The angle of elevation of top of pole from point x to horizontal ground is 32degree. If x is 68m away from the foot. Calculate height FT​

Answer:

The probability it will land on green every time is [tex]\frac{1}{27}[/tex].

Step-by-step explanation:

We are given that a spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow.

The pointer is spun three times.

As we know that the probability of an event is described as;

  Probability of an event =  [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]

Here, the favorable outcome is that the spinner will land on green every time.

So, the number of green regions = 2

Total number of regions = 3(red) + 2(green) + 1(yellow) = 6 regions

Now, the probability it will land on green every time is given by;

        Probability =  [tex]\frac{2}{6}\times \frac{2}{6}\times \frac{2}{6}[/tex]

                           =  [tex]\frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}[/tex]

                           =  [tex]\frac{1}{27}[/tex]

Hence, the probability it will land on green every time is [tex]\frac{1}{27}[/tex].

Using the concept of probability, the probability of landing on green for all 3 spins is [tex] \frac{1}{27}[/tex]

Total number of portions = (3 + 2 + 1) = 6

Recall :

Probability of rolling green on a single spin :

Therefore, the probability of obtaining green on all spins :

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Answer:

1.) ( -4, -2 ), ( -6, - 3 )

2.) ( 0, 2 ) , ( 0 , 4 )

Step-by-step explanation:

The inequality sign of >=, the greater than or equal to sign, the upper region will be shaded while for less than sign <, the lower region will be shaded.

Please find the attached file for the solution and the answer.

Answer:

Combine numerators over the common denominator to make one term

Step-by-step explanation:

Answer:

D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

[tex]$x^2+\frac{b}{a} x+\left(\frac{b}{2a} \right)^2=\frac{b^2-4ac}{4a^2} $[/tex]

[tex]\text{Consider the discriminant as }\Delta[/tex]

[tex]\Delta=b^2-4ac[/tex]

Once we got a trinomial here, just put in factored form:

[tex]$\left(x+\frac{b}{2a}\right)^2=\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \frac{ \sqrt{\Delta} }{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{\Delta}}{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{b^2-4ac}}{2a} $[/tex]

Answer:

hey hon! 2 liters is equal to 67.628 fluid ounces :) hope you have a nice day.

Answer:

-1 ( 1/3*1/3*1/3*1/3)

Step-by-step explanation:

-(3)^-4

The exponent is only affecting what is inside the parentheses

-1 * (3) ^-4

We know that a^-b = 1/a^b

-1 * 1/3^4

-1/3^4

-1 ( 1/3*1/3*1/3*1/3)

Answer:

99

Step-by-step explanation:

x = 90 x 10/100 + 90

=> x = 900/100 + 90

=> x = 9 + 90

=> x = 99

Answer:

y^6 - 9y^4 + 27y² - 27

Step-by-step explanation:

(y² - 3) (y^4 - 6y² + 9)

y^6 - 6y^4 + 9y² - 3y^4 + 18y² - 27

y^6 - 9y^4 + 27y² - 27

I have to return 400 notebooks.

Here, we have,

given that,

I order 700 notebooks by accident. I only need 3⁄7 of my order.

To determine how many notebooks you need to return, you can calculate 4/7 of your order, which represents the portion you don't need.

Let's calculate it step by step:

Calculate the number of notebooks you don't need:

4/7 * 700 = 400

we have,

I only need 3⁄7 of my order.

so, i need = 3/7 * 700

                = 300

Subtract the number of notebooks you need from the total order to find the number of notebooks you should return:

700 - 300 = 400

Therefore, you should return 400 notebooks.

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The first four terms of the given sequence are 18, 10, 6, and 4 respectively.

A sequence is an ordered list object which related and connected by a common value.

There are many sequences. They are Arithmetic sequence, Geometric sequence, and so on.

It is given that,

The first term of the sequence is a1 = 18

And the terms of the sequence are related by,

a(n + 1) = (2 + an)/2

For n = 1;

a(1 + 1) = (2 + a1)/2

⇒ a2 = (2 + 18)/2 = 10

For n = 2;

a(2 + 1) = (2 + a2)/2

⇒ a3 = (2 + 10)/2 = 6

For n = 3;

a(3 + 1) = (2 + a3)/2

⇒ a4 = (2 + 6)/2 = 4

Thus, the first four terms of the given sequence are a1 = 18, a2 = 10, a3 = 6, and a4 = 4.

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Answer:

[tex]F_{1}[/tex] = 5

Step-by-step explanation:

Given [tex]F_{1}[/tex] is perpendicular to [tex]F_{2}[/tex] then Δ ABC is right

Given [tex]F_{2}[/tex] = [tex]F_{1}[/tex]

Then using Pythagoras' identity in the right triangle

[tex]F_{1}[/tex] ² + [tex]F_{2}[/tex] ² = (5[tex]\sqrt{2}[/tex] )² , that is

2[tex]F_{1}[/tex] ² = 50 ( divide both sides by 2 )

[tex]F_{1}[/tex] ² = 25 ( take the square root of both sides )

[tex]F_{1}[/tex] = 5

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The variation p varies directly with T is written as

p = kT

where k is the constant of proportionality

To find p when T =500 we must first find the formula for the variation

That's

when p = 105 and T = 400

105 = 400k

Divide both sides by 400

So the formula for the variation is

when

T = 500

Substitute it into the above formula

That's

[tex]p = \frac{21}{80} \times 500[/tex]

Simplify

The final answer is

Hope this helps you

Incomplete Question:

The content of the pie chart is as follows:

Hamsters  = 9% ; Snakes  = 10% ; Cats  = 23%

Birds  = 21% ;  Dogs  = 26% ;  Fish  = 11%

Answer:

The number of citizens who chose cat or fish is 47,600

Step-by-step explanation:

Given

Number of citizens = 140,000

Required

Determine the number of those that chose fish or cats

First, we need to calculate the percentage of those whose pets are either cats or fish

[tex]Percentage = Cat + Fish[/tex]

Substitute 23% for cat and 11% for fish

[tex]Percentage = 23\% + 11\%[/tex]

[tex]Percentage = 34\%[/tex]

Next, is to multiply the calculated percentage by the number of citizens

[tex]Cat\ or\ Fish = Percentage * Number\ of\ Citizens[/tex]

[tex]Cat\ or\ Fish = 34\% * 140000[/tex]

[tex]Cat\ or\ fish = 47600[/tex]

Hence, the number of citizens who chose cat or fish is 47,600

the number of citizens who chose cat or fish is 47,600

= Number of citizens × total percentage

[tex]= 140,000 \times (23\% + 11\%)\\\\= 140,000 \times 34\%[/tex]

= 47,600

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Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

Area = 6.76 cm²

To find the radius substitute the value of the area into the above formula and solve for the radius

That's

[tex]6.76 = \pi \: {r}^{2} [/tex]

Divide both sides by π

We have

[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]

r = 1.46689291

We have the final answer as

radius = 1.47 cm

Hope this helps you

Answer: 1: Slope 0   Y- Intercept -5

2: Slope 0    Y- Intercept 6

Step-by-step explanation:

Answer:

Quadrilateral ABCD is a SQUARE

Step-by-step explanation:

When we are given coordinates (x1, x2) and (y1 , y2) for a Quadrilateral, we solve for the sides using this formula.

√(x2 - x1)² + (y2 - y1)²

A (3, 1), B (4, 4), C (7, 5), D (6, 2)

Side AB = A (3, 1), B (4, 4)

√(x2 - x1)² + (y2 - y1)²

= √(4 - 3)² + (4 - 1)²

= √1² + 3²

= √1 + 9

= √10

Side BC = B (4, 4), C (7, 5)

√(x2 - x1)² + (y2 - y1)²

= √(7 - 4)² + (5 - 4)²

= √3² + 1²

= √9 + 1

= √10

Side CD = C (7, 5), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 7)² + (2 - 5)²

= √(-1) ² + (-3)²

= √1 + 9

= √10

Side AD = A (3, 1), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 3)² + (2 - 1)²

= √3² + 1²

= √9 + 1

= √10

From the above calculation,

Side AB = √10

Side BC = √10

Side CD = √10

Side AD = √10

Hence, AB = BC = CD = AD

When all the side of a Quadrilateral are the same or equal to each other, it means the Quadrilateral is a square.

Therefore, Quadrilateral ABCD is a SQUARE

Answer:

The positive integer factors of 15552 that are perfect squares are;

1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184

Step-by-step explanation:

The positive integer factors of 15552 are;

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 864, 972, 1296, 1728, 1944, 2592, 3888, 5184, 7776, 15552

The perfect square integers are;

1 = 1 × 1

4 = 2 × 2

9 = 3 × 3

16 = 4 × 4

36 = 6 × 6

64 = 8 × 8

91 = 9 × 9

144 = 12 × 12

324 = 18 × 18

576 = 24 × 24

1296 = 36 × 36

5184 = 72 × 72

Therefore, the positive integer factors of 15552 that are perfect squares are;

1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184.

Answer:

9 dollars per hour

Step-by-step explanation:

36/4=9

Answer:

9

Step-by-step explanation:

4 hours : $36

1 hour : $ x

we need to find x so,

4 hours ÷ 4 = 1 hour

1 : $

since we have divided 4 by 4,

we need to do that to 36 aswell

36  ÷ 4 = 9

1 hour : $9

Answer:

1/4 or 25%

Step-by-step explanation:

Each dice has six sides, meaning the numbers that are even are: 2,4, and 6, three even numbers per dice. Meaning the chance of rolling ONE dice is 50%. So if you were to get two even numbers on TWO dice, it would be 25% hope this helps.

The odds in favor of rolling two even numbers when rolling a pair of dice would be 25% or 1/4.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Each dice has six sides, means the numbers that are even are:

2,4, and 6, three even numbers per dice.

The total number of outcomes is 6 x 6 or 36.

Meaning the chance of rolling ONE dice is 50%.

The odds in favor of rolling two even numbers when rolling a pair of dice would be 25%.

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Answer:

B) 24

D) 48

Step-by-step explanation:

Given:

Two fractions

[tex]\dfrac{1}6 \\and\\\dfrac{3}8[/tex]

To find:

Number that can be chosen as Common denominator such that numerator is also a whole number ?

Solution:

Common denominator for two fractions [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex] is chosen as LCM or multiple of LCM of (q, s).

OR

Common denominator for two fractions is chosen as the Least Common Multiple or multiple of LCM of denominators of the two fractions.

The denominators of the given fractions are 6 and 8.

Let us factorize and try to find the LCM of 6 and 8.

[tex]6 = \underline2 \times 3\\8 = \underline2 \times 2\times 2[/tex]

Common part of the denominators (as underlined) will be taken only once.

So, [tex]LCM = 2 \times 3 \times 2 \times 2 =24[/tex]

Multiples of LCM, 24 = 48

So, the correct answers are:

B) 24 and

D) 48

Answer:

-1/20

Step-by-step explanation:

For a graph like this you should make the gallons of gas on y-axis and the miles driven on the x-axis.

To find slope the formula is (y2-y1)/(x2-x1)

So in this case it is 2-4/40-0

-2/40

This reduces to -1/20

Answer:

6n = 1.50

and

13n = 3.12

Step-by-step explanation:

Here in this question, we are interested in writing equations that relate the number of ears of corn sold and the cost.

For Al’s produce stand, let the price per corn sold be n

Thus;

6 * n = 1.50

6n = $1.50 •••••••(i)

For the second;

let the price per corn sold be n;

13 * n = $3.12

-> 13n = 3.12 •••••••••(ii)

To add fractions with different denominators you must find the highest common factor (the highest number they both go into).

For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8

now, whatever you do to the bottom, you must do to the top.

So:

3 x 2 = 6 and 5 x 4 = 20

Therefore, your answer would be 6/8 + 20/8

You do that for the rest of them as well, do you get it?

Answer:

    3.  4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15

    5.  2/3  + 7/10 = 20/30 + 21/30  = (20+21)/30 = 41/30

Answer:

Hey there!

-4/3-4/5

-20/15-12/15

-32/15

Let me know if this helps :)

Answer:

  a. almost 8 years

Step-by-step explanation:

Brenda's expected annual increase in salary is ...

  $63,292 -45,258 = $18,034

If we assume that Brenda's cost of education includes going without 2 years' salary as well as the cost of tuition, her degree's total cost will be ...

  2×$45,258 +15,000 = $105,516

__

Once Brenda starts earning again, she is recovering this cost at the rate of $18,034 per year, so it will take ...

  $105,516/($18,034 /yr) = 5.85 yr

to recover that cost.

Since Brenda spent 2 years in school, from the time she decides to start school until she has recovered her cost, it will be 2 + 5.85 = 7.85 years, almost 8 years.

_____

If Brenda can continue working while going to school, she can recover her tuition cost in about 10 months after graduation.

Answer:

C

Step-by-step explanation:

Answer:

A pear is 3.4

Step-by-step explanation:

Answer: A pear cost $4.

Step-by-step explanation:

If the total price of four oranges and five pears is $32 then we could represent it by the equation  4x + 5y = 32   where x is cost of one orange and y is the cost of one pear.

The same way we could represent the second statement by the equation

3x + 2y = 17      

We know have the two systems of equations:

4x + 5y = 32

3x + 2y = 17         Solve using the elimination method

  Multiply the top equation by -3 and the down equation by 4 to eliminate x.

-3(4x + 5y) = -3(32) =  -12x - 15y = -96

 4(3x +2y) = 4(17)  =   12x + 8y = 68    

We now have the two new equations:

-12x -15y = -96      Add both equations

12x + 8y = 68            

      - 7y = -28

     y= 4    

Which means the cost of one pear is $4.

Answer: The number of pounds depend on the total price.

Step-by-step explanation:

Answer: it’s c

Step-by-step explanation:

It just is also, it’s for plato

Answer:

The height of the triangular base of the pyramid is s√3/2 units

Step-by-step explanation:

Here in this question, what we are concerned with is to calculate the height of the equilateral-triangle base of the oblique pyramid.

From the question, we are told that the equilateral triangle has a length of a units.

Let’s have a recall on some of the properties of equilateral triangles;

a. All sides are of equal lengths. Meaning side s is the length of all the sides in this case.

b. All angles are equal, meaning they are 60 degree each.

c. Dropping a perpendicular line from the top vertex to the base length will split the equilateral triangle into two right-angled triangles of angles 60 and 30 each.

So to find the height of this triangular base, we can use any of the two right angled triangles.

Kindly recall that the properties of each would be angles 30, 60 and side length s

so to calculate the height h, we can use trigonometric identities

Mathematically, the trigonometric identity we can use is the sine( side length s represents the hypotenuse, while the height h represents the opposite facing the angle 60 degrees)

Thus; we have

Sine of an angle = length of the opposite/length of hypotenuse

sin 60 = h/s

h = s sin 60

In surd form,

sin 60 = √3/2

Thus;

h = s * √3/2 = s√3/2 units

Answer:

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:

Answer:

Step-by-step explanation:

The shaded regions consist of a triangle and a semicircle

Area of shaded regions = Area of Triangle + Area of semicircle

Area of Triangle = (h x b) ÷ 2

Height, h = 10 cm

Base, b = 8 cm

Are of the triangle component = (10 x 8) ÷ 2

= 80 ÷ 2

= 40 cm^2

 Area of semicircle = πr^2 ÷ 2

Diameter, D = 8 cm

Radius, r = 8 cm ÷ 2 = 4 cm

Are of the semicircle component = [π(4^2) ÷ 2)

= 16π ÷ 2

= 16π cm^2

 Total area of shaded regions

= (40+16π) cm^2

= 8 (5 +2π) cm^2

Answer:

[tex]\boxed{\sf Area = 8\pi + 40\ cm^2}[/tex]

[tex]\boxed{\sf Perimeter = 4\pi + 22\ cm}[/tex]

Step-by-step explanation:

Area of the figure:

Firstly: Area of semicircle:

[tex]\sf \frac{\pi r^2}{2} \\Where\ r = 4 \ cm\\\frac{\pi (4)^2}{2} \\\frac{16 \pi}{2}\\8 \pi \ cm^2[/tex]

Then Area of Triangle

[tex]\sf 1/2 (Base)(Height)\\1/2(10)(4)\\10*2\\20\ cm^2[/tex]

Area of Figure = Area of Semicircle + 2(Area of triangle)

=> 8π + 2(20)

=> 8π + 40 cm²

Perimeter of Semicircle:

Firstly, we'll have to find the hypotenuse

[tex]\sf c^2 = a^2+b^2\\c^2 = 4^2+10^2\\c^2 = 16+100\\c^2 = 116\\c = 11\ cm[/tex]

Then, Perimeter of the semi-circle:

=> πr

Where r = 4 cm

=> 4π

Now, the perimeter of the whole figure:

=> 4π + 2(11)

=> 4π + 22 cm

Answer:

GREAT QUESTION!!

Step-by-step explanation:

Bases of exponential functions CANNOT be 1.

It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.

Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.

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Answer:

If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.

Step-by-step explanation:

If the base were 1, the function would be constant.

If the base were 1, the graph would be a horizontal line.

If the base were between 0 and 1, the function would be decreasing.