Answer:
144x^3+9
Step-by-step explanation:
First of all multiply 8x^2 and 18x then it is 144
danny is 22 year old. this is 6 year yonger than his sister terry write an equation that shows the relationship between the age of danny and terry. how old is terry
The equation that shows the relationship between the age of Danny and Terry is D = T - 6.
Let's represent Danny's age with the variable D and Terry's age with the variable T. We know that Danny is 22 years old, so we can write the equation D = 22.
We also know that Danny is 6 years younger than Terry, so we can write the equation D = T - 6. Now we can substitute the value of D from the first equation into the second equation to find the value of T.
D = T - 6
22 = T - 6
Add 6 to both sides of the equation:
22 + 6 = T
28 = T
So Terry is 28 years old.
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Info Sheet Math Definition
Power –
Base –
Exponent –
Coefficient –
Exponential Form –
Expanded Form –
Standard Form –
Exponent Laws –
Answer:
Power – A power is an expression that represents repeated multiplication of the same number or variable, such as a raised to the power of n, denoted by aⁿ.
Base – The base is the number or variable that is raised to a power or exponent in a power expression.
Exponent – The exponent is the number that indicates how many times the base is to be multiplied by itself in a power expression.
Coefficient – The coefficient is the numerical factor of a term that contains a variable in an algebraic expression.
Exponential Form – The exponential form is a way of writing a number using a base and an exponent, such as aⁿ, where a is the base and n is the exponent.
Expanded Form – The expanded form is a way of writing an expression as the sum or difference of its individual terms, such as (a+b)² = a² + 2ab + b².
Standard Form – The standard form is a way of writing a number using digits, such as 1234 or 1.234 x 10³.
Exponent Laws – The exponent laws are a set of rules that describe how exponents can be manipulated in algebraic expressions, including the product law, quotient law, power law, and negative exponent law. These laws help simplify and solve equations involving exponents.
Kathy saves $1 on the first day, $2 on the second day, $3 on the third day and so on,
saving an extra $1 on each subsequent day. On which day will she have $300 or more in total?
Answer:
Day 24 will be the day she'll reach $300
Step-by-step explanation:
Answer20th
Step-by-step explanation:
1) What is the period of the following trigonometric functions? a) ( f(x)=sin x) b)( f(x)=cos x) c) ( f(x)=tan x ) d) ( f(x)=sec x ) e)( f(x)=csc x ) f) ( f(x)=cot x
The periods of the given trigonometric functions are (a) 2π (b) 2π (c) π (d) 2π (e) 2π and (f) π.
The period of a trigonometric function is the smallest positive value of x for which the function repeats its values. In other words, it is the length of one complete cycle of the function. The period of the basic trigonometric functions are as follows:
a) The period of f(x)=sin x is 2π.
b) The period of f(x)=cos x is 2π.
c) The period of f(x)=tan x is π.
d) The period of f(x)=sec x is 2π.
e) The period of f(x)=csc x is 2π.
f) The period of f(x)=cot x is π.
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9. Verify that each equation is an identity. a. sin 2x = 2 tan x / 1 + tan^2 x b. tan x + cot x = 2 csc 2x
a) Sin 2x = 2 tan x / 1 + tan^2 x is an identity.
b) Tan x + cot x = 2 csc 2x is an identity.
To verify that each equation is an identity, we will simplify both sides of the equation and show that they are equal.
For part a, we will use the double angle formula for sine and the Pythagorean identity.
sin 2x = 2 sin x cos x
2 tan x / 1 + tan^2 x = 2 sin x / cos x / 1 + sin^2 x / cos^2 x
= 2 sin x / cos x / cos^2 x / cos^2 x
= 2 sin x / cos x / 1 - sin^2 x
= 2 sin x / cos x / cos^2 x
= 2 sin x cos x
Therefore, sin 2x = 2 tan x / 1 + tan^2 x is an identity.
For part b, we will use the definitions of the trigonometric functions and the double angle formula for cosecant.
tan x + cot x = sin x / cos x + cos x / sin x
= (sin^2 x + cos^2 x) / (sin x cos x)
= 1 / (sin x cos x)
= 2 / (2 sin x cos x)
= 2 / sin 2x
= 2 csc 2x
Therefore, tan x + cot x = 2 csc 2x is an identity.
In conclusion, we have verified that both equations are identities.
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T-1.3 Let W be the subspace with dimension of n-1 within vector space V. Prove that there exists a basis in vector space V (denote as S), will satisfy the condition of SO W = 0.
The proof is complete.
To prove that there exists a basis in vector space V that satisfies the condition of $W = \{0\}$, we will use the dimension theorem. The dimension theorem states that if $V$ is an $n$-dimensional vector space, then any subspace of $V$ has a dimension that is less than or equal to $n$. In this case, the given subspace $W$ has a dimension of $n-1$ and so it must be a subspace of $V$. Since the dimension of $W$ is less than the dimension of $V$, the dimension theorem states that there exists a basis in $V$ that satisfies the condition of $W = \{0\}$. Therefore, the proof is complete.
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Austin purchased a new laptop in 2018 for $1875. The laptop decreases in 7pm
value by 30% each year. What is the value of the laptop in 2022? Round to
the nearest whole dollar.
Answer:
There would be no value to the laptop. If you’re looking for the actual value, it would be worth $-375.
Step-by-step explanation:
Month Sales
Jan 34
Feb 36
Mar 39
Apr 37
May 38
June
Using exponential smoothing, with an alpha value of 0.2 and assuming the forecast for Jan is 34, what is the forecast for June?
a. 37.5
b. 36.1
c. 35.6
d. 32.4
What is the MAD value for the two-month moving average?
a. 2.67
b. 3.0
c. 4.5
d. 1.
1- The forecast for June using exponential smoothing with an alpha value of 0.2 and assuming the forecast for Jan is 34 is B. 36.1.
2- The MAD value for the two-month moving average is A. 2.67.
1- The forecast for June using exponential smoothing can be calculated as follows:
Ft = Ft-1 + α(At-1 - Ft-1)
Where Ft is the forecast for the current period, Ft-1 is the forecast for the previous period, At-1 is the actual sales for the previous period, and α is the smoothing constant.
Using the given data and an alpha value of 0.2, the forecast for June can be calculated as follows:
FJan = 34
FFeb = 34 + 0.2(34 - 34) = 34
FMar = 34 + 0.2(36 - 34) = 34.4
FApr = 34.4 + 0.2(39 - 34.4) = 35.32
FMay = 35.32 + 0.2(37 - 35.32) = 35.66
FJune = 35.66 + 0.2(38 - 35.66) = 35.87
Therefore, the forecast for June is 35.87, which is closest to option b. 36.1.
2- The MAD value for the two-month moving average can be calculated as follows:
MAD = (|34 - 35| + |36 - 34.5| + |39 - 35.5| + |37 - 37.5| + |38 - 38|) / 5 = 2.67
Therefore, the MAD value for the two-month moving average is 2.67, which is closest to option a. 2.67.
So the correct answers are B: 36.1 for the forecast for June and A: 2.67 for the MAD value for the two-month moving average.
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An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 406 ft and a distance of 891 ft from the building. What is the angle of depression from the plane to the building?
The building's depression angle relative to the plane is found as 24.49°.
Explain about the Line of Sight?The straight path an observer's eyes take to view an item is known as the line of sight. The light that bounces off an item must travel along the line of sight to the eyes in order to be seen.According to an aerial photographer who specializes in taking pictures of real estate properties.
The ideal shot should be taken at a height of around 406 feet and a distance of 891 feet from the structure.
Height h = 406 ft
Distance d =891 ft
The building's depression angle relative to the plane:
tan Ф = Height / Distance
tan Ф = 406 / 891
tan Ф = 0.455
Ф = 24.49°
Thus, the building's depression angle relative to the plane is found as 24.49°.
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What is the value of x?
Answer:
x = 106 degrees
Step-by-step explanation:
we can create a triangle with angles x, 30, and 26+18.
that means x + 30 + (26 + 18) = 180.
move the constants to one side to get x = 180 - 30 - (26 + 18) = 106
At 3pm the shadow of a lighthouse is 22 feet long. If the angle elevation with the ground is 77 degree. What is the height of the lighthouse. Round to the nearest tenth
Height of the light house is 95.6 feet .
What is trigonometric ratio?In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.
Given,
Shadow of the lighthouse = 22 feet
Angle of elevation α = 77°
Height of the light house = ?
tanα = Perpendicular/base
In this case
tanα = Height/Shadow
tan 77° = Height/22
4.33 = Height/22
Height = 22 × 4.33
Height = 95.26 ≈ 95.6 feet
Hence, 95.6 feet is height of the light house.
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How much was the initial length of the baby at birth
Answer:
19-21 inches.
Step-by-step explanation:
The average term infant's length at birth is between 19-21 inches. As would be expected, taller parents tend to produce longer neonates. At the end of their first month, most infants have increased their length by approximately 1 inch.
The quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs. The quotient of any integers (with a nonzero divisor) will be a rational number
It is true that the quotient of two integers will always result in a rational numbers, as the quotient of two integers is in fact a fraction.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by a ratio of two integers, which is in fact a fraction, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating. Examples are integers, fractions and mixed numbers.Irrational numbers are numbers that cannot be represented by a ratio of two integers, that is, they cannot be represented by fractions. They are non-terminating and non-repeating decimals, such as non-exact square roots.More can be learned about rational and irrational numbers at brainly.com/question/5186493
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I need help pls pls pls pls help quickly.
Answer:
-7/8
Step-by-step explanation:
The two coordinates shown are (0,5) and (8,-2).
The slope formula is (y2-y1)/(x2-x1).
Using that, the slope of a line passing through both points is (-2-5)/(8-0).
That reduces to -7/8.
Answer:
-7/
Step-by-step explanation:
G is inversely proportional to the square of a. If a = -3 when g = 9, find two values for a, which will make g equal 25.
If a = -3 when g = 9, the two values for a, which will make g equal 25 will be ± 9/5.
If G is inversely proportional to the square of A, then we can write the relationship as:
G = k/A^2 Where k is a constant.
We can use the given values of A and G to find the value of k:
9 = k/(-3)^2
9 = k/9
k = 81
Now we can use the value of k and the desired value of G to find the values of A:
25 = 81/A^2
A^2 = 81/25
A = ± √(81/25)
A = ± 9/5
So the two values of A that will make G equal 25 are 9/5 and -9/5.
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Which shows how to multiply 2/5×4?
Responses
2×5÷4 you will be rewarded 10 points
2 times 5 divided by 4
2×4÷5
2 times 4 divided by 5
8×2÷5
8 times 2 divided by 5
4×5÷2
Answer:
i believe this is how you solve that problem... 2÷5×4
A box is being pushed up an incline of 58 degrees with a force of 150 N (which is parallel to the incline) and the force of gravity on the box is 40 N (gravity acts straight downward). Find the magnitude of the resultant force ||FR|| and round to two decimal places.
The magnitude of the resultant force ||FR|| is 80.55 N.
The weight of the box is acting straight downward, perpendicular to the incline, so it does not affect the magnitude of the resultant force parallel to the incline. Therefore, we only need to consider the force of 150 N pushing the box up the incline.
Let's call the angle between the force of 150 N and the incline "theta". We can find theta by subtracting 58 degrees from 90 degrees (since the incline is at an angle of 58 degrees with respect to the horizontal). So:
theta = 90 degrees - 58 degrees
theta = 32 degrees
Now we can use trigonometry to find the component of the force of 150 N parallel to the incline. We'll use sine, since we know the hypotenuse (the force) and the opposite side (the component parallel to the incline):
sin(theta) = opposite/hypotenuse
sin(32 degrees) = ||FR||/150 N
Solving for ||FR||, we get:
||FR|| = 150 N * sin(32 degrees)
||FR|| ≈ 80.55 N
Therefore, the magnitude of the resultant force is approximately 80.55 N.
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F. Prime and Maximal Ideals LetAbe a commutative ring with unity, andJan ideal ofA. Prove each of the following:1 A/Jis a commutative ring with unity.2Jis a prime ideal iffA/Jis an integral domain. 3 Every maximal ideal ofAis a prime ideal. (HINT: Use the fact, proved in this chapter, that ifJis a maximal ideal thenA/Jis a field.) 4 IfA/Jis a field, thenJis a maximal ideal. (HINT: See Exercise 12 of Chapter 18.)
J is a maximal ideal.
1. To prove that A/J is a commutative ring with unity, note that the operations of addition and multiplication on A/J are well-defined and are commutative since they are inherited from the commutative ring A. Furthermore, the additive identity of A is the same as the additive identity of A/J, and therefore A/J has a unity.
2. Suppose first that J is a prime ideal of A. Then, if A/J is not an integral domain, there exist two nonzero elements x,y of A/J such that xy=0. This means that x and y are in the same coset of J in A. Thus, x-y is an element of J. Since J is prime, either x or y must be in J, which is a contradiction. Therefore, A/J is an integral domain. Conversely, if A/J is an integral domain, then the same argument can be reversed to show that J is a prime ideal.
3. If J is a maximal ideal of A, then A/J is a field by the fact proved in this chapter. Since a field is an integral domain, J is a prime ideal.
4. Suppose that A/J is a field. Then, for any ideal I of A, either I is contained in J or J is contained in I. This implies that J is a maximal ideal.
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A band expects to put 16 songs on their next CD. The band writes and records 8.75% more songs than they expect to put on the CD. During the editing process, 60% of the songs are removed. How many songs will there be on the final CD?
Answer:
Step-by-step explanation:
Given that, There are 16 songs that are put on the next CD.And there are 8.75 more songs.Also, 60% of the songs are removed. Based on the above information, the calculation is as follows:
16+(0.875 x 16)=17.4
17.4(0.60 x 17.4)= 181.656 = 182 :)
Ryan needs $30,000 for a down payment on a home in 3 years. How much does he need to deposit monthly into an account that pays 5% interest, compounded monthly, to meet his goal?
Ryan needs to make a monthly deposit of $774.08 in order to have $30,000 for a down payment on a home.
How much does he need to deposit monthly to meet his goal?To calculate the monthly deposit that Ryan needs to make in order to have $30,000 in 3 years, we can use the formula for the future value of an annuity:
FV = Pmt * [(1 + r)ⁿ - 1] / r
where FV is the future value (in this case, $30,000),
Pmt is the monthly deposit,
r is the monthly interest rate (5% / 12 = 0.00417), and
n is the number of compounding periods (36 months).
Substituting the values we have:
30,000 = Pmt * [(1 + 0.00417)³⁶ - 1] / 0.00417
38.75564454Pmt = 30,000
Pmt = 30,000/38.75564454
Pmt = $774.08
Therefore, Ryan needs to deposit approximately $774.08 each month in order to have $30,000 for a down payment on a home.
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Multiply and simplify: (4x-3)(-5x^(2)+2x-4) Choose your preferred method and submit the question.
The simplified form of [tex](4x-3)(-5x^(2)+2x-4)[/tex] is: [tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]
To multiply and simplify the given expression [tex](4x-3)(-5x^(2)+2x-4)[/tex], we can use the distributive property. This means we will multiply each term in the first parentheses by each term in the second parentheses and then combine like terms.
First, we will distribute the 4x to each term in the second parentheses:
[tex]4x * (-5x^(2)) = -20x^(3)4x * (2x) = 8x^(2)4x * (-4) = -16x[/tex]
Next, we will distribute the -3 to each term in the second parentheses:
[tex]-3 * (-5x^(2)) = 15x^(2)-3 * (2x) = -6x-3 * (-4) = 12[/tex]
Now we will combine all of the terms:
[tex]-20x^(3) + 8x^(2) - 16x + 15x^(2) - 6x + 12[/tex]
Finally, we will combine like terms:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]
So the simplified expression is:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]
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A second rectangular prism is 2 inches taller than the first.
What is the difference in the volumes of the 2 containers? Show your work.
The difference between the volume of the 2 rectangular prism containers is V = 70 inches³
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
Let the difference between the volume of the rectangular prism be D
Now , the amount of sand poured into the container = 375 inches³
And , the dimensions of the first rectangular container = 5 inches x 7 inches x 9 inches
So , the volume of the first rectangular prism V₁ = 5 x 7 x 9 = 315 inches³
where amount of sand poured into the container > volume of the first rectangular prism
Therefore , the sand cannot be poured into the prism container
b)
The height of the second rectangular container = ( h + 2 ) inches = 11 inches
So , the volume of the second prism container V₂ = 5 x 7 x 11
The volume of the second prism container V₂ = 385 inches³
And , the difference in the volumes of the 2 containers V = V₂ - V₁
On simplifying , we get
The difference between the volume of the 2 rectangular prism containers is V = 385 - 315
The difference between the volume of the 2 rectangular prism containers is V = 70 inches³
c)
The dimensions of the container which contains 375 inches³ of sand is given by V₃ = 5 inches x 5 inches x 15 inches
Hence , the volume of the rectangular prism is solved
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The complete question is :
Jack has 375 in. of sand to pour into a rectangular prism. The base of the prism is 5 inches by 7 inches and the height is 9 inches.Part A
Will the sand fit in the container? Explain why or why not.
Part B
A second rectangular prism is 2 inches taller than the first.
What is the difference in the volumes of the 2 containers? Show your work.
Part C
What are the measurements of a rectangular prism that will hold exactly 375 in. of the sand? Justify your answer.
k as the constant of variation for r varies directly as the square root of n and inversely as the square of y
The constant of variation k for this relationship is 4.
To find the constant of variation k for the given relationship, we can use the formula for direct and inverse variation:
k = (r * y^2) / √n
Where r is the variable that varies directly as the square root of n, and inversely as the square of y. To find the value of k, we can plug in the values of r, y, and n into the equation and solve for k.
For example, if r = 4, y = 2, and n = 16, we can plug these values into the equation to find k:
k = (4 * 2^2) / √16
k = (4 * 4) / 4
k = 16 / 4
k = 4
Therefore, the constant of variation k for this relationship is 4.
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How many times a wheel of 28cm diameter must rotate to go 352m?
(Take π= 22÷7)
A wheel of 28 cm diameter must rotate 400 times to go 352 m.
Let 'r' represents the radius, 'd' represents the diameter of the wheel.
Here, d = 28 cm
So, r = 14 cm
Let us assume that a wheel needs to rotate 'n' number of times.
We know that the formula for the circumference of circle is 2πr
Let 's' represents the circumference of wheel.
Using above formula,
s = 2 × π × r
s = 2 × 22/7 × 14
s = 44 × 2
s = 88 cm
Now we find the value of n.
First we convert the distance 352 m in centimeters.
352 m = 35200 cm
n = 35200 / s
n = 35200/88
n = 400
Therefore, a wheel must rotate 400 times.
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At the movie
theater, 8 tickets
cost $76.00.
How much is
each ticket?
USE A
Answer:
$9.50
Step-by-step explanation:
If there are 8 tickets and they all add up to $76, you have to divide 76 by 8 (the number of tickets)
Mav has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.She buys a new bicycle for $425.05.
She buys 4 bicycle reflectors for $15.19 each and a pair of bike gloves for $15.79.
She plans to spend some or all of the money she has left to buy new biking outfits for $29.20 each.
Write and solve an inequality which can be used to determine
�
o, the number of outfits Mav can purchase while staying within her budget.
Answer:
Inequality:
29.2x + 501.60 ≤ 560
Answer:
She may buy up to 2 reflectors.
Step-by-step explanation:
She can spend up to $560, so the total expense has to be less than or equal to $560.
total expense ≤ 560
All items she buys have a price and a number of items except for the outfits which have a price but an unknown number.
Let x = number of outfits.
total expense = $425.05 + 4 × $15.19 + $15.79 + x × $29.20
total expense = 29.2x + 501.60
Inequality:
29.2x + 501.60 ≤ 560
29.2x ≤ 58.4
x ≤ 2
She may buy up to 2 reflectors.
Find the effective interest rate for the specified
account.
nominal yield, 6.5%; compounded monthly
Question 10 answer options:
0.07%
6.70%
106.70%
0.54%
The effective interest rate for the specified account is 6.70%.
To find the effective interest rate, we can use the following formula:
Effective Interest Rate = (1 + Nominal Yield / Number of Compounding Periods) ^ Number of Compounding Periods - 1
In this case, the nominal yield is 6.5% and the number of compounding periods is 12 (since it is compounded monthly). Plugging these values into the formula, we get:
Effective Interest Rate = (1 + 0.065 / 12) ^ 12 - 1
Effective Interest Rate = (1.0054166666666667) ^ 12 - 1
Effective Interest Rate = 1.0670171619870418 - 1
Effective Interest Rate = 0.0670171619870418
Multiplying by 100 to convert to a percentage, we get:
Effective Interest Rate = 6.70%
Therefore, the effective interest rate for the specified account is 6.70%.
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Comprehensive Pre-Post Assessment Level H User name: 4724jm The total volume of the cubes in a container is 8^(7) cubic centimeters. he volume of each individual cube is 8^(2) cubic centimeters. How many cubes are in the container? Mark all that apply. 5^(8) 8^(7)*8^(-2)
The number of cubes in the container is 8^(5) and the correct answers are 8^(5) and 8^(7)*8^(-2).
The total volume of the cubes in a container is 8^(7) cubic centimetersand the volume of each individual cube is 8^(2) cubic centimeters. To find the number of cubes in the container, we need to divide the total volume by the volume of each individual cube.
This can be written as:
Number of cubes = 8^(7) / 8^(2)
Using the rule of exponents, when we divide two numbers with the same base, we can subtract their exponents. In this case, 7 - 2 = 5.
So the number of cubes in the container is:
Number of cubes = 8^(5)
Therefore, the correct answer is 8^(5).
The other option, 8^(7)*8^(-2), is also correct. This is because multiplying two numbers with the same base means we can add their exponents. In this case, 7 + (-2) = 5. So this also gives us the same answer, 8^(5).
In conclusion, the number of cubes in the container is 8^(5) and the correct answers are 8^(5) and 8^(7)*8^(-2).
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The equation a = 6 000(1 + 0. 028t) represents the amount of money earned on a savings account with 2. 9% annual simple interest
Answer:
See below.
Step-by-step explanation:
This is the correct formula for simple interest, but be careful with the numbers.
a = 6 000(1 + 0. 028t)
0.028 means 2.8% interest rate.
For 2.9% interest rate it should be
a = 6 000(1 + 0. 029t)
What percentage of college students eat the recommended five or more servings of fruits and vegetables a day?5. 4 group of answer choices 17. 3% 10% 9. 3% 5. 4%
Among the answer choices provided, the closest percentage to the actual rate is 9.3%.
For instance, a study published in the Journal of American College Health found that only 11.1% of college students in the United States consumed the recommended five or more servings of fruits and vegetables per day. Similarly, a study published in the Journal of Nutrition Education and Behavior found that only 9.2% of college students in the United States met the daily recommendations for fruit and vegetable intake.
Based on these research studies, it is clear that the percentage of college students who consume the recommended amount of fruits and vegetables daily is quite low, with estimates ranging from 6.8% to 11.1%.
Therefore, among the answer choices provided, the closest percentage to the actual rate is 9.3%.
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