Until the age of [tex]59.5[/tex] years, the amount saved from the withdrawal of funds is [tex]\$3,600.[/tex]
Used the concept of tax which states that,
A tax is an obligatory payment made by the taxpayer to the government in respect of the income earned in the previous year.
Given values:
Amount of funds: [tex]\$45,000[/tex]
Normal tax rate: [tex]20\%[/tex]
Penalty rate at [tex]59.5[/tex] years: [tex]10\%[/tex]
Step-1; Computation of after-tax amount paid at 54 years:
[tex]A_1= \text{Amount of funds} \times (1 - \text{Tax rate})[/tex]
[tex]= \$45,000 \times (1 - 0.2)[/tex]
[tex]= \$36,000[/tex]
Step-2; Computation of after-tax amount paid at 59.5 years:
[tex]A_2 = \text{Amount of funds} \times (1 - \text{Tax rate}) (1 - \text{Penalty rate})[/tex]
[tex]= \$45,000 \times (1 - 0.20) \times (1 - 0.10)[/tex]
[tex]= \$32,400[/tex]
Step-3; Computation of the amount saved;
[tex]\text{Amount saved} = A_1 - A_2\\= \$36,000 - \$32,400\\= \$3,600[/tex]
Therefore, the amount [tex]\$3,600.[/tex] was saved with the amount of [tex]\$36,000[/tex] paid-in [tex]54[/tex] years and the amount of [tex]\$32,400[/tex] paid-at [tex]59.5[/tex] years.
Learn more about taxes in the related link:
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Doug is a zookeeper in charge of monitoring the "aquatic" section at the North End Zoo. A baby dolphin was born on Wednesday and weighed 31 pounds. The dolphin is growing at an average rate of 2.3lbs per day. Write a function that can be used to find the weight, w(x), of the dolphin after x, days.
Answer:
w(x)=2.3x+31
Step-by-step explanation:
From the information given, the function would indicate that the weight of the dolphin after x days would be equal to the 31 pounds the baby weighed when it was born plus 2.3 lbs that is the average rate it is growing for the number of days:
w(x)= 2.3x+31, where:
w(x)= weight of the dolphin
x=number of days
if b=49 degrees 13' and b=10 find a
Answer:
b. 8.6
Step-by-step explanation:
Given:
B = 49° 13'
b = 10
Required:
Find a
SOLUTION:
The reference angle given = 49° 13'. Converted to degrees, we have 49.2167°.
b = Opposite side to the reference angle B = 10
a = adjacent side to angle B = ?
To find a, apply the following trigonometric ratios formula:
[tex] tan(B) = \frac{opp.}{adj.} [/tex]
[tex] tan(49.2167) = \frac{10}{a} [/tex]
Multiply both sides by a
[tex] tan(49.2167)*a = \frac{10}{a}*a [/tex]
[tex] tan(49.2167)*a = 10 [/tex]
Divide both sides by tan(49.2167)
[tex] \frac{tan(49.2167)*a}{tan(49.2167)} = \frac{10}{tan(49.2167)} [/tex]
[tex] a = \frac{10}{tan(49.2167)} [/tex]
[tex] a = 8.6 [/tex] (nearest tenth)
Answer:
B.
Step-by-step explanation:
8.6
Luke is a dog walker. He gets $10 per day for walking his neighbor's dogs. He recently snapped his surfboard and wants to buy a used surfboard for $325. If he has $142 in the bank, how many days will he have to walk the dogs to earn enough for the board?
Answer:
10$
Step-by-step explanation:
Jaxon earned $123.90 at his job when he worked for 7 hours. How much money did he earn each hour?
Answer:
$17.70
Step-by-step explanation:
123.90 / 7 = 17.7
A 20 gallon tank is 3/4 full. How many gallons are in the tank?
Answer:
15 gallons
Step-by-step explanation:
(3 / 4) * (20 US gallons)
= 15 gallons
Answer:
15 gallons are in the tank
Step-by-step explanation:
3/4(20)
write an equivalent fraction of 7/8 5/12 4/18
Answer:
Step-by-step explanation:
7/8 is 63/72
5/12 is 25/60
4/18 is 8/36
Isabella is having a party with 45 balloons. She needs 6 feet of string to attach to
each balloon. How much string would she need if it is sold by the yard? (Hint: 1
yard = 3 feet.)
Answer:
90 yards of string
Step-by-step explanation:
You multiply the 45 Balloons and 6 feet of string. Then u divide it by 3 bc there are 3 yards is a feet.
Helppp asappp pleaseee. What is the slope of a line perpendicular to the line whose equation is
2x – y = -8. Fully reduce your answer.
Answer:
-1/2
Step-by-step explanation:
2x-y=-8 --> y=2x+8 (slope: 2)
to be perpendicular, the product of two slopes should be -1
thus, the slope of a line perpendicular to this one is -1/2
HELP PLEASE ASAP
Which of the following are irrational numbers?
55
53
✓20
71
Submit
Answer: √20
Step-by-step explanation:
4.47213595 (the 5 repeats)
y=-15+3x
solve for x
Answer:
x=5+1/3y
Step-by-step explanation:
y=-15+3x
-3x=-15+y
Divide both sides of the equation by -3
x=5+1/3y
The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range
(Hope that helps (= The given says the height distribution is normally distributed with the mean height equal to 68 inches. In this case, the bell-shaped curve has a vertical symmetry at 68 inches. This means, half of the mean exceeds 68 inches while the other half has height below 68 inches.
The height range out of which only 5% of the young American men (from age 18 to 24) lie is [63.35, 72.65] (in inches)
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, let we take:
X = height of American men from age 18 to 24[a,b] = range of height (the values of X) outside which there lies only 5% of American men.Then, according to the given data, we have:
[tex]X \sim N(\mu = 68, \sigma = 2.5)[/tex]
where [tex]\mu[/tex] is mean value of X and [tex]\sigma[/tex] is standard deviation of X (both in inches).
Also, we can write:
[tex]P(X < a) + P(X > b) = 5\% = 0.05[/tex]
Since normal distribution is symmetric about its mean, we can take a and b equidistant from the mean, so as to get a symmetric range which makes much more sense than taking an asymmetric range which doesn't comply with the nature of values of X.
Thus, we have:
[tex]\mu - a = b - \mu\\b = 2\mu - a[/tex]
From this result and [tex]P(X < a) + P(X > b) = 5\% = 0.05[/tex], we get:
[tex]P(X < a) + P(X > 2\mu -a) = 0.05[/tex]
Converting X to Z(the standard normal distribution), we get;
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]P(X < a) + P(X > 2\mu -a) = 0.05\\\\P(Z < z = \dfrac{x-\mu}{\sigma} = \dfrac{a-68}{2.5}) + P(Z > \dfrac{2(68) - a - 68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > \dfrac{68-a}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > -\dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z \leq \dfrac{a-68}{2.5}) = 0.05 \: \: \: \: (\because P(Z > -k) = P(Z \leq k))\\\\2P(Z < \dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) = 0.025[/tex]
Using the z-tables, we get the value of Z for which p-value is 0.025 as
-1.96
Thus, we get:
[tex]\dfrac{a-68}{2.5} = -1.96\\\\a = 68 + (-1.96 \times 2.5)\\a = 63.35[/tex]
Thus, we get: [tex]b = 2\mu - a = 2(68) - 63.35 = 72.65[/tex]
Thus, the range is [a,b] = [63.35, 72.65]
Thus, the height range out of which only 5% of the young American men (from age 18 to 24) lie is [63.35, 72.65] (in inches)
Learn more about standard normal distribution here:
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Troy has a price chart below for various ingredients he needs to order for his sandwich bar. Sandwich Ingredients Item Cost (per pound) Onions $0.79 Tomatoes $0.93 Cheese $1.85 Ham $3.15 Turkey $3.40 Troy has to order 8 pounds of ham, 15 pounds of cheese, and 12 pounds of turkey. What is the total cost of Troy's order? $93.75 $110.25 $204.23 $293.66
Answer:
$93.75
Step-by-step explanation:
The computation of the total cost of order is shown below:
The Cost of 8 pounds of Pepperoni is
= 8 × $3.15
= 25.2
The Cost of 15 pounds of cheese is
= 15 × $1.85
= $27.75
The Cost of 12 pounds of sausage is
= 12 × $3.40
= $40.8
So, The total cost is
= $25.2 + 27.75 + $40.80
= $93.75
Answer:
a
Step-by-step explanation:
Someone pls help me.
identity property in multiplication goes to the second option
commutative property goes to the first option
identity property in addition goes to the last option
associative property goes to the fourth option
distributive property goes to the third option
I may have gotten some wrong , if I did I am very sorry,if i didnt get any wrong, then I hoped this helped!
List the least common factor for 120
and 200
Answer: Lcm = 600
Step-by-step explanation: Find the prime factorization of 120
120 = 2 × 2 × 2 × 3 × 5
Find the prime factorization of 200
200 = 2 × 2 × 2 × 5 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 2 × 3 × 5 × 5
LCM = 600
Answer:
600
Step-by-step explanation:
120= 2*2*2*3*5________eq1
200=2*2*2*5*5_________eq2
we get common factor from 1 and 2
2*2*2*5*3*5 = 600
so the least common factor is 600
1/9 of 54 bottles of water = ? bottles
Answer:
6
Step-by-step explanation:
If you divide 54 in 9 parts it will come out to 6, to check this work divide 54 by 6.
6
Step-by-step explanation:
First you would turn it into a decimal to get .111 repeating then you would multiple it by 54 to get 5.99 repeating do you would round up to get 6
Solve the proportion v/84 =2/21
Answer:
there is no solution for this equation, Hope this helps! x <3
Step-by-step explanation:
v/84=2/21
We move all terms to the left:
v/84-(2/21)=0
We add all the numbers together, and all the variables
v/84-(+2/21)=0
We get rid of parentheses
v/84-2/21=0
We calculate fractions
There is no solution for this equation
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15? Justify your answer.
Answer:
The better deal is 8 bagels for $4.15
Step-by-step explanation:
6 bagels for $3.29
3.29/ 6 = $.54833333 per bagel
8 bagels for $4.15
4.15/ 8 =$.51875 per bagel
The better deal is 8 bagels for $4.15
Answer:
buy 8 bagles
Step-by-step explanation:
because you can get more for less like if their were selling toy cars 4 for 2 and at the truth store it was 10 for 1 wich would you rather choose
help mehhhhhhhhhhhhhhhhhhhhhhh ;(
Answer:
180 minutes in 3 hours 225 miles in 3 hours
Step-by-step explanation:
A cargo plane weighed 400,000 pounds. A load of cargo was removed, and the plane weighed 348,963 pounds. Then, 15,358 more pounds of cargo were removed. How many total pounds of cargo were removed from the plane?
Answer:
364,321
384963+15358=364321
Can some one PLEASE answer these for me? (I’ll also mark you brainliest!)
AnswerAnwser key
Step-by-step explanation:
Answer:
1) -6
2) -8
3) 125185623/1000000000 ( i didn't really understand this one but i hope i got it right)
4) 1
5) 0.94736842
6) 4/5 = 5/4
I can only do up to there for now .... sorry
but i can do the second part in a few mins.
Step-by-step explanation:
i really hope this is right....
Evaluate the given question.
Answer:
In this case since you have fraction you must make sure the limit x value does not make the denominator 0. In this case it does, so you have to factor the expressions to try to cancel out like terms when dividing. Use the method of factoring polynomials to find the solution. It is too late for me but I told you how you can answer it. Once you can plug in 2 into the denominator and not get 0, you can evaluate the limit. Keep practicing!
Step-by-step explanation:
What is the solution set of the inequality for 6x – 12 > 30?
Answer:
x > 7
Step-by-step explanation:
6x - 12 > 30
add 12 to 30
6x > 42
divide 6 to 42
x > 7
Not sure if this is what you needed but hope this helped!!!
?
Select the correct answer.
No, they only have 1 corresponding equal angle.
Yes, they have 2 corresponding equal angles
No, they are not the same size.
Yes, they are the same shape.
Help
Answer:
yes they have 2 corresponding equal angles.
Solve 5(x+9) - 4 = 71 for x
Answer:
x = 6
Step-by-step explanation:
5 times x is 5x, 5 times 9 is 45; 5x+49-4; 49 minus 4 is 45; 5x+45 = 75; now minus 45 from each side so it would now be 5x = 30; now divide; 30/5 = 6.
I NEED HELP PLEASE!!!!!!!!!! O///O
How can you look at the equation of two lines and determine if they will be parallel?
Answer:
If the slope is the same but the intercept is different
i.e.
y=2x+1
y=2x+2
Step-by-step explanation:
If the slope is the same the lines are parallel, but if the y-intercept is also the same the lines have infinite solutions.
Divide. 495 ÷ 10,000 = _____ 4.950 0.0495 0.4950 0.00495
Answer:
0.0495
Step-by-step explanation:
used a calculator
0.0495.
[tex]495 / 10000 = 0.0495.[/tex]
B)
Tell whether the equation has one, zero, infinitely many solutions.
3 ( y-2) = 3y - 6
infinitely many solutions
Step-by-step explanation:Hi there !
3(y - 2) = 3y - 6
3y - 6 = 3y - 6 | + 6
3y = 3y
true ∀ y ∈ R
Good luck !
HELP ME 10 points I NEED HELP TIMED
A line passes through the points (8,-1) and (-4, 2).
What is the y-intercept of this line?
-4
-1
1
4 ?????!
Answer:
y = (-1/4)x + 1 so that the y-intercept is 1
Step-by-step explanation:
The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)
(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8
-x + 4 = 4y
y = (-1/4)x + 1 so that the y-intercept is 1
PLS HELP THIS IS HOMEWORK AND ITS DUE TOMORROW
3. Which equation can be used to find the measurement of ∠MNO, if the value of ∠LMN is 77 degrees? *
Answer:
154+2x=360
Step-by-step explanation:
Since the opposite angles are the same you add them together getting 154. You now have two unknown angles that are congruent which is expressed as 2x, and since a four sided shape always has an interior angle of 360 you set it equal. This gives you 154+2x=360.
Answer: It is the last one
154 + 2x = 360
Step-by-step explanation:
x= 103
154 + 2(103)= 360
154 + 206 =360
A,C and D are points on a circle of radius 4 cm, centre o. BA and BC are tangents to the circle. OB=10cm work out the length of arc ADC. give your answer correct to 3 significant figures
Answer:
Step-by-step explanation:
OB = 10 cm
OA = OC = Radius = 4 cm
COS <AB = OA/OB = 4/10 = 2/5 =
COS< COB = OC/OB = 4/10 = 2/5
=> <AOC = <AOB + <COB
=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)
=> <AOC = 2 Cos-¹(2/5)
=> <AOC = 2 * 66.42
=> <AOC = 132.84°
if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm
if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm