Answer:
No
Step-by-step explanation:
3(-20-3)-5>23
simplify:
3(-23)-5>23-69-5>23-74>23-74 is not greater than 23Elaine's height is 75% of her father's. If her father is 180 cm tall, how tall is Elaine?
Answer: Elaine is 135cm tall
Step-by-step explanation:
Elaine's height is 75% of her father's height.
We can calculate Elaine's height by multiplying her father's height by 75% or 0.75.
Elaine's height = 0.75 * 180 cm
= 135 cm
Therefore, Elaine is 135 cm tall.
Help please, I'm so lost
I gotchu <3
Since the vertex is (0, -3), the quadratic function can be written in vertex form as:
f(x) = a(x - 0)^2 - 3
Where 'a' is a constant that determines the shape of the parabola. Since the end behavior of the function is y --> - Infinite as x --> - infinite and y --> - Infinite as x --> + infinite, the leading coefficient 'a' must be negative.
So, f(x) = -a(x^2 - 0x) - 3
Now, using the given point (1, -7) on the parabola, we can substitute the coordinates into the function and solve for 'a'.
-7 = -a(1^2 - 0(1)) - 3
-7 = -a - 3
a = 10
Therefore, the quadratic function that satisfies the given characteristics is:
f(x) = -10x^2 - 3
Hope this helps :)
pls hurry
2. INTEREST Marty invested $2000 in an account that pays at least 4% annual interest. He wants to see how much money he will have over the next few years. Graph the inequality y ≥ 2000 (1 + 0.04) ^× to show his potential earnings.
For the given inequality substitute the coordinates of x and y to form the graph of y ≥ 2000 (1 + 0.04)ˣ.
What is compound interest?Interest that is calculated on both the initial principle and any accrued interest is known as compound interest. This implies that the interest for the subsequent period is computed using the new total amount after the interest for the prior month has been added to the principal. If the interest rate and the duration are both high, the interest might add up to a sizable amount over time. Savings accounts, investments, loans, and other financial instruments frequently use compound interest.
For the given inequality we have:
For x = 0, y = 2000.
For x = 1, y = 2000(1 + 0.04) = 2080.
Plot the points on the graph to determine the graph.
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Julian goes to a store an buys an item that costs � x dollars. He has a coupon for 20% off, and then a 4% tax is added to the discounted price. Write an expression in terms of � x that represents the total amount that Julian paid at the register.
Answer:
If Julian buys an item that costs £x, then the amount of discount he receives from the 20% off coupon is:
Discount = 0.2x
The discounted price that Julian pays after the coupon is applied is:
Price after discount = x - 0.2x = 0.8x
Next, a 4% tax is added to the discounted price, which can be calculated as:
Tax = 0.04(0.8x) = 0.032x
Therefore, the total amount that Julian paid at the register can be expressed in terms of £x as:
Total amount = Price after discount + Tax
Total amount = 0.8x + 0.032x
Total amount = 0.832x
So, the expression in terms of £x that represents the total amount that Julian paid at the register is 0.832x.
Joshua started his own lawn care business. He donates 10% of his income to a local charity, which is recognized by the IRS as a qualified charitable organization. Joshua can claim expenses from his business and charitable donations as , and they will reduce the.
first blank having: Tax credits
or
tax reductions
second having: amount of taxable income
or
amount of tax owned
Joshua started his own lawn care business. He donates 10% of his income to a local charity, which is recognized by the IRS as a qualified charitable organization. Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income.
The first blank should be filled with "tax reductions" and the second blank should be filled with "amount of taxable income."
The first blank should be filled with "tax reductions". Tax reductions reduce the amount of income that is subject to tax, whereas tax credits directly reduce the amount of tax owed.The second blank should be filled with "amount of taxable income." Business expenses and charitable donations are deductible from taxable income, meaning they reduce the amount of income that is subject to tax. By reducing the taxable income, the amount of tax owed will also be reduced.Hence, the correct statement would be: "Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income."
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a cylinder has a diameter of 10 units and a height of 20 inches what is the volume
Therefore , the solution of the given problem of volume comes out to be the cylinder has a volume of roughly 1570.796 cubic units.
What does volume mean exactly?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are the signs for cubic measurements. However, in order to determine an object's dimensions, you must also be aware of its volume. It is common practise to convert the weight of an object into weight units like grammes and kilogrammes.
Here,
The following formula can be used to determine a cylinder's volume:
Volume =π * r² * h.
where r is the cylinder's radius and h is its height, and (π) is a mathematical constant roughly equal to 3.14159.
The radius (r) of a cylinder with a diameter of 10 units would be equal to 10/2, or 5 units, which is the diameter.
We can now enter these numbers into the formula to determine the volume given that the cylinder's height (h) is 20 inches:
=> Volume = π * (5)² * 20
=> Volume = 3.14159 x 25 / 20.
(Rounded to three decimal places)
=> Volume: 1570.796 cube units
Therefore, the cylinder has a volume of roughly 1570.796 cubic units.
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Imma give h Brainliest!!!
Answer:
Yes, because of the Angle-Angle Theorem
Step-by-step explanation:
The sum of the interior angles of a triangle are 180.
Triangle on the left
180 - 90 - 42 = 48
Triangle on the right:
180 - 90 - 48 = 42
Since the angles measurements are the same, the triangles are similar.
Helping in the name of Jesus.
Answer: Yes, because of the Angle-Angle Theorem
Step-by-step explanation:
The two triangles have the same angles, so they are similar by the Angle-Angle Theorem.
Zhang walks in a straight line from the trail head at (0,0). He travels at an average rate of 3 mi/h in the direction 30° west of north. What are the coordinates of Zhang's location, relative to the trail head, after 4 hours?
Zhang's location, relative to the trail head, after 4 hours is approximately (10.392, 6) miles.
Trigonometry to find the horizontal and vertical components of Zhang's displacement vector after 4 hours, and then add these components to the coordinates of the trail head.
The horizontal component of Zhang's displacement is given by:
[tex]cos(30\℺) = \sqrt3/2[/tex]
So, the horizontal distance traveled after 4 hours is:
[tex]distance = rate \times time = 3 mi/h \times 4 h = 12 mi[/tex]
Therefore, the horizontal component of Zhang's displacement is:
[tex]\triangle x = 12 mi \times \sqrt3/2 = 6\sqrt3 mi[/tex]
The vertical component of Zhang's displacement is given by:
[tex]sin (30\℺ ) = 1/2[/tex]
So, the vertical distance traveled after 4 hours is:
[tex]distance = rate \times time = 3 mi/h \times 4 h = 12 mi[/tex]
Therefore, the vertical component of Zhang's displacement is:
[tex]\triangle y = 12 mi \times 1/2 = 6 mi[/tex]
Adding these components to the coordinates of the trail head, we get:
[tex]x = 0 + 6\sqrt 3 mi \approx 10.392 mi[/tex]
[tex]y = 0 + 6 mi = 6 mi[/tex]
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jordan drove 378 miles in 7 hours. if he can keep the same pace, how long will it take him to drive 1,188 miles?
Jordan would take 22 hours to drive 1,188 miles at the same speed he drove 378 miles in 7 hours.
How to find the time that Jordan take to drive 1,188 miles?We can use the formula:
time = distance / speed
where speed is constant, to find the time it would take Jordan to drive 1,188 miles.
The speed at which Jordan drove can be calculated as:
speed = distance / time
where distance is 378 miles and time is 7 hours.
speed = 378 / 7 = 54 miles per hour
Now, we can use the speed to find the time it would take to drive 1,188 miles:
time = distance / speed = 1,188 / 54 = 22 hours
Therefore, if Jordan can maintain the same pace, it would take him 22 hours to drive 1,188 miles.
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The radius of a semicircle is 8.4 millimeters. What is the semicircle's diameter?
Answer:
Step-by-step explanation:
8.4 x 2 = 16.8
In how many ways can two variables be chosen from X1, X2, S1, S2, S3 and assigned the value 0? ways (Type a whole number.)
There are 10 ways to choose two variables from X1, X2, S1, S2, S3 and assign the value 0.
To choose two variables from X1, X2, S1, S2, and S3, and assign the value 0, you can use the combination formula. In this case, there are 5 variables (n=5) and you want to choose 2 (r=2). The combination formula is C(n, r) = n! / (r!(n-r)!).
Applying the formula:
C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = 120 / (2! * 3!)
C(5, 2) = 120 / (2 * 6)
C(5, 2) = 120 / 12
C(5, 2) = 10
So, there are 10 ways to choose two variables from X1, X2, S1, S2, and S3, and assign the value 0.
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an assumption of the linear model of communication is the belief that _____.
The communication is a one-way process in which a message is conveyed from a sender to a receiver is one of the assumptions made by the linear model of communication.
The straightforward linear model of communication presents communication as a process with distinct beginnings and endings.
But this model ignores the fact that communication is frequently a more complex and involved process that needs context, feedback, and a variety of channels.
The linear model presumes that the message is clearly understood by the recipient and that it is received by the recipient free from distortion or interference.
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An assumption of the linear model of communication is the belief that communication is a one-way process where a sender transmits a message to a receiver through a channel. This model assumes that communication is a linear process where the sender encodes a message, which is then sent through a channel to the receiver who decodes the message.
In the linear model, the sender encodes a message, sends it through a channel, and the receiver decodes the message. This model does not account for feedback or interaction between the sender and receiver, assuming that communication is a straightforward and direct transmission of information without any complexities or interruptions.
This model assumes that there is little to no feedback or interaction between the sender and receiver, and that the message is transmitted and received accurately without any distortion. However, this assumption is often criticized for oversimplifying the complex nature of communication and ignoring the role of context and feedback in the communication process.
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a freight train left a station at 12 noon g . 4. , o~g north at a rate of 50 miles per hour. at 1:00 p.m. a passenger train left the same station, going south at a rate of 60 miles per hour. at what time were the trains 380 miles apart?
The trains will be 380 miles apart at 3:00 PM, which is 4 hours after the freight train leaves the station at 12 noon.
How to solve the problem for distance and time?We can use the formula d = rt (distance = rate x time) to calculate the distance each train has traveled during this time:
Let's call the time elapsed from 12 noon until the trains meet as t hours.
During this time, the freight train has traveled at a rate of 50 mph for t hours and the passenger train has traveled at a rate of 60 mph for (t-1) hours (since it started one hour after the freight train).
Distance traveled by freight train = 50t
Distance traveled by passenger train = 60(t-1)
The total distance between the two trains at time t is the sum of these distances, which we can write as:
Total distance = 50t + 60(t-1)
We want to find the time t at which the total distance is 380 miles. So we can set up the equation:
50t + 60(t-1) = 380
Simplifying this equation, we get:
110t - 60 = 380
110t = 440
t = 4
Therefore, the time elapsed from 12 noon until the trains meet is 4 hours. Since the passenger train left one hour after the freight train, it has been traveling for 3 hours.
So the time at which the trains are 380 miles apart is 3:00 PM (12 noon + 4 hours).
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About 16% of people who get their feet examined are found to have athlete's foot. What is the probability of a podiatrist examining five people until he finds the first patient who has athlete's foot? (0. 16)^5 (0. 84)^4(0. 16)^1 (0. 16)^4(0. 84)^1 (0. 84)5 1 − (0. 16)^4
The probability of examining the five people till first patient has athlete's foot is given by (0. 84)^4(0. 16)^1.
Percent of people have athlete foot = 16%
Let us consider the probability of success represented by p = 0.16.
Using geometric distribution,
Probability of finding first patient with athlete's foot on kth examination is given by geometric probability distribution,
P(X = k) = (1 - p)^(k - 1) × p
where X is random variable representing number of trials needed until first success.
Probability of finding the first patient with athlete's foot on the fifth examination k = 5,
⇒ P(X = 5) = (1 - p)^(5 - 1) × p
⇒ P(X = 5) = (0.84)^4 × 0.16
Simplify it we get,
⇒ P(X = 5) = 0.0473
Therefore, the probability of a podiatrist examining five people until he finds the first patient who has athlete's foot is (0. 84)^4(0. 16)^1.
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Spinning a spinner that has 5 equal sections marked 1 through 5 and anding on an even number. Find the probability and write answer in simplest form.
The probability of spinning an even number is 2/5, which can be written in simplest form.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The spinner has 5 equal sections marked 1 through 5. Two of the five numbers are even (2 and 4). Therefore, the probability of spinning an even number is:
Probability of spinning an even number = (number of even numbers) / (total number of possible outcomes)
Probability of spinning an even number = 2/5
Hence, The probability of spinning an even number is 2/5, which can be written in simplest form.
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Identify the expression that is not equivalent to 6x + 3.
The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.
For instance, "4 added to 2" will have the mathematical formula 2+4.
So, we have the expression:
= x² + 10x + 24
Now, solve when x = 3 as follows:
= x² + 10x + 24
= 3² + 10(3) + 24
= 9 + 30 + 24
= 63
Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
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Correct question:
Evaluate the expression when x = 3.
x² + 10x + 24
a. 81
b. 86
c. 63
d. 60
Find the Length of the Arc ^PQ and round your answer to the nearest Hundredth place.
Please help
The length of an arc is PQ is 9.42 units.
How to find the length of an arc?The length of an arc is PQ can be found as follows:
length of an arc = ∅ / 360 ×2πr
where
∅ = central angler = radius of the circleTherefore,
∅ = 60 degrees
r = 9 units
length of the arc = 60 / 360 × 2 × 3.14 × 9
length of the arc = 1 / 6 × 56.52
length of the arc = 56.52 / 6
length of the arc = 9.42 units
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A frog catches insects for their lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which the diagram shows.
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Flies. The second tape has 7 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Mosquitoes.
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Flies. The second tape has 7 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Mosquitoes.
The table shows the number of flies and the number of mosquitoes that the frog eats for two lunches.
Based on the ratio, complete the missing values in the table.
Day Flies Mosquitoes
Monday
15
1515
Tuesday
14
1414
are older men shorter than younger men? according to a national report, the mean height for u.s. men is 69.4 inches. in a sample of 170 men between the ages of 60 and 69, the mean height was x
If older men are shorter than younger men. However, we do have information about the mean height for U.S. men, which is 69.4 inches.
Additionally, we have a sample of 170 men between the ages of 60 and 69, but we do not have the value for the mean height of this sample (represented as "x" in the question).
If we were given the value of "x", we could compare it to the mean height for all U.S. men and potentially make conclusions about the height of older men compared to younger men.
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can someone give me the answers to these 5?? pleaseee!!
The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00
How to find the number summaries ?Calculate the MAD:
First, find the mean of the data set:
mean = (sum of all values) / (number of values)
mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10
mean = 88.00 / 10 = 8.80
Then, find the mean of these absolute deviations:
MAD = (sum of absolute deviations) / (number of values)
MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10
MAD = 4.10 / 10 = 0.41
Calculate the range:
range = maximum value - minimum value
range = 10.00 - 8.00 = 2.00
Find Q1 and Q3:
{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}
Q1 is the median of the lower half, and Q3 is the median of the upper half.
Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}
Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}
Q1 = median of lower half = 8.25
Q3 = median of upper half = 9.25
Calculate the IQR:
IQR = Q3 - Q1
IQR = 9.25 - 8.25 = 1.00
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If the area of an equilatral is 81 to the root of 3 cm squarefind the perimeter of the triangle
The perimeter of the equilateral triangle with an area of 81√3 cm² is 54 cm.
An equilateral triangle is a type of triangle in which all three sides are equal in length, and all three angles are equal to 60 degrees.
Let's denote the side length of the equilateral triangle by "a".
The formula for the area of an equilateral triangle is
Area = (√3/4) × a^2
We are given that the area is 81√3 cm², so we can set up the equation
81√3 = (√3/4) × a^2
Solving for "a", we get:
a = 18 cm
Now that we know the side length, we can find the perimeter by multiplying it by 3 (since it's an equilateral triangle):
Perimeter = 3a = 3 × 18 cm = 54 cm
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Process _____ is based on comparing the current amount of outcome variation against outcome specifications.
SPC is widely used in manufacturing, healthcare, and other industries to improve quality and efficiency.
The process you are referring to is called Statistical Process Control (SPC), which involves monitoring and analyzing a process to ensure it is within the acceptable range of variation. This is done by comparing the current amount of outcome variation against the established outcome specifications, allowing for corrective action to be taken if necessary. SPC is widely used in manufacturing, healthcare, and other industries to improve quality and efficiency.
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Process control is based on comparing the current amount of outcome variation against outcome specifications.
Process control is a management approach that involves monitoring and adjusting a process to ensure that it meets its intended outcome specifications.
The goal of process control is to maintain consistent outcomes over time, despite natural variation in the inputs or other factors that may affect the process.
In order to achieve this goal, process control typically involves monitoring the process using statistical methods and comparing the current level of variation in the process outcomes against the desired outcome specifications.
If the variation is within acceptable limits, the process is considered to be under control.
If the variation is outside of acceptable limits, the process may require adjustment or other corrective action to bring it back into control.
Overall, process control is an important tool in quality management, manufacturing, and other fields where consistent outcomes are critical to success.
By monitoring and adjusting processes over time, organizations can ensure that their products and services meet the needs and expectations of their customers, while minimizing waste, errors, and other sources of variation.
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Find the exact value of sin(a - B) if sina = -3 and sinß = 3, and the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant I.
We can use the trigonometric identity for the sine of a difference:
sin(a - B) = sin a cos B - cos a sin B
What is the exact value of sin(a - B)?We are given that sina = -3 and sinß = 3, so we need to find the cosine of each angle. Since the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant I, we can use the following relationships:
cos a = -sqrt(1 - sin^2 a) = -sqrt(1 - 9) = -sqrt(-8) = sqrt(8)i
cos ß = sqrt(1 - sin^2 ß) = sqrt(1 - 9) = sqrt(-8) = sqrt(8)i
Note that we use i to indicate the imaginary unit, since the result involves a negative square root. Therefore, we have:
sin(a - B) = sin a cos ß - cos a sin ß
= (-3)(sqrt(8)i) - (sqrt(8)i)(3)
= -3sqrt(8)i - 3sqrt(8)i
= -6sqrt(8)i
Hence, the exact value of sin(a - B) is -6sqrt(8)i.
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The exact value of sin(a - B) if sina = -3 and sinß = 3, and the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant is sin(a - B) =0
What is trigonometric identity?We apply the trigonometric identity for the sine of a difference:
sin(a - B) = sin(a)cos(B) - cos(a)sin(B)
We use Pythagorean identity to find the cosine values:
cos^2(a) = 1 - sin^2(a) = 1 - (-3)^2 = -8
cos(a) = ±√8i
cos(a) = -√8 (Since a lies in quadrant III, the cosine value is negative.)
we also have that:
cos^2(B) = 1 - sin^2(B) = 1 - 3^2 = -8
cos(B) = ±√8i
cos(B) = √8. (Since B lies in quadrant I, the cosine value is positive. )
we then substitute these values into the formula for sin(a - B):
sin(a - B) = sin(a)cos(B) - cos(a)sin(B)
= (-3)(√8) - (-√8)(3)
= -3√8 + 3√8
= 0
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data collected from several entities over a period of time (minutes, hours, days, etc.) are called...
Data collected from several entities over a period of time (minutes, hours, days, etc.) are called time series data.
What is time series data?Time series data is a type of data that is collected over a period of time, with measurements taken at regular intervals. The data is often used to track changes in a particular variable over time and to analyze patterns or trends in the data.
Examples of time series data include stock prices, temperature readings, and daily sales figures. Time series data can be used to make forecasts or predictions about future trends based on past data, and it is often analyzed using statistical methods such as trend analysis, seasonality analysis, and autocorrelation analysis.
Time series data can be represented graphically using a line chart or a scatterplot, with time on the x-axis and the variable of interest on the y-axis. Time series data can be univariate, meaning that there is only one variable being measured, or multivariate, meaning that there are multiple variables being measured at the same time.
What are statistical methods?Statistical methods are a set of techniques and procedures used to analyze and interpret data in order to draw meaningful conclusions from it. These methods involve the collection, analysis, and interpretation of data in order to identify patterns, trends, and relationships between variables.
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7) Anna wants to sell her car for $200. But before she puts an ad out, she learns
that the car is actually a speical edition, and many collectors want it. What will
she probably do to the price of her car?
Answer:
She will increase the price of the car
Step-by-step explanation:
This is because if more mass want the car, since the car is in mass demand the price should inflate in order for Anna to get the best deal for herself.
Can someone help me asap? It’s due tomorrow. Provide an explanation please.
The most representative sample is given by the following option:
20 dog owners to determine the best-selling dog food.
What is representative sampling?Representative sampling is a method of selecting a subset of individuals or objects from a larger population in a way that accurately reflects the characteristics of the population as a whole. In other words, the goal of representative sampling is to obtain a sample that is similar to the population from which it was drawn in terms of relevant variables or characteristics.
For this problem, we have that store customers are guaranteed to represent the general population in television preferences for example, however, dog owners are likely to have the best knowledge of the best selling dog food.
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1. The largest of 2 integers is one more than three times the smaller. If the sum of the two integers is 37, find the larger integer.
2. For two consecutive integers, the sum of the smaller and twice the larger is 29. Find the smaller integer.
1. we can use the first equation to find y = 3x + 1 = 3(9) + 1 = 28 So, the larger integer is 28, (2). The smaller integer is 9. The larger integer is 10, which is the next consecutive integer.
What is an integer ?An integer is a whole number ,neither a fraction or a decimal, in mathematics. Integers can be zero, positive, or negative.
Integer examples include -3, -2, -1, 0, 1, 2, 3, and so forth.
The letter "Z" stands for the set of integers.
In mathematics and allied disciplines such as computer science, physics, and finance, integers are utilized extensively.
What is a whole number ?A whole number is a non-negative integer in mathematics, which indicates that it is either a positive integer or zero.
Negative and fractional numbers are not included in whole numbers. The full integers 0, 1, 2, 3, 4, and so on are examples.
In many different branches of mathematics as well as in other disciplines, such as arithmetic, algebra, and geometry, whole numbers are used. They are also employed in daily tasks like quantity calculations and object counts.
According to question :-
Let's call the smaller integer x and the larger integer y. We know that:
y = 3x + 1 (the largest of the two integers is one more than three times the smaller)
x + y = 37 (the sum of the two integers is 37)
We can use substitution to solve for y in terms of x:
x + (3x + 1) = 37
4x + 1 = 37
4x = 36
x = 9
Now we can use the first equation to find y:
y = 3x + 1 = 3(9) + 1 = 28
So the larger integer is 28.
Let's call the smaller integer x and the larger integer y. We know that:
y = x + 1 (the integers are consecutive)
x + 2y = 29 (the sum of the smaller and twice the larger is 29)
We can substitute y = x + 1 in the second equation:
x + 2(x + 1) = 29
Simplifying and solving for x:
3x + 2 = 29
3x = 27
x = 9
So the smaller integer is 9. The larger integer is 10, which is the next consecutive integer.
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An investment of $600 is made into an account that earns 6. 5% annual simple interest for 15
years. Assuming no other deposits or withdrawals are made, what will be the balance in the
account?
According to the investment, after 15 years, the balance in the account would be $1185.
To calculate the final balance after 15 years, we can use the formula for simple interest:
Simple Interest = Principal x Interest Rate x Time
In this case, the principal is $600, the interest rate is 6.5%, and the time is 15 years.
Simple Interest = $600 x 0.065 x 15
Simple Interest = $585
So the investment of $600 earns $585 in simple interest over 15 years. To find the final balance, we add the interest earned to the initial investment:
Final Balance = Principal + Simple Interest
Final Balance = $600 + $585
Final Balance = $1185
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when solving an oblique triangle given three sides, use the ---select--- form of the law of cosines to solve for an angle.
When solving an oblique triangle given three sides, use the inverse cosine form of the Law of cosines to solve for an angle.
When solving an "oblique-triangle" given three sides, we would use the inverse cosine, form of the Law of Cosines to solve for an angle.
The "Inverse-Cosine" function allows us to find the measure of an angle when given the ratio of the lengths of the triangle's sides.
The "Law-of-Cosines" relates the lengths of the sides of a triangle to the cosine of one of its angles.
The "Law-of-Cosines" states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively:
⇒ c² = a² + b² - 2ab × cos(C),
To solve for an angle, we would rearrange the equation to find the cosine of the angle,
⇒ Cos(C) = (a² + b² - c²)/(2ab),
Then, we will take the inverse cosine of both sides of the equation to find the value of the angle,
⇒ C = cos⁻¹((a² + b² - c²)/(2ab)),
This helps us to find the measure of angle C, depending on the units used in the original triangle sides.
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The given question is incomplete, the complete question is
When solving an oblique triangle given three sides, use the _____ form of the Law of cosines to solve for an angle.
When the angle of elevation of the sun is 65°, a building casts a shadow that is 6m long. What is the height of the building to the nearest tenth of a meter?
The height of the building is approximately 18.6 meters to the nearest tenth of a meter.
What is trigonometry?Trigonometry is one of the most significant branches of mathematics, with numerous applications in a wide range of fields. The study of the relationship between the sides and angles of a right-angle triangle is the focus of the "Trigonometry" branch.
We can use trigonometry to solve this problem. Let's draw a diagram:
In the diagram, h is the height of the building, d is the distance from the building to the tip of the shadow, and the angle of elevation of the sun is 65°.
We can see that the height of the building and the distance to the tip of the shadow form a right triangle, and the angle of elevation is the angle opposite the height of the building. Therefore, we can use the tangent function to find the height of the building:
tan(65°) = h/d
Multiplying both sides by d, we get:
h = d tan(65°)
We know that the length of the shadow is 6 m, so d = 6. Substituting this into the formula, we get:
h = 6 tan(65°)
Using a calculator, we get:
h ≈ 18.6
Therefore, the height of the building is approximately 18.6 meters to the nearest tenth of a meter.
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