Step-by-step explanation:
Applying rules of exponents to solve the given problems;
4^3 x 4^5 =
5^8 ÷ 5^-2 =
(6^3 ) ^ 4 =
For these problems, the applicable rules of exponents are;
aᵇ x aⁿ = aᵇ⁺ⁿ
aᵇ ÷ aⁿ = aᵇ⁻ⁿ
(aᵇ)ˣ = aᵇˣ
For the first problem; 4³ x 4⁵
aᵇ x aⁿ = aᵇ⁺ⁿ
4³ x 4⁵ = 4³⁺⁵ = 4⁸
Second problem: aᵇ ÷ aⁿ = aᵇ⁻ⁿ
5⁸ ÷ 5⁻² = 5⁸⁻⁽⁻²⁾ = 5⁸⁺² = 5¹⁰
Third problem; (aᵇ)ˣ = aᵇˣ
(6³)⁴ = 6³ˣ⁴ = 6¹²
Solve for c.
c= -9 - 8c
c=-9-8c
+8c
9c=-9
c=-1
Hope this helps:D!!
The letter C is equal to negative one.
c = -1
Hope this helps!
A Ferris wheel is 24 meters in diameter and completes 1 full revolution in 8 minutes.A Ferris wheel is 24 meters in diameter and completes 1 full revolution in 8 minutes.
a. The completes one full rotation in 3 min,
Angular Speed = dθ/dt = 2\(\pi\)/3 rad/min
b. The angular speed obtained above, for each t minutes, the angle swept is
θ = 2\(\pi\)/3 t
c. A function of time is given by the sine function \(sin\theta=sin(\frac{2\pi }{3}t )\) and represents the elevation of the seat with respect to 3 o'clock position.
Linear and Angular Velocity:Mathematically, a velocity of an object along a straight line is called linear velocity, whereas angular velocity refers to how much an object spins, rotates, or turns. The angular velocity increases as the rotation angle increases in a certain length of time.
To find the angular speed in rad/min of a Ferris wheel of diameter 24 meter elevated 8 meters from the ground,
=> 24/8 = 3
that completes one full rotation in 3 min,
we will use the following formula
Angular Speed = dθ/dt = 2\(\pi\)/3 rad/min
b. Using the angular speed obtained above, for each t minutes, the angle swept is
θ = 2\(\pi\)/3 t
c. Boarding the Ferris wheel at 3 o'clock position t =0 and rotating with the angle in terms of time obtained above, θ = 2\(\pi\)/3 t
a function of time is given by the sine function \(sin\theta=sin(\frac{2\pi }{3}t )\)
and represents the elevation of the seat with respect to 3 o'clock position.
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Complete question is:
A Ferris wheel is 24 meters in diameter and the bottom of the Ferris wheel is 8 meters above the ground. You board the Ferris wheel at the
3 o'clock position.
a. The wheel completes one full revolution every 3 min What is the angular speed (in rad/min) that the Ferris wheel is rotating?
b. Write a formula that gives the angle measure (in radians) swept out from the 3 o'clock position, a, in terms of the number of minutes elapsed since you boarded the Ferris wheel, t
c. Define a function gives of the number of minutes elapsed since you boarded the Ferris wheel, t
An artist uses a 3-foot piece of wood to carve statues she uses 1/6 foot pieces of wood for each statue how many statues can be made from all the wood
Answer:
18
Step-by-step explanation:
Dimension of piece of wood = 3 ft
Dimension of piece of wood used for one statue = \(\frac{1}{6}\) ft
To find:
Number of statues that can be made from all the wood ?
Solution:
To find the total number of statues that can be carved from the given piece of wood, we need to divide the dimensions of given piece of wood with the piece required to carve one statue.
Formula:
\(\dfrac{a}{\frac{b}{c}} = \dfrac{a\times c}{b}\)
Number of statues that can be made:
\(\dfrac{3}{\frac{1}{6}}\\\Rightarrow \dfrac{3\times 6}{1}\\\Rightarrow \bold{18}\)
Therefore, 18 number of statues can be made.
what is 7.0893 as a decimal but in expanded form
Answer:
expanded form: 7+0.08+0.009+0.0003
Step-by-step explanation:
7 = the ones place
0.08 = hundredths place
0.009 = thousandths place
0.0003= ten thousandths place
HELP ASAP PLEASE! In Parallelogram EFGH, diagonals FH and EG intersect at point D. Give FD = x2 - 36 and DH=x^2-4x. What is HF?
Using the properties of parallelogram, measure of diagonal HF is 90.
What is parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.
Among a parallelogram's characteristics are:
The opposing sides are equal and parallel.
Angles on either side are equal.
The two diagonals are split in half.
The parallelogram is divided into two congruent triangles by each diagonal.
Given that in Parallelogram EFGH, diagonals FH and EG intersect at point D. So that, FD = DH
x² - 36 = x² - 4x
⇒ 4x = 36
⇒ x = 36/4
⇒ x = 9
So that, FD = x² - 36
FD = 9² - 36
FD = 81 -36
FD = 45
SO that, HF = 2 * FD
HF = 2*45
HF = 90
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The two segments formed as a result of a bisector will
always be______?
1Proportional
2Perpendicular
3Congruent
4Parallel
Which linear equation represents the data given in the table?
A) y = 3x + 8
B) y = 8x + 3
C) y = 3x - 8
D) y = 8x - 3
ILL GIVE BRAINLIEST HELP ASAP
Answer:
C) y = 3x - 8
Step-by-step explanation:
Hope it helps you in your learning process.
What's the value? (yelping for help)
cos(20°) is the correct answer.
Congratulations! This is the unit circle. Literally everyone hates this. Everyone takes this in Trigonometry though, and it's required. I literally failed Trigonometry because of this and had to retake it when getting my degree in Mathematics.
So, what is the x-coordinate of this? Well, for any angle or (angle in triangle) \(\alpha\), the coordinates are always (\(cos(\alpha), sin(\alpha)\)).
In this case, angle \(\alpha\) is 20°, and so the x-coordinate will be cos(20°) while the y-coordinate will be sin(20°).
Hope this helped!
Answer: cos 20
Step-by-step explanation:
Suppose two sets of test scores have the same mean, but different standard deviations, 0₁ and 02, with 02 > 0₁. Which statement best describes the variability of these data sets? (1) Data set one has the greater variability. (2) Data set two has the greater variability. (3) The variability will be the same for each data set. (4) No conclusion can be made regarding the variability of either set.
If two sets of test scores have the same mean but different standard deviations, where σ₂ is greater than σ₁ then Data set two has the greater variability it states the best description of the variability of the data sets. Which is a statement (2).
To describe the variability of these data sets, the best statement is that data set two has the greater variability. This is because variability refers to how far a set of numbers is from the mean, so if the standard deviation is greater, the variability will be greater as well. The standard deviation is a measure of how far each observation in a dataset is from the mean value.
Variability is the degree to which numbers in a set differ from one another. Two different sets of data having the same mean but different standard deviations imply that their data points are scattered at different distances from their mean.
If the standard deviation is large, it indicates that the distribution is spread out, while a small standard deviation indicates that the scores are closely bunched. In conclusion, variability is higher when the standard deviation is higher, and the statement that describes this variability of these data sets is that data set two has the greater variability. Which statement (2) describes the variability of the data sets.
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The equation below gives parametric equations and parameter intervals for the motion of a particle in the xy-plane- Identify the particle's path by findir a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion x=3t+1,y=9t2,−[infinity]
The Cartesian equation for the particle's path is y = (1/3)(x - 1)^2, representing a parabolic curve. The particle moves in the positive x-direction as t increases.
To find the Cartesian equation, we eliminate the parameter t by isolating t in one of the equations and substituting it into the other equation:
From x = 3t + 1, we can solve for t as t = (x - 1)/3.
Substituting this value of t into y = 9t^2, we get y = 9[(x - 1)/3]^2.
Simplifying the equation, we have y = (3/9)(x - 1)^2, which simplifies further to y = (1/3)(x - 1)^2.
The Cartesian equation for the particle's path is y = (1/3)(x - 1)^2. This equation represents a parabolic curve.
To graph the Cartesian equation, plot the points on the graph where x and y satisfy the equation. The graph will show a parabolic curve. Since the parameter t ranges from negative infinity to positive infinity, the particle's path extends infinitely in both directions.
The direction of motion can be determined by analyzing the coefficient of t in the parametric equation for x. In this case, the coefficient is 3, indicating that as t increases, the particle moves in the positive x-direction.
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Koshi runs in a circular path around a field so that he is always 40 yards from the center of the field. If he runs 4 laps around the field, what is the total distance Koshi runs?
A 125.6 yd
B 251.2 yd
C 502.4 yd
D 1,004.8 yd
yeah the answer is B
how did you send a request
The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?
Answer:
77.88 minutes
Step-by-step explanation:
Given that :
Mean (m) = 70
Standard deviation (s) = 10
For 80% of student to complete the exam. In the given time
Using the formula :
Zscore = (X - mean) / standard deviation
80th percentile = 80/100 = 0.8 has a Zscore = 0.7881
0.7881 = (X - 70) /10
0.7881 * 10 = X - 70
7.881 = X - 70
7.881 + 70 = X
77.881 = X
Hence, 77.88 minutes should be given
Annie wants to create a right triangle with side lengths 12 centimeters, 35 centimeters, and
37 centimeters.
Is this possible? Why or why not?
Yes, because 12 + 35 is not equal to 37.
Yes, because 12? + 352 is equal to 372
No, because 12 + 35 is greater than 37.
No, because 12? + 352 is less than 372.
Answer: yes because 12^2+35^2=37^2
Step-by-step explanation:
5.8n+3.7=29.8 pls help
Answer:
n = 4.5
Step-by-step explanation:
5.8n + 3.7 = 29.8 ( subtract 3.7 from both sides )
5.8n = 26.1 ( divide both sides by 5.8 )
n = 4.5
Answer:
so the answer to this is n= 4.5
Step-by-step explanation:
so first because you can't subtract the one with the variable you subtract 3.7 from 3.7 and 29.8 - 3.7 that cancels the 3.7 so it looks like this
5.8n + 3.7=29.8
-3.7 -3.7
5.8n = 26.1
____ ____ n= 4.5 the lines means divide
5.8 5.8
Can someone pls help me like plsssssssss
Answer:
2x-8
Step-by-step explanation:
hi
hope it helps you
thank me later
carryonlearing
Answer:
The third one is not the same (2+x-4)
Step-by-step explanation:
2x-8 is the same as -8+2x as it just switched places
With 2(x-4)
You multiply 2 with x and -4
Which is 2x-8
Thus the same
2+x-4
is not the same since if you add 2 and -4
You will get
x-2
Which is not the same as 2x-8
Hope this helps!
PLEASE HELP!
How would the graph look?
The equations of the graph from the figure are y = 4 and y = -2
Explaining the equation of the graph from the look?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that
We have two horizontal lines that pass through the points y = 4 and y = -2
This means that the equations represented on the graph are y = 4 and y = -2
So, we can conclude that none of the options are true from the options
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Find the missing term in the sequence
1, 1, 2, 3, 5, 8, __, 21, ...
Answer:
13
Step-by-step explanation:
1+1=2
1+2=3
2+3=5
3+5=8
8+blank=21
21-8=13
Answer:
13
1+1=2+3=5+8=13+21=...
A bookshelf is 48 inches long. How many books measuring 1 1/2 inches will fit on the bookshelf?
Answer:
Step-by-step explanation:
32
Answer:
67 books
Step-by-step explanation:
solved it looll
5. Solve the following using binary addition with 2's complement: a. 47-83 b. -16-131
Using Binary addition with 2's complement, the following answers are found for the given expressions:
a) 47 - 83 = 11011101 (2's complement) = -60
b) -16 - 131 = 10010011 (2's complement) = -146
a. To solve 47 - 83 using binary addition with 2's complement, we first convert the numbers to their binary representation:
47 = 00101111
83 = 01010011
Now, let's perform the subtraction using binary addition with 2's complement:
00101111 (47)
01010011 (83, 2's complement)
11011100 (2's complement of 83)
11011101 (2's complement result)
The result in binary is 11011101. To convert it back to decimal, we take the 2's complement and add 1:
= 11011101 (2's complement)
= -1
= 11011100
The decimal equivalent of the binary result is -60. Therefore, 47 - 83 = -60.
b) To solve -16 - 131 using binary addition with 2's complement, we need to convert the numbers to their binary representation:
-16 = 11110000
-131 = 10000011
Since we are subtracting, we need to find the 2's complement of the second number (131).
2's complement of 131:
Step 1: Invert the bits: 10000011 -> 01111100
Step 2: Add 1 to the inverted bits: 01111100 + 1 = 01111101
Now, let's perform the subtraction using binary addition:
11110000 (-16)
01111101 (2's complement of 131)
1 01101101 (Overflow bit)
The result in binary is 101101101, but since we are using 8-bit representation, we consider the result modulo 2^8. Therefore, the final result is 01101101, which is equal to 109 in decimal.
However, since we were subtracting, the result should be negative. To obtain the negative value, we consider the overflow bit (leftmost bit) and perform the 2's complement on the result.
2's complement of 01101101:
Step 1: Invert the bits: 01101101 -> 10010010
Step 2: Add 1 to the inverted bits: 10010010 + 1 = 10010011
Therefore, -16 - 131 = -146.
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Please help me and provide an explanation. i’m so confused. Thank you!
Mr. Green grades 2/3 of a students project in 1/4 of an hour. How many projects can he grade in one hour?
Answer:
2 2/3 projects
Step-by-step explanation:
First disect the statement.
2/3 of a project in 1/4 of an hour.
This means that she does not completely finish grading a project in a quarter hour.
We want to know how much she gets done in one whole hour, however all we know is how much she gets done in 1/4 of that time. Luckily, 1/4 times 4 is a whole hour. Since 2/3 of a project gets done in 1/4 that means if we multiply 2/3 by four we should also get how much she completes in one hour.
2/3 x 4 = 8/3
8/3 = 2 2/3 projects
You can also right these as ratios:
(2/3)/(1/4) = x/1
x = 8/3
someone help please.
A quadrilateral has no pairs of parallel sides?
What two shapes could it be?
Answer:
Two possibilities are “Kite” shaped, and either a trapezoid or trapezium
Please help me if you can thanks
\(26 sin 58°\) is the expression that represents the length of segment PR.
What is Length?The word "length" is used to describe an object's size or the separation between two points. The length of an object or the separation between two points is measured by its length. It is employed to determine an object's size or the separation between two points.
Since triangle JKL and triangle PQR are similar, we can use the similarity ratios to find the length of PR.
We know that the ratio of PR to JK is the same as the ratio of PQ to JL. We know that \(PQ = 26 and JL = 26 + 13 = 39\), so the ratio is \(26/39\).
So, \(PR = (26/39) * 13 = 26sin( JL/2) = 26sin58°\)
So the answer is \(26 sin 58°\)
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Find an equation for the contour of f(x, y) = 2x^2 y + 9x+ 15
Find an equation for the contour of f(x, y) = 2x^2
that goes through the point (5,2).
The equation for the contour of `f(x, y) = 2x^2` that goes through the point `(5, 2)` is `2x^2 = c = 50`.
The given function is given by `f(x, y) = 2x^2 y + 9x+ 15`
To find an equation for the contour of the given function, we can use the following steps:
Step 1: Replace `f(x, y)` with `c`
Step 2: Write the resulting equation as `y =` or `x =`
Step 3: Simplify the equation
Step 4: Write the equation in terms of `c` and simplify it.
Now let's solve the given problem.1. Find an equation for the contour of `f(x, y) = 2x^2 y + 9x+ 15`
First, let us replace `f(x, y)` with `c`.
Thus, `2x^2 y + 9x+ 15 = c`
This can be rewritten as `y = - 9/ (2x) - (15/ (2x^2)) + c/(2x^2)`
Hence, the equation for the contour of `f(x, y) = 2x^2 y + 9x+ 15` is `y = - 9/ (2x) - (15/ (2x^2)) + c/(2x^2)`2.
Find an equation for the contour of `f(x, y) = 2x^2` that goes through the point `(5, 2)`
The given function is `f(x, y) = 2x^2`.
If the equation has to pass through the point `(5, 2)`, then the value of `c` can be found using the given point.`f(5, 2) = 2(5)^2 = 50`
Thus, `c = 50`.
Hence, the equation for the contour of `f(x, y) = 2x^2` that goes through the point `(5, 2)` is `2x^2 = c = 50`.
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The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result  in a profit of $20 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? Use the graphical LP approach.
Answer:.
Step-by-step explanation:
Therefore, The Outdoor Furniture Corporation should produce 120 benches and 175 picnic tables to obtain the largest possible profit of $4,015.
Explanation:The given problem can be expressed in the form of a mathematical equation as: Maximize P = 9x + 20ySubject to constraints
:4x + 6y <= 120010x + 35y <= 35004x + 10y <= 12003x + 5y <= 1200x >= 0, y >= 0
Where, x = Number of Benchesy = Number of Picnic TablesFirst, we need to plot all the constraints on a graph. The shaded region in the figure below represents the feasible region for the given problem. Feasible region\(P = 9x + 20y = Z\)The feasible region is bounded by the following points:
A (0, 60)B (120, 175)C (70, 80)D (300, 0)
We need to calculate the profit at each of these points. Profit at
A(0, 60) = 0 + 20(60) = $1200Profit at B(120, 175) = 9(120) + 20(175) = $4,015
Profit at C(70, 80) = 9(70) + 20(80) = $1,630Profit at D(300, 0) = 9(300) + 20(0) = $2,700
From the above calculations, we can see that the maximum profit of $4,015 is obtained at point B (120, 175). Hence, the number of benches and tables that Outdoor Furniture should produce to obtain the largest possible profit are 120 and 175, respectively.
Therefore, The Outdoor Furniture Corporation should produce 120 benches and 175 picnic tables to obtain the largest possible profit of $4,015.
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Help please asap give an explanation too.
A tarp is used to keep the infield of a baseball field from getting wet. The infield is a square. The corners of the square tarp are anchored at each base. The tarp is 8,100 square feet.
A. What is the distance between the first and second base?
B. Is 8,100 a perfect square? Explain.
a circular pool is surrounded by a brick walkway 3 m wide. find the ra- dius of the pool if the area of the walk- way is 198 m*.
The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
\(\pi\)(R +3)^2
Area of the pool is:
\(\pi R^2\)
Now, Our equation is:;
\(\pi\)(R +3)^2 - \(\pi R^2\) = 198
\(\pi\)((R+3)^2 - \(R^2\)) = 198
Open the inner bracket :
\(\pi\)(\(R^2+6R+9-R^2\)) = 198
\(\pi\)(6R +9) = 198
6R+9 = 198/\(\pi\)
6R = 198/\(\pi\) - 9
R = (198/\(\pi\) - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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What does the 5 in the decimal .257 represent
Answer: five hundredths
A circle in the zy-Plane has a center at(3/4,1/2) and a radius that is 3/5 units long. which of the following is an equation of the circle
Answer:b
Step-by-step explanation: