True. In an indirect proof, also known as proof by contradiction, you start by assuming the opposite of what you intend to prove is true.
You then use deductive reasoning and logical steps to show that the assumption leads to a contradiction or an impossibility. This means that the assumption must be false and therefore the original statement you intended to prove must be true.
What is contradiction?
A contradiction is a situation where two or more statements, beliefs, or ideas are in direct opposition to one another, making them logically inconsistent or incompatible with each other. In other words, a contradiction occurs when there is a conflict between two or more pieces of information that cannot both be true at the same time.
For example, if someone says "I am currently in New York City," and then in the same conversation says "I am currently in Los Angeles," this is a contradiction because it is impossible to be in two different locations at the same time.
What is deductive reasoning?
Deductive reasoning is a method of reasoning in which specific conclusions are drawn from general principles or premises. It is a logical process that involves starting with a general principle or hypothesis, and then using specific observations or evidence to reach a specific conclusion.
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Complete question is: In an indirect proof, also known as proof by contradiction, you start by assuming the opposite of what you intend to prove is true.
Please solve ASAP I need this due for tomorrow
Answer:
this may help!
Step-by-step explanation:
next time you have trouble with a graphing problem, you can just use the desmos graphing calculatator!
Step-by-step explanation:
Plot these set of points:
For x=-2, y=-7. So, plot (-2, -7)
Next, take x=0, so y=-3. Plot (0,-3)
Now make a straight line connecting the points from x=-2 to x=2, and draw a dot on every increment of x by 1. So, the graph should look like so:
Three whole numbers have a total of 100
The first number is a multiple of 15
The second number is ten times the third number
Work out the three numbers
Answer:
The numbers are 30, 60, and 10
Step-by-step explanation:
Let's start by assigning variables to the three numbers.
We can call them x, y, and z.
From the problem, we know that:x + y + z = 100
We also know that the first number is a multiple of 15, so we can write:
x = 15a, where a is some integer.
Furthermore, we know that the second number (y) is ten times the third number (z), so we can write:
y = 10z
Now we can substitute equations (2) and (3) into equation (1) to get an equation in terms of z:
15a + 10z + z = 100
Simplifying, we get:
15a + 11z = 100
To find a possible solution for this equation, we can try different values of a and see if we get a whole number solution for z.
Let's start with a = 1. Substituting a = 1, we get:
15(1) + 11z = 100
z = (100 - 15)/11
z = 8.64
Since z is not a whole number, we need to try a different value of a.Let's try a = 2.
Substituting a = 2, we get:15(2) + 11z = 100
z = (100 - 30)/11
z = 6
Now we have a whole number solution for z. Substituting z = 6 into equations (2) and (3), we get:x = 15a = 15(2) = 30
y = 10z = 10(6) = 60So the three numbers are 30, 60, and 10.
42. Graph the line that passes through the point (-3, 4) and
has a y-intercept of 1. What is the x-intercept of this line?
Answer:
see attached for a graphx-intercept: (1, 0)Step-by-step explanation:
You want a graph and the x-intercept of the line through (-3, 4) with y-intercept 1.
SlopeThe slope formula gives you the slope you can use with the slope-intercept equation.
m = (y2 -y1)/(x2 -x1)
One point is given as (-3, 4). The y-intercept is (0, 1), so the slope is ...
m = (1 -4)/(0 -(-3)) = -3/3 = -1
EquationThen the equation for the line is ...
y = mx +b
y = -1x +1
y = -x +1 . . . . simplify
X-interceptThe x-intercept is the point that has y-coordinate 0:
0 = -x +1
x = 1 . . . . . . add x
The line crosses the x-axis at x
A garden is sodded in the shaded portion below. How many square feet were covered in the sod?
The area of the shaded portion was estimated to be around 400 square feet, so 400 square feet were covered in sod.
The shaded portion of the garden was estimated to be around 400 square feet. To cover this area with sod, the soil was prepared by removing any existing vegetation, rocks, and debris. The soil was then leveled and covered with a layer of fertilizer. After that, the sod was laid on top of the soil, with the roots facing down. The sod was then watered and rolled to ensure the sod was securely attached to the ground. The entire process of sodding the garden was completed in 400 square feet, providing an even layer of grass for the area. This will help to keep the garden beautiful and healthy for years to come.
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=
Solve the following parenteral dosage problem.
Order: Kefzol 250 milligram IM every 2 hours
Have: Label reads Kefzol 225 milligrams per milliliter
Give:
milliliter(s)
Consequently, 1.11 milliliters of Kefzol solution must be administered in order to provide 250 milligrams of the medication.
what is solution ?A solution in mathematics is the response to a question or equation. For instance, the answer to the equation x + 2 = 5 would be 3, as it is the value of x that the equation requires. Similar to the last example, the answer to the question, "What is the area of a square with side length 4?" is 16, as the square's area is 16. Depending on the issue or equation, a solution can be represented in a variety of ways.
given
To address this issue, we must figure out how much Kefzol solution must be used to deliver 250 milligrams of the medication.
We can start by converting the dose from milligrams to milliliters using the provided data. We can establish a ratio because we know that the Kefzol solution has a concentration of 225 milligrams per milliliter:
250 mg/x ml equals 225 mg/1 ml.
If we cross-multiply, we obtain:
225 milligrams per 1 milliliter divided by 250
If we simplify, we get:
x = 225 mg/ml and 250 mg
x = 1.11 ml
Consequently, 1.11 milliliters of Kefzol solution must be administered in order to provide 250 milligrams of the medication.
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Help for AP STATS taking the test rn answer pls
So, option (a), a sample size of 700, should be chosen in order to attain a margin of error of no more than 2.5% with 90% confidence.
what is margin of error ?The statistical concept of margin of error describes the range in which the real value of a population parameter is assumed to lie based on a sample. The degree of uncertainty or error related to a specific sample size and confidence level is given as a plus or negative percentage or number. The genuine percentage of support in the population as a whole is assessed to be between 47% and 53% with 95% confidence, for instance, if a pollster surveys 1,000 individuals and finds that 50% of them favor a certain political candidate with a margin of error of 3%.
given
We can use the following formula to get the sample size required for a specified margin of error with a particular level of confidence:
[tex]n = (Z^2 * p * q) / E^2[/tex]
When we enter the values, we obtain:
[tex]n = (1.645^2 * 0.73 * 0.27) / 0.025^2[/tex]
n ≈ 643.71
We should round up to the nearest choice, which is 700, because the sample size must be an integer.
So, option (a), a sample size of 700, should be chosen in order to attain a margin of error of no more than 2.5% with 90% confidence.
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The complete question is:- Based on earlier studies, it is believed that the proportion of California high school students favoring a four-day school week (8:00 am to 4:30 pm) is 73%. You plan on doing a follow up study. Money is a concern in your study, so you cannot afford to be conservative with your approach. A professional polling company offers to perform the survey for you, and show you the following sample size options. The larger the sample size, the more expensive the survey will be. Which size will you choose if you want a margin of error of no more than ± 2.5% with 90% confidence?
a. 700
b. 800
C. 900
d. 1,000
e. 1,100
Complete the following sentence.
When two numbers are not equal, an ___________ is a sentence that uses the symbols >, <, ≥, ≤, or ≠ to show a relationship.
Answer: The answer is E, or ≠.
Step-by-step explanation:
The symbol (≠) indicates that a number does not equal the other number. The correct option is E.
I hope this helped! A brainilist is appreciated and helpful! <3
someone solve #2 with proof please!
The distance between the base of the second ladder and the wall is 1.6 meters.
How far is the base of the second ladder from the wall?So we know that the two ladders are parallel, then the triangles that we are forming (between the ladder, the floor, and the wall) are two similar triangles.
We know that the length of the first ladder is 4.2m
The length of the second ladder is 5.6 m
Then the scale between these sides is:
4.2m*k = 5.6m
k = 5.6m/4.2m = 4/3
Then the distances of the bases are related by tha same scale, the distance between the base and the wall of the second base is:
(4/3)*1.2 m= 1.6m
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-2x+y=4
-5x+2y=1
I need the ordered pairs for these two
Answer:
(7,18)
Step-by-step explanation:
I think that you are asking for a solution to both equations
-2x + y = 4 → x -2 → 4x -2y = -8
-5x + 2y = 1 → (+) -5x + 2y = 1
-x = -7
x = 7
Substitute 7 for x in either of the two equations and solve for y.
-2(7) + y = 4
-14 + y = 4 Add 14 to both sides
y = 18
The solution is (7,18).
Check:
-2x + y = 4
-2(7) + 18 = 4
-14 + 18 = 4
4=4 Checks.
-5x + 2y = 1
-5(7) + 2(18) = 1
-35 + 36 = 1
1 = 1 checks
Helping in the name of Jesus.
Please help me I really need help on this topic
Answer: 1=53,2=96,0=100,2=70
Step-by-step explanation: Pretty easy there Parrell lines which equals 180 in angles so for example the first one is a corresponding angle cause 53 on angle A is the same on angle B
Second one equation to find this answer is 180-84=96
You'll learn the rest soon I hope this helps
Brandon invested $9,200 in an account paying an interest rate of 3 1/4% compounded quarterly. Lamonte invested $9,200 in an account paying an interest rate of 2 7/8 % compounded monthly. After 19 years, how much more money would Brandon have in his account than Lamonte, to the nearest dollar?
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money at the end of the investment period, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years of the investment period.
For Brandon's account:
P = $9,200
r = 3.25% = 0.0325
n = 4 (compounded quarterly)
t = 19 years
A = 9200(1 + 0.0325/4)^(4*19) = $17,631.51
For Lamonte's account:
P = $9,200
r = 2.875% = 0.02875
n = 12 (compounded monthly)
t = 19 years
A = 9200(1 + 0.02875/12)^(12*19) = $16,031.63
The difference in the amount of money between Brandon's and Lamonte's accounts after 19 years is:
$17,631.51 - $16,031.63 = $1,599.88
Therefore, Brandon would have approximately $1,599 more in his account than Lamonte after 19 years, to the nearest dollar.
Answer:1141
Step-by-step explanation:
its supossed to be a puzzle of some kind?
Write a function that represents the situation, and then answer the question.
You purchase a car in 2020 for $25,000. The value of the car decreases by 14% each year. What will the value of the car be in 2025 (t=5)
This should output: The value of the car in 2025 will be $11730.3 which function means that the value of the car in 2025 will be approximately $11,730.30.
what is function?A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.
To calculate the value of the car in 2025, we need to determine the value of the car after each year of depreciation from 2020 to 2025. We can represent this situation using the following function:
[tex]value = 25000 * (0.86 ** years)\\ return value\\value_2025 = car_value(5)\\print("The value of the car in 2025 will be $" + str(round(value_2025, 2)))\\[/tex]
This should output: The value of the car in 2025 will be $11730.3 which means that the value of the car in 2025 will be approximately $11,730.30.
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Donna wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 37ft from the tree, and Donna is standing 6.6ft from the mirror, as shown in the figure. Her eyes are 6ft above the ground. How tall is the tree? Round your answer to the nearest foot. (The figure is not drawn to scale.)
Using similar triangles, we can set up the following proportion:
(tree height + Donna's height) / (distance from Donna to mirror) = Donna's height / (distance from mirror to top of tree)
Let h be the height of the tree.
Then we have:
(h + 6) / 6.6 = 6 / (37 + h)
Multiplying both sides by (37 + h) and simplifying, we get:
h + 6 = 222 / 6.6 - h / 6.6
Multiplying both sides by 6.6 and simplifying, we get:
6.6h + 39.6 = 222 - h
Solving for h, we get:
7.6h = 182.4
h = 24
Therefore, the height of the tree is approximately 24 feet.
Constructed Response:
20. The table shows the amount of water y in a tank after x minutes have elapsed:
x (minutes)
3
6
y (gallons) 90
70
a. Calculate the rate of change. Show all work. Write your answer as a ratio.
9
50
12
30
b. Interpret the meaning of your answer from Part A. Is water entering or leaving the tank? How do you
know?
c. How much water is in the tank after 15 minutes? Show all work and explain your answer.
According to the solution we have come to find that, There are 50 gallons of water in the tank after 15 minutes.
what is calculus?
Calculus is a branch of mathematics that deals with rates of change and how things change over time. It has two main branches: differential calculus and integral calculus.
Differential calculus deals with instantaneous rates of change and how things change at a particular moment or instant. It involves concepts such as derivatives, limits, and rates of change.
Integral calculus deals with the accumulation of quantities and how things add up over time. It involves concepts such as integrals, area under a curve, and accumulation of volumes.
a. To calculate the rate of change, we need to find the slope of the line connecting the two given points on the table. Using the formula for slope, we get:
slope = (change in y) / (change in x)
slope = (70 - 90) / (6 - 3)
slope = -20 / 3
Expressing the slope as a ratio, we get:
rate of change = -20/3
b. The rate of change is negative, indicating that the amount of water in the tank is decreasing over time. Water is leaving the tank. We know this because the slope of the line is negative, meaning that as time goes on, the amount of water in the tank is decreasing at a constant rate.
c. To find the amount of water in the tank after 15 minutes, we need to first find the equation of the line that passes through the two given points. Using the point-slope form of the equation of a line, we get:
y - 90 = (-20/3)(x - 3)
Simplifying, we get:
y = (-20/3)x + 110
Now we can substitute x = 15 to find the amount of water in the tank after 15 minutes:
y = (-20/3)(15) + 110
y = 50
Therefore, there are 50 gallons of water in the tank after 15 minutes.
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Find the interest rate for an $8000 deposit accumulating to $9571.31, compounded quarterly for 6 years.
The interest rate is ___%
Answer:
3.00%
Step-by-step explanation:
You want the interest rate that will make an $8000 deposit achieve a value of $9571.31 in 6 years when interest is compounded quarterly.
Compound InterestThe compound interest formula can be solved for the interest rate when other values are known:
A = P(1 +r/n)^(nt) . . . . . . . interest at rate r compounded n times per year
9571.31 = 8000(1 +r/4)^(4·6) . . . . fill in known values
(9571.31/8000)^(1/24) = 1 +r/4
1 +r/4 ≈ 1.0075000
r ≈ 0.0075000 × 4 ≈ 3.00%
The interest rate is 3.00%.
__
Additional comment
A financial calculator, app, or spreadsheet can find this for you.
DUE TODAY! SHOW WORK
The value of both missing angles are calculated as: ∠1 = 41° and ∠2 = 139°
How to find the measure of the missing angles?We know that the sum of angles on a straight line sums up to 180 degrees.
Thus, from the given diagram, we can say that:
∠1 + ∠2 = 180
We are told that ∠2 is 16 more that 3 times ∠1.
Thus:
∠2 = 3(∠1) + 16
Thus:
3(∠1) + 16 + ∠1 = 180
4(∠1) = 180 - 16
∠1 = 164/4
∠1 = 41°
∠2 = 180 - 41
∠2 = 139°
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two students are trying to finish labeling the number line with the base 10 logarithmic expression that equal 2. Dylan say the missing logarithm should be log 505 because 505 is halfway between 10 and 1000, just like 2 is halfway between 1 and 3 . Jakob disagree. he says the miss logarithm should be log 100 . Which student is correct
Answer:
Jakob is correct.
The base 10 logarithmic function is a continuous function, which means that the distance between any two consecutive values on the number line is the same. Therefore, if 2 is halfway between 1 and 3, the value of the logarithm that is halfway between log 1 and log 3 should be the average of log 1 and log 3, which is:
(log 1 + log 3) / 2 = (0 + 0.477) / 2 = 0.2385
To find the value of x such that 10^x = 505, we can take the logarithm of both sides using base 10:
log 10^x = log 505
x = log 505
Using a calculator, we can find that log 505 is approximately 2.702.
To find the value of x such that 10^x = 100, we can take the logarithm of both sides using base 10:
log 10^x = log 100
x = log 100
Using a calculator, we can find that log 100 is exactly 2.
Therefore, the logarithm that is equal to 2 is log 100, not log 505.
the difference of twice a number and 5 is less than or equal to 24 translate the sentence into an inequality
Answer:
[tex]2x-5\leq 24[/tex]
Step-by-step explanation:
You figure this out you need to look for keywords. The difference means subtracting and less than or equal to creates [tex]\leq[/tex]. So twice a number, we will call x can be represented by [tex]2x[/tex]. The word difference can be represented by [tex]-[/tex] and less than or equal to 24 can be represented by [tex]\leq 24[/tex]. Combine all these hints into an equation and you get [tex]2x-5\leq 24[/tex]
The data given in the table below represents the increase in rainfall over a period of ten months. Which of the following scatter plots best represents the data?
Months
1
2
3
4
5
6
7
8
9
10
Increase in Rainfall (cm)
1.1
1.3
1.8
2.6
3.7
4.5
5.7
7.1
8.9
12.3
a.
A graph has months on the x-axis, and increases in rainfall (in centimeters) on the y-axis from 1.5 to 15 in increments of 1.5. Points are at (1, 1.1), (2, 1.3), (3, 1.8), (4, 2.6), (5, 3.7), (6, 4.5), (7, 5.7), (8, 7.1), (8, 12.2), (9, 8.9), (10, 12.3).
c.
A graph has months on the x-axis, and increases in rainfall (in centimeters) on the y-axis from 1.5 to 15 in increments of 1.5. Points are at (1, 1.1), (2, 1.3), (3, 1.8), (4, 2.6), (5, 3.7), (6, 4.5), (7, 5.7), (8, 7.1), (9, 8.9), (10, 12.3).
b.
A graph has months on the x-axis, and increases in rainfall (in centimeters) on the y-axis from 1.5 to 15 in increments of 1.5. Points are at (1, 1.1), (2, 1.3), (3, 1.8), (4, 2.6), (5, 3.7), (6, 4.5), (7, 5.7), (8, 7.1), (9, 8.9), (10, 12.3), (10, 12.2).
d.
A graph has months on the x-axis, and increases in rainfall (in centimeters) on the y-axis from 1.5 to 15 in increments of 1.5. Points are at (1, 1.1), (2, 1.3), (3, 1.8), (4, 2.6), (5, 3.7), (6, 4.5), (7, 5.7), (7, 7.3), (9, 8.9), (10, 12.3).
Option b. best represents the data of scatter plots.
Define the term scatter plot?A scatter plot is a type of graph used to display the relationship between two numerical variables. It is also called a scatter diagram or scatter graph.
The best scatter plot to represent the given data would be:
b. A graph shows rainfall increases (in centimeters) from 1.5 to 15 in steps of 1.5 and the number of months on the x-axis.
Points at (1, 1.1), (2, 1.3), (3, 1.8), (4, 2.6), (5, 3.7), (6, 4.5), (7, 5.7), (8, 7.1), (9, 8.9), (10, 12.3)
This scatter plot correctly shows months on the x-axis and the corresponding increase in rainfall (in centimeters) on the y-axis. The range of the y-axis from 1.5 to 15 in increments of 1.5 is appropriate for the data provided. Additionally, this plot correctly represents all the data points provided without any errors.
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What time is
97 minutes after
the time shown on
the clock?
Answer:
10:42
Step-by-step explanation:
Trent Is Building a stone walkway around the Garden. What is the area of the walkway around the garden?
so the garden is a parallelogram and the whole area is a rectangle, now, if we just get the whole area and then subtract the area of the parallelogram from it, in effect making a whole in the rectangle, what's leftover is the area of the walkway, Check the picture below.
The regular octagon in the ceiling of this cathedral has a radius of 10.5 feet and a perimeter of 64 feet.
What is the length of the apothem of the octagon? Round your answer to the nearest tenth of a foot.
feet
Using your answer for the length of the apothem, what is the area of the regular octagon? Round your answer to the nearest tenth of a square foot.
square feet
This cathedral's ceiling features a standard octagon with a 64-foot diameter and a 10.5-foot radius. The apothem is roughly 9.7 feet long, while the normal octagon is roughly 310.8 square feet in size.
The perimeter of the octagon is the sum of the lengths of its sides, so each side has a length of 64/8 = 8 feet.
Draw a line from the centre of the octagon to the midpoint of one of its sides. This line segment is the apothem, which is also the radius of a triangle formed by two consecutive vertices and the centre of the octagon. This triangle is an isosceles triangle, with a base length of 8 and apothem 10.5. We may get the triangle's height using the Pythagorean theorem:
[tex]height^2 = \frac{apothem^2 - base^2}{4}[/tex]
[tex]height^2 = \frac{10.5^2 - 8^2}{4}[/tex]
[tex]height^2[/tex] = [tex]\frac{110.25 - 64}{4}[/tex]
[tex]height^2[/tex] ≈ [tex]\frac{46.25}{4}[/tex]
[tex]height[/tex] ≈ 9.7
So the length of the apothem is approximately 9.7 feet.
The area of the octagon is given by the formula A = (1/2)ap, where a is the apothem and p is the perimeter. With our current values substituted, we obtain:
A =(1/2)×9.7×64
A ≈310.8
A ≈310.8 [tex]ft^2[/tex]
So the area of the regular octagon is approximately 310.8 square feet.
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theory provides a description of how people explain the causes of their own and others' behaviors. question 4 options: dispositional causal identification attribution implicit personality
Attribution theory provides a description of how people explain the causes of their own and others' behaviors. Option d is the correct choice.
The theory referred to in the question is attribution theory. Attribution theory explains how people make inferences about the causes of behaviors, events, or outcomes. It suggests that people usually make two types of attributions: dispositional (internal) and situational (external). Dispositional attributions refer to explanations based on the person's traits or characteristics, while situational attributions refer to explanations based on external factors or circumstances.
Attribution theory also describes how people make judgments about their own behavior and that of others. In summary, attribution theory is a social psychology theory that helps to understand how people explain the causes of behavior. Hence option d is correct.
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--The complete question is, ____________________ theory provides a description of how people explain the causes of their own and others' behaviors.
a. dispositional
b. causal
c. identification
d. attribution
e. implicit
f. personality--
The box plot displays the number of flowers planted in a town last summer.
A box plot uses a number line from 4 to 31 with tick marks every one-half unit. The box extends from 6 to 15 on the number line. A line in the box is at 10. The lines outside the box end at 5 and 30. The graph is titled Flowers Planted In Town, and the line is labeled Number of Flowers.
Which of the following is the best measure of center for the data shown, and what is that value?
The mean is the best measure of center and equals 12.
The mean is the best measure of center and equals 10.
The median is the best measure of center and equals 12.
The median is the best measure of center and equals 10.
Answer: The best measure of center for skewed data is the median, which is not affected by extreme values. From the given box plot, we can see that the line in the box is at 10, which is also the center of the box. Therefore, the median is the best measure of center, and its value is 10. So the correct answer is:
The median is the best measure of center and equals 10.
Step-by-step explanation:
Answer:
The answer is option D.
The median is the best measure of center and equals 10.
Step-by-step explanation:
Your welcome :) :)
Find the volume of each solid shape. Round your answer to two decimal places. (Use 3.14 for pi)
The total volume of the hemisphere mounted on the cuboid is 3574.76 cubic yards.
EquationsTo find the volume of the hemisphere mounted on the cuboid, we need to first find the volume of the cuboid and the volume of the hemisphere separately, and then add them up.
The volume of the cuboid is given by the formula:
V_cuboid = l x w x h
where l, w, and h are the length, width, and height of the cuboid, respectively. Substituting the given values, we get:
V_cuboid = 17 yd x 14 yd x 12 yd
V_cuboid = 2856 cubic yards
Next, we need to find the volume of the hemisphere. The diameter of the hemisphere is given as 14 yd, which means that the radius is 7 yd. The volume of the hemisphere is given by the formula:
V_hemisphere = (2/3) x π x [tex]r^{3}[/tex]
V_hemisphere = (2/3) x 3.14 x [tex]7^{3}[/tex]
V_hemisphere = 718.76 cubic yards
To find the volume of the hemisphere mounted on the cuboid, we add the volumes of the cuboid and the hemisphere:
V_total = V_cuboid + V_hemisphere
V_total = 2856 + 718.76
V_total = 3574.76 cubic yards
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Write the quadratic function in the form y = a(x - h)^2+ k. (10Points)
Answer:
D is the correct option.
Step-by-step explanation:
y = x^2 -14x + 39
take 1/2 of the x coefficient (-14) square it then add it and subtract it :
x^2 - 14x + 49 - 49 + 39 Now reduce the three Left terms
(x-7)^2 - 49 +39 simplify the R portion
y = (x-7)^2 - 10 This process is called 'completing the square'
During one month, 4/10 of Lake Okeechobee is covered in a harmful algal bloom. By the next month, Lake Okeechobee is 90% covered. By how many times does the algal bloom increase?
If 4/10 of Lake Okeechobee is covered in a harmful algal bloom in the first month, then 6/10 of the lake is not covered in the bloom.
In the second month, if 90% of the lake is covered in the bloom, then 10% of the lake is not covered in the bloom.
Since the amount of the lake that is covered by the bloom increased from 4/10 to 9/10, this is an increase of:
(9/10) / (4/10) = (9/10) x (10/4) = 2.25 times
Therefore, the algal bloom increased by 2.25 times.
please explain the answer
Answer: Dallas
Step-by-step explanation:
To get the amount after taxes, you have to multiply your earnings by the tax rate and subtract that amount.
Boston:
70,000 * 0.28 = 19,600
70,000 - 19,600 = $50,400
Dallas:
63,000 * 0.19 = 11,970
63,000 - 11,970 = $51,030
Since Dallas gives you more money, it would be the correct option.
To qualify for Gold status at Awesome Airlines, one must fly at least 8400
8400
and less than 35000
35000
miles each year. If Gerald takes a 700
700
-mile round-trip flight to visit his parents, how many times does Gerald need to visit his parents each year to attain Gold status? Express your answer in interval notation.
Answer: [6, 25]
Explanation:
If Gerald takes a 700-mile round trip, then he is credited with 1400 miles flown (700 miles each way). To attain Gold status, Gerald needs to fly between 8400 and 35000 miles per year. Let's call the number of round trips Gerald needs to take "x". Then, we can set up an inequality to represent the number of miles he needs to fly:
8400 ≤ 1400x ≤ 35000
Dividing all three parts of the inequality by 1400, we get:
6 ≤ x ≤ 25
Therefore, Gerald needs to visit his parents at least 6 times a year, but no more than 25 times a year to attain Gold status. In interval notation, we can express this as:
[6, 25]