Answer:
[tex]2 \frac{10}{23} [/tex]
Step-by-step explanation:
[tex] \frac{4u - 7}{ - 7} = \frac{u - 4}{4} [/tex]
Use the property of the proportion:
4 × (4u-7) = -7 × (u-4)
16u -28 = -7u + 28
16u + 7u = 28 + 28
23u = 56 / : 23
u =
[tex] 2\frac{10}{23} [/tex]
What two numbers are 7 units from 0 on a number line?
The solution to this equation is x = -7 and x = 7.
The two numbers 7 units away from 0 on a number line are -7 and 7. This can be expressed mathematically as |x-0|=7, where x is the unknown number. Solving this equation yields two solutions, x = -7 and x = 7.
To solve this equation, first subtract 0 from both sides of the equation to get |x| = 7. Then, take the absolute value of both sides of the equation to get x = 7. Finally, note that the absolute value of any number is equal to that number's positive value. Therefore, the solution to this equation is x = -7 and x = 7.
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if h(x) = 5 4f(x) , where f(1) = 5 and f '(1) = 4, find h'(1).
If h(x) = 5 4f(x) , where f(1) = 5 and f '(1) = 4, then h'(1) = 20.
To find h'(1), we need to use the chain rule of differentiation, which states that if h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).
In this case, we have h(x) = 5/4 * f(x), where f(1) = 5 and f'(1) = 4. Therefore, g(x) = x, f(x) = 5, and h(x) = 5/4 * 5 = 6.25.
To find h'(1), we need to evaluate f'(g(1)) and g'(1), then multiply them together. Since g(x) = x, we have g'(1) = 1.
Since f'(x) = 4, we have f'(g(1)) = f'(1) = 4. Therefore, h'(1) = f'(g(1)) * g'(1) = 4 * 1 = 4. However, we are looking for h'(1), so we need to multiply this by the coefficient of f(x), which is 5/4. Therefore, h'(1) = 5/4 * 4 * 1 = 20.
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three tennis balls are packaged inside a cylinder. if the diameter of the tennis ball is 7cm, what is the exact volume of the cylinder?
If the diameter of the tennis ball is 7cm. then the exact volume of the cylinder is approximately 807.96 cubic centimeters.
The volume of a cylinder is calculated using the formula
V = πr²h,
where r is the radius and h is the height.
In this case, the radius of the cylinder is equal to the radius of a tennis ball which is half its diameter or 3.5cm.
The height of the cylinder is equal to the diameter of three tennis balls or 21cm. Plugging these values into the formula gives us:
V = π * 3.5² * 21
V ≈ 807.96 cm³.
So, the exact volume of the cylinder is approximately 807.96 cubic centimeters.
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suppose that on a 100-point test, the teacher's goal is for her students' exam scores to have a standard deviation of at most 8 points. a recent sample of 25 exams has a sample standard deviation of 9.5. test whether or not her goal was achieved using a 5% level of significance. calculate the appropriate test statistic (round to 2 decimal places as needed)
we can say that the teacher's gοal οf a standard deviatiοn οf at mοst 8 pοints was achieved, at a 5% level οf significance.
What is standard deviatiοn?A measure οf a grοup οf values' variance οr dispersiοn in statistics is called the standard deviatiοn. When the standard deviatiοn is lοw, the values are mοre likely tο fall within a narrοw range, alsο knοwn as the expected value, whereas when the standard deviatiοn is high, the values tend tο be clοser tο the mean.
The lοwercase Greek letter sigma, which stands fοr the pοpulatiοn standard deviatiοn, οr the Latin letter s, which stands fοr the sample standard deviatiοn, are mοst frequently used in mathematical equatiοns and texts tο represent standard deviatiοn. Standard deviatiοn is alsο sοmetimes referred tο as SD.
suppοse that οn a 100-pοint test, the teacher's gοal is fοr her students' exam scοres tο have a standard deviatiοn οf at mοst 8 pοints.
chi²[tex]= (n-1)*s^2 /\sigma^2[/tex]
where n is the sample size, s is the sample standard deviatiοn, and sigma is the hypοthesized pοpulatiοn standard deviatiοn under the null hypοthesis.
In this case, n = 25, s = 9.5, and sigma = 8. Substituting these values, we get:
chi² [tex]= (25-1)*9.5^2 / 8^2 = 33.64[/tex]
The degrees οf freedοm fοr this test is n-1 = 24. Using a chi-squared table with 24 degrees οf freedοm, we find that the critical value fοr a οne-tailed test at a 5% level οf significance is 36.42.
Therefοre, we can say that the teacher's gοal οf a standard deviatiοn οf at mοst 8 pοints was achieved, at a 5% level οf significance.
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PLEASE HELP ASAP!!
Given: sin =-12/13 and tan ß < 0,
Find cos ß and tan ß.
let's keep in mind that the hypotenuse is just a radius unit and thus is always positive, whilst sine and cosine vary per Quadrant.
so we know the tangent is < 0, which is another way to say "tangent is negative", well, that only happens when the cosine and sine differ in sign, and that only happens in the II and IV Quadrants, so the angle β is on either of those Quadrants.
[tex]\sin(\beta )=-\cfrac{12}{13}\implies \stackrel{ \underline{IV~Quadrant} }{\sin(\beta )=\cfrac{\stackrel{opposite}{-12}}{\underset{hypotenuse}{13}}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=adjacent\\ o=\stackrel{opposite}{-12} \end{cases}[/tex]
[tex]a=\pm\sqrt{ 13^2 - (-12)^2}\implies a=\pm\sqrt{ 169 - 144 } \implies a=\pm 5\implies \stackrel{ IV~Quadrant }{a=+5} \\\\[-0.35em] ~\dotfill\\\\ \cos(\beta )=\cfrac{\stackrel{adjacent}{5}}{\underset{hypotenuse}{13}}\hspace{5em} \tan(\beta )=\cfrac{\stackrel{opposite}{-12}}{\underset{adjacent}{5}}[/tex]
the point (-5-,4) is rotated 90 degrees clockwise
Answer: (-4, 5)
Step-by-step explanation:
a publisher reports that 52% 52 % of their readers own a laptop. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 190 190 found that 45% 45 % of the readers owned a laptop. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is -2.18.
To test the claim that the percentage of readers who own a laptop is different from 52%, we can use a two-tailed z-test for proportions. The null hypothesis is that the true proportion is 52%, and the alternative hypothesis is that the true proportion is different from 52%.
The test statistic can be calculated as:
z = (p - P) / sqrt(P(1 - P) / n)
where p is the sample proportion, P is the hypothesized proportion (in this case, 0.52), and n is the sample size.
Substituting the given values, we get:
z = (0.45 - 0.52) / sqrt(0.52(1 - 0.52) / 190)
z = -0.07 / 0.039
z = -1.79
The value of -1.79 represents the number of standard deviations away from the mean of the sampling distribution of sample proportions if the null hypothesis were true. However, since we are using a two-tailed test, we need to consider both tails of the standard normal distribution.
The critical value for a two-tailed test at the 0.05 level of significance is ±1.96. Since -1.79 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the correct answer is -2.18.
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(2x-6)^2 find the square:
i looked it up but i couldn’t find how we learned it in class with other problems.
[tex](2x-6)(2x-6)[/tex]
[tex]4x^2 - 12x - 12x + 36[/tex]
Answer:[tex]\bold{4x^2 - 24x + 36}[/tex]at December 31 2024 customer advances were $12,518,000 during 2025 Bonita collected 30 million $256,000 of which customers advance advances of 26 million 182 $1000 should be recognized in income. Customer advance ________________
The remaining customer advance at the end of 2025 is $16,592,000.
How to determine Customer advance?To determine the amount of customer advance remaining at the end of 2025, we need to subtract the amount collected in 2025 from the customer advances balance at the end of 2024:
Customer advances balance at the end of 2024 = $12,518,000
Amount collected in 2025 = $30,256,000
Customer advances recognized in income in 2025 = $26,182,000
Customer advances balance at the end of 2025 = Customer advances balance at the end of 2024 + Amount collected in 2025 - Customer advances recognized in income in 2025
Customer advances balance at the end of 2025 = $12,518,000 + $30,256,000 - $26,182,000
Customer advances balance at the end of 2025 = $16,592,000
Therefore, the remaining customer advance at the end of 2025 is $16,592,000.
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Maddi has a bin shaped like a right prism. She knows that the area of the base of the bin is 14 in² and the volume of the bin is 392 in³.
What is the height of Maddi's bin?
28 in.
33 in.
38 in.
43 in.
Option A. The height of Maddi's bin is 28 inches. We know that the bin is shaped like a right prism, which means that it has a rectangular base and its sides are perpendicular to the base.
The volume of a right prism is given by the formula:
Volume = area of base x height
In this case, we are given that the area of the base is 14 in² and the volume is 392 in³. We can use these values to find the height of the prism.
Substituting the given values into the formula for the volume, we get:
392 = 14 x height
We can solve for the height by dividing both sides of the equation by 14:
height = 392/14
Simplifying this expression, we get:
height = 28
Therefore, the height of Maddi's bin is 28 inches.
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Suppose a game of 3-D tic tac toe is played on a 6x6x6 cube. How many winning lines of 6-in-a-row are there through the cube?
In the word problem , there are 84 winning lines of 6 in a row.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here on each face of a cube, there would be 6 vertical rows , 6 horizontal rows and 2 diagonal rows.
That is total of 14 rows per face.
A cube has 6 faces. Then
=> 6*14 = 84 lines.
Hence there are 84 winning lines of 6 in a row.
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in a group of 150 students 20 are freshmen 30 are sophomores 49 are juniors and 51 are senior if a student is randomly selected what is the probability that we select a sophomore before a freshmen
In a group of 150 students, 20 are freshmen 30 are sophomores 49 are juniors and 51 are seniors if a student is randomly selected the probability that we select a sophomore before freshmen is 2.69%.
So the given data we get from the question is as follows,
Total number of students, N = 150
A number of freshmen students, F = 20
The number of sophomore students, S = 30
Number of junior students, J = 49
Number of senior students, R = 51
We need to find the probability of selecting a sophomore student before a freshman student. The probability that a sophomore student is selected first,
P(S) = Number of sophomore students/Total number of students
= S/N
Probability that a freshman student is selected after a sophomore student,
P(F|S) = Number of freshman students left/Total number of students left
= F/N-1
Where N-1 is used because one student has already been selected.
The probability that a sophomore student is selected first and then a freshman student is selected,
P(S∩F) = P(S) × P(F|S)
= S/N × F/N-1
Therefore, the probability of selecting a sophomore student before a freshman student is:
P(S∩F) = S/N × F/N-1P(S∩F)
= 30/150 × 20/149P(S∩
= 0.0269 or 2.69%
Therefore, the probability of selecting a sophomore student before a freshman student is 0.0269 or 2.69%.
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X =
ML =
M
N
J 6x + 2 K
25
4x - 2
P
H
L
Answer:
x = 5 , ML = 18
Step-by-step explanation:
the midsegment NP of the trapezoid is half the sum of the bases, that is
NP = [tex]\frac{JK+ML}{2}[/tex]
25 = [tex]\frac{4x-2+6x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
50 = 10x ( divide both sides by 10 )
5 = x
Then
ML = 4x - 2 = 4(5) - 2 = 20 - 2 = 18
The table below represents a linear functions. Identify the rate of change of the function.
The linear function changes at a rate of [tex]5/4[/tex]. This implies that [tex]y[/tex] grows by [tex]5/4[/tex] units for every unit increase in [tex]x[/tex].
A linear function is which?The graph of a linear function is a direct line. The following is the form of a linear function. a + bx = y = f(x). One independent variable one and dependent variable make up a linear function.
What is an example of a linear function?A linear relation on the reference system is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) => 3x - 2 since y could be substituted with f(x).
slope = (change in y) / (change in x)
slope [tex]= (1 - (-4)) / (4 - 0)[/tex]
slope [tex]= 5 / 4[/tex]
Therefore, the rate of change of the function is [tex]5/4[/tex]. This means that for every [tex]1[/tex] unit increase in [tex]x[/tex], [tex]y[/tex] increases by [tex]5/4[/tex] units.
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A department store buys 400 shirts at a cost of $10,800 and sells them at a selling price of $30 each. Find the percent markup.
Answer:
11%
Step-by-step explanation:
find the price of the shirts before markup by dividing 10800 by 400
You get 27, which you will subtract 30 by, getting you 3.
Divide this number by 27
.11
What is the interval used in the graph shown below babysitting money
Pls help
Answer:
9
Step-by-step explanation:
1 to 10
Hence,
10 - 1 = 9
Similarly,
20 - 11 = 9
30 - 21 = 9
40 - 31 = 9
Therefore,
Interval is 9
Three friends, Jessica, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 8x^2 - 4xy + 8. The friends have already collected the following number of cans:
Jessa: 5xy + 17
Tyree: x^2
Ben: 4x^2 - 8
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work! (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all you work! (5 points)
(a) The expressiοn that represents amοunt οf canned fοοd cοllected by the three friends = 5x² + 5xy - 9
(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17
What is expressiοn?An expressiοn is a way οf writing a statement with mοre than twο variables οr numbers with οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Example: 2 + 3x + 4y = 7 is an expressiοn.
It is given that,
number οf cans cοllected by Jessa = 5xy + 17
number οf cans cοllected by Tyree = x²
number οf cans cοllected by Ben = 4x² - 8
Part(a)
tοtal number οf cans cοllected by three friends = cans cοllected by Jessa + Tyree + Ben
= 5xy + 17 + x² + 4x² - 8
= 5x² + 5xy - 9
Part(b)
the gοal οf fοοd cans cοllected = 8x² − 4xy + 8
Sο, the number οf fοοd cans still left tο cοllect = gοal - (number οf cans cοllected)
= (8x² − 4xy + 8) - (5x² + 5xy - 9)
= 8x² - 5x² - 4xy − 5xy + 8 + 9
= 3x² - 9xy + 17
Therefοre,
(a) The expressiοn that represents amοunt οf canned fοοd cοllected by the three friends = 5x² + 5xy - 9
(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17
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3y = 5x + 3
x + y = 5
Answer:
substitute the value of y
y=15-x
3(15-x)=5x+3
45-3x=5x+3
-3x-5x=3-45
-2x=42
X=21
Let f x be odd and g(x) is an even function if f(3)=2 and g(-1)=-3 find f(g(1))
the value of the given function f(g(1)) is 2 , fog is an even function
A function f is even if the equation f(x)=f(x) f (x) = f ( x) holds for every x and x in the domain of f. An even function has a graph that is geometrically symmetric with respect to the y-axis, which means that even after reflection about the y-axis, the graph does not change.
f is even (given)
∴f(−x)=f(x)
g is odd (given)
∴g(−x)=−g(x)
So,
According to question,
fog=f[g(x)]=f(y) Let [g(x)]=y
and also,
fog=f[g(−x)] ∵g(x) is odd
=f[−g(x)]
=f(−y)
=f(y)
⇒fog(x)=fog(−x)
∴fog is an even function
f(g(1)) = f(g(1)) = f(3) = 2
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The total value of the loonies and $5 bills in the cash box is $124. there are eight more $5 bills then there or loonies. how many Loonies are there?
Answer:
Step-by-step explanation:
5 added with the 15 is dollars
13. Tumblr's initial IPO was $38 per share. Anjie purchased 616 shares. What was Anjie's cost to purchase the shares?
A. $20,000
OB. $23,408
OC. $23,415
O D. $22,514
Answer:
B) $23,408
Step-by-step explanation:
to find the total cost, we need to multiply the cost per share and the number of shares:
$38 * 616 = $23,408.
[tex]e = [/tex]
What is e=? Now the only thing that problem is the best answer
Now i give you a solution:
It followed from the SPECIAL THEORY OF REIATIVITYVthat MASS and ENERGY are both but different manifestations of the SAME THING a somewhat unfamiliar conception...
Answer:
It appears that the solution you have provided is not a direct answer to the question "What is e=?". However, the statement you provided is a well-known concept in physics, where Einstein's famous equation E=mc² suggests that energy (E) and mass (m) are equivalent and interchangeable, and that they are two different manifestations of the same thing. The constant "c" in the equation represents the speed of light in a vacuum. This concept has had profound implications in the field of physics and has been used to develop nuclear energy and nuclear weapons.
Step-by-step explanation:
Here's a step-by-step explanation of Einstein's famous equation, E=mc²:
The equation E=mc² stands for "energy equals mass times the speed of light squared".
In physics, "energy" refers to the ability of a system to do work, and it is measured in joules (J).
"Mass" refers to the amount of matter in an object and is usually measured in kilograms (kg).
"c" represents the speed of light in a vacuum, which is approximately 299,792,458 meters per second (m/s).
The equation shows that energy and mass are equivalent and interchangeable. In other words, mass can be converted into energy, and energy can be converted into mass.
The conversion factor between mass and energy is the speed of light squared, which is an enormous number. This means that even a small amount of mass can produce a significant amount of energy when it is converted.
The equation has been used to explain a variety of phenomena, such as the energy released in nuclear reactions and the behavior of particles at high speeds.
It has also led to the development of nuclear energy and nuclear weapons, which rely on the conversion of mass into energy.
Overall, E=mc² is a fundamental equation in physics that has had a profound impact on our understanding of the universe and our ability to harness its energy.
The function f(x) is a cubic function and the zeros of f(x) are −5, −4 and −2. Assume the leading coefficient of f(x) is 1 1. Write the equation of the cubic polynomial in standard form.
Answer:
i don't know is correct but here The function f(x)f(x) is a cubic function and the zeros of f(x)f(x) are -5−5, 11 and 55. Assume the leading coefficient of f(x)f(x) is 11
by-step explanation:
choose the correct model from the list. are science textbook too expensive? a student sampled the price of 143 science textbook sold at the college bookstore. can the student reject the claim that the mean cost of science textbooks are no more than $200?
By hypothesis , μ ≤ $200 is the mean cost of science textbooks are no more than $200.
What does "mathematical hypothesis" mean?
A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong. An assertion that will serve as the foundation for hypothesis testing is referred to as a hypothesis in statistics (also known as a statistical hypothesis).
The statement "all fours sides of a quadrilateral measure the same, then the quadrilateral is a square" states that if true, the quadrilateral is a square.
Here n = 143
the claim that the mean cost of science textbooks are no more than $200.
H₀ : μ = $200
H₁ : μ ≤ $200
Therefore, this problem based on one sample t test for mean .
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Please help me with this scale factor problem
9/1 is the simple form in fraction .
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
1st rectangle = 15 * 45 = 675
2nd rectangle = 15 * 5 = 75
1st/2nd = 675/75
= 9/1
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Find the maximum and the minimum values of the objective function (F) =4x-y subject to the following constraints 2x+3y >= 6, 2x - 3y<=6 and y<=2.
Step-by-step explanation:
To find the maximum and minimum values of the objective function subject to the given constraints, we can use the method of linear programming.
Step 1: Convert the inequality constraints into equations by replacing the inequality signs with equality signs and adding slack or surplus variables as necessary to get the equations in the form of standard linear equations.
So the equations become:
2x + 3y + s1 = 6 (where s1 is a non-negative slack variable)
2x - 3y + s2 = 6 (where s2 is a non-negative slack variable)
y + s3 = 2 (where s3 is a non-negative slack variable)
Step 2: Write the objective function F as a linear function of the variables x and y.
F = 4x - y
Step 3: Formulate the linear programming problem in the standard form as follows:
Minimize or maximize F = 4x - y, subject to:
2x + 3y + s1 = 6
2x - 3y + s2 = 6
y + s3 = 2
where x, y, s1, s2, and s3 are non-negative variables.
Step 4: Solve the system of equations to find the feasible region.
We can solve the system of equations using matrix methods to obtain:
x = 3, y = 0, s1 = 0, s2 = 0, s3 = 2
x = 0, y = 2, s1 = 0, s2 = -6, s3 = 0
x = 0, y = 0, s1 = 6, s2 = 6, s3 = 2
x = 2, y = 0, s1 = 0, s2 = 2, s3 = 2/3
x = 1.5, y = 0.5, s1 = 0, s2 = 1.5, s3 = 1.5
x = 0, y = 2/3, s1 = 2, s2 = -2/3, s3 = 0
Step 5: Evaluate the objective function at each corner point to determine the maximum and minimum values.
F(3, 0) = 4(3) - 0 = 12
F(0, 2) = 4(0) - 2 = -2
F(0, 0) = 4(0) - 0 = 0
F(2, 0) = 4(2) - 0 = 8
F(1.5, 0.5) = 4(1.5) - 0.5 = 5.5
F(0, 2/3) = 4(0) - (2/3) = -2/3
Therefore, the maximum value of the objective function is 12, which occurs at the corner point (3, 0), and the minimum value is -2, which occurs at the corner point (0, 2).
6^(2x+1)=8^(x+1)pls solve it for me
The approximated value of x in the equation given as 6^(2x+1)=8^(x+1) is 0.192
Calculating the value of x in the equationFrom the question, the equation is given as
6^(2x+1)=8^(x+1)
Take the logarithm of both sides of the equation
So, we have
(2x + 1)log(6) = (x + 1)log(8)
Divide both sides of the equation by log(6)
So, we have
2x + 1 = (x + 1) * 1.161
So, we have
2x + 1 = 1.161x + 1.161
Evaluating the like terms, we get
0.839x = 0.161
Divide both sides by 0.839
This gives
x = 0.192
Hence, the solution is 0.192
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The coach of a soccer team keeps many stats on her team's performance.
For example, she records if the team was ahead, behind, or tied with the opponent at the end of each half.
Here is a summary of the data she got after 20 games.
End of second
half result
ahead
behind
tied
ahead
behind
tied
ahead
behind
tied
End of first half
result
ahead
ahead
ahead
behind
behind
behind
tied
tied
tied
0
Number of
games
3
4
1
3
2
1
2
3
1
Suppose the coach will continue recording the end-of-half results for 80 more games.
In how many of these 80 games will the team be ahead at the end of at most one of the halves? Use the data to make a prediction.
3
Therefore, based on the given data, we can predict that the team will be ahead at the end of at most one of the halves in 24 of the next 80 games.
What is predict?The term "predict" generally means to make an informed guess or estimate about what might happen in the future based on current information, data, or past trends. In other words, prediction involves using available information to forecast or anticipate an outcome or event that has not yet occurred. Predictions can be made in various fields such as science, economics, weather, sports, and many others. Machine learning and artificial intelligence systems also use predictive models to make forecasts and improve decision-making processes.
by the question.
Based on the given data, we can see that out of the 20 games played so far, the team was ahead at the end of both halves in 3 games, and was ahead at the end of the first half in an additional 3 games. Therefore, the team was ahead at the end of at most one of the halves in a total of 6 out of 20 games.
To predict how many of the next 80 games the team will be ahead at the end of at most one of the halves, we can use the proportion of games from the first 20 games. Specifically, we can calculate:
proportion of games with team ahead at most once = 6/20
predicted number of games with team ahead at most once in next 80 games = (6/20) x 80
predicted number of games with team ahead at most once in next 80 games = 24
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What is the area of a circle with a diameter of 12 meters? leave the answer in terms of π. 6π square meters 12π square meters 36π square meters 144π square meters
To find the area we have to calculate the radius first. Here the radius is 6m. So the area will be 36π m². Option C is the correct one.
Diameter is the straight line connecting two points on the edge of the circle, that passes through the Centre of the circle. It will be equal to two times the radius.
D = 2r
r = D/2 = 12/2 = 6m
Area of a circle can be calculated using the equation πr².
Area = π × 6² = 36π m²
So the area of the given circle with diameter will be 36π m².
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Examine the following equation.
0=−3x^2+5x+9
Which answer can be used to find the solutions to the equation using the quadratic formula?
To solve the quadratic function -3x² + 5x + 9 = 0, the formula that should be used is Option C: x = (-5 ± √133) / -6.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The quadratic formula is used to solve quadratic equations in the form of ax² + bx + c = 0, where a, b, and c are constants.
To use the quadratic formula to solve the equation -3x² + 5x + 9 = 0, we need to identify the values of a, b, and c.
In this case, a = -3, b = 5, and c = 9.
Therefore, we can use these values to plug into the quadratic formula -
x = (-b ± √(b² - 4ac)) / 2a
So the answer that can be used to find the solutions to the equation using the quadratic formula is -
x = (-5 ± √(5² - 4 × (-3) × 9)) / 2 × (-3)
Solving this equation we get -
x = (-5 ± √(25 + 108)) / -6
x = (-5 ± √133) / -6
Therefore, the solution is obtained by the equation x = (-5 ± √133) / -6.
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