Answer:
[tex]y=0.2*4^{x}[/tex]
Step-by-step explanation:
Notice when x increases 1, y is 4 times the previous one, so
the function is like [tex]y=C*4^{x}[/tex]
To determine the constant C, put any pair of (x, y)
Use x = 0, y = 0.2, so
0.2 = [tex]C*4^{0}[/tex] = C * 1 = C
then [tex]y=0.2*4^{x}[/tex]
Answer:
[tex]y=(0.2)4^x[/tex]
Step-by-step explanation:
General form of the exponential function: [tex]y=ab^x[/tex]
Substituting the first point (0, 0.2) into the function:
[tex]\implies 0.2=ab^0[/tex]
As any number to the zero power always gives one, [tex]b^0=1[/tex]
[tex]\implies0.2=a \times 1[/tex]
[tex]\implies a=0.2[/tex]
Therefore, [tex]y=(0.2)b^x[/tex]
Substituting the second point (1, 1.8) into the function:
[tex]\implies0.8=(0.2)b^1[/tex]
[tex]\implies0.8=(0.2)b[/tex]
[tex]\implies b=\frac{0.8}{0.2}[/tex]
[tex]\implies b=4[/tex]
So the final exponential equation is:
[tex]y=(0.2)4^x[/tex]
Checking the equation with the remaining two points:
[tex]x=2 \implies (0.2)4^2=3.2 \ \ \ \checkmark[/tex]
[tex]x=3 \implies (0.2)4^3=12.8 \ \ \ \checkmark[/tex]
What is the value of cos B as a simplified fraction. (Enter answer as x/y to enter the fraction).
Answer:
Cos of B = 36 / 38.884
Step-by-step explanation:
To find the cos of b you need the hypotenuse
(a)^2 + (b)^2 = (c)2
(36)^2 + (15)^2 = 1521
1521 squared is 38.884
Hypotenuse side goes on bottom and adjacent side on top
Cos of B = 36 / 38.884
The data set represents a progression of hourly temperature measurements. Use a graphing calculator to determine the quadratic regression equation for this data set. X 0 1 2 3 4 5 y 20 16 10 0 -7 -20 a. Y = 0. 795 x squared 3. 796 x 20. 180 c. Y = negative 0. 875 x squared minus 3. 596 x 20. 179 b. Y = negative 0. 795 x squared minus 3. 760 x 20. 180 d. Y = negative 0. 795 x squared minus 3. 796 x 20. 180.
A regression can be modeled by linear regression, quadratic regression, quartic regression or exponential regression
The quadratic regression equation that models the data is
[tex]\^y = -0.875\^x^2 -3.596\^x +20.179[/tex]
How to determine the regression equationThe table entries are given as:
x: 0,1,2,3,4,5
y: 20,16,10,0,-7,-20
A quadratic regression is represented as:
[tex]\^y = a\^x^2 + b\^x + c[/tex]
Using a graphing calculator to determine the quadratic regression equation, we have the following calculation summary
a = -0.875
b = -3.596
c = 20.179
Hence, the quadratic regression equation is:
[tex]\^y = -0.875\^x^2 -3.596\^x +20.179[/tex]
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Answer:
ITS C
Step-by-step explanation:
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Answer:
I believe your answer is 9
Step-by-step explanation:
The way I found this answer was by assuming that triangle CDE was expanded to get triangle FGH. So I divided 18/4 and got the answer 4.5, which means that the triangle was expanded by a factor of 4.5. So I then multiplied the similar side to HG by 4.5 which was side ED. This got me with 4.5 x 2 and I got the answer 9.
Hope this helps! :)
Someone pls show me
Answer:
x = 4
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the remote interior angles.
18x +5 = (46) +(-1 +8x)
10x = 40 . . . . . . . . . . . . . subtract (5+8x) from both sides, simplify
x = 4 . . . . . . divide by 10
__
Additional comment
The exterior angle is (18)(4) +5 = 77°. The marked unknown interior angle is -1+(8)(4) = 31°. The sum of the two remote interior angles is 46°+31° = 77°. The unmarked interior angle is 180°-77° = 103°.
A function is a type of rule in which each input results in exactly one output.
Explain why both rules above are functions
Answer:
geotheral
Step-by-step explanation:
Two friends, Justin and Andrew, had just bought their first cars. Justin uses 10 gallons of gas to drive 200 miles in his car. The table below represents the number of miles, yy, that Andrew can drive his car for every xx gallons of gas.
Answer:
andrew can drive 20 miles for every 1 gallon of gas
Step-by-step explanation:
3. A carpenter cuts a piece of lumber into two
pieces. One piece is twice the length of the other.
If the longer piece is 28 inches long, how long
was the whole piece of lumber before it was cut?
Answer:
42 inches
Step-by-step explanation:
Let x represent the length of the shorter piece then...
2x=28
Divide both sides by 2
x=14
The shorter one is 14 inches long and the longer one is 28 inches long. Now, we add these two numbers to find the original length of the lumber.
14in+28in=42 inches
Please answer this (who ever answers correctly gets brainlest)
Answer:
0.171 m
Step-by-step explanation:
First, let's determine how many mm of track he has in total...
74mm+97mm=171 mm
Now, we can set up a unit converter to convert mm to m (note that 1 mm is [tex]10^{-3{[/tex] m)...
[tex]171mm(\frac{10^{-3}m}{1mm})[/tex]
The "mm" cancels out...
[tex]171*10^{-3}m=0.171m[/tex]
Answer:
Step-by-step explanation:
74 + 97 = 171 mm
Length of the train track = 171 mm = 171÷ 1000 = 0.171 m
Which of the following best describes the graph below?
ļ ďd bd
5 4 3 2 1
1 2 3
4
&
-1
2.
2
-3
O A. It is not a function.
B. It is a many-to-one function.
C. It is a function, but it is not one-to-one.
D. It is a one-to-one function,
Answer: Most of the time, we're going to have to look at the graph of the function to determine its range. Examples. • Example 1 g(x) = 6x − 2. 3x − 4. (4).
5 pages
Step-by-step explanation:
hope this helps
The given graph is a one-to-one function
What is a function?A relation is a function if it has only One y-value for each x-value.
A function is said to be one-one if corresponding to each x we get a distinct y-value.
i.e. No two x have the same y-value.
Also it can be seen from the graph when any horizontal line is drawn parallel to the x-axis then the line intersect the curve atmost once.
it passes the horizontal line test.
Many-to-one function is a function is many to one when many x-values are mapped to same y-value.
Clearly from the graph we see that the graph is a one-to-one function.
Hence, the given graph is a one-to-one function
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Which numbers are less than 538? Select three options.
three hundred twenty-two
four hundred seventy-nine
five hundred thirty
five hundred forty
five hundred sixty-four
six hundred fifty-three
what is the area to the parallelogram
Area in picture below
Answer: 1716/25 or 16 68/25
Step-by-step explanation:
Formula: 1/2 x height x (a+b)
PLEASE ANSWER ASAP
Which THREE expressions are equivalent to: (x + 6) + (x + 6) + (x + 6) + (x + 6) O 4(x + 6) 0 2 (x + 12) 2 + 12 + 22 12 3a + 6 + 1 = 6 тиб 42 = 24
Organizing the problem:
Which THREE expressions are equivalent to:
(x + 6) + (x + 6) + (x + 6) + (x + 6)
O 4(x + 6)
0 2 (x + 12)
2 + 12 + 22
12 3a + 6 + 1 = 6
тиб 42 = 24
Out of these selections, i can only tell that number one is correct, number two isn't, and i can't tell for the rest. Please organize the question more clearly.
--Hunter
5m+3(m-3)+7=2m-1
Solve for x
Answer:
=> 5m+3(m-3)+7=2m-1
=> 5m+3m-9+7 = 2m-1
=> 8m-2 = 2m-1
=> 8m-2m = -1+2
=> 6m = 1
=> m = 1/6
in one week a farmer sells pumpkins to 60% of his customers. if 720 customers purchase pumpkins, how many total customers does the farmer have
what is the cubed root of 27?
Answer:
Cube root of 27 in radical form: ∛27???
Step-by-step explanation:
hope this helps
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Answer:
D. 14
Step-by-step explanation:
These triangles are something called a scale factor. A scale factor means when you multiply any side by that factor, you get the side of the other triangle. It is an exact copy of the triangle from before, just bigger or smaller, also known as set to scale. Here we can do 7/6 to find the scale factor (which is 1.16666666667), and multiply that factor by 12 to get 14.
If the lateral surface area of a cylinder with height 4cm is 24pi cm squared then what is its volume?
We are given –
Height of cylinder is = 4cmLateral surface area of cylinder is = 24πcm²We are asked to find volume of the given cylinder.
Let the radius be "r".Then according to the question,it’s given –
[tex]\qquad[/tex] [tex]\pink{\twoheadrightarrow\bf Curved\: surface\: area _{(Cylinder)}= 2\pi r h }[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 2\pi r h = 24 \pi[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 2\cancel{\pi} rh = 24 \cancel{\pi}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r =\dfrac{24}{2h}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \dfrac{24}{2\times 4}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \dfrac{24}{8}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \cancel{\dfrac{24}{8}}[/tex]
[tex]\qquad[/tex] [tex]\pink{\twoheadrightarrow\bf r = 3 \: cm}[/tex]
Now, Let's find volume of cylinder
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf V_{(Cylinder)} = \pi {r}^{2}h}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 3^2\times 4 [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 9 \times 4[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 36[/tex]
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf V_{(Cylinder)} = 36 \pi \: cm^3}[/tex]
Henceforth, volume of cylinder is 36π cm³.Step-by-step explanation:
Given :-
Height is = 4cmLateral surface area of cylinder is = 24πcm²to find :-
volume of the given cylinder.Solution :-
Lateral surface area of cylinder = 2πrh
24π cm = 2πrh
Cancelling π on both the sides ,
24/2h = r
putting the value of h i.e, 4 cm
24/2×4 cm = r
3 cm = radius
Now volume of Cylinder = πr²h
putting all the values ,
Volume = 3.14 × 3² × 4 cm³
Volume = 113.04 cm³
What is the equation of the line parallel to
y = 3x - 8 that passes through the point (4, 2)?
Answer:
y=3x-10
Step-by-step explanation:
A line parallel to another line has the same slope.
Therefore, we can create the equation y=3x+b.
Substituting (4,2) into y=3x+b,
2=3(4)+b
2=12+b
-10=b
y=3x-10
Therefore, the equation of the line parallel to y=3x-8 which passes through the point (4,2) is y=3x-10
Answer:
y = 3x - 10
Step-by-step explanation:
Equation: y = 3x + b
Point: (4, 2)
y = 3x + b
2 = 3 (4) + b
2 = 12 + b
b = -10
y = 3x - 10
i need answers quick thanks
What is the solution of the equation
Answer: x=-56/3 (the second answer)
Fill in the missing number. % of 96 = 24 Submit
Answer:
[tex]25[/tex]% of 96 = 24
Step-by-step explanation:
?% of 96 = 24
[tex]\frac{x}{100} =\frac{24}{96}[/tex]
[tex]x =\frac{24*100}{96}[/tex]
[tex]x = 25[/tex]%
Factor 10w^2-31w+15
I'm really stumped lol
Answer:
[tex]10 {w}^{2} - 31w + 15 \\ \\ 10 {w}^{2} - 6w - 25w + 15 \\ \\ 2w(5w - 3) - 5(5w - 3) \\ \\ (2w - 5)(5w - 3)[/tex]
# be careful #
( i ready ) i want to double check my answer
Answer:
Step-by-step explanation:
yeah you got it
what’s the slope?
50 points!! Please help
Answer:
6
Step-by-step explanation:
slope is rise/run
to get from -1 to 5 is 6 points
y axis to 1 is 1 point
6/1=6
Question 6-89a
Find the perimeter of the figure below.
15 km
4 km
7 km
10 km
[tex]\\ \tt\hookrightarrow Perimeter [/tex]
[tex]\\ \tt\hookrightarrow 15+4+7+10[/tex]
[tex]\\ \tt\hookrightarrow 19+17[/tex]
[tex]\\ \tt\hookrightarrow 36km[/tex]
Which of the following equations has both -5 and 5 as possible values of z?
z^2 =36
z^3 = 125
none of the above
The correct answer is z can take on the values of both -6 and 6, not -5 and 5.
The equation that has both -5 and 5 as possible values of z is:
[tex]z^2 = 36[/tex]
When we solve this equation, taking the square root of both sides, we get:
z = ±6
Therefore, z can take on the values of both -6 and 6, not -5 and 5.
Hence, none of the given equations have both -5 and 5 as possible values of z.For the equation z^2 = 36, we need to find the values of z that satisfy the equation. Taking the square root of both sides, we get:
z = ±√36
Simplifying the square root of 36, we have:
z = ±6
This means that z can take on the values of both -6 and 6. However, the values -5 and 5 are not solutions to this equation.
Similarly, for the equation z^3 = 125, there are no values of z that satisfy the equation for z equal to -5 or 5.
Therefore, none of the given equations, z^2 = 36 and z^3 = 125, have both -5 and 5 as possible values of z.
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The function f(x) = -(x+4)^2+5 is written in vertex form and shows that the vertex of the graph of f is located at (-4,5)
Each value of the f can be obtained from two different x-values except f(x)=5. Which best explains why f(x)=5 is the output for only one input value?
There is only one value for x that makes [tex](x+4)^2=0[/tex]
Vertex form of an expressionGiven the vertex form of the function expressed as:
[tex]f(x) = -(x+4)^2+5[/tex]
If the function f(x) = 5
[tex]5 = -(x+4)^2+5[/tex]
Subtract 5 from both sides
[tex]5 = -(x+4)^2+5\\-(x+4)^2= 5-5\\-(x+4)^2=0\\[/tex]
Hence there is only one value for x that makes [tex](x+4)^2=0[/tex]
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Given, m<7 = 108°
To find, m<3
Since both the given angles are on the same side of transversal, thus there sum is 180°
Thus, m<7 + m<3 = 180°
108° + m<3 = 180°
m<3 = 180° - 108°
m<3 = 72°
Hope this helps :)
The ratio of men to women working for a company is 7:5. If there are 192 employees total, how many women work for the company?
7:5 mean that to every 7 men there is 5 woman.
There are 54 women working for the company.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The ratio of men to women working for the company is 7:5, which means that for every 7 men, there are 5 women.
We can express this as a fraction by writing 7/7 as 1 and 5/7 as 5/7, so the ratio becomes 1:5/7.
This fraction can be rewritten as 7/7:35/7, and since the two fractions have the same denominator, we can say that the ratio is equal to 7:35.
Since there are 192 total employees, and the ratio of men to women is 7:35, we can set up the following proportion:
7/35 = x/192
We can solve this proportion by cross-multiplying:
7/35 × 192 = x
This simplifies to:
x = 54
Therefore, the company hired 54 female employees.
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