Answer:
Hank had a z-score of -1.375.
Jane had a z-score of -2.39.
Jane had the better year relative to their peers, due to her lower z-score.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Hank:
ERA of 3.36. For the males, the mean ERA was 4.449 and the standard deviation was 0.792. This means that we have to find Z when [tex]X = 3.36, \mu = 4.449, \sigma = 0.792[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.36 - 4.449}{0.792}[/tex]
[tex]Z = -1.375[/tex]
Hank had a z-score of -1.375.
Jane
ERA of 3.49. For the females, the mean ERA was 5.091 and the standard deviation was 0.669. This means that we have to find Z when [tex]X = 3.49, \mu = 5.091, \sigma = 0.669[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.49 - 5.091}{0.669}[/tex]
[tex]Z = -2.39[/tex]
Jane had a z-score of -2.39.
Which player had the better year relative to their peers, Hank or Jane
Low ERA is good, high is bad. This means that whoever had the lower z-score had the better year, and in this case, it's Jane
Energy is generated from solar & wind power. Solar power must be at most 6 units/day or the panels will burn out. Wind must be strong enough to power 1 unit/day or else the turbines won’t turn. The wind power must be less than twice the solar power less one, or the batteries won’t charge properly.
Find the optimal production of wind and solar that will maximize overall power output.
The optimal production of wind and solar that will maximize overall power output is 3 units/day of solar power and 2 units/day of wind power.
How to determine the optimal productionTo solve this question, we use the following representations
Let x be the amount of solar power generated y be the amount of wind power generated.So, the objective function is to maximize z = x + y, which represents the overall power output.
From the question, we have the following constraints:
x <= 6 (solar power must be at most 6 units/day)y >= 1 (wind power must be strong enough to power 1 unit/day)y <= 2x - 1 (wind power must be less than twice the solar power minus one)Using the Lagrangian function, we have:
L(x,y,λ1,λ2,λ3) = x + y + λ1(6-x) + λ2(y-1) + λ3(2x-y-1)
To find the optimal solution, we need to find the values of x, y, λ1, λ2, and λ3 that will make the partial derivatives of L equal to zero:
∂L/∂x = 1 + λ3 = 0
∂L/∂y = 1 - λ1 + λ2 + λ3 = 0
Using the variables x and y, we have
∂L/∂λ1 = -x + 6 = 0
∂L/∂λ2 = y - 1 = 0
∂L/∂λ3 = 2x - y - 1 = 0
Using a graphing calculator, the points that maximize the objective function are:
x = 3 and y = 2
i.e.
Power output is 3 units/day of solar power and 2 units/day of wind power.
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In a bag of marbles, 12% were red, 16% were blue, and the rest are white. If the bag has 250 marbles how many were red or blue
Answer: 70
Step-by-step explanation: First, let's find how many are worth each in numbers. Use this formula:
Part Percent * Whole number / 100
Plug in the numbers:
Red = 12 * 250 / 100
3000/100
= 30 red marbles
Blue = 16* 250 / 100
4000 / 100
= 40 blue marbles
40 + 30 = 70
White = 250 - 70
= 180 white marbles
We can check our answer by adding 12 + 16. That's 28. So by multiplying 250 by 28, we get 7000. 7000 divided by 100 = 70
70 = 70
Therefore, both statements are true
I hope this helped!
A line passing through the point (0, 4) has a slope of-2. Write the equation of the line in point-slope form.
Answer:
[tex]y-4=-2(x-0)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of -2, and contains the point (0,4).
We want to write the equation of the line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
SolvingSince we are already given the slope, we can immediately plug it into the formula.
Substitute -2 as m.
[tex]y-y_1=-2(x-x_1)[/tex]
Now, let's label the values of our points to avoid confusion and mistakes.
[tex]x_1=0\\y_1=4\\[/tex]
Substitute into the formula.
[tex]y-4=-2(x-0)[/tex]
Topic: point-slope form
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-8r-3(-6-5r)=8-5(4-2r)
Answer:
the answer I got was 18 over 1657
Step-by-step explanation:
its a fraction so the numerator is 18 and the denominator is 1657
(Multi-Step Linear Equations MC)
Determine the value of x in the equation.
three fourths times the quantity x plus 6 end quantity minus one fourth times x equals two fourths times the quantity x plus 9 end quantity
A: x = 1
B: x = 2
C: No solution
D: Infinite solutions
Answer: To solve this equation, we need to get x on one side of the equation and all the other terms on the other side.
We can start by combining like terms:
three fourths times the quantity x plus 6 end quantity minus one fourth times x equals two fourths times the quantity x plus 9 end quantity
3/4 * x + 3/4 * 6 - 1/4 * x = 2/4 * x + 2/4 * 9
3/4 * x - 1/4 * x + 3/2 = 2/4 * x + 9/2
1/2 * x + 3/2 = x + 9/4
then we can move x to the left side of the equation:
x = x + 9/4 - 3/2
x = 9/4
So the value of x is 9/4.
The answer is A: x = 1.
This is a unique solution, it means that there is only one value of x that satisfies the equation.
Step-by-step explanation:
Before the 1936 US president election, a popular poll predicted that Alfred Landon would
The correct option is a. Bias from undercoverage, is best description of the term bias.
Define the term bias from undercoverage?When you remove a portion of the population from your sample, undercoverage bias develops.
Sample isn't any longer indicative of the intended population as a result. This kind of study bias can affect non-probability sampling designs.Undercoverage bias as well as nonresponse bias may appear to be identical, but they differ greatly.
Undercoverage bias happens when certain demographic members are completely left out of the questionnaire survey you utilise for your investigation.When some of the respondents you chose to be included in your sample don't answer, nonresponse bias develops.For the stated question-
Roosevelt received support from lower-income voters and ultimately won with 62% of the vote, one of the biggest margins of victory in US presidential election history.
Thus, this clearly shows the bias from undercoverage.
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The complete question is-
Before the 1936 US presidential election, a popular poll predicted that Alfred Landon would comfortably win against Franklin D. Roosevelt. The poll randomly sampled people from sources like telephone and car registration records, but the country was in an economic crisis, so many voters without those luxuries were not included in the poll. Voters with lower incomes favored Roosevelt, who ultimately won with 62%, percent of the vote—one of the largest margins of victory ever in a US presidential election. Which type of bias does this scenario best describe?
a. Bias from undercoverage
b. Bias from using voluntary response
c. Response bias
d. Nonresponse bias
Use the table to write a linear function that relates y to x .
From the table given a linear function that relates y to x is y = -7.
What is point - slope form of line?
The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
The point - slope form of line is y - y1 = m(x - x1).
From the given table of values we have to find the linear function that relates y to x.
First to find the slope.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-7-(-7)}{0-(-2)} = \frac{0}{2} = 0[/tex]
Now consider the point - slope form of line,
y - y1 = m(x - x1).
y - (-7) = 0(x - 0)
y + 7 = 0
y = -7
Hence, from the table given a linear function that relates y to x is y = -7.
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(PRE CALC) Which graph shows the function f(x)=−ln(x−1)
Jase uses a rope as the circumference of a circle on the playground. If the rope is 6 meters long, what is the area of the circle in square
meters? Use x = 3. 14. Round to the nearest hundredth as necessary.
Answer:
279.05649m³
Step-by-step explanation:
Circumference = 2πr
6 = 2πr
6/2π = r
r = 9.424777961
Area = πr²
Area = π(9.424777961²)
Area = 279.05649m³
Maysol made 75 bracelets this month.
Last month she made 40 bracelets.
What is the percent of change
There is a 46.7% increase in the number of bracelets made.
What is Percentage?A percentage is a number or ratio that can be expressed as a fraction of 100 (100 as denominator). To calculate percent of a number, divide the number by the whole and multiply by 100.
Hence, it means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Maysol made;
This month = 75 bracelets
Last month = 40 bracelets
Change = 75 - 40
Change = 35
This means there was an increase
% increase = (35/75) x 100
% increase = 46.7%
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3+4 (r-6)=3(2+2r) 7r show work please
By solving the equation The answer is -27+17r .Because the Given question is a Equivalent Equation
Explanation3+4(r-6)= 3(2+2r)+7r
3+4r-24=6+6r+7r
3-6-24+4r+6r+7r
-24+17r
What is equivalent Equation?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
If two equations have the same solution, they are equivalent.
Equations that are equivalent can be created by adding, subtracting, multiplying, and dividing by the same number on either side of the equal sign.
Distribute the coefficients Combine any like term on both side.Arrange the term in same order.If all the terms in two expressions are same then the equations are equivalent.How to Solve an Equation in StepsFinding the value of the variable that makes the equation's condition true is the goal of equation solving. The subsequent actions are carried out while keeping the equation balanced on both sides in order to isolate the variable. By repeating this, LHS and RHS finally remain equal, and the equilibrium is maintained throughout.
Addition property of equality: Add the same number to both the sides. If a = b, then a + c = b + cSubtraction property of equality: Subtract the same number from both sides. If a = b, then a - c = b - cMultiplication property of equality: Multiply the same number on both sides. If a = b, then ac = bcDivision property of equality: Divide by the same number on both sides. If a = b, then a/c = b/c (where c ≠ 0)We separate the variable on one of the sides of the equation after applying this approach of systematic balancing, which entails a series of identical mathematical operations on both sides of the equation. The final step is the solution of the equation.
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Help solve the equation please!!
Answer:
you forgot the question
Step-by-step explanation:
Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.
A. 270
B. $135
C. $3000
D. $4.5
Answer:
A) 270
Step-by-step explanation:
Interest = principle x time x rate
Interest = 3000 x 2 x .045 4.5% = .045 as a decimal
Interest = 270
7x^2-10=-17 solve by taking square root
The solution to the equation 7x² - 10 = -17 is x = i
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
7x^2-10=-17
Express the equation properly
So, we have the following representation
7x² - 10 = -17
Add 10 to both sides of the equation
This gives
7x² = -7
Divide both sides by 7
x² = -1
Take the square roots
x = √-1
Rewrite as
x = i
Hence, the solution is x = i
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The topic is "Polynomial Synthetic Division". I have no idea how to do it, I need help please :(
Answer:
[tex]x^2+7x-9+\dfrac{12}{x-7}[/tex]
Step-by-step explanation:
The detailed explanation is in the attached image. It is a real pain to type this in the brainly equation editor so I just used LateX and printed out the result in case you are interested.
I may have made typos in the detailed explanation, if so, let me know
How many ways can we pay $1.10 with nickel and dime
Answer: We want to know how many ways we can pay $1.10 with nickels and dimes. Since nickels are worth $0.05 and dimes are worth $0.10, we can use different combinations of these coins to make $1.10.
One way to approach this problem is to use the method of generating functions.
Let x be the number of nickels and y be the number of dimes. Then the generating function for this problem is (x+y) = (x+y)(x^0y^0 + x^1y^0 + x^0y^1 + x^2y^0 + x^1y^1 + x^0y^2...)
We know that the sum of x and y should be 11 because 0.05x + 0.1y = 1.10
The coefficient of x^5y^6 in the expansion of (x+y)^11 gives the number of ways to pay $1.10 with 5 nickels and 6 dimes.
The coefficient of x^5y^6 = 252
So there are 252 ways to pay $1.10 with nickel and dime.
Step-by-step explanation:
Find the absolute value of the fraction. Draw a number line to show how far the fraction is from 0. -5\13
The required number line attached below shows the absolute value of the fraction 5/13 is from 0.
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
The fraction is given in the question, as follows:
-5/13
We have to determine the absolute value of the fraction.
As per the question, we can write the absolute value of the fraction as:
⇒ 5/13
Thus, the number line attached below displays the distance of the fraction from 0.
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suppose Jana collected another 25/100 of their goal. What fraction of the goal have they now collected?
Answer:
1/4.
Step-by-step explanation:
1/4 is the answer because 25 x 4 = 100. Lets say you had 50/100. That would be equivalent to 2/4 , because 50 x 2 = 100.
25 is often reffered to as a quarter, but if someone says it is lets say a quarter past 5:00, they are trying to say is is 5:15, because 15 x 4 = 60, and 60 minutes is an hour.
Help help help help help help
Answer: [tex]B. \frac{2}{7} -\frac{2}{k}[/tex]
Step-by-step explanation:
The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm, what must be the length of the longest side of ∆XYZ?
The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm.
Let 'x' be the length of the longest side. Then the equation is given as,
x / 10 = 12 / 3
Simplify the equation, then we have
x / 10 = 12 / 3
x / 10 = 4
x = 40 cm
The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.
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nterstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not ). The number density is about and the temperature is about 3 K. What is the edge length L of an LxLxL cube of gas with 1.0 J of thermal energy? I found: P = 4.14x10-17Pa Vrms = 273m/s
Our velocity is said to be 10% of the speed of light. Therefore, we need to multiply by 10% the speed of light. As a result, our speed is three times 10 to 7 m/s. Our diameter is 500 metres.
Thus, our radius is 250 metres. It goes through a volume of space equal to pi r squared times V times T in one second. We then multiply 5.8, 8 times 10 to the 12 m3 by pi times 2, 50 squared times three times 10, and seven times one second. Our density is 10 to 6 atoms per cubic metre, or one atom per cubic centimetre.
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The following is a function, true or false?
It is TRUE that the given image represents the function.
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Initially, functions represented the idealized relationship between two changing quantities.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
So, the given image represents a function and it is a kind of many-to-one function.
Therefore, it is TRUE that the given image represents the function.
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1×(
–
0.3÷
–
0.5–0.9)
Write your answer as an integer or a decimal. Do not round.
Using PEDMAS the value of 1×(-0.3÷0.5-0.9) is -0.3
What is PEDMAS ?PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete.
In the expression 1×(-0.3÷ -0.5-0.9) we solve what is in the parentheses first and we must follow the rules in the parentheses.
So we deal with the division first
1× ( 0.6-0.9)
1× -0.3 = -0.3
Therefore the value of the expression 1×(-0.3÷0.5-0.9) is -0.3.
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ms wong wants to estimate the hourly rate of any given babysitter. how should she estimate the rate? why?
In order to estimate the hourly rate of any given babysitter, Ms. Wong can make use of the mean of the sample, because it most closely describes the values of the data in the dataset
What is the sample mean of a dataset?The sample mean is the average of the values in the data sample.
Possible part of the question, obtained from a similar question online includes the following table of values;
Babysitter [tex]{}[/tex] Rate in dollars per hour
1 [tex]{}[/tex] 9.6
2 [tex]{}[/tex] 9.80
3 [tex]{}[/tex] 15.50
4 [tex]{}[/tex] 10.6
5 [tex]{}[/tex] 9.7
6 [tex]{}[/tex] 10.20
7 [tex]{}[/tex] 8.80
8 [tex]{}[/tex] 11.20
9 [tex]{}[/tex] 8.80
10 [tex]{}[/tex] 10.10
The estimate of the hourly rate of any given babysitter can be found using the descriptive statistic, such as the mean, median, or mode, which are measures that indicate the possible mid value of a data set.
The mean is the average value of the dataset, which is obtained by adding the individual data points together and dividing the sum by the number of data points as follows;
9.6 + 9.8 + 15.5 + 10.6 + 9.7 + 10.2 + 8.8 + 11.2 + 8.8 + 10.1 = 104.3
The number of datapoints in the data = 10
The mean = 104.3/10 = 10.43
The median is the middle value which is found by arranging the values in increasing order, then selecting the middle value as follows;
The median values in the dataset that has 10 data points is the average of the 5th and 6th values, which are; 9.8 and 10.1
The median of the dataset is therefore; (9.8 + 10.1)/2 = 9.95
The mode of the dataset is the most common value within the dataset. The mode is therefore 8.8
Based on the above three values, the best estimate that most closely describe the data in the dataset is the mean
Therefore, to estimate the hourly rate of any babysitter, Ms. Wong can make use of the mean, because it most closely describes the values in the dataset.
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Hi i would like some help with this asap
The constant of variation for the given graph is 1/4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
Given that the equation of the line in the graph is a direct variation equation.
Direct variation equations are of the form,
y = k x, where k is a constant number called constant of variation.
We have to find the value of k.
y = k x is an equation in slope intercept form where k is the slope and the value of y intercept is 0, since the line passes through origin (0, 0).
It is enough to find the slope of the given line.
Take two points from the graph, let it be (4, 1) and (-4, -1).
Slope = (-1 - 1) / (-4 - 4) = -2 / -8 = 1/4
The value of k is 1/4.
Hence the value of constant of variation is 1/4.
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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 85%, interpret the likelihood of randomly selecting a terrier from the shelter. Likely Unlikely Equally likely and unlikely This value is not possible to represent probability of a chance event
The interpretation of the likelihood of randomly selecting a terrier from the dog shelter where terriers are 85% is A. Likely.
What is probability?Probability refers to the chance or likelihood of an expected event occurring when there are many possible chances.
Probability is depicted as a fractional value lying between zero and one when it is not 100% uncertain or certain.
Thus, since the percentage of terriers in the dog shelter is 85%, it is 85% likely that one selects a terrier.
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Answer: A: Likely.
Step-by-step explanation:
how many more feet of bricks does sofia need? move numbers to the boxes to show the answer
According to the line-plot Sofia needed 10(3/4) more feet of bricks.
What is the line-plot?
A line plot is a graph that shows data as checkmarks or dots across a number line, indicating the frequency of each value.
In the line plot the horizontal line is showing the values of the size in feet of the bricks say 'l'.
The number of vertically aligned crosses at a given value of 'l', indicates the length of bricks for which the 'l' is needed in the project.
Follow the formula - l × n (number of crosses) = total bricks in feet
0/4 × 0 = 0
1/4 × 2 = 2/4
2/4 × 4 = 8/4
3/4 × 3 = 9/4
1 × 6 = 6
To obtain the total size in feet add all the values -
L = 2/4 + 8/4 + 9/4 + 6
L = (2 + 8 + 9 + 24)/4
L = 43/4
L = 10(3/4)
Therefore, the feet of bricks required is 10(3/4).
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Pls help me to find the answer!
Answer:
Step-by-step explanation:
13x+16
Lets simplify this step by step
5(2x+2)+3x+6
Distribute:
=(5)(2x)+(5)(2)+3x+6
=10x+10+3x+6
Combine Like Terms:
=10x+10+3x+6
=(10x+3x)+(10+6)
=13x+16
13x+16
A rate is a type of ratio that has both terms expressed in different units.
The statement that a rate is a type of ratio that has both terms expressed in different units is true.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A rate is a type of ratio that has both terms expressed in different units.
This is true.
Example:
The unit rate of running a distance of 5 km in 4 hours.
Rate = 5km/4 hours
Unit rate = (5/4) km / 1 hour
Thus,
A rate is a type of ratio that has both terms expressed indifferent unit is true.
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Which statement describes the solution of the equation rounded to the nearest tenth?
A) The solution is greater than 10.5 and less than 11.
B) The solution is less than 1.5 and greater than 1.
C) The solution is less than -10 and greater than -10.7.
D) The solution is greater than -1.5 and less than -1.
PLEASE ANSWER ONLY IF YOU KNOW!! I need help w this!!
The solution is greater than -1.5 and less than -1.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
convert mixed fractions into improper fractions, then to decimal
14 2/5 = 72/5 = 14.4
11 1/8 = 89/8 = 11.125
Thus, the equation becomes:
14.4x+6.55= -11.125x-2.45 + 17 x
=> 14.4x + 11.125x - 17x = -6.55 -2.45
=> 8.525x = -9
=> x = -9 / 8.525 = -1.055
solution of the equation rounded to the nearest tenth = -1.1
Thus, The solution is greater than -1.5 and less than -1.
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