Answers
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.
What is semigroup?A semigroup is a mathematical structure consisting of a set of elements along with an associative binary operation. The operation must be associative, meaning that the result of the operation is independent of the order of the operands.
We can prove this by induction. Let S be a semigroup and x1, x2, x3, ..., xn be the elements of S.
Base Case: When n = 2, then the product of x1 and x2 is x1x2.
Inductive Step: Assume that the product of x1, x2, ..., xn (in that order) is equal. Then we can prove that the product of x1, x2, ..., xn+1 (in that order) is also equal.
Let a be the product of x1, x2, ..., xn (in that order). Then a = x1x2x3....xn.
Now the product of x1, x2, ..., xn+1 (in that order) is a x xn+1. Since S is a semigroup, a x xn+1 = x1x2x3....xn x xn+1.
Since the product of x1, x2, ..., xn (in that order) is equal, a = x1x2x3....xn. Therefore, the product of x1, x2, ..., xn+1 (in that order) is also equal.
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.
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Related Questions
What is the Value of X?
Answers
The value of x is found by using the similarity theorem to create a proportion of the sides of the similar triangle, such that: x = 6 cm.
How to Find the Value of x Using Similarity Theorem?Both triangles in the image above are similar to each other based on the AA similarity theorem, which states if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are proportional.
Therefore, we will have:
x/42 = 4/28
Cross multiply:
28x = 168
x = 168/28
x = 6 cm
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2) The subtotal of your computer purchase was $398.50. If the sales tax rate is 7.25%, how much will you pay in tax for the computer?
Answers
The sale tax fοr the cοmputer is $28.89.
What is sale tax?A sales tax is a fee that is paid tο the gοvernment when certain gοοds and services are sοld. Typically, laws permit the seller tο charge the custοmer the tax at the time οf purchase. It is typically referred tο as a use tax when a tax οn gοοds οr services is paid directly tο a gοverning bοdy by a cοnsumer.
Yοur cοmputer purchase cοst $398.50 in tοtal. The sales tax is 7.25 percent.
The sale tax = cοst οf the prοduct × pecentage οf tax
Sales tax = 398.50 × 7.25%
Cοnvert percentages intο fractiοns:
Sales tax = 398.50 × (7.25/100)
Sales tax = 28.89125
sales tax ≈ 28.89
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Let f(x)=x^2+3. Find F(2)
Answers
Answer:
7
Step-by-step explanation:
When you put a value for x in a function, it means that you substitute all terms of x for that value you just substitute for x=2. The x term in the function is x^2, so that squared would be 4. You then add 3, yielding a total result of 7.
Answer:
f(2) = 7
Step-by-step:
Solution :Let f(x)=x^2+3. Find f(2)
[tex] \begin{gathered}{\longrightarrow{f(x)= {x}^{2} +3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= {(2)}^{2} +3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= {(2 \times 2)}+3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= {(4)}+3}}\end{gathered}[/tex]
[tex] \begin{gathered}{\longrightarrow{f(2)= 4+3}}\end{gathered}[/tex]
[tex]\begin{gathered}{\longrightarrow{\underline{\underline{f(2)= 7}}}}\end{gathered}[/tex]
Hence, the value of f(2) is 7.
————————————————Jeriel is driving to a concert and needs to pay for parking. There is an automatic fee of $8 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $3 for every hour he had his car in the lot. How much total money would Jeriel have to pay for parking if he left his car in the lot for 3 hours? How much would Jeriel have to pay if he left his car in the lot for
t
t hours?
Answers
Answer:
Jeriel would have to pay $17
Step-by-step explanation:
t= hours
$3 per t hour +$8 fee
t=3
3(3)+8= $17
How much would Jeriel have to pay if he left his car in the lot for t hours:
3t+8
How much total money would Jeriel have to pay for parking if he left his car in the lot for 3 hours?
$17
Nancy and George (?? relationship) form EB Corporation with the following investments: cash by Nancy of $ ; land by George (basis of $ and fair market value of $ ). EB Corporation issues …. shares of stock,....... each to Nancy and George. Thus, each receives stock in EB worth $. Which of the following statements is correct? [Hints: about section 351?]
Answers
The correct statement is that the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss under section 351 of the IRC, and each shareholder's basis in the stock received would depend on their respective contributions.
What is fair market value and stocks?Fair market value is the amount that a product would sell for on the open market if all parties were acting in their own best interests, were not subject to excessive pressure, and were given a reasonable amount of time to complete the transaction (FMV).
The given scenario describes the formation of a corporation by Nancy and George, where Nancy contributes cash and George contributes land. The corporation issues shares of stock to Nancy and George in exchange for their respective contributions.
Section 351 of the Internal Revenue Code (IRC) provides rules for the non-recognition of gain or loss on the transfer of property to a corporation in exchange for its stock. To qualify for non-recognition, certain requirements must be met, including that the transfer must be made in exchange for stock, and the transferors must be in control of the corporation immediately after the exchange.
Assuming that the requirements of section 351 are met, the transfer of the land by George to the corporation in exchange for stock should not result in any immediate tax consequences. George's basis in the stock received would be equal to his basis in the land transferred. Nancy's contribution of cash would not affect her basis in the stock received.
Therefore, the correct statement is that the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss under section 351 of the IRC, and each shareholder's basis in the stock received would depend on their respective contributions.
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Complete question is: Nancy and George form EB Corporation with the following investments: cash by Nancy of $ ; land by George (basis of $ and fair market value of $). EB Corporation issues shares of stock, each to Nancy and George. Thus, each receives stock in EB worth $.
a. the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss
b. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).
c. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).
d. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).
e. Basis of $ in the EB Corp stock, because her basis exceeded the fair market value of the land she contributed.
Marjorie teaches piano. The equation P = 35s models the
relation between her weekly profit, P, in dollars and the number
of student lessons, s, that she teaches.
a. Find Marjorie's profit for a week when she teaches no
student lessons.
b. Find the profit for a week when she teaches 20 student
lessons.
c. Interpret the slope and P-intercept of the equation.
W
Answers
Marjorie's profit for a week when she teaches no student lessons is $0. Marjorie's profit for a week when she teaches 20 student lessons is $700. The slope of the equation P = 35s is 35
How to calculate the Interpret the slope and P-intercept of the equation.a. To find Marjorie's profit for a week when she teaches no student lessons, we substitute s = 0 into the equation P = 35s:
P = 35(0) = 0
Therefore, Marjorie's profit for a week when she teaches no student lessons is $0.
b. To find the profit for a week when she teaches 20 student lessons, we substitute
s = 20 into the equation
P = 35s:
P = 35(20) = 700
Therefore, Marjorie's profit for a week when she teaches 20 student lessons is $700.
c. The slope of the equation P = 35s is 35. This means that for each additional student lesson Marjorie teaches, her profit increases by $35.
The P-intercept of the equation is 0, which represents the profit Marjorie makes when she does not teach any student lessons.
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b. Write a multiplication equation to show how the length is scaled. 4 This bar shows the length of 8 units scaled in a different way. a. Use words to describe how the length of 8 units is scaled. b. Write a multiplication equation to show how the length is scaled. 1s = 1 × Is X Use th Is 0 53 X Use the 0 Is ³/3 x
Answers
The length of the bar is doubled because it was stretched to twice the length of the original bar.
A multiplication equation that shows how the length is scaled is 2 × 8 = 16.
The length of the bar is halved because it was compressed to one-half the length of the original bar.
A multiplication equation that shows how the length is scaled is 1/2 × 8 = 4.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image (new figure) by the length of the pre-image (original figure):
Since the original bar has a length of 8 units, we can logically deduce that its length became doubled because it was expanded to twice the length of the original bar. Therefore, a multiplication equation to model this expansion is given by:
2 × 8 = 16.
Conversely, the original bar has a length of 4 units, we can logically deduce that its length was halved because it was shrunk to one-half the length of the original bar. Therefore, a multiplication equation to model this compression is given by:
1/2 × 8 = 4.
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The three sides of a triangular fence have lengths 4x + 5, y − 7, and 3x − 2. What is the total perimeter?
A) 7x + y + 10 feet
B) 7x + y − 4 feet
C) 7x + y feet
D) 4x + y − 4 feet
Answers
The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.
What is Perimeter?
Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.
Given : sides of the fence
s₁ = 4x + 5
s₂ = y − 7
s₃ = 3x − 2
We know that, perimeter of a triangle is sum of all three sides.
So, Perimeter of the fence = s₁+ s₂+ s₃
= 4x + 5 + y − 7 + 3x − 2
= 7x + y - 4 ft.
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4. A study by the Technology Services department revealed company employees receive
an average of two emails per hour. Assume the arrival of these emails is approximated
by the Poisson distribution. What is the probability that an employee received 5 or more
emails during the same period?
Answers
She received 5 or more emails in the same time period with a probability of 0.05265.
What is probability?Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
The higher the likelihood, the more likely it is that the event will take place.
So, the probability would be:
We know that λ = 2.
The formula for the poisson distribution states:
P(x = x) = (λˣ * e^⁻ˣ) / x!
P(x = 1) = (2¹ *e⁻²) / 1!
P(x = 1) = (2 * 0.1353352) = 0.2706
Then,
P(x ≥ 5) = 1 - P(x < 5)
1 - P(x < 5) = 1 - [p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4)]
We gather the individual probabilities and combine them. We can use a Poisson distribution calculator to speed up computations:
1 - P(x < 5) = 1 - (0.13534+0.27067+0.27067+0.18045+0.09022)
1 - P(x < 5) = 1 - 0.94735 = 0.05265
P(x ≥ 5) = 1 - P(x < 5) = 0.05265
Therefore, she received 5 or more emails in the same time period with a probability of 0.05265.
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Correct question:
An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. What is the probability she received 5 or more emails during the same period?
Simplify pleaseeee help I need to understand it
Answers
Answer:
hope this helps you a lot
Exo math 30 page 229
Answers
C’est un triangle rectangle donc la formule pour calculer son aire est L x l / 2
Donc 7 x 7,5 = 52.5 m2
Et on divise ça par 2 donc 52.5/2 = 26.25m
TRIANGLE POY:
C’est un triangle rectangle donc on applique la même formule L x l /2 (/ veut dire diviser )
Donc 7 x 4,6 = 32,2m2
Et on divise par 2 : 32,2 / 2 = 16.1 m2
TRIANGLE YOT
C’est un triangle rectangle
Donc on applique le théorème de Pythagore
Le côté OT^2 = YO^2 - YT^2
OT^2= 4,6^2 - 4,2^2
OT^2= 21,16 - 17,64
OT^2 = 3,52
OT= Racine carré de 3,52
Aire de ce triangle :
(4,2 x racine carré de 3,52) / 2
= environ 3,94 m2
TRIANGLE YTU
C’est un triangle rectangle (car les angled droits sont complètementaires )
Donc on applique la formule L x l / 2
Largeur = 4,2 m
Longueur = 7,5 - racine carré de 3,52 = environ 5,62
Donc aire : 4,2 x 5,62 =23,604
23,604 / 2 =13.302
Maintenant on ajoute toute les aires :
26.25 + 16.1 + 3.94 + 13.302
Donc la réponse est 59.592 m2
What factor would you need to multiply by (3d+1) to get 9d^2 + 6d + 1
Answers
Answer:
To get 9d^2 + 6d + 1 from (3d+1), you would need to multiply by 3d+1 again.
Expanding (3d+1)(3d+1), you get:
9d^2 + 3d + 3d + 1
Simplifying, you get:
9d^2 + 6d + 1
Therefore, you need to multiply (3d+1) by (3d+1) or (3d+1)^2 to get 9d^2 + 6d + 1.
Find the equation of the ellipse
Answers
The equation of the ellipse whose vertices are at (-3, -7), and (-3, 5), and focus is at (-3, 1) is; [tex]\frac{(x + 3}{8}+\frac{(y -2}{9} = 1[/tex]
What is standard form of the equation of an ellipse?The equation of an ellipse can be presented as follows;
[tex]\frac{(x - h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]
Where;
(h, k) = The coordinates of the center of the ellipse
a = The semi major axis
b = The semi minor axis
(h, k ± a) = The vertex coordinates
(h ± b, k) = The covertex coordinates
(h, k ± c) = The coordinates of the foci
c² = a² - b²
The vertex of the specified ellipse are; (-3, -1) and (-3, 5)
The focus = (-3, 1)
Therefore;
h = -3k + a = 5
k - a = -1
2·k = 4
k = 4/2 = 2
k = 2k + a = 5
2 + a = 5
a = 5 - 2 = 3
a = 3k - c = 1
2 - c = 1
-c = 1 - 2 = -1
-c = -1
c = 1
c² = a² - b²
Therefore;
1² = 3² - b²
b² = 3² - 1² = 8
b² = 8The equation of the ellipse is therefore;
[tex]\frac{(x - (-3))^2}{8} + \frac{(y-2)^2}{3^2} = \frac{(x + 3)^2}{8} + \frac{(y-2)^2}{9} = 1[/tex]Learn more on the equation of an ellipse here: https://brainly.com/question/27745454
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What is the solution to the system of equations?
3 x minus 4 y = 16. 2 x + 3 y = 5.
Answers
Answer:
It's 5
Step-by-step explanation:
i tootk the test
Step-by-step explanation:
To solve the system of equations:
3x - 4y = 16
2x + 3y = 5
We can use either substitution or elimination method. Here, we will use the elimination method:
Multiply the second equation by 4 to get:
8x + 12y = 20
Now we can add this equation to the first equation:
3x - 4y + 8x + 12y = 16 + 20
Simplifying the left side and adding the right side, we get:
11x = 36
Dividing both sides by 11, we get:
x = 36/11
Substituting this value of x into the second equation, we get:
2(36/11) + 3y = 5
Multiplying through by 11 to eliminate the fraction, we get:
72/11 + 3y = 55/11
Subtracting 72/11 from both sides, we get:
3y = -17/11
Dividing both sides by 3, we get:
y = -17/33
Therefore, the solution to the system of equations is:
x = 36/11, y = -17/33
or in decimal form,
x ≈ 3.27, y ≈ -0.52
8.2
#4
Quadrilateral LMQW is shown.
W
M
mzL-14x-10
mzM-23y-4
m/N - 6x + 22
IF LMNW is a parallelogram,
what is the value of x?
Type your answer as a whole number.
Answers
Answer:
Hi! x = 4
Step-by-step explanation:
the shape is a parallelogram!
so the opposite angles must be the same
therefore, you can equate angle L and angle N to find your x!
Hope this helps
I need the. answer asap
Answers
Answer:
(-7,2)
Step-by-step explanation:
A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 60% magical syrup by volume (and the rest is just water), and a blue potion, which is 30% magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)
(a) Find the amount of red potion (in mL) that must be added to 500 mL of blue potion in order to produce a potion that is 40% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 100 mL of a potion that is 54% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume?
Answers
Taking the quantities by volume of each potion into consideration, we can respectively answer 250ml (A), 40 mL of red and 60 mL of blue potion (B), and no (C).
How to find the solutionFor question A: Let x be the amount of red potion (in mL) that must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3(500) = 150. The total amount of syrup in the final mixture is 0.4(500 + x), and the amount of magical syrup in the final mixture is 0.4x + 150. We can set up the equation:
0.4x + 150 = 0.4(500 + x)
Solving for x, we get x = 250 mL. Therefore, 250 mL of red potion must be added to 500 mL of blue potion to produce a potion that is 40% magical syrup by volume.
For question B: Let x be the amount of red potion (in mL) and y be the amount of blue potion (in mL) that must be combined to produce 100 mL of a potion that is 54% magical syrup by volume. The amount of magical syrup in the red potion is 0.6x, and the amount of magical syrup in the blue potion is 0.3y. The total amount of syrup in the final mixture is x + y, and the amount of magical syrup in the final mixture is 0.6x + 0.3y. We can set up the equations:
x + y = 100 (equation 1)
0.6x + 0.3y = 0.54(100) (equation 2)
Solving for x and y, we get x = 40 mL and y = 60 mL. Therefore, 40 mL of red potion and 60 mL of blue potion must be combined to produce 100 mL of a potion that is 54% magical syrup by volume.
For question C: No, there does not exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume. The amount of magical syrup in the red potion is 60%, which is more than twice the amount of magical syrup in the blue potion (30%). Therefore, any combination of the two potions will always have less than 60% magical syrup by volume.
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carlos pays a monthly fee of 20$, he pays an additonal fee of 0.06 per minute of use. the least he has be charged in a month is 103.10
Answers
$103.10.
Step by step explanation:
Let's assume that Carlos uses "m" minutes in a month.
The additional fee he pays based on the number of minutes he uses would be 0.06 * m.
Therefore, his total cost in a month would be the sum of the monthly fee and the additional fee:
Total cost = Monthly fee + Additional fee
Total cost = $20 + $0.06 * m
We know that the least he has been charged in a month is $103.10.
Therefore, we can set up an inequality:
$103.10 ≤ $20 + $0.06 * m
Solving for "m":
$103.10 - $20 ≤ $0.06 * m
$83.10 ≤ $0.06 * m
m ≥ $83.10 / $0.06
m ≥ 1385
Therefore, Carlos must have used at least 1385 minutes in a month to be charged a minimum of $103.10.
In triangle PQR is equal to QR and angle R is equal to 50° then find the measure of Q
Answers
Answer:
Step-by-step explanation:
Since PQR is a triangle with QR = PQ, we have:
∠PQR = ∠QPR (since the angles opposite to equal sides are equal)
Let x be the measure of ∠QPR. Then:
∠PQR + ∠QPR + ∠R = 180° (sum of angles in a triangle)
x + x + 50° = 180°
2x = 130°
x = 65°
Therefore, the measure of ∠QPR is 65°.
What is the area of the trapezoid?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
________________________________
Answers
Answer:
144inch^2
Step-by-step explanation:
8×8=64
64÷2=32
10×8=80
80+32+32=144
Answer:
144 in
Step-by-step explanation:
Area of a trapezoid: the large base plus the small base multiplied by the height divided by two
small base:10 in
large base: 10+8+8=26
(10+26)×8 = 36×8 = 144 in
2 2
18.75 in 3 significant figures
Answers
Answer:
18.8
Step-by-step explanation:
consider rounding off 7 that becomes 8
Answer:
18.8
Step-by-step explanation:
Yes...Thats the ans...
Answer this question and explain
Answers
Answer:
I’m pretty sure it’s Salma because hers is all positive na the graph is and the graph is in quadrant 1 which is all positive
Lol please help me , cant get this right!!!
Answers
The solution of the quadratic equation x² + 10x -4 found using the quadratic formula is: x = -5 ± √29.
Explain about the quadratic formula?Sometimes, factoring the quadratic, setting its factor equal to zero, but then solving each factor is the quickest way to find the answer to "ax² + bx + c = 0" given the value of x.
Yet, there are situations when the quadratic is too complicated, it just doesn't factor in anyway, or you might not feel like factoring at all. The Quadratic Formula also can provide the solutions for you even when factoring sometimes isn't going to be successful.
The given equation:
x² + 10x -4
The general quadratic equation can be written as:
ax² + bx +c
Then, roots of the equation can be found using quadratic formula:
x = -b±√(b²-4ac))/(2a)
a = 1, b = 10 and c = -4
Put the values:
x = [ -10 ± √(10²- 4*1*(-4))]/ (2*1)
x = [ -10 ± √(100 + 16)]/ 2
x = [-10 ± √116] / 2
x = [-10 ± 2√29] / 2
x = -5 ± √29
Thus, the solution of the quadratic equation x² + 10x -4 found using the quadratic formula is: x = -5 ± √29.
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Use y = 4* to graph log4 x - 3
Answers
Therefore , the solution of the given problem of graphs comes out to be curve of y = 4x – 3 can be plot by y=4x graph.
A graph is what?Graphs are used by theoretical physicists to analytically and graphically display assertions rather than values. Typically, a graph coordinate point shows the relationship between several distinct objects. A graph is a particular kind of pas e carrier construction composed of groups and lines. The borders, also known as the channels, should be joined together with glue.
Here,
The methods below can be used to plot y = log4 x - 3 as a graph:
Move the y-axis of the graph of
=> y = log4 x down 3 units, making the horizontal asymptote y = -3 the new x-axis.
To acquire the graph of
=> y = log4 x – 3, reflect the resulting graph across the line y = x.
Here is a detailed explanation of how to plot y = log4 x - 3:
Diagram y equals 4x:
Plot the following y = 4x key locations first:
=> Y = 40 = 1 when x = 0.
=> If x = 1, then y = 41 = 4.
=> Y = 4-1 = 1/4 when x = -1.
The graph of y = 4x can be easily drawn using just these three values.
The curve of y = 4x is now 3 units lower:
To do this, take each y-coordinate and deduct 3 from it spots on the y = 4x graph. We now have the curve of y = 4x – 3:
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20
Answers
The statement that could be true for g is D. g(-13) = 20.
What statement could be true?
We are given that the function g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, and we also know that g(0) = -2 and g(-9) = 6.
We can use this information to eliminate the statements that are not true and find the one that could be true for g.
A. g(-4) = -11: Since the range of g(x) is between -5 and 45, and g(-4) is less than -5, this statement cannot be true.B. g(0) = 2: We are given that g(0) = -2, so this statement is not true.C. g(7) = -1: 7 is outside the domain of g(x), so we cannot determine the value of g(7).D. g(-13) = 20: Since g(-9) = 6 and the range of g(x) is between -5 and 45, we can see that g(x) increases as x decreases.Therefore, g(-13) is greater than g(-9) and could be 20, so this statement could be true.
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9. Use the expression 32.6 ÷ 10-5 x 8-9.16 to create an expression that includes
a set of parentheses so that the value of the expression is 43.10.
Use the expression 6.3 x 15 ÷ 3+ 6.8-28.09 to create an expression that
includes a set of parentheses so that the value of the expression is 46.25.
Answers
The first parentheses, (10-5), will calculate to 5. The second parentheses, (8-9.16), will calculate to -1.16.
The first parentheses, (3 + 6.8), will calculate to 9.8. The second parentheses, (6.3 x 15), will calculate to 94.
What are Parentheses?Parentheses are symbols used to group numbers or variables together, usually for the purpose of making calculations easier. Parentheses are commonly used to group numbers within an equation or expression and to indicate that certain operations should be performed before or after others. They are also used to clarify the meaning of a mathematical expression or to help identify the parts of an equation.
To create an expression with parentheses so that the value of the expression 32.6 ÷ 10-5 x 8-9.16 is 43.10, the following equation can be used: (32.6 ÷ (10-5)) x (8-9.16) = 43.10. The parentheses are used to ensure that the values within them are calculated first. The first parentheses, (10-5), will calculate to 5. The second parentheses, (8-9.16), will calculate to -1.16. Then the resulting equation will be 32.6 ÷ 5 x -1.16, which will equal -43.10.
To create an expression with parentheses so that the value of the expression 6.3 x 15 ÷ 3 + 6.8 - 28.09 is 46.25, the following equation can be used: (6.3 x 15) ÷ (3 + 6.8) - 28.09 = 46.25. The parentheses are used to ensure that the values within them are calculated first. The first parentheses, (3 + 6.8), will calculate to 9.8. The second parentheses, (6.3 x 15), will calculate to 94.
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The area of a plane shape is given by A=(10x-2)cm square. The area is not greater or equal to 12cm square. It is however not less than 2cm. Find the smallest possible area of this shape
Answers
Answer:
Step-by-step explanation:
We know that the area of the plane shape is given by A = (10x - 2) cm^2, and we also know that:
A is not greater than or equal to 12 cm^2 (i.e., A < 12), and
A is not less than 2 cm^2 (i.e., A > 2).
To find the smallest possible area of the shape, we need to find the smallest possible value of x that satisfies these conditions.
From the given conditions, we have:
10x - 2 < 12
10x < 14
x < 1.4
and
10x - 2 > 2
10x > 4
x > 0.4
Therefore, the smallest possible value of x that satisfies both conditions is:
0.4 < x < 1.4
To find the smallest possible area, we can substitute the lower bound of x into the area formula:
A = (10x - 2) cm^2
A = (10 × 0.4 - 2) cm^2
A = 2 cm^2
Therefore, the smallest possible area of the shape is 2 cm^2.
From the figure find x,y,z, a,b, and c
Answers
A worker's annual income is £3,000 if the first £500 is tax free and on the remaining amount tax is paid at the rate of 5 penny per pound; find the total tax paid by the man. A. £125 B. £150 C. £175 D. £350 E. £650
Answers
Answer:
The taxable income is £3000 - £500 = £2500.
The tax paid at the rate of 5 penny per pound is:
0.05 x £2500 = £125
Therefore, the total tax paid by the man is £125. Answer: A. £125
Step-by-step explanation:
Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Please help!
Answers
Answer: The height of Nasim's kite above the ground is 51.79 feet
Step-by-step explanation
Let h represent the height from Nasim hand to the kite, hence:
sin(28) = h / 105
h = 49.29
Kite height above the ground = 2.5 + 49.29 = 51.79 feet
The height of Nasim's kite above the ground is 51.79 feet
Answer:
The height of Nasim kite above the ground is 51.79 feet
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height from Nasim hand to the kite, hence:
sin(28) = h / 105
h = 49.29
Kite height above the ground = 2.5 + 49.29 = 51.79 feet
The height of Nasim kite above the ground is 51.79 feet