Answer:
[tex]T_n = \frac{2^na}{2}[/tex]
Step-by-step explanation:
Given
Bacteria splits to 2 at every 20 minutes
Required
Explain how to get the resulting number of bacteria
To do this we simply make use of geometric progression formula;
[tex]T_n = ar^{n-1}[/tex]
In this case; r = 2 (rate at which they split);
[tex]T_n = a * 2^{n-1}[/tex]
a represents the initial number of bacteria in the dish
Apply law of indices
[tex]T_n = a * \frac{2^n}{2^1}[/tex]
[tex]T_n = a * \frac{2^n}{2}[/tex]
[tex]T_n = \frac{2^na}{2}[/tex]
Assume, we want to determine the number of bacteria at the 10th 20 minutes (in other words, 200 minutes), the value of n will be 10
Indicate which property is illustrated in Step 2.
Step 1 12x + 2 + 5x + 1 = (12x + 2) + (5x + 1)
Step 2 = 12x + (2 + 5x) + 1
Step 3 = 12x + (5x + 2) + 1
Step 4 = (12x + 5x) + (2 + 1)
Step 5 = (12 + 5)x + (2 + 1)
Step 6 = 17x + 3
A.
distributive
B.
associative
C.
arithmetic fact
D.
commutative
Answer:
b
Step-by-step explanation:
You plan to rent a car from XYZ Car Rental Company for a flat rate of $35 a
day. If you plan to use the car for 3 days or fewer, you must also pay a $10
insurance fee per day. If you plan to use the car for more than 3 days, there is
a $5 insurance fee per day. Write a piecewise-defined function that models this
function.
Thanks for any help!
Answer:
The piece-wise function is;
[tex]f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}[/tex]
Step-by-step explanation:
The flat rate for renting the car = $35 per day
The amount charged as insurance fee per day for renting the car for 3 days or less = $10
The insurance fee charged per day when the car is rented for more than 3 days = $5
Let the number of days = x
Therefore, we have;
For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x
For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x
Therefore;
The charge rate for renting the car for less than or equal to 3 days = 45·x
The charge rate for renting the car for more than 3 days = 40·x
The piece-wise function can be presented as follows;
[tex]f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}[/tex]
Find an equation of the line parallel to y=x+3 and that passes through the point (1 -5)
Answer:
y=x-6
Step-by-step explanation:
Y=x+3 according to this equation, the gradient is 1 comparing to y=mx+c. so m is the gradient. so from the equation, the coefficient of x is 1. since the line is parallel so it means the new equation has the same gradient m.
y=x+c but it passes through 1,-5...when x= 1, y=-5 from here , we Can find the new intercept c. -5=1+c. so c=-5-1=-6
the new equation y=x-6
What is the quotient and remainder of 25÷3
Answer:
8 r 1
Step-by-step explanation:
Divide.
25 / 3
Think: 24 is the closest multiple to 25. 25-24 is 1. 1 cannot be divided by 3, so it is remainder
A truck parked on the street is 56 m from the base of the apartment building on the right. The angle of elevation from the truck to the top of the building is 40°. The parked truck is 49 m from the base of the apartment building on the left. The angle of elevation from the truck to the top of that building is 50°. Which building is taller?
Answer:
Building to the left is taller.
Step-by-step explanation:
Kindly refer to the attached diagram for the given dimensions.
[tex]\triangle ABR, \triangle PQR[/tex]
AB and PQ be the two buildings.
The car be parked at point R.
[tex]\angle ARB = 50^\circ\ and \\\angle PRQ = 40^\circ[/tex]
Distance of R from building bases:
BR = 49 m
QR = 56 m
Let us use tangent in [tex]\triangle PQR:[/tex]
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan40 = \dfrac{h_1}{56}\\\Rightarrow h_1 = 56 \times 0.839 \\\Rightarrow h_1 \approx 47\ m[/tex]
Let us use tangent in [tex]\triangle PQR:[/tex]
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan50 = \dfrac{h_2}{49}\\\Rightarrow h_2 = 49 \times 1.19 \\\Rightarrow h_2 \approx 58.4\ m[/tex]
So, building to the left is taller.
1-1 Relations and Functions
Marcus drives 32 miles to work each day. He records the number of minutes it takes him to drive and writes his average speed as the input
and the number of minutes as the output. He recorded his information in a table, like the one shown below.
Speed
(mph)
60
Time
(minutes)
32
45
43
55
35
50
38
62
31
If Marcus drives no faster than 65 miles per hour, what is the domain that includes all possible average speeds using interval notation?
A [0.65)
B. [65,00)
C. (0.65)
D. (65.00)
Answer:
{0, 65]
Step-by-step explanation:
A function shows the relationship between two variables (an independent and dependent variable). The independent variable is not dependent on other variables, it is considered as the input while the dependent variable is dependent on other variables and considered as output.
The speed of Marcus must not be faster than 65 mph, hence speed ≤ 65 mph. This means that Marcus can drive with speed ranging from 0 mph to 65 mph, hence 0 ≤ speed ≤ 65 mph. This is represented using the interval notation:
[0, 65]
0.401
Convert the following repeating decimals to a rational number.
Answer:
401/999
Step-by-step explanation:
0.401/100
Which list correctly orders the coefficients of the following terms from least to greatest?
81, – 4z, – 1ly, w
(1 point)
0-1ly, - 4z, w, 8z
Ow, – 4z, 81, - lly
O -1ly, - 41, 8z, u
O w, 87, - fly, – 4z
Answer:
−11y, −4z, w, 8x
Step-by-step explanation:
(PLS HELP ASAP) A basketball player scored 351 points last year. If the player plays 18 games this year, how many points will he need to average per game to beat last year’s total?
Answer:
I think it's 19 I'm pretty sure
Answer:
20
Step-by-step explanation:
The first step would be to divide 351 by 18 to see what score he would need to tie his previous record. The answer to that would be 19.5, so if you round to the nearest whole, you would get 20.
A recipe calls for 3/4 cup of sugar for every 1/2 teaspoon of cinnamon. What is the unit rate in teaspoons of cinnamon per cup of sugar?
Answer:
[tex]\frac{2}{3}[/tex] teaspoons of cinnamon per cup of sugar.
Step-by-step explanation:
A recipe calls for [tex]\frac{3}{4}[/tex] cups of sugar for every [tex]\frac{1}{2}[/tex] teaspoons of cinnamon.
For one cup of sugar;
1 × [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{2}{3}[/tex] teaspoons of cinnamon will be needed.
A Toyota Prius is 178.7 inches long. How many would you need to circle Mars’ equator, which is 13,233 mile long?
Answer:
4,691,902
Step-by-step explanation:
There are 5280 ft per mile, and 12 inches per foot. There are 178.7 inches per Prius. The number needed is ...
(13233 mi)(5280 ft/mi)(12 in/ft)/(178.7 in/Prius)
= (13233×5280×12/178.7) Prius
= 4,691,901.95 Prius
With a little squeezing, you could gain the extra 7.4 inches necessary to round this number to the next higher integer value:
4,691,902 Prius cars would be needed to circle Mars at the equator
Answer:
4,691,902
Step-by-step explanation:
took a quiz
Dave earns 7.50 per hour and has deductions if 36 per week, If Dave works 40 hours per werk, what will his next pay be for 1 week.
Answer:
$264
Step-by-step explanation:
$7.50 * 40 hrs= $300-$36=$264
Answer:
$264 for the week
Step-by-step explanation:
$7.50 per hour for 40 hours (7.50 x 40 = 300)
= $300
Deduction of $36 per week.
$300-$36= $264
Therefore, Dave's next pay for 1 week will be $264.
urgio wants to buy gifts for 8 friends. he wants to gie the same gife to all his friends and he plans to have all the gifts wrapped in additional charge for 1.50 dollars each. if sergio spends at least 70 dollars he will recieve free shipping on his order. write and inequality to determine how much sergio needs to spend on each gift to order to receive free shipping
[tex]7.25 \leqslant x[/tex]
Step-by-step explanation:
you do 1.5×8 to see how much shipping cost
you get 12 then subtract 12 from 70 and you get 58, then you do 58÷8 and you get $7.25
so he needs to spend $7.25 or more on each friend. (im pretty sure)
The amount urgio needs to spend on each gift in order to receive free shipping is 7.25.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given that urgio wants to buy gifts for 8 friends. he wants to gie the same gife to all his friends and he plans to have all the gifts wrapped in additional charge for 1.50 dollars each.
Let the cost of each gift = c
urgio is buying gifts for 8 friends = 8 gifts
Hence, the Inequality equation is written as:
(c + $1.50)× 8 ≥ $70
8c + 12 ≥ 70
8c ≥70 - 12
c ≥ 58/8
c≥ 7.25
Therefore, the amount urgio needs to spend on each gift in order to receive free shipping is 7.25
Learn more about inequality ;
brainly.com/question/14164153
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can u help me ASAP!!!! WILL MARK U BRAINLIEST IF ITS CORRECT
Answer:
OPTION 2
Step-by-step explanation:
The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.
--------------------------------------------------------------------------
HOW TO: GIVEN A GRAPH, USE THE VERTICAL LINE TEST TO DETERMINE IF THE GRAPH REPRESENTS A FUNCTION.
1.Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
2.If there is any such line, the graph does not represent a function.
3.If no vertical line can intersect the curve more than once, the graph does represent a function.
(The 2nd pic represents a graph that has a function)
delilah and group of friends had excellent service at a restaurnt they would like to give the sever 25% percent gratuity 140 bill
Answer:
35
Step-by-step explanation:
25% of 140 is 35
Answer:
35%
Step-by-step explanation:
At Statebert University, 70% of the students are female. If there are 210 male students
at Statebert U., how many female students are there?
Answer:
490 female students
Step-by-step explanation:
If 70% of students are female, 30% are male.
If 30% of students = 210 students, we can divide both sides of the equation by 3.
30/3 = 10
210/3 = 70
10% of students = 70 students
To get 70% of students, multiply both sides by 7.
10*7 = 70
70 * 7 = 490
70% of students = 490 students
Hope this helps!
Make a square number out of these cards. 1. 4. 6. 7. (make a square number out of these number)
square number of 1467=2,152,089
The solution is 1764
The number on rearranging is given by the equation A = 1764 , where the square root of the number is B = 42
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as A
Now , the set of numbers is = { 1 , 4 , 6 , 7 }
The square root of the number be B
The value of B = 42
So , the square of the number B² = 42 x 42
Square of the number B² = 1764
Therefore , the value of A = 1764
Hence , the number is 1764
To learn more about equations click :
https://brainly.com/question/19297665
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What is the difference in elevation of Mt. Blum at 7,677 feet above sea level and New Orleans at -7ft below sea level?
Answer:
7,670 ft
Step-by-step explanation:
If I'm understanding the question right, you just have to find the difference:
-7 + 7,677 = 7,670 ft
Hope this helps!
Answer:
7,670 ft
Step-by-step explanation:
To find the diffrence I just did -7 + 7,677 = 7,670 ft.
solve x^3 = 125/27 pls
Answer:
5/3
Step-by-step explanation:
Take the cube root of each of the numbers on the right
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1. 10L
2.
[tex]( \frac{p}{10} ) - 9[/tex]
Step-by-step explanation:
let length be L.
let width be W.
W = 4L
Perimeter = 2L + 2W
P = 8L + 2L
P = 10L
Given x=-3, y=6, and z=-4 3x-2y+z=
Sam is building a model of an antique car. The scale of his model to the actual car is 1:10. His model is 19.5 inches long. How long is the actual car?
Answer: 195 inches.
Step-by-step explanation:
Given: Sam is building a model of an antique car.
The scale of his model to the actual car is 1:10.
⇒Scale factor = [tex]\dfrac1{10}[/tex]
Since, Length of actual figure = (Length of model ) ÷ Scale factor.
If length of model of car = 19.5 inches.
Then, the length of the actual car = [tex]19.5\div\dfrac{1}{10}=19.5\times10=195\text{ inches}[/tex]
Hence, the length of the actual car = 195 inches.
Simplify: 675 ÷ (6 + 9 ÷ 3) A) 15 B) 9 C) 75 D) 225 E) 135
Answer:
d
Step-by-step explanation:
hope it helps
please help :d in on a time limit before it becomes late!!
The water level in the beaker was 10 mL before the small toy was placed into it. After the toy was submerged in the water, the level was 23 mL. The toy has as much volume as how many mL of water?
Answer:
volume of toy = volume of water after placing toy in it - volume of water before placing toy in it
volume of toy = 23mL - 10mL
volume of toy = 13mL
The increase in the volume of water when the toy is submerged in it is equal to the volume of the toy.
SO VOLUME OF WATER IS 13mL
9y²)³ simplified answer
Answer:
729[tex]y^{6}[/tex]
Step-by-step explanation:
(9[tex]y^{2}[/tex])^3
(9 * 9 * 9) (y* y * y * y* y* y)
5x + 3y + 5 +7a – 3x – 2y + 3 =
Answer:
8+7 times a+2 times x+y
Step-by-step explanation:
How can someone's knowledge of math be applied to be more successful life?
Pls help ASAP it’s number nine
Answer:
150°Step-by-step explanation:
[tex]Sum \:of\:angles = 360\° \\\\1/3x\° +(x-20)\° +(x-10)\° +40\° = 360\°\\\\1/3x\° +x\°-20+x\°-10+40=360\°\\\mathrm{Group\:like\:terms}\\\frac{1}{3}x\°+x\°+x\°-20-10+40=360\°\\\\\mathrm{Add\:similar\:elements:}\:x+x=2x\\\frac{1}{3}x\°+2x\°-20-10+40=360\°\\\\\mathrm{Add/Subtract\:the\:numbers:}\:-20-10+40=10\\\frac{1}{3}x\°+2x\°+10=360\°\\\\\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}\\\frac{1}{3}x\°+2x\°+10-10=360\°-10\\\\\frac{1}{3}x\°+2x\°=350\°\\[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}3\\\frac{1}{3}x\°\times \:3+2x\times \:3=350\° \times \:3\\Simplify\\x+6x=1050\°\\\\7x=1050\\\\\frac{7x}{7}=\frac{1050\°}{7}\\\\x =150\°[/tex]
3x + 11 = 2x − 5 please help
Answer:
x = -16
Step-by-step explanation:
3x+11 = 2x - 5
x +11 = -5 (Get x's on one side by substracting 2x from both sides)
x= -16 ( substract 11 from both sides to get the answer
Answer:
[tex]x=-16[/tex]
Step-by-step explanation:
[tex]3x+11=2x-5[/tex]
Subtract 11 from both sides:
[tex]\hookrightarrow[/tex] [tex]3x+11-11=2x-5-11[/tex]
[tex]\hookrightarrow 3x=2x-16[/tex]
Subtract 2x from both sides:
[tex]\hookrightarrow 3x-2x=2x-16-2x[/tex]
[tex]\hookrightarrow x=-16[/tex]
_______________________
what is the conjugate? square root of 8 - square root of 9
Answer:
-0.17157287525
Step-by-step explanation:
1. The square root of 8 will never be a whole number so it is 2.82842712475
2. Square root of 9 is 3.
3. You can already realize that the answer will not be whole or positive
4. Subtract in order.
5. The answer is -0.17157287525