The solution to the system of equations is (x, y) = (1, -1) where the given equations are 11x+9y=-20 and x=-5y-6.
What is substitution method?The substitution method is a technique used in algebra to solve systems of equations by replacing one variable with an expression containing another variable. The goal is to eliminate one of the variables so that we can solve for the other one.
According to question:We are given the following system of two equations with two variables:
11x + 9y = -20 (equation 1)
x = -5y - 6 (equation 2)
To solve the system using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the expression for that variable into the other equation. Let's solve equation 2 for x:
x = -5y - 6
Now we can substitute this expression for x into equation 1, and solve for y:
11x + 9y = -20
11(-5y - 6) + 9y = -20 (substituting x = -5y - 6)
-55y - 66 + 9y = -20
-46y = 46
y = -1
Now that we have found y = -1, we can substitute this value back into equation 2 and solve for x:
x = -5y - 6
x = -5(-1) - 6
x = 1
Therefore, the solution to the system of equations is (x, y) = (1, -1).
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auditors compared opinions about treatment (very good/acceptable/poor) at four va hospitals (labeled a,b,c,d) among veterans aged 50 and above. what are the hypotheses for a chi-square test of independence on the data? select one:
The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:
Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
The pink triangle
Step-by-step explanation:
IMPORTANT NOTE: Make sure all the units are the same and consistent
Perimeter of a figure = Total length of the outer boundary
Shape of each figure in this question = Isosceles Triangle
Perimeter of triangle = Sum of all three sides
Perimeter of pink triangle = 36m + 36m + 20m
= 92m
Perimeter of green triangle = 25m + 25m + 35m
= 85m
∴Comparing the two values calculated above, it can be observed that the pink triangle has a greater perimeter
A right triangle is describe as having an angle of measure six less than negative two times a number, another angle measure that is three less than negative one-fourth the number, and a right angle. What are the measure of the angles in degree
The angles measure 90°, -2x - 6, and -1/x - 3. ⇒ x = -44. Therefore, the required measures of the angles are 90°, 82°, and 8° in the given triangle.
A right triangle is a type of triangle where one of the angles measures exactly 90 degrees. This angle is known as the right angle, and it is formed by the intersection of the two sides of the triangle that are perpendicular to each other. The other two angles of the right triangle are acute angles, meaning they measure less than 90 degrees.
The side opposite the right angle is called the hypotenuse, and it is always the longest side of the right triangle. The other two sides are called legs, and they can be of different lengths. This theorem is one of the most important and useful tools in geometry, and it allows us to solve many practical problems involving right triangles, such as finding the height of a building.
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a garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for? (b) 65 days (d) none of
A garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for 45 days. So, the correct option is (a).
How to calculateGiven that the provision for certain men in the garrison is for 30 days. Also, given that 2/3 of them do not attend the mess, then we have to find the number of days the food will last.
The food will last longer if the number of people attending the mess is less because the same amount of food will have to be shared between fewer people. Therefore, the food will last for more than 30 days.
Let the total number of men be x, then the number of men attending the mess is (1/3)x
And the number of men not attending the mess is (2/3)x.
Therefore, the food will last for (30 × x) / (2/3)x = 45 days
Hence, the answer of the question is 46 days.
Your question is incomplete but most probably your full question was:
A garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for?
(a) 45 days
(b) 65 days
(c) 50 days
(d) none of above
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Daniel is paid an hourly rate of $9. 00 plus six percent commission on direct phone sales. Last week he worked 48 hours and received $72. 00 in commissions. What was his pay for the week?
Daniel's pay for the week was $504.00, which includes his hourly pay and his commission on direct phone sales.
To calculate Daniel's pay for the week, we need to find his total earnings, which include his hourly wage and his commission on direct phone sales.
First, let's calculate his commission on direct phone sales. We know that he received $72.00 in commissions, and we also know that his commission is six percent of his sales. So, we can use the formula:
Commission = Sales x Commission Rate
To find his sales, we can rearrange the formula to:
Sales = Commission / Commission Rate
Plugging in the given values, we get:
Sales = $72.00 / 0.06 = $1200.00
So, Daniel's direct phone sales for the week were $1200.00.
Now, let's calculate his hourly pay. He worked for 48 hours at a rate of $9.00 per hour, so his hourly earnings were:
Hourly Pay = Hours Worked x Hourly Rate
Hourly Pay = 48 x $9.00 = $432.00
Finally, we can add his commission and his hourly pay to find his total earnings for the week:
Total Pay = Hourly Pay + Commission
Total Pay = $432.00 + $72.00
Total Pay = $504.00
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Which explicit function defines this arithmetic sequence?
-351, -343, -335, -327, -319
The explicit function defines this arithmetic sequence:
C. f(n) = 8n − 359
Explicit Function:
An explicit function is a function expressed with arguments. For example, y = 4x – 7 is self-explanatory, where y is the dependent variable and depends on the independent variable x.
According to the Question:
The first element of the given arithmetic sequence is -351, and the tolerance is (-343 -(-351)) = 8. The tolerance is a multiplier of n in the explicit function.
We can identify the appropriate explicit function by finding the one that correctly describes the sequence. Evaluating each for n=1 is sufficient.
(A) f(1) = 8 -351 = -343
(B) f(1) = -8 -351 = -359
(C) f(1) = 8 -359 = -351
(D) f(1) = -8 +359 = 351
The sequence is defined by the explicit function :
f(n) = 8n -359
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[tex]f(x) = \frac{ - 3}{x - 2} + 1[/tex]
Sketch the graph of f clearly showing the asymptotes and the intercepts with the axis
Answer: Vertical asymptote = 2
Horizontal asymptote = 1
y intercept = ( 0, 5/2 )
x intercept = ( 5,0 )
Other points of graph = ( 3,-2 )
= ( 4,-1/2 )
= ( -1, 2 )
= (-2,7/4 )
= ( -3 , 8/5 )
Step-by-step explanation:
At the book store, you purchased some $5 clearance mystery books and $12 regular-priced science fiction books. How many of each did you buy if you spent a total of $126?
Answer: View answer in explanation below.
Step-by-step explanation: Let's use variables to represent the unknown quantities.
Let x be the number of $5 clearance mystery books purchased.
Let y be the number of $12 regular-priced science fiction books purchased.
We can set up a system of equations based on the given information:
5x + 12y = 126 (total amount spent)
x + y = total number of books purchased
We need to solve for x and y.
Let's use the second equation to solve for one variable in terms of the other:
y = total number of books purchased - x
Now we can substitute this expression for y into the first equation:
5x + 12(total number of books purchased - x) = 126
Simplifying and solving for x:
5x + 12total number of books purchased - 12x = 126
-7x + 12total number of books purchased = 126
-7x = -12total number of books purchased + 126
x = (12total number of books purchased - 126)/7
Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:
If total number of books purchased is 10:
x = (12(10) - 126)/7 = -6/7 (not a whole number)
If total number of books purchased is 11:
x = (12(11) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 12:
x = (12(12) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 13:
x = (12(13) - 126)/7 = 12/7 (not a whole number)
If total number of books purchased is 14:
x = (12(14) - 126)/7 = 18/7 (not a whole number)
If total number of books purchased is 15:
x = (12(15) - 126)/7 = 24/7 (not a whole number)
If total number of books purchased is 16:
x = (12(16) - 126)/7 = 30/7 (not a whole number)
If total number of books purchased is 17:
x = (12(17) - 126)/7 = 36/7 (not a whole number)
If total number of books purchased is 18:
x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)
So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.
let be the linear transformation given by let be the basis of given by and let be the basis of given by find the coordinate matrix of relative to the ordered bases and . HW6.7. Coordinate matrix for differentiation Let L :P2P be the linear transformation given by L(p(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t). Let E = (C1, C2, C3) be the basis of P2 given by el(t) = 1, ez(t) = t, ez(t) = ť. and let F = (f1, 82, 83, fa) be the basis of P3 given by fi(t) = 1, fz(t) = t, fz(t) = {2, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases & and F. LFE = Save & Grade 2 tries left Save only
The coordinate matrix LFE of L relative to the ordered bases E and F is
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex].
Since here L is a linear transformation from a vector space of dimension 3 to a vector space of dimension 4, the coordinate matrix of L relative to the given ordered bases must be a (4×3) matrix,
Linear transformation is given by,
L(P(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t)
The given basis is IP² is E = (C1, C2, C3) where, e1(t) = 1, e2(t) = t, e3(t) = t².
Also the given basis of IP³ is (f1, f2, f3, f4) where, f1(t) = 1, f2(t) = t, f3(t) = t², f4(t) = t³.
Now to find the coordinate matrix,
Now,
L(e1(t)) = 5.0 + 1.0 + 3.1 + 3t.1
= 3 + 3t
= 3f1(t) + 3f2(t) + 0.f3(t) + 0.f4(t)
L(e2(t)) = 5.0 + 1.1 + 3.t + 3t.t
= 1 + 3t + 3t²
L(e3(t)) = 5.2 + 1.2t + 3.t² + 3t.t²
= 10 + 2t + 3t² + 3t³
Now writing the coefficients as a column vector we get,
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex]
The coordinate matrix LFE of L relative to the ordered bases E and F is
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex].
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You purchased 40 shares for $3.95/sh. If you sold the shares for a total of $200. Did you net a profit or a loss?
Answer: profit
Step-by-step explanation:
3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit
a country exports crayfish to overseas markets. the buyers are prepared to pay high prices when the crayfish arrive still alive. if x is the number of deaths per dozen crayfish, the probability distribution for x is given by: a. Find k. b. Over a long period, what is the mean number of deaths per dozen crayfish? c. Find σ, the standard deviation for the probability distribution.
a country exports crayfish to overseas markets. the buyers are prepared to pay high prices when the crayfish arrive still alive. if x is the number of deaths per dozen crayfish, the probability distribution for x is given by: a. Find k. b. Over a long period
A. To find k, you need to calculate the expected value of the random variable x, which is the number of deaths per dozen crayfish. This can be done by summing up the products of all the values of x multiplied by their respective probabilities. Thus,
k = ∑(xi * Pi)
= (1 * 0.3) + (2 * 0.3) + (3 * 0.2) + (4 * 0.2)
= 2.6
B. The mean number of deaths per dozen crayfish is given by the expected value of x, which is 2.6.
C. To find the standard deviation for the probability distribution, we need to calculate the variance of x. This can be done using the formula,
σ2 = ∑((xi - k)2 * Pi)
= (0 - 2.6)2 * 0.3 + (1 - 2.6)2 * 0.3 + (2 - 2.6)2 * 0.2 + (3 - 2.6)2 * 0.2
= 0.84
Therefore, the standard deviation for the probability distribution is σ = √0.84 = 0.92.
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Fractions questions need help!
The answer to this question is 150 adults. This is calculated by subtracting the number of boys and girls from the total number of people in the museum, 250.
What is subtracting?Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.
2/5 of 250 people is equal to 100 girls. 3/10 of 250 people is equal to 75 boys. When these two numbers are subtracted from the total number of people in the museum, 250, the answer is 150 adults.
To work out the number of adults in the museum, it is important to first identify the fractions and convert them into decimals. For example, to convert 2/5 into a decimal, 2 is divided by 5, which gives an answer of 0.4. This process should be repeated for the other fractions given in this problem.
Once the fractions are converted into decimals, the next step is to multiply the decimals by the total number of people in the museum, 250. For example, 0.4 multiplied by 250 is equal to 100 girls.
Finally, the numbers of boys and girls should be subtracted from the total number of people in the museum, 250. This gives an answer of 150 adults.
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By subtracting the number of boys and girls from the total number of people in the museum, we get the number of adults that is 75.
What is subtracting?
Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.
2/5 of 250 people = 100 girls.
3/10 of 250 people =75 boys.
When these two numbers are subtracted from the total number of people in the museum, that is
250-(100+75)= 75 adults
Thus, the number of adults among the 250 people in a museum are 75.
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please help with question 6
Answer:
a = -13b = 6f(x) = (2x -1)(x -2)(x +3)Step-by-step explanation:
Given f(x) = 2x³ +x² +ax +b has a factor (x -2) and a remainder of 18 when divided by (x -1), you want to know a, b, and the factored form of f(x).
RemainderIf (x -2) is a factor, then the value of f(2) is zero:
f(2) = 2·2³ +2² +2a +b = 0
2a +b = -20 . . . . . . . subtract 20
If the remainder from division by (x +1) is 18, then f(-1) is 18:
f(-1) = 2·(-1)³ +(-1)² +a·(-1) +b = 18
-a +b = 19 . . . . . . . . . . add 1
Solve for a, bSubtracting the second equation from the first gives ...
(2a +b) -(-a +b) = (-20) -(19)
3a = -39
a = -13
b = 19 +a = 6
The values of 'a' and 'b' are -13 and 6, respectively.
Factored formWe can find the quadratic factor using synthetic division, given one root is x=2. The tableau for that is ...
[tex]\begin{array}{c|cccc}2&2&1&-13&6\\&&4&10&-6\\\cline{1-5}&2&5&-3&0\end{array}[/tex]
The remainder is 0, as expected, and the quadratic factor of f(x) is 2x² +5x -3. Now, we know f(x) = (x -2)(2x² +5x -3).
To factor the quadratic, we need to find factors of (2)(-3) = -6 that have a sum of 5. Those would be 6 and -1. This lets us factor the quadratic as ...
2x² +5x -3 = (2x +6)(2x -1)/2 = (x +3)(2x -1)
The factored form of f(x) is ...
f(x) = (2x -1)(x -2)(x +3)
a blackboard of sides 5 M 30 cm and 3m 20 CM has to be painted find the cost of the rate of rs 15 per m².
Answer: The cost of painting is Rs.254.4
Step-by-step explanation:
let l and b be the sides
here l= 5m 30cm=5.30mb=3m 20 cm=3.20m
Area of blackboard = l×b= 5.30×3.20
=16.96m²
cost of painting per m² = 15 rscost of painting per 8.5m² = 16.96 × 15 =254.4 rs
We are given that, the measures of sides of blackboard are 5 m 30 cm and 3m 20 cm.
__________________________________________
Length of the Blackboard[tex] \bf \implies5 m + 30 cm \\ [/tex]
[tex] \sf \implies 5 m + \dfrac{30}{100}m \\ [/tex]
[tex] \sf \implies 5 m + \dfrac{3\cancel{0}}{10\cancel{0}}m \\ [/tex]
[tex] \sf \implies 5 m + 0.3 m \\ [/tex]
[tex]\purple{ \bf \implies 5.3~ m } \\ [/tex]
Breadth of the Blackboard[tex] \bf \implies3 m + 20 cm \\ [/tex]
[tex] \sf \implies 3 m + \dfrac{20}{100}m \\ [/tex]
[tex] \sf \implies 3 m + \dfrac{2\cancel{0}}{10\cancel{0}}m \\ [/tex]
[tex] \sf \implies 3 m + 0.2 m \\ [/tex]
[tex] \purple{\bf \implies 3. 2 ~m} \\ [/tex]
_______________________________________________
[tex] \pink{\frak{\implies Area _{(Blackboard) }= Length \times Breadth ~m^2}} \\ [/tex]
[tex] \sf \implies Area _{(Blackboard) } = 5.3 \times 3.2 ~m^2 \\ [/tex]
[tex] \sf \implies Area _{(Blackboard) } = 16.96 m^2 \\ [/tex]
Henceforth, the cost of the rate of rs 15 per m² will be -[tex] \sf \implies 15 \times 16.96 \\ [/tex]
[tex] \pink{\sf \implies Rs ~254.4 } \\ [/tex]
Can someone help me find the elevation of the sun I need the answers that are highlighted in yellow please help image below
Answer:
Step-by-step explanation:
a. ∠ACB
b. AC
c. AB
d. BC
e. tangent, opposite, adjacent
f. m∠ACB = tan⁻¹(34/45) = 37°
Two similar solids have base areas of 47 cm² and 199 cm², as shown below.
The volume of the smaller solid is 350 cm³.
COMPLETION
50%
Calculate the volume of the larger solid correct to the nearest integer.
(4 marks)
Check the picture below.
so hmmm let's use the ratio for the areas to get the ratio of the sides, and from there, we'll get to the ratio of the volumes.
[tex]\stackrel{ \textit{Areas' ratio} }{\sqrt{\cfrac{s^2}{s^2}}}=\cfrac{s}{s}\implies \sqrt{\cfrac{47}{199}}=\cfrac{s}{s}\implies \cfrac{\sqrt{47}}{\sqrt{199}}=\cfrac{s}{s} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{Volumes' ratio} }{\sqrt[3]{\cfrac{s^3}{s^3}}}=\cfrac{s}{s}\implies \stackrel{\textit{substituting from above}}{\sqrt[3]{\cfrac{s^3}{s^3}}=\cfrac{\sqrt{47}}{\sqrt{199}}}\implies \sqrt[3]{\cfrac{350}{V}}=\cfrac{\sqrt{47}}{\sqrt{199}} \\\\\\ \cfrac{350}{V}=\left( \cfrac{\sqrt{47}}{\sqrt{199}} \right)^3\implies \cfrac{350}{V}=\cfrac{\sqrt{47^3}}{\sqrt{199^3}}\implies (350)(\sqrt{199^3})=V\sqrt{47^3} \\\\\\ \cfrac{(350)(\sqrt{199^3})}{\sqrt{47^3}}=V\implies \boxed{3049\approx V}[/tex]
Find the equation of the straight line passing through the point (0,2) which is perpendicular to the line y=1/4x+5
Answer:
y = -4x + 2
Step-by-step explanation:
you need to find the gradient first and in order to find it, you need to look at the equation of the line given
in the equation, it refers to y = mx + c and from there, the gradient is whatever the value of m is. So in this situation, m = 1/4
now that you've found your gradient, you need to get the gradient when it is perpendicular (as stated in the question) by using m¹ x m² = -1
m¹ represents the gradient of the line we have whereas m² represents the gradient of the line we want so you just have to substitute 1/4 into m¹
[tex] \frac{1}{4} \times {m}^{2} = - 1[/tex]
[tex] {m}^{2} = \frac{ - 1}{( \frac{1}{4} )} [/tex]
[tex] {m}^{2} = - 4[/tex]
now you need to find the c of the y = mx + c before you complete the equation
y = 2 (from the question)
x = 0 (from the question)
m = -4
(2) = (-4)(0) + c
2 = c
c = 2
and you just substitute everything except y into y = mx + c and you're done
y = -4x + 2
You construct three 88% confidence intervals as follows: A) A t-interval with 6 degrees of freedom. B) A t-interval with 2 degrees of freedom. C) A z-interval Assuming the mean and standard deviation are the same for all three intervals, write the three intervals (A, B, and C) in order, from narrowest to widest.
The order from narrowest to widest is: C) z-interval. A) t-interval with 6 degrees of freedom. B) t-interval with 2 degrees of freedom.
What is confidence interval?In statistics, the likelihood that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 with a 95% confidence interval of 9.50 - 10.50 is derived using a statistical model.
A confidence interval's breadth is influenced by the sample size and degree of confidence. Higher confidence levels often result in broader intervals, whereas bigger sample numbers typically result in narrower intervals.
In this instance, the three intervals have different degrees of freedom but the same 88% confidence level.
Hence, The order from narrowest to widest is: C) z-interval. A) t-interval with 6 degrees of freedom. B) t-interval with 2 degrees of freedom.
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Help!
I need your help.
Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within squareroot 2/2 units of each other.
The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.
According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.
Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.
Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.
The perimeter of the square described above is a square with a side length of square root 2 units.
Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.
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HELP PLEASE.
The options of answer to this question are:
A- 286 miles
B- 271 miles
C- 166 miles
D- 216 miles
PLEASE HELP
Answer: D - 216 miles
Explanation: The rest stop is the y-intercept in the graph because that is when he begins to travel home at a constant speed. Looking at the graph, the y-intercept falls right before 220 so the closest answer would be 216 miles.
Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck
Answer:
Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck
Step-by-step explanation:
Let's start by subtracting the base fee from the total cost:
$143.43 - $16.95 = $126.48
Now, we can divide the remaining cost by the cost per mile:
$126.48 ÷ $0.93/mile ≈ 136 miles
Therefore, Stacy drove the truck for approximately 136 miles.
Let f(x) = (x - 1)2,g(x) = e-2 , and h(x) = 1 In(1 2x) _ (a) Find the linearizations of f, g, and h at a = 0
Lf(x)=1-2x
Lg(x)=1-2x
Lh(x)=1-2x
Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
The linear approximation appears to be the best for the function (f, g, or h *h is not the answer) since it is closer to (f, g, or h) for a larger domain than it is to (f and g, g and h, f and h). The approximation looks worst for (f, g, or, h) since (f, g, or, h) moves away from L faster than (f and g, g and h, f and h) do.
We can see that the linear approximation appears to be the best for function g since it is closer to g for a larger domain than it is to f and h. The approximation looks worst for function f since f moves away from Lf faster than g and h do. Hence, the linear approximation is the worst for function f.
Given that f(x) = (x - 1)^2, g(x) = e^(-2), and h(x) = ln(1+2x) - 2x.
(a) Find the linearizations of f, g, and h at a = 0.
The linearization of f at a = 0 is given by
Lf(x) = f(0) + f'(0)(x - 0)
= (0 - 1)^2 + 2(0 - 1)(x - 0)
= -x + 1
The linearization of g at a = 0 is given by
Lg(x) = g(0) + g'(0)(x - 0)
= e^(-2) + 0(x - 0)
= e^(-2)
The linearization of h at a = 0 is given by
Lh(x) = h(0) + h'(0)(x - 0)
= (ln(1 + 2(0)) - 2(0)) + [(1/(1 + 2(0)))2 - 2](x - 0)
= -2x
Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
The graphs of f(x) = (x - 1)^2, g(x) = e^(-2), h(x) = ln(1+2x) - 2x, and their respective linear approximations Lf(x) = -x + 1, Lg(x) = e^(-2), and Lh(x) = -2x.
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Express the following as the product of prime factors in exponential form
(a) 432 (b) 729×64
Answer: 729×64 is: (3^3 × 2^3)^2
Step-by-step explanation:
(a) To express 432 as the product of prime factors in exponential form, we can follow these steps:
Divide by 2 as many times as possible until the result is odd: 432 ÷ 2 = 216 ÷ 2 = 108 ÷ 2 = 54 ÷ 2 = 27 (5 times)
Divide by 3 as many times as possible until the result is not divisible by 3: 27 ÷ 3 = 9 ÷ 3 = 3 (2 times)
Since 3 is a prime number, we cannot divide by any other prime number to obtain a smaller result. Therefore, the prime factorization of 432 is: 2^4 × 3^3.
(b) To express 729×64 as the product of prime factors in exponential form, we can follow these steps:
Rewrite each factor as a power of a prime: 729 = 3^6 and 64 = 2^6.
Multiply the powers of each prime together: (3^6) × (2^6) = 3^6 × 2^6.
Simplify the result by factoring out the highest possible power of each prime: 3^6 × 2^6 = (3^3 × 2^3)^2.
Therefore, the prime factorization of 729×64 is: (3^3 × 2^3)^2.
Answer:
Below in bold.
Step-by-step explanation:
2) 432
2) 216
2) 108
2) 54
3) 27
3) 9
3
So 432 = 2^4 * 3^3.
3)729
3)243
3)81
3)27
3)9
3
64 = 2^6
So the answer is 2^6 * 3^6
Mr. And Mrs. Smith plan to roof the cabin on
2 consecutive days. Assuming that the chance of rain is
independent of the day, what is the probability that it
will rain both days?
A. 0. 04
B. 0. 08
C. 0. 16
D. 0. 20
E. 0. 40
From the given information provided, the probability that it will rain both days is 0.04 option A.
Since we are assuming that the chance of rain is independent of the day, we can use the multiplication rule of probability to find the probability that it will rain on both days.
Let's assume that the probability of rain on any given day is p. Then, the probability of no rain on that day is 1-p.
Therefore, the probability that it will rain on both days is:
P(rain on both days) = P(rain on day 1) × P(rain on day 2)
= p × p
= p²
Since the problem does not give us a specific value of p, we cannot determine the exact probability of rain on both days. However, we can use one of the answer choices to estimate the probability of rain on both days.
Looking at the answer choices, the only choice that is a perfect square is 0.04. Therefore, we can assume that p² = 0.04, which means that p = 0.2.
So, if the probability of rain on any given day is 0.2, then the probability of rain on both days is:
P(rain on both days) = p²
= 0.2²
= 0.04
Therefore, the answer is A. 0.04.
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Kay borrows $8,750 from Chase Bank at a fixed annual interest rate of 6.2%,
where y is the number of years the loan remains unpaid. Kay waits 8 years
before beginning to repay the loan to Citibank.
Write an exponential function to represent the amount owed after t years.
O y = 8750(t) 6.2
Oy = 8750 (1.062)
Oy (t) 1.0628750
Answer:
Answer: $80,000(1+0.004)^60 + $519.17 [1-(+0.004)^60/0.004]
Step-by-step explanation:
What is the value of v i need help
Therefore , the solution of the given problem of unitary method comes out to be V has a value of -13/3.
What is a unitary method?By using preexisting variables, this common convenience, or all essential components from the initial Bishop malleable study that adhered to a specific methodology, the objective may be accomplished. If the term affirmation result does not occur, both essential components will event miss the statement; however, if it does, it then becomes possible to reach the entity once more.
Here,
TU = 4v and QR = 5v plus 17 allow us to write:
=> QR = TU + UP + PS + SR + RQ
Inputting the numbers provided yields:
=> 5v + 17 = 4v + UP + v + 26 + SR + 5v plus
When we simplify the solution, we obtain:
=> UP + SR + 6v + 26 = 0
Because UP and SR are opposite and equivalent, we can write:
=> UP = -SR
By replacing this in the preceding solution, we obtain:
=> UP - UP + 6v + 26 = 0
When we simplify the solution, we obtain:
=> 6v + 26 = 0
26 is subtracted from both parts to yield:
=> 6v = -26
When we multiply both parts by 6, we get:
=> v = -26/6
If we simplify, we get:
=> v = -13/3
V therefore has a value of -13/3.
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150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons
The total value of both bonds is $704,367,500.
Coupon payment = [tex]\frac{Coupon rate * Par value}{2}[/tex]
Coupon payment = [tex]\frac{11 * $1,000}{2}[/tex]
Coupon payment = $55
PV = [tex]55 * [1 - (1 + 0.04)^{^-40} ] / 0.04 + $1,000 / (1 + 0.04)^40[/tex]
[tex]PV = $1,026.45[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1,026.45 * 150,000 * $1,000\\Total value = $153,967,500[/tex]
[tex]PV = \frac{Price}{(1 + r)^n}[/tex]
[tex]PV = \frac{16}{(1 +0.03)^60}\\PV = $1.72[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1.72 * 320,000 * $1,000\\Total value = $550,400,000[/tex]
Therefore, the total value of both bonds is:
[tex]Total value = Value of coupon bonds + Value of zero coupon bonds\\Total value = $153,967,500 + $550,400,000\\Total value = $704,367,500[/tex]
A coupon rate is the annual interest rate paid by a bond or other fixed-income security to its bondholders or investors. It is typically expressed as a percentage of the bond's face value, also known as its par value. For example, if a bond has a face value of $1,000 and a coupon rate of 5%, the bond will pay $50 in interest each year to its bondholders. The coupon payments are usually made semi-annually or annually, depending on the terms of the bond.
The coupon rate is set when the bond is issued and remains fixed throughout the life of the bond unless the bond issuer chooses to call the bond or the bond defaults. Coupon rates are determined by a variety of factors, including market conditions, the creditworthiness of the issuer, and the length of the bond's maturity.
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Complete Question: -
The IPO Investment Bank has the following financing outstanding,
Debt: 150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons.
Preferred stock: 240,000 shares of 9 percent preferred stock with a current price of $67, and a par value of $100.
Common stock: 3,500,000 shares of common stock; the current price is $53, and the beta of the stock is.9.
Market: The corporate tax rate is 24 percent, the market risk premium is 8 percent, and the risk-free rate is 5 percent.
What is the WACC for the company? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Find the compound interest and the total amount after eight years if the interest is compounded every two years.
Principal = ₹10,000
Rate of interest = 20%
Total amount = (find)
Total interest = (find)
After 8 years, the total amount is ₹38,416 and the compound interest is ₹28,416.
What is the total amount and compound interest earned on ₹10,000 invested at 20% interest compounded every 2 years for 8 years?
To find the compound interest and the total amounts after eight year with interest compounded every two years, we'll use the compound interest formula:
Total Amount (A) = P(1 + r/n)¹/²(nt)
Where:
P = Principal = ₹10,000
r = Rate of interest = 20% = 0.2
n = Number of times the interest is compounded in a year (every 2 years, so n = 1/2)
t = Time in years = 8 years
Convert the interest rate to a decimal by dividing by 100:
20% ÷ 100 = 0.2
A = ₹10,000x (1 + 0.2¹/²)(1/2 x 8)
Calculate the expression inside the parentheses:
1 + 0.2/(1/2) = 1.4
Calculate the exponent (1/2x 8):
1/2x 8 = 4
Calculate the total amount:
A = ₹10,000 x (1.4)^4
A = ₹10,000 x3.8416
A = ₹38,416
Step 6: Calculate the compound interest:
Total interest = Total amount - Principal
Total interest = ₹38,416 - ₹10,000
Total interest = ₹28,416
So, after eight years, the total amount is ₹38,416 and the compound interest is ₹28,416.
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you roll two six-sided dice at the same time. what is the probability the second dice landed on an even number given the first one landed on an odd number?
The probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
Step-by-Step Explanation:Let A be the event that the first dice rolls an odd number, and let B be the event that the second dice rolls an even number. We want to find P(B|A), which is the probability of B given A. This can be found using the formula:P(B|A) = P(A and B) / P(A) We know that P(A) = 1/2, as half the numbers on a six-sided dice are odd.
To find P(A and B), we need to find the probability that both dice roll the desired numbers simultaneously. Since we know that the first dice rolled an odd number, only half of the numbers are possible for the second dice to be even. Therefore, P(A and B) = 1/2 x 1/2 = 1/4. So:P(B|A) = P(A and B) / P(A) = (1/4) / (1/2) = 1/2 or 0.5. Therefore, the probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
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