Peggy's method will make more money.
What is compound interest?Compound interest is the sum of interest on principal and interest on interest of previous period.
Given, that principal is same in both cases,
Also, Peggy will get total interest = 2×6 = 12%.
Whereas, Larry will get 1 % per quarter compounded quarterly.
Therefore, Larry will get (101/100)⁸%.
Hence, 12 > (101/100)^8 and Simple interest method will make more money.
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A food truck vendor averages 150 tacos sold when the price per taco is $1. A study shows that the average number of tacos sold will increase by 25 tacos for every $1 that the price per taco is
lowered
Which equation models the food truck's average sales in dollars, S, in terms of the price for taco, x?
A S = 25x + 250
B
S=-25x + 250
C S = x(25x + 250)
D
S = x(-25x + 250)
S = 25x + 250 is the equation models the food truck's average sales in dollars, S, in terms of the price for taco, x.
Define equation.Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.
Given
A food truck vendor averages 150 tacos sold when the price per taco is $1.
A study shows that the average number of tacos sold will increase by 25
tacos for every $1 that the price per taco is lowered.
The calculation needed to determine which equation best represents the food truck's average sales in dollars, s, in terms of the price per taco, x, is as follows:
S = 25x + 250
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Where is Located World of Masha and the Bear?
Answer:
Russia
Step-by-step explanation:
The original language for the show is Russian
Use a ruler and protractor to make an accurate drawing of the triangle below. Measure length x in your drawing to 1 d.p 40 20
Answer:15
Step-by-step explanation:
The seating capacity of the gym at Union Hill is 550. So far, there are 210 fans already at the basketball game. How many more fans can attend the game?
Answer:
340
Step-by-step explanation:
550 - 210 = 340
The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day?
The next time Maria will do both workouts on the same day is 15 days
When next Maria will do both workouts on the same day?Weights = every 3 days Long run = every 5 daysFind the lowest common multiple (LCM) for both weight days and long-run days
3 = 3 , 6, 9, 12, 15, 18, 21
5 = 5, 10, 15, 20, 25, 30
The lowest common multiple (LCM) for both weight days and long-run days is 15
Therefore, Maria will do both workout again in 15 days time.
Complete question:
The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day? Weights every 3 days and long run every 5 days
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pls help due now!!!!!!!!!!!!!!!!
The solution to the following system using substitution is (2,1).
What is system of equations ?
Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
[tex]$$\left[\begin{array}{c}y=-4 x+9 \\y=3 x-5\end{array}\right]$$[/tex]
Substitute y=3 x-5
[3 x-5=-4 x+9]
Isolate x for 3 x-5=-4 x+9: x=2
For y=3 x-5
Substitute x=2
[tex]y=3 \cdot 2-5[/tex]
Simplify
y=1
The solutions to the system of equations are:
y=1, x=2
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an economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in california. he believes that the mean income is $18.6, and the standard deviation is known to be $12.1. how large of a sample would be required in order to estimate the mean per capita income at the 80% level of confidence with an error of at most $0.25? round your answer up to the next integer.
Therefore , large of a sample would be required in order to estimate the mean per capita income will be $3,838.
Test statistics – what are they?You can assess the degree to which the distribution of your data conforms to that predicted underneath the null hypothesis of the statistical test you are just using by utilizing a test statistic. The data distribution, which is determined by the confidence interval and deviation from the central tendency of each observation, represents the frequency of each observation.
Here,
First step is to find z 80% confidence level
At 80% confidence level the z will be:
α/2 = 1 - 80% = 1 - 0.80 = 0.20
α/2= 0.20 / 2 = 0.01
Zα/2= Z0.01= 1.28 from z table
Now let calculate the Sample size using this formula
Sample size = n= [( Z[tex]\alpha[/tex]/2* σ ) / E]^2
Let plug in the formula
n = (1.28*12.1/0.25)^2
n= 3,838.05
n=3,838.(Approximately)
Therefore , large of a sample would be required in order to estimate the mean per capita income will be $3,838.
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kevin opened a savings account with texas national bank. his account has an apr of 1.75% compounded quarterly. if kevin opens his account with $2500, how long will it take for the account to earn $7500?
As per the concept of compound interest, it take 62.915 years for the account to earn $7500
Compound interest:
The general formula to calculate the compound interest is written as,
A = P(1 + r/n)^nt
where
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
n = number of compounding periods per unit of time
t = time in decimal years;
Given,
Compounding frequency = Quarterly
Interest rate = 1.75%
Opening balance = $2500
Final amount = $7500
Now, we have to calculate the time time for the person to achieve the final amount,
First, convert R as a percent to r as a decimal
r = R/100
r = 1.75/100
r = 0.0175 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.0175/4)] )
t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.004375)] )
t = 62.915 years
Therefore, the time required to get a total amount of $7,500.00 with compounded interest on a principal of $2,500.00 at an interest rate of 1.75% per year and compounded 4 times per year is 62.915 years.
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Gonga's health insurance deductible is $5,500. her medical bills for the year total $50,000. How much will she be required to pay out of pocket on her annual medical bills?
42,500
0
5,500
50,000
Answer:
If Gonga's health insurance deductible is $5,500 and her medical bills for the year total $50,000, she will be required to pay the first $5,500 of her medical bills out of pocket.
Step-by-step explanation:
This means that she will be required to pay a total of $5,500 out of pocket on her annual medical bills. After she has paid this amount, her health insurance will cover the remaining costs of her medical bills up to the limit of her policy.
Answer:
$5,500
Step-by-step explanation:
The enrollment for a school in 2010 was 1510 students. In 2020, the enrollment was 860 students. Find and interpret the rate of change in enrollment from 2010 to 2020.
Then the enrollment change rate from 2010 to 2020 is -52.2%.
What is rate of change?A rate of change is the rate at which one quantity changes in relation to another. For example, Change in y = change in x = change in distance = change in time.Here ,
Formulate 860 - 1510 / 1510 based on the given condition.
We have calculate the difference or sum = -650/1245
By converting a fraction to a decimal we get, = -0.52208
we have to multiply a number by its numerator and denominator by 100,
We get,
= -0.52208*100/100
-52.208/100 is the product or quotient.
Hence ,
In 2010, a school had 1510 students enrolled. In 2020, there will be 860 students enrolled. Then the enrollment change rate from 2010 to 2020 is -52.2%.
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Four of the interior angles of a pentagon are 2xº.
The fifth angle is xº.
Work out the value of xº.
Answer:
20°
Step-by-step explanation:
2x°+2x°+2x°+2x°+x°=180°
8x°+x°=180°
180°=9x°
Dbs by 9
x°=20°
A groundskeeper needs
grass seed to cover a circular field, 290 feet in diameter.
A store sells 50-pound bags of grass seed.
One pound of grass seed covers about 400 square feet
of field
What is the smallest number of bags the groundskeeper must buy to cover the circular field?
Explain or show your reasoning
The smallest number of bags the groundskeeper must buy to cover the field is 165 bags.
What is Area of a circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr²
A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.
The smallest number of bags the groundskeeper must buy to cover the field.
Diameter of the field = 290 feet
Radius = 145 feet
Area of the circular field = πr²
= 3.14 ×145²
= 66018.5ft²
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3X-y=7
4X+2Y=3
please explain each step, thank you.
Answer:
x= 1.7
y= -1.9
Step-by-step explanation:
I will be using substitution method
in the first equation i will isolate y
3x-y=7
+y +y
3x=7+y
-7. -7
3x-7=y
now since y is equal to 3x-7 we can put 3x-7 where y is in the second equation
4x+2(3x-7)=3
4x+6x-14=3
combine like terms
10x-14=3
+14 +14
10x=17
/10. /10
x= 1.7
now we fill in x in any equation to find y
i will put it into the first one
3(1.7)-y=7
5.1-y=7
-5.1. -5.1
-y=1.9
/-1. /-1
y= -1.9
hopes this helps please mark brainliest
Rewrite 1/14x^3y + 8/14 xy^2 using a common factor
Answer:
1/14 xy (x² + 8y)
Step-by-step explanation:
common factor of the number = 1/14
common factor of letter part = xy
x³ : x = x²
y : y = 1
1/14 xy (x²
x : x = 1
y² : y = y
1/14 xy (x² + 8y)
explain why a 2 x 2 matrix can have at most two distinct eigenvalues. explain why an n x 11 matrix can have at most n distinct eigenvalues.
An n x 11 matrix can have a maximum of n different eigenvalues, whereas a 2 x 2 matrix can only have a maximum of two. Below, there is a detailed explanation of this.
What is a matrix simple definition?a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
What's the matrix theory?The study of matrices is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.
solution of a 2 x 2 matrix is in given form:
|A - λI| = 0
here,
A = eigenvalue
I = identity matrix
now
|A - λI| = (a11 - λ)
(a22 - λ) - a12a21 = 0
the solutions of above equation are 2 x 2 matrix's eigenvalues.
just like this, a matrix of size n by n may have up to n different eigenvalues as its characteristic equation is a polynomial of nth degree with up to n roots (i.e. n eigenvalues). all due to the equation form: |A - I| = 0, where A is an eigen and I is an identity matrix.
by expanding the determinant:
|A - I| = (-1)
having coefficients c1, c2,..., cn, having sum = zero.
which is nth degree polynomial equation consisting of n possible solutions, that are basically n x n matrix's eigenvalues .
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A machine that drills holes for wells drilled to a depth of
72 feet in one day.
At this rate, how many hours will it take until the drill
reaches its final depth of -132 feet?
It takes 43 hours to reach final depth of -132 feet with rate of change 72 feet per day.
How to find rate of change?Depending on the context, several phrases may be used to describe rate of change. For instance, acceleration/deceleration is the rate of change with respect to speed or velocity. The slope of the line of best fit determines the pace of change in statistics and regression modeling. It is the population growth rate. Rate of change is frequently referred to as momentum in the financial markets.
The formula [tex]R=\frac{D}{T}[/tex], or rate of change equals the distance traveled divided by the time required to do so, can be used to approach rate of change problems in general. The term "distance" can be changed to another depending on the context of the issue, such as change in worth or price.
Calculation:Given,
Rate of change=72 feet per day =3 feet per hour.
Final depth=132feet;
Time taken= [tex]\frac{Final}{Rate}=\frac{132}{3} =43hours\\[/tex].
It takes 43 hours to reach final depth of -132 feet with rate of change 72 feet per day.
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A cyclist rode 3.75 miles in 0.3 hours.
a. How fast was she going in miles per hour?
b. At that rate, how long will it take her to go 4.5 miles?
The speed of a cyclist rode 3.75 miles in 0.3 hours is 0.36 hours.
Given that, a cyclist rode 3.75 miles in 0.3 hours.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
A) We know that, speed =Distance/Time
Now, speed =3.75/0.3
= 12.5 miles per hour
B) Here, distance =4.5 miles and rate =12.5 miles per hour
Now, 12.5 =4.5/Time
⇒ Time =4.5/12.5
⇒ Time =0.36 hour
Therefore, the speed of a cyclist rode 3.75 miles in 0.3 hours is 0.36 hours.
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for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
The right response is (b), as it increases the minimum sample size required to ensure a given margin of error.
What is margin of error?When a tiny sample of data from a relatively large population is estimated, this is what is meant by the term "margin of error" . The standard deviation, sample size, and desired confidence level are often the factors that control the margin of error.
calculation
Let's take a look at the values in the supplied statement to discover the missing term.
the population's standard deviation is where
m stands for "Margin of Error," and Z stands for "Empirical Value of Z-Score" at a specific confidence level.
As a result, the recommended minimum sample size for a particular degree of confidence is
⇒ (Z×σ)²/m²
The minimal sample size is directly correlated with the population's standard deviation, as shown by the calculation above.
Therefore, when the population "standard deviation" increased, the minimal sample size needed would also "rise."
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On the blueprint of a house, 44 millimeters represents 8 meters. The length of the living room is 33 millimeters on the blueprint. What is
the actual length of the living room?
Answer:
Step-by-step explanation:
The actual length of the explanation is 6 meters.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)
How to determine the correct representationsFrom the question, we have the following expression that can be used in our computation:
–3(2x – 5) < 5(2 – x)
Divide bot sides of the inequality by -1
So, we have the following representation
3(2x – 5) > -5(2 – x)
Next, we open the brackets
This gives
6x – 15 > -10 + 5x
Hence, the representation is 6x – 15 > -10 + 5x
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Complete question
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
(a) 6x – 15 > -10 + 5x
(b) 6x – 15 < -10 + 5x
(c) 3(2x – 5) > -5(2 – x)
(d) 3(2x – 5) < -5(2 – x)
Ellie and Mary went to the Stef bakery. Ellie bought 3 cakes and 6 filled donuts for $10.14. Mary bought 4 of each for $8.32. What is the price of each type of pastry?
On solving the provided question, by substitution method we got that y=1.43 and x=o.65
What is substitution method?To solve systems of linear equations, use the algebraic technique of substitution. The name of the technique implies that it involves substituting the values of variables from one equation into another.
x=cakes , y=donuts
3x+6y=$10.14 ------ eqt.1
4x+4y=$8.32 ------ eqt.2
solve eqt.1 for "y"
y=1.43
x=o.65
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The correct question is
Ellie and Mary went to the Stef bakery. Ellie bought 3 cakes and 6 filled donuts for $10.14. Mary bought 4 of each for $8.32. What is the price of each type The price of a is The price
Please answer fast loads of points!!!!!!!
Answer:
wednesday: 4
thursday: 32
Step-by-step explanation:
Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
490
472 <490<500
it fits the criteria
Given the function: y = 3x + 12 identify the independent and dependent variables.
In the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.
What is an equation?A mathematical connection in which the values of one or more independent variables uniquely determine the values of a dependent variable.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equation is y = 3x + 12. Here in the equation, the value of the y variable is dependent on the value of x. Then the x variable is independent and the y variable is dependent and depends upon the x variable.
Therefore, in the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model this situation is given by;
x + y = 461
3x + 4y = 1624
The school sold 220 students tickets and 241 adult tickets.
How to write and solve equation?let
Number of students tickets = x
Number of adults tickets = y
x + y = 461
3x + 4y = 1624
From (1)
x = 461 - y
Substitute into (2)
3x + 4y = 1624
3(461 - y) + 4y = 1624
1383 - 3y + 4y = 1624
- 3y + 4y = 1624 - 1383
y = 241
Substitute into (1)
x + y = 461
x + 241 = 461
x = 461 - 241
x = 220
In conclusion 220 students tickets and 241 adults tickets were sold.
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Solve:
3x/2-5= 7
Please give full explanation
Answer:x=8
Step-by-step explanation:
3x/2-5=7
Move all terms not containing x to the right side of the equation by adding 5 to both sides
3x/2-5+5=7+5
3x/2=12
Multiply both sides of the equation by 2/3 to isolate x.
3x/2*2/3=12*2/3
x=24/3
x=8
Answer: x= 8
Step-by-step explanation:
3x/2-5=7
3x/2 = 12
3x = 24
x= 8
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USPS offers the flat-rate shipping option below small box : 5 3/8 by 8 5/8 inches by 1 5/8 inches cost:$ 6.80 medium box: 11 7/8 inches by 3 3/8 inches by 13 5/8 cost : $13.45 large box 12 inches by 12 inches by 5 1/2 cost: $18.75 An artist makes necklaces and packs each necklace in a small jewelry box that is inches by 1 3 /4 by 2 1/4 inches by inch. A department store ordered 270 necklaces. The artist plans to ship the necklaces 3 /4 to the department store using USPS flat-rate shipping boxes. Which flat-rate box should this artist use to minimize his shipping costs?
You can mail small things weighing 70 pounds or less to any location in the US for a set price using USPS Small Flat Rate boxes. The cost of a USPS Small Flat Rate package is only $8.45.
What is USPS?The United States Postal Service (USPS), often known as the Post Office, U.S. Mail, or Postal Service, is a separate executive branch agency that is in charge of delivering postal service across the United States, including its associated states and insular territories.
It is one of the few governmental organizations that the US Constitution expressly grants authority to. 516,636 career employees and 136,531 non-career employees work for the USPS as of 2021.
The first postmaster general of the United States Postal Service, Benjamin Franklin, was appointed in 1775 during the Second Continental Congress. He also held a comparable role for the colonies of the Kingdom of Great Britain.
With the passing of the Postal Service Act in 1792, the Post Office Department was established.
Hence, A USPS Small Flat Rate box only costs $8.45.
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Find the sum of 2x2 + 5x + 7 and - 1022 - 7x + 1.
[tex](2x^2 + 5x + 7) + ( - 1,022 - 7x + 1)\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2-2x-1,014[/tex]
In 2012 there were approximately 275 students
Answer:
is there a graph available????
Step-by-step explanation:
What is 7x +3-2x - 3x simplified?
Answer:
2x+3
Step-by-step explanation:
Combine like terms.
7x-2x-3x=2x
Then add 3 to expression
Answer:
2x+3
Step-by-step explanation:
we know that we would have to add up all the commen variables first to give the most simplified answer
first take the -2x and add it with the -3x. you get -5x.
than take the -5x and add it to the 7x. you will grt 2x
lastly add them up and you get 2x+3