The number of subsets that the set has are 128 subsets.
How to find the number of subsets?First, let's remove the duplicates from the set A. The distinct elements in set A are:
A = {a, r, i, t, m, e, c}
Now, we can find the number of subsets. For each element in the set, we have two choices: either it is included in the subset, or it is not. Therefore, there are 2^n subsets for a set with n distinct elements.
In our case, n = 7, so there are 2^7 = 128 subsets for the given set A.
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A restaurant raises the price of its signature dish by 15%
The new price of the dish is 14.50
What was the original price of the dish?
Answer:
Therefore, the original price of the dish was $12.61.
Step-by-step explanation:
Let the original price of the dish be "x".
After raising the price by 15%, the new price becomes:
x + 0.15x = 1.15x
We know that the new price is $14.50, so we can set up the equation:
1.15x = 14.5
To solve for x, we can divide both sides by 1.15:
x = 14.5 / 1.15
x = 12.61 (rounded to two decimal places)
Compare the -intercepts and the rates of change of the following items.
A.The y-intercepts are the same, but the rates of change are different.
B.The items have the same y-intercept and the same rate of change.
C.The items have different y-intercepts and different rates of change.
D.The rates of change are the same, but the y-intercepts are different.
Answer:
C. The items have different y-intercepts and different rates of change
Step-by-step explanation:
Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.
Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.
Thus, we know that the rates of change are different and the y-intercepts are different for both functions.
NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality part 7a^2
The statement, "t is not less than 7" as an inequality is E. t ≥ 7.
The statement, " the negative of z is not greater than 8" is A. - z ≤ 8 .
How to represent as inequalities ?The statement "t is not less than 7" means that t can be equal to 7 or greater than 7, so we can write this as:
t ≥ 7
Therefore, the correct inequality for the statement is t ≥ 7.
Similarly, the statement "the negative of z is not greater than 8" means that the opposite of z, which is -z, can be equal to -8 or less than -8, so we can write this as:
-z ≤ 8
Multiplying both sides of the inequality by -1 gives:
z ≥ -8
Therefore, the correct inequality for the statement is z ≥ -8.
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Answer:
e) The correct option is: t≥7
The phrase "t is not less than 7" means that t can be equal to 7 or any value greater than 7, but it cannot be less than 7. Therefore, we use the greater than or equal to a symbol (≥) to represent this statement.
here's an explanation of each option:
t = 7: This statement indicates that the value of t is exactly 7. If this statement is true, then t cannot be greater than or less than 7.t > 7: This statement indicates that the value of t is greater than 7. If this statement is true, then t can be any value that is greater than 7.t < 7: This statement indicates that the value of t is less than 7. If this statement is true, then t can be any value that is less than 7.t ≤ 7: This statement indicates that the value of t cannot be greater than 7, but it can be less than or equal to 7. If this statement is true, then t can be 7 or any value less than 7.t ≥ 7: This statement indicates that the value of t cannot be less than 7, but it can be greater than or equal to 7. If this statement is true, then t can be 7 or any value greater than 7.To express the statement t≥7 as an inequality in terms of 7a^2, we can simply multiply both sides by 7a^2, like this:t * 7a^2 ≥ 7 * 7a^2
Simplifying the right-hand side of the inequality, we get:49a^2
Therefore, the inequality in terms of 7a^2 is:t * 7a^2 ≥ 49a^2
Note that this inequality is equivalent to t ≥ 7, which is what we started with.
f) The correct option is:-z ≤ 8
The phrase "the negative of z is not greater than 8" means that -z cannot be greater than 8. In other words, -z is less than or equal to 8. To express this as an inequality, we use the less than or equal symbol (≤) and write "-z ≤ 8".
here's an explanation of each option:
Note that only the first option (-z ≤ 8) accurately represents the original statement "The negative of z is not greater than 8". The other options either represent a different statement or contradict the original statement.
The statement "the negative of z is not greater than 8" can be expressed as an inequality in terms of 7a^2 as follows:
-z ≤ 8
Since we cannot multiply or divide by a negative number when we are working with inequalities, we will multiply both sides of the inequality by -1. Remember that whenever we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality symbol. So, we have:z ≥ -8
Multiplying both sides by 7a^2, we get:7a^2 * z ≥ -8 * 7a^2
Simplifying the right-hand side, we get:-56a^2
Therefore, the inequality in terms of 7a^2 is:7a^2 * z ≥ -56a^2
So, the statement "the negative of z is not greater than 8" can be expressed as the inequality 7a^2 * z ≥ -56a^2.
The sets D and E are given below.
D=(-1.2.4, 5, 8)
E=(-2,2. 3, 4, 6)
Find the union of D and E.
Find the intersection of D and E.
Write your answers using set notation (in roster form).
DUI- D
DAE = D
X
Ø
Ś
Answer:
D∪E = {-2, -1, 2, 3, 4, 5, 6, 8}D∩E = {2, 4}Step-by-step explanation:
You want the union and the intersection of the given sets D and E.
UnionThe union of the two sets is the list of elements in either set. It will contain all of the elements of D along with all of the elements of E, with duplicate values removed so that each element is only listed once.
D∪E = {-2, -1, 2, 3, 4, 5, 6, 8}IntersectionThe intersection of the two sets is the list of elements that appear in both sets. Any element that only appears in one of the sets is not part of the union.
D∩E = {2, 4}<95141404393>
Consider the graph of f(x) = (1/2)^x
Each graph shows the result of a transformation applied to function f where f(x) = (1/2)^x
1) The graph of function g is graph W because it is result of a vertivcal compression applied to graph f.
2) The graph of function g is graph X because it is result of a horizontal shift applied to graph f.
3) The graph of function g is graph Y because it is result of a reflection over y-axis applied to graph f.
4) The graph of function g is graph Z because it is result of a horizontal compression applied to graph f.
Here, a transformation applied to function f where f(x) = (1/2)^x
Consider graph W. We can observe that when the the graph of f(x) is compressed vertically then it will results in the graph of g(x)
Consider graph X. We can observe that if the the graph of f(x) is shifted horizontally right by 2 units then it will results in the graph of g(x)
Consider graph Y. We can observe that the the graph of g(x) is nothing but the reflection of f(x) over x-axis.
Consider graph Z. We can observe that when the the graph of f(x) is compressed horizontally then it will results in the graph of g(x)
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Lanzamos 1000 veces un dado de 6 caras. Calcula la probabilidad de obtener entre 400 y 500 veces un 6.
La probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de 0.
Calculando la probabilidadEste es un problema de distribución binomial con una probabilidad de éxito del evento (obtener un 6 en un lanzamiento de un dado de 6 caras) de 1/6.
Podemos utilizar una aproximación normal para la distribución binomial si el número de ensayos es grande y la probabilidad de éxito es moderada.
La aproximación normal para una distribución binomial se define como:
Z = (X - μ) / σ
donde X es el número de éxitosμ es el valor esperado de Xσ es la desviación estándar de X.El valor esperado de X es:
μ = n * p = 1000 * 1/6 = 166.67
La desviación estándar de X es:
σ = √(n * p * (1-p)) = √(1000 * 1/6 * 5/6) = 11.79
x = 400: z = (X - μ) / σ = (400 - 166.67) / 11.79 = 19.79
x = 500: z = (X - μ) / σ = (500 - 166.67) / 11.79 = 28.27
La probabilidad de obtener entre 400 y 500 éxitos se puede calcular utilizando la tabla de distribución normal estándar o una calculadora de probabilidad normal.
P(400 ≤ X ≤ 500) = P(19.79 ≤ z ≤ 28.27) = 0
Por lo tanto, la probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de aproximadamente 0.
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Q5: Triangle ABC ~ triangle DEF. Use the image to answer the question.
a triangle ABC with side AB labeled 11, side CA labeled 7.6 and side CB labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Determine the measurement of DF.
DF = 1.58
DF = 1.52
DF = 1.1
DF = 5.5
We discard the negative solution, so EF = 8.725. Now we can substitute this value into the
How to solve the question?
To solve this problem, we can use the fact that if two triangles are similar, their corresponding sides are proportional.
We are given that triangle ABC is similar to triangle DEF. Therefore, we can set up the following proportion:
AB/DE = BC/EF = AC/DF
We are given the lengths of AB, AC, and BC, so we can substitute those values into the proportion:
11/DE = 7.9/EF = 7.6/DF
We are asked to find the length of DF, so we can isolate DF by cross-multiplying:
11EF = 7.9DE
7.6EF = 11DF
Now we can set the two expressions for EF equal to each other and solve for DF:
11EF = 7.9DE
11EF/7.9 = DE
1.39EF = DE
7.6EF = 11DF
DF = 7.6EF/11
Substitute the value of DE into the expression for EF:
DF = 7.6(1.39EF)/11
DF = 1.52EF
Now we need to find the value of EF. We can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle E:
angle E = 180 - angle D - angle F
We are not given the measures of angle D or angle F, so we cannot find angle E directly. However, we do know that triangles ABC and DEF are similar, so their corresponding angles are congruent. Therefore, we can use the measures of angles A, B, and C to find the measure of angle D:
angle D = angle A
angle D = 180 - angle B - angle C
Substitute the given values for angles A, B, and C:
angle D = 56.1 degrees
angle D = 116.9 degrees
We can use the Law of Cosines to find the length of EF:
EF²= DE² + DF²- 2(DE)(DF)cos(D)
EF²= 2.2² + (1.52EF)² - 2(2.2)(1.52EF)cos(D)
Substitute the two possible values for angle D:
EF²= 2.2²+ (1.52EF)² - 2(2.2)(1.52EF)cos(56.1)
EF²= 2.2²+ (1.52EF)² - 2(2.2)(1.52EF)cos(116.9)
Simplify both expressions:
EF²= 3.2596 + 2.3104EF²- 5.7024EF
EF²= 3.2596 + 2.3104EF² + 5.7024EF
Solve for EF using either equation:
-0.3104EF² + 5.7024EF - 3.2596 = 0
-0.3104EF² - 5.7024EF + 3.2596 = 0
Solve for EF using the quadratic formula:
EF = (-b ± √(b² - 4ac))/(2a)
EF = (-5.7024 ± √(5.7024² - 4(-0.3104)(-3.2596)))/(2(-0.3104))
EF = 8.725 or EF = -4.185
We discard the negative solution, so EF = 8.725. Now we can substitute this value into the
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Answer:
a. df = 1.52
Step-by-step explanation:
11 / 5 = 2.2
so... you divide the other number by 5
7.6 / 5 = 1.52
making the length of df, 1.52
hope this helps!!! :))))
[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf
The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.
The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]
When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]
When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]
When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.
The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].
Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].
The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]
In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]
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Find an Euler path for the graph. Enter your response as a sequence of vertices in the order they are visited, for example, ABCDEA.
The given graph's Euler path is represented as a series of vertices visited in the following order: EBADCFEACBE.
What is Euler's path?A path in a finite graph known as an Euler path is one that traverses each edge precisely once while yet allowing for the revisiting of vertices.
A similar Euler trace that begins and finishes at the same vertex is known as an Euler circuit or cycle. When Leonhard Euler found a solution to the Seven Bridges of Konigsberg puzzle in 1736, it was first brought up for discussion.
A path known as an Euler path is one that utilises every edge in the graph once and only once. It doesn't have to return to the starting point because it is a path. A circuit that utilises every edge in the diagram once is known as an Euler circuit. As it is a circle, it should start and terminate at the same vertex.
If a graph has no more than two vertices of odd degree, it has an Euler path.
If every vertex has an even degree, the graph has an Euler circuit.
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Each side of a square office is 3 meters long. It will cost $87.41 per square meter to replace the carpet in the office. What would be the total cost to replace the carpet?
As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.
what is a square?The geometric shape of a square has 4 equal ends and four equal, right-angled angles (90 degrees). It is an unusual instance of a rectangle with equal sides. The symbol "" is frequently used to denote a square, which is a two-dimensional figure. A square's area is equal to the sum of its sides doubled, or s2, where s denotes the width of a side. The circumference of a square, or 4s, where s is the height of a side, is the total of the lengths among all four sides. Many real-world uses for squares can be found in the fields of mathematics, architecture, construction, and design.
given
The square office's area is:
[tex]C = 9 \times $87.41 = $786.69[/tex]
A = s2 = 3 2 = 9 metres square
To completely replace the carpet, it would cost:
Cost per square meter equals C = A.
where a square meter costs $87.41. When we change the values, we obtain:
As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.
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if x=4,then find the size of 2x+5-3x
The size of the expresssion 2x + 5 - 3x when x = 4 is 1.
What is the size of the given expression if x equal 4?Given the expression in the question:
2x + 5 - 3x
Also, x = 4
The expression 2x + 5 -3x is an algebraic expression that involves the variable x.
When we substitute x = 4 into the expression, we replace every occurrence of x with 4.
Hence
2x + 5 -3x
Replace x with 4
2(4) + 5 - 3(4)
8 + 5 - 12
Add 8 and 5
13 - 12
Subtract 12 from 13
1
Therefore, when x=4, the size of 2x + 5 - 3x is 1.
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what is 12 plus 12 and take away 67 and then add 24
Answer:
-19
Step-by-step explanation:
First you need to add all of the positive and negative numbers together, which would look like (12+12+24) + (-67) OR 48 + -67. Now add -67 to 48.
-67 + 48 is -19. Therefore the answer is -19.
IM SO SORRY IF THIS DID NOT MAKE SENSE!
Answer:12+12=24
24-67=-43
-43+24=-19
Step-by-step explanation:
Need help on this please
Answer:
Step-by-step explanation:
(-50, -20), (-60, 40)
(40 + 20)/(-60 + 50) = 60/-10= -6
y - (-20) = -6(x - (-50))
jasmine said that commutative property always works for addition but never for subtraction
No, Jasmine is not completely correct. The commutative property states that the order of the numbers can be changed without affecting the result of the operation.
In addition, the commutative property is true: a + b = b + a for any two numbers a and b.
For subtraction, the commutative property is not true in general: a - b is not equal to b - a.
However, there are some special cases where the commutative property does hold true for subtraction. For example, if a and b are equal, then a - b = b - a.
So, in general, Jasmine's statement that the commutative property never works for subtraction is not correct. While it is true that the commutative property does not hold true for subtraction in the same way that it does for addition, there are some special cases where it does apply.
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An item is worth $240 now. This is 30% of what it was originally worth. What was it originally worth?
Suppose the odds for a bet are 11: 1. Your friend tells you that he thinks the odds are too generous. Select all of the odds that are less generous.
Select all that apply.
4:1
6:1
19:1
18:1
In the ratio, the odds that are less generous is C) 19:1 and D)18:1.
What is ratio?
When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.
Here odds for bets are 11:1.
That means if for every $1 you bets, you may wins $11.
There are [tex]\frac{1}{1+11}=\frac{1}{12}=8.33\%[/tex] chance of this happens.
If the friends thinks odds are too generous , then the odds that less than generous are,
=> for 4:1 then [tex]\frac{1}{1+4}=\frac{1}{5}= 20\%[/tex]
=> For 6:1 then [tex]\frac{1}{6+1}=\frac{1}{7}= 14\%[/tex]
=> For 19:1 then [tex]\frac{1}{19+1}=\frac{1}{20}=5\%[/tex]
=> For 18:1 then [tex]\frac{1}{18+1}=\frac{1}{19}=5.2\%[/tex]
Hence the odds that are less generous is C) 19:1 and D)18:1.
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What are the factors of polynomial function g? G(x) = x^3 + 2x^2 - x - 2
To find the factors of the polynomial function g(x) = x^3 + 2x^2 - x - 2, we can use different methods such as long division, synthetic division, or grouping.
Using long division, we can divide g(x) by (x-1), which is a factor by the factor theorem:
x^2 + 3x + 2
___________________________
x - 1 | x^3 + 2x^2 - x - 2
- (x^3 - x^2)
--------
3x^2 - x
- (3x^2 - 3x)
----------
2x - 2
- (2x - 2)
--------
0
Therefore, we have factored g(x) as:
g(x) = (x - 1)(x^2 + 3x + 2)
We can further factor the quadratic term using factoring or quadratic formula to obtain the complete factorization of g(x).
The factors of polynomial function g(x) = x³ + 2x² - x - 2 are (x-1), (x+1), and (x+2).
This can be obtained by factoring the polynomial using the grouping method.
Using this method, we group the first two terms together and the last two terms together, resulting in (x²{2 + 2)(x-1) = 0. This gives us two possible roots, x = 1 and x = ±√2i.
However, as we are only interested in real factors, we only consider the real root of x = 1.
G(x) can then be divided by (x-1) using linear long division, yielding the quotient x² + 3x + 2. This quotient can then be factored as (x+1)(x+2). Therefore, the factors are (x-1), (x+1), and (x+2).
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A slow pitch softball diamond is actually a square 60' on side how far is it from home to 2nd base
Answer:
The distance from home to second base is approximately 84.85 feet in a slow pitch softball diamond that is 60 feet on each side.
Step-by-step explanation:
In a softball diamond that is 60 feet on each side, the distance from home to second base is approximately 84.85 feet. This is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the distance from home to second base forms the hypotenuse of a right triangle with legs that are each 60 / sqrt(2) feet long. Using the Pythagorean theorem, we can calculate that the distance from home to second base is approximately 84.85 feet.
Find the surface area of the figure
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where B = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
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y’all which one is it cus ion kno
How many more calories should a person on a 2000 cal diet eat for veggies then from carbs
Hence, a person on a 2000 calorie diet should eat more calories approximate ratio of 200-300 calories from vegetables and 900-1300 calories from carbohydrates.
What is the calories?A calorie is a measurement, just like a teaspoon or an inch. Calories are the amount of energy released when your body breaks down (digests and absorbs) food. The more calories a food has, the more energy it can provide to your body
How many calories take a person in vegetables and carbohydrates?The number of calories a person should consume from vegetables versus carbohydrates depends on various factors such as age, gender, activity level, body composition, and overall health status. However, in general, it is recommended that a person on a 2000 calorie diet should consume more calories from vegetables than from carbohydrates.
The United States Department of Agriculture (USDA) recommends that adults consume 2.5 to 3 cups of vegetables per day, depending on their age, gender, and level of physical activity. On a 2000 calorie diet, this would amount to approximately 200-300 calories from vegetables.
For carbohydrates, the recommended intake varies depending on the individual's energy needs, but it generally accounts for 45-65% of their total calorie intake. This equates to 900-1300 calories from carbohydrates on a 2000 calorie diet.
Therefore, a person on a 2000 calorie diet should eat more calories from vegetables than from carbohydrates, with an approximate ratio of 200-300 calories from vegetables and 900-1300 calories from carbohydrates.
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any help? i dont seem to understand which radius of circle is.
First of all, radius is half the diameter. Radius is from the center-most point of a circle straight to the edge.
Answer:
The area of the whole object is 1,237.68 m^2 (meters squared).
Step-by-step explanation:
The circles are equal to:
π * d = a
3.14 * 12 = a
37.68 = a.
Now, since the circles are half in the rectangle, it would be easier to calculate the rectangle using these halves, so the total of the half-circles outside the rectangle is equivalent to a whole circle, or 37.68. Now, let's calculate the rectangle:
20 * (30 * 2) = a
20 * 60 = a
1200 = a.
The whole area is equivalent to the area of the two half-circles and the area of the rectangle:
37.68 + 1200 = a
1237.68 = a
what is the MAD of 2,4,4,2
solve as a fraction -2 1/3 - (-5) = ?
Answer:
-2 1/3 - (-5) = -2 1/3 + 5
To add these two numbers, we need to find a common denominator. The common denominator of 3 and 1 is 3.
-2 1/3 can be written as -7/3 using the rule that a mixed number is equal to the sum of the whole number and the fraction.
So, we have:
-7/3 + 5
To add these two fractions, we need to find a common denominator. The common denominator of 3 and 1 is 3.
-7/3 can be written as -7/3 x 1/1 = -7/3.
So, we have:
-7/3 + 15/3 = 8/3
Therefore, -2 1/3 - (-5) = 8/3.
at a store 40% of all the refrigerators are silver. there are 50 silver refrigerants at the store . how many refrigerants are at the store?
Answer:
125
Step-by-step explanation:
50 refrigerators are 40% of all the refrigerators in the store.
5 refrigerators are 4% of refrigerators in the store
125 refrigerators are 100% of refrigerators in the store
therefore there are 125 refrigerators at the store.
6. What measurement do you need to calculate in order to determine the amount
of space each structure encloses? (1 point)
Hence,Volume measurement do you need to calculate in order to determine the amount of space each structure encloses .
What is the volume?We take a measurement of a shape of volume arrangement to discover how much space are contain . The volume of a body is the amount of three - dimensional space that it surrounded and it can be determine by multiplying the shape of length , breath , and width or height.
How to find volume?we can use the equation are Volume = Length x Width x Height to compute the volume of simple structure like as rectangular prisms. It may be necessary to divide more raised structures into simply shapes, determine the volume of each shape, and then add the volumes of each shape to determine the everywhere volume of the construction.
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A business owner applies for a credit card to cover $15,000 in emergency expenses. The credit card charges 17.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
$21,443.51
$21,495.64
$17,934.68
$17,956.46
Answer:
(b) $21,495.64
Step-by-step explanation:
You want to know the value of $15,000 after it has earned continuously compounded interest at 17.99% for 2 years.
Compound continuouslyThe value of an account earning interest at annual rate r compounded continuously is ...
A = P·e^(rt)
where P is the initial account value, and t is the number of years.
ApplicationIn this problem, we have P=15000, r=0.1799, and t=2, so the amount due will be ...
A = $15,000·e^(0.1799·2) ≈ $21,495.64 . . . choice B
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anyone can help with these?
Answer:
m∠B=63 degrees
AC≈23.6 units
AB≈26.4 units
Step-by-step explanation:
since the measures of ∠A and ∠C are given, we add 90 (∠C) to 27 (∠A) and x (∠B) which equals 180 by triangle angle sum theorem.
after isolating the variable, m∠B=63 degrees
we then use law of sin to find AC and AB
since [tex]\frac{sin(A)}{a}[/tex] is already given, use that to find both AC and AB
the equation for AC would be: [tex]\frac{sin(27)}{12} =\frac{sin(63)}{AC}[/tex]
the equation for AB would be: [tex]\frac{win(27)}{12} =\frac{sin(90)}{AB}[/tex]
after isolating the variables, AC≈23.6 units and AB≈26.4 units
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
The equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
How to solveWe can observe from the table that the number of books collected increases by 10 for each week.
Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:
b = mw + c
where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).
The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):
10 = 10 * 1 + c
c = 0
Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
C 17 39 511 -U D 28 4 10 6
Answer:
I'm sorry, but I'm not sure what you are trying to convey with the string of characters "C 17 39 511 -U D 28 4 10 6". It doesn't appear to be a meaningful sentence or question. Could you please provide me with more information or context so I can better understand what you are trying to communicate?
Step-by-step explanation: