If a is a set of real numbers that is bounded above and b is a set of real numbers that is bounded below, there is at most one real number that can exist in both sets.
A real number is any number that can be expressed as a decimal or fraction and exists on the number line.
If a set of real numbers, represented by a, is bounded above, it means that there exists a real number, represented by M, such that all the numbers in the set are less than or equal to M. Similarly, if a set of real numbers, represented by b, is bounded below, it means that there exists a real number, represented by m, such that all the numbers in the set are greater than or equal to m.
Now, let's consider a real number, represented by x, that exists in both sets a and b. If x exists in a, it must be less than or equal to M and if x exists in b, it must be greater than or equal to m. Hence, x must satisfy both conditions: M >= x >= m.
From these conditions, it can be deduced that M and m must be equal to x. In other words, there can only be one real number that is simultaneously the greatest value in a and the smallest value in b.
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Write at least three different inequalities the solution is x greater than -10. Find one with x on the left side that uses a less than sign
The following inequalities are,
x > -10-10 < xx ≥ -9.999...What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
We have to write three different inequalities,
In which, the solution is x greater than -10
1. It can be represented as,
x > -10
2. One on left hand side, so it is further modified as,
-10 < x
3. writing with greater equal to sign, but that x can never be equal to -10, only be greater than it
So, it can be written as
x ≥ -9.999...
Thus, three inequalities are respectively, x > -10, -10 < x, x ≥ -9.999...
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find the sample standard deviation forfind the sample standard deviation for the weights for the offensive linemen 359,297,350,254,312,250,359,253,254,326,254,331
The required standard deviation of the given data is 54.6.
How to find Standard deviation?To find the sample standard deviation for the weights of the offensive linemen, we first need to calculate the mean of the sample and then use that to find the variance and standard deviation.
Mean:
The mean (μ) is the sum of all the values in the sample divided by the number of values in the sample. In this case, the mean is:
(359 + 297 + 350 + 254 + 312 + 250 + 359 + 253 + 254 + 326 + 254 + 331) / 12 = 298.75
Variance:
The variance (σ²) is a measure of the spread of the data. It is calculated as the sum of the squared deviations of each value from the mean divided by the sample size minus one. In this case, the variance is:
( (359 - 298.75)² + (297 - 298.75)² + (350 - 298.75)² + (254 - 298.75)² + (312 - 298.75)² + (250 - 298.75)² + (359 - 298.75)² + (253 - 298.75)² + (254 - 298.75)² + (326 - 298.75)² + (254 - 298.75)² + (331 - 298.75)² ) / (12 - 1) = 2987.5
Standard Deviation:
The standard deviation (σ) is the square root of the variance. In this case, the standard deviation is:
√2987.5 = 54.59
Therefore, the sample standard deviation of the weights of the offensive linemen is 54.59 pounds.
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Math triangle word problem:
The height of the mountain above the level plain is 4465.2 feet
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
Let h represent the height of the mountain. Let d represent the distance from the plain to the mountain base
Using trigonometric ratio:
tan(32) = h/d
h = d * tan(32)
Also:
tan(36) = h / (d - 1000)
h = (d - 1000) * tan(36)
Equating:
d * tan(32) = (d - 1000) * tan(36)
d = 7145.9 feet
h = d * tan(32) = 7145.9 * tan(32) = 4465.2 feet
The height of the mountain is 4465.2 feet
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PLEASE HELP PLEASE AND THANK YOU HAVE A BLESSED DAY
the fractions with the same denominator will be 14/16 and 13/16.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
The given fraction is given are 7/8 and 13/16.
Taking lcm of the denominator will be 16
So the fraction will be 7*2 = 14
So the fractions will be 14/16 and 13/16.
Hence the fractions with the same denominator will be 14/16 and 13/16.
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Find parametric equations of the curve given by the intersection of the surfaces:
The cylinder: x2+y2=81
The surface: z=6xy
x(t) = ?
y(t) = ?
z(t) = ?
Correct Answer:
x(t) = 9cos(t)
y(t) = 9sin(t)
z(t) = 54sin(t)cos(t)
What is the parametric equation?
The parametric equation of a curve is a representation of the curve in terms of one or more independent variables (known as parameters), usually represented as t. Each parameter value t corresponds to a unique point (x, y, z) on the curve.
For the given curve, the intersection of the cylinder x² + y² = 81 and the surface z = 6xy can be found by setting the equation of the cylinder equal to the equation of the surface and solving for x, y, and z in terms of a single parameter t.
Starting with the cylinder: x² + y² = 81, we can parameterize x and y as follows:
x(t) = 9cos(t)
y(t) = 9sin(t)
Substituting these expressions into the equation of the surface:
z(t) = 6x(t)y(t) = 6 * 9cos(t) * 9sin(t) = 54sin(t)cos(t)
So, the parametric equations of the curve given by the intersection of the cylinder x² + y² = 81 and the surface z = 6xy are:
x(t) = 9cos(t)
y(t) = 9sin(t)
z(t) = 54sin(t)cos(t)
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Stories in the World's Tallest Buildings
The number of stories in each of a sample of the would's 29 tallest building follows. Construct a grouped frequency distribution and
a cumulative frequency distribution with 9 classes.
70 55 100 60 70 85 64 69 80 75
88
65 80 102 55 75 72 60 79 88
55 78 77 71 105 88 90 54 56
a. Find the class limits. The first lower class limit is 54.
b. Find the class boundaries.
c. Find the class frequency.
Class Limits
54-
Class boundaries
Frequency
The class limit or the Class width is 6.
What is measure of dispersion?Data scattering is indicated by a measure of dispersion. It provides a clear picture of their distribution while explaining the discrepancy between the data from different sources. The measure of dispersion illustrates and provides information on the range and centre value of a single item.
Dispersion, then, is the degree to which values in a distribution deviate from the distribution's mean. It offers us a sense of how different each item is from the main value and from one another.
Arrange the data in increasing order:
54 55 55 55 56 60 60 64 65 69 70 70 71 72 75 75 77 78 79 80 80 85 88 88 88 90 100 102 105
Class width = range/no of classes
No of classes=9
range=Maximum value-Minimum value=54-105=51
Class width = 51/9 = approx. 6
Hence, the class limit or the Class width= 6.
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6. Given f(x)=3x² - 2x+4, find a. ƒ(-2)= b. f(k+1)=
Answer: a. To find f(-2), substitute -2 for x in the function f(x):
f(-2) = 3(-2)² - 2(-2) + 4 = 3(4) - 2(-2) + 4 = 12 - (-4) + 4 = 16
So, f(-2) = 16.
b. To find f(k+1), substitute (k+1) for x in the function f(x):
f(k+1) = 3(k+1)² - 2(k+1) + 4 = 3k² + 6k + 3 - 2k - 2 + 4 = 3k² + 4k + 5
So, f(k+1) = 3k² + 4k + 5.
Step-by-step explanation:
binomial theorem
[tex](2x - 3y)^{7} [/tex]
The value of [tex]$(2 x-3 y)^7$$[/tex] be
[tex]$=128x^7-1344 x^6 y+6048 x^5 y^2-15120 x^4 y^3+22680 x^3 y^4-20412 x^2 y^5+10206 x y^6-2187 y^7$[/tex]
What is meant by binomial theorem?The binomial theorem states that the nth power of the sum of two numbers a and b may be written as the sum of n + 1 terms of the form for every positive integer n. Starting with n, the powers on a decrease until the final term, when the power is 0.
Statistical and probability analyses make extensive use of the binomial theorem. Because statistical and probability analyses are so important to our economy, it is quite helpful. The Binomial Theorem is used to locate equations' roots in higher powers in advanced mathematics and computation.
Let the equation be [tex]$(2 x-3 y)^7$$[/tex]
Apply binomial theorem: [tex]$(a+b)^n=\sum_{i=0}^n\left(\begin{array}{c}n \\ i\end{array}\right) a^{(n-i)} b^i$[/tex].
[tex]$$\begin{aligned}& a=2 x, b=-3 y \\& =\sum_{i=0}^7\left(\begin{array}{l}7 \\i\end{array}\right)(2 x)^{(7-i)}(-3 y)^i\end{aligned}[/tex]
substitute the values in the above equation, we get
[tex]$=\frac{7 !}{0 !(7-0) !}(2 x)^7(-3 y)^0+\frac{7 !}{1 !(7-1) !}(2 x)^6(-3 y)^1+\frac{7 !}{2 !(7-2) !}(2 x)^5(-3 y)^2+$[/tex][tex]$\frac{7 !}{3 !(7-3) !}(2 x)^4(-3 y)^3+\frac{7 !}{4 !(7-4) !}(2 x)^3(-3 y)^4+\frac{7 !}{5 !(7-5) !}(2 x)^2(-3 y)^5+$[/tex][tex]$\frac{7 !}{6 !(7-6) !}(2 x)^1(-3 y)^6+\frac{7}{7 !(7-7) !}(2 x)^0(-3 y)^7$[/tex]
simplifying the above equation, we get
[tex]$\begin{array}{ll}\frac{7 !}{0 !(7-0) !}(2 x)^7(-3 y)^0= & 128 x^7 \\ \\ \frac{7 !}{1 !(7-1) !}(2 x)^6(-3 y)^1= & -1344 x^6 y \\ \\ \frac{7 !}{2 !(7-2) !}(2 x)^5(-3 y)^2 = & 6048 x^5 y^2 \\ \\ \frac{7 !}{3 !(7-3) !}(2 x)^4(-3 y)^3= & -15120 x^4 y^3 \\ \\ \frac{7 !}{4 !(7-4) !}(2 x)^3(-3 y)^4= & 22680 x^3 y^4 \\ \\ \frac{7 !}{5 !(7-5) !}(2 x)^2(-3 y)^5= & -20412 x^2 y^5 \\ \\ \frac{7 !}{6 !(7-6) !}(2 x)^1(-3 y)^6 = & 10206 x y^6 \\ \\ \frac{7 !}{7 !(7-7) !}(2 x)^0(-3 y)^7 = & -2187 y^7\end{array}$[/tex]
Therefore, the value of [tex]$(2 x-3 y)^7$$[/tex] be
[tex]$=128x^7-1344 x^6 y+6048 x^5 y^2-15120 x^4 y^3+22680 x^3 y^4-20412 x^2 y^5+10206 x y^6-2187 y^7$[/tex]
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Find the principal value of Arctan (1.5) to the nearest minute.
Answer: You will find tan 56 degrees 18 minutes (approx) = 1.5 ... It's generally agreed that the principal value of tan inverse should lie between -90 and +90 ...
Step-by-step explanation:
Select the equation represented by the fraction strips below. 1 whole fraction strip is shown with a 1 indicated on it. Below it and to the left are 6 smaller fraction strips that are each one-twelfth the width of the whole. Another 6 fraction strips of the same size are shown further down below the image. These 6 one-twelfth-inch strips have an arrow that points from the location directly beside the first 6 one-twelfth strips. A. 6 12 − 6 12 = 0 12 B. 12 12 − 1 12 = 11 12 C. 12 12 − 2 12 = 6 12 D. 12 12 − 6 12 = 6 12 1 / 3 I NEED AN ANSWER ASAP PLEASE
The equation can be represented by 6¹/₁₂ - 6¹/₁₂ = 0. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 1 whole fraction strip is shown with a 1 indicated on it. Below it and to the left are 6 smaller fraction strips that are each one-twelfth the width of the whole.
Another 6 fraction strips of the same size are shown further down below the image. These 6 one-twelfth-inch strips have an arrow that points from the location directly beside the first 6 one-twelfth strips.
The equation for the strip can be written as:-
6¹/₁₂ - 6¹/₁₂ = 0
The correct option would be A.
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Answer 27 and 28 please!!
Answer:
27
a 43.56 inches
b 287.496 inches
28
1 1 4 8 9 27 16 64 25 125 36 216 49 343 64 512 81 729 100 1000 121 1331 144 1728Use the function B(t) = 45422 + 34.26t find the inverse of the linear model; write your function using function notation
Answer: A linear function is one whose graph is a straight line. Given the linear function B(t) = 45422 + 34.26t, its inverse function can be found by switching the places of x and y and then solving for y.
The inverse function, written in function notation, can be represented as:
B^(-1)(t) = (1/34.26)(t - 45422)
So the inverse of the linear model B(t) = 45422 + 34.26t can be written as B^(-1)(t) = (1/34.26)(t - 45422) in function notation.
Step-by-step explanation:
The equation y equals 4 times 6 to the power of t shows the number of infected people from an outbreak of the measles. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 568?
Step-by-step explanation:
By the question,
y = 4×6^t
So let y be 568,
568 = 4× 6^t
or, 6^t = 142
t =
[tex] log_{6}(142) [/tex]
Approximately,
[tex] log_{6}(142) [/tex]
weeks it takes for the infected people to be 568.
What is the period of this graph?
Answer:
4π
Step-by-step explanation:
The Period, as measured from crest-to-crest (or from trough-to-trough), is 4π, as read directly from the graph
I need and 3-4 minute explanation that’s it
Answer:
Step-by-step explanation:
Just plug in the x-intercept to find the y-intercepts. Slope is y2-y1/x2-x1, so just take any 2 y-intercepts and any 2 x intercepts to find the slope.
Please answer the attached picture
Answer:
25
Step-by-step explanation:
(f+g)(x) also stated as f(x)+g(x)
2x²+3x-2
where x=3
2(3)²+3(3)-2
2(9)+9-2
18+7
25
Which of the following sentences show correct verb tense usage? Check all that apply. When the facilitator announced a bathroom break, the seminar participants took out their iPhones and begun checking their messages a The overall outlook is favorable, so I wrote to the board chair to inform him. She has wrote him an e-mail
The sentence which show correct verb tense usage is The overall outlook is favorable.
Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.
Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.
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A student drink 32 oz energy drink containing 90 calories per 12 oz. How many calories did the student drink?
Answer:
187.5 Calories
Step-by-step explanation:
We start by multiplying 12 x 2 to get 24 which is equal to a total of 180 calories, therefore we have to subtract 32-24 to get 8oz left, we then divide 90 by 12 to get 7.5 calories which we add to the 180 from before to get a total of 187.5 Calories.
I need help with both of these can someone please help me
After the shutdown, the hospital will maintain 126 acute hospital beds available for usage.
Which categories and what is a hospital?Hospitals are classified as general, specialist, or government facilities by the source of their funding. In a medical center, nursing education and patient care are both integrated. A care facility which is smaller than a hospital is called a clinic.
If 28% of the hospital's acute card beds are going to ever be closed, that leaves 100% - 28% = 72% of such beds available for utilization.
72% of 175 beds = 0.72 x 175 = 126 beds
As a result, following the shutdown, the hospital will still have 126 basic card beds available for usage.
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2.4 divided by 0.75
The answer is 3.2
But I don’t know how to get there I only get 3 with a remainder of 15
I need to see the work please help.
Hi There! Here's your answer:
To make it easier, let's write this in fraction form:
[tex]\frac{2.4}{0.75}[/tex]
Now, multiply the numerator and denominator by 100 to remove the decimal point.
[tex]\frac{2.4}{0.75}[/tex] × [tex]\frac{100}{100}[/tex] = [tex]\frac{240}{75}[/tex]
Now, you can either divide using long division, or you can take out common factors and simplify the fraction that way.
Upon common factor simplification, we get the final fraction to be:
[tex]\frac{240}{75}[/tex] = [tex]\frac{48}{15}[/tex] (Common factor 5) = [tex]\frac{16}{5}[/tex] (Common factor 3)
Therefore, we get the final fraction as [tex]\frac{16}{5}[/tex] which is 3.2.
HOPE IT HELPS!
The recommended daily amount of sodium is 2550 mg. One can of wild rice soup contains 535.5 mg of sodium. What percent of the total recommended daily amount of sodium is in this can of soup?
Round your answer to the nearest tenth of a percent, if necessary.
21% of the total recommended daily amount of sodium is in this can of soup?
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The recommended daily amount of sodium is 2550 mg. One can of wild rice soup contains 535.5 mg of sodium. Hence:
Percentage of sodium in can = (535.5/2550) * 100% = 21%
There is 21% of sodium in can
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For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle. Interior angle = 122°; exterior angle = 58° Interior angle = 58°; exterior angle = 122° Interior angle = 82°; exterior angle = 38° Interior angle = 38°; exterior angle = 82°
Answer:
Step-by-step explanation:
the sum of the interior and the exterior angle must be 180°.
7g + 12 + 2g + 60 = 180
9g + 72 = 180
9g = 108
g = 12
interior angle = 7×12 + 12 = 96°
exterior angle = 2×12 + 60 = 84°
partition
5 over 7
into fourths and double shade
1 over 4
of
5 over 7.
.
The number of 1/4 that can be found in 5/7 will be 2 6/7
How to calculate the valueIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The number of 1/4 that can be found on 5/7 will be:
= 5/7 ÷ 1/4
= 5/7 × 4
= 20/7
= 2 6/7
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Zoey needs to order some new supplies for the restaurant where she works. The restaurant needs at least 711 glasses. There are currently 281 glasses. If each set on sale contains 10 glasses, use the drop-down menu below to write an inequality representing s, the number of sets of glasses Zoey
The x distribution must be normal in order to use a chi-square distribution to test the variance. What are some methods you can use to assess whether the x distribution is normal?
Hint: Try utilizing a goodness-of-fit test. (Select all that apply.)
a)Look at a normal quantile plot to check for a straight line.
b)Use a histogram or boxplot to check for symmetry and outliers.
c)Look at a normal quantile plot to check for a curved line.
d)Use a goodness-of-fit test to see if the distribution follows the empirical rule.
e)Look at a residual plot for a parabolic pattern.
The required methods we can use to assess whether the x distribution is normal is mentioned in (a) and (b). Options (A) and (B ) are correct
What is a normal distribution?Normal distributions can be altered to standard normal distributions by the formula:
Z = (X - μ)/σ
Where x is a value from the initial normal distribution, μ is the mean of the initial normal distribution, and σ is the standard deviation of the initial normal distribution. The standard normal distribution is periodically called the z distribution.
Here,
The methods to assess whether the x distribution is normal are:
a) Look at a normal quantile plot to check for a straight line.
b) Use a histogram or boxplot to check for symmetry and outliers.
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Listed here are some items found in the financial statements of Finzelberg. Indicate in which financial statement each item would appear.A. service revenueB. equipmentC. advertising expenseD. accounts receivableE. common stockF. interest payable
The correct answer is:
(a) Income Statement ; (b) Balance Sheet ; (c) Income Statement ; (d) Balance Sheet ; (e) Balance Sheet ; (f) Balance Sheet.
Income statementThe income statement, which is one of the so-called basic financial statements, shows how the company arrived at its financial or accounting results, which could be a profit or loss, and may be shown as a profit or loss.
In order to calculate the utility from the income the company has obtained—from which costs and expenses have been incurred—a number of processes must be taken.
Balance SheetThe balance sheet is a statement of a company's financial position at a specific time, such as at the end of the month, quarter or year. The balance sheet shows the assets and lists the responsibilities, creating a statement of what the business owns and owes.
(a) Service revenue - Income statement
(b) Equipment - Balance sheet
(c) Advertising expense - Income statement
(d) Accounts receivable - Balance sheet
(e) Common stock - Balance sheet
(f) Interest payable - Balance sheet
An investor use the information about the companies future strategy and opportunities before buying and selling of any stock . This data illustrates the dividend trend for the company.
A bank keeps track of a corporation's dividend information since it will have an impact on the balance sheet and enable banks to more effectively manage loan risk.
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(4)/(9)((3)/(2)z^(2)y^(3))^(5)
???
how do i do this ??
Answer:
The expression can be solved using algebraic methods. The result is -(2^7)z^2y^3.
Step-by-step explanation:
The solution to the equation 4/(9)((3/2)z^2y^3)^5 is y^15z^10. This can be solved by using the steps of algebraic manipulation. First, the parentheses can be simplified by multiplying the numerator and denominator together, resulting in 4/27z^2y^3. Then, the exponent can be applied to both terms, resulting in y^15z^10. Finally, this answer can be checked by substituting it into the original equation and verifying that it is true.
Given △ABC, AD and BE are medians, AD ∩BE=G. prove GD=1/3 AD
Answer: In a triangle, the medians divide the triangle into six smaller triangles with equal area. This can be proven using the fact that the medians of a triangle are concurrent, meaning they all intersect at a single point called the centroid.
Let's assume that AD = 2BE, then the area of △ADG is equal to four times the area of △BEG. This can be expressed as follows:
Area(△ADG) = 4 * Area(△BEG)
Since GD is one of the medians, it must be equal to one-third of AD. So, we can write:
GD = AD/3
Since the area of △ADG is equal to four times the area of △BEG, we can write:
Area(△ADG) = 4 * Area(△BEG)
(2BE)^2/2 * GD / 2 = 4 * BE^2/2 * EG / 2
Expanding and simplifying the above equation gives us:
BE^2 * GD / 2 = 4 * BE^2/2 * EG / 2
And, finally, dividing both sides of the equation by BE^2/2, we get:
GD = 1/3 * AD
This result holds true regardless of the relative lengths of AD and BE. Hence, the conclusion that GD = 1/3 AD is always true for any triangle △ABC where AD and BE are medians.
Step-by-step explanation:
Express the following numbers without using words.
a) China had a population of more than 1,3 billion people in 2011.
The expression of the given word phrase 1.3 billion using numbers is; 1,300,000,000.
What if the representation of the given word phrase using numbers?It follows from the task content that the concept described in the given word phrase is to be represented by a number.
On this note, since the number in discuss is; 1.3 billion where a billion represents; 1 × 10⁹.
Hence, 1.3 billion represents; 1.3 × 10⁹.
= 1,300,000,000.
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admission to a carnival costs $15 each games costs $2 to play. Which statements about the function modeling the cost to attend the carnival are True? Select all that apply
A. The slope is positive
B. The initial value is $15
C. The rate of change is $15
D. The graph has a y-intercept of 2
E. The Graph passes through the origin
Answer:
you have find if its proportianal for e thats all I know tho sorry