The sum of the first 10 terms of the arithmetic sequence is given as follows:
-40.
How to obtain the sum of an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The sum for the first n terms of an arithmetic sequence is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In which:
[tex]a_1[/tex] is the first term.[tex]a_n[/tex] is the nth term.The parameters for this problem are given as follows:
[tex]n = 10, a_1 = 5, a_n = -13[/tex]
Hence the sum is given as follows:
S = 5 x (5 - 13)
S = -40.
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The sum of the squares of three positive numbers in an ap is 155. The sum of the numbers is 21. Find the number
this was a question on my homework assignment from school but I don't know how to solve this without the height of the cone from top to bottom.
Answer: [tex]\sqrt{585}[/tex] units or [tex]3\sqrt{65}[/tex] units
Step-by-step explanation:
The formula for volume of a cone is π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]. You can find the height by plugging in 72π for volume and 3 for radius.
diameter = radius x 2, so 6/2=3 units for radius.
72π = π([tex]3^{2}[/tex])([tex]\frac{h}{3}[/tex])
72=9*[tex]\frac{h}{3}[/tex]
8 = [tex]\frac{h}{3}[/tex]
h = 24 units
The formula for slant height is [tex]\sqrt{{r}^2 + {h}^2 }[/tex]
Plug in 3 for r and 24 for h. You should get [tex]\sqrt{(9+576)}[/tex]=[tex]\sqrt{585}[/tex] or 3[tex]\sqrt{65}[/tex] as your answer.
Find the horizontal asymptote of f of x equals quantity x squared plus 3x plus 6 end quantity over quantity x squared plus 1.
The horizontal asymptote will be y = 2
What is Horizontal asymptote?
A graph's horizontal asymptote is a horizontal line y = b along which the graph approaches as the inputs approach or ∞ or –∞. A graph's slant asymptote is a slanted line y = mx + b along which the graph approaches the line as the inputs approach or ∞ or –∞
What is Square?
A square is a regular quadrilateral, which implies it has four equal sides and angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
f (x) = [tex]\frac{2x^{2}+3x+6 }{x^{2} +1}[/tex]
Here degree of numerator = degree of denominator
Hence the equation of horizontal asymptote y = 2/1
=2
Hence the equation of horizontal asymptote y=2
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The horizontal asymptote will be y = 2
What is Horizontal asymptote?
A graph's horizontal asymptote is a horizontal line y = b along which the graph approaches as the inputs approach or ∞ or –∞. A graph's slant asymptote is a slanted line y = mx + b along which the graph approaches the line as the inputs approach or ∞ or –∞
What is Square?
A square is a regular quadrilateral, which implies it has four equal sides and angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
f (x) = [tex]\frac{2x^{2} +3x+6}{x^{2} +1}[/tex]
Here the degree of numerator = degree of the denominator
Hence the equation of horizontal asymptote y = 2/1
=2
Hence the equation of horizontal asymptote y=2
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PLEASE HELP!!!! I WILL GIVE BRAINLIEST
Answer:
Below
Step-by-step explanation:
Work your way through this to make sure you understand:
The 'b' part at the bottom means you have to make SURE that BOTH of the answers actually WORK In the equation.... ONE MAY not...you have to try them both to see if one is 'extraneous' (which means 'does not work')
In how many ways can 8 persons be seated at a round table if 2 particular persons must not sit next to each other?A 40320B 5040C 3600D 720
The total number of arrangements possible if A and B must not sit together:
= 3600
Now, According to the question:
The no. of circular arrangements of n distinct items = (n-1)!
If A,B,C,D,E,F,G and H are the 8 persons to be seated around the table and A,B the 2
particular persons who must not sit together.
The total no.of circular arrangements for 8 persons = (8-1)! = 7! = 5040 --(1)
The no. of circular arrangements possible if A and B were to sit together = 6! (considering A and B as a single pair).
But, A and B can interchange their positions.
Hence, the no. of arrangements =6!×2=720×2=1440−−−−>(2)
So, the total number of arrangements possible if A and B must not sit together, = (1) - (2)
= 5040-1440
= 3600
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simplify each expression by adding or subtracting {5a2+5-a} + {6-2a+4a4}
Answer:
4a⁴ + 5a² - 3a + 11
Step-by-step explanation:
5a² + 5 - a + 6 - 2a + 4a⁴
Combine like terms.
5a² + 11 - 3a + 4a⁴
4a⁴ + 5a² - 3a + 11
Answer:
4a⁴ + 5a² - 3a + 11
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ (5a² + 5 - a) + (6 - 2a + 4a⁴)
Let's simplify the expression,
→ (5a² + 5 - a) + (6 - 2a + 4a⁴)
→ 5a² + 5 - a + 6 - 2a + 4a⁴
→ (4a⁴) + (5a²) + (-a - 2a) + (5 + 6)
→ 4a⁴ + 5a² + (-3a) + (11)
→ 4a⁴ + 5a² - 3a + 11
Therefore, this is the answer.
What are your tips for memorizing the functions sin, cos, tan, cot, csc, and sec?
The nonsense syllables Oh, Ah, and Oh-Ah (i.e. /o o. /) for O/H, A/H, and O/A can also be memorized as a substitute for the letters Sin, Cos, and Tan. For these letters, longer mnemonics like "Oscar Has A Hold On Angie" and "Oscar Had A Heap of Apples" can be used.
What is meant by function?A mathematical formula, rule, or legislation that establishes the link between the independent variable and the dependent variable (the dependent variable). At its most basic level, management is a discipline made up of the following five general tasks: organizing, staffing, leading, and controlling. A corpus of theories and practices on how to be a great manager includes these five functions. The eight categories are power, quadratic, rational, exponential, logarithmic, sinusoidal, polynomial, and linear. When examining a graph, one method is to perform a "vertical line test" to see if a relationship is indeed a function. The vertical line test can be used to determine if a graph accurately depicts a function. If a vertical line is drawn over it and is moved so that it only ever touches it once, the graph is said to be a function. If the vertical line crosses the graph multiple times, it is not a function.To learn more about function, refer to:
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Line G has a slope of 5/4. Line H is perpendicular to line G, what is the slope of line g.
Answer:
-4/5
Step-by-step explanation:
Since Line H is perpendicular to Line G, its slope is the negative reciprocal of the slope of Line G.
Line G: m = 5/4
Line H: m = -4/5
According to the NCAA, 3. 9% of female high school basketball players go onto play basketball in the NCAA. Of these players, 0. 9% are drafted into the WNBA. If you randomly select one female high school basketball player, what is the probability she will be drafted by a WNBA team?
The probability that a randomly selected female high school basketball player will be drafted by a WNBA team is 0.000351 or approximately 0.04%.
The probability of a female high school basketball player being drafted into the WNBA can be taken as a combination of two probabilities.
The probability that she will play basketball in the NCAA, which is equal to 3.9%, and the probability that she will be drafted into the WNBA given that she plays in the NCAA, which is equal to 0.9%, are both equal.
The probability can be calculated by using the formula:
P(WNBA draft) = P(NCAA) × P(WNBA draft | NCAA)
Where, P(NCAA) = 3.9 ÷ 100 which is equal to 0.039
and, P(WNBA draft | NCAA) = 0.9 ÷ 100 which is equal to 0.009
Hence, by substituting the values in the equation we get
P(WNBA draft) = 0.039 × 0.009
Which is equal to 0.000351 or approximately 0.04%
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The quadratic functions f(x) and g(x) are described in the table. x f(x) g(x) −2 4 64 −1 1 49 0 0 36 1 1 25 2 4 16 3 9 9 4 16 4 5 25 1 6 36 0 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 18 units Right by 18 units Left by 6 units Right by 6 units
Right by 6 units should f(x) be shifted to match g(x).
What is the quadratic functions?A quadratic function is a type of mathematical function that can be represented by an equation in the form of ax^2 + bx + c, where x is a variable, a, b, and c are coefficients, and a ≠ 0. Quadratic functions are commonly used in various fields including physics, engineering, and finance, to model various real-world phenomena.
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which of the following statistics are unbiased estimators: a) all these (sample mean, sample proportion, and sample variance) b) the sample proportion c) the sample variance d) the sample mean
All these (sample mean, sample proportion, and sample variance) are the statistics are unbiased estimators.
What is meant by unbiased estimator?The difference between an estimator's expected value and the actual value of the parameter under consideration is known as bias in statistics. Unbiased estimators or decision rules are referred to as unbiased. "Bias" is a statistical term for an estimator's objective property.An estimator's expected value must exactly match the population parameter's value in order for it to be considered impartial. The discrepancy between an estimator's expected value and the parameter value is known as bias. The estimator has bias if this difference is not zero.Given a straightforward random sample, the sample mean is an unbiased estimator of the population parameter because, over a large number of samples, it does not consistently overestimate or underestimate the true population mean.Learn more about unbiased estimator refer to :
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A and B are oppoite vertice of a regular ix-ide hape, the point C and D are the midpoint of two oppoite ide. The area of the regular ix-ided hape i 60. Determine the product of the length of the line AB and CD!
The product of AB and CD in a regular hexagon with an area of 60 is (40 / √3) / 2.
To find the product of the length of AB and CD in a regular hexagon, we have to initially calculate the length of one side of the hexagon and later use that information to find the length of AB and CD.
Let us say that the length of one side of the hexagon = s.
W.k.t the area of the hexagon = 60, so we can use the formula for the area of a regular hexagon:
Area = (3 * √3) / 2 * [tex]s^2[/tex]
Making this equal to 60 and solving s:
60 = (3 * √3) / 2 * [tex]s^2[/tex]
120 = 3 * √3 * [tex]s^2[/tex]
40 = √3 * [tex]s^2[/tex]
(40 / √3) = [tex]s^2[/tex]
Taking the square root of both sides:
s = (40 / √3)^(1/2)
Now that we found the length of one side of the hexagon, So we can use that to find the length of AB and CD.
AB = the length of one side of the hexagon times the square root of 3, CD = the length of one side of the hexagon divided by 2.
So,
AB = s * √3
CD = s / 2
Now, we can find the product of AB and CD by multiplying them together:
AB * CD = s * √3 * s / 2
AB * CD = (s^2 * √3) / 2
AB * CD = (40 / √3) / 2
So the product of AB and CD in a regular hexagon with an area of 60 is equal to (40 / √3) / 2.
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Kevin's bank offered him a 4. 5% interest rate for his mortgage. If he purchases 3 points, what will be his new rate?
The new interest rate for his mortgage would be 3.75%.
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.
Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.
A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)
New interest rate=4.5%-0.75%=3.75%
Thus, The new interest rate for his mortgage would be 3.75%.
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Which would cause a shift in the supply curve?
The supply curve shifts as a result of every factor but a change in market price. The movement along the supply curve and the change in price are correlated.
What is meant by supply curve?The supply curve can change depending on a number of variables, such as shifts in production costs (such as raw material and labor prices), advancements in technology, the level of competition and the number of sellers/producers, as well as the regulatory and tax environment.
Although a shift in the quantity supplied or along the supply curve for a given commodity or service is frequently brought about by a change in price, the supply curve itself does not alter as a result.
Input prices, weather conditions, technological advancements, as well as governmental taxes, regulations, and subsidies, can all modify the supply curve for goods and services, resulting in a different quantity being delivered for a given price.
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Show that each term in the following equation has units of lb/ftº. Consider u as velocity, y as length, x as length, p as pressure, and u as absolute viscosity
The equation [tex]p*u*(dy/dx)[/tex]has units of[tex]lb/ftº[/tex], which is derived by multiplying the units of each of the three terms in the equation: [tex](lb/ft²)(ft/s)(1/ft).[/tex]
[tex]p*u*(dy/dx)[/tex]
[tex]lb/ftº = (lb/ft²)(ft/s)(1/ft)[/tex]
[tex]= (lb/ft²)(ft/s)(ftº)= lb/ftº[/tex]
1. The first term in the equation is pressure, p, which is measured in units of [tex]lb/ft².[/tex]
2. The second term is absolute viscosity, u, which is measured in units of ft/s.
3. The third term, [tex](dy/dx)[/tex] is the derivative of y with respect to x, and has units of 1/ft.
4. Multiplying the three terms together gives a result of[tex](lb/ft²)(ft/s)(1/ft)[/tex]which is equal to[tex]lb/ftº.[/tex]
The equation[tex]p*u*(dy/dx)[/tex] has units of [tex]lb/ftº[/tex], which is derived by multiplying the units of each of the three terms in the equation: [tex](lb/ft²)(ft/s)(1/ft).[/tex]
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at a point on the ground 50 meters from the foot of a tree, the angle of elevation of the top of the tree is 48 degrees. find the height of the tree to the newest hundredth of a meter.
When measured from a position on the ground 50 meters away from a tree, the height of the tree is 55.5 meters to the nearest hundredth of a meter.
what is trigonometry ?The association between triangle line angle lengths and angles is examined in the mathematics discipline known as trigonometry. The application of geometry in astronomical inquiry gave rise to the area's first appearance in the 18th century, roughly in the third centuries BC. Exact approaches mathematics focuses on certain right triangle and how they could be applied to operations. In trigonometry, there are six well-known trigonometric functions. They are identified by their various names and buzzwords: sine, cosine, parallel, cotangent, hyperbolic tangent, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly of right triangles. The features of all geometric forms are studied in geometry.
given
Base = 50, Elevation Angle = 48
An angle's opposite or adjacent side is its tan.
Tan (48),
height/distance, = 50*tan (48),
height, or 55.5 feet.
When measured from a position on the ground 50 meters away from a tree, the height of the tree is 55.5 meters to the nearest hundredth of a meter.
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don't quite understand. can someone explain pls?
The two column proof showing that m∠AKG = m∠HKB is as below and explained.
How to interpret two column proof?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The two column proof showing the vertical angles are explained below.
Statement 1: Segment GH Intersects Segment AB at K
Reason 1: Given
Statement 2: m∠AKG + m∠GKB = 180°
m∠GKB + m∠HKB = 180°
Reason 2: Definition of supplementary angles
Statement 3: m∠AKG + m∠GKB = m∠GKB + m∠HKB
Reason 3: Substitution property
Statement 4: m∠AKG = m∠HKB
Reason 4: Subtraction property
Now, supplementary angles are defined as angles that sum up to 180 degrees and that is why m∠AKG + m∠GKB = 180° and m∠GKB + m∠HKB = 180°
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Find the slope of a line parallel to the line whose equation is x + 2y = -14. Fully
simplify your answer.
Answer:
So first solve the equation given
X+2y=-14
-x -x
-----------------
2y=-x-14
---- ---------
2 2
y=- 1/2x-7
this would be your parallel line equation because y=-1/2x-7
Parallel lines have the same slope
Perpendicular lines have a negative reciprocal slope (so -2 would be positive 1/2)
Hope this helps!
Please leave a comment if I made a mistake, I will correct it!
below is a sketch of the region bounded by the line y=4−2x, the line y=0, and the line x=0
[tex]y = 4-2x , y = 0 , x = 0[/tex] The region is a triangle with the upper right corner at (2, 4).
1. Start by drawing the three lines: the line [tex]y=4−2x[/tex], the line y=0, and the line x=0.
2. Find the coordinates of the upper right corner of the region. To do this, we need to find the point where the two lines y=4−2x and x=0 intersect. We can solve this by setting y=4−2x and x=0, which gives us the point (0, 4). This is the upper right corner of the region.
3. The region is a triangle with the upper right corner at (2, 4).
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In the figure ABCD is a cyclic find the measure of each angles
The angle relations in a cyclic quadrilateral are discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that ABCD is a cyclic quadrilateral.
A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords.
The opposite angles of a cyclic quadrilateral have a total of 180°.
For a cyclic quadrilateral with successive sides a, b, c, d, semi - perimeter s, and angle A between sides a and d, the angle relations for a cyclic quadrilateral as -
Cosine {A} : [tex]${\displaystyle \cos A={\frac {a^{2}-b^{2}-c^{2}+d^{2}}{2(ad+bc)}}}[/tex]Sine (A) : [tex]$\sin A={\frac {2{\sqrt {(s-a)(s-b)(s-c)(s-d)}}}{(ad+bc)}}[/tex]tan (A/2) : [tex]$\tan {\frac {A}{2}}={\sqrt {\frac {(s-a)(s-d)}{(s-b)(s-c)}}}.[/tex]The angle θ between the diagonals that is opposite sides a and c satisfies -[tex]$\tan {\frac {\theta }{2}}={\sqrt {\frac {(s-b)(s-d)}{(s-a)(s-c)}}}.[/tex]
If the extensions of opposite sides a and c intersect at an angle φ, then -[tex]${\displaystyle \cos {\frac {\varphi }{2}}={\sqrt {\frac {(s-b)(s-d)(b+d)^{2}}{(ab+cd)(ad+bc)}}}}[/tex]
Therefore, the angle relations in a cyclic quadrilateral are discussed above.
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1)The time (in minutes) that it takes a mechanic to change oil has an exponential distribution with mean 20.
a) Find P(X < 25), P(X > 15), and P(15 < X < 25)
b) Find the 40th percentile
a) P(X<25) = 0.7135 P(X>15) = 0.4724 P(15<X<25)=0.1859 and The 40th percentile is : 10.2165
What is exponential distribution?The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a certain event occurs. It refers to a system in which things proceed continuously and separately at such an average speed that is constant.
Let X = The time (in minutes) that it takes a mechanic to change oil
We have,
X = Exp (mean = 20)
The distribution function of X is: F(x) = P (X < x) = 1 - e{-x/20}
a) Consider, P (X < 25) = F(25)
= 1 - e{-25/20}
= 0.7135
Consider, P( X > 15)
= 1 - P (X < 15)
= 1 - 1 - e{-15/20}
= 0.4724
Consider, P(15 < X < 25)
= P (X < 25) - P (X < 15)
= 1 - e{-25/20} - 1 - e{-15/20}
= 0.1859
Hence,
P(X<25) = 0.7135 P(X>15) = 0.4724 P(15<X<25)=0.1859
b) We want to find x such that P(X<x) =0.40
Consider, P (X < x) = 0.40
1 - e{-x/20} = 0.40
x = 10.2165
Hence, The 40th percentile is : 10.2165
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if f(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and \" f '(6) = 6\" , find f '(1).
The value of the composite function F(1) is 6.
Composite function;
When the result of one function is utilized as the input for another, this is known as a composite function.
Composite function;
F(x) = f(xf(xf(x)))
Also, we have
f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6,
Substitute 1 for x in the equation F(x) = f(xf(xf(x)))
So, we have
F(1) = f(xf(xf(1)))
From the question
f(1) = 4
So, we have
F(1) = f(xf(4))
From the question
f(4) = 6
So, we have
F(1) = f(6)
As a general rule
If f '(4) = 5 then f(6) = 6
So, we have
F(1) = 6
Hence, the value of the function F(1) is 6
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How do you simplify 2 + square root of 60 all divided by 4?
The simplified expression is [1 + √15]/2
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
2 + √60]/4
So, we have
2 + 2√15]/4
Divide
1 + √15]/2
Hence, the expression is [1 + √15]/2
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21.1.4 Quiz: Thinking Chronologically
Question 5 of 5
Which timeline correctly organizes the founding of important world religions?
O A
B.
О с.
O D.
World Religions
Christianity was founded about 2,000 years ago.
• Islam was founded about 1,400 years ago.
.
Hinduism was founded about 3,500 years ago.
.
• Buddhism was founded about 2,500 years ago.
• Judaism was founded about 4,000 years ago.
·
← PREVIOUS
Buddhism
Judaism
Christianity
Hinduism
Judaism
Buddhism
Judaism
Islam
Christianity
Christianity
Islam
Christianity
Islam
Islam
Hinduism
Judaism
Hinduism is one of the suggested timelines for the foundation of significant world religions. Islam Buddhism Christianity The right answer is C.
Whose faith is the most popular worldwide?With more than two billion adherents, Christianity is the largest of the world's main religions. Christianity, which has been around for around 2,000 years, is founded on the life and teachings of Jesus. Faith and reason have always been seen as the basis of religious beliefs. There are reportedly 10,000 different religions in the globe, although almost all of them have localised, insignificant followings.
Which seven world religions are there?JUDAISM.
CHRISTIANITY.
ISLAM.
HINDUISM.
BUDDHISM.
SIKHISM.
ANIMISM.
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If I paid $625 interest on $5000 that I borrowed at 5%, how many years did I borrow it? *Remember, I = P x R x T help fast
A bag contains 5 black pencils and 3 yellow pencils. What is the
probability of drawing 1 black pencil and 2 yellow pencils without
replacement?
The probability of drawing 1 black pencil and 2 yellow pencils without replacement is 0.035714.
The probability of drawing 1 black pencil and 2 yellow pencils without replacement can be calculated by multiplying the individual probabilities of drawing each pencil.
The first step is to calculate the probability of drawing a black pencil which is 5/8. Then, the probability of drawing the first yellow pencil is 4/7 and the probability of drawing the second yellow pencil is 3/6.
To find the probability of drawing all three pencils, you multiply these three probabilities together:
5/8 × 4/7 × 3/6 = 0.035714.
This result represents the probability of drawing 1 black pencil and 2 yellow pencils in that order without replacement.
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Question: Which function is best represented by this graph?
Responses: f(x)=x2+2x−1 f(x)=x2−2x−1 f(x)=x2+2x f(x)=x2−2x
The quadratic function best represented by the graph is given as follows:
f(x) = x² + 2x.
How to model the quadratic function?The quadratic function of roots x* and x** is given by the rule presented as follows:
y = a(x - x*)(x - x**).
In which a is the leading coefficient.
The roots are given on the graph by the values of x when the graph crosses the x-axis, hence they are given as follows:
x* = -2, x* = 0.
Hence:
y = a(x + 2)(x)
When x = -1, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a(-1 + 2)(-1)
-a = -1
a = 1.
Meaning that the function is defined as follows:
f(x) = x² + 2x.
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A student is buying single-serve breakfast meals for the next 9 days. The options are meat bowl, vegetarian bowl, cereal bowl, and taco bowl. How many different selections could the student make?
The student has 36 different combinations of breakfast options to choose from (4 options x 9 days).
To determine this:
The student has four different options for breakfast each day for 9 days, so the number of different selections could be calculated as 4 options x 9 days = 36 different selections.
This means that the student has 36 different combinations of breakfast options to choose from, as they can choose one option each day for 9 days. The options are meat bowl, vegetarian bowl, cereal bowl, and taco bowl, and they can choose any combination of these options for their 9 days of breakfast.
For example, they can choose a meat bowl on day 1, a vegetarian bowl on day 2, a cereal bowl on day 3, a taco bowl on day 4, and so on, or they can choose the same option every day, or they can mix and match their options in any combination they like.
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there are nine different positions on a baseball team. if a team has 15 players how many different line-ups can the team make? (assume every player can play every position.) the team can make different line-ups. baseball games consist of nine innings. a team wants to change its line-up every inning. if no game goes to extra innings, and a season consists of 66 games, how many complete seasons can the team play without repeating a line-up?
There are 18 seasons and the number of different line-ups the team can make is 24310
A) We are given the team has 17 players and there are 9 different positions in the team.
This is a combination question and thus, the number of different line-ups the team can make is;
C(17, 9) = 24310
B) We are told the basketball games consist of 9 innings.
Thus,
Number of games you can fill = 24310/9 = 2701.1111
And then we are told a season consists of 147 games.
Thus;
The number of complete seasons can the team play without repeating a line-up = 2701.1111/147 ≈ 18 seasons.
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Zach’s car travels 21 miles on 1 gallon of gas. Write an equation to represent the relationship between the gas Zach’s car uses and the distance he travels. Then solve the equation to see how far Zach travels on a trip if he uses 16 gallons of gas
The equation to see how far Zach travels is y = 21x and Zach traveled 336 miles using 16 gallons of gas.
What is the equation to see how far Zach travels on a trip?Number of miles traveled Zach's car traveled= 21 miles
Quantity of gallons used = 1 gallon
y = kx
Where,
x = total gallons used
k = unit rate of miles per gallon
y = Number of miles traveled
So,
21 = k × 1
21 = k
y = 21x
Hence,
if he uses 16 gallons of gas
y = kx
y = 21 × 16
y = 336 miles
In conclusion, Zach's car traveled 336 miles.
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