75° 30’ convert into radian

The cartesian equation and domain and range will be Domain: - 2 ≤ x ≤ 2;

Range:  - 2 ≤ y ≤ 2;

We square the following equations to obtain the cartesian equation, and then we add:

Suppose that P0 has coordinates x0,y0,z0, and n has components a,b, and c. Let P, with coordinates x,y, and z, be an arbitrary point on the plane. A Cartesian equation of the plane is what this is. in which d is a constant ax0 + by0 + cz0.

x2(t) = 4cos2(t), y2(t) = 4sin2(t).

So, x2 + y2 = 4(cos2(t) + sin2(t)), or x2 + y2 = 4

We have a circle with a radius of two and a center at the origin.

Domain: - 2 ≤ x ≤ 2;

Range:  - 2 ≤ y ≤ 2;

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The full and correct question would be:

find the cartesian equation and domain and range of this

For the pair of parametric equations below, eliminate the parameter to find its Cartesian equation. Also, specify the domain and range of your equation using interval notation.

x(t)=2cos(t)

y(t)=2sin(t)

Answer:

2200

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) f(-4) = 15

since x < -1

the function will be :-

-5x - 5

= -5(-4) - 5

= 20 - 5

= 15

(b) f(-1) = -2

since x >= -1

the function will be:-

x^2 + 2x - 1

= (-1)^2 +2(-1) - 1

= 1 - 2 - 1

= -2

(c) f(1) = 2

since x >= -1

the function will be:-

x^2 + 2x - 1

= (1)^2 + 2(1) - 1

= 1 + 2 - 1

= 2

1) The 6th term of the geometric sequence is;  a₆ = 486

2) The 9th term of the geometric sequence is; a₉ = 729

The formula for the nth term of a geometric sequence is;

aₙ = a₁rⁿ⁻¹

where;

a₁ is first term

r is common ratio

n is position of term

1) The parameters are;

First term; a₁ = 2

common ratio; r = 3

Thus, the 6th term is;

a₆ = 2 * 3⁶⁻¹

a₆ = 2 * 3⁵

a₆ = 486

2) The parameters are;

First term; a₁ = 1/3

common ratio; r = 3

Thus, the 9th term is;

a₉ = (1/3) * (3)⁸⁻¹

a₉ = (1/3) * 3⁷

a₉ = 729

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The solution to the inequality is 1/3 ≤ x < 7

For the first inequality:

2x + 1 ≤ 5x

Solving for x:

2x + 1 - 5x ≤ 0

-3x + 1 ≤ 0

-3x ≤ -1

x ≥ 1/3

For the second inequality:

3x + 5 > 4x - 2

Solving for x:

3x + 5 - 4x + 2 > 0

-x + 7 > 0

x < 7

The set of all real numbers that satisfy both inequalities is:

1/3 ≤ x < 7

Graphically, this is represented on the number line

|----|---|---|---|---|---|---|---|---|---|

1/3                                        7

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4 thread of 2(1/7) inches can be made from 8(3/4) inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Thread = 2(1/7) inches

Total length = 8(3/4) inches

The number of 2(1/7) inches thread.

= 8(3/4) ÷ 2(1/7)

= 8(3/4) / 2(1/7)

= 35/4 x 7/15

= 7/4 x 7/3

= 49/12

= 4.08

= 4

Thus,

4 thread of 2(1/7) inches can be made.

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The answer is c. lower than 215.3. If the CPI were recalculated with 1995 as the reference year, then the CPI for 2008 would be lower than 215.3.

This is because the CPI is calculated based on the cost of goods and services relative to the cost of the same goods and services in the reference year.

Since prices have generally increased since 1995, the cost of goods and services in 2008 will be higher than the cost of the same goods and services in 1995. Therefore, the CPI for 2008 will be lower than the CPI for 1995, which is currently 215.3.

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The statement that is true about the transformation of segment AB is;

AB is reflected over the y-axis and is congruent to the image.

A reflection is a type of transformation that behaves like a mirror. Thus, It swaps all pairs of points that are on exactly opposite sides of the line of reflection. The line of reflection can be defined by an equation or by two points it passes through.

Now, the transformation rule for reflection about the y-axis is;

(x, y) = (-x, y)

In this graph, it is exactly a reflection about the y-axis and as such we can say that option A is the correct answer.

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Answer:

101,168

Step-by-step explanation:

The value of 6 in the given number 35,629 is the hundreds value.

35,629.

You are trying to find a number in which the number 6 is in 1/10th of the value of the original number. In this case, divide the hundreds value by 10:

100/10 = 10

Place the value 6 in the tens digit place value for any number.

101,168 can be a answer choice.

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Answer: 5,211 dollars

Step-by-step explanation: Our first approch to this is to find the number of Gala and Honeycrisp(HC) Trees are there.

We are given the number of total trees (81 trees) and the ratio between Gala and HC trees  (5 to 4). This means for every set of 9 trees, 5 will be Gala and 4 will be HC. We can create the equation

9x = 81

5x = number of gala trees

4x = number of HC trees

x represents the number of sets of 9 trees so in this case, there will be 9 sets if you solve for x.

9x = 81

divide both sides by 9

x = 9

We can plug this back into the 2 other equations that represent the number of each tree so

5(9) = 45 gala trees,

4(9) = 36 HC trees

This makes sense since 45+36 = 81 so it adds up

Now to find the amount of money just take the amount of each trees we have and multiply it by the pounds each tree made then multiply it by the price each pound makes.

45 gala trees * 25 pounds * 1.52 dollars = 1,710 dollars

and

36 HC trees * 25 pounds * 3.89 dollars = 3,501 dollars

Finally, add both of them up to get the total profit

1,710 + 3,501 = 5211 dollars

Answer:

40 hot dogs and 90 sodas were sold at the football game.

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations. Let's use:

➽"x" to represent the number of hot dogs sold

➽"y" to represent the number of sodas sold

We are given the following information:

♦The total revenue from hot dogs and sodas is $300.

♦The number of sodas sold is 10 more than two times the number of hot      dogs sold.

From this information, we can create the following equations:

▷[tex]\tt{3x + 2y = 300}[/tex] (The total revenue from hot dogs and sodas)

▷[tex]\tt{y = 2x + 10}[/tex] (The number of sodas sold is 10 more than two times the    number of hot dogs sold)

Now, we can solve this system of equations using the substitution method. Substitute the second equation into the first equation:

Simplify and solve for x:

Now that we have the number of hot dogs sold (x = 40), we can find the number of sodas sold by substituting x back into the second equation:

So, 40 hot dogs and 90 sodas were sold at the football game.

________________________________________________________

Number of hot dogs sold = 40

Number of sodas sold = 90

The school earned $300 in total, this confirms our answer.

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________________________________________________________

The nearest tenth of a year, about 11 years 5 months  long will it be until the value of the car is 7900 dollars

For $25,000, a brand-new car is bought. The automobile loses 14% of its value annually.

x=6.3.

Using the conditions stated, come up with:

20500 . 1 - 14% x 7900

Determine the difference or total:

First, we convert R percent to r a decimal,

which is 14%/100, which is 0.14 each year. Next, we solve for t by using the ratio

(1/0.14)(20500/7900) - 1),

which gives us 11.39 years.

At a basic interest rate of 14% per year, it will take 11.39 years to accumulate a total of $20,500.00 from the principle and interest on a $7,900.00 starting point (about 11 years 5 months).

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Answer: 6.3

Step-by-step explanation: just because

Compare the volume and surface area, it can be said that the volume of the sphere is approximately equal to the volume of the cube, but the cube has a greater surface area.

It is the space occupied by a body, it is calculated by multiplying its dimensions, for example: length, height and width.

Information about the problem:

Using the formula of the volume and the surface area of the sphere we get:

v(sphere)= 4/3 (π * r³)

v(sphere)= 4/3 *π*(4)^3 in^3

v(sphere)= 268.08 in^3

Rounding down = 268 in^3

surface area(sphere) = 4*π*r²

surface area(sphere) = 4*π*(4)^2

surface area(sphere) = 201.062 in^2

v(cube)= l³

v(cube)=(6.45)^3

v(cube)= 268.34 in^3

Rounding down = 268 in^3

surface area(cube) = 6*l²

surface area(cube) = 6 * (6.45)^2

surface area(cube) = 249.62 in^2

Therefore:

The volume of the sphere is approximately equal to the volume of the cube, but the cube has a greater surface area.

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Answer:

B X^6 Y^3

Step-by-step explanation:

Answer:

lets say you decide to take three part-time jobs: Work at a convenience store 60% of your time, and earn $11.00 an hour. Referee games at your city park 25% of your time, and earn $19.00 an hour. Do your elderly neighbor’s housework 15% of your time, and earn $16.00 an hour. What will your average hourly wage be? Enter your answer up to two decimal places. its on edmentum.

For this it's going to be 13.75. The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job): 0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.

Answer:

y=2x+9

Step-by-step explanation:

Point of intersection of y=3 & x+y=0

Point of intersection of y=3 & x+y=0put x=3 in x+y=0

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2y−3=2[x+3]

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2y−3=2[x+3]y=2x+6+3

y=2x+9

For the treatment of issues with the bile and pancreatic ducts, endoscopic retrograde cholangiopancreatography (ERCP) combines upper gastrointestinal (GI) endoscopy and x-rays.

ERCP is a procedure that doctors utilize to treat bile and pancreatic duct issues. If they want to treat issues during the procedure, medical professionals also utilize ERCP to identify issues with the pancreatic and bile ducts. Instead of using ERCP for diagnosis alone, clinicians may choose to use noninvasive tests, which do not physically enter the body. Noninvasive procedures like magnetic resonance cholangiopancreatography (MRCP), a form of magnetic resonance imaging (MRI) NIH external link, are less dangerous and can also identify a wide range of issues with the bile and pancreatic ducts.

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The vertex is (21, 125210)

The vertex shows that the overall value of home in 21 years after 2020,i.e., in 2041 is 125210 dollars.

What is quadratic equation in math?

A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic.            

                         Equations with quadratic terms are another name for them. The quadratic equation is expressed in its general form as ax2 + bx + c = 0. When the numerical coefficients a, b, and c are present and x is an unknown variable.

The overall value of a home is modeled by

v(x) = 210x²-4400x+125000

This is a quadratic function which is of the form ax²+bx+c ⇒ x²+(b/a)x+(c/a)

The vertex of a quadratic function is the point where the rate of change of function is zero.

x-coordinate of the vertex is given by (-b/2a) and the y-coordinate is the corresponding y-value to the x-coordinate of the vertex.

Hence here, x-coordinate = -(-4400/210) = 20.95 ≈ 21

y-coordinate = 210 x 21²-4400 x 21+125000 = 125210

The vertex is (21, 125210).

The vertex shows that the value of home in 21 years after 2020,i.e., in 2041 is 125210 dollars.

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1) The value of AA is [tex]\left[\begin{array}{ccc}25&0&0\\0&4&0\\0&0&16\end{array}\right][/tex]. 2) By solving the matrix equation, we got [tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-131 \\-1\\7\end{array}\right][/tex]. 3) The value of x and y is -4 and 18

1) A = [tex]\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right][/tex]                

AA =  [tex]\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right][/tex]   [tex]\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right][/tex]  

AA = [tex]\left[\begin{array}{ccc}(-5)^2&0&0\\0&(-2)^2&0\\0&0&(-4)^2\end{array}\right][/tex]

AA = [tex]\left[\begin{array}{ccc}25&0&0\\0&4&0\\0&0&16\end{array}\right][/tex]

2)We are given            x₁ - 2x₂ + 3x₃ = 24

                                      -x₁ + 3x₂ - x₃ = -11

                                   2x₁ - 5x₂ + 5x₃ = 24

Now, AX = B

[tex]\left[\begin{array}{ccc}1&-2&3\\-1&3&-1\\2&-5&5\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right][/tex]

As, AX = B => X = BA⁻¹      --(1)

Here A⁻¹ = (1/|A|)adjA

Where adjA is Adjoint of matrix A

|A| = 1

AdjA = [tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]

Therefore, A⁻¹ = [tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]

Using (1)

X = [tex]\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right][/tex][tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right][/tex][tex]\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-131 \\-1\\7\end{array}\right][/tex]

3)  [tex]\left[\begin{array}{ccc}x+2&6&-5\\7&2y&2x\\2x+6&6&-5\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2x+6&6&-5\\7&18&-8\\3&-8&11\end{array}\right][/tex]

So, x + 2 = 2x + 6

       2x - x = 2 - 6

              x = -4

     2y = 18

       y = 9

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The required value of x in a similar triangle is given as x = 24.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
As both the triangles are similar,
AB / XY = BC / ZY
x /18 = 16/12
x = 4/3 × 18
x = 24

Thus, the required value of x in a similar triangle is given as x = 24.

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The clock, which is equal to 30 cm multiplied by pi (3.14), or 94.2 cm, in one hour.

Clock is an instrument used to measure and indicate time. It is one of the oldest human inventions, measuring time in units of seconds, minutes, hours, days, weeks, months, and years. Clocks are used in many different contexts, including to regulate the timing of activities, to measure the duration of events, to indicate the time of day, to give a signal at a specific time, and to keep track of time.

The tip of the minute hand of a circular clock moves around the circumference of the clock in one hour. The circumference of the clock is equal to the diameter of the clock multiplied by pi (3.14). The diameter of the clock is equal to twice the length of the minute hand, or 30 cm. Therefore, the tip of the minute hand moves around the circumference of the clock, which is equal to 30 cm multiplied by pi (3.14), or 94.2 cm, in one hour.

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The probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0152.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given the mean diameter of the bolt = 145 mm

variance = 49

random sample = 34

to find the probability when the population mean by more than 2.6 mm

calculating probability by z-score

z = (x - μ)/σ

σ = √(varience/n)

σ = √(49/34)

σ = 1.2004

and x - μ = 2.6

substitute the value in the formula,

z = 2.6/1.2004

z = 2.1659

so P(x - μ < 2.6) = 0.98484

and  P(x - μ > 2.6)  = 0.015158 = 0.0152

Hence probability is 0.0152.

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The value vt= 305 shows the distance travelled.

Given:

If a car travels at a constant speed of v miles per hour for t hours, it will travel vt miles.

we have v= 61 and t= 5

So, vt = 61 x 5 = 305

As, we know from the formula

speed = distance/ time

distance = speed x time

here speed= v, time= t

So, the value vt= 305 represents the distance travelled when speed is 61 and time is 5.

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Answer: Lowest: Qatar, Highest: Denmark

Hope this helps :)

Step-by-step explanation:

Philippines - About $2.59 per gallon (USD)

USA - About $3.51 per gallon

India- About $4.83 per gallon (USD)

Qatar - About $2.18 per gallon (USD)

Denmark- About $5.93 per gallon

The slope of the tangent line is 12.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, a function f(x) = 3x²+1, has a rate of change at x = 2

We are asked to calculate the instantaneous rate of change and slope of secant,

Instantaneous Rate of Change

We can approximate to the value of the slope of one function P(x) by computing the slope of the secant line as:

m = f(x+Δx) - f(x) / Δx

Where Δx is an infinitesimal change of x, as small as we want.

The given function is = f(x) = 3x²+1

Let Δx = 0.1

m = f(2+0.1) - f(2) / 0.1

= 14.23 - 13 / 0.1

= 12.3

Now we use a smaller infinitesimal or differential

Δx = 0.01

m = f(2+0.01) - f(2) / 0.01

= 0.1203 / 0.01

= 12.03

We can see the slope is getting closer to 12 as the infinitesimal tends to 0,

Hence, we can estimate the slope of the tangent line is 12

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True. Personal observation permits a system analyst to confirm the veracity of comments provided by interviewees and to establish if procedures run as reported.

Personal observation enables the analyst to gather firsthand information about the procedures and operations being used in an organization. This information can then be compared with what was stated during the interviews to verify the accuracy of the statements made. By observing the actual processes, the analyst can identify any discrepancies or areas for improvement, allowing for a more comprehensive and effective analysis.

The ease of learning and implementation of personal observation as a method for system analysis can vary depending on several factors such as the complexity of the system, the experience and training of the analyst, and the availability of resources.

In general, personal observation is a straightforward technique, but it can be time-consuming and requires careful planning and execution. The analyst must have strong analytical and observation skills and the ability to identify and document relevant information. Proper training and experience can help make the learning and implementation process smoother.

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By integration by parts, the integral ∫ 4 · x · e³ˣ dx = (4 / 3) · x · e³ˣ - ∫ (4 / 3) · e³ˣ dx is an alternative form of integral ∫ 4 · x · e³ˣ dx. (Correct choice: A)

Herein we find the case of an integral of a product of two functions that cannot be integrated by means of a single integral and algebraic substitution, this can be found alternatively by definition of integration by parts:

∫ u dv = u · v - ∫v du

First, define functions u and dv:

u = 4 · x

dv = e³ˣ dx

Second, find functions du and v:

du = 4 dx

v = (1 / 3) · e³ˣ

Third, find the alternative integral equation:

∫ 4 · x · e³ˣ dx = (4 / 3) · x · e³ˣ - ∫ (4 / 3) · e³ˣ dx

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The situations described are A : subjective, B : classical, C : empirical, D : subjective and E : empirical.

In Classical probability, probability of an event is found using the basic probability formula assuming the outcomes in a sample space are equally likely.

In Empirical probability, experiment is actually done and record the outcomes.

In subjective probability, probability is based completely on the intuition or guess.

A : Recruiters are making a wild guess that there is an 80% chance that remote hiring will increase in 2023. This is a subjective probability.

B : This is classical probability because the probability is found by the basic formula, Number of nurses divided by total number of medical employees = 10/20 = 0.50.

C : This is an empirical probability because the experiment of survey is already done to find that there is a 73% chance that a randomly selected adult will say that he/she is playing games on mobile phones.

D : This is a subjective probability because the climate change expert made a educated guess.

E : This is an example of empirical probability because, the probability is known according to the Sharaf DG records.

Hence the situations are classified as classical empirical and subjective probability.

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Answer:

Step-by-step explanation:

I'll do the first part for you:

The number of 3/4 in 2 is [tex]=2/\frac{3}{4}[/tex]

That is the division equation.  Rearrange it to make the multiplication equation.  keep...change...flip.  Change the division to a multiplication and flip the fraction:

The number of 3/4 in 2 =[tex]=2.\frac{4}{3}[/tex]

The approximate mass of the brain of a mouse that has a mass of 64 grams is 2 grams

We have been given:

Weight: 64 grams

The mouse's brain's approximate mass must be determined.

This inquiry is based on the calculation used to determine an object's mass of an animal brain.

Let B represent the estimated brain mass in grams and m represent the brain mass of a mammal in grams.

By applying the method to determine a mammal's brain mass,

[tex]B=\frac{1}{8} m^{\frac{2}{3} }[/tex]

Taking into account that m = 64 grammes,

[tex]B=\frac{1}{8}(64)^{\frac{2}{3} }[/tex]

[tex]B=\frac{1}{8}(4^{3} )^{\frac{2}{3} }[/tex]

B = 16/8

B = 2 grams

Consequently, a mouse's brain weighs around 2 grams.

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