what are the values of x?​

The rate of growth of the plant is 2 centimeters per week.

Calculate the change in height divided by the change in time (weeks) to find the plant's growth rate.

To calculate the rate of growth of the plant, we need to determine the change in height per week.

Given:

Initial height = 4 cm

Final height = 12 cm

Weeks = 4

To find the rate of growth, we can use the formula:

Rate of growth = (Final height - Initial height) / Weeks

Substituting the given values into the formula:

Rate of growth = (12 cm - 4 cm) / 4 weeks

Rate of growth = 8 cm / 4 weeks

Rate of growth = 2 cm/week

Therefore, the rate of growth of the plant is 2 centimeters per week.

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Based on fractional subtraction, Emily must walk ¹/₂₀ miles after dinner to meet her target walking distance of ⁴/₅ miles daily.

A fraction represents a portion or part of a whole value.

Subtractions involving fractions can be accomplished by finding the common factor of the denominators as follows:

The target walking distance that Emily set = ⁴/₅ miles

The distance Emily covered to work = ²/₅ miles

The distance Emily covered during lunchtime = ¹/₄ miles

The distance that Emily needs to walk after dinner to meet her set target = ¹/₂₀ (⁴/₅ - ²/₅ - ¹/₄)

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To stay healthy, Emily decided to walk 4/5 miles every day. She walked 2/5 miles to work and walked 1/4 mile at lunchtime. How much more does she need to walk after dinner if she wants to meet her target distance? ​

We play total of 4.5 hours of video games on Friday and Saturday.

An expression in math is a statement having minimum of two numbers or variables or both and an operator connecting them.

To get total hours played on Friday and Saturday, we will subtract the sum of hours played from the mean of 1.5 hours per day for the five days given.

The total hours played on Friday and Saturday will be:

= (Mean hours per day * 7) - (Sum of hours played on Sunday to Thursday)

= (1.5 * 7) - (1.75 + 1 + 0.5 + 1.5 + 1.25)

= 10.5 - 6

= 4.5 hours.

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The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

The mean of the data is 9 students because there are 45 students total and 5 meetings.

When 15 students attend the next meeting, the mean increases to 10.5 students because there are now 60 students total and 6 meetings.

Mean of the first 5 meetings:

There are 45 students total.

There are 5 meetings.

Therefore, the mean is:

= 45 / 5

= 9 students.

There are 60 students total.

There are 6 meetings.

Therefore, the mean is:

= 60/6

= 10 students.

The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

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Answer:

288in³

Step-by-step explanation:

volume for one = 12 X 6 X 2 = 144.

for two books, it is 2 X 144 = 288in³

The walkway is 12 feet 9 inches long.

To find the total length of the walkway, we need to add the lengths of the three boards together.

The first board is 3 feet 7 inches long, which can be written as 3'7".

The second board is 5 feet 4 inches long, which can be written as 5'4".

The third board is 3 feet 10 inches long, which can be written as 3'10".

Now, let's add the lengths together:

3'7" + 5'4" + 3'10"

When adding feet and inches, we need to carry over any extra inches beyond 12 to the feet.

Adding the inches first:

7" + 4" + 10" = 21"

Now, let's add the feet:

3' + 5' + 3' = 11'

So, the total length of the walkway is 11 feet 21 inches.

We need to convert the inches to feet by dividing by 12:

11' + 21" ÷ 12 = 11' + 1'9" = 12'9"

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Formula for slant height:

[tex]l = \sqrt{ {r}^{2} + {h}^{2} } [/tex]

We dont have height so we will find it with the help of area

[tex] \sf \: area = \pi {r}^{2} + \sqrt{ {r}^{2} + {h}^{2} } [/tex]

[tex] \sf \: 31.4 = 3.14 \times {2}^{2} + \sqrt{ {2}^{2} + {h}^{2} } [/tex]

[tex] \sf \: 31.4 = 3.14 \times 4 + \sqrt{ 4 + {h}^{2} } [/tex]

[tex] \sf \: 31.4 =12.56 + \sqrt{ 4 + {h}^{2} } [/tex]

[tex] \sf \: 31.4 - 12 .56 = \sqrt{ 4 + {h}^{2} } [/tex]

[tex] \sf \: 18.84 = \sqrt{ 4 + {h}^{2} } [/tex]

[tex] \sf \: 18.84 ^{2} = 4 + {h}^{2} [/tex]

[tex] \sf \: 354.9456 - 4 = {h}^{2} [/tex]

[tex] \sf \: 350.9456 = {h}^{2} [/tex]

[tex] \sf \: h = \sqrt{ 350.9456}[/tex]

[tex] \sf \: h = 18.73[/tex]

Now put this in the first formula to find slant height (l)

[tex] \tt \: l = \sqrt{ {r}^{2} + {h}^{2} } [/tex]

[tex] \tt \: l = \sqrt{ {2}^{2} + {18.73}^{2} } [/tex]

[tex] \tt \: l = \sqrt{ 4 + 350.8129 } [/tex]

[tex] \tt \: l = \sqrt{ 354.8129 } [/tex]

[tex] \tt \: l = 18.83[/tex]

The calculated values of A and p that satisfy the equation y = Ax - 2p are A = -2.6 and p = -0.626

From the question, we have the following parameters that can be used in our computation:

Points = (-0.68, 3.02) and (1.07,-1.53)

The equation is of the form

y = Ax - 2p

Using the given points, we have

3.02 = -0.68A - 2p

-1.53 = 1.07A - 2p

Subtract the eqations

-0.68A - 1.07A = 3.02 + 1.53

So, we have

-1.75A = 4.55

This gives

A = -2.6

Recall that

3.02 = -0.68A - 2p

So, we have

3.02 = 0.68 * 2.6 - 2p

Evaluate

2p = -1.252

Divide by 2

p = -0.626

Hence, the values of A and p are A = -2.6 and p = -0.626

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Question

The variables x and y satisfy the equation y = Ax - 2p, where A and p are constants. The graph of In y against In x is a straight line passing through the points (-0.68, 3.02) and (1.07,-1.53).

Find the values of A and p.​

A relation R on a set X means , R is a subset of the Cartesian product Xⁿ, where n is the number of components of the relation.

Now, A relation R on a set X, where n is the arity or number of components of the relation, is a mathematical phrase that denotes that R is a subset of the Cartesian product Xⁿ

For example,

If X = 1, 2, 3, for instance, and R is a relation on X such that R = 1, 2, 3, then n=2.

We can see that R is a subset of X in this instance, which is composed of the elements (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), and (3,1), (3,2), (3,3).

Since each member of R is an ordered n-tuple consisting of n items that belong to X, it follows that if R is belong in Xⁿ, it is a relation on the set X.

Thus, A relation R on a set X means , R is a subset of the Cartesian product Xⁿ, where n is the number of components of the relation.

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To find the length of DE in circle D, we can use the properties of a circle and the given information.

In a circle, if two chords intersect, the product of the segments of one chord is equal to the product of the segments of the other chord. In this case, we have chord EF intersecting chord DE at point D.

Let x represent the length of segment DE, and y represent the length of segment DF. Therefore, the length of segment EF would be (x + y).

According to the chord-chord power theorem:

DE * EF = DF * DF

Substituting the given values:

x * (x + y) = y * y

x^2 + xy = y^2

We are also given that angle EDF measures 70 degrees. According to the angle intercepting chord theorem, the intercepted arc EF is twice the measure of angle EDF. So, the measure of arc EF is 2 * 70 = 140 degrees.

Now, we can use the length of arc EF to find the ratio of the lengths of segments EF and DF.

The ratio of the lengths of the intercepted arcs is equal to the ratio of the lengths of the corresponding chords. Therefore:

EF / DF = arc EF / arc DF

(x + y) / y = 140 / 360 [Using the measure of the intercepted arcs]

Simplifying this equation:

(x + y) / y = 7 / 18

Cross-multiplying:

18(x + y) = 7y

18x + 18y = 7y

18x = 7y - 18y

18x = -11y

Dividing by -11:

x = -11y / 18

We need to find the value of x, which represents the length of segment DE. Since segment lengths cannot be negative, we can disregard the negative sign.

x = 11y / 18

Substituting this value of x in the equation x^2 + xy = y^2:

(11y / 18)^2 + (11y / 18) * y = y^2

Simplifying:

121y^2 / 324 + 11y^2 / 18 = y^2

Multiplying through by 324:

121y^2 + 594y^2 = 324y^2

715y^2 = 324y^2

715y^2 - 324y^2 = 0

391y^2 = 0

y^2 = 0

Since y^2 = 0, it implies that y = 0. This means that segment DF has zero length.

Now, substituting y = 0 into the equation x = 11y / 18:

x = 11 * 0 / 18

x = 0

Therefore, the length of DE is 0.

In conclusion, the length of DE is 0.

I cannot load the image that you have provided this is what the answer is according to the text provided.

The equation that would be the line of best fit is B. y = 1/50x

The line of best fit is a line that best describes the relationship between two variables. In this case, the two variables are the total number of watches manufactured and the number of defective watches. The line of best fit is determined by finding the line that minimizes the sum of the squared vertical distances between the line and the data points.

The line of best fit for the scatter plot is y= 1/50x. This line passes through the center of the data points, which means that it minimizes the sum of the squared vertical distances between the line and the data points. The slope means that for every 50 watches manufactured, there is one defective watch.

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The mean number of text messages that Julianna sent per day is 7.

To calculate the mean number of text messages that Julianna sent per day, we need to sum up the number of text messages she sent each day and divide it by the total number of days.

Total number of text messages sent:

13 + 0 + 4 + 4 + 5 + 6 + 17 = 49

Total number of days: 7

Mean = Sum of all observations/number of observations

Mean =Total number of text messages sent/Total number of days

Mean number of text messages per day: 49 / 7

= 7

Therefore, 7 is the  mean number of text messages that Julianna sent per day.

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Use julianna’s text message data to answer the questions.

Text messages sent:

Sun: 13 Mon: 0 tues: 4 wed: 4 thurs: 5 fri: 6 sat: 17

1. What was the mean number of text messages that julianna sent per day ?

A. 4

B.6

C.8

D.7

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

The expression that shows the result of that transformation are:

3f(x) = 3.4ˣ

f(3x)=4³ˣ

f(x+3)=4ˣ⁺³

f(x)+3=4ˣ+3.

The given function is f(x) =4ˣ.

We have to find the transformations applied to the function f(x).

Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.

f(x) =4ˣ

We have to find 3f(x), f(3x), f(x+3) and f(x)+3.

3f(x) = 3.4ˣ

f(3x)=4³ˣ

f(x+3)=4ˣ⁺³

f(x)+3=4ˣ+3.

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Yes, the product of X and Y, that is X × Y is a set.

Given that, the product X×Y is a set because X×Y⊂PP(X∪Y).

A set is defined as a collection of elements or members, and X × Y meets this criteria as it is a collection of ordered pairs of elements from X and Y.

We can also prove this using set theory. The expression X × Y⊂PP(X∪Y) means that the set X × Y is a subset of the power set of the union of X and Y.

The power set of a set A is a set of all subsets of A, which means that PP(X∪Y) includes all of the possible combinations of the elements from X and Y.

So, the fact that X × Y⊂PP(X∪Y) proves that it is a subset of a set and thus is a set itself.

Yes, the product of X and Y, that is X × Y is a set.

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Answer: 10 cheeseburgers

Step-by-step explanation: 25/2.5=10

Answer:

10

Step-by-step explanation:

To determine the number of cheeseburgers you can get with $25, you can divide the total amount of money by the cost of each cheeseburger.

$25 ÷ $2.50 = 10

Therefore, with $25, you can get 10 cheeseburgers if each cheeseburger costs $2.50.

Answer:

Surface Area = 63.5 ft².

Step-by-step explanation:

Length: 3.5 ft

Width: 4.5 ft

Height: 2 ft.

Surface Area = 2(Area of Base) + (Perimeter of Base) × Height

       Area of Base = Length × Width

       Area of Base = 3.5 ft × 4.5 ft = 15.75 ft²

       Perimeter of Base = 2(Length) + 2(Width)

       Perimeter of Base = 2(3.5 ft) + 2(4.5 ft) = 7 ft + 9 ft = 16 ft

Substitute these values into the surface area formula:

Surface Area = 2(Area of Base) + (Perimeter of Base) × Height

Surface Area = 2(15.75 ft²) + (16 ft) × (2 ft)

Surface Area = 31.5 ft² + 32 ft²

Surface Area = 63.5 ft²

Therefore, the surface area of the given prism with dimensions 3.5 ft, 4.5 ft, and 2 ft is 63.5 ft².

The length of B'C' from the given quadrilateral A'B'C'D' is 3 units. Therefore, option D is the correct answer.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Here, AB = A'B' = 7 units

AD = A'D'= 6 units

DC = D'C'= 4 units

BC = B'C' = 3 units

Therefore, option D is the correct answer.

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Answer:

x = 36.1°

Step-by-step explanation:

In the Right-angled triangle, opposite side of angle x and adjacent side of angle x is given, and we have to find the angle x. To find angle x, we can use the trigonometry ratio 'tan x'.

           [tex]\sf Tan \ x = \dfrac{opposite \ side \ of \ \angle X}{adjacent \ side \ of \ \angle x}[/tex]

                     [tex]\sf = \dfrac{22}{30}\\\\ = 0.73[/tex]

                  [tex]x = arctan \ (0.73)[/tex]

                      = 36.13

                  x = 36.1°

Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two: , the raw score is relatively lower than the mean.

If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.

A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two:

If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.

To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.

In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.

By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.

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The standard deviation of the number of education majors in the sample is 0.3.

The standard deviation of the number of education majors in the sample is calculated as follows;

σ = √ [(N - n) x n(N - k) / ((N - 1) x N²)]

Where

The standard deviation of the number of education majors in the sample is calculated as;

σ = √[(200 - 30) x 30(200 - 60) / ((200 - 1) x 200²)]

= √[(170 x 30 x 140 / (199 x 40000)]

= √(714000 / 7960000)

= 0.3

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Answer:

The volume of the shipping box is 3434.6 in³ (to the nearest tenth).

The length of the longest item that will fit inside the shipping box is 26.8 inches (to the nearest tenth).

Step-by-step explanation:

The shipping box can be modelled as a cuboid.

A cuboid is a three-dimensional geometric shape with six rectangular faces and right angles between adjacent faces.

The volume of a cuboid can be calculated by multiplying its length (L), width (W), and height (H) together.

From the given diagram, the width of the cuboid is 16 inches and its height is 12 inches. Therefore, we need to find the measure of its length in order to calculate its volume.

As all sides of a cuboid have interior angles of 90°, and we have been given the face diagonal of the base (24 inches), we can use Pythagoras Theorem to calculate the length (L).

[tex]\begin{aligned}L^2+16^2&=24^2\\L^2+256&=576\\L^2&=320\\L&=\sqrt{320}\\L&=8\sqrt{5}\; \sf in\end{aligned}[/tex]

Substitute L = 8√5, W = 16 and H = 12 into the formula for the volume of a cuboid to calculate the volume of the shipping box:

[tex]\begin{aligned}\sf Volume&=\sf L \cdot W \cdot H\\&=8\sqrt{5} \cdot 16 \cdot 12\\&=128\sqrt{5} \cdot 12\\&=1526\sqrt{5}\\&=3434.60041...\\&=3434.6\; \sf in^3\end{aligned}[/tex]

Therefore, the volume of the shipping box is 3434.6 in³ to the nearest tenth.

[tex]\hrulefill[/tex]

In a cuboid, there are two types of diagonals: face diagonals and body diagonals.

The body diagonal of a cuboid is the longest line that can be drawn inside the cuboid. Therefore, to find the length of the longest item that will fit inside the shipping box, we need to calculate the body diagonal of the cuboid.

The formula for the body diagonal of a cuboid is:

[tex]\sf Body \;diagonal=\sqrt{L^2+W^2+H^2}[/tex]

Substitute L = 8√5, W = 16 and H = 12 into the formula to find the body diagonal of the cuboid (marked as a red dashed line on the given diagram):

[tex]\begin{aligned}\sf Body \;diagonal&=\sf \sqrt{L^2+W^2+H^2}\\&=\sqrt{(8\sqrt{5})^2+16^2+12^2\\&=\sqrt{320+256+144}\\&=\sqrt{720}\\&=26.8328157...\\&=26.8\; \sf in\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the length of the longest item that will fit inside the shipping box is 26.8 inches, to the nearest tenth.

The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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The probability of winning the jackpot with one ticket is P ( A ) = 1/34

Given data ,

To calculate the probability of winning the jackpot in the lottery, we need to determine the total number of possible outcomes (the sample space) and the number of favorable outcomes (winning outcomes).

Total number of possible outcomes:

For the white balls, there are 43 numbers to choose from, and we need to select 5 distinct numbers in any order. This can be calculated using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of options and r is the number of selections. In this case, we have 43 white balls and need to choose 5, so the number of possible outcomes for the white balls is:

C(43, 5) = 43! / (5! * (43 - 5)!) = 43! / (5! * 38!) = 43 * 42 * 41 * 40 * 39

For the gold ball, there are 34 numbers to choose from, and we need to select 1 number. So the number of possible outcomes for the gold ball is simply 34.

Therefore, the total number of possible outcomes is:

Total outcomes = (43 * 42 * 41 * 40 * 39) * 34

Number of favorable outcomes (winning outcomes):

To win the jackpot, we need to match all 5 distinct numbers from the white balls and the number on the gold ball. Since order doesn't matter for the white balls, we can use the combination formula again:

C(n, r) = n! / (r! * (n - r)!)

In this case, we have 43 white balls and need to choose 5, so the number of favorable outcomes for the white balls is:

C(43, 5) = 43! / (5! * (43 - 5)!) = 43 * 42 * 41 * 40 * 39

For the gold ball, there is only 1 winning number.

Therefore, the number of favorable outcomes is:

Favorable outcomes = (43 * 42 * 41 * 40 * 39) * 1

Probability of winning the jackpot:

The probability of winning the jackpot is the ratio of the number of favorable outcomes to the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes

Plugging in the values, we get:

Probability = [(43 * 42 * 41 * 40 * 39) * 1] / [(43 * 42 * 41 * 40 * 39) * 34]

Simplifying, we find:

Probability = 1 / 34

Hence , the probability of winning the jackpot with one ticket in this lottery is 1 in 34.

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

[tex]\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}[/tex]

The formulas for the area of a regular polygon and the area of a circle given their radii are:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Therefore, the area of the regular pentagon is:

[tex]\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}[/tex]

The area of the circumcircle is:

[tex]\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}[/tex]

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

[tex]\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}[/tex]

                                                 [tex]\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}[/tex]

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

16 liters of the 10% acid solution should be in the mixture.

Step-by-step explanation:

Let x represent the volume of the 10% acid solution to be added.

The volume of pure acid added would be (90 - x).

The equation to solve is: 0.1x + (90 - x) = 0.84(90)

Simplifying, we get: 0.1x + 90 - x = 75.6

Combining like terms, we have: -0.9x + 90 = 75.6

Subtracting 90 from both sides: -0.9x = -14.4

Dividing by -0.9: x = 16

Therefore, 16 liters of the 10% acid solution should be in the mixture.

The probability of the intersection P(A∩B) is 0

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 12

Intersection = 0

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For the intersection events, we have

P(A∩B) = 0/36

Evaluate

P(A∩B) = 0

Hence, the probability of P(A∩B) is 0

Read more about probability at

brainly.com/question/251701

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