what is the equivalent expression for:
m - (8 -3m)
The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 4.3% per hour. How many hours does it take for the size of the sample to double? Note this is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answer:
16.12 hours
Explanation:
A continuous exponential growth model is given below:
[tex]P(t)=P_oe^{rt}[/tex]• The growth rate, r = 4.3% = 0.043
,• t = time in hours
,• Po = Initial population
,• P(t) = Present population
We want to find the number of hours it takes the population to double. That is if the initial population, Po = 1
• The present population, P(t) = 1 x 2 = 2.
Substitute these values into the model above to get:
[tex]2=1(e^{0.043t})[/tex]Since natural logarithm(ln) is the inverse of exponential, take the natural logarithm of both sides to remove the exponential operator.
[tex]\begin{gathered} \ln (2)=\ln (e^{0.043t}) \\ \ln (2)=0.043t \end{gathered}[/tex]Divide both sides by 0.043.
[tex]\begin{gathered} \frac{\ln (2)}{0.043}=\frac{0.043t}{0.043} \\ t=\frac{\ln(2)}{0.043} \\ t\approx16.12 \end{gathered}[/tex]It will take 16.12 hours for the size of the sample to double.
Find each quotient. All final answers must be in simplest form.9x3y2 + 15x2y - 6x2/ 3x2 = X^2 + 8x - 163xy^2 + 5y + 2 3xy^2 + 5y - 2 3xy^2 - 5y - 2
ok
[tex]\begin{gathered} \frac{9x^3y^2+15x^2y-6x^2}{3x^2}\text{ = }\frac{9x^3y^2}{3x^2}\text{ + }\frac{15x^2y}{3x^2}\text{ - }\frac{6x^2}{3x^2} \\ \text{ = 3xy}^2\text{ + 5y - 2} \end{gathered}[/tex]The answer is on the second row. 3xy^2 + 5y - 2
1. Think of a real-life situation, where knowing the percent error would be helpful.2. In a short paragraph, describe the situation and include the percent error. Explain why knowing the percent error is helpful.
SOLUTION:
The percent erroris helpsful in many situations. An example will be when conducting
Angle JKL is an equilateral triangle jk=13x+5 KL=17x-19 and JL=8x+35
The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
An equilateral triangle is a shape with three sides that have an equal measure of side length.
The 3 sides of triangle JKL are equal to each other, therefore we can equate any of the two sides together to find the unknown variable called x.
So, JK = KL
JK = 13x + 5
KL + 17x - 19
13x + 5 = 17x - 19
Collect like terms;
17x - 13x = 19 + 5
4x = 24
x = 24/4
x = 6
We can now proceed to find the sides;
JK = 13x + 5
13 x 6 + 5
= 78 + 5
= 83
JK = 83
KL = 17x - 19
= 17 x 6 - 19
= 102 - 19
= 83
KL = 83
JL= 8x + 35
= 8 x 6 + 35
= 48 + 35
= 83
JL = 83
Hence, The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
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Is the following a power function, a polynomial, both, or neither?f(x)=−17x^5
Answer:
Both
Explanation:
Given the function:
[tex]f(x)=-17x^5[/tex]• A power function is a function with a whole number as its exponent.
,• A monomial is a polynomial that has only one term.
The given funtion has 5 as its exponent, thus, it sis a power function. Furthermore, it is a monomial, thus it is also a polynomial.
f(x) is both a power function and a polynomial.
Which are the better statistics to use to compare the team scores
Step 1
We are given two team scores
Required; Which are the better statistics to use to compare the team scores
Step 2
The box plot displays the 5 number summary
-Minimum data value
-Maximum data value
-Median
-First Quartile, and
Third Quartile
The Interquartile Range (IQR) of the data can also be calculated by finding the difference between the First Quartile, and the third Quartile.
The Interquartile Range (IQR) helps us to determine the variability of the data set. The IQR is often seen as a better measure of spread than the range as it is not affected by outliers.
The median that is gotten from the box pot measures the center tendency of the data. The median is the most informative measure of central tendency for skewed distributions or distributions with outliers.
Therefore, the better statistics to use for comparing the scores of the teams are;
Median and IQR.
Rudy has $90,000 in a savings account that earns 10% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
The total interest earned by Rudy on the principal is $9000
Amount in Rudy's saving account = $90,000
Interest rate per year = 10%
The formula for simple interest is given:
A loan or deposit's principal amount serves as the foundation for simple interest. Compound interest, on the other hand, is calculated based on both the initial principal and the interest that is added to it each period.
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Substituting the values in the formula we get:
Simple interest = 90000*10*1/100
= 9000
So, the interest amount is $9000
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Select the table that represents a linear function. (Graph them if necessary.)
OA. x 0 1 2 3
y 2 3 6 11
OB. x 0 1 2 3
y 1 3 9 27
OC. x 0123
y 0149
OD. x 012
3
y 39 15 21
Answer:
The last table represents a linear function.
As x increases by 1 unit, y increases by a constant of 6 units
The equation of the function is
y = 6x + 3
Step-by-step explanation:
How do I solve 5/9x+ 6=10?
Due to the inaccuracy of the provided information, we will suppose that the original expression is
[tex]\frac{5x}{9}+6=10[/tex]Solve for x as shown below
[tex]\begin{gathered} \Rightarrow\frac{5x}{9}+6-6=10-6 \\ \Rightarrow\frac{5x}{9}=4 \\ \Rightarrow(9)\frac{5x}{9}=(9)4=36 \\ \Rightarrow5x=36 \\ \Rightarrow(\frac{1}{5})5x=\frac{1}{5}\cdot36 \\ \Rightarrow x=\frac{36}{5} \end{gathered}[/tex]Therefore, the answer is x=36/5
A family has 6 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 6 girls if it is known the family has at least one girl.
The probability that the family has 6 girls if it is known the family has at least one girl is; 3.125%
What is the Probability?
We are told that each child has the same chance of being a boy or a girl and as such we can say that probability is 1 in 2, or 0.50 or 50%.
Since the family must have at least one girl, if we assume that the first child is a girl, the the probability of the second child being a girl is 50%.
The probability of the other 5 children all being girls is:
(1/2) * (1/2) * (1/2) *(1/2) * (1/2) = 1/32.
This Probability expressed as a decimal or percentage represents a probability that we have as; 1/32 = 0.03125 = 3.125%.
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Given the following: P(A)=0.28, P(B)=0.64, P(B|A)= 0.37, calculate P(A and B)
By definition of conditional probability you know that
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]Now, replace the values that you have and solve for P(A and B)
[tex]\begin{gathered} P(B|A)=\frac{P(A\cap B)}{P(A)} \\ 0.37=\frac{P(A\cap B)}{0.28} \\ \text{ Multiply by 0.28 on both sides of the equation} \\ 0.37\cdot0.28=\frac{P(A\cap B)}{0.28}\cdot0.28 \\ \text{ Therefore,} \\ 0.1036=P(A\cap B) \end{gathered}[/tex]A board 172 inches wide is cut to three-fourths of its original width
Answer: 129 inches
Step-by-step explanation:
172 inches x 3/4 original with = 129 inches
Each relationship below compares the shaded portion the part to the entire figure the whole complete the table 6'60'600'32
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a portion of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Percent refers to one hundred percent.
A decimal is a number divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of full and partially whole quantities.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
A ratio displays the multiplicity of two numbers. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.
Percentage Decimal Fraction Ratio
6% 0.06 6 / 100 6:100
60% 0.6 60 / 100 60:100
600% 6 600 / 100 = 6 / 1 6:1
32% 0.32 32 / 100 32:100
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There are 151 people in the 6th
grade class. It costs $24 for each
person to go snorkeling. How
much did they pay altogether?
Answer:
Step-by-step explanation:
it cost $3,624
2x – 1 over 5 - 3x +2 over 4
we have
(2x-1)/5-(3x+2)/4
{4(2x-1)-5(3x+2)}/20
{8x-4-15x-10}/20
{-7x-14}
5-(3x+2)/4
4(2x-1
What are the x intercept of the equation f(x)=3(x-7)(4x+2)
The x-intercepts are
x = 7
and
x = -1/2
SOLUTION:
we need to find the value of x where y or f(x) is 0
the expression x-7 will be zero if x=7
the expression 4x+2 will be zero if x = -1/2
Given P250/75R18 tires, what would be the Circumference in inches of the tire?
Given data:
The given radius of the tire is r=18 in.
Th expression for the circumference is,
C=2πr
Substitute the given values in the above expression.
C=2(3.14)(18)
=113.04 in
Thus, the circumference of the tire is 113.04 inn.
what is probability that it is from the 70s is
Given :
the total number of collections = 60 vinyl
There are six from the 70s
So, the probability that is from 70s is :
[tex]\frac{6}{60}=\frac{1}{10}[/tex]ryan is buying pencil boxes. he wnats to buy the box that will fit the most markers. he can choose between the following 3 options
Answer:
what r the 3 following options??
Step-by-step explanation:
Give a parametric representation of the parabola y = (x+7)^2 -5
We have to find the parametric representation of the parabola y = (x+7)² - 5, which is represented in vertex form.
Parametric representations use a third variable on which we define x and y.
We will call this variable t.
We can start with defining t as:
[tex]\begin{gathered} t=x+7 \\ \Rightarrow x(t)=t-7 \end{gathered}[/tex]We then have already x in function of t.
Then, we can use the definition of t to find y(t):
[tex]\begin{gathered} y(t)=(x(t)+7)^2-5 \\ y(t)=(t-7+7)^2-5 \\ y(t)=t^2-5 \end{gathered}[/tex]We then have x and y defined in function of t.
Answer: we can represent the parabola in a parametric form as
x(t) = t-7
y(t) = t² - 5
The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?
Answer: 156.86
Step-by-step explanation:
cual es la raiz cuadrada de 4096 y 529
The square root of 4096 is 64 and the square root of 529 is 23.
The square root of a number x in mathematics is a number y whose square (the outcome of multiplying the number by itself, or y·y), is equal to x.
For instance, since 4² = (-4)² = 16, 4 and -4 are the square roots of 16.The square root of x is rational if and only if x is a rational integer that can be expressed as the ratio of two perfect squares. (The square root of 2 for proof that this number is illogical; the quadratic irrational for evidence against all non-square natural numbers.) The square root function changes rational numbers into algebraic numbers, which are a superset of rational numbers.The given numbers are 4096 and 529.
Let us find the factors of 4096:
4096 = 2¹²
Therefore the square root of 4096 = √4096 = √(2¹²) = 2⁶ = 64 .
Let us find the factors of 529:
4096 = 23 × 23
Therefore the square root of 529 = √529 = √(23²) = 23 .
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Disclaimer : The question in English is :
What is the square root of 4096 and 529.?
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if a varies equal directly with b, and a=8 when b=20 what is the value of a when b= 14.5
b. Triangle DEF with coordinates D(-2, 2), E (1,5), and F (4, -1) is rotated 90° counterclockwise aboutthe origin
a cylinder shaped popcorn
Answer
Option C is correct.
Volume = 1,413 in³
Explanation
The volume of a cylinder is given as
Volume = πr²h
where
π = pi = 3.14
r = radius of the cylinder = ½ (Diameter) = ½ (10) = 5 inches
h = height of the cylinder = 1.5 feet = 1.5 (12 inches) = 18 inches
The conversion from feet to inches was done using 1 feet = 12 inches
So, we can calculate the volume now
Volume = πr²h
Volume = (3.14) × (5²) × (18)
Volume = 1,413 in³
Hope this Helps!!!
Simplify 3^2 + 3(6 - 2^2) ÷ 6.
Fractions simplification
Apply PEMDAS method. Eliminate parenthesis first.
Then (3^2 + 3•6 - 3•2^2 )/ 6 = (3^2 + 3•6 - 3•2^2 )/ 6
now eliminate exponents
= [3• 3 + 3•6 + 3•4] / 6
= 3•5/6 now multiplicate
3•5= 15
Then
= 15/6 = 2 + 3/6 = 2 + 1/2 = 2.5
Hey there Ms or Mr could you please help me out with this problem? Just a heads up, this is my assignment not a quiz. My assignment is about distance and midpoint formula.
EXPLANATION
Let's see the facts:
Midpoint = (-2,5)
A=(4,7)
Let the point of B as B=(x,y)
Then,
[tex]\frac{x+4}{2}=-2,\frac{y+7}{2}=5[/tex]Multiplying the frist equation by 2:
[tex]x+4=-2\cdot2[/tex]Subtracting -4 to both sides:
[tex]x=-4-4[/tex]Simplifying:
[tex]x=-8[/tex]Multiplying the second equation by 2:
[tex]y+7=2\cdot5[/tex]Subtracting -7 to both sides:
[tex]y=10-7=\text{ 3}[/tex]The coordinates of the point B are:
B=(-8,3)
Find the value of sin t if tan t = 1 and pi/2 < t < 3pi/2
The value of sin t = sin 135° = 1/√2
What are trigonometric functions?The trigonometric functions are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions[1][2]. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given; tan t = 1
And the given condition is π/2 < t < 3π/ 2
this mean t lies in the 2nd quadrant because the value of t lies between 90 and 270 degrees.
This means tan t = tan (90 + 45)= cot 45 = 1
thus t = 235 degree
And thus sin t = sin 135 ° = sin (90+ 45) = cos 45 ° = 1/ √2
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the supplement of an angle is 30 degrees more than the measure of the
what is the measure of
the angle?
angle,
Answer:
x = 75°
Step-by-step explanation:
supplementary angles sum to 180°
let x be the angle then x + 30 is the supplementary angle , so
x + x + 30 = 180
2x + 30 = 180 ( subtract 30 from both sides )
2x = 150 ( divide both sides by 2 )
x = 75
x + 30 = 75 + 30 = 105
the angle is 75° and the supplementary angle is 105°