Answer:
An equivalent function to the given function is;
[tex]f(x)=6(8)^x[/tex]Explanation:
Given the function;
[tex]f(x)=6(2)^{3x}[/tex]we want to find an equivalent function to the given function;
Applying the rules of exponent;
[tex]\begin{gathered} f(x)=6(2)^{3x}=6(2^3)^x \\ =6(2\times2\times2)^x \\ =6(8)^x \end{gathered}[/tex]Therefore, An equivalent function to the given function is;
[tex]f(x)=6(8)^x[/tex]The sum of two numbers is 21. The second number is six times the first number. Work out the two numbers. Write your ansWwers on one line.
A: What two integers does square root of 37 fall between
B: Estimate The Decimal To The Nearest Tenth
A . [tex]\sqrt{37}[/tex] falls between integers 6 and 7
B. The decimal to the nearest tenth = 6.1
A. How are the two integers calculated?
[tex]\sqrt{37}[/tex] = 6.082 , falls between integers 6 and 7
What are integers?
A collection of integers is created if negative numbers are mixed in with whole numbers.Positive, negative, and zero are all examples of integers. Fractions and decimals are not included in integers. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division.B: Estimate The Decimal To The Nearest Tenth
[tex]\sqrt{37}[/tex] = 6.082
To estimate the decimal to the nearest tenth , we check the number in the hundredth place first which is 8.Since the hundredth place value number 8 is greater than 5 , we add a number to the tenth place .So the tenth place number changes from 0 to 1.[tex]\sqrt{37}[/tex] = 6.082 = 6.1
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How much money did Annie actually spend?
Write a expression to represent the amount of money that Annie spent. Was
your estimation an overestimation or underestimation? Why do you
think that might be?
Considering Annie bought 5 pounds of apples, 4 pounds of oranges, and 3 pounds of bananas, and each pound of apple costed $1.75, orange $2.35 and bananas $1.50,
(i) Annie had to spend an exact amount of $22.65, to buy all the above mentioned fruits.
(ii) The amount of money that Annie spent on the fruits, can be represented by the expression [(1.75 * 5) + (2.35 * 4) + (1.50 * 3)]
(iii) Rounding the prices to the nearest whole dollar and estimating the total amount Annie spent, our estimation is an overestimation compared to the actual price Annie had spent.
As per the question statement, no information is provided about Annie's expenditure, and hence, we are considering that, Annie bought 5 pounds of apples, each pound costing $1.75, 4 pounds of oranges, each pound costing $2.35 and 3 pounds of bananas, each pound costing $1.50.
We are required to calculate:
(i) The exact amount Annie spent on the fruits.
(ii) A mathematical expression to represent the amount of money that Annie spent.
(iii) To determine whether it is an overestimation or underestimation if we round the prices to the nearest whole dollar and estimate the total amount Annie spent.
Starting with (i) and (ii),
Total amount Annie actually spent on her fruits
= [{(price of per pound apple) * (number of pounds of apple she bought)} + {(price of per pound orange) * (number of pounds of orange she bought)} + {(price of per pound banana) * (number of pounds of bananas she bought)}
= $[(1.75 * 5) + (2.35 * 4) + (1.50 * 3)]
= $(8.75 + 9.40 + 4.50)
= $22.65
And, the amount of money that Annie spent on the fruits, can be represented by the expression [(1.75 * 5) + (2.35 * 4) + (1.50 * 3)].
Now solving (iii), first, we need to round off the prices to the nearest whole dollar and then estimate the total amount Annie spent.
Now, $1.75 dollars rounded off the prices to the nearest whole dollar will become $2.
Similarly, $2.35 dollars rounded off the prices to the nearest whole dollar will become $2,
And, $1.50 dollars rounded off the prices to the nearest whole dollar will become $2.
That is, the rounded-off per pound cost of apples is $2, that of oranges is $2 and of bananas is also $2.
Therefore, on the same consideration that, Annie bought 5 pounds of apples, 4 pounds of oranges, and 3 pounds of bananas, the estimated total amount she spent on the fruits based on the above mentioned rounded-off per pound costs will be equal to
$[(2 * 5) + (2 * 4) + (2 * 3)] = ${10 + 8 +6) = $24
Since (24 > 22.60), thus, we can conclude that rounding-off the prices to the nearest whole dollar and estimating the total amount Annie spent, our estimation is an overestimation compared to the actual price Annie had spent.
Expression: In mathematics, an expression is a finite combination of terms containing number or variables or both, connected by operator symbols in between, that is well-formed according to rules of mathematics.Round-off: In Mathematics, rounding-off a number can be done to a whole number or decimal number, to make it simpler by keeping its value intact but closer to the next number.To learn more about Rounding-off and expressions, click on the link below.
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Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are
(
3
x
−
4
)
feet,
(
x
2
−
1
)
feet, and
(
2
x
2
−
15
)
feet.
What is the perimeter of the triangle if
x
=
4
?
Responses
16
feet
16 feet
40
feet
40 feet
76
feet
76 feet
80
feet
The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively. The perimeter of the triangle is 42 feet.
Given that,
Kat is using reflective orange paint to outline a triangle stage prop. The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively.
We have to find if x = 4, what is the triangle's perimeter.
The perimeter of the triangle is equal to sum of the three sides of the triangle.
=3x - 4 + x² - 1 + 2x² - 15
=3x²+3x-20
Take the x value as 4
We get,
=3(4)²+3(4)-20
=3×16+3×4-20
=48+14-20
=62-20
=42
Therefore, The perimeter of the triangle is 42 feet.
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4. Which of the following is a binomial with degree 3?
3x+3x²
2xy²
2+5x-3x³
2x³ + xy
2x³ + XY is a binomial with a degree of 3
What is binomial?An algebraic expression containing only two terms is called a binomial. This is a binomial polynomial. It is also called the sum or difference of two or more monomials. This is the simplest form of a polynomial. A binomial is a polynomial with only terms. For example, x 2 is a binomial where x and 2 are two separate terms. Also, the coefficient of x is 1, the exponent of x is 1, and 2 is a constant here. Therefore, an A-binomial is a two-term algebraic expression that contains a variable, a coefficient, an exponent, and a constant.
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due now pls explain how you got the anser
The graph that shows the in the table is option (D)
From the table
The cost for hiring a plumber for zero hours = $50
The cost for hiring a plumber for 1 hours = $80
The cost for hiring a plumber for 2 hours = $110
The cost for hiring a plumber for 3 hours = $140
The domain is the set of all possible inputs.
The range is the set of all possible output
Here we have to plot the graph using the number of hours in the x axis and cost of hiring a plumber in y axis
The graph on option (D) matches the values in table. Because
At x= 0, y=50
At x= 1, y=80
At x= 2, y= 110
At x= 3, y= 140
Hence, the graph that shows the in the table is option (D)
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Functions W and Z are both linear functions of x. Which statement comparing the functions is true? Select all that apply. A. The slope of Function W is less than the slope of Function Z. B. The slope of Function W is equal to the slope of Function Z. C. The slope of Function W is greater than the slope of Function Z. D. The y-intercept of Function W is less than the y-intercept of Function Z. E. The y-intercept of Function W is equal to the y-intercept of Function Z. F. The y-intercept of Function W is greater than the y-intercept of Function Z
The correct options are:
B. The slope of Function W is greater than the slope of Function Z.
F. The y-intercept of Function W is greater than the y-intercept of Function Z.
Let's find the slope (m) and y-intercept (b) of each function to see which one compares the two functions accurately.
Function W:
The slope of Function B, using two points on the line, (0, -1) and (2, 0):
m = ( y₂ - y₁ )/ (x₂ - x₁ )
m = [ 0 - (- 1 )]/( 2- 0 ) = 0.5
The y-intercept will be when x = 0. Therefore, from the graph, the y-intercept is b = -1.
For Function Z:
The slope of Function Z, using two pairs of values from the table of values for function Z, ( 0, - 2 ) and ( 2, - 1.5 ):
m = ( y₂ - y₁ )/ (x₂ - x₁ )
m = ( - 1.5 - ( -2 ) )/( 2 - 0 )
m = 0.5/2 = 0.25
The y-intercept is the value of y when x = 0.
From the table when x = 0, y = - 2. Therefore, the y-intercept is b = - 2.
Thus, the following statements that compare both functions are TRUE:
B. The slope of Function W is greater than the slope of Function Z.
This is TRUE because 0.5 is greater than 0.25.F. The y-intercept of Function W is greater than the y-intercept of Function Z.
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Use point-slope form to write the equation of a line that passes through the point (20,19)(20,19) with slope 55.
The equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.
As given in the question,
Line passes through the point ( x₁ , y₁ ) = ( 20, 19)
Slope of the line that passes through (20 , 19) is 55
Equation of a line in point-slope form that passes through the point (20,19) with slope 55
y - y₁ = m ( x- x₁)
⇒ y - 19 = 55 (x - 20)
⇒ y -19 = 55x - 1100
⇒ y= 55x - 1091
Therefore, the equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.
The complete question is:
Use point-slope form to write the equation of a line that passes through the point (20,19) with slope 55.
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Find the coordinate of the midpoint of the segment with the given endpoints.
-8 and -6.
The distance between the points is 2: x2 - x1 = -6 + 8. So, the midpoint would be located on a point that is half of this distance from both points.
2/2 = 1
-6 - 1 = -7
-8 + 1 = -7
-7 has a distance of 1 from both -8 and -6, so this is the midpoint.
For any long-distance call T-Mobile charges a base rate of $15 per month plus $0.0
that you are on the phone, while Verizon charges a base rate of only $10 per month, but charges $0.10 per minute for long distance calls. Write the equation that represents the total cost for one month of long distance calls for each company, where y is total cost and x is the amount of minutes used
T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.
How to estimate total cost?Given: While Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls, T-Mobile has a base fee of $15 per month plus $0.05 for each minute you are on the phone.
We have to estimate how long would you need to call for them to charge the same amount.
Let the equation be 15 + 0.05 x = 0.10 x
⇒ 0.05 x - 0.10 x = -15
simplifying the above equation, we get
⇒ -0.05 x = -15
⇒ 0.05x = 15
⇒ x = 15 / 0.05
⇒ x = 300 minutes
Therefore, 300 minutes long would you need to call for them to charge the same amount.
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A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 16 feet
more than the length of the shortest side. Find the dimensions if the perimeter is 156 feet.
The length of three sides will be 35 feet, 70 feet and 51 feet
Define Perimeter of triangle
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
Perimeter of Triangle = side1 + base + side2
Let, the shortest side of the triangle = x
The other side length is = 2x
and, the length of third side is = x + 16
given perimeter = 156 feet
We know, perimeter of triangle = a + b +c
where, 'a' and 'c' stands for sides of triangle
and, b stands for base
hence, the expression will be according to formula,
x + 2x + x + 16 = 156
solve for 'x'
4x + 16 = 156
4x = 156 - 16
x = 140/4
x = 35
2x = 2 * 35 = 70
x + 16 = 35 + 16 = 51
Therefore, the length of three sides will be 35 feet, 70 feet and 51 feet.
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A youth organization raised $15, 336 by selling gift baskets. Five different
teams sold the baskets. Martin's team sold 48 baskets, Amy's team sold 138
baskets, Sharon's team sold 77 baskets, Juan's team sold 250 baskets, and
Dee's team sold 126 baskets.
Part A
Each gift basket was the same price. What was the price of one basket?
Two or more expressions with an Equal sign is called as Equation. Price of each basket is 24.ice of each basket is 24.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given A youth organization raised $15, 336 by selling gift baskets.
Martin's team sold : 48 baskets
Amy's team sold : 138 baskets
Sharon's team sold :77 baskets
Juan's team sold : 250 baskets
Dee's team sold : 126 baskets
Let x be the price of each basket.
Let us form a equation by given data
48x+138x+77x+250x+126x=$15, 336
639x=$15, 336
Divide both sides by 639
x=24
Hence price of each basket is 24.
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Polly is an artist, and she sells posters at a local café. When she sells x posters, she makes f(x) dollars.
What does f(5)=10 tell you?
The expression f(5)=10 tells us that if Polly is an artist and sells posters at a local cafe then it means that Polly makes 10 dollars when she sells 5 posters.
According to the question,
We have the following information:
Polly sells x posters then she makes f(x) dollars.
We have the following expression:
f(5) = 10
So, it simply means that in place of x in f(x) we have f(5) then we have 5 in place of x.
f(x) is the amount made in dollars. So, the total amount Polly made is 10 dollars.
Hence, the expression f(5) = 10 clearly states that Polly sold 5 posters as an artist and made 10 dollars out of it.
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Asymptote (horizontal) of f(x)=2(3)^-x
The Value of the horizontal asymptote is 0
What is horizontal asymptote?
The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute [tex]x=[/tex]±∞. We can also find the vertical asymptote.
now we are given a function
[tex]f(x)=2(3)^{-x}[/tex]
Now substitute x=±∞ in the equation, as the x in denominator we get
f(x)= 0
This is the value of the horizontal asymptote
Hence the value of horizontal asymptote comes out to be 0
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before the early 1990s, a telephone area code in the us consisted of three digits, where the first was not 0 or 1, the second was 0 or 1, and the third was anything except 0. how many area codes were possible?
Number of possible area codes = 144
The telephone area codes consist 3 digits.
The possible digits are 1, 2, 3,4,5,6,7,8,9,0. That is, a total of 10 digits.
The first digit was not 0 or 1. So the remaining are 2,3,4,5,6,7,8,9. There are 8 possibilities in first place.
The second digit is either 0 or 1. So there are only two possibilities for second place.
The third digit was anything except 0. So the third digit has 9 possibilities.
The total possibilities of the three digit number is the product of possibilities of digits in each place.
Hence, Number of possible area codes = 8 x 2 x 9 = 144
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6. A spool of ribbon has 100 meters(m) on it. How many millimeters does the spool of ribbon have?
In order to determine how many millimeters the spool has, you take into account the following identity:
1 meter = 1000 millimeters (1 m = 1000mm)
Then, you can proceed as follow:
100 m = 100(1m) = 100 (1000 mm) = 100,000 mm
where you have multiplied by 1000 the given quantity in meters, that is, you replace the unit meter (m) by its equivalence in millimeters (1000 mm)
That is, 100 meters are equivalent to 100,000 millimeters
What is the answer pls
Answer: 11.2
Step-by-step explanation: In order to find the length of n, you can use the given angle measure and base length as well as a trig ratio. Since 6.2 is adjacent to angle N, you can use tangent (opposite/ adjacent).
tan (61) = n/6.2
(multiply by 6.2 on both sides to isolate n)
• 6.2 • 6.2
tan (61) • 6.2 = n
11.185 = n
~11.2 = n.
(3x²y) . (2xy³) . (4x²y²)
Answer:
24[tex]x^{5}[/tex][tex]y^{6}[/tex]
Step-by-step explanation:
(3x²y) × (2xy³) × (4x²y²)
= 3 × 2 × 4 × x² × x × x² × y × y³ × y²
= 24 × [tex]x^{(2+1+2)}[/tex] × [tex]y^{(1+3+2)}[/tex]
= 24[tex]x^{5}[/tex][tex]y^{6}[/tex]
(Please help) Write an equation of the line
The equation of the line is y = -x + 3
How to find the equation of a line
Equation of a straight line is usually of the form y = mx + c
where:
m = slope
c = y intercept
slope = ( 5 - -2 ) / ( -2 - 5 )
= ( 5 + 2 ) / -7
= 7 / -7
= -1
The y intercept is found from the graph to be 3
the equation of lthe line is
y = -1 ( x ) + 3
y = -x + 3
Therefore the equation of the line as gotten from the graph is y = -x + 3
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-1/9 divided by 3/4
-4/27
1/12
1/12
4/27
Answer:
-4/27
Step-by-step explanation:
say we use a 5% p-value cutoff. do we reject the null, fail to reject the null, or are we unable to tell using our staff confidence interval?
1. Reject the null.
2. Data is consistent with the null hypothesis.
3. Unable to tell using our staff confidence interval.
What are confidence interval?A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used. Confidence intervals are used by statisticians to assess a sample variable's level of uncertainty. For instance, a researcher might randomly select many samples from the same population, compute a confidence interval for each sample, and then examine how well each sample might reflect the true value of the population variable. The generated datasets are all unique, some of which contain the genuine population parameter and others which do not. An unknown population parameter is most likely to be found inside a range of values that is bounded above and below the statistic's mean.
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Need help college math algebra
What equation matches this situation?
John wants to buy an MP3 Player that costs $30.98. How much change did he receive if
he gives the cashier $40.
Answer: If John gives the cashier $40 he will get 9.02 change back because $40.98 - $30.98 = $9.02
1.are the events not on a leash and retriever independent 2.what is the probability that a dog that is a retriever is on a leash3.what is the probability that a dog that is not on a leash is not a retriever?4.what is the probability that a dog is not a retriever and is on a leash?
The total number of dogs are 135.
The number of Retrievers dogs are 35.
The number of off leashed playing dogs are 47.
Determine the number of dogs that are not Retrievers.
[tex]\begin{gathered} NR=135-35 \\ =100 \end{gathered}[/tex]Determine the number of dogs that are not retrievers and not lleashed.
[tex]47-10=37[/tex]So table can be filled as,
Not on a leash leashed Total
Retrievers 10 25 35
Not a Retrievers 37 63 100
Total 47 88 135
1.
The events are indpendent if occurence of event does not affect the other event. But it can be observed that not on a leash and retriever depend on each other. So event not on a leash and retriever are not indpendent.
4.
The number of dogs that are not retriever and is on a leash are 63. So probability is,
[tex]\begin{gathered} P\text{ (R'}andL\text{)}=\frac{63}{135} \\ =\frac{7}{15} \end{gathered}[/tex]What is the slope of the line that passes through the point (4,7) and (7,16)
Answer: The slope is 3.
Step-by-step explanation: Hope this helps :)
At the toy store you could get 2 board games for $8.36. Online the price for 3 board games is $12.84. Which place has the highest price for a board game?
An online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
From the data given:
At the toy store, you could get 2 board games for $8.36.
Each board game cost = 8.36/2 = $4.18
Online the price for 3 board games is $12.84.
Each board game costs = 12.84/3 = $4.28
4.28 > 4.18
Thus, an online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.
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Part A = Gil is shopping for books and CDs. He buys 4 books and no CDs for a total of $32. Write an equation that represents the relationship between the cost of a book, y, and the cost of a CD, x, in standard form.
Part B= what is the slope of the equation?
what do electrons wear on their feet
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Which of the following is the prime factorization of 10? a1 x 10 b2 x 2 x 5 c5 x 5 d2 x 5
a=1×10, b=2×2×5, c=5×5 and d=2×5. Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.
Given that,
a=1×10, b=2×2×5, c=5×5 and d=2×5
We have to find the prime factorization of 10.
A natural number other than 1 is said to have a prime factor if its only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. So, let's take something like the number 20 as an example. That can be divided into two components. We can say, "Well, that's 4 times 5." Note that the number five is a prime.
Option a is 1×10
1×10=10
Option a is a prime factor of 10.
Option b is 2×2×5
2×2×5=10×2
Option b is a prime factor of 10.
Option c is 5×5
5×5=25
Option c is not a prime factor of 10.
Option d is 2×5
2×5=10
Option d is a prime factor of 10.
Therefore, Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.
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if the sample size were to increase, all other numbers remaining the same, what would be the impact on the standard error? the standard error would:
If the sample size were to increase, and all other numbers remaining stays the same, then the standard error would be less.
Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.
SE = SD / √n
where SE = standard error
SD = sample standard deviation
n = sample size
Increasing the sample size, n, while the samples remain the same(hence, the standard deviation will be the same), will result to smaller standard error.
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