Answers
Answer:
abbbcab(a) [tex]7^{4}[/tex] (b) [tex](\frac{4}{9}) ^{17}[/tex] (c) [tex]4^{-4}[/tex] (d) [tex]8^{-3}[/tex]Step-by-step explanation:
1. The moment he started: 3 bacteria
1st hour: 3*2 bacteria = 3*[tex]2^{1}[/tex] bacteria
2nd hour: 3*2*2 bacteria = 3*[tex]2^{2}[/tex] bacteria
3rd hour: 3*2*2*2 bacteria = 3*[tex]2^{3}[/tex] bacteria
etc.
Each hour the number of bacteria multiplies by 2 (the power of 2 is increased by 1), therefore, [tex]B=3*(2)^{n}[/tex]
2. Exponential function has the form of [tex]f(x)=ab^{x}[/tex]
if a is greater than 0 and b is greater than 1, then it's exponential growth.
The answer is:
[tex]y=4^{x}[/tex] (4 > 1)
3. If smth increases by 2.5% each time, that means that at first you had 100% and then it became 100%+2.5% = 102.5%. So each time we multiply the value by 1.025 (100*1.025=102.5).
4. Linear equation form: [tex]y=ax+b[/tex]
Quadratic equation form: [tex]y=ax^{2} + bx + c[/tex]
Exponential equation form: [tex]y=ab^{x}[/tex]
In this case, a = 3.8, b = -5.5, c = -4.8
5. (a) square root
(b) linear
(c) exponential
(d) quadratic
6. Each year the car's worth is multiplied by 0.82 (82%). Therefore, after n years, the value will be: V = 27 500 * [tex]0.82^{n}[/tex]
7. Neither first, nor second differences are constant in case of an exponential relation, because we do not add but multiply.
Ex. [tex]y=2^{x}[/tex]
values: 1 2 4 8 16 32...
1st diff: 1 2 4 8 16...
2nd diff: 1 2 4 8...
8. (a) [tex]7^{11} / 7^{7} = 7^{11-7} = 7^{4}[/tex]
(b) [tex](\frac{4}{9})^{12} *(\frac{4}{9})^{5} =(\frac{4}{9} )^{12+5}=(\frac{4}{9})^{17}[/tex]
(c) [tex]4^{11} / (4^{5})^{3} =4^{11} / 4^{5*3}=4^{11} /4^{15}=4^{11-15}=4^{-4}[/tex]
(d) [tex]8^{-6}*8^{3}=8^{-6+3}=8^{-3}[/tex]
Related Questions
Evaluate 1/4 c + 3d when c = 6 and d = 7
Answers
Answer:
SolutioN :
Just plug in the values of c & d in the given expression and calculate :[tex] \longrightarrow \bf \: \frac{1}{4} \times 6 + 3 \times 7[/tex]
[tex] \longrightarrow \boxed{\bf{ \frac{45}{2} }}[/tex]
Our final answer is 45/2 .--------------HappY LearninG <3 -------
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Evaluate 1/4c+3d when c=6, and d=7.
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
Replace c with 6, and d with 7:-
[tex]\Large\text{$\displaystyle\frac{1}{4} (6)+3(7)$}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\Large\text{$\displaystyle\frac{1}{4} \times\frac{6}{1}+21$}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\Large\text{$\displaystyle\frac{6}{4} +21$}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\Large\text{$\displaystyle\frac{6}{4}+\frac{84}{4}$}[/tex]
[tex]\bigstar[/tex] Adding the numerators,
[tex]\Large\text{$\displaystyle\frac{90}{4}$}[/tex]
[tex]\bigstar[/tex] Finally, Reducing the fraction:-
[tex]\Large\text{$\displaystyle\frac{45}{2}$}[/tex]
[tex]\Uparrow[/tex] [tex]\mathbb{OUR\:SIMPLIFIED\:EXPRESSION}[/tex]
Good luck with your studies.[tex]\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
Janette measures the heights in inches of some of the flowers in her garden to see which ones are growing more. the heights are listed below. which line plot represents the data correctly? 7 1 2 7 7 1 2 6 3 4 7 1 4 7 1 4 7 1 4 7 6 1 2 7 3 4 7 3 4 6 3 4 8 1 4 7 7 1 2 7 7 1 4 7 7 1 2 7 1 2 a. a line plot named b. a line plot named c. a line plot named d. a line plot named
Answers
The line plot that represents the height of the flowers in the garden is the line plot named a.
What is a line plot?A line plot is a diagram that is used to represent data. The line plot is made up of dots that are used to represents the frequency with which the number appears.
Please find attached the line plot that represents the answer. To learn more about line plots, please check: https://brainly.com/question/16321364
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A bus stops at a bus stop every 45 minutes. Once a person gets to the bus stio, what is the probability they will wait for no more than 20 minutes?
Answers
Answer:
≈ [tex]44.4%[/tex][tex]%[/tex]%
Step-by-step explanation:
The person will wait for no more than 20 minutes if they arrive when the bus is going to stop in 20 minutes, which means that they must arrive 25 minutes after the previous bus stops. So the probability that the person will not wait for more than 20 minutes will be [tex]\frac{20}{45}[/tex] which is about 44.4%.
A bag contains 5 red marbles, 5 white marbles, and 8 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red
Answers
Answer:
15
----
153
15=6+3+1
153=18×17÷2
The area of a rectangle is 20. The length is 5, and the width is the √x. What is the value of x? What is the width of the rectangle?
A. The value of x is 4. The width is 16.
B. The value of x is 16. The width is 4 or –4.
C. The value of x is 4. The width is 2.
D. The value of x is 16. The width is 4.
Answers
Answer:
D
Step-by-step explanation:
5([tex]\sqrt{x}[/tex]) = 20 Divide by 5
[tex]\sqrt{x}[/tex] = 4 Square both sides
x = 16
Widths can't be negative
Answer: D
Step-by-step explanation:
A = LW
[tex]\sqrt{x}[/tex] * 5 = 20
[tex](\sqrt{x} * 5)^{2} = 20^{2}[/tex] (square both sides)
x * 25 = 400
25x = 400
[tex]\frac{25x}{25} = \frac{400}{25}[/tex] (divide both sides by 25)
x = 16
[tex]\sqrt{16} = 4[/tex]
x = 16, and the width is 4.
Last semester 150 out of thwhat is the 800 student at jungle junior high made the honor roll
what percent of the students made the honor roll
Answers
Answer:
Your sentence got cut out or sum.
Step-by-step explanation:
I'm assuming it's asking: What is 150 out of 800?
If so:
150/800 --> 3/16
3/16 --> Percent Form: 18.75%
Final Answer: 18.75%
substitution. y = x − 35 y=-4x
Answers
Answer:
(7, - 28 )
Step-by-step explanation:
y = x - 35 → (1)
y = - 4x → (2)
substitute y = x - 35 into (2)
x - 35 = - 4x ( add 4x to both sides )\
5x - 35 = 0 ( add 35 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
substitute x = 7 into either of the 2 equations
substituting into (1)
y = 7 - 35 = - 28
solution is (7, - 28 )
Glass A contains 100 ml of water and glass B contains 100 ml of wine. A 10 ml spoonful of wine is taken from Glass B and mixed thoroughly with the water in Glass A. A 10 ml spoonful of the mixture from A is returned to B. Is there now more wine in the water or more water in the wine
Answers
Answer:
More wine in the water
Step-by-step explanation:
Hope this helped
Two whole number, three over five of the pupils in a school are boys. If there are 96 girls and the school,how many pupils are there in the school?
Answers
Answer:
106 students
Step-by-step explanation:
If you take the 2 3/5 and covert it into a whole number by: 2×3+5 = 10
and then you have 96 girls so you add the whole number you got that is 10 and the 96 girls
=96+10= 106 students
⋆ ˚｡⋆୨୧˚hope this helped˚୨୧⋆｡˚ ⋆
Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house. how long does it take jasmin to rake leaves at the second house.
Answers
The Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house.
From the problem:
[tex]= \rm 2\dfrac{1}{3}\times \dfrac{1}{2}[/tex]
[tex]= \rm \dfrac{7}{3}\times \dfrac{1}{2}[/tex]
[tex]= \rm \dfrac{7}{6}[/tex]
[tex]= \rm 1\dfrac{1}{6}[/tex]
Thus, the Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.
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What is the complete factorization of x2 4x − 45? a. (x 15)(x − 3) b. (x − 9)(x 5) c. (x 9)(x − 5) d. (x − 15)(x 3)
Answers
The complete factor of the expression x² + 4x - 45 is (x - 5)(x + 9)
How to determine the complete factorization?The expression is given as:
x² + 4x - 45
Expand the equation
x² + 4x - 45 = x² + 9x - 5x - 45
Factorize the expression
x² + 4x - 45 = x(x + 9) - 5(x + 9)
Factor out x + 9
x² + 4x - 45 = (x - 5)(x + 9)
Hence, the complete factor of the expression x² + 4x - 45 is (x - 5)(x + 9)
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Answer:
Factor x2+4x−45 using the AC method. (x+9) (x−5)
Step-by-step explanation: so B
help me please!!! i cant do these
Answers
Answer:
sec(B)=b. ab/bc
sin(B)=c. ac/ab
csc(B)=f. ab/ac
cot(B)=a. bc/ac
tan(B)=e. ac/bc
cos(B)=d. bc/ab
Step-by-step explanation:
SOHCAHTOA
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
SHACHOCotAO
Secant=Hypotenuse/Adjacent
Cosecant=Hypotenuse/Opposite
Cotangent=Adjacent/Opposite
help asap pls pls pls
Answers
Answer:
the answer is 13, all you had to do was substitute 5 for N, so all you had to do was 3 + 2(5) which is 13
Fine the length of the third side. If necessary, write in simplest radical form
Answers
Answer:
7.2
Step-by-step explanation:
(6)^2 + (4)^2
36 + 16
52
square root of 52 = 7.2
Thomas found a box that had a volume of 150 in3. He measured the height of the box to be 2 inches and the length was 10 inches more than the width. What is the width of the box?
7 inches
11 inches
15 inches
5 inches
Need help Bad
Answers
Answer:
D) 5 inchesStep-by-step explanation:
GivenA box with the volume of 150 in³
Dimensions of the box are
2, x and x + 10, where x- width, (x + 10) - lengthThe volume of the box is
V = lwhSubstitute the values and solve the equation for x
x(x + 10)*12 = 150x(x + 10) = 75x² + 10x - 75 = 0x² - 5x + 15x - 75 = 0x(x - 5) + 15(x - 5) = 0(x - 5)(x + 15) = 0x - 5 = 0 or x + 15 = 0x = 5 or x = - 15 (discarded as negative value)The width of the box is 5 in
Correct choice is DSolve for X
13=270 (0.5)^x/7
Answers
Answer:
Step-by-step explanation:
Which is the graph of the circle (x−2)2+(y−1)2=25?
Answers
Answer: y=-x+31/2
Step-by-step explanation:
2x-4+2y-2=25
2y=-2x+31
y=-x+31/2
You must really like math to want to answer this ngl
Answers
Answer:
a) 2/10
b) 3/20
c) option 2
Step-by-step explanation:
Find the volume of the cylinder.
Answers
Answer:
120 i am sorry if i am wrong
Step-by-step explanation:
the volume of the cylinder is 120 cm
I have tried my hardest on studying this
question i am sorry if its wrong
What is -8.2 ÷ 4.32 = ?
Answers
Answer:
-8.2 / 4.32 is an infinite nummber but an aproximate is -1.9 or -2
Step-by-step explanation:
Write the converse of the following statements:
1. If two angles are both obtuse, the two angles are equal.
2. If 3 - 2x = 13, then x = -5.
3. If 2 angles are supplementary, then they are not equal.
Answers
For the first statement the converse is two angles are equal if the two angles are both obtuse, for second "x = -5 if the equation is 3 - 2x = 13" for third Two angles are not equal if 2 angles are supplementary.
What is the converse of a statement?A conditional statement with the antecedent and effect reversed is known as a converse statement.
We have statement:
1. If two angles are both obtuse, the two angles are equal.
Converse: The two angles are equal if the two angles are both obtuse.
2. If 3 - 2x = 13, then x = -5.
Converse: x = -5 if the equation is 3 - 2x = 13
3. If 2 angles are supplementary, then they are not equal.
Converse: Two angles are not equal if 2 angles are supplementary.
Thus, for the first statement the converse is two angles are equal if the two angles are both obtuse, for second "x = -5 if the equation is 3 - 2x = 13" for third Two angles are not equal if 2 angles are supplementary.
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someone pls help it is due on monday and thank you
The next model of a sports car will cost more than the current model. The current model costs . How much will the price increase in dollars? What will be the price of the next model?
Increase in price:
Price of next model:
Answers
Answer:
Step-by-step explanation:
1. Given that $53000 represents 100% of the original cost. You know that 6.9% as a percentage is equivalent to 0.069 as a decimal.
Increase in price:
= 53000 * 0.069
= $3657
2. The question states that the price of the car model is increasing, so you must add the original cost to the increase in price.
Price of next model:
= 53000 + 3657
= $56657
helpppppopppppoppppppp
Answers
write as improper fraction,
5/4 / 39/8
5/4 x 8/39 = 40/156
40/156 = 10/39
Mala walks her dog 3 times a day.
Each walk 3/4 ismile
Which expression tells how many miles Mala walks her dog each day?
Answers
Answer:
3/4 x 3 (top right)
Step-by-step explanation:
one you selected is incorrect
What is the area of a triangle with a base of 9 units and a height of 7 units?
Answers
Answer:
31.5 units.
Step-by-step explanation:
The area is the height times the base divided by 2.
9x7 = 63
63/2 = 31.5
How many millimeters are in 27 centimeters? (2 points)
a
27 mm
Ob
270 mm
Ос
2,700 mm
Od
27,000 mm
Answers
Step-by-Step Explanation:
We know,
1 cm = 10 mm
1mm = 1/10 cm
Therefore,
27 cm = 27 * 10 = 270 mm
The sum of two integers is 9 and their product is 18. What are the integers?
Answers
Answer:
The integers are 2.
Step-by-step explanation:
Answer: 3 and 6
Step-by-step explanation:
3+6=9
3x6=18
The circumference of a circle is approximately 43.96 centimeters. what is the radius of the circle? use 3.14 for radius.
Answers
Answer:
7 cm
Step-by-step explanation:
The circumference of a circle is given in terms of its radius by the formula ...
C = 2πr . . . . where r represents the radius
__
Using the given values in the formula, we can find the radius to be ...
C/(2π) = r
43.96/(2×3.14) = r = 7 . . . . cm
The radius of the circle is 7 cm.
a girl exercises every day for half an hour how many minutes in total for over 5 days
Answers
Answer:
150 minutes
Step-by-step explanation:
30 × 5 = 150 minutes
the formula for converting degrees fahrenheit (f) to degrees kelvin (k) is:
solve for f, in terms of k
k=5/9(f+459.67)
Answers
Answer:
See below
Step-by-step explanation:
K = 5/9 (F + 459.67) Multiply both sides by 9/5
9/5 K = F + 459.67 Subtract 459.67 from both sides
9/5 K - 459.67 = F