HELP PLS I NEED THIS TODAY
What are the similarities and differences between number 1 and 3?
What are the similarities and differences do you see between 3 and 4
For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #3 is continuous
WILL GIVE BRAIN
Answers
The correct responses for the arithmetic and exponential sequence and function are;
1. First part; 32 pennies
Second part; Approximately 50 days
2. 24.6 gallons
3,738.5 minutes
3. $67.2
Approximately 24 months
4. 1106.14 gallons
66.56 minutes
The difference is 1 is an arithmetic sequence while 3 is an exponential function
What is a an arithmetic sequence?An arithmetic sequence is a group of numbers in which the difference between subsequent terms is a constant
1. The given parameters are;
The initial amount Savannah placed in the piggy bank = 5 pennies
The amount given to Savannah each day = 3 pennies
Required;
First part;
The amount Savannah will have after 10 days
Solution;
The mathematical model for the situation is an arithmetic sequence or progression
The equation for an arithmetic progression is;
[tex]a_n = a_1 + (n - 1) \times d[/tex]
Where;
[tex]a_n[/tex] = The amount after n days
[tex]a_1 [/tex] = The first amount Savannah placed in the piggy bank = 5 pennies
n = The number of days
d = The common difference between the amount present in consecutive days = 3 pennies
The amount after 10 days is therefore;
[tex]a_{10} = 5 + (10 - 1) \times 3=32[/tex]
The money after 10 days is 32 pennies
Second part;
The number of days it would take for there to be $1.50 in the piggy bank.
Solution;
100 pennies = $1.00
Therefore;
$1.50 = 150 pennies
Which gives;
150 = 5 + (n - 1) × 3
(n - 1) × 3 = 150 - 5 = 145
(n - 1) × 3 = 145
n - 1 = 145 ÷ 3
n = 145 ÷ 3 + 1 ≈ 49.3 ≈ 50
It will take approximately 50 days for the amount in the piggy bank to be $1.50
2. The volume of the pool = 1,500 gallons
The initial amount of water in the pool = 5 gallons
The rate at which water enters the pool = 2 gallons in 5 minutes
Required;
First part
The volume of water in the pool after 50 minutes
Solution;
2 gallons in 5 minutes = (2/5) gallons/minute = 0.4 gallons/minute
Therefore;
[tex]a_{50} = 5 + (50 - 1) \times 0.4 =24.6[/tex]
After 50 minutes, 24.6 gallons will be in the pool
Second part;
The time it will take to fill the pool is given by the equation;
[tex]1500 = 5 + (n - 1) \times 0.4[/tex]
number
Which gives;
n = 3738.5
It will take 3,738.5 minutes to fill the pool
3. The formula for finding the amount in the account is the compound interest formula;
[tex]\displaystyle{A = P\cdot (1 + r)^n }[/tex]
Where;
A = The amount in the account after n months
P = The initial amount in the account = $50.0
r = The interest rate = 3.0%
n = The number of periods (months)
After 10 months, we have;
[tex]\displaystyle{A = 50 \times (1 + 0.03)^{10} \approx 67.2 }[/tex]
The amount in the account after 10 months is therefore, approximately $67.2
Second part;
Double the initial amount is 2×$50 = $100
Which gives;
[tex]100 = \displaystyle{50 \times (1 + 0.03)^{n} \approx 67.2 } [/tex]
Which gives;
n ≈ 23.45
Therefore it will take approximately 23.45 months or approximately 24 months for the amount to double
4. Using the exponential function formula, we have;
Number of 5 minutes in 50 minutes = 10
[tex] \displaystyle{1500 \times (1 - 0.03)^{10} \approx 1106.14} [/tex]
The water remaining after 50 minutes is approximately 1106.14 gallons
The time it takes for there to be less than 1,000 gallons in the pool is given as follows;
[tex] \displaystyle{ 1000= 1500 \times (1 - 0.03)^{n}} [/tex]
Which gives;
n = 13.3
Therefore;
The water in the pool will be less than 1000 gallons after 13.3, 5 minute periods or 13.3 × 5 minutes≈ 66.56 minutes
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Related Questions
Suppose that kellogg believes that the average weight for a box of frosted flakes is 18 ounces. As part of a quality control effort, they sample 30 boxes and find that the mean of those 30 boxes is 18. 2 ounces. Historical records show that the standard deviation of the filling process is 0. 32 ounces. How likely is it for the sample mean to have been 18. 2 ounces or larger if the actual mean is 18 ounces and the standard deviation of the filling process is 0. 32 ounces? round your answer to four decimal places.
Answers
If the actual mean is 18 ounces, there is a 0.0003 chance that the sample mean was 18.2 ounces or more.
Given that 18 ounces are what Kellogg estimates to be the typical weight of a box of Frosted Flaked. The average weight of the 30 cartons they sampled was 18.2 ounces. According to past data, the filling procedure's standard deviation is 0.32 ounces.
Let Y be a box weights random variable.
μ = 18 ounces
SD = 0.32 ounces
The sample size and mean are provided as,
Sample size (n) = 30
Sample mean (y) = 18.2
Y then follows roughly the standard deviation N(μ = 18, SD = 0.32)
Z score appears as:
[tex]z = \frac{\sqrt{n}(y-u)} {SD}[/tex]
where z is a normal standard variable having a mean of 0 and a standard deviation of 1.
Since sample size n is 30 and the standard deviation is given. y follows approximately Normal distribution
If the actual mean is 18 ounces, the likelihood that the sample mean will have been 18.2 ounces or more is given as,
[tex]P[Y \geq 18.2] = P [\frac{\sqrt{n(y - u)} }{SD} \geq \frac{\sqrt{30}(18.2- 18) }{0.32}\\ \\ =P [z\geq \frac{\sqrt{30}* 0.2 }{0.32}]\\ \\= P [z\geq \frac{1.0954}{0.32}]\\ \\=P [z\geq 3.4233]\\\\= 0.0003[/tex]
Therefore, if the actual mean is 18 ounces, there is a 0.0003 chance that the sample mean was 18.2 ounces or more.
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3. Consider drawing a hand of five cards. What is the probability that:
a. The first card is a king.
Answers
The probability that the first card is a king is 0.08.
Which is probability?
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics. The likelihood that something will occur is essentially what is meant by probability. This is the fundamental theory of probability, which is also used to calculate the probability distribution, and it is from it that you will discover the likelihood of various outcomes in a random experiment.
A deck of cards contains 52 cards.
Sample space = 52
there are 4 kings in a deck of cards.
Therefore the probability that the first card is a king = 4/52
=0.0769 approximately = 0.08
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A given line passes through the points
(
−
2
,
15
)
and
(
6
,
−
5
)
. What is the equation of a line that is perpendicular to the given line that passes through the point
(
5
,
−
5
)
? Write your answer in slope-intercept form.
Answers
Answer:
hggssssssssssssssssssss
PLEASE HELP i only have 20 points...
Answers
Answer:
I would say corresponding angles are converse
Step-by-step explanation:
I'm not that sure though, but I'm looking at my notes and it's kind of similar to the fact that it's corresponding
PLEASE HELP ME ASAP
Answers
Answer:
C is the correct graph.
Step-by-step explanation:
Since (0, 0) satisfies the inequality, we draw a dashed line and then shade in the region that has the origin.
Estimate the quotient of 35 ÷ 0.7.
3.5
5
50
70
Answers
Answer:
your answer would be 50.
Step-by-step explanation:
Answer: 3.5
Step-by-step explanation: 0.7 rounds to 10, and 35 divided by 10 is 3.5
Please help and thanks!!! :))
Answers
Step-by-step explanation:
the same scale factor has to apply to all sides.
we see for the left vertical side that for C it is 3 units long, for D it is 2 units long.
so, the scale factor is
3/2 = 1.5
to go from D to C we have to multiply all lengths by 1.5.
Directions: Solve each problem. Show all of your work.
1) Maribel has seven piles of three slices of pizza and seven slices left over. Bruno has four
groups of five slices of pizza and two slices left over. Who has more pizza? Write an
expression. Draw a diagram and then solve.
Answers
A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction.
Maribel has :
total slice of pizza left = 3 x7 +7 = 28 slice.
Bruno has :
total slice of pizza left = 4x 5 + 2 = 22 slice.
Since Maribel has More Pizza .
What is a fraction ?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.Fractions are an important foundation for learning more advanced mathematics. As a student's first introduction to abstraction in mathematics, fractions provide the best introduction to algebra in elementary and middle school.To learn more about : Fraction
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Each marble bag sold by alan's marble company contains 6 orange marbles for every 5 yellow marbles. if a bag has 40 yellow marbles, how many orange marbles does it contain?
Answers
Answer:
48 orange marbles
Step-by-step explanation:
[tex] \frac{6}{5} = \frac{x}{40} [/tex]
[tex]5x = 240[/tex]
[tex]x = 48[/tex]
Solve for k.
2k 3k +4
k=
Answers
Answer:
incomplete question
SOLUTION STEPS
k+2k+3k+4k
Combine k and 2k to get 3k.
3k+3k+4k
Combine 3k and 3k to get 6k.
6k+4k
Combine 6k and 4k to get 10k.
10k
Select the correct answer.
Which expression is equivalent to this polynomial?
4x²²+27
A.(2x + 3√/3i)(2x - 3√/3i)
B.(2x + 9) (2z -3i)
C. (2x + 3√3)²
D.(2x + 3√3)(2x - 3√/3)
Answers
None of the expressions is equivalent to the given polynomial.
What is a polynomial?
A polynomial is a mathematical statement that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminates (also known as variables) and coefficients. Numerous branches of mathematics and science use polynomials. For instance, they are used to define polynomial functions, which show up in contexts ranging from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximation other functions. Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems. In higher mathematics, polynomials are used to build algebraic varieties and polynomial rings, two fundamental ideas in algebra and algebraic geometry.
None of the given expressions is equivalent to the given polynomial.
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I need help pleaseee
Answers
Answer: Degree of Polynomial: 12
Step-by-step explanation:
To determine the degree, you add the exponents for each term and find the highest sum.
Between 11 (9+2), 2, and 12 (8+1+3), 12 is highest.
Is -24.5 bigger than 26
Answers
Answer:
89
Step-by-step explanation:
Answer:
NO
Step-by-step explanation:
is having -$50 bigger than having $50??
Roxanne claims that all linear equations represent proportional relationships. Which statement explains whether Roxanne is correct?
A Yes, because all linear equations have graphs that are straight lines.
B No, because not all linear equations have graphs that pass through the origin.
C Yes, because all proportional relationships can be expressed as linear equations.
D No, because not all proportional relationships can be expressed as linear equations.
Answers
Roxanne claims that all linear equations represent proportional relationships. So, this statement "Yes, because all linear equations have graphs that are straight lines." makes him correct.
When there is a proportionate relationship between two variables, the other variable changes at a consistent pace regardless of how the first variable changes, grows or shrinks. A constant ratio between the two variables can be thought of as the constant rate.
Equations, graphs, and tables that use proportions can be used to show proportional relationships. A broad structure is followed by the proportional relationship equation, which will be taught in this session. Straight lines are used to illustrate the graphs. The tables are sets of numbers that are always paired in the same ratio.
Hence the correct option is A
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40 POINTS
The table shows the distance, y, a greyhound dog can travel (in feet) in x seconds.
Time, x (seconds) Distance, y (feet)
0 0
5 220
10 440
15 660
Based on the information in the table, which equation can be used to represent the relationship between time and the distance a greyhound dog can travel?
Answers
The equation that can be used to represent the proportional relationship between time and the distance a greyhound dog can travel is:
y = 44x.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality, as follows:
y = kx.
In which k is the constant of proportionality, also representing the rate between the output and the input for any pair of (input, output) except (0,0).
From the table of distances and time given in this problem, the constant is found as follows:
k = 220/5 = 440/10 = 660/15 = 44.
Hence the constant is of 44 and the relation is given by:
y = 44x.
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Order the values from least to greatest:
9/4 , 160%, 1.8, 16/5 , 220%, and 2.1
Answers
The values from the least to greatest is 160%, 1.8, 2.1, 220%, 16/5 .
In the question ,
it is given that
the values 9/4 , 160%, 1.8, 16/5 , 220%, and 2.1
to arrange the values , we first need to simplify all the values .
(i) the value 9/4 = 2.25
(ii) 160% = 160/100 = 1.60
(iii)the value 1.80
(iv) Simplifying 16/5 , we get 3.20
(v) Simplifying 220% = 220/100 = 2.20
(vi) the value 2.10
the least value is 1.60 which is 160%.
the greatest value is 3.20 which is 16/5 .
Therefore ,the values from the least to greatest is 160%,1.8,2.1,220%,16/5 .
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dang this hard, i need some help
Answers
Hello!
Part (A)
[tex]\text{Mean} = \dfrac{\text{sum of all salaries}}{\text{number of workers}} =\dfrac{13500 + 27500+13750 + 79000+ 19250 + 29000+21000}{7} \\\\\text{Mean}= 29000 \text{ dollars}[/tex]
Part (B)
==> The mean of other six worker's salary
[tex]\text{Mean}= \dfrac{\text{sum of the 6 worker's salary}}{\text{number of workers} }=\dfrac{13500+27500+13750+19250+29000 + 21000}{6} \\\\ \text{Mean}= \dfrac{124000}{6}=20,666.67 \text{ dollars}[/tex]
Hope that helps!
Find the distance between two numbers on a number line. Write your answer as a decimal-2.2,8.4 the distance between two numbers is
Answers
The distance between these two numbers on a number line is equal to -10.6.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
In Mathematics, a number line can be used to determine the difference between two numbers such as -2.2 and 8.4. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
Now, we can determine the distance by taking the difference between both values as follows:
Distance = -2.2 - 8.4
Distance = -10.6.
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What is 80000*60/70[64+87)/6
Answers
Answer: 1725714.28571
Answer:
12080000/7 or 1725714.28571
Step-by-step explanation:
The sum of the first 333 terms of a geometric series is 171171171 and the common ratio is \dfrac23
3
2
start fraction, 2, divided by, 3, end fraction.
What is the first term of the series?
Answers
The first term of the geometric progression will be 81.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.
Given that the common ratio of the geometric series is ( 2 / 3 ) and the sum of the first four terms is 171.
The first term of the geometric series will be calculated as:-
[tex]S_n = a_1\dfrac{(r^n-1)}{r-1}[/tex]
[tex]171 = a_1\dfrac{(\dfrac{2}{3}^3-1)}{\dfrac{2}{3}-1}[/tex]
a₁ = ( 171 x 9 ) / 19
a₁ = 9 x 9
a₁ = 81
Therefore, the first term of the geometric progression will be 81.
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The distance between Town A and Town
B on a map is 15.6 cm. If the scale is 1 cm =
12 miles, what is the actual distance
between towns?
Answers
Answer:
187.2
Step-by-step explanation:
if the scale is 1:12 then you would need to multiply 12 by the 15.6 which gets you 187.2 miles.
the quotient of 9660 and 460
Answers
Answer:
21-- 9660 / 460 = 21
Answer:
9660/460 = 21
Step-by-step explanation:
find the image of the point A(2,3) rotating about the point (0,0) through plus 90 degree
Answers
Answer:
3,-2
Step-by-step explanation:
3,-2
What is 10+10? I’ll give brainliest
Answers
Answer:
Step-by-step explanation:
20
Determine if the given lines are parallel, perpendicular or neither. line a: 6x - 12y = -24 line b: 3y = 2x + 18
Answers
Answer: n = 1/2; m = 2/3
Step-by-step explanation:
A ⇒ 12 y = 6x + 24
[tex]y=\frac{n}{2}+2[/tex]
[tex]n=\frac{1}{2}[/tex]
B ⇒ 3y = 2x + 18
[tex]y=\frac{2}{3}n+6[/tex]
[tex]m=\frac{2}{3}[/tex]
∴ Lines are neither because slop diff.
Which of the following is equivalent to 57x + 19y + 5x?
57x + 24xy
57x + 5x + 19y
57x(19y + 5x)
5x(57x + 19y)
HELP PLS ASAP
Answers
Answer:
57x + 5x + 19y by the commutative property for addition.
For f(x) = √x and g(x) = x + 9, find the following functions.
a. (f o g)(x) =
(Simplify your answer.)
b. (g o f)(x) =
(Simplify your answer.)
c. (f o g)(7) =
(Simplify your answer.)
d. (g o f)(7) =
(Simplify your answer.)
Show your work below.
Answers
Part a
[tex](f \circ g)(x)=f(g(x))=\sqrt{x+9}[/tex]
Part b
[tex](g \circ f)(x)=g(f(x))=\sqrt{x}+9[/tex]
Part c
[tex](f \circ g)(7)=\sqrt{7+9}=4[/tex]
Part d
[tex](g \circ f)(7)=\sqrt{7}+9[/tex]
Write an algebraic expression for the word phrase.
4 less than the product of y and 12
a) 12y + 4
b) 4 − 12y
c) 12y − 4
d) 12y − 4y
Answers
Answer:
c
Step-by-step explanation:
the product (multiply ) of y and 12 is 12y and 4 less than 12y is
12y - 4
Answer:
12y - 4.
Step-by-step explanation:
The product is 12y and we subtract 4 from it.
A principle of $1500 is invested at 7.25% interest compounded annually how much will the investment be worth at five years
Answers
Answer: $2128.52
Step-by-step explanation:
[tex]1500(1+.0725)^{5}[/tex]
An architect is building a model for her project propasal. In the model 3 cm equals 20 ft. If the length of the model is 61 cm how long will the building be?round if nessasary.
Answers
Answer: 406.67 ft
Step-by-step explanation:
(20x60)/3
1220/3
= about 406.66667
= 406.67