The equation A(t) = 900(0.85)t represents the value of a motor scooter t years after it was purchased. Which statements are also true of this situation?
Answer:
When new, the scooter cost $900
Step-by-step explanation:
The complete question in the attached figure
we have
[tex]A(t)=900(0.85)^t[/tex]
This is a exponential function of the form
[tex]A(t)=a(b)^t[/tex]
where
A(t) ----> represent the value of a motor scooter
t ----> the number of years after it was purchased
a ---> represent the initial value or y-intercept
b is the base of the exponential function
r is the percent rate of change
b=(1+r)
In this problem we have
[tex]a=\$900\\b=0.85[/tex]
The base b is less than 1
That means ----> is a exponential decay function (is a decreasing function)
Find the percent rate of change
[tex]b=(1+r)\\0.85=1+r\\r=0.85-1\\r=-0.15[/tex]
Convert to percentage (multiply by 100)
[tex]r=-15\%[/tex] ---> negative means is a decreasing function
Verify each statements
case A) When new, the scooter cost $765.
The statement is false
Because the original value of the scooter was $900
case B) When new, the scooter cost $900
The statement is true (see the explanation)
case C) The scooter’s value is decreasing at a rate of 85% each year
The statement is false
Because the scooter’s value is decreasing at a rate of 15% each year (see the explanation)
case D) The scooter’s value is decreasing at a rate of 0.15% each year
The statement is false
Because the scooter’s value is decreasing at a rate of 15% each year (see the explanation)
I got the first two can you help me with the last one PLZ
3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising.
(a) Is this an arithmetic or geometric sequence?
(b) How can you find the next number in the sequence?
(c) Give the rule you would use to find the 20th week.
1. Geometric Sequence
2. [tex]a_n = a_{n-1} * 3[/tex]
3. [tex]a_n = 6 * (3)^{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
6, 18, 54, 162,....
Here
[tex]a_1 =6\\a_2 = 18\\a_3 = 54[/tex]
(a) Is this an arithmetic or geometric sequence?
We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.
We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r
[tex]r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3[/tex]
As the common ratio is same, the given sequence is a geometric sequence.
(b) How can you find the next number in the sequence?
Recursive formulas are used to find the next number in sequence using previous term
Recursive formula for a geometric sequence is given by:
[tex]a_n = a_{n-1} * r[/tex]
In case of given sequence,
[tex]a_n = a_{n-1} * 3[/tex]
So to find the 5th term
[tex]a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486[/tex]
(c) Give the rule you would use to find the 20th week.
In order to find the pushups for 20th week, explicit formul for sequence will be used.
The general form of explicit formula is given by:
[tex]a_n = a_1 * r^{n-1}[/tex]
Putting the values of a_1 and r
[tex]a_n = 6 * (3)^{n-1}[/tex]
Hence,
1. Geometric Sequence
2. [tex]a_n = a_{n-1} * 3[/tex]
3. [tex]a_n = 6 * (3)^{n-1}[/tex]
Keywords: Geometric sequence, common ratio
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Joe went to a market and bought 5 carrots for a total of $10.50. If each carrot cost the same amount, how many dollars did each carrot cost? Express your answer as a decimal to the nearest hundredth
Final answer:
Each carrot cost $2.10, found by dividing the total cost of $10.50 by the number of carrots, which is 5.
Explanation:
The student’s question relates to the basic concept of unit price in mathematics. Joe bought 5 carrots for a total of $10.50. To find out how much each carrot cost, we divide the total cost by the number of carrots.
Here’s the calculation step-by-step:
Determine the total cost of the carrots, which is $10.50.
Determine the number of carrots bought, which is 5 carrots.
Divide the total cost by the number of carrots: $10.50 / 5 = $2.10.
So, each carrot costs $2.10 when expressed as a decimal to the nearest hundredth.
Show work for answer please
Answer:
x = - 3
Step-by-step explanation:
Given
7 + x - 3 = x - 5 - 3x ( simplify both sides )
4 + x = - 2x - 5 ( add 2x to both sides )
4 + 3x = - 5 ( subtract 4 from both sides )
3x = - 9 ( divide both sides by 3 )
x = - 3
What percent is equivalent to StartFraction 1 Over 25 EndFraction? 4% 5% 20% 25%
Convert the fraction to a decimal:
1/25 = 0.04
Multiply by 100 to get the percent:
0.04 x 100 = 4%
The fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have a fraction:
= 1/25
In decimal:
= 0.04
In percent:
= 0.04×100
= 4%
Thus, the fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.
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Jesse has 2 coupons, but can only use one of them. Coupon A is for $10 dollars off an item. Coupon B is for 25% off an item. The product he is buying costs $42. Which coupon is the better deal?
Answer:
coupon b offers $10.50 off whereas the other is only for $10 off
Step-by-step explanation:
25%*42=10.5
9. Evaluate f(x) = -2х2 - 4 fоr x = 3.
o
О-22
o
etric
o
О-18
o
О-10
The value of function f (x) at x = 3 is,
⇒ f (3) = - 22
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = - 2x² - 4
Now, Put x = 3 in above function we get;
⇒ f (x) = - 2x² - 4
Put x = 3;
⇒ f (3) = - 2 (3)² - 4
⇒ f (3) = - 2 x 9 - 4
⇒ f (3) = - 18 - 4
⇒ f (3) = - 22
Thus, The value of function f (x) at x = 3 is,
⇒ f (3) = - 22
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Average of -3,0,7,-2
Answer:
The average would be 0.5
Step-by-step explanation:
Answer: 0.5
Step-by-step explanation: To find the average, we begin by adding the numbers so we have -3 + 0 + 7 + -2 which is 2.
Now we divide 2 by the number of numbers in the data set which is 4.
2 divided by 4 is 0.5 so the average of these numbers is 0.5.
Which is the best buy?
a. $19.25 for 11 candy bars
b. $22.62 for 13 candy bars
c. $15.39 for 9 candy bars
d. $17.30 for 10 candy bars
Answer:
a=$1.75 per candy bar
b=$1.74 per candy bar
c=$1.71 per candy bar
d=$1.73 per candy bar
Option C is the better buy.
Hope this helps!
What is the value of
2x4 + 5x when x = 6?
What is the slope of f(x)=4/5x-8
Answer:
the slope is 4/5
Step-by-step explanation:
because i learn that
The product of two numbers is 20. If one of the numbers is 5/14, what is the other number
Answer:
56 is the other number
Step-by-step explanation:
let the first number be a
the other number is 5/14 from the question
a x 5/14 = 20
5a/14 = 20
5a = 14 x 20 = 280
a = 280/5 = 56
What’s is a,b and c and explain if you can please
Answer:
Are you VSCO??
Step-by-step explanation:
The greatest common factor is simply which factors of each number are shared between them. Factors are numbers that multiply together to get a certain number.
For example, a) 2x, 4
The factors of 2x are 2 and x
The factors of 4 are 2 and 2
The factors that are shared between them is 2, so the greatest common factor is 2 in this case.
For 2x^2, 4x it's easier to write it out:
The factors of 2x^2 are 2, x, x
The factors of 4x are 2, 2, x
Because they both have 2 and x, the greatest common factor is 2x in this case.
The Gonzalez family has a combined monthly income of $1850. Their food budget is $ 380 per month. What percent of their monthly income is budgeted for food? (Round your answer to the nearest whole percent.)
Answer:
21 percent of their monthly income is budgeted for food.
Step-by-step explanation:
Given:
The Gonzalez family has a combined monthly income of $1850.
Their food budget is $380 per month.
Now, to find the percent of their monthly income is budgeted for food.
Total income = $1850.
Food budget = $380.
Now, to get the percent of the food budget:
[tex]\frac{380}{1850} \times 100[/tex]
[tex]=\frac{38000}{1850}[/tex]
[tex]=20.54\%.[/tex]
Thus, the percent nearest to whole = 21%.
Therefore, 21 percent of their monthly income is budgeted for food.
Simplfy the expression 3x+4(x-6)-3(x-7)
Answer:
the answer is 4x-3
Step-by-step explanation:
To simplify the expression 3x + 4(x - 6) - 3(x - 7), distribute the multiplication across the parentheses, combine like terms, and simplify to get the final result: 4x - 3.
To simplify the expression 3x + 4(x - 6) - 3(x - 7), follow these steps:
Distribute the 4 into the second parenthesis: 4 imes x - 4 imes 6 which gives 4x - 24.
Distribute the -3 into the third parenthesis: -3 imes x + (-3) imes (-7) which gives -3x + 21.
Combine like terms with the rest of the expression: 3x + (4x - 24) + (-3x + 21).
Add/subtract the x terms and constant terms: 3x + 4x - 3x (which simplifies to 4x) and -24 + 21 (which simplifies to -3).
The simplified form of the expression is 4x - 3.
How many hours will it take to complete a 63-km bike ride if you go 20 km per
hour the whole time?
Answer: time = 3.15 hrs
Step-by-step explanation:
distance = 63km
speed = 20km/hr
time = ?
speed = distance / time
therefore :
time = distance / speed
time = 63/20
time = 3.15 hours
Answer: 3 for whole numbers, but if you want to be exact, 3 and 3/20 (three and three twentieths)
Step-by-step explanation:
20 times 3 is 60, and there is 3 left so you would make it a fraction since it won't divide into 20.
What is the sum of the measures of the interior angles of a hexagon?
Answer:
720°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6 ( number of sides of a hexagon ), thus
sum = 180° × 4 = 720°
The sum of the measures of the interior angles of a hexagon is [tex]720^{\circ}[/tex]
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain. The bounded plane region, the bounding circuit, or the two together, may be called a polygon. A hexagon is a six-sided polygon or [tex]6-[/tex]gon. Interior angles are those that lie inside a polygon.
The total of the internal angles of any simple hexagon is [tex]\boldsymbol{720^{\circ}}[/tex]
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2. In the Practice Book, underline details that
ook, underline details that explain the main idea that it is possible to link
machine to mind. Describe how these details explam
Well, what is the story?
sure, what. you will have to do is to fomulate the links between the human brain and what a computer does, i prefer a mind map, then find the common procedures and use it in your answer
Choose the best answer.
Jim Tree sold 3 items for cash.
Where would Jim list the amount received?
-Equipment Assets
-Other Assets (includes -receivables)
-Cash Assets
-Owner's Equity
-Liabilities - Accounts -Payable
Answer:
Cash assets is the answer
A rectangular garage is 12 meters long and 10 meters wide. What is its perimeter?
What are the x- and y-intercepts of -6x+4y=96
Answer:
Step-by-step explanation:
to find the x intercept, sub in 0 for y and solve for x
-6x + 4y = 96
-6x + 4(0) = 96
-6x = 96
x = -96/6
x = -16.....ur x intercept is -16 or (-16,0) <===
to find the y intercept, sub in 0 for x and solve for y
-6x + 4y = 96
-6(0) + 4y = 96
4y = 96
y = 96/4
y = 24....so ur y int is 24 or (0,24) <===
[tex]\text{Find the x and y intercepts:}\\\\\text{x intercepts:}\\\\\text{Plug in 0 to y}\\\\-6x+4(0)=96\\\\\text{Solve:}\\\\-6x+4(0)=96\\\\-6x=96\\\\\text{Divide both sides by -6}\\\\\boxed{x=(-16,0)}\\\\\text{y intercept:}\\\\\text{Plug in 0 to x}\\\\-6(0)+4y=96[/tex]
[tex]\text{Solve:}\\\\-6(0)+4y=96\\\\4y=96\\\\\text{Divide both sides by 4}\\\\\boxed{y=(0,24)}[/tex]
Please help with these 4 problems. See attachment
What is the answer to |x-4|<13
Answer:
The solution is -9 < x < 17.Step-by-step explanation:
|x-4|<13.
The above equation means, whatever the actual value of x is, the value of (x - 4) must be greater than - 13 and less than 13.
Hence, -13 < x - 4 < 13 or, -9 < x < 17. The value of x will be in between -9 and 17. The value of x can not be -9 or 17.
i give up i might have to pull an allnighter
Answer:
Yes, they are congruent
Step-by-step explanation:
Yes, they are congruent because all the side and angle lengths are congruent.
Answer:
Yes
Step-by-step explanation:
3q - 16q = 7 + 2(-89 – 3)
Answer:
q = 177/13
Step-by-step explanation:
3q - 16q = 7 + 2(-89 – 3)
-13q = 7 + 2(-92)
-13q = 7 - 184
-13q = -177
q = (-177)/(-13)
q = 177/13
QUESTION 10.2 Two mechanics worked on a car. The first mechanic charged $ 95 per hour, and the second mechanic charged $ 75 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $ 1800 . How long did each mechanic work?
Mechanic A worked for 15 hours and mechanic B worked for 5 hours.
Step-by-step explanation:
Given,
Per hour charges of mechanic A = $95
Per hour charges of mechanic B = $75
Total hours worked = 20
Total amount charged = $1800
Let,
x represent the number of hours of mechanic A
y represent the number of hours of mechanic B
According to given statement;
x+y=20 Eqn 1
95x+75y=1800 Eqn 2
Multiplying Eqn 1 by 95
[tex]95(x+y=20)\\95x+95y=1900\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](95x+95y)-(95x+75y)=1900-1800\\95x+95y-95x-75y=100\\20y=100[/tex]
Dividing both sides by 20
[tex]\frac{20y}{20}=\frac{100}{20}\\y=5[/tex]
Putting y=5 in Eqn 1
[tex]x+5=20\\x=20-5\\x=15[/tex]
Mechanic A worked for 15 hours and mechanic B worked for 5 hours.
Keywords: linear equation, elimination method
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The first mechanic worked for 15 hours while the second mechanic worked for 5 hours.
Let's denote the number of hours worked by the first mechanic as x and the number of hours worked by the second mechanic as y.
We know two things:
The total hours worked by both mechanics is 20:⇒ x + y = 20
The total charges for both mechanics is $1800:⇒ 95x + 75y = 1800
Using the first equation, we can express y in terms of x:⇒ y = 20 - x
Substitute this value of y into the second equation:⇒ 95x + 75(20 - x) = 1800
Distribute and combine like terms:⇒ 95x + 1500 - 75x = 1800
⇒ 20x + 1500 = 1800
⇒ 20x = 300
⇒ x = 15
So the first mechanic worked for 15 hours. To find the second mechanic's hours, substitute x back into y = 20 - x:⇒ y = 20 - 15 = 5
Thus, the second mechanic worked for 5 hours.
Complete question:
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $75 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1800. How long did each mechanic work?
The sum of two numbers is 119. If 4 times the smaller number is subtracted from the larger number the result is nine. Find a two numbers.
The larger number is 97 and smaller number is 22.
Step-by-step explanation:
Let,
The two numbers are x and y.
According to given statement;
x+y=119 Eqn 1
y-4x=9 Eqn 2
Subtracting Eqn 2 from Eqn 1
[tex](x+y)-(y-4x)=119-9\\x+y-y+4x=110\\5x=110[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{110}{5}\\x=22[/tex]
Putting x=22 in Eqn 1
[tex]22+y=119\\y=119-22\\y=97[/tex]
The larger number is 97 and smaller number is 22.
Keywords: linear equation, elimination method
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Xander needs to collect at least 120 cans for a food drive to earn community service credit. He has already collected 64 items. Choose the inequality and solution to represent the number of cans, c, that Xander must still collect.
Answer:
Step-by-step explanation:
so he needs to collect at least 120 cans....and he already has 64
c + 64 > = 120 (thats a greater then or equal sign)
c > = 120 - 64
c > = 56....he needs to collect at least 56 more
To represent the number of cans that Xander must still collect to reach at least 120 cans, use the inequality c >= 120 - 64. The solution to the inequality is c >= 56.
Explanation:To represent the number of cans that Xander must still collect to reach at least 120 cans, we can use the inequality:
c >= 120 - 64
This inequality represents that Xander must collect a number of cans that is greater than or equal to the difference between the desired total (120) and the number of cans he has already collected (64).
The solution to the inequality is:
c >= 56
This means that Xander must still collect at least 56 more cans to reach his goal.
What is the domain and range of the relation shown in the table?
x y
0 3
5 4
9 2
32 7
domain: {0, 5, 9, 32} range: {y|y∈R}
domain: {x|x∈R} range: {2,3,4,7}
domain: {0, 5, 9, 32} range: {2,3,4,7}
domain: {2,3,4,7} range: {0, 5, 9, 32}
Answer:
domain: {0, 5, 9, 32} range: {2,3,4,7}
Step-by-step explanation:
we know that
For a set of ordered pairs, the first elements of each ordered pair represents the domain of the function and second elements of each ordered pair represents the range of the function.
The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
In this problem we have
values of x ----> [tex]\{0,5,9,32\}[/tex]
values of y ----> [tex]\{2,3,4,7\}[/tex]
therefore
domain: {0, 5, 9, 32} range: {2,3,4,7}
Will someone please help me?
Answer:
The number of viruses was 2 times greater than bacteria.
Step-by-step explanation:
The number of viruses was [tex]2*10^9[/tex], and the number of bacteria was [tex]1*10^9[/tex].
To find how many times was the virus number greater than the bacteria number, we just divide the virus number by bacteria number:
[tex]\frac{ virus\:number }{bacteria\:number} =\frac{2*10^9 }{1*10^9} = 2*\frac{10^9}{10^9} =2[/tex]
Viruses are 2 times greater.
Answer:
Viruses are 2 times of the bacteria.
Step-by-step explanation:
Given:
Number of viruses = [tex]2\times 10^9[/tex]
Number of bacteria = [tex]1\times 10^9[/tex]
We have to found how many times viruses are greater than the bacteria.
To find how many times,we can divide both the numbers to compare its values.
Lets
Numerator = Number of viruses
Denominator = Number of bacteria
Dividing both we have,
⇒ [tex]\frac{2\times 10^9}{1\times 10^9}[/tex]
⇒ [tex]2\times 10^(^9^-^9)[/tex] ...[tex]\frac{ab^x}{cb^y}=\frac{ab^x^-^y}{c}[/tex]
⇒ [tex]2\times 10^0[/tex] ...[tex]a^0=1[/tex]
⇒ [tex]2[/tex]
So the viruses are 2 times of the bacteria.