The equation of the new graph g(x) is expressed as g(x) = 4^x + 6
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the function f(x) = 4^x
If the function is shifted 6 units up, the function g(x) is derived by adding 4 to the function f(x). The resulting function is given as;
g(x) = f(x) + 6
g(x) = 4^x + 6
Hence the equation of the new graph g(x) is expressed as g(x) = 4^x + 6
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How many 3-coin combinations exist if we can choose from
pennies, nickels, dimes, and quarters?
select one:
a. 20
b. 4!
o
c.4.
o
d. 12
There are four numbers of 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.
How to solve probability combinations?The coins to select from are nickels, dimes, quarters, and half-dollars;
Thus;
Coins (n) = 4
The number of coin to select is:
Coin (r) = 3
The coin combination is then calculated using:
Combination = ⁴C₃
Apply the combination formula, we have;
Combination = 4
Thus, there are four number 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.
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Answer:
12
Step-by-step explanation:
took the exam
Harmony earns a $42,000 salary in the first year of her career. Each year, she gets a 4%, percent raise.
Which expression gives the total amount Harmony has earned in her first n years of her career?
Answer:
42000*1.04^(n-1)
Step-by-step explanation:
4% is equal to 0.04, a raise is 1+0.04=1.04
1.04 is now the number we are multiplying by to get a new yearly salary for Harmony.
42000*1.04^(n-1) since n is how many years after she has the job you have to raise it to the power and subtract one.
Write an equation of the line that passes through $\left(-1,\ 7\right)$ and is perpendicular to the line $y=-\frac{1}{8}x-1$ .
Equation of the line which is passing through the points [tex](-1,7)[/tex] and perpendicular to the line [tex]$y=-\frac{1}{8}x-1$[/tex]
is [tex]y=8x+15[/tex]
How to find the equation which passing through one point [tex](-1,7)[/tex]and perpendicular to the equation [tex]$y=-\frac{1}{8}x-1$[/tex] ?
We know that the equation of line in form of slope and point is
[tex]y-y_{1} =m(x-x_{1} )[/tex]
So first equation of line which is passing through point [tex](-1,7)[/tex] is
[tex]y-7=m_{1} (x-(-1))\\y-7=m_{1}(x+1)[/tex].....(a)
Line [tex]$y=-\frac{1}{8}x-1$[/tex] perpendicular to the line (a)
And we know when two lines are perpendicular then
[tex]m_{1} m_{2} =-1[/tex]
So [tex]m_{1} =-1/m_{2}[/tex]
and we know [tex]m_{2} =-1/8[/tex]
So
[tex]m_{1} =-1/\frac{-1}{8} \\=-1*8/-1\\=8[/tex]
The equation of the line is
[tex]y-7=8(x+1)\\y-7=8x+8\\y=8x+8+7\\y=8x+15[/tex]
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Whoever helps first get brainiest
Answer:
75
Step-by-step explanation:
Use PEMDAS (Perenthesis, Exponents, Multiply, Divide, Add, Subract)
45/5-6+24*3
9-6+24*3
9-6+72
3+72
75
Answer:
75
Step-by-step explanation:
PEMDAS:
45/5=9
24*3=72
9-6+72=75
Which statement is the most appropriate comparison of the spreads?
Option D. The most appropriate comparison for the spread is that the interquartile range for town A, 15 degrees is less than that of B.
How to solve for the interquartile rangeThe inter quartile is solved as Q3 - Q1
This is seen as
For Town A,
30 - 15 = 15 degrees
For town B
40 - 20 = 20 degrees.
Hence we can see that 15 is less than 20, so town A is less than town B. The answer is option D.
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Calculate how long it would take for an investment of R9000 to double if the simple interest rate is 11% per annum.
Answer:
9.09 years
Step-by-step explanation:
Use the simple interest formula
A=P(1+rt)
18000=9000(1+.11*t), solve for t
t = 9.0909
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).The graph represents the piecewise function:
The definition of the piecewise function is given as follows:
[tex]f(x) = x + 3, -3 \leq x < 1[/tex].[tex]f(x) = 5, -1 \leq x \leq 1[/tex].What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
Researching this problem on the internet, for x equal or greater than -3 and less than -1, the function is a line with a slope of 1 that goes through (-3,0), hence the definition is found as follows:
y = x + b
0 = -3 + b
b = 3
Then:
[tex]f(x) = x + 3, -3 \leq x < 1[/tex].
For x between -1 and 1, inclusive, the function is constant at 5, hence the definition is:
[tex]f(x) = 5, -1 \leq x \leq 1[/tex].
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Find the unknown angle
x
4
z
y
A 12-ounce cup of juice contains 70 percent fruit and 30 percent water. If combined with 16 ounces of juice that contain 10 percent fruit and 90 percent water, what portion of the mixture is fruit?
Write the answer to the nearest hundredth
The portion of the mixture that is fruit to the nearest hundredth is 10.00 ounces
Percentage12 ounce juice:
Water = 30%Fruits = 70%= 70/100 × 12
= 0.7 × 12
= 8.4 ounces
Water = 30%
16 ounces;
Water = 90%Fruits = 10%= 10/100 × 16
= 0.1 × 16
= 1.6 ounces
Portion of mixture that is fruits = 8.4 ounces + 1.6 ounces
= 10.00 ounces
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If the probability of a student taking a math class is 0.70, the probability of taking a physics class is 0.30, and the probability of taking a math class and a physics class is 0.15, what is the probability of a student taking a math class or a physics class
The probability of a student taking a math class or a physics class is [tex]0.85[/tex] when the probability of a student taking a math class is [tex]0.70[/tex], the probability of taking a physics class is [tex]0.30[/tex], and the probability of taking a math class and a physics class is [tex]0.15[/tex]
How can we find the probability of taking math class or a physics class ?
Given in the question probability of the student taking class
[tex]p(M)=0.70\\p(P)=0.30\\p( M and P)=0.15[/tex]
So we use the probability union intersection formula
[tex]p(M or P)=p(M)+p(P)-p(M and P)[/tex]
Substitute the values
[tex]p(M or P)=0.7+0.3-0.15\\=0.85[/tex]
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WILL MAKE BRAINLIEST!! Solve for b
Answer: 32
Step-by-step explanation:
The line is straight meaning 180 angle. When finding B you subtract 148 by 180 which would be 32.
) Suppose that we have a bucket of 30 red balls and 70 blue balls. If we pick 20 balls uniformly out of the bucket, what is the probability of getting exactly k red balls
Answer: 30%
Step-by-step explanation:
Complete the recursive formula of the geometric sequence -0.25\,,-2\,,-16\,,-128,...−0.25,−2,−16,−128,...minus, 0, point, 25, comma, minus, 2, comma, minus, 16, comma, minus, 128, comma, point, point, point.
b(1)=b(1)=b, left parenthesis, 1, right parenthesis, equals
b(n)=b(n-1)\cdotb(n)=b(n−1)⋅b, left parenthesis, n, right parenthesis, equals, b, left parenthesis, n, minus, 1, right parenthesis, dot
The recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]
How to determine the recursive formula?The sequence is given as:
[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]
The first term of the above sequence is
[tex]b(1) = -0.25[/tex]
Calculate the common ratio using
r = b(2)/b(1)
So, we have:
r = -2/-0.25
Evaluate
r = 8
So, we have:
[tex]b(n) = b(n-1)\cdot 8[/tex]
Hence, the recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]
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Complete question
Complete the recursive formula of the geometric sequence
[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]
[tex]b(1) =[/tex]
[tex]b(n) = b(n-1)\cdot[/tex]
Surface area=
Volume =
Help me please thanks
Answer this one please!
Daphne is calculating the total asset turnover ratio of a company. Under which accounting principle would she value the assets of the company at their original cost? A. accrual method of accounting B. historical cost accounting C. business entity concept D. going concern concept
The accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.
What is historical cost accounting?Historical cost accounting is an accounting method for recording the value of fixed assets under US GAAP where the value of an asset on a balance sheet is equal to the cost of acquiring the asset.
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In Circle P, chord AB measures 4x - 6 centimeters and chord CD measures 6x - 12
centimeters. If Segment AB and Segment CD are each 4 centimeters from P, find AP.
Answer:
5 cm
Step-by-step explanation:
When two chords are equidistant from the center of the circle, the two chords have equal length. Therefore, the length of chord AB, 4x - 6, is equal to the length of chord CD, 6x - 12.
4x - 6 = 6x - 12
6 = 2x
x = 3
Now that we know x = 3, we can substitute the value back into the original expression, 4x - 6, to find the length of chord AB.
AB = 4x - 6 = 4*3 - 6 = 12 - 6 = 6 cm
When measuring the distance between a line and a point, we create a segment through the point perpendicular to the line. In Geometry, we also learn that the perpendicular bisector of a chord in a circle contains the center of the circle.
In this case, the gray line perpendicularly bisects segment AB. PX is 4 cm long and AX is 3 cm long (because AX is half the length of AB). Notice that triangle AXP is a right triangle, so we can use Pythagorean Theorem to find AP.
[tex]AP^{2} = AX^{2} +PX^{2}[/tex]
[tex]AP = \sqrt{3^{2} +4^{2} }[/tex]
[tex]AP =\sqrt{9+16}[/tex]
[tex]AP = \sqrt{25}[/tex]
[tex]AP = 5[/tex]
Can u guys pls help me with this homework
The value of √(7 * 23 - 1)/8 is 4.47, the values of a, b and c are -14/11, -10/11 and 3, respectively and the area of the shape is 5√5 + 5 square meters
How to evaluate the radical expression?The question goes thus:
If √5 = 2.236, evaluate √(7 * 23 - 1)/8
We have:
√(7 * 23 - 1)/8
Evaluate the product of 7 and 23
√(7 * 23 - 1)/8 = √(161 - 1)/8
Evaluate the difference of 161 and 1
√(7 * 23 - 1)/8 = √160/8
Evaluate the quotient of 160 and 8
√(7 * 23 - 1)/8 = √20
Express 20 as the product 4 and 5
√(7 * 23 - 1)/8 = √(4 * 5)
Expand the product
√(7 * 23 - 1)/8 = √4 * √5
Express √4 as 2
√(7 * 23 - 1)/8 = 2 * √5
Substitute √5 = 2.236
√(7 * 23 - 1)/8 = 2 * 2.236
Evaluate the product
√(7 * 23 - 1)/8 = 4.472
Approximate
√(7 * 23 - 1)/8 = 4.47
Hence, the value of √(7 * 23 - 1)/8 is 4.47
How to simplify the radical expression?The expression is given as:
(3√2 + 5√6)/(3√2 - 5√6)
Rationalize the above expression
(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)
Evaluate the product
(3√2 + 5√6)²/((3√2)² - (5√6)²)
Simplify the denominator
(3√2 + 5√6)²/(18 - 150)
This gives
[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)
Simplify the numerator
[168 + 120√3]/(-132)
Simplify the fraction
-14/11 - 10√3/11
Hence, the values of a, b and c are -14/11, -10/11 and 3, respectively
How to determine the area?The area is calculated as:
A = 1/2 * (Sum of parallel bases) * Height
So, we have:
A = 1/2 * (4 + 3√5 + 6 - √5) * √5
Evaluate the like terms
A = 1/2 * (10 + 2√5) * √5
Evaluate the product
A = (5 + √5) * √5
Evaluate the product
A = 5√5 + 5
Hence, the area of the shape is 5√5 + 5 square meters
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A type of sampling in which individuals to be interviewed are selected based on their proportion or quota in the general population being polled is known as
A type of sampling in which individuals to be interviewed are selected based on their proportion or quota in the general population being polled is known as public opinion.
What is sampling type of public opinion ?
A survey that measures the entire target population is called a census. A sample refers to a group or section of a population from which information is to be obtained. Survey samples can be broadly divided into two types: probability samples and super samples.
The collective opinion of large segment of the population on an issue, candidate or public policy on which the public may be much divided and lake a consensus.
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Allen is 5 feet 9 inches tall, terrel is 6 feet 2 inches tall. what is the average height
The average height is [tex]5feet[/tex] and [tex]11.5[/tex] inches if Allen is [tex]5 feet 9 inches[/tex] tall and Terrel is [tex]6 feet 2 inches[/tex] tall.
How to find the average height ?
Allen height is [tex]5feet ,9inches[/tex]
Terrel height is [tex]6feet,2inches[/tex]
And we know that [tex]1feet=12inches[/tex]
So Allen height is
[tex]=5*12+9\\=60+9\\=69 inches[/tex]
And Terrel height is
[tex]=6*12+2\\=72+2\\=74inches[/tex]
Average of the Allen and Terrel height is
[tex]\frac{69+74}{2\\} \\=143/2\\=71.5inches[/tex]
And average height in feet is [tex]5feet,11.5inches[/tex]
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Your family is going on vacation for two nights. You don't want to spend more than $135 on a hotel room for your vacation. Write an inequality to represent how much you can spend each night on your hotel room.
Answer:
Step-by-step explanation:
$135 is less than or equal to 2 nights at the hotel (h)
135</=2h
A rectangular box with a square base, an open top, and a volume of 32,000 cm3 is to be made. What is the minimum surface area for the box
the minimum surface area for the box is 4800 cm².
Forming the Equation of SurfaceArea
It is given that the given rectangular box is square-based and top is open. hence, it consists of square and 4 rectangles.
Let the side of the square be a, and height of the box be h.
Then, the total surface area of the box will be given by,
S = a² + 4ah _________ (1)
Also, it is given that the volume of the box is, V = 32000 cm³
The volume of the rectangular box, V = a² h
Eliminating One of the Variables From the Equation
The volume of the rectangular box, V = a² h
⇒ a² h = 32000
⇒ h = 32000/a² _______ (2)
Substituting this value of h in equation (1), we get,
S = a² +4a(32000/a²)
S = a²+128000/a
Minimizing the Surface Area Equation
To find the minima, put, dS/da = 0
dS/da = 2a-128000/a²
⇒ 2a-128000/a² = 0
Multiplying the whole equation with a², we get,
2a³-128000 = 0
⇒ 2a³ = 128000
⇒ a³ = 128000/2
⇒ a³ = 64000
⇒ a = 40 cm
Calculating the Minimum Surface Area
From, equation (2), h = 32000/(40)²
h = 32000/1600
h = 20 cm
Now, substituting the computed values of a and h in equation (1), we get,
S = (40)² +4(40)(20)
S = 1600 +3200
S = 4800 cm²
∴ The minimum surface area of the box is 4800 cm².
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If p(a) = 2/3, p(b) = 4/5, and p(anb) = 3/5, what is P( AuB) ( the n is the arc shape direction, so is the u)
By the inclusion/exclusion principle,
[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]
[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]
[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]
[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]
9. Two hexagons are similar in shape. The larger hexagon has an area of
7350 mm². Find the area of the smaller hexagon.
22,509.3 mm²
12,862.5 mm²
4,214.3 mm²
2,400 mm²
Answer:
2400 mm^2.
Step-by-step explanation:
The ratio of their areas = ratio of the squares of their sides.
So x / 7350 = 40^2 / 70^2 where x is area of smaller hexagon.
x = 7350 * 40^2 / 70^2
= 2400 mm^2.
The area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.
The areas of two similar figures are in the ratio which is equal to the square of the ratio of their corresponding sides.
If we have two figures A and B, and they are similar, then we can say that:
(Area of A)/(Area of B) = {(Side of A)/(Side of B)}².
In the question, we are informed that the two hexagons are similar in shape.
We are asked to find the area of the smaller hexagon, given the larger hexagon has an area of 7350 mm².
As the two hexagons are similar, we can show that:
(Area of the smaller hexagon)/(Area of the larger hexagon) = {(Side of the smaller hexagon)/(Side of the larger hexagon)}².
The side of the smaller hexagon is given to be 40mm, whereas the corresponding side of the larger hexagon is given to be 70 mm.
Thus, we can show that:
(Area of the smaller hexagon)/7350 = {40/70}²,
or, Area of the smaller hexagon = (16/49)*7350 = 16*150 mm² = 2400 mm².
Thus, the area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.
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Fill out First row is standard form
Second row is Factored Form already done for you.
Answer:
(x + 6)(x - 2) = x² + 4x - 12
(x + 2)(x - 8) = x² - 6x - 16
(x + 6)(x - 6) = x² - 36
(x - 5)(x - 1) = x² - 6x + 5
(x - 4)(x - 10) = x² - 14x + 40
(x + 2)(x + 5) = x² + 7x + 10
Step-by-step explanation:
Use FOIL.
(x + 6)(x - 2) =
F - first: x × x = x²
O - outer: -2 × x = -2x
I - inner: 6 × x = 6x
L - last: 6 × -2 = -12
(x + 6)(x - 2) = x² - 2x + 6x - 12
Now, combine like terms.
(x + 6)(x - 2) = x² + 4x - 12
(x + 2)(x - 8) = x² - 6x - 16
(x + 6)(x - 6) = x² - 36
(x - 5)(x - 1) = x² - 6x + 5
(x - 4)(x - 10) = x² - 14x + 40
(x + 2)(x + 5) = x² + 7x + 10
Zoe went out to her garden and cut 19 roses from the first rose bush, 28 roses from the second rose bush, 37 roses from the third rose bush, and 46 roses from the fourth rose bush. What kind of sequence is this?
Based on the given scenario, the kind of sequence explained is an arithmetic sequence
SequenceFirst bush = 19 rosesSecond bush = 28 rosesThird bush = 37 rosesFourth bush = 46First term, a = 19
Second term, a + d
28 = 19 + d
28 - 19 = d
9 = d
Common difference, d = 9Third term, a + 2d
= 19 + 2(9)
= 19 + 18
= 37
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describe how the graph is transformed from its parent function?
Answer:
It is stretched taller by a factor of 2.
Please help me
Marking brainliest for smart answer
Answer:
58%
Step-by-step explanation:
47/81 x 100%
≈ 58%
Hope it helps : )
Find the greatest common factor of the
following monomials:
33c 27c^4
The greatest Common factor of monomials [tex]33c[/tex] and [tex]27c^4[/tex] is [tex]3c[/tex]
How we can find the GCF of monomials ?
Monomials are [tex]33c[/tex] and [tex]27c^4[/tex]
We can write the monomials in fraction form
[tex]33c=11*3*c[/tex]
[tex]27c^4=3*9*c*c*c*c[/tex]
----------------------------------
So we can see the common factor is [tex]3c[/tex]
The Greatest Common Factor of [tex]33c ,27c^4[/tex] is [tex]3c[/tex]
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A variable that can only take on specific numeric values is called a _____. Group of answer choices categorical variable discrete random variable continuous random variable categorical variable
A variable that can only take on specific numeric values is called A discrete random variable.
According to the statement
A variable which is used to select a specific numeric value and we have to find a those variable
A discrete random variable is one which may take on only a countable number of distinct values.
So, A variable that can only take on specific numeric values is called A discrete random variable.
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