[tex]y = (1/5) x^5 + Ce^ {(-x^5)}[/tex] is the general solution of the given differential equation.
The given differential equation is:
y' + 5x⁴ y = x⁴
To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is [tex]e^{(int 5x^4 dx)}[/tex]:
[tex]e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}[/tex]
The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is [tex]e^{(x^5)}[/tex]:
[tex]e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)[/tex]
Now we can recognize the left-hand side as the product of the derivative of the product of [tex]e^{(x^5)[/tex]and y:
[tex](d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}[/tex]
Integrating both sides with respect to x, we get:
[tex]e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C[/tex]
where C is the constant of integration. Dividing both sides by [tex]e^{(x^5)}[/tex], we get the general solution:
[tex]y = (1/5) x^5 + Ce^(-x^5)[/tex]
where C is an arbitrary constant.
[tex]y = (1/5) x^5 + Ce^{(-x^5)}[/tex] is the general solution of the given differential equation.
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Question: You Invest $2000 At 5% Per Year, Compounded Semi-Annually. How Long In Months, Will It Take For The Investment To Triple
The time taken to triple the principal investemet for an interest compounded semi-annually is approximately 267 months.
What is the time taken to tripple the principal amount?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
P = principal amount (initial investment) = $2000
A = final amount (triple the initial investment) = 3 × $2000 = $6000
r = interest rate per period = 5%
n = number of compounding periods per year n = 2
t = time in years = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05
Plug the given values into the above formula and solve for time taken t.
[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\t = \frac{In(\frac{A}{P}) }{n(In( 1 + \frac{r}{n}) } \\\\t = \frac{In(\frac{6000}{2000}) }{2(In( 1 + \frac{0.05}{2}) } \\\\t = 22.246\ years \\\\t = 267\ months[/tex]
Therefore, the time taken is approximately 267 months.
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Factories 2p^2-60p-128
Answer:
2(p - 32)(p + 2)
Step-by-step explanation:
2p² - 60p - 128 ← factor out common factor 2 from each term
= 2(p² - 30p - 64) ← factor the quadratic
consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)
the factors are - 32 and + 2 , since
- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then
p² - 30p - 64 = (p - 32)(p + 2) , so
2p² - 60p - 128 = 2(p - 32)(p + 2)
The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:
a = 2, b = -60, c = -128
The product of a and c is:
ac = 2 × (-128) = -256
We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:
1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256
We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.
We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.
We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:
2p² - 60p - 128 = 2(p - 4)(p - 32)
Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).
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A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of
h, in cm?
A 4x
B 10x
C h = 4x
D h = 10x
Answer:A
Step-by-step explanation:
To determine the possible values of h, we can apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have side lengths measuring 3x cm, 7x cm, and h cm. Therefore, the possible values of h must satisfy the following conditions:
h + 3x > 7x
h + 7x > 3x
3x + 7x > h
Simplifying these inequalities, we have:
h > 4x
h > -4x (since we have h + 7x > 3x, we can subtract 7x from both sides)
10x > h
From these conditions, we can conclude that h must be greater than 4x and less than 10x. So, the expression that describes the possible values of h is:
h > 4x and h < 10x
Alternatively, we can write it as:
4x < h < 10x
Therefore, the correct option is A) 4x.
darwin's geometric ratio of increase pertains specifically to
Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.
In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.
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how many of these 64 possible offspring have skin that is darker than their parents?
To determine the number of offspring with skin darker than their parents, we need more information about the specific genetic inheritance patterns and traits involved.
The answer depends on factors such as the dominance or recessiveness of genes controlling skin color, the genotype of the parents, and the specific combination of alleles passed on to the offspring.
Without additional information, it is not possible to provide an accurate count of the number of offspring with darker skin. Genetic inheritance is a complex process that involves multiple genes and interactions, making it necessary to consider specific genetic traits and their inheritance patterns to determine the outcome.
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what is the coefficient of y²z
Answer:
1
You're welcome!
A coefficient is a constant which stands in front of a variable
For example, the coefficient of 3x is 3.
Or, the coefficient of 9xy is 9
Same with 2x^2*z. 2
In this case, because there is nothing visible, the coefficient is 1.
Someone help me how to do this? I don’t remember
The value of x such that f(x) = -24 is given as follows:
x = -3.
How to solve the function?The exponential function in the context of this problem is defined as follows:
[tex]f(x) = -3(0.5)^x[/tex]
The numeric value of the function is given as follows:
f(x) = -24.
Hence we can equal the definition to -24 to obtain the value of x, as follows:
[tex]-3(0.5)^x = -24[/tex]
[tex]0.5^x = 8[/tex]
We have that:
2³ = 8.[tex]0.5^x = 2^{-x}[/tex]Hence:
[tex]2^{-x} = 2^3[/tex]
x = -3.
Which is the solution to the exponential function in this problem.
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. Which numbers round to 4,100 when
rounded to the nearest hundred?
Answer: 4140, 4060, and 4109
Step-by-step explanation:
4140: looking at the tens place (4) it is less than 5 so it rounds to 4100
4060: the tens place (6) is bigger than 5 so you add a 1 to the hundreds place everything behind it becomes a 0. and equal to 4100.
4109: everything behind becomes a 0
The organized list shows the sample space of picking a marble, replacing it, and picking another marble, from a bag with green (G), orange (O), and black (B) marbles.
{(G, G), (G, O), (G, B), (O, G), (O, O), (O, B), (B, G), (B, O), (B, B)}
Part A
What is the probability of picking at least one green marble?
A.) 1 1/9
B.) 1/3
C.) 4/9
D.) 5/9
Part B
If you repeat this experiment 450 times, how many repetitions do you predict will result in picking the same color marble?
a) The probability of picking at least one green marble is given as follows: 5/9, option D.
b) The expected number of repetitions with the same color is given as follows: 150 repetitions.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The number of outcomes in this problem is given as follows:
9.
The number of outcomes in which at least one green was picked is:
5.
Hence the probability is of:
p = 5/9.
3 outcomes had the same color, (G,G), (O,O) and (B,B), hence the probability is given as follows:
p = 3/9
p = 1/3
Out of 450 repetitions, the amount is given as follows:
E(X) = 1/3 x 450 = 150 repetitions.
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pls help if you can , it’s due at 12
Answer:
25.54
Step-by-step explanation:
SOH CAH TOA
v
Cos 0 = [tex]\frac{adj}{hyp}[/tex]
-------------------------------------------
11.
Cos 20° = [tex]\frac{adj}{hyp}[/tex]
Cos 20° = [tex]\frac{24}{x}[/tex]
*Rearrange*
[tex]x[/tex] = [tex]\frac{24}{Cos 20}[/tex]
*Cos 20° = 0.9397*
[tex]x[/tex] = [tex]\frac{24}{0.9397}[/tex]
[tex]x[/tex] = 25.5400659785
Nearest tenth: 25.54
Water is being pumped into a pool at a constant rate P(t):
P(t)
=1170 gal/hour
- for 10 hours, where t is the number of hours since pumping began. The pool contained 1200 gallons of water at t= 0. However, there is a crack in the pool that is
getting larger over time. Water leaks from the pool at a rate L(t):
L(t)=0.3e' gal/hour
_during the same 10 hours.
a. What is the rate of change of water in the pool at t=5 hours?
b. Write an integral expression to calculate the total volume of water in the pool at t= 10 hours. Calculate the volume of water in the pool at t= 10 hours in
gallons.
c. What is the average rate of change of water in the pool over the 10 hours? Indicate units.
d. Find the absolute maximum volume of water, in gallons, in the pool over the interval, 0
Correct answers -
a.Rate of change of water in the pool at t= 5 hours
b. Total volume of water in the pool at t=10 hours
c. Average rate of change of water in the pool = 389.31 gallons/hour
To answer the given questions, let's go step by step:
a. To find the rate of change of water in the pool at t=5 hours, we need to calculate the difference between the rate of water being pumped into the pool and the rate of water leaking from the pool at that specific time.
Rate of change of water in the pool at t=5 hours = P(5) - L(5)
P(5) = 1170 gal/hour (given)
L(5) = [tex]0.3e^5[/tex] gal/hour (given)
Substituting the values into the equation:
Rate of change of water in the pool at t= 5 hours = 1170 - [tex]0.3e^5[/tex]
b. To write an integral expression to calculate the total volume of water in the pool at t=10 hours, we need to integrate the rate of water being pumped into the pool over the time interval [0, 10] and subtract the integral of the rate of water leaking from the pool over the same interval.
Total volume of water in the pool at t=10 hours = ∫[0,10] P(t) - ∫[0,10] L(t) dt
P(t) = 1170 gal/hour (given)
L(t) = [tex]0.3e^t[/tex] gal/hour (given)
Calculating the integrals:
∫[0,10] P(t) dt = ∫[0,10] 1170 dt = 1170t | [0,10] = 1170 × 10 - 1170 × 0 = 11700 gallons
∫[0,10] L(t) dt = ∫[0,10] 0.3[tex]e^t[/tex] dt = 0.3 ∫[0,10] [tex]e^t[/tex]dt = 0.3 ([tex]e^t[/tex]) | [0,10] = 0.3 × ([tex]e^{10} - e^0[/tex]) ≈ 0.3 × (22025 - 1) ≈ 6606.9 gallons
Total volume of water in the pool at t=10 hours = 11700 - 6606.9 ≈ 5093.1 gallons
c. To find the average rate of change of water in the pool over the 10 hours, we need to divide the change in volume by the time interval.
Average rate of change of water in the pool = (Change in volume) / (Time interval)
Change in volume = Total volume of water in the pool at t=10 hours - Initial volume of water in the pool
Change in volume = 5093.1 - 1200 = 3893.1 gallons
Time interval = 10 hours
Average rate of change of water in the pool = 3893.1 / 10 = 389.31 gallons/hour
d. To find the absolute maximum volume of water in the pool over the interval [0,10], we need to find the maximum value of the volume function within that interval.
To determine this, we can find the critical points by setting the derivative of the volume function equal to zero and check the endpoints of the interval.
Since the volume function is not provided, we cannot directly find the absolute maximum volume without additional information.
Final answers-
a.Rate of change of water in the pool at t= 5 hours
b. Total volume of water in the pool at t=10 hours
c. Average rate of change of water in the pool = 389.31 gallons/hour
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A student found the value of the expression
10
1
4
−
6
7
8
.
The student subtracted the whole numbers first and then subtracted the lesser fraction from the greater fraction to find the answer.
Which steps correct the error in the student’s thinking?
The steps correcting the error;
Step 1: Convert the mixed fraction to improper fractions
Step 2: Find the lowest common factor
27/8
What is a fraction?A fraction can be defined as the part of a whole number, variable or element.
The different types of fractions are;
Simple fractionsComplex fractionsProper fractionsImproper fractionsMixed fractionsFrom the information given, we have that;
10 1/4 - 6 7/8
First, convert the mixed fractions to improper fractions, we have that;
Multiply the numerator of the fraction by the whole number then add the numerator
41/4 - 55/8
Find the LCM
82 - 55 /8
subtract the value
27/8
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a product must pass an initial inspection, where the probability that it will be rejected is 0.4. if it passes this inspection, it also must pass a second inspection where the probability that it will be rejected is 0.3. what is the probability that it will pass both inspections?
Therefore, the probability that the product will pass both inspections is 0.42.
To find the probability that the product will pass both inspections, we need to multiply the probabilities of passing each inspection:
P(passing both inspections) = P(passing first inspection) * P(passing second inspection | passed first inspection)
The probability of passing the first inspection is 1 - 0.4 = 0.6 (since the probability of rejection is 0.4).
The probability of passing the second inspection, given that the product passed the first inspection, is 1 - 0.3 = 0.7 (since the probability of rejection is 0.3).
So, we have:
P(passing both inspections) = 0.6 * 0.7 = 0.42
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last month, the number of covid-19 cases in a given county was 8. assuming this is the expected number in the current month, what is the probability of having no more than 5 cases this month.
Answer:
The probability of having no more than 5 cases this month is 0.421.
We can calculate this probability by using the following formula:
P(X <= 5) = ∑_{x=0}^5 P(X = x)
where P(X = x) is the probability of having x cases.
The probability of having 0 cases is 0.316, the probability of having 1 case is 0.368, the probability of having 2 cases is 0.201, the probability of having 3 cases is 0.075, and the probability of having 4 cases is 0.031.
Plugging these values into the formula, we get the following:
P(X <= 5) = 0.316 + 0.368 + 0.201 + 0.075 + 0.031 = 0.421
Therefore, the probability of having no more than 5 cases this month is 0.421.
Step-by-step explanation:
A cylindrical tank of water with radius 10.5cm and height 20cm is emptied into another cylindrical tank of radius 10cm. Find the height of the new tank to 2 decimal places. Take π(22/7)
Answer:
The height of the new cylindrical tank is approximately 54.10 cm when rounded to two decimal places.
Step-by-step explanation:
Find the volume of the water in the original tank using the formula for the volume of a cylinder:
V1 = π(10.5cm)^2(20cm) ≈ 6939.25 cm^3
Since the amount of water is conserved, set the volume of the water in the new tank equal to V1:
V2 = π(10cm)^2(h)
π(10.5cm)^2(20cm) = π(10cm)^2(h)
Simplifying, we get:
4410 = 100h
h ≈ 44.10 cm
However, this is the height that the water would reach if it was poured into a cylinder with a radius of 10 cm. To find the actual height of the new tank, add the radius of the new tank (which is also 10 cm) to this height:
h_new = h + r = 44.10 + 10 = 54.10 cm
Therefore, the height of the new tank is approximately 54.10 cm when rounded to two decimal places.
show a+c = b+d
............
a+c = b+d , because angle c = angle b and a = d
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Angles on parallel lines can be alternate, corresponding or verically opposite to each other. And when they have these properties, the angles are equal to reach other.
b = c , since b+y = 360 and c+y = 360
and also a + x = 180
d + x = 180
therefore a = d
Therefore;
in b+d , we can substitute c for a and b for c
therefore b+d = a+c
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4. If the equation (x + 10)x= 0 is true, which statement is also true according to the zero product
property?
A. Only x = 0
B. Either x = 0 or x + 10 =0
2
C. Either x = 0 or 10x = 0
D. Only x + 10 = 0
5. What are the solutions to the equation (10x) (3x - 9) = 0?
A.
10 and 3
-10 and 9
1
B.
C. 10 and 3
D 10 and 9
-
The correct statement according to the zero product property is the one in option B.
Which statement is also true according to the zero product property?The zero product property says that if the product of two numbers A and B is zero, then either A or (and) B are equal to zero.
Then if:
(x + 10)*x = 0
Then we have that either:
x = 0
or:
x + 10 = 0
x = -10
Then the correct option is B:
"Either x = 0 or x + 10 =0"
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Here is a trapezium ABCD. 20 cm A 8 cm C 14 cm B Diagram NOT accurately drawn Angle DAB = angle ABC = 90° AD = 20 cm AB= 8 cm BC= 14 cm Calculate the area of the trapezium ABCD.
The area of the trapezium ABCD is 136 square cm
Calculating the area of the trapezium ABCD.From the question, we have the following parameters that can be used in our computation:
The image of the trapezium (see attachment)
The area of the trapezium ABCD is calculated as
Area = 1/2 * Sum of opposite sides * Height
When the given values are substituted in the above equation, we have the following equation
Area = 1/2 * (14 + 20) * 8
Evaluate the sum
Area = 1/2 * 34 * 8
Evaluate the products
Area = 136
Hence, the area of the trapezium ABCD is 136 square cm
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if log 7 equals a and log 8 equals b then log 224 equals
A: a + 5/3b
B: a + 4b
C: 4a + B
D: 4ab
E: none of the above
If log 7 equals a and log 8 equals b then log 224 equals: E: none of the above.
What is log?Simplify the expression for log (224) by using:
log (ab) = log (a) + log (b) and log (a/b) = log (a) - log (b):
So,
log (224) = log ( 7 × 8 × 4)
= log (7) + log (8) + log (4)
Since log(4) = 0 (since 4 = 2^2)
Simplify
log(224) = log (7) + log (8) + log (4)
= log 7 + log 8
= a + b
Therefore the correct option is E.
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Which of the possibilities below represents the mood and figure of the following argument: Some dictators are not warmongers. Since no dictators are egomaniacs, and some egomaniacs are warmongers. Group of answer choices
AEO - 1
IEO - 1
EIO - 4
IOE - 2
The mood of the argument is categorical and the figure is EIO. To determine the mood and figure of the given argument, we'll first identify the premises and conclusion, and then assign the appropriate categorical proposition to each statement.
The argument can be rewritten as:
Premise 1: Some dictators are not warmongers. (Some D are not W)
Premise 2: No dictators are egomaniacs. (No D are E)
Premise 3: Some egomaniacs are warmongers. (Some E are W)
Conclusion: Some dictators are not warmongers. (Some D are not W)
Now, let's assign the categorical propositions to each statement:
Premise 1: I (Some D are not W)
Premise 2: E (No D are E)
Premise 3: I (Some E are W)
Conclusion: O (Some D are not W)
The mood of the argument is IEO.
Next, we'll determine the figure by looking at the placement of the middle term (E) in the premises:
Premise 2: No D are E (subject-middle term)
Premise 3: Some E are W (middle term-predicate)
The figure is 1 because the middle term is the subject of one premise and the predicate of the other premise.
So, the mood and figure of the argument are IEO-1. Therefore, the correct answer is:
IEO - 1
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0.000000000996 in a scienific notation pls help 30 POINTS
Answer:
scienific
Step-by-step explanation:
2.
JA = 5, AL = 9, and LK= 15. What is the length of JK?
A. 6
B. 11
C. 15
D. 19
The value of length JK is 11
What is tangent of a circle?A tangent is a straight line that touches any part of the circumference. A circumference is the outer body of a circle.
A theorem of tangency states that if lines comes from thesame point of a circumference and meet at a point , then the lines are equal.
Therefore we can say that;
JA = JB = 5
AL = LC = 9
CK = LK - LC
= 15 -9
= 6
BK = LK = 6
therefore ;
JK = BK + JP
= 6+5
= 11
Therefore the value of JK is 11
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Sophia spends a total of $6.30 on cheese. She buys 500g of Cheddar cheese and 200g of Stilton cheese. The cost of the Cheddar cheese is $9.20 for 1kg. Work out the cost of 1kg of the Stilton cheese
Answer:
The price would be 7.20
Step-by-step explanation:
Could anyone help me with this?
For the given right angle triangle ABC (A) option is the correct answer.
We have,
A right triangle, also known as a right-angled triangle, or more technically an orthogonal triangle, was originally known as a triangle, is a triangle with one right angle and two perpendicular sides. Trigonometry is based on the relationship between the sides and various angles of a right triangle.
What is the correct statement for right triangle ABC ?
Cos A = Sin ( 90˚- A )
Since at 90˚ Sine function convert into cosine function and (90˚- A) results in first quadrant where sine function is positive.
Therefore Cos A = Cos A
Hence the correct option is (a) option Cos A = Sin ( 90˚- A )
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complete question:
attached below.
Urgent!! Will give brainliest :)
The better statistics to compare the distribution are given as follows:
A. Mean and standard deviation.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.
The standard deviation of a data-set is calculated as square root of the sum of the differences squared between each observation and the mean of the data-set, divided by the cardinality of the data-set.
These two measures should be used as both distributions in this problem are symmetric, meaning that they do not contain outliers.
If the distribution contained outliers, then the median and the IQR should have been used.
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I need some help please, How can you map figure P onto figure Q?
Answer:
6 units right
Step-by-step explanation:
To translate figure P onto figure Q, just translate the figure 6 units to the right.
A person invests 9500 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 22600 dollars?
Answer:
10.6
Step-by-step explanation:
To find out how long the person must leave the money in the bank until it reaches $22,600, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (22600 dollars in this case)
P = the principal amount (9500 dollars)
r = the annual interest rate (5.75% expressed as 0.0575)
n = the number of times the interest is compounded per year (in this case, annually, so n = 1)
t = the time in years
Substituting the given values into the formula, we have:
22600 = 9500(1 + 0.0575/1)^(1*t)
Simplifying:
2.3789 = (1.0575)^t
To solve for t, we take the logarithm of both sides:
log(2.3789) = log((1.0575)^t)
Using logarithm properties, we can bring the exponent down:
log(2.3789) = t * log(1.0575)
Now, we can solve for t by dividing both sides of the equation:
t = log(2.3789) / log(1.0575)
Using a calculator, we find:
t ≈ 10.6
Therefore, the person must leave the money in the bank for approximately 10.6 years to reach $22,600.
in garland, texas, it rained 4(1/2) in. on monday. on tuesday, it rained 0.03 in. less than on monday. how much did it rain on tuesday.
It rained approximately 4.47 inches on Tuesday.
The meaning of SUBTRACT is to take away by or as if by deducting. How to use subtract in a sentence.
On Monday, it rained 4(1/2) inches.
On Tuesday, it rained 0.03 inches less than on Monday.
To find out how much it rained on Tuesday, we need to subtract 0.03 inches from the rainfall on Monday.
4(1/2) inches - 0.03 inches = 4.5 inches - 0.03 inches = 4.47 inches
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Please help!
I will mark brainliest to correct answer.
1/2 is the probability that the number will add up to more than 4. Option C is correct
Application of probabilityProbability is defined as the likelihood or chance that an event will occur.
Probability = Expected/Total
From the given spinner, the total outcome is expressed according to the permutation
For orange spin
3P2 = 3!
3P2 = 6
For green spin
4P2 = 4!/2!
4P2 = 12
If they are both spinned, the probability that the sum will be more than 4 are:
Expected (orange) = {(2,3)}
Expected (green) = {((1, 3), (3, 4) (2, 4), (2,3)}
Pr(number added is 4) = 1/6 + 4/12
Pr(number added is 4) = 2+4/12
Pr(number added is 4) = 1/2
Hence the probability that the number will add up to more than 4 is 1/2
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Mandy's Candies is most famous for their homemade fudge and homemade toffee. They make an average of 149 pounds of fudge and toffee combined each month. They sell a pound of fudge for $8.12 and a pound of toffee for $7.62. Mandy's averages $1,169.38 each month in fudge and toffee sales. On average, how many pounds each of fudge and toffee does Mandy's Candies sell in one month?
A.
57 fudge; 92 toffee
B.
68 fudge; 81 toffee
C.
71 fudge; 78 toffee
D.
74 fudge; 75 toffee
Mandy's Candies sells an average of 68 pounds of fudge and 81 pounds of toffee each month. Option B
How to find how many pounds each of fudge and toffee does Mandy's Candies sell in one monthUsing a system of equations to solve this
Let f be the number of pounds of fudge sold each month, and
t be the number of pounds of toffee sold each month.
Then we have:
f + t = 149 (equation 1)
8.12f + 7.62t = 1169.38 (equation 2)
We can solve for f in equation 1:
f = 149 - t
Substituting this into equation 2, we get:
8.12(149 - t) + 7.62t = 1169.38
Simplifying and solving for t, we get:
1209.88 - 0.5t = 1169.38
0.5t = 40.5
t = 81
Substituting this back into equation 1, we get:
f + 81 = 149
f = 68
Therefore, Mandy's Candies sells an average of 68 pounds of fudge and 81 pounds of toffee each month.
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