Hello, I really appreciate your help! Thanks!


Tricia uses the Fermi process to estimate the number of buckets of sand she could store in a warehouse. The buckets are shaped like cylinders. The warehouse is shaped like a rectangular prism.


She estimates the buckets have a height of 15 inches and a diameter of 20 inches.

She estimates the warehouse is 250 feet long, 80 feet wide, and 20 feet high.

Which expression should Tricia use in the process?




A) 7×10^9/5×10^4 ​


​B) 5×10^6/5×10^3 ​


C) ​7×10^8/5×10^3 ​


​D) 5×10^7/5×10^4 ​

Answer:

144, 36, 9, 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex]

Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give

Multiply both sides by 4, then

[tex]a_{n-1}[/tex] = 4[tex]a_{n}[/tex]

Given a₄ = 2 [tex]\frac{1}{4}[/tex], then

a₃ = 4 × a₄ = 4 × 2[tex]\frac{1}{4}[/tex] = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

The first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_n=\dfrac{a_n-1}{4}[/tex]

Given the fourth term, we require to work back to the third term, second, and so on. Rearrange the formula to give.

Multiply both sides by 4, then

a[tex]_{n-1}[/tex] = 4a[tex]._n[/tex]

Given a₄ = 2, then

The first four terms will be calculated as given below:-

a₃ = 4 × a₄ = 4 × 2 = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

Therefore, the first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

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Answer:

1 : 1000

In the real life, it measures as:

62 mm = 62000 mm = 6.2 m

54 mm = 54000 mm = 5.4 m

It ask how large is it, I don't know if you want area or primeter, so I will give you both of them.

Area:

6.2 x 5.4 = 33.48 m^2

Primeter:

(6.2 + 5.4)2 = 23.2 m.

Answer:

2000 m/h

Step-by-step explanation:

speed = distance/time

Mila's distance was (2/3)·(750 m) = 500 m, so her speed was ...

(500 m)/(1/4 h) = 2000 m/h

Mila swam 500 meters in 0.25 hours. Hence, her average speed was 2000 meters/hour.

To calculate Mila's average speed, first we need to calculate the distance she swam. Mila swam 2/3 of Logan's distance, which is 2/3 * 750 meters = 500 meters.

Now, we need to find out how long she swam in hours as her time was given in quarters of an hour. As Mila swam for 1/4 of an hour, this translates to 1/4 * 60 minutes = 15 minutes, or 0.25 in hours.

Speed is calculated as distance/time, therefore Mila's average speed is 500 meters/0.25 hours = 2000 meters/hour.

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I'm only doing these because it's about a pet pig named Hammy.

5.

rate = distance / time

a.

rate: 36 inches per 3 seconds

b

unit rate: 12 inches per second

c

5 seconds × 12 inches per second = 60 inches

d

144 inches / 12 inches per second = 12 seconds

6.

a.

[tex] \frac 4 7 \div \frac 3 5 = \frac 4 7 \times \frac 5 3 = \dfrac{20}{21}[/tex]

b.

[tex]2 \frac 2 5 \div 1 \frac 7 9 = \frac{12}{5} \div \frac{16}{9} = \frac{12}{5} \times \frac{9}{16} = \dfrac{27}{20} [/tex]

c

[tex]3.24 \div 1.5 = 3.24 \div \frac 3 2 = 3.24 \times \frac 2 3 = 6.48/3 = 2.16[/tex]

d

[tex] \frac 8 9 \div 3\frac 1 3 = \frac 8 9 \times \frac{3}{10} = \dfrac{4}{15}[/tex]

Answer:

Step-by-step explanation:

(a) Hammy's rate is 36 inches in 3 sec.

(b) Hammy's unit rate is (36 inches) / (3 sec) = 12 in/sec

(c) In 5 sec Hammy can run (12 in/sec)(5 sec) = 60 in

(d) time = distance/rate, so here the time is (144 in) / (12 in/sec) = 12 sec

(6a) 4/7 divided by 3/5 is equivalent to 4/7 times 5/3, which comes out to 20/21.

(6b) Convert 2  2/5 to 12/5 and 1  7/9 to 16/9.  Then invert the second improper fraction and multiply:  12/5 times 9/16 = 108/80, or 27/20.

(6c)  3.24 divided by 1.5 is equivalent to 3.24 times 2/3:  2.16, or 2  4/25

(6d) 8/9 divided by 3  1/3 is equivalent to 8/9 times 3/10, or 24/90, or 4/15.

Answer:

You add them together and divide it by how many number there are.

Step-by-step explanation:

For example lets say we need to find the average of 12, 15, 18, and 24.

You would do 12+15+18+24

You will get a sum of 69

Then since there are 4 numbers you do 69 divided by 4 and get a quotients of 17.25.

Therefore 17.25 is the average of all four numbers.

[tex]\begin{array}{c|c|c}\underline{\quad (x,y)\quad}&\underline{\quad y=2x\quad }&\underline{\quad Answer\quad }\\(-1, a_o)&a_o=2(-1)&a_o=-2\\(0, a_1)&a_1=2(0)&a_1=0\\(1, a_2)&a_2=2(1)&a_2=2\\(2, a_3)&a_3=2(2)&a_3=4\\(3, a_4)&a_4=2(3)&a_4=6\\(4, a_5)&a_5=2(4)&a_5=8\end{array}[/tex]

Answer:

(-2, 4)

Step-by-step explanation:

One of the equations is already solved for y, so let's solve the other one for y and by the transitive proprerty of equality, if y = y, then what those y's are equal to are equal to each other.  Solving the first equation for y:

x + y = 2 so

y = -x + 2

Let's fill that in for y in the second equation.  Where

[tex]y=\frac{1}{2}x+5[/tex], making the substitution,

[tex]-x+2=\frac{1}{2}x+5[/tex]

Combining like terms and getting the x on one side and the constant on the other side of the equals sign:

[tex]-\frac{3}{2}x=3[/tex]

The product of a fraction and its reciprocal is 1 so we will multiply both sides by

[tex]-\frac{2}{3}[/tex] to get:

[tex](-\frac{2}{3})(-\frac{3}{2})x=(3)(-\frac{2}{3})[/tex]

and we end up with x = -2.

Now that we know that, we can sub that in for x in either one of the original equations.  I chose the first one:

If x + y = 2, then -2 + y = 2

and y = 4

Therefore, the solution set is (-2, 4)

Step-by-step explanation:

A number cubed is equal to the product of 52 and the square of the number.

Answer:

ZX

Step-by-step explanation:

A diameter is a chord of a circle that passes through the center of the circle.

A chord of a circle is a segment inside the circle whose endpoints are on the circle.

Chords of the circle:

ZY, ZX, YW, UV

Of all those chords, only two pass through the center of the circle:

ZX, YW

Of the two diameters, only one is a choice:

ZX

Answer: B. ZX

Answer:

zx

Step-by-step explanation:

A pex

Answer:

216°

Step-by-step explanation:

Both chords are the same length, so the left and right arcs are both 72°.  The whole circle is 360°, so:

72° + 72° + x = 360°

x = 216°

Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=3\\ b=2 \end{cases}\implies \cfrac{(x-0)^2}{3^2}+\cfrac{(y-0)^2}{2^2}=1\implies \cfrac{x^2}{9}+\cfrac{y^2}{4}=1[/tex]

Perimeter of the square backyard=56m

Perimeter of a square=4*side

Side=

56=4*side

56/4=side

side=14 cm

Area of a square=side*side

=14*14

=196cm^2

So,the area of the square backyard is 196m^2.

Answer:

A=196

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

  (x, y) = (-3, 5)

Step-by-step explanation:

There are many ways to solve a system of two equations with two unknowns. Almost all of them involve reducing the system to one equation in one unknown. (Graphical solution, as in the attachment, bypasses that algebraic manipulation.)

In general, the first step is to look at the equations to see if ...

If the first condition is true, then the system may be easily solved by "substitution." The expression you have for one of the variables can be substituted for that variable in the other equation.

If the second condition is true, you can add the equations to eliminate the variable with opposite coefficients. (Opposites add to give zero.)

Here, the third condition holds: the coefficient of x in the first equation (4) is simply related to the coefficient of x in the second equation (8) by a factor of 2.

___

So, we can eliminate the x-variable from the system of equations by multiplying the first equation by -2 and adding that result to the second equation:

  -2(4x +2y) +(8x +5y) = -2(-2) +(1)

  -8x -4y +8x +5y = 4 +1 . . . . eliminate parentheses

  y = 5 . . . . . . . . . . . . . . . . . . . collect terms

Now, we can substitute this value into either equation to find the value of x. Using the first equation, we get ...

  4x +2(5) = -2

  4x = -12 . . . . . . . subtract 10

  x = -3 . . . . . . . . . divide by 4

The solution to the system of equations is (x, y) = (-3, 5).

ANSWER

[tex]x = 140 \degree[/tex]

EXPLANATION.

The two tangents each meet the radius at 90° each.

This implies that,

[tex]x + 40 + 90 + 90 = 360[/tex]

The sum of interior angles of a Quadrilateral is 360°

We simplify to get

[tex]x + 40 = 180[/tex]

[tex]x = 180 - 40[/tex]

[tex]x = 140 \degree[/tex]

The answer is 4. All of the above I googled it

Answer:

b 125

Step-by-step explanation:

first you know that you have 2 and 5 as similar numbers you both square them so that they become a ratio of area which is 4/25 after you do 4/25=20/x and you do cross multiply then you find 125. hope that helped understand.

Answer:

B.

Step-by-step explanation:

o find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

Answer:

15.5 in

Step-by-step explanation:

Use property of secant and tangent segments in the circle:

If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

In your case,

Tanget - x in

External secant - 10 in

Total secant - 10+14 in

So,

[tex]x^2=10\cdot (10+14)\\ \\x^2 =10\cdot 24\\ \\x^2 =240\\ \\x\approx 15.5\ in[/tex]

Answer:

Step-by-step explanation:

No solution

Answer:

First, before I answer, he or she forgot the n/3.

So the problem is n/3 + (-4) = 2

The answer is 6

Step-by-step explanation:

First, simply + -4 to -4, because different signs subtract

Second subtract -4 + 2 which equals 2

Now multiply 3 ( came from n/3) with 2

And its 6

I hope I helped you!!!

Answer:

[tex]\large\boxed{a.\ -44}[/tex]

Step-by-step explanation:

[tex]\dfrac{y}{4}+8=-3\qquad\text{subtract 8 from both sides}\\\\\dfrac{y}{4}+8-8=-3-8\\\\\dfrac{y}{4}=-11\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{y}{4\!\!\!\!\diagup_1}=(4)(-11)\\\\y=-44[/tex]

Answer:

a.  -44.

Step-by-step explanation:

y/4 + 8 = -3

Subtract 8 from both sides:

y/4 = -3 - 8

y/4 = -11

Now multiply both sides by 4:

y = 4 * -11 = -44 (answer).

Answer:

  n(n+1)

Step-by-step explanation:

Only the last two formulas work for n=1; only the last formula works for n=2.

For n=1

  3n = 3 ≠ 2

  n² -1 = 0 ≠ 2

  n² +1 = 2

  n(n+1) = 2

For n=2

  n²+1 = 5 ≠ 6

  n(n+1) = 6 . . . . . this last formula works for the given sequence

Answer:

  congruent triangles

Step-by-step explanation:

The complete reason is, "corresponding parts of congruent triangles are congruent." This reason is sometimes abbreviated CPCTC.

It can be helpful to note that the previous step concluded that the relevant triangles are congruent.

Answer:

5. Congruent triangles

Step-by-step explanation:

Congruent Triangles : When two triangles are congruent, all its three sides are equal and have the same angles.

So in conguent traingles,

ΔADB ≅ BDC

Therefore, AB = DC and AD = BC

Thus this completes the missing information that proves that the quadrilateral ABCD ia a parallelogram, then its opposite sides are congruent.

Answer:

Step-by-step explanation: You are given the equation of -7x+6y=9 and -2x-5y=16 and you are asked to find what x=? and what y=?

First step is to write down the problem

-2x-5y=16

next add 5y over the equal sign.

-2x=5y+16

Next is too divide by -2

-2x/-2=5y+16/-2

after solving you get

x=-2.5y-8

now you substitute the equation into the other formula to get

-7(-2.5y-8)+6y=9

then solve by doing -7*-2.5y and -7*-8 to get 17.5y and 56 which will give you

17.5y+56+6y=9

Next you subtract 56 to the other side to get 9-56 or -47 now you have

17.5y+6y=-47

next is too add the 17.5y and 6y together to get 23.5y

23.5y=-47

next is too divide by 23.5

23.5y/23.5=-47/23.5

solve to get y=-2, now this is half you the problem

Step two is too substitute what y=-2 into the equation of x=-2.5y-8 to get

x=-2.5(-2)-8

Solve to get

x=5-8

Solve again to get

x=-3

Your answers are x=-3 and y=-2

Answer:

x = -3 and y = -2

Step-by-step explanation:

It is given that,

-7x + 6y = 9

   ----(1)

-2x - 5y = 16    -------(2)

To find the solution of given equations

eq(1) * 2 ⇒

-14x + 12y = 18 ------(3)

eq(2) * 7 ⇒

-14x - 35y = 112   ---(4)

eq (3) - eq(4) ⇒

-14x + 12y = 18 ------(3)

-14x - 35y = 112   ---(4)

    0   4y = -94

y = 94/(-47) = -2

Substitute the value of y in eq (2)

-2x - 5y = 16    -------(2)

-2x - 5*-2 = 16

-2x +10 = 16

-2x = 6

x = 6/-2 = -3

Therefore x = -3 and y = -2

Answer:

b = √(c^2 - a²)

Step-by-step explanation:

Start with the given c = √a^2 + b^2.  Squaring both sides, we get:

c² = a² + b².

We want to iosolate b² and then b.

So:  subtract a² from both sides, resulting in:

c² - a² = b²

Taking the square root of both sides, we get:

√b² = √(c² - a²)

and so:

b = √(c^2 - a²)

To solve the Pythagorean theorem equation for b, isolate b on one side by first squaring both sides. Move the a^2 term to the other side of the equation, then take the square root of both to solve for b. The solution is b = √(c^2 - a^2).

The formula mentioned, c = √a^2 + b^2, represents the application of the Pythagorean theorem for right-angled triangles. To solve this equation for b, you would have to isolate b on one side. Start by squaring both sides of the equation, which gives: c^2 = a^2 + b^2. Then, move a^2 to the other side of the equation to isolate b^2 assuming c^2 > a^2. This gives you: b^2 = c^2 - a^2. Then, take the square root of both sides, which gives: b = √(c^2 - a^2).

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Answer:

4th option

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{1+\sqrt{3}}[/tex]

In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with [tex]1-\sqrt{3}[/tex], as shown below:

[tex]\frac{1}{1+\sqrt{3}}\\=\frac{1}{1+\sqrt{3}} \times \frac{1-\sqrt{3}}{1-\sqrt{3}}\\=\frac{1-\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}\\\\ =\frac{1-\sqrt{3}}{1-3}\\\\ =\frac{1-\sqrt{3}}{-2}\\\\ =\frac{-1(1-\sqrt{3})}{2}\\\\ =\frac{-1+\sqrt{3}}{2}[/tex]

Thus, 4th option gives the correct answer.

Answer:

The right option is D -1+√3/2

Step-by-step explanation:

To find the quotient of the sure function 1/1+√3, we will rationalize the surd function by multiplying the numerator and the denominator of the surd by the conjugate of its denominator.

Given he denominator to be 1+√3, the conjugate of 1+√3 is 1-√3

Multiplying by 1-√3 will result in the following;

1/1+√3×1-√3/1-√3

= 1-√3/(1+√3)(1-√3)

= 1-√3/1-√3+√3-√9

= 1-√3/1-√9

= 1-√3/1-3

= 1-√3/-2

= -(1-√3)/2

= -1+√3/2

The right option is D -1+√3/2

Answer:  272

Step-by-step explanation:

f(x) = 4x         g(x) = 3x - 5

(g × f)(x) = (4x)(3x - 5)

             = 12x² - 20x

(g × f)(-4) = 12(-4)² - 20(-4)

               = 12(16) + 80

               = 192 + 80

              = 272

Hi!

To solve this, first let's decide what quadrant the 135 degrees lies in. Starting in quadrant one, it would end up landing in quadrant 2.

Coordinates:

(cos, sin)

In quadrant 2, the y value (sin) as a coordinate would be positive, therefore our final answer should be positive.

180 - 135 = 45

Therefore our reference angle will be sin45.

We should know that sin45 is equal to [tex]\cfrac{\sqrt{2} }{2}[/tex]

Now, remember that our final answer should be positive. We don't have to change this because it's already positive, so your final answer is:

[tex]\cfrac{\sqrt{2} }{2}[/tex]

The exact value of sin 135 degrees is - (√2)/2.

The unit circle and trigonometric identities can be used to calculate the sine of 135 degrees.

We can determine the location of the point on the unit circle that corresponds to an angle of 135 degrees by utilizing the unit circle. It is located in the third quadrant.

In the first and second quadrants, the sine function is positive; however, the third and fourth quadrants are where it is negative.

We can use the fact that the sine of an angle equals the y-coordinate of the point on the unit circle corresponding to that angle to determine the precise value.

The sine of 135 degrees is negative because the third quadrant's y-coordinate is negative.

We can determine the precise sine value of 135 degrees by using a reference angle.

In the third quadrant, the reference angle for 135 degrees is 45 degrees (180 degrees - 135 degrees).

The sine of a 45-degree angle is (2)/2 or 1/sqrt(2).

The sine of 135 degrees is a negative number because the reference angle is in the third quadrant.

Consequently, (2)/2 is the precise value of sin 135 degrees.

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The  fraction of the animals at the shelter are dogs 74/100 or 37/50

A relative value indicating hundredth parts of any quantity.

Given:

74% of the animals at an animal shelter are dogs.

We know the percent is considered as 100.

If we need to estimate anything in percent we compare it with 100%.

So,  fraction of the animals at the shelter are dogs be,

=74% of 100%

=74/100*100/100

= 74/100

=37/50

Hence,  fraction of the animals at the shelter are dogs be is 74/100 or37/50.

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Answer:

2(2r + 1)(2r - 5)

Step-by-step explanation:

Given

8r² - 16r - 10 ← factor out 2 from each term

= 2(4r² - 8r - 5)

To factorise the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

product = 4 × - 5 = - 20 and sum = - 8

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5 ( factor the first/second and third/fourth terms )

= 2r(2r + 1) - 5(2r + 1) ← factor out (2r + 1) from each term

= (2r + 1)(2r - 5), so

4r² - 8r - 5 = (2r + 1)(2r - 5) and

8r² - 16r - 10 = 2(2r + 1)(2r - 5) ← in factored form

The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

It is Given that

8r² - 16r - 10

= 2(4r² - 8r - 5)

To factorize the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5

= 2r(2r + 1) - 5(2r + 1)

= (2r + 1)(2r - 5),

4r² - 8r - 5 = (2r + 1)(2r - 5)

and

8r² - 16r - 10 = 2(2r + 1)(2r - 5)

The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .

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Answer:

The value of slope m = -1

Step-by-step explanation:

x = -2 + 4t

and y = 1 + 4t

Solving the both equations

x +2 = 4t

=> t = (x+2)/4     eq(1)

y-1 = 4t

=> t = (y-1)/4      eq(2)

Putting eq(1) = eq(2) as left hand side of both equations are same

(x+2)/4 = (y-1)/4

Cross multiplying

4(x+2) = 4(y-1)

4x + 8 = 4y -4

4x +4y = -4 -8

4x + 4y = -12

4(x+y) = -12

x+y = -12/4

x+y = -3

y = -x -3

The slope intercept form of line is:

y = mx + b

where m is the slope. Comparing with y = -x-3

The value of slope m = -1

The slope of the line defined by the parametric equations x=-2+4t and y=1+4t is mathematically given as

m = -1

Question Parameter(s):

the parametric equations x=-2+4t and y=1+4t

Generally, the equation for the Equations   is mathematically given as

x=-2+4t

y=1+4t

Therefore

t = (x+2)/4..1

t = (y-1)/4 ...2

 Hence

(x+2)/4 = (y-1)/4

4(x+2) = 4(y-1)

y = -x -3

In conclusion, slope intercept

y = mx + b

Hence

y = -x-3

The slope is m = -1

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