The formula to calculate the magic number in MLB is: Magic number = 163 - (number of wins by leading team) + (number of losses by trailing team) - 1.
The "magic number" in Major League Baseball (MLB) represents the combination of wins by the leading team and losses by the trailing team required for the leading team to clinch a playoff spot. To calculate the magic number, follow these steps:
1. Determine the total number of games in the season. In MLB, this is typically 162 games.
2. Subtract the number of games in the season from 163. For example, 163 - 162 = 1.
3. Subtract the number of wins by the leading team from 163. For example, if the leading team has 90 wins, 163 - 90 = 73.
4. Add the result from step 2 to the result from step 3. For example, 73 + 1 = 74.
5. Finally, subtract the number of losses by the trailing team from the result of step 4. For example, if the trailing team has 80 losses, 74 - 80 = -6. In this case, the magic number is zero, meaning that the leading team has already clinched a playoff spot.
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Name
Period
Practice
Example 1
FINANCE Caldonia deposits $150 into an account that pays 7.3% annual interest compo
quarterly.
1.
GO Practice S
a. Write an equation to represent Caldonia's account balance after t years.
b. Write and use a system of equations to determine how many years it will take for the
account reach $200. Round to the nearest year.
It takes for the account to reach $200 is 4 years.
What is Compound Interest?Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.
Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.
[tex]A = P(1 +\frac{r}{n})^n^t[/tex]
where:
A = the total account balance after t years
P = the initial deposit $150
r = the annual interest rate =0.073
n = the number of compounding periods per year, which is 4 (quarterly) in this case
t = the number of years the money is in the account
Now let us substitute the values
[tex]A = 150(1 + \frac{0.073}{4} )^4^t[/tex] is the equation to represent Caldonia's account balance after t years.
Now let us determine the number of years it will take for the account to reach $200.
[tex]200 = 150(1 + \frac{0.073}{4} )^4^t[/tex]
200=150(1+0.01825)^4t
[tex]1.333=1.018^4^t[/tex]
Take log on both sides
log1.333=4tlog(1.018)
0.1248=4t 0.0077
0.1248=0.0309t
Divide both sides by 0.0309
t=4.038
Hence, it takes 4 years to reach account balance of $200
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The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides.
The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.
The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.
To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.
The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.
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Dominique is selling merchandise for a school fundraiser. she is selling calendars for $8 each and coffee mugs for $10 each. she must sell at least $600 of merchandise, including at least 40 calendars, to meet her goals. if x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario? 8x 10y > 600 and y > 40 8x 10y > 600 and x > 40 8x 10y ≥ 600 and y ≥ 40 8x 10y ≥ 600 and x ≥ 40
By answering the given question, we may state that Hence, the interest appropriate response is X = 40 and 8x + 10y = 600
what is interest ?Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to calculate interest. The most typical technique to figure out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a friend and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.
Selling x calendars will cost 8x, while selling y mugs will cost 10y. The scenario is therefore represented by the following system of inequalities in order for her to reach her objective of selling at least $600 worth of stuff, including at least 40 calendars:
(Total cost of goods sold must be at least $600; 8x + 10y)
x ≥ 40 (must sell at least 40 calendars) (must sell at least 40 calendars)
In the first inequality, you'll see that we used the symbol "" rather than ">" since Dominique needs to sell at least $600 worth of goods, not just more than $600.
Hence, the appropriate response is
X = 40 and 8x + 10y = 600
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Your company manufactures hot water heaters. The life spans of the products are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years.
a) You are buying a new hot water heater, based on the information in the problem, between how many years would you expect your hot water heater to last. (Give a range of numbers). Explain your answer.
b) You want to set the warranty on your product so that you have to replace at most 5% of the hot water heaters that you sell. How many years should you claim on your warranty? (Round answer to nearest whole number of years.) Explain your answer.
we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell.
What is mean ?
Mean can be defined as the ratio of sum of the given observations and total number of observations.
a) Since the life spans of the hot water heaters are normally distributed with a mean of 13 years and a standard deviation of 1.5 years, we can use the empirical rule to estimate the range of years we would expect the hot water heater to last. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
Using this information, we can estimate that the range of years we would expect the hot water heater to last is approximately 10.5 to 15.5 years. This is because one standard deviation below the mean is 13 - 1.5 = 11.5 years, and one standard deviation above the mean is 13 + 1.5 = 14.5 years. Therefore, we can reasonably expect the hot water heater to last between 10.5 and 15.5 years with about 95% confidence.
b) To set the warranty on the product so that we have to replace at most 5% of the hot water heaters that we sell, we need to find the number of years that corresponds to the 5th percentile of the distribution. This is the value below which 5% of the data falls.
We can use a standard normal distribution table or a calculator to find the z-score corresponding to the 5th percentile, which is -1.645. We can then use the formula z = (x - mu) / sigma to find the number of years, x, that corresponds to this z-score.
-1.645 = (x - 13) / 1.5
Solving for x, we get x = 10.83 years.
Therefore, we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell
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Work out the length x in the triangle below. If your answer is a decimal, give it to 1 d.p.
area = 42 m²
Answer:
The length of side x in the given triangle is 12 m.
Step-by-step explanation:
To calculate length x in the given triangle, use the Area Sine Rule.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area Sine Rule} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]
The given values are:
a = 14 mb = xC = 30°A = 42 m²Substitute the given values into the formula:
[tex]\implies 42=\dfrac{1}{2} \cdot 14 \cdot x\cdot \sin30^{\circ}[/tex]
Multiply 1/2 · 14 = 7:
[tex]\implies 42=7x\sin30^{\circ}[/tex]
Divide both sides of the equation by 7:
[tex]\implies 6=x\sin30^{\circ}[/tex]
Calculate sin30°:
[tex]\implies 6=\dfrac{1}{2}x[/tex]
Multiply both sides of the equation by 2:
[tex]\implies 12=x[/tex]
Therefore, the length of side x in the given triangle is 12 m.
A 2-column table titled f (x + 1) = 4 (f (x)) has 5 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5. Column 2 is labeled f (x) with entries 4, a, b, c, 1,024. What are the missing values in the table representing the recursively defined geometric sequence? a = b = c =.
Answer:
16, 64, 256
Step-by-step explanation:
Two sprinters, nick and ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10. 8 seconds, and his team has a mean time of 11. 4 seconds and a standard deviation of 0. 4 seconds. Ryan has a time of 11. 2 seconds, and his team has a mean of 11. 5 seconds and a standard deviation of 0. 1 seconds. Who has the faster time when compared to each of their teams?.
Ryan has the faster time when compared to each of their teams,
"Information available from the question"
The time taken by Nick is 10.8 seconds.
The mean time taken by Nick is 11.4 seconds.
The standard deviation of Nick is 0.4 seconds.
The time taken by Ryan is 11.2 seconds.
The mean time taken by Ryan is 11.5 seconds.
The standard deviation of Ryan is 0.1 seconds.
The z-score of Nick is:
[tex]z_1=\frac{10.8-11.4}{0.4}[/tex]
[tex]z_1=-1.5[/tex]
The z-score of Ryan is:
[tex]z_2=\frac{11.2-11.5}{0.1}[/tex]
[tex]z_2=-3[/tex]
Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams.
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Holly picks 125 she spends 35 on gas for her car
which model represtant how much money holly spent
The second option is the correct representation of the given context.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number.
The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
Look at the model, it starts at 125 and drops to 90.
If she has $125 and spends $35 on gas, the remaining balance is reduced by that amount.
125 - 35 = 90.
Q. Holly has $125 she spends $35 on gas for her car which model represents how much money holly has left?
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Can you please find the exact value of X?
Answer:
10[tex]\sqrt{50}[/tex]
Step-by-step explanation:
Since it's a isosceles right triangle, so
x^2+x^2=100^2
2x^2=10000
x^2=5000
x=[tex]\sqrt{5000}[/tex]=10[tex]\sqrt{50}[/tex]
A regular hexagon has six congruent sides. If the length of each side is represented by the expression 7x+4. What expression is equivalent to the perimeter of the figure
Answer:
42x + 24
Step-by-step explanation:
6(7x + 4)
42x + 24
I need some help please
Answer:
[tex]x = - \frac{2}{9} [/tex]
Answer: [tex]\text{x} = \boldsymbol{-\frac{2}{9}}[/tex]
2 goes in the green box up top
9 goes in the gray box down below.
=========================================
Work Shown:
[tex]-2(4+3\text{x}) = 3(\text{x}-2)\\\\-8-6\text{x} = 3\text{x}-6\\\\-6\text{x}-3\text{x} = -6+8\\\\-9\text{x} = 2\\\\\text{x} = \boldsymbol{-\frac{2}{9}}\\\\[/tex]
A letter in the word ACCEL is chosen 50 times. Results are shown in the table below
What is the experimental probability of choosing a C?
Answer:
Step-by-step explanation:
C is chosen 12 times (7 + 5)
You have 50 total picks.
So the experimental probability is 12/50.
Value of T please and thank you !!!!
the value of "t" will be 28 degrees for the given circle.
What are the properties of a circle?The following four properties and their proofs were introduced:
1: The angles at the center and at the circumference of a circle are subtended by the same arc.
2: Angles at the circumference are subtended by a diameter.
3: Angles at the circumference of a circle subtended by the same arc.
Given, a circle with an angle between two secants of 28 degrees.
From the intersecting Secant theorem of a circle:
The angle between secant = bigger arc -smaller arc)/2
In our case,
28 = (3t -t)/2
2t/2 = 28
t = 28
therefore, the value of "t" will be 28 degrees for the given data.
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Classify the following triangle check all that apply 36,8.68,7,54,5.1
We can see that the triangle is given as one of the angles is 90 degrees . The triangle is a right-angle triangle, and scalene also.
What is a right-angled triangle?A right-angled triangle is a triangle having one of its angles with measure of 90°
The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.
We can see that the triangle is given as one of the angles is 90 degrees and the other two angles are 36 and 54 degrees.
If one of the angles is 90° then the triangle is a right-angled triangle.
Also, the length of the two sides is given as 8.66 units and 5.1.
We have already concluded that the triangle is a right-angle triangle, so all the three sides of the triangle must be different.
This implies that the triangle is scalene also.
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You pick a card at random.
4 5
6 7 8 9
What is P(5)
Write your answer as a percentage.
Total cards = 4 (6,7,8,9), If the card is not 9, the required card will be (6,7,8), Number of cards that are not 9 is 3, Probability = expected/total P( 5) = 3/4 and the probability of picking 5 is 16.67%.
What is Probability?
The probability of an occurrence is a number used in science to describe how likely it is that the event will occur. It is stated as a number between 0 and 1, or, when using percentage notation, in the range between 0% and 100%.The higher the probability, the more likely it is that the event will occur. The probability is typically expressed as the proportion of positive outcomes to all outcomes in the sample space.It is written as Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).Simple probability calculations can be done by adding the probabilities together.Calculating a result or the likelihood that an event will occur is known as simple probability.Probability statistics are used by insurance firms to estimate the likelihood of having to pay out a claim. A simple probability is computed by dividing a particular event by all potential outcomes.There are a total of 6 numbers in the grid, and only one of them is 5. Therefore, the probability of selecting 5 is:
P(5) = 1/6
To write this as a percentage, we multiply by 100:
P(5) = 1/6 * 100% = 16.67%
Therefore, the probability of picking 5 is 16.67%.
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is (bc^2)/a^3b^2c^-2*(2a^-4b^3c^-4)^4 equal to (16c^20/a^13b^13)
Answer: No.
Step-by-step explanation: Unless I read and calculated wrongly, it should be equal to 2b^4/(a^3b^2c^2-2)a^4c^2 -1/256
Please help quick I don’t have much time!!!
The missing values in table should be completed as follows;
X(input) Y(output)
10 19
12 23
Rule: y = 2x - 1.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (3, 5), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:
y - 5 = (11 - 5)/(6 - 3)(x - 3)
y - 5 = 6/3(x - 3)
y = 2(x - 3) + 5
y = 2x - 1
When x(input) = 10, the y(output) is given by:
y = 2x - 1
y = 2(10) - 1
y = 20 - 1
y = 19.
When y(output) = 23, the x(input) is given by:
y = 2x - 1
23 = 2x - 1
2x = 24
x = 12.
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Build subtraction equations using the indicated
18-x-x-x=0
x=6 is the solution to the equation 18 - x - x - x = 0.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
One way to build a subtraction equation using the indicated expression is:
18 - x - x - x = 0
Add the like terms
18 - 3x = 0
Now let us solve for x
we can isolate x on one side of the equation by subtracting 18 from both sides:
-3x = -18
Divide both sides by -3 to find the value of x:
x = 6
Therefore, a solution to the equation 18 - x - x - x = 0 is x = 6.
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which equation has a slope of -1 and passes through the point (4,-5)
Answer:
y = -x - 1
Step-by-step explanation:
y = mx +c
y = -x + c [ m = slope]
As the line passes through (4,-5)
-5 = -4 + c [Substituting value of x and y]
c = -1 [Solving the above equation]
a ramp 46 ft long rises to a platform. the bottom of the platform is 20 fr from the foot of the ramp. Find x, the angle of elevation of the ramp
The angle of elevation is 66.50 degrees
How to determine the angle of elevationFrom the question, we have the following parameters that can be used in our computation:
Rise = 46 ft
Length = 20 ft
The angle of elevation, x is calculated as
tan(x) = 46/20
Evaluate
tan(x) = 2.3
Take the arc tan of bth sides and evaluate
x = 66.50
Hence, the angle is 66.50 degrees
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how many possibilities are there for a four digit pin where no digit is repeated?
The total number of possibilities for four digit pin with the condition of no digit is repeated is equal to 5040.
Total number of digit used to form pin = 4
Condition is : No digit is repeated.
Number of digits are :
( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )
Total digits are = 10
Number of possibilities to form four digit pin with no digit repeated
= ¹⁰P₄
= ( 10! ) / ( 10 - 4 )!
= ( 10 × 9 × 8 × 7 × 6! ) / 6!
= 10 × 9 × 8 × 7
= 5040
Therefore, the total number of possibilities to form four digit pin with the given condition is equal to 5040.
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What are the outliers of the data set?
13, 24, 25, 25, 25, 26, 27, 27, 27, 28, 36
Select EACH correct answer.
A helicopter flying a search pattern flies 2
miles in a straight line, turns 90°
left, flies 1
more mile, then turns and returns to its starting location. What is the total distance flown to the nearest tenth of a mile?
Answer:
Total distance flown = 5.2 miles
Step-by-step explanation:
The path of the helicopter is that of a right triangle with the first stretch of 2 miles as one leg and the other stretch 90° left as the other leg.
The return trip direct to starting point is the hypotenuse of the right triangle
By the Pythagorean theorem if c is the hypotenuse and a, b are the two legs
c² = a² + b²
Letting a = 2mi and b= 1mi,
c² = 2² + 1²
c² = 4 + 1
c² = 5
c = √5 (only positive square root considered)
c =2.236 mi
c = 2.236 mi to the nearest tenth
Total distance = 2 + 1 + 2.236
= 5.236
= 5.2 mi to the nearest tenth
Solve the system of equations.
x + y = 8
y = x2 – 4
(3,5) and (-4,12)
(-3,11) and (4,4)
(4,4) and (5,3)
(12,-4) and (7,1)
Answer:
A) [tex](3,5)[/tex] and [tex](-4,12)[/tex]
Step-by-step explanation:
[tex]x+y=8\\x+(x^2-4)=8\\x^2+x-4=8\\x^2+x-12=0\\(x-3)(x+4)=0\\x_1=3,\,x_2=-4\\\\x_1+y=8\\3+y=8\\y_1=5\\\\x_2+y=8\\-4+y=8\\y_2=12[/tex]
Can one report both student T test and Mann-Whitney U test to denotes significant difference ?
Yes, both tests can be reported to denote a significant difference. The T-test is used for normally distributed data, whereas the Mann-Whitney U test is used for non-normally distributed data.
Yes, both the Student's T-test and the Mann-Whitney U test can be used to denote a significant difference. The Student's T-test is used to compare the means of two normally distributed samples and determine if the difference in means is statistically significant. The Mann-Whitney U test is used to compare the means of two non-normally distributed samples and determine if the difference in means is statistically significant. Both tests are used to test the null hypothesis that the means of the two samples are the same. If the null hypothesis is rejected, it can be concluded that the difference between the means is statistically significant. Both tests provide a measure of the strength of the evidence against the null hypothesis, which can be used to determine if the difference between the means is significant.
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PLEAS ONLY ANSWER IF YOU KNOW
The missing reasons for the proof are given as follows:
1) AB/DB = CB/EB - Given
2) ∠ABC ≅ DBE - Opposite Angles
3) ΔABC ~ ΔDBE - Angle - Side - Side Postulate.
What does the Angle - Side - Side Postulate say?
The Angle-Side-Side (ASA) Postulate states that if two angles and a side of one triangle are congruent to two angles and the corresponding side of another triangle, then the two triangles are congruent.
In other words, if two triangles have the same orientation and their corresponding angles and sides match in size, the two triangles are identical. The ASA Postulate can be used to determine the congruence of triangles and to prove theorems and solve problems in geometry and related fields.
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Which relation is NOT a function?
{(10, –4), (–10, 14), (14, –10)}
{(–4, –10), (–2, –4), (–10, –1), (–1, –7), (1, 10), (–3, –1)}
{(–4, 10), (14, 3), (15, 14), (10, 3)}
{(11, 16), (12, 14), (14, 14), (11, 13), (21, 12)}
{(11, 16), (12, 14), (14, 14), (11, 13), (21, 12)}
This is because the the number 11, an x-value, is used twice and if an x-value is used more than once then it is not a function. A function is a relation between sets where there is only one output for each input
Which unit of measurement is part of the metric system?
O pound
Oliter
O quart
O foot
PQRS is parallelogram. If PS = 15, then QR =
Answer:
QR = 15
Step-by-step explanation:
Opposite sides of parallelograms are congruent. This means that their lengths are the same.
Hence,
PS = 15 = QR.
The table of values represents a linear function.
X Y
-2. 1
0. -9
2. -19
4. -29
6. -39
Complete the equation below to represent the function defined by the table in the form
y = mx + b.
Answer:
5 mx plus b which you have to do 5 plus m to get 5m which is ur answer