Answer:
Provided an explanation below.
The examples are not asking you to solve, only to simplify the expression
For the examples you posted, not sure if you want the solutions are not; I have gone ahead and simplified
[tex]1.\; -8x^3y^5\\\\2\; \dfrac{2y^3}{3}\\\\3.\; They are both equal\\\\4.\; 3x^2\\\\[/tex]
Step-by-step explanation:
First let's understand what an exponent is.
When a number or a term or an expression is multiplied repeatedly by itself, an exponent can be used to represent this situation
for example,
5 x 5 x 5 x 5 x 5 x 5 = 5⁶ since 5 is multiplied by itself 6 times
Here the number being multiplied(5) is called the base and the number of times it is multiplied(6) is called the exponent.
There are some rules regarding exponentiation
1 Zero Exponent
Any number raised to the power zero is 1
[tex]4^0 = 1\\\\123.456^0 = 1\\\\x^0 = 1[/tex]
2. Negative Exponent
If the exponent if negative, the expression is equivalent to the reciprocal of the term raised to the positive exponent
In general
[tex]a^{-m} = \dfrac{1}{a^m}\\\\and\\\\\dfrac{1}{a^{-m}} = a^m\\\\[/tex]
Examples:
[tex]x^-1 = \dfrac{1}{x}\\\\\left({x + y}\right)^{-a} = \dfrac{1}{(x+y)^a}[/tex]
[tex]\dfrac{1}{x^{-3}} = x^3[/tex]
3. Product Rule
When you multiply exponents with the same base the exponents get added
In general
[tex]\displaystyle {a^m a^n = a^{m + n}}[/tex]
Examples
[tex]x^3x^6 = x^{(3+6)} = x^9\\\\[/tex]
4. Quotient Rule
When you divide an exponentiated term by another exponentiated term with the same base the resulting exponent is the difference between the two exponents:
In general
[tex]\dfrac{a^m}{a^n} = a^{m-n[/tex]
Examples
[tex]\dfrac{y^3}{y^2} = y^{3-2} = y^1 = y[/tex]
5. Power Rule 1
An exponent term raised to another power will be the base raised to the product of the two exponents
In general
[tex](a^m)^n = a^{mn}[/tex]
[tex](x^3)^4 = x^{3 \cdot 4} = x^{12}[/tex]
6. Power Rule 2
If the base is the product of two or more terms and the whole expression is raised to a power then each individual term gets raised to that power.
[tex](ab)^m = a^mb^m\\\\(2x^3y^2z^4)^4 = 2^4x^{3.4}y^{2.4}z^{4.4} = 16x^{12}y^8z^{16}[/tex]
7. One exponent
Any term raised to the power 1 is itself
[tex]a^1 = a[/tex]
example: 5¹ = 5
x¹ = x
You may have to use some or all of the rules when confronted with a specific problem
There are plenty of excellent resources on the web which can explain far more lucidly than I can.
Here are a few. Just search for them and you will get the site links
LibreTexts, OpenStax, cK-12.org etc
As for the specific examples you posted:
[tex]1. (4xy^2)(-2x^2y3)\\[/tex]
Multiply the constant coefficients: 4 x -2 = -8Multiply each term with the same base by the other term with the same base[tex]\textrm{2. }\dfrac{6y^2}{18x}\cdot 2xy[/tex]
[tex]\mathrm{Cancel\:}\dfrac{6y^2}{18x}:\quad \dfrac{y^2}{3x}\\\\[/tex]3. Which expression has the greater value?
[tex]2^3.2^5 \; or\; \dfrac{4^7}{4^3}[/tex]
[tex]2^3\cdot2^5 = 2^8\\\\\dfrac{4^7}{4^3}= 4^{7-3}=4^4\\\\\mathrm{Since \;4 = 2^2, 4^4 = (2^2)^4=2^8}[/tex]
[tex]4. \dfrac{\left(3x^{\frac{1}{3}}\cdot 3x^{\frac{7}{3}}\right)}{3x^{\frac{2}{3}}}[/tex]
[tex]\\\\\\\mathrm{Cancel\:the\:common\:factor:}\:3[/tex]A drone rises 18 m every three seconds. After five seconds, the drone is at a height of 40 m how many meters is a drone rise each second
The height rises by the drone each second is 6 meters.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a drone rises 18 m every three seconds. After five seconds, the drone is at a height of 40 m.
The height will be calculated as:-
3 sec = 18 meters
1 sec = 18 / 3 meters
1 sec = 6 meters
Hence, the height in 1 second will be 3 meters.
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A 1.25” diameter shaft is being stretched by a load of 39,000 lb. Calculate the stress on the part.
I got 31784.84108 psi
is this correct?
It has a diameter of 1.25 inches and yield stress of 63,000 psi. Find the variable component stress.
Calculate the stress at the component?alternative the fee of weight for pressure in the formula for stress, σ = F/A, wherein F is the force and A is the vicinity of go-phase.
In easy phrases we can define pressure because the pressure of resistance per unit area, provided by means of a frame against deformation. strain is the ratio of force over area (S =R/A, in which S is the strain, R is the inner resisting force and A is the move-sectional location).
while the forces acting on the frame are trying to squash it's far compression. The method underneath is used to calculate the pressure: strain =force/ cross-sectional location. σ= F/A.
If we are about to layout a beam or a member. We need strain fee to evaluate with extraordinary pass-sectional shapes and distinct material homes to reach at a feasible section.”
Therefore, It has a diameter of 1.25 inches and yield stress of 63,000 psi.
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Salim has a flock of 300 chickens, 15% of which are infected with a virus. He plans on taking an SRS of 7 chickens to test for the virus. Which of the following would find the probability that exactly 4 of the 7 chickens sampled have the virus? Choose 1 answer: (0) (0.15)*(0.85) © ()(0.15)*(0.85) (390) (0.1 (0.15)*(0.85) (0.15) (0.85) (0.15)*(0.85)
The probability of exactly 4 of the 7 hens contracting the disease is ⁷C₄(0.15)⁴(0.85)³.. The ideal response is (A).
How can the binomial distribution be used to calculate probability?
The binomial theorem, which can be expressed as (a + b)n = nC0anb0 + nC1an1b1 + nC2an2b2 +....+ nCna0bn, is the foundation of the binomial distribution.Events must be independent of one another and have probabilities that add up to 1 in order for the probability to be used.
Due to that,There is a 15% chance that the chicken will be affected it is spelled as as,
15% P(infected)
= 15/100
= 0.15
Consequently, the likelihood of avoiding diseased chicken is,
P(not contaminated) = 1 - 0.15= 0.85
Seven chickens in all will be used for the test.
Now, the binomial distribution may be used to determine the likelihood of having exactly 4 sick chickens.
nCxpxqnx is a general expression for the binomial distribution.
n = 7 and x = 4 for the case where p = P(infected) and q = P(not infected) are given
Consequently, the likelihood is given as,
P = 7C4(0.15)4(0.85)3 (Exact 4 are infected).
Therefore, the likelihood that the virus infects precisely 4 out of the 7 chickens sampled is ⁷C₄(0.15)⁴(0.85)³.
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Directions: solve for x round to the nearest tenth
To solve for x in this problem, we need to use the Law of Cosines.
Solve for x round to the nearest tenth?This law states that in any triangle, the sum of the squares of the lengths of the two sides is equal to the square of the length of the third side.In this case, we have two sides, AB and BC, and we need to find the measure of angle A.We can set up the equation as follows:
a² = b² + c² - 2bc cos(x)
We can substitute the values for a, b, and c, which are 22, 10, and 10 respectively. This gives us the equation:
22² = 10² + 10² - 2(10)(10) cos(x)
Simplifying the equation gives us:
484 = 200 - 200cos(x)
Therefore,
200cos(x) = 284
We can divide both sides by 200 to get cos(x) = 1.42.
We can take the inverse cosine of both sides to get x = 54.15°.
Rounding to the nearest tenth, x = 54.
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Ms. Morales bought the kiddie pool shown below for her children. A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
A) 5,832π in.^3
B) 6,561π in.^3
C) 7,776π in.^3
D) 8,748π in.3
The water volume in the kiddie pool is 6561π [tex]in^{3}[/tex], the correct answer is B. 6561π [tex]in^{3}[/tex].
The volume can be found by using cylinder volume formula V = π[tex].r^{2}.h[/tex]
Find the height of the waterSo, the kiddie pool has 6561π [tex]in^{3}[/tex] of water.
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Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle’s name blank and write CNBD for “Cannot be determined” in place of the rule. ∆RED = ∆___ By rule ________
ΔRED ≅ ΔBUL, by rule SSA criterion.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the triangles,
ΔRED and ΔBUL.
And given:
RE ≅ BU
RD ≅ BL
And ∠RDE ≅ ∠BLU.
Hence,
ΔRED ≅ ΔBUL, by SSA criterion.
Therefore, ΔRED ≅ ΔBUL, by SSA criterion.
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find a time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec i
The average velocity of the top of the ladder on this time interval is 8.75.
What is an average velocity?
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
Here, we have
Given: time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec.
v = Δy/Δt = 20 = (0 - √625 - (7+2a)²)/(9-a)
-20 = (-√4(144 - 7a - a²)/(9-a)
10 = √(16 + a)(9 - a)/(9-a)
10 = √(16 + a)/(9 - a)
a = √884/101 = 8.75
Hence, the average velocity of the top of the ladder on this time interval is 8.75.
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I need to understand quadratic graphs. eg. y=x^2 +2x -3
A quadratic graph is a type of parabolic graph that can be represented by the equation y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of this equation is a parabola that opens either up or down, depending on the value of a.
The equation y = x^2 + 2x - 3 is an example of a quadratic graph. It can be written in the standard form of a quadratic equation as y = x^2 + 2x - 3, where a = 1, b = 2 and c = -3.
The x^2 term in the equation is known as the quadratic term, and it is responsible for the parabolic shape of the graph. The x term and the constant term, 2x and -3, respectively, determine the location of the vertex and the direction of the parabola.
The vertex of the parabola is the point where the parabola changes direction. It can be found by using the formula x = -b/2a, which in this case is x = -2/2 = -1 and y = f(-1) = -1.
The graph of y = x^2 + 2x - 3 is a parabola that opens upwards and the vertex of the parabola is (-1,-1)
In summary, a quadratic graph is a parabolic graph represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. The x^2 term gives the parabolic shape to the graph, the x term and the constant term determine the vertex and the direction of the parabola respectively.
Then Venn diagram shows sets shade (A n B) ‘U C’
The diagram of the required shaded region of the Venn representing the set of elements (A ∩ B)' ∪ C, created with MS Word, is attached.
What is a Venn diagram?A Venn diagram consists of circles or curved enclosures, representing sets, located in a universal set which is a rectangle.
The sdets shown in the Venn diagram = Set A, Set B, and Set C
The required region to be shaded in the Venn diagram = (A ∩ B)' ∪ C'
A ∩ B (A intersection B) is the set of elements common to both Set A and Set B
(A ∩ B)' (A intersection B) complement is the set of all elements which are not in the set of elements common to both Set A and Set B
(A ∩ B)' ∪ C (A intersection B) comliment union C; The set of elements not in the intersection of Set A and Set B, but contains the elements in Set C
(A ∩ B)' ∪ C' (A intersection B) comliment union C complement; The set of elements not in the intersection of Set A and Set B, but includes elements in the universal set, excluding all elements in the Set C.
The required shaded region is; A ∩ (B ∪ C)', B ∩ (A ∪ C)' and (A ∪ B ∪ C)'
Please find attached the diagram of the Venn diagram, created with MS Word, with the shaded region representing (A ∩ B)' ∪ C'
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Determine which of the lines, if any, are parallel or perpendicular. Explain. Line a passes through (2, 10) and (4,13). Line b passes through (4,9) and (6, 12) Line c passes through (2, 10) and (4,9). are parallel. The slopes are perpendicular to The slopes are
Line A is parallel to line B
We know, the slope of the line joining two points [tex](x_{1} ,y_{1} )[/tex] , [tex](x_{2} ,y_{2} )[/tex] is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2}- x_{1}}[/tex]
Line A is passing through (2, 10) and (4,13).
The slope of line A
[tex]m_{1} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{13 - 10}{4-2} =\frac{3}{2}[/tex]
Line B is passing through (4,9) and (6, 12)
The slope of line B
[tex]m_{2} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{12 - 9}{6-4} =\frac{3}{2}[/tex]
Line C is passing through (2, 10), and (4,9).
The slope of line C
[tex]m_{3} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{9- 10}{4-2} =\frac{-1}{2}[/tex]
We also know that if the slope of two lines is equal that is [tex]m_{1} = m_{2}[/tex] then the lines are parallel and
if the slope of the two lines has a relation [tex]m_{1} * m_{2} = -1[/tex] , the lines are perpendicular to each other.
Here, since the slope of lines A and lines B are equal.
Hence, line A is parallel to line B.
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The perimeters of a triangle is 19 feet. One side of the triangle is 3 times the second side. The third side is 4 feet longer than the second side. Find the kength of each side?
Answer:
9 ft, 3 ft 7, ft
Step-by-step explanation:
Perimeter = 19 ft
Let side 2 = x
Side 1 = 3x
Side 3 = x + 4
perimeter = 3x + x + x + 4 = 19
5x + 4 = 19
5x = 15
x = 3
Side 1: 3x = 3(9) = 9
Side 2: x = 3
Side 3: x + 4 = 3 + 4 = 7
Answer:
9 ft, 3 ft 7, ft
Find the general solution, in implicit form, to the differential equation dy/dx = 9 + 5x ^1/2 / 8+ (13y)^1/2 x>0, y>0Then, rearrange the solution that you get into the form f (x,y) = C, for some constant C.
A general solution is one which involves the integer 'n' and gives all solutions of a trigonometric equation.
What is general and particular solution of differential equation?A specific differential equation solution is one with the formula y = f(x), which lacks any arbitrary constants. The arbitrary constants a and b are used in the differential equation's general solution, which has the form y = f(x) or y = axe + b.The differential equation's solution can be quickly and easily found by integrating each variable once it has been separated. The formulas are: f(x)dx+g(y)dy=0, where f(x) and g(y) are respectively constants or functions of x and y.Any equation involving the unknown function y=f(x) and one or more of its derivatives is known as a differential equation. A function y=f(x) that satisfies the differential equation when f and its derivatives are replaced into the equation is a solution to a differential equation.Given data :
dy / dx = 9 + [tex]\frac{9 + (5x)^{1/2} }{8 + (13y)^{1/2} }[/tex] ; x > 0
The general solution of a differential equation in implicit form is obtained as follows
dy / dx = h(x) / g(y)
g(y)dy = {8 + (13y)^{1/2}
h(x) dx = {9 + (5x)^{1/2}
F(x,y) = C
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Consider the sampling distribution of a sample ed toward the o th m an obtained by random sampling from an infinite population. This e me that is highly skewed toward the larger values. a. How is the mean of the sampling distribution related to the mean of the population? b. How is the standa rd deviation of the sampling distribution related to the standard deviation of the population? c. How is the shape of the sampling distribution affected by the sample size?
The mean of the sampling distribution is related to the mean of the population, the standard deviation of the sampling distribution is related to the standard deviation of the population and the shape of the sampling distribution is affected by the sample size.
a. The mean of the sampling distribution is related to the mean of the population. The mean of the sampling distribution is an estimate of the population mean and is usually denoted by x⁻. The mean of the sampling distribution is expected to be close to the population mean, as the sample size increases. However, if the sample size is small, there will be more variation in the sample means and the sample mean will not be an accurate estimate of the population mean.
b. The standard deviation of the sampling distribution is related to the standard deviation of the population. The standard deviation of the sampling distribution is an estimate of the population standard deviation and is usually denoted by s. The standard deviation of the sampling distribution is expected to be smaller than the population standard deviation, as the sample size increases. The standard deviation of the sampling distribution is also affected by the sample size, it decreases as sample size increases.
c. The shape of the sampling distribution is affected by the sample size. As the sample size increases, the shape of the sampling distribution becomes more normal and less skewed, regardless of the shape of the population. The larger the sample size, the less spread in the sample means and more likely that the sample mean will be close to the population mean.
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In each of the following scenarios, state what type of distribution should be used to model the response Y: Binomal, Multinomial, Poisson, or Normal. a. The response is if an employed person commutes more than 10 minutes to work. b. The response is how many days a week an employed person commutes more than 10 minutes to work c. The response is how many minutes a week a student studies. d. The response is what blood type a subject is (A,B,AB, or O)
A. Binomial distribution. B. Poisson distribution. C. Normal distribution. D. Multinomial distribution. is the types of distribution as given in the conditon below.
A binomial distribution should be utilized since the answer—whether or not an employed person commutes more than 10 minutes to work—is a yes or no question.
B. The answer is the percentage of days a week on which a working person travels more than 10 minutes to go to work. The Poisson distribution should be utilized since the number of days is a count variable and the mean number of days does not always equal the variance.
C. The answer is the number of minutes a student studies each week. Since the number of study minutes is a continuous variable with an equal mean and variance, the normal distribution should be applied.
D. The answer is the subject's blood type (A,B,AB, or O). Given that there are four alternative outcomes for blood type, multinomial distribution should be employed.
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Point A is 4 miles due west of home. Point B is 6 miles due north of
home. Point C is 7 miles due east of home. Kayla goes on a bike trip
along the triangular path from home to point A, to point B, to Point
C and back to home. How far, in miles, does Kayla travel?
The distance covered on the triangular path to home along point A to B to C is 23.42 miles.
What is Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Given that the trip to home goes from point A to point B and then to point C.
The path traced thus, represents the hypotenuse of the two triangles. Triangle BHA and triangle BCH.
The Pythagorean theorem is given as follows:
a^2 + b^2 = c^2
For triangle BHA substitute the value of a = 4 and b =6.
4^2 + 6^2 = c^2
16 + 36 = c^2
c = 7.21
For triangle BHC, substitute the value of a = 7 and b =6.
7^2 + 6^2 = c^2
49 + 36 = c^2
c = 9.21
Now, from point B to point H the additional distance is 7 miles, hence the total distance traveled is:
D = 7.21 + 9.21 + 7
D = 23.42
Hence, the distance covered on the triangular path to home along point A to B to C is 23.42 miles.
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Consumer Reports gave a report about the life (hours) of size AA batteries in toys. A total of 16 random toys were tested which gave a mean life of 3.58 hours with sample standard deviation of 1.85 hours. a. The packaging for the batteries claims that the AA batteries last around 5 hours in toys. Does the sample differ from the claim? a = .05 b. Would your answer change if a - .001? Explain.
a. To determine if the sample differs from the claim, we can use a hypothesis test. The null hypothesis is that the mean life of the AA batteries in toys is 5 hours, and the alternative hypothesis is that the mean life is different from 5 hours.
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Using a t-test with a significance level of 0.05, we can calculate the t-statistic and the p-value.
The t-statistic is calculated as (mean - hypothesized mean) / (standard deviation / sqrt(sample size))
t = (3.58 - 5) / (1.85 / sqrt(16)) = -2.06
The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true.
p-value = P(t < -2.06) = 0.048
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that the sample mean of 3.58 hours differs significantly from the claim of 5 hours.
b. The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true. If we change the significance level to 0.001, the p-value would be less than 0.001, which would still be less than the new significance level. Therefore the conclusion would still be the same, the sample mean of 3.58 hours differs significantly from the claim of 5 hours.
However, it's worth mentioning that a lower significance level (0.001) would require a stronger evidence against the null hypothesis, therefore it would be more stringent in accepting the alternative hypothesis.
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4y squared - 3y squared
Answer:
y²
Step-by-step explanation:
4y² - 3y² = (4 - 3) × y² = 1y² = y²
find the smallest positive real number $c,$ such that for all nonnegative real numbers $x$ and $y,$ \[\sqrt{xy} c |x - y| \ge \frac{x y}{2}.\]
The smallest positive real number c that satisfies the above inequality is [tex]$c = \frac{2}{\sqrt{xy}}[/tex]
We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized. We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. The smallest positive value that c can take is[tex]$\frac{2}{\sqrt{xy}}$[/tex].
We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized.
We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$c \ge \frac{2}{\sqrt{xy}|x - y|}$[/tex]. The smallest positive value that c can take is [tex]$\frac{2}{\sqrt{xy}}$[/tex].
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The constellation whose stars are used as pointers to the north celestial pole in the northern hemisphere at this time in history is:
A) Ursa Minor, the Little Bear, containing the bright star Polaris.
B) Leo, the Lion, containing the bright star Regulus.
C) Boötes, the Herdsman, containing the bright star Arcturus.
D) Ursa Major, the Big Dipper.
The correct option is (A). The correct answer is Ursa Minor, the Little Bear, containing the bright star Polaris.
Whereas stars spin or revolve from the northern hemisphere is the center of the sky, also known as the North Celestial Pole. Additionally, it marks the precise location of the Polaris or Northern Star constellation in full view. In addition, this served as a point of reference for the construction of sundials in earlier times.
When people go outside, especially at night, and try to find the Polaris constellation, it is evident that the stars close to this star formation circle in an east-to-west direction, in contrast to the northern star, which makes no movement whatsoever as the evening wears on.
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What solid will this lesson focus on?A- rectangular solidB- coneC- regular square pyramidD- triangular prism
Solid will this lesson focus on the regular square pyramid
Regular square pyramid.
The justification is stated below:
Four triangular faces, five vertices, and eight edges make up the typical square pyramid's square base. The main formulae for a square pyramid are volume and surface area.
By definition, a regular square pyramid is one that has a base that is square, meaning that each of its sides is the same length.
Because it has an apex, a height, lateral faces that are congruent isosceles triangles, and slant height, you can tell that it is a pyramid (the altitude of the lateral faces).
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In an office7by 9 chairs have wheels what is the ratio between the number if chairs with wheels and those without wheels
The ratio for number of chairs with wheels and number of chairs without wheels is 7:2.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
The ratio value is given as 7/9.
There are 7/9 chairs that are with wheels.
This means that the total number of chairs is 9.
Out of the 9 chairs 7 chairs have wheels.
The number of chairs that have no wheels is -
Total number of chairs - Number of chairs with wheels
= 9 - 7
= 2
So, the number of chairs with no wheels is 2
The ratio for number of chairs with wheels to no wheels is -
7:2
Therefore, the ratio value is obtained as 7:2.
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Write the equation for the trend line in y=mx+b form.
Answer:
y=3/2x+86
Step-by-step explanation:
y=Mx+b
M is the slope and b is the y intercept. The slope of a line is rise/run, in this case 3/2 and the y intercept is where the line goes through the y axis which for this problem, is 86. So y=3/2x+86
If it took Rachel and David 10 minutes to play a game of checkers, and they started playing at 2:25 P.M., at what time did they finish playing the game?
Answer:
2:35
Step-by-step explanation:
you are gust adding so 25 +10 = 35
A cash bix of$1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. Hiw many each bill does it contain?
Answer:
10 $1 bills
7 $5 bills
Step-by-step explanation:
Let s = number of $1 bills.
Let f = number of $5 bills.
1s + 5f = 45
s = f + 3
f + 3 + 5f = 45
6f = 42
f = 7
s = f + 3 = 7 + 3 = 10
10 $1 bills
7 $5 bills
Graph the system on a separate piece of paper and determine the number of solutions it has. If it has one solution determine its coordinates.
y = x - 3
y = -5x + 3
A) no solution
B) 1 solution (-2 , 1)
C) 1 solution (1 , -2)
D) infinitely many solutions
If there is only one answer, it is the coordinates. y = 1/2x - 1, y = 4x + 6 equals (0,6) (-3/2, 0), and so forth.
What is meant by equations? The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is something like 4 + 6 = 10.Given,
y = 1/2x - 1
y= 4x + 6
You may also rapidly graph them on paper as follows.
To get two points for each line, find the x and y intercepts for each line.
y = 1/2x - 1
(0, -1) (2, 0)
For the next line
y= 4x + 6
(0, 6) (-3/2, 0)
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consider the following function f(x) 6x2 x3 find f' (x) f' (x) ~3x2 + 12x find the equation of the tangent line to the given curve at the point (1, 5). y =
The equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.
The given function is f(x) = 6x2 - x3.
We need to find the equation of the tangent line to the given curve at the point (1, 5).
To find the equation of the tangent line, we need to find the slope of the tangent line. The slope of the tangent line is given by the derivative of the curve at the given point.
The derivative of the given curve is f' (x) = 3x2 + 12x.
Substituting the value of x as 1, we get the slope of the tangent line at (1, 5) as f' (1) = 3(1)2 + 12(1) = 15.
Therefore, the equation of the tangent line at (1, 5) is given by y – 5 = 15(x – 1).
This can be simplified to y = 15x – 10.
Hence, the equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.
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Boris is making iced tea. He has a container that has a volume of 7.6 dm3 to hold the iced tea. Find how many kiloliters of iced tea will completely fill the container. Use the table of conversion facts, as needed.
The capacity of the container is equal to 7.6 × 10⁻³ kiloliters.
How many kiloliters are required to fill a container?
This is a unit conversion question, in which we need to determine how many kiloliters are equivalent to the capacity of a container.
According to capacity tables, a cubic decimeter or 1000 cubic centimeters equals a liter. Then, we can determine the number of kiloliters by using the following cross multiplication:
x = 7.6 dm³ × (1 L / 1 dm³) × (1 kL / 1000 L)
x = 7.6 × 10⁻³ kL
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jim holzman at ace ticket has a few premium seats in the front row. he would like to find out how much extra he can charge for those tickets, relative to identical seats right behind in the second row. to do so, he decided to run a survey.
The price difference, which can then be used to determine the extra he can charge for the front row tickets.
To calculate the price difference between the front row and second row tickets, Jim should first identify the mean price of the second row tickets, P2. He can then compare the mean price of the second row tickets to the mean price of the front row tickets, P1. He can then calculate the price difference between the two rows by subtracting the mean price of the second row tickets from the mean price of the first row tickets, (P1-P2). This will give him the price difference, which can then be used to determine the extra he can charge for the front row tickets.
For example, if the mean price of the second row tickets, P2, is $15 and the mean price of the first row tickets, P1, is $20, then the price difference would be $5, meaning he can charge an extra $5 for the front row tickets.
Formula: Price Difference = P1 - P2
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9 less than 10 and 6 times the letter n
The statement '9 less than 10 and 6 times the letter n' in the mathematical form will be 9 < 10 + 6n.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
The statement is '9 less than 10 and 6 times the letter n'.
Convert the statement into a mathematical form. Then we have
9 < 10 + 6n
Simplify the inequality, then we have
9 < 10 + 6n
6n > - 1
n > - 1/6
The statement '9 less than 10 and 6 times the letter n' in the mathematical form will be 9 < 10 + 6n.
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the following equation can be used to model the deflection of a sailboat mast subject to a wind force:
d^2y/dz^2 = f/2EI*(L-z)^2
where f = wind force, E = modulus of elasticity, L = mast length, and I = moment of inertia. Calculate the deflection if y = 0 and dy/dz = 0 at z = 0. Use parameter values of f = 60, L = 30. E = 1.25*10^8, and I = 0.05 for your computation.
Use mid-point method to find y, up to z = 30, with a step size of 2, Use excel for performing the calculations, and clearly mark the variables
The midpoint method is a numerical integration technique for solving ordinary differential equations. To use it to solve the given equation, we start by discretizing the interval [0, L] into smaller steps of size h = 2, and use the midpoint of each interval to estimate the deflection at that point. Here's the algorithm:
Initialize z = 0, y = 0, and dydz = 0
Repeat the following steps for z = z + h until z = 30:
a. Calculate f1 = dydz
b. Calculate ymid = y + h/2 * f1
c. Calculate f2 = d2y/dz2 = f/2EI * (L-z-h/2)^2
d. Update y = y + h * f2
e. Update dydz = dydz + h * f2
The final value of y is the estimated deflection at z = 30.
The midpoint method is a numerical integration technique for solving ordinary differential equations. To use it to solve the given equation, we start by discretizing the interval [0, L] into smaller steps of size h = 2, and use the midpoint of each interval to estimate the deflection at that point. Here's the algorithm:
Initialize z = 0, y = 0, and dydz = 0
Repeat the following steps for z = z + h until z = 30:
a. Calculate f1 = dydz
b. Calculate ymid = y + h/2 * f1
c. Calculate f2 = d2y/dz2 = f/2EI * (L-z-h/2)^2
d. Update y = y + h * f2
e. Update dydz = dydz + h * f2
The final value of y is the estimated deflection at z = 30.
Plugging in the given parameter values, we have:
f = 60, E = 1.25 * 10^8, I = 0.05, L = 30
h = 2
z = 0, y = 0, dydz = 0
while z < 30:
f1 = dydz
ymid = y + h/2 * f1
f2 = f/2EI * (L-z-h/2)^2
y = y + h * f2
dydz = dydz + h * f2
z = z + h
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