The simplified form of the expression is a³ which is calculated by using the properties of exponents.
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.
Typically, a superscript to the right of the base indicates the exponent. Then, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most succinctly, "b to the nth."
The given expression is a³(2a² + 4bc⁴)⁰.
From the properties of exponents we know that:
a⁰ = 1
Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1
Therefore the total value of the exponential expression is a³
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A car travels for 15km in a city at a Certain speed-Dutside the city it travels 72km at twice its former speed. If the total travelling time is 1hour 8minutes find the average speed .
If the total traveling time is 1 hour 8 minutes f the average speed is 45 km/h.
This is a problem from time and distance. We can solve this equation by following a few steps.
Let's assume the car travel in the city for t minutes and the average speed is v.
According to the question, the car travel outside the city for, (68- t) minutes as 1 hour 8 minutes is equal to 68 minutes.
Therefore, the average speed (v) in the city = 15/t km/minute as v = s/t where v represents the speed, t represents the taken time and s represents the distance.Hence, the speed outside the city = 72/(68- t) km/minute.As per the question, Outside the city, it travels at twice its former speed v.
Now, we can form an equation, 2 (15/t) = 72/(68- t).
Let's simplify the given equation. 30/t = 72/(68- t)
Or, 72t = 30(68- t) [cross multiplication]
Or, 72t = 2040 - 30t
Or, 102t = 2040 [add with +30t both sides]
Or, t = 2040/102
Or, t = 20 [dividing by 102 both sides]
Therefore we can conclude that the average speed ( km/h) is (15×60) / 20 = 45 km/h.
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Supposed that you purchased an old property for $120,000. You decide to mark
up the value by 40% before you put it on the market. If your real estate agent
charges 5.5% commission on the sale, how much did you make on the sale?
Answer:
158,760$
Step-by-step explanation:
120,000$ + 40%=168,000$-5.5%=158,760$
need help assap look in the picture
Answer:
8
Step-by-step explanation:
To find the perimeter, you must add the lengths of all sides.
In this question the perimeter is given, which is 63.
63 = 12 + 12 + 3x + 2x + 1 + x + 2
1. Add the numbers
63 = 12 + 12 + 3x + 2x + 1 + x + 2
12 + 12 + 1 + 2 = 27
63 = 27 + 3x + 2x + x
2. Combine Like Terms
63 = 27 + 3x + 2x + x
x = 1
3x + 2x + 1x = 6x
63 = 27 + 6x
3. Move Variable to the left
63 = 27 + 6x
63 = 6x + 27
4. Subtract 27 from both sides, the opposite of adding 27
63 = 6x + 27
63 - 27 = 6x + 27 - 27
36 = 6x
5. Divide by the same factor, the opposite of multiplying 6
36 = 6x
36/6 = 6x/6
6. Cancel out the 6s but leave the x
36/6 = 6x/6
x = 6
So, now that we know that x = 6 we can solve the expression, x + 2, to find out the length of the side BC.
6 + 2 = 8
hat is the expected share return given the following macro-economic probabilities? Probability of recession 20% - Share return 5%; Probability of steady state 60% - Share return 10%; Probability of boom 20% - Share return 15%
Based on the probability of the macro-economic probabilities and the share returns, the expected share return can be found to be 10%.
How to find the expected share return?The expected share return based on the economic probabilities can be found by the formula:
= (Probability of recession x Share return in recessions) + (Probability of steady state x Share return in steady state) + (Probability of boom x Share return in boom)
Solving for the expected share return gives:
= (20% x 5%) + (60% x 10%) + (20% x 15%)
= 1% + 6% + 3%
= 10%
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ill give brainliest if i can have help, i am having trouble turning on axis, can someone explain? (refer to image somewhere lol)
Answer:
a=2,-2 b=-5,-1 c=-1,-2
Step-by-step explanation:
you just put the shape the opisite way
Find the expected value E(X) of the following data. Round your answer to one decimal place.AnswerHow to enter your answer (opens in new window)6P(X = x) 0.1x789100.2 0.2 0.2 0.3
[tex]E(X)=\Sigma xP(x)[/tex][tex]\begin{gathered} (6\times0.1)+(7\times0.2)+(8\times0.2)+(9\times0.2)+(10\times0.3) \\ \\ =8.4 \end{gathered}[/tex]
Note ; We multiplied each of the x-values with their probabilities and obtain the sum of all. This gives the expected value.
Give a formular on how to calculate growth rate
Answer:
Straight-line percent change method example
Growth rate = (489 - 402) / 402. Absolute change = 87 (489 - 402) Growth rate = 0.2164 (87 / 402) Percent change = 21.64% (0.2164 x 100)
An investment grows by 4% per year for 5 years. By what percent does it increase over the 5-year period?
Given: GC bisects FGH. Determine the missing measure.a. m
Given that line segment, GC bisects ∠FGH
I made a sketch of the angles, they are not at scale.
That segment GC is an angle bisector indicates that it divides ∠FGH into halves. To determine the measure of the ∠FGC and ∠CGH you have to divide the measure of FGH by 2.
[tex]\angle\text{FGC}=\angle\text{CGH}=\frac{\angle\text{FGH}}{2}[/tex]a) ∠FGH=86º
[tex]\begin{gathered} \angle\text{FGC}=\frac{\angle FGH}{2} \\ \angle\text{FGC}=\frac{86º}{2} \\ \angle\text{FGC}=43º \end{gathered}[/tex]So, in this case, the measure of ∠FGC is 43º.
b) For this item you have to determine the measure of ∠FGH given that the measure of one of the angles determined by the bisector is ∠CGH. To determine the measure of ∠FGH you have to multiply ∠CGH by 2
[tex]\begin{gathered} \angle\text{FGH}=2\cdot\angle\text{CGH} \\ \angle\text{FGH}=2\cdot28º \\ \angle\text{FGH}=56º \end{gathered}[/tex]Multiple choice triangle. im pretty sure its pythagorean theorem but please let me know
To solve this triangle, we cannot use either the Pythagorean Theorem or the Law of Cosines. We need more information.
Conversely, we can use SOHCAHTOA, in the sense that we can use the SOH part of this (Sine = opposite side over hypotenuse), that is, we can use angle 33 as the reference angle, and we have a right triangle here. Then, using trigonometric ratios, we can use:
[tex]\sin (\theta)=\frac{opp}{hyp}\Rightarrow\sin (33)=\frac{x}{29}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]We also can use the Law of Sines to solve it:
[tex]\frac{x}{\sin(33)}=\frac{29}{\sin(90)}\Rightarrow\frac{x}{\sin(33)}=\frac{29}{1}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]Therefore, we can solve this triangle using both Law of Sines and SOHCAHTOA. (We can select two options: c and d.)
i need help plsssssssssss ill put 20 points
The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
What is Arithmetic sequence?
An arithmetic sequence is ordered set of numbers that have common difference between each consecutive term.
Given that;
The Arithmetic sequence are;
a) 35, 32, 29, 26 ...
b) - 3, -23, - 43, -63
c) -34, -64, -94, - 124
d) - 30, - 40, - 50, -60
Now, The common difference of an arithmetic sequence is calculated by the difference between each consecutive term.
For Arithmetic sequence a;
Common difference = 32 - 35 = -3
And, For Arithmetic sequence b;
Common difference = - 23 - (-3)
= - 23 + 3
= - 20
For Arithmetic sequence c;
Common difference = - 64 - (-34)
= - 64 + 34
= - 30
For Arithmetic sequence d;
Common difference = - 40 - (-30)
= - 40 + 30
= - 10
Thus, The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
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Find the Slope of the line through the points (4, -5) and (2, 2) then graph it.Slope =
The Slope of the line through the points (4, -5) and (2, 2) then graph it. Slope [tex]m=-\frac{7}{2}$$[/tex]
Slope between two points: [tex]$\quad$[/tex]Slope [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]
[tex]$$\begin{aligned}&\left(x_1, y_1\right)=(4,-5),\left(x_2, y_2\right)=(2,2) \\&m=\frac{2-(-5)}{2-4}\end{aligned}$$[/tex]
Refine
[tex]m=-\frac{7}{2}$$[/tex]
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
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for which values of (A) the system has at least one solution
Answer
The values of a that ensures that the system has at least one solution is
a > (21/127)
Explanation
We are told to find the values of a that ensures that the system has at least one solution. The system of equations include
3 (a - 5x) < 1 + x
2 - (x/2) > 3 + 5 (x - a)
To do this, we need to solve the expressions
3 (a - 5x) < 1 + x
3a - 15x < 1 + x
We can rewrite this as
1 + x > 3a - 15x
x + 15x > 3a - 1
16x > 3a - 1
Divide both sides 16
[tex]\begin{gathered} \frac{16x}{16}>\frac{3a-1}{16} \\ x>\frac{3a}{16}-\frac{1}{16} \end{gathered}[/tex]We then solve the second one. But to do this, let's multiply through by 2
2 - (x/2) > 3 + 5 (x - a)
4 - x > 6 + 10 (x - a)
we can rewrite as
6 + 10 (x - a) < 4 - x
6 + 10x - 10a < 4 - x
10x + x < 10a - 6 + 4
11x < 10a - 2
Divide both sides by 11
[tex]\begin{gathered} \frac{11x}{11}<\frac{10a-2}{11} \\ x<\frac{10a}{11}-\frac{2}{11} \end{gathered}[/tex]The two solutions are
x > (3a/16) - (1/16)
x < (10a/11) - (2/11)
To find a lasting solution, we need the inequality sign to be the same, so, we need to multiply through one of the equations by -1
x > (3a/16) - (1/16)
-x < (-3a/16) + (1/16)
So, the system of equations become
-x < (-3a/16) + (1/16)
x < (10a/11) - (2/11)
We can then add the two equations
-x + x < (-3a/16) + (1/16) + (10a/11) - (2/11)
0 < (-3a/16) + (10a/11) + (1/16) - (2/11)
0 < -0.1875a + 0.9091a + 0.0625 - 0.1818
0 < 0.7216a - 0.1193
Rewrite
0.7216a - 0.1193 > 0
0.7216a > 0.1193
Divide both sides by 0.7216
(0.7216a/0.7216) > (0.1193/0.7216)
a > 0.1653
a > (21/127)
Hope this Helps!!!
The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The range of the function is determined as 1 ≤ M ≤ 6.5 kg.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Also we can defined a domain of a function as all the possible values that go into a function.
From the graph the range of the function of the mass of the bucket is calculated as follows;
The minimum value of the mass of the bucket = 1
The maximum value of the mass of the bucket = 6.5 kg
The range of the function (mass, M of the bucket) = {1, 2, 3, 4, 5, 6.5 kg}
1 ≤ M ≤ 6.5 kg
Thus, the range of the function includes numbers ranging from 1 to 6.5 kg. That is {1, 2, 3, 4, 5, 6.5 kg}.
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When you mix two colors of paint in equivalent ratios, the resulting color is 1 po always the same. ***How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green?*** cups of cups of blue paint yellow paint 2 10 1 Your answer
Since question is incomplete, I will try my best to complete it my way:
It is given that 2 cups of blue with 10 cups of yellow make up green.
Question asks how many cups of yellow would i need to mix with 1 cup of blue to make same shade of green.
So,
2 cup with 10 cup
We divide each by 2, to get:
2/2 = 1
10/2 = 5
This means:
1 cup with 5 cup
Or,
1 cup blue with 5 cup yellow.
So, we arrive at our answer:
with 1 cup of blue, we need to fix 5 cups of yellow to get same shade of green.
John is a software salesperson. His base salary is $2300 and he makes $70 more for every copy of English is Fun he sells. His total pay, P (in dollars), after selling c copies is given by the following.
P=70c+2300
(a) If john’s total pay is $4750, how many copies did he sell?
(b) What is john’s total pay if he sells 25 copies?
Answer:
A - 35 copies
B - $4050
Step-by-step explanation:
A-
2300 + 70c = 4750
70c = 4750 - 2300
70c = 2450
c = 35
He sold 35 copies
B-
P = 2300 + 70(25)
P = 2300 + 1750
P = $4050
Total if he sold 25 copies: $4050
A couple has two children. Let A be the event that their first child is a boy, and note that P(A) = 51.2%. Let B be theevent that their second child is a girl, with P(B) = 48.8%.A and B are independent events. What is the probability that the couple has a first child that is a boy and a second childthat is a girl?Give your answer as a decimal rounded to two decimal places.
Answer:
P(A and B) = 0.25
Step-by-step explanation:
Since P(A) and P(B) are independents events, The probability P(A) and P(B) occurs consecutively is P(A)*P(B):
P(A and B) = P(A)*P(B)
P(A and B) = 0.512*0.488
P(A and B) = 0.25
Refer to the number line. Find the coordinate of point X such that the ratio of BX to XF is 3:2
Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.
What is Coordinate?
A combination of numbers that use the vertical and horizontal separations out from two reference axes to define a point's location on a coordinate plane. Typically expressed by the x-value & y-value pair (x,y).A group of variables that accurately depict a stance.The first number on a graph represents the distance along, while the second number represents the distance upward or downward.Total coordinates son number line from -7 to +7 =15
Number line ratio that has to be provided = 3:2
Let the coordinate be provided is x.
Therefore, 3x+2x=15
⇒5x=15
⇒x=3
Coordinate X
3x=3(3)=9
9th coordinate from -7 = 1 i.e. D
Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.
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You are designing a rectangular poster to contain 70 cm2 of printing with a 2 cm margin at the top and bottom and a 4 cm margin on the left and right. Determine, to two decimal places, the length of the poster required so as to minimize the amount of paper used.
The dimension of minimum paper size would be 18 inches by 9 inches.
What dimensions will minimize the amount of paper used?Let the paper size be x inches in length and y inches in width.
The length of the printed space would be x-8 inches and width would be y-4 inches.
Print area would thus be (x-8)(y-4)=50.
From this [tex]$y=4+\frac{50}{x-8}=\frac{4 x+18}{x-8}$[/tex]
Also from the same equation on simplifying, it is x y-8 y-4 x+32=50.
Since the area of the paper of size x inches by y inches is xy, let it be denoted as A.
Thus
[tex]$A-8 y-4 x=18$[/tex] Or [tex]$A=8 y+4 x+18$[/tex]
[tex]$A=\frac{32 x+144}{x-8}+4 x+18$[/tex].
For minimum paper size [tex]$\frac{d A}{d x}$[/tex] must be =0, hence,
[tex]$\frac{d A}{d x}=\frac{32(x-8)-(32 x+144)}{(x-8)^2}+4=0$[/tex]
[tex]$\frac{-400}{(x-8)^2}+4=0$[/tex]
(x-8)² = 100
x-8 = 10
[tex]$\mathrm{x}=18$[/tex], hence [tex]$\mathrm{y}=4+\frac{50}{x-8}=9$[/tex]
Dimension of minimum paper size would be 18 inches by 9 inches.
The complete question is:
You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?
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I need to Know how to find the maximum and the minimum values of a function?
Answer:
Step-by-step explanation:
first you need to figure out what your solving for We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
A fisher finder shows a large fish at 13 ft below the surface and a smaller fish 4 ft below surface. what is the expressions that are equivalent to the distance between the fish
Answer:
Distance = 9 ft
Explanation:
We can represent the position of the large fish with the number -13 because it is 13ft below the surface. In the same way, we can represent the position of the smaller fish with the number -4.
Then, the distance between the fish will be the absolute value of the difference between their positions. So, the expressions that are equivalent to the distance between the fish are:
| - 13 - ( - 4) | = | - 13 + 4| = 9
or
| -4 - (- 13) | = | - 4 + 13 | = 9
Therefore the distance between the fish is 9 ft
You have a solution that is 18.5% methyl alcohol. If the bottle contains 1.43 L of solution, what is the volume in milliliters of methyl alcohol?
We have the next given information:
-18.5% is the percentage of methyl alcohol
- The bottle contains 1.43 L
Now, we need to convert the percentage into a decimal.
Then 18.5% = 0.185
We need to determinate the volume in millimeters for methyl alcohol:
If 143L of solution contains 18.5% of methyl alcohol. Therefore:
The volume of methyl alcohol = 1.43 * 0.185
= 0.26455 L
Then, we need to convert Liters to milliliters:
1L ---------------------------- 1000ml
0.26455 L ------------------ x
Where x = (0.26455 L*1000ml)/1L
x =264.55ml
-3(x+3)+11=14
(steps included)
Answer:
-4
Step-by-step explanation:
-3(x+3)+11=14
-3·x-3·3+11=14
-3x-9+11=14
-3x+2=14
-3x=14-2
-3x=12
x=12÷(-3)
x=-4
m multipled by the square of n
Answer:
mn²
Step-by-step explanation:
the square of n is n² and m multiplied by this is
mn²
Given the graph of a function f. Identify function by name. Then graph the indicated functions. State the domain and the range in set notation.A) f(x-1) -3B) -f(x)
Answer:
For f(x);
The domain is;
[tex]D\colon x=(-\infty,\infty)[/tex]The range is;
[tex]R\colon y=\lbrack0,\infty)[/tex]Graphing those points for function A, we have;
The domain and range of the given function A is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=\lbrack-3,\infty) \end{gathered}[/tex]Graphing those points for function B, we have;
The domain and range of the given function B is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=(-\infty,0\rbrack \end{gathered}[/tex]Explanation:
Given the function in the attached image;
The function is a square function and can be written as;
[tex]f(x)=x^2[/tex]The domain is;
[tex]D\colon x=(-\infty,\infty)[/tex]The range is;
[tex]R\colon y=\lbrack0,\infty)[/tex]A.
[tex]f(x-1)-3=(x-1)^2-3[/tex]B.
[tex]-f(x)=-x^2[/tex]Graphing the functions;
For A;
[tex]\begin{gathered} f(1-1)=(1-1)^2-3=-3 \\ (1,-3) \\ f(3-1)=(3-1)^2-3=1 \\ (3,1) \\ f(-1-1)=(-1-1)^2-3=1 \\ (-1,1) \end{gathered}[/tex]Graphing those points for function A, we have;
The domain and range of the given function A is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=\lbrack-3,\infty) \end{gathered}[/tex]For B;
[tex]\begin{gathered} -f(x)=-x^2 \\ -f(0)=-0^2 \\ (0,0) \\ -f(2)=-2^2=-4 \\ (2,-4) \\ -f(-2)=-(-2)^2=-4 \\ (-2,-4) \end{gathered}[/tex]Graphing those points for function B, we have;
The domain and range of the given function B is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=(-\infty,0\rbrack \end{gathered}[/tex]How many points of intersection are there between the graphs of the two hyperbolas?
The graphs of the hyperbola have zero point of intersection.
What is the point of intersection?The point of intersection is the point where two or more functions meet.
The given parameters;
3x² – 4y² + 4x – 8y +4= 0
3x² + y² + 4x – 3y +4= 0
To find the points of intersection, we simply equate both equations.
So;
3x² – 4y² + 4x – 8y +4= 3x² + y² + 4x – 3y +4
Now Cancel out the common terms
y² - 3y = - 4y² - 8y
Collect like terms;
y² + 4y²= 3y - 8y
5y² = - 5y
Divide through by 5
y² = -y
Divide through by y
y = -1
Hence, the graphs of the hyperbola have zero point of intersection.
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Find the volume of the solid to the nearest unit. 13 A 6 A drawing not to scale 3 O 546 ft 3 O 1092 ft 3 O 273 ft 3 O 422 ft
Volume = Area of the base * height
Area of the base = (7 * 6) / 2
Area of the base = 42/2
Area of the base = 21ft^2
Volume of the prism = 21 * 13
Volume of the prism = 273 ft^3 The thi
The mass of a bull is 325 kg. This is 175 kg more than the mass of a calf. The mass of a calf is 107 kg less than the mass of a cow.
Calculate the mass of a cow
Answer:
257 kg
Step-by-step explanation:
Hello!
Given Info:Bull = 325 kgCalf = 175 kg less than BullCow = 107 kg more than the calfCalf:325 - 175150Cow:150 + 107257The mass of the cow is 257 kg.
the store purchased a produce for 1 dollar and sells it for 6 what is the mark up as a precent?
Pls help asap
Answer:
[tex]1 \div 6 = 0.16 \times 100 = 16.6 percent[/tex]
that's all I know
(b) The area of a rectangular pool is 8075 m².If the length of the pool is 95 m, what is its width?Width of the pool: ]m
The area of a rectangle is:
[tex]A=wl[/tex]where w is the width and l is the length. Plugging the values we have and solving for w:
[tex]\begin{gathered} 8075=95w \\ w=\frac{8075}{95} \\ w=85 \end{gathered}[/tex]Therefore the width is 85 meters.