The final value of a_5 is 27a.
The equation a_n=a_{n-1}+5a is a recursive formula that gives the value of a_n in terms of the value of a_{n-1}. To find the value of a_5, we need to apply this formula repeatedly, starting with the given initial value of a_1=7a.
Using the recursive formula:
a_2 = a_1 + 5a = 7a + 5a = 12a
a_3 = a_2 + 5a = 12a + 5a = 17a
a_4 = a_3 + 5a = 17a + 5a = 22a
a_5 = a_4 + 5a = 22a + 5a = 27a
so a_5 = 27a
This is the final result and no need to calculate more.
Thus the final value of a_5 is 27a.
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4/5 + 3/4= asap PLEASEEE
What are the properties of addition and subtraction?
Answer:
Step-by-step explanation:
In addition and subtraction, the identity is 0. In multiplication and division, the identity is 1. That means that if 0 is added to or subtracted from n, then n remains the same. Also, if n is multiplied or divided by 1, then n remains the same
ORRRRRRRRR
Five Properties of Addition
Closure property of Addition.
Commutative property of Addition.
Associative property of Addition.
Additive identity property of Addition.
Additive inverse property of Addition.
PLEASE HELP PICTURE ATTACHED
Answer:
11. ∠5 and ∠7 are corresponding angles
12. ∠1 and ∠8 are alternate exterior angles
13. ∠3 and ∠6 are alternate interior angles
14. ∠6 and ∠7 are consecutive interior angles.
15. ∠1 = 58
∠2 = 122
∠3 = 58
∠5 = 122
∠6 = 58
∠7 = 122
∠8 = 58
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the image below is the one you need to solve
Option c: y = -x + 5 represents scatter plot 1, Option g: The relationship is not linear represents scatter plot 2, Option a: y = 3x represents scatter plot 3, and Option f: y = x + 3 represents scatter plot 4.
What is a scatter plot?
The graphs that show the association between two variables in a data set are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.
The given equations are -
a. y = 3x
b. y = 4x - 2
c. y = -x + 5
d. y = -5x
e. y = -2x - 4
f. y = x + 3
g. The relationship is not linear.
The first scatter plot is going from positive y-axis to positive x-axis in a linear form. The graph for the equation that goes from positive y-axis to positive x-axis is y = -x + 5.
The second scatter plot is a curved parabola going and not a linear plot. So, the scatter plot is said to be a non-linear scatter plot.
The third scatter plot is going from positive x-axis to infinity in a linear form. The graph for the equation that goes from x-axis to infinity is y = 3x.
The fourth scatter plot is going from positive y-axis to infinity in a linear form. The graph for the equation that goes from positive y-axis to infinity is y = x + 3.
Therefore, scatter plot 1 is represented by equation y = -x + 5, scatter plot 2 is not linear, scatter plot 3 is represented by equation y = 3x and scatter plot 4 is represented by equation y = x + 3.
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What's the value of the following game: You roll a 100 sided die with sides 1-100. You can either take this number of dollars, or pay $1 to roll again. You can keep on paying $1 to roll for as long as you like.
You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
Can a die have 100 sides?The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."
optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.
Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:
1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)
2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1
[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]
[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]
maximizing E w.r.t. x,
dE/dx = 0
2x^2 - 400x + 19600 = 0
x = ( 400+/- sqrt(160000-4*2*19600) ) / 4
Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4
x = 85.85786
We just have to calculate E(x=85) and E(x=86) and compare.
E((x=86) = 87.35 and E(x=85) = 87.33
so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
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Chapter 3 Lesson 4 Arithmetic Sequence
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
What is Arithmatic Sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence. As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulae for arithmetic sequences.
The equation to determine the nth term in an arithmetic series
The formula for calculating the sum of an arithmetic sequence's first n terms
There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."
Option 1, 4 and 6 are in Arithmatic Sequence as
In 1:
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
again in 4 :
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
and in 6
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
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Please help I have a learning disability and need help with this.
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
( 3 6) 9 and 3 (6 9)
yes, it uses the Associative Property
yes, it uses the Commutative Property
yes, it uses the Identity Property
no they are not equivalent
Answer:
No, they are not equivalent.
Step-by-step explanation:
The first expression, (3 6) 9, is equal to 9, while the second expression, 3 (6 9), is equal to 3. The two expressions are not equivalent because they do not produce the same result when the operations are carried out. The properties of associativity, commutativity, and identity do not apply to these expressions.
Answer:
no they are not equivalent
Step-by-step explanation:
The two expressions are not equivalent. This is because the distributive property does not apply in this case, as the parentheses on the left side of the expression have precedence over the parentheses on the right side. Therefore, the expression on the left side would be evaluated first, resulting in a different answer than the expression on the right side.
I need the answer to this question please!
5 * root(x ^ 2, 3) is the equivalent expression.
Why do roots grow in numbers?Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.
Only if the numbers under the radical sign are equal can you add or subtract square roots themselves. The original number will still be in the radical sign after adding or subtracting the coefficients (numbers in front of the radical sign). Implement the suggested action.
5 * root(x ^ 2, 3) is the equivalent expression.
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Animal House Rescue is holding a fundraiser raffle. They sell 2,980 tickets for $1 each for a prize telescope valued at $425. What is the expected gain or loss to a participant purchasing ten tickets?
Answer:
Gain: $415
Loss: $10
Step-by-step explanation:
money earned - money spent = gain/loss
The gain is when the participant wins the telescope:
telescope = $425 ==> money earned
10 tickets * $1 = $10 for tickets ==> money spent
$425 - $10 = $415
Loss is when the participant doesn't get the telescope:
$0 ==> money earned (No money earned)
10 tickets * $1 = $10 for tickets ==> money spent
$0 - $10 = -$10 gained
-$10 gained ==> $10 lost
Cherri brought $2,100 computer on an installment plan. She made a $400 down payment, and she has to make a monthly payment for $79. 50 for the next two years. How much interst will she pay
If Cherri brought $2100 computer on an installment plan and made $400 down payment and monthly payment for $79. 50 for the next two years, then the interest amount is $208 .
the cost of the computer is = $2100 ;
the amount paid as down payment is = $400 ;
the amount that will be paid in monthly installment is = $79.50 ;
the time for the loan is = 24 months ;
So , the amount paid as installment is 24 months is = [tex]24 \times79.50[/tex]
= $1908 .
So , the total amount paid by Cherri with installment plan is = [tex]\$1908+\$400[/tex]
= $2308 .
So , the interest amount paid is = [tex]\$2308-\$2100[/tex]
= $208 .
Therefore , Cherri will pay $208 as interest .
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A test has a mean of 75 with a standard deviation of 5. Which of the following scores is within one standard deviation of the mean
The score interval that is within one standard deviation of the mean is
(70 , 80).
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.
Some of the properties of the standard deviation are:
1. It cannot be negative
2. It is only employed to calculate the spread or dispersion around a data set's mean
3. It displays the degree of deviation from the mean value
4. The larger the spread, the more standard deviation, with data of about the same mean.
Given,
The mean of the test μ = 75
The standard deviation σ = 5
We are asked to find the scores within one standard deviation of the mean.
This means that the scores should be in the interval ( μ - σ , μ + σ )
μ - σ = 75 - 5 =70
μ + σ = 75 + 5 = 80
Therefore the scores should be in the interval = ( 70,80), which is within one standard deviation of the mean.
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What is a 2 step equation that equals to 14
Answer:
2x + 1 = 29
Step-by-step explanation:
There are a lot of answers.
2x + 1 = 29
2x + 1 = 29 Subtract 1 from both sides
2x = 28 Divide both sides by s
x = 14
Start off knowing that x will be 14, then multiply 14 by some number and then add or subtract some number from that and put that on the other side of the equal sign.
x = 14
14 x 2 = 28 and then add 1 to that to get 29
2x + 1 = 29
Answer: Do you want x=14 or for it to equal 14, because I have it both ways. For x=14, an acceptable two step equation would be 2x-5=23. If you want it to equal 14, then you can write 5x-1=14
Step-by-step explanation:
For x=14:
2x-5=23
Add 5 on both sides
2x=28
x=14
For the equation to equal 14:
5x-1=14
Add one on both sides
5x=15
x=3
A window is to be built in the shape of a rectangle surmounted by an isosceles
triangle. The area of the window must be 6m2. Use Lagrange Multipliers to find
the width and height of the rectangle for which the perimeter of the window will be
as small as possible. (Clarications: (1) A rectangle surmounted by a triangle has
the shape of a stick drawing of a house as might be drawn by a child, a rectangle
with a triangle on top. (2) The window's perimeter is made up of three sides of
the rectangle and the two equal length sides of the triangle. Draw a diagram! (3)
This may require some industrial strength algebra!)
The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).
What is the Lagrange multiplier?
The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.
To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.
Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.
The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))
The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6
The Lagrange equation is
L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)
To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:
∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0
∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0
∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0
Solving these equations simultaneously will give us the critical points of the function.
We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))
We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)
Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).
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How do you solve a 2 step equation 7th grade?
The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .
What is a Two Step Equation ?
The Two Step Equation can be defined as the equations that can be solved exactly within two steps.
When solving the two step equation, we have to perform the operation on both sides of equals to sign.
To solve the equation we need to perform same operation on both sides of equation.
For Example ⇒ Solve [tex]3x+3=12[/tex] ;
Step1 : we Subtract 3 from both sides to isolate the variable x.
⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]
⇒ [tex]3x = 9[/tex]
Step2 : We Divide both the sides of equation by 3 and solve for x.
⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]
⇒ [tex]x = 3[/tex] ;
Therefore , the given equation is solved in two steps .
The given question is incomplete , the complete question is
How do you solve a 2 step equation ?
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How do you choose which variable to eliminate when doing elimination method?
Choose the variable whose numerical coefficients are smaller or have a smaller common multiple.
What is Elimination Method ?In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
Elimination Method for a System of EquationsPut the two equations in standard form.Alternate the coefficients of one variable.To remove one variable, add the equations produced by Step 2.Find the solution for the last variable.Fill in one of the original equations with the solution from Step 4.Elimination has less steps than substitution. Elimination reduces the possibilities of mistakes as compared to other methods. Elimination is quicker.To learn more about Elimination Method refer to :
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Tell you
Try It!
Write an inequality to represent each situation.
a. Harry is taller than 60 inches.
b. Sherry is not 4 years old.
c. Hank has at least $7. 50.
The inequality to represent each situation is Harry > 60 inches, Sherry ≠ 4 years, and Hank ≥ $7.50.
a) Harry: This inequality states that Harry is taller than 60 inches. This is likely referring to Harry's height, as most people measure height in inches. This inequality can also be written as Harry ≥ 60 inches, emphasizing that Harry is at least 60 inches tall.
b) Sherry: This inequality states that Sherry is not equal to 4 years. This could be referring to Sherry's age, as it is common to measure age in years. This inequality can also be written as Sherry ≠ 4 years, emphasizing that Sherry is not exactly 4 years old.
c) Hank: This inequality states that Hank is greater than or equal to $7.50. This is likely referring to Hank's amount of money, as it is common to measure money in dollars. This inequality can also be written as Hank ≥ $7.50, emphasizing that Hank has at least $7.50.
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Jean Junction is selling jeans at 15% off the regular price the regular price is $25 per pair what is the discount amount
Answer:
15% off means take $3.75 off the regular price
Step-by-step explanation:
$25(0.15) = $3.75
$25 - $3.75 = $21.75 sale price
24,000 at 5 5% for 5 years
Answer:660,000
Step-by-step explanation:
principle= 24,000
rate=5.5%
time = 5years
simple interest= P×R×T
. =24000×5.5×5
. = 660,000
Do isosceles triangles have 3 congruent angles?
Yes, isosceles triangles have three congruent angles.
An isosceles triangle is a triangle with at least two congruent sides and two congruent angles. The two congruent sides and two congruent angles form an isosceles triangle. The two congruent angles are known as the base angles, and they are opposite to the two congruent sides. The third angle in an isosceles triangle must also be congruent to the two base angles in order for the triangle to be true. This is because the angles of a triangle must always sum up to 180 degrees. Therefore, isosceles triangles have three congruent angles. These angles are all equal in measure and have the same shape. The angles of each isosceles triangle can be different from other isosceles triangles, but the angles are still congruent to each other. Therefore, isosceles triangles have three congruent angles.
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a form of reasoning called is the process of forming general ideas and rules based on your experiences and observation
A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.
What is the Induction?The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.
The action or process of inducting someone to a position or organization.
We have given that,
A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.
As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.
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find the length of side xx in simplest radical form with a rational denominator.
For given right triangle, the length of hypotenuse x = 4/√3
Here we have been given a 30° - 60°- 90° right triangle.
A side opposie to angle 60 degrees measures 2 units.
And x is the hypotenuse of right tirnagle.
To find the value of x, consider sine of angle 60 degrees.
sin(60°) = (opposite side of angle 60°) / hypotenuse
From tirgonometric table, sin(60°) = √3 / 2
So, above equation becomes,
√3/ 2 = 2/x
x = 2 × (2/√3)
x = 4/√3
We can see that the value of x is in in simplest radical form with a rational denominator.
Therefore, x = 4/√3
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Simplify: [tex]\frac{32a^2bc^3}{20abc}[/tex]
The fractions is simplified to 8ac²/ 5
What is a fraction?A fraction can be described as the part of a whole element, number or variable.
There are different types of fractions, which includes;
Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractionsExamples of improper fractions; 5/3, 7/5
Examples of proper fractions; 3/4, 5/6
Examples of mixed fractions; 3 1/2, 4 5/6
Examples of simple fractions; 1/2 , 1/ 4
From the information given, we have that;
[tex]\frac{32a^2bc^3}{20abc}[/tex]
This is simplified to;
32 × a × a × b × c × c × c/ 20 × a × b × c
Divide the common terms
8ac²/ 5
Hence, the fractions is 8ac²/ 5
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at the age of 7, john is one of the tallest kids in his class. John is just a few inches shorter than his older brother Matthew, who, at the age of 12 is one of the shortest kids in his class
In the given case, Matthew would have a negative z score and John would have a positive z score.
A z-score is a measurement of how far an observation or data point is from the distribution's mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative. Therefore, it is possible that John's z-score would be positive, showing that he is taller than the average for his age group if he is one of the tallest children in his class at the age of 7.
In contrast, if 12-year-old Matthew is among the smallest students in his class, it is likely that his z-score will be negative, suggesting that he is shorter than the norm for his age group. Therefore, John would have a positive z-score but Matthew would have a negative one if he is shorter than average for his age group.
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The area of the triangle is no more than 30 square inches. Right and solve inequality that represents a.
(HELP ASAP!)
The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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A bacteria population has been doubling each day for the last 5 days. It is currently 100,000. What was the bacterial population 5 days ago?
It becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.
Logarithms arise in problems of exponential growth
and decay because they are inverses of exponential functions. Because of the Laws of Logarithms, they also turn out to be useful in the measurement of the loudness of sounds, the intensity of earthquakes, and other processes that occur in nature
We can write an exponential function to represent the situation.
We know that the current population is 100,000.
The population doubles each day.
The standard exponential function is given by P(t) = A (2)^t
Since our current population is 100,000, a = 100000.
Since our rate is doubling, r = 2.
So
P(t) = 100000 (2)^t
We want to find the population five days ago.
So, we can say that t = -5. The negative represent the number of days that has passed.
Therefore
P(-5) = 100000 (2)^-5 =100000*(1/32) =3125
However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.
We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:
P(t) = A (2)^t
After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:
100000 =A[tex]2^5[/tex]
And solving for A, we acquire :[tex]\frac{100000}{2^5}[/tex]
=3125
So, our function in terms of the original day is:
P(t) = 3125 (2)^t
So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.
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What is the number of terms in the expansion of 2x 3y 2 )( 2x 3y 2 2?
The number of terms in the expansion of [tex](2x^3y^2)(2x^2y^3)[/tex] is 12.
When expanding the product of two polynomials, the number of terms in the expansion is equal to the product of the number of terms in each polynomial. In this case, the first polynomial has 1 term (2x^3y^2) and the second polynomial has 1 term (2x^2y^3), so the number of terms in the expansion will be 1*1=1.
A polynomial function is one in which the variable's non-negative integer powers or positive integer exponents are the only parts of the equation. Examples of polynomial functions include quadratic, cubic, and other equations. An example of a polynomial with an exponent of 1 is 2x+5.
However, the expression provided is not a polynomial, it is a number.
[tex]2x^3y^2 * 2x^2y^3 = 4x^5y^5[/tex]
It is just one term.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 25, 150, 900, ... Find the 9th term.
Answer:80
Step-by-step explanation:by5 will be this and 20 by 10 mulltiply 60 by 9
5 mop and 7 broom cot a total of $855. 0. A mop cot $15. 00 more than a broom. Find the cot of:
a) 1 mop
b) 1 broom
pleae how working
the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
What is the system of equations?
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.
To find the cost of a mop and a broom, we can set up a system of equations using the information given:
Let x be the cost of a broom
Let y be the cost of a mop (which is $15 more than a broom)
From the problem, we know that:
y = x + 15 (since a mop costs $15 more than a broom)
5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)
We can substitute the first equation into the second equation:
5x + 7(x + 15) = 855
5x + 7x + 105 = 855
12x = 750
x = 62.5
Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
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Which bag of potatoes is the better deal?
Answer:
5 kg.
Step-by-step explanation:
2 kg for $0.96 is more expensive than 5 kg for $1.95
The depth of water in a tank oscillates sinusoidally once every
8 hours. If the smallest depth is 6. 6 feet and the largest
depth is 9. 4 feet, find a possible formula for the depth in terms
of time t in hours. Assume that at t=0 the water level is at
the average of the depth and is rising.
.
The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
To learn more about Sinusoidally function , refer:
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