On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:
x = 1.49y
-1.49y + x = 0
-149y + 100x = 0
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The linear equation in the required form is: x - 1.49y = 0
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."
Using this information, we can write:
x = 1.49y
To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.
Subtracting 1.49y from both sides, we get:
x - 1.49y = 0
So the linear equation in the required form is:
x - 1.49y = 0
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The numbered disks shown are placed in a box and one disk is selected at random. Find the probability
The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
What is the calculation for this?1. Let's calculate the probability of selecting a blue disk
We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is = 3/8
2. Let's calculate the probability of selecting the blue disk labeled with number 2 =
We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is = 1 /3
3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:
Probability of selecting a 2 given that a blue disk is selected =
3/8 x 1/3 = 3/24 = 1/8
Thus,it is correct to state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
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Full Question:
See attached image.
➡) Complete the expression to show the total
points Roopesh earns if 2 beanbags land on
the board and 2 beanbags land in the hole.
2.5
2.2 ? ▼
Answer:
Step-by-step explanation:
8 points
Systolic blood pressures are approximately Normal with a mean of 120 and a standard deviation of 8.
a. What percentage of people have a systolic blood pressure above 130 (hypertension)?
b. What percentage of people have a systolic blood pressure between 120 and 130?
c. What is the range of systolic blood pressures for the middle 60% of the population?
d. Suppose people with systolic blood pressures in the top 15% of the population have their blood pressures monitored more closely by health care professionals. What systolic blood pressure would qualify a person for this additional monitoring?
About 9.1% of people have a systolic blood pressure above 130.about 34.1% of people have a systolic blood pressure between 120 and 130.
What is percentage?A number can be expressed in fractions of 100 using a percentage. When expressing it, the notation %, which stands for "per hundred," is frequently used. 50%, for instance, equals 50/100, or the percentage 1/2.
a. To find the percentage of people with a systolic blood pressure above 130, we need to find the area under the normal curve to the right of 130. Using a standard normal distribution table or a calculator, we can find that this area is approximately 9.1%. Therefore, about 9.1% of people have a systolic blood pressure above 130.
b. To find the percentage of people with a systolic blood pressure between 120 and 130, we need to find the area under the normal curve between 120 and 130. Using a standard normal distribution table or a calculator, we can find that this area is approximately 34.1%. Therefore, about 34.1% of people have a systolic blood pressure between 120 and 130.
c. To find the range of systolic blood pressures for the middle 60% of the population, we need to find the two values of systolic blood pressure that separate the centre 60% of the normal curve's area under the curve. Using a standard normal distribution table or a calculator, we can find that these values are approximately 111.4 and 128.6. Therefore, the range of systolic blood pressures for the middle 60% of the population is approximately 111.4 to 128.6.
d. To find the systolic blood pressure that qualifies a person for additional monitoring if they are in the top 15% of the population, we need to find the value of systolic blood pressure that separates the top 15% of the area under the normal curve from the rest. Using a standard normal distribution table or a calculator, we can find that this value is approximately 131.4. Therefore, a systolic blood pressure of 131.4 or higher would qualify a person for additional monitoring.
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a. approximately 10.56% of people have a systolic blood pressure above 130.
b. approximately 39.44% of people have a systolic blood pressure between 120 and 130.
c. a systolic blood pressure of 128.32 or higher would qualify a person for additional monitoring if they are in the top 15% of the population.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
a. To find the percentage of people with a systolic blood pressure above 130, we need to calculate the area under the standard normal curve to the right of the z-score corresponding to a systolic blood pressure of 130.
z = (130 - 120) / 8 = 1.25
Using a standard normal distribution table or calculator, we find that the area to the right of z = 1.25 is 0.1056 or 10.56%. Therefore, approximately 10.56% of people have a systolic blood pressure above 130.
b. To find the percentage of people with a systolic blood pressure between 120 and 130, we need to calculate the area under the standard normal curve between the z-scores corresponding to systolic blood pressures of 120 and 130.
z1 = (120 - 120) / 8 = 0
z2 = (130 - 120) / 8 = 1.25
Using a standard normal distribution table or calculator, we find that the area between z = 0 and z = 1.25 is 0.3944 or 39.44%. Therefore, approximately 39.44% of people have a systolic blood pressure between 120 and 130.
c. To find the range of systolic blood pressures for the middle 60% of the population, we need to find the z-scores corresponding to the 20th and 80th percentiles of the standard normal distribution, which are -0.84 and 0.84, respectively.
The corresponding systolic blood pressures are:
lower limit: z1 * 8 + 120 = 113.68
upper limit: z2 * 8 + 120 = 130
Therefore, the range of systolic blood pressures for the middle 60% of the population is approximately 113.68 to 130.
d. To find the systolic blood pressure that qualifies a person for additional monitoring if they are in the top 15% of the population, we need to find the z-score corresponding to the 85th percentile of the standard normal distribution.
Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 85th percentile is 1.04.
The corresponding systolic blood pressure is:
systolic blood pressure = z * 8 + 120 = 128.32
Therefore, a systolic blood pressure of 128.32 or higher would qualify a person for additional monitoring if they are in the top 15% of the population.
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a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.if the call lasted x minutes and x is an integer greater than 3, which of the following expresses the cost of the call in dollars?
The equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).
What is linear equation?A linear equation has the formula y = mx + b, where x and y are variables, m is the angle of the line's slope, and b denotes the y-intercept (the location where the line crosses the y-axis). On a graph, this equation represents a straight line.
The y-intercept of a linear equation, which is determined by the value of b, is first plotted on a graph. The slope is then used to determine further points along the line. How much y changes for each unit of x is indicated by the slope. For instance, if the slope is 2, then y grows by 2 for every unit increase in x.
Given that, a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.
Let us suppose number of minutes = x.
Then,
Cost = 0.75 + 0.15(x - 3)
hence, the equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).
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The complete question is:
Let S be the universal set, where: S={1, 2, 3,…, 18, 19, 20}
Let sets A and B be subsets of S, where:
n(A ∪ B ∪ C) = 16
n(A u B u C) = 2.
How to solve for the setTo find the number of elements in the set ( A cup B cup C), we need to find the union of the sets A, B, and C. This can be done by combining all the elements in A, B, and C, and then removing any duplicates.
So, (A ∪ B ∪ C) = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 20}
Therefore, n(A ∪ B ∪ C) = 16.
To find the number of elements in the set ( A ∩ B ∩ C), we need to find the intersection of the sets A, B, and C. This can be done by finding the elements that are common to all three sets.
So, (A ∩ B ∩ C) = {8, 20}
Therefore, n(A u B u C) = 2.
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Mrs. Sawyer is interested in a particular bracelet. Its original price was $37,260, but it is now marked down by 45%. What is the price of the bracelet now?
Answer: 20,493
Step-by-step explanation:
%45 off of $37,260 is the same as (45 x 45) / 100 which equals to: 16,767
Then do: 37,260 - 16,767 = 20,493
And there you have it! Hope this helps!!
Find f. f ″(x) = −2 + 24x − 12x2, f(0) = 2, f ′(0) = 16
[tex]f''(x)=-2+24x-12x^2\hspace{5em}f'(0)=16\hspace{5em}f(0)=2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \displaystyle \int~(-2+24x-12x^2)dx\implies -2x+12x^2 - 4x^3 + C=f'(x) \\\\\\ \stackrel{\textit{since we know that}}{f'(0)=16}\hspace{5em}-2(0)+12(0)^2-4(0)^3+C=16 \\\\\\ C=16\hspace{5em}\stackrel{\textit{so then we know that}}{-2x+12x^2 - 4x^3 + 16=f'(x)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\displaystyle \int~(-2x+12x^2 - 4x^3 + 16)dx\implies -x^2+4x^3-x^4+16x+C=f(x) \\\\\\ \stackrel{\textit{since we know that}}{f(0)=2}\hspace{5em}-(0)^2+4(0)^3+16(0)+C=2 \\\\\\ C=2\hspace{5em}\boxed{-x^2+4x^3-x^4+16x+2=f(x)}[/tex]
A rocket is launched in the air. Its height in feet is given by h(t)=−16t^2 +24t where
t represents the time in seconds after launch. How long is the rocket in the air?
Taking into account the zeros of a quadratic function, the time of the rocket when it is in the air is equal to 1.5 seconds.
Zeros of a functionThe points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
The zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
In a quadratic function that has the form:
f(x)= ax² + bx + c
the zeros or roots are calculated by:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
Time of he rocket in the airA rocket launched with height function h(t)= -16t²+ 24t
where
't' represents the time in seconds'h' is the height of rocket.Time for which rocket is in the air given by h(t) = 0, so:
0= -16t²+ 24t
where:
a= -16b= 24c= 0Solving:
[tex]x1=\frac{-24+\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]
[tex]x1=\frac{-24+\sqrt{24^{2}} }{2x(-16)}[/tex]
[tex]x1=\frac{-24+24 }{2x(-16)}[/tex]
[tex]x1=\frac{0 }{-32}[/tex]
x₁= 0
and
[tex]x2=\frac{-24-\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]
[tex]x2=\frac{-24-\sqrt{24^{2} } }{2x(-16)}[/tex]
[tex]x2=\frac{-24-24}{2x(-16)}[/tex]
[tex]x2=\frac{-48}{-32}[/tex]
x₂= 1.5
Therefore, the time of the rocket in the air is 1.5 seconds.
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Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmission. The results are displayed below.
Because automatic automobile frequency is different from the dealership, there will be an association.
A frequency chart is what?A list of objects is contained in a frequency table together with the frequency of each item.
The quantity of times that an event or value occurs is its frequency.
A frequency table, then, is a table that contains some facts and their frequency.
Considering the dealership's frequency schedule for both manual and automatic.
We can see that whereas manual transmission dealerships all use the same frequencies, automatic transmission dealerships use distinct frequencies. Since there is a relationship between the two, there will be an association.
Because automatic automobile frequency is different from dealership frequency, there will therefore be a link.
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The complete question is:
Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmission. The results are displayed below.
Select the correct answer.
Using a table of values, what is the solution to this equation?
7/ x + 2 = log (x + 5)
Answer:
Step-by-step explanation:
pleasse help these are the first questions and I am struggling so hard
The solution to the word problems are:
1) ∠JML = 63°
2) The center of the circle is (4, -4) and Radius = 4
3) The required measurement of the table cloth should be:
48 in x 36 in
4) The correct option of the similar triangles is:
UY/UV = UZ/ZW
How to solve algebraic word problems?1) The angle subtended by an arc at the Centre is twice the angle subtended at the circumference . More simply, the angle at the centre is double the angle at the circumference. Thus:
∠JML = 126/2 = 63°
2) The general formula for equation of a circle is expressed as:
(x - h)² + (y - k)² = r²
where:
(h, k) is the coordinate of the center of the circle
r is the radius
We are given the circle equation as:
(x + 4)² + (y - 4)² = 16
This can be rewritten as:
(x + 4)² + (y - 4)² = 4²
Thus:
Coordinates of center = (4, -4)
Radius = 4
3) The required measurement of the table cloth should be:
48 in x 36 in
4) Since both triangles are similar, then it means ratio of corresponding sides will be equal and as such:
UY/UV = UZ/ZW
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amber and bethan tries a number of sweets and shares them in the ratio 2:1
The ratio of the number of sweets that Amber has to the number of sweets that Callum has is 16:9.
What is ratio?A quantitative comparison of two or more quantities that shows their relative sizes is called a ratio.
In terms of how many times one is greater or less than the other, it describes the relationship between the two quantities.
Let's assume that Amber and Bethan bought x number of sweets, then Callum and David also bought x number of sweets.
According to the problem, Amber and Bethan share the sweets in the ratio 2:1. Therefore, Amber has (2/3)(x) sweets and Bethan has (1/3)(x) sweets.
Also, Callum and David share the sweets in the ratio 3:5. Therefore, Callum has (3/8)(x) sweets and David has (5/8)(x) sweets.
Now, we can find the ratio of the number of sweets that Amber has to the number of sweets that Callum has as follows:
Amber/Callum = [(2/3)(x)]/[(3/8)(x)] = (16/9)
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Find an expression which represents the difference when (5x + 6y) is subtracted
from (2x + 7y) in simplest terms.
Answer: -3x+y
Step-by-step explanation:
This is a subtraction problem and "from" means it's the 1st number so
(2x+7y) - (5x + 6y) be careful to distribute negative
2x +7y - 5x -6y
-3x+y
To find the simplest expression when (5x + 6y) is subtracted from (2x + 7y), we subtract the coefficients of like terms. This gives us -3x + y as the final result.
Explanation:The expression represents the difference when (5x + 6y) is subtracted from (2x + 7y) can be found using the properties of addition and subtraction for algebraic expressions. We will combine like terms to simplify.
So, Subtract (5x + 6y) from (2x + 7y), it's like saying (2x + 7y) - (5x + 6y) this will give us:
-3x + y is the final expression in the simplest form.
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Find the area of parallelogram VW XY. Round your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation
A=bh for a parallelogram. The diagram is flipped(turn your paper)
b=9
h=6.7
A=(9)(6.7)=60.3 in²
Use the frequency distribution to complete parts (a) through (e)
For the frequency distribution table;
1. The total number of observation is 24.
2. The width of each class is 11
3. The midpoint of the second class is 26
4. The model class is 65-75
5. The class limits of the next class is 76-86
How do we find the width, model, midpoint and next class limit for the frequency distribution table?For the frequency distribution table,
1. Total observation is the sum of the frequency:
2 + 3 + 5 + 6 + 0 + 8 = 24
2. The width is the first limit lower class - first limit of upper class.
21-10 = 11 or 32-21 = 11
3. The midpoint of class 2 is 21 + 31 = 52/2 = 26
4. The class with the highest frequency is the model class
5. Next class lower limit = 75 + 1 = 76
Next class upper limit = 75 + 11 = 86
Use the frequency distribution to complete parts (a) through (e).
Class Frequency
a) Determine the total number of observations. 10-20 2
b) Determine the width of each class. 21-31 3
c) Determine the midpoint of the second class. 32-42 5
d) Determine the modal class (or classes). 43-53 6
e) Determine the class limits of the next class 54-64 0
if an additional class were to be added. 65-75 8
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14. Joey gets paid $ 4.50 per hour for
babysitting. How much will he
make if he babysits for 6 hours?
(Answer: $__:__)
11
Answer:
$27.00
Step-by-step explanation:
6 × $4.50 = $27.00
Answer:27
Step-by-step explanation:
4.50 x 6 = 27
Toss a fair coin n = 1 time. The distribution of x
the number on the upper face is flat or
uniform
Answer:1
Step-by-step explanation:
A bus traveled on a level road for 3 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 2 hours. Find the average speed on the level road if the entire trip was 290 miles.
Answer:
Let's call the average speed on the winding road "x". Then, the average speed on the level road is "x + 20".
We know that the bus traveled on the winding road for 2 hours, so the distance traveled on the winding road is:
distance = rate × time = x × 2 = 2x
We also know that the bus traveled on the level road for 3 hours at an average speed of "x + 20", so the distance traveled on the level road is:
distance = rate × time = (x + 20) × 3 = 3x + 60
The total distance traveled is 290 miles, so we can write:
2x + 3x + 60 = 290
Combining like terms and solving for x, we get:
5x + 60 = 290
5x = 230
x = 46
Therefore, the average speed on the winding road is 46 mph, and the average speed on the level road is:
x + 20 = 46 + 20 = 66 mph.
Let S be the universal set, where:
S= {1, 2, 3,..., 18, 19, 20}
Let sets A and B be subsets of S, where:
Answer:
Step-by-step explanation:
Therefore, the height of the tower is approximately 121.4 meters.
The graph and table each show a proportional relationship between the number of miles traveled and the
advertised number of gallons of gas used for the two car models, A and B, respectively. Based on the
graph and table, car A can travel how many times the distance car B can travel when both cars use
1 gallon of gas? Write your answer as a decimal.
Enter your answer in the box
1.25
To answer this question, we need to compare the ratios of miles traveled to gallons of gas used for car A and car B when they both use 1 gallon of gas.
For car A, we can see from the graph that 50 miles are traveled for every 2 gallons of gas used, or in other words, 25 miles are traveled for every 1 gallon of gas used. Therefore, car A can travel 25 times the distance for 1 gallon of gas.
For car B, we can see from the table that 40 miles are traveled for every 2 gallons of gas used, or in other words, 20 miles are traveled for every 1 gallon of gas used. Therefore, car B can travel 20 times the distance for 1 gallon of gas.
To compare the two ratios, we can divide the ratio of miles traveled to gallons of gas used for car A by the ratio for car B:
25/20 = 1.25
Therefore, car A can travel 1.25 times the distance car B can travel when both cars use 1 gallon of gas.
in how many ways can the letters of MCHNLRN be arranged
Answer:
2520
Step-by-step explanation:
There are 7 letters in MCHNLRN and they can be arranged into 7 ways:
7! = 5040 ways in total
However, the letter 'N' is repeated so we have to divide it by 2.
5040 ÷ 2 = 2520 ways
Answer:
2,520 ways
Step-by-step explanation:
MCHNLRN has 7 letters with one repetition.
therefore, =7!/2!
=2,520 ways
Student loans and credit cards are two kinds of loans that most often have ________. a. No fees b. Low fees c. Compounding interest d. No late penalties
Student loans and credit cards are two kinds of loans that most often have c. Compounding interest.
What is compounding interest ?It's vital to understand that compound interest charges interest not solely on the borrowing amount but also the accruing interest. Failure to make timely payments can cause a notable rise in the owed total over an extended period of time.
Late fees and penalties are common for student loans and credit cards; thus, comprehending the repayment responsibilities as described within the terms and conditions becomes paramount for borrowers.
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List the angle measures of △IJK in order from smallest to largest. Assume that x is a positive number
Therefore , the solution of the given problem of angles comes out to be
∠I < ∠J <∠K is the increasing order of angle.
An angle's meaning is what?A skew greatest and smallest walls are located where the roads leading to its ends meet. A crossroads could be where two paths converge. Angle is another outcome of two things interacting. They mimic dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various ways between their endpoints.
Here,
Using the provided image, we can calculate the angle measures of the IJK in the following order, from smallest to largest:
∠I: This angle seems to be the smallest one in the IJK system.
∠J: This angle seems to be the following bigger angle in IJK.
∠K: This angle seems to be the biggest one in IJK, according to K.
Therefore , the solution of the given problem of angles comes out to be
∠I < ∠J <∠K is the increasing order of angle.
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pic below
Which statement is supported by the information in the graph?
Answer B The income in Year 5 was twice the income in Year 1.
A Expenses have increased $200,000 each year over the last 5 years.
C The combined income in Years 1, 2, and 3 was equal to the combined expenses in Years 1, 2, and 3.
D The combined expenses in Years 3 and 4 were $300,000 more than the combined income in Years 3 and 4.
Correct option is D. the combined expenses are $300,000 more than the combined income.
What is the bar chart?In business, economics, statistics, and science, bar charts are frequently used to display and compare data. When dealing with data that can be divided into discrete categories, like nominal or ordinal data, they are especially helpful.
According to the Income and expenses graph;
We can verify each options one by one.
A. Expenses have increased $200,000 each year over the last 5 years:
If we see the graph for expenses in each year that is increased by $100,000 not the $200,000 over the last 5 years.
So, the option is wrong.
B. The income in Year 5 was twice the income in Year 1:
Income in year 1 = $600,000
Income in year 5 = $900,000
We can see here, income is not just double.
So, the option is wrong.
C. The sum of all expenses in Years 1, 2, and 3 was the same as the sum of all income in those years:
combined income in Years 1, 2, and 3 = $600,000 + $600,000 + $400,000 = $1600,000
combined expenses in Years 1, 2, and 3 = $400,000 + $500,000 + $600,000 = $1500,000
Both are not equal.
So, the option is wrong.
D. The total amount expenses in Years 3 and 4 were $300,000 more than the total amount income in Years 3 and 4:
combined expenses in Years 3 and 4 = $600,000 + $700,000 = $13,00,000
combined income in Years 3 and 4 = $400,000 + $600,000 = $10,00,000
We can see here the combined expenses are $300,000 more than the combined income.
So, the option is correct.
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i need help (see picture)
Answer:
Please refer to the attachment
Step-by-step explanation:
Substitute x-values in g(x).
Eg. g(x) at x=0 is g(0)
=> -5(0) -5
= (-5)
What percent larger is 20.49 trillion to 4.00 trillion
20.49 trillion is 412.25% larger than 4.00 trillion.
How to calculate a percentage increase?To calculate the percentage increase of a value from an initial value to a final value, you can use the following formula:
increase in percentage = ((final value - initial value) / initial value) x 100%
Percentage increase is useful in a variety of contexts, including: Finance, Sales, Economics, Science, Education. Percentage increase is a useful tool for measuring growth or change over time and comparing different values.
To find the percentage increase, we first need to calculate the difference between the two numbers:
20.49 trillion - 4.00 trillion = 16.49 trillion
Next, we can divide the difference by the original amount (4.00 trillion) and multiply by 100 to get the percentage increase:
(16.49 trillion / 4.00 trillion) * 100 = 412.25%
Therefore, 20.49 trillion is 412.25% larger than 4.00 trillion.
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Draw a point that belongs to the solution region of this system of inequalities.
y > 1.5 +4
y
+ 6
Drawing Tools
Select
Point
Click on a tool to begin drawing.
-10
-8
-6
-2
10-
8
4
2-
-2
2
Delete
3
Undo
6
8
Reset
10
The point (2, 7) belongs to the solution region of the system of inequalities.
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The system of inequalities given is:
y > 1.5x + 4
y > -x + 6
One point that belongs to the solution region of this system of inequalities is (2, 7).
To check if this point satisfies the system of inequalities, we can substitute the values of x and y into each inequality:
For the first inequality, y > 1.5x + 4, we have:
7 > 1.5(2) + 4
7 > 7
This is true, so the point (2, 7) satisfies the first inequality.
For the second inequality, y > -x + 6, we have:
7 > -(2) + 6
7 > 4
This is also true, so point (2, 7) satisfies the second inequality.
Therefore, points (2, 7) belong to the solution region of the system of inequalities.
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Expand (x+2y) in ascending powers of x.
Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.
what is exponents ?Exponents, usually referred to as powers and indices, are a type of mathematical operation that requires increasing a base number to a specific exponent. You can multiply the minimum amount by itself a given number of times using the exponent. For instance, the number 2 raised toward the power of 3 (printed as 23) is equivalent to 2 x 2 x 2, which is 8. Exponents are frequently employed in scientific notation, algebra, and other areas of mathematics to express extremely big or extremely small integers.
given
The distributive property of multiplication is used to multiply out the expression when expanding (x+2y) in ascending powers of x.
[tex](x + 2y) = x + 2yx^0[/tex]
By remembering that every number raised to the power of zero equals 1, we may simplify the second term. We thus have:
(x + 2y) = x + 2y(1) (1)
When we multiply the expression, we get:
(x + 2y) = x + 2y
Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.
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Determine the area of the given region.
[tex]\displaystyle \int_{0}^{\frac{\pi }{3}}~\sin(x)dx\implies \left.\cfrac{}{} -\cos(x)\right]_{0}^{\frac{\pi }{3}}\implies\left( -\cfrac{1}{2}\right) ~~ - ~~(-1)\implies \cfrac{1}{2}[/tex]
Which type of function best models the data in each table? Use differences or ratios. X-0, 1, 2, 3, 4
Y-0,1.5,6,13.5,24
Answer:
To determine the type of function that best models the data in the table, we can observe the differences or ratios between successive values of y.
Using differences:
The first differences between successive values of y are:
1.5 - 0 = 1.5
6 - 1.5 = 4.5
13.5 - 6 = 7.5
24 - 13.5 = 10.5
The second differences between successive values of y are:
4.5 - 1.5 = 3
7.5 - 4.5 = 3
10.5 - 7.5 = 3
Since the second differences are constant, the function that best models the data is a quadratic function.
Using ratios:
The ratios between successive values of y are:
1.5/0 = undefined
6/1.5 = 4
13.5/6 = 2.25
24/13.5 ≈ 1.78
Since the ratios are not constant, the function that best models the data is not an exponential function.
Therefore, the type of function that best models the data in the table is a quadratic function. We can try to find a quadratic function of the form y = ax^2 + bx + c that passes through the given points. Using the first three points, we get the system of equations:
a(0)^2 + b(0) + c = 0
a(1)^2 + b(1) + c = 1.5
a(2)^2 + b(2) + c = 6
Solving this system of equations, we get:
a = 3/2
b = 0
c = 0
Therefore, the quadratic function that best models the data is y = (3/2)x^2.
