Answer:
0.196 lbs
Step-by-step explanation:
The area of the cross section is the difference of the areas of circles with the different diameters. The volume of the pipe material is the product of its cross section area and its length:
V = π(D² -d²)L/4 = π(0.82² -0.75²)36/4 ≈ 3.107 . . . in³
Then the weight of the material is this volume multiplied by the density.
W = V·δ = (3.107 in³)(0.063 lb/in³) ≈ 0.196 lb
Finding the weight of the PVC pipe involves calculating the volumes of the outer and inner cylinders then finding the difference, which is multiplied by the weight per cubic inch of PVC.
Explanation:The weight of a 36 inch piece of PVC pipe can be calculated using the formula for the volume of a cylinder and the given weight per cubic inch of PVC material. Firstly, calculate the volume of the outer cylinder, which we know the diameter and length (or height). The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. We need to halve the diameter to get the radius, which gives us 0.82/2 = 0.41 inches.
Secondly, we calculate the volume of the inner cylinder in the same way, except we use the inner diameter, which is 0.75 inches, halved gives us a radius of 0.375 inches. The volume of material used is then the volume of the outer cylinder minus the volume of the inner cylinder. Lastly, multiply the volume of material by the weight per cubic inch to get the total weight.
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Help with these questions!
Step-by-step explanation:
An inscribed angle is half the arc angle.
m∠MNQ = 80°/2
m∠MNQ = 40°
The angle between two chords is the average of the arc angles.
m∠AMB = (80° + 85°) / 2
m∠AMB = 82.5°
Figure ABCD is a parallelogram.
5x + 3
What is the value of x?
Answer:
x=7
Step-by-step explanation:
Since this is a parallelogram, you can say that the 5x+3 will equal to 38 in this situation. 38-3 =35.
[tex]\frac{35}{5} \\\\x=7[/tex]
So the answer is 7
Find the volume and surface area of the composite figure. Give four answer in terms of π.
Answer:
V = 99π in³; S = 81π in²
Step-by-step explanation:
Volume is that of a hemisphere of radius 3 in together with that of a cylinder of radius 3 in and height 9 in.
V = (2/3)πr³ +πr²h = (πr²)(2/3r +h)
= 9π(2 +9) = 99π . . . . in³
__
The area is that of a hemisphere, the side of the cylinder, and the circular bottom of the cylinder.
S = 2πr² +2πrh +πr² = πr(2r +2h +r)
S = 3π(6+18 +3) = 81π . . . . in²
Which is an exponential growth function?
A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find the value of the home after x years?
f(x) = 120,000(1.055x)
f(x) = 120,000(0.055)x
f(x) = 120,000(1.055)x
f(x) = [(120,000)(1.055)]x
Answer:
[tex]f(x)=120,000(1.055)^{x}[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
f(x) a home's value
x the number of years
a is the initial value
b is the base
b=(1+r)
r is the rate of grown
we have
a=$120,000
r=5.5%=5.5/100=0.055
b=1+0.055=1.055
substitute
[tex]f(x)=120,000(1.055)^{x}[/tex]
Answer:
It is In fact C. f(x) = 120,000(1.055)x
Step-by-step explanation:
Took this on Edg, it's right.
What is the product of (3a + 2)(4a2 – 2a + 9)?
Answer:
12a^3 + 2a^2 + 23a + 18
Step-by-step explanation:
Please use the " ^ " symbol to represent exponentiation: 4a^2 – 2a + 9.
Now carry out the multiplication as follows:
First, multiply each term in 4a^2 – 2a + 9 by 3a: 12a^3 - 6a^2 + 27a.
Next, multiply each term in 4a^2 – 2a + 9 by 2: 8a^ 2 - 4a + 18.
Now combine like terms:
12a^3 - 6a^2 + 27a
8a^ 2 - 4a + 18
---------------------------------
12a^3 + 2a^2 + 23a + 18
Round to estimate the answer, and then solve to find the correct answer. Explain whether your estimate was reasonable: A T. Rex dinosaur eats ten twelfths of a plant and then eats two twelfths of the plant later. How much of the plant did the dinosaur eat in total?
Answer:
1 plant
Step-by-step explanation:
The T.Rex dinosaur eats ten twelffths of a plant and later eats two twelfths of a plant. In total, the T.Rex dinosaur ate:
[tex]\frac{10}{12} + \frac{2}{12} =\frac{12}{12}=1[/tex]
Therefore, the dinsaur in total ate one entire plant.
It's better to solve the problem by using fractions instead of decimals. If we had used decimals the response would be the following:
[tex]0.833333+0.166666=0.999999[/tex] which can be rounded to 1.
What are the discontinuity and zero of the function f(x) = x^2+5x+4/x+4
Answer:
The zeros of our function f is at x=-1.
The discontinuity is at x=-4.
These are correct if the function is [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] .
Please let know if I did not interpret your function correctly.
Step-by-step explanation:
I imagine you mean [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] but please correct me if I'm wrong.
The zero's of a rational expression occur from it's numerator.
That is, in a fraction, the only thing that makes that fraction 0 is it's numerator.
So we need to solve [tex]x^2+5x+4=0[/tex] for x.
The cool thing is this one is not bad to factor since the coefficient of x^2 is 1. When the coefficient of x^2 is 1 and you have a quadratic, all you have to do is ask yourself what multiplies to be c and adds to be b.
[tex]x^2+5x+4[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=5,c=4[/tex].
So we are looking for two numbers that multiply to be c and add to be b.
We are looking for two numbers that multiply to be 4 and add to be 5.
Those numbers are 1 and 4 since 1(4)=4 and 1+4=5.
The factored form of [tex]x^2+5x+4[/tex] is [tex](x+1)(x+4)[/tex].
So [tex]x^2+5x+4=0[/tex] becomes [tex](x+1)(x+4)=0[/tex].
If you have a product equals 0 then at least one of the factors is 0.
So we need to solve x+1=0 and x+4=0.
x+1=0 when x=-1 (subtracted 1 on both sides to get this).
x+4=0 when x=-4 (subtracted 4 on both sides to get this).
The zeros of our function f is at x=-1 and x=-4.
Now to find where it is discontinuous. We have to think 'oh this is a fraction and I can't divide by 0 but when is my denominator 0'. If the value for the variable is not obvious to you when the denominator is 0, just solve x+4=0.
x+4=0 when x=-4 (subtracted 4 on both sides).
So we have a contradiction at one of the zeros so x=-4 can't be a zero.
The discontinuity is at x=-4.
Answer:
This function is discontinuous at x = 4, and has a zero at x = -1.
Step-by-step explanation:
If x = -4, the denominator will be zero and thus the function will be undefined. Thus, the discontinuity is at x = -4.
To find the zero(s): Set the numerator = to 0, obtaining
x^2+5x+4 = 0. Factoring this, we get (x + 4)(x + 1) = 0. Thus, we have a zero at x = -1.
Notice that f(x) can be rewritten as
x^2 + 5x + 4 (x+4)(x+1)
f(x) = -------------------- = ---------------- = x + 1 for all x other than x = -4.
x + 4 (x+4)
This function is discontinuous at x = 4, and has a zero at x = -1.
Please help me with this problem
Answer:
g(x) = -5x
Step-by-step explanation:
If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right. That point will be reflected through the x-axis to land at (1, -5). That means that the equation of the new line would be
g(x) = -5x
A reflection across the x -axis would have the opposite value of the output.
If the value is a positive value, the mirrored value would be a negative value.
The function of g(x) would be g(x) = -5x
please help
Solve for the indicated variable in the literal equation
Ax + By = C for x
Answer:
x = (C-By)/A
Step-by-step explanation:
Ax + By = C
Subtract By from each side
Ax + By-By = C-By
Ax = C -By
Divide each side by A
Ax/A = (C-By)/A
x = (C-By)/A
Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school:
What is the minimum number of at-the-door tickets she needs to sell to make her goal?
A,333
B.334
C.66
D.67
Answer: The answer would be 333
Step-by-step explanation: Hope this was helpful
To make at least $5,000, Anna must sell a minimum of 200 at-the-door tickets priced at $25 each. This is the minimum required, but the venue's capacity allows for selling up to 400 tickets to potentially exceed the fundraising goal.
Explanation:The question asks us to calculate the minimum number of at-the-door tickets Anna needs to sell to meet the fundraiser target of at least $5,000, given the constraints of the venue capacity and the ticket prices. This can be solved by first identifying the total amount needed to be raised and then calculating the number of at-the-door tickets needed if no pre-sale tickets are sold.
Since at-the-door tickets sell for $25 each, we divide the total amount Anna wants to raise ($5,000) by the price of each at-the-door ticket:
$5,000 ÷ $25 = 200 tickets
This means Anna will have to sell at least 200 at-the-door tickets to raise $5,000. However, the venue limits the capacity to 400 people, and it is not specified how many pre-sale tickets are sold. To ensure reaching the target, assuming no pre-sale tickets are sold, Anna should aim to sell all 400 tickets at the door. Selling any fewer at the door would require pre-sale tickets to make up the difference to reach the $5,000 target.
Therefore, the minimum number of at-the-door tickets Anna needs to sell to reach the $5,000 goal is 200, although to fully utilize the venue's capacity and potentially exceed the target, she can sell up to 400 tickets at the door.
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What is the approximate length of arc s on the circle below? Use 3.14 for pi. Round your answer to the nearest tenth.
A. 5.6 in.
B. 6.3 in.
C. 14.3 in.
D. 25.1 in.
Answer:
B 6.3
Step-by-step explanation:
r = 8
l = 2*3.14*r
l = 50.24
s=l/360*45
s≈6.3
For this case we have that by definition, the arc length is given by:
[tex]Al = 2 \pi * r *\frac {a} {360}[/tex]
Where:
r: It's the radio
a: It is the angle of the sector
Then, according to the data we have:
[tex]Al = 2 \pi * 8 * \frac {45} {360}\\Al = 2 * 3.14 * 8 * \frac {45} {360}\\Al = 50.24 * \frac {45} {360}\\Al = 6.28[/tex]
Rounding we have 6.3in
Answer:
Option B
What number fits the sequence, and why?
What is the actual sequence?
Answer:
The number is 15.
Step-by-step explanation:
If you look closely, the sum of any two adjacent boxes in the bottom row gives the number in the top row. For example, the sum of the first two boxes 27 and 18 gives the number 45.
27+18 = 45
Similarly,
21+x = 36 (Third and fourth boxes in bottom row)
Solving, we get x=15.
We can confirm this by checking with the last two boxes.
x+13 = 28
x=15
So, the answer is 15.
Please mark Brainliest if this helps!
In your drawer you have 10 white socks, 6 black socks, 4 brown socks and 2 blue socks. Your roommate is still asleep, and you cannot turn the light on while you get dressed. You reach in blindly and grab two socks. What is the probability of pulling out a matching pair of black socks?
Answer: Required probability is,
[tex]\frac{36}{231}[/tex]
Step-by-step explanation:
Given,
White socks = 10,
Black socks = 6,
Brown socks = 4,
Blue socks = 2,
Total socks = 10 + 6 + 4 + 2 = 22,
Thus, the total ways of choosing any 2 socks = [tex]^22C_2[/tex],
Now, the ways of choosing a black socks = [tex]^6C_1[/tex]
Thus, ways of choosing a pair of black socks = [tex]^6C_1\times ^6C_1[/tex]
Hence, the probability of pulling out a matching pair of black socks
= [tex]\frac{^6C_1\times ^6C_1}{^{22}c_2}[/tex]
= [tex]\frac{36}{231}[/tex]
Natasha places an online order for plate holders to display her antique plates. She chooses a specific site because it has a promotional offer of 15% off on all purchases. She orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each. There is no sales tax on her purchase, but she must pay a flat rate of $5.35 for shipping and handling. What is the total of Natasha?s online purchase?
Answer:
Total online purchase is $26.473 .
Step-by-step explanation:
As given
Natasha places an online order for plate holders to display her antique plates.
Natasha orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each.
Thus
Total purchase of Natasha = Number of large holders × Cost of each large holder + Number of medium holders × Cost of each medium holder + Number of small holders × Cost of each small holder .
Put all the values in the above
Total purchase of Natasha = 3 × $4.95+ 2 × $3.25 + 2 × $1.75
= $14.85 + $6.5 + $3.5
= $ 24.85
As given
Site has a promotional offer of 15% off on all purchases.
15% is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Discount amount = 0.15 × Total purchase of Natasha .
= 0.15 × $24.85
= $ 3.7275
Thus
Total purchase of Natasha after discount = Total purchase of Natasha - Discount amount .
= $24.85 - $3.7275
= $ 21.1225
As given
Natasha must pay a flat rate of $5.35 for shipping and handling.
Thus
Total online purchase of Natasha = Total purchase of Natasha after discount + Flat rate for shipping and handling .
Total online purchase of Natasha = $21.1225 + $5.35
= $ 26.4725
= $26.473 (Approx)
Therefore the total online purchase is $26.473 .
Answer:
the order Natasha places is as follows;
3 large holders - $4.95 each - 4.95*3 = 14.85
2 medium holders - $3.25 each - 3.25*2 = 6.5
2 small holders - $1.75 each - 1.75*2 = 3.5
Total value for purchases is - 14.85 + 6.5 + 3.5 = 24.85
she gets 15% for all purchases therefore she has to pay only 85% of the purchase value
$24.85 * 85% = $21.1225
She has to pay an additional $5.35 for shipping and handling
therefore the total amount she has to pay is = 21.1225 + 5.35
total amount = 26.4725 this rounded off to second decimal place,
correct answer
C - $26.47
Florence Tyler invests $6,500 in a 4-year certificate of deposit that earns interest at an annual rate of 5% compounded daily. The amount per $1.00 is 1.221386. What is the interest earned to the nearest cent?
Answer:
The total interest earned is $1,439.
Step-by-step explanation:
Consider the provided information:
Florence Tyler invests $6,500 in a 4-year certificate of deposit that earns interest at an annual rate of 5% compounded daily.
Now, Use the formula: [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where, A is the total amount (after adding interest), P is the principal (investment or loan), r is the interest rate, n is compound, and t is the time (in years).
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]A=6500(1+\frac{0.05}{365} )^{4(365)}[/tex]
[tex]A=6500(1.00014)^{1460}[/tex]
[tex]A=6500(1.22139)[/tex]
[tex]A=7939.00918[/tex]
Therefore total interest earned is:
$7,939.00 - $6500 = $1,439.00
Hence, interest earned is $1,439.
The variable z is directly proportional to x. When x is 6, z has the value 60. What is the value of z when x = 11?
Answer:
110
Step-by-step explanation:
z is apparently 10 times x.
10 times 11 is 110.
Finley's mother bought soda for her slumber party that has 10 people. Her mother bought 6 liters of soda. How many milliliters of soda can each child have?
Answer:
Step-by-step explanation:
5/3lit
Answer:young boy
Step-by-step explanation:two two
What is the solution of the equation x2 − 12x = 8?
Answer:
x = 12.63 or x= -0.63
Step-by-step explanation:
From my understanding the question is x² - 12x = 8
This will be solved through a quadratic equation formula.
Step 1: Form a quadratic equation
x² - 12x = 8
x² - 12x - 8 = 0
Step 2: Apply the quadratic formula
a = 1, b = -12, c = -8
x = -b±√b²-4ac
2a
x = -(-12)±√(-12)²-4(1)(-8)
2(1)
Step 3: Find the value of x
x = 12±4√(11
2
x = 12+4√(11) or x = 12-4√(11)
2 2
x = 12.63 or x= -0.63
!!
Determine whether the given value is a statistic or a parameter. A sample of employees is selected and it is found that 55 % own a vehicle. Choose the correct statement below. a. Parameter because the value is a numerical measurement describing a characteristic of a sample. b. Statistic because the value is a numerical measurement describing a characteristic of a sample. c. Statistic because the value is a numerical measurement describing a characteristic of a population. d. Parameter because the value is a numerical measurement describing a characteristic of a population.
Answer:
b. Statistic
Step-by-step explanation:
b. Statistic because the value is a numerical measurement describing a characteristic of a sample.
Answer:
Option b
Step-by-step explanation:
Given that a sample of employees is selected and it is found that 55 % own a vehicle.
Before we answer the questions let us understand the difference between a parameter and a statistic.
Parameters are numbers that summarizes the data of a population. But statistics are numbers that summarizes the data of a sample.
Sample is a subset of population i.e. a small portion of the whole population is sample.
Here 55% is the proportion of the sample of employees. Since this is a number summarizing the data about a sample this is called statistic.
b. Statistic because the value is a numerical measurement describing a characteristic of a sample.
The Discriminant of a quadratic equation is -6. What types of solutions does the equation have?
Answer:
2 complex conjugates
Step-by-step explanation:
The discriminate is the part of the quadratic formula that is under the radical sign. If the discriminate is negative, that means that the solutions, both of them, are complex conjugates, aka imaginary solutions.
For this case we have that by definition, the discriminant of an equation is given by:
[tex]D = b ^ 2-4 (a) (c)[/tex]
We have the following cases:
[tex]D> 0:[/tex] Two different real roots
[tex]D = 0:[/tex]Two equal real roots
[tex]D <0:[/tex] Two different complex roots
In this case we have to:
[tex]D = -6[/tex], [tex]-6 <0[/tex] , Then we have two different complex roots.
Answer:
OPTION B
A company manufactures three types of cabinets. It makes 110 cabinets each week. In the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. The next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.
In the first week, the number of type-1 cabinets produced was , the number of type-2 cabinets produced was , and the number of type-3 cabinets produced was .
Type cabinet 1 answer - 10 , 15 , 25 ,30
Type 2 - 20 , 25 , 30 , 45
Type 3 - 35 , 45 , 55, 65
WHEN YOU COMMENT PLEASE BE ONE HUNNA PERCENT!! AND JUST GIVE ME THE ANSWER
Answer:
In the first week, the number of type-1 cabinets produced was 15, the number of type-2 cabinets produced was 30, the number of type-3 cabinets produced was 65.Step-by-step explanation:
If we let a, b, c represent the numbers of type-1, type-2, and type-3 cabinets produced in the first week, respectively, we can write three equations in these unknowns:
a + b + c = 110 . . . . . total cabinets for the first weeka + 2b - c = 10 . . . . relationship of quantities in the first week3a +0b +c = 110 . . . . total cabinets in the second weekIt can be convenient to let a machine solver find the solution to this set of equations. Most graphing calculators can handle it, along with several web sites.
__
Solving by hand, we can subtract the second equation from twice the first. This gives ...
2(a +b +c) -(a +2b -c) - 2(110) -(10)
a +3c = 210 . . . . simplify
Subtracting this from 3 times the third equation gives ...
3(3a +c) -(a +3c) = 3(110) -(210)
8a = 120 . . . . . simplify
a = 15 . . . . . . . divide by 8
Using this in the third equation of the original set, we have ...
3·15 +c = 110
c = 65 . . . . . . subtract 45
Then, in the first equation, we get ...
15 + b + 65 = 110
b = 30 . . . . . . . subtract 80
The solution is (type-1, type-2, type-3) = (15, 30, 65) for the first week.
The problem provides a set of linear equations. Solving this system by substitution or elimination method will give the number of cabinets of each type produced each week. The equations are formed based on the conditions provided in the problem.
Explanation:From the information provided, we can use a system of equations to solve this. Let's denote the number of type-1 cabinets made in the first week as x , the number of type-2 cabinets as y, and the number of type-3 cabinets as z. The first condition in the problem gives us the equation x + 2y = z + 10. The total number of cabinets produced in each week is 110, so we get the equation x + y + z = 110 for the first week. From the second week's conditions, we know that no type-2 cabinets were made (y=0), the number of type-3 cabinets was the same (z=z) and the number of type-1 cabinets was three times as much as the first week (x=3x), this means 3x + 0 + z = 110.. Solving this system of equations will provide the number of cabinets produced for each type.
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8. In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 28 vowels and 12 consonants, what is the probability you will choose a consonant and then a vowel?
Answer:
The probability that you will choose a consonant and then a vowel is 0.21....
Step-by-step explanation:
Total no of tiles = 28 + 12 = 40
First you should choose a consonant = 12/40
Second you should choose a vowel = 28/40
So the probability you choose a consonant and then a vowel:
= 12/40 * 28/40
=336/1600
=0.21
So the probability that you will choose a consonant and then a vowel is 0.21....
Assume that the wooden triangle shown is a right triangle.
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram.
Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
a.
a^2 + b^2 = c^2
The legs are a and b. c is the hypotenuse.
Let a = 6x + 9y; b = 8x + 12y; c = 10x + 15y
The equation is:
(6x + 9y)^2 + (8x + 12y)^2 = (10x + 15y)^2
b.
Now we square each binomial and combine like terms on each side.
36x^2 + 108xy + 81y^2 + 64x^2 + 192 xy + 144y = 100x^2 + 300xy + 225y^2
36x^2 + 64x^2 + 108xy + 192xy + 81y^2 + 144y^2 = 100x^2 + 300xy + 225y^2
100x^2 + 300xy + 225y^2 = 100x^2 + 300xy + 225y^2
The two sides are equal, so it is an identity.
Answer:
see below
Step-by-step explanation:
a The pythagorean theorem is a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + b^2 = c^2
(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2
b solve
(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2
(6x+9y)(6x+9y) + (8x+12y)(8x+12y) = (10x + 15y)(10x+15y)
Factor out the common factors
3(2x+3y)3(2x+3y) + 4(2x+3y)4(2x+3y) = 5(2x+3y)5(2x+3y)
Rearrange
9 (2x+3y)^2 +16 (2x+3y)^2 = 25(2x+3y)^2
Divide each side by(2x+3y)^2
9 (2x+3y)^2/ (2x+3y)^2 +16 (2x+3y)^2/(2x+3y)^2 = 25(2x+3y)^2/(2x+3y)^2
9 + 16 = 25
25=25
This is true, so it is an identity
“Write each of the following expression in the form ca^pb^q where c,p and q are numbers.” The first problem is “(2a^2)^3/b”.
So what I’m wondering is what kind of math this is b/c I’ve never seen this before. Also, if anyone can solve this first problem to give me a sense of how to do it, thank you!
Answer:
[tex]8a^6b^{-1}[/tex]
Step-by-step explanation:
This is math that involves the properties of exponents. For this problem, three rules are used:
[tex](ab)^c=a^cb^c\\\\(a^b)^c=a^{bc}\\\\a^{-b}=\dfrac{1}{a^b}[/tex]
So, your expression can be written as ...
[tex]\dfrac{(2a^2)^3}{b}=\dfrac{2^3(a^2)^3}{b^1}=8a^6b^{-1}[/tex]
The mathematics involved is about exponential notation and algebraic expressions. The expression (2a^2)^3/b simplifies to 8a^6b^-1.
Explanation:The math involved here is known as exponential notation and algebraic expressions. In the given expression (2a^2)^3/b, the power rule of exponents can be applied, where to simplify the power of a power, we multiply the exponents. Therefore, (2a^2)^3 becomes 2^3 * (a^2)^3 which equals 8a^6. The expression then becomes 8a^6/b. This can be rewritten as 8a^6b^-1 (since anything divided by b can be written as multiplied by b^-1) adhering to the ca^pb^q format. So, the equivalent form of the given expression is 8a^6b^-1.
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Browning Labs is testing a new growth inhibitor for a certain type of bacteria. The bacteria naturally grows exponentially each hour at a rate of 6.2%. The researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. The sample currently contains 100 bacteria.The container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. However, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. They would like to determine the possible number of bacteria in the container over time.Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.
Hey! I just answered this on plato. the answer is that it includes negative factors, which makes not all solutions viable.
Answer:
Look at the attachment
Step-by-step explanation:
First we need to find out the equations that will represent each inequality:
For the bacteria:
This is an exponential growth equation, the formula is simple:
y≤[tex]n*(1+r)^{x}[/tex] where n is the starting point of the sample, r is the rate and x is the variable dependent on time so:
y≤[tex]100*(1+0.062)^{x}[/tex]
y≤[tex]100*(1.062)^{x}[/tex]
For the container:
This is a line equation, following the formula:
y<mx+b where m is the slope or growing rate (100 more per hour), and b is the starting point (300 bacteria)
y< 100x+300
The graph will be like is showed in the attachment, and the solution is the intersecting area to the right of both functions, since they are trying to find out if the inhibitor works, the rate of growth will be equal or smaller than 6.2% thus closing in to 100 bacterias as a constant in time if it works.
If two spheres have the same center but different radii, they are called concentric spheres.
True
False
Answer:
False
Step-by-step explanation:
If two spheres have the same center but different radii, they are NOT called concentric spheres. They would be called congruent circles if they have the same center but different radii.
Answer:
false
Step-by-step explanation:
Applying the ceiling function. Please help me. 30 points to who can answer me correctly please.
Explanation:
A fraction of an hour costs the same as an hour.
actual time ⇒ time charged ⇒ cost of parking
5 min ⇒ 1 hour ⇒ $3
1 hour ⇒ 1 hour ⇒ $3
1 hour 50 min ⇒ 2 hours ⇒ $6
2 hours ⇒ 2 hours ⇒ $6
2 hours 1 min ⇒ 3 hours ⇒ $9
3 1/2 hours ⇒ 4 hours ⇒ $12
Determine if the sequence is algebraic or geometric, and find the common difference or ratio.
x 1 2 3 4
f(x) 3 9 27 81
A.) Algebraic, common difference = 3
B.) Algebraic, common difference = 6
C.) Geometric, common ratio = 3
D.) Geometric, common ration = 6
Answer:
Option C.) Geometric, common ratio = 3
Step-by-step explanation:
we know that
In a Geometric Sequence each term is found by multiplying the previous term by a constant
The constant is called the common ratio
In this problem we have
For x=1, f(1)=3
For x=2, f(2)=9
For x=3, f(3)=27
For x=4, f(4)=81
so
f(2)/f(1)=9/3=3 -----> f(2)=3*f(1)
f(3)/f(2)=27/9=3 -----> f(3)=3*f(2)
f(4)/f(3)=81/27=3 -----> f(4)=3*f(3)
f(n+1)/f(n)=3 -----> f(n+1)=3*f(n)
therefore
This is a Geometric sequence and the common ratio is equal to 3
The sequence is a geometric sequence with a common ratio of 3.
Explanation:The sequence given is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio can be found by dividing a term in the sequence by its preceding term. For example, if we divide the second term (9) by the first term (3), we get 3. The same goes for the rest of the terms in the sequence. Therefore, the correct answer is Option C: Geometric, common ratio = 3.
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In the figure below, if angle ZYX measures 23 degrees, then arc XY measures 45 degrees.
Answer:
FALSE
Step-by-step explanation:
Assuming ZY is a tangent, the measure of the arc will be twice the measure of the angle. If the angle ZYX is 23°, the measure of arc YX will be 46°.
MAJOR HELP!
Imagine you are at home watching television. You are sitting 6 feet away from your TV which is hung on the wall and the top of it is 8 feet off the ground. Which of the following functions correctly represents the angle θ that you make with the top of your television?
Answer: Option A
[tex]\theta=tan^{-1}(\frac{8}{6})[/tex]
Step-by-step explanation:
We can model the situation by means of a right triangle.
Where the angle [tex]\theta[/tex] is the angle that you make with the top of the TV.
Then the horizontal distance of 6 feet is the adjacent side and the vertical distance of 8 feet is the opposite side to the angle the.
By definition of the [tex]tan(\theta)[/tex] function we know that:
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Therefore:
[tex]tan^{-1}(\frac{8}{6})=\theta[/tex]
[tex]\theta=tan^{-1}(\frac{8}{6})[/tex]
Answer:
CORRECT
Step-by-step explanation: