Simplify the expression five to the third power +3(5-3)
Answers
Answer:
Step-by-step explanation:
The expression +3(5-3) can be simplified using the order of operations (PEMDAS) as follows: first, we need to perform the exponentiation operation, which gives us 125.
Then, we need to perform the operation inside the parentheses, which gives us 6. Finally, we multiply 3 by 6, giving us 18. Therefore, the simplified expression is 125 + 18 = 143.
To further explain this solution, we use the order of operations, which is a set of rules that dictate the order in which operations must be performed when evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, which represents the order of operations from left to right.
In this expression, we first need to evaluate the exponentiation operation, which is 5 to the third power. This gives us 125. Next, we need to perform the operation inside the parentheses, which is 5-3. This gives us 2. We then multiply 3 by 2, which gives us 6. Finally, we add 125 and 6, giving us 131.
It is important to follow the order of operations when simplifying an expression to ensure that we obtain the correct result. By using PEMDAS, we can systematically simplify an expression step-by-step, avoiding any potential errors and obtaining a clear and concise solution.
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Related Questions
If 2/3 of a woman’s age is 38 what is her age? Please help quickly I’m in a hurry.
Answers
Answer:
57
Step-by-step explanation:
Multiplying both sides by 3/2 to solve for x will give us her age:
(3/2)(2/3)x = (3/2)*3
x =57
Victoria buys a two-gallon bottle of juice for $48.64. What is the unit rate of the cost of the juice per fluid ounce? 1 gallon = 1 gallon= 4 quarts 4 quarts 1 quart = 1 quart= 2 pints 2 pints 1 pint = 1 pint= 2 cups 2 cups 1 cup = 1 cup= 8 fluid ounces 8 fluid ounces Before you try that problem, answer the question below. How many fluid ounces of juice did Victoria buy?
Answers
Answer:
.19
Step-by-step explanation:
48.64/256=.19
T/F: it is best to plan future activities for the group during the middle of the group
Answers
Answer:
False.
Step-by-step explanation:
It's ok to plan future activities for the group, but it's best to plan in the beginning of the group.
what is x+5=8 step by step
Answers
Answer:
x = 3
Step-by-step explanation:
x+5=8
x+5-5=8-5
X=3
Answer:
x = 3
Step-by-step explanation:
basically 2 ways
1st: Transposing
1) x + 5 = 8
2) transpose or transfer +5 to the other side
NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)
3) x = 8 - 5
x = 3
2nd: Property of Equality (whatever u do one one side, you do the same to the other)
1) x + 5 = 8
2) x + 5 - 5 = 8 - 5
x = 3
the main focus is to isolate x, or to make it be alone in one side of the equation
What is a possible value for the missing term of the geometric sequence?
54, ___, 1944, ...
Answers
Answer:
324
Step-by-step explanation:
The missing term in this geometric sequence is the geometric mean of 54 and 1944.
\( \sqrt{54 \times 1944} = \sqrt{104976} = 324\)
Answer:
324
Step-by-step explanation:
The formula for the missing term in a geometric sequence is the square root of x times y.
given that $n > 1$, what is the smallest positive integer $n$ whose positive divisors have a product of $n^6$?
Answers
The smallest positive integer n whose positive divisors have a product of n^6 is 2^6.
To find the smallest positive integer n satisfying the given condition, we need to consider the prime factorization of n. Since the product of positive divisors is equal to n^6, each prime factor of n must appear with an exponent that is a multiple of 6.
The smallest prime number is 2. If we raise 2 to the power of 6, we get 64, which satisfies the condition. Moreover, there is no smaller prime number that meets the requirement because any smaller prime raised to the power of 6 would result in a larger product.
Therefore, the smallest positive integer n whose positive divisors have a product of n^6 is 2^6, which is equal to 64.
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Steel sheet length 2400 mm, wide 1200 mm, how many number of pieces 300 mm×200 mm for cutting.
6 12 24 48
Answers
The correct answer is 48 pieces.
To determine the number of pieces that can be cut from the steel sheet, we need to divide the dimensions of the steel sheet by the dimensions of each piece to see how many can fit.
Calculate the number of pieces along the length:
The length of the steel sheet is given as 2400 mm, and each piece has a length of 300 mm. By dividing the total length by the length of each piece, we get 2400 mm ÷ 300 mm = 8. This means we can cut 8 pieces along the length of the steel sheet.
Calculate the number of pieces along the width:
The width of the steel sheet is given as 1200 mm, and each piece has a width of 200 mm. By dividing the total width by the width of each piece, we get 1200 mm ÷ 200 mm = 6. This means we can cut 6 pieces along the width of the steel sheet.
Calculate the total number of pieces:
To find the total number of pieces, we multiply the number of pieces along the length by the number of pieces along the width: 8 pieces × 6 pieces = 48 pieces.
Therefore, the correct answer is 48 pieces.
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At theage of 27, to save for retirement, you decibe to deposit %50 at the end of each month in an IRA that pays 5% compounded monthly.
a. Use the following formula to determine how much you will have in the IRA when you retire at age 65.
A= P[(1+r)^t-1] / r or A=P[(t=r/n)^nt-1 / (r/n)
b. Find the interest
Answers
Interest = A - (50 * 456)
To determine how much you will have in the IRA when you retire at age 65, we can use the formula A = P[(1 + r)^t - 1] / r, where A is the future value, P is the monthly deposit, r is the monthly interest rate, and t is the number of months.
a. In this case, the monthly deposit is 50, the monthly interest rate is 5% or 0.05, and the number of months is (65 - 27) * 12 = 456 (from age 27 to 65).
Using the formula, we can calculate:
A = 50[(1 + 0.05)^456 - 1] / 0.05
b. To find the interest, we can subtract the total deposits from the future value:
Interest = A - (P * t)
In this case:
Interest = A - (50 * 456)
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in a survey of 2000 people, 55% of people said they don't watch tv during the week. The survey was used to estimate the number of people in a town of 28408 who don't watch tv during the week. the margin of error is 2.9%. Based on the survey, what are the estimated minimum and maximum of people in this town who don't watch tv.
Answers
The estimated minimum and maximum people who don't watch television in the town would be :
Minimum = 14,804 peopleMaximum = 16, 469 peopleHow to find the maximum and minimum ?According to the survey, 55% of the 2000 people surveyed said they don't watch TV during the week. When applied to the population of the town, we are therefore looking at 55 % not watching tv during the week.
However, we are given a margin of error of 2. 9 % which means the minimum people who abstain from television in the week are:
= ( 55 % - 2. 9 % ) x 28, 408
= 14, 801 people
The maximum would be :
= ( 55 % + 2. 9 % ) x 28, 408
= 16, 448 people
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What is the equation of the line that is perpendicular to a line with a slope of 2 and intersects that line at (4,2)?
Answers
Answer:
y = (-1/2) x + 4
Step-by-step explanation:
Given line has slope 2 so the perpendicular line has the slope is -1/2 because ⊥ lines have their slopes negative reciprocal.
Both lines intersect at (4, 2) so this point belongs to both lines.
→general equation of a line y = mx+b where m = slope, b = y-intercept
→the equation for the line that has slope m = -1/2, is y = (-1/2) x+ b ( we do not know b now but will find it)
→we know that the point ( 4, 2) belongs to this line so the equation works for (x= 4, y= 2), substitute those values in the equation y = (-1/2) x+ b
2 = (-1/2)*4+ b which gives us b = 2+ (1/2)*4= 2+ 4/2 = 2+ 2 = 4
The equation of the line that is perpendicular to a line with a slope of 2 and intersects that line at (4,2) is y = (-1/2) x + 4
What are the vertices of ΔA'B'C' if ΔABC is dilated by a scale factor of 3?
Answers
The vertices of ΔA'B'C' can be found by multiplying the coordinates of the vertices of ΔABC by the scale factor of 3.
Therefore, if the coordinates of the vertices of ΔABC are (x₁,y₁), (x₂,y₂), then the coordinates of the vertices of ΔA'B'C' are (3x₁,3y₁), (3x₂,3y₂), and (3x₃,3y₃). This is because a dilation stretches or shrinks a shape by a factor, and the coordinates of the vertices are affected accordingly.
Step 1: Identify the coordinates of the vertices of ΔABC. Let's assume the vertices are A(x₁,y₁), B(x₂, y₂), and C(x₃, y₃).
Step 2: Multiply each coordinate by the scale factor of 3:
A'(3x₁,3y₁), B'(3x₂, 3y₂), and C'(3x₃, 3y₃).
Step 3: Write down the coordinates of the new vertices A', B', and C' after dilation.
The vertices of ΔA'B'C' are A'(3x₁,3y₁), B'(3x₂, 3y₂), and C'(3x₃, 3y₃).after dilating ΔABC by a scale factor of 3.
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(a) Derive the class equation of a finite group G.
(b) Prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique.
Answers
a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.
b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.
(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).
To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:
|G| = |Z(G)| + ∑ |[a]|
where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].
The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:
Z(G) = {z in G | gz = zg for all g in G}
The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.
The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.
By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.
(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.
If a Sylow p-subgroup is normal, then it is unique:
Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.
If a Sylow p-subgroup is unique, then it is normal:
Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.
Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.
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Which model shows and angle that appears to represent 45/360 of a circle
Answers
A protractor is a tool used for measuring and drawing angles. It is typically a semi-circular piece of plastic or metal with a degree scale marked along its curved edge.
The scale typically ranges from 0 to 180 degrees, which covers half a circle. To measure or draw an angle of 45 degrees, you would line up the protractor's baseline with one arm of the angle and use the degree scale to find 45 degrees. If you are drawing the angle, you would then use a straightedge to extend the other arm of the angle from the point where it intersects the 45-degree mark on the protractor.
It's important to note that the 45-degree angle represents 45/360 of a full circle, which is equal to one-eighth of a full rotation. This means that if you were to rotate the angle around its vertex, it would make one-eighth of a full circle before aligning with its original position.
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HELP LAST QUESTION......
c) The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
The volume of the smallest container is one-third the volume of the largest
container.
The volume of the middle-sized container is two-thirds the volume of the largest
container. What is the volume of each container?
Answers
Answer:
9424.78cm^3
3141.59cm^3
6282.67 cm^3
Step-by-step explanation:
the equation for a cylinder's volume is pi(r)^2(height)
The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3 (remember the units!)
The volume of t he smallest cylinder is 1/3 the largest or: 9424.78/3 = 3141.59cm^3 (remember the units!)
The volume of the medium cylinder is 2/3 the largest or 9424.78(2/3) = 6282.67 cm^3
Explain how can the sum 18 + 81 be rearranged using decomposition to become 27 + 72 without using the sum of 99. [Hint: Below is an example of 16 + 61 can be rearranged to give 25 + 52, where both sums add up to 77 16 + 61 = (15 + 1) + (10 + 51) = (15 + 10) + (1 + 52) = 25 + 52]
Answers
The sum 18 + 81 has been rearranged using decomposition to become 27 + 72 without using the sum of 99.
How to add numbers by decomposition?We are told to explain how the sum 18 + 81 can become 27 + 72 using decomposition.
The decomposition of 18 gives us:
18 = 10 + 8
The decomposition of 81 gives us:
81 = 80 + 1
Arranging the decomposed numbers to form the preferred sum is:
18 + 81 = (10 + 8) + (80 + 1)
Using algebra properties, we can rewrite it as:
(10 + 80) + (8 + 1)
= 27 + 72
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Which of the following tables represents a linear relationship that is also proportional?
(A)
x −1 0 1
y 0 2 4
(B)
x −3 0 3
y −2 −1 0
(C)
x −2 0 2
y 1 0 −1
(D)
x −1 0 1
y −5 −2 1
Answers
Answer: 我不知道你好
Step-by-step explanation:
What is the range of the graph
Answers
Answer:
You're correct the answer is B) \(-5 \leq y \leq -1\)
Step-by-step explanation:
The key behind this problem is think about the function \(\sqrt[3]{x}\) and think what happen when you plug in values in it.
So we're going to try with some simply values for evaluate
\(\sqrt[3]{-8} = -2\)
\(\sqrt[3]-1} = -1\)
\(\sqrt[3]{0} = 0\)
\(\sqrt[3]{1} = 1\)
\(\sqrt[3]{8} = 2\)
How you can see when plug in a negative number the function return a negative number, but when you plug in a positive number the function return a positive number (this isn't a proof of this happen in each value of the given interval, but is a good way of demonstrate the relation). This means that when you plug in a value this value is greater than the value of before, so the function is increasing it's outputs.
Now this is good because that's mean that the limits of the range are the limits of the domain evaluates in the function (because the smaller input give us the smaller output and the same with the greater). But the given function have different operation in it, so you have to interpret this operations of this way:
When you have a negative value in the \(x\) like in this occasion (\(\sqrt[3]{-x}\)) the function reflex it's values with respect to the y axis (image put the functions in a mirror a draw the given image in the same cartesian plane).And you have a -3 this is move each value of the function 3 units down.So with this information you evaluate each limit of the domain \(\{-8, 8\}\) in the function and get the limits for the range.
\(f(-8) = \sqrt[3]{-(-8)} -3= \sqrt[3]{8} -3 = 2 -3 = -1\)
\(f(8) = \sqrt[3]{-8} -3= -2 -3 = -5\)
So the range of the function in the given interval is equal to \(\{-1, -5\}\) in the interval notation is equal to \(-5 \leq y \leq -1\)
Order of operation help I have 4 min left on my timer . NO LINKS
Answers
Answer:
13
Step-by-step explanation:
Just In case you want explanation-
1. 4 squared Meaning 4 x 4 = 16
2. 16 x 6 = 96
3x 6 = 18
96- 18 = 78
in the denominator, 25/ 5 = 5
11 minus 5 = 6
78 divided by 6
it gives you 13
Answer:
13
Step-by-step explanation:
Order of operations:
Parenthesis, exponents, multiplication and division, addition and subtraction
A coach buys a uniform and a basketball for each of the 12 players on the team. Each basketball costs $8. The coach spends a total of $288 for uniforms and basketballs.
Enter the cost, in dollars, of 1 uniform.
Answers
16
Step-by-step explanation:
if you multiply 12 by 8 you get 96 so then you would subtract 96 from 288 and get how much he would spend on all of them then i think you would need to divide 192 from 12 and get 16.so i think the answer is 16 correct me if im wrong
Santosh spent $200, before tax, on a DVD player and DVDs. The player cost $120, new DVDs cost $15 and used DVDs cost $5. Santosh purchased the same number of new and uses DVDs. Write and solve an equation to find the number of each type of DVD Santosh purchased.
Answers
Answer:
Santosh purchased 4 new and 4 used DVDs.
Step-by-step explanation:
From the information given, as you know that Santosh spent $200 and that the DVD player cost $120, you can say that the new and used DVDs cost $80, which can be expressed as:
15x+5y=80, where:
x refers to the number of new DVDs
y refers to the number of used DVDs
Now, as the statement indicates that Santosh purchased the same number of new and used DVDs, this means that x is equal to y and you can replace y with x and solve for x:
15x+5x=80
20x=80
x=80/20
x=4
According to this, the answer is that Santosh purchased 4 new and 4 used DVDs.
Juan compro un plasma en cuotas que costó $8000 si le faltan pagar 3 cuotas y ya pagó $6500 ¿cual es el valor de cada cuotas fijas?
Answers
Answer:
El valor de cada cuota fija es de $500.
Step-by-step explanation:
Para encontrar el valor de cada cuota fija, puedes calcular la diferencia entre lo que Juan ha pagado y el valor que costó el plasma para saber cuál es el monto que aún debe. Después, debes dividir la cantidad que aún debe pagar entre tres que es el número de cuota pendientes para encontrar el valor de cada cuota teniendo en cuenta que son fijas:
8000-6500=1500
1500/3=500
De acuerdo a esto, la respuesta es que el valor de cada cuota fija es de $500.
Answer 1-5 for each! I’ll mark as brainiest
Answers
Answer:
4 because I had this quiz and I got 80
Solve for x in the rectangle below.
Answers
the answer for x is 1
The diameter of a circle is 9 ft. Find its area to the nearest tenth.
Answers
Answer:
= 28.3
Step-by-step explanation:
3.14*9
= 28.26
= 28.3
Sheila needs to spin a number greater than 2 to win. On the game spinner below, what is the probability of her winning?
Answers
Answer:
4
Step-by-step explanation:
I think I'm not sure but please let me know if it is helpful
Which value for the variable w makes the value of this expression 10?
50/w
A. w = 1/5
B. w = 5
C. w = 60
D. w = 500
Answers
Answer:
5
Step-by-step explanation:
50/5=10
therefore 5 is your answer
Answer:5
Step-by-step explanation:
If a family has five girls and plans to have another child, answer the following if the probability of the event of a boy being born is \( \frac{1}{2} \), and births are independent events. a. What is
Answers
In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.
The previous births do not affect the probability of the next birth since each birth is an independent event.
The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.
Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.
In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.
Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.
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There are 14 dogs at the dog park on a busy Saturday. 2 of them are springer spaniels.
What is the probability that a randomly selected dog is a springer spaniel?
Write your answer as a fraction or whole number.
Answers
Answer:1/7
Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.
Due to 14.28% rise in the price of milk, the milkman is able to purchase 20 liters less of milk for Rs. 5600. Find the original price of milk.
Answers
The original price of milk is Rs. 14.
Let the original price of milk be Rs. x and the original quantity of milk purchased be y liters. After the rise, the new price of milk becomes 14.28% + 100% of the original price of milk i.e. (100% + 14.28%) = 114.28% of the original price of milk. Therefore, the new price of milk becomes (114.28/100)*x = 1.1428x. Now, due to the 14.28% rise in price, the milkman is able to purchase 20 liters less of milk for Rs. 5600. Using this information, let's set up an equation as follows:(x/y) - (1.1428x)/(y - 20) = 5600/y where the left-hand side of the equation represents the original cost of the milk minus the new cost of the milk after the price rise. The above equation can be simplified as follows:(x/y) - (1.1428x)/(y - 20) = (5600/y) * (y/(5600 + 20x)).After simplification, the equation becomes :x(y - 20) = (5600 + 20x)*y. Now, substitute the values given in the question to get the original price of milk as follows: x(y - 20) = (5600 + 20x)*y x(y - 20) = 5600y + 20xy - 400xy = 5600yx - 20xy - 5600y = -400xy = (5600y)/(x - 20y) = 5600/400 = 14.
Original price=Rs14
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: Consider the following vector field. F(x,y,z)=5yzlnxi+(9x−8yz)j+xy6z3k (a) Find the curl of F evaluated at the point (7,1,3). (b) Find the divergence of F evaluated at the point (7,1,3).
Answers
(a) The curl of F at the point (7, 1, 3) = 27i + 15ln(7)j - 8k
(b) The divergence of F at the point (7, 1, 3) = 9/7.
(a) To evaluate the curl of the vector field F(x, y, z) = 5yzln(x)i + (9x - 8yz)j + xy^6z^3k, we compute the cross product of the gradient operator with the vector field.
The curl of F is obtained by:
curl(F) = ∇ x F
Let's compute the individual components of the curl:
∂/∂x (xy^6z^3) = y^6z^3
∂/∂y (5yzln(x)) = 5zln(x)
∂/∂z (9x - 8yz) = -8y
Therefore, the curl of F is:
curl(F) = (y^6z^3)i + (5zln(x))j - 8yk
Now, let's evaluate the curl at the point (7, 1, 3):
curl(F) = (1^6 * 3^3)i + (5 * 3 * ln(7))j - 8k
= 27i + 15ln(7)j - 8k
(b) To obtain the divergence of F, we compute the dot product of the gradient operator with the vector field:
div(F) = ∇ · F
The divergence is obtained by:
∂/∂x (5yzln(x)) = 5yz/x
∂/∂y (9x - 8yz) = -8z
∂/∂z (xy^6z^3) = 3xy^6z^2
Therefore, the divergence of F is:
div(F) = (5yz/x) + (-8z) + (3xy^6z^2)
= 5yz/x - 8z + 3xy^6z^2
Now, let's evaluate the divergence at the point (7, 1, 3):
div(F) = 5(1)(3)/7 - 8(3) + 3(7)(1^6)(3^2)
= 15/7 - 24 + 63
= 9/7
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