Answer:
[tex]\textsf{1.} \quad y=a \cdot 2^5\;\;\textsf{(where $a$ is the initial population)}[/tex]
[tex]\textsf{2.} \quad 2^{-3}[/tex]
[tex]\textsf{3.} \quad y=a \cdot 2^{2}\;\;\textsf{(where $a$ is the initial population)}[/tex]
[tex]\textsf{4.} \quad y=a \cdot 2^{8}\;\;\textsf{(where $a$ is the initial population)}[/tex]
[tex]\textsf{5.} \quad 64[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question 1Given that organism A's population doubles every day for the first 5 days:
b = 2x = 5Therefore, an exponential expression to express organism A's population growth in the first 5 days is:
[tex]\boxed{y=a \cdot 2^5}[/tex]
(where a is the initial population).
Question 2Given expression showing organism A's decrease in population over the next 3 days:
[tex]\left(2^{-1}\right)^3[/tex]To rewrite the expression with the same base but one exponent,
[tex]\textsf{apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{-3}[/tex]
Question 3Combine the increase and decrease in organism A's population after 8 days by multiplying the rates. So the exponential expression for the total change in organism A's population after 8 days is:
[tex]\implies y=a \cdot 2^5 \cdot 2^{-3}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies y=a \cdot 2^{5-3}[/tex]
[tex]\implies y=a \cdot 2^{2}[/tex]
Question 4As organism B's population grows at the same rate as organism A, but is not infected with the virus, its population doubles each day. Therefore, an exponential expression showing its increase in population over the same 8 days is:
[tex]\boxed{y=a \cdot 2^8}[/tex]
where a is the initial population.
Question 5To calculate how many times greater organism B's population is than organism A's population after 8 days, divide the expression for organism B by the expression for organism A:
[tex]\implies \dfrac{a \cdot 2^8}{a \cdot 2^2}[/tex]
[tex]\implies \dfrac{2^8}{2^2}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 2^{8-2}[/tex]
[tex]\implies 2^6=64[/tex]
if h(x)=(f o g)(x) and h(x)=\sqrt[4]{x+7} find g(x) if f(x)= \sqrt[4]{x+1}
The function g(x), considering that h(x) is the composite function of f(x) and g(x), is given as follows:
g(x) = x + 6.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
h(x) = (f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The functions for this problem are defined as follows:
[tex]h(x) = \sqrt[4]{x + 7}[/tex][tex]f(x) = \sqrt[4]{x + 1}[/tex]Hence the function g(x) is defined as follows:
g(x) = x + 6.
As the application of the composite function is given as follows:
[tex]h(x) = (f \circ g)(x) = f(x + 6) = \sqrt[4]{x + 6 + 1} = \sqrt[4]{x + 7}[/tex]
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A parabola can be drawn given a focus of (-8,6) and a directrix of y=0. Write the equation of the parabola in any form
A parabola with focus of (-8, 6) and a directrix of y = 0. has the equation of the parabola as (x + 5)² = 8 (y - 3)
How to write the equation of parabola with directrix of y = 0 and focus of (-8, 5)Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The focus
F (h, k + p) = (-8, 6)
h = -8
k + p = 6
P in this problem, is the midpoint between the focus and the directrix
P = (6 - 0) / 2 = 3
p = 3
the vertex
v(h, k)
h = -8
k + p = 6, k = 3
v(h, k) = v(-8, 3)
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - (-8))² = 4 * 3 (y - 3)
(x + 5)² = 8 (y - 3)
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A company sells wireless speakers for $140 each. To produce a batch of n wireless speakers, there is a cost of $78 per
wireless speaker and a fixed or setup cost of $11,200 for the entire batch. Determine a function that gives the profit in
terms of the number of wireless speakers produced. What is the number of wireless speakers that must be produced and
sold in order for the company to break even?
The number of wireless speakers that must be produced and sold in order for the company to break even is 186 and the profit function can be given as 62n -11200.
What is equation?An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.
Given;
A company sells wireless speakers for $140 each,
cost of $78 per wireless speaker and the fixed cost is $11200,
Write the function of cost as shown below,
Cost price = 11200 + 78n
Here, n is the number of speakers
Calculate the profit as shown below,
profit = 140n - 11200 - 78n
profit = 62n -11200
Calculate the breakeven point as shown below.
62n -11200 = 0
n = 11200 / 62
n = 180.6
n = 181
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X
-2
2246
y
-5
5
05
10
15
Which best describes the function represented by the
table?
O direct variation; k =
O direct variation; k =
NS
52
O inverse variation; k = 10
O direct variation; k
=
10
The function is best described by option B direct variation; k= 5/2.
What is direct variation?When two variables are related in a way that one is a constant multiple of the other, this is referred to as direct variation.
The direct variation is given as follows y ∝ x.
The equation is thus of the form y = kx.
Using the given values in the table:
Consider x=-2 and y= -5
Substitute the values in y=kx.
-5 = -2k
Divide both sides of the equation by -2.
[tex]\frac{-5}{-2} = \frac{-2}{-2}k \\k =\frac{5}{2}[/tex]
The equation is [tex]y=\frac{5}{2} x[/tex] [ equation 1]
Check equation 1 for a different value in the table using the constant value k.
Let x= 4 and y = 10.
[tex]y = \frac{5}{2} x\\10 = \frac{5}{2} (4) \\10 = 10[/tex]
The equation holds true; hence the function is best described by direct variation; k = 5/2.
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How can I say "my pleasure" in French?
Answer:
My pleasure in French is Mon Plaisir
Answer:
You can say ''my pleasure '' in French ''
Step-by-step explanation:
mon plaisir
how do I solve this by elimination?
4x + 10y = -12
-4X - 7Y = 0
Answer:
[tex]x=7, y=-4[/tex]
Step-by-step explanation:
[tex](4x+10y)+(-4x-7y)=-12+0 \implies 3y=-12 \implies y=-4 \\ \\ 4x+10(-4)=-12 \implies x=7 \\ \\ \therefore x=7, y=-4[/tex]
Given: quadrilateral MATH; M(-5,-2), A(-3,2),
T(3,2) and H(1,-2)
Prove: MATH is a parallelogram
Answer:
If both of the opposite sides are parallel then the quadrilateral is a parallelogram. If the slopes are the same and the constants are different than the lines are parallel.
Step-by-step explanation:
If both of the opposite sides are parallel then the quadrilateral is a parallelogram. If the slopes are the same and the constants are different than the lines are parallel.
(-32) ( 3,2) and side (-5,-2) (1,-2)
(-3, 2) (3,2)
Slope [tex]\frac{2-2}{3- -3}[/tex] = [tex]\frac{0}{6}[/tex] = 0
y-intercept
2 = 0(3) + b
2 = b
Equation
y = 0x + 2
y = 2
(-5,-2) ( 1,-2)
slope [tex]\frac{-2 - -2}{1 - -5}[/tex] = [tex]\frac{0}{6}[/tex] = 0
y-intercept
-2 = 0(1) + b
-2 = b
Equation
y = 0x - 2
y = -2
These sides are parallel because the slope is the same and the y-intercepts are different.
Sides (-3,2) (-5,-2) and (3,2) (1,-2)
(-3,2) (-5,-2)
slope [tex]\frac{-2 -2}{-5 - -3}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
y-intercept
-2 = (2)(-5) + b
-2 = -10 + b
8 = b
Equation:
y = 2x + 8
(3,2) (1,-2)
slope [tex]\frac{-2-2}{1-3}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
y-intercept
2 = (2)(3) + b
2 = 6 + b
-4 = b
Equation
y = 2x -4
The sides are parallel because the slopes are the same, but the y-intercept are different.
Given:
Quadrilateral MATH with vertices M(-5,-2), A(-3,2), T(3,2) and H(1,-2)Recall properties of a parallelogram:
Opposite sides are parallel, and congruent;Diagonals bisect each-other.Prove that same applies to the given quadrilateral.
1) Opposite sides are: MH & AT and MA & TH.
MH and AT have same y-coordinates and therefore both are horizontal, hence parallel.
Their lengths:
MH = 1 - (-5) = 6 units,AT = 3 - (-3) = 6 units.Same can be proved for MA &TH.
2) Find the midpoint of diagonals MT and AH.
Midpoint of MT:
x = (-5 + 3)/2 = - 2/2 = - 1,y = (-2 + 2)/2 = 0/2 = 0.Midpoint of AH:
x = (-3 + 1)/2 = - 2/2 = - 1,y = (2 - 2)/2 = 0/2 = 0.Both diagonals have same midpoint (-1, 0). This proves that diagonals bisect each-other.
Therefore MATH is a parallelogram.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 4/5x + 8
Step-by-step explanation:
y-intercept = b = 8
Use the points (-10,0) and (0,8) to find the slope (m)
m = (8 - 0)/(0 - (-10)) = 8/10 = 4/5
y = mx + b
y = 4/5x + 8
How many solutions does this equation have? 2x + 2x + 2 = 4 + 2x
The number of solutions the equation 2x + 2x + 2 = 4 + 2x have is 1
How many solutions does this equation have?From the question, we have the following parameters that can be used in our computation:
2x + 2x + 2 = 4 + 2x
Subtract 2x from both sides of the equation
So, we have the following representation
2x + 2 = 4
Subtract 2 from both sides of the equation
So, we have the following representation
2x = 2
Divide both sides by 2
x = 1
Hence, the equation has 1 solution
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If sin(0) = 0.731, then csc(0) = 2.212.
O True False
The statement is true that sin(0) = 0.731, then csc(0) = 2.212.
What are trigonometric functions?The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of the lengths of the two sides. All geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more, utilize them extensively.Check your understanding of the six trigonometric ratios: sine, cosine, tangent, cotangent, secant, and cosecant. One way to recall the sine, cosine, and tangent ratios in a right triangle is to see them as strings of letters, like SOH-CAH-TOA in English: Sine = Opposite Hypotenuse. Hypotenuse + Adjacent = Cosine. Opposite and adjacent is a tangent. Sine, Cosine, and Tangent are the three primary trigonometric operations. The first trigonometric identity we have is that.To learn mor about trigonometric functions refer to:
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Hector left his house at (-9,9) on a map of Coleville and walked to the zoo at (-9,2). From there he walked
east to his friend's house. He walked a total distance of 24 blocks.
If each unit on the map represents one block, what are the coordinates of Hector's friend's house?
Answer:
(-33,2)
Step-by-step explanation:
evaluate 9 to the power of -0.5
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]9^{-0.5}[/tex] to make the exponent positive, put it over 1.
[tex]\frac{1}{9^{0.5} }[/tex] another way to write this is
[tex]\frac{1}{\sqrt{9} }[/tex]
[tex]\frac{1}{3}[/tex]
Which of the following scenarios creates LESS interest over time:
Borrowing $1750 for six months at a simple interest rate of 7%
OR
Borrowing $1750 for five months at a simple interest rate of 9%
The scenario that will bring about less interest will be Borrowing $1750 for six months at a simple interest rate of 7%.
How to calculate the interest?It should be noted that the simple Interest is calculated by using the formula thus:
= Principal × Rate × Time
Borrowing $1750 for six months at a simple interest rate of 7%. The simple interest will be:
= $1750 × 7% × 6/12
= $61.25
Borrowing $1750 for five months at a simple interest rate of 9%. The simple Interest will be:
= $1750 × 9% × 5/12
= $65.64
Therefore, Borrowing $1750 for six months at a simple interest rate of 7% has less simple interest.
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What is the scale factor of dec to abc decimal form only 
The scale factor from the given similar triangles is 3.5 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle ABC and triangle DEC are similar.
DE=6, AB=21, DC=4, EC=2x+3, and BC=13x-1.5.
Since, ΔABC similar to ΔDEC
So, AB/DE =AC/DC =BC/EC
21/6 =13x-1.5/2x+3
7/2 =13x-1.5/2x+3
7(2x+3)=2(13x-1.5)
14x+21=26x-3
26x-14x=21+3
12x=24
x=2
So, EC=2x+3 =7 and BC=13x-1.5 =24.5
Now, AB/DE =BC/EC
21/6=24.5/7=3.5
Therefore, the scale factor is 3.5 units.
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y=5/2x-4 point slope form
Answer: 5/2
Step-by-step explanation:
Slope = 5/2
If a₁ = 1 and an = -5an-1 then find the value of a6. Please a need Help to solved
Answer Im not exactly sure
Step-by-step explanation:
sharmila recived 81 texts in 9 minutes
Answer:
Step-by-step explanation:
81 texts in 9 hours
So you do 81 divided by 9
Which givrs you 9 text an hour
Using the balance sheet, calculate XYZ Company's
total assets.
XYZ Company
Balance Sheet
Assets
Liabilities
Cash
$35,000
Notes $45,000
Inventory $41,000 Wages $56,000
Property $124,000
Equity
Stock
$50,000
Investment $49,000
Total Assets: Total Liabilities+ Equity:
Total Assets = $ [?]
The total assets of the company if assets are Cash $35,000, Inventory $41,000, Property $124,000, The liabilities are Notes $45,000, and Wages $56,000 is $200000.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
The assets are Cash $35,000, Inventory $41,000, Property $124,000,
The liabilities are Notes $45,000, Wages $56,000
The Equity are Stock $50,000, Investment $49,000
Calculate the total assets as shown below,
the total assets = 35000 + 41000 + 124000
the total assets = 200000
Calculate the total liabilities and equity as shown below,
The total liabilities and equity = 45000 + 56000 + 50000 + 49000
The total liabilities and equity = 200000
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How can i Decrease 180 by 20%
Answer:
144
Step-by-step explanation:
divide 20 by 100 and multiply by the amount. The amount in this case is 180. Subtract the number from 180. Youll get 36, so subtract 36 from 180 and youll get 144.
For each figure below, determine if it has rotational symmetry.
If it does, give the smallest angle of rotation needed for the figure to appear unmoved.
A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.
A square is divided into four congruent sides, hence it has rotational symmetry, while the unit circle, over which the figures are rotated, is of 360º, hence the angle is given as follows:
360/4 = 90º.
The second figure has three equal arrows, hence it also has rotational symmetry, with an angle given as follows:
360/3 = 120º.
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Misaki is measuring her office, which is rectangular. The length of the room is 9 ft and the perimeter is 42 ft.
Which equation represents the perimeter in terms of the width, w?
- 2(9+w)=42
- 2(9)+w=42
- 2(18+w)=42
- 2(w)+9=42
The correct equation which represents the perimeter in terms of the width, w is,
⇒ 2 (9 + w) = 42
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Misaki is measuring her office, which is rectangular.
And, The length of the room is 9 ft and the perimeter is 42 ft.
Now, We know that;
⇒ Perimeter of rectangle = 2 (Length + Width)
Here, The length of the room is 9 ft and the perimeter is 42 ft.
So, We can formulate;
⇒ Perimeter of rectangle = 2 (Length + Width)
⇒ 42 = 2 (9+ w)
Thus, The correct equation is,
⇒ 42 = 2 (9+ w)
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Help ASAP, please math question
The length of the skid marks is 336 feet
How to determine the length of the skid marks?
Since the formula s = √(21d) relates the speed (s) of the car and the length of skid (d).
If the car is traveling at 84 miles per hour, we can determine the length of the skid marks by substituting s = 84 into the formula and then solve for d. That is:
s = √(21d)
84 = √(21d)
84² = 21d
7056 = 21d
21d = 7056
d = 7056/21
d = 336 feet
Thus, length of the skid marks is 336 feet
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help please. And can I have the explanation so I can understand better, thank you!!
-3
-2
449
(-2,-2)2
A
(2, 2)
2
3
The distance of AB = [? ]
Round to the nearest tenth.
Hint: d= √(x₂ −×1 )² + (Y2 − Y1)²
Enter
The distance between the points (-2, -2) and (2, 2) will be 4√2 units.
What is the distance between two points?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The two points are given below.
(-2, -2) and (2, 2)
Then the distance between the points are given as,
D² = (2 + 2)² + (2 + 2)²
D² = 4² + 4²
D² = 16 + 16
D² = 32
D = 4√2 units
The distance between the points (-2, -2) and (2, 2) will be 4√2 units.
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Which symbol replaces ? to make the statement true?
2 x 18 - 18 ? 2 x [28-3 x (2+4)]
will mark brainliest and will give thanks
Which symbol replaces ? to make the statement true?
2 x 18 - 18 ? 2 x [28-3 x (2+4)]
will mark brainliest and will give thanks
the answer : <
use distributive property to remove parenthesis -4(-6v-4w+1)
Answer:
To use the distributive property to remove the parentheses in the expression "-4(-6v-4w+1)", you need to distribute the negative 4 to each of the terms inside the parentheses. This gives you the following:
(-4*-6v) + (-4*-4w) + (-4*1)
Simplifying this expression, we get:
24v + 16w - 4
Step-by-step explanation:
Answer:
24v + 16w - 4
Step-by-step explanation:
use distributive property to remove parenthesis -4(-6v-4w+1)
-4(-6v - 4w + 1) =
24v + 16w - 4
Miguel has $20. He spends $6.00 on a movie ticket, $3.85 for snacks, and $2.00 for bus fare each way. How much money does Miguel have left?
The amount of money left with Miguel is $8.15
How to calculate the amount of money that Miguel will have after his expenses?Miguel has $20
He spends $6 on movie ticket
He spends $3.85 for snacks
He also spends $2 for bus fare
The total expenses is
6 + 3.85 + 2
= 11.85
The amount left is
20- 11.85
= 8.15
Hence Miguel has $8.15 left
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A scale drawing of tv is shown. If the width of the actual television is 4 feet what is the area of the tv
Answer:
788.48 sq feet
Step-by-step explanation:
Because you have to multplie
What is x ?
x(x)=25
2. The rate at which glaciers melt is increasing globally. The Saskatchewan Glacier near Banff has receded 1.5 km in the last 75 years. The Peyto Glacier shown below receded 1320 m from 1923 to 1993. Which glacier had the greater annual rate of melting?
Answer:
Saskatchewan Glacier
Step-by-step explanation:
You want to know the greater rate, 1.5 km in 75 years, or 1320 m between 1923 and 1993.
RatesThe rate of glacier recession is the ratio of distance to time:
Saskatchewan Glacier
(1500 m)/(75 yr) = 20 m/yr
Peyto Glacier
(1320 m)/(1993 -1923 yr) = 1320/70 m/yr ≈ 18.86 m/yr
The Saskatchewan Glacier had a greater annual rate of melting.
