%

Die: 50%

Step-by-step explanation:

Well for the spinner it depends on the amount of numbers it has,

in this case we’ll use 6.

So The probability of landing on the even numbers in a 6 numbered spinner.

2, 4, 6

3/6

50%

Your average die has 6 sides so the odd numbers are,

1, 3, 5

3/6

50%