Answer:
below
Step-by-step explanation:
Need the diagram......
Determine by inspection (that is, with only minimal calculations) if the given vectors form a linearly dependent or linearly independent set. Justify your answer u = [3]
[-1]
v=[6]
[-4]
w=[1]
[7]
a. Linearly dependent. Notice that u V 3w b. Linearly independent. If {u1, u2, . . ., um} is a set of vectors in Rn and n < m, then the set is linearly independent. c. Linearly dependent. Notice that v - 2u, so 2u- d. Linearly independent. The vectors are not scalar multiples of each other. e. Linearly dependent. If (ui, u2, ..., um) is a set of vectors in R" and n< m, then the set is linearly dependent.
a. Linearly dependent. Notice that u = 3w, so w can be written as a scalar multiple of u, meaning the set is linearly dependent.
b. Linearly independent. The vectors are not scalar multiples of each other, meaning they are linearly independent.
c. Linearly dependent. Notice that v = -2u, so v can be written as a scalar multiple of u, meaning the set is linearly dependent.
d. Linearly independent. The vectors are not scalar multiples of each other, meaning they are linearly independent.
e. Linearly dependent. If (ui, u2, ..., um) is a set of vectors in R" and n < m, then the set is linearly dependent. This means that the set of vectors {u, v, w} is linearly dependent as n = 2 and m = 3.
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Let f and g be the functions in the table below. x f(x) g(x) f '(x) g'(x)
1 3 2 4 6
2 1 3 5 7
3 2 1 7 9 (a) If F(x) = f(f(x)), find F '(1).
F '(1) = ___________________.
(b) If G(x) = g(g(x)), find G'(2).
G'(2) = ___________________.
The value of function f' (x)=28 and G' (x)=63
x f(x) g(x) f' (x) g' (x)
1 3 2 4 6
2 1 3 5 7
3 2 1 7 9
F(X)=f(f(x))
F' (X)=(F' (f(x)) x F' (x)⇒ (chain rule)
F' (1)=F' (F(1)x f' (1))
=f' (3) x f' (1) (( ∵ f(1)=3))
=7 x 4 (∵f' (3)=7, f' (1)=4))
=28
G(x)=g(g(x))
G' (x)=g' (g(x) X g' (x) ⇒ (chain rule)
G' (2)=g' (g(2) x g' (2)
=g' (3) x g' (2) (∵g(2)=3))
=9x7 ((∵g' (3)=9, g' (2)=7))
=63
The chain rule is a formula in calculus that expresses the derivative of the composition of two differentiable functions f and g in terms of f and g's derivatives.
d/dx(f(g(x)=f'(g(x)g'(x).
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any local College 63 of the male students are smokers in 147 or non-smokers the female students 70 or smokers and 130 are non-smokers a male student and a female student from the college are randomly selected for a survey what is the probability that both are smokers
Answer:
To find the probability that both a randomly selected male student and a randomly selected female student are smokers, we can use the formula for conditional probability: P(A and B) = P(A) * P(B|A), where A is the event that the male student is a smoker and B is the event that the female student is a smoker.
First, we need to find the probability that a randomly selected male student is a smoker:
P(A) = (number of male smokers) / (total number of male students) = 63 / (63 + 147) = 63/210
Next, we need to find the probability that a randomly selected female student is a smoker, given that the male student is a smoker:
P(B|A) = (number of female smokers and male smokers) / (number of male smokers) = 70 / 63
Finally, we can find the probability that both students are smokers by multiplying these two probabilities together:
P(A and B) = P(A) * P(B|A) = (63/210) * (70/63) = 0.09
So the probability that both a randomly selected male student and a randomly selected female student are smokers is 0.09 or 9%.
Step-by-step explanation:
PLEASE HELP ANSWER!
There are 108 major sources of pollen in state A. These pollen sources are categorized as grasses, weeds, and treesIf the number of weeds is 7 less than thrice the number of grasses, and the number of trees is 3 more than thrice the number of grasses, find the number of grasses, weeds, and trees that are major pollen sources.
Answer: 16 grasses, 41 weeds, and 51 trees
Step-by-step explanation:
You can use a variable for the different pollen sources. Use g for grass, w for weeds, and t for trees. w=3g-7. t=3g+3. g+w+t=108. In that last equation, you can substitute other values for w and t. g+(3g-7)+(3g+3)=108. combine like terms to get, 7g-4=108. This equation simplifies to g=16. Substitute 16 for g in the first 2 equations, and find that w=41, and t=51.
(Sorry if my explanation didn't make sense)
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. -7x - 10y = -83 4x - 10y = 16 O Subtract to eliminate y. Subtract to eliminate x. Add to eliminate x. Add to eliminate y.
If a variable needs to be eliminated, to solve -7x - 10y = -83 4x - 10y = 16, the correct first step is to:
Subtract to eliminate y.
In order to solve a system of linear equations, we can use elimination method. The goal of elimination method is to simplify the system of equations by making one of the variables disappear or equal to zero.
Here, the system of equations is:
-7x - 10y = -834x - 10y = 16To eliminate one of the variables, we can add or subtract the equations so that one of the coefficients cancels out.
In this case, we want to eliminate y. We can do that by subtracting the first equation from the second equation.
When we subtract the first equation from the second equation, the y-term will cancel out because the coefficients are the same:
-7x - 10y = -834x - 10y = 16--------- (subtract the two equations)
11x = 99
Now, we only have one variable, x, and we can easily solve for it:
x = 9
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Find sin\alpha +cos\alpha if sin\alpha *cos\alpha =(3)/(8).
By algebra properties and trigonometric formulas, the trigonometric equation sin α + cos α is equal to √7 / 2.
How to derive the value of a trigonometric equation
In this problem we find the definition of trigonometric equation, whose value must be found by means of algebra properties and trigonometric formulas. First, write the entire formula:
sin α + cos α
Second, square the formula:
(sin α + cos α)² = sin² α + 2 · sin α · cos α + cos² α
Third, simplify the formula and clear sin α + cos α:
(sin α + cos α)² = 1 + 2 · sin α · cos α
sin α + cos α = √(1 + 2 · sin α · cos α)
Fourth, find the value of the resulting trigonometric equation:
sin α + cos α = √[1 + 2 · (3 / 8)]
sin α + cos α = √7 / 2
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Write a congruence statement for the above triangles pt.2
The value of angle A and C is 14° and 121° respectively
What is the sum of angle in a triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
The sum of angle in a triangle is 180°
Therefore 45+6x-5+x-7 = 180
collect like terms
45-5-7+6x+x =180
33+7x = 180
7x = 180 - 33
7x = 147
x = 147/7
x= 21
therefore the value of angle A = ( 21-7) = 14°
and angle C = 6(21) - 5
C = 126-5
C = 121°
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at a cinema, films are shown on screen 1 and screen 2 customers pay full price or child price there are three times as many customers in screen 2 as in scree 2 73 customers paid child price complete the frequency tree
348 are the total number of customers visited the theatre.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that at a cinema, films are shown on screen 1 and screen 2
screen 2 customers pay full price or child price
There are three times as many customers in screen 1.
68 customers paid child price in screen 1
In screen 1 the number of customers are 87
In screen 2 the number of customers are three times the screen 1.
87×3=261 in screen 2.
72 are full in screen 1.
53 are in child of screen 2
208 in screen 2 full screen
261+87=348
Hence, 348 are the total number of customers visited the theatre.
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What is negative 2.48 rounded to the nearest hundredth
Answer:
it's already rounded to the nearest hundredth
Step-by-step explanation:
because there is no numbers after the hundredth.
Daniel's Print Shop purchased a new printer for $35,000. Each year it depreciates (loses value) at a rate of 5%. What is the initial value?
Answer:
The equation need to solve this problem is y=a(b)^x
a= the starting value
b= the rate of change
x= the time
to get the rate of change do the following:
add 1 to the percentage of change (only if value is growing)
subtract the percentage from one (only if value is decaying)
Since the printer is depreciating it is a decay.
The rate of change for this problem is showed below.
1-0.05
0.95 is the rate of change.
Below is the equation for the problem.
y=35000(0.95)^4 Work the problem.
Y=35000(0.814506250
Y=28507.71875 Since we are working with money we round to two decimal places.
The printer's value after four years is $28,507.72.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
f'(-3.5) ≈ 0.8292
f'(2) ≈ 5.277
f'(4) ≈ 10.34
Step-by-step explanation:
You want the approximate derivative of f(x) = 8·1.4^x using h=0.001 at x = {-3.5, 2, 4}.
DerivativeThe derivative is approximated by the formula ...
[tex]f'(x)\approx\dfrac{f(x+h)-f(x)}{h}\\\\f'(x)\approx\dfrac{f(x+0.001)-f(x)}{0.001}\qquad\text{for $h=0.001$}\\\\f'(x)\approx\dfrac{8\cdot1.4^{x+0.001}-8\cdot1.4^x}{0.001}\qquad\text{using the given $f(x)$}[/tex]
The calculation for different values of x is tedious, but not difficult.
For example, ...
f'(-3.5) = (8·1.4^-3.499 -8·1.4^-3.5)/0.001 = (2.4648358 -2.4640066)/0.001
= 0.0008292/0.001
f'(-3.5) = 0.8292
The remaining f'(x) values are shown in the attached table in the column f₁(x₂).
__
Additional comment
When function evaluation is repeated for different values, it is usually convenient to let a calculator or spreadsheet do the math. You can enter the formula once and have it evaluated as many times as you need.
The formula shown can be simplified to f'(x) ≈ 8000(1.4^(x+.001) -1.4^x), reducing the tedium by a small amount. The second attachment shows a different calculator using this formula.
Write an explicit formula for a_n , the nth term of the sequence 25, 33, 41
The explicit formula for aₙ is a formula for the nth term of this sequence aₙ = 8n + 17.
What is the explicit formula?
The explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by Riemann for the Riemann zeta function.
The formula for the nth term of this sequence is a_n = 8n + 17.
This means that each term in the sequence is equal to 8 multiplied by the position of the term (n) plus 17.
For example, the first term (n = 1) is 25, which can be calculated as 8 * 1 + 17 = 25.
The second term (n = 2) is 33, which can be calculated as 8 * 2 + 17 = 33, and so on.
hence, the explicit formula for aₙ is a formula for the nth term of this sequence is aₙ = 8n + 17.
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A deposit of $10,000 is made
in a savings account for which the interest is compounded continuously. The balance will double in 12 years.
(a) What is the annual interest rate for this account?
(b) Find the balance after 1 year.
(c) The effective yield of a savings plan is the percent increase in the balance after 1 year. Find the effective yield.
Explain or show work
Answer:
(a) 5.78%
(b) $10,594.63
(c) 5.95%
Step-by-step explanation:
You want the annual rate, the 1-year balance, and the effective yield on an account in which $10,000 is deposited, and the value doubles in 12 years.
(a) Annual rateThe compound interest formula is ...
A = Pe^(rt)
where P is the amount invested at annual rate r for t years, and A is the account balance.
Solving for r, we have ...
ln(A/P)/t = r
The account value will have doubled when A/P = 2, so the rate is ...
r = ln(2)/12 ≈ 0.057762 ≈ 5.78%
The annual rate is about 5.78%.
(b) 1-year balanceThe balance after 1 year is ...
A = 10000·e^(ln(2)/12·1) = 10000·2^(1/12) = 10594.63
The balance after 1 year will be $10,594.63.
(c) Effective yieldThe APR (r) will be ...
A = P(1 +r)^t
10594.63 = 10000(1 +r)¹
r = 10594.63/10000 -1 = 0.059463 ≈ 5.95%
The effective yield is about 5.95%.
SOLVE: A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing. The upper bound for the 95 percent confidence interval for the true proportion of customers who pay within a month would be:
Answer:Yes
because there were at least 10 "successes" and at least 10 "failures" in the sample
Step-by-step explanation:
Answer:
20% or 0.2
Step-by-step explanation:
→ 32 ÷ 160
common factor
→ = ⅕
convert the number
→ = 20% or 0.2
hope this helps!
the sum of the perimeter of an equilateral triangle and a square is 10 find the dimensions of the triangle and the square that produce a minimum total area
The dimensions of the square is [tex]\frac{30}{9+4 \sqrt{3}}[/tex] and equilateral triangle is [tex]& \frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex] that produce a minimum total area.
The sum of the perimeter of an equilateral triangle and a square is 10
Differentiation is a derivative of the value of an independent variable that can be used to measure features of an independent variable per unit change.
The objective is to find the dimensions of the equilateral triangle and square that produce a minimum total area.
Consider,
⇒4a+3b=10
⇒4a=10-3b
⇒a=[tex]\frac{10-3b}{4}[/tex]
The total area of the circle and square is,
[tex]A=a^2+\frac{\sqrt{3}}{4} b^2[/tex]
Substitute the value of a in the formula,
[tex]$$\begin{aligned}A & =\left(\frac{10-3 b}{4}\right)^2+\frac{\sqrt{3}}{4} b^2 \\& =\frac{100-60 b+9 b^2}{16}+\frac{\sqrt{3}}{4} b^2 \\& =\frac{100-60 b+9 b^2+4 \sqrt{3} b^2}{16} \\& =\frac{100-60 b+(9+4 \sqrt{3}) b^2}{16}\end{aligned}$$[/tex]
Differentiate the total area and equate with 0 ,
[tex]$$\begin{aligned}\frac{d A}{d r} & =\frac{0-60+2(9+4 \sqrt{3}) b}{16} \\0 & =\frac{0-60+2(9+4 \sqrt{3}) b}{16} \\\end{aligned}$$[/tex]
[tex]0-60+2(9+4 \sqrt{3}) b & =0 \\2(9+4 \sqrt{3}) b & =60[/tex]
And,
b[tex]=\frac{30}{9+4 \sqrt{3}}[/tex]
Substitute the value of b in the value of a,
[tex]$$\begin{aligned}a & =\frac{10-3\left(\frac{30}{9+4 \sqrt{3}}\right)}{4} \\& =\frac{90+40 \sqrt{3}-90}{4(9+4 \sqrt{3})} \\& =\frac{40 \sqrt{3}}{4(9+4 \sqrt{3})} \\& =\frac{10 \sqrt{3}}{9+4 \sqrt{3}}\end{aligned}$$[/tex]
a[tex]& =\frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex]
Therefore, the dimensions of the square is [tex]\frac{30}{9+4 \sqrt{3}}[/tex] and equilateral triangle is [tex]& \frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex] that produce a minimum total area.
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What equation does this set of algebra tiles represent?
x
1
1
1
1
1
1
1
1
=
1
1
1
1
1
1
1
1
1
1
1
1
Combine like terms on each side of the equation. For example, write 3 instead of 1 + 1 + 1.
The equation of the set of algebra tiles is x + 8 = 12.
What are algebra tiles?Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have been demonstrated to offer solid examples.
Given set,
x 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1
the set has one positive x and eight positive units,
the equation is x + 8.
and on the right side of the equation, there are 12 positive units,
equation is x + 8 = 12
Hence the equation s x + 8 = 12.
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Answer:
x + 8 = 12.
Step-by-step explanation:
in case you need it (x=4)
compare proof by contradiction and proof by contrapositive and provide an example of one or the other.
Contrapositive represents the implication of conditional statement to the logical statement if p then q to be false where as contradiction we prove that our supposition is false that implies the given condition is true.
Comparison in the proof of contrapositive and contradiction:
Contrapositive represents the hypothesis is true that implies conclusion is also true or the conclusion is false that implies hypothesis is also false.
Example of contrapositive: For any integer a , b a + b ≥ 17 , a≥9 , b≥ 9.
Using contrapositive :
If a < 9 , b < 9 then a + b < 17
a < 9, b < 9 consider a ≤8 , b≤8
a + b = 8 + 8
= 16
< 17
It proves a < 9 , b < 9 then a + b < 17 implies ,when a≥9 , b≥ 9 then
a + b ≥ 17 .
Contradiction : Here we suppose the statement which is against the required statement and prove it wrong which implies our given statement is true.
Example: For any integer a, a² is even then a is even .
Here we assume a is an odd integer then prove it wrong.
Therefore, comparing contrapositive and contradiction provides contrapositive is conditional to logical and contradiction required to our supposition is wrong.
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write and solve system of equations - an adult ticket to a museum costs $3 more than a childrens ticket. when 200 adult tickets and 100 childrens tickets are sold, the total revenue is $2100. what is the cost of a childrens ticket
Answer:
$5
Step-by-step explanation:
Let the cost of a children's ticket be x.
The cost of an adults ticket would be x + 3. (adult ticket costs $3 more than a children's ticket.)
200 adult tickets would cost 200(x+3), and 100 children's ticket would cost 100x.
The combined costs of children's ticket and adult would be 200(x+3) + 100x.
Using these information, the equation: 200(x+3) + 100x = 2100 can be formed.
200(x+3) + 100x = 2100
200x + 600 + 100x = 2100
300x = 1500
x = 5
The children's ticket cost $5.
Double check.
200*8 + 100*5 = 2100.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations that have the same solution are:
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
Options B, C, and D are the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We have,
2.3p - 10.1 = 6.5p - 4 - 0.01p
2.3p - 6.5p + 0.01p = 10.1 - 4
2.31p - 6.5p = 6.1
-4.19p = 6.1
p = -6.1/4.19
p = -1.5
Now,
Solve for p.
2.3p – 10.1 = 6.4p – 4
2.3p - 6.4p = 10.1 - 4
-4.1p - 6.4
p = -6.4/4.1
p = -1.6
2.3p – 10.1 = 6.49p – 4
2.3p - 6.49p = 10.1 - 4
-4.19p = 6.1
p = -1.5
230p – 1010 = 650p – 400 – p
230p - 649p = 1010 - 400
-419p = 610
p = -1.5
23p – 101 = 65p – 40 – p
23p - 64p = 101 - 40
-41p = 61
p = -1.5
2.3p – 14.1 = 6.4p – 4
2.3p - 6.4p = 14.1 - 4
-4.1p = 10.1
p = 2.5
Thus,
Equations that have the same solution
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
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On his last history test, Marty only missed one question. He received -3 points for that question. His friend Julie forgot to study and missed six questions. If each question was worth the same amount of points, how many points did Julie receive for those six questions? -12 -18 -6 -9
Answer:
-18
Step-by-step explanation:
missing 1 question means losing 3 points so if we mutliply the amout of questions he missed, 6, times the points yoy lose per question,3, we get 18.
Evaluate Expression.
5a-30
a=6
Answer: 0
Step-by-step explanation:
Step 1: Substitute the a as 6.
Step2: 5*(a) =5*6, which equals 30
Step 3: 5(6) - 30= 0
i am 20 years older than twice my daughter's age, and i am 34 years old. How old is my daughter?
Your daughter is 7 years old.
Step-by-step explanation:1. Express the ages as variables.
Let "x" be your age.
According to the statement, your age is 34. Thus, x= 34.
Let "y" be the age of your daughter.
According to the statement, your daughter's age is given by the following equation:
[tex]2y+20=x\\ \\2y+20=34[/tex]
2. Solve the equation for "y". Start by subtracting "20" on both sides of the equation.[tex]2y+20-20=34-20\\ \\2y=14[/tex]
3. Divide by "7" on both sides of the equation.[tex]\frac{2y}{2} =\frac{14}{2} \\ \\y=7[/tex]
4. Verify the answer.Let's see if number 7 makes the original condition be true.
So, you are 20 years older than twice your daughter's age. Let's multiply your daughter○s age by 2 and add 20, it should return your age (34).
[tex]2(7)+20=\\ \\14+20=\\ \\34[/tex]
That's correct, it means that 7 is the correct answer.
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Question 1(Multiple Choice Worth 2 points)
(03.03 MC)
What are the zeros of the function f(x)=x4-x2-2
+/-3,+/-i
+/-2,+/-i
+/-squareroot of 2, +/- i
+/-squareroot of 3, +/- i
Please explain :)
The zeros of the function f(x) = x^4 - x² - 2 are given as follows:
+/-squareroot of 2, +/- i
How to obtain the zeros of the function?The function for this problem is defined as follows:
f(x) = x^4 - x² - 2
The zeros are the values of x for which:
f(x) = 0.
Applying the transformation y = x², the function can be reduced to a quadratic function as follows:
y² - y - 2 = 0.
Hence:
(y - 2)(y + 1) = 0.
Meaning that the solutions for y are given as follows:
y - 2 = 0 -> y = 2.y + 1 = 0 -> y = -1.Then the solutions for x are given as follows:
y = -1 -> y = x² -> x = +/- iy = 2 -> x = +/-squareroot of 2Meaning that the third option is correct.
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The following table (Table C2.1) is a partial listing of the sales transactions for the Watson Distributing Company for the year ended December 31, 200X. Select the first three sample items from the population using the following techniques. a. The systematic selection technique with a random starting point of 13 and a sampling interval of 30. b. The probability-proportional-to-size sampling selection technique with a random starting dollar of $17,240 and a sampling interval of $220,000. c. The random-number table selection technique using Figure 2.1 on pp. 24-25. Using the last four digits of the invoice number, begin at row (0004) and column (01), continuing across the row and then down to the beginning of the next row.
The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.
Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.
Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.
The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.
The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.
The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.
The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.
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Find the X and Y Intercepts for y=-1/4x+1
g(x)=-3x^2 + 2x-6
h(x)=-4-x
Find: g(x ) - h(x)
Answer: g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.
Step-by-step explanation: The expression g(x) - h(x) can be found by subtracting h(x) from g(x).
g(x) = -3x^2 + 2x - 6
h(x) = -4 - x
So,
g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.
A basketball game is 40 minutes long. Carter plays 5 8 of a basketball game. To calculate how many minutes Carter played, find an equivalent fraction to 5 8 with a denominator of 40. Select the correct calculation. A. 5 × 8 8 × 8 = 40 64 ; 64 minutes B. 5 × 8 8 × 5 = 40 40 ; 40 minutes C. 5 × 5 8 × 5 = 25 40 ; 25 minutes D. 5 × 4 8 × 5 = 20 40 ; 20 minutes
Calculate the time value, at the end of the fifth year, of a 5-year annuity that pays $200
every month, starting from the beginning of the second month, when the continu-
ously compounded interest rate is 9.959%. Give your answer to the nearest dollar.
Answer:
The time value, at the end of the fifth year, of a 5-year annuity that pays $200 every month, starting from the beginning of the second month, when the continuously compounded interest rate is 9.959%, is $11,828. To calculate this, we can use the formula A = PMT x [((1 + r)n - 1) / r], where PMT is the payment amount, r is the continuously compounded interest rate, and n is the number of payments. In this case, PMT = $200, r = 0.09959, and n = 60. Plugging these values into the formula, we get A = $200 x [((1 + 0.09959)60 - 1) / 0.09959] = $11,828.
Solve the system of equations using substitution. Show work please.
y = 3x - 2
y = x + 2
The solution to the system of equations is x = (y + 2) / 3 and y = 2.5.
What is the equations ?Equations are mathematical statements that express the relationship between two or more variables. An equation typically consists of an equal sign, two expressions containing the variables, and the equals sign is used to show that the two expressions on either side of it are equal in value. Equations are used to solve problems, make predictions, and describe patterns.
Let's start by solving for x in the first equation:
y = 3x - 2
Add 2 to both sides of the equation:
y + 2 = 3x
Divide both sides of the equation by 3:
(y + 2) / 3 = x
Now that we've solved for x, we can substitute x into the second equation.
y = x + 2
Substitute (y + 2) / 3 for x:
y = (y + 2) / 3 + 2
Simplify the left side of the equation:
y = (y + 2 + 3) / 3
Multiply both sides of the equation by 3:
3y = (y + 5)
Subtract y from both sides of the equation:
2y = 5
Divide both sides of the equation by 2:
y = 5 / 2
y = 2.5
Therefore, the solution to the system of equations is x = (y + 2) / 3 and y = 2.5.
To learn more about equations
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Cindy is making fruit salads and fruit smoothies. The salad recipe requires 1/3 cup of strawberries and the smoothie recipe calls for 3/4 cup of strawberries. Her friend Borling is helping make the food.How many cups of strawberries would be required for both girls and two of their friends?
The fruit salad recipe requires 1/3 cup of strawberries and the smoothie recipe requires 3/4 cup of strawberries. So in total, 1/3 + 3/4 = 5/12 cup of strawberries are required for both recipes.
Now we know that Cindy and Borling are both making the recipes. So we need to multiply the 5/12 cup of strawberries by 2 to find out how many cups of strawberries are needed for both of them.
5/12 cup * 2 = 10/12 cup or 5/6 cup of strawberries.
Now if two more friends are joining them, we need to multiply the 5/6 cup of strawberries by 4 to find the total number of cups of strawberries required for all 4 of them.
5/6 cup * 4 = 2 and 1/6 cups.
So in total, 2 and 1/6 cups of strawberries would be required for both girls and two of their friends.
Answer:
Find x.
1/3+3/4=x
4/12+9/12=x
13/12=x
1 1/12 cups of strawberries for one person.
3*1 1/12=3 1/4
3 1/4 cups of strawberries in total for both girls and two of their friends.Step-by-step explanation:
