Farmers Products Inc. should disclose a contingent liability in its 2016 financial statements for the lawsuit filed against them due to a collision caused by one of their delivery truck drivers.
Based on the information provided, it appears that as of the date of the financial statements (March 3, 2017), Farmers Products would need to disclose a contingent liability related to the lawsuit filed against them by the other driver.
A contingent liability is a potential liability that may arise from past events but the outcome is uncertain and will depend on future events. In this case, the lawsuit filed against Farmers Products by the other driver represents a potential liability that may result in damages being awarded against the company.
Under accounting standards, a contingent liability should be disclosed in the notes to the financial statements if it is probable that a liability has been incurred and the amount of the liability can be reasonably estimated. In this case, it is probable that Farmers Products may be liable for damages resulting from the accident and the estimated damages fall within a reasonable range of $6,000 to $10,000.
Therefore, in the notes to its 2016 financial statements, Farmers Products should disclose the existence of the lawsuit and the potential liability that may result. The disclosure should also include an estimate of the potential damages, if any, and any other relevant information about the lawsuit.
The question is incomplete; please see below for the whole question -
On December 4, 2016, Dan Johnson, a Farmers Products Inc. delivery truck driver, ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other car filed a lawsuit against Farmers Products for vehicle damages. Damage to this vehicle was estimated to be between $6,000 and $10,000, with no value within that range being more likely than any other. Farmers Products' 2016 financial statements were released on March 3, 2017.
1. Prepare the disclosures and/or journal entries that Farmers Products should include in its financial statements for the fiscal year ending December 31, 2016.2. How would the disclosures and/or journal entries alter if Farmers Products employed IFRS versus US GAAP?
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The Venn diagram shows below the number of customers in a restaurant who ordered a starter or a dessert. A customer is picked at random. If they ordered a dessert, what is the probability that they did *not* order starter? Give your answer as fraction in its simplest form.
Answer:
Step-by-step explanation:
23 people ordered dessert.
8 of these ordered only a dessert.
P(not starter | ordered dessert) [tex]=\frac{8}{23}[/tex]
If agent D was able to reduce their average Handling Time by 10% what would thier average handling time be
The new average handling time for Agent D would be 90% of their original handling time.
What are Percentages?A percentage is a way of expressing a number as a fraction of 100. It is typically represented using the percent sign (%) and is often used to describe the amount or proportion of something in relation to a whole. Percentages are commonly used in a variety of fields, such as finance, mathematics, and statistics.
Let's say the original average handling time for Agent D was "x" units (e.g. seconds, minutes, etc.). If Agent D was able to reduce their average handling time by 10%, their new average handling time would be:
New average handling time = x - 0.1x
Simplifying the expression on the right-hand side:
New average handling time = 0.9x
Therefore, the new average handling time for Agent D would be 90% of their original handling time.
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6. The picture at the right shows the garden in Robert's
yard. He wants to cover the garden with plastic be-
cause of a sudden drop in temperature. How many
square yards of plastic does he need?
12 ft
15 ft
9 ft
Answer:
To determine the area of the garden that needs to be covered with plastic, we need to multiply the length by the width of the garden. However, we need to convert the measurements to the same unit of measurement. Let's convert the measurements into yards since we need to find the area in square yards. 12 ft = 4 yards 15 ft = 5 yards 9 ft = 3 yards Now, we can calculate the area: Area = Length x Width Area = 5 yards x 4 yards Area = 20 square yards Therefore, Robert needs 20 square yards of plastic to cover his garden.
Jake and Steve are calculating the volume of a triangular prism. Who calculated the volume incorrectly? What is the student's error?
Answer: Jake solved it incorrectly.
Step-by-step explanation: His equation was supposed to be (7/2*35/2) *18
Given sinx=3/5 and is in quadrant 2, what is the value of tan x/2 ?
Answer:
[tex]\tan \left(\dfrac{x}{2}\right)=3[/tex]
Step-by-step explanation:
Trigonometric ratios are the ratios of the sides of a right triangle.
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
The sine trigonometric ratio is the ratio of the side opposite the angle to the hypotenuse.
Given sin(x) = 3/5, the side opposite angle x is 3, and the hypotenuse is 5.
As we have two sides of the right triangle, we can calculate the third side (the side adjacent the angle) using Pythagoras Theorem.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore:
[tex]\implies A^2+3^2=5^2[/tex]
[tex]\implies A^2+9=25[/tex]
[tex]\implies A^2+9-9=25-9[/tex]
[tex]\implies A^2=16[/tex]
[tex]\implies \sqrt{A^2}=\sqrt{16}[/tex]
[tex]\implies A=4[/tex]
Use the cosine trigonometric ratio to find the value of cos(x), remembering that cosine is negative in Quadrant II.
[tex]\implies \cos x=-\dfrac{4}{5}[/tex]
Now we have the values of sin(x) and cos(x) in Quadrant II, we can use the tangent half angle formula to find the value of tan(x/2).
[tex]\begin{aligned}\implies \tan \left(\dfrac{x}{2}\right)&=\dfrac{\sin x}{1+\cos x}\\\\&=\dfrac{\frac{3}{5}}{1-\frac{4}{5}}\\\\&=\dfrac{\frac{3}{5}}{\frac{1}{5}}\\\\&=\dfrac{3}{5} \cdot \frac{5}{1}\\\\&=3\end{aligned}[/tex]
Therefore, the value of tan(x/2) is 3.
What is the frequency of the sinusoidal graph?
the frequency of the sinusoidal graph is 1/π.
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. a. Sketch this exponential probability distribution. b. What is the probability that the arrival time between vehicles is 12 seconds or less? c. What is the probability that the arrival time between vehicles is 6 seconds or less? d. What is the probability of 30 or more seconds between vehicle arrivals?
After answering the presented question, we can conclude that the probability of 30 or more seconds between vehicle arrivals is approximately 0.082.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.
exponential probability distribution
[tex]P(X ≤ 12) = ∫[0,12] f(x) dx = ∫[0,12] (1/12) * e^(-x/12) d\\P(X ≤ 12) = [-e^(-x/12)] [0,12] = -e^(-1) + 1 ≈ 0.632\\P(X ≤ 6) = ∫[0,6] f(x) dx = ∫[0,6] (1/12) * e^(-x/12) dx\\P(X ≤ 6) = [-e^(-x/12)] [0,6] = -e^(-1/2) + 1 ≈ 0.393\\[/tex]
Therefore, the probability that the arrival time between vehicles is 6 seconds or less is approximately 0.393.
P(X ≥ 30) = 1 - P(X < 30) = 1 - P(X ≤ 30) = 1 - ∫[0,30] f(x) dx
[tex]= 1 - ∫[0,30] (1/12) * e^(-x/12) dx[/tex]
[tex]P(X ≥ 30) = 1 - [-e^(-x/12)] [0,30] = e^(-2.5) ≈ 0.082[/tex]
Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.082.
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The superintendent of a school district wants to predict next year‘s middle school lunch count the graph shows the results of a survey randomly selected middle school students she conducted a survey and which randomly select the middle school students rest do you typically buy a school lunch each week approximately 63% of students responded they do not typically buy a school lunch if the district has 5000 middle school students next year about how many students plan to buy lunch one and two days a week 
1850 students are expected to buy lunch one or two days a week next year.
what is a percentage?A ratio or figure stated as a fraction of 100 is called a percentage. The sign "%" is frequently used to indicate it as a percentage or a component of a total.
If 63% of the students do not typically buy a school lunch, then 37% of the students do typically buy a school lunch.
Let's assume that x students plan to buy lunch one or two days a week.
Then, the number of students who do typically buy a school lunch can be estimated as:
0.37(5000) = 1850
Let's assume that p% of the students plan to buy lunch one or two days a week. Then, we can set up the following equation:
p% of (5000) = x
To solve for x, we need to convert the percentage to a decimal by dividing by 100:
p/100 × 5000 = x
Simplifying the equation, we get:
50p = x
We can substitute this equation into the original equation to get:
0.37(5000) = 50p
Simplifying and solving for p, we get:
1850 = 50p
p = 37
Therefore, approximately 37% of the 5000 middle school students, or 1850 students, are expected to buy lunch one or two days a week next year.
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Light travels 1.8x10^7 kilometers in one minute. How far does it travel in 6 minutes?
Consider a triangle ABC like the one below suppose that C equals 32 vehicles 44 and C equals 27° the figure is not drawn to scale solve the triangle
On solving the provided question we can say that As a result, the triangle is resolved.
what is trigonometry?The study of the relationship between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their potential applications in computations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric shapes.
We now have all of the information we require to solve the triangle. We now have:
a = 55.815 sin(A) (A
b = 55.815 sin(B) (B)
c = 32
A + B + C = 180°
B = 153° - A
To find the values of A and B, we can use a calculator. We get:
A ≈ 83.814°
B ≈ 42.186°
32 / sin(27°) = a / sin(A)
a ≈ 54.482
AB ≈ 54.482
BC ≈ 39.343
AC ≈ 22.414
A ≈ 83.814°
B ≈ 42.186°
C ≈ 27°
As a result, the triangle is resolved.
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Find the slope of a line perpendicular to the line whose equation is 2x + 3y = 24.
Fully simplify your answer.
The slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2
What is Equation?An equation is a statement that two expressions are equal. It contains one or more variables and may also contain constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
To find the slope of a line perpendicular to the line whose equation is [tex]2x + 3y = 24[/tex], we need to first find the slope of the given line.
We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:
[tex]2x + 3y = 24[/tex]
[tex]3y = -2x + 24[/tex]
[tex]y = \huge \text(-\dfrac{2}{3}\huge \text )x + 8[/tex]
So the slope of the given line is -2/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of -2/3.
The negative reciprocal of a number is the number flipped upside down and then negated. So the negative reciprocal of -2/3 is:
[tex]-1 \div \huge \text(-\dfrac{2}{3}\huge \text )=\dfrac{3}{2}[/tex]
Therefore, the slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2
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Four transformations of the function f (x ) = 2x are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
For the four transformations based on f(x)= [tex]2^{x}[/tex],
1)6f(x)= 6 [tex]2^{x}[/tex]
2)f(6x)= [tex]2^{6x}[/tex]
3)f(x+6)=[tex]2^{x+6}[/tex]
4)f(x)+6 = [tex]2^{x}[/tex]+6
What are transformations?
Transformations in any given function is changing its original form to nre form by flipping, rotating, shifting, enlarging and compressing the function. We can move the given function up or down as per the given conditions by adding up or subtracting the constant in y axis. We can move the given function left or right as per the given conditions by adding up or subtracting the constant in x axis. We can stretch or compress the function about x or y axes. Also we can also flip,reverse the function, reflect about axes or enlarge the functions.
Here given that function f(x)= [tex]2^{x}[/tex]
From the given graph we can identify few points for the given function:
(-1,0.5); (0,1); (1,2); (2,4); (3,8); (4,16); (5,32); (6,64) and so on.
Now to identify the transformations, we can substitute the tranformed value of x in the function:
1)6 f(x) = 6 . [tex]2^{x}[/tex] {as we know that f(x)= [tex]2^{x}[/tex]}
∴6 f(x) will be equal to 6 . [tex]2^{x}[/tex]
2)f(6x) : for this we can replace 'x' by '6x'
f(6x) = [tex]2^{6x}[/tex]
3)f(x+6): for this function replace 'x' by 'x+6'
f(x+6)=[tex]2^{x+6}[/tex]
4)f(x)+6 : substitute f(x)= [tex]2^{x}[/tex], we get
f(x)+6 = [tex]2^{x}[/tex]+6
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The height above the ground in feet of a football thrown into the air from the balcony of a house is -12t + 20t + 30, where t is the time in seconds since the ball was thrown. How high above the ground is the balcony?
Answer: The height above the ground in feet of a football thrown into the air from the balcony of a house is given by the expression:
h(t) = -12t^2 + 20t + 30
where t is the time in seconds since the ball was thrown.
To find the height of the balcony above the ground, we need to determine the initial height of the football when it was thrown from the balcony. This initial height corresponds to the value of h(0), since the time elapsed since the throw was zero at that moment.
Therefore, we can substitute t = 0 into the expression for h(t):
h(0) = -12(0)^2 + 20(0) + 30 = 30
This means that the balcony is 30 feet above the ground.
Hence, the height of the balcony above the ground is 30 feet.
Step-by-step explanation:
Please help asap!!!
The exact values of trigonometric functions are, respectively:
sin (u + v) = - 13 /85
tan (u + v) = - 13 / 84
How to find the exact values of trigonometric functions
In this problem we need to determine the exact values of trigonometric functions, this can be done by using trigonometric formulas and relationships between trigonometric functions. We need to use the following expressions:
sin² x + cos² x = 1
sin (u + v) = sin u · cos v + cos u · sin v
tan x = sin x / cos x
tan (u + v) = (tan u + tan v) / (1 - tan u · tan v)
Where x, u, v are measured in radians.
Now we proceed to determine the exact values of each function:
cos u = √[1 - (- 3 / 5)²]
cos u = 4 / 5
sin v = √[1 - (15 / 17)²]
sin v = 8 / 17
sin (u + v) = (- 3 / 5) · (15 / 17) + (4 / 5) · (8 / 17)
sin (u + v) = - 13 /85
tan u = (- 3 / 5) / (4 / 5)
tan u = - 3 / 4
tan v = (8 / 17) / (15 / 17)
tan v = 8 / 15
tan (u + v) = (- 3 / 4 + 8 / 15) / [1 - (- 3 / 4) · (8 / 15)]
tan (u + v) = - 13 / 84
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Let f(x) = (x + 3)(x + 4) and g(x) = 1 3 (x + 3)(x − 4). The graphs of each are shown below.
Which graph represents which polynomial function? Explain how you can determine this without
using graphing software
Answer: We can determine which graph represents which polynomial function by analyzing the factors of each function.
First, let's consider f(x) = (x + 3)(x + 4). The factors are (x + 3) and (x + 4). When we multiply these factors together, we get a quadratic polynomial with a positive leading coefficient. This means that the graph of f(x) will be a parabola that opens upward.
Next, let's consider g(x) = 1/3(x + 3)(x − 4). The factors are (x + 3) and (x - 4). When we multiply these factors together and simplify, we get a quadratic polynomial with a leading coefficient of 1/3. This means that the graph of g(x) will also be a parabola that opens upward, but it will be narrower than the graph of f(x).
Based on this analysis, we can determine that the graph of f(x) corresponds to the wider parabola, and the graph of g(x) corresponds to the narrower parabola. We can also determine this without using graphing software by noting that f(x) has roots at x = -3 and x = -4, while g(x) has roots at x = -3 and x = 4. The graph of f(x) must therefore intersect the x-axis at -3 and -4, while the graph of g(x) must intersect the x-axis at -3 and 4. By examining the graphs, we can see that the wider parabola intersects the x-axis at -3 and -4, so it corresponds to f(x), while the narrower parabola intersects the x-axis at -3 and 4, so it corresponds to g(x).
Step-by-step explanation:
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Adele and her brother ran a race. Adele reached the finish line in 37.45 seconds and her brother reached the finish line 2.1 seconds later. How long did it take Adele's brother to run the race?
Answer:
It took Adele's brother 37.45 + 2.10 = 39.55 seconds to run the race.
The combined city/highway fuel economy of a 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range of 21mpg to 26mpg answer A and B URGENT
a)The range of 95% of the data is from 21 mpg to 26 mpg, which is a range of 5 mpg.
b)We need a sample size of 543 to estimate the mean with 98% confidence and an error of 0.25 mpg
What is Empirical Rule for a normal distribution?
If a dataset is normally distributed, we can expect that about 68% of the data points will fall within one standard deviation of the mean, about 95% of the data points will fall within two standard deviations of the mean, and about 99.7% of the data points will fall within three standard deviations of the mean. This rule is a useful guideline for understanding the spread of data in a normal distribution.
(a) Using Method 3 (the Empirical Rule for a normal distribution), we know that for a normally distributed random variable, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.
Since the range of the combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is from 21 mpg to 26 mpg, the midpoint of the range is (21 + 26) / 2 = 23.5 mpg.
Using the Empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the range of 95% of the data is from 21 mpg to 26 mpg, which is a range of 5 mpg.
We can set up the following equation to solve for the standard deviation, σ:
2σ = 5
σ = 5 / 2
σ = 2.5
Therefore, the estimated standard deviation is 2.5 mpg. Rounded to 4 decimal places, the estimated standard deviation is 2.5000 mpg.
(b) The formula for the margin of error is:
Margin of error = z-value×(standard deviation / √(sample size))
We want the margin of error to be 0.25 mpg and the confidence level to be 98%. Since we are using a z-value, we can look up the z-value for a 98% confidence level in a standard normal distribution table.
The z-value for a 98% confidence level is approximately 2.33 when rounded to 3 decimal places.
Plugging in the given values, we have:
0.25 = 2.33×(2.5 / √(sample size))
Solving for the sample size, we get:
√(sample size) = 2.33 × (2.5 / 0.25)
√(sample size) = 23.3
sample size = (23.3)²
sample size = 542.89
Rounded to the nearest whole number, we need a sample size of 543 to estimate the mean with 98% confidence and an error of 0.25 mpg.
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Suppose that A and B are independent events such that P (A) - 0.10 and P (B) - 0.60.
Find P(A n B) and P (A U B).
Answer:
Step-by-step explanation:
Since A and B are independent events, we can use the formula:
P(A ∩ B) = P(A) x P(B)
P(A ∩ B) = 0.10 x 0.60
P(A ∩ B) = 0.06
So the probability of both events A and B occurring is 0.06.
To find P(A U B), we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.10 + 0.60 - 0.06
P(A U B) = 0.64
Therefore, the probability of either A or B occurring (or both) is 0.64.
Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x. Rstudio
a) [25, 2.081]
b) [25, 1.981]
c) [25, 1.681]
d) [25, 1.581]
e) [80, 1.681]
[ 25 , 1.581 ] is the pair that is the mean and standard error of x.
What does standard error mean?
A statistical concept known as the standard error uses standard deviation to assess how well a sample distribution represents a population.
The standard error of the mean describes the statistical variation between a sample mean and the population's actual mean. Measures of variability include standard error and standard deviation: The standard deviation describes variation within a single sample.
n = 80
μ = 25
σ² = 200
mean of x = μ = 25
standard error = √ σ²/n
= √200/80
= 1.581
= [ 25 , 1.581 ]
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The Griffins bought a $292,000 house. They made a down payment of $48,000 and took out a mortgage for the rest. Over the course of 30 years they
monthly payments of $1462.91 on their mortgage until it was paid off.
Question 13
(a) What was the total amount they ended up paying for the house (including
the down payment and monthly payments)?
$
(b) How much interest did they pay on the mortgage?
$
The Griffins ended up paying a total of $575,647.60 for the house. The Griffins paid a total of $331,647.60 in interest over the 30-year period
What is interest rate?Interest rate refers to the percentage of the principal amount charged by a lender to a borrower for the use of money over a certain period of time.
According to question:(a) The total amount they ended up paying for the house can be calculated by adding the down payment to the total amount paid in monthly mortgage payments over the 30-year period:
Total amount paid = down payment + (monthly payment x number of payments)
Number of payments = 30 years x 12 months/year
= 360
Total amount paid = $48,000 + ($1462.91 x 360)
= $48,000 + $527,647.60
= $575,647.60
Therefore, the Griffins ended up paying a total of $575,647.60 for the house.
(b) The total amount of interest paid on the mortgage can be calculated by subtracting the amount borrowed (i.e., the purchase price minus the down payment) from the total amount paid over the 30-year period:
Total interest paid = total amount paid - amount borrowed
Amount borrowed = $292,000 - $48,000 = $244,000
Total interest paid = $575,647.60 - $244,000 = $331,647.60
Therefore, the Griffins paid a total of $331,647.60 in interest over the 30-year period.
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Change into passive voice a. They bring food for us.
Answer:
Food is brought for us by them.
Answer:
Food is brought for us by them.
Step-by-step explanation:
Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
x = 2;
y = √3
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{y}{1} [/tex]
Cross-multiply to find y:
[tex]y = 1 \times \tan(60°) = 1 \times \sqrt{3} = \sqrt{3} [/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {1}^{2} [/tex]
[tex] {x}^{2} = ( { \sqrt{3}) }^{2} + {1}^{2} = 3 + 1 = 4[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{4} = 2[/tex]
Are these ratios equivalent?
6 teal sweatshirts to 8 purple sweatshirts
15 teal sweatshirts to 13 purple sweatshirts
True
False
Answer:
False
Step-by-step explanation:
Purple: 13÷8= 1.625
Teal: 15÷6= 2.5
The ratios don't have the same scale factor. Therefore they are not equivalent fractions.
Analyze the diagram below and complete the instructions that follow.
Find sin 45°.
A.
112
B. √√√2
L
45°
sin 45° = opposite/hypotenuse = x/√2x = √2/2. The answer is B. √2/2.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of trigonometric functions, which are functions that relate the angles of a triangle to the ratios of the lengths of its sides.
The triangle shown in the diagram is a right triangle with one angle of 45 degrees, which means that the other two angles must measure 45 degrees each as well.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can label the sides of the triangle as follows:
The side opposite the 45-degree angle is x.
The side adjacent to the 45-degree angle (and opposite the other 45-degree angle) is also x.
The hypotenuse is the longest side of the triangle and is labeled as √2x.
Using the definition of sine, we have:
sin 45° = opposite/hypotenuse = x/√2x = √2/2
Therefore, the answer is B. √2/2.
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How much will you owe at the end of 10 years and a month, if you decide to pay your yearly bonus at the end of each year toward reducing your outstanding loan amount for a loan with the following details? Loan amount PV $320,000 Rate of interest APR 4.750% p. y. c. w. Loan term NPER 15 years Bonus payment at end of each year $4,500 Group of answer choices $21,619.43 $41,033.68 $58,527.87 $74,315.75
The correct option is $58,527.87
To solve this problemUsing the loan details and bonus payment provided, the remaining balance on the loan at the end of 10 years and a month can be calculated as follows:
Number of payments made = 10 years * 12 months/year + 1 month = 121
Monthly interest rate = 4.75% / 12 = 0.3958%
Yearly bonus payment = $4,500
Using the PMT function in Excel, the monthly payment on the loan can be calculated as:
PMT(0.003958, 15*12, 320000) = -$2,378.03
Since the bonus payment is made once a year, it can be applied as a lump sum to the remaining balance at the end of each year. Therefore, the remaining balance after 10 years and a month can be calculated as:
Remaining balance = PV(0.003958, 5*12, -2378.03, 0, 0) - 4500
where PV is the present value function.
Solving this equation yields:
Remaining balance = $58,527.87
Therefore, the answer is $58,527.87.
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What is the perimeter of a rectangle with a base of 9 ft and a height of 10 ft?
Answer: The perimeter of a rectangle is found by adding up all four sides. For this rectangle with a base of 9 ft and a height of 10 ft, the two base sides have a length of 9 ft each, and the two height sides have a length of 10 ft each. Therefore, the perimeter is:
P = 2(9 ft) + 2(10 ft) = 18 ft + 20 ft = 38 ft
So the perimeter of the rectangle is 38 feet.
Step-by-step explanation:
How will the product change if one number is increased by a factor of 12 and the other is decreased by a factor of 4
If one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will be multiplied by a factor of 3.
Let's suppose we have two numbers, A and B, and we want to know how their product will change if one number is increased by a factor of 12 and the other is decreased by a factor of 4.
The initial product of the two numbers is:
A x B
If we increase A by a factor of 12, the new value of A will be 12A. If we decrease B by a factor of 4, the new value of B will be B/4. Therefore, the new product of the two numbers will be:
(12A) x (B/4) = (12/4) x A x B = 3AB
So the new product of the two numbers will be three times the initial product. In other words, if one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will increase by a factor of 3.
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If trapezoid QRST is dilated about the origin by a scaled (k) of 2, what is the resulting coordinate of point T”?
Using dilation, we can find the coordinates of the new trapezoid and the coordinates of T" is (-6, -4).
Define dilation?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale-factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation maths, but the square's shape doesn't change.
In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.
Here in the question,
The coordinates of point T = (-3, -2)
Now, the trapezoid is dilated about the origin.
The scale factor here is. k = 2.
The new coordinates of the point T":
x coordinate = -3 × 2 = -6
y coordinate= -2 × 2 = -4
The coordinates of T" = (-6, -4).
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what is a fraction between 6/7 and 1
Answer:
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sandhyamahilane1116
24.02.2021
Math
Secondary School
answered • expert verified
What is a fraction between 6/7 and 1 whole?
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amitnrw
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Given : 6/7 and 1 whole
To Find : a fraction between 6/7 and 1 whole
Solution:
There exist Infinitely many rational between two different rational numbers
There can be Different ways to find rational number in between two number
one way is to find mean of number
= (6/7 + 1)/2
= 13/14
13/14 is a fraction between 6/7 and 1 whole
6/7 = 18/21
1 = 21/21
19/21 , 20/21 are fraction between 6/7 andfraction
Whats the value of x?
Answer:
x = 25
Step-by-step explanation:
By the angle sum property,
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 175
x = 25
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Answer:
x = 25
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180 and 7x=175
7x = 175
x = 25
so x is most likely the answer
x=25 Give her BRAINLEST for figuring it out first