In 2011 Clayton Kershaw earned $500,000 pitching for the LA Dodgers. In 2019, his salary was $31,000,000. Answer the three parts below. Clearly show all work and reasoning.
A) Kershaw pitched in 32 games in 2011. What was his salary per game in 2011?
B) He pitched in 28 games in 2019. What was his salary per game in 2019? Round to the nearest cent.
C) Did he earn more per game in 2019 than he did for the entire 2011 season?
Answer:
A. $15,625 per game
B. $1,107,142.86 per game
C. he earned $607,142.86 more per game in 2019 than he did for the entire 2011 season
Step-by-step explanation:
His salary in 2011 = $500,000
His salary in 2019 = $31,000,000
A) Kershaw pitched in 32 games in 2011. What was his salary per game in 2011?
Kershaw's salary per game = Total salary / Total number of games
= $500,000 / 32 games
= $15,625 per game
B) He pitched in 28 games in 2019. What was his salary per game in 2019? Round to the nearest cent.
Kershaw's salary per game = Total salary / Total number of games
= $31,000,000 / 28 games
= $1,107,142.8571428
To the nearest cents
= $1,107,142.86 per game
C) Did he earn more per game in 2019 than he did for the entire 2011 season?
$1,107,142.86 per game - $500,000
= $607,142.86
Yes, he earned $607,142.86 more per game in 2019 than he did for the entire 2011 season
Answer:
A. $15,625 - game
B. $1,107,142.86 - game
C. Kersh earned $607,142.86 more per game in 2019 than he did for the entire 2011 season ($500k)
How many gallons each of 30% alcohol and 5% alcohol should be mixed to obtain 25gal of 25% alcohol?
Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.
We want the total amount to by 25 gal, then we have:
\(x+y=25\)We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:
\(\begin{gathered} 0.3x+0.05y=0.25(25) \\ 0.3x+0.05y=6.25 \end{gathered}\)Hence we have the system of equations:
\(\begin{gathered} x+y=25 \\ 0.3x+0.05y=6.25 \end{gathered}\)To solve the system we solve the first equation for y:
\(y=25-x\)then we plug this value of y in the second equation:
\(\begin{gathered} 0.3x+0.05(25-x)=6.25 \\ 0.3x+1.25-0.05x=6.25 \\ 0.25x=6.25-1.25 \\ 0.25x=5 \\ x=\frac{5}{0.25} \\ x=20 \end{gathered}\)Once we have the value of x we plug it in the expression we found for y:
\(\begin{gathered} y=25-20 \\ y=5 \end{gathered}\)Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.
I need help solving for X
Answer:
x= 10
Step-by-step explanation:
The total measure of this degree is 90, since it's a right angle.
So, the equation would be: 5x+4x= 90.
Step 1- Add common variables.
(5x+4x)= 90
9x= 90
Step 2- Divide 9 to both sides.
9x= 90
9 9
x= 10
Hope this helps! :)
How many cubic centimetres would you place in a tub of water to displace 1 L of water?
1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water
What is conversion of units?Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.
From the information given, we have that;
Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water
So, we have that there is 1 liter of water in the tub
In order to displace, you need to put something in that is the same amount
Now, let's convert the units
1 liter = 1000 cubic cm
Hence, you need 1000 cubic cm to displace 1 liter
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Explain
Design of experiments
(DOE) using a similar example (but not the same) as given in class about
the cake making process?
Design of Experiments (DOE) is a statistical methodology that is used to systematically change input variables or process parameters to discover the effect of these changes on the output variables.
DOE is a critical tool used in the manufacturing industry, pharmaceuticals, and many other sectors. The cake making process is a simple example of how DOE is used. Consider a case where we want to optimize a recipe for a cake mix.
The following are some input factors that might affect the quality of the cake mix:
The response variable for the experiment is cake texture, as it will be measured using the following factors:
After determining the response and input variables, the next step is to identify levels and ranges for the input factors. As an example, we may use the following levels for the input variables:
Amount of butter: 25, 50, 75, 100
Sugar concentration: 20, 30, 40, 50
Egg yolk quantity: 1, 2, 3, 4
Amount of flour: 100, 200, 300, 400
Baking temperature: 150, 160, 170, 180
Mixing time: 5, 10, 15, 20
In a standard DOE, a full factorial experiment is carried out in which every possible combination of the different levels of input variables is tested. The output of each test run is then recorded, and statistical analysis is performed to identify which input variables have the greatest effect on the output variables.
By using DOE, we can optimize the recipe for a cake mix by finding the ideal combination of input variables that result in the best cake texture.
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determine the value of from the plot of log(δ[i−3]/δ) versus log[s2o2−8]0 using data in trials 1, 2, and 3.
The value of m for this experiment will be the same regardless of the units used for δ[i-3]/δ and s2o2-8 for the given oxidation state.
The oxidation state, or oxidation number, of an atom describes the degree of oxidation (loss of electrons) of the atom in a compound. The oxidation state is used to determine oxidation-reduction reactions. Oxygen's oxidation state is -2 in virtually all compounds, with two exceptions: peroxides and superoxides. The oxidation state of O2-2 in peroxides (e.g. H2O2) is -1, and the oxidation state of O2- in superoxides (e.g. KO2) is -1/2.
Logarithmic scales are used to compare very large or very small values that are hard to compare on a linear scale. It is represented as ln. It is the inverse operation of exponentiation using the Euler's number (e) as the base, which is approximately equal to 2.71828.The following formula is used to calculate the slope (m) of a line in a graph:
m = Δy / Δx
Where,Δy is the change in y-axis (vertical) coordinates,Δx is the change in x-axis (horizontal) coordinates.For this experiment, the value of m can be calculated using the graph of log(δ[i-3]/δ) versus log[s2o2-8]0 for trials 1, 2, and 3.
The slope of the line in the graph is equivalent to m. The formula for the slope of the line in the graph can be written as:
m = (y2 - y1) / (x2 - x1)Where (x1,y1) and (x2,y2) are two points on the line
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Tanner is building birdhouses in shop class, and he has a total of 495 nails on hand. A small birdhouse requires 25 nails and a large birdhouse requires 59 nails.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
An inequality in standard form that describes this situation is 25x + 59y ≤ 495.
How to write an inequality that represents this situation?In order to write an inequality that represents or describes this situation, we would assign variables to the number of nails required by the small birdhouse and large birdhouse respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the small birdhouse.Let the variable y represent the large birdhouse.Since Tanner has a total of 495 nails on hand and a small birdhouse requires 25 nails while a large birdhouse requires 59 nails, an inequality that represents or describes this situation can be written as follows;
25x + 59y ≤ 495.
In conclusion, we can reasonably infer and logically deduce that the total number of nails required by both the small birdhouse and large birdhouse is less than or equal to 495 nails.
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Subtract 11b^2-
4b + 7 from b^2 + 8b-9.
Your answer should be a polynomial in standard form.
Answer: -10b^2+ 12b-16
Step-by-step explanation: i just know its right.
The points M, N, O and P all lie on the same line segment, in that order, such that the
ratio of MN NO: OP is equal to 3: 4: 3. If MP = 20, find MN.
Answer: MN=6
Step-by-step explanation:
\(\displaystyle\\MN=\frac{20*3}{3+4+3} \\\\MN=\frac{60}{10}\\\\ MN=\frac{6*10}{10}\\\\MN=6\)
Change each radian measure to degree measure
Answer:
13)60°
14)90°
15)-270°
16)-180°
17)30°
18)150°
19)120°
20)300°
21)210°
22)-315°
23)450°
24)720°
25)-1260
26)-810°
27)45°
28)135°
29)-300°
30)15°
31)1170°
32)-240°
Step-by-step explanation:
of the first 11 questions on a test, a student must answer 7. of the second 5 questions, the student must answer 3. in how many ways can this be done
The number of ways the student answer the questions = 3300
In this question, we have been given that out of the first 11 questions on a test, a student must answer 7. of the second 5 questions, the student must answer 3.
We need to find the number of ways the student answer the questions.
of the first 11 questions on a test, a student must answer 7.
Let n1 be the number of ways this can be done.
n1 = 11C7
n1 = 330
of the second 5 questions, the student must answer 3.
Let n2 be the number of ways this can be done.
n2 = 5C3
n2 = 10
So, the required combination would be,
n = n1 * n2
n = 330 * 10
n = 3300
Therefore, the number of ways the student answer the questions = 3300
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For each of the following scenarios, determine whether the mean or median better represents the data (place a check mark in the appropriate box). For each case, explain why you chose that particular average. The following three scenarios below do not have a specific data set. Be sure to consider all possibilities/outcomes! "Create" a data set if you need to.
In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..
1. Scenario: Income distribution of a population
- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.
2. Scenario: Exam scores in a class
- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.
3. Scenario: Housing prices in a city
- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.
Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.
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6th attempt on posting this question and getting an answer :,)
Help haha..?
Answer:
GCF: (x + 2)(9x + 6)
Step-by-step explanation:
Given the algebraic expression, 9x(x + 2) + 6(x + 2), where the greatest common factor (GCF) must be taken out:
Solution:Since (x + 2) are common between the two groups, then we can group 9x and 6 together.
In other words:
= 9x(x + 2) + 6(x + 2)
= (9x + 6)(x + 2)
If we perform the FOIL method onto (9x + 6)(x + 2), it will result in the following trinomial:
(9x + 6)(x + 2)
= 9x² + 18x + 6x + 12
= 9x² + 24x + 12
Verify Solution:In order to see why this works, let's go back to the original problem, as if we're trying to determine the resulting trinomial:
Given: 9x(x + 2) + 6(x + 2)
Distribute 9x and 6 into the parenthesis:
= 9x² + 18x + 6x + 12
Combine like terms:
= 9x² + 24x + 12 ⇒ As we can see, this trinomial matches our solution.
Therefore, the correct answer is: (x + 2)(9x + 6).
Triangle FUN has vertices located at F(-1,-4) U (3,-5) N(2,6) find the length and slope of UF
Answer:
Slope = - 1/4Length = \(\sqrt{17}\) units---------------------------
Use slope equation:
m(UF) = (-4 - (-5)) / (-1 - 3)m(UF) = 1 / (-4)m(UF) = - 1/4Use distance equation:
\(d(UF)=\sqrt{(-1 - 3)^2+(-4-(-5))^2} =\sqrt{16+1}=\sqrt{17}\)The figure shows the size of a pool. 6 ft 4 ft 16 ft What is the volume of the pool? A. 60 ft³ B. 224 ft3³ 12 ft O C. 1728 ft³ D. 3136 ft³ 8 ft 14 ft h
The volume of the pool is 768 cubic feet.
What is the Volume?
In mathematics, volume refers to the amount of space occupied by a three-dimensional object. It is a measure of the total amount of space enclosed within the boundaries of an object. The volume of an object is usually measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³).
To find the volume of the pool, we need to multiply its length, width, and depth. Looking at the figure, we see that the length of the pool is 16 ft, the width is 6 ft, and the depth is 8 ft.
So, the volume of the pool is:
V = length x width x depth = 16 ft x 6 ft x 8 ft = 768 cubic feet
Hence, the volume of the pool is 768 cubic feet.
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Factor the expression below.
x² - 64
A. (x+3)(x-8)
B. (x-8)(x-8)
C. (x - 16)(x - 4)
D. (x+16)(x-2)
Answer:
(x + 8) (x - 8)
Step-by-step explanation:
To factorise the expression follow the steps:
Think the factorising means you want like:-
( x + _ ) ( x + _ )
Now, add the numbers to get 0 & multiple together to get -64
-64 = 8 x -8
8 + -8 = 0
Now fill the numbers in the factorising mean which will give you,
( x + _ ) ( x + _ ) --> ( x + 8 ) ( x - 8 )
Therefore, the answer will be: ( x + 8 ) ( x - 8 )
I hope this will help you :)
Answer:
b
Step-by-step explanation:
HELP!! Which property is illustrated? 40 POINTS!!
6(5+7)= 6(5)+6(7)
Answer:
42
Step-by-step explanation:
I hope I helped
Answer:
distribute
Step-by-step explanation:
the parenthesis
please help asap!!!!!
Answer:
61% close to 3/5 but its just 61/100
Step-by-step explanation:
First add up all the times rolled in or equal to number 4 rolled
thats 61 now we need to find the total which when added is an even 100 so its a 61% chance
The mean monthly rent of students at Oxnard university is 970 with a standard deviation of 204. John`s rent is 1390. What is his standardized z-score? Is john`s rent an outlier? How high would the rent have to be to qualify as an outlier
Answer:
Standardized z score = 2.06
His house rent is not an outlier
Step-by-step explanation:
The mean monthly rent of students at Oxnard university is 970 with a standard deviation of 204. John`s rent is 1390. What is his standardized z-score? Is john`s rent an outlier? How high would the rent have to be to qualify as an outlier
We solve using z score formula
= z = (x-μ)/σ, where
x is the raw score = 1390
μ is the population mean = 970
σ is the population standard deviation = 204
His z score is calculated as:
z = 1390 - 970/204
z = 2.06
No his house rent is not an outlier
what is the circumference of the circle of parallel of latitude 40°
Answer:
The circumference of a circle with a latitude of 40 degrees is 251.33
WET TEDDY BEARS, GET YOUR WET TEDDY BEARS
(Liberty Mutual)
Step-by-step explanation:
Hell yes, I'll take 5 please
Answer:
Yes! Wet teddy bears are fire! I'll take 4, pls!
Step-by-step explanation:
help pls
15. In a parallelogram ABCD, AB = 7.2 cm and the perpendicular from Con<br />AB is 4.5 cm find its area.
Answer: The area of the parallelogram ABCD = 32.4 sq. cm
Step-by-step explanation:
Given: In parallelogram ABCD, AB = 7.2 cm and the perpendicular drawn from C (altitude) on AB is 4.5 cm i.e.e height =4.5 cm.
Area of parallelogram = \((Base \times height)\)
Then, Area of parallelogram ABCD = \(7.2\times4.5\)
= \(32.4\ cm^2\)
Therefore , the area of the parallelogram ABCD = 32.4 sq. cm
etermine the an so that the equation [infinity] n=1 nan xn−1 2 [infinity] n=0 an xn = 0 is satisfied. try to identify the function represented by the series [infinity] n=0 an xn.
The value of an depends on the exponents and the pattern of the series. By identifying the conditions that satisfy the equation, we can determine the specific values of an. The function represented by the series is an alternating series based on the pattern observed.
To determine the value of an that satisfies the equation ∑[n=1 to ∞] an xn-1 + ∑[n=0 to ∞] an xn = 0, we need to analyze the coefficients and exponents of the series.
By examining the terms in the equation, we can identify a pattern that allows us to find a solution for an. The function represented by the series ∑[n=0 to ∞] an xn can then be determined based on the values of an and the corresponding exponents.
The equation can be rewritten as ∑[n=1 to ∞] an xn-1 + an xn = 0. Notice that the terms involving xn-1 and xn have a common factor of an. Factoring out an, we get an(xn-1 + xn) = 0. For this equation to hold true for all values of x, either an = 0 or xn-1 + xn = 0.
If an = 0, then it does not contribute to the series. However, if xn-1 + xn = 0, we can solve for xn-1 = -xn. This suggests that the function represented by the series is an alternating series, where the terms alternate between positive and negative values.
In summary, the value of an depends on the exponents and the pattern of the series. By identifying the conditions that satisfy the equation, we can determine the specific values of an. The function represented by the series is an alternating series based on the pattern observed.
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The value of a professional basketball player's autograph rose 10% in the last year. It is now worth $286.00. What was it worth a year ago?
What is the value of the expression 20 ÷ 4 + (6 x 2) − 2?
15
17
22
28
Yolanda has quarters, Q, and dimes, D, in her coin jar. She has a total of 31 coins.
The total amount of money in the jar is $4.75\$4.75$4.75 . Write two equations that could be used to find the number of quarters and the number of dimes in the jar.
Solve the equations to find out how many quarters and
how many dimes Yolanda has in her jar.
Answer:
11 Quarters 20 Dimes
Step-by-step explanation:
Q+D=31
25Q +10D = 475 (miltiplied all by 100 to avoid decimals)
Multiply the first by -10(to eliminate D)
-10Q - 10D = - 310
25Q+10D = 475
ADD BOTH( D will cancel)
15Q = 165
Q= 11
31-11 =20 (dimes =20)
11x0.25 = 2.75
20x0.10=2
2.75+2 = $4.75
Considerable research is being done in bioremediation - the use of living organisms to clean up pollution. In a recently conducted experiment, researchers used fungi to degrade hydrocarbons, the by-products of incomplete combustion of fossil fuels. These by-products can cause cancer, and their accumulation in water and soil poses an environmental hazard. 0.83 0.91 1.00
1.08 1.08 1.09
1.10 1.23 1.36 In order to be cost-effective, a minimum of 1.00 micromoles/minute/gram of soil of a particular hydrocarbon must be degraded. The researchers added fungi and growth media (essentially sugar) to the soil in 9 containers with random samples of soil and obtained the following degradation rates in micromoles/min/gram:
(a) The sample mean =1.076 and the sample standard deviation=0.158. Calculate and interpret the standard error of the mean for these data.
(b)Construct and interpret a 90% confidence interval for the mean degradation rate. Can the researchers be confident that this process will be cost-effective?
Standard error of the mean is 0.05267 in (a). The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to (b).
What does standard error mean?The group mean's likelihood to vary from a sampling distribution is indicated by the standard deviation of a mean, or merely standard error. It reveals how much is the sample imply would change if a research were to be repeated with fresh samples drawn from a particular population.
(a)
Sample size, n = 9
Sample standard deviation, S = 0.158
Standard error of the mean,
\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)
(b)
Since we do not know the distribution of the parent population or the population standard deviation, and further the sample size, n = 8 < 30,
Therefore we will use the t-distribution to construct the confidence interval for the true population mean α
Sample size, n = 9
Sample mean, r = 1.076
Sample standard deviation, S = 0.158
Standard error of the mean,
\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)
Level of confidence, c (in percentage) = 90
α = (1-(c/100) = 0.1
Degrees of freedom, df = n-1 = 9 - 1 = 8
The critical t-score, \(\mathrm{t}_{\mathrm{c}}\) is the
t-score corresponds to the given level of confidence and degrees of freedom :
\(\begin{aligned}& P\left(x > t_{d f}\right)=\Rightarrow / 2 \\& \Rightarrow \\& P\left(x > t_8\right)=0.1 / 2=0.05 \\& \Rightarrow t_c=1.86\end{aligned}\)
The confidence interval is calculated as:
\(\mathrm{Cl}=\bar{x} \pm\left(\mathrm{t}_{\mathrm{c}}\right)^*\left(\sigma_{\bar{x}}\right)\)
= 1.076 ± (1.86)*(0.05267)
= 1.076± 0.098
= (1.076 - 0.098, 1.076 + 0.098)
= (0.978, 1.174)
The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to this information.
The mean degradation rate must be higher than 1 for the process to be cost-effective.
However, because the 90% confidence interval does not completely fall above 1, the experts cannot be certain that the process will be cost-effective.
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Solve for c law of sines
Answer:
c/sin(60°) = 14/sin(25°)
c = 14sin(60°)/sin(25°) = 28.7
2. find out the h.c.f
2a , 1st exp= a2 + ab
= a(a+b)
2nd exp = a2-b2
= (a+b) (a-b)
HCF = (a+b)
b, 1 st exp= (a+b)2
= (a+b)(a+)
2 nd exp = a2-b2
= (a+b) ( a-b)
HCF = (a+b)
c, 1 st exp= (a-1)2
= (a+1) (a-1)
2nd exp= a2-1
= (a+1)(a-1)
HCF = (a-1)
d, 1st exp= (x-2)(x-3)
= x(x-3)-2(x-3)
= x2 - 3x - 2x + 6
= x2- 5x+ 6
= x2 - (3+2)x + 6
=x2 -3x-2x+ 6
= x(x-3) -2(x-3)
=(x-3)(x-2)
2 nd exp = (x+2) (x-3)
= x( x-3) + 2 (x-3)
= x2 - 3 x+ 2x -6
= x(x-3) + 2(x-3)
=(x-3) ( x+ 2)
HCF = (x-3)
int \( a[4]=\{1,2,3,4\} \) int \( { }^{*} p=a \); What is the value of \( *(p+3) ? \)
The value of the expression is 4.
The code :
int a[4] = {1, 2, 3, 4};
int *p = a;
what is *(p + 3)?
The variable a is an array of integers, and the variable p is a pointer to the first element of the array.
The expression *(p + 3) is the value of the element of the array that is 3 elements after the element that p points to.
Since p points to the first element of the array, the expression *(p + 3) is the value of the fourth element of the array, which is 4.
Therefore, the value of the expression is 4.
Here is a breakdown of the code:
int a[4] = {1, 2, 3, 4}: This line declares an array of integers called a and initializes it with the values 1, 2, 3, and 4.
int *p = a; This line declares a pointer to an integer called p and initializes it with the address of the first element of the array a.
what is *(p + 3)?: This line asks what the value of the expression *(p + 3) is.
The expression *(p + 3) is the value of the element of the array that is 3 elements after the element that p points to.
Since p points to the first element of the array, the expression *(p + 3) is the value of the fourth element of the array, which is 4.
Therefore, the value of the expression is 4.
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Correct Question :
Int a[4]={1,2,3,4}, int *p=a. What is the value of *(p+3)?