Put in the formula
[tex]\\ \rm\Rrightarrow A=P(1+r)^t[/tex]
[tex]\\ \rm\Rrightarrow 7255=6000(1+0.055)^t[/tex]
[tex]\\ \rm\Rrightarrow 1.20917=(1.055)^t[/tex]
[tex]\\ \rm\Rrightarrow ln1.20917=tln1.055[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{ln1.20917}{ln1.055}[/tex]
[tex]\\ \rm\Rrightarrow t=3.5years[/tex]
Answer:
4 years (nearest year) or
3.5 years (nearest tenth) or
3 years, 6 months and 17 days (most accurate)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
A = $7,255P = $6,000r = 5.5% = 0.055Substitute the given values into the formula and solve for t:
[tex]\implies \sf 7255=6000(1+0.055)^t[/tex]
[tex]\implies \sf 7255=6000(1.055)^t[/tex]
[tex]\implies \sf \dfrac{7255}{6000}=(1.055)^t[/tex]
Take natural logs of both sides:
[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= \ln (1.055)^t[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= t\ln (1.055)[/tex]
[tex]\implies \sf t=\dfrac{\ln \left(\dfrac{7255}{6000}\right)}{\ln (1.055)}[/tex]
[tex]\sf \implies t=3.547416819...[/tex]
Therefore, the number of years the principal was invested is:
4 years (nearest year)3.5 years (nearest tenth)3 years, 6 months and 17 daysLearn more about compound interest here:
https://brainly.com/question/27806277
https://brainly.com/question/27747709
A king decided to pay a knight one inch of gold for each day's protection on a 6-day trip. The king took a gold bar 6 inches long and paid the knight at the end of each day; however, he made only two cuts. How did he do this?
A king gives 1 inch per day to the knight as there are three pieces of length 1, 2, and 3 inches.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
A king decided to pay a knight one inch of gold for each day's protection on a 6-day trip. The king took a gold bar 6 inches long and paid the knight at the end of each day.
The gold is divided into 2 parts.
First at the 1-inch mark, then the second mark will be
For the second mark, there are two conditions.
Condition 1 = mark can be made at 4 inches, then the next piece will be of 2 inches.
There will be a total of three pieces of 3 inches, 1 inch, and 2 inches.
Condition 2 = Mark can be made at 5 inches, then the next piece will be of 1 inch.
There will be a total of three pieces of 3 inches, 1 inch, and 2 inches.
The division is shown below.
The king will take 1 inch back from the knight and give him 2 inches.
According to the condition = A king gives 1 inch per day to the knight as there are three pieces of length 1, 2, and 3 inches.
So on the first day, 1 inch will be given. On the second day, he will give 2 inches and take 1 inch. On the third day, he will give 3 inches and take back 2 inches. On the fourth day, he will give 1 inch. On the fifth day, he will give 2 inches and take back 1 inch. On the sixth day, he will give 1 inch.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
Solve the inequality.
Answer:
D. t < -4 or t > 5
Step-by-step explanation:
Inequality 1
5t - 1 < -215t < -20t < -4Inequality 2
4t + 2 > 224t > 20t > 5⇒ t < -4 or t > 5
⇒ Option D
Graph
Answer:
[tex]\sf D. \quad t < -4, t > 5[/tex]
Step-by-step explanation:
Given system of inequalities:
[tex]\begin{cases}5t-1 < -21\\4t+2 > 22\end{cases}[/tex]
Solve the inequalities by isolating t.
Inequality 1
[tex]\sf \implies 5t-1 < -21[/tex]
[tex]\implies \sf 5t-1+1 < -21+1[/tex]
[tex]\sf \implies 5t < -20[/tex]
[tex]\sf \implies 5t \div 5 < -20 \div 5[/tex]
[tex]\sf \implies t < -4[/tex]
Inequality 2
[tex]\sf \implies 4t+2 > 22[/tex]
[tex]\sf \implies 4t+2-2 > 22-2[/tex]
[tex]\sf \implies 4t > 20[/tex]
[tex]\sf \implies 4t \div 4 > 20 \div 4[/tex]
[tex]\sf \implies t > 5[/tex]
Therefore, the solution to the system of inequities is:
[tex]\sf t < -4, t > 5[/tex]
When graphing inequalities:
< or > : dashed lines≤ or ≥ : solid line< or ≤ : shading under the line> or ≥ : shading above the lineTherefore, to graph the given system of inequalities:
Draw a straight dashed line at t = -4 and shade under the line.Draw a straight dashed line at t = 5 and shade above the line.(Refer to attachment for the graph).
Learn more about inequalities here:
https://brainly.com/question/27959739
https://brainly.com/question/27947009
Reid, the second-place finisher, developed a cramp with 3 tenths of the race remaining. How many miles did Reid run without a cramp?
Answer:
He ran .7 miles without a cramp
Step-by-step explanation:
hail 0.5 inch deep and weighing 1800 pounds covers a roof. the hails weight varies directly with its depth. write an equation that relates d and w. then predict the weight on the room of hail that is 1.75 inches deep
In a directly proportional relationship, increasing one variable will increase another. The weight of the roof whose depth is 1.75 inches is 6,300 pounds.
What is the directly proportional relationship?In a directly proportional relationship, increasing one variable will increase another. This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.
Let there are two variables p and q. Then, p and q are said to be directly proportional to each other if p = kq, where k is some constant number called the constant of proportionality.
Given the hail's weight varies directly with its depth. Therefore, the relation can be written as,
Weight ∝ Depth
W∝D
Introducing the constant to remove the proportionality we will get the equation as,
W = kD
1800pounds = k × 0.5 inches
3600ponds/inches = k
Now, the weight of the roof whose depth is 1.75 inches can be written as,
W = kD
W = 3600 × 1.75
W = 6,300 pounds
Hence, the weight of the roof whose depth is 1.75 inches is 6,300 pounds.
Learn more about directly proportional relationship:
https://brainly.com/question/13082482
#SPJ1
Could you help me with this for 50? points.
Prove algebraically that the straight line with equation x =2y+5 is a tangent to the circle with equation x ² +y ²
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
x = 2y + 5 ...1
x² + y² = 5 ...2
If the intersection of the point of the circle and line is one. Then the line is tangent to the circle.
Then from equations 1 and 2, we have
(2y + 5)² + y² = 5
4y² + 25 + 20y + y² - 5 = 0
5y² + 20y + 20 = 0
5y² + 10y + 10y + 20 = 0
5y (y + 2) + 10(y + 2) = 0
(5y + 10)(y + 2) = 0
y = -2, -2
Then the value of y is unique then the value of x will be unique.
The value of x will be
x = 2(-2) + 5
x = -4 + 5
x = 1
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ1
Explain the meaning of the scale 1 :2.5
Based on the picture below what would the genotypes of the parent plants be? Use the other questions to help you answer this.
Thank you so much.
Answer:
ant sorry you no entendía
7. In which step does a mistake first occur? 8÷2+ (3 x 3-2) Step 1: 8÷2 + (3 x 1) Step 2: 8÷2+3 Step 3: 4+3 Step 4: 7
Answer: Step 1
A mistake first happens in Step #1. PEMDAS is not followed correctly.
(PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction)
When solving 8÷2+(3x3-2), you first move left to write and solve the problems working through the correct order of operations.
Correct Steps:
1) 8÷2 + (3x3-2)
2) 4 + (9-2)
3) 4 + 7
4) 4+7 = 11
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z. The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases. The demand for Model Z is estimated as D(p) = 180 + 10q - 4p, where p is the price of Model Z. Consider the following two statements: 1. If the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X 2. If the average gasoline price q increases by $1, the demand at the revenue- maximizing price (i.e., D(p*)) increases by a factor of Y What is X/Y?
The ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
What is a mathematical model?A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z.
The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases.
The demand for Model Z is estimated as
[tex]D(p) = 180 + 10q - 4p[/tex]
Here, p is the price of Model Z.
Consider the following two statements:
1. When the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X.[tex]D(p) = 180 + 10q - 4p\\D(p) = 180 + 10(q+1) - 4(p+X)[/tex]
2. When the average gasoline price q increases by $1, the demand at the revenue-maximizing price (i.e., D(p*)) increases by a factor of Y.[tex]D(p)+Y = 180 + 10q - 4p\\(D(p)+Y) = 180 + 10(q+1) - 4(p+X)\\Y= 180 + 10(q+1) - 4(p+X)-D(p)\\[/tex]
Put the value of demand at the revenue-maximizing price as,
[tex]Y= 180 + 10(q+1) - 4(p+X)-(180 + 10q - 4p)\\Y= 180 + 10q+10 - 4p-pX-180 - 10q + 4p\\Y= 10 -pX\\1=\dfrac{10}{Y}-\dfrac{pX}{Y}\\\dfrac{10}{Y}=\dfrac{pX}{Y}\\\dfrac{10}{pY}=\dfrac{X}{Y}[/tex]
Thus, the ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
Learn more about the mathematical model here;
https://brainly.com/question/4960142
#SPJ1
Identify the steps for proving ADDC.
A. 1. BD BD by the reflexive property
2. AABD=ACBD by SAS
3. ADDC by CPCTC
B. 1. BD BD by definition of an isosceles triangle
2. AABD = ACBD by SAS
3. ADDC by CPCTC
C. 1. BD BD by the reflexive property
2. AABD = ACBD by CPCTC
3. ADDC by SAS
D. 1. BD BD by definition of an isosceles triangle
2. AABD = ACBD by CPCTC
3. ADDC by SAS
John has a monthly net income of $2,376.80. John allots 20% of his income for food, which amounts to
Answer: 20% of 2,7376.80 = 475.36
Step-by-step explanation:
2,376.80(0.2)=475.36
Question 11(Multiple Choice Worth 5 points)
(03.06A LC)
Which statement is true for the equation 2x - 2x - 7 = -7?
O It has infinitely many solutions.
O It has two solutions.
O It has one solution.
It has no solution.
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
2x-2x-7=-7
We need to solve it first as follows:
[tex]2x-2x-7=-7[/tex]
[tex]2x-2x=-7+7[/tex]
[tex]0=0[/tex]
Since L.H.S. = R.H.S.
So, it satisfies the equation for all x.
So, there will be infinitely many solutions.
Hence, Option 'a' is correct.
what is the exact value of cosC
Answer:
[tex]cosC = \frac{\sqrt{161} }{15}[/tex]
Step-by-step explanation:
[tex]cosC = \frac{\sqrt{161} }{15}[/tex]
CosC = adj/hyp
Avery had $25.75 in her wallet. If she bought lunch with 87 dollars from her wallet, how much money did she have in her wallet
after lunch?
A. $16.00
B. $17.45
C. $17.00
D. $17.75
Answer is D even tho u typo it i still got it so u do 25.75 from 8.00 yw.
The diameter of a circle is 2 miles. What is the circle's area?
d=2 mi
square miles
Use 3.14 for л.
Answer:
A= 3.14
Step-by-step explanation:
The formula for finding the area of a circle is A=π r²
The radius = half of the diameter so that makes the radius 1 in this case.
When you plug in the values for the equation you get A= 3.14*1²
Answer:
3.14
Step-by-step explanation:
The Formula for area of a circle is л times r^2. R(radius) is half of D(diameter )in which this case is 1. So 1^2 = 1 times л which is 3.14. 3.14 times 1 = 3.14 as answer.
someone help with the answer
The answer is
for parallel : y= 4/7-5x/7
for perpendicular: y=10+7x/5
What is slope- intercept equations?The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b.
Given line: 5x+7y=9
when our intersection point is (5,-3) the constant
5x+7y
= 5(5)+7(-3)
= 25-21
=4
hence, 5x+7y=4
slope intercept form
7y= 4-5x
y= 4/7-5x/7
Now, for perpendicular lines:
swap the coefficients on x and y with negative sign of x in 5x+7y=9
7x-5y= constant
again, when our intersection point is (5,-3) the constant must be
7x-5y
= 7(5)-5(-3)
=35+15
=50
7x-5y=50
slope intercept form so we solve for y:
y= (50+7x)/5
y=10+7x/5
Learn more about intercept equation here:
https://brainly.com/question/13300036
#SPJ1
A water park has pools, slides, and rides
that, in total, make use of 4.6 x 10^5
gallons of water. They plan to add a ride
that would make use of an additional
6.7 x 10^4 gallons of water. Use scientific
notation to express the total gallons of
water made use of in the park after the
new ride is installed.
Answer:
5.27×10^5 gallons
Step-by-step explanation:
Adding numbers in scientific notation requires that their powers of ten match. Here, we can rewrite the smaller number so its power of ten matches that of the larger number.
__
4.6×10^5 +6.7×10^4
= 4.6×10^5 + 0.67×10^5
= 5.27×10^5
The park will use 5.27×10^5 gallons of water after the new ride is installed.
__
This kind of calculation can be done easily by your scientific calculator or a spreadsheet. You may have to set the display mode to scientific notation.
3X minus 2Y is equal to or greater than or equal to four
Answer:
3x- 2y
Step-by-step explanation:
its defintly not = to four because you cant subtract two diffrent varibles so it should be less then
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, what is the volume of the water that was displaced (in cubic inches)?
The volume of the water that was displaced will be 0.06 cubic feet.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
mass = density × volume
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water.
Then the volume of the water that was displaced will be
We know that the density of the water is 62.4 pounds per cubic foot.
Then we have
3.7 = 62.4 × volume
Volume = 0.059
Volume ≅ 0.06 cubic-foot
To learn more about the density refer to the link;
brainly.com/question/952755
#SPJ1
It takes 5 gardeners 48 hours to landscape a gArden how long w I'll it take 8 gardeners to landscape same garden
The time is taken by the 8 gardeners to landscape the same garden will be 30 hours.
What are ratios and proportions?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
It takes 5 gardeners 48 hours to landscape a garden.
Then the time taken by the 8 gardeners to landscape the same garden will be
The relationship between the gardeners and time is inversely proportional. Then we have
Let x be the time taken by the 8 gardeners. Then we have
8x = 5×48
x = 30 hours
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ1
What are the solutions to the following system?
-2x² + y = -5
y=-3x² +5
O (0, 2)
O (1,-2)
o o (12,-1) and (-√2-1)
(
o (V5,-10) and (-15.-10)
The solutions to the equation -2x² + y = -5 and y=-3x² +5 are (√2,-1) and (-√2-1) option third is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
We have given expressions:
-2x² + y = -5 ..(1)
y=-3x² +5 ...(2)
From the equation (2) take the value of y and plug it in the equation (1)
-2x²-3x²+5 = -5
-5x² = -10
x = ±√2
Plug this value in the equation (2), we get value of y:
y = -1
Thus, the solutions to the equation -2x² + y = -5 and y=-3x² +5 are (√2,-1) and (-√2-1) option third is correct.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ1
help will mark Brainliest
A rectangular park has a perimeter of 374 feet and a length of 65 feet.
What is the width of the park?
Answer: 122
Step-by-step explanation:
▪︎ Perimeter = (width + length) * 2
374 = (width + 65) * 2
width + 65 = 374 / 2
width + 65 = 187
width = 187 - 65
width = 122
You work at a restaurant and the head manager has sent you to purchase livestock for an experiment. You want to grow the meat for the food right at the restaurant. You have been given 500 gold coins to spend at the store to purchase the livestock. Each sheep costs 12 gold coins, while each chicken costs seven.
If you purchase 32 sheep, how many chickens can you buy? Show all of your work. Hint: you don’t have to spend every coin.
Write an inequality that represents this situation.
If you want to buy twice as many chickens as sheep, what is the maximum number of sheep you can buy? Show all of your work.
Make a graph of the inequality from #2. Remember to label all parts of the graph. Label the intercept points.
Part 2: The animals you bought for the restaurant are doing quite well. You purchased an initial flock of 30 sheep and 20 chickens. The chickens and sheep have been breeding very successfully, and the flocks are growing. The sheep breed at a rate so that they will double every year. The chickens breed faster than the sheep (it helps when you can lay multiple chicks from one hen at a time!) The population of the chickens multiplies by 2.2 each year. (For all of these problems round to the nearest animal.)
5. How many sheep will there be in five years? Show all of your work.
6. Create an exponential equation to represent this situation.
7. How many chickens will there be in eight years? Show all of your work.
8. Create an exponential equation to represent this situation.
9. During what year will there be more chickens than sheep? Show your work or explain how you know.
10. Plot the two curves on a graph together. Remember to label all parts of the graph.
11. What is the domain of each function?
12. What is the y-intercept for each function? Explain what this number means in the context of this situation.
13. Your field can support a maximum of 3000 animals before you run out of vegetation and space. During what year will you need to purchase more land to house the animals?
The number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where 'a' is a constant and a>1
Total coins = 500 gold coin
Each sheep costs 12 gold coins, while each chicken costs 7 gold coins.
If purchased 32 sheep, so the total cost for the 32 sheep:
= 32×12
= 384
Remaining gold coin = 500 - 384 = 116 gold coin
Number of chicken can purchase in 166 gold coin = 116/7 = 16.57 ≈ 16
Inequality for the above scenario:
Let x be the number of sheep and y be the number of chickens.
12x + 7y ≤ 500
If you want to buy twice as many chickens as sheep.
y = 2x
12x + 7y = 500
After solving both the equation:
x = 19.23 ≈ 19 (Number of sheep)
y = 38 (double the number of sheep)
For the part 2:
The exponential equation for the sheep:
[tex]\rm y = 30(2)^x^-^1[/tex]
After 5 years, plug x = 5
[tex]\rm y = 30(2)^4[/tex]
y = 480 sheep
The exponential equation for the chicken:
[tex]\rm y = 20(2.2)^x^-^1[/tex]
After 8 years, plug x = 8
[tex]\rm y = 20(2.2)^7[/tex]
y = 4988.71 ≈ 4988 chickens
Similarly, you can find the rest of the data using the above equation.
Thus, the number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.
Learn more about the exponential function here:
brainly.com/question/11487261
#SPJ1
The cylinder shown has a volume of 30 cubic units. The
cone and the cylinder have the same height and the same
base. What is the volume of the cone?
S.
Cylinder. V = Th
Cone: V = : 1 / ²
Please help no links or you will get reported
The volume of the cone will be 10 cubic units.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the cube or cuboid.
Given that:-
The cylinder shown has a volume of 30 cubic units.The cone and the cylinder have the same height and the same base.The volume of the cone will be:-
Vc = Vcyl
[tex]\dfrac{1}{3} \pi r^2h\ \ \ =\ \ \pi r^2h[/tex]
Vc = (1 / 3) Vcyl
Vc = ( 1 / 3 ) x 30
Vc = 10 cubic units
Therefore the volume of the cone will be 10 cubic units.
To know more about Volume follow
https://brainly.com/question/1972490
#SPJ1
1. Kyle put $300 of his birthday money in the bank. The bank offers an annual interest rate of 4%, compounded twice a
year. How much money will Kyle have after three years?
Answer:
300(1 + 0.04/2)3(2) = $337.85
Step-by-step explanation:
A conclusion that is proved to be true by deductive reasoning is called a theorem.
True
False
Answer:
True,
Step-by-step explanation:
In math we prove the theorem using known axioms in Math.
Answer: True
Step-by-step explanation:
How do you simplify this problem?
Answer:
x/y.
Step-by-step explanation:
Deal with each number or letter at a time:
3 / 3 = 1
x^3/x^2 = x
y^4 / y^5 = y^-1 = 1/y
z / z = 1
So the answer is 1*x * 1/y * 1
= x/y.
Solve for in each of the following statements. ( is the smallest positive integer to make each statement true.)
5+43≡ 9
18 − 12÷3≡ 5
3+5≡0 11
There is no variable unfortunately
We have to change question little bit
#1
5+43=9x9x=48x=48/9#2
Rest are also meaningless as there is no variable
#3
(3+5)x=0.118x=0.11x=0.11/8