Which expressions are equivalent to 6\cdot6\cdot6\cdot6\cdot66⋅6⋅6⋅6⋅66, dot, 6, dot, 6, dot, 6, dot, 6 ?

Answers

Answer 1

The expressions equivalent to 6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 are 1296\cdot396\cdot2376 and 839808\cdot36.

Find out which expression is equivalent to the given expressions?

We can use the associative property of multiplication to group the factors in different ways while preserving their product. For example, we can group the first four 6's together and then multiply by the remaining 6 and 66:

6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 = (6\cdot6\cdot6\cdot6)\cdot(6\cdot66)\cdot(6\cdot6\cdot66)

= 1296\cdot396\cdot2376

Alternatively, we can group the last two 6's together and then multiply by the remaining factors:

6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 = (6\cdot6\cdot6\cdot6\cdot66)\cdot(6\cdot6)

= 839808\cdot36 is the equivalent expression.

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Related Questions

Mr. Smith invested $2500 in a savings account that earns 3% interest compounded


annually. Find the following:


1. Is this exponential growth or exponential decay?


2. Domain


3. Range


4. Y-intercept


5. Function Rule

Answers

The 99% confidence interval for the population mean is between 39.18 and 62.82, assuming that the population is normally distributed.

How to find the range of the population?

To construct a confidence interval for the population mean, we need to make certain assumptions about the distribution of the sample data and the population. In this case, we assume that the population is normally distributed, the sample size is small (less than 30), and the standard deviation of the population is unknown but can be estimated from the sample data.

Using these assumptions, we can calculate the confidence interval as:

CI = X ± tα/2 * (s/√n)

Where X is the sample mean, tα/2 is the critical value of the t-distribution with degrees of freedom (n-1) and a confidence level of 99%, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the provided data, we get:

CI = 51 ± 2.898 * (17/√18)

CI = (39.18, 62.82)

Therefore, with 99% confidence, we can estimate that the population mean is between 39.18 and 62.82 based on the provided data.

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Estimate the radius of the object. Round to the nearest hundredth if necessary.


C = 8. 9 mm


radius: about


mm

Answers

The estimated radius of the object is about 1.42 mm.

The given information is that the circumference( C) of the object is8.9 mm.

We know that the formula for the circumference of a circle is given by  

C =  2πr  

where r is the compass of the circle.  

To estimate the compass, we can rearrange the formula as

  r =  C/ 2π  

Substituting the given value of C, we get

  r = 8.9/ 2π

we can  estimate this expression to get  

r ≈1.42 mm( rounded to two decimal places)

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Two days after he bought a speedometer for his bicycle; Lance brought it back (0 the Yellow Jersey Bike Shop. FThele problemn with this speedomeler;' Ba Lance complained to the clerk "Yesterday [ cycled the 22-mile Rogadzo Road Trail in 70 minutes and nOt once did the speedometer read above [5 miles per hour"" Yeah?" responded the clerk " What' $ the problem?" To explain Lance's complaint, first compute his average velocity: (Use decimal notation. Give your answer tO two decimal places ) average velocity: DNE mileshcur Incorrecr

Answers

Therefore, Lance's average velocity was 15.43 miles per hour.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

We can compute Lance's average velocity by dividing the total distance he cycled by the time it took him, and then converting the units to miles per hour.

Total distance: 22 miles

Time: 70 minutes = 70/60 hours

= 7/6 hours

Average velocity = Total distance / Time

= 22 / (7/6)

= 15.43 miles per hour (rounded to two decimal places)

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Question 6 < - Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.16). L(x) = In(1.16) Question Help: Video Message instructor Submit Question Question 5 Use linear ap

Answers

The linear approximation of f(x) = ln(x) at x = 1 is L(x) = x - 1. Using this approximation, we can estimate ln(1.16) to be approximately 0.16.

The formula for the linear approximation of a function f(x) at a point x = a is given by L(x) = f(a) + f'(a)(x - a), where f'(a) is the derivative of f(x) evaluated at x = a.

In this case, f(x) = ln(x), so f'(x) = 1/x by the derivative of natural logarithm.

We are asked to find the linear approximation of f(x) = ln(x) at x = 1, so a = 1 in the formula.

Plugging in the values, we get L(x) = ln(1) + 1( x - 1) = x - 1.

Now, we can use this linear approximation L(x) = x - 1 to estimate ln(1.16) by plugging in x = 1.16, as given in the question.

L(1.16) = 1.16 - 1 = 0.16, which is our estimated value for ln(1.16) using the linear approximation.

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dylan used a styrofoam cone to make a floral arrangement. the cone had a radius of 4.5 inches and a height of 6 inches. what is the volume of this cone? (round your answer to the nearest tenth.)

Answers

The volume of this cone is approximately 127.2 cubic inches

Hi! To calculate the volume of the Styrofoam cone used by Dylan to make a floral arrangement, we can use the formula for the volume of a cone: V = (1/3)πr²h. The cone had a radius of 4.5 inches and a height of 6 inches.

Substituting these values into the formula, we have:
V = (1/3)π(4.5)²(6)

V ≈ 127.2 cubic inches (rounded to the nearest tenth).

So, the volume of this cone is approximately 127.2 cubic inches.

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The number of coyotes found in certain state counties is decreasing at a rate of 4. 5% per year. A wildlife biologist recently counted 100 coyotes in one tri-county area. The biologist uses a function to model the population over time and then uses this model to predict the coyote population. Which function model did the biologist correctly use to predict when the population would be fewer than 50 in this tri-county area?

Answers

The biologist predicts that the population would be fewer than 50 in approximately 30 years from the initial count.

The biologist likely used the exponential decay function to model the coyote population over time. This function takes the form:

P(t) = P0 * (1 - r)^t

Where:
P(t) is the population at time t,
P0 is the initial population (100 coyotes),
r is the rate of decrease (0.045 or 4.5%),
t is the time in years.

To predict when the population would be fewer than 50, the biologist would solve the equation:

50 = 100 * (1 - 0.045)^t

t = 30

This equation can be used to find the value of t, which represents the number of years it takes for the population to decrease to fewer than 50 coyotes in the tri-county area, which is 30 years.

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Leo is going to use a random number generator

400

400400 times. Each time he uses it, he will get a

1

,

2

,

3

,

4

,

1,2,3,4,1, comma, 2, comma, 3, comma, 4, comma or

5

55.

Answers

It sounds like Leo will be using a specific type of random number generator that produces only five possible outcomes: 1, 2, 3, 4, or 555. It seems that the generator produces a repeating pattern of four numbers (1, 2, 3, 4) followed by a fifth number (555).

If Leo uses this generator 400400400 times, then he will get 100100100 repetitions of the pattern. This means that he will get 100100100 x 4 = 400400400 numbers 1, 2, 3, or 4, and 100100100 occurrences of the number 555.

It is important to note that this type of random number generator is not truly random, as it is not generating numbers with equal probability. Instead, it is producing a predetermined sequence of numbers. This means that if Leo knows the pattern, he could predict the next number that will be generated with certainty.

In general, it is important to use truly random number generators for many applications, such as cryptography or scientific simulations, where the results need to be unpredictable and unbiased.

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the chance of rain on a random day in May in Gwinnett is about 30%. Using this empirical probability, what would you estimate the probability of having NO rain for an entire week (7 days)?

Answers

The probability of having NO rain for an entire week (7 days) is 0.9998

Estimating the probability of having no rain

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

P(Rain) = 30%

Given that the number of days is

n = 7

The probability of having no rain for an entire week is calculated as

P = 1 - P(Rain)ⁿ

Where

n = 7

Substitute the known values in the above equation, so, we have the following representation

P = 1 - (30%)⁷

Evaluate

P = 0.9998

Hence, the probability is 0.9998

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Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches

Answers

The radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches is approximately 36.7 inches.

To find the radius of an eyebrow window, we first need to understand its shape. An eyebrow window is a type of arched window that has a curved shape similar to that of an eyebrow. The shape of an eyebrow window is created by a combination of a circular arc and a straight line.

To find the radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches, we need to use some geometry formulas. The height of the eyebrow window represents the height of the circular arc, and the width represents the diameter of the circle.

The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. To find the diameter, we divide the width by pi (3.14). So, the diameter is 62.8/3.14 = 20 inches.

The height of the circular arc is half of the width, which is 18.5/2 = 9.25 inches. To find the radius, we use the formula for the height of a circular arc, h = r(1-cos(a/2)), where h is the height, r is the radius, and a is the angle of the arc.

The angle of the arc can be found using trigonometry. The sine of half the angle is equal to the height divided by the radius. So, sin(a/2) = h/r. Solving for a, we get a = 2arcsin(h/r).

Plugging in the values, we get a = 2arcsin(9.25/r). To find the radius, we solve for r using a calculator or algebra. The radius is approximately 36.7 inches.

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solve for b

18, b, 27, 22
(round your answer to the nearest tenth
b=[?]

Answers

The length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.

What is the sine rule

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

18/sin22° = b/sin27°

b = (18 × sin27°)/sin22° {cross multiplication}

b = 21.8144

Therefore, the length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.

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Please help and explain if possibile

Answers

The missing lengths of triangles are 5in, 5mi, 13.9km,13.3mi respectively.

What is triangle?

A triangle is a closed, two-dimensional geometric figure with three straight sides and three angles.

What is Pythagorean theorem?

The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the three sides of a right-angled triangle.

According to given information:

Using the Pythagorean theorem [tex](a^2 + b^2 = c^2)[/tex], we can solve for the missing side in each triangle.

Triangle 1:

[tex]a = 12 in\\\\c = 13 in\\\\a^2 + b^2 = c^2\\\\12^2 + b^2 = 13^2\\\\144 + b^2 = 169\\\\b^2 = 25\\\\b = \sqrt{(25)}\\\\b = 5 in[/tex]

Therefore, the length of the missing side in Triangle 1 is 5 in.

Triangle 2:

[tex]a = 4 mi\\\\b = 3 mi\\\\c = x\\\\a^2 + b^2 = c^2\\\\4^2 + 3^2 = x^2\\\\16 + 9 = x^2\\\\25 = x^2\\\\x = \sqrt{(25)}\\\\x = 5 mi[/tex]

Therefore, the length of the hypotenuse in Triangle 2 is 5 mi.

Triangle 3:

[tex]a = x\\\\b = 11.9 km\\\\c = 14.7 km\\\\a^2 + b^2 = c^2\\\\x^2 + 11.9^2 = 14.7^2\\\\x^2 = 14.7^2 - 11.9^2\\\\x^2 = 192.36\\\\x = \sqrt{(192.36)}\\\\x = 13.9 km[/tex]

Therefore, the length of the height in Triangle 3 is 13.9 km.

Triangle 4:

[tex]a = x\\\\b = 6.3 mi\\\\c = 15.4 mi\\\\a^2 + b^2 = c^2\\\\x^2 + 6.3^2 = 15.4^2\\\\x^2 = 15.4^2 - 6.3^2\\\\x^2 = 178.09\\\\x = \sqrt{(178.09)}\\\\x = 13.3 mi[/tex]

Therefore, the length of the height in Triangle 4 is 13.3 mi.

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Boris needs to read 2 novels each month.let n be the number of novels boris needs to read in m months.write an equation relating n to m. then use this equation to find the number of novels boris needs to read in 17 months.equation:number of novels in 17 months: i novels

Answers

Solving the equation, Boris needs to read 34 novels in 17 months.

Given that Boris needs to read 2 novels each month.

To relate the number of novels Boris needs to read (n) to the number of months he has to read them (m), we can use the equation:
n = 2m

This equation states that the number of novels (n) is equal to two times the number of months (m) since Boris needs to read 2 novels each month.

Now, to find the number of novels Boris needs to read in 17 months, we can substitute m = 17 into the equation:
n = 2m
n = 2(17)
n = 34

Therefore, Boris needs to read 34 novels in 17 months to meet his goal of reading 2 novels each month.


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CD is a perpendicular bisector of chord AB and a chord through CD passes through the center of a circle. Find the diameter of the wheel.



The figure shows a circle. Points A, C, B, E lie on the circle. Chords A B and C E intersect at point D. The length of segment A B is 12 inches. The length of segment C D is 4 inches.




715 in.



10 in.



1425 in.




1215 in.



Need Help ASAP please!!!

Answers

We know that the diameter of the wheel is 1215 inches

Since CD is a perpendicular bisector of AB, it means that CD passes through the center of the circle. Let O be the center of the circle. Then OD is the radius of the circle.

Since chord CE passes through the center O, it is a diameter of the circle. Therefore, CE = 2OD.

Let's use the intersecting chords theorem to find OD.

According to the intersecting chords theorem,

AC * CB = EC * CD

We know that AC = CB (since they are radii of the same circle) and CD = 4 inches. We also know that AB = 12 inches. Let's call the length of segment AE x. Then the length of segment EB is 12 - x.

So we have:

x * (12 - x) = EC * 4

Simplifying:

12x - x^2 = 4EC

Rearranging:

EC = 3x - x^2/4

Now let's use the intersecting chords theorem again, but this time for chords AB and CD:

AC * CB = AD * DB

We know that AC = CB and AB = 12 inches. Let's call the length of segment AD y. Then the length of segment DB is 12 - y.

So we have:

x^2 = y * (12 - y)

Simplifying:

y^2 - 12y + x^2 = 0

Using the quadratic formula:

y = (12 ± sqrt(144 - 4x^2))/2

We can discard the negative solution (since y is the length of a segment, it cannot be negative), so:

y = 6 + sqrt(36 - x^2)

Now let's use the fact that CD is a perpendicular bisector of AB to find x.

Since CD is a perpendicular bisector of AB, it divides AB into two segments of equal length. Therefore,

AD = DB = 6

Using the Pythagorean theorem in triangle ACD:

AC^2 + CD^2 = AD^2

Substituting the values we know:

x^2 + 4^2 = 6^2

Solving for x:

x = sqrt(20)

Now we can find EC:

EC = 3x - x^2/4

Substituting x:

EC = 3sqrt(20) - 5

Finally, we can find OD:

AC * CB = EC * CD

Substituting the values we know:

(2OD)^2 = (3sqrt(20) - 5) * 4

Simplifying:

OD^2 = 12sqrt(20) - 20

OD = sqrt(12sqrt(20) - 20)

We are asked to find the diameter of the circle, which is twice the radius:

Diameter = 2OD = 2sqrt(12sqrt(20) - 20)

This is approximately equal to 1215 inches.

So the answer is:

The diameter of the wheel is 1215 inches.

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The dotted line is the perpendicular bisector of side AB. The distance between points E and A is 7 units. What is the distance between points E and B? Explain or show your reasoning

Answers

The distance between points E and B is (2/3)*AB, or (2/3)*(7+x) units.

Since the dotted line is the perpendicular bisector of side AB, it means that it cuts the line AB into two equal halves. Thus, the distance between points E and the dotted line is equal to the distance between point A and the dotted line.

We know that the distance between points E and A is 7 units, and since the dotted line bisects AB, the distance between point A and the dotted line is equal to the distance between point B and the dotted line. Let's call this distance 'x'.

Therefore, we have two equal distances (7 units and 'x') that add up to the length of AB. This means that:

AB = 7 units + x

However, we also know that the dotted line is the perpendicular bisector of AB, meaning that it forms right angles with both A and B. This creates two right-angled triangles, AED and BED, where DE is the perpendicular line from point E to AB.

Using Pythagoras' theorem, we can find the length of DE in terms of 'x':

(DE)² + (AE)² = (AD)²

(DE)² + (7)² = (AB/2)²

(DE)² + 49 = (AB²)/4

(DE)² = (AB²)/4 - 49

(DE)² = (AB² - 196)/4

(DE)² = (x²)/4

DE = x/2

Therefore, the distance between points E and B is equal to the length of DE plus the distance between point B and the dotted line, which is also equal to 'x'. Therefore, the distance between points E and B is:

EB = (x/2) + x = 1.5x

We can substitute this into the equation we found earlier:

AB = 7 units + x

AB = 7 units + (2/3)*EB

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prove that the following triangles are congurent

Answers

Answer:

Step-by-step explanation:

Congruent triangles are triangles that are the same shape and same size.

So if they look the same and have the same dimension like area and perimeter then they are congruent.

Name
Chapter
5
1.On a calendar, each day is represented by a rectangle. To keep track of the date, you cross off the
previous day by connecting one pair of opposite corners of the rectangle, as shown.
10
E 177
11
F18
12
b. List the five triangle congruence theorems.
G10
a. Classify AABE by its sides and by measuring its angles. Explain your reasoning.
D
Date
c.For each of the triangle congruence theorems you listed in part (b), prove that AFBC = ACGF
using that theorem. (You will need to write five different proofs.)

Answers

The triangle theorems will be:

Side-Side-Side (SSS) Congruence Theorem:Side-Angle-Side (SAS) Congruence Theorem:Angle-Side-Angle (ASA) Congruence Theorem:Hypotenuse-Leg (HL) Congruence Theorem:Angle-Angle-Side (AAS) Congruence Theorem

How to explain the theorem

Side-Side-Side (SSS) Congruence Theorem: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.

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Emir earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded monthly. After 9 years, there is $400. 00 in the account. How much did Emir earn doing odd jobs?

Round your answer to the nearest cent

Answers

Emir earned approximately $207.05 doing odd jobs.

Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:

x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05

Therefore, Emir earned approximately $207.05 doing odd jobs.

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What is the variance of the following set of data?


4, 44, 404, 244, 4, 74, 84, 64

Answers

The variance of the given data set is 18603.39.

To find the variance of the given data set {4, 44, 404, 244, 4, 74, 84, 64}, follow these steps:

Step 1: First, we need to find the mean of the data set:

Mean = (4 + 44 + 404 + 244 + 4 + 74 + 84 + 64) / 8 = 120.5

Step 2: Next, we calculate the deviation of each data point from the mean:

(4 - 120.5) = -116.5

(44 - 120.5) = -76.5

(404 - 120.5) = 283.5

(244 - 120.5) = 123.5

(4 - 120.5) = -116.5

(74 - 120.5) = -46.5

(84 - 120.5) = -36.5

(64 - 120.5) = -56.5

Step 3: Now, we square each deviation:

[tex](-116.5)^2 = 13556.25\\(-76.5)^2 = 5852.25\\(283.5)^2 = 80322.25\\(123.5)^2 = 15252.25\\(-116.5)^2 = 13556.25\\(-46.5)^2 = 2162.25 \\(-36.5)^2 = 1332.25\\(-56.5)^2 = 3192.25[/tex](-116.5)^2 = 13556.25

Step 4: We add up all the squared deviations:

13556.25 + 5852.25 + 80322.25 + 15252.25 + 13556.25 + 2162.25 + 1332.25 + 3192.25 = 130223.75

Step 5: We divide the sum of the squared deviations by the number of data points minus 1 to get the variance:

Variance = 130223.75 / 7 = 18603.39 (rounded to two decimal places)

Therefore, the variance of the data set is 18603.39.

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Can someone help answers this! Remember to Fill in the Drop Boxes

Answers

The line y=10x will in this instance pass through most of the data points, demonstrating that it is a good fit for the data.

A good line of fit should travel across the greatest number of data points and exhibit a positive connection.

What exactly is a scatter plot?

A relationship between two variables in which rising values of one cause rising values of the other. On a scatter plot, it is shown as a positive slope.

The line y=10x will in this instance pass through most of the data points, demonstrating that it is a good fit for the data.

The line will be favourably sloped, so as the duration of an accessible bike rental increases, so does the total cost charged.

The scatterplot confirms this, proving that the line y=10x is a good match for the data.  

This indicates that the data points are nearly aligned with the line but not exactly so.

A good line of fit should travel across the greatest number of data points and exhibit a positive connection.

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If (arc)mEA=112* and m

Answers

If angle of arc EA is 112 degrees then value of arc IV is 36 degrees by  outside angles theorem

Given that Arc EA measure is One hundred twelve degrees

By Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs

(112-x)/2=38

112-x=38×2

112-x=76

112-76=x

36 degrees = angle IV or x

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Use the Chain Rule to find Oz/as and Oz/ot. sin(e) cos(6), = st*, Q = st дz as az at 1 x

Answers

the Chain Rule to find Oz/as and Oz/ot for the expression sin(e) cos(6), we first need to break it down into its component parts.

Let u = sin(e) and v = cos(6), so that our expression becomes u*v.

Now we can find the partial derivative of Oz/as by using the Chain Rule:

Oz/as = (dOz/du) * (du/as) + (dOz/dv) * (dv/as)

Since Oz = st*, we have dOz/du = st and dOz/dv = t*, so we can substitute those values in:

Oz/as = (st) * (dcos(e)/das) + (t*) * (-sin(6)/das)

To simplify this expression, we need to find the partial derivative of u and v with respect to as:

du/as = (dcos(e)/das)

dv/as = (-sin(6)/das)

Substituting those values back into our original expression for Oz/as, we get:

Oz/as = st * du/as + t* * dv/as

Oz/as = st * (dcos(e)/das) + t* * (-sin(6)/das)

Finally, we can simplify this expression by factoring out the common factor of das:

Oz/as = (st * dcos(e) - t* * sin(6)) / das

To find Oz/ot, we can follow the same steps but with respect to ot instead of as:

Oz/ot = (dOz/du) * (du/ot) + (dOz/dv) * (dv/ot)

Since Oz = st*, we have dOz/du = st and dOz/dv = t*, so we can substitute those values in:

Oz/ot = (st) * (-sin(e)/dot) + (t*) * (-6sin(6)/dot)

To simplify this expression, we need to find the partial derivative of u and v with respect to ot:

du/ot = (-sin(e)/dot)

dv/ot = (-6sin(6)/dot)

Substituting those values back into our original expression for Oz/ot, we get:

Oz/ot = st * du/ot + t* * dv/ot

Oz/ot = st * (-sin(e)/dot) + t* * (-6sin(6)/dot)

Finally, we can simplify this expression by factoring out the common factor of dot:

Oz/ot = (-sin(e)st - 6sin(6)t*) / dot
To find ∂z/∂s and ∂z/∂t using the Chain Rule, let's first define the given functions:

1. z = st (where s and t are variables)
2. s = sin(e) (where e is a variable)
3. t = cos(θ) (where θ is a variable)

Now, apply the Chain Rule to find ∂z/∂s and ∂z/∂t:

Chain Rule states: ∂z/∂x = (∂z/∂s) * (∂s/∂x) + (∂z/∂t) * (∂t/∂x)

1. Find ∂z/∂s:
Since z = st, ∂z/∂s = t

2. Find ∂z/∂t:
Since z = st, ∂z/∂t = s

Now we have ∂z/∂s and ∂z/∂t. You can use these expressions to find the desired derivatives by substituting the given functions for s and t.

∂z/∂s = t = cos(θ)
∂z/∂t = s = sin(e)

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Angle BCD is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 13 centimeters. What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box.

Answers

Answer:12.4

Step-by-step explanation:

18^2-13^2=155
Square root of 155 to the nearest tenth is 12.4

Name:


Date:


Lesson 02. 05: Module Two Project-Based Assessment


Printable Assessment Module Two Project Based Assessment


Module Two Project-Based Assessment


Part 1


The table shows the measurements of shooting stars that were measured. Use the table


to complete the activities below.


Shooting star length


(in feet)


Number


10


2


8


10


6


8


6


10


7


8


10





4


1. Compare the sizes. Think about the number of Xs that would appear on the line plot.


Write the shooting star lengths in the correct box.


Fewer than 5 Xs


More than 5 Xs


COM


10


2. Complete the line plot for the given set of data.


Lengths of Shooting Stars


7


O


2


Measurement in feet

Answers

5 or more Xs

How to complete the line plot?

To complete the activities based on the given data:

Compare the sizes: By looking at the shooting star lengths, we can determine the number of Xs that would appear on the line plot. The shooting star lengths "10" and "8" appear more than 5 times, so they would be placed in the "More than 5 Xs" box. The shooting star lengths "6" and "4" appear fewer than 5 times, so they would be placed in the "Fewer than 5 Xs" box.

Complete the line plot: Using the given set of data, we can create a line plot to represent the lengths of shooting stars. We mark each measurement on the number line and place an X above the corresponding value.

The line plot would have an X above the number 10, 8, 6, and 4, each representing the occurrence of shooting stars with those lengths.

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Please help with this​

Answers

a) The table is completed as follows:

x = -5, y = -3.x = 0, y = 2.x = 3, y = 5.

b) The graph is given by the image presented at the end of the answer.

How to calculate the numeric value of a function or of an expression?

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

y=  x + 2.

Hence the numeric values of the function are given as follows:

x = -5, y = -5 + 2 = -3.x = 0, y = 0 + 2 = 2.x = 3, y = 3 + 2 = 5.

Then the graph is constructed connecting two of these points and tracing a line through them.

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Issac wants to save up some money to buy a new smartphone, so he babysits on the weekends. There is a proportional relationship between the time Oscar spends babysitting(in hours) , z, and the amount of money he earns babysitting(in dollars) , y. What is the constant of proportionality? Write your answer as a whole number or decimal

Answers

The constant of proportionality represents the rate at which Issac earns money while babysitting and can be found by dividing the amount of money he earns by the time spent babysitting.

Let's say that Issac earns $10 per hour of babysitting. Then, the constant of proportionality would be:

$10 per hour = $10/1 hour = 10

Therefore, the constant of proportionality is 10, which means that Issac earns $10 for every hour of babysitting. This relationship is an example of proportionality because the amount of money earned is directly proportional to the time spent babysitting. As Issac spends more time babysitting, he will earn more money in a proportional relationship.

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100-3(4. 25)-13-4(2. 99) SOMEONE PLSS HELP MEE THIS IS DIE TMRW!!

Answers

The simplified expression of 100-3(4. 25)-13-4(2. 99) is 48.29.

What is PEMDAS?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.

To simplify the expression 100-3(4.25)-13-4(2.99), you can follow the order of operations (PEMDAS) which is:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using this order, you can simplify the expression as follows:

100 - 3(4.25) - 13 - 4(2.99)

= 100 - 12.75 - 13 - 11.96 // multiply 3 and 4 with their respective numbers

= 62.29 - 13 - 11.96 // perform subtraction within parentheses

= 48.29 // perform final subtraction

Therefore, the simplified expression is 48.29.

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Two straight lines cross at a point.
b+c+d=280°
Work out the sizes of angles a, b, c and d.
a
b
d.
C
Not drawn accurately

Answers

Answer:

a = c = 80°b = d = 100°

Step-by-step explanation:

You want the measures of the angles where lines cross if the sum of three of them is 280°.

Linear pair

Angle b and c form a linear pair, so ...

  b + c = 180°

Substituting that into the given equation, we have ...

  b + c + d = 280°

  180° + d = 280°

  d = 100°

Vertical angles

Angles in this figure that do not share a side are vertical angles, hence congruent.

  b = d = 100°

  c = 180° -b = 180° -100° = 80° . . . . using the linear pair relation

  a = c = 80°

For the cost function C(x) = 6000 + 242 + 0.005.03 find: A) The production level that will minimize the average cost. B) The minimal average cost.

Answers

To find the production level that will minimize the average cost, we need to differentiate the cost function with respect to x and set it equal to zero. So:

C'(x) = 0.005x^2 + 242x + 6000
0 = 0.005x^2 + 242x + 6000
Using the quadratic formula, we get:
x = (-242 ± sqrt(242^2 - 4(0.005)(6000))) / (2(0.005))
x = (-242 ± sqrt(146416)) / 0.01
x = (-242 ± 382) / 0.01
x = -14,000 or 27,000

Since the production level cannot be negative, we can discard the negative solution and conclude that the production level that will minimize the average cost is 27,000 units.

To find the minimal average cost, we need to plug the production level back into the cost function and divide by the production level. So:

C(27,000) = 6000 + 242(27,000) + 0.005(27,000)^2
C(27,000) = 6,594,000
Average cost = C(27,000) / 27,000
Average cost = 6,594,000 / 27,000
Average cost ≈ 244.22

Therefore, the minimal average cost is approximately $244.22.
To answer your question, first, let's correct the cost function, which should be in the form of C(x) = Fixed cost + Variable cost. Assuming it is C(x) = 6000 + 242x + 0.005x^2.

A) To find the production level that will minimize the average cost, we need to first determine the average cost function, which is AC(x) = C(x)/x. So, AC(x) = (6000 + 242x + 0.005x^2)/x.

Now, find the first derivative of AC(x) concerning x, and set it equal to zero to find the minimum point:

d(AC(x))/dx = 0

The first derivative of AC(x) is:

d(AC(x))/dx = (242 + 0.010x - 6000/x^2)

Setting this to zero and solving for x will give us the production level that minimizes the average cost:

242 + 0.010x - 6000/x^2 = 0

Now, you can solve for x using numerical methods, such as Newton-Raphson or others. After solving for x, you will get the production level that minimizes the average cost.

B) To find the minimal average cost, plug the production level x you found in part A into the average cost function, AC(x):

Minimal Average Cost = AC(production level)

This will give you the minimal average cost for the given cost function.

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roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax what was the total for rogers purchased

Answers

After the discount and the tax, the amount that Roger pays is $45.41

How to find the final price?

We know that Roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax, then the total cost before the discount and tax is:

C = 12.00 + 34.50 = 46.50

Now we apply the discount and the tax (as factors in a product) to get:

C' = 46.50*(1 - 0.1)*(1 + 0.085) = 45.41

That is the amouint that Roger pays for the two items.

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A ring-shaped region is shown below.
Its inner radius is 9m, and its outer radius is 13m.
Find the area of the shaded region.
Use 3.14 for Pie. Do not round your answer.

Answers

The area of the ring-shaped region with radii of 9m and 13m is approximately 276.32 square meters.

What is Area?

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

What is Perimeter?

The perimeter of a shape is defined as the total distance surrounding the shape. It is the length of any two-dimensional geometric shape's outline or boundary.

According to the given information:

The given shape is a two concentric circles with radii of 9m and 13m, we can calculate the area of this region using the formula for the area of a circle:

Area of shaded region = Area of outer circle - Area of inner circle

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

Area of inner circle = π(9)^2 = 81π

Area of outer circle = π(13)^2 = 169π

Area of shaded region = 169π - 81π = 88π

Using the value of π = 3.14, we get:

Area of shaded region = 88π = 88(3.14) = 276.32 square meters (rounded to two decimal places)

Therefore, the area of the ring shaped region with radii of 9m and 13m is approximately 276.32 square meters.

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