Step-by-step explanation:
x²-6x+9=0
using the almighty formula where a=1 , b=-6 , c=9
When solving the equation 3(x-2)=-12, what is a possible first step?
A) Distributing the 3 into each term of the parenthesis.
B) She could either divide by 3 or distribute 3 into the parenthesis
C) Adding 2 to each side of the equation
D) Subtracting 2 on each side of the equation
E) Dividing each side of the equation by 3
F) none of the answer choices tell what the first step could be.
Answer:
A
Step-by-step explanation:
The summaries of data from the balance sheet, income statement, and retained earnings statement for two corporations, Walco Corporation, and Gunther Enterprises, are presented below for 2017.
Determine the missing amounts. Assume all changes in stockholders equity are due to changes in retained earnings
Walco Corporation Gunther Enterprise
Beginning of year Total assets $100,000 $159,000
Total liabilities 73,000 $_____ (d)
Total stockholders' equity $_____ (a) 67,500
End of year Total assets $_____ (b) 190,000
Total liabilities 128,000 50,000
Total stockholders' equity 54,000 $_____ (e)
Changes during year in retained earnings Dividends $_____ (c) 4,900
Total revenues 219,000 $_____ (f)
Total expenses 167,000 79,000
The missing amounts for Walco Corporation and Gunther Enterprises assuming all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.
a) Total liabilities + Total stockholders' equity = Total assets
Total liabilities + $54,000 = $100,000
Total liabilities = $46,000
(b) Total assets = Total liabilities + Total stockholders' equity
Total assets = $128,000 + $54,000
Total assets = $182,000
(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $167,000 - $4,900
Changes during year in retained earnings = $47,100
The missing values for Gunther Enterprises:
(d) Total liabilities + Total stockholders' equity = Total assets
$67,500 + $(e) = $159,000
$(e) = $91,500
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $(f) - $79,000 - $4,900
Changes during year in retained earnings = $(f) - $83,900
Using the balance sheet equation, we can find the missing values:
(d) Total liabilities = Total assets - Total stockholders' equity
Total liabilities = $159,000 - $67,500
Total liabilities = $91,500
(e) Total stockholders' equity = Total assets - Total liabilities
Total stockholders' equity = $190,000 - $50,000
Total stockholders' equity = $140,000
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $79,000 - $4,900
Changes during year in retained earnings = $135,100
Therefore, the missing amounts are:
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
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HELP PLEASE … Assuming the input of energy continues for another 2.5 seconds, where will the particle be?
A) cannot be determined
B) positive maximum
C) negative maximum
D) equilibrium
Answer:
To determine the position of a particle given the input of energy, we need to know the type of energy input and the initial position and velocity of the particle. Without this information, we cannot determine the position of the particle after 2.5 seconds.
Therefore, the answer is A) cannot be determined.
Step-by-step explanation:
ABOVE
Write the expression in complete factored
form.
b2(p + 3) + q(P + 3) =
A bag of oranges weighs 1.5 kg to the nearest 100 g. Complete the error interval, where x is the weight of the oranges.
Move the manilla point as close to the circle as possible so that the blue arc almost disappears keep the manilla point on the circle
What previously learned theorem do these transformations reveal
A theorem which these transformations reveal include the following: theorem of intersecting secants.
What is the theorem of intersecting secants?In Mathematics and Geometry, the theorem of intersecting secants states that when two lines intersect outside a given circle, the measure of the angle formed by these intersecting lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, the value of any of the angle subtended by the intersecting lines can be calculated by using the following mathematical equation:
m∠a = One-half(y – x).
m∠a = ½(y – x).
Where:
x and y represent the angles formed by the intersecting lines.
Therefore, the theorem of intersecting secants describe these set of transformations.
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Write each equation in slope-intercept form. Identify the slope and y-intercept.
x - 3y = 12
*Work must be shown.*
Answer:
slope is 1/3
y-intercept is -4
Step-by-step explanation:
x - 3y = 12
3y = x - 12
y = 1/3x - 4
according to y = mx + b, m is slope and b is y-intercept
slope is 1/3
y-intercept is -4
Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton. Which of the following statements is true? If she rejects this egg, returns it to the carton, and randomly picks again, these will be dependent events. If she uses this egg in a recipe and picks another one from the carton, these will be dependent events. Whether or not these are dependent or independent events depends on what color egg Caris chooses next. If she uses this egg in a recipe and picks another one from the carton, these will be independent events.
Answer:
Step-by-step explanation:
i think you have to times it
Mrs Smith walks a half a mile a day after work. She works five days a week. How many yards will she have walked for the week by Friday morning?
The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.
One week has seven days in total.
Mrs. Smith walks half a mile each day after work, she walks a total of
0.5 miles/ day × 7 days/ week = 3.5 miles/ week
Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.
Therefore,
0.5 miles/ day × 4 days = 2 miles
To convert miles to yards, we can use the fact that there are 1760 yards in one mile:
2 miles/week × 1760 yards/mile = 3520 yards/week
Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.
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Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and
letting all the kite's string play out. He measures the angle of elevation from his hand
to the kite to be 24°. If the string from the kite to his hand is 105 feet long, how many
feet is the kite above the ground? Round your answer to the nearest tenth of a foot if
necessary.
Answer: 46.0 ft
Step-by-step explanation:
[tex]\text{sin} \ 24^o=\dfrac{x}{105}[/tex]
[tex]x=105 \ \text{sin 24}^o[/tex]
So, the distance above the ground is [tex]\text{105 sin} \ 24^o+3.25\thickapprox \boxed{46.0 \ \text{ft}}[/tex]
compute the zeros of the polynomial 4x2 - 4x - 8
Answer:
(2, 0) and (-1, 0)
Step-by-step explanation:
[tex]4x^2 - 4x - 8 = 0 \text{ // Divide by 4} \\x^2 - x - 2 = 0\\\\x_{1, 2} = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times (-2)}}{2\times1}\\\\x_{1, 2} = \frac{1 \pm \sqrt{1 + 8}}2\\\\x_{1, 2} = \frac{1 \pm \sqrt9}2\\\\x_{1, 2} = \frac{1 \pm 3}2\\\\x_1 = \frac{1 + 3}2 = \frac42 = 2\\\\x_2 = \frac{1 - 3}2 = \frac{-2}2 = -1[/tex]
Therefore, the zeroes are (2, 0) and (-1, 0).
What is result of following operation(4623. 56)10+ (110011. 11)2whare (110011. 11(2 mean that 110011. 11as a number express in base 2
The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].
A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:
System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-
[tex](4623.56)_{10} , (110011.11)_{2}[/tex]
these are in decimal and binary system respectively.
now, we will express them in same system ( here we choose decimal system).
[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]
Now, addition is done below:-
4623.56+51.75= 4675.31.
hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]
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the cylinder has a volume of 45 cubic inches and a height of 5 inches what is the raduis of the cylinder
The radius of the cylinder is 3 inches.
What is the volume of a cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases and a curved lateral surface connecting the two bases. The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex], where r is the radius of the base, h is the height of the cylinder, and π is a constant value approximately equal to 3.14.
Calculating the value of radius :
We are given that the cylinder has a volume of 45 cubic inches and a height of 5 inches. Using the formula for the volume of a cylinder, we get:
[tex]V = \pi r^2h[/tex]
Substituting the given values, we get:
[tex]45 = \pi r^2(5)[/tex]
Simplifying the equation, we get:
[tex]9 = r^2[/tex]
Taking the square root of both sides, we get:
[tex]r = \pm 3[/tex]
Since the radius cannot be negative, we take the positive value of r, which is:
r = 3 inches
Therefore, the radius of the cylinder is 3 inches.
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The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with radius 83,000,000 mi. Find the linear speed of XYZ in miles per hour. The linear speed is approximately ______ miles per hour. (Round to the nearest integer as needed.)
The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with a radius of 83,000,000 mi. The linear speed of XYZ in miles per hour is approximately 1,093,333 miles per hour.
What is the orbit and what is the linear speed?
An orbit refers to the path taken by an object, such as a planet, as it circles around another object, such as a star. The speed of the planet is its rate of movement, measured in linear units like miles or kilometers per hour, as it travels around the orbit.
These are terms that are important to understanding the solution to the problem provided. The linear speed of XYZ in miles per hour is approximate _____ miles per hour. (Round to the nearest integer as needed.)
The planet XYZ travels around the star ABC in a circular orbit that takes 24 hours to complete. The orbit is a circle with a radius of 83,000,000 miles.
To find the linear speed of XYZ in miles per hour, it is necessary to use the formula for the circumference of a circle.
Circumference = 2πr Circumference
=2πr Substitute 83,000,000 for r in the formula.
Circumference = 2π(83,000,000)
Circumference = 522,000,000 π
The orbit's circumference is 522,000,000 π miles.
The distance traveled by XYZ in one hour is the linear speed. The linear speed of XYZ in miles per hour is calculated as follows:
Speed = Distance/TimeSpeed
= Circumference/24Speed
= (522,000,000 π)/24
Speed = 21,750,000 π
The linear speed of XYZ in miles per hour is 21,750,000 π miles per hour.
To get an approximate answer, π is equal to 3.14.
Speed ≈ 21,750,000 (3.14)
Speed ≈ 68,295,000
The linear speed of XYZ in miles per hour is approximately 68,295,000 miles per hour. Rounded to the nearest integer, the linear speed is approximately 1,093,333 miles per hour.
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Using the inverse transform method for discrete distribution, define a process for generating random variates from a binomial distribution with N 6 and p 0.4. (sixth decimal place.)
The another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
The process of generating random variates from a binomial distribution using the inverse transform method for discrete distribution is done as follows:Step 1: Determine the probability mass function (pmf) of the binomial distribution with parameters n and p. For example, for a binomial distribution with n = 6 and p = 0.4, the pmf is given by:P(X=k) = (6 choose k)(0.4)^k(1-0.4)^(6-k), where k=0,1,2,3,4,5,6Step 2: Calculate the cumulative distribution function (CDF) of the binomial distribution by summing the pmf up to each value of k. The CDF is given by:F(k) = P(X ≤ k) = ΣP(X=i) for i=0 to k, where k=0,1,2,3,4,5,6Step 3: Generate a uniform random variate, U, between 0 and 1. For example, U=0.23456.Step 4: Find the smallest value of k such that F(k) ≥ U. This value of k is the random variate X. For example, if U=0.23456, then F(0)=0.10737, F(1)=0.38223, and F(2)=0.74304. Since F(1) is the smallest value of F(k) that is greater than or equal to U, X=1. Therefore, a random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=1.To find another random variate from the same distribution, repeat steps 3 and 4. For example, U=0.987654, F(0)=0.10737, F(1)=0.38223, F(2)=0.74304, F(3)=0.91892, F(4)=0.98544, and F(5)=0.99856. Since F(3) is the smallest value of F(k) that is greater than or equal to U, X=3. Therefore, another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
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The town council of Finleyville is meeting to discuss emergency evacuation plans. Finleyville is in a state where hurricanes occur. Some town councillors believe the town's emergency evacuation plan needs to be changed because there has been an increase in natural disasters in the area. Other town councilors believe the plan is fine as it is. The following chart was presented to the town council. Which statement best describes the information presented in the chart?
a graph showing the number of hurricanes of category 1 or higher that happened during a specific series of years. Between 1980?1989 there were 13; from 1990?1999 there were 14; from 2000?2009 there were 23; and from 2010?2017 there were 10.
The number of hurricanes has decreased steadily since 1980.
There have been fewer hurricanes because of a change in temperature.
The number of hurricanes was increasing but has decreased in recent years.
There are more tornadoes in Finleyville than there are hurricanes.
The statement that best describes the infοrmatiοn presented in the chart is: "The number οf hurricanes was increasing but has decreased in recent years."
What are hurricanes ?Hurricanes, knοwn generically as trοpical cyclοnes, are lοw-pressure systems with οrganized thunderstοrm activity that fοrm οver trοpical οr subtrοpical waters. They gain their energy frοm warm οcean waters.
The chart shοws the number οf hurricanes οf categοry 1 οr higher that οccurred during specific series οf years, and it indicates that the number οf hurricanes increased frοm 13 in 1980-1989 tο 23 in 2000-2009, and then decreased tο 10 in 2010-2017.
Therefοre, the chart suggests that the number οf hurricanes was increasing, but it has decreased in recent years. The chart dοes nοt prοvide any infοrmatiοn abοut tοrnadοes in Finleyville οr the relatiοnship between the number οf hurricanes and temperature.
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The statement that best describes the information in the graph is: "The number of hurricanes has increased but decreased in recent years." The graph shows that the number of Category 1 or greater hurricanes increased from 1980 to 2009, but decreased from 2010 to 2017.
How could 1/5 + -4/5 be modeled on a number line
The expression 1/5 + -4/5 has plotted on the number line
To model 1/5 + (-4/5) on a number line, we can start by placing a point at 0 on the number line. Then we can represent 1/5 by placing another point to the right of 0, one-fifth of the distance from 0 to 1. We can represent -4/5 by placing a point to the left of 0, four-fifths of the distance from 0 to -1.
To add these two points together, we start at the point representing 1/5 and move four-fifths of the distance towards the left, since -4/5 is negative. The resulting point represents the sum of 1/5 and -4/5.
To solve this problem algebraically, we can add the two fractions together by finding a common denominator:
1/5 + (-4/5) = 1/5 - 4/5
= (1-4)/5
= -3/5
= -0.6
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in august 2012, tropical storm isaac formed in the caribbean and was headed for the gulf of mexico. there was an initial probability of .69 that isaac would become a hurricane by the time it reached the gulf of mexico (national hurricane center website, august 21, 2012). a. what was the probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico (to 2 decimals)? b. two days later, the national hurricane center projected the path of isaac would pass directly over cuba before reaching the gulf of mexico. hurricanes that reach the gulf of mexico have a .08 probability of having passed over cuba. tropical storms that reach the gulf of mexico have a .20 probability of having passed over cuba. how did passing over cuba alter the probability that isaac would become a hurricane by the time it reached the gulf of mexico? use the above probabilities to answer this question. p(c|h) (to 2 decimals) p(c|t) (to 2 decimals) p(h|c) (to 4 decimals) c. what happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as cuba? select (to 2 decimals) to (to 4 decimals).\
By using Bayes' theorem in probability.
a) The probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico is 0.31.
b) P(H|c) = 0.4493
c) It can be observed that the likelihood of a tropical storm developing into a hurricane decreases slightly when it passes over Cuba. This can be inferred from the fact that the conditional probability of a hurricane forming given that the storm has passed over Cuba (P(H|c) = 0.4493) is lower than the initial probability of 0.69.
a) The probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is:
P(not hurricane) = 1 - P(hurricane) = 1 - 0.69 = 0.31
So the probability is 0.31 (to 2 decimals).
b) We need to use Bayes' theorem to calculate the probabilities:
P(c|H) = P(H|c) * P(c) / P(H)
P(c|T) = P(T|c) * P(c) / P(T)
where c denotes passing over Cuba, H denotes becoming a hurricane, and T denotes remaining a tropical storm.
From the problem, we have:
P(H) = 0.69
P(T) = 1 - P(H) = 0.31
P(c|H) = 0.08
P(c|T) = 0.20
To calculate P(c), we need to use the law of total probability:
P(c) = P(c|H) * P(H) + P(c|T) * P(T)
= 0.08 * 0.69 + 0.20 * 0.31
= 0.1228
Now we can calculate P(c|H) and P(c|T):
P(c|H) = 0.08 * 0.69 / 0.1228
= 0.4493 (to 2 decimals)
P(c|T) = 0.20 * 0.31 / 0.1228
= 0.5065 (to 2 decimals)
To calculate P(H|c), we use Bayes' theorem again:
P(H|c) = P(c|H) * P(H) / P(c)
= 0.08 * 0.69 / 0.1228
= 0.4493 (to 4 decimals)
c) Passing over a landmass such as Cuba can alter the probability of becoming a hurricane because it can either enhance or weaken the storm. In this case, we can see that the probability of becoming a hurricane is actually slightly lower when a tropical storm passes over Cuba, as P(H|c) = 0.4493 is lower than the initial probability of 0.69. However, it is important to note that this is just one example and the effect of passing over a landmass can vary depending on many factors.
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assuming the conditions for inference have been met, does the coffee shop owner have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5 percent level of significance? conduct the appropriate statistical test to support your conclusion.
The coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
What is proportion ?
A proportion refers to the number or fraction of individuals or items that exhibit a particular characteristic or have a certain attribute, relative to the total number or sample size being considered. It is often expressed as a ratio or percentage.
To test whether the distribution of sales is proportional to the number of facings, we can use the chi-squared goodness of fit test. The null hypothesis for this test is that the observed data follows a specific distribution (in this case, a proportional distribution), while the alternative hypothesis is that the observed data does not follow that distribution.
To conduct the test, we first need to calculate the expected frequency for each category assuming a proportional distribution. We can do this by multiplying the total number of sales (610) by the proportion of facings for each brand:
Starbucks: 610 x 0.3 = 183
Dunkin: 610 x 0.4 = 244
Peet's: 610 x 0.2 = 122
Other: 610 x 0.1 = 61
Next, we calculate the chi-squared statistic using the formula:
χ² = Σ((O - E)² / E)
where O is the observed frequency and E is the expected frequency. The degrees of freedom for this test are (k-1), where k is the number of categories. In this case, k = 4, so the degrees of freedom are 3.
Using the observed and expected frequencies from the table, we get:
χ² = ((130-183)²/183) + ((240-244)²/244) + ((85-122)²/122) + ((155-61)²/61) = 124.36
Looking up the critical value of chi-squared for 3 degrees of freedom and a significance level of 0.05, we get a value of 7.815. Since our calculated χ² value of 124.36 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that the observed distribution of sales is not proportional to the number of facings.
Therefore, the coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
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Blaine works for a battery manufacturing company. he wants to develop a method to test the batteries made each day to determine if they work. which method would provide the most valid results?
Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.
A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.
The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.
Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
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the nutty professor sells cashews for $7.70 per pound and brazil nuts for $4.80 per pound. how much of each type should be used to make a 27 pound mixture that sells for $6.41 per pound?
The amount that each type would be 11.87 lbs of cashews and 15.13 lbs of brazil nuts
1. First, find the total cost of 27 lbs of the mixture: 27 lbs x $6.41/lb = $171.07.
2. Next, find the cost of cashews and brazil nuts in the mixture. Cashews cost $7.70/lb and brazil nuts cost $4.80/lb.
3. Subtract the cost of the brazil nuts from the total cost of the mixture: $171.07 - (27 lbs x $4.80/lb) = $105.27.
4. Divide the cost of the cashews ($105.27) by the cost of one pound of cashews ($7.70): $105.27/$7.70 = 13.66 lbs.
5. Subtract the number of pounds of cashews (13.66) from the total pounds of the mixture (27) to find the number of pounds of brazil nuts: 27 - 13.66 = 15.13 lbs.
6. Therefore, the mixture should contain 11.87 lbs of cashews and 15.13 lbs of brazil nuts.
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a person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1. find the expectation of this game. is the game fair?
A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value
How do we determine the expected value of the game?We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.
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two people standing at different locations are looking at a tall building. person a angle of elevation to the building is 35 degrees. person b angle of elevation is 77 degrees. the building is 8 miles away from person b. how far away is person a from the building?
Therefore, Person A is approximately 95.17 miles away from the building.
To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.
Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.
Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.
First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:
height = 8tan(77) ≈ 61.23 miles.
Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:
x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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j by 9 and then multiply the quotient by 2
The sequence of the questions is [tex]J/9[/tex] when you multiply [tex]J[/tex] by [tex]9[/tex] and the quotient by [tex]2[/tex].
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the result, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.
Is quotient the same as answer?The result of dividing two integers is known as the quotient. Six divided into two results in the number three. Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the two digits enters the first.
[tex]2 * (J/9)[/tex]
This means you first divide [tex]J[/tex] by [tex]9[/tex] to get the quotient, and then multiply the quotient by [tex]2[/tex]. So the order of operations is:
[tex]J/9[/tex]
Multiply the quotient by [tex]2[/tex]
For example, if [tex]J = 45[/tex], then:
[tex]J/9 = 45/9 = 5[/tex]
[tex]2 * (J/9) = 2 * 5 = 10[/tex]
So the result of multiplying [tex]J[/tex] by [tex]9[/tex] and then multiplying the quotient by [tex]2[/tex], when [tex]J = 45[/tex], is [tex]10[/tex].
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Rina is climbing a mountain. She has not
yet reached base camp. Write an inequality
to show the remaining distance, d, in feet
she must climb to reach the peak.
The distance she must climb to reach the peak is greater than 2,663 feet. An inequality to show the remaining distance, d, in feet she must climb to reach the peak is d > 2,663.
Inequlity represents a relationship between two values that is not equal. That is inequlity means no equal and the symbols which used for not equal is ≠ and for comparison are < , > , ≤ , ≥. For example, ax > b etc. We have, Rina is climbing a mountain and mountain height present in above figure. See the figure carefully, the main two points in figure are the following: height of mountain peak
= 12,358 feet
height of base camp = 9,695 feet
we have to write an inequality for the remaining distance, d, in feet. Also, it is specified that she has not reached base camp yet. So, his climbed distance is less than 9,695 feet. Let the remaining distance be 'd feet '. From the above figures, d + base camp height > 12,358
Substract 9695 from both sides
=> d > 12,358 - 9,695
=> d > 2,663
Hence, required inequalty is d > 2,663.
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Complete question:
Rina is climbing a mountain. She has not yet reached base camp. Write an inequality to show the remaining distance, d, in feet she must climb to reach the peak. See tha above figure.
(-6, -2) (-2, 0) what is solution to system of equations?
Note that the solution of the system of equations will be (-6, -2). (Option A)
What is a system of equation?
A system of equations is a collection of two or more equations with a shared set of unknown variables. The goal is to find the values of the variables that satisfy all the equations simultaneously.
Note that System of equations is represented by two straight lines on a graph.
And solution of the system of equations is the point of intersection of these lines, because that is the point where the values from both functions satisfy all the equations simultaneously.
From the graph attached, two straight lines represent the system of equations.
And the point of intersection of these lines is the solution.
Therefore, solution of the system of equations will be (-6, -2). (Option A)
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Full Question:
Although part of your question is missing, you might be referring to this full question:
What is the solution to the system of equations?
A (-6,2-)
B (-2, 6)
C (6,2)
D (-2,-6)? See attached image.
17- 20: In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%."17. What is the population of interest?18. What is the sample being used?19. What is the population parameter of interest, and what is the correct notation for this parameter? What is the relevant statistic?20. Find an interval estimate for the parameter of interest. Interpret it in terms of dissatisfaction in the quality of education students receive. Use two decimal places in your answer.
17. The population of interest is U.S. adults (age 18 and over).
18. The sample being used is 1,012 randomly selected U.S. adults (age 18 and over).
19. The population parameter of interest is the percentage of U.S. adults (age 18 and over) who are dissatisfied with the quality of education students receive in kindergarten through grade 12. The correct notation for this parameter is p and the relevant statistic is 53%.
20. The interval estimate for the parameter of interest is 49% - 57%, which indicates that between 49% and 57% of U.S. adults (age 18 and over) are dissatisfied with the quality of education students receive in kindergarten through grade 12.
Triangle lmn will be dilated with respect to the origin by a scale factor of 1/2
what are the new coordinates of L’M’N’
The triangle LMN, with vertices L(6, −8), M(4, −4), and N(−12, 2), dilated with respect to the origin by a scale factor of 1/2, results in triangle L'M'N', with vertices L'(3, -4), M'(2, -2), and N'(-6, 1)
To dilate a triangle with respect to the origin, we need to multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is 1/2, so we multiply each coordinate by 1/2.
The coordinates of L' are obtained by multiplying the coordinates of L by 1/2:
L'((1/2)6, (1/2)(-8)) = (3, -4)
The coordinates of M' are obtained by multiplying the coordinates of M by 1/2:
M'((1/2)4, (1/2)(-4)) = (2, -2)
The coordinates of N' are obtained by multiplying the coordinates of N by scale factor 1/2:
N'((1/2)×(-12), (1/2)×2) = (-6, 1)
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The given question is incomplete, the complete question is:
Triangle LMN with vertices L(6, −8), M(4, −4), and N(−12, 2) is dilated with respect to origin by a scale factor of 2 to obtain triangle L′M′N′. What are the new coordinates of L′M′N′ ?
Keilantra and Samantha work at a dry cleaners ironing shirts. Keilantra can iron 30 shirts per hour, and Samantha can iron 15 shirts per hour. Keilantra and Samantha worked a combined 11 hours and ironed 240 shirts. Graphically solve a system of equations in order to determine the number of hours Keilantra worked, x, and the number hours Samantha worked, y.
Answer: Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours
Step-by-step explanation:
We will use the variables x and y the question provides. We know the time worked by each person added together will equal the combined total time. We can write an equation to show this using addition.
x + y = 11 hours
Next, we know that Keilantra ironed 30 per hour, Samantha ironed 15 per hour and that they ironed 240 shirts. We can write another equation to represent this using addition and multiplication.
30x + 15y = 240
Next, we will graph these two equations. See attached. The solution is the point of intersection written as (x, y). This is (5, 6) meaning that Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours.
Find the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3)
Answer: The given equation 2x + 5y = 10 can be rewritten in slope-intercept form (y = mx + b) by solving for y:
2x + 5y = 10
5y = -2x + 10
y = (-2/5)x + 2
where the slope is -2/5.
Since we want to find the equation of a line parallel to this one, the slope of the new line will also be -2/5. We can use the point-slope form of the equation of a line to find the equation of the new line, using the point (0,-3):
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting m = -2/5, x1 = 0, and y1 = -3, we get:
y - (-3) = (-2/5)(x - 0)
y + 3 = (-2/5)x
y = (-2/5)x - 3
Therefore, the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3) is y = (-2/5)x - 3.
Step-by-step explanation:
Answer:
2x + 5y = - 15
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + 5y = 10 ( subtract 2x from both sides )
5y = - 2x + 10 ( divide through by 5 )
y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{2}{5}[/tex] x + c
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - [tex]\frac{2}{5}[/tex] x - 3 ← equation of parallel line in slope- intercept form
multiply through by 5 to clear the fraction
5y = - 2x - 15 ( add 2x to both sides )
2x + 5y = - 15 ← in standard form
