The solution for y in the expression is y = -53 and y = 63
How to determine the solution for y?From the question, the expression is given as
y = 5 ± 58
We start by expanding the expression
So, we have the following representation
y = 5 - 58 and y = 5 + 58
Evaluate the sum and the difference of the like terms in the above expression
So, we have the following representation
y = -53 and y = 63
Hence, the solution is
y = -53 and y = 63
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suppose that the mean weight of king penguins found in an anarctic colony last year was 15.4 kilograms and the standard deviation was 2.5 kilograms. you want to test the null hypothesis that the mean penguin weight this year does not differ from last year. assume that the standard deviation has not changed. you are planning to measure a random sample of 100 penguins. at 10% significance level, find the critical values for the test.
we are 90% confident that the mean penguin height lies in the range:
14.99 and 15.81
A popular deviation (or σ) is a degree of the way dispersed the facts is on the subject of the imply. Low popular deviation way facts are clustered across the imply, and excessive popular deviation shows facts are greater unfold out. What is the usual deviation example? Consider the facts set: 2, 1, 3, 2, four.
The imply and the sum of squares of deviations of the observations from the imply could be 2.four and 5.2, respectively. Thus, the usual deviation could be √(5.2/5) = 1.01. Standard deviation tells you ways unfold out the facts is. It is a degree of the way some distance every determined fee is from the imply. In any distribution, approximately 95% of values could be inside 2 popular deviations of the imply.
Given sample mean=x=15.4 kg
sample standard deviation=s=2.5 kg
sample size=n=100 penguins
z multiplier for 90 CI is 1.645
90% CI for population mean is given by:
[tex]X+Z_{\frac{\alpha }{2} } * \frac{Z}{\sqrt[]{N} }[/tex]
15.4 (±)1.645(2.5)/sqrt(100)
15.4(±)1.645(2.5)/10
15.4 (±) 0.41125
15.4-.41125<μ<15.4+.41125
14.98875<μ<15.81125
we are 90% confident that the mean penguin height lies in the range
14.99 and 15.81
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using the following information. coefficients intercept −12.8094 independent variable 2.1794 anova df ss ms f regression 1 12,323.56 12,323.56 90.0481 residual 8 1,094.842 136.8553 total 9 13,418.4 what is the standard error of the estimate? multiple choice 136.8552 1,094.842 11.6985 13,418.4
The Standard error of the estimate is 11.6985
The standard error of estimate is the measure of variation of an observation made around around the regression line
Simply, It is used to check the accuracy of prediction made with the regression line. A standard deviation which measures the variation in the set of data from its mean, the standard error of estimate also measured the variation in actual values of Y from the computed values of Y on the regression line.
Given in the question,
coefficient of y-intercept = -12.8094
Coefficient of x = 2.1794
N-1 = 9
=> N = 10
SSE = 1094.842
Standard error of estimate = √SSE(N-2)
where , SSE is sum of square of error
S.E = √(1094.842)/ (10-2)
=> √(1094.842)/8
=> √136,855
=> 11.6985 is standard error
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The formula A=6V^2/3 related the surface Area ‘A’, in square units, of a cube to the volume ‘V’, in cubic units. What is the volume, in cubic inches, of a cube with surface area of 396.
536.2 cubic inches is the volume of a cube with surface area of 396.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
[tex]A=6V^{\frac{2}{3}}[/tex]
A is surface Area ‘A’, in square units, of a cube
V is volume of cube in cubic units.
We need to find the volume, in cubic inches, of a cube with surface area of 396.
A=396
We need to find V
[tex]V^{\frac{2}{3} } =A/6[/tex]
=396/6
=66
[tex]V=66^{\frac{3}{2} }[/tex]
V=536.2 cubic inches
Hence, 536.2 cubic inches is the volume of a cube with surface area of 396.
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tasmanian automobile licence plates consist of three capital letters (a through z) followed by three digits (0 through 9). how many different tasmanian license plates are possible?
tasmanian license plates are 8,000,000 combinations possible
In probability, what do combination and permutation mean?
Combinations and permutations may appear to be synonyms. However, they are defined differently in probability theory. Combinations: The sequence of results is irrelevant. Permutations: The sequence of events matters.
If an event is made up of numerous other events (i.e., when it is a list), we may calculate the probability that it will occur with the help of permutations and combinations. If the sequence of the events doesn't matter, we have a combination; if it does, we have a permutation. A permutation can be defined as an ordered combination.
An ordered combination is what is meant by a permutation.
The number of permutations of n objects, taken r at a time, is calculated using the formula below:
P(n,r)=n!(n-r)!
The following formula calculates the number of combinations of n objects taken r at a time: C(n,r)=n!/(n-r)!r!
there are 26^3 combinations of letters. And 10^3 combinations of numbers.
So the total combinations is 26^3 x 10^3 = 17,576,000
Many license plates don’t allow vowels a,e,i,o,u,and y which would accidentally form some awkward words…
Then you’d have 20^3 x 10^3 = 8,000,000 combinations.
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Find the value of so that the graph of the equation has the given y-intercept
Y= -1/3x + 5/6k; b= -10
The value of 'k' will be;
⇒ k = - 12
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph of the equation has the given y-intercept are;
⇒ Y= -1/3x + 5/6k; b= -10
Now,
Since, The equation of line in point-slope form will be;
⇒ y = mx + b
Here, The equation is,
⇒ Y= -1/3x + 5/6k
Hence, The y - intercept (b) = 5/6k
But here, b = - 10
So, We get;
⇒ 5/6 k = - 10
Solve for k as;
⇒ 5k = - 10 × 6
⇒ 5k = - 60
⇒ k = - 12
Thus, The value of 'k' will be;
⇒ k = - 12
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The of the degrees of each factor is the degree of the product.
Answer:The degree of the product is equal to the sum of the degrees of the factors.
Step-by-step explanation:
ar chie and bijan share some money in the ratio 7 : 11. bijan gets £132. how much money does archie get?
Archie will get $84.
We have given that,
archie and bijjan share some money in the ratio 7:11 and bijjan get $132.
We have to find how much money will archie get.
Let us consider x as a money
i.e. 7x:11x
bijjan gets $132
means 11x = 132
x = [tex]\frac{132}{11}[/tex]
x = 12
Therefore archie's money,
7x=7(12) = 84
Hence archie get $84.
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. The concept of ratio defines us to compare two quantities while the proportion is an equation that shows that two ratios are equivalent.
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explain how the is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers.
Nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.
What is birth weight?
The body weight of a newborn is referred to as birth weight. Infants of European descent typically weigh between 2.5 and 4.5 kilogrammes at birth, with an average of 3.5 kilograms. South Asian and Chinese babies weigh about 3.26 kilogrammes on average.
Babies born to nonsmokers typically weighed between 1,000 and 5,000 grammes. Babies born to smokers often ranged in weight from 500 to 4500 grammes.
However, we also notice some significant variations between the two groups' normal ranges of birth weights. With fewer infants in the lower weight ranges, nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.
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what is the recursive formula
Answer: The recursive formula generate term at a time by relating the term to one or more previous terms
Step-by-step explanation: The formula for recursive is
f(1)=6,f(n)=f(1)+f(n-1),n>1
there are 38 different time periods during which classes at a university can be scheduled. if there are 677 different classes, what is the minimum number of different rooms that will be needed?
The minimum number of different rooms that will be needed = 18
We know that the Pigeonhole Principle states that if N objects are placed into k boxes, then at least one box contains at least N/k objects.
In this question, we have been given there are 38 different time periods during which classes at a university can be scheduled.
if there are 677 different classes, we need to find the minimum number of different rooms that will be needed.
There exists a time period will have at least 677/38 = 18 classes during
it.
Therefore, 18 different rooms will be needed.
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PLS HELP!!! I really need help!
Use substitution to solve the system.
5x + 4y = 9
-2x + y = -14
Answer:
x = 9/5 − 4y/5
x = 7 + y/2
Step-by-step explanation:
Move all terms that dont contain x to the right side and solve.
length
Quantity
amount of substance
luminous intensity
US Customary Units
inch (in), foot (ft), yard (yd), mile (mi)
ounce (oz), pound (lb), ton (tn)
fluid ounce (fl oz), pint (pt), quart (qt),
gallon (gal)
second (sec), minute (min), hour (hr)
degrees Fahrenheit ("F)
SI Units
kilometer (km), meter (m), centimeter
(cm), millimeter (mm)
second (s)
Kelvin (K)
kilogram (kg), gram (g), milligram (mg)
ampere (A). milliampere (mA)
mole (mol)
candela (cd)
Answer:
Step-by-step explanation:
All units of a physical measure are linked via a conversion factor. On this web page for every unit you can find the conversion factor compared to the base unit (SI unit).
To do a conversion (or equivalent) you must multiply the value to be converted by the conversion factor of the start unit and then divide the result by the conversion factor of the destination unit.
For example, we want to know how many centimeters equals 12 yards?
# convert the units in meters (which is the SI base unit for the lengths)
# 1 yard = 0.9144 meters
# 1 centimeters = 0.01 meters
# derive the conversion factor between the yard and centimeters by dividing the factors found
# 0.9144/0.01 = 91.44
# 1 yd = 91.44 cm
# now we multiply the amount to be converted by the conversion factor found
# 12 * 91.44 = 1097.28
# result: 12 yd equals 1097.28 cm
Unit conversion tool implements this simple algorithm.
A drummer and a guitarist each wrote songs for their band. The guitarist wrote 10 fewer than twice the number of songs that the drummer wrote. They wrote a total of 50 songs. Write the system of equations that models this situation if the drummer wrote d songs and the guitarist wrote g songs.
Answer:
Step-by-step explanation:
no
The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each
year from 2010 through 2016 can be approximated by the models = 254 − 9 + 1. 12 and = 341 +
3. 2 where t is the year.
Write a function P that represents the annual profit of the company.
(Profit = Revenue − Cost)
A function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .
Describe the term Function?Function: A relationship between two variables, one of which is dependent on the other and the other of which is independent, is represented by an expression.The overall cost incurred by a business (or organization) for one employee over the course of a year is known as the annual cost.We provided Cost C. ( in thousand of dollar)
And a company's revenue R (in thousands of dollars).
C is the cost function.
C = 254 - 9t + (1.1)t²Revenue function R = 341 - 3.2t where t time in year .The value t = 9 is 9 years.
If P is the Annual profit. Then,
Profit = Revenue − Cost
P = R - C
P = 341 - (3.2)t - 254 - 9t + (1.1)t²
= (1.1)t² - (12.2)t + 87
Thus, a function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .
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Complete Question:
The annual cost C in thousands of dollars and revenue R in thousands of dollars for a company each year from 2010 through 2016 can be approximated by the models C = 254 − 9t + 1.1t2 and R = 341 + 3.2t where t is the year, with t = 10 corresponding to 2010.
(a) Write a function P that represents the annual profit of the company.
Find an equation that is perpendicular to 4x+3y=12
Answer:
Step-by-step explanation
x=2
1. Claude can do 120 jumping jacks in 2 minutes.
Write an equation to represent how many jumping
jacks Claude can complete in 5 minutes.
five hamburgers cost 5.25 at this rate what is the cost of 8 hamburgers
Answer: 8.4
Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4
mary has 16 forks and 12 knives to place in silverware holders at the fast food restaurant where she works. she wants to distribute them equally, with no forks or knives left over. what is the greatest number of silverware holders mary can stock?
The greatest number of silverware holders Mary can stock is 4, each containing 4 forks and 3 knives so that no fork or knife is left over and are distributed equally.
What is distribution?
When a quantity is to be distributed equally into a certain number of groups, we divide the quantity by the number of groups.
Equating number of silverware stocks :Given: 16 Forks and 12 knives
To find: number of silverware stocks = ?
As we know that the knives and forks should be distributed equally in each silverware holder, 4 forks and 3 knives will go into each of the silverware holder.
Now, we need number of silverware holders each having same number of forks and knives.
4 forks×4 = 16
3 knives× 4 = 12
∴ Number of silverware holders Mary requires to distribute knives and forks equally with no left over is 4.
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find the probability if two dice are rolled. (enter the value of probability in decimals. round the answer to three decimal places.)
The probability of getting a total of 8 when two dice are rolled is 0.139.
Probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be represented by proportions on a 0–1 scale.
A single die will have six sides with the numbers: 1, 2, 3, 4, 5, and 6. Each of these events is equally likely to occur if the dice are rolled fairly. So the probability of getting any side of the number is 1/6. Therefore, the probability of getting 1 in dice is 1/6, 2 is 1/6, and so on.
Therefore, the total possible outcomes are the multiplication of the total possible outcomes on dice 1 and dice 2, which is 36.
This possible outcome of rolling two dice is given by,
[tex]\left\{\begin{array}{ccccccc}(1, 1)&(1, 2)& (1, 3)&(1, 4)&(1, 5)&(1, 6)\\(2, 1)&(2, 2)&(2, 3)&(2, 4)&(2, 5)&(2, 6)\\(3, 1)&(3, 2)&(3, 3)&(3, 4)&(3, 5)&(3, 6)\\(4, 1)&(4, 2)&(4, 3)&(4, 4)&(4, 5)&(4, 6)\\(5, 1)&(5, 2)&(5, 3)&(5, 4)&(5, 5)&(5, 6)\\(6, 1)&(6, 2)&(6, 3)&(6, 4)&(6, 5)&(6, 6)\end{array}\right\}[/tex]
The probability of getting a total of 8 from both dice is given by, (2, 6) (3, 5) (4, 4) (5, 3) (6, 2). So the number of favorable outcomes is 5 and the total outcome is 36. The probability is P(getting a total of 8 from both dices)=5/36= 0.139.
The answer is 0.139.
The complete question is -
Consider rolling dice and getting a total of 8. Find the probability of two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places).
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tion for y: 2x + 3y = -6. Then, answer the questions that follow.
formed equation, what is the slope of the linear equation 2x + 3y = -6?
to find solutions to the linear equation.
x
Lesson 17 Problem Se
Transformed Linear Equation:
y
Answer:
The slope is -2/3
Step-by-step explanation:
2x + 3y = -6
We want to find the slope, so we need to get the equation in slope intercept form y = mx+b where m is the slope and b is the y intercept
Subtract 2x from each side
3y = -2x+6
Divide each side by 3
y = -2/3x +2
The slope is -2/3
Determine whether or not each of the following have the well-ordering property (i.e. whether "WOP(A;)" holds/is true or if is fails/is false). If for a set Ai, WOP(Ai) fails, then give a nonempty subset Eị of the set Aj which has no least element, i.e. give a subset that serves as a counterexample to "WOP(A;)", in other words give a witness that shows that the well- ordering property fails. 1 (iv) A4 = {5i +į lien} = {} \}} (v) A5 ne Z\ {0} n (vi) A6 = {-5, 7, 10, 13}
(iv) set A₄ holds well ordering property.
(v) set A₅ does not hold well ordering property.
(vi) set A₆ holds well ordering property.
(iv) A₄ = {5i+1/i I i ∈ N}
= { 5(1) + 1/1, 2(2)+1/2, 5(3)+1/3, 5(4)+1/4, .....}
= {5+1, 10+1/2, 15+1/3, 20+1/4, ....}
Elements of the set A₄ are distinct and increasing and 6 is the least elements of A₄.
set A₄ holds well ordering property.
(v) A₅ = { 1/n I n ∈ ZI }
= {1,1/2,1/3,1/4,1/5,....}
A₅ does not hold well ordering property.
(vi) A₆ = {-5,7,10,13}
A₆ is the finite set and all elements are distinct .
For any sub sets of A₆ there exists a dense elements.
A₆ holds well deseriving property.
Hence we get the required answer.
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Which criteria for triangle congruence allows you to immediately conclude that the triangles.
We may determine that the triangles are congruent based on the (B) HL criterion right away.
What are HL criteria?According to the HL Postulate, a right triangle's hypotenuse and leg are congruent if they are also congruent with the hypotenuse and leg of another right triangle.
So, we can see from the accompanying figure that these two triangles share a center line that is parallel to the base.
The two triangles are therefore right-angled triangles.
The hypotenuse of two triangles being congruent is then mentioned as a further argument.
Triangle congruence according to the HL criterion allows for a quick determination of congruence.
Therefore, we may determine that the triangles are congruent based on the (B) HL criterion right away.
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Complete question:
Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?
A) SAS
B) HL
C) AAS
D) none
Mercury orbits the Sun 3 times in 264 days.
a. How many times does Mercury orbit the Sun in 440 days?
Mercury orbits the Sun__________ times in 440 days.
Question 2
b. How many days does it take Mercury to orbit the Sun 8 times?
It takes Mercury_________ days to orbit the Sun 8 times.
Answer:
a. 15 days
b. 704 days
Step-by-step explanation:
a.264+88+88=440
b.It takes mercury 264 days to orbit the sun 3 times which means all you have to do is
264+264=528+264=792-88=704
3 + 3 = 6 + 3 = 9- 1 = 8
an executive hires 3 office workers from 8 applicants. (a) in how many ways can the selection be made?
The number of ways can the selection be made is 84.
Given:
an executive hires 3 office workers from 8 applicants.
a ) .
Number of ways = C ( 8 , 3 )
C ( n , r ) = n! / ( n - r ) ! r!
C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!
= 8! / 5! * 3 !
= 8 * 7 * 6 * 5! / 5! * 3!
= 56 * 6 / 3!
= 56 * 6 / 3 * 2 * 1
= 56 * 3 / 2 * 1
= 28 * 3 / 1
= 28 * 3
= 84 ways
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Use the unit fraction 1/5 to represent the space between the tick marks on the number line. Write an expression involving subtraction that is being modeled. Then find the difference.
Please help asap now !!!!!
Answer:
220.25
Step-by-step explanation:
881 divided by 4 is 220.25
A company that makes hair-care products had 8000 people try a new shampoo. Of the 8000 people, 48 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
0.6% of the people had a mild allergic reaction
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A company that makes hair-care products had 8000 people try a new shampoo.
In the 8000 people, 48 had a mild allergic reaction.
We need to find the percent of the people had a mild allergic reaction
We have to find what is 48 percent in 8000.
x×8000=48
Divide both sides by 8000
x=48/8000
x=0.006
Now we need to multiply by 100 as it is a hundredth part.
0.006×100
0.6
Hence, 0.6% of the people had a mild allergic reaction
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The parking garage at the airport has 625 parking spaces. 92% of the spaces are empty. How
many empty spaces are there in the parking garage?
Answer:
575 empty spaces
Step-by-step explanation:
If 625 --> 100% then
X --> 92%
X= (625 * 92)/100
X= 575
let $s$ be the set of the 2005 smallest positive multiples of 4, and let $t$ be the set of the 2005 smallest positive multiples of 6. how many elements are common to $s$ and $t$? (a) 166 (b) 333 (c) 500 (d) 668 (e) 1001
The number of elements that are common to S and T are 668 elements ,
the correct option is (d) .
In the question ,
it is given that ,
the set S is the set of 2005 positive multiple of 4
that is S = {4,8,12,16,....}
and the set T is the set of 2005 positive multiple of 6
that is T = {6,12,18,24,....}
and since the least common multiple , LCM of 4 and 6 is = 12,
So , elements that are common to set S and T must be multiples of 12.
Since, 4 × 2005 = 8020 and 6 × 2005 = 12030,
the several multiples of 12 that are in set T won't be in set S,
but all multiples of 12 that are in set S will be in set T.
So we have to find the number of multiples of 12 that are in set S.
and since 4 × 3 = 12, that means every 3rd element of set S will be a multiple of 12.
which is = 2005/3 = 668 .
Therefore , there are 668 elements that are common .
The given question is incomplete , the complete question is
Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. how many elements are common to S and T ?
(a) 166 (b) 333 (c) 500 (d) 668 (e) 1001
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Please answer! Another math prob!
Gavin worked 7 hours tutoring and 3 hours landscaping.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Gavin is working for making $14 per hour tutoring and $13 per hour landscaping.
And, Last week Gavin worked a total 10 hours and earned $137.
Now,
Let number of hour for tutoring = x
And, Number of hour for landscaping = y
Since, Gavin is working for making $14 per hour tutoring and $13 per hour landscaping and earned $137.
So, We can formulate;
⇒ 14x + 13y = 137 ..(i)
And, Last week Gavin worked a total 10 hours.
So, We get;
⇒ x + y = 10 ..(ii)
Multiply by 13 in equation (ii) and subtract from (i0, we get;
⇒ 14x + 13y - 13x - 13y = 137 - 130
⇒ x = 7
And, x + y = 10
⇒ 7 + y = 10
⇒ y = 10 - 7
⇒ y = 3
Thus, Gavin worked 7 hours tutoring and 3 hours landscaping.
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