Step-by-step explanation:
To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.
(a) What was the total amount Linda ended up paying for the equipment
(including the down payment and monthly payments)?
How much on loan:
12,200 - 1,600 = $10,600 loan amount
How much paid on loan:
$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan
Total paid:
= loan amount + amount paid on loan
$10,600 + $$11,608.28
= $22,208.28 paid overall
________________________________________
(b) How much interest did Linda pay on the loan?
= loan amount - amount paid on loan
= $11,608.28 - $10,600
= $1,009.28 paid in interest
The total cost of a plane ride, C, is given below as a function of the time flown, m, in minutes.
C = $33.00 + $1.20m
If a customer spends $267.00 on a plane ride, how many minutes does the ride last?
A. 250
B. 195
C. 223
D. 325
The number of minutes is 195 minutes when the customer spends $267.00. The correct option is B.
How to calculate the time?From the information, the total cost of a plane ride, C, is given as a function
C = $33.00 + $1.20m
where n = number of minute
Since the customer spends $267.00 on a plane ride, this will be:
C = = 33.00 + $1.20m
33 + 1.2m = 267
Collect like terms
1.2m = 267 - 33
1.2m = 234
Divide
m = 234 / 1.2
m = 195
Minutes used is 195 minutes
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round square root of 4004 to the nearest integer
A patient is using a bicycle as part of their physiotherapy routine. The diameter of the bicycle’s wheel is 590 mm. While in session, the wheel is rotating at a speed of 82 rpm (revolutions per minute). If the patient is riding the bicycle for 1 h and 10 minutes, determine the number of kilometres the patient has travelled. Round to the nearest tenth.
The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.
What is the distance?The distance is the length from one point to the end.
For our purpose, distance represents the product of speed and time.
Diameter of the bicycle's wheel = 590 mm
Speed (Revolutions) per minute = 82 rpm
Time riding the bicycle = 1 hr and 10 minutes = 70 minutes
1 Kilometer = 1,000,000 Millimeters
Distance per rotation = pi x diameter
= 3.14 x 590
= 1,852.6 mm/minute
Total distance traveled in kilometers = (1,852.6 x 82 x 70) ÷ 1,000,000
= 10,633,924 ÷ 1,000,000
= 10.6 kilometers
Thus, we can conclude that the patient traveled 10.6 kilometers by bicycling for one hour and 10 minutes.
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The function C(x)=−21x+2025 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $24?
The least number of items that can be produced so that the average cost is no more than $24 is 95.
According to the question,
We have the following information:
The function C(x)=−21x+2025 represents the cost to produce x items.
Cost should be no more than $24.
So, we have the following inequality to find the number of items:
-21x+2025 ≤24
Subtracting 2025 from both sides:
-21x≤24-2025
-21x ≤ -2001
Dividing both sides by -21:
x ≤ 2001/21
x ≤95.28
Hence, the least number of items that can be produced so that the average cost is no more than $24 is 95.
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Evergreen Landscaping bought 7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270. The next week the firm bought 5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015. Pea gravel costs $28 less per ton than topsoil. Find the cost per ton for each item.
The cost of topsoil per ton would be $48.
The cost of pea gravel per ton is $20.
The cost of mulch per ton is $479.
What is the linear equations in two variable?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.
We have,
7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.
5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.
Let,
cost of topsoil per ton = x
cost of pea gravel per ton = x - 28
cost of mulch per ton = m
7x + 6m + 3(x - 28) = 3270
7x + 6m + 3x - 84 = 3270
10x + 6m = 3270 + 84
10x + 6m = 3354 -------------(i)
5x + 5m + 5(x - 28) = 3015
5x + 5m + 5(x - 28) = 3015
10x + 5m = 3015 - 140
10x + 5m = 2875 -----------(II)
Subtracting equation (II) from (I), we get
10x + 6m = 3354
- 10x + 5m = 2875
Solving we get
m = 479
Put m = 479 in equation(I), we get
10x + 6m = 3354
10x + 6(479) = 3354
10x = 480
x = 480/10
x = 48
Hence,
The cost of topsoil per ton would be = x = $48.
The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.
The cost of mulch per ton = m = $479.
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95 POINTS
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answer: 33577
Step-by-step explanation:
3x3x5x7x7 = 2205
The lifetimes of batteries created by a company are normally distributed with a
mean of 105 hours and a standard deviation of 12 hours. What percentage of these batteries will last between 90.6 and 109.8 hours?
Answer:
84.6
Step-by-step explanation:
Children at nutrition are either playing or sitting down resting. The ratio of kids playing to resting is 3:1. If there are 8 children resting, then how many are playing?
Answer: 24 kids playing
Step-by-step explanation: Since the ratio of the kids playing and resting is 3:1, and there are 8 kids resting, replace the 1 with 8, and multiply the 3 with 8 to make the equation balanced. 24:8!
Martha's employee benefits include family health-care coverage. She contributes 18% of the
cost. Martha gets paid biweekly and $108.00 is taken out of each paycheck for family health-care
coverage. How much does her employer contribute annually for the family coverage?
use dollar sign, decimal and comma
The family coverage paid by Martha's employer for health care coverage is $2592.
What is a health care coverage?
Health insurance is a sort of insurance that pays for unexpected medical costs brought on by a disease. These expenditures may be associated with the price of hospitalisation, or the cost of medical visits.
Main body:
Let the total biweekly salary of Martha be x.
Therefore according to question :
18% of x =$108
(18/100)*x =108
x= 600
Martha earns $600 biweekly.
monthly earning of Martha be 600*2 =$1200
Therefore total coverage annually = 108*total salary day
=108*24
=$2592
Hence the answer is $2592.
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1/3a^2+a=0
It's rather urgent, please or else I will fail my semester...
The solution of the equation given as 1/3a² + a=0 is a = 3
How to determine the solution to the equation?From the question, we have the following equation that can be used in our computation:
1/3a^2+a=0
Rewrite the equation properly
So, we have
1/3a² + a=0
Multiply through the above equation by 3
So, we have the following equation
3 * (1/3a² + a) =0 * 3
Evaluate the products
So, the equation becomes
a² + 3a = 0
Next, we divide through the equation by the variable a
This gives
a + 3 = 0
Subtract 3 from both sides of the equation
i.e. Add -3 to both sides of the equation
a = -3
The above equation cannot be solved further.
So, we leave it like that and stop solving
Hence, the solution to the equation is a = -3
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One spring day, Harper noted the time of day and the temperature, in degrees
Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 58° F. For the
next 3 hours, the temperature rose 4° per hour. For the next 5 hours, it rose 1° per
hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the
temperature was 70° at midnight. On the set of axes below, graph Harper's data.
The graph that shows Harper's data about temperature and time is shown below .
The graph is a relation that represents the relationship between two variables on the x and y axis .
In the question ,
Harper's data of time of day and the temperature, in degrees Fahrenheit is given,
the temperature at 6 a.m. = 58° F
for the next 3 hours the temperature rose 4° each hour means
in 3 hours it will rise 12°
So , the temperature at 9 a.m. = 70° F
For the next 5 hours, it rose 1° per hour which means
in 5 hours it will rise 5°
So , the temperature at 2 p.m. = 75° F
The temperature then stayed steady until 6 p.m. which means
temperature at 6 p.m. = 75° F
For the next 2 hours, the temperature dropped 1° per hour , which means
temperature at 8 p.m. = 73° F
the temperature at midnight = 70° F
So , from the above data the graph is shown below .
Therefore , The graph that shows Harper's data about temperature and time is shown below .
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How did you compute sums of dollar amounts that were not whole numbers? For example, how did you compute the sum of $5.89 and $1.45? Use this example to explain your strategy.
The Sum of dollars in decimal is not a whole number.
Whole numbers are made up of natural numbers plus the number zero. In mathematics, the set of whole numbers is symbolized by the symbol W and is given as W = {0, 1, 2, 3, 4, …}.
To calculate a number of dollars that is not a whole number.
As an example, consider the sum of $5.89 and $1.45:
$5.89 + $1.45
Taking the whole numbers first:
$5 + $1 = $6
Take the sum of the decimals :
$0.89 + $0.45 = $1.34
sum of original whole + sum of decimal whole
$6 + $1 = $7
Remaining decimal: $1.34 - $1 = $0.34
$7 + $0.34 = $7.34
Therefore $7.34 is not a whole number
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16 2/3-15 1/6+1.3/2.5x1.56x0.4
HELP ASAP
Answer:
Step-by-step explanation:
The answer would be 1.82448
Fill in the blank, rounding the result to exactly three significant digits when necessary
81 m = ___ ft
Two people are jogging around a circular track in the same direction one person can go to completely around the track in 21 minutes the second person takes 18th if they both start running in the same direction at the same time how long will it take them to be together at this place if they continue to run
Answer:
n * 21 = m * 18 one runs n laps and one runs m laps to again be together at the same place
7 n = 6 m divide by 3
one runs 7 * 18 = 126 min
the other runs 6 * 21 = 126 min
After 126 min they will be together at the start
Find the GCF of 21 and 28.
Answer: 7
Step-by-step explanation:
Answer:
7 is the GCF of 21 and 28
Step-by-step explanation:
The GCF of 21 and 28 is 7. To calculate the greatest common factor (GCF) of 21 and 28, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 21 and 28, i.e., 7.
2. Sketch a list or tree diagram to represent
the sample space of flipping a penny, a nickel,
and a dime one time each.
There are total 8 possible outcomes if we flip penny , nickel , dime together. We can show these outcomes by the Tree diagram or by listing each outcome separately.
The one way to create an organized list to represent the sample space
Penny NICKEL DIME
H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T
The another way to create an organized list to represent the sample space is to make a tree diagram .
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6.) One clothing Store has a dress for $6.20
and a belt for $3.50. Customers
buy 3 dresses for $15.20. How much
would be saved by buying 3 dresses
Than by buying per piece?
Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present.
How many yards does he have left?
Step-by-step explanation:
Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present. How many yards does he have left?
5/6 - 2/6 = 3/6
3/6 reduces to 1/2 yards left
Karen is waiting for a pot of soup to cook off before serving it. After 4 3/4 min the soup has cooled from 100°C to 78° C. What was the average change in temperature each minute.
Answer:
Karen is waiting for a pot of soup to cool off before serving it. After 4 min the soup has cooled from 100°C to 78°C. What was the average change in temperature each minute?
✓ Answer:It went down 5.5°C a minute.Step-by-step explanation:You have to look for the difference of 100 and 78, which is …
In 5-10, match each expression with the correct value
Trignometric equation can be used to answer this:
What is trignometric equation?A trigonometric equation is any equation that contains a trigonometric function. Up until now we have introduced trigonometric functions, but not fully explore them. In the lessons within this SparkNote on trigonometric equations, we'll learn exactly how to solve trigonometric equations.As mentioned in Trigonometric Identities, a trigonometric equation that holds true for any angle is called a trigonometric identity. There are other equations, though, that only are true for certain angles. They are generally known as conditional equations, but in this text we'll just call them equations. We'll learn some techniques for solving general equations, as well as how to derive an infinite number of solutions to an equation based on a single solution to that equation.acc to our question-
5. cos(75)= 2-√3
6. tan(22/7)= 1+√2
7. sin 3π/6= √2-√√2/2
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If a = 4, then a³ + a=
I know the answer but can someone explain step by step
Answer:
D) 16
Step-by-step explanation:
A=4
[tex]a^3[/tex]/a=?
[tex](4^3)[/tex]/(4)=?
64/4=16
Classify the polynomial by its degree: 4m³-9x² + 10
A) 0
B) 1st
C) 2nd
D) 3rd
E) 4th
what percent of factors of 21! are odd?
Step-by-step explanation:
here's the answer, all of them
It takes Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Assuming Abby doesn't stop, what is her average speed from Ashdown to Carton to 1 dp?
The average speed for the given situation is 56 mph.
Given that, Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
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.
Now, distance = Speed × Time
= 60 × 3
= 180 miles
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Now, Time = 30/40
= 0.75 hours
Total time =3+0.75=3.75 and total distance =180+30=210
Then average speed = 210/3.75
= 56 mph
Therefore, the average speed for the given situation is 56 mph.
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A Calculator salesman’s monthly income is $1500 salary plus a commission of 7% of his sales over $5000 what was his income the month that he sold $11,470 in calculators
$142428 income earned. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services.
What is commission?A type of variable-pay compensation for goods or services sold are commissions. Salespeople are frequently encouraged and rewarded with commissions. Additionally, commissions can be created to promote particular sales habits. For instance, commissions may be decreased while providing significant discounts.
Let X be the sales for a man
so7% of sales=7x/100
Total that needs to be earned=$11470
So,
Total needs to be earned= salary +commission on sale
11470=1500+7x/100
11470-1500=7x/100
9970=0.7x
X=9970/0.7
X=142428
Therefore $142428 income earned .
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The doubling period of a bacterial population is 20 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0?
Find the size of the bacterial population after 3 hours.
The initial population of the bacterial population at time t = 0, can be found to be 1,406.25.
The size of the bacterial population after 3 hours is 720,000.
How to find the bacterial population?The doubling period of the bacterial population is said to be 20 minutes. The number of doubling periods in 120 minutes is:
= 120 / 20
= 6 doubling periods
The initial population is:
= Population at 120 minutes / 2 ^ number of doubling periods
= 90,000 / 2⁶
= 1,406.25
The bacterial population at 3 hours is:
= Bacterial population at t = 0 x 2 ^ number of doubling periods in 3 hours
= 1,406.25 x 2 ^ (180 minutes in 3 hours / 20)
= 1,406.25 x 2⁹
= 720,000
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Glass cases how many gumballs are in the gumball machine one student guesses 456 counting it was determined that they were actually 408 gumballs in the machine what is the percent error of the guess
According to the solving the percent error = 11.764%
What does "percent mistake" mean?The percent error is the distinction between the estimated value and the real value in relation to the actual value. In those other words, the relative error is multiplied by 100 to calculate the percent error.
What does a high percent error rate mean?The difference between an approximate number and an exact value is measured in percent error. The bigger the percentage error, the further your estimated value deviates from the known value; conversely, the smaller the percentage error, more closer your approximation to the true value.
According to the given data:Actual value = 408
Expected value = 456
We know that the percent error :
= (expected value - actual value)/actual value.
= (456 - 408)/ 408
= 48/408
= 11.764
= 11.764%
According to the solving the percent error = 11.764%
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Given CB || ED,;CB=ED prove CBF= EDF using isometric ridged transformation outline the necessary transformation to prove CBF = EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements
The given triangle is rotated about 180 degrees and as such, we can say that the triangle CBF is congruent to the triangle EDF.
How to prove congruent angles?
From the attached image, we see that CB is parallel to ED. We also see that the transversal lines are BD and CE.
The point E will become the image of point C by a rotation of 180° around the point F.
Now, the point D will be the image of point B by a rotation of 180° around the point F.
Rotation is a type of transformation and as such ΔEDF will be the image of ΔCBF.
Therefore we can conclude that ΔCBF ≅ ΔEDF
The second way to prove this congruency is as follows;
∠B = ∠D (Due to the fact that alternate angles are congruent)
∠C = ∠E (Due to the fact that alternate angles are congruent)
Now, since CB ≅ ED , then it means that ΔCBF ≅ ΔEDF by SAS congruency postulate
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height $h$, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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