Answer:
-1/2
Step-by-step explanation:
x^2- 16^x = 0x^2 = 16^xx^2 = 4^2xx = 4^xlogx = xlog41/x×logx = log4log(x^1/x) = log4x^(1/x) = 4At this point you can guess and try. And it seems that x = -1/2, lets check:
(-1/2)^(1 /-1/2)= (-1/2)^-2= 2^2= 4So, this is correct: x= -1/2
Please answer this correctly without making mistakes
Shortest is Vindale to Wildgrove to Clarksville
18.9 + 13.2 = 32.1 km.
Refer to the following wage breakdown for a garment factory:
Hourly Wages Number of employees
$4 up to $7 18
7 up to 10 36
10 up to 13 20
13 up to 16 6
What is the class interval for the preceding table of wages?
A. $4
B. $2
C. $5
D. $3
Answer:
The class interval is $3Step-by-step explanation:
The class interval is simply the difference between the lower or upper class boundary or limit of a class and the lower or upper class boundary or limit of the next class.
In this case for the class
$4 up to $7 18 and
$7 up to $10 36
The lower class boundary of the first class is $4 and the lower class boundary of the second class is $7
Hence the class interval = $7-$4= $3A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2
Answer:
3
Step-by-step explanation:
let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room
A living room is two times as long as the bedroom, so:
A = 2X
A living room is one and one-half times as wide as a bedroom, so:
B = 1.5Y
The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y
So, AB in terms of XY is:
A*B = (2X)*(1.5Y) = 3(X*Y)
It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the bedroom.
convert the equation y= -4x + 2/3 into general form equation and find t the values of A,B and C.
Answer:
Standard form: [tex]12x+3y-2=0[/tex]
A = 12, B = 3 and C = -2
Step-by-step explanation:
Given:
The equation:
[tex]y= -4x + \dfrac{2}3[/tex]
To find:
The standard form of given equation and find A, B and C.
Solution:
First of all, let us write the standard form of an equation.
Standard form of an equation is represented as:
[tex]Ax+By+C=0[/tex]
A is the coefficient of x and can be positive or negative.
B is the coefficient of y and can be positive or negative.
C can also be positive or negative.
Now, let us consider the given equation:
[tex]y= -4x + \dfrac{2}3[/tex]
Multiplying the whole equation with 3 first:
[tex]3 \times y= 3 \times -4x + 3 \times \dfrac{2}3\\\Rightarrow 3y=-12x+2[/tex]
Now, let us take all the terms on one side:
[tex]\Rightarrow 3y+12x-2=0\\\Rightarrow 12x+3y-2=0[/tex]
Now, let us compare with [tex]Ax+By+C=0[/tex].
So, A = 12, B = 3 and C = -2
find the exact value of sin 0
Answer:
12/13
Step-by-step explanation:
First we must calculate the hypotenus using the pythagoran theorem
5²+12² = (MO)² MO = [tex]\sqrt{5^{2}+12^{2} }[/tex] MO = 13Now let's calculate sin0
sin O = 12/13So the exact value is 12/13
Answer:
C.) 12/13
Step-by-step explanation:
In a right angle triangle MN = 12, ON = 5 and; angle N = 90°
Now,
For hypotenuse we will use Pythagorean Theorem
(MO)² = (MN)² + (ON)²
(MO)² = (12)² + (5)²
(MO)² = 144 + 25
(MO)² = 169
MO = √169
MO = 13
now,
Sin O = opp÷hyp = 12÷13
Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000. If a person is about to take the test what is the probability that he or she will make a score of 650 or more?
Answer:
0.0668 or 6.68%
Step-by-step explanation:
Variance (V) = 10,000
Standard deviation (σ) = √V= 100
Mean score (μ) = 500
The z-score for any test score X is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = 650:
[tex]z=\frac{650-500}{100}\\z=1.5[/tex]
A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]
The probability is 0.0668 or 6.68%
The probability that he or she will make a score of 650 or more is 0.0668.
Let X = Scores made on a certain aptitude test by nursing students
X follows normal distribution with mean = 500 and variance of 10,000.
So, standard deviation = [tex]\sqrt{10000}=100[/tex].
z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].
The probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]
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You are selling your product at a three-day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money on the first two days and lose money on the third day
Answer:
The required probability = 0.144
Step-by-step explanation:
Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%
Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.
That would be;
P(making money) * P(making money) * P(losing money)
Kindly recollect;
P(making money) = 60% = 60/100 = 0.6
P(losing money) = 40% = 40/100 = 0.4
The probability we want to calculate is thus;
0.6 * 0.6 * 0.4 = 0.144
The owner of a shoe store wanted to determine whether the average customer bought more than $100 worth of shoes. She randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below.
Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is greater than $100 and then draw a conclusion in the context of the problem. Use α=0.05.
125 99 219 65 109 89 79 119 95 135
Select the correct answer below:
A) Reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
B) Reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
C) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Answer:
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Step-by-step explanation:
We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;
X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.
Let [tex]\mu[/tex] = average customer bought worth of shoes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $100 {means that the mean is smaller than or equal to $100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $100 {means that the mean is greater than $100}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = $113.4
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $42.78
n = sample of receipts = 10
So, the test statistics = [tex]\frac{113.4-100}{\frac{42.78}{\sqrt{10} } }[/tex] ~ [tex]t_9[/tex]
= 0.991
The value of t-test statistics is 0.991.
Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.
Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean is smaller than or equal to $100.
If w'(t) is the rate of growth of a child in pounds per year, what does 7 w'(t)dt 4 represent? The change in the child's weight (in pounds) between the ages of 4 and 7. The change in the child's age (in years) between the ages of 4 and 7. The child's weight at age 7. The child's weight at age 4. The child's initial weight at birth.
Complete Question
If w'(t) is the rate of growth of a child in pounds per year, what does
[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] represent?
a) The change in the child's weight (in pounds) between the ages of 4 and 7.
b) The change in the child's age (in years) between the ages of 4 and 7.
c) The child's weight at age 7.
d) The child's weight at age 4. The child's initial weight at birth.
Answer:
The correct option is option a
Step-by-step explanation:
From the question we are told that
[tex]w'(t)[/tex] represents the rate of growth of a child in [tex]\frac{pounds}{year}[/tex]
So [tex]{w'(t)} \, dt[/tex] will be in [tex]pounds[/tex]
Which then mean that this [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] the change in the weight of the child between the ages of [tex]4 \to 7[/tex] years
An airplane descends during the last hour of it's flight to prepare for landing. It's altitude changes at an average of -0.15 km per minute for those 60 minutes. (What is the product) How does the elevation of the airplane change in that hour? The elevation of the airplane _________ by ______ km. increases 60 decreases 9 0.15
WILL GIVE BRAINLIEST, THANKS AND FIVE STARS
Answer:
The elevation of the airplane decreases by 9 km.
Step-by-step explanation:
We use the distance-rate-time formula: d = rt.
Here, the rate is r = 0.15 km/min and the time is t = 60 min. Simply plug these into the formula:
d = rt
d = 0.15 * 60 = 9 km
So, the change in elevation in the last 60 minutes is 9 km. However, note that the rate is negative (-0.15 km/min), which means that the elevation actually is decreasing.
Thus, the answer is: the elevation of the airplane decreases by 9 km.
~ an aesthetics lover
Answer:
The elevation of the airplane _decrease_ by __9____ km
Step-by-step explanation:
Take the rate and multiply by the time to get the distance traveled
-.15 km per minute * 60 minutes
- 9 km
The plane will go down 9 km in that 60 minutes
Calculate the length of the unknown side of this right angled triangle
Answer:
12.04
Step-by-step explanation:
Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,
[tex]a^2 + b^2 = c^2[/tex]
We already have a and b which are 8 and 9 so we plug them in.
[tex](8)^2 + (9)^2 = c^2[/tex]
64 + 81 = c^2
145 = c^2
c = 12.04 rounded to the nearest hundredth.
Thus,
the unknown side is about 12.04.
Hope this helps :)
Write these numbers in standard form 0.000 05
Answer:
5x 10 ^-5
Step-by-step explanation:
UHM that would be
NaN × [tex]10^{0}[/tex]
I hope this helps!
so my reasoning... Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
Please help. I’ll mark you as brainliest if correct!
Answer:
8lb of the cheaper Candy
17.5lb of the expensive candy
Step-by-step explanation:
Let the cheaper candy be x
let the costly candy be y
X+y = 25.5....equation one
2.2x +7.3y = 25.5(5.7)
2.2x +7.3y = 145.35.....equation two
X+y = 25.5
2.2x +7.3y = 145.35
Solving simultaneously
X= 25.5-y
Substituting value of X into equation two
2.2(25.5-y) + 7.3y = 145.35
56.1 -2.2y +7.3y = 145.35
5.1y = 145.35-56.1
5.1y = 89.25
Y= 89.25/5.1
Y= 17.5
X= 25.5-y
X= 25.5-17.5
X= 8
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4 and x = -9 b. x = 4 and x = -9 c. x = -4 and x = 9 d. x = 4 and x = 9
Answer:
c. x = -4 or x = 9Step-by-step explanation:
[tex]\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}[/tex]
Domain:
[tex]x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3[/tex]
solution:
[tex]\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}[/tex]
use (a - b)(a + b) = a² - b²
[tex]\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}[/tex]
multiply both sides by (x - 3) ≠ 0
[tex]\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}[/tex]
cancel (x - 3)
[tex]\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3[/tex]
subtract [tex]\frac{4(x-3)}{x}[/tex] from both sides
[tex]\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}[/tex]
cross multiply
[tex](4)(x)=(x+3)(-x+12)[/tex]
use FOIL
[tex]4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36[/tex]
subtract 4x from both sides
[tex]0=-x^2+12x-3x+36-4x[/tex]
combine like terms
[tex]0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36[/tex]
change the signs
[tex]x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0[/tex]
The product is 0 if one of the factors is 0. Therefore:
[tex]x-9=0\ \vee\ x+4=0[/tex]
[tex]x-9=0[/tex] add 9 to both sides
[tex]x=9\in D[/tex]
[tex]x+4=0[/tex] subtract 4 from both sides
[tex]x=-4\in D[/tex]
Historically, the proportion of students entering a university who finished in 4 years or less was 63%. To test whether this proportion has decreased, 114 students were examined and 51% had finished in 4 years or less. To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased (at the 5% level of signficance), what is the critical value
Answer:
z(c) = - 1,64
We reject the null hypothesis
Step-by-step explanation:
We need to solve a proportion test ( one tail-test ) left test
Normal distribution
p₀ = 63 %
proportion size p = 51 %
sample size n = 114
At 5% level of significance α = 0,05, and with this value we find in z- table z score of z(c) = 1,64 ( critical value )
Test of proportion:
H₀ Null Hypothesis p = p₀
Hₐ Alternate Hypothesis p < p₀
We now compute z(s) as:
z(s) = ( p - p₀ ) / √ p₀q₀/n
z(s) =( 0,51 - 0,63) / √0,63*0,37/114
z(s) = - 0,12 / 0,045
z(s) = - 2,66
We compare z(s) and z(c)
z(s) < z(c) - 2,66 < -1,64
Therefore as z(s) < z(c) z(s) is in the rejection zone we reject the null hypothesis
Determine whether 52c2y4 is a monomial, binomial, trinomial, or other polynomial.
Answer: Monomial.
Step-by-step explanation:
Ok, when we have a polynomial with only one term, this is a monomial.
If the polynomial has two terms, this is a binomial.
If the polynomial has 3 terms, this is a trinomial.
And so on.
In this particular case we have:
52*c^2*y^4
Where c and y may be variables.
We can see that here we have only one term, so this would be a monomial.
(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)
Answer:
binomial.
Step-by-step explanation:
The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.
What is the total amount of 2/5+5/3+9/3 and the lowest common denominator?
The lowest common denominator is lcm(5, 3), which is 15.
The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].
Solve the proportion below.
X =
A. 24
B. 49
c. 27
D. 6
Answer:
A. 24
Step-by-step explanation:
4/9 = x/54
x= 54*4/9 ===== multiplying both sides by 54
x= 24
Answer is 24, choice A is correct one
9. A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?
Answer: 97
Step-by-step explanation:
Formula to compute the required sample size :
[tex]n= (\dfrac{\sigma\times z_{\alpha/2}}{E})^2[/tex]
, where [tex]\sigma[/tex] = standard deviation
E= Margin of error
[tex]z_{\alpha/2}[/tex] = Two tailed z-value.
Here, E= 20
[tex]\sigma[/tex] = 100
For 95% confidence level: [tex]z_{\alpha/2}[/tex] =1.96
Required sample size:
[tex]n=(\dfrac{100\times1.96}{20})^2\\\\=(5\times1.96)^2\\\\=96.04\approx97[/tex]
Hence, the required sample size : 97
What is (6b +4) when b is 2?
Answer:
16
Step-by-step explanation:
6*2 = 12
12 + 4 = 16
Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 64 + x2 − y2 R = {(x, y): x2 + y2 ≤ 64}
The area of the surface above the region R is 4096π square units.
Given that:
The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]
The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].
To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.
The integral for the area is given by:
[tex]Area = \int\int_R f(x, y) dA[/tex]
To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.
Using polar coordinates, we can parameterize the region R as follows:
x = rcos(θ)
y = rsin(θ)
where r goes from 0 to 8, and θ goes from 0 to 2π.
Now, rewrite the integral in polar coordinates:
[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]
Now, we can integrate with respect to r first and then with respect to θ:
[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]
Integrate with respect to r:
[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]
Now, we can integrate with respect to θ:
[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]
Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))
Area = 4096π + 128(0) - 0
Area = 4096π square units
So, the area of the surface above the region R is 4096π square units.
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A man bought certain number of litches
at 20 per Rs 100 and an equal no. of 30 per
Rs 100. He mixed them and sold them at
25
per Rs 100. Find his
gain or loss
percent?
Answer: The loss is 4%
Step-by-step explanation:
Lets call litches that are 20 pcs per Rs 100 - litches A
that are 30 pcs per Rs 100- litches B
So a man can buy 2 pcs A per Rs 10
and 3 pcs B per Rs 10
OR
6x pcs A per Rs 30x
and 6x pcs B per Rs 20x
Now he gonna sell the 12x litches for y Rs
Lets find y from the proportion
12x cost y
25 cost 100
y/12=100/25
y=48 Rs
So the man bought 6x A + 6x B for 20x+30x=50 Rs
And then he sold them for 48 Rs
Obviously the man gonna loose the money.
Lets find the losses in %
(50-48)/50*100=200/50=4%
The loss is 4%
Use all the information below to find the missing x-value for the point that is on this line. m = - 1 / 3 b = 7 ( x, 4 )
Answer:
[tex]\boxed{x = 9}[/tex]
Step-by-step explanation:
m = -1/3
b = 7
And y = 4 (Given)
Putting all of the givens in [tex]y = mx+b[/tex] to solve for x
=> 4 = (-1/3) x + 7
Subtracting 7 to both sides
=> 4-7 = (-1/3) x
=> -3 = (-1/3) x
Multiplying both sides by -3
=> -3 * -3 = x
=> 9 = x
OR
=> x = 9
Answer:
x = 9
Step-by-step explanation:
m = -1/3
b = 7
Using slope-intercept form:
y = mx + b
m is slope, b is y-intercept.
y = -1/3x + 7
Solve for x:
Plug y as 4
4 = 1/3x + 7
Subtract 7 on both sides.
-3 = -1/3x
Multiply both sides by -3.
9 = x
In an ANOVA the F-calculated for the treatment 4.76 with 3 degrees of freedom in the numerator and 6 degrees of freedom in the error term. What is the approximate p-value
Answer:
0.0499
Step-by-step explanation:
The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.
The p-value shows that the for 5% level of significance the null hypothesis can be rejected.
plzzzzz helpp j + 9 - 3 < 8
Answer:
j < 2
Step-by-step explanation:
Simplify both sides of the inequality and isolating the variable would get you the answer
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
7/44
Step-by-step explanation:
First find the total number of presidents.
2 + 7 + 13 + 12 + 7 + 3 = 44
There were 7 presidents that were 45-49 when elected. Divide this number by the total number of presidents to find the fraction.
7/44 ≈ 0.159
Suppose Miss Roxanne Davenport is 25 years old right now and puts away $1,800 per quarter in an account that returns 6% interest. a.) How much will be in the account when she turns 65? b.)What is her total contribution to the account?
Answer:
a. Total amount after 65 years = $1179415.39
b. The total contribution to the account = $288000
Step-by-step explanation:
Given annuity amount = $1800
Total number of years for contribution = 65 – 25 = 40 years
Interest rate = 6%
a. Total amount after 65 years = Annuity[((1+r)^n -1) / r]
Total amount after 65 years = 1800×((1+.06/4)^(4 × 40) - 1)/(.06/4)
Total amount after 65 years = $1179415.39
b. The total contribution to the account =1800 × 4 Quarter × 40 Years
The total contribution to the account = $288000
You are mandated to pick 45 units per hour. You work 8.5 hours a day (minus a 1/2 hour lunch), Monday to Friday. How many units should you be picking each week?
Answer:
1912.5 unitsStep-by-step explanation:
Firstly let us calculate the amount of hours you will have to work in a week.
Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.
Hence in a week you will work 8.5*5= 42.5 hours in a week
Since in 1 hours you are mandated to pick 45 units
Hence in 42.5 hours you will pick 42.5*45= 1912.5 units