Determine if the following ratios form proportions.

1.) 1 to 3 and 7 to 21

2.) 3 to 4 and 24 to 18

3.)1:5 and 6:30

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Veremos que el volumen total que cabe en el pilón es 2,800 m^3

Sabemos que el pilón tiene una capacidad máxima V.

Tambíen sabemos que de momento, el pilón tiene 1,600 m^3 de agua, y esto es equivalente a 4/7 de la capacidad máxima.

Entonces podemos plantear:

(4/7)*V = 1,600m^3

Podemos resolver esta ecuación para V si multiplicamos ambos lados por (7/4), así obtenemos:

V = (7/4)*1,600m^3 = 2,800 m^3

Es decir, el volumen total que cabe en el pilon es 2,800m^3

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The SSS Similarity Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are similar. This theorem is also known as the Side-Side-Side Similarity Theorem or the SSS Similarity Postulate.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SSS or Side-Side-Side Similarity.
If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
From this result, we can conclude that-
∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
Hence, we have described the SSS similarity theorem.

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In variables estimation sampling, the sample standard deviation is used to calculate the: sample size.

This is further explained below.

Generally, In the process of estimating variables using samples, the sample standard deviation is what is utilized to compute the size of the sample.

In conclusion, The process of selecting the total number of observations or duplicates that will be included in a statistical sample is known as "sample size determination." In any kind of empirical research where the purpose is to draw conclusions about a population based on a sample, the size of the sample being investigated is an essential component.

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Answer:

3

Step-by-step explanation:

Answer:

21 divided by 3 = 7

Step-by-step explanation:

hope this helps

Answer: a. 2

Step-by-step explanation:

A minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean, assuming a normal distribution of the number of words per sentence in the book and a population standard deviation of 4 words.

To determine the minimum sample size needed to be 95% confident that the sample mean is within 2 words of the true population mean, we can use the formula for the margin of error:

Margin of error = z * (standard deviation / sqrt(n))

Where z is the z-score for the desired confidence level, standard deviation is the population standard deviation (given as 4 words), and n is the sample size.

We want the margin of error to be no more than 2 words, so we can set up the inequality:

z * (4 / √n) ≤ 2

To find the value of z for 95% confidence level, we can use a z-table or calculator and find that z = 1.96.

Substituting this value into the inequality and solving for n, we get:

1.96 * (4 / √n) ≤ 2

Simplifying and solving for n, we get:

n >= 61.05

Since we can't have a fractional sample size, we can round up to the nearest whole number and conclude that a minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean.

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Answer:

N^6

= n*n*n*n*n*n

Step-by-step explanation:

Answer:

  a) 22e^-0.01t kilograms

  b) about 19.906 kilograms

Step-by-step explanation:

You want an equation for the amount of salt in a 15 kL brine tank initially containing 22 kg of salt if 150 L/min of the contents is replaced by pure water.

The quantity of salt s(t) in kilograms can be described by the differential equation ...

  s(0) = 22; s'(t) = -150/15000·s(t)

The solution can be found by separation of variables.

  \(\displaystyle\dfrac{ds}{dt}=-0.01s\\\\\int{\dfrac{1}{s}}\,ds=-0.01\int{}\,dt\\\\\ln{s}=-0.01t+c_1\\\\s=c_2\cdot e^{-0.01t}\qquad\text{where $c_2$ is $s(0)=22$}\\\\\boxed{s(t)=22e^{-0.01t}}\)

The amount of salt remaining after 10 minutes is ...

  s(10) = 22·e^(-0.01·10) = 22·e^-0.1

  s(10) ≈ 19.906 . . . . kilograms

There is about 19.906 kg of salt in the tank after 10 minutes.

__

Additional comment

The initial rate of change of the amount of salt is -22/100 kg/min, so after 10 minutes, we expect an approximate reduction by 2.2 kg to 19.8 kg. Since the rate slows as salt is removed, the value 19.9 kg after 10 minutes is reasonable.

There are a couple of places where the integration constant can be put in the equation for the salt quantity. As a multiplier of the exponential function, its value is found in a straightforward way.

The 8th percentile of a normally distributed random variable X with mean μ=47 and standard deviation σ=8 is approximately 36.88.

To find the 8th percentile of a normally distributed random variable, you can use the z-score formula and the standard normal distribution table as follows:

For a normally distributed random variable X with mean μ and standard deviation σ, the z-score is given by;

z=(X-μ)/σ

To find the 8th percentile, we need to find the z-score such that the area to the left of that z-score is 0.08 in the standard normal distribution table.

By consulting the table, we find that the z-score corresponding to 0.08 is -1.405

Thus, we have;

z=-1.405

= (X-47)/8

Solving for X, we get;

X = 47 - 1.405(8)

≈ 36.88

Therefore, the 8th percentile of a normally distributed random variable X with mean μ=47 and standard deviation σ=8 is approximately 36.88.

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Given the following question:

Now for part two:

Find the amount of money after 17 weeks

After 17 weeks she will have 960 dollars.

Required surface area is 100 in² and volume is 60 in³of each solid to the nearest tenth.

What is the surface area and volume of cuboid ?

Surface area of a cuboid = \(2(lb + bh + lh)\)

and volume of a cuboid = \(lbh\)

Where,

\(l = \)Length of the cuboid

\(b = \)Breadth of the cuboid

\(h = \)Height of the cuboid

Given, figure is a cuboid and according to figure length of the figure is 5 in and breadth of the figure is 2 in and height of the figure is 6 in.

We want to find surface area and volume of the given figure.

Here,

\(l = 5 \: in \\ b = 2 \: in \\ h = 6 \: in\)

So, required surface area =

\(2(5 \times 2 + 2 \times 6 + 5 \times 6) \\ = 2(10 + 12 + 30) \\ = 2 \times 52 \\ = 104 \: {(in)}^{2} \)

and volume

\( = 5 \times 2\times 6 \\ = 60 \: ({in})^{3} \)

Therefore, surface area is 104 in²

and nearest 10th value of 104 is 100.

So, required surface area is 100 in²

and volume is 60 in³

Nearest 10th value of 60 is also 60.

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Answer:

Distributive Property

Step-by-step explanation:

4(x-6)=5.4x-24

4x-24=5.4x-24

Answer:

vanilla small= 14

lemon large= 25

Step-by-step explanation:

total= 120

120÷3= 40

each of flavoured cake have 40

lemon= 40 - 26= 14

vanilla= 40- 15= 25

The function g(x), which is the reflection across the x-axis of f(x) = 10|x - 5| - 9 is given by g(x) = -10|x + 5| + 9

To find g(x), which is the reflection across the x-axis of f(x) = 10|x - 5| - 9,

we follow these steps

Step 1: Replace f(x) with -f(x) to reflect it across the x-axis.

The negative symbol reflects the function across the x-axis.

Hence, we get -f(x) = -10|x - 5| + 9.

Step 2: Replace x with -x to reflect it again across the y-axis.

Hence, we have -f(-x) = -10|(-x) - 5| + 9.

Step 3: Simplify -f(-x) by performing the required operations.

-f(-x) = -10|-x - 5| + 9 = -10|x + 5| + 9.

Therefore, the function g(x), which is the reflection across the x-axis of f(x) = 10|x - 5| - 9 is given by g(x) = -10|x + 5| + 9.

A reflection across the x-axis changes the sign of the y-coordinate only, whereas a reflection across the y-axis changes the sign of the x-coordinate only.

So, we replace f(x) with -f(x) to reflect across the x-axis.

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Since it's going up and down, my guess would be the second answer slope = undefined.

Answer:

The Correct answer is slope=Undefined

Answer:

0.25 or 5/12 - 1/6

Step-by-step explanation:

-1/2(-5/6+1/3), do PMDAS. (-5/6) = -0.833 (repeated) and (1/3) = 0.333 (repeated) and you add them both (-0.833 + 0.333) = -0.5 and -1/2 = -0.5 and when you multiply them both it would equal 0.25. or another explanation for the answer is 5/12 = 0.41666666666 and 1/6 = 0.16666666666 and when you subtract them both you get 0.25, I hope this was helpful.

Answer:

c

Step-by-step explanation:

it just is

Answer:

C

Step-by-step explanation:

It just is

Step-by-step explanation:

An equation involving x and y, which is also a function, can be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” and means that y is a function of x.

Lily spent $39.3 at the amusement park.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra we use variables like x, y, and z along with numbers.

Let the money spent by Mandy and Jeremy be 'x' and 'y' respectively.

We have given,

Mandy spent = $16. 25

Jeremy spent = x + $3. 40 = $16. 25 + $3. 40 = $19.65

Lily spent = y × 2 = $19.65 × 2

 Lily spent = $39.3

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The fraction of the sheet that Amelia used for each card is 1/18 sheets.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

First of all, we would determine the total number of sheet of construction paper used as follows;

Total number of sheet of construction paper used = 6 × 3

Total number of sheet of construction paper used = 18 sheets.

Now, we can determine the fraction of the sheet used by Amelia as follows;

Fraction of sheet = 1/3 × 1/6

Fraction of sheet = 1/18 sheets.

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Complete Question:

Amelia had 1/3 of a sheet of construction paper to make 6 greeting cards. What fraction of the sheet did she use for each card?

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

Explanation:

x = number of minutes

y = amount of grain left over, in cubic meters

We can abbreviate "cubic meters" into "m^3" without quotes of course.

The silo holds 2000 m^3 of grain. This is the initial value, so it is the y intercept. This means b = 2000. If the silo wasn't completely full, then we'd have to use a different initial value.

The slope is -9 because the amount of grain decreases by 9 cubic meters per minute. We can think of it like

slope = rise/run = (change in y)/(change in x)

slope = (change in grain)/(change in time)

Saying slope = -9/1 means the change in grain is -9 m^3 and the change in time is 1 minute.

Because the slope is -9, we say that m = -9

Therefore, we go from y = mx+b to y = -9x+2000

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

Note how plugging x = 0 into the equation leads to

y = -9x+2000

y = -9*0+2000

y = 0 + 2000

y = 2000

Showing that after 0 minutes, aka at the start, we have 2000 m^3 of grain.

Then at the x = 1 minute mark, we have...

y = -9x+2000

y = -9*1+2000

y = -9+2000

y = 1991

Showing that the silo lost 9 m^3 of grain since 2000-1991 = 9.

The graph y = -9x+2000 is a straight line that goes through the two points (0,2000) and (1,1991).

Answer:

(4c + b)(12c - b)

Step-by-step explanation:

- b² + 48c² + 8bc ← rearrange

48c² + 8bc - b² ( split the middle term )

= 48c² + 12bc - 4bc - b² ( factor first/second and third/fourth terms )

= 12c(4c + b) - b(4c + b) ← factor out (4c + b) from each term

= (4c + b)(12c - b)

Answer:

Standard form

Step-by-step explanation:

In this question, we have to figure out what form the equation is.

Our options are: point-slope form, slope-intercept form, and standard form.

Our forms are structed as followed below:

Point-slope form: y - y1 = m(x - x1)

Slope-intercept form: y= mx + b

Standard form: Ax + By = C

Now, we just need to find out which form the equation resembles.

You would notice that the linear equation "2x + 4y = 12" follows the structure of the standard form.

Side-by-side comparison:

2x + 4y = 12

Ax + By = C

Therefore, your answer would be standard form.

Answer:

y-y1=m(x-x1)

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

y=1/2x+3

Answer:

Step-by-step explanation:

m = 1/2

Equation of line: y - y₁ = m(x - x₁)

x₁ = 2  & y₁ = 4

\(y -4 = \dfrac{1}{2}(x - 2)\\\\y - 4 =\dfrac{1}{2}x -2*\dfrac{1}{2}\\\\y-4=\dfrac{1}{2}x -1\\y = \dfrac{1}{2}x -1+4\\\\y=\dfrac{1}{2}x+3\)

Answer:

Red balls - 20

Blue balls - 50

Step-by-step explanation:

4 + 10 = 14

4/14 × 70

= 20

10/14 × 70

= 50

The given expression, cos(pi/12)cos(5pi/12) + sin(pi/12)sin(5pi/12), is equivalent to 1/2.

The given expression is:

cos(pi/12)cos(5pi/12) + sin(pi/12)sin(5pi/12)

To find an equivalent expression, we can use the trigonometric identity for the cosine of the difference of two angles:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Comparing this identity to the given expression, we can see that A = pi/12 and B = 5pi/12. So we can rewrite the given expression as:

cos(pi/12)cos(5pi/12) + sin(pi/12)sin(5pi/12) = cos(pi/12 - 5pi/12)

Using the trigonometric identity, we can simplify the expression further:

cos(pi/12 - 5pi/12) = cos(-4pi/12) = cos(-pi/3)

Now, using the cosine of a negative angle identity:

cos(-A) = cos(A)

We can simplify the expression even more:

cos(-pi/3) = cos(pi/3)

Finally, using the value of cosine(pi/3) = 1/2, we have:

cos(pi/3) = 1/2

So, the equivalent expression is 1/2.

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Answer:

6/2 = 3

Step-by-step explanation:

there are 2 people, when you divide the 6 trout by the 2 people, they will each get 3 fishes

Answer:

This property is known as the associative property

Step-by-step explanation:

In the associative property, you rearrange the numbers so they make the most sense in what position they are in.

Hope this helps! :)

Answer:

associate property

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