Answer:
To find the lower and upper quartiles and the interquartile range, we first need to order the data from smallest to largest:
20, 22, 25, 28, 29, 30, 32, 33, 34
Next, we find the median (middle value) of the entire dataset:
Median = (29 + 30) / 2 = 29.5
This median value divides the data into two halves. We then find the median of the lower half of the data, which includes all values less than or equal to 29.5:
Lower half: 20, 22, 25, 28, 29
Median of lower half = (25 + 28) / 2 = 26.5
This value, 26.5, is the lower quartile (Q1).
Similarly, we find the median of the upper half of the data, which includes all values greater than or equal to 29.5:
Upper half: 30, 32, 33, 34
Median of upper half = (32 + 33) / 2 = 32.5
This value, 32.5, is the upper quartile (Q3).
Finally, we can calculate the interquartile range (IQR) as the difference between the upper and lower quartiles:
IQR = Q3 - Q1 = 32.5 - 26.5 = 6
Therefore, the lower quartile is 26.5, the upper quartile is 32.5, and the interquartile range is 6.
17 feet 2 inches= Inches
Answer:
206 inches
Step-by-step explanation:
1 feet = 12 inches
17 feet = 17 x 12 = 204 inches
17 feet 2 inches = 204 + 2 = 206 inches
So, 17 feet 2 inches = 206 inches
A chemical company makes two brands of antifreeze. The first brand is 55% pure antifreeze, and the second brand is 85% pure antifreeze. In order to obtain 90 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Therefore , the solution of the given problem of percentage comes out to be 15 gallons of the first brand and 75 gallons of the second brand must be utilised
What is percentages?In statistics, a figure or metric than may be presented as a percentage or 100 is denoted by the abbreviation "a%". Another unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this. Additionally, there are no indications or predetermined ratios of any component to the whole. Numbers are effectively integers since they frequently add up to 100.
Here,
Let's write "x" for the first brand's (55% pure antifreeze) number of gallons and "y" for the second brand's (85% pure antifreeze) number of gallons.
Given:
90 gallons of mixture total are required.
Antifreeze content in the mixture should be 80%.
Based on the information provided, we can construct the following system of equations:
Formula 1: x + y = 90
Formula 2: 0.55x + 0.85y = 0.80 * 90
=> x = 90 - y
=> 0.55(90 - y) + 0.85y = 0.80 * 90
=> 49.5 - 0.55y + 0.85y = 72
=> 0.30y = 22.5
=> y = 75
=> x = 90 - 75
=> x = 15
In order to get 90 gallons of a mixture that contains 80% pure antifreeze, 15 gallons of the first brand and 75 gallons of the second brand must be utilised.
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if 3+1=34
2+2=44
2+3=65
5+3=158
7+2=?
Answer:
7 + 2 = 149 here.
7 × 2 = 14, and 7 + 2 = 9.
PLEASE HELP!!! MIDDLE SCHOOL MATH
Based on the scatter plot below, which is a better prediction for y when x = 74?
PLEASE LOOK AT THE PICTURE!!!!!!!!!!!!!!
The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.
How to find the better prediction ?Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.
From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.
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. Keisha's employer deducts 0.2 times
her wages in payroll taxes. How much is
deducted when Keisha earns $132?
You have to find what 0.2 of 132 is
132 x 0.2 = 26.40
The answer [tex]\boxed{\bold{\$26.40}}[/tex]
I need help please!!!
Answer:
a. Plot the points on the graphing calculator, then generate a logarithmic regression equation.
y = 34.17860108 - 5.682632245ln(x)
b. Setting this equation equal to 10, we have x = 70.44 mph
c. If x = 75 mph, then y = 9.64.
Flying against the wind, an airplane travels 6390 kilometers in 9 hours. Flying with the wind, the same plane travels 2970 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 810 km/h and the rate of the wind is 90 km/h.
Explain the term rate
Rate is a measure of the speed or frequency of change of a quantity over time or space. It is expressed as a ratio between two quantities, such as distance travelled per unit of time or number of occurrences per unit of time. Rates are commonly used in mathematics, science, and economics to analyze and compare different phenomena.
According to the given information
Let's let x be the rate of the plane in still air and y be the rate of the wind. When flying against the wind, the plane's effective speed is (x - y) km/h, and when flying with the wind, its effective speed is (x + y) km/h.
From the information given in the problem, we can set up two equations to represent the plane's distance travelled when flying against and with the wind:
6390 = 9(x - y)
2970 = 3(x + y)
Solving for x and y in these equations, we find that x = 810 and y = 90. So the rate of the plane in still air is 810 km/h and the rate of the wind is 90 km/h.
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What is the equation in point-slope form of the line that passes through the points (7,5) and (−4,−1) ? Responses y+1=67(x+4) y plus 1 equals fraction 6 over 7 end fraction left parenthesis x plus 4 right parenthesis y+1=611(x+4) y plus 1 equals fraction 6 over 11 end fraction left parenthesis x plus 4 right parenthesis y+4=116(x+1) y plus 4 equals fraction 11 over 6 end fraction left parenthesis x plus 1 right parenthesis y−1=611(x−4)
The line that goes through the specified points has the equation into point-slope form is [tex]y+1=6/11(x+4)[/tex].
What is a straight line equation?X-axis points equal (7, -4).
Y-axis points are equal to (5, -1).
To determine the equation of the line passing through the specified points in point-slope form:
A straight line equation's direction and steepness are commonly described by its slope, which is also known as a line's gradient.
In mathematics, the following formula yields the slope of a line:
Slope(m) = [tex]y2-y1/x2-x1[/tex]
slope= [tex]\frac{-1-5}{-4-7}[/tex]
slope= 6/11
To find point slope:
[tex]y-y1=m(x-x1)\\y-(-1)=6/11(x-(-4)\\y+1=6/11(x+4)[/tex]
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Five cards are dealt from a standard deck. What is the probability that at least four of them are hearts?
Step-by-step explanation:
To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.
There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.
Now, there are two possible scenarios that would result in at least four hearts:
Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).
Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.
So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
Plugging in the values and simplifying, we get:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
= (715 * 39 + 1287) / 2,598,960
= 27,885 / 2,598,960
≈ 0.0107566
So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.
A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar. At this rate, how many cups of sugar should be used if 5 cups of flour included?
According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product
According to the given information:If the recipe requires 2 cups of flour for every 2/3 cups of sugar, we can write this relationship as:
2 cups of flour : 2/3 cups of sugar
To find out how many cups of sugar should be used if 5 cups of flour are included, we can set up a proportion:
2 cups of flour / 2/3 cups of sugar = 5 cups of flour / x cups of sugar
where x is the number of cups of sugar we want to find.
To solve for x, we can cross-multiply:
2 cups of flour * x cups of sugar = 2/3 cups of sugar * 5 cups of flour
2x = (2/3) * 5
2x = 10/3
x = 5/3
Therefore, According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
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Apples $1.20 per pound how much would it cost for 2.5 pounds of apples?
Answer: $3.00
Step-by-step explanation:
To figure this out, we can use the following formula:
[tex]\textsf{Cost per pound x number of pounds we want to buy}[/tex]
In this case, we want to buy 2.5 pounds of apples, so we can multiply 2.5 by $1.20 to get the total cost:
[tex] \textsf{2.5 x 1.20 = 3} [/tex]
So, 2.5 pounds of apples will cost $3.00
A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.
The work done in stretching a spring is given by the formula:
W = (1/2)k[tex]x^{2}[/tex]
where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.
To find the spring constant k, we can use the given information:
F = kx
where F is the force applied to the spring. Rearranging this equation, we get:
k = F/x
Substituting the given values, we get:
k = 350 N / 30 cm = 11.67 N/cm
Now, we can find the work done in stretching the spring from 10 cm to 40 cm:
W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])
where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).
Substituting the values, we get:
W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])
W = (1/2) * 11.67 N/cm * (1600 [tex]cm^{2}[/tex] - 100 [tex]cm^{2}[/tex])
W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]
W = 10,837.5 joules (J)
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Can anybody help me
The Swamis family went on a vacation. They recorded the number of miles they drove each day. The mileage is shown in the table. Day 1 2 3 4 5 Distance (mi) 248 176 379 263 202
a) The mean of the mileage is 90.4 miles per day
b) The median of the mileage is 255.5 miles
Given data ,
Let the data be represented as A
Now , the value of A is
A = { 248 176 379 263 202 }
And , Mean = (248 + 176 + 379 + 263 + 202) / 5 = 452 / 5 = 90.4 miles per day (rounded to one decimal place)
Therefore, the mean of the data is 90.4 miles per day.
To find the median of the data, we need to first put the distances in order from least to greatest:
176, 202, 248, 263, 379
There are 5 data points, so the median is the middle value.
Median = (248 + 263) / 2 = 511 / 2 = 255.5 miles
Hence , the median of the data is 255.5 miles
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The complete question is attached below :
The Swamis family went on a vacation. They recorded the number of miles they drove each day. The mileage is shown in the table. Day 1 2 3 4 5 Distance (mi) 248 176 379 263 202 What is the mean of the data? ____miles What is the median of the data? ______miles
please help me solve the bonus question
Answer: a = 5 and k = 1/2
Step-by-step explanation:
We are given that the function is defined by:
f(x) = 16 + a(3^(kx))
We need to find the real numbers a and k such that f(0) = 21 and f(4) = 61. Using the given values of f(0) and f(4), we can form a system of two equations:
f(0) = 16 + a(3^(k(0))) = 21
f(4) = 16 + a(3^(k(4))) = 61
Simplifying the first equation, we get:
16 + a(3^0) = 21
16 + a = 21
a = 5
Substituting this value of a into the second equation, we get:
16 + 5(3^(4k)) = 61
5(3^(4k)) = 45
3^(4k) = 9
We know that 3^2 = 9, therefore
4k = 2
=> k = 2/4
=> k = 1/2
Therefore, the real numbers a and k that satisfy the given conditions are a = 5 and k = 1/2. So the function is:
f(x) = 16 + 5(3^(x/2))
The solution to the equation give us an approximate that x = 1.55.
What is the solution to the equation?To solve this equation, we can start by subtracting 4 from both sides to isolate the exponential term:
3.5^x + 4 - 4 = 11 - 4
This simplifies to:
3.5^x = 7
Next, we can take the logarithm of both sides with base 3.5 to eliminate the exponent:
log(3.5^x) = log(7)
Using the property of logarithms that log(a^b) = b*log(a), we can rewrite the left side as:
x*log(3.5) = log(7)
Now, we can solve for x by dividing both sides by log(3.5):
x = log(7) / log(3.5)
Plugging in the values, we get:
x = 0.84509804001 / 0.54406804435
x = 1.55329475566
x ≈ 1.55.
Answered question "Solve the equation 3.5^x + 4 = 11"
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Kelly is making a bubble mixture for kids to play with at a backyard party. She adds 1/4 of a cup of corn syrup to 6 cups of soap and water.
She wants to make more bubble mixture and has 18 cups of the soap and water mixture to use.
How much corn syrup does she need to add?
A. 2/3 of a cup of corn syrup
B. 3 cups of corn syrup
C. 3/4 of a cup of corn syrup
D. 3 1/4 cups of corn syrup
Answer: C. 3/4 of a cup of corn syrup
Step-by-step explanation:
We will set up a proportion to help us solve.
[tex]\displaystyle \frac{1/4\text{ cup corn syrup}}{6\text{ cups of soap and water}} =\frac{x\text{ cups corn syrup}}{18\text{ cups of soap and water}}[/tex]
Next, we will cross-multiply.
1/4 * 18 = 6 * x
9/2 = 6x
Lastly, we will divide both sides of the equation by 6.
x = 3/4 of a cup of corn syrup
C. 3/4 of a cup of corn syrup
Please help me. Giving brainliest to whoever answers it!!!
The algebraic expression that represents the age of Ethan's dad is 4a - 5
How to represent the situation as an algebraic expression?Let's start by defining a variable to represent Ethan's age. We'll call this variable "a".
According to the problem, Ethan's dad is five years younger than four times Ethan's age. So, if we multiply Ethan's age by 4 and then subtract 5 years, we'll have the age of Ethan's dad.
Algebraically, we can represent this as:
4a - 5
Therefore, the algebraic expression that represents the age of Ethan's dad is 4a - 5.
Solve the equation [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex]?Solve for x by simplifying both sides of the equation and isolating the variable.
[tex]3\frac{2}{3}x=2\frac{2}{5}[/tex]
Convert mixed numbers to improper fraction :
[tex]3\frac{2}{3} =\frac{11}{3}[/tex]
[tex]\frac{11}{3}x=2\frac{2}{5}[/tex]
Convert mixed numbers to improper fractions:
[tex]2\frac{2}{5} = \frac{12}{5}[/tex]
[tex]\frac{11}{3}x=\frac{12}{5}[/tex]
Multiply both sides by 3
[tex]11x=\frac{36}{5}[/tex]
Divide both sides by 11
[tex]x=\frac{36}{55}[/tex]
Therefore, [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex] = [tex]x=\frac{36}{55}[/tex]
Steve sold 252 fruit baskets for the fundraiser. Therefore, we can find how many baskets Evie sold by using the ratio of her sales to Steve's sales, which is given as 25 baskets for each 100 baskets Steve sold.
We can set up a proportion to solve for the number of baskets Evie sold:
25/100 = x/252
Here, x represents the number of fruit baskets Evie sold.
To solve for x, we can cross-multiply and simplify:
25 * 252 = 100 * x
6300 = 100x
x = 63
Therefore, Evie sold 63 fruit baskets for the fundraiser.
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The piecewise function g(x) is shown in the graph.
Graph with three pieces. The first piece is a horizontal line from the left with an open right endpoint at negative 2 comma negative 1. The second piece is curved with a solid point at negative 1 comma 0, which ends at 1 comma 1. The last piece starts with a solid circle at 0 comma 1 and increases to the right as it passes through 4 comma 5.
Which of the following represents g(x)?
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than or equal to x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than or equal to x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).
What represents g (x)?Looking at the graph, we can see that:
g(x) is equal to -2 for x ≤ -1.g(x) is a quadratic function that passes through the point (-1,0) and (1,1), with a vertex at (0,1), for -1 < x ≤ 0.g(x) is a linear function that passes through the point (0,1) and (4,5), for x > 0.Thus, the correct piecewise function that represents g(x) is:
g(x) = {-2 if x ≤ -1
{ (x-1)^2 if -1 < x ≤ 0
{ -x+1 if x > 0
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In the diagram below DE is parallel to XY what is the value of X
Since this is about the angle theorem and the angle theorem is a theorem that helps us know the relationship between angles. Being a corresponding angle, x = 105°. Hence option A is correct.
What are corresponding angles?A corresponding angle is an angle that occupies the same relative position as another angle elsewhere in the diagram. The corresponding angle in planar geometry occurs when a transverse line crosses his two straight lines. Two angles correspond or relate to each other by being on the same side of the horizontal line. One is the exterior angle (outside the parallel lines) and the other is the interior angle (inside the parallel lines).
You can see that the transversal line intersects two parallel lines DE and XY. From the transversal theorem of angles in mathematics, we know that when a transversal line intersects two parallel lines, the corresponding angles formed are congruent and therefore equal to each other.
In this question we see that one of the angles is 105°. Therefore x° is congruent to it, x = 105°.
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The complete question is as follows:
Which of the points below correctly plots the point (2,7π/4)?
Points are plotted on a polar graph.
Answer: E is correct
Step-by-step explanation:
Remember that the coordinates (2,7π4) tell us the radius r=2 and the angle θ=7π4. So the point should be on the circle labeled 2 and form an angle of 7π4 with the positive x-axis. Point E is the correct point.
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest) 905, 940, 955, 965, 1020, 1040, 1045, 1085, 1090, 1105 Send data to calculator Suppose that one of the people moves. His rent changes from $905 to $ 1055 Answer the following (a) What happens to the mean ? decreases by It increases by s Box It stays the same . (b) What happens to the median ? It decreases by s It increases by It stays the same .
Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.
What is mean?The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.
Here,
The average rent is determined by adding up all the rents and dividing by the total number of rents.
This is known as the mean.
Given that the person's rent increased by
=>$150, $1055 - $905 = $150.
The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.
The mean would therefore rise by
=> $150/10
=> $15.
(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.
The new median would be the middle value of the revised list, which would include the new price of $1055,
if one person's rent increased from $905 to $1055.
The median would rise given that $1055 is more expensive than $1020.
Thus , it increases by.
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Is the range a subset or a proper subset of the codomain?
A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.
What is a subset?A set that includes all or a portion of another set's elements is known as a subset. For instance, because every even integer is also an integer, the set of even integers is a subset of the set of integers. A subset that contains some, but not all, of the members of another set is said to be a proper subset. Because it contains some, but not all, of the positive integers, the set of positive integers less than 10 is a valid subset of the set of positive integers.
A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.
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Find the area of each triangle.
Step-by-step explanation:
the area of a right-angled triangle is
leg1 × leg2 / 2 =
sin(angle)×baseline × cos(angle)×baseline / 2 =
sin(angle)×cos(angle) × baseline² / 2
4 = sin(30)×baseline = 0.5 × baseline
baseline = 4/0.5 = 8 units
Pythagoras gives us the third side = cos(30)×baseline :
8² = 4² + side²
64 = 16 + side²
48 = side²
side = sqrt(48) = sqrt(16×3) = 4×sqrt(3) units
so, the area of the triangle is again
sin(30)×baseline × cos(30)×baseline / 2 =
= 4 × 4×sqrt(3) / 2 = 2×4×sqrt(3) = 8×sqrt(3) units² =
= 13.85640646... units²
If the point (1,5) lies on a circle with center (0,0), determine which point in quadrant 2 that also lies on the circle.
Answer:
If the point (1,5) lies on a circle with center (0,0), then the radius of the circle is the distance from the center to the point (1,5), which is:
r = sqrt((1-0)^2 + (5-0)^2) = sqrt(26)
So the equation of the circle is:
x^2 + y^2 = 26
To find a point in quadrant 2 that lies on the circle, we need to find a point with a negative x-coordinate and a positive y-coordinate that satisfies this equation.
Among the given options, only (a) (-5,1) and (e) (-2,3) have a negative x-coordinate. Let's check if they satisfy the equation of the circle:
For point (a) (-5,1):
x^2 + y^2 = 26
(-5)^2 + 1^2 = 26
25 + 1 = 26
This point does not lie on the circle.
For point (e) (-2,3):
x^2 + y^2 = 26
(-2)^2 + 3^2 = 26
4 + 9 = 26
This point also does not lie on the circle.
Therefore, among the given options, there is no point in quadrant 2 that lies on the circle.
Step-by-step explanation:
since the center of the circle is at the origin, that means that the circle is evenly going through all four quadrants - one quarter arc after the other.
the point (1, 5) is in the first quadrant (upper right one, positive x, positive y).
the circle arc in the second quadrant (upper left one, negative x, positive y) is the mirrored image of the arc in the first quadrant across the y-axis.
so, the point on it gets mirrored too.
that means, it's coordinates are then the same y and the x is converted to its negative value :
(-1, 5)
that is the easily identifiable point in the second quadrant that has to be on the circle.
Find the length of FG.
The length of FG chord is 5 units.
What bout chord?
A chord is a line segment that joins two points on the circumference of a circle. More specifically, a chord is a straight line that intersects a circle at two points, and the segment of the line between these two points is called a chord.
The length of a chord can be calculated using the Pythagorean theorem, given the radius of the circle and the distance between the two points on the circumference. The length of a chord is always less than or equal to the diameter of the circle.
Chords have various applications in geometry, trigonometry, and calculus. For example, in trigonometry, the chord function is defined as the ratio of the length of a chord to the radius of the circle. In calculus, chords are used in the definition of the derivative, which is the slope of the tangent line to a curve at a given point.
According to the given information:
2(x + 2 )= ( 5 x - 5 )
2x + 4 = 5x -5
9 = 3x
3 = x
The length of FG is = x+2 = 3+2 = 5 units
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The length of FG chord is 5 units.
What bout chord?
A chord is a line segment that joins two points on the circumference of a circle. More specifically, a chord is a straight line that intersects a circle at two points, and the segment of the line between these two points is called a chord.
The length of a chord can be calculated using the Pythagorean theorem, given the radius of the circle and the distance between the two points on the circumference. The length of a chord is always less than or equal to the diameter of the circle.
Chords have various applications in geometry, trigonometry, and calculus. For example, in trigonometry, the chord function is defined as the ratio of the length of a chord to the radius of the circle. In calculus, chords are used in the definition of the derivative, which is the slope of the tangent line to a curve at a given point.
According to the given information:
2(x + 2 )= ( 5 x - 5 )
2x + 4 = 5x -5
9 = 3x
3 = x
The length of FG is = x+2 = 3+2 = 5 units
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The concentration C of a drug in a patient's bloodstream t hours after injection is given by C(t) = 100t/2 t^2 + 85.
Use a calculator to approximate the time when the concentration is highest. (Round your answer to two decimal places.)
Approximately 1.18 hours the concentration is highest.
The given function is c(t)=100t/t² +85.
When the concentration is highest, the function becomes
100t/t² +85 =0
100/t +85=0
100+85t=0
85t=100
t=100/85
t=1.18 hours
Therefore, approximately 1.18 hours the concentration is highest.
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plot 1 2/5 - 1/2 - 2 1/10 on a number line
A graph of the data set is shown in the image attached below.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a number line as shown in the image attached below.
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Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
a. What was the book value of the equipment at December 31 the end of the fifth year?
b. Assume that the equipment was sold on April 1 of the sixth year for $105,800.
1. Journalize the entry to record depreciation for the three months until the sale date.
2. Journalize the entry to record the sale of the equipment.
The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000
Accumulated Depreciation $66,000
How to solve the question?
a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:
Depreciation Expense = (Cost - Residual Value) / Useful Life
Depreciation Expense = ($212,000 - $14,000) / 15
Depreciation Expense = $13,200 per year
The accumulated depreciation for five years is therefore:
Accumulated Depreciation = Depreciation Expense x Number of Years
Accumulated Depreciation = $13,200 x 5
Accumulated Depreciation = $66,000
The book value of the equipment at December 31 of the fifth year is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - $66,000
Book Value = $146,000
b.
To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.
Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)
Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)
Depreciation Expense for the Sixth Year = $9,900
The journal entry to record depreciation for the three months until the sale date would be:
Depreciation Expense $9,900
Accumulated Depreciation $9,900
To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.
The book value of the equipment at the time of the sale is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - ($13,200 x 5.25)
Book Value = $141,450
Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:
Cash $105,800
Loss on Sale of Equipment $35,650
Equipment $212,000
Accumulated Depreciation $66,000
The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.
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Kelly’s bill at a restaurant came to $21.52. If she decides to leave a 18% tip, how much of a tip did she leave
Answer:
$3.87 for the 18% tip.
Drag each tile to the correct box.
A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Sample A Sample B Sample C
x g(x)
0 60
1 120
2 240
3 480
Sample C starts
with 600 bacteria and
increases at a
rate of 20%.
f(x)=200(3/2)x^
Order the samples by their average growth rate over the interval [1, 3], from least to greatest.
Sample C
Sample A
Sample B
pleaseeee help thank youuu
we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.
How to solve the question?
To determine the average growth rate of each sample over the interval [1, 3], we need to calculate the ratio of the change in bacteria population to the change in time for each sample, and then take the average of these ratios over the given interval.
For Sample A, the change in bacteria population over the interval [1, 3] is 480 - 120 = 360, and the change in time is 3 - 1 = 2. So the average growth rate of Sample A over this interval is 360/2 = 180 bacteria per hour.
For Sample B, the change in bacteria population over the interval [1, 3] is 480 - 240 = 240, and the change in time is 3 - 1 = 2. So the average growth rate of Sample B over this interval is 240/2 = 120 bacteria per hour.
For Sample C, the change in bacteria population over the interval [1, 3] is (1.2600)(1.2*1.2 - 1) = 345.6, and the change in time is 3 - 1 = 2. So the average growth rate of Sample C over this interval is 345.6/2 = 172.8 bacteria per hour.
For Sample A, the growth rate is the highest, followed by Sample C and then Sample B. Therefore, the order of the samples by their average growth rate over the interval [1, 3] from least to greatest is Sample C, Sample A, and Sample B.
It's important to note that the growth rate of Sample C is not constant but increases over time due to the 20% increase in the initial bacteria population. The exponential function f(x) = 200(3/2)in power x represents this growth, and we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.
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Your complete question is :-A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Sample A Sample B Sample C
x g(x)
0 60
1 120
2 240
3 480