Answer:
a) I think Aaron is correct.
Step-by-step explanation:
Aaron and Blake are having a disagreement during math class. Aaron says 0.3838 is a terminating decimal while Blake says it's a repeating decimal.
a) I think Aaron is correct.
b) If we convert the decimal into fraction then this will give
[tex]0.3838 = \frac{3838}{10000} = \frac{1919}{5000}[/tex]
c) So the fraction [tex]\frac{1919}{5000}[/tex] has an exact value of 0.3838 and this does not repeat. Hence, this is a terminating decimal. (Answer)
Susie wants to deposit $6000 into a savings account and plans to leave her money in the account for 10 years. The bank offers two types of savings accounts
• Account 1: offers 4.5% simple interest.
• Account 2: offers 4% interest compounded annually.
Which statement about the savings accounts is true?
A. Susie should invest her money in Account 1 because the account will earn $300.00 more in interest than Account 2 after 10 years.
B. Susie should invest her money in Account 1 because the account will earn $436.35 more in interest than Account 2 after 10 years.
C. Susie should invest her money in Account 2 because the account will earn $617.82 more in interest than Account 1 after 10 years.
D. Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years.
Answer:
Option D
Step-by-step explanation:
step 1
Account 1
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\r=4.5\%=4.5/100=0.045[/tex]
substitute in the formula above
[tex]A=6,000(1+0.045*10)[/tex]
[tex]A=6,000(1.45)[/tex]
[tex]A=\$8,700[/tex]
step 2
Account 2
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\ r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=6,000(1+\frac{0.04}{1})^{1*10}[/tex]
[tex]A=6,000(1.04)^{10}[/tex]
[tex]A=\$8,881.47[/tex]
step 3
Find the difference
[tex]\$8,881.47-\$8,700=\$181.47[/tex]
therefore
Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years
What property is 3(x-y)=3x-3y
Answer:
The distributive property is used
Step-by-step explanation:
3(x - y) = 3x - 3y Distribute the 3 to the (x - y)
Which are true of the function f(x)=49(1/7)^x
select three options.
1) the domain is the set of all real numbers
2) the range is the set of all real numbers
3) the domain is x>0
4) the range is y>0
5) as x increased by 1, each y-value is one seventh of the previous y-value
The Option (1),(4) and (5) are correct.
Step-by-step explanation:
The function given to us is : y= f(x) =49(1/7)^x
The following statements are true regarding the above function is
As you can see that the value of y(49)is defined for all values of x , so the Domain is the set of all values of x , which is set of all real numbers.X is defined for all values of y. So the Range of all the values that y can take is also set of all real numbers greater than zero, i.e y>0.As x increased by 1, each y-value is one seventh of the previous y-valueAnswer:
The correct options are 1, 4 and 5.
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is initial value and b is growth factor.
Domain of this function is all real numbers. If a>0, then range is all positive numbers.
The given function is
[tex]f(x)=49(\frac{1}{7})^x[/tex]
where, a =49 and b=1/7.
It is an exponential function. So, the domain is the set of all real numbers.
Since, a=49 which is a positive value, therefore the range is y>0.
The value of b is 1/7, it means as x increased by 1, each y-value is one seventh of the previous y-value.
Therefore, the correct options are 1, 4 and 5.
A bakery has 36 glazed donuts on display.This is 80% of the total number of donuts what is the total number of donuts in the bakery
Answer:
45
Step-by-step explanation:
Given:
A bakery has 36 glazed donuts on display.
This is 80% of the total number of donuts.
Question asked:
what is the total number of donuts in the bakery ?
Solution:
Let total number of donuts in the bakery = [tex]x[/tex]
80% of total number of donuts = 36 (given)
[tex]80\% of x = 36[/tex]
[tex]\frac{80x}{100} = 36[/tex]
Multiplying both side by 100
[tex]80x = 3600[/tex]
Dividing both side by 80
[tex]x = 45\\[/tex]
Thus, the number of donuts in the bakery is 45
Is 9 bigger than negative 10??
Answer:
Yes 9 is larger than -10
Step-by-step explanation:
Any positive number is larger than a negative number
Answer: yes
Step-by-step explanation: this is so because on the number line 9 comes first while -10 is far behind from -1
Arrange the following measurement in order from smallest to largest. 2000 milititers 4.1 liters 0.7 liters
answer is
o.7 liters 2000 milliliters and 4.1 liters
Step-by-step explanation:
1 / 5
1 \text{ liter} ={1{,}000}\text{ milliliters}1 liter=1,000 milliliters1, start text, space, l, i, t, e, r, end text, equals, 1, comma, 000, start text, space, m, i, l, l, i, l, i, t, e, r, s, end text
So, 1 \text{ milliliter} = \dfrac1{1{,}000}\text{ liter}1 milliliter=
1,000
1
liter1, start text, space, m, i, l, l, i, l, i, t, e, r, end text, equals, start fraction, 1, divided by, 1, comma, 000, end fraction, start text, space, l, i, t, e, r, end text
Hint #22 / 5
We know \maroonD{0.7}0.7start color #ca337c, 0, point, 7, end color #ca337c liters is less than \greenD{4.1}4.1start color #1fab54, 4, point, 1, end color #1fab54 liters. But where does \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters fit?
We need to convert \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters to liters before we can compare.
Hint #33 / 5
\begin {aligned}{\blueD{2{,}000} \text{ mL}}&= {\blueD{2{,}000} \text{ mL}}\times \dfrac{1 \text{ L}}{{1{,}000 \text{ mL}}} \\\\ &= {\dfrac{\blueD{2{,}000} \cancel{\text{ mL}}}{1}}\times \dfrac{1 \text{ L}}{{1{,}000 \cancel{\text{ mL}}}} \\\\ &=\dfrac{\blueD{2{,}000}\text{ L} }{1{,}000}\\\\ &=\blueD{2{,}000}\text{ L}\div1{,}000\\\\ &=\blueD{2}\text{ L} \end{aligned}
2,000 mL
=2,000 mL×
1,000 mL
1 L
=
1
2,000
mL
×
1,000
mL
1 L
=
1,000
2,000 L
=2,000 L÷1,000
=2 L
What is the value of 4x 3+4x when x=4
Final answer:
The value of 4x when x=4 is 16, and for proportions like 1:2=4:x, you'd get x=8 by cross multiplying.
Explanation:
The value of 4x when x=4 is simply 4 multiplied by 4, which equals 16. This calculation is a basic algebraic operation, and it should not be confused with more complex problems. For example, if you're trying to solve a proportion like 1:2=4:x, you'd set up a proportion to figure out the value of x. To solve for x you can use the cross multiplication method, resulting in 1x = 8, hence x = 8.
Final answer:
The value of 4x^3 + 4x when x=4 is found by substituting 4 into the expression and simplifying step by step, resulting in a final answer of 272.
Explanation:
When answering a question such as "What is the value of 4x3 + 4x when x=4," we need to substitute the value of x into the expression and simplify.
Let's break it down step-by-step:
Substitute x with 4 into the expression: 4(4)3 + 4(4).
Calculate the exponent: (4)3 = 4 x 4 x 4 = 64.
Multiply by 4: 4 x 64 = 256.
Add the second term: 256 + 4(4).
Perform the second multiplication: 4 x 4 = 16.
Add the two results together: 256 + 16.
Get the final answer: 272.
The value of 4x3 + 4x when x=4 is 272.
If r=4 units and x=8 units then what is the volume of the cylinder?
Answer:
To answer this you will use the formula V = pi x radius ^2 x height. The substitution for this would be 3.14 x 4^2 x 8. The approximate answer is 401.92 cubic units. 3.14 is an approximation of pi.
Note: It does not say that x is the height, but this is the only piece of information missing without an obvious label, so I am using it as the height.
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Step-by-step explanation:
What is the solution to this system?
Y=-5x+8,y=11/7x-4/7
Answer:
Step-by-step explanation:
hello : the system is : y =-5x+8...(*)
y =11/7x-4/7 ...(**)
by (*) and (**) : 11/7x-4/7 = -5x+8
multiply by 7 : 11x-4 = -35x+56
11x+35x = 56+4
46x = 60
x = 60/46 = 30/23
continu.....put the value for x in (*) or (**)
Leroy is going to take a flight from Buffalo, New York, to Dallas, Texas. The
flight leaves Buffalo at 10:15 a.m. Buffalo time and arrives in Dallas at 1:33
p.m. Dallas time. If Buffalo is in the eastern time zone and Dallas is in the
central time zone, how long is the flight?
Use the following to help you answer the question,
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
O
A. 4 h 18 min
O
O
O
B. 5 h 18 min
C. 2 h 18 min
D. 3 h 18 min
Answer:
A- 4h 18min
Step-by-step explanation:
First you look at the data provided that shows that this is this latest time, so when it is 10:15 in buffalo, it is 9:15 in Dallas. He arrives in Dallas at 1:33, so you can either think in central time which is 9:15-1:33, or in eastern time which is 10:15-2:33. From there you can subtract 15 from 33 getting 18, and from 10 o’clock to 2 o’clock (or 9 o’clock to 1 o’clock) is 4 hours.
I need this asap so if you can help that would be amazing . I can boost the points to more than 50 comment if you want more...
Multiply the number amount of cartridges by the number of books and add that tot he number of cartridges by the number of magazines.:
This needs to be either less than or equal tot he total cartridges she wants to use
40B + 30M ≤ 300
Do the same with pages:
200B + 80M ≤ 1200
The measure of <B is (3x - 4) and the measure of
<D is (2x-6)”. What are the measures of angles B
and D?
m<B=
m<D =
Step-by-step explanation:
Given information is insufficient for finding the measures of angles B and D.
Answer:
110 and 70
Step-by-step explanation:
A farmer has two pieces of land in a parallelogram shape on the same base. He grows vegetables and flowers in two triangular pieces of land as shown in diagram.
Q: Check whether the two triangular pieces of land are equal in area.
Step-by-step explanation:
In trapezoid ABCF, AB || CF.
Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.
[tex] \therefore Ar(\parallel^{gm} ABEF) = Ar(\parallel^{gm}ABCD)\\... (1)\\\\
\because\: Ar(\parallel^{gm} ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\
\&\: Ar(\parallel^{gm}ABCD)\\= Ar(\triangle BCE) +Ar(\square ABED)....(3) [/tex]
From equations (1), (2) & (3), we find:
[tex] Ar(\triangle AFD) + Ar(\square \: ABED) \\ = Ar(\triangle BCE) +Ar(\square ABED)
\\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}}
\\ [/tex]
Thus, the two triangular pieces of land are equal in area.
Hence proved.
The area of a rectangular sandbox is (5x + 40) feet. Factor 5x + 40 to find possible
dimensions of the sandbox.
The possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].
Important information:
The area of the rectangular sandbox is [tex]5x+40[/tex].We need to find the possible dimensions of the sandbox.
Area of a rectangle:Formula for the area of a rectangle is:
[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
Factorize the given expression to find the possible dimensions of the sandbox.
[tex]5x+40=5x+5\times 8)[/tex]
[tex]5x+40=5(x+8)[/tex]
Thus, the possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].
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ifyou choose one without looking, the probability you choose a green marble is StartFraction 20 Over 40 EndFraction
. How can you write this probability as a decimal? Write this probability as a decimal. Use a word or phrase to describe this probability.
How do you change the fraction to a decimal?
A.
Multiply the numerator and denominator by 3.
B.
Divide the numerator by the denominator.
C.
Divide the denominator by the numerator.
D.
Multiply the numerator by the denominator.
a) To write the probability as a decimal, we divide the numerator (20) by the denominator (40). This gives us the decimal representation of the probability.
b) To change the fraction to a decimal, we divide the numerator by the denominator.
So, the correct answer is option B: Divide the numerator by the denominator.
Explanation:
To change the fraction [tex]\( \frac{20}{40} \)[/tex] to a decimal, we perform the division [tex]\( \frac{20}{40} \)[/tex].
[tex]\[ \frac{20}{40} = 0.5 \][/tex]
Therefore, the probability of choosing a green marble as a decimal is 0.5.
For the function defined by f(x)=12/x^2, what is the constant proportionality
A. 120
B.undefined
C. 12
D.1200
Answer:
12
Step-by-step explanation:
What is 3 4/15 divided by ( 8 times 6 3/10
A train has 3 passenger cars and each car has 4 columns of seats and each column holds 40 passengers. If one of the cars has 15 people standing in addition to all of the sitting passengers, and the rest of the cars are full without anyone standing, how many passengers are on the train?
Answer:
There are a total of 495 people on the train
Step-by-step explanation:
Let's identify what we know:
1) The train has 3 passenger cars
2) Each passenger car has 4 columns, and each can accommodate 40 people.
3) All three passenger cars are full, but one of them has 15 additional people standing.
We can create a formula to model the problem:
x = ((3 x 4) x 40) + 15
x = the total number of passengers!
There are a total of 180 people sitting, and 15 additional people standing in one of the passengers cars, equaling a total of 495 passengers on the train.
The train has a total of 495 passengers.
Explanation:To calculate the number of passengers on the train, we first need to determine the seating capacity of each car. Since each car has 4 columns of seats and each column holds 40 passengers, each car can seat a total of 4 x 40 = 160 passengers.
Next, we need to account for the 15 people standing in one of the cars. This means that one car has 160 + 15 = 175 passengers.
Finally, since the rest of the cars are full without anyone standing, we can assume that the other two cars also have 160 passengers each. Therefore, the total number of passengers on the train is 175 + 160 + 160 = 495.
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The length is 3 inches more than twice the width. Which expression represents the perimeter of the frame in inches?
2w+3
Answer:
[tex](6W+6)\ in[/tex]
Step-by-step explanation:
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex] ----> equation A
where
L is the length
W is the width
we have
The length is 3 inches more than twice the width
so
[tex]L=2w+3[/tex] ----> equation B
substitute equation B in equation A
[tex]P=2(2W+3+W)[/tex]
Combine like terms
[tex]P=2(3W+3)\\P=(6W+6)\ in[/tex]
What is the nth term of the geometric sequence -2,10,-50
Answer:
[tex]T_n=-1(-5)^n^-^1[/tex]
Step-by-step explanation:
We are given;
A geometric sequence;
-2,10,-50
Required to determine the nth term
The nth term in a geometric sequence is given by the formula;
[tex]T_n=a_1r^n^-^1[/tex]
where [tex]a_1[/tex] is the first term and r is the common ratio;
In this case;
[tex]a_1=-2[/tex]
r = 10 ÷ -2
= -5
Therefore;
To get the nth term in the given geometric sequence we use;
[tex]T_n=-1(-5)^n^-^1[/tex]
Thus, the nth term is [tex]T_n=-1(-5)^n^-^1[/tex]
-8x+2y=-2
4x+4y=-4
What is the solution to the system
The solution to system is x = 0 and y = -1
Solution:
Given system of equations are:
-8x + 2y = -2 ----------- eqn 1
4x + 4y = -4 ---------- eqn 2
We have to solve the system of equations
We can solve the equations by elimination method
Multiply eqn 2 by 2
8x + 8y = -8 ------ eqn 3
Add eqn 1 and eqn 3
-8x + 2y = -2
8x + 8y = -8
( + ) ---------------
0x + 2y + 8y = -2 - 8
10y = -10
Divide both sides by 10
y = -1
Substitute y = -1 in eqn 1
-8x + 2(-1) = -2
-8x - 2 = -2
-8x = -2 + 2
x = 0
Thus the solution to system is x = 0 and y = -1
Tina wants to run 12 3/5 miles over 7 days she wants to run the same distance each day how far must she run each day
To find out how much Tina needs to run each day, divide the total miles she wants to run by the number of days. The result is that Tina needs to run 1.8 miles each day.
Explanation:To find out how far Tina must run each day, we need to divide the total distance she plans to run by the number of days she plans to run. Tina wants to run 12 3/5 miles over 7 days. As a first step, convert her mixed number to an improper fraction. 12 3/5 is equivalent to 63/5.
Now, to find the distance she must run each day, simply divide 63/5 miles by 7 days. Carrying out this division gives us distance of 9/5 miles per day, or in decimal form, 1.8 miles per day.
So, Tina should run 1.8 miles each day to reach her goal.
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mira's kitchen holds up to 103.468 liters of water. round this amount to the nearest liter WORTH: 10 PTS
Answer:
It would round down to 103 liters.
Step-by-step explanation:
c) Find the value of x:
5x + 2 = 4x + 8
Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will not be used.
To find the circumference of a circle, use the formula C = 2πr. To find the area, use the formula A = πr^2.
Explanation:The question asks to match each circular flower bed on the left to its circumference and its area on the right. In order to find the circumference of a circle, we use the formula C = 2πr, where r is the radius of the circle.
To find the area of a circle, we use the formula A = πr^2. We can use these formulas to calculate the circumference and area of each circular flower bed and match them to the options on the right.
For example, if a circular flower bed has a radius of 3 meters, we can find its circumference by plugging the radius into the formula: C = 2π(3) = 6π meters. Similarly, we can find its area by plugging the radius into the formula: A = π(3^2) = 9π square meters.
PLEASE ANSWER ASAP
Talk of the Town is a cell phone provider. They charge by the month. The first month of service costs $72.99. The second month of service costs $101.44. The third month of service costs $129.89. Write an equation in the form of
y=c+d(x−1)
to represent this situation. Explain how you got your equation.
Answer:
[tex]y=72.99+28.45(x-1)[/tex]
Step-by-step explanation:
Linear Modeling
Some situations in real life are bound to be modeled as mathematical functions. A model allows scientists and analysts to take decisions based on predicted values coming from those models.
To construct them we usually take or measure values of the variables of interest and find the general equation of the model. In this case, we'll find the relation between the service costs (y) of a cell phone provider and the number of months (x).
There are three points available: ( 1 , 72.99 ) , ( 2 , 101.44 ) , ( 3 , 129.89 ) and we only need two to find a function of the form
[tex]y=c+d(x-1)[/tex]
We'll use the first two points and use the third point to verify the validity of the model. Let's plug in the first point:
[tex]72.99=c+d(1-1)[/tex]
Operating
[tex]72.99=c\\c=72.99[/tex]
Now for the second point
[tex]101.44=72.99+d(2-1)[/tex]
Operating and rearranging
[tex]d=101.44-72.99=28.45[/tex]
Our model is complete:
[tex]\boxed{y=72.99+28.45(x-1)}[/tex]
Let's check the third point ( 3 , 129.89 ) by plugging x=3
[tex]y=72.99+28.45(3-1)=72.99+56.9=129.89[/tex]
The point belongs to the function.
Final answer:
The cell phone provider's escalating monthly charges can be represented by a linear equation, demonstrating the initial cost plus the consistent monthly increase. The equation is y = 72.99 + 28.45(x - 1).
Explanation:
To find the equation representing the cell phone provider Talk of the Town, we observe the costs for the first three months: $72.99 for the first month, $101.44 for the second, and $129.89 for the third. The increase in cost from one month to the next is consistent, increasing by $28.45 each time. This situation can be expressed as a linear equation in the form y=c+d(x−1), where y is the total cost, c is the starting value, d is the difference per period, and x represents the month number.
To find c (the initial cost), we look at the first month's charge: $72.99. d, the monthly increase, is $28.45. Thus the equation for the total cost of service from Talk of the Town over x months is y = 72.99 + 28.45(x - 1). This equation accounts for the initial cost in the first month and the consistent monthly increase thereafter.
When a=2 b=3 and c=5 what is the value of a(b+c)
Show how you got the answer
Answer:
B =
Step-by-step explanation:B + C would be 8 because B=2 and C=5. 5 + 8 is 8
32h = 288 solve for h
Answer:
h= 9
Step-by-step explanation:
you divide both sides by 32
and 288 divided by 32 is 9
with a head wind, it takes 7 hours to fly 2800 miles from miami to seattle. with a tailwind, and the same airspeed, it takes 5 hours to fly in the opposite direction, from seattle to miami. find the airspeed and the windspeed
Answer:
Plane speed: 480mph
Wind speed: 80mph
Step-by-step explanation:
Miami to Seattle: time = 7hrs
Speed (s) = 2800mph
D = speed/time = 2800/7
= 400mph
Seattle to Miami:
Same speed = 2800mp
Time = 5hrs
Distance (D) = speed/time
= 2800/5 = 560mph
Let p be speed of plane and w wind speed.
Therefore, P+w = 560. . .1
P-w = 400. . .2
2p = 960
P = 960/2 = 480
Therefore, P + w = 560
480 + w = 560
W = 80mph
While P = 480mph
Right and solve an equation that can be used to find the width of the backyard that is 120 feet long and has a perimeter of 330 feet
The width of backyard is 45 feet.
Step-by-step explanation:
Given,
Length of backyard = 120 feet
Perimeter of backyard = 330 feet
Width of backyard = w
Perimeter = 2(Length + Width)
[tex]330=2(120+w)\\330=240+2w\\330-240=2w\\90=2w\\2w=90[/tex]
Dividing both sides by 2
[tex]\frac{2w}{2}=\frac{90}{2}\\w=45[/tex]
The width of backyard is 45 feet.
Keywords: perimeter, division
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