What would the polar coordinate graph of r^2=81cos2θ like?

The exponents a and b in the simplified expression are:

a = 1

b = 7

Remember the rules for exponents:

[tex]a^x*a^y = a^{x + y}\\\\a^x/a^y = a^{x - y}\\\\(a^x)^y = a^{x*y}[/tex]

Now we need to use these rules to simplify our expression:

[tex]\frac{x^2(y^3)^4}{x*y^5}[/tex]

We can rewrite that as:

[tex]\frac{x^2(y^3)^4}{x*y^5} = \frac{x^2}{x} *\frac{(y^3)^4}{y^5} = x^{2 - 1}\frac{y^{3*4}}{y^5} \\\\= x*y^{12 - 5} = x*y^7[/tex]

Then the values of a and b are:

a = 1

b = 7

Learn more about exponents at:

https://brainly.com/question/847241

#SPJ1

[tex]\text{t = total}[/tex]

[tex]\text{equation:} \ t = 25x + 50[/tex]

[tex]m=25[/tex]

[tex]\text{The slope is} \ \bold{25}[/tex]

The width of the rectangle is 6 centimeters

We know that the area of a rectangle is given by the formula

A = L x W

where A is the area, L is the length, and W is the width.

In this problem, we are given the length of the rectangle (L) as 9 centimeters and the area (A) as 54 square centimeters. We can use these values to find the width (W) of the rectangle.

We can start by substituting the given values into the formula

54 = 9 x W

Next, we can solve for the width (W) by dividing both sides of the equation by 9

54 / 9 = W

Simplifying the left-hand side, we get

W = 6 centimeter

Learn more about area here

brainly.com/question/20693059

#SPJ4

I have solved the question in general, as the given question is incomplete.

The complete question is:

The length of a rectangle with area 54 square centimeters is 9 centimeters. What is the width of the rectangle

Annabelle supplied 121.35 pounds of shrimp, Curly Q supplied 96.9 pounds of shrimp, and Slojoe supplied 72.81 pounds of shrimp.

The three shrimp boats, Annabelle, Curly Q, and Slojoe, collectively supplied 242.7 pounds of shrimp to Hudson's, 217 pounds to Captain J's, and 159.3 pounds to Mainstreet.

Annabelle supplied 50% of its catch to Hudson's, 20% to Captain J's, and 30% to Mainstreet. Therefore, Annabelle supplied: (242.7 x 0.5) = 121.35 pounds of shrimp to Hudson's, (217 x 0.2) = 43.4 pounds of shrimp to Captain J's and (159.3 x 0.3) = 47.79 pounds of shrimp to Mainstreet.

In total, Annabelle supplied = 121.35 + 43.4 + 47.79 = 212.54

Curly Q supplied 40% of its catch to Hudson's, 40% to Captain J's, and 20% to Mainstreet. Therefore, Curly Q supplied (242.7 x 0.4) = 96.9 pounds of shrimp to Hudson's, (217 x 0.4) = 86.8 pounds of shrimp to Captain J's, and               (159.3 x 0.2) = 31.86 pounds of shrimp to Mainstreet.

In total, Curly Q supplied = 96.9 + 86.8 + 31.86 = 215.56

Slojoe supplied 30% of its catch to Hudson's, 40% to Captain J's, and 30% to Mainstreet. Therefore, Slojoe supplied (242.7 x 0.3) = 72.81 pounds of shrimp to Hudson's, (217 x 0.4) = 86.8 pounds of shrimp to Captain J's, and              (159.3 x 0.3) = 47.79 pounds of shrimp to Mainstreet.

In total, Slojoe supplied = 72.81 + 86.8 + 47.79 = 207.4

Know more about pounds here:

https://brainly.com/question/30400939

#SPJ11

Number of students at preschool are four-years-old in the program is 6

If 16 students are four-years-old, then the remaining students must be older than four. Let's call the number of older students "x". Then the total number of students is

16 + x

Now we know that 3/8 fraction of the total students attend the full-day program. So we can set up an equation

3/8 (16 + x) = number of students in full-day program

To solve for the number of four-year-old's in the program, we need to find 3/8 of the number of four-year-old's (16). We can do this by multiplying 16 by 3/8

16 x 3/8 = 6

Learn more about fraction here

brainly.com/question/29276116

#SPJ4

Answer:

x^2 + 7x - 18 = (x + 9)(x - 2)

The difference between length and width is x + 9 - (x - 2) = x + 9 - x + 2 = 11.

the answer is (D) 3/10. we know that the arrow landed on the red section 15 times out of 50 total spins. So we can find by  the experimental probability of landing on the red section

what is probability ?

Probability is a measure of the likelihood or chance that a particular event will occur. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen. A probability of 0.5 means that the event is equally likely to occur or not occur.

In the given question,

The experimental probability of an event is defined as the ratio of the number of times the event occurred to the total number of trials. In this case, we want to find the experimental probability of landing on the red section.

From the given data, we know that the arrow landed on the red section 15 times out of 50 total spins. So the experimental probability of landing on the red section is:

P(Red) = Number of red spins / Total number of spins

= 15/50

= 3/10

Therefore, the answer is (D) 3/10.

To know more about  probability , visit:

https://brainly.com/question/30034780

#SPJ1

Answer:

4.85 ft

Step-by-step explanation:

Answer:

What is 16.00 to 1 decimal place?" is the same as asking, "What is 16.00 rounded to one decimal point?" or "How to round 16.00 to one decimal place."

The main point (pun intended), is that you want to round 16.00 to one digit or place after the decimal point. Thus, we want to eliminate the last digit in 16.00. To eliminate the last digit, we use the following One Decimal Place rules to get the answer:

One Decimal Place Rule #1: If the last digit in 16.00 is less than 5, then remove the last digit.

One Decimal Place Rule #2: If the last digit in 16.00 is 5 or more and the second to the last digit in 16.00 is less than 9, then remove the last digit and add 1 to the second to the last digit.

One Decimal Place Rule #3: If the last digit in 16.00 is 5 or more and the second to the last digit in 16.00 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.

When rounding 16.00 to one decimal place we use One Decimal Place Rule #1. Therefore, the answer to "What is 16.00 rounded to 1 decimal place?" is:

Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is 8.

The binomial distribution is a type of probability distribution that computes the probability of a given number of successes in a fixed number of independent tests with two possible results: success and failure. Furthermore, the following are the features of the binomial distribution:

The trial is identical, with two possible outcomes: success and failure.

The probability of success (p) and failure (q = 1 - p) remains constant throughout the trials.

All trials are independent of one another.

The formula for a standard deviation for binomial distribution is given by:

[tex]$\sqrt{npq}$$[/tex]

Where n is the sample size, p is the probability of success, and q is the probability of failure.

Therefore, given that the percentage of students planning to go to graduate school is 20%, the probability of success (p) is 0.2, and the probability of failure (q) is 0.8. The sample size (n) is 400.

Thus, the standard deviation can be calculated as follows:

[tex]$$\sqrt{npq} = \sqrt{400\times 0.2\times 0.8} \approx 8$$[/tex]

Therefore, the standard deviation of this binomial distribution is 8.

To know more about the "standard deviation": https://brainly.com/question/24298037

#SPJ11

The dimensions of the final flag and the number of pieces of construction paper it took would be 9 inches tall and 18 inches long.

Three (3) pieces of  9" x 12" construction paper are needed.

First, let's find out the dimensions of the flag. The flag is twice as long as it is tall. If the height of the flag is H, then the length L would be 2H.

Since there are three equally sized vertical bars, the length of the flag would be 3 times the width of the green bar:

L = 3(18 - a)

Now, we know that L = 2H. So,

2H = 3(18 - a)

Given that the construction paper is 9" x 12", we can try to create the flag with the minimum amount of overlap a. Since the height of the flag should be equal to the short side of the construction paper, H = 9 inches.

Now we can plug in the value of H in the equation we derived above:

2(9) = 3(18 - a)

18 = 54 - 3a

3a = 36

a = 12

Now we can calculate the dimensions of the final flag:

H = 9 inches

L = 2H = 2(9) = 18 inches

Find out more on dimensions of flags at https://brainly.com/question/30202139

#SPJ1

We use the symbol '[tex]\bar{x}[/tex]' to represent the mean arsenic level in the sample, and 'p' to represent the proportion of health issues in the sample.

The mean tells us about the average arsenic level in the sample, while the proportion tells us about the fraction or percentage of individuals in the sample who have health issues.

First, let's talk about the mean arsenic level in the sample. The mean is a measure of central tendency that tells us about the average value of a dataset. In this case, we are interested in finding the average arsenic level in our sample. The symbol we use to represent the mean is '[tex]\bar{x}[/tex]' (pronounced x-bar). So, if we have a sample of n arsenic level readings, we would calculate the mean arsenic level as follows:

[tex]\bar{x}[/tex] = (x₁ + x₂ + x₃ + ... + xₙ) / n

Here, 'xi' represents the ith observation in our sample. By summing up all the observations and dividing by the sample size, we get the mean arsenic level.

Now, let's move on to the proportion of health issues in the sample. Proportion is a statistic that tells us what fraction or percentage of a sample has a certain characteristic.

To know more about proportion here

https://brainly.com/question/30657439

#SPJ4

Answer:

[tex]{ \colorbox{lightgreen}{can \: be \: simplified}} \\ \dashrightarrow \: { \sf{ \blue{9x + 6x}}} \: \: \: \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \: \: \: \\ { \sf{ = (9 + 6)x}} \\ { \underline{ \sf{ \: = 15x \: \: \: \: \: \: \: \: \: \: }}} \\ \\ \dashrightarrow \: { \sf{ \blue{4x + x}}} \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (4 + 1)x}} \\ { \underline{ \sf{ \: = 5x \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \\\dashrightarrow \: { \sf{ \blue{y + 2y}}} \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (1 + 2)y}} \\ { \underline{ \sf{ \: = 3y \: \: \: \: \: \: \: \: \: \: \: \: }}}[/tex]

[tex]{ \colorbox{lightgreen}{cannot \: be \: simplified}} \\ \dashrightarrow \: { \sf{2x + 3y}} \\ \dashrightarrow \: { \sf{7y + 1 \: \: }} \\ \dashrightarrow \: { \sf{4y + 4x}}[/tex]

Answer:

Step-by-step explanation:

try 39

Answer:

-24

Step-by-step explanation:

Hey there!

First we need to find the ratio

ratio = -6/-3 = 2

r = 2

-3, -6, -12, ? , -48

T1 = a

T2 = ar

T3 = ar²

T4 = ar³

T5 = ar⁴

And so on...

T1 means first term, T2 means second term

We're finding the fourth term which is T4

Remember T1 = a = -3

So, T4 = ar³

= -3 × 2³

= -3× 8

= -24

Therefore, the fourth unknown term is -24

You're welcome y'all

The triangle congruency postulate that proves both triangles are congruent is: SSS

There are different triangle congruence postulates such as:

SSS: This denotes Side Side Side Congruency Postulate

SAS: Side angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

Now, from the given two triangles, we can see the following:

BC ≅ UW

AC ≅ UV

AB ≅ VW

Thus, the three sides are congruent and as such it is congruent by SSS congruency postulate

Read more about Congruency Postulate at: https://brainly.com/question/29268713

#SPJ1

The values of x and y in the cyclic quadrilateral are 107 degrees and 75 degrees

From the question, we have the cyclic quadrilateral

In a cyclic quadrilateral, opposite angles are supplementary, meaning they add up to 180 degrees. This property is known as the "Opposite Angles Theorem."

For example, angles A and C are opposite angles, and they are both subtended by diameter BD.

Similarly, angles B and D are opposite angles, and they are both subtended by diameter AC.

Therefore, we can state that in a cyclic quadrilateral, the sum of opposite angles is 180 degrees

So, we have

x = 180 - 73 = 107

y = 180 - 105 = 75

Hence, the value of x is 107 degrees

Read more about cyclic quadrilateral at

https://brainly.com/question/29704807

#SPJ1

The total number of students in Ms. Persons class is 24.

An equation is simply a mathematical formula that expresses the equality of two expressions.

Given the data in the question:

Lets y be the number of students in the class

Hence:

[tex]75\% \ \text{of y = 18}[/tex]

[tex]\text{Lets find y}[/tex]

[tex](\dfrac{75}{100} ) \times y = 18[/tex]

[tex]75 \times y = 18 \times 100[/tex]

[tex]75 \times y = 1800[/tex]

[tex]y = 1800 \div 75[/tex]

[tex]y = 24[/tex]

Therefore, the total number of students in Ms. Persons class is 24.

The factored form of the polynomial after factoring out the greatest common factor is 3s^(2) (s + 2)

The greatest common factor (GCF) of a polynomial is the largest factor that is common to all the terms in the polynomial. To find the GCF of a polynomial, we need to factor each term into its prime factors, and then identify the factors that appear in all the terms.

To factor out the greatest common factor from the given polynomial, we need to find the largest monomial that divides each term in the polynomial.

The first step is to identify the common factors of the two terms. In this case, both terms have a factor of 3 and a factor of s^2. So, we can factor out 3s^2 from both terms

3s^(3) + 6s^(2) = 3s^(2) (s + 2)

Learn more about greatest common factor here

brainly.com/question/29584814

#SPJ4

Answer:

-157.7

Step-by-step explanation:

Subtract 12.3 from 23 to get 10.7

10.7 - (166.4 + 2), next add 166.4 and 2 to get 168.4

10.7 - 168.4, finally subtract 168.4 from 10.7 to get -157.7

The five number summary is: Minimum: 60 Q1 (first quartile): 63 ,Median: 70Q3 (third quartile): 75, Maximum: 79

To find the five number summary of the data set 72, 60, 64, 75, 79, 63, 70, 61, 78, follow these steps:

1. Arrange the data in ascending order: 60, 61, 63, 64, 70, 72, 75, 78, 79

2. Identify the minimum value (smallest number): 60

3. Identify the maximum value (largest number): 79

4. Calculate the median (middle number): There are 9 data points, so the median is the 5th number: 70

5. Calculate the first quartile (Q1): The lower half of the data set is 60, 61, 63, 64, 70. The median of this lower half is the

middle number, which is 63.

6. Calculate the third quartile (Q3): The upper half of the data set is 70, 72, 75, 78, 79. The median of this upper half is

the middle number, which is 75.

The five number summary is:

Minimum: 60

Q1 (first quartile): 63

Median: 70

Q3 (third quartile): 75

Maximum: 79

for such more question on Median

https://brainly.com/question/14532771

#SPJ11

We can write this expression as a product of two factors:

(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)

HOW TO WRITE expression as a product.?

To write an expression as a product means to represent the expression as the multiplication of two or more factors. The process of writing an expression as a product depends on the type of expression and the algebraic techniques that are available.

Here are some general steps that can be followed to write an expression as a product:

Look for common factors: If there are common factors in the expression, they can be factored out using the distributive property. For example, in the expression 3x + 6, we can factor out 3 to get 3(x + 2).

Use algebraic identities: There are many algebraic identities that can be used to factor expressions. For example, the difference of squares identity (a² - b²= (a + b)(a - b)) can be used to factor expressions that are in the form of a difference of squares.

Look for patterns: Sometimes, expressions can be factored by recognizing patterns. For example, the expression x² + 2x + 1 can be factored as (x + 1)²by recognizing that it is a perfect square trinomial.

Use polynomial division: If the expression is a polynomial with higher degree, polynomial division can be used to factor it into linear and quadratic factors.

Use the quadratic formula: If the expression is a quadratic trinomial that cannot be factored easily, the quadratic formula can be used to find the roots of the equation, which can then be used to write the expression as a product of linear factors.

Overall, writing an expression as a product requires a good understanding of algebraic techniques and a lot of practice.

We can use the formula for the sum of cubes to write the expression as a product:

(a + 1) + x³ = (a + 1 + x)(a² - a x + x²) + x³

Expanding the first factor on the right-hand side using the distributive property, we get:

(a + 1 + x)(a²- a x + x²) + x^3 = a³- a² x + a x² + a² + a x + x²+ x³

Collecting like terms, we can write this expression as a product of two factors:

(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)

To know more about expression visit :-

https://brainly.com/question/1859113

#SPJ1

If Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie can skip up to 15 days and still finish crocheting at least 3 blankets before she wants to donate them to the homeless shelter.

Let's first calculate how much of a blanket Darcie can crochet in 60 days if she works every day:

1/15 blanket per day * 60 days = 4 blankets

Since Darcie wants to crochet a minimum of 3 blankets, we know that she needs to work for at least 3/4 of 60 days. Let x be the number of days Darcie can skip and still finish the blankets:

(60 - x) * 1/15 >= 3

Simplifying this inequality, we get:

4 - 1/15x >= 3

1/15x <= 1

x <= 15

Therefore, Darcie can skip up to 15 days and still finish crocheting at least 3 blankets before she wants to donate them to the homeless shelter.

Learn more about number of days here:https://brainly.com/question/9286901

#SPJ1

Answer: is it an A.P or G.P

The length of AC is approximately 29.4 units.

We can use the Pythagorean theorem and the fact that the two triangles ABD and CBD are similar to solve for the length of AC:

Let's denote the length of AB as a and the length of BC as b.

From triangle ABD, we have:

a^2 + 18^2 = c^2 (where c is the length of AC)

From triangle CBD, we have:

b^2 + 6^2 = c^2

Since the two triangles ABD and CBD are similar, we have:

a/b = 18/6 (because the altitude BD divides the hypotenuse AC into segments with lengths of 18 and 6, respectively)

Simplifying, we get:

a/b = 3

a = 3b

When we enter this into the initial equation, we obtain:

(3b)^2 + 18^2 = c^2

9b^2 + 324 = c^2

Substituting this into the second equation, we get:

b^2 + 6^2 = 9b^2/4 + 81

Simplifying, we get:

3b^2/4 = 45

b^2 = 60

Substituting this back into the equation for c^2, we get:

9(60) + 324 =c^2

c^2 = 864

Taking the square root of both sides, we get:

c ≈ 29.4

Therefore, the length of AC is approximately 29.4 units

Learn more about Pythagorean theorem

https://brainly.com/question/23060414

We have that, when testing a certain type of truck tire on rough terrain, it is observed that 25% of the trucks fail to complete the test without blowout, the probability that of the next 15 trucks tested, at least one will not able to complete the test run without an explosion is 0.987

Given that when testing a certain type of truck tire on rough terrain, it is found that 25% of the trucks do not complete the test without blowout.So, the probability that a truck completes the test without a blowout is:

P (A complete truck test without blowout) = 1 - P (A complete truck test without an explosion) = 1 - 0.25 = 0.75

Now, we need to find the probability that of the next 15 trucks tested, at least one will not complete the test without an explosion. This can be found using the complement rule. The complement of the probability that at least one truck does not complete the test without a blowout is the probability that all 15 trucks complete the test without a blowout.

P(All 15 trucks complete the test without a blowout) = P(One truck completes the test without a blowout) x P(A second truck completes the test without a blowout) x ... x P(The fifteenth truck completes the test without a blowout) = 0.75 x 0.75 x ... x 0.75 (15 times)= 0.75^15= 0.013

But we need the probability that at least one truck fails to complete the test without a blowout, which is the complement of the above probability.

P(At least one truck does not complete the test without blowout) = 1 - P(All 15 trucks complete the test without blowout)= 1 - 0.013= 0.987

Therefore, the probability that of the next 15 trucks tested, at least one will not be able to complete the test run without an explosion is 0.987.

See more information about probability in: https://brainly.com/question/24756209

#SPJ11

The population of a town increases by 9.2% annually.

Exponential growth is a process where a quantity grows at a constant percentage rate over time. This means that the rate of growth of the quantity itself increases as the quantity becomes larger.

The context that represents exponential growth is:

The population of a town increases by 9.2% annually.

Exponential growth occurs when a quantity grows at a constant percentage rate over time. In this case, the population of the town is growing at a constant rate of 9.2% per year, which means that the population is increasing exponentially over time.

The other options describe either decay (the radioactive compound decaying at a rate of 25% per hour) or decreasing quantities (the town's population shrinking at a rate of 3.5% every year or the fixed monthly cost of the music service).

For example, let's say that a population of rabbits grows at a rate of 10% per year. If there are initially 100 rabbits, we can use the formula to calculate the population after 5 years:

y = 100 * (1 + 0.10)^5 = 161.05

This means that after 5 years, there will be approximately 161 rabbits, which is a 61% increase from the initial population of 100 rabbits.

Learn more about Exponential growth visit:

https://brainly.com/question/12490064

#SPJ1

In perspective of this, the function that degrades as input values go closer to both negative and positive infinity is [tex]g(x) = -2x^3 - 4x^2 +9[/tex] and the appropriate response is (2).

Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function seems to be a rule that generates a unique outcome one per input x in mathematical. A mapping as well as transformation in mathematics represents a function.

(1) [tex]f(x) = x^3 - 4x^2 + x[/tex]

x3 and -4x2 become extremely big negative numbers as x approaches negative infinity, and x becomes a very large negative number. As a result, f(x) approaches infinity. [tex]x^3[/tex] and [tex]-4x^{2}[/tex] become extremely big positive values as x approaches positive infinity, and x becomes a very large positive number. As a result, f(x) approaches infinity. As a result, f(x) does not decrease when the input values approach negative and positive infinity.

(2) [tex]g(x) = -2x^3 - 4x^2 +9[/tex]

When x approaches negative infinity, the negative integers -2x3 and [tex]-4x^{2}[/tex] grow very big, and 9 becomes negligible. As a result, g(x) approaches infinity. When x approaches positive infinity, the negative integers -[tex]2x^3[/tex] and [tex]-4x^{2}[/tex] grow very big, and 9 becomes negligible. As a result, g(x) approaches infinity. As a result, g(x) diminishes as the input values approach negative and positive infinity.

(3) [tex]h(x) = x^4 - 4x^3 + 2x + 8[/tex]

When x approaches negative infinity, the negative integers [tex]x^4[/tex] and [tex]-4x^3[/tex] grow very big, whereas 2x and 8 become unimportant. As a result, h(x) approaches infinity. When x approaches positive infinity, the positive integers [tex]x^4[/tex] and [tex]-4x^3[/tex] grow very big, whereas 2x and 8 become unimportant. As a result, h(x) approaches infinity. As a result, h(x) does not decrease when the input values approach negative and positive infinity.

(4) [tex]r(x) = -x^4 + 9x^3 + x^2 + 8x + 2[/tex]

When x approaches negative infinity, the negative numbers [tex]x^4[/tex] and [tex]9x^3[/tex] grow quite big, whereas [tex]x^2[/tex], 8x, and 2 become unimportant. As a result, r(x) approaches infinity. When x approaches positive infinity, the negative integers  [tex]-x^{4}[/tex] and [tex]9x^{3}[/tex] grow quite big, whereas [tex]x^2[/tex], 8x, and 2 become unimportant. As a result, r(x) approaches infinity. As a result, r(x) diminishes as the input values approach negative and positive infinity.

To know more about function visit:

https://brainly.com/question/31035045

#SPJ1

Answer:

Step-by-step explanation:

the measurements are a Pythagorean triple, therefore it is a right triangle, where 3 and 4 are the legs and 5 is the hypotenuse, we use the formula 1/2 × b × h

A = 1/2 × b × h.

A = 1.5 × 4

A = 6"^2