The functions f(x) = √16^x and g(x) = ∛64^x increase at the same rate as x increases.
Explanation:The functions f(x) = √16ˣ and g(x) = ∛64ˣ are related in the way they grow or decrease as x increases. Let's analyze each function:
For the function f(x) = √16ˣ, as x increases, the value of f(x) also increases. This is because when x increases, 16^x becomes larger, and taking the square root of a larger number results in a larger value for f(x).
For the function g(x) = ∛64ˣ, the same logic applies. As x increases, the value of g(x) also increases. This is because when x increases, 64ˣ becomes larger, and taking the cube root of a larger number results in a larger value for g(x).
Therefore, both functions f(x) and g(x) increase at the same rate as x increases. None of the given options accurately describe the relationship between the graphs of f(x) and g(x).
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Answer:
A.
Step-by-step explanation:
Average annual rainfall totals for cities in New York are listed below.
Rochester 0.97 meters
Ithaca 0.947 meters
Saratoga Springs 1.5 meters
New York City 1.268 meters
a. Put the rainfall measurements in order from least to greatest. Write the smallest total rainfall in word form and expanded form.
b. Round each of the rainfall totals to the nearest tenth.
c. Imagine New York City’s rainfall is the same every year. How much rain would fall in 100 years?
d. Write an equation using an exponent that would express the 100-year total rainfall. Explain how the digits have shifted position and why.
Answer:
a) Order: 0.947 < 0.97 < 1.268 < 1.5
b)Smallest total rainfall = 0.947 meters in Ithaca
c) 100 years total rainfall = [tex]126.8 \text{ meters} = 1.268\times 10^2[/tex]
Step-by-step explanation:
We are given the following data in the question:
City: Rochester Ithaca Sara-Toga New-York
Rainfall(meters): 0.97 0.947 1.5 1.268
a) Order:
0.947 < 0.97 < 1.268 < 1.5
Ithaca < Rochester < New-York < Sara-Toga
Smallest total rainfall = 0.947 meters in Ithaca
Expanded form: [tex]0.947 = 9\times \frac{1}{10} + 4\times\frac{1}{100} + 7\times \frac{1}{1000}[/tex]
Word form: seven thousandths and ninety four hundredths.
b) Round off to nearest tenths
Rochester - 1.0 meters
Ithaca - 0.9 meters
Sara-Toga - 1.5 meters
New-York - 1.3 meters
c) [tex]\text{Rainfall in 100 years} = \text{Annual rainfall}\times 100 = 1.268\times 100 = 126.8 \text{ meters}[/tex]
d) 100 years total rainfall = [tex]126.8\text{ meters} = 1.268\times 10^2 = 0.1268\times 10^3[/tex]
The points shifted because we have to multiply 1.268 by 100. This would again result in shifting the point towards right.
Final answer:
The rainfall totals ordered from least to greatest are Ithaca, Rochester, New York City, Saratoga Springs. Rounded to the nearest tenth, New York City would receive 126.8 meters of rain in 100 years, represented as 1.268 x 10^2 with the base ten exponent indicating multiplication by 100.
Explanation:
Ordering Rainfall Totals and Mathematical Operations
To answer the student's question regarding the average annual rainfall totals for cities in New York:
Ordering from least to greatest: Ithaca (0.947 meters), Rochester (0.97 meters), New York City (1.268 meters), Saratoga Springs (1.5 meters). The smallest total rainfall (Ithaca) in word form is nine hundred forty-seven thousandths and in expanded form is 0.9 + 0.04 + 0.007.
Rounding to the nearest tenth: Rochester (1.0 meters), Ithaca (0.9 meters), New York City (1.3 meters), Saratoga Springs (1.5 meters).
Rainfall in 100 years: New York City's rainfall of 1.268 meters every year would result in 126.8 meters of rain in 100 years.
Equation with exponent: The equation to express the total 100-year rainfall for New York City is 1.268 meters x 100 years. Using an exponent, this is written as 1.268 x 102. The digits shift two places to the left because the base ten exponent indicates the value should be multiplied by 100.
The figures above are based on the provided data and standard mathematical operations such as ordering, rounding, and multiplication with exponents.
What is 0.9 7/8 0.86 written from least to greatest
Answer: 0.86 0.875 0.9
Step-by-step explanation: 7/8 is 8.75 in decimal form, so above would be the answer from least to greatest.
Answer: 0.86, 7/8, 0.9 is least to greatest
Step-by-step explanation:
The seats at a football stadium are on a slope with gradient of 1/2. What is the height of the bottom seats?
Answer:
ANS IS 2m
Step-by-step explanation:
we can solve it by using coordinate geometry
Answer:
Height of the bottom seats is 2 meter.
Step-by-step explanation:
It has been given in the question seats are located on a slope having gradient [tex]\frac{1}{2}[/tex]
We have to find the height h of the bottom seats.
Since gradient = [tex]tan\theta=\frac{1}{2}[/tex]
Therefore, from the figure attached,
[tex]tan\theta =\frac{(12-h)}{20}[/tex]
[tex]\frac{1}{2}=\frac{(12-h)}{20}[/tex]
12 - h = [tex]\frac{20}{2}[/tex]
12 - h = 10
h = 12 - 10
h = 2 m
Therefore, height of the bottom seats if 2 m.
Given the function, d(t) = 50t, the variable t represents which of the following? Select all that apply. input output function independent variable dependent variable
Answer:
Input
Independent variable
Step-by-step explanation:
we know that
Independent variables, are the values that can be changed or controlled in a given model or equation
Dependent variables, are the values that result from the independent variables
we have the function
[tex]d(t)=50t[/tex]
In this problem
This is a proportional relationship between the variables d and t
The function d(t) represent the dependent variable or the output
The variable t represent the independent variable or input
Answer:
Independent variable
Step-by-step explanation:
Given is a function
[tex]d(t) = 50t[/tex]
We have to find the independent and dependent variable in this equation
In scientific analysis, the independent variable is one which is changed to get some results for tests. Dependent variable is one which changes according to changes in independent variable
Here we find the term t is independent as it can be changed independently and d(t) can be analysed for various values of t
Thus the dependent variable [tex]d(t)[/tex] a function of t is tested for various values of independent variable t.
Is this equation an identity?
-5w − 8 = 1 − 2w
Answer:
-3w = 9
w = -3
yes, it is an identity
Simplify the expression 3(x + 2)(x2 − x − 8). 3x3 + 3x2 − 30x − 48 3x3 + x2 − 10x − 16 3x3 − 30x2 − 12x − 48 3x3 − 4x2 − 30x − 4
Answer:
3x^3 + 3x^2 − 30x − 48
Step-by-step explanation:
3( x + 2 )( x^2 − x − 8 )
= ( 3( x + 2 ))( x^2 + − x + − 8 )
= ( 3( x + 2 ))( x^2 ) + ( 3( x + 2 ))( −x ) + ( 3( x + 2 ))( −8 )
= 3x^3 + 6x^2 − 3x^2 − 6x − 24x − 48
3x^3 + 3x^2 − 30x − 48
Answer:
The correct option is A) [tex]3x^3+3x^2-30x-48[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]3\left(x+2\right)\left(x^2-x-8\right)[/tex]
Distribute 3 as shown
[tex]\left(3x+6\right)\left(x^2-x-8\right)[/tex]
Distribute parentheses as shown.
[tex]3xx^2+3x\left(-x\right)+3x\left(-8\right)+6x^2+6\left(-x\right)+6\left(-8\right)[/tex]
[tex]3x^2x-3xx-3\cdot \:8x+6x^2-6x-6\cdot \:8[/tex]
[tex]3x^3-3x^2-24x+6x^2-6x-48[/tex]
Add and subtract like terms
[tex]3x^3+3x^2-30x-48[/tex]
Hence, the correct option is A) [tex]3x^3+3x^2-30x-48[/tex]
the product of 3 and a number is the same as 30 less thrice that same number
Answer:
11
Step-by-step explanation:
So, we can say that
3 × X - 3 = 30
3 × X = 30+3
3 × X = 33
X = 33/3
X = 11
Which point lies below the x-axis and to the right of the
y-axis?
Answer:
Quadrant IV
Step-by-step explanation:
The points (x,y) such that
y < 0 and x>0, i.e. quadrant IV of the plane.
Number A is 5342. Number B is 11124 greater than A. Number C is 3104 less than B. What is the total value of numbers A,B and C?
Answer:
B - 16466
C - 13362
total value - 35170
Step-by-step explanation:
to find B add 11124 to 5342 (11124+5342=16466)
to find C subtract 3104 from 16466 (16466-3104=13362)
total value - add them all together
Your class started at 12:12PM and ended at 12:50PM. What angle did the minute hand of a watch sweep through during the class?
A. 132
B. 228
C. 153
D. 168
What is 456698 in word form
Answer:
four hundred and fifty six thousand six hundred and ninety eight
Martinez quilt is made of 6 red square and 18 blue squares. Which ratio compares the number of blue squares to the total number of squares
A) 1:3
B) 3:1
C)1:4
D) 3:4
A room has a length of 12.62 ft and a width of 10.2 ft. Find the perimeter of the room with the correct number of significant digits.
Answer:
45.6 ft
Step-by-step explanation:
The room is a rectangle. The perimeter of a rectangle is
perimeter = 2L + 2W
perimeter = 2(12.62 ft) + 2(10.2 ft)
perimeter = 25.24 ft + 20.4 ft
perimeter = 45.64 ft
Since 10.2 ft has only 3 significant digits, the answer must also have only 3 significant digits.
Answer: perimeter = 45.6 ft
5. A group of four friends attended a movie togene.
Each friend bought a movie ticket and a bottle o
water. The total they paid was $30. If each movie
ticket cost $5.50, how much did each bottle of
water cost?
if a scale factor is grater than 1, then your figure gets
Answer:
multiplied
Step-by-step explanation:
Answer:
If a scale factor is greater than 1, then your figure gets bigger.
Step-by-step explanation:
For scale factors, you are multiplying the scale factor to get the desired outcome. If the scale factor is greater than 1, you are multiplying by a whole number, which would be ≥ the original number. If the scale is 1, then it would be = too the original number. If the scale factor is a fraction, then the figure would be scaled down.
~
pls help me out least question :)
Answer:
A
Step-by-step explanation:
percent of each number
71.33 % of 54
Answer:
38.5182
Step-by-step explanation:
54 • 0.7133 is 38.5182.
BRAINLIEST + 30 POINTS! Please help ASAP!
(Please explain your work if you can, i'm confused by this module so it'd really help!)
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
Answer:
we know that
By alternate interior angles
m∠PRD=m∠APR -------> equation
m∠PRD=120°
so
m∠APR=120°
m∠APR=m∠APQ+m∠QPR ---------> equation
m∠APQ=62°
m∠QPR=x°
Substitute the values in the equation 120=62+x
x=120-62
x=53
therefore
the answer is
The measure of angle x is equal to 53 degrees
Because the lines are parallel the lower outside angle given as 155 is equal to the opposite angle, which is made up of X and 62.
To find X subtract 62 from 115:
X = 115 - 62
X = 53
Need help with 3 and 4
Answer:
3. 9.2 mL; 4. 0.25 mL
Step-by-step explanation:
3. 12 mL syringe
The arrow points to the first division between 9 mL and 10 mL.
There are five divisions, so
5 divisions = 1.0 mL or
1 division = 0.2 mL
The reading is
9.0 mL + 0.2 mL = 9.2 mL
4. 0.5 mL syringe
The arrow points to the fifth division between 0.20 mL and 0.30 mL.
There are 10 divisions, so
10 divisions = 0.10 mL or
1 division = 0.01 mL
5 divisions = 0.05 mL
The reading is
0.20 mL + 0.05 mL = 0.25 mL
Babatunde has a mass of 78kg. What would Babatunde weigh on the Moon? (The gravitational field strength on the Moon is 1.6N/kg.)
Answer:
Babatunde weigh on the Moon would be 124.8 N
Step-by-step explanation:
* The wight of an object on the earth is mg , where m is the the
mass of the object in kg and g is the acceleration of gravity which
is 9.8 m/s²
* The mass of an object on earth is the same as the mass of the
same object on the moon but the weight of the object on the
earth is different from the weight of the same object on the
moon because the gravity on the earth different from on the moon
* The wight on the moon is mg , where m is the the mass of the
object in kg and g is gravitational field strength on the Moon
which is 1.6 N/kg
∵ Babatunde has a mass of 78 kg
∵ The mass on the moon = the mass on the earth
∵ On the moon the gravitational field strength is 1.6N/kg
∵ Weight = mg
∴ Babatunde weigh = 78 × 1.6 = 124.8 N
* Babatunde weigh on the Moon would be 124.8 N
Babatunde's weight on the Moon is calculated by multiplying his mass (78 kg) by the Moon's gravitational field strength (1.6 N/kg), resulting in 124.8 newtons.
Explanation:Calculating Babatunde's Weight on the MoonTo calculate Babatunde's weight on the Moon, we use the formula for weight, which is the product of mass and gravitational field strength. On Earth, the average acceleration due to gravity is approximately 9.8 m/s², and on the Moon, it is about 1.6 N/kg. Babatunde's mass on Earth is 78 kg. Therefore, to calculate his weight on the Moon, we multiply his mass by the Moon's gravitational field strength.
Weight on the Moon = Mass × Gravitational field strength on the Moon
Weight on the Moon = 78 kg × 1.6 N/kg
Weight on the Moon = 124.8 N
Babatunde would weigh 124.8 newtons on the surface of the Moon, significantly less than his weight on Earth due to the Moon's lower gravitational pull.
What is the vertex of angle 4 in this diagram?
To increase an amount by 7% what single multiplier would you use?
QUESTION:To decrease an amount by 7% what single multiplier would you use?
ANSWER: You want 7% less than 100%, so the answer is (100%-7%)=93% =0.93.
Hope this helped! Enjoy! :)
What is 7.0717 million in figures. ?
7.0717 million
Lets see:
1 million = 1.000.000
So, 7.0717 million = 7.071.700
7.071.700 can be read as "seven million seventy one thousand and seven hunred"
If you wanna split it you can split in
seven million = 7 million
seventy one thousand = 71 thousand
seven hundred = 7 hundred
How many hours are equal to 150 minutes?
Answer:
2Hours and 30 mins. 2 1/2
Step-by-step explanation:
3x60=180 since there is 60 minutes in an hour There is no possible ways to get an exact number.
Answer:
2.5 hours
Step-by-step explanation:
Just divide your total number of minutes by 60, which is how many minutes are in an hour to receive your answer of 2.5!
What is the combined length of all the pieces Meg measured? Write an equation using a variable to show your work.
Lengths of wire
1 - 3 inches
2 - 5 inches
3 - 6 inches
3 - 7 inches
1 - 9 inches
Answer:
The combined length is 61 inches
Step-by-step explanation:
we know that
To find out the combined length of all the pieces Meg measured, multiply each measure by the number of pieces and then sum all the values
Let
x -----> the combined length
we know that
we have
1 piece of 3 inches
2 pieces of 5 inches
3 pieces of 6 inches
3 piece of 7 inches
1 piece of 9 inches
so
[tex]x=(1)(3)+ (2)(5)+(3)(6)+(3)(7)+(1)(9)\\x=3+10+18+21+9\\x=61\ in[/tex]
therefore
The combined length is 61 inches
14% of 81 is what number?
Answer:
11.34
hope it helps. :)
6.) A kennel owner has 168 feet of fencing with which
to enclose a rectangular region. He wants to subdivide
this region into three smaller rectangles of equal
length. If the total area to be enclosed 832 ft-, what are
the possible dimensions of the region?
Answer:
The possible dimensions of the region are
52 ft by 16 ft
32 ft by 26 ft
Step-by-step explanation:
Let
x -----> the length of the rectangular region
y ----> the width of the rectangular region
we know that
The perimeter of a rectangle is equal to
[tex]P=2(x+y)[/tex]
Remember that
A kennel owner wants to subdivide this region into three smaller rectangles of equal length
so
we also have to take into account the divisions
[tex]P=2(x+y)+2y[/tex]
[tex]P=2(x+2y)[/tex]
we have
[tex]P=168\ ft[/tex]
[tex]168=2(x+2y)[/tex]
simplify
[tex]84=(x+2y)[/tex] -----> [tex]x=84-2y[/tex] -----> equation A
The total area to be enclosed is 832 ft^2
The area is equal to
[tex]A=xy[/tex]
so
[tex]832=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]832=(84-2y)y[/tex]
[tex]832=84y-2y^2[/tex]
[tex]2y^2-84y+832=0[/tex]
Solve the quadratic equation by graphing
The solution are y1=16 ft, y2=26 ft
see the attached figure
For
[tex]y=16\ ft\\x=84-2(16)=52\ ft[/tex]
For
[tex]y=26\ ft\\x=84-2(26)=32\ ft[/tex]
therefore
The possible dimensions of the region are
52 ft by 16 ft
32 ft by 26 ft
9. We measure time in hours.
Suppose 12 noon is represented by the integer 0.
a) Which integer represents 1 P.M. the same day?
b) Which integer represents 10 A.M. the same day?
c) Which integer represents 12 midnight the same day?
d) Which integer represents 10 P.M. the previous day?
Describe the strategy you used to find the integers.
Answer:
for a
the integer 1 will be represented by 1 pm the same day
for b
-2 will be represented by 10 am
for C:
12 midnight will be represented by 0
for D:
the integer 10 will be represented by that .
Using a number line, integers can be used to represent the following given day time in hours as shown in the diagram below:
a. Integer 1 represents 1 P.M.
b. Integer -2 represents 10 A.M.
c. Integer -12 represents 12 midnight.
d. Integer 10 represents 10 P.M.
Recall:
Integers are numbers that have no fractional parts. They are whole numbers.Integers includes 0, negative, and positive numbers.Integers on a number line has been shown below to illustrate how they can represent measure of time in hours if 12 noon is integer 0.
From the image given showing the integers on a number line, the following integers and their respective day time they represent are:
a. Integer 1 represents 1 P.M.
b. Integer -2 represents 10 A.M.
c. Integer -12 represents 12 midnight.
d. Integer 10 represents 10 P.M.
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How much would $300 invested at 9% interest compounded continuously be worth after 3 years? Round your answer to the nearest cent.
$300*e^(0.09*3) = $392.99.
the answer is $392.99
A cardboard box, which weighs 0.6 pounds empty, is filled with 15 bags of beans and a 4-pound bag of rice. the total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6+15b+4=25.6 . In this situation, what does the solution to the equation represent?
Answer:
the weight of a bag of beans
Step-by-step explanation:
You have an equation representing the total weight of a box, 15 bags of beans, and a bag of rice. You want to know the meaning of the variable b in the equation ...
0.6 +15b +4 = 25.6
Sum of weightsEach term in the equation is the weight of something.
The first term (0.6) is the weight of the empty box.
The second term (15b) is the weight of 15 bags of beans. In this context, we assume the meaning of 'b' is the weight of 1 bag of beans.
The third term (4) is the weight of a bag of rice.
The term on the right of the equal sign (25.6) is the total of the other weights.
SolutionThe unknown value in the equation is the value of 'b', the weight of a bag of rice. When we solve for that value, we get ...
4.6 +15b = 25.6
15b = 21
b = 21/15 = 7/5 = 1.4
When this value is multiplied by bags, the result is pounds. That means the units of 'b' are "pounds per bag", the weight of one bag of rice.
The solution (b=1.4) represents the weight of one bag of rice.
The solution to the given equation represents the weight of one bag of beans. The variable 'b' represents this weight in the equation, and by solving, we can find this value.
Explanation:The equation 0.6+15b+4=25.6 represents a situation where a cardboard box, which is empty weighs 0.6 pounds, is filled with 15 bags of beans and a 4-pound bag of rice, leading to a total weight of 25.6 pounds. Here, the variable 'b' represents the weight of one bag of beans. To find this value, we rearrange the equation and isolate 'b', leading to the equation b=(25.6-0.6-4)/15. We then calculate the righthand side to get the weight of a bag of beans. The solution to the equation is the weight of one bag of beans.
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