Answer: $41.3
Step-by-step explanation:
this month late = 158 - 40 = 118
7× $0.05 = $0.35
118 × $0.35 = $41.3
For the functions below, what is the direction of fastest increase at (1, 1, 1)? (a) f(x, y, z) = 1/x² + y² + 22
(b) f(x, y, z) = 4xy + 4yz + 4xz 6 (c) f(x, y, z) x2 + y2 + z2
Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.
For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[2/x³, 2y, 22] = [2, 2, 22].
The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].
Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[2x, 2y, 2z] = [2, 2, 2].
As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.
Step-by-step explanation:
What are the domain and range of the logarithmic function?
The domain and range of the logarithmic function is given by:
Domain= [ 0 , ∞ ) and Range = { y ∈ R }.
As given in the question,
Let y = logₐ x be the given logarithmic function.
Logarithmic function is defined for all the positive values.
Domain of the logarithmic function is given by x∈ R , x > 0.
Range of the logarithmic function is inverse of the domain of the exponential function.
x = e^y
Here y is set of all the real numbers.
Range of logarithmic function is set of all the real numbers.
Therefore, domain of the logarithmic function is set of all real number greater than zero and range of the logarithmic function is the set of all the real numbers.
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What is a 2 step equation example?
The general two steps to solve the two-step equations are:
Step 1: Addition and subtraction to isolate the variable.
Step 2: Multiplication or division to determine the value of the variable.
Now, According to the question:
Solving Two Step Equations:
Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:
Step 1: Addition and subtraction to isolate the variable.
Step 2: Multiplication or division to determine the value of the variable.
Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:
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If $3x 7\equiv 2\pmod{16}$, then $2x 11$ is congruent $\pmod{16}$ to what integer between $0$ and $15$, inclusive
2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.
If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.
To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.
First, we can solve for x in the given equation:
3x 7 is congruent to 2 mod 16
3x is congruent to 2 mod 16
x is congruent to 6 mod 16
Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:
2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16
So the solution is that 2x 11 is congruent to 13 mod 16.
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Tom is adding soil to his raised garden bed. The depth of the soil is currently 8 inches, and for each bag of soil he adds, the depth will increase by 1/2 of an inch. You can use a function to describe the depth of the soil in the garden bed after Tom adds x bags of soil.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x.
The function that describes the depth of the soil is h(x) = -(1/2)x + 8.
Where x is the number of bags of soil.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Depth of the soil = 8 inches
One bag of soil increases by 1/2 of an inch.
Now,
The function denotes the depth of the soil.
h(x) = -(1/2)x + 8
Where x is the number of bags of soil
Thus,
The function is h(x) = -(1/2)x + 8.
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5
1 point
Eliana measures outdoor temperatures in an area each day for a week at exactly 2:00 p.m. The
temperatures she records are all between 25 °C and 30 °C. Eliana concludes that the climate of the
area is tropical.
What is the most important reason why her conclusion might not be correct?
she made her conclusion based only on temperature and not also on precipitation
she took the temperature readings at the same time each day
she made her conclusion based on only one week of data instead of over a long period of
time
she did not calculate the average of her data
It is possible for a valid argument to have a false conclusion as long as at least one premise is false.
Conclusions might be true or erroneous.?When the premises are genuine, validity guarantees a true conclusion; when the premises are wrong, validity provides no assurance. Even in a legitimate argument, faulty premises might lead to either a true or erroneous conclusion. In many cases, it was chance rather than reasoning that led to the correct conclusion.
Avoid including: Important evidence or analysis that was not provided in the main body for a stronger conclusion paragraph.Generic closing phrases (for example, “In conclusion…”)Weak remarks that undercut your argument (for example, “There are valid points on both sides of this debate.”)
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Work out the equation of the line shown below.
Give your answer in the form y = mx + c, where m and c are
integers or fractions in their simplest forms.
to get the equation of any straight line, we simply need two points off of it, let's use those from the picture below.
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{-100})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{140}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{140}-\stackrel{y1}{(-100)}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{(-10)}}} \implies \cfrac{140 +100}{30 +10} \implies \cfrac{ 240 }{ 40 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-100)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-10)}) \\\\\\ y +100 = 6 ( x +10)\implies y+100=6x+60\implies {\Large \begin{array}{llll} y=6x-40 \end{array}}[/tex]
Evaluate the expression 2(b+4), when b=5
The evaluation of the expression 2(b + 4) when b = 4 is 18
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: 2(b + 4)
Values: b = 5
Substitute the known values in the above equation, so, we have the following representation
2(b + 4) = 2 * (5 + 4)
Evaluate the products
This gives
2(b + 4) = 10 + 8
Evaluate the like terms in the equation
So, we have the following representation
2(b + 4) = 18
Using the above as a guide, we have the following:
The solution is 18
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Suppose x is 5 and y is 7. Choose the value of the following expression: (x != 7) && (x <= y) a. false b. true c. 0 d. null Suppose that x is an int variable. Which of the following expressions always evaluates to true? a. (x > 0) || ( x <= 0) c. (x > 0) && ( x <= 0) b. (x >= 0) 11 (x == 0) d. (x > 0) && (x == 0)
1)correct option is b) true
2)Which of the following expressions always evaluates to true?
correct option is d)(x > 0) && (x == 0)
given that
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Many authors make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects.
x = 5 and y = 7
Choose the value of the following expression: (x != 7) && (x <= y)
a. false
b. true
c. 0
d. null
(5! = 7) && (5<=7)
5 ≠ 7
correct option is b) true
Suppose that x is an int variable.
Which of the following expressions always evaluates to true?
a. (x > 0) || ( x <= 0)
b. (x > 0) && ( x <= 0)
c. (x >= 0) 11 (x == 0)
d. (x > 0) && (x == 0)
a) x = 1,2,3.... || x =0,-1,-2,-3......
b)x = 1,2,3.... && x = 0,-1,-2,-3,.....
c) x = 0,1,2,3..... 11 x = 0
d) x = 1,2,3.... && x = 0
correct option is d)(x > 0) && (x == 0)
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It is known that the percent of red M&Ms is 35% in each package. Don went to the vending machine and bought a package of M&Ms. In his package he counted 52 MaMs and 18 were red. If 35% is the true parameter then what is the probability that a package of getting no more than 18 out of 52 M&Ms red?
35% in each package is red.
that means nothing else than for every M&M you pick, the probability is 35% (or 0.35) that is is red.
it also means the probability to get anything but red is 1 - 0.35 = 0.65 (65%).
if I understand you correctly, the question is for the probability that there are no more than 18 red M&Ms in a package of 52.
in other words, the probabilty that there are exactly 18, or exactly 17, or exactly 16 ... or exactly 1, or no red M&Ms.
the probability to get exactly 18 red out of 52 is
0.35¹⁸ × 0.65³⁴
for one of the combinations.
and we have C(52, 18) possible combinations :
52! / (18! × (52-18)!) = 52! / (18! × 34!)
18 red = 0.35¹⁸ × 0.65³⁴ × C(52, 18) = 0.115457378...
17 red = 0.35¹⁷ × 0.65³⁵ × C(52, 17) = 0.110273578...
16 red = 0.35¹⁶ × 0.65³⁶ × C(52, 16) = 0.096708177...
15 red = 0.35¹⁵ × 0.65³⁷ × C(52, 15) = 0.077665254...
14 red = 0.35¹⁴ × 0.65³⁸ × C(52, 14) = 0.056935055...
13 red = 0.35¹³ × 0.65³⁹ × C(52, 13) = 0.037956703...
12 red = 0.35¹² × 0.65⁴⁰ × C(52, 12) = 0.022909582...
11 red = 0.35¹¹ × 0.65⁴¹ × C(52, 11) = 0.012452595...
10 red = 0.35¹⁰ × 0.65⁴² × C(52, 10) = 0.006056874...
9 red = 0.35⁹ × 0.65⁴³ × C(52, 9) = 0.002615926...
8 red = 0.35⁸ × 0.65⁴⁴ × C(52, 8) = 0.000993712...
7 red = 0.35⁷ × 0.65⁴⁵ × C(52, 7) = 0.000328083..
6 red = 0.35⁶ × 0.65⁴⁶ × C(52, 6) = 9.271902896e-005
5 red = 0.35⁵ × 0.65⁴⁷ × C(52, 5) = 2.198201902e-005
4 red = 0.35⁴ × 0.65⁴⁸ × C(52, 4) = 4.252473918e-006
3 red = 0.35³ × 0.65⁴⁹ × C(52, 3) = 6.446899235e-007
2 red = 0.35² × 0.65⁵⁰ × C(52, 2) = 7.183687719e-008
1 red = 0.35 × 0.65⁵¹ × C (52, 1) = 5.231817386e-009
0 red = 0.35⁰ × 0.65⁵² × C(52, 0) =
= 0.65⁵² = 1.868506209e-010
the probability to have no more than 18 reds is the sum of all that :
0.540472593...
13. Solve:* 3b⁴ x 6b² =
Answer:
18b^6
Step-by-step explanation:
3b⁴ x 6b²
What is the solution to this system of linear equations x − 3y − 2x 3y 16?
solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9
What is linear equation?An algebraic expression that shows a relationship between two variables that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.
.
What is the solution of the system of linear equation?we are given, two linear equations x - a -3y = 0
and a - 2x -3y - 16 =0
from the first equation, x = a + 3y
we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0
a - 2a - 6y - 3y -16 = 0
- a - 9y -16 =0
- (a + 16) = 9y
y = - (a+16) / 9
now we put the value of y in the equation, x = a + 3y
get, x = a+ 3 [ - (a+16)] / 9
x = a + [ - (a+16)] / 3
x = (3a - a -16) / 3
x = (2a - 16)/ 3
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Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. Which describes the solution set of the inequality.
Answer:
It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.
To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:
5(-0.3) + 1.5 ≥ 4
This simplifies to:
-1.5 + 1.5 ≥ 4
Which further simplifies to:
0 ≥ 4
Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.
Step-by-step explanation:
What is a real solution set?
A solution set is the set of all variables or numbers that makes the equation true.
What is a real number solution set?If solving a linear equation leads to a true statement is equal to 0 = 0 the equation is an identity. Its solution set is all real numbers.A solution set is the set of values that satisfy a given set of equations or inequalities. The feasible region of a constrained optimization problem is the solution set of the constraints.
How many real solutions are possible?There are three possibilities for the number of real solutions of a quadratic equation, and those are that a quadratic equation can have no real solutions, exactly one real solution, or exactly two real solutions.Zero is considered to be both a real and an imaginary number.
Now we can find solution set by solving the equation.
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What are the 3 steps to solving a two step equation?
Answer:
Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes
1.3584655000
2.85760000
3.146737000
4.5555627000
5.7777000
please help
Step-by-step explanation:
1. Eliminate any constant that is on the same side as the variable.
2. Use inverse operations to isolate the variable by itself.
3. Whatever you do to one side you do to the other.
Today you ran seven-eighths of a mile. Yesterday you ran three-fourths of a mile. How much farther did you run today?
You ran 1/8 of miles more today than yesterday.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
Miles you ran yesterday is three fourths of a mile.
Let 1 mile be M.
Miles you ran yesterday = 3/4 M
Today you ran seven-eighths of a mile.
Miles you ran today = 7/8 M
Difference of miles = 7/8 M - 3/4 M
3/4 is same as 6/8.
Difference of miles = 7/8 M - 6/8M
= 1/8 M
Hence you ran 1/8 of miles more than yesterday.
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hello!!!! please help me with this- i will you give brainlist :]
The completed blanks in the statement are underlined as follows
Standard form: x⁶ + 53x⁵ + 2x⁴ - 2The degree is 6 . The leading coefficient is 1This is called a polynomial because it has 4 termsHow to complete the blanks in the statementFrom the question, we have the following parameters that can be used in our computation:
A mathematical expression
The mathematical expression is given as
2x⁴ + 53x⁵ - 2 + x⁶
The standard form
To do this, we rearrange the expression from the highest power to the least
So, we have the following representation
x⁶ + 53x⁵ + 2x⁴ - 2
The degree
This is the highest power in the expression
So, the degree is 6
The leading coefficient
This is the coefficient of the term that has highest power of x
So, the leading coefficient is 1
The name of the expression
The expression has 4 terms
So, the name is a polynomial
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We have a drawer with 30 pairs of different socks. How many (individual) socks do we need to pull from the drawer before getting one pair for certain
Answer:
60 because their a 2 induivedinal in 1 sock.
Step-by-step explanation:
30 x 2 = 60
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 112.
x+4
The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
perimeter of a rectangle = length + length + width + width
length + length + width + width = perimeter of a rectangle
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
So ,The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
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7. $5,000 was invested at a simple interest
rate. In 15 years, the account was worth
65 hundred dollars. What was the interest
rate?
A 0.2%
B 1.5%
C 2%
D 2.15%
Answer:
C. 2%
Step-by-step explanation:
(6500-5000) / 15 / 5000 x 100% = 1500 / 15 / 5000 x 100% = 100 / 5000 x 100% = 0.02 x 100% = 2%
find the area of the rectangle whose length is 16cm and breath is 8am
Answer:128 cm^2
Step-by-step explanation:
A boat is traveling due east for 130 miles. The boat travels another 72 miles at a bearing N38E. Determine the distance, direction angle, and bearing of the boat from its original location.
The distance and bearing of the boat from its original location are about 183.33 miles, N71.97°E
What is the bearing of a location?A bearing is a description of the amount by which a north or south headed line is deflected in the eastern or western direction.
The initial direction in which the boat is traveling = Due east
The distance the boat travels in the direction due east = 130 miles
The distance the boat travels in the direction N38°E = 72 miles
Therefore;
The distance the boat has traveled from its original location is found using the law of cosines as follows;
The included angle between the 130 miles distance the boat travels east and the 72 miles distance the boat travels N38°E = 90° + 38° = 128°
Let d represent the distance of the boat from its original location, we get;
d² = 130² + 72² - 2 × 130 × 72 × cos(128°) ≈ 33609.1828181
d ≈ √(33609.1828181) ≈ 183.33
The distance of the boat from its original location is about 183.33 miles
Let the angle formed by the direction of the boat to its destination and the path the boat travels east, according to the law of sines, we get;
183.33/(sin(128°) ≈ 72/(sin(B))
(sin(B)) ≈ 72 × (sin(128°))/183.33
m∠B ≈ arcsin(72 × (sin(128°))/183.33) ≈ 18.03°
The bearing of the boat from its original location is; N(90° - 18.03°)E = N71.97°E
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What does FG mean in functions?
FG stands for Function Generator, which is a device that produces electrical signals with a function of frequencies and amplitudes. It is commonly used in scientific laboratories to generate signals for testing and research purposes.
A function generator is an electrical device used to generate electrical signals with a range of frequencies and amplitudes. It is commonly used in scientific laboratories to generate test signals for testing and research purposes. Function generators typically consist of an oscillator, amplifier, and waveform selector. The oscillator generates a signal of a given frequency and amplitude, while the amplifier adjusts the output voltage. The waveform selector allows the user to choose from a variety of waveforms, such as sine, square, triangle, and sawtooth. Function generators can be used to simulate various types of electrical signals, such as AC and DC signals, as well as a variety of noise signals. They are also used to test various types of electronic components, such as transistors and capacitors, and to conduct research in fields such as telecommunications and signal processing. The acronym FG stands for Function Generator.
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A boy wants a game which cost $180, but he only has 1/3 of the money, how much more money does he need to buy the game?
Answer: $120
Step-by-step explanation:
So you find 1/3 of 180, basically, you multiply them which is 60.
So if he has a third of the money, he has $60, but he needs 180. So we subtract $180 (how much money he needs) from $60 (the money he has). Which is 120 dollars, so the boy needs $120.
Or 2/3 more.
How do you solve this?.....Katherine has a loyalty card good for a 3% discount at her local grocery store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answer:
Step-by-step explanation:
To find the number Katherine should multiply the prices on the tags by to find the price she would have to pay before tax, we need to calculate the inverse of the discount percentage, which is 1 - (discount percentage / 100).
Given that the discount is 3% and we want to find the price after the discount, that means:
1 - (3/100) = 1 - 0.03 = 0.97
So, the number Katherine should multiply the prices on the tags by to find the price she would have to pay, before tax, in one step, is 0.97. Multiplying the price of an item by 0.97 is equivalent to subtracting 3% from the original price, which is the same as finding the final price after the discount.
For example, if an item is priced at $10, Katherine can multiply this by 0.97 to find that the final price she would have to pay before tax is $9.7
10*0.97 = 9.7
SinA + cosA = √2, prove that tanA + cotA = 2
[tex]sin(A)+cos(A)=\sqrt{2}\hspace{10em}tan(A)+cot(A)=2 \\\\[-0.35em] ~\dotfill\\\\ tan(A)+cot(A)=2\implies \cfrac{sin(A)}{cos(A)}+\cfrac{cos(A)}{sin(A)}=2 \\\\\\ \cfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}=2\implies \boxed{\cfrac{1}{cos(A)sin(A)}=2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]sin(A)+cos(A)=\sqrt{2}\implies (~~sin(A)+cos(A)~~)^2=(\sqrt{2})^2 \\\\\\ sin^2(A)+2sin(A)cos(A)+cos^2(A)=2 \\\\\\ 2sin(A)cos(A)+sin^2(A)+cos^2(A)=2\implies 2sin(A)+1=2 \\\\\\ 2sin(A)cos(A)=1\implies \boxed{2=\cfrac{1}{cos(A)sin(A)}}[/tex]
now, another way to look at this identity will be as a unified system of equations
[tex]\begin{cases} (~~sin(A)+cos(A)~~)^2=2\\\\ ~~ ~tan(A)+cot(A)=2 \end{cases}\implies (~~sin(A)+cos(A)~~)^2=tan(A)+cot(A)[/tex]
and we'd end up with the same rigamarole.
Please help
me find the product
Answer:
cant answer sorry i didnt realize it was an equation
Step-by-step explanation:
What is the coefficient of x² in 2 X² x³?
The coefficient of x² in 2 x² x³ is 2 n with number.
2 x² x³
= 2 x² (x³)
= 2 x² (x x x)
= 2 x² x x x
The coefficient of x² is 2.The expression 2 x² x³ can be written as 2 x² (x³). This can be further simplified to 2 x² (x x x). The coefficient of x² is 2, which means that the coefficient of x² in 2 x² x³ is 2. The coefficient of a term is the numerical factor of the term, or the number that is multiplied with the term. In this case, the coefficient of x² is 2, as it is the number multiplied with x².
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Let's say you accepted a part-time job working in a bakery. The baker sells a bag of rolls containing 13 rolls (or a
baker's dozen). The baker made 158 rolls before leaving for the evening. He asks you to make sure each roll is
packaged before going home. What is the greatest number of bags you will need, and should you try to sell any
extra rolls so as not to have leftovers?
Answer:
52 bags and 2 extra
Step-by-step explanation:
Simply divide the no. of rolls by no. of rolls per bag
Answer:
12 bags
Step-by-step explanation:
158 rolls ÷ 13 rolls/bag = 12.15 bags
You will have 12 full bags plus about 2 extra rolls left over, which you can try to sell separately or as a "pack" of 2. Or, you can sell one overstuffed bag with 2 extra rolls in it (for a total of 15 rolls) for a little extra on the price.
please give a step by step explanation please
The radius of a sphere whose surface area is 324*pi cm² is:
R = 9 cm.
What is the radius of the sphere in the image?We know that the surface of a sphere of radius R is given by:
S = 4*pi*R^2
Where pi = 3.14
Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:
S = 324*pi cm² = 4*pi*R^2
We can divide both sides by pi, so we get:
324 cm^2 = 4*R^2
Now we can solve that equation for R, we will get:
R^2= (324 cm^2)/4 = 81cm^2
R = √(81 cm^2)
R = 9cm
The radius of the sphere is 9cm.
Learn more about spheres by reading:
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