The system of equations that represent this situation is given as follows:
d + m = 120.7d = 2m.How to model the system of equations?The variables for the system of equations are given as follows:
Variable d: number of kilograms of dark chocolate.Variable m: number of kilograms of milk chocolate.The total weight is of 120 kg, hence the first equation is given as follows:
d + m = 120.
Her recipe calls for twice the amount of dark chocolate as milk chocolate, hence the second equation is given as follows:
d = 2m.
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erify that the following function is a probability mass function, and determine the requested probabilities. [give exact answers in form of fraction.]
The probability of x = 1 is 0.2,x = 2 is 0.3, x = 3 is 0.5
Let X be a random variable with the following probability mass function:
f(x) =
x = 1: 0.2
x = 2: 0.3
x = 3: 0.5
This is indeed a probability mass function because the values of f(x) are all greater than or equal to 0, and the sum of the values of f(x) is equal to
To calculate the probability of x = 1, we can use the formula for probability mass functions: P(X = x) = f(x).
Therefore, the probability of x = 1 is 0.2.
To calculate the probability of x = 2, we can use the same formula: P(X = x) = f(x).
Therefore, the probability of x = 2 is 0.3.
To calculate the probability of x = 3, we can use the same formula: P(X = x) = f(x).
Therefore, the probability of x = 3 is 0.5.
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complete question
What is the probability of x = 1, x = 2, and x = 3?
You() watch what you are saying.the boss is very upset today.
Answer: Noted
Step-by-step explanation: do not p$ss off boss
Q y r z s x+2 3x-8 solve for x
A)12
B)10
C)11
D)13
Answer:
ANSWER IS B
Step-by-step explanation:
given a table of values of f(x) below, which table represents f-1(X)
The table that represents f⁻¹(x) in the attached figure
What is a function?A relation is a function if it has only One y-value for each x-value.
we know that, If (x,y) is a solution of f(x)
then (y,x) is a solution of f⁻¹(x)
In this problem, the ordered pairs in the table that represent f(x) are
(-2,11),(-1,8),(0,5),(1,2),(2,-1)
therefore, The ordered pairs that represent f⁻¹(x) are
(11,-2),(8,-1),(5,0),(2,1),(-1,2)
Hence, the table that represents f⁻¹(x) in the attached figure
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Choose the word or phrase that correctly completes the sentence.
Andrew wrapped his
sisters
sisteres'
sisters'
sister's
I don't know this yet.
present.
Answer:
answer is sister's.
Step-by-step explanation:
sisters mean more than one sister.
sisterses isn't a word.
sisters' also isn't a word.
sister's is a word and it means that she has possession of something or that she owns something.
For two linear functions f and g , (f+g)(x)=-6x-2 and (f-g)(x)=-2x+4 . Find( f(g(x)))
Need help ASAP!!
Answer:
(-6x-2)(2x+4)
-12x+24x-4x+6
=8x+6
which choice is equivalent to the product below
√6×√3
Answer:
Step-by-step explanation:
The expression √3 × √5 × √6 is equivalent to the expression 3 × √10. Then the correct option is B.
What is an equivalent expression?
The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ √3 × √5 × √6
Simplify the expression, then the value of the expression will be given as,
⇒ √3 × √5 × √(3 ×2)
⇒ √3 × √5 × √3 × √2
⇒ 3 × √(5 × 2)
⇒ 3 × √10
The articulation √3 × √5 × √6 is comparable to the articulation 3 × √10. Then, at that point, the right choice is B.
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×==3
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Answer: 3√2
Step-by-step explanation: I just took the test
identify each of the following as examples of nominal, ordinal, discrete, or continuous variables. (a) a poll of registered voters as to which candidate they support.
The candidate is an example of a nominal variable. Since candidates are identified through their names, the variable is qualitative in nature. Moreover, since names are all the voters have to go by, there is thus no inherent ordering in the candidates.
About nominal variableNominal variable is a variable with the lowest level of measurement scale and can only be used for qualitative classification or categorization. That is, these variables can only be measured in terms of whether the characteristics of an object can be distinguished from other characteristics, but we cannot measure or even rank these categories.
For example, we can say that the genders of the 2 people are different, one is female and the other is male. Here we can distinguish the characteristics of the two, but we cannot measure and say which is "more" or which is "less" from the quality represented by the variable.
We can only assign codes/labels to these two characteristics, for example the number 0 for women and the number 1 for men. The code/number label can be exchanged. The code there only serves as a differentiator between the two objects and does not indicate order or continuity. The number 1 does not indicate higher or better than 0.
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Y’all, I need help ;-; 14) Maya's cat eats 4 ounces of cat food each day. Maya bought a 26 pound bag of cat food.
How many 4- ounce servings are in the 26 pound bag?
A) 6
B) 224
C) 104
D) 416
After Game 6 of the 2016 NBA Finals, Frank put down an even-money $100,000 bet on the Cavs to win Game 7 (and therefore, the championship). So, if the Cavs win, he wins $100,000, and if the Cavs lose, he loses $100,000. Suppose Frank has a logarithmic utility-of-wealth function: U(w) = ln(w), and his current wealth is $1,000,000 (one million dollars). Given that he accepted this bet, what can we determine about p, the probability with which Frank believes the Cavs will win Game 7? The goal of this problem is to figure this out. The subparts below will walk you through figuring this out
a) Write down an expression for Frank’s expected utility of wealth, as a function of p, if he takes the bet. [Remember to take into account his current wealth level as well as how winning or losing will change it.]
b) Frank’s other option is to reject the bet. What will his utility of wealth be if he rejects the bet?
c) If he accepts the bet, we know that the utility given for (a) must be larger than the utility given for (b). Write down and solve the inequality. You should be able to determine either a lower bound or upper bound for p, e.g. p ≤ 0.25 or p ≥.80.
d) Suppose Frank’s utility-of-wealth function was less curved, i.e. closer to a straight line. How would the bound from (c) change? Remember, the bound defines the range of possible probabilities p for him to accept the bet. Explain why it would be larger or smaller.
Frank's expected utility of wealth function if he takes the bet is U(w) = $1,000,000 + p(ln($100,000)) + (1-p)(ln($900,000)). If Frank accepts the bet, the probability p must be greater than or equal to 0.8.
a) Frank's expected utility of wealth if he takes the bet is U(w) = $1,000,000 + p(ln($100,000)) + (1-p)(ln($900,000))
b) If Frank rejects the bet, his utility of wealth will be U(w) = ln($1,000,000)
c) U(w) = $1,000,000 + p(ln($100,000)) + (1-p)(ln($900,000)) ≥ ln($1,000,000)
p(ln($100,000)) + (1-p)(ln($900,000)) ≥ ln($1,000,000) - $1,000,000
p(ln($100,000)) + (1-p)(ln($900,000) - ln($1,000,000)) ≥ -$1,000,000
p(ln($100,000) - ln($1,000,000)) + (1-p)(ln($900,000) - ln($1,000,000)) ≥ -$1,000,000
p(ln($100,000/$1,000,000)) + (1-p)(ln($900,000/$1,000,000)) ≥ -$1,000,000
p(ln(0.1)) + (1-p)(ln(0.9)) ≥ -$1,000,000
p(ln(0.1)) ≥ -$1,000,000 - (1-p)(ln(0.9))
p ≥ (-$1,000,000 - (1-p)(ln(0.9)))/(ln(0.1))
p ≥ -$1,000,000/(ln(0.1)) - (1-p)(ln(0.9))/ln(0.1)
p ≥ 0.8
d) If Frank's utility of wealth function was less curved, i.e. closer to a straight line, the bound from (c) would be larger. This is because, with a less curved utility of wealth function, Frank would be less risk-averse and therefore more likely to accept the bet.
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The perimeter of a triangle is 45 feet. The ratio of the lengths of the three sides is 2:3:4. Find the measure of each side. Show your work. Compare and contrast this problem with the extended ratios for the angles of a triangle. Find the sides of the triangle: Equation: 4+3+2=9 Side length 1: 10 Side length 2: 15 Side length 3: 20
The measures of side lengths of triangle are 10 feet, 15 feet and 20 feet.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that perimeter of a triangle is 45 feet.
ratio of the lengths of the three sides is 2:3:4
We have to find the measure of each side.
Let us consider the side lengths are 2x, 3x, and 4x.
2x+3x+4x=45
Add the like terms
9x=45
Divide both sides by 9
x=5
Side lengths are 2x = 2×5 = 10 feet,
3x = 3× 5 = 15 feet, and 4x = 4 ×5 = 20 feet.
Hence, the measures of side lengths of triangle are 10 feet, 15 feet and 20 feet.
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let f and g be continuous at a. which of the following functions is not necessarily continuous at a ?
Answer:
if f and g are functions such that f+g is continuous, at least one of f or g must be continuous.
Step-by-step explanation:
Solving inequality #4
25 points!!
Answer:
-5 <= x < 3
Step-by-step explanation:
The left end of the inequality is -5 with a closed circle so it has an equal sign with it
The right end of the inequality is 3 with an open circle so it will not have an equals sign.
The line is in the middle of the points so the variable is in the middle.
-5 <= x < 3
Answer:
The inequality shown is Interval Notation[tex] - 5 \leqslant y < 3[/tex]
Allonzo deposits $3000 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the first six years?
The interest will he be paid in the first six years is $360.
What is Simple Interest?Simple interest is the cost of borrowing money that does not take compounding into consideration. In other words, just the principal is affected by simple interest.
Formula: (P x R x T)/100
Given:
P= $3000
R= 2%
T = 6 years
Using Simple interest
= (P x R x T)/100
= ( 3000 x 2 x 6)/100
= 30 x 2 x 6
= $360
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On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below.
x 0 1 2 3 4 5 Total
P(x) .04 .43 .29 .18 .05 .01 1.00
(a) Calculate the mean and standard deviation.
The mean of the data-set is given as follows:
E(X) = 1.8.
The standard deviation of the data-set is given as follows:
S(X) = 1.
How to obtain the mean and the standard deviation?The mean is given by the sum of all the outcomes multiplied by their respective probabilities, hence:
E(X) = 0 x 0.04 + 1 x 0.43 + 2 x 0.29 + 3 x 0.18 + 4 x 0.05 + 5 x 0.01
E(X) = 1.8.
The standard deviation is given by the square root of the sum of the difference squared between each outcome and the mean, multiplied by their respective probabilities, hence:
S(X) = sqrt[(0 - 1.8)² x 0.04 + (1 - 1.8)² x 0.43 + (2 - 1.8)² x 0.29 + (3 - 1.8)² x 0.18 + (4 - 1.8)² x 0.05 + (5 - 1.8)² x 0.01]
S(X) = 1.
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in the racially charged language case, which of the following is not one of the edi initiatives discussed in the case group of answer choices create an inclusive community where all students thrive. establish goals to retain underrepresented groups. allow flyers using racial slurs. implement a 12-week training program.
Allow flyers using racial slurs is not one of the EDI initiatives discussed in the case.
The EDI initiatives discussed in the case include creating an inclusive community where all students thrive, establishing goals to retain underrepresented groups, and implementing a 12-week training program. To create an inclusive community, the school administration must first determine the current state of the campus environment. This can be done through surveys and focus groups, which allow the administration to identify what areas need improvement and how best to address them. Establishing goals to retain underrepresented groups involves setting specific goals for the recruitment and retaining of underrepresented groups, such as increasing the number of faculty or students from underrepresented groups. Finally, implementing a 12-week training program requires developing an educational program to teach students about diversity, equity, and inclusion, and providing the necessary resources to ensure that these lessons are successfully implemented.
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Mrs. Chen said she had 1,152 file folders in the 4 boxes on her desk. Maria used the expression 1,152÷4 to determine how many file folders were in each box. Which statement explains the first step to finding out how many file folders were in each box?
The expression 1,152 ÷ 4 determines the number of file folders in each box.
What is expression ?
Expression is a sentence with a minimum of two numbers or variables and at least one operation. This operation can be addition, subtraction, multiplication, or division
The first step in finding out how many file folders were in each box is to perform the division 1,152 ÷ 4.
This division gives the number of file folders in each box by dividing the total number of file folders (1,152) by the number of boxes (4).
The expression 1,152 ÷ 4 determines the number of file folders in each box.
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the following data show the number of hours worked by 200 statistics students. number of hours frequency 0 - 9 40 10 - 19 50 20 - 29 70 30 - 39 40 determine the probability of a student working 19 hours or less.
To determine the probability of a student working 19 hours or less, we need to find the cumulative frequency of students working 19 hours or less.
From the data, the cumulative frequency of students working 19 hours or less is 40 + 50 = 90. The total number of students is 200. Therefore, the probability of a student working 19 hours or less can be calculated as:
P(working 19 hours or less) = cumulative frequency of students working 19 hours or less / total number of students
P(working 19 hours or less) = 90 / 200
P(working 19 hours or less) = 0.45
So, the probability of a student working 19 hours or less is 0.45 or 45%.
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Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.) C = 127o a = 2, b = 6
The area of the triangle is approximately 33.8 square units.
Heron's formula is applicable to all types of triangles. Heron's formula is used to compute the area of a triangle, and every sort of triangle in the world has an area.
So, if the three sides of a triangle are known, Heron's formula may be used to directly determine the area.
We can use the Law of Cosines to find the third side of the triangle, then use Heron's formula to find the area.
First, we find the third side, c:
c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 2^2 + 6^2 - 2 * 2 * 6 * cos(127)
c = sqrt(40 - 24 * cos(127))
Next, we use Heron's formula to find the area of the triangle:
s = (a + b + c) / 2
area = sqrt(s * (s-a) * (s-b) * (s-c))
area = sqrt((7.82 + 3) * (7.82 - 2) * (7.82 - 6) * (3))
area = sqrt(45.82 * 5.82 * 1.82 * 3)
area = sqrt(1138.3916)
area = 33.75
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joshua worked five hours,katleho worked for three hours and pevashnee worked for four hours if they paid R288 divide money between the three
Answer:
Step-by-step explanation:
5h + 3h + 4h = R288
12h = R288
h = R24
Josh, 5 hours at R24/hour = R120
Katleho, 3 hours at R24/hour = R72
Pevashnee, 4 hours at R24/hour = R96
Check your work: 120 + 72 + 96 = 288
help please!!!!!!!!!!!!!!!!!!!
The sequence as shown is a geometric sequence.
What is a geometric sequence?We know that the geometric sequence is the kind of sequence in which there is the common ratio. We can tell that for the geometric sequence we have;
U(n) = Tr^n-1
Where T is the first term and then r is the common ration while n is the number of terms.
Given the fact that we have the terms in the sequence as 81, 27, 9, 3, 1. We can see that the common ratio of the sequence is given as;
r = T2/T1 = 27/81
1/3
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The heights of Ross, Matt, Martin, Jonah, and Jared are 6 feet, 5.8 feet, 5.5 feet, 6 feet, and 5.7 feet respectively. The median of these five heights is:
5.8 is the median of 6 feet, 5.8 feet, 5.5 feet, 6 feet, and 5.7 feet heights
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The median of a set of numbers is the middle value when the values are arranged in order from smallest to largest.
The heights of Ross, Matt, Martin, Jonah, and Jared are:
5.5, 5.7, 5.8, 6, 6
Arranged in order from smallest to largest, the middle value is 5.8 feet, so the median height of the five individuals is 5.8 feet.
Hence, 5.8 is the median of 6 feet, 5.8 feet, 5.5 feet, 6 feet, and 5.7 feet heights
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Round to 2 decimal places. 8 of the company’s trucks from their pool of 37 trucks needed brake maintenance. What percent of the truck pool needed brake maintenance?
Answer:
21.62%
Step-by-step explanation:
trucks needed maintenance = 8
truck's pool = 37
%age of the trucks needed maintenance
= (8 / 37) * 100
= 21.62%
when you collect data, you can compare and contrast results. based on your results, which of the following is the strongest base?
When collect data, we can compare and contrast results. based on the results, Ammonia has the strongest base.
Ammonia characteristicsThe following are some of the characteristics of ammonia:
Ammonia is a colorless gas but has a very strong odor. Ammonia dissolves easily in water, under standard conditions, one liter of water can dissolve 1180 liters of ammonia. Ammonia melts easily, liquid ammonia can freeze at -78 degrees Celsius. Ammonia melts or under normal conditions at a temperature of 30 to 40 degrees Celsius. Ammonia boils at -33 degrees Celsius. Ammonia is corrosive to tin and copper. Ammonia is used for cosmetic ingredients, for example to mix hair dye, and to straighten hair.Learn more about ammonia at https://brainly.com/question/15409518.
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Which graph represents the function f(x) = -x-2?
Answer:
Here's the graph. If you want just go onto desmos and write y=-x-2 and it'll be there as well.
Step-by-step explanation:
Simplify
5x^2 - x + 9= [?]
x=3
[tex]5x^2-x+9[/tex] when x is equal to 3
Substitute for x with the given value(3):
[tex]5(3)^2-3+9[/tex]
[tex]5(9)-3+9[/tex]
[tex]45-3+9[/tex]
[tex]=\boxed{51}[/tex]
Answer:
it equals 231
Step-by-step explanation:
5x3 is 1515x15 is 225225-3= 222222+9=231The height above the ground of a passenger on a Ferris wheel t minutes after the ride begins is modeled by the differentiable function H, where H(t) is measured in meters. Which of the following is an interpretation of the statement H'(7.5) = 15.708?
The statement "H'(7.5) = 15.708" means that the rate of change of the height of the passenger on the Ferris wheel at 7.5 minutes after the ride begins is 15.708 meters per minute.
The statement H'(7.5) = 15.708 is an interpretation of the derivative of the function H at time 7.5 minutes. The derivative of a function represents the rate of change of the function, and it is calculated by taking the limit of the ratio of the change in the function to the change in its independent variable (in this case, time). H'(7.5) represents the rate of change of the height of the passenger at 7.5 minutes into the ride. The value of 15.708 means that the height of the passenger is increasing by 15.708 meters per minute at 7.5 minutes into the ride.
At 7.5 minutes into the ride, the passenger's height is changing at a rate of 15.708 meters per minute. This means that the passenger is moving upward at a speed of 15.708 meters per minute at this particular time. The derivative of a function at a specific point gives us the rate of change of the function at that point, and in this case, it gives us the speed at which the passenger's height is changing at 7.5 minutes into the ride.
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Worth 25 points! Pls show work on both questions inside of the picture.
The area of the composite figure is 54 in².
The perimeter of the composite figure is 35 in.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The composite figure has 3 shapes.
Triangle and 2 rectangles.
Now,
Base = 3 in
Height = 4 in
Area of the triangle.
= 1/2 x base x height
= 1/2 x 3 x 4
= 6 in²
Now,
Length = 5 in
Width = 4 in
Area of the rectangle.
= length x width
= 5 x 4
= 20 in²
Now,
Length = 4 in
Width = 7 in
Area of the rectangle.
= length x width
= 4 x 7
= 28 in²
Now,
Area of the composite figure.
= 6 + 20 + 28
= 54 in²
Now,
The perimeter of the composite figure.
= 12 + 7 + 4 + 3 + 5 + 4
= 35 in
Thus,
The area is 54 in².
The perimeter is 35 in.
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8n = 10.80 solve for n
Answer:
1.35
Step-by-step explanation:
10.80 divided by 8
n = 1.35
Eric has a riddle: "I am thinking of a fraction that is equivalent to
2
5
and the numerator is 18 less than the denominator."
What is Eric's fraction? Explain how you know.
Answer:
To obtain the fraction first we need to obtained the number. The number can be identified by using algebraic expression.
The fraction is .
Given:
The given fraction is .
Let the numerator is .
The numerator is 18 less than denominator is , the fraction is .
Write the algebraic expression as per question to find the number.
Calculate the fraction.
Thus, the fraction is .
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Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
assume top a, bottom b
so a/b =2/5
so a=2/5b
b=a+18 = 2/5b+18
so 3/5b = 18
b = 30
a=12