a potter forms a piece of clay into a right circular cylinder. as she rolls it, the height h of the cylinder increases and the radius r decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by 0.5 centimeters per second. what is the rate at which the radius is changing when the radius is 7 centimeters and the height is 6 centimeters?

x = milliliters of 40% alcohol

y = milliliters of 20% alcohol

so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]

The value of x and y in the angles are 15.6 and 10.5 respectively.

When parallel lines are cut by a transversal lines, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, line XD, TZ, YF and LP are parallel to each other.

WC is the transversal line.

Hence,

m∠CNL = 6x - 17.6

m∠FBH = 12y - 22

m∠THR = 3x + 29.2

Hence,

180 - (12y - 22) = 6x - 17.6(corresponding angles)

Corresponding angles are congruent

180 - 12y + 22 = 6x - 17.6

6x + 12y = 180 + 22 + 17.6

6x + 12y = 219.6

Therefore,

180 - (3x + 29.2) = 12y - 22 (alternate angles)

Alternate angles are congruent .

180 - 3x - 29.2 = 12y - 22

180 + 22 - 29.2 = 12y + 3x

172.8 = 3x + 12y

combine the equation

6x + 12y = 219.6

3x + 12y = 172.8

subtract equation(ii) from equation(i)

3x = 46.8

x = 46.8 / 3

x = 15.6

12y = 219.6 - 6(15.6)

12y = 219.6 - 93.6

12y = 126

y = 126 / 12

y = 10.5

Therefore,

x = 15.6

y = 10.5

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The ratio of x:y  is 4:3.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categories ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.

Given:

15% of x=20% of y

So,

15 / 100 × x = 20 / 100 × y

3 / 20x = 1/5y

x / y = 1/5 x 20/3

x / y = 4/3

Hence, the ratio of x:y  is 4:3.

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59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other

The figure that is formed is the following with the respective measurements, now to calculate the area we need the height, for Pythagoras we have:

17 ²= h ² + 8 ²

h ² = 289 - 64

h ² = 225

h = 15

now the figure area is as follows:

A = h × (b + a) / 2

b long side 20 m and short side 12 cm, replacing:

A = 15 × (12 + 20) / 2

A = 240 m²

We are told that each can of weed killer can cover up to 100m ^ 2

Thus:

240/100 = 2.4, so you would need 3 cans of weedkiller

each can costs 19.75, which means that the total cost is:

19.75 × 3 = 59.25 euros

Hence 59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn.

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Answer:

its A

Step-by-step explanation:

:)

The formula for getting the volume of a sphere is:

where r = radius of the sphere.

Let's plug into the formula the given radius of the sphere in the question.

Then solve.

Multiply 10 cm by itself three times.

Multiply 1000 by 4, then divide by 3.

Rounding the calculated volume to the nearest whole number, the volume of the sphere is 1,333π cm³ (Option D or 4)

Answer:

The volume of the sphere is 1,333π cm³ (Option D or 4)

The equation of the graph of g is represented by y  - 6 =  (x-2)²

The very first step in balancing a variable equation is to correctly identify the specific values of the variables that lead to equality.

The graph of the function is f is y = x²

Now we can see that the graph of g is translated to 2 units to the right and 6 units up.

We know from the properties of translation that when the graph moves 2 units to the right we get the equation as y = (x-2)²

Again when the graph moves 6 units up wards the graph changes by

y  - 6 =  (x-2)²

Therefore the equation of g is  y  - 6 =  (x-2)²

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Answer:

x = 130°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 50° + 80° = 130°

Answer: 130

Step-by-step explanation:

180 = y + 50 + 80

y = 50

180 - y = x

x = 130

The equation for the purchase of n number of notebooks by Caitlin is

4n = c , where c is representing the cost that Caitlin paid.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.

the price for one notebook was = $4 each

n number of notebooks were purchased by caitlin

therefore the cost price of 4 notebooks will be = 4 * n

as per given in the question cost price = c

therefore the equation formed will be

4n = c

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The customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).

We are given with the cost of ham is $2.49 per pound and

Cost of swiss cheese is $3.79 per pound.

So, the cost of 2 pounds of ham will be given as-

= 2× $2.49

= $4.98

Since, the customer has a total of  $9.50 to spend on 2 pounds of ham and some cheese,

∴ Let the number of pounds of cheese she can purchase be x.

Then the equation will be this:

2.49*2 + 3.79*x = 9.50

4.98 + 3.79x = 9.50

Subtracting 4.98 from each side we get-

4.98 -4.98 + 3.79x = 9.50-4.98

3.79x = 4.54

x  [tex]=\frac{4.54}{3.79}[/tex]

x = 1.19788 pounds of cheese (approximately 1.2 pounds).

Hence, the customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).

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Answer:

39.

Step-by-step explanation:

50779 divided by 590 is 86, with a remainder of 39.

Explanation

We are given the measure of arc PR = 118°.

We are required to find m∠PQR.

We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:

Hence, the answer is:

But since Q is the measure of the angle, then the final answer is 118°.

Answer:9 days

Step-by-step explanation:A lot of division is required, but because 8.75 probably isn't an answer, I rounded up to 9.

The graph of the quadratic equation:

y = x^2 -8x + 16

Can be seen in the image at the end.

First, we have a quadratic function:

y = x^2 -8x + 16

To graph this we need to find some points on the parabola, to do that, we will evaluate it in some values of x.

if x = 0

y = 0^2 - 8*0 + 16 = 16

So we have the point (0, 16)

if x = 1

y = 1^2 - 8*1 + 16 = 9

So we have the point (1, 9)

if x = -1 we have:

y = (-1)^2 - 8*-1 + 16 = 23

So we have the point (-1, 23)

And so on, once you have enough points, you can graph them in a coordinate axis and then draw a parabola that connects them, the graph of the quadratic equation can be seen in the image below.

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[tex](\frac{3}{8} )^{-2}[/tex]

[tex](\frac{8}{3})^{2}[/tex]

[tex](\frac{8}{3} )\times(\frac{8}{3} )[/tex]

[tex]\frac{8\times8}{3\times3}[/tex]

[tex]\frac{64}{9}[/tex] or [tex]7.1111111[/tex]

Answer: there is no picture again. just take a good guess

Step-by-step explanation:

The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.

Given,

x + 3 is greater than or equal to 2x - 6

That is,

x + 3 ≥ 2x - 6

Solve for x in this solution.

So,

x + 3 ≥ 2x - 6

Here,

6 + 3 ≥ 2x - x

Then,

9 ≥ x

That is,

The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.

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In the graph, which compares the snowfall for the same three months last year and this year, you can see that the total snowfall for last year was 36.4 inches. how much more snow fell over the course of three months this year than did so last year: 5.45

what is the explanation?

The first step is to calculate the amount of snowfall from the previous year, which are:

12.6+6+9.2

=27.8

The next stage is to calculate how much snow has fallen this year, which includes:

10+15.75+7.5

=33.25

Now let's compare the snowfall over the first three months of current year to that of last year.

33.25-27.8

=5.45

In conclusion Graph showing snowfall during the same three months last year and this year, if the total snowfall for last year was 36.4

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If the knowledge that an event "a" has occurred implies that another event "b" cannot occur, then the events "a" and "b" are said to be disjoint events.

As per the question statement, the knowledge that an event "a" has occurred implies that another event "b" cannot occur.

We are required to determine the characteristic name for the above mentioned events.

And here, if event "a" occurs, even "b" does not, implying the fact that, events "a" and "b" cannot occur simultaneously. Hence, as per the above definition of disjoint events,  the events "a" and "b" are be disjoint.

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If a circle has a circumference of 320 cm, then its radius can be calculated as 50.92 cm according to the formula of circumference of a circle.

In geometry, the circumference can be defined as the perimeter of a circle or an ellipse. It can also be said as the linear distance present around it.

To better describe it, you can imagine that if a circle is opened out and placed as a straight line, then the total length of that straight line can be described as the circumference of the circle.

It is synonymous to perimeter, but the terminology can only be used with circled and ellipses. It is the curved length of the object. In this case, the object is mostly 2 dimensional but sometimes 3 dimensional objects can also be placed to take out their circumference with other methods.

In this particular question,

2[tex]\pi[/tex]r = 320

⇒ r = 320/2[tex]\pi[/tex]

⇒ r = 50.92

⇒ r ≈ 51 cm

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The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).

According to the question,

We have the following information:

Akela drew smaller arrays to find the product of a larger array.

Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).

Now, to find the correct option, we will look for these two in options:

So, the option that has both of them is  7*6 = (4*6) + (3*6).

Now, we can verify whether the sides of the equation given are correct or not.

We have:

7*6 = 42

On right hand side, we have:

(4*6) + (3*6)

24+18

42

Hence, the correct option is 4th one.

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Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.

H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3

Ha : at least one Pij ≠ Pi · Pj

We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;

e = (Row total) x (Column total) /Total sample size

We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where

x² =Σ(a - e)²/e

Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get

X² = 68.732

Rejection Region → X² ≥ 13.277

Test statistic → X² = 68.732

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

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The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

         4x+2x+5x+50= 180

        = 6x+5x+50 =180

        combine 6x and 5x

        =  11x

         11x+50= 180

        subtract 50 both sides

        11x = 180- 5

        =  130

        11x=130

        x= 130/11

          11.81

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The value of y when x = -7 according to the function defined y = w(x) is; 9.

It follows from the task content that the value of y when x = -7 is to be determined according to the given expression; y = w(x).

Since it follows from the task content that;

y = w(x)

Therefore, it follows that when; x = -7; we have;

y = w(-7).

However, recall from the function instances given that; w(-7) = 9;

Therefore, y = w(-7) = 9.

Ultimately, the value of y when x = -7 as required in the task content is; 9.

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Answer: Width = 8/20 ÷ 7/8  = 8/20 x 8/7   = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !

Answer: (-5, 8)

Step-by-step explanation:

       The x-coordinate is responsible for left and right, and the y-coordinate is responsible for up and down translations. Coordinate points are written as (x, y).

(-8, 9) ➜ (-8 + 3, 9 - 1) ➜ (-5, 8)

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Answer:

Perimeter (to the nearest tenth) = 24.3

Step-by-step explanation:

Applying logarithm properties, the solution of the highlighted question is given as follows:

x = 4.

The logarithmic equation is given as follows:

[tex]\log_{a}(x + 2) = \frac{1}{3}\log_{a}{8} + \log_{a}{3}[/tex]

First, we apply the power rule, meaning that the multiplying coefficient of the logarithm can be the power of the given term, hence:

[tex]\frac{1}{3}\log_{a}{8} = \log_{a}{8^{\frac{1}{3}}} = \log_{a}{\sqrt[3]{8}} = \log_{a}{2}[/tex]

Then the equivalent expression is:

[tex]\log_{a}(x + 2) = \log_{a}{2} + \log_{a}{3}[/tex]

Now we apply the product rule, as the sum of two logarithms of same base can be written as a single logarithm, keeping the base and multiplying the terms.

Hence the equivalent expression is:

[tex]\log_{a}(x + 2) = \log_{a}{(2 \times 3)}[/tex]

[tex]\log_{a}(x + 2) = \log_{a}{6}[/tex]

The logarithm function is one-to-one, meaning that if they have the same input, they will have the same output, hence we can solve for x as follows:

x + 2 = 6

x = 6 - 2

x = 4.

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Answer:

86

Step-by-step explanation:

I'll assume the expression is meant to be 10^2 - 5a +6

4a- 3 =13

4a = 16

a = 4

10^2 - 5a +6

10^2 - 5(4) +6

10^2 - 20 +6

100 - 14 = 86