Answer:
$1386.
Step-by-step explanation:
We have been given that Zack deposited $1,200 in a savings account that paid 7.75% simple interest. We are asked to find the balance in his account at the beginning of the third year.
The balance in the account at the beginning of the third year will be equal to balance in the account at the end of 2nd year.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon converting our given interest rate in decimal form we will get,
[tex]7.75\%=\frac{7.75}{100}=0.0775[/tex]
Upon substituting our given values in simple interest formula we will get,
[tex]A=\$1200(1+0.0775\cdot 2)[/tex]
[tex]A=\$1200(1+0.155)[/tex]
[tex]A=\$1200(1.155)[/tex]
[tex]A=\$1386[/tex]
Therefore, an amount of $1386 will be in Jack's account at the beginning of third year.
20 how much metal is needed to smelt a cubical metal box with outer side 12 inches long if the thickness of its walls should be exactly 3 inches?
You roll two fair dice, a green one and a red one. (a) what is the probability of getting a sum of 6? (enter your answer as a fraction.)
Answer:
Step-by-step explanation:
The Temple in Jerusalem was destroyed in the year A.D.________.
46
63
70
80
The provincial governors in Rome were given orders to openly persecute the Christians by Emperor ________.
Caligula
Caesar
Trajan
Constantine
The Roman emperor who passed a decree to require everyone to participate in the cult of emperor worship was:
Caligula
Caesar
Trajan
Decius
Fill in the blanks.
1 Peter 3:17: "For it is__________if God should will it so, that you suffer for doing what is right rather than for doing what is wrong."
What was the most damaging charge brought against the Christians in Rome?
They were constant law-breakers who did not discharge their duties to the state.
They were somewhat secretive in their worship.
They stirred up riots.
They would not engage in emperor worship.
1. The Temple in Jerusalem was destroyed in the year of 70 AD.
The first Temple was built by King Solomon for seven years in the 10th century BC. The first Temple was destroyed by the Babylonians in 586 BC. The construction of the new Temple began 535 BC and it is completed in 516 BC. The rebuilding of the Temple was approved by Darius I. It was, however, destroyed by the Romans in 70 AD. Despite the fact that the Temple was destroyed, all the outer walls still stand, and for a long time, it was believed that only the west wall stood.
The provincial governors in Rome were given orders to openly persecute the Christians by Emperor Trajan.
This can be concluded from the letter sent to him by Pliny, governor of Bithynia (province of Asia Minor). He had doubts about the investigation and the way of punishing those who were accused as Christians because he never been present at any trials of Christians. This implies that there have already been trials for Christians and that he did not know the details about Trajan’s decree of prosecuting Christians.
The Roman emperor who passed a decree to require everyone to participate in the cult of emperor worship was Decius.
Emperor Decius (249-251) announced the edict that orders everyone to do sacrifice to the Roman gods and to him personally. According to the edict, the sacrifice had to be carried out in the presence of a Roman magistrate who issued a certificate that this had been done. There is no evidence that it was directed against the Christians, but it was fatal for them because was contrary to their beliefs.
1 Peter 3:17: "For it is better, if God should will it so, that you suffer for doing what is right rather than for doing what is wrong."
The quote is from the First Epistle of Peter, which is part of the New Testament. It is written by Peter the Apostle in Rome (where he was a bishop) as the letter which is sent to believers in Asia Minor who were persecuted and tortured.
The most damaging charge brought against the Christians in Rome was that they were constant law-breakers who did not discharge their duties to the state.
The Roman authorities consider Christians as opponents of the state that promoted treasonous activities and they were apprehended for disobedience. Suspected Christians have often refused to deviate from Christianity in order to comply themselves with acts of a state cult, which was understood as a public cancellation of loyalty to the state.
In a certain skyscraper, the elevator whisk you a restaurant in the skyscraper at a speed of 500 feet in 60 seconds. If the restaurant is 300 feet up, how long will it take you to reach the restaurant by elevator?
Answer:
The elevator will take you up at 300 feet in 36 seconds.
Step-by-step explanation:
Let the time taken to go up 300 feet be = t seconds
Given is that the elevator takes you up at 500 feet in 60 seconds.
So, we can derive a relation as:
[tex]\frac{500}{60}= \frac{300}{t}[/tex]
=> [tex]500t=300\times60[/tex]
=> [tex]500t=18000[/tex]
t = 36 seconds
So, the elevator will take you up at 300 feet in 36 seconds.
The amount of money, in dollars, in an account after t years is given by A = 1000(1.03)t. The initial deposit into the account was $ a0 and the interest rate is a1% per year. Only enter numbers in the boxes. Do not include any commas or decimal points.
A system of equations is graphed on the coordinate plane. y=−x+5y=2x−1 What is the solution to the system of equations? Enter the coordinates of the solution in the boxes.
Answer:
[tex](2;3)[/tex]
Step-by-step explanation:
We can find the solution directly on the graph. The solution of a system of equations is the intersections between the two lines. Remember that each equation in this case represent a line, where the common points are always shown as an intersection.
To prove this result, we can apply other methods. Using the substitution method, we have to isolate one variable from one equation and then replace it in the other equation, like this:
[tex]\left \{ {{y=-x+52'} \atop {y=2x-1}} \right.[/tex]
The variable y is already isolated, now we just replace the first equation in the second:
[tex]-x+5=2x-1\\5+1-2x+x\\6=3x\\x=\frac{6}{3}=2[/tex]
Then, we replace the x-value in one equation, no matter which one:
[tex]y=2x-1\\y=2(2)-1\\y=4-1=3[/tex]
Therefore, we found that the solution is[tex](2;3)[/tex]
SHALL CROWN BRAINLIEST!
Which sentence uses a double negative correctly?
A. I was not displeased by my performance at the recital.
B. I don't have no hat to wear to the game.
C. Fernando's parents won't give him no money for lunch.
D. Molly never gets no respect from her sister.
I vaguely suspect the answer is A, but I need someone to confirm my suspicions.
Answer:
it's A u were correct
Step-by-step explanation:
Calculate the slant height for the given square pyramid. Round to the nearest tenth.
Pyramid base = 6 cm
Height = 5 cm
A. 6.2 cm
B. 5.8 cm
C. 7.8 cm
D. 7.2 cm
the answer would have to be 7.8
Answer: 7.8
Step-by-step explanation:
Write 5 thousand, 456 and 68 hundredths in standard form, word form, and point form. Can someone help! :,)
The required form can be given as,
5 thousand into standard form can be given as = 5000,
456 in word form would be written as four hundred fifty-six,
68 in point form 0.68
Given that,
To write 5 thousand, 456 and 68 hundredths in standard form, word form, and point form.
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
5 thousand = 5000
456 in word form = four hundred fifty-six
Point form of 68 hundredths, = 0.68
Thus, the solution is given above in the solution part,
Learn more about the number system here:
https://brainly.com/question/22046046
#SPJ2
Alex is making a nut mixture to sell at the local farmer's market. He mixes 2 pounds of cashews with a nut mixture that is 40% cashews. The resulting mixture is 52% cashews. How many pounds of nut mixture does Alex make?
Mr. Martinez mixes a 90% sugar cinnamon flavored solution with a 75% sugar cherry flavored solution to make 12 gallons of a new product. The new product is 85% sugar. How much of the cherry flavored solution did he use?
Mr.Acosta works in the lab at a pharmaceutical company. He needs 26 liters of a 36% acid solution to test a new product. His supplier only ships a 42% and a 29% solution. How much of the 42% solution will Mr.Acosta need to use?
PLEASE SHOW WORK!!
What is the Greatest Common Factor of 12 and 36? (1 point)
2
4
6
12
The greatest Common factor of 12 and 36 is 12.
A number that divide another number is called factor.
Factors of 12 is 2, 3, 4, 6, 12
Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.
Therefore, the greatest common factor of 12 and 36 is 12.
Learn more about factor here:
https://brainly.com/question/29167102
#SPJ2
What number should be added to the expression x²+14x to change it into a perfect square trinomial?
7
14
28
49
Final answer:
To transform x²+14x into a perfect square trinomial, add 49 to it, which is the square of half the coefficient of x.
Explanation:
The number that should be added to the expression x²+14x to change it into a perfect square trinomial is obtained by taking half of the coefficient of x, which is 14, and then squaring that value. Therefore, (14 / 2)² = 7² = 49. So, the number to be added to make x²+14x a perfect square trinomial is 49.
Anybody have the answer to this?
grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee. If h represent the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?
We find that Grayson charges more than Ian when the number of hours of service h is less than 2.
To determine for how many hours Grayson charges more than Ian, we can set up an equation where the cost of Grayson's tax preparation service is greater than Ian's service. Grayson charges $35 per hour plus a $35 administration fee, while Ian charges $45 per hour plus a $15 administration fee. The number of hours for which the service is required is represented by h.
Grayson's total charge for h hours would be:
Grayson's Cost = $35h + $35
Ian's total charge for h hours would be:
Ian's Cost = $45h + $15
To find the number of hours where Grayson's cost is more than Ian's cost, we set Grayson's Cost > Ian's Cost:
$35h + $35 > $45h + $15
Simplifying, we get:
$35h - $45h > $15 - $35
-$10h > -$20
Dividing both sides by -10 (and remembering to reverse the inequality when dividing by a negative):
h < 2
Thus, Grayson charges more than Ian for fewer than 2 hours of tax preparation.
Consider the image of ABC for the translation (x, y) --> (x + 4, y - 2). What is the ordered pair of C'?
Which equation is correct for the perpendicular bisector of the line segment whose endpoints are (−1,1) and (7,−5)?
What is the square root of 252 in simplest radical form?
The square root of 252 in simplest radical form is 6√7.
Explanation:To find the square root of 252 in simplest radical form, we can break it down into its prime factors. The prime factorization of 252 is 2 * 2 * 3 * 3 * 7. To simplify the square root, we group the factors into pairs and put one factor from each pair outside the square root and leave the other inside. In this case, we have (2 * 3) * (2 * 3) * 7. Simplifying this further, we get 6 * 6 * 7, which equals 252.
Learn more about Square Roots here:
https://brainly.com/question/1540542
#SPJ11
Directions - Write The Correct Number In Each Blank To Show The Community Property Of Addition.
Question —> 48 + 14 = 62; Therefore, _____ + 48 = 62
The diameter of a circle is 8 kilometers. What is the angle measure of an arc kilometers long?
This is the angle measured in radians for an arc that is 1 kilometre long is [tex]\({\theta = \frac{360}{\pi^2}}\)[/tex] radians.
To find the angle measure of an arc in radians, we use the formula:
[tex]\[ \text{Angle in radians} = \frac{\text{Arc length}}{\text{Radius}} \][/tex]
Given that the diameter of the circle is 8 kilometres, we can find the radius by dividing the diameter by 2:
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{8 \text{ km}}{2} = 4 \text{ km} \][/tex]
The arc length is given as [tex]\(\pi\)[/tex] kilometres. Now we can calculate the angle in radians subtended by the arc:
[tex]\[ \theta = \frac{\text{Arc length}}{\text{Radius}} = \frac{\pi \text{ km}}{4 \text{ km}} = \frac{\pi}{4} \][/tex]
However, this is not the final answer. We need to find the angle measured in degrees. To convert radians to degrees, we use the conversion factor:[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]
Thus, the angle in degrees is:
[tex]\[ \theta_{\text{degrees}} = \theta_{\text{radians}} \times \frac{180}{\pi} = \frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45 \text{ degrees} \][/tex]
Now, we need to find the angle measured in radians that correspond to an arc length of 1 kilometre. Using the same formula:
[tex]\[ \theta_{\text{1 km}} = \frac{1 \text{ km}}{4 \text{ km}} = \frac{1}{4} \text{ radians} \][/tex]
To find the number of radians in the entire circle, we multiply by [tex]\(2\pi\)[/tex](since the circumference is [tex]\(2\pi r\)[/tex] and the radius is 4 km):
[tex]\[ \text{Full circle in radians} = 2\pi \times 4 \text{ km} = 8\pi \text{ radians} \][/tex]
Now, we want to find how many times the arc length of 1 km fits into the full circle's circumference:
[tex]\[ \text{Number of arcs} = \frac{8\pi \text{ radians}}{1/4 \text{ radians}} = 32\pi \][/tex]
This represents the number of times the 1 km arc goes around the circle, which is also the measure of the angle in radians that corresponds to a 1 km arc. Since the full circle is [tex]\(360\)[/tex] degrees, the angle measured in degrees for the 1 km arc is:
[tex]\[ \theta_{\text{1 km degrees}} = 32\pi \times \frac{180}{\pi} = 32\pi \times \frac{360}{2\pi} = 32 \times 180 = 5760 \text{ degrees} \][/tex]
However, this is not the final answer. We made a mistake in the calculation. We should not multiply the number of arcs by the full circle's degrees. Instead, we should divide the full circle's degrees by the number of arcs to find the angle measure for one arc:
[tex]\[ \theta_{\text{1 km degrees}} = \frac{360}{32\pi} = \frac{360}{\pi} \times \frac{1}{32} = \frac{360}{\pi^2} \times \frac{\pi}{32} = \frac{360}{\pi^2} \text{ degrees} \][/tex]
To convert this back to radians, we multiply by [tex]\(\frac{\pi}{180}\)[/tex]:
[tex]\[ \theta_{\text{1 km radians}} = \frac{360}{\pi^2} \times \frac{\pi}{180} = \frac{360}{\pi^2} \text{ radians} \][/tex]
This is the angle measured in radians for an arc that is 1 kilometre long.
How many times do you need to divide by ten to get from 3731.7 to 373.17
What does (p⋅c)(2) mean about the horse-drawn carriage tour company?
c(2) = 50 +5(2) = 60
p(2) = 80-2(2) = 76
60 * 76 = 4560 when the price is 60
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Let, The amount invested in Account A=x
Then, the amount invested in Account B=2000-x
The formula of Simple Interest =[tex] \frac{Principle*Rate*Time}{100} [/tex]
Interest earned in Account A in 1 year=[tex] \frac{x*3*1}{100} [/tex]
Interest earned by Account A=[tex] \frac{3x}{100} [/tex]
Interest earned in Account B in 1 year=[tex] \frac{(2000-x)*5*1}{100} [/tex]
Interest earned by Account B=[tex] \frac{5(2000-x)}{100} [/tex]
Total Interest Earned= Interest earned by Account A+ Interest earned by Account B
Total Interest Earned=[tex] \frac{3x}{100} [/tex]+[tex] \frac{5(2000-x)}{100} [/tex]
75=[tex] \frac{3x}{100} [/tex]+[tex] \frac{10000-5x)}{100} [/tex]
75=[tex] \frac{3x+10000-5x)}{100} [/tex]
Multiply by 100 on both sides
75*100=[tex] \frac{100(10000-2x))}{100} [/tex]
7500=10000-2x
Let us subtract 7500 from both sides
7500-7500=10000-7500-2x
0=2500-2x
Adding 2x on both sides, we get
0+2x=2500-2x+2x
2x=2500
To solve for x, divide by 2 on both sides
2x/2=2500/2
x=1250
So, The Amount invested in Account A= $1250
The Amount invested in Account B= $2000-1250=$750
the manager of and apartment complex will install new carpeting in a studio apartment. The floor plan is shown at the right. What is the total area that needs to be carpeted?\
help with 1 and 2 only
To keep heating costs down for a structure, architects want the ratio of surface area to volume as small as possible. An expression for the ratio of the surface area to volume for the square prism shown is 2b+4h/bh. Find the ratio when b=12 ft and h=18ft.
Final answer:
The ratio of surface area to volume for the square prism is 4/9 when b = 12 ft and h = 18 ft.
Explanation:
The expression for the ratio of surface area to volume of the square prism is 2b + 4h/bh. To find the ratio when b = 12 ft and h = 18 ft, substitute these values into the expression.
Ratio = 2(12) + 4(18)/(12)(18)
= 24 + 72/216
= 96/216
= 4/9
Therefore, the ratio of surface area to volume for the given square prism is 4/9 when b = 12 ft and h = 18 ft.
The ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is calculated using the formula 2b + 4h / bh, which results in a ratio of 4 / 9 ft⁻¹.
Explanation:The student has asked to find the ratio of surface area to volume for a square prism when given specific dimensions. The formula provided is 2b + 4h / bh, where b is the base length and h is the height of the prism. To find the ratio for b = 12 ft and h = 18 ft, we substitute these values into the formula:
Ratio = (2 × 12 ft) + (4 × 18 ft) / (12 ft × 18 ft) =
24 ft + 72 ft / 216 ft² =
96 ft / 216 ft².
After performing the calculations, we simplify the expression to get the ratio:
Ratio = 96 ft / 216 ft² = 4 / 9 ft⁻¹.
Thus, the ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is 4 / 9 ft⁻¹.
A 5-digit combination lock with digits 0-9 can be opened only if a correct combination of digits is chosen. Find the probability of guessing the correct combination if:
When fritz drives to work his trip takes 40 minutes, but when he takes the train it takes 30 minutes. find the distance fritz travels to work if the train travels an average of 15 miles per hour faster than his driving. assume that the train travels the same distance as the car?
John says the transformation rule (x, y) es002-1.jpg (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, ???2). What was his error?
We are given transformation rule
(x, y) --> (x + 4, y + 7).
The coordinate of the pre-image is (4,5).
The coordinate of the transformed image is (0,-2).
Please see, if we apply
(x, y) --> (x + 4, y + 7) rule.
(4,5) coordinate would become (4 +4 , 5+7 ) = (8,12).
But we need (0,-2) instead of (8,12).
Let us reverse operation in the given rule and check.
Let us change (x + 4, y + 7) to (x-4, y-7) and now check.
(4,5) coordinate would become (4-4 , 5-7) = (0,-2).
So, we got exact coordinate of the transformed image.
Therefore, error was
(x, y) --> (x + 4, y + 7) rule should be (x, y) --> (x - 4, y - 7) rule.
Transformation involves changing the position of a point.
John's error is that, he subtracted the points instead of adding them.
The pre-image is given as:
[tex]\mathbf{(x,y) = (4,5)}[/tex]
The image is given as:
[tex]\mathbf{(x,y) = (0,-2)}[/tex]
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex]
When the rule [tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex] is applied on [tex]\mathbf{(x,y) = (4,5)}[/tex], we have:
[tex]\mathbf{(x,y) = (4+4,5+7)}[/tex]
[tex]\mathbf{(x,y) = (8,12)}[/tex]
Hence, John's claim is incorrect.
His error is that, he subtracted the points instead of adding them.
Read more about transformations at:
https://brainly.com/question/11709244
A wheelchair ramp has a slope of 1:12 (1 foot of rise over a horizontal distance of 12 feet). To the nearest 0.1 foot, how many feet of ramp will be needed to rise 3 feet? (Round the angle of incline to the nearest 0.01°.)
Quick Fix Inc. repairs bikes. The company’s revenue is modeled by the function R(h)=220h−160 for every h hours spent repairing bikes. The company’s overhead cost is modeled by the function C(h)=20h^2−400.
After how many hours does the company break even?
Final answer:
Quick Fix Inc. breaks even after 7 hours of labor. This is determined by setting the revenue function equal to the overhead cost function and solving for the variable h (hours), which results in a quadratic equation that factors to reveal the break-even point.
Explanation:
To find out after how many hours Quick Fix Inc. breaks even, we need to set the company's revenue function equal to its overhead cost function. The revenue function is given by R(h) = 220h - 160 and the overhead cost function is given by C(h) = 20h2 - 400. The break-even point occurs when R(h) = C(h).
To solve for h (hours), we rearrange the equation: [tex]20h^2 - 220h + 160 + 400 = 0, or \\20h^2 - 220h + 560 = 0.[/tex]
Divide through by 20 to simplify: [tex]h^2 - 11h + 28 = 0.[/tex]
Factoring the quadratic equation gives us: (h - 7)(h - 4) = 0.
Set each factor equal to zero and solve for h: h - 7 = 0 or h - 4 = 0, thus h = 7 hours or h = 4 hours.
Since we are looking for a positive number of hours, we need to test which solution makes sense in the context of the problem. After examining both possibilities, we conclude that the company breaks even at 7 hours, because at 4 hours, the cost would still exceed the revenue.
Evaluate g(x) = 0.023x^3 + 0.4x^2 − 2.1x + 8.3 for x = 2 and x = 4.