Answer:
450 km
Step-by-step explanation:
Let's say Va is the speed of the car from city A, Ta is the time it spent traveling, and Da is the distance it traveled.
Similarly, Vb is the speed of the car from city B, Tb is the time it spent traveling, and Db is the distance it traveled.
Given:
Va = Vb - 10
Ta₁ = Tb₁ = 5
Ta₂ = Tb₂ + 4.5
Db₂ = 150
Find:
D = Da₁ + Db₁ = Da₂ + Db₂
Distance = rate × time
In the first scenario:
Da₁ = Va Ta₁
Da₁ = (Vb - 10) (5)
Da₁ = 5Vb - 50
Db₁ = Vb Tb₁
Db₁ = Vb (5)
Db₁ = 5Vb
So:
D = Da₁ + Db₁
D = 10Vb - 50
In the second scenario:
Da₂ = Va Ta₂
Da₂ = (Vb - 10) (Tb₂ + 4.5)
Da₂ = Vb Tb₂ + 4.5Vb - 10Tb₂ - 45
Db₂ = Vb Tb₂
150 = Vb Tb₂
Substituting:
Da₂ = 150 + 4.5Vb - 10Tb₂ - 45
Da₂ = 105 + 4.5Vb - 10Tb₂
Da₂ = 105 + 4.5Vb - 10 (150 / Vb)
Da₂ = 105 + 4.5Vb - (1500 / Vb)
So:
D = Da₂ + Db₂
D = 105 + 4.5Vb - (1500 / Vb) + 150
D = 255 + 4.5Vb - (1500 / Vb)
Setting this equal to the equation we found for D from the first scenario:
10Vb - 50 = 255 + 4.5Vb - (1500 / Vb)
5.5Vb - 305 = -1500 / Vb
5.5Vb² - 305Vb = -1500
5.5Vb² - 305Vb + 1500 = 0
11Vb² - 610Vb + 3000 = 0
(Vb - 50) (11Vb - 60) = 0
Vb = 50, 5.45
Since Vb > 10, Vb = 50 km/hr.
So the distance between the cities is:
D = 10Vb - 50
D = 10(50) - 50
D = 450 km
I need help with Math Homework
Answer:
Your answer should be -8.
a+b= 17, ab=70, Find the value of |a-b|
Answer:
3
Step-by-step explanation:
there are two solutions in the given system of two equations:
a=10; b=7 and a=7; b=10.
|a-b|=3.
To estimate μ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 81 full professors. The sample mean is = $77,220 and the sample standard deviation is s = $4500. A 98% confidence interval for μ is _____.
Answer with explanation:
Sample mean of 81 full Professor = $ 77,220
Sample Standard Deviation (S)= $ 4500
Sample mean= $77,220
[tex]Z_{98 \text{Percent}=\frac{98}{100}}\\\\Z_{98 \text{Percent}=0.8365}\\\\Z_{\text Score=\frac{\bar x -\mu}{\sigma}}\\\\0.84=\frac{77220- \mu}{4500}\\\\\mu=77220-3780\\\\ \mu=73440[/tex]
So, When , z=98% , then Mean Salary ( μ)=73,440
Electric power costs 17.8 cents per kWh in Los Angeles in July 2017 (compared to the national average of 14.3 cents per kWh). How much did it cost (in cents) to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017? Assume 3 significant digits in your answer.
The cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017 is:
4.45 cents
Step-by-step explanation:Electric power costs 17.8 cents per kWh in Los Angeles in July 2017.
Now we are asked to find the cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017.
We know that: 1 w=0.001 kW
This means that:
1500 W= 1.500 kW
Also, it is used for 10 minutes
i.e. 1/6 hours
Hence, the electric power used to run the hair dryer is: 1.500×(1/6)
i.e. Electric power to used by hair dryer is: 0.25 kWh
Cost of 1 kwh is: 17.8 cents
This means that cost of 0.25 kwh is: 17.8×0.25
= 4.45 cents
Hence, the answer is:
4.45 cents
Find how much should be invested to have $14,000 in 10 months at 9.1% simple interest.
Answer:
[tex]\$13,013.17[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10/12\ years\\ P=?\\ A=\$14,000\\r=0.091[/tex]
substitute in the formula above
[tex]\$14,000=P(1+0.091*(10/12))[/tex]
[tex]P=\$14,000/(1+0.091*(10/12))[/tex]
[tex]P=\$13,013.17[/tex]
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $35. For one performance, there were 45 tickets sold in all, and the total amount paid for them was $1375
. How many tickets of each type were sold?
For this case we propose a system of equations:
x: Variable representing the anticipated tickets
y: Variable representing the same day tickets
So:
[tex]x + y = 45\\25x + 35y = 1375[/tex]
We clear x from the first equation:
[tex]x = 45-y[/tex]
We substitute in the second equation:
[tex]25 (45-y) + 35y = 1375\\1125-25y + 35y = 1375\\10y = 1375-1125\\10y = 250\\y = 25[/tex]
We look for the value of x:
[tex]x = 45-25\\x = 20[/tex]
Thus, 20 of anticipated type and 25 of same day type were sold.
Answer:
20 of anticipated type and 25 of same day type were sold.
Answer: 20 advance tickets and 25 same-day tickets.
Step-by-step explanation:
Set up a system of equations.
Let be "a" the number of advance tickets and "s" the number of same-day tickets.
Then:
[tex]\left \{ {{25a+35s=1375} \atop {a+s=45}} \right.[/tex]
You can use the Elimination method. Multiply the second equation by -25, then add both equations and solve for "s":
[tex]\left \{ {{25a+35s=1,375} \atop {-25a-25s=-1,125}} \right.\\.............................\\10s=250\\\\s=\frac{250}{10}\\\\s=25[/tex]
Substitute [tex]s=25[/tex] into an original equation and solve for "a":
[tex]a+(25)=45\\\\a=45-25\\\\a=20[/tex]
what is the y-coordinate of the vertex of the parabola?
f(x)= -x^2 - 2x +6
Answer:
7
Step-by-step explanation:
The function can be written in vertex form as ...
f(x) = -(x +1)^2 +7
The vertex is then identifiable as (-1, 7). The y-coordinate is 7.
_____
Vertex form is ...
f(x) = a(x -h)^2 +k
where "a" is the vertical scale factor, and (h, k) is the vertex point. It is convenient to arrive at this form by factoring "a" from the first two terms, then adding and subtracting the square of the remaining x-coefficient inside and outside parentheses.
f(x) = -(x^2 +2x) +6
f(x) = -(x^2 +2x +1) + 6 -(-1) . . . . completing the square
f(x) = -(x +1)^2 +7 . . . . . . . . . . . . vertex form; a=-1, (h, k) = (-1, 7)
The y-coordinate of the vertex of the parabola defined by the function f(x)= -x² - 2x + 6 is 3. This is found by using the vertex formula and then substituting the x-coordinate back into the original function.
To find the y-coordinate of the vertex of the parabola defined by the quadratic function f(x)= -x² - 2x + 6, we can use the vertex formula for a parabola in standard form, which is y = ax² + bx + c. The x-coordinate of the vertex is given by the formula -b/(2a), and the y-coordinate can then be calculated by applying the x-coordinate to the original function.
First, let's find the x-coordinate of the vertex:
a = -1 (coefficient of x²)b = -2 (coefficient of x)x-coordinate of the vertex, x_v = -(-2)/(2*(-1)) = -(-2)/(-2) = 1
Now, substitute x_v back into the function to find the y-coordinate:
y-coordinate of the vertex, y_v = f(1) = -1² - 2*1 + 6 = -1 - 2 + 6 = 3
Therefore, the y-coordinate of the vertex is 3.
If the nominal interest rate is 6 percent and the rate of inflation is 10 percent, then the real interest rate is A. -16 percent. B. 4 percent. C. -4 percent. D. 16 percent.
Answer: C. -4 percent
Step-by-step explanation:
Nominal interest rate is the interest rate before taking inflation into account.
Real interest rate takes the inflation rate into account.
The equation that links all three values is
nominal rate - inflation rate = real rate
6 - 10 = -4
-4 percent
The real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate. In this case, the real interest rate is -4%, suggesting an investor would lose value due to inflation.
Explanation:The calculation of the real interest rate involves subtracting inflation from the nominal interest rate. This is essential since inflation erodes the purchasing power of money, making it an important factor to consider when dealing with interest rates. In this case, you need to subtract the inflation rate (10 percent) from the nominal interest rate (6 percent).
So, performing this calculation:
6% (Nominal Interest Rate) - 10% (Inflation Rate) = -4%
Thus, in this scenario, the correct option would be C. -4 percent. This implies that an investor would actually lose ground when considering the effect of inflation.
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The n candidates for a job have been ranked 1, 2, 3, . . . , n. Let X be the rank of a randomly selected candidate, so the X has the pmf p(x) = 1/n, if x = 1, 2, 3 . . . n, 0, otherwise. This is called the discrete uniform distribution. Compute E(X) and Var(X). (Hint: the sum of the first n positive integers is n(n + 1)/2, whereas the sum of their squares is n(n + 1)(2n + 1)/6.)
By definition of expectation,
[tex]\displaystyle E[X]=\sum_xx\,P(X=x)=\sum_{x=1}^n\frac xn=\frac{n(n+1)}{2n}=\boxed{\frac{n+1}2}[/tex]
and variance,
[tex]V[X]=E[(X-E[X])^2]=E[X^2-2X\,E[X]+E[X]^2]=E[X^2]-E[X]^2[/tex]
Also by definition, we have
[tex]E[f(X)]=\displaystyle\sum_xf(x)\,P(X=x)[/tex]
so that
[tex]E[X^2]=\displaystyle\sum_{x=1}^n\frac{x^2}n=\frac{n(n+1)(2n+1)}{6n}=\frac{(n+1)(2n+1)}6[/tex]
and finally,
[tex]V[X]=\dfrac{(n+1)(2n+1)}6-\dfrac{(n+1)^2}4=\boxed{\dfrac{n^2-1}{12}}[/tex]
Answer:
[tex]\frac{n^{2} - 1 }{12}[/tex]
Step-by-step explanation:
Data:
We collect the variables and simplify the result:
E[X] = [tex]\SIGMA \\[/tex]Σ x · p(x) = [tex]\frac{1}{n}[/tex]= ....
E[X²] =∑ x²· p(x) = ∑x²·[tex]\frac{1}{n}[/tex] = ....
Var [X] = E[X²] - E[X]² = ...
We then use the identities:
∑x = [tex]\frac{n(n+1)}{2}[/tex] and ∑ x² = [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
simplifying the identities above gives:
[tex]\frac{n^{2-1} }{12}[/tex]
The long jump record, in feet, at a particular school can be modeled by f(x) = 19.6 + 2.5ln(x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 11 years after record started being kept? Round your answer to the nearest tenth.
Answer:
25.8
Step-by-step explanation:
A. The point-slope form of the equation of a line is y ? y1 = m(x ? x1), where m is the slope and (x1, y1) is a point on the line. Write the equation of the line in point-slope form perpendicular to the graph of y = 1/2x -7 passing through the point (6, 5).
B. Write an equation of the perpendicular bisector of JK, where J = (?8, 4) and K = (4, 4).
Can you show work please.
Answer:
A.
[tex]y - 5 = -2(x-6)[/tex]
Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.
Then apply point-slope form.
B. The answer is x = 6.
The midpoint of JK is
[tex]\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)[/tex]
The line that goes through JK is just a horizontal line [tex]y = 4[/tex] because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, [tex]x = 6[/tex].
3x3 matrix A. r1(3 -2 0) r2(0 1 1) r3(2 -1 0). don't calculate A^-1 or raise any matrix to a power first. calculate det(2A^-2)
Answer with explanation:
For, a 3 × 3, matrix
[tex]r_{1}=(3,-2,0)\\\\r_{2}=(0,1,1)\\\\r_{3}=(2,-1,0)[/tex]
which are entries of First, Second and Third Row Respectively.
So, if written in the form of Matrix (A)
[tex]A=\left[\begin{array}{ccc}3&-2&0\\0&1&1\\2&-1&0\end{array}\right][/tex]
⇒Adjoint A= Transpose of Cofactor of A
[tex]a_{11}=1,a_{12}=2,a_{13}=-2\\\\a_{21}=0,a_{22}=0,a_{23}=-1\\\\a_{31}=-2,a_{32}=- 3,a_{33}=3\\\\Adj.A=\left[\begin{array}{ccc}1&0&-2\\2&0&-3\\-2&-1&3\end{array}\right][/tex]
⇒≡ |Adj.A|=1 ×(0-3) -2×(-2-0)
= -3 +4
=1 --------(1)
⇒For, a Matrix of Order, 3 × 3,
| Adj.A |=| A|²---------(2)
[tex]|2 A^{-2}|=2^3\times |A^{-2}|\\\\=2^3\times |A|^{-2}\\\\=\frac{8}{|A^{2}|}\\\\=\frac{8}{|Adj.A|}\\\\=\frac{8}{1}\\\\=8[/tex]
--------------------------------------------(Using 1 and 2)
[tex]\rightarrow|2 A^{-2}|=8[/tex]
Multiply Conjugates
(r+1/4)r-1/4)
Answer:
[tex]\large\boxed{\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\left(\dfrac{1}{4}\right)^2=r^2-\dfrac{1^2}{4^2}=r^2-\dfrac{1}{16}[/tex]
[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]\left(r+\dfrac{1}{4}\right)\left(r-\dfrac{1}{4}\right)=r^2-\dfrac{1}{16}[/tex]
Find(f/g)(x)for the following functions.
Answer:
[tex]x^{2} \neq -\frac{1}{14}[/tex]
Step-by-step explanation:
The equation will hold true as long as the denominator does not equal zero:
so take the denominator and set it equal to zero and find x. when you find x, that will be your answer:
-14x^2 -1=0
-14x^2=1
-x^2=1/14
x^2=-1/14
what is the value of X
Answer:
The value of x = 96°
Step-by-step explanation:
Here we consider two angles be <1, <2 and < 3, where <1 is the linear pair of angle measures 130° and <2 be the linear pair of angle measures 134°
To find the value of m<1
m<1 = 180 - 130 = 50°
To find the value of m<2
m<2 = 180 - 134 = 46°
To find the value of m<3
By using angle sum property,
m<1 + m<2 + m< 3 = 180
m<3 =180 - (m<1 + m<2)
= 180 - (50 + 46 = 96
= 84°
To find the value of x
Here x and <3 are linear pair,
x + m<3 = 180
x = 180 - m<3
= 180 - 84 = 96°
Therefore the value of x = 96°
What side lengths should be used to model the rectangle?
A rectangle with an area of x2 - 4x - 12 square units is
represented by the model
(x + 2) and (x-6)
(x+6) and (x - 2)
(x + 2) and (x - 10)
(x + 10) and (x - 2)
-X
-
+X
-
-
- -
- -
-
-
- -
- -
+X
For this case we have that by definition, the area of a rectangle is given by:
[tex]A = ab[/tex]
Where:
a, b: They are the sides of the rectangle
We have as data that the area of the rectangle is given by:
[tex]x ^ 2-4x-12[/tex]
IF we factor the expression, we must find two numbers that when multiplied give as a result "-12" and when summed give as result "-4". These numbers are: -6 and +2:
[tex](x-6) (x + 2)[/tex]
Thus, the sides of the rectangle are given by:
[tex](x-6) (x + 2)[/tex]
Answer:
Option A
Graph y ≥ -x^2 - 1. Click on the graph until the correct graph appears.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y\geq -x^{2}-1[/tex]
The solution of the inequality is the shaded area above the solid line of the equation of the parabola [tex]y= -x^{2}-1[/tex]
The vertex of the parabola is the point (0,-1)
The parabola open downward (vertex is a maximum)
using a graphing tool
see the attached figure
For each of the following statements, state whether it is true (meaning, always true) or false (meaning, not always true): Let X and Y be two binomial random variables. (a) If X and Y are independent, then X+Y is also a binomial random variable.
Answer:
yes
Step-by-step explanation:
it is absolutely true that biononmials always gives biononmials when added
If X and Y are independent, then X+Y is not a binomial random variable and so it is a false statement.
What is the sum of independent binomial random variables?This term is known to be a binomial random variable that occurs when all the parts of the variables is said to have similar success probability.
The best method to check if two random variables are said to be independent is through the calculation of the covariance of the two specific random variables.
Note that if If the variables are said to be independent (X and Y), then their difference is said to be not binomially distributed.
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The population of a culture of cells grows according to the function P(t)= 90t/ t + 1, where t> or =0 is measured in weeks. Complete parts (a) and (b) below.
What is the average rate of change in the population over the interval [0,24]?
Answer:
The average rate of change is [tex]\frac{18}{5}[/tex]
Step-by-step explanation:
Given function that shows the population of a culture of cells,
[tex]P(t)=\frac{90t}{t+1}------(1)[/tex]
Where, t represents the number of weeks.
Thus, the average rate of change in the population over the interval [0,24],
[tex]m=\frac{P(24)-P(0)}{24-0}[/tex]
From equation (1),
[tex]=\frac{\frac{90\times 24}{24+1}-\frac{90\times 0}{0+1}}{24}[/tex]
[tex]=\frac{\frac{2160}{25}-\frac{0+1}{0}}{24}[/tex]
[tex]=\frac{2160}{25\times 24}[/tex]
[tex]=\frac{2160}{600}[/tex]
[tex]=\frac{18}{5}[/tex]
Please help me! Struggling with Geometry! 45 points (proofs)
Answer:
Step-by-step explanation:
It’s nothing
We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. We choose a coin at random, toss it, and it comes heads. What is the probability that the opposite face is tails?
Answer:
50% chance
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
There are 3 coins, and each coin has 2 possible outcomes. So there are a total of 6 possible outcomes.
Of these 6 outcomes, 3 are heads. Of these 3, only 1 has tails on the opposite face.
So the probability is 1/3.
We can also show this using conditional probability:
P(A|B) = P(A∩B) / P(B)
Probability that A occurs, given that B has occurred = Probability that both A and B occur / Probability that B occurs
Here, A = tails on opposite face and B = heads.
P(A|B) = (1/6) / (3/6)
P(A|B) = 1/3
Five infinity stones cost $16.80. What is the price per infinity stone ?
Answer:
The price is $3.36 per infinity stone
Step-by-step explanation:
we know that
Five infinity stones cost $16.80
so
To find the price of each infinity stone (unit rate) divide the total cost by five
[tex]\frac{16.80}{5} =3.36\frac{\$}{infinity\ stone}[/tex]
What is the probability that a randomly drawn hand of four cards contains all black cards or all face cards? The probability is 6 Round to four decimal places as needed.)
Answer: 0.05699
Step-by-step explanation:
The total number of cards in a deck = 52
The total number of black cards = 26
Then ,[tex]\text{P(Black)}=\dfrac{C(26,4)}{C(52,4)}=0.00182842367\approx0.00183[/tex]
The total number of face cards = 12
Then , [tex]\text{P(Face)}=\dfrac{C(12,4)}{C(52,4)}\approx0.05522[/tex]
The number of cards that are black and face cards = 6
Then , [tex]\text{P(Black and Face )}=\dfrac{C(6,4)}{C(52,4)}\approx0.00006[/tex]
Then , the probability that a randomly drawn hand of four cards contains all black cards or all face cards is given by :-
[tex]\text{P(Black or Face)}=\text{P(Black)+P(Face)-P(Black and Face)}\\\\\Rightarrow\ \text{P(Black or Face)}=0.00183+0.05522-0.00006\\\\\Rightarrow\ \text{P(Black or Face)}=0.05699[/tex]
how the graph does the graph behave as x approaches positive or negative infinity. does it keep going at the same rate or does it approach a value but never touch it ?
The graph approaches positive infinity at a constant rate.
The end behavior of this graph is:
As x → -∞, f(x) → +∞
For the first notation it looks at the behavior of the left side of the graph. As x approaches negative infinity (or positive xs) y or f(x) approaches positive infinity (or positive ys)
and
As x → +∞, f(x) → +∞
For the second notation it looks at the behavior of the right side of the graph. As x approaches positive infinity (or positive x's) y or f(x) approaches positive infinity (or positive ys)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: The graph approaches positive infinity at a constant rate.
Step-by-step explanation:
translate the phrase into an Algebraic Expression and Simplify : The Result of Increasing the product of a number x and 9 by 4
Answer:
[tex]y =( x +9 )\times 4[/tex]
simplified
[tex]y = 4x + 48[/tex]
Step-by-step explanation:
first know that the result would be y or f(x), because it's the function applied to x that makes it y. so its starts with either y= or, f(x)=
increasing by a number is multiplying, the word and is used for addition so
+9 ×4 will be in the equation
used PEMDAS, distribution, and combining like terms to simplify
What is the length of side s of the square shown below?
Answer:
C
Step-by-step explanation:
The Pythagorean Theorem tells us that
a^2 + b^2 = c^2
a = b = s because a right angle and a 45 degree angle leaves only 45 degrees which means that both acute angles are 45 degrees
c = 2
2s^2 = 2^2 Divide by 2
s^2 = 4/2
s^2 = 2 Take the square root of both sides.
sqrt(s^2) = sqrt(2)
s = sqrt(2)
Answer:
C: square root of 2.
Step-by-step explanation:
Ignore the picture that shows option D, jcherry99's description is correct.
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
Answer that question with all work shown. Thanks
Answer:
a_n=-\frac{1}{4 a_{n-1}
Step-by-step explanation:
The recursive formula for the geometric sequence is given by:
a_n = a_{n-1} \cdot r
where,
r is the common ratio terms
-16, 4, -1, ...
This is a geometric sequence.
Here, and
Since,
ans so on .....
Substitute the given values we have;
⇒
Therefore, the recursive formula for the following geometric sequence is,
Answer:
[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]
Step-by-step explanation:
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
Here the common difference of two terms are not same.
LEts find the common ratio. To find common ratio, divide the second term by first term
[tex]\frac{4}{-16} =\frac{-1}{4}[/tex]
[tex]\frac{-1}{4} =\frac{-1}{4}[/tex]
So common ratio is -1/4
Recursive formula is
[tex]A_n= A_{n-1} (r)[/tex]
'r' is the common ratio.
Recursive formula becomes
[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]
if u are 4/7 mile from your home and u can walk 4 5/7 miles per hour , How long will it take for u to walk to your home ????? A) 4/33 hour B) 80/49 hours C) 20/231 hour D) 80/49 hours E) 132/49 hours Which one is the best Answer ..
Answer:
A) 4/33 hour
Step-by-step explanation:
This is a distance = rate * time problem
We are given the distance and the rate, now we need to solve for the time:
[tex]\frac{4}{7}=4\frac{5}{7}t[/tex]
Let's change that mixed fraction into an improper one:
[tex]\frac{4}{7}=\frac{33}{7}t[/tex]
Now to solve for t we can multiply the 33/7 by its recirocal:
[tex](\frac{7}{33})\frac{4}{7}=\frac{33}{7}(\frac{7}{33})t[/tex]
Multiplying a fraction by its reciprocal = 1, so that leaves only a t on the right:
[tex](\frac{7}{33})\frac{4}{7}=t[/tex]
The 7's cancel out on the left and that leaves you with
[tex]t=\frac{4}{33}hr[/tex]
Suppose you invest $150 a month for 5 years into an account earning 7% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 23 years. How much will you have in the end?
Answer:
About 0.3 billion dollars
Step-by-step explanation:
5 years = 60 months.
The 150 of the first month will be 150*1.07^60 in 5 years.
The 150 of the second month will be 150*1.07^59 in 5 years.
The 150 of the third month will be 150*1.07^58 in 5 years.
And so forth.
So we sum that up:
( sum_(n=1)^(60) 150×1.07^n)
And multiply with
× 1.07^(5×23)
to account for the increase in value in the following 23 years.
The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 153 cm2, what is the length of the diagonal?
Give your answer to 2 decimal places.
If anyone could explain this I would appreciate it, all the answers I kept getting on similar questions were a few numbers off and I don't know why.
Answer:
diagonal ≈ 18.43 cm
Step-by-step explanation:
Let L represent the length of the rectangle. Then the width is ...
w = 2L -4 . . . . . . 4 less than twice the length
The area is ...
A = wL = (2L -4)L = 2L² -4L
The area is said to be 153 cm², so we have ...
2L² -4L = 153
2L² -4L -153 = 0 . . . . . . subtract 153 to put into standard form
We can find the solution to this using the quadratic formula. It tells us the solution to ax²+bx+c=0 is given by ...
x = (-b±√(b²-4ac))/(2a)
We have a=2, b=-4, c=-153, so our solution for L is ...
L = (-(-4) ±√((-4)²-4(2)(-153)))/(2(2)) = (4±√1240)/4
Only the positive solution is of interest, so L = 1+√77.5.
__
Now we know the rectangle is 1+√77.5 long and -2+2√77.5 wide. The diagonal (d) is the hypotenuse of a right triangle with these leg lengths. Its measure can be found from ...
d² = w² +L² = (-2+2√77.5)² +(1+√77.5)²
It can work well to simply evaluate this using a calculator, or it can be simplified first.
d² = 4 -8√77.5 +4·77.5 + 1 +2√77.5 +77.5 = 392.5 -6√77.5
Taking the square root gives the diagonal length:
d = √(392.5 -6√77.5) ≈ 18.43 . . . . cm