Only the integer 12 is a divisor of every other integer which is a part of the set S.
This is a classic problem where we are asked to find such an integer that is going to be a divisor of the above set S of integers. The set S of integers consists of those integers that when squared are both divisible by 24 and 108. Now we know 24 can be written as 2*2*2*3 and similarly 108 can be written as 2*2*3*3*3. The smallest perfect square (n^2) which is a multiple of both 24 and 108 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.
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HELPPPP I NEED HELP!!!!
Answer:
مرتم باشگاه ورزشی خیلی علاقه داشتم خیلی قشنگ بی که خیلی تخفیف فایل که خیلی خوعه بچه آخر بی
Answer:
After four bites, Alice would be 256 inches tall.
An exponential function that models this growth would be f (x) = 64.22 where x is the number of bites she takes.
If Alice doesn't take any bites (zero bites), her height would be 64 inches.
are true statements.
If Alice takes two bites, she will be 256 inches tall. is false and After three bites, Alice would be 192 inches tall is also false.
Determine a definite integral that represents the area. region in the first quadrant within the limacon r = 5 + sin(o)
The area of the region in the first quadrant within the limacon r = 5 + sin(o) is 25π/2 + 5π - 2.
The definite integral that represents the area of the region in the first quadrant within the limacon r = 5 + sin(o) is given by:
∫0π/2 (5 + sin(o))2 do
This integral can be evaluated by using the formula for the area of a circle, A = πr2, and converting it to polar coordinates. Since the radius of the limacon is given by r = 5 + sin(o), the area of the region within the limacon is calculated by:
A = ∫0π/2 (5 + sin(o))2 do
= ∫0π/2 (25 + 10 sin(o) + sin2(o)) do
= 25π/2 + 5π - (cos(π/2) - cos(0))
= 25π/2 + 5π - 2
Therefore, the area of the region in the first quadrant within the limacon r = 5 + sin(o) is 25π/2 + 5π - 2.
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The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.
Shawn should use the point-slope formula ⇒ y - y₁ = m(x - x₁) and the y-intercept is -12.
We already know that the point-slope formula goes as such -
⇒ y - y₁ = m(x - x₁)
We have also been told that the slope of the line is 4 and the line passes through the point (1,-8). So, point (1,-8) = (x₁ , y₁) and the slope, m = 4.
Using the given values and the formula of point-slope, we get -
⇒ y - (-8) = 4(x - 1)
⇒ y + 8 = 4x - 4
⇒ 4x - y = -12
⇒ y = 4x - 12
This is the equation of the line.
From this, we get the y-intercept = -12
The complete question that you might be looking for is given below -
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept, and what is the y-intercept of the line?
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Which of the following tables represents a proportional relationship between x and y?
The numbers in table are in proportion. Therefore, option B is the correct answer.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Here,
From the table A:
1/5 = 3/15 = 5/20 = 7/28
1/5 = 1/5 ≠ 1/4 = 1/4
Here, numbers are not in proportion.
From the table B:
3/9 = 5/15 = 7/21 = 8/24
1/3 = 1/3 = 1/3 = 1/3
The numbers are in proportion.
From the table C:
4/12 = 6/18 = 7/28 = 9/36
1/3 = 1/3 ≠ 1/4 ≠ 1/4
The numbers are not in proportion.
From the table D:
2/8 = 3/12 = 4/16 = 5/30
1/4 = 1/4 = 1/4 ≠ 1/6
The numbers are not in proportion.
Therefore, option B is the correct answer.
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Find the recursive formula for the geometric sequence. Then find a5,
2, 14, 98, 686, ...
A) an = an - 1 . 7; 33,614
B) an = an - 1 . 7; 693
C) an = an - 1 . 7; 4,802
D) an = an - 1 . 7; 98
an = an - 1 . 7; 4,802 is the recursive formula for the geometric sequence.
What exactly is a geometric series?
A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.
2, 4, 8, 16, 32, 64,..., which has a common ratio of 2, is an illustration of a geometric sequence.
2, 14, 98, 686, ...
as shown in total
2 * 7 = 14 14 * 7 = 98 98 * 7 = 686
So aₙ = aₙ₋¹
a₅ = a₄ . 7
= 686 . 7 = 4802
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The electric potential as a function of position y in a region of space is given by the equation V(y)=4y2 - 3y. Which of the following is correct for the magnitude of the electric field at position (2,6)?
The electric field is the derivative of the electric potential with respect to position. So we can find the electric field by finding the derivative of V(y) with respect to y.
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variablevariable).
dV/dy = 8y - 3
So, at position y=6, the electric field is E = dV/dy = 8*6 - 3 = 45
Therefore, the magnitude of the electric field at position (2,6) is 45 N/C.
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factorise the following:
4p + 10
Answer:
2(2p+5)
Step-by-step explanation:
4p + 10
taking common values
2(2p+5)
The expression 4p + 10 can be factored by grouping the like terms together.
4p + 10 can be factored as:
2(2p + 5)
This is the prime factorization of the given expression. Here we have factored out the common factor 2 from 4p and 10. This is the most simplified form of the expression.
Solar panel position
For locations between 20° and 60° north latitude a solar collector panel should be mounted so that its angle with the horizontal is 20°
greater than the local latitude. Consequently, the solar panel mounted on a roof forms a 54° angle with the horizontal. The bottom edge of the 12-ft long panel is resting on the roof and the high edge is 5 feet above the roof. What is the total area of the rectangular solar collector panel?
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
A=12h
sin54°= h/5
ℎ= 5 / sin54°
h= sin54° / 5
Therefore: A=12 * sin54° / 5
74.164 feet2
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
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-25 POINTS-
Y=-X+[?]
Don’t need to explain. guessers will be reported
Answer:
the first one is 16=-4+12
from here you can solve
Step-by-step explanation:
Answer:
the answer is 20
Step-by-step explanation:
y= –x+z
1. 16= –4+z
16+4=z
20=z
z=20
2. 15= –5+z
15+5=z
20=z
z=20
z=20 is true
An artist wants to paint a canvas based on a photograph that measures 4 inches by 5 inches. based on the canvas prices listed in the table, the artist could use canvases at which prices to make a painting that is proportional to the photograph? click on the canvas prices you want to select. $6.43, $11.65,$18.47, $22.80.
The artist wants to paint a canvas that is proportional to the photograph, which measures 4 inches by 5 inches.
To calculate the proportionality, we will use the formula for converting inches to centimeters. 1 inch is equal to 2.54 centimeters. Therefore, 4 inches is equal to 10.16 centimeters and 5 inches is equal to 12.7 centimeters. Therefore, the artist should purchase canvases that are 10.16 centimeters by 12.7 centimeters in size. This will correspond to the following canvas prices: $6.43, $11.65, $18.47, and $22.80. By purchasing these canvases, the artist will ensure that the painting is proportional to the photograph.
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During _____________, the cell uses information from messenger RNA to produce proteins. Responses A respirationrespiration B transcriptiontranscription C amino acid sequencingamino acid sequencing D translationtranslation
Answer:
D) During translation, the cell uses information from messenger RNA to produce proteins.
Step-by-step explanation:
Hope it helps! =D
Departmental allocation of overheadThe firm is considering a switch to departmental rates for MOH.XYZ will use machine hours (MH) to allocate Assembly Dept. costs. Of the $2,430,000 of MOH, the firm determined that $1,620,000 is related to the Assembly Dept. and $810,000 is related to the Packaging Dept.• Basic units6,000 MH in Assembly• Deluxe units 30,000 MH in Assembly• Total 36,000 MH in Assemblya) Assembly dept. allocation rate = Assembly dept. MOH allocated to Basic = Assembly dept. MOH allocated to Deluxe= XYZ will use labor dollars (DL$) to allocate Packaging Dept. costs• Basic units $990,000 DL$ in Packaging• Deluxe units $360,000 DL$ in Packaging• Total$1,350,000 DL$ in Packagingb) Packaging dept. allocation rate = Packaging dept. MOH allocated to Basic = Packaging dept. MOH allocated to Deluxe = c) Total cost for Basic = Total cost for Deluxe = d) Cost/unit for Basic = Cost/unit for Deluxe =
Assembly dept. allocation rate = $45 per MH; Packaging dept. allocation rate = $0.60/DL$; Total cost for Basic = $864,000; Total cost for Deluxe = $1,566,000; Cost/unit for Basic = $144/unit; Cost/unit for Deluxe = $52/unit.
a) Assembly dept. allocation rate = $1,620,000 MOH / 36,000 MH = $45 per MH
Assembly dept. MOH allocated to Basic = 6,000 MH * $45/MH = $270,000
Assembly dept. MOH allocated to Deluxe = 30,000 MH * $45/MH = $1,350,000
b) Packaging dept. allocation rate = $810,000 MOH / $1,350,000 DL$ = $0.60/DL$
Packaging dept. MOH allocated to Basic = $990,000 DL$ * $0.60/DL$ = $594,000
Packaging dept. MOH allocated to Deluxe = $360,000 DL$ * $0.60/DL$ = $216,000
c) Total cost for Basic = $270,000 + $594,000 = $864,000
Total cost for Deluxe = $1,350,000 + $216,000 = $1,566,000
d) Cost/unit for Basic = $864,000 / 6,000 units = $144/unit
Cost/unit for Deluxe = $1,566,000 / 30,000 units = $52/unit
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Assume that for dry rice and beans:
1 basin =20 cups
40 basins ≈ 1 sack
(a) A sack contains 100 kg of rice.
Estimate the number of kilograms of rice in 1 başin.
Estimate the number of grams of rice in 1 cup.
(b) A trader buys a sack of rice for 6 000 and sells it at 200 per basin.
Estimate the profit on a sack of rice.
(c) A trader charges #5 000 for a sack and 140 for a basin for beans.
Four women buy a sack of beans between them. They share the beans equally.
How many basins does each woman get?
How much does each woman save by buying the beans in this way?
(a) 1 sack of rice contains 100 kg of rice. If 1 basin of rice is equal to 20 cups, then 1 sack is equal to 40*20 = 800 cups.
Therefore, 1 basin of rice contains 100/40 = 2.5 kg of rice.
1 cup of rice contains 2.5/20 = 0.125 kg of rice.
(b) A trader buys a sack of rice for 6 000 and sells it at 200 per basin. If 1 sack contains 800 cups of rice, then the total revenue from a sack of rice is 800*200 = 160,000.
Therefore, the profit on a sack of rice is 160,000-6,000 = 154,000
(c) A trader charges #5 000 for a sack of beans and 140 for a basin. If four women buy a sack of beans between them, they share the beans equally, so each woman gets 1/4 of a sack of beans, which is equal to 1/440 = 10 basins of beans.
Each woman gets 10 basins of beans which cost 14010 = 1,400. If they had bought the beans individually at 140 per basin, they would have spent 140*10 = 1,400.
So each woman saves 5,000/4 = 1,250 by buying the beans in this way.
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A grocery supplier believes that the mean number of broken eggs per dozen is 0.6, with a standard deviation of 0.5. Olaf buys 3 dozen eggs without checking them.
a. How many broken eggs does Olaf expect to get?
b. What's the standard deviation?
c. Is it necessary to assume the cartons of eggs are independent? Why?
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
a. Olaf expects to get 1.8 broken eggs.
b. The standard deviation is 0.5.
c. Yes, it is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs, and if they are not independent, the probability of one carton containing broken eggs will influence the other cartons.
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
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There were seven serving lines at the
annual pancake breakfast. The total
number of people served at each of
the seven lines were 126, 118, 127, 134,
98, 132, and 121. What was the median
number of people served?
Answer: 126
Step-by-step explanation: Given that the median is the middle number in a sorted, ascending, or descending list of numbers and can be more descriptive of that data set than the average. We know that we need to put the numbers in order from greatest to least or least to greatest first.
Step 1: Ordering the numbers (from least to greatest)
98,118,121,126,127,132,134
Step 2: Finding the value in the middle
98,118,121, 126 ,127,132,134
We now know that 126 is the median number of people served.
Answer: 126 is the median number of people served.
Step-by-step explanation:
The median is found by arranging the data points in a set from lowest to greatest. Once this is done, if there are an odd number of data points, simply find the number in the middle. If there is an even number, find the average of the two middle numbers. Here, you would arrange the numbers as such, 98,118,121,126,127,132,134. Once this is done, since there are seven lines (an odd number of data points, therefore), figure out which number is in the middle, and here it is 126. Hence, the median is 126 (people)
Answer all 3 as soon as any can
The domain of the expression is all real numbers except where the expression is undefined.
How do you find the domain and range?In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).
Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money.
Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range. A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavour will be provided.
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which choice is equivalent to the product below? √6/8 x √6/18
Answer: √6/8 x √6/18
Step-by-step explanation: The square root of A over B is the same as the squared of A, so it's important to know that before I start with this product. To go over the square.
I can do that if I combine the two square roots under the exact square root. This is only for multiplication.
I could take the square root of the term separately
Since I'm using fractions, I'll add the tops and bottoms to the equation.
The square root is eight times 18 and the squared root is six times six. It is the square to 36 over. It's eight times 18. There are 44 items.
The square to 36 is a question. I don't know what time it gives me. There were 36. 36 times six is 6. Six Over would be this. What time gives me 1 44?
Twelve times. 6/12 would be the day. It doesn't want me to reduce that, but I could.
The answer would be 6/12.
Plsssss help number one and two!!!!!!!
According to the Pythagorean Theorem 1. b = 122. a = 1/4 for more detail scroll down.
What is the Pythagorean Theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as an equation: c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
1. To use the Pythagorean theorem to find the length of side b, you can use the equation: c^2 = a^2 + b^2. In this case, c = 15 and a = 9, so you can substitute those values into the equation and solve for b:
15^2 = 9^2 + b^2
225 = 81 + b^2
b^2 = 225 - 81
b^2 = 144
b = sqrt(144)
b = 12
2. In the second case a is unknown and the other two sides are in fraction form, so we can use Pythagorean theorem to find the value of a.
The equation is c^2 = a^2 + b^2
(5/12)^2 = a^2 + (4/12)^2
25/144 = a^2 + 16/144
a^2 = 9/144
a = sqrt(9/144)
a = sqrt(1/16)
a = 1/4
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PLEASE HELP
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the equation -10 + 6( h - 8 ) = -4( 2h + 3 ) to answer Parts A, B, and C below.
Part A: What property can be used to eliminate the parentheses in the equation?
Part B: Solve the equation. Show all work.
Part C: Verify the solution. Show all work.
The distributive property is used eliminate the parentheses in the equation and the solution of the equation is not correct.
What property can be used in the equation?Part A: The distributive property can be used to eliminate the parentheses in the equation.
Part B: Using the distributive property, we get:
-10 + 6h - 48 = -8h - 12
6h + 8h = 48 + 10 -12
14h = 70
Now we divide both sides by 14:
h = 70/14
h = 5
Part C: To verify the solution, we can substitute 5 back into the original equation and see if both sides are equal.
-10 + 6(5 - 8) = -4(2(5) + 3)
-10 + 6(-3) = -4(10 + 3)
-10 - 18 = -4(13)
-28 = -52
Thus, the solution is not correct.
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Answer:
Part A: The distributive property can be used to eliminate the parentheses in the equation.
Part B: Using the distributive property, we get:
-10 + 6h - 48 = -8h - 12
6h + 8h = 48 + 10 -12
14h = 70
Now we divide both sides by 14:
h = 70/14
h = 5
Part C: To verify the solution, we can substitute 5 back into the original equation and see if both sides are equal.
-10 + 6(5 - 8) = -4(2(5) + 3)
-10 + 6(-3) = -4(10 + 3)
-10 - 18 = -4(13)
-28 = -52
Thus, the solution is not correct.
Step-by-step explanation:
what is the value of -6 ^ 3
Answer:
-216
Step-by-step explanation:
[tex]-6^3\\-6*-6*-6 = -216[/tex]
URGENT!!!
Consider the graph of the polynomial function y=f(x) given below. The graph continues forever at both ends. Determine the following features (make sure you write all intervals in interval notation and all intercepts as points):
(A) State the domain and range.
(B) State the x-intercepts.
(C) State the y-intercept.
(D) State the interval(s) for which the function is increasing.
(E) State the interval(s) for which the function is decreasing.
(F) State the interval(s) for which the function is constant.
(G) State any symmetry about any axis and/or the origin.
(H) Determine whether the function is even, odd, or neither.
The features of the given polynomial graph are;
A) Domain: (-∞, ∞)
Range: (-∞, 16)
B) The x-intercepts are; (-2√2, 0), (0, 0), (2√2, 0)
C) The y-intercept is; (0, 0)
D) The interval(s) for which the function is increasing is; (-∞, -2) and (0, 2)
E) The interval(s) for which the function is decreasing. is; (-2, 0) and (2, ∞)
F) The graph has no constant interval.
G) It is symmetrical about the y-axis
H) Even function
How to find the domain and range of a polynomial graph?The domain of a function is defined as the set of all possible input values for which the function holds. The range of a function is defined as the set of all possible output values for all possible input values.
A) The x-values intervals we reckon will be positive and negative infinity as the graph extends till infinity. However, the maximum value of the y-values will be 16 while the minimum is negative infinity.
B) The x-intercepts are the points where the graph crosses the x-axis and they are; (-2√2, 0), (0, 0), (2√2, 0)
C) The y-intercepts are the points where the graph crosses the y-axis and it has the coordinate; (0, 0)
D) Looking at the given graph, it is increasing when the curve rises and in this case it is; (-∞, -2) and (0, 2)
E) Looking at the given graph, it is decreasing when the curve descends and in this case it is; (-2, 0) and (2, ∞)
F) The graph has no constant interval.
G) It is symmetrical about the y-axis
H) The function is an even function
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Jan had 1/4 pound of chocolate and shared it among her eight friends. How much
did each person get?
Zach had eight candy bars and gave each friend 1/4 of a candy bar. How many
people did he share with?
2 and 1/4 chocolate and shared it among her eight friends.
24 people did he share with candy bar.
What is meant by chocolate ?
The cacao tree's seeds are extremely bitter and must be fermented in order to produce a flavorful product.The seeds are dried, washed, and roasted after fermentation. The shell is taken off to create cocoa nibs, which are then ground to create cocoa mass, a kind of pure chocolate.Chocolate liquor is the result of boiling the cocoa material to a liquid state.It is also possible to chill the liquor and separate it into the two ingredients cocoa solids and cocoa butter.Baking chocolate, often known as bitter chocolate, is made only of cocoa butter and solids in different ratios.Dutch cocoa can be made by alkalizing powdered baking cocoa, which has more fiber than cocoa butter.To learn more about chocolate refer to
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Help with homework please!
The exponential depreciation rate to the nearest tenth of a percent is -0.2%.
How to calculate the exponential depreciation rate?we need to use the exponential decay formula to find exponential rate.
A = A0 * e^(-rt)
where:
A0 = initial value of car (52,000)
A = final price of the car (45,000)
t = elapsed time (32 months)
r = exponential depreciation rate
Rearrange the formula to solve for the exponential depreciation rate "r".
r = -ln(A/A0) / t
Insert value:
r= -ln(45,000 / 52,000) / 32
r = -0.067115074/32
r = -0.002097288
The exponential depreciation rate, expressed as a percentage to the nearest tenth of a percent, is obtained by multiplying by 100.
r = -0.002097288 * 100
r = -0.21D
44 Therefore, the exponential depreciation rate to the nearest tenth of a percent is -0.2%.
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Suppose that a sample of size 100 is selected from a population with unknown variance. If this information is used to construct a confidence interval for the population mean, which of the following statements is true?O The sample standard deviation cannot be used to estimate the population standard deviation because the sample size is too small, O The 2-score must be used in computing the limits for the confidence interval O The sample must be normally distributed O The population is assumed to be normally distributed
In the given case, the population is assumed to have a normal distribution.
When creating a confidence interval for the population mean with a sample size of 100, the population is taken to have a normal distribution. This is due to the Central Limit Theorem, which asserts that regardless of the population distribution's form, the distribution of the sample means approaches a normal distribution as the sample size increases.
Therefore, it is safe to infer that the population mean is normally distributed when the sample size is large enough, for instance, n>30. Additionally, it is also ideal to conclude that the population mean has a normal distribution since a sample size of 100 is greater than 30.
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the present age of neha is 4 times the age of her 4 year old son.if her son is presently 14years old, find neha's present age.
Answer: 40
Step-by-step explanation:
Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
y = 3z2 − 3x2
(Write an equation for the cross section at z = −1
using x and y.)
(Write an equation for the cross section at z = 0
using x and y.)
(Write an equation for the cross section at z = 1
using x and y.)
(Write an equation for the cross section at y = −1
using x and z.)
(Write an equation for the cross section at y = 0
using x and z.)
(Write an equation for the cross section at y = 1
using x and z.)
(Write an equation for the cross section at x = −1
using y and z.)
(Write an equation for the cross section at x = 0
using y and z.)
(Write an equation for the cross section at x = 1
using y and z.)
Answer:
Cross section at z = -1: y = 3(-1)^2 - 3x^2 = -3x^2
Cross section at z = 0: y = 3(0)^2 - 3x^2 = -3x^2
Cross section at z = 1: y = 3(1)^2 - 3x^2 = -3x^2
Cross section at y = -1: x^2 = (3z^2+1)/3; x = sqrt((3z^2+1)/3) or x = -sqrt((3z^2+1)/3)
Cross section at y = 0: x = 0;
Cross section at y = 1: x^2 = (3z^2-1)/3; x = sqrt((3z^2-1)/3) or x = -sqrt((3z^2-1)/3)
Cross section at x = -1: z^2 = (3y+1)/3; z = sqrt((3y+1)/3) or z = -sqrt((3y+1)/3)
Cross section at x = 0: z = 0;
Cross section at x = 1: z^2 = (3y-1)/3; z = sqrt((3y-1)/3) or z = -sqrt((3y-1)/3)
Step-by-step explanation:
Let V be the set of functions f : R 5 R. For any two functions f , g in V , define the sum f + g to be the function given by (f + g)(x) = f(x) + g(x) for all real numbers x. For any real number c and any function f in V , define scalar multiplication c f by (cf)x) = cf(x) for all real numbers x. Answer the following questions as partial verification that V is a vector space. (Addition is commutative:) Let f and g be any vectors in V . Then f(x) + g(x) = for all real numbers x since adding the real numbers f(x) and g(x) is a commutative operation. zero vector exists:) The zero vector in V is the function f given by f(x) = for all x_ (Additive inverses exist:) The additive inverse of the function f in V is a function g that satisfies f(x) + g(x) for all real numbers X. The additive inverse of f is the function g(x) for all x. (Scalar multiplication distributes over vector addition:) If c is any real number and and g are two vectors in V , then c(f + g)(x) = c(f(x) + g(x)) =
V is a set of functions that map from [tex]R^5[/tex] to R. It is a vector space because it has a commutative addition operation, a zero vector, additive inverses, scalar multiplication that distributes over vector addition, associativity of vector addition, a multiplicative identity for scalars, and a multiplicative inverse for non-zero scalars.
cf(x) + cg(x) for all real numbers x.
Associativity of vector addition: Let f, g, and h be any vectors in V. Then (f + g) + h = f + (g + h) for all real numbers x.
Existence of a multiplicative identity for scalars: The multiplicative identity for scalars in V is 1, such that for any vector f in V, 1f(x) = f(x) for all real numbers x.
Existence of a multiplicative inverse for nonzero scalars: For any nonzero real number c, there exists a multiplicative inverse 1/c such that c(1/c)f(x) = f(x) for all real numbers x and for any vector f in V.
All these properties are the standard conditions for a vector space, therefore V is a vector space.
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Tickey and Sixpence collected money for charity in the ratio of 5:2 respectively. Sixpence collected R600 less than Tickey. Determine the total amount collected by Tickey and Sixpence.
Answer:
2100
Step-by-step explanation:
let the unknown be x
5 : 2
x. 600
cross multiply
2x=3000
x= 3000
2
x=. 1500 .
Total amount collected= 1500+600
=2100
For a system to be closed under an operation, and when any two elements in the system are combined using the operation, the result must still be an element of that system. For instance, when any two natural numbers (1, 2, 3, . . .), are added together, the result will always be a natural number. When answering the following questions, consider the system of all polynomial equations and the system of all rational equations.
Part A
Which systems are closed under addition? If either system is not closed under addition, provide a counterexample
Part B
Which systems are closed under subtraction? If either system is not closed under subtraction, provide a counterexample.
Part C
Which systems are closed under multiplication? If either system is not closed under multiplication, provide a counterexample.
Part D
Which systems are closed under division? If either system is not closed under division, provide a counterexample.
Part E
Based on which operations the system of polynomial equations is closed under, which system of numbers is most similar to the system of polynomial equations? Explain your answer, and provide any needed counterexamples.
Part F
Based on which operations the system of rational equations is closed under, which system of numbers is most similar to the system of rational equations? Explain your answer, and provide any needed counterexample
The answers to all parts is shown below.
What are Numbers?An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labelling. Thus, mathematics is built on numbers.
1. Real numbers are "closed" under addition Integers are "not closed" under division. Irrational numbers are "not closed" under multiplication. Rational numbers are "closed" under subtraction.
2. Rational numbers are "closed" under subtraction. If an operation is closed under a set of numbers that means that the result of the operation will always be within that same set of numbers.
3. The closure property of multiplication holds for natural numbers, whole numbers, integers and rational numbers.
4. Rational numbers are closed under division as long as the division is not by zero. Irrational numbers are not closed under addition, subtraction, multiplication or division.
5. The whole number system and the polynomial system are nearly identical. Actually, there are not many differences between polynomial functions and our whole number system. We employ a base-10 (decimal) approach for counting. The above-mentioned polynomial is an example of a "base x" system.
6. The system of polynomials is almost the same with the system of whole numbers.
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9. Hachi uses 2 tablespoons of peanut butter on each slice of toast she prepares. Let s represent the number of slices of toast, and let t represent the number of tablespoons of peanut butter she needs. Write an equation to represent this relationship, and use it to determine how many tablespoons of peanut butter she would need for 5 slices of toast.
The following vitamins, minerals, and nutrients are particularly notable in each 2-tablespoon (tbsp) portion of smooth peanut butter: Protein. Protein content per 2-tbsp portion of peanut butter is 7.02 grammes (g).
How much protein is in 2 spoons of peanut butter?Although peanut butter is high in protein, vitamins, and minerals, it may also be quite calorie-dense, salty, and high in unsaturated fat. Given that many commercial brands include sugar and oil additives, low-sugar homemade peanut butter can be a decent alternative.Nutrients included in peanuts and peanut butter could help people with their blood sugar levels and heart health.Depending on how peanut butter is incorporated into a person's diet, it may aid in weight loss or weight gain during bodybuilding or weightlifting.The high calorie and fat content of peanut butter, however, means that it should only be consumed in moderation.In this piece, we examine the advantages of consuming peanut butter and outline its hazards.The Complete Question.
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