Answer:
[tex]y=250(5)^x[/tex]
Step-by-step explanation:
The growth of a population of bacteria can be represented by exponential growth function,
[tex]y=a(1+r)^x[/tex]
where,
y = the population of the bacteria after x hours,
x = the number of hours,
a = initial population of bacteria,
r = rate of growth,
At the beginning the number bacteria was 250 and the population of bacteria quadruples every hour i.e rate of growth is 400% or 4 per hour.
Putting all the values,
[tex]y=250(1+4)^x[/tex]
[tex]\Rightarrow y=250(5)^x[/tex]
Your parents are renting an apartment for you when you go away to college. An annual contract is $502.00/month with a 2-month penalty if you break the lease. The month-to-month contract is $615.00/month. How much is the difference in payments if you stay the whole year?
Answer:
The month-to-month contract will cost an extra $1356.
Step-by-step explanation:
"An annual contract is $502.00/month with a 2-month penalty if you break the lease."
If you stay the whole year, and you pay $502 per month, you pay 12 * $502 = $6024 for the entire year.
"The month-to-month contract is $615.00/month."
If you stay the entire year, you pay 12 * $615 = $7380.
The difference is $7380 - $6024 = $1356
1.) you have a credit card with an initial balance of $3,168 and an interest rate of 12.75 % APR if you make no payments on the car for 3 months how much is your balance by the end of the third month?
A.) $3,571.92
B.) $3,270.06
C.) $3,201.66
D.) $3,860.43
2.) your gross pay is $2,759 your involuntary deductions are FICA 7.65 percent Federal withholding 12% and state withholding 7% how much are you allowed for housing and fixed expenses?
A.) $772.52
B.) $993.24
C.) $728.54
D.) $566.64
3.) You are paid $8.25/hour. You work 35 hours/week for 3 weeks. Your involuntary deductions are FICA (7.65%), federal withholding (13%), and state withholding (9%). How much is your realized income?
A 203.13
B 866.25
C 288.75
D 609.39
Answer:
1.) [B]
2.) [C]
(3.) [D]
Step-by-step explanation:
1.) Initial amount = $3168
Annual percentage rate = 12.75
per month percentage rate = 1.06%
Interest after 3 months = P*R*T/100
= 3168*1.06*3/100
= 100.74 (aprox)
Balance after 3 months = 3168-100.74
= $3270.06 (aprox) (B.)
2.) Gross pay = $2759
Total interest rate = 7.65%+12%+7% = 26.65%
interest amount= 26.65% *2759 =$728.24 (aprox)
Housing and fixing expenses= $728.54 (C.)
3.) 1 hour = $8.25
1 week= 35 hours
3 weeks = 35*3 hours = 105 hours
Total income= 105 hours = $8.25*105= $866.25
Total interest to be deducted = 7.65+13+9 = 29.65 %
Income after deducting interest = $866.25-256.843 = $609.407
(D.)
The answers are:
1) C - $728.54
2) D - $609.39
3) B - $3,270.06
Point M is the midpoint of AB. The coordinates of point A are (-7,2) and the coordinates of M are (-2,2). What are the coordinates of point B?
Answer:
(-9/2,2)
Step-by-step explanation:
Midpoint equals (x1+x2)/2, (y1+y2)/2
Answer:
(-9/2,2)
Step-by-step explanation:
Wyatt is training for a race. He will run 3 4 of a mile a day for 8 days. How far will Wyatt run altogether?
FAST!!!!!!!!!! PLZ im timed
Hello!
3 8 24 6
- x - = _ = - OR 6
4 1 4 1
Answer: 6 OR 6/1
Hope this helps! ~Pooch ♥
Answer:
6 miles.
Step-by-step explanation:
I believe your trying to say 3/4
3/4 x 8
3/4 x 8/1
24/4 = 6
triple of a number x decreased by one
Answer:
3x-1
Step-by-step explanation:
if you triple x, you multiply x 3 times
Sin (3pi/4) =_____ please help!!!
[tex]sin\frac{3}{4}\pi=sin(\pi-\frac{\pi}{4})=sin\frac{\pi}{4}=\frac{\sqrt2}{2}[/tex]
Which inequality best represents that ice cream at −3°C is cooler than ice cream at 1°C?
A. −3°C > 1°C
B.−3°C < 1°C
C. 1°C > 3°C
D. 1°C < −3°C
Answer: Choice B
"ice cream at -3 degrees C is cooler than ice cream at 1 degree C"
-3 is smaller than 1
-3 < 1
Keep the order the same even though 1 > -3 is also possible, but fortunately this isn't listed.
a train travels 160 km in 2 h what is the trains average speed in km/h
Answer:
80km/h
Step-by-step explanation:
we know that the train is 160 km in 2 hours we need to find how much is in 1 hour you divide 160÷2= 80 so it means that there is 80 km in 1 hour which is "80 km/h"
Susie has $15.66 to spend on lunch for herself and her friend. If she spends an equal amount on each person. How much will susie spend on each of them?
Answer:
7.83
Step-by-step explanation:
Susie will spend $7.83 on each person
Susie has a total amount of $15.66 to spend on lunch for both her and her friend
She wants to spend an equal amount on both her and her friend
Hence, since she wants to spend equal amount on herself and her friend it can be calculated as follows
= 15.66/2
= 7.83
Hence Susie will spend $7.83 on herself and friend
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Find the slope of the line through each pair of points.
6) (-2,-1), (-1,0)
7) (-7,-4), (-13,-13)
8) (-14,-14), (-11,-9)
9) (17,-13), (-7,-13)
10) (7,4), (15,-18)
11) (4,14), (-2,17)
12) (-18,-10), (-18,15)
13) (13,-15), (14,-3)
14) (5,5), (-11,-6)
15) (3, -19), (-7,11)
Answer:
M=slope
(6) m=1
(7) m=3/2
(8)m=5/3
(9) m=0
(10) m=-11/4
(11) m=-1/2
(12) Undefined
(13) m=12
(14) m=11/16
(15) m=-3
Hope this would HELP
Step-by-step explanation:
what is the r^2 value of the following data to three decimal places???
Answer:
0.783
Step-by-step explanation:
To find first r and then r square for the data
correlation coefficient of x and y = Cov (x,y)/std dev x * std dev Y
Cov (x,y) = E(xy) -E(x)E(y)
Hence calculations would be as follows:
x y xy
1 2 2
2 10 20
5 5 25
7 18 126
10 25 250
Mean 5 12 84.6
Cov E(xy)-E(x)E(y) 24.6
r 0.884640297
r^2 0.782588454
so answre is 0.783 after rounding off.
Elise took out a payday loan for $500 due in 2 weeks that charges an $80 fee. What is the periodic interest rate of the loan?
The periodic interest rate of Elise's payday loan is calculated by dividing the $80 fee by the $500 borrowed, resulting in a rate of 16% for the 2-week period.
To calculate the periodic interest rate of Elise's payday loan, we need to consider the fee charged as the interest for the period of the loan, since the loan is due in 2 weeks, which is a half-month period. Elise is being charged an $80 fee on a $500 loan, and this fee represents the interest for the loan's term.
Therefore, we can calculate the periodic interest rate by dividing the interest by the principal and the number of periods.
Here's the calculation:
Interest (Fee) = $80
Principal (Amount borrowed) = $500
Periodic interest rate = Interest / Principal
Periodic interest rate = $80 / $500 = 0.16 or 16%
Since the period is 2 weeks, we could express this interest rate on a monthly basis if needed by scaling the bi-weekly rate to a monthly rate. However, the loan terms only mention a 2-week period, so the periodic interest rate for the loan's duration is 16%.
Which statement can be used to fill in the blank? (Pictures included)
Answer:
Look up the definition of that and then examples I’m in your class my names Joe
Step-by-step explanati
How do I graph y=6x+4
The graph of the linear equation y = 6x + 4 is drawn below.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The equation is given below:
y = 6x + 4
Convert the equation into intercept form, then we have
y = 6x + 4
6x - y = - 4
x / (-0.667) + y / 4 = 1
The graph of the equation is given below.
More about the linear equation link is given below.
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Solve the system of equations.
Answer:
X=9 and Y=81
Step-by-step explanation:
For this case we have a system of two equations with two unknowns:
[tex]y = 9x\\y = 2x + 63[/tex]
Matching we have:
[tex]9x = 2x + 63[/tex]
subtracting 2x on both sides of the equation:
[tex]9x-2x = 2x-2x + 63\\7x = 63[/tex]
Dividing between 7 on both sides of the equation:
[tex]\frac {7x} {7} = \frac {63} {7}\\x = 9[/tex]
We find the value of y:
[tex]y = 9 (9)\\y = 81[/tex]
ANswer:
[tex]x = 9\\y = 81[/tex]
What are the real and imaginary parts of the complex number? 9+7i
An i is an imaginary value. So 7i is the imaginary part and 9 is the real part.
Hope this helps!!
Complex number is the number which is the combination of the real numbers and imaginary number. For the given complex number the real part is 9 and the imaginary part is 7.
Given information-
The complex number given in the problem is,
[tex]9+7i[/tex]
What is complex number?Complex number is the number which is the combination of the real numbers and imaginary number.
The complex number written in the form of,
[tex]a+bi[/tex]
Here [tex]a[/tex], [tex]b[/tex] are the real number and [tex]i[/tex] is the imaginary number called iota.
The value of the iota [tex]i[/tex] is,
[tex]i=\sqrt{-1}[/tex]
The complex number is made of two parts, the real part is [tex]a[/tex] and the imaginary part is [tex]b[/tex] for the above example.
Compare the given complex number with above complex number to find out the real and imaginary part of the complex number.
[tex]9+7i[/tex]
Here [tex]a[/tex] is 9 and [tex]b[/tex] is 7. Thus for the given complex number the real part is 9 and the imaginary part is 7.
Learn more about the real and imaginary parts of the complex number here;
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evaluate: 5–^2 =
WILL MARK AS BRAINLIEST
When you have a negative exponent, you move it to the other side of the fraction to make the exponent positive.
For example:
[tex]x^{-2}[/tex] or [tex]\frac{x^{-2}}{1}=\frac{1}{x^2}[/tex]
[tex]\frac{1}{y^{-2}}=\frac{y^2}{1}[/tex] or y²
So:
[tex]5^{-2}=\frac{1}{5^2}=\frac{1}{25}[/tex]
Your answer is B
The correct evaluation of [tex]5^{-2}[/tex] is [tex]\frac{1}{25}[/tex]
How to evaluate the expression?We know that [tex]a^{-b}[/tex] can be written as [tex]\frac{1}{a^{b} }[/tex]∴ [tex]5^{-2}[/tex] can be written as [tex]\frac{1}{5^{2} }[/tex]
So, [tex]5^{-2}[/tex] = [tex]\frac{1}{25}[/tex]
Option B is correct.
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The grade that a student scores on her math test is inversely proportional to the number of hours a week that she plays video games. She scores a 73.6 on a test when she plays 10 hours of video games per week. If this relationship continues at the same rate, what score can she expect on her math test if she plays video games for only 8 hours a week?
Answer:
She would make a 78.88% on a test if she played video games for only 8 hours a week.
Step-by-step explanation:
10 hours of video games=73.6% on a test.
8 hours of video games=x% on a test.
A proportion just doesn’t work out for this problem, so here’s what I did.
100-73.6=26.4
26.4 times .8 =21.12
100-21.12 equals 78.88
If you wanted to know what she would make on her test if she played video games for 6, 4, or 2 hours a week, you could do this.
78.88-73.6=5.28
There are increments of -5.28% for every 2 hours of video game play.
As you keep adding, here are the results.
6- 84.16%
4- 89.44%
2- 94.72%
0- 100%
After 18 hours of gameplay in a week, you would get 4.96% on a test, and then a 0 on not even completing the 19th hour.
A rectangle has an area (x2-17x+72) square units.Since the area of a rectangle is determined using the formula, A= lw, what could be the length and width of the rectangle
Answer:
length: 9
width: 8
Step-by-step explanation:
you would need to factorise the equation in order to work out the length and width of the rectangle
so to factorise x^2 -17x +72, you will need to numbers that multiply to make 72 and add to make -17
the numbers are -9 and -8
so the factorised equation is (x-9)(x-8)
if you equate it to 0 you get 9 and 8 as values for x
since the length is longer than the width
the length is 9 and the width is 8
Mr. Geyer dog weighs 32.01 pounds if he goes on a die and loses 5.89 pounds how much will he weigh
Answer: 27.12
Step-by-step explanation:
32.01
-5.89
27.12
HELP!!! ASAP PLEASE
The answer is A. An equation is when two quantities are equal to each other, thus having an equal sign.
What is the area of this parallelogram
20
28
30
35
How many centimeters are in 7 feet, given that 1 inch = 2.5 centimeters?
Answer:
210 cm
Step-by-step explanation:
We need to convert 7 ft to cm
We know that 1 ft = 12 inches
7 ft * 12 inches/1 ft = 84 inches
We know that 1 inch = 2.5 cm
( 1 inch is really 2.54 cm but you question says 2.5 cm)
84 inches * 2.5 cm/1 inch = 210 cm
Harvey the wonder hamster can run 3 1/6 km in 1/4 hour harvey runs at a constant rate what is his average speed in kilometers per hour
what is the domain of f(x) = 4^x?
Answer:
The domain are all real numbers, there are no restrictions on the value x can be the domain is the set of all real numbers.
Answer:
All real numbers.
D is the correct option.
Step-by-step explanation:
The given function is [tex]f(x)=4^x[/tex]
Domain is the set of x values for which the function is defined.
In this exponential function, no matter we take which x values, the function remains defined for all real values of x.
Therefore, the domain of the given exponential function is All real numbers.
D is the correct option.
"If parallel lines have a transversal, then corresponding angles are congruent."
On the fence, lines A and B are parallel and line C is a transversal. How many pairs of corresponding angles are available on the picture to use to prove the theorem? Which given pair of angles can be used?
A) 2 pairs; ∠5 and ∠1;
B) 2 pairs; ∠5 and ∠7;
C) 4 pairs; ∠2 and ∠4
D) 4 pairs; ∠3 and ∠5;
Answer:
Option C. 4 pairs; ∠2 and ∠4
Step-by-step explanation:
we know that
In the figure
[tex]m<6=m<1[/tex] -----> by corresponding angles
[tex]m<3=m<7[/tex] -----> by corresponding angles
[tex]m<5=m<8[/tex] -----> by corresponding angles
[tex]m<2=m<4[/tex] -----> by corresponding angles
therefore
Are available [tex]4[/tex] pairs of corresponding angles
The answer is the option C
-46 times a number minus 19 is equal to 86 less the number
Answer:
-46 * x - 19 = -86
Step-by-step explanation:
this a word problem!
lets break it down
-46 times a number
this will be -46 * x
minus 19 is equal to 86 less the number
-46 * x - 19 = -86
To solve the equation "-46 times a number minus 19 is equal to 86 less the number", we can simplify the equation by combining like terms and isolating x. The solution is x = -105/45 or approximately -2.33.
Explanation:To solve the equation -46 times a number minus 19 is equal to 86 less the number, we can first simplify the equation. Let's call the number x. So, -46x - 19 = 86 - x. We can solve for x by combining like terms and isolating x on one side of the equation. Adding x to both sides gives -45x - 19 = 86. Then, adding 19 to both sides gives -45x = 105. Finally, dividing both sides by -45 gives x = -105/45, which simplifies to x = -7/3 or approximately -2.33.
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help me!! need help!!!!! 10 minutes due!
Answer:
3
Step-by-step explanation:
The slope is 3 because the equation is y=mx+b. If you add in the terms m=3 and b=0. It is y=3x. M is the slope, so the slope is 3!
The green line below
Answer:
A D E are all true. The others are false and should not be checked.
Step-by-step explanation:
A crosses the x axis at (- 2.5,0)
B is false. The line does not go through (0,0) which is the origin.
C is false. The green line is not perpendicular to anything.
D is true. It crosses the y axis at (0,5)
E is true. It is on the xy plane.
F is false. It is not parallel to either axis.
3 is what percent of 12
Answer:
25%
Step-by-step explanation:
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage of 3 in 12 is 25%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
3 and 12.
The percentage of 3 in 12.
= 3/12 x 100
= 1/4 x 100
= 25%
Thus,
The percentage of 3 in 12 is 25%.
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