Toby submitted the following work when asked to convert 12 2/3 to an improper fraction

The 15th term of the geometric progression is 9,565,94.

A geometric progression can be expressed as an = a1rn-1 for some a1 and r. You are told that a2 * a4 = 2a5 and a1 + a2 + a3 + a4 = 80.

From the first equation, a2 = a1 r, a4 = a1 r3, and a5 = a1 r4. This tells us that

a1 r a1 r3 = 2 a1 r4

The r's and one a1 cancel leaving a1 = 2.

Now, plugging similarly into a1 + a2 + a3 + a4 = 80,

2 + 2r + 2r2 + 2r3 = 80

r3 + r2 + r + 1 = 40

In general, the easiest way to solve a cubic is by graphing, but here you know the answer will be a small integer, so just try a few. If we try r=3, we get 27 + 9 + 3 + 1 = 40 so r = 3.

So the geometric sequence here is an = 2 3n-1. The 15th term is then:

a15 = 2*3^14

a15 = 9,565,938.

Full question:

A G.P, the product of the 2nd and the 4th term is double the 5th term, and the sum of the first 4th terms is 80. find the 15th term.

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Answer:

B

Step-by-step explanation:

Graph B represents a linear function.

Notice that graph D also shows a line, but it is not the graph of a function, since it doesn't pass the vertical line test for functions.

Graph A shows a quadratic function, and graph C shows likely an exponential function. It is graph B the one that is linear, and a function as well.

Answer: It is B.

Step-by-step explanation:

A is a quadratic function

B is a linear function because it is a straight line and every input has exactly one output.

C is a is not straight

D failed the vertical line test.

Answer:

B)  13

Step-by-step explanation:

Given equation:

\(4(y-3)+19=59\)

Subtract 19 from both sides:

\(\implies 4(y-3)+19-19=59-19\)

\(\implies 4(y-3)=40\)

Divide both sides by 4:

\(\implies \dfrac{4(y-3)}{4}=\dfrac{40}{4}\)

\(\implies y-3=10\)

Add 3 to both sides:

\(\implies y-3+3=10+3\)

\(\implies y=13\)

Check by substituting y = 13 into the original equation:

\(\begin{aligned}\implies 4(13-3)+19 & = 4(10)+19\\& = 40+19\\& = 59\end{aligned}\)

Hence verifying that y = 13.

Answer:

B.) y = 13

Given expression:

\(\sf \rightarrow 4(y-3)+19 = 59\)

Solving steps:

\(\sf \rightarrow 4(y-3)= 59-19\)

\(\sf \rightarrow 4(y-3)=40\)

\(\sf \rightarrow y-3=10\)

\(\sf \rightarrow y=10+3\)

\(\sf \rightarrow y=13\)

Answer:

a) 3

b) \(\frac{3}{2}\)

Step-by-step explanation:

Ewen has 48 white tiles and 16 blue tiles.

(a) Write down the ratio of the number of white tiles to the number of blue tiles.

Give your ratio in its simplest form.

The cost of each white tile was £2

The cost of each blue tile was £4

(b) Work out the ratio of the total cost of the white tiles to the total cost

of the blue tiles.

Answer:

a) Since they are 48 white tiles and 16 blue tiles, ratio of the number of white tiles to the number of blue tiles is the number of white tiles divided by the number of blue tiles. Therefore:

Ratio of white tiles to the blue tiles = number of white tiles/number of blue tiles = \(\frac{48}{16}=3\)

b)  total cost of the white tiles = number of white tiles × cost of each white tile = 48 tiles × £2 per tile = £96

total cost of the blue tiles = number of blue tiles × cost of each blue tile = 16 tiles × £4 per tile = £64

ratio of the total cost of the white tiles to the total cost  of the blue tiles = total cost of the white tiles/total cost  of the blue tiles = \(\frac{96}{64}=\frac{3}{2}\)

Answer:

I see what's happening here

You're face to face with greatness

And it's strange

You don't even know how you feel

It's adorable

It's nice to see that humans never change

Open your eyes, let's begin

Yes it's really me, breathe it in

I know it's a lot, the hair, the bod

When you're staring at a demigod

So what can I say except

You're welcome

For the tide, the sun, the sky

Hey, it's okay, it's okay

You're welcome

I'm just an ordinary demiguy

What can I say except

You're welcome

For the tide, the sun, the sky

Hey, it's okay, it's okay

You're welcome

I'm just an ordinary demiguy

Honestly, I can go on and on

I could explain every natural phenomenon

The tide, the grass, the ground

Oh, that was me I was messing around

I killed a snake, I buried its guts

Sprouted a tree, now you've got coconuts

What's the lesson?

What is the takeaway?

Don't mess with Maui when he's on a breakaway

And the tapestry here in my skin

Is a map of the victories I win

Look where I've been, I make everything happen

Look at that mean mini Maui just tikkity tappin'

Singing and scratchin'

Flipping and snappin'

People are clappin', hearing me rappin'

And bring the chorus back in

Well anyway, let me say you're welcome

For the wonderful world you know

Hey, it's okay, it's okay

You're welcome

Well, come to think of it, I gotta go

Hey, it's your day to say

You're welcome

'Cause I'm gonna need that boat

I'm sailing away, away

You're welcome

'Cause Maui's the ultimate guy

You're welcome!

You're welcome!

Step-by-step explanation:

Answer:

2101=64...............

Answer:

638 miles

Step-by-step explanation:

Key skills needed: Proportions, Unit Rates

1) The car can go 464 miles with 16 gallons of gasoline. We need to find how many miles each gallon gasoline results in.

To find the miles per gallon, we would do 464 miles/16 gallons --> 29 mpg

This means each gallon lets the car run 29 miles.

2) To find out how many miles 22 gallons is, we then do 29 x 22, which is 638 miles.

Therefore, your answer is 638.

Hope you understood and have a nice day!!

Since a= 10, we know that b = 4a - 5

 --> b = 4(10) - 5 = 40 - 5 = 35

By looking at the table at the left, the value of of c that goes with a when a = 10 is

--> 19.

So b = 35 and c = 19.

Hope that helps!

Answer:

|X-Y|<=10

Step-by-step explanation:

X-Y<=10

And

X-Y>= -10

but then it cannot be solved unless one of the variables is known.

The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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Step-by-step explanation:

1) Cotangent is cosine over sine.

From unit circle, cos 30° = ½√3 and sin 30° = ½

cot 30° = cos 30° / sin 30°

cot 30° = (½√3) / ½

cot 30° = √3

2) Cosecant is the inverse of sine.

From unit circle, sin π/4 = 1/√2

csc π/4 = 1 / sin π/4

csc π/4 = 1 / (1/√2)

csc π/4 = √2

On solving the provided question, we can say that the - by solving algebraic equation x= 0 and y= 4.

A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases. Check out algebraic expressions as well. Equations, or the equal sign, simply indicate equality. With mathematics, and algebraic expression is one that is constructed using variables, constant algebraic numbers, and algebraic operations. An algebraic expression is, for instance, 3x2 2xy + c.

y+ (2/3)x = 4

12—3y

3y +6x 12

2x+3y=12

by subtracting2frorn1.

4x=o

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Answer:

  D.  10 square units

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

__

This triangle has a base of 4 units and a height of 5 units. (These dimensions can be counted from the graph, or found by subtracting coordinate values.) Its area is ...

  A = 1/2(4 units)(5 units) = 10 square units

_____

Additional comment

The first two coordinates lie on the line x=0. The length of that segment is the difference of the y-values: 4 -(-1) = 5.

The first and last coordinates lie on the line y=-1. The length of that segment is the difference of the x-values: 4 -0 = 4.

The point estimate for the plants' survival rate in the humid environment is 42%.

To calculate the point estimate, divide the number of successful outcomes (plants alive) by the total number of trials (total plants). In this case, 21 plants were alive out of 50, so the calculation would be 21/50.

This gives you a decimal (0.42), which you can convert into a percentage by multiplying by 100, resulting in 42%. The point estimate represents the proportion of plants that survived in the humid environment after one month, providing an indication of the new environment's effect on the plants' survival.

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Answer:

8/20

Step-by-step explanation:

This answer is 8/20 because they’re only 8 chocolates in the whole bag. So it is the amount you have over the total.

Answer:

Option (1)

Step-by-step explanation:

Formula to get the area of a circle is given by,

Area = πr²

Here r = radius of the circle

Since, Radius of a circle = \(\frac{\text{Diameter}}{2}\)

Therefore, Radius of the circle with diameter = 31.6 cm will be,

Radius = \(\frac{31.6}{2}\)

            = 15.8 cm

Now Area of the circle = π(15.8)²

                                      = 249.64π cm²

                                      = 783.87 cm²

                                      ≈ 783.9 cm²

Therefore, Option (1) will be the correct option.

Answer:

10 boxes

Step-by-step explanation:

Take the number of fossils and divide by the number per box to determine the number of boxes

60/6 = 10

She needs 10 boxes

Answer:

10 boxes

Step-by-step explanation:

60 fossils are evenly distirbutd into x number of boxes so that there are 6 fossils in each box.

The equation will look like:

\(6x=60\\x= 10\)

Hope this helped!

The number-of-times the "number-6" go into the "number-60" is exactly "10-times".

When we divide the "number 60" by "6", we are asking how many times the "number 6" can be evenly divided into "60" without any remainder.

In other words, we are searching for the quotient of the division operation.

To find the quotient, we divide the "number 60" by "6",

On dividing "60" by "6", the result is "10", which means that the "number 6" can go into "60" exactly "10 times", because "6" multiplied by "10" equals "60", with no remainder.

Therefore, exactly "10-times" the "number-6" go into "60".

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that there is no total computable function f(x, y) with the given property.

To prove this, we can assume that such a function f(x, y) exists and use it to show that the Halting problem is decidable. The Halting problem is the problem of determining whether a given program will halt or run forever on a given input. It is known to be undecidable, meaning that there is no algorithm that can solve it for all cases.

However, if we have a function f(x, y) that can tell us in how many steps a program will halt (or that it will not halt), then we can use it to decide the Halting problem. Given a program P and input I, we can construct a new program P.(Cy) that simulates P on I and counts the number of steps it takes for P to halt (or runs forever). Then, we can use f(P.(Cy), y) to determine whether P halts on I or runs forever. If f(P.(Cy), y) returns a number less than or equal to the number of steps that P actually takes to halt on I, then we know that P halts on I. Otherwise, we know that P runs forever on I.

Since the Halting problem is undecidable, we cannot have a function f(x, y) that solves it in the given way. Therefore, there is no total computable function f(x, y) with the property that if P.(Cy) stops, then it does so in f(x, y) or fewer steps.

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The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

the slope is 2

Step-by-step explanation:

use the two points to find the slope

start at the blue point go up 4 then over 2 to get to the red point.

the slope of 4/2 in other words 2

Answer:

Step-by-step explanation:

They appear to be linear so that's easy enough to find out. What we are being asked is to find the equation represented by each table. Knowing that they are linear, we need the slope of each one and then the y-intercept of each one (each "one" being each table). Let's begin with the y-intercept. The y-intercepts exist where x = 0. In the first table, where x = 0, y = -4; in the second table, where x = 0, y = 3.

The equation we will finally fill in is y = mx + b, where m is the slope and b is the y-intercept.

Solving for slope in the first table:

\(m=\frac{-4-(-7)}{0-(-1)}=\frac{3}{1}=3\) and the equation for this table is

y = 3x - 4

Solving for the slope in the second table:

\(m=\frac{3-4}{0-(-1)}=\frac{-1}{1}=-1\) and the equation for this table is

y = -1x + 3 or just y = -x + 3

That's the system, which happens to be choice D

Answer:

B

Step-by-step explanation:

All you have to do is analyze the formula that fits, and it is easier while using the table, bonus that the answers for the second table are different. That's what I have done.

Answer:

A. Actute triangle

Step-by-step explanation:

Is A because an acute triangle is a triangle where all the angles are the same.

Can not be B. because isosceles triangles have two sides that are the same which doesn't relate to angles.

Can not be C. because equilatiral triangles are triangles with sides that are all the same.

Can not be D. because for a triangle to be obtuse one of the angles needs to be greater that 90 degrees.

So it has to be A.

Answer:

y-3=2x-4

Step-by-step explanation:

a. H: δ>100 is a legitimate statistical hypothesis because it is a statement about a population parameter (δ) and it is testable using statistical methods.
b. H: x=45 is a legitimate statistical hypothesis because it is a statement about a population parameter (x) and it is testable using statistical methods.
c. H: s<.20 is a legitimate statistical hypothesis because it is a statement about a population parameter (s) and it is testable using statistical methods.
d. H: δ1/δ2 <1 is a legitimate statistical hypothesis because it is a statement about a population parameter (δ1 and δ2) and it is testable using statistical methods.
e. H: X-Y=5 is a legitimate statistical hypothesis because it is a statement about a population parameter (X and Y) and it is testable using statistical methods.
f. H: גּ<.01 is a legitimate statistical hypothesis because it is a statement about a population parameter (λ) and it is testable using statistical methods, with the parameter being the rate parameter of an exponential distribution used to model component lifetime.

Here are the answers for each assertion:

a. H: δ>100 - This is a legitimate statistical hypothesis because it states a specific direction for the population parameter (delta).

b. H: x=45 - This is not a legitimate statistical hypothesis because it refers to a sample statistic (x) rather than a population parameter.

c. H: s<.20 - This is not a legitimate statistical hypothesis because it refers to a sample statistic (s, sample standard deviation) instead of a population parameter.

d. H: δ1/δ2 <1 - This is a legitimate statistical hypothesis because it specifies a relationship between two population parameters (delta1 and delta2).

e. H: X-Y=5 - This is not a legitimate statistical hypothesis because it refers to sample statistics (X and Y) rather than population parameters.

f. H: λ<.01 - This is a legitimate statistical hypothesis because it states a specific direction for the population parameter (lambda) related to the exponential distribution for component lifetime.

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Answer:

34/45 pi

Step-by-step explanation:

To change from degrees to radians, multiply by pi/180

136 * pi/180

34/45 pi

Step-by-step explanation:

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Answer:

x= 17

Step-by-step explanation:

x+2x+20+7x-10 = 180

10x+10 = 180

10x = 180-10

x = 170/10

x = 17

Data set A is the correct match for the shape depicted in the image, where the mean, median, and mode are all equal to 40.

The first data set, A, matches with the shape depicted in the image. The mean, median, and mode are all equal to 40.
To understand what these measures represent, let's break them down:
- Mean: The mean is the average of all the values in a data set. In this case, all the values in data set A must add up to 40 when divided by the number of values.
- Median: The median is the middle value in a data set when arranged in ascending order. In this case, the median is also 40, which means that half of the values in data set A are below 40 and half are above 40.
- Mode: The mode is the value that appears most frequently in a data set. Here, 40 is the mode because it occurs more often than any other value in data set A.
Therefore, data set A is the correct match for the shape depicted in the image, where the mean, median, and mode are all equal to 40.

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