The measure of angle ∠A will be 53.13.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
The two sides are perpendicular = 9.2 and the base is 7.2. The angle ∠A will be calculated as:-
tan(A) = P / B
A = tan⁻¹ ( 9.2 / 7.2 )
A = 53.13°
Therefore, the measure of angle ∠A will be 53.13.
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Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of pi (no approximations).
The requried area of the shaded region is 4.56 square centimeters.
What is the area of the circle?The area of a circle is given by the pie times square of the radius.
Area of circle = πr²
Here,
A right triangle is inscribed in a circle where the diameter of the circle is the hypotenuse of the right triangle,
So from the figure,
The area of the shaded region is given by the difference between the semi-circle LMN and the area of the right triangle LMN
The diameter of the circle is given by trig ratios,
sin 45 = 4/d
d = 4√2 So the radius will be d = 2√2
Now,
As hypotenuse is the diameter of the circle,
So LM = MN
Now,
Area of shaded region = area of semi-circle - an area of a triangle
Area of shaded region = πr²/2 - 1/2 × base × height
Area of the shaded region = 3.14 × [2√2]²/2 - 1/2 × 4 × 4
Area of shaded region = 4.56 cm²
Thus, the requried area of the shaded region is 4.56 square centimeters.
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Members of a soccer team suspect the coin used for the coin toss at the beginning of their games is unfair. They believe it turns up tails less often than it should if it were fair. The coach of the team decides to flip the coin 100 times and count the number of tails. His trial results in 35 tails. He decides to carry out a significance test. What is the p-value he obtains and the general conclusion that can be made at a 99% significance level?.
The p-value he obtains and the general conclusion that can be made at a 99% significance level is 0.01
A p-value is a measure of the evidence against a null hypothesis. In this case, the null hypothesis is that the coin is fair and equally likely to turn up heads or tails.
The coach carries out a significance test to determine if the number of tails in his trial of 100 flips is significantly different from what would be expected if the coin were fair.
The p-value is calculated by comparing the observed number of tails (35) to the expected number of tails (50, if the coin were fair) using a binomial distribution.
This involves finding the probability of observing 35 or fewer tails in 100 flips, assuming the null hypothesis is true. If this probability is low (i.e. if the p-value is small), then it suggests that the coin is not fair and that the observed difference is unlikely to have occurred by chance.
At a 99% significance level, a common threshold used in statistical tests, the p-value needs to be less than 0.01 to reject the null hypothesis and conclude that the coin is not fair.
If the p-value obtained is less than 0.01, then we can conclude with 99% confidence that the coin is biased towards heads. On the other hand, if the p-value is greater than 0.01, then we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the coin is unfair.
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Micro economics, I will give brainliest if you get this correct
Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources
Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.
Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.
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A middle school with z students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts a and b.
LOADING... Click the icon to view the table of activities.
Question content area bottom
Part 1
a. Write an expression in the table for each activity to represent the number of students who enjoy that activity most.
Activity
Word Description
Expression
Drama
22 more than one-eighth of the students
one eighth s plus 26
1
8s+26
Baseball
24 fewer than five-eighths of the students
three eighths s minus 28
3
8s−28
Dance
27 more than one-eighth of the students
one eighth s plus 30
1
8s+30
(Use integers or fractions for any numbers in the expression.)
The system of equations are
a) Drama = ( 1/8 )s + 22
b) Baseball = ( 5/8 )s - 24
c) Dance = ( 1/8 )s + 27
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of students be represented as s
a)
For Drama , it is 22 more than one-eighth of the students
On simplifying the equation , we get
Drama = ( 1/8 )s + 22
b)
For Baseball , it is 24 fewer than five-eighths of the students
On simplifying the equation , we get
Baseball = ( 5/8 )s - 24
c)
For Dance , it is 27 more than one-eighth of the students
On simplifying the equation , we get
Dance = ( 1/8 )s + 27
Hence , the equations are solved
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Paul gross weekly salary is $456 what is the maximum monthly rent he can afford?
Answer:
A metal disk 12cm in diameter and 5cm thick is melted down and cast into a cylindrical bar of diameter 5cm . How long is the bar
How can i learned maths hardly?
Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.
Some tips that may help you learn maths quickly and efficientlyStart with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.
Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.
Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.
Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.
Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.
Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.
Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.
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Four of the following statements are correct descriptions of a Normal curve. Which one is NOT a characteristic of a Normal curve?
A. It is symmetric.
B. Its spread increases as its mean increases.
C. It is bell-shaped.
D. Its mean is equal to its median.
E. It is single-peaked (unimodal).
(D) Its mean is equal to its median is NOT a characteristic of a Normal curve.
While it is true that the mean and median are equal in a symmetrical distribution like the Normal curve, not all distributions with equal mean and median are symmetrical and Normal.
In a Normal distribution, the mean, median, and mode are equal and located at the center of the bell-shaped curve. However, in a skewed distribution, the mean and median may still be equal but the distribution will not be symmetrical or bell-shaped.
The most important continuous probability distribution in probability theory and statistics is known as the Normal Distribution, commonly known as the Gaussian Distribution.
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Will give brainliest
Answer:
Below
Step-by-step explanation:
f(x) = x^2+ 6x -5 Use Quadratic Formula with a = 1 b = 6 c = -5
to find :
x = - 3 ± [tex]\sqrt{17}[/tex]
YOU GUYS I’M BEGGING YOU
A ball is dropped from a height of 64 feet. It
rebounds three-fourths of the height from which it falls every time it hits the ground. Write a function that models the height the ball
reaches after each time it hits the ground.
Answer:
This is a standard problem if GP (Geometric Progression) as the height of the ball is getting reduced by 25% every-time it touches the ground.
Step-by-step explanation:
Solve the equation AB=BC for A, assuming that AB and C are square matrices and Bis invertible.?
[tex]A = B^-1 * BC[/tex]
Since B is invertible, it can be used to solve the equation.
1. Calculate the inverse of B, [tex]B^-1[/tex].
2. Multiply[tex]B^-1[/tex] with BC, to obtain A.
Assuming that AB and C are square matrices and B is invertible, the equation AB=BC can be solved for A. To do this, we first need to calculate the inverse of B, [tex]B^-1[/tex]. The inverse of a matrix is defined as the matrix which when multiplied to the original matrix, yields the identity matrix. Once we have the inverse of B, we can use it to solve the equation by multiplying [tex]B^-1[/tex] with BC, which will give us A. This works because when we multiply a matrix by its inverse, the result is always the identity matrix. Hence, by multiplying the inverse of B with BC, we can obtain A.
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Each of 8 students reported the number of movies they saw in the past year. Here is what they reported. 4, 17, 17, 20, 13, 4, 16, 18 Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
Answer:
13.6
Step-by-step explanation:
To find the mean number of movies that the students saw, we add up all the reported numbers of movies and then divide by the total number of students (which is 8 in this case).
Adding up the reported numbers of movies:
4 + 17 + 17 + 20 + 13 + 4 + 16 + 18 = 109
Dividing by the number of students:
109/8 = 13.625
Rounding to the nearest tenth:
Mean number of movies seen = 13.6
Therefore, the mean number of movies that the students saw, rounded to the nearest tenth, is 13.6.
Answer: 13.6
Step-by-step explanation:
Your basically finding the average:
(4+17+17+20+13+4+16+18)/8 = 13.6
Bodin Company manufactures finger splints for kids who get tendonitis from playing video games. The firm had the following inventories at the beginning and end of the month of January. Jan 1 Jan 31 Finished goods$125,000 $117,000 Work in process 233,000 251,000 Raw material 133,000 124,000 The following additional data pertain to January operations. Raw material purchased$190,000 Direct labor 350,000 Actual manufacturing overhead 170,000 Actual selling and administrative expenses 110,000 The company applies manufacturing overhead at the rate of 60 percent of direct-labor cost. Any overapplied or underapplied manufacturing overhead is accumulated until the end of the year. Compute the company's prime cost for January.
The company's prime cost for January is 556000.
As per the data given:
Bodin Company manufactures finger splints for kids who get tendonitis from playing video games.
The firm had the following inventories at the beginning and end of the month of January.
January 1 January 31
Finished goods---------$125,000----------------$117,000Work in process--------$233,000---------------$251,000Raw material-------------$133,000----------------$124,000The following additional data pertain to January operations.
Raw material purchased------------------------------------$190,000Direct labor------------------------------------------------------350,000 Actual manufacturing overhead--------------------------170,000Actual selling and administrative expenses----------110,000Here we have compute the company's prime cost for January.
First add Raw materials, January 1 with Raw materials purchased and then subtract Raw materials, January 31 from this sum and then later add up the Direct labor to the result.
The final result will be the prime cost for January
Raw materials, January 1_______133000(+) Raw materials purchased____190000(-) Raw materials, January 31____117000Raw materials used___________206000(+) Direct labor______________ 350000Prime cost__________________556000Therefore the prime cost is 556000.
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Mark has a bag containing a mixture of 30 green and white
marbles. Without looking, he guesses that half of the marbles in
the bag are green. He randomly selected 1 marble from the bag,
recorded the color, and returned the marble to the bag. After 15
trials, Mark has drawn 10 green marbles and 5 white marbles.
Which of the conclusions below is best supported by his data?
The best conclusion is:
The bag contains more green Marbles than white marbles.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
The bag contains 10 green marbles and 20 white marbles.
The bag contains an equal amount of each color.
The bag contains more green than white marbles.
After 15 trials, Mark has drawn 10 green marbles and 5 white marbles
So, the Probability of Total green Marbles
= (10/15) x 30
= 20
Probability of Total White Marbles
= (5/15) x 30
= 10
So, The bag contains more green Marbles than white marbles.
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Find the average rate of change on the interval [-3, 4].
The average rate of change of f(x) over the interval is 15/7
What is the average rate of change of f(x) over the intervalFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
f(-3) = -4
f(4) = 11
The average rate is then calculated as
Average rate = [f(4) - f(-3)]/[4 + 3]
Substitute the known values in the above equation, so, we have the following representation
Average rate = (11 + 4)/(4 + 3)
Evaluate
Average rate = 15/7
Hence, the average rate is 15/7
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Complete question
Find the average rate of change on the interval [-3, 4].
X f(x)
-3 -4
4 11
PLS!!!!!!!!!!!!!!!!! HELP ME ASAP. The director of a youth soccer league asked the coaches to survey the members of their teams about their years of experience playing soccer.
Maya's coach gathered data from her team, the Dragons, and displayed the results in the line plot shown below.
The league director combined the data from all 120 athletes in the league and created the box-and-whisker plot shown below to display the data.
34
This question has 3 parts. Be sure to complete all parts.
A
Type your response in the box.
What is an example of a question that the data displays can be used to answer about Maya's team but not about the whole league? Answer the question, and explain why it cannot be answered about all the players in the league.
Answer: A Parameter is a value that represents a property of a population. This could be the population mean.A statistic is a value that represents a property of a sample. This could be the sample mean.In the given scenario, the population is the entire 14 teams.
Step-by-step explanation: I hope this helps^^
If f(x) = +8, what is f(x) when x = 10?
04
09
O 13
O 36
Answer:
Evaluate the function for x = 10 , that is substitute 10 into any x in the function.
f(10) = 102+8=5+8=13
Step-by-step explanation:
I hope it helps you
The value of function f(x) at x= 10 is 13.
The correct option is C.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
f(x) = x/2 + 8
Now, we have to find the value of function at x= 10.
So, put the value x= 10 the f(x) we get
f(10)= 10/2+ 8
f(10) = 5 + 8
f(10) = 13
Thus, the required value is 13.
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What is the greatest common factor (GCF) of 9 and 18
Answer: 9
Step-by-step explanation:
Find the factors (numbers that the given number can be divided by to make a whole number) of each number:
9: 1,3,9
18: 1,2,3,6,9,18
It's quite easy here because the numbers are small but if you get bigger numbers, it might be helpful to draw out a prime factorization tree. And then multiply together all the common prime numbers. (I haven't explained this in great detail but if you want to know leave a comment :))
Kayla rolls a die 84 times. How many times can she expect to roll a 3?
A. 14
B. 21
C. 12
D. 18
Answer:
[tex]\huge\boxed{\sf 14\ times}[/tex]
Step-by-step explanation:
Formula:[tex]\displaystyle Probability = \frac{Possible \ no. \ of\ events}{Total \ number\ of \ events}[/tex]
Solution:If we roll a die 1 time, the probability of obtaining a 3 is:
= 1 / 6
Because a die has total 6 faces, out of which 3 is only 1.
But, if we roll it 84 times, it becomes:
= [tex]\displaystyle \frac{1}{6} \times 84[/tex]
= 84/6
= 14 times[tex]\rule[225]{225}{2}[/tex]
5
Select the correct answer.
2
2
Which of the following inequalities is graphed on the coordinate plane?
O A. y 2 2z + 2
OB. y< 2z+ 2
O c.
y > 2z + 2
OD. y ≤ 2z + 2
The Answer Is A
Its hard to explain but the answer is A
Calculate the distance between the points J=(-4, 0) and E = (4, 7) In the coordinate plane.
Round your answer to the nearest hundredth.
E
Distance: I
The distance between the points J=(-4, 0) and E = (4, 7) In the coordinate plane is, 10.63 units
How to calculate distance between two points ?The distance between two points in the coordinate plane can be calculated using the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
The given points
J=(-4, 0) and E = (4, 7),
we have:
x₁ = -4, y₁ = 0
x₂ = 4, y₂ = 7
Plugging in these values into the distance formula, we get:
d = √((4-(-4))² + (7-0)²)
= √(8² + 7²)
= √(64 + 49)
= √113
= 10.63 (rounded to the nearest hundredth)
So, the distance between points J and E is approximately 10.63 units.
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Dave spent $6 on a pack of 3 test tubes. Which shows the money spent per test tube?
An expression which shows the money spent per test tube is u = 6/3.
How to determine the unit price?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the unit price, we would determine the unit rate for one pack of 3 test tubes by using the following mathematical expression;
Unit price = Cost of test tubes/Number of test tubes
Substituting the given parameters into the unit price formula, we have the following;
Unit price = $6/3
Unit price = $2.
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Given the following segment lengths, find the length of segment AB.
AC : 10
EC : 16
ED :4
Show all your work
2.5 is the length of segment AB.
What is line segment ?
A line segment in geometry has two unique points on the line that define its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.
In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.
BD ║ AE
Δ CBD ≈ ΔCAE by AA similarity corresponding sides are proportional .
CB/CA = CD/DE ⇒ CB/10 = EC - ED/16
CB/10 = 16 - 4/16 ⇒ CB/10 = 12/16
CB = 12 * 10/16 = 7.5
AB= AC - CB = 10 - 7.5
AB = 2.5
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how do you graph 3x+2y=12 on a graph? i need to graph y=5x-7 and 3x+2y=12 to see where they intersect.
The solution of the system of equations is equal to (2, 3).
What is a point of intersection?In Mathematics, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (2, 3).
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(-2 -2) and y=8/3x-5 in slope intercept form
The equation of a line perpendicular to line y = 8/3x-5 in slope-intercept form that contains point (-2, -2) is y = -3x/8 - 11/4.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
8/3 × m₂ = -1
m₂ = -3/8.
At data point (-2, -2), a linear equation of this line can be calculated in point-slope form as follows:
y - (-2) = -3/8(x - (-2))
y + 2 = -3/8(x + 2)
y = -3x/8 - 3/4 - 2
y = -3x/8 - 11/4
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What is t statistic table ?
The t statistic table is the t-test table is used to evaluate proportions combined with z-scores.
In Statistics, a t-test, can be expressed similarly as a statistical hypothesis test where the test statistic maintains a student’s t-distribution, if the null hypothesis is set. Hence, we know we can use the t-test table here.
The t-test table is used to evaluate proportions combined with z-scores. This table is used to find the ratio for t-statistics. The t-distribution table displays the probability of t-values from a given value. The acquired probability is the t-curve area between the t-distribution ordinates, i.e., the given value and infinity.
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Why do we use p hat in statistics?
In statistics, p hat is used as an estimator of the population proportion (p) of a categorical variable. It is the sample proportion of the variable, which is calculated as the number of occurrences of a particular category in the sample divided by the total sample size.
The reason why p hat is used is that it provides an estimate of the unknown population proportion based on a representative sample. By using p hat, we can draw inferences about the population proportion with a certain level of confidence. This is important in hypothesis testing and confidence interval estimation, where we want to make statements about the population based on the information gathered from a sample.
Using p hat as an estimator of p is also beneficial because it has desirable statistical properties, such as being an unbiased estimator, having a sampling distribution that approaches normality, and having a known standard error.
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What is 56 prime factors?
The prime factorization of 56 is the process of breaking 56 down into its prime factors. The prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.
One way to calculate the prime factorization of 56 is to use a factor tree. To begin, find two numbers that multiply together to equal 56. The two factors that multiply together to equal 56 are 8 and 7. Since 8 and 7 are both prime numbers, they can be written as the prime factors of 56: 56 = 8 x 7.In mathematical terms, the prime factorization of 56 can be expressed as 56 = 2 x 2 x 2 x 7, where 2 is multiplied by itself three times and then multiplied by 7. This is because 56 can also be written as 2 x 2 x 2 x 7, which is the same as 8 x 7.The prime factorization of 56 can also be expressed as the product of the prime exponents: 56 = 2^3 x 7^1. Here, 2 is raised to the third power, and 7 is raised to the first power. This expression is equivalent to 8 x 7.In summary, the prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.
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Please answer ASAP (show work)!
The width of a mirror is 2 in. Less than its length. The area of the mirror is 168 in. sq. Find the dimensions of the mirror.
Work Shown:
x = length
x-2 = width
area = length*width
area = x(x-2)
x(x-2) = 168
x^2-2x = 168
x^2-2x-168 = 0
Plug a = 1, b = -2, c = -168 into the quadratic formula.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-168)}}{2(1)}\\\\x = \frac{2\pm\sqrt{676}}{2}\\\\x = \frac{2\pm26}{2}\\\\x = \frac{2+26}{2} \ \text{ or } \ x = \frac{2-26}{2}\\\\x = \frac{28}{2} \ \text{ or } \ x = \frac{-24}{2}\\\\x = 14 \ \text{ or } \ x = -12\\\\[/tex]
Ignore x = -12 since we cannot have a negative length.
The only practical solution is x = 14.
If x = 14, then x-2 = 14-2 = 12
The rectangular mirror is 14 inches by 12 inches
Check: area = length*width = 14*12 = 168
The answers are confirmed.
what is 193 lbs to kg ?
Since 1 lbs is 2.2046 kilogram. Therefore, 193 lbs is 87.5433 kilograms.
Pound:
Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.
Kilogram:
The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.
According to the Question:
We can use the following formula to convert Pounds to kilogram :
X(kg) = y(lb) × 0.45359237
Converting 193 lbs to kilograms:
To convert 193 pound to kilogram:
⇒ X(kg) = 193(lbs) × 0.45359237
= 87.5433 kilogram
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What could you multiply the top equation by to be able to add the equations and eliminate the x-values in this system?
You should multiply the top equation by 3 to be able to add the equations and eliminate the x-values in this system.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
2x + 5y = 5 .........equation 1.
-6x + 7y = -37 .........equation 2.
By multiplying equation 1 by 3, we have:
3(2x + 5y = 5) = 6x + 15y = 15 ......equation 3
By adding equation 2 to equation 3, we have:
6x + 15y = 15
-6x + 7y = -37
22y = -22
y = -22/22
y = -1.
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