The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
To purchase 13700 worth of restaurant equipment for her business.
Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.
The total amount Maria ended up paying for the equipment will be
Total amount = 371.16 × 3 × 12 + 1500
Total amount = $14,861.76
The interest of Maria on the loan will be
Interset = [(14861.76 – 13700) / 13700] x 100
Interset = 8.48%
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There are 192 pencils in 8 Super Saver packs. If there are the same number of pencils in each Super Saver pack, how many pencils are in 5 packs?
Rasberry Crazy Ants, a species found in wall sockets, cellphones, and television sets are
slowly spreading across Texas and are poised to spread across the entire South. Named for
Texas exterminator Tom Rasberry, who spotted ants moving in an erratic swarm in 2002,
the destructive ants are now in 23 counties in Texas, the Austin American-Statesman
recently reported. Although their march in impossible to stop, it is also quite slow. They travel at an average speed of 1.8 feet per day.
a. At that rate, how long will the swarm that is presently centered in Austin, Texas, take to reach your home? Express your answer in the timeframe that is most appropriate.
b. Do you need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren? Explain why or why
not.
The average time taken to travel to Toronto by the swarm of Rasberry Crazy Ants is 12,947 Years
What is the calculation for the above Solution?To arrive at the solution above, we need to look at the information given and the information assumed.
Step 1 - Information given:
Step 2 - Information assumed:
The swarm are travelling to the location of the student which is assumed to be Toronto.
Hence,
Time taken for the swam to get to Toronto (TTS) =
Distance between Austin, Texas and Toronto (DBTT) / Average distance covered per day by the Rasberry Ants. (ADC)
Estimated distance between Austin Texas and Toronto = 2592.6 Kilometers
Time travelled per day by the ants (In Km) = 0.00054864
Thus,
TTS = DBTT/ADC
= 2592.6 /0.00054864
≈ 4,725,503.06 days or
≈ 12,947 Years
Do I need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren?The answer to both questions is NO.
The average life expectancy in Toronto (as at 2022) is 80 years. Assuming I was born today, it is expected that the time between now and when my last grand child will die is about:
80 x 3 = 240 years.
Given that the ants have to travel 12,947 to get to Toronto, the possibility of my grand children seeing them is zero.
Besides, even if they by chance got to Toronto and infested my grandchildren's residence, they would have nothing to worry about because Rasberry Crazy Ants are 100% harmless.
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NS,
Word problem on unit rates associated with ratios of whole...
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) Greg bought 16 pounds of sugar for $8.
C
How many dollars did he pay per pound of sugar?
dollars per pound
(b) It takes 76 pounds of seed to completely plant a 12-acre field.
How many pounds of seed are needed per acre?
pounds per acre
|||
Answer:
Define different tipes of discontuinity of a function .also,write the condition for increasing, decreasing and concave of function
a.- Representa el cálculo del porcentaje de cada par de artículos y marca el que es más conveniente comprar.
1 el par de zapatos cuesta $90.Por la compra de dos pares , tienes el 25% del descuento total
2 el par de zapatos cuesta $90.El segundo par de zapatos esta con el 40% de descuento
El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.
¿Cual opción es más conveniente?
En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.
Entonces el costo por 2 pares es:
C = ($90 + $90)*(1 - 25%/100%)
Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:
C = ($180)*(0.75) = $135.
En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.
C = $90 + $90*(1 - 40%/100%) =
C = $90 + $90*(0.6) = $144
Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.
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If ANYONE ANSWERS I WILL GIVE THEM BRAINLIEST PLEASE HELP ME!!
If an investment account is leveraged by a ratio of 5:1, by how much would the value of the security invested need to drop before the value of the account falls to $0?
20%
50%
10%
5%
Answer:
From what my calculations said its 20%
Please help
Follow the steps to find the area of the shaded region.
First use the formula below to find the area of the whole sector.
Sector Area= ( angle of sector/360). R2
Sector Area = ? Cm^2
Round to four decimal places.
14 cm
46°
14 cm
The area of the sector, to 4 decimal places, is: 78.6794 cm².
How to Find the Area of a Sector of a Circle?Area of sector = ∅/360 × πr².
Given the following:
∅ = 46°Radius (r) = 14 cmArea of sector = 46/360 × π(14²)
Area of sector ≈ 78.6794 cm²
The area of the sector is approximately 78.6794 cm².
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Please help!!
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation
(-4,5) y=1/3x +6
Answer:
The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Multiplication of slope of two perpendicular lines is = -1
first line is y= [tex]\frac{1}{3}[/tex]x +6
slope of this line is [tex]\frac{1}{3}[/tex]
So the slope of the second line is : [tex]\frac{-1}{3}[/tex]
Equation of line would be written by using :
(y - y1) = m(x - x1)
here the line passing through (-4,5)
put the values in equation
y -5 =[tex]\frac{-1}{3}[/tex][x - (-4)]
3y - 15 = -x -4
3y = -x +11
y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
So The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
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A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means is greater than 8.8 hours? Express your answer as a percent rounded to hundredths of a percent.
Using the normal distribution, it is found that 7.64% of of sample means are greater than 8.8 hours.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 8.4, \sigma = 1.77, n = 40, s = \frac{1.77}{\sqrt{40}} = 0.2799[/tex]
The proportion of sample means greater than 8.8 hours is one subtracted by the p-value of Z when X = 8.8, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.8 - 8.4}{0.2799}[/tex]
Z = 1.43
Z = 1.43 has a p-value of 0.9236.
1 - 0.9236 = 0.0764.
7.64% of of sample means are greater than 8.8 hours.
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Can u help me with this I don’t understand
Answer:
D -6, 15
Step-by-step explanation:
Because 3,11 is the middle, and 12,7 is the other end, you can do
12 - 3 = 9
3 - 9 = 6
then
11 - 7 = 4
11 + 4 = 15
so
6 is you x and 15 is your y
Using the Empirical Rule, it is found that:
Scores between 80% and 96% are within 2 standard deviations of the mean.
68 scores are within one standard deviation of the mean.
It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:
88 - 2 x 4 = 80%.
88 + 2 x 4 = 96%.
68% are within 1 standard deviation of the mean, hence, out of 100:
0.68 x 100% = 68 scores.
What is the median of the above answer? Pls help fast.
Considering that the mean of the normal distribution is the same as the median, the median is of 88%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the normal distribution, the median is the same of the mean, that is, the median is of 88%.
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what is the mid point of 3,2 and -3,4?
Answer
(0,3)
Step-by-step explanation:
from mid point (x+x)/2, (y+y)/2((3+-3)/2,(2+4)/2)(0/2, 6/2)(0, 3)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The intervals in which a function is decreasing has a negative slope. and for given graph, the required intervals are :
[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Find the domain and range of the relation graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-1, 3][/tex]Range: [tex][0, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Find the equation of the line with slope 43 and y-intercept (0,−3).
[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex] Equation: [tex]\bullet[/tex] y=43x-3 ✅
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
Do you need to know the equation of the line with a slope of -43 and a y-intercept of (0,-3)? No problem! Luckily, there's a formula to find it! (:
The Slope Intercept FormulaThe slope intercept formula, [tex]\boldsymbol{y=mx+c}[/tex], comes in handy when we need to find the equation of a line!
In this formula,
"m" denotes the slope"c" denotes the y intercept-- ↩
This particular question provides us both "m" and "c."
m=43c=-3 (It's the second co-ordinate, the y co-ordinate, in the point "(0,-3)"Stickin the values
[tex]\boldsymbol{y=43x+(-3)}[/tex]
Simplify!
[tex]\boldsymbol{y=43x-3}[/tex]
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. \: Dream big. }[/tex]
--
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If x is a positive integer, what is the value of x for the equation (x!-(x-3)!)\23=1?
I think the first step is knowing (x!-(x-3)!) equals to 23, but after that i'm stuck, can someone help me?
[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
Sianna bought 3 pens, 4 notebooks, and a calculator. The calculator cost $25. If x represents the cost of each pen and y represents the cost of each notebook, which expression represents the amount of change Sianna should receive from $50?
3x + 4y +25
50 – (3x + 4y)
50 – (3x + 4y + 25)
3x + 4y + 25 + 50
Answer:
50 – (3x + 4y + 25)
Step-by-step explanation:
To see how much change she is gonna receive we need to find how much she spent on the items and add them all up:
The calculator was $25
The price of pens and notebooks are unknown so they are represented with x and y respectively.
With given information we can write the following equation to see the change she will receive:
50 – (3x + 4y + 25)
You started this year with $413 saved and you continue to save $21 per month.
Write an equation to model this situation (use m for months and s for savings)
Answer:
y = 21x + 413
Step-by-step explanation:
Use y = mx + b
m represents the slope which in this case is 21.
b represents the y - intercept which in this case is 413.
Now, just fill in the variables.
y = 21x + 413
Hope this helps!
In what table does y vary directly with x?
Answer:
The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways. for some constant k. The k is called the constant of proportionality. Therefore a chance of probability is a binary table.
Step-by-step explanation:
Find all real zeros of the function.
Answer:
Zeros: 0, 1, and 7
Step-by-step explanation:
Given function: f(x) = 3x(x - 1)²(x - 7)²
To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.
1. Substitute f(x) = 0:
[tex]\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2[/tex]
2. Divide both sides by 3:
[tex]\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2[/tex]
3. Separate into possible cases:
[tex]\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0[/tex]
4. Simplify:
[tex]\sf a)\ x = 0\ \textsf{[ already simplified ]}[/tex]
[tex]\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1[/tex]
[tex]\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7[/tex]
Therefore, the zeros of this function are: 0, 1, and 7.
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At the start of the week, Monique’s savings account had a balance of $326. She made a $45 withdrawal each day for seven days. During that week, she also made two deposits of $125 each. Which integer represents the balance in Monique’s account at the end of the week?
–891
–261
261
891
Answer:
C. 261
Step-by-step explanation:
45 times 7= 315
326-315=11
125 times 2=250
250+11=261
so the answer is C. $261
What is the inverse of p>q
Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.
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Find the quotient: (9mn2)(−3m6n)33m10n3
The quotient is -27m/ 55.
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
(9mn²)(−3m*6n)÷33m*10n³
=9mn² *(-18mn) / 330mn³
= -162m²n³/ 330mn³
= -27m/ 55
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Needa line segment has endpoints P(-8,7) and Q(6,-3). What is the midpoint of the segment?
Answer:
1/2(6-8), 1/2(-3+7)=-1,2
Answer: C - (-1, 2)
Step-by-step explanation:
Huilan is years 15 younger than Thomas. The sum of their ages is 73 . What is Thomas's age?
thomas age:44
huilan age: 29
Step-by-step explanation:
h = t + 15
t + t + 15 = 73
2t = 73 - 15
2t = 58
t = 29
DOES THE THE NUMBER LINE GOES ON FORVEVER
Answer:
Yes.
Step-by-step explanation:
In mathematics, a number line ends in arrows on both sides, signifying it going infinite in the positive and negative directions.
Answer:
Yes.
Step-by-step explanation:
A number line is infinite in both directions it faces. This means left or right there is a infinite amount of numbers.
Next
Pretest: Coordinate Geometry
7
Select the correct answer from each drop-down menu.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
The
✓of their slopes is
so the lines are
I
Because both lines have the same slope but different y-intercepts, we conclude that the lines are parallel.
What can we conclude about the two given lines?
Here we have the two lines:
6x - 2y = -2
y = 3x + 12
If we write both of these in the slope-intercept form, we get:
y = (-2 - 6x)/-2 = 3x + 1
y = 3x + 12
So, as you can see, both lines have the same slope but different y-intercepts. That means that the two lines are parallel, so they never do intercept.
Then we can conclude that the correct option is parallel.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt{Yes, there's a local maximum at -9,} [/tex] [tex] \texttt{and it is 9} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
By Observing the graph, we can easily conclude that there's a local maxima at -9
[tex] \textsf{And f(-9) = 9} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Raul's pet store has a play area that can fit up to 30 cats and dogs. His son is allergic to cats so the pet store never has more than 8 cats in the play areas.
How many of each type of pet can they have at the
pet store?
Write a system of inequalities.
Answer:
Step-by-step explanation:
Let :
C = number of cats
D = number of dogs
Raul's pet store has a play area that can fit up to 30 cats and dogs.
C + D = 30
The pet store never has more than 8 cats in the play areas.
C < 9(there can never be 9 or more cats)
As or the number of dogs :
C + D = 30
C = 30 - D
Since we know that C < 9. To get the number of dogs allowed, we just plug in 30 - D for C.
30 - D < 9
30 - 9 < D
or
D > 21
(dogs have to be 22 or more)
Which explicit formula models this situation
Answer:
The formula is: y = y•e^(-k•x)
In this specific case the function is: 512•e^(-x/1.44)
The number of players in the round 7 is 4
Use the Change of Base Formula to solve each equation.
3x = 27.3
Answer:
9.1
Step-by-step explanation:
3(9.1)=27.3
27.3÷3=×
×=9.1
