At any time t (in hours), there are 216(t +18) of Type A bacteria in a sample and 362t + 8 of Type B bacteria in a sample. After how many hours will the number of type A bacteria be less than the type B bacteria?
Answers
1. The given situation can be described in the following inequality:
[tex]216^{(t+18)}<36^{(2t+8)}[/tex]2. To solve the prevous inequality, proceedas follow:
write 216 as 6^3 and 36 as 6^2, then, apply log_6 both sides:
[tex]\begin{gathered} 6^{3(t+18)}<6^{2(2t+8)} \\ \log _66^{3(t+18)}<\log _66^{2(2t+8)} \\ 3(t+18)<2(2t+8) \end{gathered}[/tex]then, solve for t, as follow:
[tex]\begin{gathered} 3t+54<4t+16 \\ 3t-4t<16-54 \\ -t<-38 \\ t>38 \end{gathered}[/tex]Hence, from t = 38 hours the number of type A bacteria will be less than the type B bacteria
3. In a number line, you obtain:
Related Questions
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-interceptform.x1520253035HHHу160200240280320An equation of the line in point-slope form is
Answers
Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Explanation:
To write an equation of the line in point-slope form that passes through the given points in the table, we need to pick any two of the points in the table for x and y axis and find the changes of x and y
Points chosen: (20, 200) and (15, 160)
m = slope = (change in y)/ (change in x)
[tex]\begin{gathered} m\text{ = }\frac{200-160}{20-15}\text{ = }\frac{40}{5} \\ m\text{ = 8} \end{gathered}[/tex]Point-slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1)\text{ then we would pick any of the points used earlier} \\ U\sin g\text{ (15, 160)} \\ y\text{ - 160 = 8( x - 15)} \\ y\text{ - 160 = 8x -120} \\ y\text{ =}8x\text{ + 40} \end{gathered}[/tex]The equation in the slope intercept form:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = 8x + 40} \\ \text{where m = 8 b = intercept = 40} \end{gathered}[/tex]Hence, Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Solve for x: 6x + 3 = 5x - 8
О -11
О 11
о
О -5
0
О 5
F
Answers
Answer:
6x+3=5x-8
6x-5x= -8-3(match the like terms)
x= -11
jaylens snow cone stand went thourgh 10 bags of ice in the first hour it was open and 8 1/6 simplify your answer and write it as a fraction or as a whole or mixed number
Answers
The fraction form of 8 1/6 is 49/8 as the definition of fraction says, "An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided".
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction merely informs us of the number of parts that make up the whole. The slash that is written between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction.
Here,
8 1/6=(6*8+1)/8
=49/8
According to the definition of a fraction, which states that it is "a number represented mathematically as a quotient, where the numerator and denominator are divided," the fraction form of 8 1/6 is 49/8.
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write and equation in slope-intercept form to represent each table x-3,6,9,12 y-5, -1, -7, -13
Answers
The equation that represents the table, in slope-intercept form, is: y = -2x + 11.
How to Write the Equation of a Line in Slope-intercept Form?The slope-intercept form of an equation that represents a line is expressed as y = mx + b, where:
m = slope = change in y / change in x.b = y-interceptUsing two pairs of values from the table, (6, -1) and (9, -7):
Slope (m) = (-7 -(-1)) / (9 - 6)
Slope (m) = -6/3
Slope (m) = -2.
Find the y-intercept, b, by substituting m = -2 and (x, y) = (6, -1) into y = mx + b:
-1 = -2(6) + b
-1 = -12 + b
-1 + 12 = b
b = 11
To write the equation, substitute m = -2 and b = 11 into y = mx + b:
y = -2x + 11
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3 times x increased by 20 as a algebraic expression
Answers
Answer:
3x+20
Step-by-step explanation:
“3 times x” means 3x
and “increased by 20” means to add 20 to the equation.
if you were to solve this equation, the answer to the first step would be 6.666!
divide each side by 3. 3/3 is 1, and 20/3 is 6.666! therefore, the 1 cancels out and you get this number, which is the value of x.
now, for the second step, you would get 39.998, which is your overall answer! all you have to do is replace x with the answer from the previous step (6.666)
i hope this helped!!
number 8 State how you know each pair of triangles are congruent
Answers
trianglesPairs of congruent triangles
Triangles A is congruent since UV = WX
Triangle Δ KLJ = Δ MNO and are congruents
Triangle Δ UGI ≠ Δ MNO ≠ ΔKLJ is congruent
<
An inequality is shown.
-2x+12<18
What is the solution to the inequality?
0x<3
x>3
Answers
Answer:
-3 < x
Step-by-step explanation:
first of all get the positive x on one side, so we have
12 < 18 + 2x ( positive x is easier to work with)
then, get only x on one side
-6 < 2x
simplify
-3 < x
Vivian has $535 in her stavings account and she has to pay $5.00 each month for her cell phone Reza has $145 and he saves $25 each month for his job walking the dogs at this rate when will they had the same amount of money and how much will they have
Answers
Answer: $456
Step-by-step explanation: They will both have the same amount of money at 7 months
which value of x below will solve equation 3/4x+10=4
Answers
3/4x+10=4
Then solve for x
3/4x = 4 - 10
x = (4-10)/(3/4)
. = -6/3/4
. = -24/3
. = -8
In consecuence , answer IS
x= -8
?
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
Area of Irregular Shapes
Nov 03, 2-44:03 PM
Answer:
9
3
20 POINTS PLEASE HELP !!!!!
Answers
Area of irregular shape is 41.13m².
Define area.The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
Given,
Area of irregular shape = Area of rectangle + Area of semicircle
Area of rectangle = Length × Breadth
Area of rectangle = 9 × 3
Area of rectangle = 27 m²
Area of semicircle:
1/2πr²
1/2 × 3.14 × 3²
14.13 m²
Area of irregular shape = 27 + 14.13
Area of irregular shape = 41.13
Area of irregular shape is 41.13m².
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Solve the quadratic equation using the quadratic formula or completing the square. Show exact answers in simplified, radical form; no rounded decimals 2x^2-4x+3=0
Answers
The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula
Given,
In the question:
The equation is :
2x^2-4x+3=0
To solve by using the quadratic formula :
Now, According to the question;
[tex]2x^2 -4x+3=0[/tex]
Identify the coefficients
a = 2, b = -4 , c = 3
Use the quadratic Formula :
x = (-b±√(b²-4ac))/(2a)
Substitute into values above formula :
x = -(-4) +√(-4)²-4x 2 x 3))/(2x2) or
x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)
Determine the sign for exponential or radical expressions
x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)
x = 4 -√16-4x 2 x 3))/(2x2)
Calculate the product or quotient
x = 4 -√16-24/4
x = 4 -√-8/4
x = 4 - √-8 x √-1/ 4
x = [tex]\frac{4\sqrt{2^2.2 } }{4}[/tex] x [tex]\sqrt{-1}[/tex]
Simplify the radical expression:
x = [tex]\frac{4 - 2\sqrt{2} . \sqrt{-1} }{4}[/tex]
Rewrite by definition i = [tex]\sqrt{-1}[/tex]
x = [tex]\frac{4-2\sqrt{2i} }{4}[/tex]
x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex]
Hence, The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula .
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24. Find fl-1).For questions 24-27, use the graph below.25. Find f(4).26. Find f(-3).27. If f(x) = 9, find x.
Answers
Let's start by calculating the value for f(-1).
For this we go to the graph and count the number of squares to the left of the axis to be at -1. In this case f(-1) would be 5.
Now let's calculate f(4)
For this case the value of f(4) would be 0.
Similarly we calculate f(-3). As you can see in the graph it would be 6.
The last scenario would be for when f(x) = 9, we look for that value on the curve and realize that it corresponds to x = 1.
Torren deposits $4500 in an account earning 2% interest, compounded annually. The equation that represents this situation is:A(n) = 4500(1 + 0.02) - 1How much will he have in the account at the beginning of year 8? Round youranswer to the nearest dollar.A. $5169B. $32,130C. $16,124D. $5272
Answers
Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
The following formula can be used to calculate the compound interest.
[tex]A(n) = P(1 + r)^{(t- 1)}[/tex]
where,
A(n) denotes the final sum.
P stands for the initial deposit.
r denotes the interest rate (in decimal).
t denotes the time (in year).
The compound interest will be C.I = A - P in this case.
We are given in the question;
The account's initial deposit is $4500, and the term is 8 years.
As a result,
A = 4500 and
t = 8
As we all know, interest is compounded once a year.
We shall divide the interest rate in percentage form by 100 to convert it to decimal form.
r = 2% = 2/100
⇒r = 0.02
The given equation is
[tex]A(n) = 4500(1 + 0.02)^{(n- 1)}[/tex]
Substituting the given values in the above equation, we will get,
[tex]A(n) = 4500(1 + 0.02)^{(8- 1)}[/tex]
[tex]A(n) = 4500(1 + 0.02)^{7}[/tex]
[tex]A(n) = 4500 \times 1.14868[/tex]
[tex]A(n) = 5169.06[/tex]
[tex]A(n) = 5169[/tex]
Thus, Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
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Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b equals one half question markgraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative 3 times pi over 2 comma negative 2 and negative pi comma negative 1 and negative pi over 2 comma 0 to the right asymptotic to the line x equals 0 and another piece that increases from the left in quadrant 4 asymptotic to the line x equals 0 passing through the points pi over 2 comma negative 2 and pi comma negative 1 and 3 times pi over 2 comma 0 to the right asymptotic to the line x equals 2 times pigraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative pi comma negative 2 and 0 comma negative 1 and pi comma 0 to the right asymptotic to the line x equals 2 times pigraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative 3 times pi over 2 comma 1 to the right asymptotic to the line x equals negative pi and another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative pi passing through the point negative pi over 2 comma 1 to the right asymptotic to the line x equals 0 and continuing periodicallygraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 7 times pi over 4 passing through the point negative 3 times pi over 2 comma negative 1 to the right asymptotic to the line x equals negative 5 times pi over 4 and another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 5 times pi over 4 passing through the point negative pi comma negative 1 to the right asymptotic to the line x equals negative 3 times pi over 4 and continuing periodically
Answers
In general, given
[tex]y=a*tan(bx-c)+d[/tex]b is related to the period of the function, such that, in the case of the tangent function,
[tex]period=\frac{\pi}{b}[/tex]Remember that the period of tan(x) is equal to pi.
Therefore, in our case,
[tex]\begin{gathered} b=\frac{1}{2} \\ \Rightarrow period=\frac{\pi}{\frac{1}{2}}=2\pi \end{gathered}[/tex]The period of the function is 2pi, which means that it repeats every 2pi units.
Thus, the answer is the first graph, the one shown below.
A lawnmower designer wants to build a lawnmower that measures
8 feet in height, 3 feet width, and 7 feet in length. She needs to construct a three dimensional model of the lawnmower. First, determine
the width for the scale model given a height of 10 inches?
Answers
The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.
What is width of the scale model given a height of 10 inches?It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.
According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.
Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;
8/10 = 3/x
x = ( 10 × 3 ) / 8
x = 30/8
x = 3.75 inches.
Therefore, the width on the scale as required is; 3.75 inches.
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How do you decide how well data represent
a population?
Use examples to explain.
Answers
The data that represent a population is helpful when we have to find the information only about one field.
In the given question we have decide how well data represent a population.
The total group you want to make judgments about is referred to as a population. Data is a set of quantitive data which refers the population only in numbers. So the data is only helpful when we have to find the only in small amount and only one field.
Data collection from a large population is typically only simple when the population is small, approachable, and cooperative.
Example: Gathering information from a population
A high school administrator is looking for trends in the final exam results of all graduating seniors. They use the entire population dataset since they are only interested in applying their findings to the graduating seniors in this high school. So the data is useful.
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HELP QUICK 30 POINTS!!!!
What equation is graphed in this figure?
A. y−4=−2/3(x+2)
B. y+2=−3/2(x−2)
C. y+1=−2/3(x−3)
D. y−3=3/2(x+1)
Answers
Answer:
B is correct. The slope is -3/2.
Answer:D
Step-by-step explanation:
Mia is deciding between two truck rental companies. Company A charges an initial fee of $30 for the rental plus $3 per mile driven. Company B charges an initial fee of $85 for the rental plus $2 per mile driven. Let AA represent the amount Company A would charge if Mia drives xx miles, and let BB represent the amount Company B would charge if Mia drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Mia needs to drive 80 miles with the rented truck.
Answers
Answer:
(a.): Company A: 3x + 30; Company B: 2x+85
(b.) Company B is cheaper as it would cost $245 for Mia to drive 80 miles
Step-by-step explanation:
The equations we need are linear and we can think of them as such. x represents the slope (cost per mile) and the initial fee represents our y-intercept or constant (amount paid before Mia ever drives)
(a.): Thus, for company A, we have y = 3x + 30 and for company B we have y = 2x + 85.
(b.) Since we know that Mia needs to drive 80 miles, we plug this into x for both companies and find which one is lower
Company A: 3(80) + 30 = $270
Company B: 2(80) + 85 = $245
Company B's price would be lower for Mia's needs.
Attendance at october fest was 15% more than last year. this year's attendance was 1785 people. find the number of people who attended the festival last year. rounded to the nearest person
Answers
Using the concept of equations, 1552 people attended the festival last year.
What are algebraic equations?Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.
An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.
Let the number of people who attended the festival last year =x
Then, we can write an equation as
1785=1.15 × x
x = 1785/1.15
=1552 people
So, last year's attendance = 1552
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According to the rules of significant figures:1.25 × 200 = 300True orFalse
Answers
According to the rules of significant figures:
1.25 × 200 = 300
the answer is
TRue
there is a step missing from the solution. Which equation is the missing step?
Answers
To determine the next step, we need to slove the expression.
divide both sides by -1:
[tex]\begin{gathered} \frac{8}{-1}=\frac{-\sqrt[]{0.025x+7}}{-1} \\ -8=\sqrt{0.025x +7} \end{gathered}[/tex]Square both sides of the equation:
[tex]\begin{gathered} 8^2=(\sqrt{0.025x +7})^2 \\ 64\text{ = 0.025x + 7 } \\ 64\text{ - 7 = 0.025x } \\ 57\text{ = 0.025x } \\ Hence,\text{the missing step: }64\text{ = 0.025x + 7 (option B)} \end{gathered}[/tex]What is the reciprocal of 1 1/8 ?
Answers
Answer:
0.8 repeated
Step-by-step explanation:
Because it is
Tim buys a torch and a battery
The torch costs eleven times as much as the battery
Tim pays with a £10 note and gets £4.84 change
How much does the battery cost?
Answers
The cost of battery is £0.43.
Given,
In the question:
Tim buys a torch and a battery
The torch costs eleven times as much as the battery and
Tim pays with a £10 note and gets £4.84 change.
To find the how much does the battery cost?
Now, According to the question:
Let cost of battery = £ x
So, Cost of torch = £ 11x
Based on the given conditions :
=> x + 11x = £ 10 - £ 4.84
=> 12x = £ 5.16
=> x = £ 5.16/ 12
=> x = £ 0.43
Hence, The cost of battery is £0.43.
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One third times the difference of thirty and a variable is three fourths. one third times the quantity 30 minus y equals three fourths one third times the quantity y minus 30 equals three fourths one third times 30 minus y equals three fourths one third times y minus 30 equals three fourths
Answers
The original statement is same as third statment and value of y is 27.
Writing the equation form for each statement -
Let the variable be represented as y.
One third times the difference of thirty and a variable is three fourths1/3(30 - y) = 3/4
one third times the quantity 30 minus y equals three fourths1/3×30 - y = 3/4
one third times the quantity y minus 30 equals three fourths1/3×y - 30 = 3/4
one third times 30 minus y equals three fourths1/3(30 - y) = 3/4
one third times y minus 30 equals three fourths1/3(y - 30) = 3/4
Based on the interpretation of all the sentences in equation form, we find the statement 3 to be same as original statement. Solving the equation to get the value of y.
1/3(30 - y) = 3/4
10 - y/3 = 3/4
10 = 3/4 + y/3
10 = (3×4 + y×4)/12
10×12 = 12 + 4y
4y + 12 = 120
4y = 120 - 12
4y = 108
y = 27
Hence, the value of y is 27.
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Answer:
the answer is A.
1 over 3 (30 - y) = 3 over 4
Simplify the equation 10x - 8x +2 + 10
Answers
And then add 2 and 10 =12
Steps
10x-8x=2x
2+10=12
2x+12
which value represents between 11% and 17%?
Answers
0.159 - A
It is between 11% and 17%
Which table shows a function that is decreasing only over the interval (-1, infinity)
Answers
The last table shows the function that is decreasing only over the interval [tex](-1, \infty)[/tex].
From given tables we clearly see that in below table, the functions are decreasing as 'x' increases
x f(x)
-3 -5
-1 -1
-1 -1
0 0
1 -4
2 -8
We need to find interval [tex](-1, \infty)[/tex].
In first table,f(x)=-5,-2,-1,2. Here the functions are in increasing order
In second table, f(x)=-7,-6,1,-1. Here the functions does not follow a specific order
in third table, f(x)=-1,2,1,-6, Here also the functions does not follow a specific order.
In fourth table, f(x)=1,0,-4,-8. Here the functions are in decreasing order.
Hence, the fourth table shows the function that deceases over interval [tex](-1, \infty)[/tex].
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What is the value of x in the triangle?
a 30-60-90 triangle with long leg length x and shorter leg length of 7 times the square root of 3
Answers
Answer:
sin 30 = 7 *3^1/2 / c
sin 60 = x / c definition of 30-60-90 -
sin 30 / sin 60 = 7 * 3^1/2 / x = .5 / .866 = .577
x = 7 * 3^1/2 / .577 = 21
Check: tan 30 = 7 * 3^1/2 / 21 = .577 = tan 30
what is evaluate 5-(6/3)
Answers
I need help evaluating/answering this!
Answers
The value of the expression is equal to 6.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is [3(6-14)]/(-4). The value of the expression will be calculated below,
E = [3(6-14)]/(-4).
Simply the expression by using mathematical operations,
E = [3( -8)]/(-4).
E = 3 x 2
E = 6
Therefore, the value of the expression is equal to 6.
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