What is the measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R =
Answers
The measure of the angles of the triangles are 90° , 67.380° and 22.620°
What is the law of sines?The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.
Law of Sines :
a / sin A = b / sin B = c / sin C
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of ∠PQR = 90°
The measure of side PR = 13 cm
The measure of side PQ = 5 cm
The measure of side QR = 12 cm
From the law of sines , we get
a / sin A = b / sin B = c / sin C
Substituting the value sin the equation , we get
12 / sin P = 13 / sin 90°
From the trigonometric relations , sin 90° = 1
So , Multiply by sin P on both sides of the equation , we get
sin P = 12/13
Taking inverse on both sides of the equation , we get
sin⁻¹ ( 12/13 ) = 67.380°
Therefore , the measure of ∠QPR = 67.380°
And , the measure of ∠PRQ = 180 - ( 90° + 67.380° )
The measure of ∠PRQ = 22.620°
Hence , the angles of triangles is solved
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Related Questions
what is the probability of finding 3 or fewer defects in carpet roll? using the poisson distribution.
Answers
a. the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.
b. the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.
A) The probability of finding exactly 6 defects in a carpet roll can be calculated using the Poisson probability formula:
P(X = 6) = (e^-λ) * (λ^6) / 6!
where λ = 2.0 (the average number of defects per roll), and e is the mathematical constant approximately equal to 2.71828.
Plugging in the values, we get:
P(X = 6) = (e^-2) * (2^6) / 6! = 0.0403
So the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.
B) To find the probability of finding 3 or fewer defects in a carpet roll, we need to calculate the cumulative probability:
P(X ≤ 3) = Σ_{i=0}^3 P(X = i) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
where P(X = i) is the probability of finding exactly i defects, which can be calculated using the Poisson probability formula.
Plugging in the values and adding the probabilities, we get:
P(X ≤ 3) = (e^-2) + (e^-2) * (2^1) / 1! + (e^-2) * (2^2) / 2! + (e^-2) * (2^3) / 3!
P(X ≤ 3) = 0.135
So the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.
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Complete question:
The World Carpet and Rug Company buys medium grade carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution,
A) What is the probability of finding exactly 6 defects in a carpet roll chosen at random?
b) What is the probability of finding 3 or fewer defects in a carpet roll?
Kim was solving a problem using the six steps first she read the promblem then she wrote down the facts and figures next she knew she had to find a relation between what’s given and what
Answers
Kim was solving a problem using the six steps first she read the problem then she wrote down the facts and figures next she knew she had to find a relation between what’s given and what's asked for.
After that, she formulated a plan or strategy to solve the problem. Then, she carried out the plan and solved the problem. Finally, she checked her answer to see if it made sense and if it was reasonable.
These six steps are often used in problem-solving and are a useful way to approach a problem systematically. By following these steps, one can ensure that all the relevant information is taken into consideration, a plan is developed to solve the problem, and the solution is verified before presenting it as the final answer.
The six steps are:
1. Determining the problem statement.
2. Identifying the main causes of the problem.
3. Developing viable solutions relevant to the problem.
4. Selecting one solution among the options.
5. Applying the solution on the problem at hand.
6. Evaluating the effect of the solution on the problem.
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Use the Polygon tool to draw a rectangle with a length of 6 units and a height of 4 units. One of the sides of the rectangle falls on line CD , and the rectangle has a vertex of C.
Each segment on the grid represents 1 unit
Answers
The image below (see attachment) illustrates how the rectangle with a vertex of C and a side on line CD is built.
A rectangle can be thought of as a four-sided polygon with two opposite pairs of equal sides and four interior angles that are each 90 degrees. At each corner or vertex, the two sides come together at an angle. Rectangles differ from squares in that their opposite sides are of equal length. Additionally, it is known as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. As a result, the rectangle with the stated lengths and a vertex of C is built as shown in the image attached below (see attachment).
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Write the following ratio using fractional notation.
2 to 9
Answers
The correct way to write the ratio using fractional notation is [tex]\frac{2}{9}[/tex] (two-ninths).
What is a fraction?In math, a fraction is a mathematical expression that shows pars in a whole. Due to this, fractions include a numerator (number placed above) and a denominator (number placed below).
How to write a ratio as a fraction?Ratios and fractions are equivalent, which means you just need to make sure the first number is the numerator and the second number is the denominator. Moreover, the fraction should be simplified if possible. Based on this, the fraction is:
[tex]\frac{2}{9}[/tex]
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what is the sentence
Answers
Answer: Unclear
Step-by-step explanation: I can't see your image/sentence, so I can't help u
question 6 options: if a cell phone tower is 24 meters tall and casts a shadow 45 meters long, then how long of a shadow will be cast by a nearby marble column that is 8 meters tall?
Answers
If a cell phone tower is 24 meters tall and casts a shadow 45 meters long, then 15 m long of a shadow will be cast by a nearby marble column that is 8 meters tall.
A Cell phone tower is 24 meters tall.
Casts of a shadow is 45 meters long.
A nearby marble column that is 8 meters tall.
We have to determine the how long of a shadow will be cast by a nearby marble column.
Since, the triangle △PQR∼△MNO
So from the diagram
MN/PQ = ON/RQ
8/24 = x/45
Multiply by 45 on both side, we get
x = 8/24 × 45
x = 360/24
x = 15
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0
a) What is a fraction between 25% and
50%? How do you know?
Answers
Answer:
30/100
Step-by-step explanation:
25%= 25/100
50%= 50/100
3/100 is in the middle of the two fractions. So one of the possible answer can be 30/100 or 30%
Answer:
[tex]\sf \dfrac{2}{5}[/tex]
Step-by-step explanation:
"per cent" means "per hundred". Therefore, to change a percent to a fraction, remove the % sign and place the number as the numerator of a fraction with 100 as the denominator.
[tex]\sf 25\%=\dfrac{25}{100}[/tex]
[tex]\sf 50\%=\dfrac{50}{100}[/tex]
Any percent between 25% and 50% can be written as a fraction in the same way.
Choose a number between 25 and 50, place it as the numerator of a fraction with 100 as the denominator:
[tex]\sf \dfrac{40}{100}[/tex]
Now reduce the fraction to its simplest term by dividing the numerator and denominator by the greatest common factor (GCF):
[tex]\sf \dfrac{40 \div 20}{100\div 20}=\dfrac{2}{5}[/tex]
Therefore, the fraction ²/₅ is between 25% and 50% as it is equivalent to 40%.
A ball is thrown vertically upward. After t seconds, its height / (in feet) is given by the function ()-100r-16r². What is the maximum height that the ball
will reach?
Do not round your answer.
Height:fect
X
G
Answers
Find the roots using the quadratic formula
25
4. '
-6.25,0
There are 30 students in Mrs. Taylor ’ s kindergarten class. If there are twice as many students with blond hair as with blue eyes, 6 students with blond hair and blue eyes, and 3 students with neither blond hair nor blue eyes, how many students have blue eyes?
Answers
Answer:
11
Step-by-step explanation:
Let e represent the number of students with blue eyes. Then the number of students with blond hair is 2e. The total number of students is ...
3 + e + 2e -6 = 30
We subtracted 6 because the expressions e and 2e cause the 6 students with both blond hair and blue eyes to be counted twice.
3e = 33 . . . . add 3 and simplify
e = 11
11 students have blue eyes.
Answer:
11
Step-by-step explanation:
11
venn daigram
Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equipment will cost $1200.
Henry orders 600 shirts and determines that the profit for his new business is modeled by the function P = 22x - 1200. What is the domain of this function in this context?
{0 ≤ x ≤ 600}
{0 ≥ x ≥ 600}
{-1,200 ≤ x ≤ 2,000}
all real numbers
Answers
The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.
What is the domain of a function?The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.
The domain of this function in this context is {0 ≤ x ≤ 600}.
This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.
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The diagram shows a circle with centre O.
A, B, C & D lie on the circumference of this circle.
Given that AC is a diameter of the circle and ∠DCA = 51° and ∠BCA = 26°, find the size of ∠DAB as highlighted in the diagram.
Answers
CDA AND ABC ARE 90’ due to it being formed by the diameter
So,
ACB + BAC + ABC = 180
Thus BAC=64’
DCA + CDA + CAD = 180’
CAD=39’
BAC + CAD = 103’ = DAB
This meal cost $29 the 40% coupon is applied followed by 7% sales tax rate
What is the total with the discount and tax
Answers
Answer:
12.41
Step-by-step explanation:
[tex]29 \times 0.40 = 11.6[/tex]
[tex]11.6 \times 0.07 = 0.812[/tex]
[tex]0.812 + 11.6 = 12.412[/tex]
Since f(1)=0 for f(x)=x^6-x^4+2x^2-2, we can conclude that x−1 is a factor of f(x) .
true or false?
Answers
For f(1) = 0 the statement is true that (x - 1) is the factor of the function.
What are polynomials?Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given a function,
f(x) = x⁶ - x⁴ + 2x² - 2
and f(1) = 0
substitute the values,
f(x) = x⁶ - x⁴ + 2x² - 2
f(1) = 1⁶ - 1⁴ + 2(1)² - 2
f(1) = 0
so when x = 1 function is zero,
so x - 1 = 0 and (x - 1) is one of the factor of function f(x).
Hence the statement is true.
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find the probability (a) that at least one of the three events occurs. (b) exactly one of the three events occurs.
Answers
Let assume the probability of the three events as P(A), P(B), and P(C), respectively. Then:
(a) The probability that at least one of the three events occurs is given by:
P (A or B or C) = 1 - P (not A and not B and not C) = 1 - P (not A) * P (not B) * P (not C)
where P (not A) is the complement of P (A), and similarly for P (not B) and P (not C).
(b) The probability that exactly one of the three events occurs can be calculated by adding the probabilities of each event occurring individually and then subtracting the probability that two events occur simultaneously.
P (exactly one) = P(A) + P(B) + P(C) - 2 * P (A and B) - 2 * P (A and C) - 2 * P(B and C) + 3 * P (A and B and C)
Note that the above formulas assume that the events are mutually exclusive and exhaustive, meaning that one and only one of the events must occur and the sum of the probabilities of the individual events is equal to 1.
If this is not the case, the probabilities need to be adjusted accordingly.
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You spin the spinner once.
3 4 5
What is P(greater than 4 or less than 5)?
Write your answer as a percentage.
Answers
The value of P(greater than 4 or less than 5) is 66.7%
How to evaluate the probabilityFrom the question, we have the following parameters that can be used in our computation:
Spinner = 3 4 5
Using the above as a guide, we have the following:
4 or 5 = 2
Total = 3
So, we have
P(greater than 4 or less than 5) = 2/3
Evaluate
P(greater than 4 or less than 5) = 66.7%
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There is three-fourths of a shell pile left, and Terrence has sorted four-sixths of it.
How much of the shells did he sort?
twelve twenty-fourths
sixteen-eighteenths
twelve-sixteenths
seven-tenths
Answers
Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.
What is a fractional value?A fractional value is a value that represents a portion or part of the total value.
Fractional values can be depicted as proper, improper, or complex fractions. They can also be depicted as decimals or percentages.
The remaining quantity of the shell pile = ³/₄
The quantity sorted by Terrence = ⁴/₆
The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%
Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.
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the total of two number is 146
one of the number is a multiple of 11
the other one is a multiple of 17, find the two numbers
Answers
The two amount of numbers are 11 and 135. 11 is a multiple of 11 and 135 is a multiple of 17. The sum of the two numbers is 146.
Step 1: One of the numbers is a multiple of 11
Let the number be 11x, where x is an integer
Step 2: The total of the two numbers is 146
Therefore, 11x + 17y = 146, where y is an integer
Step 3: Solve the equation
11x + 17y = 146
11x = 146 - 17y
x = (146 - 17y) / 11
Step 4: Find the two numbers
x = (146 - 17y) / 11
For y = 1, x = 11
Therefore, the two numbers are 11 and 17.
The two numbers that add up to 146 are 11 and 135. 11 is a multiple of 11, which means it is divisible by 11 without any remainder. 135 is a multiple of 17, which means it is divisible by 17 without any remainder. When these two numbers are added together, the sum is 146. This means that 11 and 135 are the two numbers that add up to 146. 11 is a multiple of 11 and 135 is a multiple of 17, which explains why the sum of the two numbers is 146. The two numbers together can be used to represent a variety of different mathematical equations, such as the addition of two integers or the multiplication of two fractions. Knowing the two numbers that add up to 146 can be useful in a variety of different scenarios, such as solving math problems or accounting for the total of two items.
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Paul has a collection of nickels and dimes that has a total value of
$12.50. He has 150 coins in all. How many dimes does Paul have?
50
75
100
134
Answers
Answer:
100 dimes.
Step-by-step explanation:
Two equations.
First modeling the total money with x as nickels and y as dimes.
0.05x + 0.1y = 12.50
Second, modeling the amount of coins.
x + y = 150
Which you can alter to substitute for in the first equation.
x = 150 - y
Subsitute.
0.05(150 - y) + 0.1y = 12.50
7.5 - 0.05y + 0.1y = 12.50
0.05y = 5
y = 100
Paul has 100 dimes and 50 nickels.
Solve x 2 − 2 x − 4 = 0
Answers
x equals 1 ± the square root of 5 end root
The product of a number and -7 increased by 9, is at most 16
Answers
The required number would be -23 for the given statement.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
Let the required number would be x.
As per the question, we can write the algebraic form would be as:
-7(x + 7) = 16
Using the distributive property,
-7x - 49 = 16
-7x = 16 + 49
-7x = 65
x = -65/7
x = -23
Thus, the required number would be -23.
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The question seems incomplete, the complete question would be as:
The product of a number and -7 increased by 9, is at most 16. Find the number.
Identify the diameter of circle A.
Answers
The diameter of circle A is equal to line segment TB.
What is a circle?In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
Based on the information provided about circle A, we can reasonably infer and logically deduce that its diameter is represented by line segment TB. Furthermore, the radius of circle A can be calculated as follows;
Diameter = radius + radius
Diameter = TA + AB
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a man has five pairs of socks, of which no two pairs are the same color. he randomly selects two socks from a drawer. what is the probability that he gets a matched pair? 118. bookshelf ord
Answers
The probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer is 5/45, or approximately 0.11.
To calculate the probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer, we need to consider the number of possible combinations of socks that result in a match and divide that by the total number of possible combinations of two socks.
The man has a total of 5 pairs of socks, or 10 socks, so there are 10 choose 2, or 45, possible combinations of two socks. Out of these, 5 of them result in a match, because there are 5 pairs of matching socks in the drawer.
Therefore, the probability of getting a matched pair of socks is 5/45, or approximately 0.11. This means that there is an 11% chance that the man will select a matched pair of socks if he randomly selects two socks from the drawer.
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The density of a certain type of wood is 353 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345 kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample?
Answers
Answer:
.99
Step-by-step explanation:
345/353 =0.98
cube root =0 .99
so each edge is 0.99 m
The volume of the wood sample is calculated using the given density and mass. Given that this sample is a cube, the volume is also equal to the cube of the edge length. Therefore, finding the cube root of the volume gives us the edge length, which is about 0.99 meters.
Explanation:The density of a material is defined by the ratio of its mass to its volume, expressed by the formula density = mass/volume. Given that the mass of the sample is 345 kg and the density is 353 kg/m³, you can calculate the volume by rearranging the formula to volume = mass/density. So, the volume comes out to be approximately 0.977 cubic meters. Now, since the sample is a cube, all sides are equal. The volume of a cube is given by the formula volume = edge ^ 3 (edge length cubed). You are hence looking to find the cube root of the volume, which is approximately 0.99 meters. Therefore, the length of one edge of the wood sample is approximately 0.99 meters to the nearest hundredth of a meter.
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PLS HELP WILL GIVE BRAINIEST IF CORRECT
Of the people who fished at Clearwater Park today, 54 had a fishing license, and 36 did not. Of the people who fished at Mountain View Park today, 90 had a license, and 10 did not. (No one fished at both parks.)
Suppose that one fisher from each park is chosen at random. What is the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license?
Do not round your answer.
Answers
The probability of choosing a fisher from Clearwater who had a license is 54/(54+36) = 0.6, and the probability of choosing a fisher from Mountain View who did not have a license is 10/(10+90) = 0.1.
Assuming that the choices are independent, the probability of both events happening together is the product of their probabilities:
P(Clearwater had a license and Mountain View did not have a license) = P(Clearwater had a license) x P(Mountain View did not have a license)
= 0.6 x 0.1
= 0.06
Therefore, the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06.
Answer:
The probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06
Step-by-step explanation:
To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events both occurring is equal to the product of their individual probabilities.Let event A be the event that a fisher chosen from Clearwater Park had a license, and let event B be the event that a fisher chosen from Mountain View Park did not have a license. Then, we need to find the probability of A and B occurring together, which we can write as P(A and B).
Using the given information, we can calculate the probabilities of events A and B as follows:
P(A) = 54/(54+36) = 0.6 (the proportion of fishers at Clearwater Park with a license)
P(B) = 10/(90+10) = 0.1 (the proportion of fishers at Mountain View Park without a license)
Since the events are independent (since no one fished at both parks), we can use the multiplication rule to find the probability of A and B occurring together:
P(A and B) = P(A) * P(B) = 0.6 * 0.1 = 0.06
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending.
y = -10x + 1500
This means y is the altitude with -10ft decent every x minutes when the initial altitude is 1500Ft
Part A: Create a table for the values when x = 0,5,8,10,10
Show your work with the equation used to identify the values you put in the table when X = 0,5,8,10 and 30.
Part B: identify the altitude after 5 minutes and after 30 minutes. use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals. Starter: The plane's altitude after 5 minutes would be _________. After 30 minutes, the plane's altitude would be ________.
Then describe if the plane is in the air or on the ground at those times.
Answers
The equation of line is y = -10x + 1500 , where the slope is m = -10
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y = -10x + 1500 be equation (1)
where x is the number of minutes
and y is the altitude in feet
when x = 0
Substituting the value of x = 0 in the equation , we get
y = 1500 feet
when x = 5
Substituting the value of x = 5 in the equation , we get
y = -10 ( 5 ) + 1500
y = -50 + 1500
y = 1450 feet
when x = 8
Substituting the value of x = 8 in the equation , we get
y = -10 ( 8 ) + 1500
y = -80 + 1500
y = 1420 feet
when x = 10
Substituting the value of x = 10 in the equation , we get
y = -10 ( 10 ) + 1500
y = -100 + 1500
y = 1400 feet
when x = 30
Substituting the value of x = 30 in the equation , we get
y = -10 ( 30 ) + 1500
y = 300 + 1500
y = 1200 feet
So , the plane's altitude after 5 minutes would be 1450 feet and after 30 minutes, the plane's altitude would be 1200 feet
Now , the plane will reach the ground when y = 0
0 = -10x + 1500
10x = 1500
x = 150 minutes
Hence , the equation of line is y = -10x + 1500
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Compute $\dfrac{\sqrt{150}}{\sqrt{96}}$.
Answers
The solution is 5/4.
What is Square root?A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
here, we have,
√150/√96
=√6√25/√6√16
=5√6/4√6
=5/4
Hence, The solution is 5/4.
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the degree to which any differences in the outcome variables are different related to the experimental treatment is:
Answers
The degree of effect refers to the extent to which any differences in the outcome variables are related to the experimental treatment. It can be quantified using various statistical measures and is an important consideration in experimental design and analysis. However, it is not the only factor to consider, and other factors such as the magnitude of effect and potential confounding variables should also be taken into account.
In experimental design and analysis, the degree to which any differences in the outcome variables are related to the experimental treatment is an important consideration. This is typically referred to as the "degree of effect" or "degree of difference."
The degree of effect refers to the extent to which the experimental treatment produces differences in the outcome variables being measured. This can be quantified using various statistical techniques, such as the analysis of variance (ANOVA) or regression analysis, which compare the variation in the outcome variable between groups or over time. It is typically expressed as a statistical measure, such as a p-value or a confidence interval, which indicates the level of confidence that can be placed in the observed differences. A low p-value or a narrow confidence interval indicates a high degree of effect, indicating that any observed differences are likely to be related to the experimental treatment rather than chance or other factors.
In addition to the degree of effect, it is also important to consider the magnitude or size of the effect. This refers to the extent or strength of the differences between the treatment groups, and can be expressed using various effect size measures, such as Cohen's d or eta-squared. A larger effect size indicates a stronger or more meaningful difference between the groups, and is generally considered to be more important than a smaller effect size.
However, it is important to note that the degree of effect and magnitude of effect are not the only factors to consider when evaluating the results of an experiment. Other factors, such as the study design, sample size, and potential confounding variables, can also affect the interpretation of the results and the conclusions that can be drawn.
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how many distinct ordered pairs of positive integers $(m,n)$ are there so that the sum of the reciprocals of $m$ and $n$ is $\frac14$?
Answers
There are no such pairs. The sum of the reciprocals of any two positive integers is always greater than[tex]$\frac14$[/tex].
The sum of the reciprocals of any two positive integers is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex], which is always greater than [tex]$\frac14$[/tex]. Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex]
For any two positive integers m and n, the sum of their reciprocals is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex] which is always greater than [tex]$\frac14$[/tex] This is because [tex]\frac{1}{m}$ ,$\frac{1}{n}[/tex] are both positive numbers, and so their sum must be greater than [tex]$\frac14$[/tex]Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex].
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Nevaeh invested $660 in an account paying an interest rate of 3\tfrac{1}{4}3 4 1 % compounded continuously. Jonathan invested $660 in an account paying an interest rate of 3\tfrac{1}{8}3 8 1 % compounded monthly. After 14 years, how much more money would Nevaeh have in her account than Jonathan, to the nearest dollar?
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Nevaeh would have $54 more in her account than Jonathan, to the nearest dollar.
Let's denote the amount of money Nevaeh has in her account after t years as A, and the amount of money Jonathan has in his account after t years as B.
We can use the formula for continuously compounded interest:
Compound interest finds its usage in most of the transactions in the banking and finance sectors and other areas.
[tex]A = 660 * e^(0.0334 * t)[/tex]And for monthly compounded interest:
[tex]B = 660 * (1 + 0.003125)^(12 * t)[/tex]We can plug in t = 14 to get the amounts for each person after 14 years:
[tex]A = 660 * e^(0.0334 * 14)[/tex][tex]B = 660 * (1 + 0.003125)^(12 * 14)[/tex]The difference between these amounts is the amount by which Nevaeh would have more money in her account than Jonathan, to the nearest dollar:
difference = A - B
difference = round(difference)
Using a calculator, we find that:
difference = 977.78 - 923.61 = 54.17
So, Nevaeh would have $54 more in her account than Jonathan, to the nearest dollar.
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where will the ball be after being thrown straight up from the ground at 112 feet per second after 7 seconds?
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The ball will be 864 feet above the ground after 7 seconds. The equation for calculating the height of an object after a certain amount of time given a certain initial velocity is: h = v_0 * t - 0.5 * g * t^2
The equation for calculating the height of an object after a certain amount of time given a certain initial velocity is:
h = v_0 * t - 0.5 * g * t^2
where h is the height, v_0 is the initial velocity, t is the time, and g is the acceleration due to gravity (9.81 m/s^2).
In this case, h = 112 feet/sec * 7 sec - 0.5 * 9.81 m/s^2 * (7 sec)^2
h = 864 feet
The ball will be 864 feet above the ground after 7 seconds.
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