Answers
The simplified expression is y.
To solve the expression [tex](x^2 y^5 / x^3 y^8) \times (x^5 y^6 / x^4 y^2)[/tex], we can simplify and perform the necessary operation
Let's break it down step by step:
Step 1: Simplify the expression inside the parentheses.
[tex](x^2 y^5 / x^3 y^8) \times (x^5 y^6 / x^4 y^2)[/tex]can be simplified as follows:
= [tex](x^{(2-3)} y^{(5-8)}) \times (x^{(5-4) }y^{(6-2)})[/tex]
= [tex](x^{(-1)} y^{(-3)}) \times (x^1 y^4)[/tex]
= [tex](1/x y^{(-3)}) \times (x y^4)[/tex]
=[tex]x^0 \times y^{(-3+4)[/tex]
= [tex]1 \times y^1[/tex]
= y
Therefore, the simplified expression is y.
The explanation is as follows:
We can simplify the given expression by applying the laws of exponents. In this case, when dividing two terms with the same base (x or y), we subtract their exponents. Additionally, any term raised to the power of 0 is equal to 1.
After simplifying the expression, we find that the answer is y. This means that the original expression[tex](x^2 y^5 / x^3 y^8) \times (x^5 y^6 / x^4 y^2)[/tex]simplifies to just y.
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Related Questions
Chandler decided to go cliff jumping into the lake at his cottage. He started on the cliff at 32 ft above sea level. He jumped for 40 feet! How far below sea level did Chandler end up?
Answers
Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.
Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.
Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):
32 feet - 40 feet = -8 feet
It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level
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Answer:
-8 feet
Step-by-step explanation:
You are using a magnifying glass that shows the image of an object that is six tin image of the termite seen through the magnifying glass. 9.5 mm The image length through the magnifying glass is millimeters.
Answers
When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.
When using a magnifying glass, the image of an object appears larger. In this case, the termite is being viewed through a magnifying glass that magnifies the image by a factor of six. The actual length of the termite is not mentioned in the given information. However, it is stated that the length of the image seen through the magnifying glass is 9.5 mm.To determine the actual length of the termite, we can divide the length of the image by the magnification factor. Therefore, the actual length of the termite would be 9.5 mm divided by 6, which is approximately 1.58 mm.Therefore, when viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.For more questions on magnifying glass
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Find the measure of the red arc or angle
Answers
The measure of the intercepted arc PS in the circle is 80 degrees.
What is the measure of arc PS?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the diagram:
Inscribed angle R = 40 degrees
Intercepted arc PS = ?
Plug the given value into the above formula and solve for arc PS.
Inscribed angle = 1/2 × intercepted arc.
40 = 1/2 × intercepted arc PS
Intercepted arc PS = 40 × 2
Intercepted arc PS = 80°
Therefore, arc PS measure 80 degrees.
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Verify the identity.
cos x/1+sin x = sec x - tanx
Answers
Answer:
See below for proof
Step-by-step explanation:
[tex]\displaystyle \frac{\cos x}{1+\sin x}=\frac{\cos x(1-\sin x)}{(1+\sin x)(1-\sin x)}\\\\\frac{\cos x}{1+\sin x}=\frac{\cos x(1-\sin x)}{1-\sin^2x}\\\\\frac{\cos x}{1+\sin x}=\frac{\cos x(1-\sin x)}{\cos^2x}\\\\\frac{\cos x}{1+\sin x}=\frac{1-\sin x}{\cos x}\\\\\frac{\cos x}{1+\sin x}=\frac{1}{\cos x}-\frac{\sin x}{\cos x}\\\\\frac{\cos x}{1+\sin x}=\sec x-\tan x[/tex]
C In circle K, segment is tangent to the circle at point A. If the radius of the circle has a length of 5 units and the tangent has a length of 12 units, then what is the length of ?
Answers
The length of segment BC is approximately 10.92 units.
To find the length of segment BC, we can use the properties of a tangent to a circle.
In a circle, a tangent is perpendicular to the radius drawn to the point of tangency. Therefore, triangle ABC is a right triangle with AB as the hypotenuse.
Given that the radius of the circle is 5 units and the tangent AB has a length of 12 units, we can apply the Pythagorean theorem to find the length of segment BC.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the other two sides (BC and AC).
Applying the theorem to triangle ABC:
AB^2 = BC^2 + AC^2.
Substituting the given values:
12^2 = BC^2 + 5^2.
144 = BC^2 + 25.
Rearranging the equation:
BC^2 = 144 - 25.
BC^2 = 119.
Taking the square root of both sides:
BC = √119.
Therefore, the length of segment BC is approximately equal to √119 units.
Since it's not possible to represent the square root of 119 exactly as a whole number or fraction, we can leave the answer as √119 or approximate it as a decimal. The decimal approximation for √119 is approximately 10.92.
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NO LINKS!! URGENT HELP PLEASE!!
Find the probability of each event.
28. One day, 9 babies are born at a hospital. Assuming each baby has an equal chance of being a boy or girl, what is the probability that exactly 4 of the 9 babies are girls?
29. A gambler places a bet on a horse race. To win, he must pick the top 3 finishers in order. 13 horses of equal ability are entered in the race. Assuming the horses finish in random order, what is the probability that the gambler will win his bet?
Answers
Answer:
28. 0.2461 or 24.61%.
29. 0.00058275 or 0.058275%.
Step-by-step explanation:
Question 28:
we can use the binomial probability formula to calculate the probability:
[tex]\boxed{\bold{P(X = k) = (nCk) * p^k * (1 - p)^(n - k)}}[/tex]
Where:
P(X = k) is the probability of getting exactly k successesnCk is the number of combinations of n items taken k at a timep is the probability of a single successn is the total number of trialsIn this case, we have n = 9 babies, and each baby has a 50% chance of being a girl (p = 0.5). We want to find the probability that exactly 4 of them are girls (k = 4).
Using the formula, we can calculate the probability as follows:
[tex]\bold{P(X = 4) = (9C4) * (0.5)^4 * (1 - 0.5)^(9 - 4)}[/tex]
Calculating the values:
(9C4) = 126 (0.5)^4 = 0.0625(1 - 0.5)^(9 - 4) = 0.5^5 = 0.03125Now, we can substitute these values into the formula:
P(X = 4) = 126 * 0.0625 * 0.03125 = 0.2461 or 24.61%
Therefore, the probability that exactly 4 out of 9 babies are girls is approximately 0.2461 or 24.61%.
Question 29:
We need to calculate the number of possible outcomes to calculate this probability, where the gambler correctly predicts the top 3 finishers in order and divides it by the total number of possible outcomes.
The total number of possible outcomes is the number of permutations of 13 horses taken 3 at a time.
This can be calculated as:
[tex]13P3 = \frac{13! }{(13 - 3)! }= \frac{13! }{ 10! }=\frac{13*12*11*10! }{ 10! }= 13 * 12 * 11 = 1,716[/tex]
Now,
To calculate the number of favorable outcomes where the gambler predicts the top 3 finishers correctly, we need to consider that there is only one correct order for the horses to finish.
Therefore, there is only one favorable outcome.
The probability of the gambler winning his bet is given by:
[tex]\boxed{\bold{P\:(winning) = \frac{Number\: of \:favorable\: outcomes }{ Total \:number \:of \:outcomes}}}[/tex]
[tex]P(winning) = \frac{1 }{1,716}=0,00058275 \: or\:0.058275%[/tex]
Therefore, the probability that the gambler will win his bet is approximately 0.00058275 or 0.058275%.
Answer:
28) 0.246 = 24.6%
29) 1/286 = 0.350%
Step-by-step explanation:
Question 28We can model the given scenario as a binomial distribution.
Binomial distribution[tex]X \sim \text{B}(n,p)[/tex]
where:
X is the random variable that represents the number of successes.n is the fixed number of independent trials.p is the probability of success in each trial.Given the probability that a baby is born a girl is 0.5, and the number of babies is 9:
[tex]\boxed{X \sim \text{B}(9,0.5)}[/tex]
where the random variable X represents the number of babies who are girls.
To find the probability that at exactly 4 babies are girls, we need to find P(X = 4).
To do this, we can use the binomial distribution formula:
[tex]\boxed{\displaystyle \text{P}(X=x)=\binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}}[/tex]
Substitute the values of n = 9, p = 0.5 and x = 4 into the formula:
[tex]\begin{aligned}\displaystyle \text{P}(X=4)&=\binom{9}{4} \cdot 0.5^4 \cdot (1-0.5)^{9-4}\\\\&=\dfrac{9!}{4!\:(9-4)!} \cdot 0.5^4 \cdot 0.5^{5}\\\\&=126 \cdot 0.0625 \cdot 0.03125\\\\& = 0.24609375\end{aligned}[/tex]
Therefore, the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.
We can also use the binomial probability density function of a calculator to calculate P(X = 4).
Inputting the values of n = 9, p = 0.5 and x = 4 into the binomial pdf:
[tex]\text{P}(X=4)=0.24609375[/tex]
Therefore, this confirms that the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.
[tex]\hrulefill[/tex]
Question 29To calculate the probability that the gambler will win his bet, we need to determine the number of favorable outcomes (winning combinations) and the total number of possible outcomes.
The gambler wins if he picks the top three horses in any order. There are 6 ways for the three winners to be arranged in the top three.
There are a total of 13 horses in the race.
The number of ways to choose the first-place horse is 13. After the first-place horse is chosen, there are 12 remaining horses, so the number of ways to choose the second-place horse is 12. Finally, after the first two horses are chosen, there are 11 remaining horses, so the number of ways to choose the third-place horse is 11.Therefore, the total number of possible outcomes is:
[tex]13 \times 12 \times 11 = 1716[/tex]
Therefore, the probability that the gambler will win his bet is:
[tex]\begin{aligned} \sf Probability &=\sf \dfrac{Favorable \;outcomes}{Total\;outcomes}\\\\&=\dfrac{6}{1716}\\\\&=\dfrac{1}{286}\\\\ & \approx0.350\%\; \sf (3\;d.p.)\end{aligned}[/tex]
Four equal-sized equilateral triangles form a larger equilateral triangle, as shown
below.
EF-2a
ED=3b
a) Express FB in terms of b
b) Express FD in terms of a and b
c) Express CB in terms of a and b
Give each answer in its simplest form
Answers
a) To express FB in terms of b, we need to consider the relationship between FB and EF. Since EF is equal to 2a, we can substitute this value into the expression for FB:
FB = EF - FB
= (2a) - (2a)
= 0
Therefore, FB is equal to 0 in terms of b.
b) To express FD in terms of a and b, we can use the given relationship between ED and FD. ED is equal to 3b, so we can substitute this value into the expression for FD:
FD = ED - FB
= (3b) - (0)
= 3b
Therefore, FD is equal to 3b in terms of a and b.
c) To express CB in terms of a and b, we need to consider the relationship between CB and EF. Since EF is equal to 2a, we can substitute this value into the expression for CB:
CB = EF - EB
= (2a) - (FB + FD)
= (2a) - (0 + 3b)
= 2a - 3b
Therefore, CB is equal to 2a - 3b in terms of a and b.
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent.
Answers
The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3
To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:
Since for all x > 0, we have:
Thus, by the limit comparison test:
converges if and only if converges.
We can evaluate using the power rule of integration:
where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:
∫(1/x^4) dx from 1 to infinity = lim as b → infinity
=>
=> 0 - (-1/3)
=> 1/3
Since the integral dx converges by comparison to a convergent integral, and its value is 1/3.
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Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1
Review the simple interest rate based on FICO scores to answer the question:
FICO Score Simple Interest Rate
800–850 5.295%
740–799 6.597%
670–739 9.132%
580–669 10.358%
300–579 14.313%
Kamryn plans to borrow $13,250.00 with a simple interest rate loan. Determine the amount of interest Kamryn will save if she is able to raise her credit score from 665 to 680.
Answers
Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.
According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.
Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.
Interest = Principal * Rate
= $13,250.00 * 0.10358
≈ $1,370.56
Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.
Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.
Calculating the interest with a credit score of 680:
Interest = Principal * Rate
= $13,250.00 * 0.09132
≈ $1,210.57
Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.
Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
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Select the correct answer. Given: is a rectangle with vertices , , , and , where . Prove: is a square. Statements Reasons 1. is a rectangle with vertices , , , and . 1. given 2. units 2. ? 3. units 3. distance formula 4. 4. ? 5. is a square. 5. ? What is the correct order of reasons that complete the proof?
Answers
The correct order of reasons that complete the proof is:
Given
AB = 6 units
BC = 4 units
AC = 4 units
Diagonals are congruent
AC = BD = 4 units
ABCD is a rhombus
ABCD is a square.
Based on the given statements and reasons, let's determine the correct order of reasons to complete the proof that ABCD is a square.
Given: ABCD is a rectangle with vertices A, B, C, and D.
Reason: Given.
AB = 6 units.
Reason: The length of AB is given as 6 units.
BC = 4 units.
Reason: The length of BC is given as 4 units.
AC = 4 units.
Reason: Since ABCD is a rectangle, opposite sides are equal. Therefore, AB = CD = 6 units and BC = AD = 4 units.
Diagonals are congruent.
Reason: In a rectangle, the diagonals are congruent. Therefore, AC = BD.
AC = BD = 4 units.
Reason: From reason 4, we know that AC = 4 units. From reason 5, we know that AC = BD.
ABCD is a rhombus.
Reason: In a rhombus, all sides are equal, and opposite angles are congruent. Since AC = BD = 4 units (reason 6), ABCD satisfies the properties of a rhombus.
ABCD is a square.
Reason: In a square, all sides are equal, and all angles are right angles. Since ABCD is a rectangle (reason 1) and a rhombus (reason 7), it must also be a square.
Therefore, the correct order of reasons that complete the proof is:
Given
AB = 6 units
BC = 4 units
AC = 4 units
Diagonals are congruent
AC = BD = 4 units
ABCD is a rhombus
ABCD is a square.
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In a certain year, there were 300 congressional
seats in a country's congress. The population of
one state was 1,312,127 and its standard quota
was 7.2513. Find the country's population in the
given year.
The country's population was
(Type a whole number.)
people.
Answers
Answer:
There would be 54,307,200 people
Step-by-step explanation:
[tex]24\ \textgreater \ 6x-3[/tex]
Answers
Answer:
x < 4.5
Step-by-step explanation:
To solve the inequality 24 > 6x - 3, we can follow these steps:
Start by adding 3 to both sides of the inequality to isolate the term with the variable:
24 + 3 > 6x - 3 + 3
This simplifies to:
27 > 6x
Divide both sides of the inequality by 6 to solve for x:
27/6 > 6x/6
Simplifying further:
4.5 > x
Therefore, the solution to the inequality 24 > 6x - 3 is x < 4.5.
Hope this helps!
The solution to the inequality is :
↬ [tex]\bf{x < \dfrac{9}{2}}[/tex]
Solution:
Let's solve [tex]\bf24\:\textgreater\:6x-3}[/tex].
First, add 3 to each side:
[tex]\sf{24+3\:\textgreater \:6x}[/tex]
[tex]\sf{27 > 6x}[/tex]
Divide each side by 6
[tex]\sf{27/6 > x}[/tex]
[tex]\sf{x < 27/6}[/tex]
[tex]\sf{x < 9/2}[/tex]
Hence, x < 9/2PLEASE HELP
I need this done is 13 minutes.
Polygon ABCD with vertices at A(1,-1) B(3,-1), C(3,-2) and D(1-2) is dilated to create polygon ABCD with vertices at A’(2,-2), B(6,-2), C’(6,-4) and D’(2,-4). Determine the scale factor used to create the image
A. 3
B. 2
C. 1/2
D. 1/3
Answers
The correct answer is B. 2, as the scale factor used to create the dilated polygon is 2.
To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original polygon ABCD and the dilated polygon A'B'C'D'.
Let's calculate the lengths of the corresponding sides:
Side AB: The length of side AB is 3 - 1 = 2 units in the original polygon. In the dilated polygon, the length of side A'B' is 6 - 2 = 4 units.
Side BC: The length of side BC is -2 - (-1) = -1 units in the original polygon. In the dilated polygon, the length of side B'C' is -4 - (-2) = -2 units.
Side CD: The length of side CD is 1 - 3 = -2 units in the original polygon. In the dilated polygon, the length of side C'D' is 2 - 6 = -4 units.
Side DA: The length of side DA is -1 - (-2) = 1 unit in the original polygon. In the dilated polygon, the length of side D'A' is -2 - (-4) = 2 units.
Now, let's compare the corresponding side lengths:
AB: A'B' = 4 units / 2 units = 2
BC: B'C' = -2 units / -1 units = 2
CD: C'D' = -4 units / -2 units = 2
DA: D'A' = 2 units / 1 unit = 2
The scale factor used to create the image is the ratio of the corresponding side lengths.
In this case, all the corresponding side lengths have a ratio of 2.
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Find a basis of the subspace
Find a basis of the subspace of R4
that consists of all vectors perpendicular to both
[1,0,5,-9] and [0,1,9,-7].
Answers
A basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7] is [-5, -9, 5].
To find a basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7], we can use the concept of the cross product.
Let's consider the vectors [1,0,5,-9] and [0,1,9,-7] as vectors A and B, respectively.
We can find a vector C that is perpendicular to both A and B by taking the cross product of A and B.
C = A × B
To compute the cross product, we can use the following determinant formula:
C = [i, j, k]
[1, 0, 5]
[0, 1, 9]
Expanding the determinant, we have:
C = (0 × 9 - 1 × 5)i - (1 × 9 - 0 × 5)j + (1 × 5 - 0 × 1)k
= -5i - 9j + 5k
Therefore, we have found a vector C that is perpendicular to both [1,0,5,-9] and [0,1,9,-7], which is C = [-5, -9, 5].
To find a basis of the subspace, we can use this vector C as the basis vector. Since it is the only vector in the subspace, it forms a basis.
So, a basis of the subspace that consists of all vectors perpendicular to both [1,0,5,-9] and [0,1,9,-7] is [-5, -9, 5].
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In quadrilateral ABCD, angle A is 72, angle B is 94, and angle C is 113. What is angle D
Answers
Angle D measures 81 degrees in quadrilateral ABCD.
We have,
To find the measure of angle D in quadrilateral ABCD, we can use the fact that the sum of the angles in any quadrilateral is always 360 degrees.
Let's denote angle D as x. Given that angle A is 72 degrees, angle B is 94 degrees, and angle C is 113 degrees, we can set up the equation:
72 + 94 + 113 + x = 360
Combining the known angle measures:
279 + x = 360
To solve for x, we can subtract 279 from both sides of the equation:
x = 360 - 279
x = 81
Therefore,
Angle D measures 81 degrees in quadrilateral ABCD.
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7 cameras cost $308. The cost of each camera is the same. What is the cost of each camera?
Answers
Answer:
$44
Step-by-step explanation:
Hello!
It said that 7 cameras cost $308, right?
If each camera costs the same, it means that 7 cameras with the same value equal $308.
If we use this in an equation, and if x is a variable we want to solve, it would be:
7x = 308.
If 7x = 308, it would be
308/7 =
44.
So, $44 is the answer.
PLEASE HELP!!!
Triangle ABC has vertices at A(-5,2), B(1,3), and C(-3,0). Determine the coordinates of the vertices for the image of the pre image is translated 4 units right.
A. A’(-9,2),B’(-3,3), C’(-7,0)
B. A’(-4,6),B’(0,7),C’(1,0)
C. A’(-1,2),B’(5,3),C’(1,0)
D. A’ (-5,-2), B’(-1,-1), C’(-3,-4)
Answers
The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
What is translation on a coordinate plane?Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.
During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.
Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.
So,
[tex]\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}[/tex]
[tex]\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}[/tex]
[tex]\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}[/tex]
Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
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Imagine looking for a certain angle whose cosine is positive and whose sine is negative.
Part 1: Name the two quadrants in which cosine is positive.
Part 2: Name the quadrants in which sine is negative.
Part 3: Use the information in parts a and b to identify the quadrant in which cosine is positive and sine is negative.
Part 4: Write down one angle, in degrees, that has a negative sine and a positive cosine.
Part 5: Using your calculator, confirm your choice by writing the cosine of your angle and the sine of your angle below.
Answers
The two quadrants in which cosine is positive are the first quadrant (Q1) and the fourth quadrant (Q4).
How to explain the informationPart 2: The quadrants in which sine is negative are the third quadrant (Q3) and the fourth quadrant (Q4).
Part 3: Based on the information from parts 1 and 2, the quadrant in which cosine is positive and sine is negative is the fourth quadrant (Q4).
Part 4: One angle that has a negative sine and a positive cosine in the fourth quadrant is 135 degrees (or 3π/4 radians).
Part 5: Using a calculator, we can confirm the values of cosine and sine for 135 degrees:
Cosine of 135 degrees: cos(135°) ≈ -0.7071 (rounded to four decimal places)
Sine of 135 degrees: sin(135°) ≈ -0.7071 (rounded to four decimal places)
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what’s the answer ?
Answers
247.75
Uh I can't explain well so heres the answer
247.75
If the point (-9,2) is a solution to a linear equation, the point (2,-9) will be a solution to it's inverse. True False
Answers
If the point (-9,2) is a solution to a linear equation, the point (2,-9) will be a solution to it's inverse is false.
If the point (-9,2) is a solution to a linear equation, it means that when you substitute x = -9 and y = 2 into the equation, it satisfies the equation and makes it true.
However, the point (2,-9) will not necessarily be a solution to the inverse of that equation.
To find the inverse of a linear equation, you need to switch the x and y variables and solve for the new y.
So if the original equation is in the form y = mx + b, the inverse will be in the form x = my + b.
Therefore, the point (2,-9) will only be a solution to the inverse equation if substituting x = 2 and y = -9 into the inverse equation makes it true.
It cannot be determined just based on the fact that (-9,2) is a solution to the original equation.
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Find the length of side X in simple radical form with a rational denominator
Answers
The length of side X in simple radical form with a rational denominator is 10/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 2 × 5/√3
Hypotenuse, x = 10/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
Answers
The calculation of this can be done by first determining the future value of the monthly payments of $327.50
The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,
which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.
The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35
This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.
Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.
for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).
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Find the measurement of WX
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The measure of the arc angle WX is 100 degrees.
How to find the arc angle ?The arc angle WX can be found as follows:
The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.
Therefore,
arc WY = 2(75)
arc WY = 150 degrees
Therefore, let's find the arc angle WX as follows:
arc angle WX = 360 - 150 - 110
arc angle WX = 210 - 110
arc angle WX = 100 degrees
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Answer:kkkkkkkkkkkkkkkkkkkkkkkkkkk mean ok 26 times
The mean number of covid 19cases is 26.68347575 Adoctor in german stated that the missing value A in the table is less than 8 million . verify . showing all calculations whether the doctor's statement is valid
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1. The hormone that results in diabetes mellitus when it is deficient is insulin.
2. The organ that secretes insulin is the pancreas.
3. Two other hormones that influence the glucose level of the blood are:
1. Glucagon: It is produced by the alpha cells of the pancreas and increases blood glucose levels by promoting the breakdown of glycogen in the liver.
2. Cortisol: It is produced by the adrenal glands and helps regulate glucose metabolism by promoting gluconeogenesis (conversion of proteins and fats into glucose) and reducing glucose uptake by peripheral tissues.
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Find the variance of the data. 22, 34, 7, 27, 25 x = 23 Variance (²) = [?]
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Therefore, the variance (²) of the data. 22, 34, 7, 27, 25 x = 23 is 79.6.
Variance calculation
To find the variance of a set of data, you can follow these steps.
Calculate the mean of the data set.
Mean = (22 + 34+ 7 +27 +25)= 23.
Substract the mean from each data point and square.
(22 -23)² =1
(34 -23)² =121
(7-23)² =256
(27-23)² =16
(25 -23)² =4
Find the mean of the squared differences.
The mean of squared differences = (1 + 121+ 256+ 16+ 4) /5 = 79.6
Therefore, the variance (²) is 79.6.
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A basket had 15 mangoes. A monkey came and took
away two-fifths of the mangoes. How many mangoes
were left in the basket
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Total mangoes: 15
Leftover mangoes after monkey took two fifth:
2/5 * 15
= 6
So, two-fifths of the mangoes are 6.
Now calculating leftover:
15 - 6
= 9 mangoes(ANSWER)
Refer to the information below to answer Questions 1 to 4. 1. Billy's gross pay is K850.00 Billy is taxed 12% on his taxable income, and contributes 7% to Nusfund. His loan deduction is 5%. What is his net pay? (1 mark)
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The Billy's net pay is K646
The given information are; Billy's gross pay is K850.00, he is taxed 12% on his taxable income, and contributes 7% to Nusfund. His loan deduction is 5%.
To find out his net pay, the following steps must be taken:Firstly, calculate Billy's tax amount, Nusfund contribution, and loan deduction by using their respective percentages and the gross pay.
tax amount= 12/100 × 850= K102 Refund contribution= 7/100 × 850= K59.50Loan deduction= 5/100 × 850= K42.50 Secondly, the sum of all the deductions made from the gross pay is calculated to obtain the total deductions.
Total deductions= K102 + K59.50 + K42.50= K204The final step is to subtract the total deductions from the gross pay to find Billy's net pay. Net pay= K850 − K204= K646.
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A line with of -10 passes through the Points (4, 8) and (5, r) what is the valué of r
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The value of [tex]\(r\)[/tex] is [tex]\(r = -2\)[/tex], according to the given cartesian points.
To find the value of [tex]\(r\)[/tex], we can use the slope-intercept form of a linear equation, [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope of the line. Given that the line has a slope of [tex]\(-10\)[/tex] and passes through the cartesian points [tex]\((4, 8)\)[/tex]and \[tex]((5, r)\)[/tex], we can calculate the slope as follows:
[tex]\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{r - 8}}{{5 - 4}} = r - 8\][/tex]
Since the slope is [tex]\(-10\)[/tex], we can equate it to the calculated slope and solve for [tex]\(r\)[/tex]:
[tex]\[-10 = r - 8\][/tex]
Simplifying the equation, we have:
[tex]\[r - 8 = -10\][/tex]
Adding [tex]\(8\)[/tex] to both sides, we get:
[tex]\[r = -10 + 8\][/tex]
Therefore, the value of [tex]\(r\)[/tex] is [tex]\(r = -2\)[/tex].
In conclusion, the value of [tex]\(r\)[/tex] in the line with a slope of [tex]-10[/tex] passing through the points [tex](4, 8)[/tex] and [tex](5, \(r\))[/tex] is [tex]\(r = -2\)[/tex]. This satisfies the equation and represents the y-coordinate of the second point. This value of [tex]r[/tex] indicates that the second point lies on the line with a slope of -[tex]10[/tex] passing through ([tex]4,8[/tex]).
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(q9) Find the volume of the solid obtained by rotating the region enclosed by the curves
and y = x2 about the y-axis.
Answers
The volume of the solid obtained by rotating the region enclosed by the curves [tex]y=\sqrt{x^3}[/tex] and [tex]y = x^2[/tex] about the y-axis is [tex]\pi/14[/tex] . option B
To determine the solid's volume after rotating the area bounded by curves
[tex]y = \sqrt{x^3}[/tex] and [tex]y = x^2[/tex]
We can apply the cylindrical shell approach to the y-axis.
First, let's locate the spots where the two curves intersect:
[tex]\sqrt{x^3} = x^2[/tex]
Squaring both sides:
[tex]x^3 = x^4[/tex]
Rearranging:
[tex]x^4 - x^3 = 0[/tex]
Factorizing [tex]x^3(x - 1) = 0[/tex]
Therefore, the locations of intersection are x = 0 and x = 1.
The integral for the solid's volume must then be set up using cylindrical shells. The following formula determines the volume of a cylindrical shell:
V is equal to 2[a, b] x * h(x). dx where a and b are the integration limits, x is the shell's radius, and h(x) is the height of the shell.
The radius of the shell in this instance is x, while the height of the shell is the ratio of the two curves: [tex]h(x) = \sqrt{x^3} - x^2.[/tex]
Since those are the locations of intersection, the range of integration's bounds is 0 to 1.
The integral then becomes:
∫[tex]V = 2\pi [0, 1] x * (\sqrt{x^3} - x^2) dx[/tex]
We can simplify the formula inside the integral in order to evaluate it:
V = 2π ∫[0, 1] (x^(5/2) - x^3) dx
We can integrate each word by applying the power rule for integration as follows:
[tex]V = 2\pi [(2/7)x^{(7/2)} - (1/4)x^{4}] |[0, 1][/tex]
Calculating the limits of the definite integral:
[tex]V = 2\pi [(2/7)(1^{(7/2))} - (1/4)(1^{4)}] - 2\pi [(2/7)(0^{(7/2})) - (1/4)(0^{4)}][/tex]
Simplifying further:
V = 2π [(2/7) - (1/4)]
V = 2π (8/28 - 7/28)
V = 2π/28
Simplifying the fraction:
V = π/14 ,Therefore, the correct answer is option B.
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