According to the information, it can be inferred that the F bacterium had a greater growth over time. Additionally, the population of G si will exceed the population of F because it has an x exponent.
What do the functions express?The functions express the relationship between the number of bacteria and time. In accordance with the above, the function of the bacterium A, expresses that the number of bacteria grows 36 individuals every hour.
36 * 1 = 3636 * 2 = 7236 * 3 = 10836 * 4 = 144On the other hand, the function of B expresses that the individuals grow exponentially in 3. According to the above, at some point the exponent of 3 will be so great that it will be able to exceed the number of individuals of A. (not in the first four hours).
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The rectangular floor of a classroom is 32 feet in length and 28 feet in width. A scale drawing of the floor has a length of 16 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answer:
Step-by-step explanation: the answer would be 60.
A women is 159 1/4 cm tall and her son is 147 6/8 cm how taller is the women
Answer: 11 1/2 cm or 11.5 cm
Step-by-step explanation:
To see how much taller the woman is than her son, we will subtract the son's height from the woman's height. We can convert these fractions into decimals to make it easier to subtract.
159 1/4 - 147 6/8 = 159.25 - 147.75 = 11.5 = 11 1/2 cm
how many 3/4 cup servings are in a 12 cup bottle of lemonade? (must be solved using fractions - show your work).
Answer:
16
Step-by-step explanation:
we need to find how many servings can be made out of 12cups of lemonade if each serving is 3/4th of a cup . For that you just need to divide the total quantity of lemonade with each serving as ,
= 12 ÷ 3/4
= 12 * 4/3
= 4*4
= 16
And we are done!
What fraction of 6 naira is 6 Kobo
The part 6 kobo as required in the task content represents 1% of the whole, 6 naira.
What percentage of 6 naira is 6 kobo?It follows from the task content that the percentage of 6 naira which 6 kobo represents is to be determined.
On this note, it follows from currency conversion that 1 naira is equivalent to 100 kobo.
Hence , 6 naira = 600 kobo
The percent as required to be determined can be evaluated as follows;
6 / 600 = percent / 100.
Percent = 1%.
Ultimately, the fraction of 6 naira which 6 kobo represents is; 1%.
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I need help with this problem
An increasing exponential function is defined as follows:
y = a(1 + r)^x.
In which:
a is the initial value.r is the growth rate, as a decimal.For this problem, the function is given as follows:
y = 20000(1.14)^t.
In which the parameters are given as follows:
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the sum of three fractions is 6.if 18/7 and5/6 are two of the fractionsfind the third fraction
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
First, we need to solve for a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To get the common denominator between [tex]\frac{18}{7}[/tex] and [tex]\frac{5}{6}[/tex], we multiply their denominators.
7 × 6 = 42Now, we know the fractions would look like this:
[tex]\frac{?}{42} \frac{?}{42}[/tex]To solve for the numerators, we can use these equations:
18 × 6 = 1085 × 7 = 35Now, the fractions look like this:
[tex]\frac{108}{42}[/tex] and [tex]\frac{35}{42}[/tex]Adding them together:
[tex]\frac{108}{42} +\frac{35}{42} = \frac{143}{42}[/tex]Now, we can convert this into a mixed number.
[tex]\frac{143}{42} = 3\frac{17}{42}[/tex]Now that we have this, we can subtract that from 6 to get the missing value.
[tex]6 - 3\frac{17}{42}[/tex][tex]=2\frac{25}{42}[/tex]Therefore, the third fraction is [tex]2\frac{25}{42}[/tex].
I need help with this question(Divide.
Express your answer as a decimal.
51
÷
6
=
51÷6) the first person answer get 10 points thanks for the help!
Answer:
Below
Step-by-step explanation:
51÷6= 51/6 = 8 3/6 = 8 1/2 = 8.5
6
This graph represents one of the following descriptions. Which one?
a. A phone loses 80% (20% left) of its value every year after purchase: the relationship between the number of years since purchasing the phone and the value of the phone.
b. The number of stores a company triples approximately every 5 years: the relationship between the number of years and the number of stores.
c. A camera loses 40% (60% left) of its value every year after purchase: the relationship between the number of years since purchasing the camera and the value of the camera.
2. A small town's population has grown at a rate of 6% per year. The initial population of the town was 5,600. A nearby town had an initial population of 10, 200 people but is declining at a rate of 4% per year.
a. Write two equations to model the population of each town.
Let Pa represents the first town's population and t represents years. Let Pa represents the second town's population and t represents years.
b. Use your equation to predict the number of years when the two towns will have the same population. About how many people will be in each town at that time?
sjdffdghddffffdbdbbfbdhdbdbfbd
Which of the following is the correct answer?
From the given data value of function f ' (- 10) is,
⇒ f ' (- 10) = 0.035
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.
Given that;
Table for the given data is shown.
Now, We have to find the value of f ' (- 10).
Since, - 10 is in between - 11 and - 9.
Hence, The slope given the value of f ' (- 10) as;
⇒ f ' (- 10) = (1.12 - 1.05) / (- 9 - (- 11))
⇒ f ' (- 10) = (0.07/2)
⇒ f ' (- 10) = 0.035
Thus, From the given data value of f ' (- 10) is,
⇒ f ' (- 10) = 0.035
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Q4 The following square is made up of
rectangles and a compound shape.
Write a simplified expression for each
area making up the square.
6x +1
x+1
x + 2
2x + 2
3x + 1
B
D
3x + 1
A
E
4x + 1
C
x+2
Step-by-step explanation:
The given figure consists of some rectangles and square making up a bigger square.
As we know that,
area of rectangle= length*breadth, so
Area of rectangle A :-
A = lb
A = (6x+1)(x+2)
A = 6x(x+2)+1(x+2)
A = 6x² + 12x + x + 2
A = 6x² + 13x + 2
Area of rectangle B :-
A = (2x+2)(3x+1)
A = 2x(3x+1)+2(3x+1)
A = 6x² + 2x + 6x + 2
A = 6x² + 8x + 2
Area of rectangle C :-
A = (x+1)(x+2+2x+2)
A = (x+1)(3x+4)
A = 3x² + 4x + 3x + 4
A = 3x² + 7x + 4
Area of rectangle D :-
A = (3x+1)(3x+1)
A = 9x² + 3x + 3x + 1
A = 9x² + 6x + 1
Area of rectangle E :-
A = (6x+1-3x-1 )(2x+2+3x+1)
A = 3x(5x+3)
A = 15x² + 9x
Hence these are the simplified expressions making up the area of the whole square .
And we are done!
what are the excluded values?
After divide, the solution of the expression is,
⇒ x (x + 2y) / 5
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ (x² - 4y²) ÷ (5x - 10y) / x
Now, We an simplify as;
⇒ (x² - 4y²) ÷ (5x - 10y) / x
⇒ (x² - (2y)²) ÷ (5x - 10y) / x
⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x
⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)
⇒ x (x + 2y) / 5
Thus, The solution of the expression is,
⇒ x (x + 2y) / 5
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a boy owns 8 pairs of pants, 5 shirts, 3 ties and 6 jackets. how many different outfits can he wear to school if he must wear one of each item?
The boy can wear 720 different outfits to school if he must wear one of each item, we need to find the number of combinations of one pair of pants, one shirt, one tie, and one jacket. The number of different combinations of pants he can wear is 8.
The number of different combinations of shirts he can wear is 5.
The number of different combinations of ties he can wear is 3.
The number of different combinations of jackets he can wear is 6.
To find the total number of different outfits, we multiply the number of combinations of each item:
8 * 5 * 3 * 6 = 8 * 90 = 720
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9.5% of Undergraduate students study abroad. 60% of those who study abroad are female. 49 % of those who do not study abroad are female. calculate probability of a female student studying abroad .
The probability of a female student studying abroad is 9.5%. 60% of those who study abroad are female, while 49% of those who do not study abroad are female.
P(Female studying abroad) = P(Female and Studying Abroad) / P(Female)
P(Female and Studying Abroad) = 0.095 × 0.60 = 0.057
P(Female) = 0.095 × 0.60 + 0.905 × 0.49 = 0.902
P(Female studying abroad) = 0.057 / 0.902 = 0.063
Therefore, the probability of a female student studying abroad is 0.063.
The probability of a female student studying abroad is 9.5%. This means that out of all the undergraduate students, 9.5% of them are female and are studying abroad. It is also important to note that out of those who study abroad, 60% are female, while 49% of those who do not study abroad are female. This means that more female students are likely to study abroad than male students, as the percentage of female students studying abroad is higher than the percentage of male students studying abroad. It is also important to note that the overall percentage of female students studying abroad is lower than the overall percentage of male students studying abroad, as the number of female students who study abroad is lower than the number of male students who study abroad. Therefore, the probability of a female student studying abroad is 9.5%.
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Explain the process and the properties you have to use to solve the logarithmic equation: log_3(x) + log_3(4) - 2log_3(3) = 2
The solution to the logarithmic equation is; x = 81/4
How to solve Logarithmic Equations?We want to solve the logarithmic equation;
log₃x + log₃4 - 2log3 = 2
From property of logarithms, we know that;
logₐ4 = log 4/log a
Similarly we know that;
log a + log b = log (ab)
log a - log b = log (a/b)
Thus;
log₃x + log₃4 - 2log₃3 = 2 is;
(log₃4x) - 2log₃3 = 2
(log₃4x) - log₃3² = 2
log₃(4x/3² ) = 2
3² = 4x/9
4x = 9 * 9
4x = 81
x = 81/4
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how can you find a 30% increase of some thing which started at 50? 
increase=(30/100)*50
=15
so,
value after increase
=50+15
=65
factor completely: (x^4)+(2x^3)-2x-1
The factored form of the polynomial is x³( x + 2 ) - 1 ( 2x + 1 ).
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that the polynomial is (x⁴)+(2x³)-2x-1. The expression will be factorized as below:-
E = (x⁴)+(2x³)-2x-1.
E = x² ( x² + 2 ) -1 ( 2x + 1 )
Hence, the factorized form of the polynomial is x² ( x² + 2 ) -1 ( 2x + 1 ).
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To solve for the lengths of the right triangle sides, which equation is correct?
According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2},[/tex] Option D is accurate since[tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]
The Pythagorean Theorem: What is it?The Pythagorean Theorem, also known as the Equation, is the fundamental Cartesian geometry relationship between a right triangle's three sides.
The Pythagorean Theorem states that the sum of the squares that thus span the angles of a right triangle is equal to the number that crosses the right triangle's rectangular prism opposite any right angle. Sometimes it is expressed using the general geometric notation [tex]a^{2} + b^{2} = c^{2}[/tex]
Given,
according to the diagram
in right triangle
[tex](base )^{2} + (perpendicular) ^{2} = (hypotenuse)^{2}[/tex]
[tex](2x-10 )^{2} + x^{2} = (3x)^{2}[/tex]
According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2}[/tex],
Option D is accurate since [tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]
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2. Find the value(s) of t that make V(t) = 4 true.
Explain what the value(s) tell us about the volume of
water in the cooler.
Step 1: Solve the equation V(t) = 4 for t. To solve the equation V(t) = 4 for t, divide both sides of the equation by 11, which gives us t = 4/11.
Step 2: Interpret the result. The value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.
Therefore, the value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.
Since there are more molecules in larger volumes than smaller ones, the pace of cooling will be slower if the water's volume is increased. Losing the heat energy from all the molecules will therefore take longer.
The question is incomplete and requires further explanation. For the mentioned part, the information is not significant to determine volume of water in the cooler.
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Solve for x. 6(x-2) = 4x-2 *
Answer:
x=5
Step-by-step explanation:
distribute: 6x-12=4x-2
subtract 4x and add 12 on both sides: 2x=10
Solve each system by elimination -6x+4y=-28 and 6x+7y=11
Answer:
[tex]x=\dfrac{40}{11}, \quad y=-\dfrac{17}{11}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-6x+4y=-28\\6x+7y=11\end{cases}[/tex]
To solve by the method of elimination, add the equations together to eliminate the terms in x.
[tex]\begin{array}{crcccl}&-6x & + & 4y & = & -28\\+&(6x & +&7y&=&\;\;\:11)\\\cline{2-6}\vphantom{\dfrac12}&&&11y&=&-17\\\cline{2-6}\end{array}[/tex]
Solve the equation for y:
[tex]\implies y=-\dfrac{17}{11}[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 6x+7\left(-\dfrac{17}{11}\right)=11[/tex]
[tex]\implies 6x-\dfrac{119}{11}=11[/tex]
[tex]\implies 6x=\dfrac{240}{11}[/tex]
[tex]\implies x=\dfrac{240}{11\cdot 6}[/tex]
[tex]\implies x=\dfrac{40 \cdot \diagup\!\!\!\!\!6}{11\cdot \diagup\!\!\!\!\!6}[/tex]
[tex]\implies x=\dfrac{40}{11}[/tex]
Therefore, the solution is:
[tex]x=\dfrac{40}{11}, \quad y=-\dfrac{17}{11}[/tex]
6 lb 3 oz − 2 lb 7 oz
Can you please find the perimeter of the blueprint room in feet? And could you find the area of the blueprint room in sqaure feet.
2 of the walls are 11 and 11, there's 3 more walls to find. Break thr room into rectangles and then do Base × height then add both rectangles together.
Based on the information in the graph, it can be inferred that the perimeter of the room is 44 feet.
How to find the perimeter of the room in the graph?To find the perimeter of the room in the graph we must apply the following formula:
Perimeter = base + upper base + left side + right sideAccording to the above, if each of the sides is 11 feet long we have two alternatives
perimeter = 4 * 11perimeter = 11 + 11 + 11 + 11In both operations the result would be 44.
Based on the above, the perimeter of the room would be 44 feet.
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A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. Using computer software, the coach achieves a linear model by taking the log of each launch angle and plotting against the log of each height.
A graph titled log (height) versus log (launch angle) has log (launch angle) on the x-axis, and log (height) on the y-axis. The points increase in a line with positive slope.
A graph titled residuals versus log (launch angle) has log (launch angle) on the x-axis, and residual on the y-axis. The points curve down, and then up.
Based on the scatterplot and residual plot, which type of model would best summarize the relationship between launch angle and punt height?
A linear model is appropriate because the residual plot shows a random scatter.
A logarithmic model is appropriate because logarithms were used to transform the data sets.
A power model is appropriate because the scatterplot of log angle and log height is roughly linear.
An exponential model is appropriate because the scatterplot of log angle and log height is roughly linear.
Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.
What is Scatter plot?The graphs known as scatter plots show how two variables within a data collection relate to one another. Both a two-dimensional plane and the Cartesian system are used to represent the data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or characteristic. Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.
According to Scatter plot, the relation between log(height) and log(launch angle) is linear.
Let, us consider log(height) = m log(launch angle) + b
Height = [tex]10^{(log(launch angle))}[/tex] + b
Height = [tex](launch angle)^{m}[/tex] + 10ᵇ
Height = (10)ᵇ + [tex](launch angle)^{m}[/tex]
Thus, the relation of height and launch angle is in power mode.
Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.
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write each answer as a fraction
he value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7
Trigonometry identity for a right triangleAccording to the trigonometry identity
tan Ф = opposite/adjacent
sin Ф = opposite/hypotenuse
cos Ф = adjacent/hypotenuse
From the given triangle;
AC = 7
AB = 17
BC = 4√15
Determine the following trigonometry given
cos B = BC/AB
cos B = 4√15/17
sinB = AC/AB
sin B = 7/17
sinA = cos B = 4√15/17
tan B = AC/BC
tan B = 7/4√15
tan A = BC/AC
tan A = 4√15/7
The value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7
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PLEASE HELP ME ON THIS I’ll make you brainliest I swear
The graph of the given quadratic function, y = -0.5(x + 5)(x - 3), is shown below
Graph of a Quadratic functionFrom the question, we are to draw the graph of the given quadratic function.
The given quadratic function is
y = -0.5(x + 5)(x - 3)
To plot the graph of the given quadratic function, we will determine the value pairs that satisfy the equation
When x = -5
y = -0.5(-5 + 5)(-5 - 3)
y = -0.5(0)(-8)
y = 0
When x = -2
y = -0.5(-2 + 5)(-2 - 3)
y = -0.5(3)(-5)
y = 7.5
When x = 0
y = -0.5(0 + 5)(0 - 3)
y = -0.5(5)(-3)
y = 7.5
When x = 2
y = -0.5(2 + 5)(2 - 3)
y = -0.5(7)(-1)
y = 3.5
When x = 3
y = -0.5(3 + 5)(3 - 3)
y = -0.5(8)(0)
y = 0
When x = -5
y = -0.5(5 + 5)(5 - 3)
y = -0.5(10)(2)
y = -10
Using the value pairs above, the graph of the given function is shown below
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Evaluate the expression for the given value of the variables.
0. 5c -2. 7d
c=13, d = 2
0. 50 -2. 7d = (Type an integer or a decimal. )
When the value of c is 13 and d = 2, then the value of the expression
0. 5c -2. 7d is 1.1
It is given that the expression for the given value of the variables is
0. 5c -2. 7d
If the value of c is 13 and the value of d is 2, then the value of expression is
0. 5c -2. 7d
putting the value of 'c' and 'd'
0. 5c -2. 7d = 0.5(13) - 2.7(2)
0. 5c -2. 7d = 6.5 - 5.4
0. 5c -2. 7d = 1.1
so, the value of the expressions for the given value of the variables i.e., c = 13 and d = 2 is 1.1
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Where are the asymptotes for the following function located?
f (x) = StartFraction 14 Over (x minus 5) (x + 1) EndFraction
x = –1 and x = 5
x = –1 and x = 14
x = 1 and x = –5
x = 14 and x = 5
The asymptotes for the function are:
x = 5 and x = -1.
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
There are three types of asymptotes.
1) Horizontal asymptotes
2) Vertical asymptotes
3) Oblique asymptotes
Now,
Horizontal asymptotes.
f(x) = 14 / (x - 5)(x + 1)
f(x) = 14/(x² + x - 5x - 5)
f(x) = 14 / (x² - 4x - 5)
The degree of the numerator is less than the denominator.
So,
Horizontal asymptotes.
y = 0
i.e
The x-axis.
Now,
Vertical asymptotes
f(x) = 14 / (x - 5)(x + 1)
Simplify in its lowest term.
Now,
Set the denominator to zero.
So,
(x - 5) ( x + 1) = 0
x - 5 = 0
x = 5
And,
x + 1 = 0
x = -1
Now,
Since there is a horizontal asymptote there are no oblique asymptotes.
Thus,
The asymptotes for the function are:
x = 5 and x = -1.
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Answer:
A. x = -1 and x = 5Step-by-step explanation:
Using Pythagorean Theorem
calculate the diagonal
distance from point
(-2,12) to (2,2)
Answer:
10.8 units or [tex]2\sqrt{29}[/tex] units
Step-by-step explanation:
The line drawn connecting two points on a graph is known as a line segment.
The formula used to calculate the length of a line segment is derived from the Pythagorean Theorem
Length of a line segment: [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2}}[/tex]
= [tex]\sqrt{[2-(-2)]^{2} + (2-12)^{2} }[/tex]
= [tex]\sqrt{(2+2)^{2} +(-10)^{2} }[/tex]
= [tex]\sqrt{4^{2} + 100}[/tex]
= [tex]\sqrt{16 +100}[/tex]
= [tex]\sqrt{116}[/tex]
= [tex]\sqrt{4}[/tex]×[tex]\sqrt{29}[/tex]
= [tex]2\sqrt{29}[/tex] units
Diagonal distance = 10.8 units (Rounded to 3 significant figures)
Which equation is graphed here?
A. y+5=-3/2(x-4)
B. y-5=-2/3(x+4)
C. y-5=-3/2(x+4)
D. y-4=-3/2(x+5)
The equation of the graphed line is expressed as: A. y + 5 = -3/2(x - 4).
How to Write the Equation of a Line?The equation that represents a line can be written in point-slope form as y - b = m(x - a), where a point on the line is (a, b) and the slope is m.
Slope (m) = rise/run = -3/2
Substitute a point on the line (a, b) = (4, -5) and m = -3/2 into y - b = m(x - a):
y + 5 = -3/2(x - 4)
The equation is: A. y + 5 = -3/2(x - 4).
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