The number of bald eagles in the state in the winter of 1999 is 273.909, where The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function.
by the given information the equation is
[tex]f(x) = -3.439(x)^4 + 35.952(x)^3 - 99.139(x)^2 + 41.541(x) + 178.192[/tex]
where x = number of years since 1996
The given quartic function must be changed to x = 3 in order to determine the number of bald eagles in the state during the winter of 1999:
[tex]f(3) = -3.439(3)^4 + 35.952(3)^3 - 99.139(3)^2 + 41.541(3) + 178.192[/tex]
When we condense this expression, we get:
f(3) = -3.439(81) + 35.952(27) - 99.139(9) + 41.541(3) + 178.192
f(3) = -1107.759 + 970.104 - 892.251 + 124.623 + 178.192
f(3) = 273.909
Hence, in the winter of 1999, there were roughly 273.909 bald eagles in the state.
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Find the expected number of flips of a coin, which comes up
heads with probability 0.5,
that are necessary to obtain either h, h, h or t, t, t.
The expected value of X is given byE(X) = 1/p= 1/(1/4) = 4
To obtain either h, h, h or t, t, t, let's consider the sequence h, h, h, t, t, t. The probability of obtaining h, h, h or t, t, t is (1/2)^3 + (1/2)^3 = 1/4. Also, the probability of the first head or tail occurring on the nth flip is (1/2)^n-1. If X denotes the number of flips of a coin required to get h, h, h or t, t, t, then X has a geometric distribution with parameter p = 1/4. Hence, the expected value of X is given byE(X) = 1/p= 1/(1/4) = 4The expected number of flips of a coin, which comes up heads with probability 0.5, that are necessary to obtain either h, h, h or t, t, t is 4.
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Verify
(N+3)!÷n+ =(n+1)(n+2)(n+3)
Answer:
True
Step-by-step explanation:
A factorial means a number multiplied by all of the positive integers before it. That means both n+3! and n! have a common factor of n!. When you take out this factor of N, the fraction (n+3)!/n! ‘s denominator would be one, and the numerator would have all of the positive integers before n+3 and also being greater than n. Thus, (n+1)(n+2)(n+3)
Write a vertical motion model in the form ()=−++h of , open t close , equals negative 16 , t squared , plus , v sub 0 , t plus , h sub 0 for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height.
Initial velocity: 32 ft/s; initial height: 20 ft
Answer:
h(t)=−16t²+v
0 t+h 0
for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height. Initial velocity: 32 ft/s; initial height: 20 ft
Step-by-step explanation:
the attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend. the ratios for the three days were equivalent. complete the table. day hybrids total fri. sat. sun.
The table below shows the number of hybrid vehicles and the total number of vehicles in the parking lot for each day of the weekend:
Day Hybrids Total
Fri x y
Sat x y
Sun x y
Since the ratios for the three days were equivalent, this means that the fraction of hybrid vehicles to total vehicles was the same for each day. In other words:
x/y = x/y = x/y
Therefore, the values of x and y must be the same for each day. This means that the number of hybrid vehicles and the total number of vehicles in the parking lot were the same for each day of the weekend.
In conclusion, the table should be completed with the same values of x and y for each day, as shown below:
Day Hybrids Total
Fri x y
Sat x y
Sun x y
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Can someone please help me if they cannnn :(
Step-by-step explanation:
Your debt ratio is the ratio of the credit limit you have spent.
Your debt ratio is the amount you have spent on the credit card/ the limit
You have spent $9000- $3200 = $5800
Debt ratio = 5800/9000
=58/90 = 29/45
2. Acceptable ratio is less than 43%
Is 29 out of 45 less than 43%
Convert 29/45 to percentage
29/45 /100/1 = 64.44%
You have exceeded acceptable ratio at 64.4%
Answer:
Your debt ratio is the percentage of your credit limit that you have spent.
spent $9000- $3200 = $5800
Debt to income ratio = 5800/9000 = 58/90 = 29/45
2. A satisfactory ratio is less than 43%.
Is 29 percent of 45 less than 43%?
29/45 converted to a percentage 29/45 /100/1 = 64.44%
Step-by-step explanation:
Brainliest pls
Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?
Option C requires the examination of the data on bowling scores to find out what Molly's mean score is, and this constitutes a statistical inquiry that can be resolved with the information that has been gathered.
The statistical question that can be answered from the data is: C) What was Molly's average bowling score?
Option A is not a statistical question because it only concerns Molly's personal feeling towards one of her bowling scores.
Option B is a factual question that does not require statistical analysis.
Option D is also a factual question that does not require statistical analysis.
However, option C involves analyzing the bowling scores data to determine Molly's average score. This is a statistical question that can be answered using the collected data.
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Complete question:
Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?
A) Which bowling score made Molly the proudest?
B) How many times did the bowling club meet?
C) What was Molly's average bowling score?
D) On what day did the bowling club begin?
PLEASE I NEED THE AWNSER IN 2 MIN
Match the situation with the correct ratio. Don't forget that you can write a ratio three ways! Also remember the different ways to find equivalent ratios (simplify, rename, table, graph, tape diagram). Make sure you pay attention to the order!! Only enter CAPITAL letters with no spaces or numbers. (Your answer should look something like this WTYUSR)
*
1. 6:15 has a ratio of 2:5
2. 10:40 has a ratio of 1:4
3. 6:28 has a ratio of 3:14 but it would be 12:56 based on the answer choices
4. 15:25 has a ratio of 3:5 but it would be 15:25 based on the answer choices
Patients arrive at a hospital emergency department according to a Poisson distribution with an average of 9 per hour. (a) What is the probability that exactly 7 patients will arrive during a 90 minutes period? (b) What is the probability that at least 30 minutes will pass until the next patient arrives? (c) If one hour has passed and no patient has arrived, what is the probability that the next patient arrives during the following 20 minutes? Problem 4: [9 points] Patients arrive at a hospital emergency department according to a Poisson distribution with an average of 9 per hour. (a) What is the probability that exactly 7 patients will arrive during a 90 minutes period? (b) What is the probability that at least 30 minutes will pass until the next patient arrives? (c) If one hour has passed and no patient has arrived, what is the probability that the next patient arrives during the following 20 minutes?
The probability that the next patient arrives during the following 20 minutes is approximately 0.776.
(a) The probability that exactly 7 patients will arrive during a 90-minute period can be found by using the Poisson distribution formula.Poisson distribution formula:P(X = x) = (e-λ * λx) / x!Where: λ is the average number of events per unit of time or space, x is the number of occurrences, e is the exponential constant equal to 2.71828.x! means x factorial that is x(x − 1)(x − 2)⋯(2)(1).Here, λ = 9/60 = 0.15 (since there are 9 arrivals in one hour, there would be 9/60 arrivals in 1 minute)We are to find the probability of exactly 7 patients arriving in 90 minutes.The time period is 90/60 = 1.5 hours. Hence, λ = 0.15 × 1.5 = 0.225P(X = 7) = (e-λ * λ7) / 7! = (e-0.225 * 0.2257) / 7! = 0.085 ≈ 0.09Therefore, the probability that exactly 7 patients will arrive during a 90 minutes period is approximately 0.09(b) We can calculate the probability of at least 30 minutes passing until the next patient arrives by using the cumulative distribution function (CDF) of the exponential distribution.Exponential distribution formula:f(x) = λe-λxwhere λ is the rate parameter, x is the time period, and e is the exponential constant equal to 2.71828.The mean waiting time between two successive arrivals is 60/9 = 6.67 minutes.Hence, λ = 1/6.67 = 0.15The probability of at least 30 minutes passing until the next patient arrives can be calculated as follows:P(X > 0.5) = 1 - P(X ≤ 0.5) = 1 - (1 - e-λx) = e-λx = e-0.15×0.5 ≈ 0.776Therefore, the probability that at least 30 minutes will pass until the next patient arrives is approximately 0.776.(c) The probability that the next patient arrives during the following 20 minutes can be calculated as follows:P(X > 1) = 1 - P(X ≤ 1) = 1 - (1 - e-λx) = e-λx = e-0.15×1/3 ≈ 0.776Therefore, the probability that the next patient arrives during the following 20 minutes is approximately 0.776.
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r=1.94668
r=2.94668
r=3.94668
r=0.94668
The correlation coefficient for the SAT math score and the GPA of the students is given as follows:
r=0.94668.
What is a correlation?A correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is represented by the symbol "r" and ranges from -1 to 1.
The value of the correlation coefficient indicates the strength of the linear relationship between the variables. The closer the value of "r" is to -1 or +1, the stronger the linear relationship between the variables. A value of 0 indicates that there is no linear relationship between the variables.
The correlation coefficient is calculated inserting the points of the data-set into a correlation coefficient calculator.
The points from the graph are given as follows:
(595, 3.4), (520, 3.2), (715, 3.9), (405, 2.3), (680, 3.9), (490, 2.5), (565, 3.5).
Inserting these points into a calculator, the coefficient is given as follows:
r = 0.94668.
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Order the set of numbers from least to greatest.
-4.33, 4.67 , 4 1/2
Oa. 4.67, 4 -4.33
Ob. 4,-4.33, 4.67
Oc. -4.33, 4.67, 4
Od.-4.33, 4, 4.67
What are the solutions to the system of equations below?
7x - 5y = 38
2x+10y = -12
Answer:
Step-by-step explanation:
To solve this system of equations, we can use either substitution or elimination method.
Let's use the elimination method to eliminate y.
Multiplying the first equation by 2 and the second equation by 5, we get:
14x - 10y = 76
10x + 50y = -60
Now, we can add the two equations to eliminate y:
(14x - 10y) + (10x + 50y) = 76 - 60
Simplifying the left side and right side, we get:
24x = 16
Dividing both sides by 24, we get:
x = 2/3
Now that we have the value of x, we can substitute it back into either of the original equations to find y.
Let's substitute it into the first equation:
7x - 5y = 38
7(2/3) - 5y = 38
Simplifying and solving for y, we get:
-5y = 38 - 14/3
-5y = 100/3
y = -20/3
Therefore, the solution to the system of equations is (x, y) = (2/3, -20/3).
algebra 2 assignment three variable HELPPP 13 points
The team scored 2 field goals, 2 safeties, and 4 touchdowns.
Define the term equation?A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.
The football team scored 8 times and a total of 38 points.
Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.
We know, T = F + S and F + S = 4
Substituting, T = F + S into the equation for total points,
we get, 7T + 3F + 2S = 38
Solving for F and S, we get F = 2 and S = 2.
Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.
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Solve for F and S then get F = 2 and S = 2.
The team scored 4 touchdowns, 2 field goals, and 2 safeties.
How to calculate DF score?The football group scored 8 times, totaling 38 points.
Let,
T is the no.of touchdowns,
F is the no.of field goals, and
S is the no.of safeties.
Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).
Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.
Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.
We know that,
T = F + S and
F + S = 4
For total points, put T = F + S into the equation.
We get,
7T + 3F + 2S = 38
Solve for F and S,
we get,
F = 2 and S = 2.
As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.
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5a. Evaluate \( \lim _{x \rightarrow \frac{\pi}{2}-} \tan (x) \). (Hint: Rewrite \( \tan (x) \) as \( \frac{\sin (x)}{\cos (x)} \).)
lim_{x\to{\frac{\pi}{2}}^-} \tan x is 0.
The given function can be rewritten as;$$\frac{\sin x}{\cos x}$$Let us calculate the left hand limit$$\lim_{x\to{\frac{\pi}{2}}^-} \frac{\sin x}{\cos x}=\lim_{x\to{\frac{\pi}{2}}^-} \frac{1}{\cos x}= \frac{1}{\cos \frac{\pi}{2}}=0$$Thus, the evaluation of $$\lim_{x\to{\frac{\pi}{2}}^-} \tan x$$ is 0.
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Which ordered pair is the solution to tue system if equations below when using matrix tool 3x+y=17 2x-y=8
The solution of the system of equations is (4, 5).
How to solve the system of equations?Here we have the system of equations:
3x + y = 17
2x - y = 8
We would want tosolve this using matrices, then we need to solve:
[tex]\left[\begin{array}{ccc}3&1\\2&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\8\end{array}\right][/tex]
If we add the first and second equations (or the rows of the first matrix) then we will get:
[tex]\left[\begin{array}{ccc}3&1\\5&0\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\25\end{array}\right][/tex]
Then we have:
5y = 25
y = 25/5
y = 5
And now that we know the value of y we can input it in any of the equations to find x.
3x + y = 17
3x + 5 = 17
3x = 17 - 5 = 12
x = 12/3 = 4
The solution is (4, 5).
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Please help me desperately need help
Answer:
9) 15
10)22
11)25
Step-by-step explanation:
9)
[tex]area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\[/tex]
substitute:
=2x+7
=2(7)+1
=15
10)
[tex]area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x[/tex]
substitute:
=3x-2
=3(7)+1
=22
11)
[tex]area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25[/tex]
(x+42)
3x
please help
Given:-
A right angle is given to us.It is made up of two angles (x+42)° and 3x°.To find:-
The value of " x " .Solution:-
Here the sum of the two unknown angles will be 90° as they are the angles which make up 90° . So that;
[tex]\implies x^o + 42^o + 3x^o = 90^o \\[/tex]
[tex]\implies 4x^o = 90^o - 42^o \\[/tex]
[tex]\implies 4x^o = 48^o \\[/tex]
[tex]\implies x =\dfrac{48}{4} \\[/tex]
[tex]\implies \boxed{ x = 12} \\[/tex]
Hence the value of x is 12 .
and we are done!
Answer this question
Answer:
5/2
Step-by-step explanation:
substitute the values into the cosine rule:
(2[tex]\sqrt{7}[/tex])² = ((2x - 1)² + (2x + 1)²) - 2(2x - 1)(2x + 1)cos(60))
work out each part separately:
(2[tex]\sqrt{7}[/tex])² = 28
(2x - 1)² = 4x² - 4x + 1
(2x + 1)² = 4x² + 4x + 1
(2x - 1)² + (2x + 1)² = (4x² - 4x + 1) + (4x² + 4x + 1) = 8x² + 2
2((2x - 1)(2x + 1)cos(60)):
(2x - 1)(2x + 1) = 4x² - 1
cos(60) = √1/2 = 1/2
2(4x² - 1)(1/2) = 4x² - 1
substitute back in:
28 = (8x² + 2) - (4x² - 1)
28 = 4x² + 3
25 = 4x²
25/4 = x²
x = √(25/4)
x = 5/2
x/5+9=11 so I need to get it solved by using 2 Step Equation with Multiplication
Step 1: Isolate x/5 by subtracting 9 from both sides:
x/5 + 9 -9 = 11 -9
x/5 = 2
Step 2: Isolate x by multiplying both sides by 5:
5 · x/5 = 2 · 5
x = 10
The solution is 10.
The fork length r (in centimeters) of a requiem shark can be approximated by r = 0.83t + 1.13, where t is the total length (in centimeters) of the shark. Find the inverse of the function.
The inverse of the function is t = (r - 1.13) / 0.83.
What is function ?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. A function can be thought of as a rule or a machine that takes an input value and produces a corresponding output value.
The given equation is: r = 0.83t + 1.13
To find the inverse of the function, we need to solve the equation for t.
r = 0.83t + 1.13
Subtract 1.13 from both sides:
r - 1.13 = 0.83t
Divide both sides by 0.83:
(r - 1.13)/0.83 = t
So the inverse function is:
t = (r - 1.13)/0.83
Or we can write it as:
[tex]f^{(-1)(r)} = (r - 1.13)/0.83[/tex], where [tex]f^{(-1)}[/tex] represents the inverse function.
Therefore, the inverse of the function is t = (r - 1.13) / 0.83.
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Incorrect Your answer is incorrect. Find the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, -8). D M-D = 00 X
The midpoint of the line segment joining the points C and D is M = (-4, 0).
How to calculate the midpoint MThe coordinates of the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, -8) can be found using the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
So, for C = (0, 8) and D = (-8, -8), we have:
M = ((0 + (-8))/2, (8 + (-8))/2)
M = (-4, 0)
Therefore, the midpoint of the line segment joining the points C and D is M = (-4, 0).
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A container holds 3.5 ounces of tablets. How many grams does the container hold?
The container holds 99.223 grams of tablets.
How to convert ounces to grams?One-sixteenth of a pound is represented by the weight measurement called an ounce (oz). A slice of bread and a pencil are two items that weigh about one ounce. One fluid ounce is the same as one-eighth of a cup in terms of volume. A medication cup has a volume of roughly one liquid ounce.
To convert ounces to grams, we can use the conversion factor 1 oz = 28.3495 g.
So, the container holds:
[tex]$3.5\ \text{oz} \times 28.3495\ \frac{\text{g}}{\text{oz}} = 99.223\ \text{g}$[/tex]
Therefore, the container holds 99.223 grams of tablets.
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Let U= {q, r, s. t, u, v, w, x, y,z}
A= {q, s, u, w, y}
B= {q, s, u, w, y}
C= {v, w, x, y, z}
12. A∩B'
A.) {r, s, t, u, v, w, x, z}
B.) {t, v, x}
C.) {u, w}
D.) {q, s, t, u, v, w, x, y}
The intersection of A and B' is an empty set because there are no elements that are in both A and B'. The correct answer is (option E) the empty set.
What is a set ?
A set is a collection of distinct objects, called elements or members, that are well-defined and unordered.
We can start by finding the complement of set B, which consists of all the elements in U that are not in B:
B' = {r, t, v, x, z}
Then, A ∩ B' consists of all the elements that are in A and also in B':
A ∩ B' = {u, w, y} ∩ {r, t, v, x, z} = { }
Therefore, The intersection of A and B' is an empty set because there are no elements that are in both A and B', the correct answer is (option E) the empty set.
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Given the expression
Choose all the equivalent expressions as your answer.
b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.
d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.
What is an equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value(s) fοr the variable(s).
Given expression y√x
a. Is not equivalent as power is rational and exponent are non equal,
b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex]
= [tex]\dfrac{\sqrt{x} }{\frac{1}{y}}[/tex]
= y√x
Thus, b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.
c. Is not a n equivalent expression at has a different variable.
d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex]
[tex]\rm\sqrt{ (xy^2)} }[/tex]
[tex]\rm y \sqrt{ (x)} }[/tex]
Thus, d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.
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anyone know this , i need help again lol
Check the picture below.
The graph of an exponential function is shown in the figure below.
The horizontal asymptote is shown as a dashed line.
Find the range and the domain
Answer:
dghcŕhĝt5dfg9yd6grdy6cjbjbknygug4ximpohyvug5h7h6g6
major axis 12 units long and parallel to the y-axis, minor axis 8 units long, center at (-2,5)
center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1
The dimensions of the given ellipse are major axis 12 units long and parallel to the y-axis, minor axis 8 units long, and the center is located at (-2,5).Let us find the standard form equation of the ellipse. The standard form equation of an ellipse is given by:(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1Where (h, k) is the center of the ellipse, a is the distance from the center to either the x-axis or the y-axis, and b is the distance from the center to the other axis. Therefore, for the given ellipse, the equation of the ellipse in standard form is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1Thus, the standard form equation of the ellipse whose major axis is 12 units long and parallel to the y-axis, minor axis 8 units long, and center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1.
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Given that q is indirectly proportional to r, if q=2.8 when r=11.25, what is q when r=5.25 ?
The value of q is 6
How to calculate the value of q?The constant is k
The first step the to calculate the value of the constant which is k
k= qr
Write out the parameters given in the question
The value of q is 2.8
The value of r is 11.25
k= 2.8 × 11.25
= 31.5
The value of q can be calculated by the value of k which is 31.5 and r which is 5.25
k= qr
31.5= q × 5.25
31.5= 5.25q
q= 31.5/5.25
q= 6
Hence the value q is 6
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The tennis balls in a bag are either white or yellow. If the ratio of white balls to yellow balls is 3/10. Which of the following could not be the number of balls in the bag
The number of balls, given the ratio of white balls to yellow balls that could not be in the bag is C. 42 balls.
How to find the ratio ?The number of balls that could not be in the bag, given the ratio of white balls to yellow balls, is the number that would not give a whole number when multiplied by the ratio of white balls to yellow balls.
26 balls :
= 3 / ( 10 + 3 white balls ) x 26
= 3 / 13 x 26
= 6 balls
39 balls :
= 3 / 13 x 39
= 9 balls
42 balls :
= 3 / 13 x 42
= 9.69 balls
There therefore cannot be 42 balls.
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Options for this question include:
2639425265someone please help me thank u
Answer:
C, E
Step-by-step explanation:
You want to identify the true statements about the end behavior, symmetry, domain, and range of g(x) = -5x² and f(x) = 5x-10.
End behaviorThe function g(x) is of even degree (the exponent is 2), and the function f(x) is of odd degree (the exponent is 1). An even-degree function cannot have the same end behavior as an odd-degree function.
RangeThe range of any odd-degree polynomial function is (-∞, +∞).
Any even-degree polynomial function will have a global maximum or minimum so cannot have the same range. The range of g(x) is (-∞, 0].
DomainThe domain of any polynomial function is "all real numbers." Both f and g have the same domain.
SymmetryAn even-degree function may have an axis of symmetry. An odd-degree function cannot be symmetrical about any line. The functions cannot have the same symmetry.
Points of intersectionTwo polynomial functions may have a number of points of intersection equal to the highest degree. That means a degree-1 and a degree-2 function may have up to 2 points of intersection. These two functions intersect twice, as the graph in the attachment shows.
The elongation α
of a planet is the angle formed by the planet, earth, and sun. It is known that the distance from the sun to Venus is 0. 723AU
(see Exercise 65 in Section 6. 2 ). At a certain time the elongation of Venus is found to be 39. 4∘.
Find the possible distances from the earth to Venus at that time in Astronomical Units (AU)
The possible distances from the Earth to Venus at the time of an elongation of 39.4 degrees are 0.709 AU and 1.333 AU.
The elongation of a planet is the angle formed when the planet, Earth, and Sun are in a straight line. At a certain time, the elongation of Venus was found to be 39.4 degrees. To find the possible distances from the earth to Venus at that time in Astronomical Units (AU), the Law of Cosines can be used.
The Law of Cosines states that for a triangle with sides a, b, and c and angles A, B, and C, c2 = a2 + b2 - 2abcosC.
In this case, a is the distance from the sun to Venus (0.723 AU), b is the distance from the Earth to Venus, and C is the elongation (39.4 degrees).
Therefore, b2 = 0.7232 + b2 - 2(0.723)(b)cos39.4.
Solving for b, we get b = 0.709 AU and b = 1.333 AU, so the possible distances from the Earth to Venus are 0.709 AU and 1.333 AU.
Learn more about Law of Cosines here:
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