Expand the square. Remember that
(a - b)² = a² - 2ab + b²
With a = 5√3 and b = √27, we have
(5√3 - √27)² = (5√3)² - 2 (5√3) √27 + (√27)²
… = 25•3 - 10√81 + 27
… = 75 - 10√(9²) + 27
… = 102 - 10•9
… = 102 - 90
… = 12
a scientist notes that the number of bacteria in a colony is 50.3, hours later she notes that the number of bacteria has increased to 80. if this rate of growth continues, how much more time will it take for the number of bacteria to reach 1119?
The time it would take for the bacteria to reach 1119 is 5.83 hours
Calculations and Parameters:Given the function:
[tex]Pt= P_0e^k^t[/tex]
Initial amount= 50amount after 3 hours= 80To find the exponential growth;
80 = [tex]50e^k^*^3[/tex]
[tex]k= 1.6/3\\k= 0.533[/tex]
If there is a constant growth, then to get to 1119:
1119= [tex]50e^0^.^5^3^3^*t[/tex]
3.8 = 0.533*t
t= 5.83 hours
Therefore, it would take 5.83 hours for the bacteria to increase to 1119.
Read more about exponential growth here:
https://brainly.com/question/2456547
#SPJ1
What is the remainder when f(x) = x³- 13x² + 40x + 18 is divided by x-7? Show your work.
Answer:
remainder = 4
Step-by-step explanation:
using the remainder theorem
when f(x) is divided by (x - a) then the remainder is f(a)
so when f(x) is divided by (x - 7) the remainder is f(7) , that is
f(7) = 7³ - 13(7)² + 40(7) + 18
= 343 - 13(49) + 280 + 18
= 343 - 637 + 298
= 4
Hence, the remainder is [tex]4[/tex].
What is the remainder value?
The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.
Applying the remainder theorem
In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].
So, here when [tex]f(x)[/tex] is divided by [tex](x - 7)[/tex] the remainder is [tex]f(7)[/tex], that is
[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]
Hence, the remainder is [tex]4[/tex].
To know more about the remainder
https://brainly.com/question/11230333
#SPJ2
Help help help help help me
Answer:
Step-by-step explanation:
What is the minimum of the data?
0
5
7
13
Answer:
b; [5]
Step-by-step explanation:
i took the quiz
Question 9
Expand and simplify (2x-7)(3x-8).
Answer:
=> Expand by applying the FOIL method
[tex]2x\cdot \:3x+2x\left(-8\right)-7\cdot \:3x-7\left(-8\right)[/tex]
=> combine like terms
[tex]6x^2-37x+56[/tex]
37-(y-19)=2y this is a problom from rsm
Answer:
y = 56/3
Step-by-step explanation:
Distribute:
37 - (y - 19) = 2y
37 - y + 19 = 2y
Add the numbers:
37 - y + 19 = 2y
56 - y = 2y
Rearrange the terms:
56 - y = 2y
-y + 56 = 2y
Solution:
y = 56/3
Suav left his house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then he stopped and went into the store for 2 minutes. From there, he drove in the same direction at a speed of 4 blocks per minute until he got to the bank, which is 16 blocks away from the store. He stopped at the bank for 4 minutes. Then he drove home at a speed of 6 blocks every minute. Make a graph of showing the number of blocks away from home that Suav is xx minutes after he leaves his house, until he gets back home.
The graph for Suav's trip is attached along with the values derived from the information provided.
What is the explanation for the graph?The key to understanding the graph is that every time spent while he was on the way to the back and back are all added cumulatively.
So when he stops at the store which is 8 blocks away from home, the time spent is recorded as 4 + 2 at location 8 blocks.
It is also to be noted that the time spent is plotted on the x-axis and the blocks away from home on the y-axis.
Learn more about graphs at:
https://brainly.com/question/19040584
#SPJ1
The ratio for sin B?
Answer:
[tex]d)~ \dfrac{20}{29}[/tex]
Step-by-step explanation:
[tex]\sin B = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\~~~~~~~~=\dfrac{AC}{AB}\\\\~~~~~~~~=\dfrac{20}{29}[/tex]
(05.06)Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.
Which graph best represents the scenario described?
The graph third represents the provided situation first line increases and then constant then again increases and becomes constant.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.
Based on the information given we can say graph third represents the situation.
First Keisha ran to swim practice so the line first increases and then she but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes which means the line should be constant.
Again they both ran so line increases.
Then they both stayed for 1 hour, so the line should be constant.
Thus, the graph third represents the provided situation first line increases and then constant then again increases and becomes constant.
Learn more about the line chart here:
brainly.com/question/23680294
#SPJ1
for what value of x is the rational expression below equal to zero?
3x+15
———
6-x
[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]
Answer:
the answer= -5
Can y’all help find the surface area please and thank you
To find the area of a complex shape:
⇒ must cut the whole shape into a simpler shape
square with side lengths of 4 in2 triangles with a base of 4 in. and a height of 8 in.2 triangles with a base of 4 in. and a height of 10 in.Let's calculate:
Area of 2 triangles with a base of 4 in. and a height of 8 in.[tex]Area = \frac{1}{2}*4*8 + \frac{1}{2}*4*8=16+16=32\\[/tex]
2 triangles with a base of 4 in. and a height of 10 in.[tex]Area = \frac{1}{2}*4*10 + \frac{1}{2}*4*10=20+20=40[/tex]
square with side lengths of 4 in[tex]Area = 4 * 4=16[/tex]
Total Area: 32 + 40 + 16 = 88 in²
Answer: 88 in²
Hope that helps!
Patrick buys a wrench with a listed price of $22. Which of these coupons will deduct the most from Patrick's purchase price?
A. Save $5 + 10%
B. Save $10
C. 15% off
D. Save 25%
Answer:
B: Save $10
Step-by-step explanation:
A: $14.80, B: $12, C:$18.70, D: $16.50
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.
Answer:15
Step-by-step explanation:
A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.
Let the distance of the ladder from the wall be x
The length of the ladder = x+3
The ladder touches the wall at a vertical height of 9 feet.
(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem
x^2 + 6x+ 9 = x^2 + 81
x^2- x^2 +6x = 81-9
6x= 72
x= 12
Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.
Pippa has a box containing n pens.
there are only black pens and red pens in the box.
the number of black pens in the box is 3 more than the number of red pens.
pippa is going to take at random 2 pens from the box.
the probability that she will take a black pen followed by a red pen is
9
35
find the possible values of n.
show clear algebraic working.
The possible values of N from the given probability parameters is; N equals 15 or 21
How to Solve Algebra Problems?We are told that;
Number of pens in the box = N
Let the number of red pens be x
Thus; number of black pens = x + 3
Thus;
x + x + 3 = N
x = (N - 3)/2
The probability that she will take a black pen followed by a red pen is;
P(she will take a black pen followed by a red pen) = (x + 3)/N * x/(N - 1)
Plugging in he relevant values and solving for N gives ;
Solving for N gives N equals 15 or 21
Read more about Algebra at; https://brainly.com/question/723406
#SPJ
Type the correct answer in each box. write each answer as a fraction, using / for the fraction bar. wesley draws a card at random from a well-shuffled deck of playing cards. the probability that wesley draws an ace or a jack is . the probability that wesley draws a number card or a black card is .
The probability that Wesley draws an ace or a jack is 0.154 and the probability that Wesley draws a number card or a black card is 0.846
The probability of Ace or jackIn a standard deck of cards, we have:
Total = 52
Ace = 4
Jack = 4
Ace and Jack = 0
The probability is then calculated as:
P = P(Ace) +P(Jack) - P(Ace and Jack)
This gives
P = 4/52 + 4/52 - 0/52
Evaluate
P = 0.154
Hence, the probability that Wesley draws an ace or a jack is 0.154
The probability of Number card or black cardIn a standard deck of cards, we have:
Total = 52
Number card = 36
Black = 26
Number card and Black = 18
The probability is then calculated as:
P = P(Number card) +P(Black card) - P(Both)
This gives
P = 36/52 + 26/52 - 18/52
Evaluate
P = 0.846
Hence, the probability that Wesley draws a number card or a black card is 0.846
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
Answer: my guess is 4/13 and 11/13
Step-by-step explanation:
sorry if im wrong
The table represents a function.
X
-6
-2
6203
f(x)
3
1
4
-2
What is f(-2)?
0-3
O-1
0 1
0 3
What is the length of HI? (Giving 40 points please hurry!)
Answer: Hope this helps you!
3
Step-by-step explanation:
9 (total amount) - 6 (1 part of it) = 3 (the other part of it)
Brainliest?
Can someone please help me? I put the answer at 47.1 but it says it's wrong.
Answer:
47.14 cm
Step-by-step explanation:
Circumference :
π x diameterπ x 1515π15 x 22/7330/747.14 cm (approximately)the average of 5 girls is 6 yrs. the average of 4 of them is 16½. what is d age of d fifth gal
Answer:
This assumes the question should read:
"The average of 5 girls is 16 [not 6] yrs. the average of 4 of them is 16½. what is d age of d fifth gal
The age, d, is 14 years.
Step-by-step explanation:
When the girl with age d is not included, the average goes up to 16.5 years. Let's define GroupA as the sum of the ages of the 4 girls whose average age is 16.5 years. d is the age of the girl that is removed from the average.
We know that all the girls (GroupA + d) have an average age of 16 years:
(GroupA + d)/5 = 16 years [Add the ages for all the girls (GroupA and d) and divide by 5 to obtain the average age for the larger group].
We know that when d is removed, the average for the 4 remaining girls (GroupA) is 16.5 years:
(GroupA)/4 = 16.5 years
This tells us the sum of the ages for GroupA:
GroupA = 4*(16.5)
GroupA total = 66 years
From above: (GroupA + d)/5 = 16 years
Since GroupA = 66 years, (66 years + d)/5 = 16 years
(66 years + d) = 90 years
d = 14 years
The hour and minute hand of a clock form an angle that constantly changes. During each hour of the day,the clock hands will form right, acute and obtuse angles. Assume the hour hand points directly at the hour.Write a time of day when the two clock hands form each tyep of angle
The each type of angle are discussed below
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
If the hours hand point to the hour 1 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 2 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 3 and minute hand at 12 then
angle will be right angle .
If the hours hand point to the hour 4 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 5 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 6 and minute hand at 12 then
angle will be straight angle .
If the hours hand point to the hour 7 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 8 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 9 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 10 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 11 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 12 and minute hand at 12 then
angle will be Complete angle.
Learn more about angle here:
https://brainly.com/question/12129157
#SPJ1
which sequence of transformations could be used to move triangle RST so it completely covers triangle R”S”T?
Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
Consider triangle ABC. What is b?
which unit of measure would be appropriate for the area of a bulletin board that is 2 meters tall and 6 meters wide
Answer:The entire area would be 12 square meters.
Step-by-step explanation:
2 x 6 square meters = 12 square meters. which is the entire area.
A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling the number 2.
If there is more than one element in the set, separate them with commas.
The sample space S = {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}
What is sample space?It is defined as the space in which all possible outcomes are represented in a list form for a particular event.
We have:
A number cube with faces labeled from 1 to 6 will be rolled once.
Let S is the sample space:
As we know, the sample space is the set of all possible outcomes:
S = {1, 2, 3, 4, 5, 6}
The total number of outcomes:
n(S) = 6
The outcomes for the event of rolling the number 2.
E = {2}
n(E) = 1
Thus, the sample space S = {1, 2, 3, 4, 5, 6} describing all possible outcomes and outcomes for the event of rolling the number 2 is E = {2}
Learn more about the sample space here:
https://brainly.com/question/17144524
#SPJ1
25 Select the correct answer. What is the average rate of change of f(x), represented by the graph, over the interval [-1, 2]? A. -2.5 B. -2 C. 2.5 D. 3 E. 6
The average rate of change of the function over the interval [-1, 2] is: C. 2.5.
How to Find the Average Rate of Change?The average rate of change over an interval of a function is: f(b) - f(a) / b - a.
Given the interval [-1, 2]:
a = -1; f(a) = -5
b = 2; f(b) = 2.5
Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3
Average rate of change = 2.5 (option C).
Learn more about average rate of change on:
https://brainly.com/question/11627203
#SPJ1
It's the last second of a playoff basketball game and Bridget has three free throws she must make to seal the win she typically makes about 75% of her free throws what is the probability that Bridget makes all three free throws to win the game
The probability that Bridget makes all three free throws to win the game is; 42.2%
How to find the probability?
We are told that the probability of Bridget making her free throw correctly is 75%.
Now, if she has to get all three free throws correctly, then the probability for that is;
P(3 free throws correct) = 0.75 * 0.75 * 0.75
P(3 free throws correct) = 0.421875 ≈ 42.2%
Read more about Probability at; https://brainly.com/question/251701
#SPJ1
K, L, and M are points on the circle. KS is a tangent to the circle at K. KM is a diameter and triangle KLM is isosceles. Find the value of z.
Using the circle theorems, the value of z is 45
Circle GeometryFrom the question, we are to determine the value of z
From the given information,
KM is a diameter
∴ ∠KLM = 90° (Angle in a semicircle)
Also, ΔKLM is isosceles
∴ ∠KML = ∠MKL (Base angles of an isosceles triangle)
Then,
∠KML + ∠MKL + ∠KLM = 180° (Sum of angles in a triangle)
2× ∠KML + 90° = 180°
2× ∠KML = 180° - 90°
2× ∠KML = 90°
∠KML = 90°/2
∠KML = 45°
Now, we can observe that
z° = ∠KML (Angles in alternate segment)
But,
∠KML = 45°
∴ z = 45
Hence, the value of z is 45
Learn more on Circle Geometry here: https://brainly.com/question/17074363
#SPJ1
Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.
Rectangular Prism A:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
Rectangular Prism B:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³
Surface Area to Volume Ratio = 43/28
Mensuration of SolidsGiven Data
Rectangular prism A
Length = 2 inches
Width = 7 inches
Height = 8 inches
Surface Area
A=2(wl+hl+hw)
A=2(7*2+8*2+8*7)
A=2(14+16+56)
A= 172 inches²
Volume
Volume = L*W*H
Volume = 2*7*8
Volume = 112 inches³
Surface Area to Volume Ratio
= 172/112
= 43/28
Learn more about Mensuration of Solids here:
https://brainly.com/textbook-solutions/q-7-composite-figures-use-diagram-backpack-right
#SPJ1
An unusual number cube (with 6 sides) has the numbers 2, 2, 4, 4, 6, and 6 on its faces.
It is rolled once. Match the outcome to its probability.
1. P(2 or 4)
2. A(multiple of 2)
3. P(multiple of 3)
4. P(odd prime numbers)
2/3
0
1
1/3
Answer:
1. P(2 or 4) - 2/3
2. P(multiple of 2) - 1
3. P(multiple of 3) 1/3
4. P(odd prime numbers) 0
Step-by-step explanation:
Good luck lol
P(2 or 4) = 2/3
P( multiple of 2) = 1
P( multiple of 3) = 1/3
P(odd prime numbers) = 0
What is probability?Probability is the likelihood of an event happening or not.
Analysis:
possible outcome = (2,2,4,4,6,6) = 6
P(2 or 4)
n( 2) = required outcome = (2,2) = 2
P(2) = 2/6 = 1/3
n(4) = (4,4) = 2
P(4) = 2/6 = 1/3
P(2 or 4) = 1/3 + 1/3 = 2/3
n( multiple of 2) = (2,2,4,4,6,6) = 6
P( multiple of 2) = 6/6 = 1
n(multiple of 3) = (6,6) = 2
P(multiple of 3) = 2/6 = 1/3
P(odd prime numbers) = 0
Learn more about probability: brainly.com/question/24756209
#SPJ1
Is 3²+3³ equal to 3⁵?
( yes, no ) the expressions (are, are not ) equal
Answer: No the expressions are not equal
Work Shown:
3² = 3*3 = 9
3³ = 3*3*3 = 27
3²+3³ = 9+27 = 36
3⁵ = 3*3*3*3*3 = 243
The 3²+3³ = 36 doesn't match up with 3⁵ = 243
Therefore, the two expressions are not equal.
Answer:
Step-by-step explanation:
No, the expressions are not equal.
3^2 + 3^3 = 9 + 27 = 36
3^2 * 3^3 = 3^5
keep the base the same and add the exponents