Answer:
In 20 years, the population will be about 80.3 thousand people
Step-by-step explanation:
If our first time is 0 and the population that goes along with that time is 70,000, we have a coordinate point where x is the time (0), and y is the population at that time (70). Our next time is 10 years later, when the population is 75,000. The coordinate point for that set of data is (10, 75). Now we will use those 2 points in the standard form of an exponential equation to write the model for this particular situation.
Exponential equations are of the form
[tex]y=a(b)^x[/tex]
where x and y are the coordinates from our points, one at a time; a is the initial value, and b is the growth rate. Filling in an equation with the first set of data:
[tex]70=a(b)^0[/tex]
Anything raised to the power of 0 = 1, so b to the power of 0 = 1 and we simply have that a = 70.
Now we use that value of a along with the x and y from the next coordinate pair to solve for b:
[tex]75=70(b)^{10}[/tex]
Begin by dividing both sides by 70 to get
[tex]1.071428571=b^{10}[/tex]
Undo the power of 10 on the right by taking the 10th root of both sides:
[tex](1.071428571)^{\frac{1}{10}}=(b^{10})^{\frac{1}{10}}[/tex]
On the right side we simply have b now, and on the left we have
1.006923142=b
Now we have a and b to write the model for this situation:
[tex]y=70(1.006923142)^x[/tex]
We need to find y, the population, in x = 20 years:
[tex]y=70(1.006923142)^{20}[/tex]
Raise the parenthesis to the 20th power giving you
y = 70(1.147959784) and
y = 80.3 thousand people
Final answer:
The exponential growth function that fits the given data is y(t) = a * (1 + r)^t. Using this function, we can find the population 20 years from now.
Explanation:
The exponential growth function that fits the given data is:
y(t) = a * (1 + r)^t
where:
a represents the initial population (70,000)r represents the growth rate per yeart represents the time in yearsTo find the growth rate per year, we can use the formula: r = (P/P0)^(1/t) - 1
Given that the population is projected to be 75,000 in 10 years, we can substitute these values into the formula to find the growth rate:
r = (75,000/70,000)¹/¹⁰ - 1 ≈ 0.035
The exponential growth function becomes:
y(t) = 70,000 * (1 + 0.035)^t
To find the population 20 years from now, we can substitute t = 20 into the exponential growth function:
y(20) = 70,000 * (1 + 0.035)²⁰ ≈ 95,212
The student business club on your campus has decided to hold a pizza fund raiser. The club plans to buy 50 pizzas from Dominos and resell them in the student center. Based upon the specials advertised on the Dominos website, what will you need to charge per slice (assume 8 slices per pizza) in order to break even? Since this is a fund raiser, what would you suggest charging for each slice and, based on this, what would the net profit be to this club? Why do you feel breakeven analysis is so crucial in the development of new products for businesses?
Answer:
2.50 per slice would be okay because most people would order 2 slices and that would have them give you an even 5.00. Net profit for this would be 464.00
Step-by-step explanation:
The specials advertised on Domino's website is 5.99 for each pizza, 8 slices.
The break even price is 1.34 per slice. This is important to know because a business never wants to take a loss.
To break even, the club would need to charge $2 per slice. However, for fundraising, they might charge $3 per slice, giving a net profit of $400. Breakeven analysis is crucial in business as it helps in decision making and financial planning.
Explanation:Based on the information given, we see that the business club wants to purchase 50 pizzas from Domino's and resell them on campus. Assuming each pizza costs $16 (as per the example given for Authentic Chinese Pizza), the initial cost for the club would be $800 (50 pizzas x $16).
To calculate the break-even price per slice, we would need to divide the total cost by the total number of slices: $800 / (8 slices x 50 pizzas) = $2 per slice. However, since this is a fundraiser, the club might want to add in a margin to generate profit, so they might charge for example $3 per slice, resulting in a profit of $1 per slice, or $400 total.
The breakeven analysis is crucial in the development of new products because it helps businesses determine the minimum production and sales levels they must achieve to avoid losing money. This is useful for decision making and financial planning in any business operation.
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Liz earns a salary of $2,500 per month, plus a commission of 7% of her sales. She wants to earn at least $2,900 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Answer:
The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]
Step-by-step explanation:
Let
x----> amount in sales this month
we know that
[tex]7\%=7/100=0.07[/tex]
The inequality that represent this situation is equal to
[tex]2,500+0.07x\geq2,900[/tex]
Solve for x
Subtract 2,500 both sides
[tex]0.07x\geq2,900-2,500[/tex]
[tex]0.07x\geq400[/tex]
Divide by 0.07 both sides
[tex]x\geq400/0.07[/tex]
[tex]x\geq \$5,714.29[/tex]
therefore
The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]
Prove that for all real numbers x, if 2x+1 is rational then x is rational
Answer with explanation:
It is given that, for all real numbers x, if 2 x+1 is rational .
When you will look at the expression ,2 x +1
⇒1 is rational
⇒2 x will be rational, because the expression , 2 x+1, is rational.
⇒2 x is rational, it means , x will be rational,because 2 is rational.
Some important rules considering rational and irrational
1.⇒Product of rational and rational is Rational.
2.⇒Product of Irrational and Rational is Irrational.
3.⇒Product of Irrational and Irrational may be irrational or rational.
≡2 x →is rational, 2 is rational number ,so x will be rational also.
If 2x+1 is rational, hence 2x is rational subtracting 1 which is also rational. Assuming 2x is expressible as a/b, then x is a/2b, again showing x is rational.
Explanation:To prove that if 2x+1 is rational, then x must also be rational, we must understand the definition of rational numbers and basic properties of arithmetic operations involving rational numbers. A number is considered rational if it can be written as the quotient of two integers (where the denominator is not zero). Given that the sum of two rational numbers is also rational, if 2x+1 is rational, and we know that 1 is rational (since 1 can be written as 1/1), then 2x must be rational because rational minus rational yields a rational result.
Now, assuming 2x is rational, we can express it as a fraction [tex]\frac{a}{b}[/tex], with a and b being integers and b non-zero. Since the multiplication of a rational number by an integer is also rational, and knowing that 2 is an integer, we can then say that x, which is [tex]\frac{a}{2b}[/tex], is also rational. This is because we can express the result of [tex]\frac{a}{2b}[/tex] with integers in the numerator and the denominator.
A mile-runner’s times for the mile are normally distributed with a mean of 4 min. 3 sec. (This would have to be expressed in decimal minutes -- 4.05 minutes), and a standard deviation of 2 seconds (0.0333333··· minutes (the three dots indicate a repeating decimal)). What is the probability that on a given run, the time will be 4 minutes or less?
Answer: 0.0668
Step-by-step explanation:
Given: Mean : [tex]\mu=\text{4 min. 3 sec.=4.05 minutes}[/tex]
Standard deviation : [tex]\sigma = \text{2 seconds=0.033333 minutes }[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 4 minutes , we have
[tex]z=\dfrac{4-4.05}{0.03333}\approx-1.5[/tex]
The P-value = [tex]P(z\leq-1.5)=0.0668072\approx0.0668[/tex]
Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668
The probability that on a given run, the time will be 4 minutes or less is approximately 6.68%.
Explanation:To find the probability that on a given run, the time will be 4 minutes or less, we need to calculate the z-score for 4 minutes and then use the standard normal distribution table to find the probability. The z-score can be calculated using the formula (x - mean) / standard deviation. In this case, the z-score is (4 - 4.05) / 0.0333333⋯ = -1.50. Looking up the z-score in the standard normal distribution table, we find that the probability is approximately 0.0668 or 6.68%.
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1) Find the lump that must be deposited today to have a future value of $ 25,000 in 5 years if funds earn 6 % componded annually.
Answer: $ 18681.45
Step-by-step explanation:
Given: Future value : [tex]FV=\$25,000[/tex]
The rate of interest : [tex]r=0.06[/tex]
The number of time period : [tex]t=5[/tex]
The formula to calculate the future value is given by :-
[tex]\text{Future value}=P(1+i)^n[/tex], where P is the initial amount deposited.
[tex]\Rightarrow\ 25000=P(1+0.06)^5\\\\\Rightarrow\ P=\dfrac{25000}{(1.06)^5}\\\\\Rightarrow\ P=18681.4543217\approx=18681.45[/tex]
Hence, the lump that must be deposit today : $ 18681.45
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x → (π/2)+ cos(x) 1 − sin(x)
Answer:
The limit of the function at x approaches to [tex]\frac{\pi}{2}[/tex] is [tex]-\infty[/tex].
Step-by-step explanation:
Consider the information:
[tex]\lim_{x \to \frac{\pi}{2}}\frac{cos(x)}{1-sin(x)}[/tex]
If we try to find the value at [tex]\frac{\pi}{2}[/tex] we will obtained a [tex]\frac{0}{0}[/tex] form. this means that L'Hôpital's rule applies.
To apply the rule, take the derivative of the numerator:
[tex]\frac{d}{dx}cos(x)=-sin(x)[/tex]
Now, take the derivative of the denominator:
[tex]\frac{d}{dx}1-sin(x)=-cos(x)[/tex]
Therefore,
[tex]\lim_{x \to \frac{\pi}{2}}\frac{-sin(x)}{-cos(x)}[/tex]
[tex]\lim_{x \to \frac{\pi}{2}}\frac{sin(x)}{cos(x)}[/tex]
[tex]\lim_{x \to \frac{\pi}{2}}tan(x)}[/tex]
Since, tangent function approaches -∞ as x approaches to [tex]\frac{\pi}{2}[/tex]
, therefore, the original expression does the same thing.
Hence, the limit of the function at x approaches to [tex]\frac{\pi}{2}[/tex] is [tex]-\infty[/tex].
The function cos(x)/(1-sin(x)) approaches an indeterminate form as x approaches π/2 from the right. By applying L'Hopital's Rule, we find that the limit is equivalent to the limit of tan(x) as x approaches π/2 from the right. However, tan(π/2) is undefined, so the limit does not exist.
Explanation:In this question, we are asked to find the limit of the function cos(x)/(1-sin(x)) as x approaches π/2 from the right. We can't directly substitute x = π/2 because it makes the denominator zero, yielding an indeterminate form of '0/0'.
So, we use L'Hopital's Rule, which states that the limit of a ratio of two functions as x approaches a particular value is equal to the limit of their derivatives.
The derivative of cos(x) is -sin(x) and the derivative of (1-sin(x)) is -cos(x). Using L'Hopital's Rule, we can now re-evaluate our limit substituting these derivatives.
lim [x → (π/2)+] (-sin(x)/-cos(x)) = lim [x → (π/2)+] tan(x)
When substituting x = π/2 into tan(x), we realize that the tan(π/2) is undefined, so the answer is the limit does not exist.
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Help me ! Please for summer school
Answer:
The correct answer option is C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex].
Step-by-step explanation:
We are given that two line segments AB and CD are formed from the points A ([tex](x_1, y_1)[/tex], B ([tex](x_2, y_2)[/tex], C ([tex](x_3, y_3)[/tex] and D ([tex](x_4, y_4)[/tex].
We are to determine which condition needs to be met in order to prove that AB is perpendicular to CD.
When slopes of two perpendicular lines are multiplied, they give a product of -1.
Hence option C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex] is the correct answer.
The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. What is the probability that a randomly selected broiler weighs more than 1,454 grams?
Answer:
Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)
Step-by-step explanation:
Given:
Weights of Broilers are normally distributed.
Mean = 1387 g
Standard Deviation = 161 g
To find: Probability that a randomly selected broiler weighs more than 1454 g.
we have ,
[tex]Mean,\,\mu=1387[/tex]
[tex]Standard\,deviation,\,\sigma=161[/tex]
X = 1454
We use z-score to find this probability.
we know that
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]z=\frac{1454-1387}{161}=0.416=0.42[/tex]
P( z = 0.42 ) = 0.6628 (from z-score table)
Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 = 0.3372
Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)
i need geometry help pleas will give brainliest
Area of the shaded segment=
6π-9√3un^2
12π-9√3un^2
9π-9√3un^2
Answer:
6π - 9√3 unit^2
Step-by-step explanation:
Area of sector
= 1/6(π (6)^2
= 6π
Area of triangle = √3/4 (6)^2 = 9√3
Area of the shaded segment = Area of sector - Area of triangle
= 6π - 9√3 unit^2
to the risk of sounding redundant.
[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}-sin(\theta ) \right)~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ °rees\\ \cline{1-2} r=&6\\ \theta =&60 \end{cases}\implies A=\cfrac{6^2}{2}\left(\cfrac{\pi 60}{180}-sin(60^o ) \right) \\\\\\ A=18\left( \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} \right)\implies \boxed{A=6\pi -9\sqrt{3}}\implies \implies A\approx 3.26[/tex]
How do you convert 7/2^6 to decimal please? ( seven over 2 to the power of 6)
You just put the expression in a calculator! We have
[tex]\dfrac{7}{2^6} = \dfrac{7}{64}=0.109375[/tex]
Evaluate the function at the given value of the independent variable. Simplify the results. (If an answer is undefined, enter UNDEFINED.) f(x) = x3 − 49 x f(x) − f(7) x − 7 =
To evaluate the function f(x) = 5x² + 7 at a given value, substitute that value into the function and simplify. The resulting answer is the function's value at that point. For the difference quotient f(x) - f(7)/(x - 7), the value is undefined if x = 7.
To evaluate the function f(x) = 5x² + 7 at a given value of the independent variable and simplify the results, we simply plug in the value of the independent variable into the function. For example, if we want to evaluate f at x = 3, we would calculate f(3) = 5(3)² + 7 = 5(9) + 7 = 45 + 7 = 52. Thus, the evaluated function at x = 3 is 52.
If we were to find the difference quotient f(x) - f(7)/(x - 7), we would need to plug in a value for x that is not 7, as the expression is undefined for x = 7. For any other value of x, we substitute x into the function, subtract f(7), and divide by (x - 7). If x = 7, the result is UNDEFINED.
Solve the following problem. PV=$24,122; n = 70; i = 0.024; PMT ?; PMT = $ (Round to two decimal places.)
Answer:
The payment per period is $714.82.
Step-by-step explanation:
Given information: PV=$24,122; n = 70; i = 0.024
The formula for payment per period is
[tex]PMT=\frac{PV\times i}{1-(1+i)^{-n}}[/tex]
Substitute PV=$24,122; n = 70; i = 0.024 in the above formula.
[tex]PMT=\frac{24122\times 0.024}{1-(1+0.024)^{-70}}[/tex]
[tex]PMT=\frac{578.928}{0.80989084337}[/tex]
[tex]PMT=714.822256282[/tex]
[tex]PMT\approx 714.82[/tex]
Therefore the payment per period is $714.82.
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. Find the probability that it takes at least 8 minutes to find a parking space. (Round your answer to four decimal places.)
Answer: 0.0668
Step-by-step explanation:
Given: Mean : [tex]\mu = 5\text{ minutes}[/tex]
Standard deviation : [tex]\sigma = 2\text{ minutes}[/tex]
The formula to calculate z is given by :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
To check the probability it takes at least 8 minutes (X≥ 8) to find a parking space.
Put X= 8 minutes
[tex]z=\dfrac{8-5}{2}=1.5[/tex]
The P Value =[tex]P(z\geq1.5)=1-P(z\leq1.5)=1- 0.9331927=0.0668073\approx0.0668[/tex]
Hence, the probability that it takes at least 8 minutes to find a parking space = 0.0668
The probability that it takes atleast 8 minutes to find a parking space is 0.0668
Given the Parameters :
Mean = 5 minutes Standard deviation = 2 minutes X ≥ 8First we find the Zscore :
Zscore = (X - mean) / standard deviationZscore = (8 - 5) / 2 = 1.5
The probability of taking atleast 8 minutes can be expressed thus and calculated using the normal distribution table :
P(Z ≥ 1.5) = 1 - P(Z ≤ 1.5)
P(Z ≥ 1.5) = 1 - 0.9332
P(Z ≥ 1.5) = 0.0668
Therefore, the probability, P(Z ≥ 1.5) is 0.0668
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when are the expressions 3x +12 and 3(x+4) equvialent
Answer:
For any value of x
Step-by-step explanation:
Solve by using system of equations!
3x+12
3(x+4)=3x+12
3x+12=3x+12
x=x
This means that any value of x would create the same answer for both equations.
Answer:
Always.
Step-by-step explanation:
Always. This is true by distributive property.
The 5 hour energy drink should keep a person feeling awake while driving for 5 hours, regardless of their age. Stacy just doesn't believe it. So she has 50 twenty year olds, 50 thirty year olds, 50 forty year olds, and 50 fifty year olds consume a 5 hour energy drink, and then Stacy measured participants' awakeness after 5 hours of driving. What test should she use to analyze her results?
Answer:
a. Single-sample Z-Test
b. Single-sample t-test
c. Independent-measures t-test
d. Repeated-measures t-test (Paired-samples t-test)
e. Independent-measures ANOVA
Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a standard deviation of 1800 hours and a mean life span of 20,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 17,659 hours. Round your answer to four decimal places.
Answer: 0.9032
Step-by-step explanation:
Given: Mean : [tex]\mu = 20,000\text{ hours}[/tex]
Standard deviation : [tex]\sigma = 1800 \text{ hours}[/tex]
The formula to calculate z is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 17659
[tex]z=\dfrac{17659-20000}{1800}=−1.30055555556\approx-1.3[/tex]
The P Value =[tex]P(z>-1.5)=1-P(z<1.3)=1- 0.0968005\approx0.9031995\approx 0.9032[/tex]
Hence, the probability that the life span of the monitor will be more than 17,659 hours = 0.9032
To find the probability that the life span of the monitor will be more than 17,659 hours, use the z-score formula and the standard normal distribution table. The probability is approximately 0.0968.
Explanation:To find the probability that the life span of the monitor will be more than 17,659 hours, we need to calculate the z-score and use the standard normal distribution table. The z-score is calculated as:
z = (x - μ) / σ
Where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = 17,659, μ = 20,000, and σ = 1800. Plugging these values into the formula, we get:
z = (17659 - 20000) / 1800 = -1.3
Now, we can look up the probability corresponding to the z-score -1.3 in the standard normal distribution table. The probability is approximately 0.0968. Therefore, the probability that the life span of the monitor will be more than 17,659 hours is approximately 0.0968.
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Fast! Which of the following are characteristics of the graph of the square root
parent function? Check all that apply.
Answer:
Only choices B and C are correct.
Step-by-step explanation:
The square root parent function is [tex]f(x)= \sqrt{x}.[/tex]
The function [tex]f(x)[/tex] is not a linear function, therefore it's graph cannot be a straight line. This rules out choice A.
The function [tex]f(x)[/tex] is defined at [tex]x=0[/tex] because [tex]f(0)= \sqrt{0} =0[/tex]. This means that choice B is correct.
The function [tex]f(x)[/tex] is only real for values [tex]x\geq 0[/tex], because negative values of [tex]x[/tex] give complex values for [tex]f(x)[/tex]. This means that choice C is correct.
The function [tex]f(x)[/tex] can take only positive values which means it is confined to only the I quadrant, and is not defined in quadrants II, III, and IV. This rules out Choice D.
Therefore only choices B and C are correct.
Answer:
B & C
Step-by-step explanation:
B and C are the answers
How to integrate with steps:
(4x2-6)/(x+5)(x-2)(3x-1)
[tex]\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx[/tex]
You have a rational expression whose numerator's degree is smaller than the denominator's. This tells you you should consider a partial fraction decomposition. We want to rewrite the integrand in the form
[tex]\dfrac{4x^2-6}{(x+5)(x-2)(3x-1)}=\dfrac a{x+5}+\dfrac b{x-2}+\dfrac c{3x-1}[/tex]
[tex]\implies4x^2-6=a(x-2)(3x-1)+b(x+5)(3x-1)+c(x+5)(x-2)[/tex]
You can use the "cover-up" method here to easily solve for [tex]a,b,c[/tex]. It involves fixing a value of [tex]x[/tex] to make 2 of the 3 terms on the right side disappear and leaving a simple algebraic equation to solve for the remaining one.
If [tex]x=-5[/tex], then [tex]94=112a\implies a=\dfrac{47}{56}[/tex]If [tex]x=2[/tex], then [tex]10=35b\implies b=\dfrac27[/tex]If [tex]x=\dfrac13[/tex], then [tex]-\dfrac{50}9=-\dfrac{80}9c\implies c=\dfrac58[/tex]So the integral we want to compute is the same as
[tex]\displaystyle\frac{47}{56}\int\frac{\mathrm dx}{x+5}+\frac{10}{35}\int\frac{\mathrm dx}{x-2}+\frac58\int\frac{\mathrm dx}{3x-1}[/tex]
and each integral here is trivial. We end up with
[tex]\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx=\frac{47}{56}\ln|x+5|+\frac27\ln|x-2|+\frac5{24}\ln|3x-1|+C[/tex]
which can be condensed as
[tex]\ln\left|(x+5)^{47/56}(x-2)^{2/7}(3x-1)^{5/24}\right|+C[/tex]
Calculate ∬y dA where R is the region between the disks x^2+y^2 <=1 & x^2+(y-1)^2 <=1
Show all work. (Also explain why you split up the regions)
Let's first consider converting to polar coordinates.
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\begin{cases}x^2+y^2=1\iff r=1\\x^2+(y-1)^2=1\iff r=2\sin\theta\end{cases}[/tex]
We have
[tex]1=2\sin\theta\implies\sin\theta=\dfrac12\implies\theta=\dfrac\pi6\text{ or }\theta=\dfrac{5\pi}6[/tex]
Then [tex]\mathrm dA=r\,\mathrm dr\,\mathrm d\theta[/tex] and the integral is
[tex]\displaystyle\iint_Ry\,\mathrm dA=\int_{\pi/6}^{5\pi/6}\int_{2\sin\theta}^1r^2\sin\theta\,\mathrm dr\,\mathrm d\theta=\boxed{-\frac{\sqrt3}4-\frac{2\pi}3}[/tex]
Which is an equation of a circle with center ( -5, -7) that passes through the point ( 0, 0 ) brainly
Answer:
(x+5)^2+(y+7)^2=74
Step-by-step explanation:
So we are given this (x+5)^2+(y+7)^2=r^2
We need to find r so just plug in your point (0,0) for (x,y) and solve for r :)
(0+5)^2+(0+7)^2=r^2
25+49=r^2
74=r^2
So the answer is (x+5)^2+(y+7)^2=74
Answer:
(x+5)^2+(y+7)^2=74
Step-by-step explanation:
2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Mr. Profit had a taxable income of $35,000. He figured his tax from the table above. 1. Find his earned income level. 2. Enter the base amount. = $ 3. Find the amount over $ = $ 4. Multiply line 3 by % = $ 5. Add Lines 2 and 4 = $ 6. Compute his monthly withholding would be = $
The total tax comes to $5,173.50, with a monthly withholding of approximately $431.13.
To calculate Mr. Profit's federal income tax based on a taxable income of $35,000 in 2007, we need to find the correct tax bracket and perform a series of calculations:
Earned income level: Based on the provided information, an income of $35,000 falls into the third bracket (over $31,850 but not over $77,100).Enter the base amount: The base amount for this bracket is $4,386.Find the amount over: The amount over $31,850 is $35,000 - $31,850, which equals $3,150.Multiply line 3 by the percentage: Multiply the amount over $31,850 by the rate of 25%, which is $3,150 * 25% = $787.50.Add lines 2 and 4: Adding the base amount to the above calculation gives us the total tax: $4,386 + $787.50 = $5,173.50.Compute his monthly withholding: To find the monthly withholding amount, we divide the total tax by 12 months: $5,173.50 / 12 = $431.125.Therefore, Mr. Profit's federal income tax for 2007 would be $5,173.50, and his monthly withholding would be approximately $431.13.
Mr. Profit's earned income level is $35,000. The base tax is $4,386, with an additional tax of $787.50 for amounts over $31,850. Monthly withholding comes to approximately $431.13.
To calculate Mr. Profit's tax liability based on his taxable income, we need to identify which tax bracket his income falls into and then compute the tax accordingly.
Given that Mr. Profit has a taxable income of $35,000, he falls into the 25% tax bracket, where the taxable income is over $31,850 but not over $77,100.
The tax table for this bracket is:
Base tax for incomes from $7,825 to $31,850: $788
The marginal tax rate for income over $31,850: 25%
Let's compute the tax following the provided steps.
Earned Income Level
Mr. Profit's earned income level is his taxable income:
Earned Income Level = $35,000
Base Amount
The base tax amount for his tax bracket:
Base Amount = $4,386
Amount Over
The amount over the lower bound of his tax bracket:
Amount Over = $35,000 - $31,850 = $3,150
Multiply by Percentage
Multiply the amount over by the tax rate for his bracket (25%):
Multiply Line 3 by 25% = $3,150 \times 0.25 = $787.50
Add Base and Multiplication Result
Add the base amount and the calculated tax from step 4:
Add Lines 2 and 4 = $4,386 + $787.50 = $5,173.50
Compute Monthly Withholding
Given that there are 12 months in a year, compute the monthly withholding:
Compute monthly withholding [tex]= $5,173.50 \div 12 \approx $431.13[/tex]
Thus, rounding to two decimal places, we have :
Earned Income Level: $35,000
Base Amount: $4,386
Amount Over: $3,150
Multiply Line 3 by Percentage: $787.50
Add Lines 2 and 4: $5,173.50
Compute monthly withholding: $431.13
The complete question is : 2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Mr. Profit had a taxable income of $35,000. He figured his tax from the table above. 1. Find his earned income level. 2. Enter the base amount. = $ 3. Find the amount over $ = $ 4. Multiply line 3 by % = $ 5. Add Lines 2 and 4 = $ 6. Compute his monthly withholding would be = $
Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. Determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.
Answer:
sales are increasing at the rate of 6000 units per week
Step-by-step explanation:
Your demand equation appears to be ...
4p³ +x² =38400
Then differentiation gives ...
12p²·p' +2x·x' = 0
Solving for x', we get ...
x' = -6p²·p'/x
Filling in the given values, we find the rate of change of sales to be ...
x' = -6(20²)(-0.20/wk)/80 = 6/wk . . . . . in thousands of units/wk
Sales are increasing at the rate of 6000 units per week.
Find a parametrization for the curve「and determine the work done on a particle moving along Γ in R3 through the force field F:R^3--R^3'where F(x,y,z) = (1,-x,z) and (a) Im (Γ) is the line segment from (0,0,0) to (1,2,1) (b) Im (Γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) Im (Γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)
a. Parameterize [tex]\Gamma[/tex] by
[tex]\vec r(t)=(t,2t,t)[/tex]
with [tex]0\le t\le1[/tex]. The work done by [tex]\vec F[/tex] along [tex]\Gamma[/tex] is
[tex]\displaystyle\int_\Gamma\vec F\cdot\mathrm d\vec r=\int_0^1(1,-t,t)\cdot(1,2,1)\,\mathrm dt=\int_0^1(1-t)\,\mathrm dt=\boxed{\frac12}[/tex]
b. Break up [tex]\Gamma[/tex] into each component line segment, denoting them by [tex]\Gamma_1[/tex] and [tex]\Gamma_2[/tex], and parameterize each respectively by
[tex]\vec r_1(t)=(1-t,t,t)[/tex] and[tex]\vec r_2(t)=(2t,1+t,1+t)[/tex]both with [tex]0\le t\le1[/tex]. Then the work done by [tex]\vec F[/tex] along each component path is
[tex]\displaystyle\int_{\Gamma_1}\vec F\cdot\mathrm d\vec r_1=\int_0^1(1,t-1,t)\cdot(-1,1,1)\,\mathrm dt=\int_0^1(2t-2)\,\mathrm dt=-1[/tex]
[tex]\displaystyle\int_{\Gamma_2}\vec F\cdot\mathrm d\vec r_2=\int_0^1(1,-2t,1+t)\cdot(2,1,1)\,\mathrm dt=\int_0^1(3-t)\,\mathrm dt=\frac52[/tex]
giving a total work done of [tex]-1+\dfrac52=\boxed{\dfrac32}[/tex].
c. Parameterize [tex]\Gamma[/tex] by
[tex]\vec r(t)=(\cos t,\sin t,1)[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the work done by [tex]\vec F[/tex] is
[tex]\displaystyle\int_\Gamma\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}(1,-\cos t,1)\cdot(-\sin t,\cos t,0)\,\mathrm dr=-\int_0^{2\pi}(\sin t+\cos^2t)\,\mathrm dt=\boxed{-\pi}[/tex]
Solve the following system of equations
3x - 2y =55
-2x - 3y = 14
Answer:
The solution is:
[tex](\frac{137}{13}, -\frac{152}{13})[/tex]
Step-by-step explanation:
We have the following equations
[tex]3x - 2y =55[/tex]
[tex]-2x - 3y = 14[/tex]
To solve the system multiply by [tex]\frac{3}{2}[/tex] the second equation and add it to the first equation
[tex]-2*\frac{3}{2}x - 3\frac{3}{2}y = 14\frac{3}{2}[/tex]
[tex]-3x - \frac{9}{2}y = 21[/tex]
[tex]3x - 2y =55[/tex]
---------------------------------------
[tex]-\frac{13}{2}y=76[/tex]
[tex]y=-76*\frac{2}{13}[/tex]
[tex]y=-\frac{152}{13}[/tex]
Now substitute the value of y in any of the two equations and solve for x
[tex]-2x - 3(-\frac{152}{13}) = 14[/tex]
[tex]-2x +\frac{456}{13} = 14[/tex]
[tex]-2x= 14-\frac{456}{13}[/tex]
[tex]-2x=-\frac{274}{13}[/tex]
[tex]x=\frac{137}{13}[/tex]
The solution is:
[tex](\frac{137}{13}, -\frac{152}{13})[/tex]
Answer:
x = 411/39 and y = -152/13
Step-by-step explanation:
It is given that,
3x - 2y = 55 ----(1)
-2x - 3y = 14 ---(2)
To find the solution of given equations
eq(1) * 2 ⇒
6x - 4y = 110 ---(3)
eq(2) * 3 ⇒
-6x - 9y = 42 ---(4)
eq(3) + eq(4) ⇒
6x - 4y = 110 ---(3)
-6x - 9y = 42 ---(4)
0 - 13y = 152
y = -152/13
Substitute the value of y in eq (1)
3x - 2y = 55 ----(1)
3x - 2*(-152/13) = 55
3x + 304/13 = 55
3x = 411/13
x = 411/39
Therefore x = 411/39 and y = -152/13
Which number is irrational?
A. 0.14
B.1/3
C. Square root 4
D. Square root 6
Answer:
[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Let's define irrational by stating what rational means first, and the use the process of elimination.
A rational number is one that can be expressed as a ratio. When dividing the numerator of this ratio by the denominator, we will either get a whole number, a decimal that repeats a pattern, or we will get a decimal that terminates.
.14 terminates, so it is rational
1/3 divides to .333333333333333333333333333333333333333 indefinitely, so it is rational
square root of 4 is 2, a whole number, so it is rational
the square root of 6, to 9 decimal places, is 2.449489743... and it goes on without ending and without repeating. So this is the only irrational number of the bunch.
Answer:
D
Step-by-step explanation:
please help, Drag the values to order them from least to greatest, with the least at top
Step-by-step explanation:
The square root of 17 is 4.12. Minus one equals 3.12
The square root of 5 is 2.23.
pi+7 equals 10.142. Divided by five equals around 2.
so you end up with, 3.12, 2.23, and 2.1
Find the absolute maximum and minimum values of f(x.y)=x^2+y^2-2x-2y on the closed region bounded by the triangle with vertices (0,0), (2,0), and (0,2)
Try this suggested solution, note, 'D' means the region bounded by the triangle according to the condition. It consists of 6 steps.
Answers are underlined with red colour.
The equation P=31+1.75w models the relation between the amount of Tuyet’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Find Tuyet’s payment for a month when 12 units of water are used.
Answer: [tex]P = \$\ 52[/tex]
Step-by-step explanation:
We have the equation [tex]P = 31 + 1.75w[/tex] where P represents the payment and w represents the amount of water used.
To calculate the monthly payment that corresponds to 12 units of water you must do [tex]w = 12[/tex] in the main equation and solve for the variable P.
[tex]P = 31 + 1.75w[/tex]
[tex]P = 31 + 1.75(12)[/tex]
[tex]P = 31 + 21[/tex]
[tex]P = 52[/tex]
Tuyet's payment for a month when 12 units of water are used is $52.
Explanation:To find Tuyet's payment for a month when 12 units of water are used, we can substitute 12 for 'w' in the equation P = 31 + 1.75w and solve for P.
P = 31 + 1.75(12)
P = 31 + 21
P = 52
Therefore, Tuyet's payment for a month when 12 units of water are used is $52.
Learn more about water bill payment here:https://brainly.com/question/33583861
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Two balls are drawn at random from an urn containing six white and nine red balls. Recall the equatio n for an. r) given below. C(n,r) (a) Use combinations to compute the probability that both balls are white. (b) Compute the probability that both balls are red. (a) The probability that both balls are white is (Type an integer or a decimal. Round to two decimal places as needed.)
Answer: (a) [tex]\dfrac{1}{7}[/tex] (b) [tex]\dfrac{12}{35}[/tex]
Step-by-step explanation:
Given: Number of white balls : 6
Number of red balls = 9
Total balls = 15
(a) The probability that both balls are white is given by :-
[tex]\dfrac{^6C_2}{^{15}{C_2}}\\\\=\dfrac{\dfrac{6!}{2!(6-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{1}{7}[/tex]
∴ The probability that both balls are white is [tex]\dfrac{1}{7}[/tex] .
(b) The probability that both balls are red is given by :-
[tex]\dfrac{^9C_2}{^{15}C_2}\\\\=\dfrac{\dfrac{9!}{2!(9-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{12}{35}[/tex]
∴ The probability that both balls are red is [tex]\dfrac{12}{35}[/tex] .
Which of the following graphs could represent a quartic function?
Answer:
Graph A
Basically a graph of a function will have no turns if linear, 1 turn if quadratic, 2 turns if cubic, and 3 terms if quartic.
Graph A has a small turn on its right side.
Step-by-step explanation:
I love the way this other guy explained it, basically you count the turns that it says. i.e quartic = 4, so 4 turns, so A in this case
This was so confusing and I've been learning it for over a week and never understood it but literally took me 2 seconds to read his answer and understand it perfectly