Answer:
Zeroes & Multiplicity:
x = 0 : Multiplicity = 2
x = -6/5 : Multiplicity = 9
x = 8 : Multiplicity = 2
Step-by-step explanation:
The equation provided is: [tex]f(x)=x^2(5x+6)^9(x-8)^2[/tex]
Factored Form:We're given the polynomial in factored form, which just means the polynomial is broken down into each of its factors. This is a really convenient form to have a polynomial in as we can easily find the zeroes of the polynomial.
This is due to the Zero Property of Multiplication, which essentially states zero times any number results in zero. So we just have to set each factor equal to zero, and solve, since if one of the factors is zero, then the entire thing becomes zero.
So this gives us the following equations:
[tex]x^2=0\implies x = 0\\\\(5x+6)^9=0\implies x = -\frac{6}{5}\\\\(x-8)^2=0\implies x = 8[/tex]
Now for the multiplicity, we just look at the exponent of the factor we set equal to zero. So x^2 gives us a zero of x = 0, and the exponent is 2, which is also the multiplicity of this zero.
The (5x + 6)^9 gives us a zero of x = -6/5, and the exponent is 9, which is also the multiplicity of the zero. Same thing applies for the zero at x = 8, which has a multiplicity of 2.
in a data set consisting of 30 positive integers, the minimum value is 13. the number 6 is added to the original set to create a set of 31 positive integers. which of the following measures must be 7 greater for the new data set than for the original data set?
a. The mean
b. The median
c. The range
d. The standard deviation
The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set.
The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.
The formula for the mean is: Mean = (Sum of Values)/(Number of Values)
For the original data set: Mean = (Sum of Values)/30
For the new data set: Mean = (Sum of Values + 6)/31
Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.
The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.
The formula for the median is: Median = (n+1)/2
For the original data set: Median = (30+1)/2 = 15.5
For the new data set: Median = (31+1)/2 = 16.5
Therefore, the median for the new data set must be 7 greater than the median for the original data set.
The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.
The formula for the range is: Range = (Largest Value) - (Smallest Value)
For the original data set: Range = (Largest Value) - 13
For the new data set: Range = (Largest Value + 6) - 13
Therefore, the range for the new data set must be 7 greater than the range for the original data set.
The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.
The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)
For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)
For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)
Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.
The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set
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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 to proportion and what theorem it is please help
The missing side is AJ and the theorem is, the ratio of corresponding sides of a similar triangle are equal
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
The corresponding sides are FJ , AJ and CF and AC
The ratio of these corresponding sides are equal. i.e
FJ/AJ = CF/AC
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prove that 32^5-16^5+2^19 is divisible by 63
Answer:
see below
Step-by-step explanation:
32^5 - 16^5 +2^19 = (2*16)^5 - 16^5 +2^19
= 2^5 *16 ^ 5 - 16^5+ 2^19
=32* 16 ^ 5 - 16 ^ 5 + 2^19
=31 * 16^5 + 2^19
=31 *2 ^(4*5) + 2^19
= 31 *2^20 + 2^19
= 62 *2^19 + 2^19
=63*2^19
so it's dvisible by 63
Reflect the point in the x-axis followed by the y-axis
Please do graph too ty.
Answer:
A(-3, 4) reflected across x-axis ==> A'(-3, -4)
A'(-3, -4) reflected across y-axis ==> A"(3, -4)
Graph attached
Step-by-step explanation:
The point is (-3, 4) shown as point A on attached graph
When reflected across the x-axis to point A' the x-coordinate does not change but the y-coordinate is the negative of the original y-coordinate
Therefore A (-3, 4) ⇒ A' (-3, -4)
When A' is reflected across the y-axis to A" the x-coordinates change sign but y-coordinates stay unchanged
A'(-3, -4) ⇒ A" (3, -4)
So the final point is A"(3, -4)
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.
an important component of measurements is using the right/appropriate unit for what is being measured! what unit would you use to measure the length of our classroom (assume any classroom).
The required unit would you use to measure the length of our classroom are meters or feet.
What are measurement tools?The usual measurement equipment is composed of thermometers, rulers, yardsticks, scales, beakers, protractors, clocks, and measuring tape. Knowing how to use each instrument properly can make measuring more accurate and enjoyable. Each tool has a unique purpose.
According to question:To measure the length of a classroom, you would use the unit of meters or feet.
These are commonly used units for measuring length or distance. For example, you might say "The length of the classroom is 10 meters" or "The classroom is 30 feet long". The specific unit used might depend on the location and the system of units (metric or imperial) that is commonly used in that area.
It's important to choose a unit that is appropriate for the task at hand, and to be consistent in using that unit throughout the measurement process.
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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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why is the cutting edge of the knife made very thin ?
Due to the edge's significantly smaller surface area and increased pressure, it is simpler to force your palm through. You don't need to move the butter around as much because the edge is narrower.
What does a knife's cutting edge look like?The blade's edge is its cutting edge. It stretches all the way from the knife's tip to its heel. Heel: Opposite the tip, the heel is the back portion of the edge.
A knife's edge is how thick?Knives should have a thickness of between.013" and.25" to be considered optimum. Kitchen knives are typically slimmer, whereas survival blades are typically thicker.
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When a scientific name is used more than once in the text, it is appropriate to write both the genus and the species name the first time and then abbreviate the genus name every time.
It is true when a scientific name appears more than once in the text, it is appropriate to write both the genus and species name the first time and then abbreviate the genus name every time after that.
Binominal nomenclature:Binominal nomenclature, also referred to as binary nomenclature or binomial nomenclature, is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, though they can be based on words from other languages. Binomial nomenclature is also known as the "two-term naming system" or "two-name naming system" and is used in taxonomy.
A name of this type is known as a binomial name (which is also abbreviated to just "binomial"), a binomen, a binominal name, or a scientific name. It was also known as a Latin name unofficially at one point in time.
The name's second component, the specific name or particular epithet, differentiates the species within the genus while the first component, the generic name, specifies the genus to which the species belongs.
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Is the ordered pair (4,1) a solution of the system of linear equations:
-x + y = -3
x + 3y = 6
a. yes
b. no
Answer:
no
Step-by-step explanation:
-x+y=-3
-4+1=-3
which is correct
x+3y=6
4+3×1=6
4+3=6
which is incorrect because 4+3=7
What percent is modeled by the grid? A grid model with 100 squares. 33What percent is modeled by the grid? A grid model with 100 squares. 33 squares are shaded. 23% 30% 33% 40% squares are shaded. 23% 30% 33% 40%
Answer:
33%
Step-by-step explanation:
There are 33 squares out of 100 that are shaded
33/100
Percent means out of 100
33%
Or
A ratio that compares a number to 100 can be written as a percent. So in this problem, since the figure has 33 out of 100 boxes shaded, we have the ratio 33/100 which can be written as 33%.
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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The two triangles are similar.
What is the value of x?
The value of x for the similar triangles is equal to 7.
How to calculate for x for the similar trianglesWe have the triangles to be similar, this implies that the length 2x - 2 of the smaller triangle is similar to the length 3x of the larger triangle
and the length 8 of the smaller triangle is similar to the length 6+8 = 14 of the larger triangle
so;
(2x - 2)/3x = 8/14
14(2x - 2) = 8 × 3x {cross multiplication}
28x - 28 = 24x
28x - 24x= 28 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7.
Therefore, the value of x for the similar triangles is equal to 7.
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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
An investor has two bonds in his portfolio. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity equal to 8.2%. One bond, Bond C, pays an annual coupon of 10%; the other bond, Bond Z, is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 8.2% over the next 4 years, what will be the price of each of the bonds at the following time periods? Assume time 0 is today. Fill in the following table. Round your answers to the nearest cent.
T Price of Bond C Price of Bond Z
0 $
$
1
2
3
4
Answer:
Step-by-step explanation:
The price of Bond C at time t can be calculated using the formula:
P_C = (C / (1 + r)^t) + (F / (1 + r)^(n))
where C is the coupon payment, r is the yield to maturity, t is the time period, n is the number of years until maturity, and F is the face value.
Similarly, the price of Bond Z at time t can be calculated using the formula:
P_Z = F / (1 + r)^(n + t)
Substituting the values:
C = 100 (10% of $1,000)
r = 0.082
n = 4
F = $1,000
T Price of Bond C Price of Bond Z
0 $1,000 $1,000
1 $1,082 $961.67
2 $1,167.24 $926.58
3 $1,259.51 $893.63
4 $1,360.29 $862.54
The prices are rounded to the nearest cent.
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.
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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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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please help!! it’s due in today and i have no idea what u do ahha!!!
Answer:
90000000000
Step-by-step explanation:
3*1 plus 8 zeros
*
3*1 plus 2 zeros
so 300000000 * 300=
90000000000
find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x= 1+4t-t^2, y= 2-t^3 at t=1. dy/dx = -3/2 at t=1. where do i go from here?
The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
find value of x and y :
x= 1+4t-t²
Substitute t=1
x= 1+4(1)-1² =1+4-1 = 4
y= 2-t³
Substitute t=1
y= 2-1³ = 2-1 = 1
Given slope, m= -3/2
point slope form of line :
y-y1=m(x-x1)
y-1=-3/2(x-4)
=>2(y-1) = -3(x-4)
=> 2y-2 = -3x+12
=> 2y = -3x+12 + 2
=> 2y = -3x+14
=> y= (-3/2)x + 7
The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
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The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
find value of x and y :
x= 1+4t-t²
Substitute t=1
x= 1+4(1)-1² =1+4-1 = 4
y= 2-t³
Substitute t=1
y= 2-1³ = 2-1 = 1
Given slope, m= -3/2
point slope form of line :
y-y1=m(x-x1)
y-1=-3/2(x-4)
=>2(y-1) = -3(x-4)
=> 2y-2 = -3x+12
=> 2y = -3x+12 + 2
=> 2y = -3x+14
=> y= (-3/2)x + 7
The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
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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 1728In the figure below, the segments AB and AC are tangent to the circle centered at O. Given that AC=9 and OA= 10.6, find OB.
6.1 is the value of OC in right triangle .
What is a right-angle triangle, exactly?
Any angle that is a right angle or has one of its internal angles equal to 90 degrees is considered to be in a right-angled triangle.
In light of this, this triangle is sometimes referred to as the right triangle or the 90-degree triangle.
Triangles AOB and AOC are right triangles
In the right triangle AOC
OC = OB
OA² = OC² + AC²
10.9² = OC² + 9²
OC² = 118.81 - 91
= 37.81
OC = 6.1
OB = OC = 6.1
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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:
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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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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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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George took home a net pay of $1, 300on their paycheck this week. They worked 60 hours during this specific pay period and had deductions that totaled $200, what is their hourly rate of pay?
$25 per hour, is their hourly rate of pay.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Net pay= $1300
Deductions= $200
Hours worked= 60
then,
Total pay=$1300+ $200
= $1500.
Since her net pay is the money left after deductions, so we add the netpay and deductions to get her total pay.
Therefore, to find her hourly pay, we simply divide the total pay by the hours worked,
so we have 1500/60= $25/hour
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To qualify for Gold status at Awesome Airlines, one must fly at least 7000
and less than 30800
miles each year. If Jordan takes a 700
-mile round-trip flight to visit his parents, how many times does Jordan need to visit his parents each year to attain Gold status? Express your answer in interval notation.
[10 , 44) is the interval of the number of times, Jordan need to visit his parents each year to attain Gold status.
What is interval notation?Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers.
Given,
To qualify for gold status
one must fly at least 7000 and less than 30800 miles each year.
Jordan takes 700 miles trip to visit his parents.
No. of trips to fly at least 7000 miles = 7000/700 = 10 trips
No of trips to fly 30800 miles = 30800/700 = 44 trips.
If no. of trips is x, Jordan should take {x | 10 ≤ x < 44} trips.
No. of trips Jordan should take is [10 , 44).
Hence, Number of trips Jordan should take is [10 , 44) .
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nitially, suppose that only adventurous citizens buy tickets at 7 flags. each adventurous citizen has an individual demand given by qa
The number of possible combinations for this scenario is 35
A combination is a way of selecting items from a set, where the order of the items does not matter.
Let's assume that each adventurous citizen has a demand for visiting three flags. This means that each citizen wants to visit three flags out of the seven available flags. To find the number of possible combinations, we can use the formula for combinations, which is:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of flags available (7), and r is the number of flags that each citizen wants to visit (3). So, the number of possible combinations is:
C(7, 3) = 7! / (3! * (7 - 3)!) = 35
This means that there are 35 different combinations of flags that an adventurous citizen can choose from at 7 flags amusement park.
Complete Question:
Initially, suppose that only adventurous citizens buy tickets at 7 flags. each adventurous citizen has an individual demand given by those 3 flags. Find the number of possible combinations for this one.
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