The classification of student class designation (freshman, sophomore, junior, senior) is an example of a categorical random variable. The correct option is A.
What is a random variable?A random variable is a numerical or categorical quantity whose value is unknown but whose behavior can be forecast based on data that has been measured or observed. Random variables are typically used to represent quantities that fluctuate over time or are subject to chance occurrences.
The types of random variables are as follows:
i) Categorical random variable: This type of variable contains categorical data or data that are descriptive in nature. It is used to classify items or events into categories, which can be named or identified. For example, a set of data that includes categories like gender, eye color, or country of origin.
ii) Discrete random variable: This type of variable takes on discrete values, which means it can only take on whole numbers. For example, the number of cars sold at a dealership on any given day is a discrete random variable because it can only take on integer values.
iii) Continuous random variable: This type of variable takes on continuous values, which means it can take on any value within a given range. For example, the temperature in a room can take on any value between a certain minimum and maximum value.
Therefore, the correct option is A.
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Complete the following activity by identifying the location of the muscles, bones, and sensory organs.
Part One
1. Label each of the following body parts on the two pictures below: muscles, bones, and sensory
organs.
2. In the space provided, describe the function of each body part you labeled.
Name: Date:
Lesson 13.04: Building Muscles
Lesson Assessment: Building Muscles
Muscles:
Bones:
Sensory organs:
Muscles:
Part Two
In the space provided, describe how the bones, muscles, and sensory organs all work together.
I can give you with a general explanation of the functions of muscles, bones, and sensitive organs, as well as how they work together.
Muscles are responsible for movement and give the force needed to move bones. They're attached to bones via tendons and work in dyads or groups to produce coordinated movement. Muscles are also responsible for maintaining posture and generating heat.
Bones give a rigid frame for the body, cover internal organs, and serve as attachment points for muscles. They also store minerals similar as calcium and produce blood cells in the bone gist.
sensitive organs, similar as the eyes, cognizance, nose, and skin, descry and respond to stimulants in the terrain. They transmit information to the brain, which processes the information and generates an applicable response.
All three body corridor work together in the musculoskeletal system to produce movement, maintain posture, and respond to external stimulants. Muscles attach to bones and work together to produce coordinated movement. sensitive organs descry stimulants in the terrain and transmit information to the brain, which coordinates muscle movement and generates a response. Bones give the rigid frame and attachment points for muscles, as well as cover internal organs.
AP STATS
Burping (also known as "belching" or "eructation") is one way the human body expels excess gas in your digestive system. It occurs when your stomach fills with air, which can be caused by swallowing food and liquids. Drinking carbonated beverages, such as soda, is known to increase burping because its bubbles have tiny amounts of carbon dioxide in them.
As an avid soda drinker and statistics student, you notice you tend to burp more after drinking root beer than you do after drinking cola. You decide to determine whether there is a difference between the number of burps while drinking a root beer and while drinking a cola. To determine this, you select 20 students at random from high school, have each drink both types of beverages, and record the number of burps. You randomize which beverage each participant drinks first by flipping a coin. Both beverages contain 12 fluid ounces. Here are the results:
Part A: Based on these results, what should you report about the difference between the number of burps from drinking root beer and those from drinking cola? Give appropriate statistical evidence to support your response at the α = 0.05 significance level.
Part B: How much of a difference is there when an individual burps from drinking root beer than from drinking cola? Construct and interpret a 95% confidence interval.
Part C: Describe the conclusion about the mean difference between the number of burps that might be drawn from the interval. How does this relate to your conclusion in part A?"
The mean number of burps after drinking root beer is between 0.66 and 4.24 burps fewer than after drinking cola.
What is the definition of a mean number?Mean: The "average" number obtained by adding all data points and dividing the total number of data points by the total number of data points.
Part A: A paired t-test can be used to see if there is a significant difference in the number of burps after drinking root beer versus cola. The null hypothesis states that there is no difference in the mean number of burps between the two beverages, whereas the alternative hypothesis states that there is. Using a two-tailed test with a significance level of = 0.05, we find that the t-value is -3.365 and the p-value is 0.003. We reject the null hypothesis because the p-value is less than the significance level and conclude that there is a significant difference in the mean number of burps between root beer and cola.
Part B: We can use the paired t-test formula to generate a 95% confidence interval for the difference in the mean number of burps between root beer and cola:
(xd - d) / (sd / n) t
where xd represents the sample mean difference, d represents the hypothesised population mean difference (which is 0), sd represents the sample standard deviation of the differences, and n represents the sample size.
We calculate the sample mean difference to be -2.45 and the sample standard deviation of the differences to be 2.69 using the data in the table. We get a t-value of -3.365 with 19 degrees of freedom after plugging in these values. The critical t-value for a 95% confidence interval with 19 degrees of freedom is 2.093, according to a t-distribution table.
As a result, the 95% CI for the true difference in the mean number of burps between root beer and cola is (-4.24, -0.66). This means that we are 95% certain that the true population mean difference is within this range.
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HELP PLS combine the like terms 3x+5-x+3+4x
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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Can anyone solve this ???
The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.
How do you depict a relationship of recurrence?As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.
We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:
Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:
Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)
Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)
(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)
Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)
(b), we can use the just-proven formula:
A = ln(1, 2,...) + ln + ln (89)
= ln(j=1 to 89) prod
sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).
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there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3 rd row, and so on. if the price per ticket is $32, how much will be the total sales for a one-night concert if all seats are taken?
Answer:
Step-by-step explanation:
To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.
To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:
S = n/2 * (a + l)
where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.
In this case, we have:
n = 20 (since there are 20 rows)
a = 25 (since there are 25 seats in the first row)
d = 2 (since the difference between each row is 2 seats, the common difference is 2)
We can use d to find the last term as well:
l = a + (n-1)*d
l = 25 + (20-1)*2
l = 25 + 38
l = 63
Now we can plug these values into the formula:
S = 20/2 * (25 + 63)
S = 10 * 88
S = 880
So there are 880 seats in total.
To find the total sales, we just need to multiply by the price per ticket:
total sales = 880 * $32
total sales = $28,160
Therefore, the total sales for a one-night concert with all seats taken would be $28,160.
question 962946: if a triangle with all sides equal length has a perimeter of 15x 27, what is an expression for the length of one of it's sides?
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27.
Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
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The general form of the equation of a circle is x2 y2 8x 22y 37 = 0. the equation of this circle in standard form is (x )2 (y )2 = . the center of the circle is at the point ( , ).
The centre οf the circle is (-4, -11).
What is a circle's general equatiοn?We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.
Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.
Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.
Let's separate the terms with x frοm the terms with y:
[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]
We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16
Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:
[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]
The equatiοn can nοw be written in standard fοrm:
[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]
The circle's centre is (-4, -11).
As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).
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An electric dipole with its center located at the origin of a Cartesian coordinate system oscillates along the z axis, creating an electromagnetic wave. At a position on the y axis far from the origin, what is the polarization of the wave and which axis are the magnetic (a) The wave is polarized parallel to the a axis and the magnetic field lines are parallel to b The wave is polarized parallel to the z axis and the magnetic field lines are parallel to (c) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (d) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (e) The wave is polarized parallel to the z axis and the magnetic field lines are parallel to field lines parallel to? the y axis the axis the r axis the z axis the z axis
The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.
The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.
The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.
According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.
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josh borrowed $250 from his mother to buy an electric scooter. josh will pay her back in 1 year with 3% simple annual interest. how much interest will josh pay?
The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.
What is interest rate?Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.
The interest rate formula is:
Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}
Here,
Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.
The amount of interest that Josh will pay is calculated as:
Interest = Principal Amount × Rate of Interest × Time
Interest = 250 × 3
Therefore, Josh will pay his mother $7.50 in interest for the loan.
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Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
a. 1
b. x.x’
c. 1+ x.x’
d. (1+ x.x’)^2
e. exp (x+x’), for x.x’ ER
f. min (x.x’) for x.x’ E Z
Answer:
Step-by-step explanation:
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
In the above video lecture, we verified the following result: Computing the gradient of n
Rn (θ) = 1/n Σ (y^(t) - θ.x^(t)^2 / 2
t=1
we get ΔRn (θ) = Aθ-b (=0) where A= n n
A = 1/n Σ x^(t) (x^(t))^T , b = 1/n Σ y^(t) x^(t)
t=1 t=1
Now, what is the necessary and sufficient condition that Aθ - b = 0 has a unique solution?
- None of A's entries is 0. - A is invertible.
- A's dimension is the same as that of θ's
The direction of the steepest descent, which is used to find the minimum value of a function.
The necessary and sufficient condition that Aθ-b = 0 has a unique solution is: A is invertible.What is computing?Computing is a part of computer science that focuses on computer programs, including their software and hardware. It is concerned with designing algorithms to solve problems and creating software that will run these algorithms. As a result, computing is a field of study that is concerned with the process of creating algorithms and software.InvertibleAn invertible matrix is a matrix in which the determinant is not zero. An invertible matrix is also referred to as a non-singular matrix. An invertible matrix has a unique inverse. The rank of an invertible matrix is equal to its dimension. An invertible matrix can be used to solve a system of linear equations.GradientA gradient is a vector field in which the direction of the vector points to the steepest increase in a function, and the magnitude of the vector is the rate of increase in that direction. The gradient of a function is a vector field that is a derivative of the function. The gradient is used in multivariable calculus to solve optimization problems. The gradient is used to find the direction of the steepest ascent, which is used to find a maximum value of a function. It is used to find the direction of the steepest descent, which is used to find the minimum value of a function.
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Gill opened an account at a different bank. The banks rate of interest was 6%. After one year the bank paid Gill interest. The amount in her account was now $2306
Answer:
Step-by-step explanation:
To solve this problem, we can use the formula for calculating simple interest:
I = P * r * t
where:
I = interest earned
P = principal (initial amount of money)
r = rate of interest
t = time (in years)
We can rearrange the formula to solve for the principal:
P = I / (r * t)
In this case, we know that Gill earned $2306 in interest after one year at a rate of 6%. So:
I = $2306
r = 0.06
t = 1 year
Substituting these values into the formula, we get:
P = $2306 / (0.06 * 1)
P = $38,433.33
Therefore, the initial amount of money that Gill deposited into her account was $38,433.33.
5x-2=3(x+4)
What is the value of X
Answer:
[tex]\large\boxed{\textsf{x = 7}}[/tex]
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to find the value of x.}[/tex]
[tex]\textsf{We should simply isolate the x so that it's only on one side.}[/tex]
[tex]\large\underline{\textsf{How?}}[/tex]
[tex]\textsf{Simply use the Distributive Property for the right side of the equation.}[/tex]
[tex]\textsf{Simplify the equation to where x is by itself.}[/tex]
[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{The Distributive Property is a Property that allow us to distribute expressions further.}[/tex]
[tex]\textsf{Commonly, the form is a(b+c); Where b and c are multiplied by a.}[/tex]
[tex]\large\underline{\textsf{Use the Distributive Property;}}[/tex]
[tex]\mathtt{5x-2=3(x+4)}[/tex]
[tex]\mathtt{5x-2=(3 \times x)+(3 \times 4)}[/tex]
[tex]\mathtt{5x-2=3x+12}[/tex]
[tex]\large\underline{\textsf{Add 2 to Both Sides of the Equation;}}[/tex]
[tex]\mathtt{5x-2 \ \underline{+ \ 2}=3x+12 \ \underline{+ \ 2}}[/tex]
[tex]\mathtt{5x=3x+14}[/tex]
[tex]\large\underline{\textsf{Subtract 3x from Both Sides of the Equation;}}[/tex]
[tex]\mathtt{5x-3x=3x-3x+14}[/tex]
[tex]\mathtt{2x=14}[/tex]
[tex]\large\underline{\textsf{Divide the Whole Equation by 2;}}[/tex]
[tex]\mathtt{\frac{2x}{2} = \frac{14}{2} }[/tex]
[tex]\large\boxed{\textsf{x = 7}}[/tex]
Answer:
[tex] \sf \: x = 7[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x - 2 = 3(x + 4)
Then the value of x will be,
→ 5x - 2 = 3(x + 4)
→ 5x - 2 = 3(x) + 3(4)
→ 5x - 2 = 3x + 12
→ 5x - 3x = 12 + 2
→ 2x = 14
→ x = 14 ÷ 2
→ [ x = 7 ]
Hence, the value of x is 7.
The island of Martinique has received $32,000
for hurricane relief efforts. The island’s goal is to
fundraise at least y dollars for aid by the end of
the month. They receive donations of $4500
each day. Write an inequality that represents this
situation, where x is the number of days.
An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.
What is inequality?Inequality is an algebraic statement that two or more mathematical expressions are unequal.
Inequalities can be represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount received by the island = $32,000
The daily receipt of donations = $4,500
Let the number of days = x
Let the funds raised for aid = y
Inequality:y ≤ 32,000 + 4,500x
Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.
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What is an equation of the line that passes through the point (5,1) and is parallel to
the line x +y = 9?
The line x + y = 9 is y = -x + 6 is keeps through the point (5,1).
To find the equation of the line that passes through the point (5,1) and is parallel to the line x + y = 9, we need to first find the slope of the line x + y = 9.
Rearranging the equation in slope-intercept form, we get y = -x + 9
The slope of this line is -1, since the coefficient of x is -1.
Since the line we want to find is parallel to this line, it will have the same slope of -1.
Using the point-slope form of a line, the equation of the line passing through the point (5,1) and with a slope of -1 is: y - 1 = -1(x - 5)
Simplifying and rearranging the equation, we get:
y - 1 = -x + 5
y = -x + 6
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Complimentary Event The compliment of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted E (read "E bar"). Rule for Complimentary Events P(E)=1-P(E) or P(E)=1-P(E) O P(E)+P(E)=1 Example # 12: The probability that Mary can work a problem is 70%. Find the probability that Mary cannot work the problem. Example # 13: In 2004, 57.2% of all enrolled college students were females. Choose one enrolled student at random. What is the probability that the student was a male?
The student is male, which is P(male).Using the rule of complementary events, P(male) = 1 - P(female)P(male) = 1 - 0.572 = 0.428Therefore, the probability that the student is male is 0.428 or 42.8%.
The complimentary event is a part of probability theory. It is the event that occurs when the event E does not occur. In other words, it is a set of outcomes in the sample space that are not included in the outcomes of event E. The notation for the complement of E is E'. Rule for Complimentary EventsThe rule for complementary events can be expressed in two ways:
P(E) = 1 - P(E)P(E) + P(E') = 1Example # 12:Let the probability that Mary can work a problem be P(E) = 0.70.We need to find the probability that Mary cannot work the problem, which is P(E').Using the rule of complementary events,P(E') = 1 - P(E)P(E') = 1 - 0.70 = 0.30Therefore, the probability that Mary cannot work the problem is 0.30 or 30%.Example # 13:Let P(female) be the probability that the student is female. We are given that P(female) = 0.572.
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In data analytics, a _____ refers to all possible data values in a certain dataset
In data analytics, a population refers to all possible data values in a certain dataset.
What is data analytics?Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.
The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.
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Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b
The upper bound of a + b can be found by adding the upper bounds of a and b.
For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.
For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.
So the upper bound of a + b is:
5.5 + 3.5 = 9
Therefore, the upper bound of a + b is 9cm.
How do I solve this?
Answer:
X+4
Step-by-step explanation:
Area = l *b
x^2 + 13x + 36 = (X+9) * b
x^2 + 9x + 4x + 36 = (X+9) * b
X(X+9) + 4(X+9) = (X+9) * b
(X+4) (X+9) = (X+9) * b
b = (X+4)
Solve the triangle PQR (find the measures of ∠P, ∠Q, and side PQ).
(I need help finding both angle measure and side measure, please and thank you!)
Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
What precisely is a triangle?A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.
Here,
The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:
=> PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)
=> PQ² = 9² + 12² - 2(9)(12)cos(62°)
=> PQ² ≈ 110.03
=> PQ ≈ 10.49
As a result, side PQ is roughly 10.49 units long.
The rule of sines can then be used to determine the dimensions of angles P and Q:
=> sin(∠P) / PQ = sin(62°) / PR
=> sin(∠P) / 10.49 = sin(62°) / 9
=> sin(∠P) ≈ 0.6322
=> ∠P ≈ 39.39°
=> sin(∠Q) / PQ = sin(77°) / QR
=> sin(∠Q) / 10.49 = sin(77°) / 12
=> sin(∠Q) ≈ 0.8559
=> ∠Q ≈ 58.10°
As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
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Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
x cos y = 1, (2, pi/3), Find the derivative.
The derivative of the implicit function x · cos y = 1 at point (2, π / 3) is equal to y' = √3 / 6.
How to find the derivative of a function by implicit differentiation
In this problem we find the case of a implicit function of the form f(x, y), whose derivative must be found. This can be done by implicite differentiation, whose procedure is shown:
Derive the function by derivative rules.Clear y' within the resulting expression. Substitute x and y.Step 1 - Derive the expression by derivative rules:
cos y - x · sin y · y' = 0
Step 2 - Clear y' within the expression:
y' = cos y / (x · sin y)
Step 3 - Clear x and y in the resulting expression:
y' = cos (π / 3) / [2 · sin (π / 3)]
y' = 1 / [2 · tan (π / 3)]
y' = √3 / 6
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use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.
To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.
Let's consider a cross section of the solid taken at a distance x from the center of the circle.
Since the cross section is an equilateral triangle, all its sides have the same length.
Let this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:
[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]
Therefore, the area of the cross section at a distance x from the center of the circle is:
[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]
Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):
[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]
To find the limits of integration for y, we need to consider the equation of the circle:
[tex]x^2 + y^2= 3^2[/tex]
Solving for y, we get:
[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]
Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:
[tex]y = 3*\sqrt{3}[/tex]
Substituting this into the integral, we get:
[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]
[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]
Integrating, we get:
[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]
[tex]= 81/2*\sqrt{3}[/tex]
Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units
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Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
Answer: 12.84
Step-by-step explanation:
if x = 3.2 and y = 6.1 and Z = 0.2
then plug in the numbers
(3.2)(0.2) + (6.1)(2)
0.64 + 12.2 = 12.84
Any variable next to a number means multiplication.
if I was wrong lmk
Triangle ABC has coordinates A(4,1), B(5,9),and C (2,7). If the triangle is translated 7 units to left, what are the coordinates of B'?
Answer:
(-2,9)
Step-by-step explanation:
when moving it 5 units left on the x axis it would be 5-7
So in turn you would be given (-2,9)
Because the y stays the same you would still have (?,9)
Using c use the best term to identify the following.
The correct definition for the lines drawn to circle with centre C are:
FA is an secant.CD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.Explain about the circle?A circle is a spherical shape without boundaries or edges.
A radius describes the distance radiating from the centre.The Diameter passes through the centre of the circle in a straight line.The distance travelled through a circle is its circumference.A line that precisely crosses a circle at one point is said to be tangent.The circular region is divided into two sections by a circle's chord. The term "circular segment" refers to each component.The major segment and minor segment are distinguished by the arcs they contain. The major segment contains the minor arc.Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:
FA is an secantCD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.know more about the circle,
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Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie
reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.
Answer:
45 yo
Step-by-step explanation:
Let's start by defining some variables to represent the ages of Ted and Rosie:
- Let's call Ted's current age "T"
- Let's call Rosie's current age "R"
From the problem statement, we know that:
- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:
T = 5(R - (T - R))
Simplifying this equation, we get:
T = 5(R - T + R)
T = 10R - 5T
- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:
R + T = 72 - T
We now have two equations with two variables. We can use substitution to solve for T.
Substitute the second equation into the first equation to eliminate R:
T = 10R - 5T
T = 10(72 - T) - 5T
T = 720 - 15T
16T = 720
T = 45
Therefore, Ted's current age is 45.
#1 Brainlist!
Answer and show steps and I will make you brainlist.
Answer:
Multiplying the second equation by 5, we get:
15x + 20y = 180
Now, we can add this equation to the first equation:
26x = 208
x = 8
Substituting x = 8 in the second equation:
3(8) + 4y = 36
4y = 12
y = 3
Therefore, the solution to the system is (8, 3).
