Answer:
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. If the diameter of each circular light is 7 inches, the radius would be half of that, or 3.5 inches.
Therefore, the area of one circular light would be:
A = π * 3.5^2 = 3.5^2 * π = 12.25 * π square inches.
Since there are three circular lights, the total area of all three would be:
3 * 12.25 * π = 36.75 * π square inches.
Step-by-step explanation:
pls mark brainlist
the following data set represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 suppose that the last value, 75, was mistakenly recorded as 5. what measure(s) of the typical value in a data set would be affected by this error? select all that apply.
The following measures of typical value in a data set would be affected by the error:
Mean: The mean is the sum of all the values divided by the number of values. If one value is significantly different from the rest, it can significantly affect the mean. In this case, the mean would be affected because the value of 5 is much lower than the other values in the data set, which would cause the mean to be lower than it should be.
Median: The median is the middle value in a data set. If the error is low enough, it may not affect the median, but if it is low enough to move the value of 5 to the middle of the data set, the median would be affected.
In conclusion, the mean and median of this data set would be affected by the error of recording the value of 75 as 5.
The mode, mean and median of this data set would be affected by the error of recording the value of 75 as 5.
Given that, a data set represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 suppose that the last value, 75, was mistakenly recorded as 5.
so, here, due to mistake the mode, mean and the median will be affected.
Adding a data point to the set, or taking one away, can affect the mean, median, and mode.
If we add a data point that's above the mean, or take away a data point that's below the mean, then the mean will increase.
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Write an equity find X. Make sure you use ""="" sign in your answer.
Equity is generally defined as the difference between the value of a company’s assets and its liabilities, and is typically expressed as a dollar amount.
The formula for equity is: Equity = Assets - Liabilities To calculate equity, you would first need to calculate the value of all of the company’s assets, such as cash, investments, inventory, property, and equipment. Then, you would need to calculate the value of all of the company’s liabilities, such as accounts payable, short and long-term debt, and any other financial obligations. Once the value of the assets and liabilities have been calculated, the difference between them is the company’s equity. For example, if a company has total assets of $4,000 and total liabilities of $2,500, the equity can be calculated as follows :Equity = Assets - Liabilities Equity = $4,000 - $2,500 Equity = $1,500
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Kellys last quiz scores were 79,89,86, and 93. What must her next score be to obtain an average that is more than 88
Answer: To find out what Kelly's next score must be in order to obtain an average that is more than 88, we first need to find the current average of her scores. To do this, we add up her current scores and divide by the number of scores:
(79 + 89 + 86 + 93) / 4 = 337 / 4 = 84.25
Since the current average is 84.25, which is less than 88, Kelly must score higher than 88 on her next quiz to bring the average up to more than 88. To be specific, Kelly must score at least 89 on her next quiz.
Step-by-step explanation:
how many pattern block trapezoids would create 2 hexagons
There are 12 trapezoids needed to create two hexagons with pattern blocks.
1. To create two hexagons with pattern blocks, you will need 12 trapezoids.
2. Each hexagon consists of six trapezoids.
3. Since you need two hexagons, you will need 12 trapezoids in total.
In order to create two hexagons with pattern blocks, you will need to use 12 trapezoids in total. Each hexagon consists of six trapezoids, so you will need two hexagons to use all twelve trapezoids. The two hexagons can be formed by arranging the trapezoids in a pattern of two triangles, two parallelograms, two rhombuses, and two trapezoids. With these 12 trapezoids, you will be able to create two complete hexagons.
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Answer:
Step-by-step explanation:
how many pattern blocks triangles would create 1 hexagon
what is the point estimator for the proportion of registered voters expressed concern about a loosening of restrictions? b. determine the margin of error for this poll assuming a confidence level of 95%
The point estimator for the proportion of registered voters expressed concern about a loosening of restrictions is 0.58. The margin of error for this poll is 3.6%.
The point estimator for the proportion of registered voters expressing concern about a loosening of restrictions is:
58/100 = 0.58 or 58%
To determine the margin of error for this poll assuming a confidence level of 95%, we can use the following formula:
margin of error = zsqrt(p(1-p)/n)
where z is the z-score for the desired confidence level (1.96 for 95%), p is the point estimator for the proportion (0.58), and n is the sample size (900).
So, the margin of error is:
1.96sqrt(0.58(1-0.58)/900) ≈ 0.036 or 3.6%
Therefore, the margin of error for this poll is 3.6%.
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____The given question is incomplete, the complete question is given below:
Read the following news article and then answer the two questions at the end According to an NBC News/Wall Street Journal poll released Sunday, 58 percent of registered voters expressed concern about a loosening of restrictions compared with 32 percent who worried that the restrictions would stay in place for too long 3 percent said they were concerned about both scenarios. A mere 3 percent said the pandemic had no impact on their lives, compared with 77 percent who said it had affected them either in a very major way" or "fairly major way The sample size was 900 registered voters a What is the point estimator for the proportion of registered voters expressed concern about a loosening of restrictions b. Determine the margin of error for this poll assuming a confidence level of 95%.
Can somebody help me out here, please?
The addition and subtraction of the fractions by finding the LCD gives:
NUMBER 1: (8y-49) /(y²-49)
NUMBER 2: (x+10) /(2x+8)
NUMBER 3: (7a-2)/10b
NUMBER 4: 1
How to add and subtract the fractions by finding the LCD?Least Common Denominator (LCD) refers to the smallest multiple that two or more denominators have in common, and is used in operations involving fractions.
NUMBER 1
y/(y²-49) - 7(y+7) = y/[(y+7)(y-7)] - 7(y+7)
LCD of (y+7)(y-7) and (y+7) is (y+7)(y-7):
= [y + 7(y-7)] / [(y+7)(y-7)]
= [y + 7y-49)] / [(y+7)(y-7)]
= (8y-49) / (y+7)(y-7)
= (8y-49) /(y²-49)
NUMBER 2
1/2 + 3/(x + 4) = [1(x+4) + 3*2] /[2(x+4)]
= [x+4 + 6] /[2(x+4)]
= (x+10) /(2x+8)
NUMBER 3
(a+2)/4b + (a-1)/10b + (a-3)/5b = [5(a+2) + 2(a-1) + 4(a-3)]/20b
= [5a+10 + 2a-2 + 4a-12]/20b
= (14a-4)/20b
= 2(7a-2)/20b
= (7a-2)/10b
NUMBER 4
x/(x+1) - 1/(x-1) + 2x/(x²-1) = [x(x-1) - 1(x+1) + 2x]/(x²-1)
= [x²-x -x-1 + 2x]/(x²-1)
= (x²-1)/(x²-1)
= 1
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HELPPPPP i don't know how to do these, I missed the first quarter of math
The domain of the relation is 0, 2, 3, and 7.
The range of the relation is 1 and 3.
How to find the domain and range of a relation?The domain of a function is the set of all possible inputs for the function. The domain of a relation is the independent variable of the relation. The domain of the relation are the x values.
Therefore, the domain of the relation are 0, 2, 3 and 7.
The range of the relation is the set of the second coordinates from the ordered pairs. The range is the output of the relation. The range are the y axis values.
Therefore, the range of the relation are 1 and 3.
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dr. raynor, a school psychologist, tracks the number of students that are reported by teachers as having concerning behaviors in the classroom. at the end of the year, she calculated that 12.4% of the students in her school have been identified as having behaviors that impact their performance in the classroom. she understands that there is a margin of error to this estimate and reports that the number of children who have behavior problems at school may be as low as 10.2% and as high as 14.6%. what is the term used to describe the 12.4% calculation made by dr. raynor?
Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.
The 12.4% calculation made by Dr. Raynor is referred to as a confidence interval. A confidence interval is a range of numbers that is likely to contain a population parameter. In this case, the population parameter is the percentage of students in the school with concerning behaviors that impact their performance in the classroom. To calculate the confidence interval, Dr. Raynor first determined the sample proportion, which is 12.4%. Then, she used the following formula to calculate the confidence interval:
Confidence Interval = (Sample Proportion ± Margin of Error)
In this case, the margin of error was 2.2%, which is calculated by multiplying the sample proportion by 1.96 (1.96 being the critical value for a 95% confidence interval). Thus, the confidence interval of 10.2% to 14.6% was determined. This confidence interval means that Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.
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30 percent of what number is 15
Step-by-step explanation:
50
because 50*(30/100)=1500/100
then it gives 15
so the 30 percent of a number is 15 that number is 50.
The requried, 30 percent of 50 is 15, as of the given condition.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
We can use algebra to solve the problem.
Let's call the number we're looking for "x". Then we can translate the problem statement into an equation:
30% of x is 15:
0.3x = 15
To solve for x, we can divide both sides of the equation by 0.3:
x = 15 ÷ 0.3
x = 50
Therefore, 30 percent of 50 is 15.
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In a lottery, the top cash prize was $693 million, going to three lucky winners. Players pick five different numbers from 1 to 51
and one number from 1 to 42. -
A player wins a minimum award of $400 by correctly matching four numbers drawn from the white balls (1 through 51) and
matching the number on the gold ball (1 through 42). What is the probability of winning the minimum award?
The probability of winning the minimum award is.
(Type an integer or a simplified fraction.)
Answer:
1/237.12.
Step-by-step explanation:
The probability of winning the minimum award can be calculated by multiplying the probability of picking 4 numbers correctly from 1 to 51 and then multiplying by the probability of picking 1 number correctly from 1 to 42.
The probability of picking 4 numbers correctly from 1 to 51 is given by the formula:
(number of combinations of 4 numbers from 51) / (number of combinations of 5 numbers from 51)
= (51 choose 4) / (51 choose 5)
= 51! / (4! * 47!) / (51! / (5! * 46!))
= (51 * 50 * 49 * 48) / (5 * 4 * 47 * 46)
= 19600 / 10,946
= 1/5.6 approximately
The probability of picking 1 number correctly from 1 to 42 is given by the formula:
1/42
The final probability of winning the minimum award is given by multiplying the above two probabilities:
1/5.6 * 1/42 = 1/237.12
So, the probability of winning the minimum award is approximately 1/237.12.
State the maximum and minimum values if they exist.
The maximum and minimum values are 34.5 and 2
How to determine the maximum and minimum valuesfrom the question, we have the following parameters that can be used in our computation:
P = 2x + 7y
Subject to:
4x - 2y <= 5
x >= 1
0 <= y <= 4
Next, we plot the constraints on a graph
From the graph, we have the following vertices
(1, 0), (4, 0) and (3.25, 4)
This gives
P = 2(1) + 7(0) = 2
P = 2(4) + 7(0) = 8
P = 2(3.25) + 7(4) = 34.5
Hence, the minimum is 2 and the maximum is 34.5
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A, b and c are integers. They are the length, width and height of a cuboid respectively. It has a volume of 12cm^3, and the top faces has an area of 4 cm^2. If the cuboid is longer than it is width, what are a, b and c?
The length is 1 and width is 4 and height is 3.
In geometry, a cuboid is a solid or three-dimensional shape. A convex polyhedron bounded by 6 rectangular faces with 8 vertices and 12 sides is called a cuboid. A cuboid is also called a cuboid. A cuboid with six square faces is called a cube. An example of a real cube is a rectangular box. In mathematics, we can observe other shapes that are exactly the same as the cuboid. They are cuboid, cuboid, right prism, cuboid, cuboid, cuboid. Learn more about cuboids here
has a volume of 12cm^3
volume of cuboid is = length*width*height.
a*b*c = 12
and the top faces has an area of 4 cm^2
op faces has an area = a*b.
ab = 4
a = length
b = width
ab = 4 = 1x4 = 2x2
and a = 1
b = 4 because the cuboid is longer than it is width
now
abc = 12
ab = 4
c = 12/ab
c = 12/4
c = 3
length = 1 width = 4 height = 3
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A baker initially makes 10 loaves of bread and sells 2 loaves each day.
How many loaves of bread does the baker have at the end of the second day?
Answer:6
Step-by-step explanation:
day one-2 bread
day two-4 bread
10-4=6
6 at the end of the day
The number of loaves of bread remaining at the end of second day = 6 loaves of bread
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
Let number of loaves of bread remaining at the end of second day be A
The total number of loaves of bread = 10 loaves
The number of loaves of bread sold each day = 2 loaves
Substituting the values in the equation , we get
So , the number of loaves of bread remaining at end of first day = 10 - 2 = 8
Now , the number of loaves of bread remaining at end of second day = 8 -2
The number of loaves of bread remaining at the end of second day = 6
Therefore , the value of A is 6 loaves of bread
Hence , the equation is A = 6 loaves
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Mr. Steiner purchased a car for about $14,000. Assuming his loan was
compounded monthly at an interest rate of 4. 9% for 72 months:
p=
r=
n=
t=
A. How much will he have paid total?
B. How much more did he pay than the price of the car?
Mr. Steiner will need to pay $18774 in total and he paid $4774 more than the actual price of the car.
we know that the amount of money earned, in compound interest after t years is showed as, A(t) = P (1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]
here, we know that A(t) is the amount of money after t years.
P is the initial sum of money, know as principal,
r is the interest rate as a decimal value,
n is the number of times that interest is compounded per year,
and
t is the time in years for which the money is invested or borrowed.
now here we know,
P = 14000, r = 0.049, n = 12, t = 6
when we have all values we can find,
A(t) = P(1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]
A(6) = 14000 (1+[tex]\frac{0.049}{12}[/tex])¹²ˣ⁶
A(6) = 18774
therefore we know that Mr. Steiner needs to pay $18774 in total.
now,
18774 - 14000 = 4774
therefore we get to know that Mr. Steiner paid $4774 more than the actual price of the car.
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Mrs. Martinez and Ms. Jones' classes are competing for best average homework completion over the course of the semester.
According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.
How do average and mean differ?The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.
Comparing the median and average.By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.
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Find the Slope of line LM algebraically.
L(-1,-5)M(-4,-2)
Answer:
-2+5/-4+1= -1
Step-by-step explanation:
put y2 minus y1 over x2 minus x1
A new refrigerator comes packaged in a box shaped like a rectangular prism. The base of the box measures 6 feet by 12 feet. The total surface area of the box is 396 square feet. What is the height of the box in feet?
Answer:
7 feet
Step-by-step explanation:
You want the height of a 6' by 12' cuboid box that has a total surface area of 396 square feet.
Surface areaThe formula for the surface area of a cuboid is ...
SA = 2(LW +H(L+W))
ApplicationFor the given box, this is ...
396 = 2(6·12 +H(6+12))
198 = 72 +18H . . . . . . . . . . divide by 2
126 = 18H . . . . . . . . . . . subtract 72
7 = H . . . . . . . . . . . . divide by 18
The height of the box is 7 feet.
A rental car company charges $74.90 per day to rent a car and $0.13 for every mile driven. Tyee wants to rent a car, knowing that:
Answer:
74.90d + 0.13m = Total cost of the car rental
Step-by-step explanation:
Hmmm you didn't give enough information but....
let d represent the number of days
let m represent the number of miles driven
74.90d + 0.13m = Total cost of the car rental
For example Tyee rents the car for 2 days and drives 100 miles
149.8 + 13 = Total cost of the car rental.
$162.8 is the Total cost of the car rental.
when constructing a confidence interval for a difference between two population proportions, why is it important to check that the number of successes and the number of failures in each sample is at least 10? select the correct answer.
Why is it crucial to ensure that each sample has at least 10 successes and failures when building a confidence interval for the difference between two population proportions. This will allow us to select a sample distribution for p1-p2 that is roughly normal.
A distributor is a business that takes part in the value chain's distribution step. Making a good or service available to the consumer or business user who wants it is the process of distribution. This might be done by the producer or service provider directly or through indirect channels like distributors or intermediaries. Distribution is one of the four elements of the marketing mix, along with the other three being the product, pricing, and promotion. The broad strategic goal and objective of a corporation should guide distribution decisions. The main task of strategic planning is to develop a thorough distribution plan. At the strategic level, there are three basic distribution tactics: mass, selective, and exclusive distribution.
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What does it mean for an event to be unusual? Why should the cutoff for identifying unusual events not always be 0.05? Choose the correct answer below A. An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem. B. An event is unusual if it has a high probability of occurring The choice of the cutoff should consider the context of the problem. C. An event is unusual if it has a probability equal to 0 The choice of a cutoff should consider the context of the problem. D. An event is unusual if it has a probability equal to 1 The choice of a cutoff should consider the context of the problem.
The Correct option Will be An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem i.e. A.
What exactly is probability?The likelihood of an event is expressed by probability. The occurrence of a random event is the subject of this mathematical field of study. The value is between zero and one. In mathematics, probability is a tool for calculating the likelihood that certain events will take place.
Probability is the possibility of something happening. The probability distribution also makes use of this central concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood that a specific event will occur.
What does it mean when an event is unusual or out of the ordinary?When something unusual happens, it does not happen frequently in terms of sight or sound.
The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.
Now,
As an unusual event has low probability because it does not happen often and The same cutoff should not be used to detect unexpected events all of the time. Choosing a cutoff is subjective, and it should consider the repercussions of erroneously labelling an occurrence as rare.
Hence,
An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem.
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A system of equations has one line with a positive slope and one line with a negative slope. which of the following statements is true?
A. There is not enough information to know whether the system is consistent or inconsistent.
B. The lines are parallel to each other.
C. The system is consistent.
D. The system is inconsistent.
The system is consistent.
What is meant by consistent?
A system of equations is said to be consistent when they have atleast one solution in common.
A system of equations has one line with a positive slope and one line with a negative slope
The system has 1 line with a positive slope, so a line that has a positive slope is going to be rising from left to right.
The second line that has a negative slope. So just a line ,it is decreasing. Now a negative slope means the line, falls from left to right or is downward sloping.
If 1 line has a positive slope and 1 line has a negative slope, then at some point those lines are going to intersect, which will be the solution to the system.
Hence, the system is consistent.
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2/5 of a gal used 1/4 for coffee. How much milk in cups
The cups of milk required for the ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee is given by 2.4 cups.
Here,
( 2 / 5 ) of a gallons is equal to 0.4 gallons.
( 1 / 4 ) of gallons used for coffee that is equal to 0.25 gallons.
Total gallons left after coffee is equal to
= ( 0.4 ) - ( 0.25 )
= ( 0.15 )gallons
Conversion of gallons to cups is given by :
1 gallon = 16 cups
⇒ ( 0.15 )gallons = 0.15 × 16 cups
⇒ ( 0.15 )gallons = 2.4 cups of milk used.
Therefore, the 2.4 cups of milk is used when ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee.
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Find the perimeter of the rectangle in the given diagram.
Recall: To find the perimeter of a rectangle, add all of its sides.
15
Perimeter =
9
A
The perimeter of the rectangle in the given diagram is: D. 42 units.
How to determine the perimeter of this rectangle?In order to determine the perimeter of this rectangle, we would have to find the length of the third side of the right-angled triangle by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
9² + b² = 15²
81 + b² = 225
b² = 225 - 81
b = √144
b = 12 units.
Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.P = 2(9 + 12)
P = 42 units.
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A cylindrical jar of radius 6 cm contains water. How many iron spheres each of radius 1.5 cm are required to raise the level of water by 2 cm?
16 iron spheres each of radius 1.5 cm are required to raise the level of water by 2 cm
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, A cylindrical jar of radius 6 cm contains water.
Therefore, the volume of the cylinder is π(6²)h = 36πh.
Given, The height raises by 2cm therefore, 36π(h + 2).
We know, The volume of a sphere is, (4/3)πr³
= (4/3)π(1.5)³.
= (4/3)π×3.375.
= (13.5/3)π.
let, We need 'x' number of spheres.
Therefore, 36πh + (13.5/3)πx = 36π(h + 2).
36πh - 36π(h + 2) = - (13.5/3)πx.
36h - 36(h + 2) = - (13.5/3)x.
108h - 108(h + 2) = - 13.5x.
108(h - h - 2) = - 13.5x.
108(-2) = - 13.5x.
x = 216/13.5.
x = 16.
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Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
Answer:
<A=45°,<B=65°,<C=70°
Step-by-step explanation:
<A=3(x+5)=3x+15
<B=5x+15
<C=7x
sum angles in a triangle is 180°
so,<A+<B+<C=180
(3x+15)+(5x+15)+(7x)=180
C.L.T
3x+5x+7x+15+15=180
15x+30=180
15x=180-30
15x=150
divide both sides by 15
x=10
<A=3(x+5)=3(10+5)=3(15)=45°
<B=5(10)+15=50+15=65°
<C=7(10)=70°
terry invests a sum of money at a rate of 3.7% p.a. compound annually. After 4 years he withdraws $2000, and moves the moves the remaining money into an account earning 4.5% p.a. compounded annually. After 3 more years, there is $5635.66 in the account. How much did terry initially invest?
Answer:
To solve it, you need to use compound interest. Let me show you how.
Let P be the initial amount that Terry invested. Then after 4 years, the amount in the account is:
P × (1 + 0.037)^4
After withdrawing $2000, the remaining amount is:
P × (1 + 0.037)^4 - 2000
This amount is then moved to another account earning 4.5% p.a. compounded annually. After 3 more years, the amount in the account is:
(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3
We are given that this amount is equal to $5635.66. So we can write an equation:
(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3 = 5635.66
Simplifying the equation, we get:
P × 1.1597 - 2000 = 5635.66 / 1.1406
Adding 2000 to both sides, we get:
P × 1.1597 = 5635.66 / 1.1406 + 2000
Dividing both sides by 1.1597, we get:
P = (5635.66 / 1.1406 + 2000) / 1.1597
Using a calculator, we get:
P ≈ 5000.01
Therefore, Terry initially invested about $5000.01.
Step-by-step explanation:
1/2 of 2/3 = 1/2 of ____ third(s) = ____ third(s)
The product of 1/2 and 2/3 is equivalent to one third
Taking the product of fractions
Fractions are expressions written as a ratio of two integers. For instance a/b is a fraction
Given the expression below
1/2 of 2/3
This can also be written as;
1/2 of 2/3 = 1/2 of two thirds
Simplify
1/2 * 2/3 = 2/6
1/2 of 2/3 = 1/3
Hence the resulting value of the expression is one third
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Find X then find angle RB
The value of x is 11 and arc RB = 150°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
We know that,
∠RDB = 1/2(RB - EC)
So, substituting the values,
5x - 10 = 1/2(13x + 7 - 60)
10x - 20 = 13x - 53
3x = 33
x = 11
So, arc RB = 13 x 11 + 7 = 150°.
Hence, arc RB = 150°.
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Select the correct answer. Rewrite the expression using only positive integer exponents. (m2/3n-1/3)^6
A. m9/n18
B. n18/m9
C. m4/n2
D. n2/m4
Answer:
C. m4/n2 :))))
at noon, a ship leaves a harbor and sails south at 20 knots. four hours later, a second ship leaves the harbor and sails east at 15 knots. when will the ships be 100 nautical miles apart? round to the nearest minute. note that 1 knot = 1 nautical mile per hour.
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:
[tex]a^2 + b^2 = c^2[/tex]
We can use the Pythagorean theorem to find the distance between the two ships at any given time:
d² = (20t)² + (15(t-4))²
Simplifying this equation, we get:
d² = 400t² + 225(t² - 8t + 16)
d² = 625t² - 1800t + 3600
d = √(625t²- 1800t + 3600)
We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:
100 = √(625t² - 1800t + 3600)
Squaring both sides, we get:
10000 = 625t² - 1800t + 3600
Rearranging, we get:
625t² - 1800t - 6400 = 0
Using the quadratic formula, we get:
t = (1800 ± √(1800² + 46256400)) / (2*625)
t = (1800 ± 3900) / 1250
t = 3.84 or t = 8.16
So the time elapsed for the second ship is:
t2 = t + 4
t2 = 7.84 or t2 = 12.16
We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:
d = √((163.2)² + (62.4)²) = 174.9 nautical miles
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
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