Step-by-step explanation:
Set each binomial equal to 0, solve for x.
[tex](x + 5) = 0[/tex]
[tex]x = - 5[/tex]
[tex](x - 2) {}^{2} = 0[/tex]
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
The zeroes are -5, and 2(with a multiplicity of 2)
We have a degree of 3.
[tex](x + 5)(x {}^{2} - 4x + 4)[/tex]
the first term in each binomail when using FOIL, become x^3 since that is the highest degree, 3 is the degree of c.
Answer for free9+10 =
Answer: 19
Step-by-step explanation:
Answer:19
Step-by-step explanation: 10 add the 9
given an integer x and an array of numbers, find if two numbers in the array sum up to x. (or, find the pair of numbers whose sum is closest to x.)
The program for finding the two numbers in the array sum up to x is made.
Explain the term sorting?Sorting involves putting data into a meaningful order so how you can more efficiently evaluate it. For instance, if you want to plot a graph of sales performance, you could wish to sort the sales data per calendar month.Array A[n], x
Sort by the use of Mergesort ------- O(nlogn)Initialize 2 index variables to estimate candidit.Initialize 1st to that leftmost index: l = 0Initializ 2nd to that rightmost index: r = n - 1While l < r -----------O(n)if A[l] + A[r] == x; return trueelse if A[l] + A[r] < sum; increment lelse decrement rreturn falseTime Complexity:
As was covered in class, step one employs mergesort, which has an O(nlogn) complexity.
Since the worst-case scenario involves traversing through the full array, step three consumes O(n) time.
Total Running Time = O(nlogn + n) = O(nlogn)
Thus, the program for finding the two intergers in the array sum up to x is made.
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I need help with the last part. I don’t know what to do with the pi part. If someone can help, that would be great!!
Answer:
Error: 131π
Surface Area = 131π=411.5 yd^2
Step-by-step explanation:
All the other steps were correct but 131π = 411.5486376, so there's no way the person should have gotten 411.3 yd^3.
Finally, if we round 411.5486376 to the nearest tenth, we get 411.5 yd^2.
Carrie is creating a painting for art class. The width of the canvas is 5 inches greater than the height of the canvas. Write a simplified equation in terms of h (the height) for the perimeter, p, of the canvas. (Please show work!)50 points!!!!!!
Length is 4 ft and width is is 3ft.
What is width ?
The "size" of a body is measured in geometry by its mean width; for more information on the various body measures, see Hadwiger's theorem. One must take into account -dimensional hyperplanes parallel to a specific direction in where is the n-sphere.
[tex]\begin{aligned}& w^2+(w+1)^2=5^2 \\& \frac{w^2+w^2+2 w+1}{}=25 \\& 2 w^2+2 w-21\end{aligned}[/tex]
[tex]\begin{aligned}& 2 w^2+2 w-24=0 \\& w^2+w-12=0\end{aligned}[/tex]
[tex]\begin{gathered}(w-3)(w+4)=0 \\w=3,-4\end{gathered}[/tex]
The width must be three because we can't have negative widths. Since the length is four feet, we have the dimensions of our poster.
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Triangle ABC and DEF are similar what is the measure of side DF?
Answer:
15
Step-by-step explanation:
25 / 15 = 1.666...
9 x 1.666.... = 15
Answer:
Step-by-step explanation:
375
if they are simiar than 15 from abc would have been the same length
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Moussa sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
81 visitors purchased no costume.
6 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a decimal to the nearest hundredth.
The probability that the next person will purchase more than one costume will be 1/30.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Total visitors of a day = 81 + 6 + 3 = 90
The number of purchasing more than one costume = 3
Probability of purchasing more than one costume = 3/90 = 1/30
Hence"The probability that the next person will purchase more than one costume will be 1/30".
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-5y^2+17y-84 / y^3+12y^2+36y partial fraction decompostion
[tex]5y^2+17y-84 / y^3+12y^2+36y[/tex] partial fraction decomposition is [tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
What is partial fraction decomposition?Partially decomposing a rational fraction, also known as partially expanding it, in algebra includes expressing the fraction as the sum of a polynomial and one or more fractions with a lower common denominator.
One technique for breaking down rational expressions into smaller partial fractions is partial fraction decomposition. This method serves the integration process better.
In order to integrate a rational function, it is condensed to a valid rational function. The integrand can be expressed as the sum of more elementary rational functions through the use of partial fraction decomposition.
Therefore, starting with the simplified solution and proceeding backwards, the final expression is “decomposed” into the original polynomial fractions.
[tex]= -5y²+ 17y-84 / y³+12y²+36y[/tex]
[tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
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PLEASE HELP ASAP
Choose the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power end quantity all raised to the negative third power.
−76
1 divided by 7 raised to the third power
negative 1 divided by 7 raised to the sixth power
718
The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.
What is power?
The power (or exponent) of a number says how many times to use the number in multiplication. It is written as a small number to the right and above the base number.
The expression 7 raised to the negative second power times 7 raised to the third power is equivalent to 7 raised to the (negative second + third) power, which is 7 raised to the first power. This is equal to 7.
The quantity 7 raised to the first power all raised to the negative third power is equal to 7 raised to the (first + negative third) power, which is 7 raised to the negative second power.
Therefore, the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power all raised to the negative third power is 7 raised to the negative second power, which is 1/7^2 = 1/49.
Hence, The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
Answer:
Step-by-step explanation:
1) She can use the CUADRATIC FUNCTION for to solve
2) She can use factorization for to solve
3) She can use the ZERO method for to solve
Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to two decimal places.)f(t) = 2 cos t + sin 2t[0,pi/2]____min____max
The absolute minima of the function is at 12.85 and the absolute maxima is at 15.42.
Let the function be ,
f(t) = 5t + 5 cot( t/2 ).
first derivative of the function,
f'(t)
= d/dt ( 5t + 5 cot(t/2))
= d/dt(5t) + d/dt ( 5 cot (t/2))
= 5 - 5/2cos^2(t/2)
Taking the derivative equal to 0,
f'(t) = 0
t = pi/2 , 3pi/2 f
On evaluating the equation wrt to obtained critical value,
we will get ,
absolute minimum value 12.85
absolute maximum value 18.56.
The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.
The terms "local maxima" and "local minima" refer to additional maxima and minima of a function that are not its absolute maxima and minima.
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cassie prepaid a 6-month membership to the summer lotus yoga studio. she received a one-time discount of $40 for prepaying. cassie paid a total of $650.
The amount which Cassie will pay the studio per month will be $115.
The equation by taking data from the question will be
6m - 40 = 650
6m−40=650
On solving this we get ,
6m = 610
m = 115
The regular cost per month is $115.
The above question is an example of multi-step equation.
Multi-step equations are algebraic expressions that must be solved using more than one operation, such as subtraction, addition, multiplication, division, or exponentiation. When solving multi-step equations, it is critical to understand the order of operations.
Solve an equation with a single unknown variable, x, by using algebraic operations on both sides of the equation to isolate x. The goal is to select an algebraic operation sequence that will leave x on one side of the equal sign and put everything else on the other side.
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A sweater is priced at $60 normally. It is on sale for $45. By what percentage was the
sweater's price decreased?
What is the relationship between multiplying polynomials and factoring? How are these two concepts related? How can they be used to check your work? Give an example and work it out to explain your reasoning. Be sure to explain how your example shows the relationship you describe.
Things you MUST include:
- A verbal/written explanation that describes the relationship between the two concepts. (3 points)
- An example that shows how multiplying polynomials
Explain how your example shows the relationship. (2 points)
By spreading (by multiplying) that 3 back in, we may obtain our original expression 12.
What do you mean by Factoring of polynomial?
The process of multiplying polynomial factors is known as factoring polynomials. A polynomial of degree "n" in variable x is an equation of the form axn + bxn-1 + kcxn-2 +....+kx+ l, where each variable has a constant acting as its coefficient. A polynomial is an expression that has a constant and a variable together with an addition or a subtraction sign between them.
Factors of polynomials are zeros of polynomials that may be expressed as another linear polynomial. If we divide a given polynomial by any of its components after factorization, the residual will be zero.
Contingents: 1, 2, 5, and 7.variables: x, y, and hTerms: 3x, 8y, and 2h (terms are often separated by a + or a -).(Note that words can also include variables and constants)
Formulas: 3x+1, 4x +5, 2h + 2wEquations: P = 2h + 2w, x = 4, y = x + 2One of the variables or constants that is multiplied by another factor to create a phrase is called a factor. Factors 4 and x make up the phrase 4x. To factor is to divide the object of the multiplication. Therefore, factoring "disassembles" the result of multiplication.
We frequently need to factor a term in order to "solve" (that is, get the value of, say, x) an equation
For Example:
The operation of factoring falls in between multiplication and dividing. Let's examine the following statement:
3x + 12
We can factor out the third because 3x and 9 both share the number three:
3x ÷ 3 = x 12 ÷ 3 = 4
We set it aside what's left after factoring out 3:
3(x + 4)
By spreading (by multiplying) that 3 back in, we may obtain our original expression: x * 3 = 3x 4 * 3 = 12.
We now have: 3x + 12
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solve the equation
-(1+7x)-6(-7-x)=36
The solution to the equation is x = -1.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
To solve this equation, we need to use the order of operations to simplify the expression on the left side of the equal sign.
The order of operations tells us that we should perform operations within parentheses first, then perform any exponents or radicals, then perform any multiplications or divisions (working from left to right), and finally perform any additions or subtractions (also working from left to right).
Using the order of operations, we can simplify the left side of the equation as follows:
-1 - 7x - 6(-7 - x) = 36
(-1 - 7x) - 6(-7 - x) = 36
-1 - 7x - (-42 - 6x) = 36
-1 - 7x + 42 + 6x = 36
5x + 41 = 36
5x = -5
x = -1
Therefore, the solution to the equation is x = -1.
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Evaluate b(-7), when b(c) = 2c³5c² - 6c - 13.
Answer:
168015
Step-by-step explanation:
b(c) = 2c³5c² - 6c - 13
b(7)=2(7)³5(7)²-6(7)-13
b(7)=2(343)5(7)²-6(7)-13
b(7)=(686) 5(49)-6(7)-13
b(7)=(686) (245)-6(7)-13
b(7)=(686) (245) -42-13
b(7)=168070-42-13
b(7)=168028-13
b(7)=168015
(Usually this is how you would solve it but because there was no sign between the 2c^35c^2 I got sort of confused so I just multiplied, if wrong I'm sorry..)
[tex]b(-7)=-168041[/tex].
Step-by-step explanation:1. Write the function.[tex]b(c)=2c^{3} 5c^{2} -6c-13[/tex]
2. Substitute "c" by "-7" in the function.[tex]b(-7)=2(-7)^{3} 5(-7)^{2} -6(-7)-13[/tex]
3. Calculate.[tex]b(-7)=2(-343) 5(49) -(-42)-13\\ \\b(-7)=-168070 +42-13\\ \\b(-7)=-168041[/tex]
In each blank below a single digit is inserted such that the following six three-digit numbers, in this order, form an arithmetic sequence: 1_ _, _ _ 9, 2 _ 2, _ 6 _, 2 _ _, _ 3 _What is the value of the next number in the sequence?
The series appears to be 166, 199, 232, 265, 298, 331
With examples, define sequence?
A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.
In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.
The last number of the common difference must end in 3
And this must be a 2 digit number
So....the first number must end in 6
The the 4th number must be 265
So..... the 5th number must end in 8
And the last digit of the last term must end in 1 [ and begin with 3 ]
Putting all this together we have that
265 + 2d = 331
2d = 66 ⇒ d = 33
So the first term must be 265 - 3 (66) = 166
the series appears to be 166, 199, 232, 265, 298, 331
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HELP NOW 50 POINTS IMPORTANT!
Using the image of the blank check below, match each item with what would go in that space.
Column A
1.
Date:
Date
2.
Who the check is being written to:
Who the check is being written to
3.
Amount of check, written in numeric format:
Amount of check, written in numeric format
4.
Amount of check, written in word format:
Amount of check, written in word format
5.
A description of what the check is for:
A description of what the check is for
6.
The checking account owner's signature:
The checking account owner's signature
Column B
a.Item 1
b.Item 4
c.Item 3
d.Item 5
e.Item 6
f.Item 2
Answer:
HOPE IT HELPED
Step-by-step explanation:
Date is item 2
Who the check is being written to is item 1
Amount of check, written in numeric format is item 3
Amount of check written in word format is item 4
A description of what the check is for is item 5
The checking account owner's signature is item 6
A 0.60-kg basketball is dropped out of a window that is 6.1mabove the ground. The ball is caught by a person whose handsare 1.5m above the gound.1. How much work is done on e the ball by its weight?What is the gravitational potential energy of the basketball,relative to the ground, when it is ... 2. released and 3. caught?4. How is the change (PEf- PE0) in the ball'sgravitational potential energy related to the workdone by its weight?
The work that gravity does;
W = F.S = mgΔh
In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.
W = mgΔh
g = 9.8 m/s²
Δh = 4.6 m
m = 0.60 kg
W = 0.60 x 9.80 x 4.6
W = 2.7 J
The source of gravitational potential energy in relation to the ground is;
U = mgh
The release point therefore
Ug = mgh(0)
U0 = 0.60 x 9.8 x 6.1
U0 = 35.87 J
At the point of release
U(gf) = mgh(f)
U(gf) = 0.60 x 9.80 x 1.5
U(gf) = 8.820 J
Gravitational potential energy changes are;
ΔU(g) = U(gf) - U0
ΔU(g) = 8.820 J - 35.87 J
ΔU(g) = -27.05 J
Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.
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The size of a wolf population in a national park increases according to the formula y=y₀ e^{0.027 t}, where t is time in years and y₀ is the initial population at time 0 . If the size of the current population is 58 wolves, find how many wolves there will be in 5 years.
In 5 years, there will be ? wolves.
(Round to the nearest whole number as needed.)
There will be 66 wolves there will be in 5 years according to given exponential function.
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main body:
given = y=y₀ e^{0.027 t}
here , y₀ = 58
t = 5 years
y = 58 e^(0.027 * 5)
y = 58 e^(0.135)
y = 58 * 1.144537
y = 66.383133
y = 66
Hence there will be 66 wolves there will be in 5 years.
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The data in the table represent the height of an object over time. Which model best represents the data ? Height of an Object quadratic, because the height of the object increases or decreases with a multiplicative rate of change quadratic, because the height increases and then decreases Time (seconds) 0 1 2 Heiaht(feet) 5 50 70 48 3 exponential, because the height of the object increases or decreases with a multiplicative rate of change exponential , because the height increases and then decreases
Since the data in the table represent the height of an object over time, a model which best represents the data is: B. quadratic, because the height increases and then decreases.
What is a quadratic equation?In Mathematics, a quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
Additionally, the standard form of a quadratic equation in mathematics is given by the following mathematical expression:
ax² + bx + c = 0
In Mathematics, the graph of all quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve.
In conclusion, we can logically deduce that the graph of a quadratic equation (function) would always form a parabolic curve with the data value increasing on one end and decreasing on the other end as shown in the image attached below.
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Complete Question:
The data in the table represent the height of an object over time.
Which model best represents the data?
quadratic, because the height of the object increases or decreases with a multiplicative rate of change
quadratic, because the height increases and then decreases
exponential, because the height of the object increases or decreases with a multiplicative rate of change
exponential, because the height increases and then decreases
Write the expression as a number in scientific notation.
quantity 8 times 10 squared end quantity times quantity 3.2 times 10 to the fifth power end quantity all divided by the quantity 4 times 10 cubed
7.2 x 107
7.2 x 104
6.4 x 107
6.4 x 104
The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)
Simplify the expression, then we have
⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)
⇒ [(25.6 × 10⁷)] / (4 × 10³)
⇒ 6.4 × 10⁷⁻³
⇒ 6.4 × 10⁴
The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.
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Find the area of the shaded region, the graph to the right, depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The area of the shaded region is ——?
Round to four decimal places as needed
Answer:
68%
Step-by-step explanation:
93 is 7 pts BELOW 100 this represents -7 /15 = -.4666 Z-score
From Z-score table this represents .3192 ..or 31.92 % to the LEFT of the 93 ...... to the RIGHT is 100% - 31.92 % = ~ 68%
Given: Line m is parallel to line n
prove : <1 is supplementary to < 3 HELP PLEASE
Supplementary angles are two angles whose combined angle is 180 degrees. As shown below, the table of the proof that (1) is an addition to (3) can be completed.
What are Supplementary angles?Supplementary angles are two angles whose combined angle is 180 degrees. When a straight line crosses another line, two angles are created on either side of the initially imagined straight line. Two sets of additional angles make up those two-two angles. This implies that a straight line will be formed by the outside sides of any extra angles that are positioned next to one another.
For the demonstration that 1 is an addition to 3, the preceding table can be completed as shown below.
1) Line m in is parallel to line n;
2) ∠1 = ∠2 → Corresponding angles
3) m∠1 = m∠2 → Definition of Congruent angles
4) ∠2 and ∠3 for a linear pair → Adjacent angles on a straight line
5) ∠2 is supplementary to ∠3 → Definition of linear pair
6) m∠2 + m∠3 = 180° → Definition of supplementary angles
7) m∠1 + m∠3 = 180° → Substitution Property
8) ∠1 is supplementary to ∠3
As a result, the table containing the proof that item 1 is an addition to item 3 can be completed as displayed above.
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A family rents a truck to move from Buffalo to Chicago. The rental has a base cost of $49.95, plus, an additional cost of $1.19 per mile driven. The family also pays for gas, which costs $3.89 per gallon. The truck’s average gas mileage is 18 miles per gallon. The family decided to take a rest in Cleveland, what would be the distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85?
By solving a linear equation, we will see that the distance is 479.98 miles.
How to find the distance?We know:
The rental has a base cost of $49.95 plus $1.19 per mile.
There is also an extra cost of $3.89 per gallon of gas, and with one gallon they can travel 18 miles, then there is another extra cost of:
$3.89/18 per mile.
Then, if you travel x miles, the total cost is given by the linear equation:
C(x) = $49.95 + ($1.19 + $3.89/18)*x
We want to find the value of x, number of miles, such that the total cost is $724.85, then we need to solve:
$724.85 = $49.95 + ($1.19 + $3.89/18)*x
Let's solve that for x:
$724.85 - $49.95 = ($1.19 + $3.89/18)*x
$674.90 = ($1.19 + $3.89/18)*x
$674.90/($1.19 + $3.89/18) = x
479.98 = x
So the distance is 479.98 miles.
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The teacher is planning a party for the students. She needs to pick 2 of 6 dinners to offer and 3 to 5 desserts. How many different combinations can she pick?
She can choose from the various combinations of 6 of 2, 5 to 3.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence.
A permutation and a combination can be distinguished by how they are ordered.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence. Combination is one of the various methods for selecting elements from a huge collection of objects without taking the order into account.Permutations and combinations are the several ways that items from a set can be chosen, usually without replacement, to generate subsets.The order matters, for instance, if you have a lock that requires four digits to unlock. You cannot type the same numbers in any other order (for example, 6 8 2 3) and expect the lock to open if the right values are 8 3 6 2! That's a permutation, so.Explanation:
2 of 6 = 6 of 2
3 to 5 = 5 to 3.
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How much money does Dana Jones have after 7 years if she invests $ 1100 at 5% interest compounded continuously?
Dana Jones has $__-after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
Dana Jones has amount after 7 years is $1560.97.
What is compounded continuously?
Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.
Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.
We have to find the amount after 7 years.
Consider, the formula
A = Pe^rt
where,
A is the amount after t years
P is the invested amount
r is the interest rate
t is the number of years
Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.
[tex]A = 1100e^0^.^0^5^(^7^)\\A = 1560.9743\\A = 1560.97[/tex]
Hence, Dana Jones has amount after 7 years is $1560.97.
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A hose fills a hot tub at a rate of 3.49 gallons per minute. How many hours will it take to fill a 343-gallon hot tub? Question content area bottom Part 1 It will take enter your response here hours to fill the hot tub.
Answer:
answer = 98.2808022923 i think
can someone help me with this thank you
Answer:
a, b, d: No
c: Yes
Step-by-step explanation:
You want to identify statements that are and are not the negation of "I am not drawing a rectangle."
NegationThe negation of a statement is a statement using the same subject and predicate, but with the opposite truth value.
The negation of ...
I am not drawing a rectangleis the statement ...
I am drawing a rectangleStatements about circles are irrelevant, as are statements about any action other than drawing (or not drawing).
In how many ways can the digit in the number 7,600,000 be arranged
Answer:Answer to Solved In how many ways can the digits in the number 7, ... Question: In how many ways can the digits in the number 7, 600,000 be arranged?
1 answer
·
Top answer:
Concept used : The number of permutations (arrang...
Step-by-step explanation:
What is greater 7/8 or 5/6?
Answer:
7/8
Step-by-step explanation:
First, we need to get 7/8 and 5/6 to the same denominator which is 48. 7/8 becomes 42/48 whilst 5/6 becomes 40/48
we can simply put them both with the same denominator and check, the larger numerator will be it.
so hmmm let's multiply one by the denominator of the other
[tex]\cfrac{7}{8}\hspace{5em}\cfrac{5}{6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}\cdot \cfrac{6}{6}\implies \cfrac{42}{48}\hspace{5em}\cfrac{5}{6}\cdot \cfrac{8}{8}\implies \cfrac{40}{48}\hspace{9em}\boxed{\cfrac{42}{48} ~~ {\Large \begin{array}{llll} > \end{array}}~~ \cfrac{40}{48}}[/tex]