Answer:
look below
Step-by-step explanation:
To determine the upper-tail critical value of the test statistic for a chi-square test for independence in a contingency table, you can use a table of critical values for the chi-square distribution or you can use a statistical software package or calculator to compute the critical value.
In each of the following circumstances:
a. a=0.05, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.05.
b. a=0.01, r=5, c=6: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.
c. a=0.01, r=5, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.
d. a=0.01, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.01.
e. α=0.01, r=6, c=5: The critical value would be the upper-tail critical value of the chi-square distribution with 6 degrees of freedom and an alpha level of 0.01.
It's important to note that the critical value is dependent on the degrees of freedom and the alpha level, so you will need to use the appropriate values for these parameters in order to determine the correct critical value.
The arts & crafts club is selling candles to raise money. It costs $100 to rent a booth to sell the candles in. Materials to decorate the booth cost $32.50. The candles cost $2.50 each to make and the club sells them for $5 each. How many candles must be sold to break even?
We know that we need to sell out 53 candles to break even using mathematical operations.
What are mathematical operations?
The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, the total expense of the shop:
$100 + $32.50 = $132.50
No, the candle costs $2.50.
The selling price of a candle is $5.
Profit in each candle is: 5 - 2.50 = $2.50
A number of candles that we need to sell to break even are:
132.50/2.50
53
Therefore, we know that we need to sell out 53 candles to break even using mathematical operations.
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Suppose 41% of the registered voters in a country are Republican. If a sample of 488 voters is selected, what is the probability that the sample proportion of Republicans will be greater than 44%?
The probability that the sample's Republican percentage will be higher than 44% is 0.089.
What is probability?Probability is a metric used to express the possibility or chance that a particular event will occur.
Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
To determine the probability of a sample proportion, the normal probability is used as the z-test statistic of one sample proportion.
When the sample size is big, the z-test statistic, a normal test statistic, is employed.
So, the probability will be:
We know that the sample size is n = 488 and the proportion is p = 0.41.
Now, obtain P(p > 0.44) as follows:
[tex]\begin{aligned}& P(\hat{p} > 0.44)=1-P\left(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \leq \frac{0.44-p}{\sqrt{\frac{p(1-p)}{n}}}\right) \\& P(\hat{p} > 0.44)=1-P\left(Z \leq \frac{0.44-0.41}{\sqrt{\frac{0.41(1-0.41)}{488}}}\right) \\& P(\hat{p} > 0.44)=1-P(Z \leq 1.347)\end{aligned}[/tex]
Excel function for the p-value:
P(p > 0.44) = 1 - 0.911
P(p > 0.44) = 0.089
Therefore, the probability that the sample's Republican percentage will be higher than 44% is 0.089.
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Find the missing number so that the equation has infinitely many solutions.
–2x + 8= __x + 8
a
3
b
-4
c
8
d
-2
Answer:
-2
Step-by-step explanation:
If both sides are identical, there will be infinitely many solutions.
Help asap
Brainliest to best answer
7) ∠EFG = 88 degree
8) DC and AB are parallel to each other.
AE and AB are perpendicular to each other
CG and AB are perpendicular to each other.
9) ∠ACD = 102 degree
What do you mean by co interior angle?
Co-interior angles, or consecutive interior angles, are two angles on the same side of a transverse line. Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary.
7) Given :
∠EFG = 32 degree
∠GFH = 56 degree
∠EFG = ∠EFG + ∠GFH = 32 + 56 = 88 degree
Therefore, ∠EFG = 88 degree
8) DC and AB are parallel to each other.
AE and AB are perpendicular to each other
CG and AB are perpendicular to each other.
9) As AB and CD are parallel to each other therefore , ∠BAC and ∠ACD are cointerior angle and sum of co interior angles is 180 degree.
6x + 6 + 9x - 6 = 180
15x = 180
x = 180/15 = 12
∠ACD = (9x - 6) degree = 9(12) - 6 = 108 - 6 = 102
Therefore, ∠ACD = 102 degree
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Factor a²+4 b² completely.
a²+4b²=_____
Answer: The expression a²+4b² can be factored in the following way:
a²+4b² = (a² + 2ab + 2ab + 4b²)
= (a+b)²
In general, the square of a binomial (a+b) can be written as (a+b)² = a² + 2ab + b². This is known as the "square of a sum" formula. In this case, we can apply this formula to the binomial a+b to obtain a² + 2ab + b² = (a+b)². We can then use the fact that the square of a binomial can be written as the square of each term plus twice the product of the two terms. This allows us to write the expression as (a+b)² = a² + 2ab + b² = a² + 2ab + 2ab + 4b² = (a² + 2ab + 2ab + 4b²) = (a²+4b²). Therefore, the fully factored form of a²+4b² is (a+b)².
The corner convenience store sells candy in 20 c, 30 c, and 50 c packages, List all the ways in which Waylon can spend exactly $3.00 on candy.
The possible ways the corner convenience store can sell candy packages to spend at least $3.00 is
How to solve equations?An equation is a mathematical model showing the equality of two opposite sides or an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given parameters are
20c, 30c and 50c
Least cost =$3
Let the possible ways be x
20x+30x+50x=3.00
Solving the equation we have:
100x=3.00
make x the subject
100x=3
x=3/100
This can be expressed in decimal as 0.03
In conclusion, he can sell it in 3/100 or 0.03 ways to spend at least $3.00 on a candy.
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If the ratio of perimeters is 2:9, then the ratio of areas is?
Group of answer choices
2:9
5:21
4:81
8:729
Answer:
4:81
Step-by-step explanation:
κμΛζΖυ
The ratio of area of squares is 4:81. Therefore, option C is the correct answer.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of perimeters of a squares is 2:9.
We know that, perimeter of square is 4a, where a is side of a square
Now, 4x/4y =2/9
x/y =2/9
As we know area of square is a², where a is side of a square
So, x²/y² =2²/9²
x²/y² =4/81
The ratio of area of squares is 4:81. Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
If the ratio of perimeters of a squares is 2:9, then the ratio of their areas is
A) 2:9
B) 5:21
C) 4:81
D) 8:729
Help
The Christmas cheer from the crowd singing in the park brings up the Clausometer to 80%!
What is this number written as a fraction in simplest form?
The number written as a fraction in simplest form is 4/5
What is this number written as a fraction in simplest form?From the question, we have the following parameters that can be used in our computation:
Clausometer = 80%
Turn the percentage to fraction
So, we have the following representation
Clausometer = 80/100
Divide 80 and 100 by 10
So, we have the following representation
Clausometer = 8/10
Divide 8 and 10 by 2
So, we have the following representation
Clausometer = 4/5
Hence, the fraction is 4/5
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You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
Find the critical value that corresponds to a confidence level of 99.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
The critical value that corresponds to a confidence level of 99% is, 2.58.
What is a 3 decimal place number?1 decimal place (tenths) 2 decimal places (hundredths) 3 decimal places (thousandths) 4 decimal places (ten-thousandths)
Consider a random variable X that follows a Binomial distribution with parameters, sample size n and probability of success p.It is provided that the distribution of proportion of random variable X, , can be approximated by the Normal distribution.The mean of the distribution of proportion is, The standard deviation of the distribution of proportion is, .Then the confidence interval for the population proportion p is:The confidence level is 99%.
The significance level is:
Compute the critical value as follows:
That is:
Use the z-table for the z-value.
For z = 2.58 the P (Z < z) = 0.995.
And for z = -2.58 the P (Z > z) = 0.005.
Thus, the critical value is, 2.58.
active attachment
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 87.3% of confidence, our significance level would be given by and . And the critical value would be given by:And we can use the following excel codes to find the solution:"=NORM.INV(0.0635,0,1)"
"=NORM.INV(1-0.0635,0,1)"
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". The margin of error is the range of values below and above the sample statistic in a confidence interval. Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". The population proportion have the following distribution (assuming the normal approximation)Solution to the problemThe confidence interval for the mean is given by the following formula: In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 87.3% of confidence, our significance level would be given by and . And the critical value would be given by:And we can use the following excel codes to find the solution:
"=NORM.INV(0.0635,0,1)"
"=NORM.INV(1-0.0635,0,1)"
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if an ionic oxide has both x amount of fe2 and y amount fe3 , where x and y do not have to be integers, the formula would be (fe2 )x(fe3 )yoz. calculate the amount of oxide ions, z, in terms of x and y (an algebra problem).
Fe^2 + → Fe^3 + + e^- is an example of oxidation
How many oxidations do Fe3+ and Fe2+ ions have?
For instance, the oxygen ion O2+ has an oxidation number of 2 because it can contribute two electrons, whereas the iron ion Fe3+ has an oxidation number of +3 because it can take on three electrons to establish a chemical bond.
[tex]$\mathrm{Fe}_3 \mathrm{O}_4$[/tex] contains [tex]$\mathrm{F}$ e[/tex] atoms of both[tex]$+2$ and $+3$[/tex]oxidation number.
It is a stoichiometric mixture of[tex]Ferrous $(\mathrm{FeO})$[/tex]
and Ferric [tex]$\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ oxides combined as $\mathrm{FeO} \cdot \mathrm{Fe}_2 \mathrm{O}_3$.[/tex]
[tex]Oxidation state of oxygen in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ is $-2$.[/tex]Let the oxidation state of [tex]$\mathrm{Fe}$ in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ be $\mathrm{x}$ and $y$[/tex]
As we know that the sum of the oxidation states of all the atoms or ions in a neutral compound is zero.
ThereforeOxidation state of [tex]$\mathrm{F}$ e in $\mathrm{F}$ eO-[/tex]
&[tex]x+(-2)=0 \\& \Rightarrow x=2[/tex]
Oxidation state of[tex]$\mathrm{F}$ e in $\mathrm{Fe}_2 \mathrm{O}_3-$[/tex]
&[tex]2(\mathrm{y})+3(-2)=0 \\& \Rightarrow 2 \mathrm{y}=6 \\& \Rightarrow \mathrm{y}=3\end{aligned}[/tex]
Hence the oxidation number of [tex]$\mathrm{Fe}$ in $\mathrm{Fe}_3 \mathrm{O}_4$ are $+2$ and $+3$[/tex]respectively.
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Please help me with this! Thank you so much ahead!
The area of the shaded region will be equal to 120 square cm.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that the sides of the rectangle are 24 cm and 10 cm. The area of the shaded region will be calculated by subtracting the area of the whole rectangle and the area of the triangle which is not shaded.
Area of the shaded region = ( 24 x 10 ) - ( 1/2 x 24 x 10)
Area of the shaded region = 240 - 120
Area of the shaded region = 120 square cm
Therefore, the area of the shaded region will be equal to 120 square cm.
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59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible)
The probability that a resident own a cat or a dog is 48%
How to determine the probability a resident own a cat or a dogFrom the question, we have the following parameters that can be used in our computation:
P(Own a cat) = 70%
P(Own a dog) = 59%
P(Own a cat and a dog) = 42%
The probability a resident own a cat or a dog is then calculated as
Probability a resident own a cat or a dog = P(Own a cat) + P(Own a dog) - P(Own a cat and a dog)
Substitute the known values in the above equation, so, we have the following representation
Probability a resident own a cat or a dog = 70% + 59% - 42%
Evaluate the sum and the difference
Probability a resident own a cat or a dog = 48%
Hence, the probability is 48%
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Complete question
59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find:
the probability a resident own a cat or a dog
(round to 4 decimal places where possible)
Line p passes through points (8, 7) and (4, 4). Line q is parallel to line p. What is the slope of line q?
Answer:
slope of line q = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
calculate the slope of line p using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )
m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes
then slope of line q = [tex]\frac{3}{4}[/tex]
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20 year mortgage from her bank. What formula could you type into Excel to determine what the largest mortgage loan she can afford?
The biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.
What are excel formulas?A formula in Microsoft Excel is an expression that modifies values in a set of cells.
Even if the result is incorrect, these formulas nonetheless return a result.
We may execute calculations like addition, subtraction, multiplication, and division using Excel formulae.
To make complex computations simpler, Excel features prewritten formulas known as functions.
A function takes one or more values, runs an operation, and then outputs the outcome to a cell.
Arguments are the values that you pass to a function.
So, in the given situation of Jenny, the excel formula PV(.035/12, 15*12, -485)will be used to determine the largest mortgage loan she can afford.
Therefore, the biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.
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Complete question":
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20-year mortgage from her bank. What formula could you type into Excel to determine the largest mortgage loan she can afford is?
(A) PV(.035/12, 15*12, -485)
(B) PMT(.035/12, 15*12, -485)
(C) PV(.035, 15*12, -485)
(D) 390*.035/20
A phone company offers two monthly plans plan a cost $19 plus an additional $0.11 for each minute of calls plan b has no initial fee but costs $0.15 for each minute of costs For what amount of calling do the two plans cost the same? What is the cost when the two plans cost the same?
When the costs of the two plans are equal, plan A will cost $37.81, whereas plan B will cost $25.65.
To find the number of calls at which the two plans cost the same, we need to set the costs equal to each other and solve for the number of minutes. The cost of plan A is $19 + $0.11 per minute, and the cost of plan B is $0.15 per minute. Setting these equal to each other, we get:
$19 + $0.11 per minute = $0.15 per minute
We can then solve for the number of minutes by dividing both sides by the per-minute cost:
$19 / $0.11 per minute = $0.15 per minute / $0.11 per minute
This simplifies to:
171 minutes = 135 minutes
Therefore, the two plans cost the same at 171 minutes of calling.
To find the cost at this point, we can substitute 171 minutes back into either of the original cost equations:
Plan A: $19 + $0.11 per minute × 171 minutes = $19 + $18.81 = $37.81
Plan B: $0.15 per minute × 171 minutes = $25.65
Thus, the cost when the two plans cost the same is $37.81 for plan A and $25.65 for plan B.
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A Question 9 (2 points) Retake question
Evaluate the function f(x), if f(x) = 4x - 2, what is the value of f(3)?
Enter your answer in the box below.
f(3) =
A
A Question 10 ( 2 points) Retake question
A function f(x) is graphed on the coordinate plane. What is the function rule in slope-intercept form?
- Rule written in function notation (1 point)
- Correct slope and intercept (1 point)
Solve the system using substitution.
5x + 3y = -4
y - 2x = 6
([?], [ ])
What is the rate of change of the function y=-5x+3
Answer:
-5
Step-by-step explanation:
The rate of change, also known as slope, would be -5.
Slope can be found with two points and the formula y minus y divided by x minus x or the change of y divided by the change in x.
To identify the slope on the equation is easy since this is slope-intercept form.
y=mx+b
where m is the slope
m in this case is -5, so -5 is your answer
Suppose that the functions g and f are defined as follows.
g(x)=(x+6)(x+6)
f(x)=-6 x+7
(a) Find g/f
(b) Find all values that are NOT in the domain of g/f}. If there is more than one value, separate them with commas.
By using the concept of function, it can be calculated that-
a) [tex]\frac{g}{f}(-4) = \frac{4}{31}[/tex]
b) The point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are -
g(x) = (x + 6)(x + 6)
f(x)= -6x+7
[tex]\frac{g}{f}(x) = \frac{g(x)}{f(x)} = \frac{(x+6)(x+6)}{-6x+ 7} = \frac{(x+6)^2}{-6x + 7}[/tex]
[tex]\frac{g}{f}(-4) = \frac{g(-4)}{f(-4)} = \frac{(-4+6)^2}{-6(-4) + 7} = \frac{4}{31}[/tex]
b) [tex]\frac{g}{f}(x)[/tex] is not defined if -6x + 7 = 0
[tex]\frac{g}{f}(x)[/tex] is not defined if [tex]x = \frac{7}{6}[/tex]
So the point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex].
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what would 10 possibly be? please help me thank u :)
- have a wonderful day/ night <3
The distance is 244.56 feet, in feet, between point K and point L.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Recall the Pythagorean theorem formula:
a² + b² = c²
Given that Kim is standing on the deck, point k, which is 140.75 feet above ground level.
Louise point L, is standing 200ft from the base of the lighthouse directly below Kim’s position.
Thus the distance, in feet, between point K and point L
Replacing by the values we have;
200 ² + 140.75² = KL²
KL² = 59810.56
KL = 244.56
The distance is 244.56 feet, in feet, between point K and point L.
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on average, the number of days it takes for a caterpillar to become a butterfly is 15 days with a standard deviation of 3.5 days.
If there are 10000 caterpillars at a sanctuary, how many out of the 10000 would you expect to become a butterfly in 17.8 days or more?
2,200 caterpillars are expected to become a butterfly in 17.8 days or more.
Step-by-step explanation:1. Find the Z value of 17.8.Formula: Z= (x-bar-mean)/σ: where x-bar is the score to which we are calculating a Z value; mean is just the arithmetic mean of the sample or population, and σ is the standard deviation of the sample or the population. Check attached image 1 below.
Substitute and calculate:
[tex]Z=(17.8-15)/3.5\\\\ Z=0.8[/tex]
2. Find the probability.For this solution, we are going to b e using Microsoft Excel's tools to calculate the probabilities. Check attached image 2.
[tex]IP(Z\leq 17.8)=0.7881[/tex]
This is the probability that any caterpillar becomes a butterfly in 17.8 days or less. This is how Microsoft Excel calculates probabilities for default. Now, in order to get the probability that the problem asks for (17.8 days or more) we just need to do the following operation:
[tex]1-0.778=0.222[/tex]
3. Calculate the amount of caterpillalrs.[tex](0.222)(10,000)=2,220[/tex]
4. Conclude.2,200 caterpillars are expected to become a butterfly in 17.8 days or more.
twice the number of x
9. ΔRWS ≅ ΔTUV
Find the values of x and y
[tex]VT=SR \implies 3y+7=25 \implies \boxed{y=6} \\ \\ \\ ○\ m\angle UTV=180^{\circ}-90^{\circ}-29^{\circ}=61^{\circ} \\ \\ \angle WRS \cong \angle UTV \implies 8x-27=61 \implies \boxed{x=11}[/tex]
A parachutist's rate during a free fall reaches 55 meters per second. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 15 seconds of free fall? In your computations, assume that meter is equal to 3.3 feet. Do not round your answers.
The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
A parachutist's rate during a fast drop arrives at 55 meters each second. In your calculations, accept that the meter is equivalent to 3.3 feet.
Convert the speed into feet per second. Then we have
S = 55 x 3.3
S = 181.5 feet per second
The parachutist fall during 15 seconds of free fall will be given as,
D = 181.5 x 15
D = 2,722.5 feet
The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.
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Which of the following forms of organization is a separate legal entity?
A corporation—also known as a C corp—is a legal entity distinct from its owners.
What is a corporation?A corporation also referred to as a C corp, is a separate legal entity from its owners.
Corporations are able to generate revenue, pay taxes, and face legal consequences.
The strongest protection against personal liability is provided to owners by corporations, although forming a corporation is more expensive than creating other types of entities.
A corporation is a collection of people or a business that has been given legal status as a single entity by the state and is used for specific legal purposes.
Early corporations were created with a charter.
The majority of governments currently permit the registration of new corporations.
Therefore, a corporation—also known as a C corp—is a legal entity distinct from its owners.
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Correct question:
Which form of organization is a separate legal entity?
If I earn one dollar every second how many hours would it take for me to get to 230,000 dollars?
Answer:
It will take 64 hours
Step-by-step explanation:
It will be more specifically 63.889 hours, but rounding up it's 64
A teacher gives students independent reading 1/2 time for 1 hour,three times a week.Represent the total amount of reading time for a week as a mixed number and an improper fraction.
The reading time calculated to be
1 1/2 represented as mixed fraction3/2 represented as improper fractionHow to determine the the reading timeThe problem involves multiplication of fractions
The fraction required are:
let the reading time be x
1/2 time for 1 hour = 1/2 * x = x/2
three times a week
= x/2 * 3
= 3x/2
The reading time is 3/2 improper fraction and 1 1/2 mixed fraction
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One label on a package of bolts says that each bolt has a diameter of 0.45 inch. To be in the package, the percent error of the diameter must be less than 3%. A test on the production line shows a bolt with a diameter of 0.46 inch. Should this bolt go into the package?
This bolt should go into the package. The percentage of error is 2.22% which is less than 3%.
What is the meaning of error?
The discrepancy between a variable's observed value and its actual but unseen value
Given that the diameter of each bolt is 0.45 inch.
The percentage of error the diameter of each bolt must be less than 3%.
A bolt picks for a test. The diameter of the bolt is 0.46 inch.
The formula of percent error is
The difference of the diameters/ the original diameter of bolt )× 100%
= [(0.46 - 0.45)/0.45] × 100%
= (0.1/0.45) × 100%
= 0.0222 × 100%
= 2.22%
The percentage of error is less than 3%. So the lot is good to go.
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6. Mrs. Ramirez' groceries cost $50 before tax, and the total including sales tax was $55. What is
the sales tax rate that Mrs. Ramirez paid?
Answer:sales tax rate would be 0.1
using the formula
Sales tax rate = Sales tax percent / 100
if 3 -letter words'' are formed using the letters a, b, c, d, e, f, g, how many such words are possible for each of the following conditions:
The possible number of 3 -letter words that can be formed with given conditions.
(a) No condition is imposed: 343
(b) No letter can be repeated in a word: 210
(c) Each word must begin with the letter 'a' : 49
(d) The letter 'c' must be at the end: 49
(e) The second letter must be a vowel: 98
In this question we have been given that 3 -letter words' are formed using the letters a, b, c, d, e, f, g.
We need to find the possible number of 3 -letter words that can be formed with given conditions.
(a) No condition is imposed.
the possible number of 3 letters words would be,
7³ = 343
(b) No letter can be repeated in a word.
Using the formula of Permutation,
^{7}P_3 = 7!/(7 - 3)!
= 210
(c) Each word must begin with the letter a.
If each word begins with letter 'a' there would be possible combinations of remaining 6 letters at 2nd and 3rd position of 3-letter word.
So, the possible number of 3 letters words would be,
7² = 49
(d) The letter c must be at the end.
If each word ends with letter c there would be possible combinations of remaining 6 letters at 1st and 2nd position of 3-letter word.
So, the possible number of 3 letters words would be,
7² = 49
(e) The second letter must be a vowel.
In the 3 letter word, the second letter must be vowel which is either a or e.
So, the possible number of 3 letters words would be,
49 + 49 = 98
Therefore, the possible number of words would be (a) No condition is imposed: 343
(b) No letter can be repeated in a word: 210
(c) Each word must begin with the letter 'a' : 49
(d) The letter 'c' must be at the end: 49
(e) The second letter must be a vowel: 98
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The complete question is:
3 -letter words'' are formed using the letters a, b, c, d, e, f, g. How many such words are possible for each of the following conditions?
(a) No condition is imposed.
(b) No letter can be repeated in a word.
(c) Each word must begin with the letter a.
(d) The letter c must be at the end.
(e) The second letter must be a vowel.