It looks like you have
[tex]\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}[/tex]
Substituting these in to the plane equation, we have
[tex]4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2[/tex]
When [tex]t=-2[/tex], we get the point
[tex]\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}[/tex]
jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
The monthly payment is $796.40.
The total amount she would deposit is $286,705.51
The total interest earned is $513,294.49
What is the monthly payment, total amount deposited and interest?The payments made by Jessica are known as deferred annuities. Deferred annuities are when a series of payments are made in exchange for an amount of money in the future.
The formula that can be used to determine the amount of monthly deposit is: future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 6%/12 = 0.5%
n = number of years = 30 x 12 = 360
Annuity factor = ](1.005^360) - 1] / 0.005 = 1004.515
Monthly payments = 800,000 / 1004.515 = $796.40
Total amount she would deposit = monthly payment x number of years x number of months in a year
$796.40 x 30 x 12 = 286,705.51
Total interest earned = value of the retirement account - total amount deposited
800,000 - 286,705.51 = 513,294.49
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Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur
The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
How to calculate the profit?From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.
It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.
The loss will be:
= 2,000,000 - 1,500,000
= 500,000
Therefore, the information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
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A 2-liter bottle of juice costs $2.80. A box containing six 1/2 liter bottles sells for $3.90. Which option has a higher cost per liter? What is that cost?
A. 2-liter bottle; $1.40
B. Box of six 2-liter bottles; $1.30
C. 2-liter bottle; $2.80
D. Box of six-liter bottles; $3.90
Answer:
A. 2-liter bottle;$1.40
Step-by-step explanation:
We have to find out which option has the higher cost per liter. To do this we must find out how much each option would be if it was a liter.
1st set up each equation
2-liter = $2.80 we can divide by 2 on both sides of the equal sign and we get 1 liter = $1.40.
6(1/2) liter bottles = $3.90 this becomes 3 liters = $3.90 then we divide by 3 on both sides of the equal sign and we get $1.30
2nd we compare
$1.40(2 liter bottle) > $1.30 (6 1/2 liter bottles)
If the volume of the cone is 180 in³, what is its surface area?
Answer:
Hi, to find the surface area of a cone is πrl
if your radius and length is given.
hope this helps (•‿•)
2/120=X/80=Y/300
x=? & y=?
X=1.33
Y=4.9875;approx. 5.0
Answer:
(2/120=X/80)=Y/300
2×80=120×X
X=160/120
X=1.33
X/80=Y/300
But X=1.33
By substituting
X=1.33, We have that
1.33/80=Y/300
80×Y=1.33×300
80Y=399
Y=399/80
Y=399/80
Y=5.0 approx.
The percentage of each transaction contributed to the total transactions in the same Account. Use BASE_EQUIV_AMT as the unit.
The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:
Cash Account:1. Service Revenue $900 = 8%
2. Owner's Equity, Barbara Hanson $2,200 = 19.8%
3. Accounts Receivable $750 = 6.8%
5. Note Payable $6,000 = 54.1%
6. Unearned Revenue $1,250 = 11.3%
Total cash receipts = $11,100
Service Revenue:1. Cash $900 = 70.6%
4. Accounts Receivable $375 = 29.4%
Total $1,275
How is the percentage computed?The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.
Percentage values show the degrees of relationship among variables.
The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.
Transaction Analysis:1. Cash $900 Service Revenue $900
2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200
3. Cash $750 Accounts Receivable $750
4. Accounts Receivable $375 Service Revenue $375
5. Cash $6,000 Note Payable $6,000
6. Cash $1,250 Unearned Revenue $1,250
Question Completion:The following transactions occurred during July:
1. Received $900 cash for services provided to a customer during July.
2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.
3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.
4. Provided services to a customer on credit, $375.
5. Borrowed $6,000 from the bank by signing a promissory note.
6. Received $1,250 cash from a customer for services to be rendered next year.
Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.
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in mongolia the temperature can dip down to -45C in January. The temperature in July may reach 40C. What is the temperature range in Mongolia?
Answer:
85 C
Step-by-step explanation:
Temperature range means the difference between the maximum and minimum in temperature for an area. 40C-(-45C)=85 C
From the top of the Eiffel tower, which is 984 feet tall, you look down and see your friend at a 60°
angle of depression. How far is your friend from the foot of the tower?
The answer is 492 feet.
If we picture the scenario as a right triangle, using trigonometric ratios, this problem can be solved.
cos 60° = x / 984
1/2 = x/984
x = 984/2
x = 492 feet
ASAP help me with this PLEASE
Answer:
98 degrees
Step-by-step explanation:
In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.
Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"
So using all the known values we can set up the following equation:
[tex]2x+64+100=360[/tex]
Simplify on the left side
[tex]2x+164=360[/tex]
Subtract 164 from both sides
[tex]2x=196[/tex]
Divide both sides by 2
[tex]x=98[/tex]
Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.
Ramiro was on a 2-day road trip. On the first day he drive at an average speed 40 mph. On the second day he drove at an average speed of 60 mph. If he drove 2 hours. If he drove 2 hours longer and went 20 miles farther on the first day, find the total distance Ramiro traveled on his first road trip
The total distance Ramiro travelled is 380 miles.
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).
Parts of an EquationThere are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
let x be the first day hours
let y be the second day hours.
now,
x = y + 2
40x = 60y + 20
Putting x= y+2
40(y + 2) = 60y + 20
40y + 80 = 60y + 20
60 = 20y
y = 3 hours
For, first day
x = y + 2
x = 3 + 2
x = 5 hours
Thus,
Total distance = 40(5) + 60(3)
=200 + 180
=380 miles
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Did you ever purchase a bag of M & M Peanut candies and wonder about the distribution of the colors ? A recent article reported that 30 percent of the candies are brown , 20 percent yellow , 20 percent red , 20 percent green , and 10 percent orange . A one - pound bag of M & M peanut candies was purchased at Wal - Mart here in Lubbock . A total of 188 candies were in the bag , with 67 brown , 22 yellow , 51 red , 24 green , and 24 orange .
Filling in the frequency table according to the colors observed and expected on the M & M Peanut candies is as follows:
Frequency Table:Color Brown Yellow Red Green Orange Total
Absolute FrequenciesObserved Frequency 67 22 51 24 24 188
Expected Frequency 56 38 38 38 18 188
Relative Frequencies:
Observed Frequency 36% 12% 27% 13% 13%
Expected Frequency 30% 20% 20% 20% 10%
What is a frequency table?A frequency table is a display of the number of occurrences of a particular value or characteristic.
A frequency table makes it easy to display and interpret a distribution of data.
The absolute frequencies shows the absolute values of the observed and expected frequencies, while the relative frequencies shows the percentage values of the observed and expected frequencies.
Data and Calculations:Color Brown Yellow Red Green Orange Total
Observed Frequency 67 22 51 24 24 188
Expected Frequency 30% 20% 20% 20% 10% 100%
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Question Completion:Fill in the following table on the frequency of the colors, indicating the absolute and relative frequencies of the distributions.
What is the common denominator of x+5/x+8=1+6/x+1?
Answer:
(x+8) (x+1)
Step-by-step explanation:
To find the common denominator, we need to find the least common multiple of the terms in the denominator
(x+8) from the first term
(1) from the second term
(x+1) from the third term
The least common denominator is
(x+8) (1)(x+1)
Simplifiying
(x+8) (x+1)
So confused please help me thank u
What is 500$ invested at 8% for 6 and a half years?
Answer:
$824.56
Step-by-step explanation:
Use the compound interest formula which is A = P(1+r/n)^nt
1st using the given information we are going to find out values:
P is our initial amount of $500
r is the annual rate of interest (expressed as a decimal) 8% becomes 0.08.
n is how many times interest is compounded per year, in this case since its not stated we are going to assume its annually, so n is 1
t is how long the money is deposited (in years) so t is 6.5
A is our final amount
2nd plug in our values into the equation
Plugging all these values we get A = 500 (1 +0.08/1)^(0.08)(6.5)
A = $824.56
PLEASE HELP ASAP PLEASE PLEASE
Answer:
transitive property
Step-by-step explanation:
This is the answer by definition.
The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.
In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.
According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."
According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.
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do the quantities combine?
Answer:
D
Step-by-step explanation:
Widrawal is - 30
Deposit is +30
-30+30 = 0
Madison finished 4/5 of her homework before dinner. What percent of Maddison’s homework is left to finish?
Answer:
1/5 of it
Step-by-step explanation:
5/5 represents all of her homework
5/5-4/5= 1/5
4/5 represents the homework she did before dinner
1/5 represents the homework left to do
Determine the relationship between the angle θ of a circular sector of a circumference of radius 10 cm and the area Aθ of the sector; and calculate the area for an angle of π/4
The area is:
A = (θ/2)*R^2
The circumference is:
C = θ*R
And the area of the circle when the angle is π/4 is: 39.25 cm^2
How to find the area in terms of the angle?
For a circle of radius R, the area is:
A = pi*R^2
where pi = 3.14
And the circumference is:
C = 2*pi*R
Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
And the circumference is:
C = (θ/2pi)*2pi*R = θ*R
Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4
Replacing that in the area equation, we get:
A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2
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Barbara runs once around the track in 3 minutes 45 seconds. Liad runs around the track in 2
minutes 30 seconds. At these rates, after 10 minutes of running, the distance Barbara has run is
what fractional part of Liad's?
Answer:
2/3rds of liad's run
Step-by-step explanation:
3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps
2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps
(8/3)/4 = 2/3
Given the property:
a = am-n, for a 0
am
an
Explain the three cases for:
a. 0
b. 0
c.m=n
Could you try reposting the question clearly
A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 3 hours there will be 780 bacteria.
(a) Express the population after t hours as a function of t.
population: ? (function of t)
(b) What will be the population after 3 hours?
(c) How long will it take for the population to reach 1870 ?
The solutions to the exponential growth problem are:
A. [tex]P(t) = 260e^0.3662t[/tex]
B.[tex]P(3) = 260e^0.3662(3) = 779[/tex]
C.3.367 hours
What is the formular for the exponential growth problem?The exponential growth problem obeys the equation:
P(t) = P0ekt
P0=population
time t
We can find the value of k At t=3 hours as,
780 = 260e^k(3)
k = (1/3) ln(780/260) hours-1 ≅ 0.3662 hours-1
A. [tex]P(t) = 260e^0.3662t[/tex]
B. [tex]P(3) = 260e^0.3662(3) = 779[/tex]
C. 1870 = 260e^0.3662t
To Solve for t, w2e make t the subject of the formula
t = ln(1870/260) / 0.3662 hours = 3.367 hours
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(4x + 5) - (2x - 3)
Answer:
2x + 8
Step-by-step explanation:
(4x + 5) - (2x - 3)
4x + 5 - 2x + 3
2x + 8
Answer: 2x+8
Step-by-step explanation:
4x+5-2x+3
=2x+8
Karin has 13 coins (2 quarters, 6 dimes, 4 nickels, and 1 penny) in a piggy bank. She turns the bank
upside down and shakes the bank until a coin falls out, puts it aside, and the shakes until another coin
falls out.
What is the probability that the first coin is a nickel and the second coin is a quarter?
Select one:
OOO O
2 63 23
39
01/3
118
Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is: 2/39.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Hence:
For the first coin, out of 13 coins, 4 are nickels, hence the probability is 4/13.For the second coin, considering that a nickel was taken first, 2 out of 12 coins will be quarters, hence the probability is 2/12 = 1/6.Then the probability for both coins is:
p = 4/13 x 1/6 = 4/78 = 2/39
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Equivalent fraction statement
Answer:
x=18
Step-by-step explanation:
[tex]\frac{4}{12} =\frac{6}{x} \\[/tex]
[tex]\frac{4}{12}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{6}{x}[/tex]
[tex]\frac{2}{6} = \frac{6}{x}[/tex]
2×3 =6
6×3=18
x=18
need answers right now
tysm
If the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.
Given the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1).
We are required to find the area of the rhombus when the fourth point Z is plotted.
We have to plot the points of the rhombus in the graph. We know that all the sides of the rhombus should be equal to each other. So by adjusting the blocks in the graph we will be able to plot Z as (-2,3).
In this way the diagonals are ZX and WY.
ZX=[tex]\sqrt{(3-3)^{2} +(6+2)^{2} }[/tex]
=[tex]\sqrt{64}[/tex]
=8 units
WY=[tex]\sqrt{(1-5)^{2} +(2-2)^{2} }[/tex]
=[tex]\sqrt{16}[/tex]
=4 units
Area of rhombus=1/2 *([tex]d_{1} *d_{2}[/tex])
=1/2* (8*4)
=8*2
=16 Square units.
Hence if the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.
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Can someone please help meee<3
Answer:
36
Step-by-step explanation:
[tex]\sqrt{24a}=12\sqrt{6} \\ \\ 24a=864 \\ \\ a=36[/tex]
simply the following expression by combining like terms 5w + 7v - 8w + v - w + 2y
PLEASE HELP ASAP!!! ALSO PLEASE ADD A DESEND EXPLANATION!! Find the original price if the price was: $8a after 60% increase.
Answer: $3.2a
Step-by-step explanation: We need to decrease $8a by 60 percent because $8a is the price after a 60% increase. 8 x 6/10 is 48/10 which as a mixed number is 4 8/10 or 4.8. Now, we subtract 4.8 from 8 which yields our answer of 3.2.
Tried doing it myself multiple times , multi choice question, not getting any availabile answer.
Answer: The given integral is impossible to solve.
Step-by-step explanation: I tried solving it right now with integration by parts and trigonometric substitution, and I was unable to solve it.
So I looked at two math solvers and tried inputting the question, and it either says "There is nothing more you can do with this problem," or "We are unable to solve this problem."
First, let's substitute [tex]x=\frac w4[/tex] and [tex]dx=\frac{dw}4[/tex] to get rid of the fraction.
[tex]\displaystyle \int \csc^6\left(\dfrac w4\right) \cot^4\left(\dfrac w4\right) \, dw = 4 \int \csc^6(x) \cot^4(x) \, dx[/tex]
Recall that
[tex]\cot^2(x) + 1 = \csc^2(x)[/tex]
[tex]\dfrac{d}{dx} \cot(x) = -\csc^2(x)[/tex]
We can the rewrite the integrand as
[tex]\displaystyle 4 \int \csc^6(x) \cot^4(x) \, dx = 4 \int \left(\cot^2(x) + 1\right)^2 \cot^4(x) \csc^2(x) \, dx[/tex]
then substitute [tex]y=\cot(x)[/tex] and [tex]dy=-\csc^2(x)\,dx[/tex] to get
[tex]\displaystyle -4 \int (y^2 + 1)^2 y^4 \, dy[/tex]
Expand the integrand.
[tex]\displaystyle -4 \int (y^4 + 2y^2 + 1) y^4 \, dy = -4 \int (y^8 + 2y^6 + y^4) \, dy[/tex]
Now integrate with the power rule.
[tex]\displaystyle -4 \left(\frac{y^9}9 + \frac{2y^7}7 + \frac{y^5}5\right) + C[/tex]
[tex]\displaystyle -\frac{4y^9}9 - \frac{8y^7}7 - \frac{4y^5}5 + C[/tex]
Put everything back in terms of [tex]x[/tex], then [tex]w[/tex].
[tex]\displaystyle -\frac{4\cot^9(x)}9 - \frac{8\cot^7(x)}7 - \frac{4\cot^5(x)}5 + C[/tex]
[tex]\displaystyle \boxed{-\frac49 \cot^9\left(\dfrac w4\right) - \frac87 \cot^7\left(\dfrac w4\right) - \frac45 \cot^5\left(\dfrac w4\right) + C}[/tex]
Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415. How much interest did they pay due to financing?
The interest due on financing option is $307.50
What is interest on financing?
Interest on financing is the extra amount paid by the couple when their total payments are compared to the cash price of $6,230.
The total payments would be the 25% down payment plus the sum of the twelve monthly payments of $415 each
Down payment=cash price*25%
Down payment=$6230*25%
Down payment=$1,557.50
Total monthly payments=amount of each monthly payment*number of monthly payments
monthly payment=$415
number of monthly payments=12
Total monthly payments=$415*12
Total monthly payments=$4,980
Total payment under financing=Down payment +Total monthly payments
Total payment under financing=$1,557.50+$4,980
Total payment under financing=$6,537.50
Interest=$6,537.50-$6,230
Interest on financing=$307.50
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