That sounds like a smart plan! Before investing his savings, Jose should do some research to determine the best investment strategy for his goals.
What is research?
He will need to consider factors such as his risk tolerance, the potential return on investment, and the length of time he has to invest. Once he has identified an investment strategy that aligns with his goals, he should start investing his savings.
Over time, as his investments generate returns, he can use these returns to fund his business venture. It is important for Jose to regularly monitor his investments and adjust his strategy as needed to ensure that he is on track to achieve his goals. With careful planning and a well-executed investment strategy, Jose can achieve his goal of retiring early and starting his own coaching classes.
What is an investment ?
An investment refers to the purchase of an asset with the goal of generating income, capital appreciation, or both. The asset could be anything of value, such as stocks, bonds, real estate, commodities, or mutual funds. Investors typically make an investment with the expectation of earning a return on their investment over a period of time.
The return could be in the form of interest, dividends, or capital gains, depending on the type of investment. Investors may choose to invest in different types of assets based on their investment goals, risk tolerance, and investment horizon. The process of investing involves conducting research, analyzing market trends, and making informed decisions based on the available information.
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Complete question is: Jose is a middle-aged professor who wants to retire early and start his own coaching classes. He decides to invest his savings and use the returns to fund his business venture. Before investing his savings, Jose should do some research to determine the best investment strategy for his goals.
Need help with this
5. The value of angle LNM in the given circle is 54 degrees. 7. The value of angle ABC is 51 degrees.
What is a circle?A circle is a two-dimensional shape made up of a collection of points that are spaced uniformly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius. The centre, the radius, and the diameter of a circle may be seen in the following illustration.
5. The angle subtended by the two chords is half the measure of the angle at the center.
Thus,
angle LNM = 1/2 (angle LPM)
Substitute the value of angle LPM = 108, thus:
angle LNM = 1/2(108) = 54 degrees.
Hence, the value of angle LNM in the given circle is 54 degrees.
7. For measure angle ABC we have:
16x-26 = 2(5x+11)
16x-10x = 22+26
6x=48
x = 8
Substituting the value of x we have:
5(8) + 11 = 40 + 11 = 51
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The mean per capita daily water consumption in a village in Bangladesh is about 83 liters per person and the standard deviation is about 11.9 liters person. Random samples of size 50 are drawn from this population and the mean of each sample is determined . Probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person.
the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability theory is a branch of mathematics that deals with the study of random events and their probabilities
In the given question,
We are given that the population mean per capita daily water consumption is 83 liters and the standard deviation is 11.9 liters. We are also given that random samples of size 50 are drawn from this population and the mean of each sample is determined.
We can use the central limit theorem to approximate the distribution of the sample means. According to the central limit theorem, the distribution of the sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
So, for a sample size of 50, the standard deviation of the sample mean is:
standard deviation of sample mean = 11.9 / √(50) = 1.68
To find the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person, we need to find the z-scores corresponding to these values and use the standard normal distribution table or calculator to find the probability.
The z-score for 80 liters per person is:
z = (80 - 83) / 1.68 = -1.79
The z-score for 82 liters per person is:
z = (82 - 83) / 1.68 = -0.60
Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score between -1.79 and -0.60 is 0.1271.
Therefore, the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%
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Find the domain and range for y=4x^2+24x+13 and f(x)=-5x+20x-7
All real numbers make up the domain of a linear function, hence the domain of [tex]f(x)=-5x+20x-7[/tex] is [tex](-\infty , \infty )[/tex] . The range of a linear function is also the set of all real numbers, hence [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).
What is domain and range?For the formula, [tex]y = 4x2 + 24x + 13[/tex]
All real numbers make up the domain of a polynomial function, hence the domain of y=4x2+24x+13 is [tex](-\infty , \infty )[/tex]
We can use calculus or the square root method to determine the function's range. At x=-3, where y=1, the function's minimal value is found. As a result, the function's range is [tex][1, \infty )[/tex].
Using the formula [tex]f(x)=-5x+20x-7:[/tex]
Using related words together, we obtain [tex]f(x)=15x-7.[/tex]
Therefore, All real numbers make up the domain of a linear function, hence the domain of [tex]f(x)=-5x+20x-7[/tex] is [tex](-\infty , \infty )[/tex] . The range of a linear function is also the set of all real numbers, hence [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).
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is 0.0505505550... a rational number?
The number "0.0505505550..." is an irrational number. The reason for it is that the number can't be expressed as the quotient of two integers. SInce it has the ellipsis (...) at the end, it indicates that the number isn't showing all its significant figures, therefore, can't be represented as the ratio of two integers. Thus, it is irrational.
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Answer:
No, it's not
Step-by-step explanation:
A rational number can be written in the form [tex]\sf{\dfrac{p}{q}}[/tex], where q ≠ 0.
While an irrational number cannot be written in such a form.
Well, not only can't we express 0.0505505550... as [tex]\sf{\dfrac{p}{q}}[/tex], we also see three dots in the end that indicate that the number goes on forever.
It's impossible to express a number that goes on for ever, as a fraction.
Therefore the number is irrational.
Write a mathematical expression to represent the following statement.
'Two less than a number plus twenty.'
Answer: (n - 2) + 20
Step-by-step explanation:
We will create a mathematical expression using the statement given. 'Less' implies subtraction, let n be a number.
'than a number' ➜ n
'Two less' ➜ - 2
'plus twenty.' ➜ + 20
'Two less than a number plus twenty.' ➜ (n - 2) + 20
How many people can you allow on a
beach if the lifeguards want to have
30 sq ft per person and the beach is
1,000 ft long and 200 ft wide? Round
to a whole number.
Answer:
Rounding down to a whole number, we get:
6,666 people
Step-by-step explanation:
First, we need to calculate the total area of the beach:
1000 ft x 200 ft = 200,000 sq ft
Next, we divide the total area by the desired area per person:
200,000 sq ft ÷ 30 sq ft per person = 6,666.67 people
Factor 16x2 – 49.....
Answer:
(4x+7)(4x-7)
Step-by-step explanation:
Use DoS (x+y)(x-y)=x^2-y^2
22-1x5-4 to the second
The value of a given arithmetic expression is 1.
We have given that an arithmetic expression -
22-(1×5)-4 to the seccond
So we can write it -
22-(1×5)-4²
we shall solve it with the help of the BODMASS rule
BODMAS Rule: The BODMAS Rule is a crucial mathematical tool for resolving issues. It is a technique for using an arithmetic expression to resolve mathematical problems. The abbreviation BODMAS stands for brackets, order of powers or roots, division, and multiplication. S indicates for subtraction, whereas A stands for addition.
according to BODMASS
first, solve the brackets and square,
=22-(5)-16
now subtract all
=22-21
=1
The complete question is
Solve the given arithmetic expression -
22-(1×5)-4 to the seccond
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which of the following statements is false 1) sin45=cos45 2)cos110=sin80 3)sin30=cos40 5) sin0=cos90
The false statement is 3)sin30=cos40.
This is because the sine of 30 degrees is 0.5, whereas the cosine of 40 degrees is approximately 0.766. These two values are not equal to each other.
The following claims, however, are accurate:
The sine of 45 degrees is equal to the cosine of 45 degrees (both are equal to approximately 0.707).The cosine of 110 degrees is equal to the sine of 80 degrees.The sine of 0 degrees (or any multiple of 360 degrees) is equal to 0, and the cosine of 90 degrees (or any odd multiple of 90 degrees) is also equal to 0.Therefore, the false statement is 3)sin30=cos40.
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a) Write 1 as a decimal rounded to 1 significant figure.
b) Write
2
as a decimal rounded to 3 significant figures.
Since it is less than 5, we do not round up, and our final answer is 2.00.
What is decimal round?Decimal rounding is a process of changing a number to a certain number of decimal places, based on a specified rounding rule. In decimal rounding, the digits to the right of the specified decimal place are examined to determine whether rounding is necessary. If the digit immediately to the right of the specified decimal place is 5 or greater, the number is rounded up by adding 1 to the last digit of the specified decimal place. If the digit is less than 5, the number is rounded down by simply dropping the digits to the right of the specified decimal place.
(a). To round 1 to 1 significant figure, we only keep the leftmost digit, which is 1. Therefore, 1 rounded to 1 significant figure is 1.
(b) . To write 2 as a decimal rounded to 3 significant figures, we start by identifying the leftmost significant digit. In this case, it is the digit 2. We then count two more digits to the right, which gives us 2.00. Finally, we look at the next digit, which is 0. Since it is less than 5, we do not round up, and our final answer is 2.00.
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Express the following argument mathematically and give the rule(s) that could be used to prove or disprove them. a. The children are sick. The doctors are not here. Therefore the doctors are not here and the children are sick. [2 marks]?
Answer:
Step-by-step explanation:
Let A represent "The children are sick."
Let B represent "The doctors are not here."
Argument: A and ¬B
Rule(s) used to prove or disprove: Conjunction (AND)
Solve the problem in the picture please!
x^2-16÷ (x-16 )(x+4)
= (x^2)-(4^2)÷ (x-16)(x+4)
= (x+4)(x-4)÷ (x-16) (x+4)
=(x-4)÷(x-16)
Let a, b, and m be positive integers, where = a, and
4
=b. Which of the following numbers could be m?
The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.
What do you mean by term Integers?A whole number that can be either positive, negative, or zero is known as an integer. It is a number without a decimal or fractional component. Integer examples include: -3, -2, -1, 0, 1, 2, 3, etc
Lets check if 4 and 6 are divisible by both a and b and is a positive integer,
F. 124:
124/4 = 31, is a positive integer
124/6 = 20.6 is a not positive integer
Thus, 124 is not m.
G. 222:
222/4 = 55.5, is a not positive integer
Thus, 222 is not m.
H. 310:
310/4 = 77.5, is a not positive integer
Thus, 310 is not m.
J. 480:
480/4 = 120, is a positive integer
480/6 = 80 is a positive integer
Thus, 480 is m.
K. 544:
544/4 = 136, is a positive integer
544/6 = 90.6 is not a positive integer
Thus, 544 is not m.
Thus, The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.
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Complete question:
Two gears turn together. Each time Gear A makes 36 turns, Gear B makes 27 turns. How many turns does Gear A make When Gear B makes 90 turns?
In the proportion, Gear A makes 120 turns when Gear B makes 90 turns.
What is Proportion?
A proportion is a statement that two ratios or fractions are equal. It shows the relationship between two or more quantities that are proportional to each other.
The gears have a fixed ratio of rotations, which is determined by the number of teeth on each gear.
To find out how many turns Gear A makes when Gear B makes 90 turns, we can set up a proportion:
=> [tex]\frac{36}{27} =\frac{ x}{90}[/tex]
where x is the number of turns Gear A makes.
To solve for x, we can cross-multiply:
=> 36 × 90 = 27 × x
=> 3240 = 27x
=> x = 120
Therefore, Gear A makes 120 turns when Gear B makes 90 turns.
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Evaluate the expression m^2+7m-6 when m=5
Answer:
54 =)
Step-by-step explanation:
m^2+7m-6
5^2+7(5)-6
25+35-6
Answer is 54
Help with math problems
Answer:
Step-by-step explanation:
Sorry, i can't "add up to five attachments" because i say only answer.
1.(−24,8)
2.[−3,1]
3.[−3,4]
4. (−3,5)
5 and 6 no answer (check my attachments)
7. (−∞,−8)v(4,+∞)
8 (−∞,1)v(7,+∞)
9. (−∞,−3]v[6,+∞)
10. (−∞,−3]v[2,+∞)
11. (−∞,∞)
12. (−∞,∞)
13. (−∞,−[tex]\frac{21}{4}[/tex]]v[[tex]\frac{15}{4}[/tex],+∞)
14.[-[tex]\frac{4}{5}[/tex],[tex]\frac{8}{5}[/tex]]
15. (-[tex]\frac{17}{3}[/tex];5)
16. (−∞,−14]v[22,+∞)
17. no answer (how 5 and 6)
18. (−∞,∞)
19. (−2,[tex]\frac{2}{3}[/tex])
20. (−∞,−4)v(−[tex]\frac{2}{3}[/tex],+∞)
Scott Salman, a travel agent, is paid on variable commission, is married, and claims four withholding allowances. He receives 3% of the first $20,000 in sales, 4% of the next $10,000 in sales, and 6% of all sales over $30,000. This week he has sales of $45,550 and the following deductions: FICA, Medicare, federal withholding, state disability insurance, state withholding, a retirement contribution of $45, a savings bond of $50, and charitable contributions of $20. Find his net pay after subtracting all of his deductions.
Scott Salman's net pay after subtracting all of his deductions is $1,620.26.
How To calculate Scott Salman's net pay?
To calculate Scott Salman's net pay, we need to first calculate his commission earnings and then subtract all of his deductions.
Commission Earnings:
3% of the first $20,000 in sales = $600
4% of the next $10,000 in sales = $400
6% of all sales over $30,000 = 6% × ($45,550 - $30,000) = $930
Total commission earnings = $600 + $400 + $930 = $1,930
Now we can calculate his gross pay by adding his commission earnings to his base salary:
Gross Pay:
Base salary = 0 (not given)
Commission earnings = $1,930
Total gross pay = $1,930
Next, we need to calculate his deductions. We'll assume the following rates for each deduction:
FICA: 7.65%
Medicare: 1.45%
Federal withholding: based on the IRS tax tables (not provided)
State disability insurance: 1%
State withholding: based on the state tax tables (not provided)
Retirement contribution: $45
Savings bond: $50
Charitable contributions: $20
Deductions:
FICA = 7.65% × $1,930 = $147.45
Medicare = 1.45% × $1,930 = $27.99
Federal withholding = based on the IRS tax tables (not provided)
State disability insurance = 1%×$1,930 = $19.30
State withholding = based on the state tax tables (not provided)
Retirement contribution = $45
Savings bond = $50
Charitable contributions = $20
Total deductions = $147.45 + $27.99 + $19.30 + $45 + $50 + $20 = $309.74
Finally, we can calculate Scott Salman's net pay by subtracting his total deductions from his gross pay:
Net Pay:
Gross pay = $1,930
Total deductions = $309.74
Net pay = $1,930 - $309.74 = $1,620.26
Therefore, Scott Salman's net pay after subtracting all of his deductions is $1,620.26.
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Help plssssssssssssssss
find the length of the arc
(50 points)
can mark brainly
Answer: i'm going to assume, this needs to be a full answer
meaning this would be
43.9823 inches (or 44 if fully rounded)
basically, to find arc length, you take the given degrees shown (210) and divide it over the full length of the circle (360)
dividing this gives us 58.333333 (repeated forever) or 7/12
then we need to find the circumference, which is c=pid (or c=pi times diameter)
so we would do 24 multiplied by 3.14159 (this is standard amount of numbers for naturally calculating pi in equations) and we get 75.39816
finally, we need to multiply 75.39816 to 7/12, and we will get 43.98226
which when rounded to the 4th digit will give us 43.9823
Answer with step-by-step explanation:
The formula to find the arc length of a circle is:
[tex]\sf \red {Arc\: length = \frac{\theta}{360} *2 \pi r}[/tex]
PQ major arc length
[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{210}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{15825.6}{360} \\\\\sf Arc\: length = 43.96\: in[/tex]
PQ minor arc length
[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{150}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{11304}{360} \\\\\sf Arc\: length = 31.4\: in[/tex]
Solve for x. Round to the nearest tenth of a degree, if necessary.
E
2.6
F
to
3.4
G
The answer of the given question based on the triangle is the value of angle G or x is approximately 52.6° degrees (rounded to the nearest tenth of a degree).
What is Trigonometric function?Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). Trigonometric functions can be used to solve problems involving angles and sides of right triangles, as well as to model periodic phenomena such as waves and oscillations.
To find angle G, we need to use the trigonometric function tangent since we know the opposite and adjacent sides of angle G in the right triangle EFG.
Recall that the tangent of an angle is defined as the ratio of the opposite side to the adjacent side, i.e.,
tan(G) = opposite/adjacent = FG/EF
Substituting the given values, we get:
tan(G) = 3.4/2.6 = 1.3076
Using a calculator, we can find the inverse tangent of 1.3076, which gives us:
G ≈ [tex]tan^{-1}[/tex](1.3077) ≈ 52.6° degrees
Therefore, the value of angle G is approximately 52.6° degrees (rounded to the nearest tenth of a degree).
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To make marbled paper, Shannon filled a rectangular 279/10cm by 178/10cm dish with water. Then they gently swirled paint on top of the water. let a represent the area of the dish.
Select 1 multiplication and 1 division equation to represent the relationship.
choose 2 answers
A) 178/10 x a = 279/10
B) 178/10 x 279/10 = a
C) 279/10 ÷ 178/10 = a
D) a ÷ 178/10 = 279/10
The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:
a = (279/10) cm x (178/10) cm
Simplifying this expression, we get:
a = 4953/100 cm^2
So, the correct equations are:
B) 178/10 x 279/10 = a
and
D) a ÷ 178/10 = 279/10
Add the expressions.
the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity
negative 3 over 12 times p plus negative 1
7 over 16 times p minus 1
3 over 8 times p minus 15
7 over 8 times p plus negative 15
Please help me and tell me what is did wrong I picked The second one
An addition of the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity is: C. 3 over 8 times p minus 15.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expressions:
Expression = -8 - 1/4(p)
Expression = 5/8(p) - 7
By adding the two expressions, we have:
Addition = -8 - 1/4(p) + 5/8(p) - 7
Addition = -8 - p/4 + 5p/8 - 7
Addition = -15 +(-p/4 + 5p/8)
Addition = -15 +(-2p + 5p)/8
Addition = -15 + (3p)/8
Addition = 3p/8 - 15
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The sum of the digits of a two digit number is 10. When the digits are reversed, the number increases by 18. Find original number.
Answer:
Step-by-step explanation:
10x+y=10y+x-18 multiply the tens digit by 10 and leave the one's digit alone
9x=9y-18 divide by 9
x=y-2
x-y=-2
x+y=10
add above two equations
2x=8 divide by 2
x=4
y=10-4=6
numbers are 46 and 64
64=46+18 4+6=10
The cost of a small business is given by the expression 3000 + 12x, where x is the number of units produced. The business will be profitable whenever its profit y exceeds its cost.
If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
The profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex] .
What is the profitable for all values?To determine which graph corresponds to the given situation, we need to understand the relationship between cost, profit, and revenue.
The revenue (R) of a small business is given by the product of the price per unit (p) and the number of units sold (x):
[tex]R = px[/tex]
The profit (P) of a small business is the difference between its revenue and cost (C):
[tex]P = R - C = px - (3000 + 12x) = (p - 12)x - 3000[/tex]
The profit will be positive when P > 0, which means that the revenue is greater than the cost:
[tex](p - 12)x > 3000[/tex]
[tex]x > 3000/(p - 12)[/tex]
This inequality tells us that the business will be profitable for all values of x greater than [tex]3000/(p - 12).[/tex]
Graph A: This graph shows a linear revenue function (R = 20x) and a linear cost function [tex](C = 3000 + 10x).[/tex] The profit function [tex](P = R - C)[/tex] is also linear.
To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex]. However, we cannot determine if this corresponds to the given situation without knowing the price per unit.
Graph B: This graph shows a linear revenue function [tex](R = 25x)[/tex] and a quadratic cost function [tex](C = 3000 + 15x + 0.5x^2).[/tex] The profit function [tex](P = R - C)[/tex] is also quadratic. To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex] .
We can solve for the roots of the quadratic equation [tex]P = 25x - (3000 + 15x + 0.5x^2) = -0.5x^2 + 10x - 3000[/tex] and find the interval of x-values for which [tex]P > 0.[/tex]
This corresponds to the range of x-values for which the graph of P is above the x-axis. We can see that this region is shaded in blue, so Graph B corresponds to the given situation.
Graph C: This graph shows a linear revenue function [tex](R = 15x)[/tex] and a linear cost function [tex](C = 3000 + 20x).[/tex]The profit function [tex](P = R - C)[/tex] is also linear.
To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex]. However, we can see that the profit function intersects the x-axis at [tex]x = 150.[/tex]
Therefore, the profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex].
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A rectangle has side lengths of 5 inches and 5–√ inches. Which statement must be true about the area of the rectangle?
The area of a rectangle is represented by an irrational number because the product of the two side lengths is an irrational number. This is because the product between an integer and an irrational number leads to another irrational number, which is the right answer.
What is the area of the rectangle?A rectangle is a four-sided flat geometric form with right angles on all four sides. It is a quadrilateral, which implies that it has four sides. A rectangle's opposite sides are parallel and equal in length, whereas its adjacent sides are perpendicular to one other. A rectangle's area is computed by multiplying its length by its width, and its perimeter is computed by summing the lengths of all four sides.
According to this question, we know the lengths of the two sides of the rectangle, the length of a side is an positive integer and the length of the other one is an positive irrational number. The area of the rectangle is the product of the two sides lengths mentioned above.
By algebra, we know that the product between an integer and an irrational number leads to other irrational number. Therefore, the area of the rectangle is represented by an irrational number.
A = 3 x [tex]\sqrt{5}[/tex]
A = 3[tex]\sqrt{5}[/tex]
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The complete question is: A rectangle has side lengths of 3 inches and 5–√ inches. Which statement must be true about the area of the rectangle?
solve for y
3(3y-8)=21
Answer:
y = 5
Step-by-step explanation:
3(3y-8)=21
expand:
9y - 24 = 21
+24 to both sides to get 9y on its own.
9y = 45
divide both sides by 9 to get y on its own.
therefore
y = 5
hope this makes sense!
Answer: Solve for
y
by simplifying both sides of the equation, then isolating the variable.
y≈−1.21698677,2.94165923
Step-by-step explanation:
CIRCLES GEO !!
7. Is DE tangent to circle C
8. ST is tangent to circle Q. Find the value of r.
9. Find the value(s) of x.
The value of x is approximately equals to 30.4 and the value of r is approximately 9.24.
What is circle ?
In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.
Is DE tangent to circle C?
Yes, DE is tangent to circle C. This is because a tangent to a circle is a line that intersects the circle at exactly one point, and in this case, DE intersects circle C at point E and only touches the circle at that point.
ST is tangent to circle Q. Find the value of r.
Since ST is tangent to circle Q at point T, the radius of the circle Q is perpendicular to ST at T. Therefore, triangle SRT is a right triangle, where RS is the hypotenuse and ST is the adjacent side to the angle at S. We can use the Pythagorean theorem to find the length of the hypotenuse:
We know that ST = 10 and RT = r, so we can substitute these values to get:
[tex]RS^{2}[/tex] = 100+ [tex]r^{2}[/tex]
We also know that RS = 2r, so we can substitute this value to get:
4[tex]r^{2}[/tex]= 100 + [tex]r^{2}[/tex]
3[tex]r^{2}[/tex] = 100
[tex]r^{2}[/tex] = 100/3
r ≈ 9.24
Therefore, the value of r is approximately 9.24.
Find the value(s) of x.
Since AB is a diameter of circle C, triangle ABC is a right triangle with right angle at B. Therefore, we can use the Pythagorean theorem to find the length of BC:
We know that AB = 26 and AC = x + 8, so we can substitute these values to get:
[tex](x + 8)^{2}[/tex]= 676 + [tex]BC^{2}[/tex]
We also know that BC = x - 2, so we can substitute this value to get:
[tex](x + 8)^{2}[/tex]= 676 + [tex](x - 2)^{2}[/tex]
[tex]x^{2}[/tex]+ 16x + 64 = 676 + [tex]x^{2}[/tex]- 4x + 4
20x = 608
x = 30.4
Therefore, the value of x is 30.4.
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A student is to be selected randomly from a group of students. For each classification of freshman and sophomore, there is a math major, an art major, and a biology major. The probability of each individual being selected is given in the following table: Math Art Biology Freshman 0.12 0.09 0.18 Sophomore 0.23 0.27 0.11 (a) Find the probability that a freshman is selected. (b) Find the probability that an art major is chosen. (c) Find the probability that a freshman math major or a sophomore biology major is chosen.
The probability that a freshman is selected is 0.39. the probability that an art major is chosen is 0.36. the probability that a freshman math major or a sophomore biology major is chosen is 0.23.
(a) To find the probability that a freshman is selected, we need to add up the probabilities of selecting any of the three types of majors among the freshman group. Thus:
Probability of selecting a freshman = Probability of selecting a freshman math major + Probability of selecting a freshman art major + Probability of selecting a freshman biology major
Probability of selecting a freshman = 0.12 + 0.09 + 0.18
Probability of selecting a freshman = 0.39
(b) To find the probability that an art major is chosen, we need to add up the probabilities of selecting an art major from both the freshman and sophomore groups. Thus:
Probability of selecting an art major = Probability of selecting a freshman art major + Probability of selecting a sophomore art major
Probability of selecting an art major = 0.09 + 0.27
Probability of selecting an art major = 0.36
(c) To find the probability that a freshman math major or a sophomore biology major is chosen, we need to add up the probabilities of selecting a freshman math major and a sophomore biology major. Thus:
Probability of selecting a freshman math major or a sophomore biology major = Probability of selecting a freshman math major + Probability of selecting a sophomore biology major
Probability of selecting a freshman math major or a sophomore biology major = 0.12 + 0.11
Probability of selecting a freshman math major or a sophomore biology major = 0.23
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On a certain day, Miquel. had a credit of $75 in her checking account and spent $240. Which represents the total change in his account that day?
A. $315
B. $365
C. -$135
D. -$165
SHOW YOUR WORK!!
Answer:
B. $365
Step-by-step explanation:
What is the answer?
Answer:?
The differentiation of the trigonometric function gives:
dy/dx = sin(x) - cos(x)
How to differentiate the function?Here we want to find dy/dx for:
y = sec⁻¹(x) + csc⁻¹(x)
Remember that these two are the inverses of the sine and cosine function, then we can write that just as:
y = cos(x) + sin(x)
Now the differentiation is part by part, we know that:
d(cos(x))/dx = -sin(x)
d(sin(x))/dx = cos(x)
Then:
dy/dx = sin(x) - cos(x)
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