Answers
The value of cos(2x+y) is -12/65.
Describe cosine ?Cosine, commonly denoted as cos, is a mathematical function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In other words, it is the ratio of the length of the adjacent side of an angle to the hypotenuse of the right triangle containing that angle. Cosine is one of the basic trigonometric functions, along with sine and tangent, and is widely used in mathematics, physics, and engineering to model various phenomena.
Cosine is periodic with a period of 2π, and its values range from -1 to 1. When the angle is 0°, the cosine is equal to 1, indicating that the adjacent side of the triangle is equal to the hypotenuse.
We can use the trigonometric identities for cosine to find cos(2x+y), using the values of x and y given:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
To find cos(2x), we can use the double angle identity for cosine:
cos(2x) = cos²(x) - sin²(x)
To find cos(x) and sin(x), we can use the fact that x = sin⁻¹(4/5) and the Pythagorean theorem:
sin(x) = 4/5
cos(x) = √(1 - sin²(x)) = √(1 - 16/25) = 3/5
Substituting these values into the double angle identity, we get:
cos(2x) = cos²(x) - sin²(x) = (3/5)² - (4/5)² = -7/25
To find sin(2x), we can use the double angle identity for sine:
sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5) = 24/25
To find cos(y) and sin(y), we can use the fact that y = tan⁻¹(12/5) and the Pythagorean theorem:
sin(y) = 12/13
cos(y) = 5/13
Substituting these values into the expression for cos(2x+y), we get:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
= (-7/25)(5/13) - (24/25)(12/13)
= -60/325
= -12/65
Therefore, cos(2x+y) = -12/65.
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Related Questions
Another Statistics Card Question
You are dealt a hand of five cards from a standard deck of 52 cards. What is the probability of being dealt three cards of one denomination and two of another?
Answers
The odds against this happening are 48:25 . For this we have to know the meaning of probability.
How to find the Probability?I showed that out of 22100 possible deals, there are 3744 ways to get a pair and 52 ways of getting 3 of a kind that makes a total of 3796 ways to get a pair or 3 of a kind.
If we multiply this by 3! then we get 22776 possible permutations that result in 3 of a kind or in a pair.
To get the number of permutations of deals where the first two cards are a pair, we note that the first card could be any one of the 52 in the pack.
The second card must be one of the 3 remaining cards that pairs up with the first one and then there are 50 cards that could be selected for the third.
That makes a total of 52×3×50=7800 permutations.
[tex]\frac{7800}{22776} = \frac{27}{73}[/tex]
The odds against this happening are 48:25
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Simplify:
cos^2(a) /( sin(a)-1)
Answers
[tex]\cfrac{cos^2(a)}{sin(a)-1}\implies \cfrac{1-sin^2(a)}{sin(a)-1}\implies \cfrac{\stackrel{ \textit{difference of squares} }{1^2-sin^2(a)}}{sin(a)-1} \\\\\\ \cfrac{[1-sin(a)][1+sin(a)]}{sin(a)-1}\implies \cfrac{~~\begin{matrix} [1-sin(a)] \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~[1+sin(a)]}{-[~~\begin{matrix} 1-sin(a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~]}\implies -[1+sin(a)][/tex]
Answer:-1
Step-by-step explanation:
[tex]\frac{cos^{2}a}{sina-1} \\cos^{2}a=\frac{1+cos2a}{2}\\\frac{\frac{1+cos2a}{2}}{sina-1}=\frac{1+cos2a}{2(sina-1)}=\frac{1+cos2a}{2sina-2}=\frac{1+cos2a}{-(2-2sina)}\\1-2sina=cos2a\\\frac{1+cos2a}{-(1+(1-2sina))}=\frac{1+cos2a}{-(1+cos2a)}=-1[/tex]
Find the area of Length = 15 m, breadth = 9 m
Answers
Answer:
135 square meters
Step-by-step explanation:
Area = Length x Breadth
15 m x 9 m = 135 square meters.
Answer:
135m
Step-by-step explanation:
l×b = Area
15×9 = 135m
What are the coordinates of point A(-22, 1) after it is reflected across the x-axis?
O A) (22,1)
O B) (1.-22)
oc) (23,-1)
OD) (-2,-1)
Answers
The required correct answer is (D) (-22, -1).
What is reflected across the x-axis?By graphing y=-f(x), we can reflect the graph of any function f about the x-axis, and by plotting y=f, we can reflect the graph about the y-axis.(-x). By graphing y=-f, we can even mirror it about both axes.(-x).
According got question:When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
Therefore, to find the coordinates of point A after it is reflected across the x-axis, we change the sign of the y-coordinate of A.
So, if the original coordinates of point A are (-22, 1), the coordinates of A after it is reflected across the x-axis are (-22, -1).
Therefore, the correct answer is (D) (-22, -1).
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If someone help I’ll be thankful!!!
Answers
Answer:
m<v = m<w
Step-by-step explanation:
I do not know how to explain it. CD are parallel with those to lines. They ahve the same degree as the other two angles.
<y = <z are opposite angle.
<w + <x = 180 are suplementary angle which mean they add up to 180.
translate this phrase into an algebraic expression.
The sum of 15 and twice Jose’s score
use the variable j to represent Jose’s score
Answers
Answer:
15 + 2j
Step-by-step explanation:
Sum, which means addition, is used to say that 15 will be added to something.
That "something" is twice Jose's score, which is 2 * j, since j is the score.
15 + 2 * j, or just 15 + 2j
Hei can someone help me with math homework
Answers
It would take approximately 12.5 hours for only pipe A to fill the pool, 168 hours for only pipe B, 48.6 hours for only pipe C, and 3.5 hours for all pipes.
What is equations ?
An equation is a mathematical statement that shows two expressions to be equal to each other. It typically contains one or more variables, and solving the equation involves finding the values of the variables that make the equation true. Equations are used in many areas of mathematics, science, engineering, and other fields to describe relationships between different quantities or to solve problems. Examples of equations include linear equations, quadratic equations, and differential equations.
Let's represent the amount of work done by each pipe per hour:
Pipe A: a
Pipe B: b
Pipe C: c
From the problem, we know that:
a + b = 1/9.5 (1) (pipes A and B take 9.5 hours to fill the pool)
b + c = 1/6 (2) (pipes B and C take 6 hours to fill the pool)
a + c = 1/10 (3) (pipes A and C take 10 hours to fill the pool)
We can solve this system of equations to find the values of a, b, and c:
Adding (1) and (2), we get:
a + 2b + c = 1/9.5 + 1/6
Multiplying both sides by 2, we get:
2a + 4b + 2c = 1/4.75 + 1/
Simplifying, we get:
2a + 4b + 2c = 13/28 (4)
Adding (1) and (3), we get:
2a + b + c = 1/9.5 + 1/10
Multiplying both sides by 20, we get:
40a + 20b + 20c = 2 + 1.9
Simplifying, we get:
40a + 20b + 20c = 3.9 (5)
Now we can solve for a, b, and c using (4) and (5). Multiplying (4) by 5 and subtracting (5) from it, we get:
6b = 1/28
Simplifying, we get:
b = 1/168
Substituting b into (1), we get:
a = 1/9.5 - 1/168
Simplifying, we get:
a = 1/12.32
Substituting b into (2), we get:
c = 1/6 - 1/168
Simplifying, we get:
c = 7/336
Now we can find the time it takes for each pipe to fill the pool individually:
Only pipe A: 1/a = 12.32 hours ≈ 12.5 hours
Only pipe B: 1/b = 168 hours
Only pipe C: 1/c = 48 hours ≈ 48.6 hours
All pipes: 1/(a+b+c) = 3.46 hours ≈ 3.5 hours (using the values we found for a, b, and c)
Therefore, it would take approximately 12.5 hours for only pipe A to fill the pool, 168 hours for only pipe B, 48.6 hours for only pipe C, and 3.5 hours for all pipes.
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Can anyone help me with number 3?
Answers
Answer:
the least is 40 the greatest is 49
Step-by-step explanation:
Answer:
40 the greatest is 49
Step-by-step explanation:
The function f(x) = 2x3 - 6x2 _ 210x + 7 is increasing on the inverval
(-00, A]U |B, ∞), and decreasing on the interval [4, B].
A =
and B =
Answers
The critical points are A = -5 and B = 7, and the function is increasing on the interval (-∞, -5] ∪ [7, ∞), and decreasing on the interval [-5, 7].
What is the value of A and B along the intervalTo find A and B, we need to find the critical points of the function f(x) and determine the intervals of increase and decrease.
First, we find the derivative of f(x) as:
f'(x) = 6x^2 - 12x - 210
Next, we find the critical points by setting f'(x) = 0:
6x^2 - 12x - 210 = 0
Simplifying, we get:
x^2 - 2x - 35 = 0
Factoring, we get:
(x - 7)(x + 5) = 0
So the critical points are x = 7 and x = -5.
Now we can determine the intervals of increase and decrease. We create a sign chart based on the sign of f'(x) in each interval:
Interval | f'(x) | f(x) increasing/decreasing
(-∞, -5) | - | decreasing
(-5, 7) | + | increasing
(7, ∞) | - | decreasing
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Prove that the roots of x² + (1-k)x+k-3=0 are real for all real values of k.
Answers
Answer:
Step-by-step explanation:To prove that the roots of the equation x² + (1-k)x + k-3 = 0 are real for all real values of k, we need to show that the discriminant of the equation is non-negative for all values of k.
The discriminant of a quadratic equation ax² + bx + c = 0 is given by b² - 4ac. If the discriminant is positive, then the equation has two distinct real roots; if it is zero, then the equation has one real root (a repeated root); and if it is negative, then the equation has no real roots.
So, in this case, the discriminant of the equation is:
(1-k)² - 4(1)(k-3)
= 1 - 2k + k² - 4k + 12
= k² - 6k + 13
We need to show that k² - 6k + 13 ≥ 0 for all real values of k.
To do this, we can complete the square:
k² - 6k + 13
= (k - 3)² + 4
Since the square of any real number is non-negative, we have (k-3)² ≥ 0 for all k, which means that (k-3)² + 4 ≥ 4.
Therefore, k² - 6k + 13 ≥ 4 for all real values of k, which means that the discriminant of the quadratic equation x² + (1-k)x + k-3 = 0 is non-negative for all real values of k. Hence, the roots of the equation are real for all real values of k.
For the quadratic equation x² + (1-k)x+k-3=0, we have:
a = 1
b = 1-k
c = k-3
Using the quadratic formula, we can find the roots of the equation:
x = (-b ± sqrt(b²-4ac))/2a
Substituting in the values of a, b, and c, we get:
x = (-(1-k) ± sqrt((1-k)² - 4(1)(k-3)))/2(1)
Simplifying, we get:
x = (k-1 ± sqrt((k-1)² - 4(k-3)))/2
Expanding the square inside the square root, we get:
x = (k-1 ± sqrt(k² - 2k + 1 - 4k + 12))/2
Simplifying further, we get:
x = (k-1 ± sqrt(k² - 2k + 13))/2
In order for the roots to be real, the expression inside the square root must be non-negative. That is:
k² - 2k + 13 ≥ 0
To find the values of k that satisfy this inequality, we can use the quadratic formula again:
k = (2 ± sqrt(4 - 4(1)(13)))/2
k = 1 ± sqrt(-44)/2
Since the square root of a negative number is not a real number, there are no real values of k that satisfy this inequality. Therefore, the roots of x² + (1-k)x+k-3=0 are real for all real values of k.
Triangle L M N LMN is similar to triangle O P R OPR. Find R O RO. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
Answers
Cross multiply - 1643 = 17x
Divide - x = 96.64706…
Round - x ≈ 96.6
A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s before
Firework A. How many seconds after Firework B launches will both fireworks explode?
Firework A : 320 ft/s
Firework B : 220 ft/s
Both fireworks will explode ___ seconds after Firework B launches.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
Answers
Both fireworks will explode at time 0.55 seconds after Firework B launches.
What is distance?Distance is a unit of measurement for the separation between two places. This scalar number is typically expressed in terms of metres, feet, or miles. Depending on the situation, other distance formulae can be used, such as the geometry distance formula or the physics average speed formula. Displacement, a vector quantity that considers the direction of motion, is distinct from distance. Distance is the overall length of an object's route, whereas displacement is the change in an object's location from its beginning position to its end position.
Let us suppose time = t.
Given that, Firework B is launched 0.25 s before Firework A.
Time taken for Firework A to explode after Firework B launches is t - 0.25.
The distance traveled by each firework is given by:
Distance of Firework A = 320t
Distance of Firework B = 220(t - 0.25) = 220t - 55
Since both fireworks explode at the same height, their distances traveled must be equal. Therefore:
320t = 220t - 55
100t = 55
t = 0.55 seconds
Hence, both fireworks will explode 0.55 seconds after Firework B launches.
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[tex]2.3x^{2} +\frac{69}{465} =?[/tex]
Answers
Answer: To solve this expression, we need to simplify it using the order of operations (PEMDAS) and perform the indicated operations:
2.3x^2 + 69 / 465
First, we need to simplify the fraction 69/465. Both the numerator and denominator have a common factor of 3, so we can simplify the fraction by dividing both by 3:
69 / 465 = 23 / 155
Now we can substitute this simplified fraction back into the original expression:
2.3x^2 + 23 / 155
The expression is now in simplified form, and there are no more operations we can perform. So this is the final answer.
Alternatively, if the expression was meant to be solved for x, we would need an equation (e.g., 2.3x^2 + 69 / 465 = some value) in order to solve for x. As it stands, we cannot solve for x with the given expression.
Step-by-step explanation:
The circumference of a circle is 28 in.
What is the diameter of the circle?
Responses
28 over pi, in.
14 over pi, in.
square root of 28 over pi end root, in.
14π−−√ in.
I think it is 28/pi but I would like to make sure
Answers
The diameter οf the circle is 28/π inches οr apprοximately 8.89 inches (rοunded tο twο decimal places).
The fοrmula fοr the circumference (C) οf a circle is given by:
C = 2πr
where r is the radius οf the circle.
If the circumference οf the circle is 28 inches, we can sοlve fοr the radius by dividing bοth sides οf the equatiοn by 2π:
C/2π = r
Substituting the given value οf C = 28, we get:
r = 28/2π
r = 14/π
Finally, tο find the diameter (d) οf the circle, we multiply the radius by 2:
d = 2r
Substituting the value οf r = 14/π, we get:
d = 2(14/π) = 28/π
Therefοre, the diameter οf the circle is 28/π inches οr apprοximately 8.89 inches (rοunded tο twο decimal places).
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Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
Answers
The requried, we would expect 8 of the next 16 muffins sold to be bran muffins.
Out of a total of 50 muffins sold, 25 were bran muffins. That means that the proportion of bran muffins to total muffins sold is:
25 / 50 = 1/2
To find how many of the next 16 muffins sold would be bran muffins, we can multiply the proportion of bran muffins by the total number of muffins:
(1/2) * 16 = 8
Therefore, we would expect 8 of the next 16 muffins sold to be bran muffins.
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NO LINKS!!! URGENT HELP PLEASE!!!
Please help me with #20, 22, and 24
Answers
Answer:
see the work below
Step-by-step explanation:
20.) x = √32²+32² = √2048 = 45.25
y = 32(sin60) = 27.7
z = 32(cos60) = 16
22.) x = 7√3 / cos60 = 24.25 = 14√3
y = 14√3 / tan30 = 42
sin30 = 14√3 / (z+7√3)
z + 7√3 = 14√3 / sin30
z = 14√3/√sin30 - 7√3 = 36.37 = 21√3
24.) z = 18(tan30) = 10.4
h = √10.4² + 18² = √432 = 20.785
x = y
2x² = 20.785²
x = √20.785²/2 = 14.7
y = 14.7
Answer:
Question 20:
x = 32√2 unitsy = 16√3 unitsz = 16 unitsQuestion 22:
x = 14√3 unitsy = 42 unitsz = 21√3 unitsQuestion 24:
x = 6√6 unitsy = 6√6 unitsz = 6√3 unitsStep-by-step explanation:
45-45-90 triangleA 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2. Therefore, the formula for the ratio of the sides is b : b : b√2 where:
b is each side opposite the 45 degree angles (legs).b√2 is the side opposite the right angle (hypotenuse).30-60-90 triangleA 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:
c is the shortest side opposite the 30° angle.c√3 is the side opposite the 60° angle.2c is the longest side (hypotenuse) opposite the right angle.Question 20Side x is the hypotenuse of a 45-45-90 triangle with congruent legs measuring 32 units. Therefore b = 32.
[tex]\implies x=b\sqrt{2}=32\sqrt{2}\; \sf units[/tex]
Side y is the side opposite the 60° angle in a 30-60-90 triangle with a hypotenuse of 32 units. Therefore, 2c = 32 so c = 16.
[tex]\implies y = c\sqrt{3}=16\sqrt{3}\; \sf units[/tex]
Side y is the side opposite the 30° angle in the same 30-60-90 triangle.
[tex]\implies z=c = 16\; \sf units[/tex]
Question 22Side x is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 7√3 units. Therefore c = 7√3.
[tex]\implies x=2c=2 \cdot 7 \sqrt{3}=14\sqrt{3}\; \sf units[/tex]
Therefore, other leg of the same triangle (opposite the 60° angle) measures c√3 = 7√3 · √3 = 21 units.
Side y is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 21 units. Therefore c = 21.
[tex]\implies y=2c=2 \cdot 21 = 42\; \sf units[/tex]
Side z is the leg of the same 30-60-90 triangle opposite the 60° angle.
[tex]\implies z=c\sqrt{3}=21\sqrt{3}\; \sf units[/tex]
Question 24Side z is the side opposite the 30° angle in a 30-60-90 triangle with the other leg (opposite the 60° angle) measuring 18 units. Therefore, c√3 = 18, so c = 18/√3 = 6√3 units.
[tex]\implies z=c = 6\sqrt{3}\; \sf units[/tex]
Therefore, the hypotenuse of the same triangle measures 2c = 12√3 units.
Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 12√3 units. Therefore b√2 = 12√3, so b = 6√6.
[tex]\implies x=6 \sqrt{6}\; \sf units[/tex]
[tex]\implies y=6 \sqrt{6}\; \sf units[/tex]
(ii) Find Z if -18=Z-3+2Z
Answers
Answer: Z=-5
Step-by-step explanation:
we want to group Z on only one side of the equation
-18=Z-3+2Z
-18-Z-2Z=-3 (subtract Z and 2Z from both sides, to remove Z from one side and to move it to the other side)
-3Z=-3+18 (regroup Z and add 18 on both sides, to have Z on only one side)
-3Z=15 (add -3+18)
3Z=-15 (multiply both sides by -1 to get a positive Z)
Z=-5 (divide both sides by 3)
45°, 35.8°, x°
Find the missing measure with the given measure
Answers
Answer:
a = 45 b = 35.8 c = 57.503
Step-by-step explanation:
there
a scientist is conducting experiments on two bacteria cultures. the table shows the functions representing the growth rate of each bacteria culture, where x represents the number of days since the start of the experiment, and x>(or equal to) 0
A. 2.9 Days
B.5.8 Days
C.36.6 Days
D. 106.0 Days
Answers
The approximate value of x which the number of bacteria would approximately be the same include the following: A. 2.9 Days.
What is an exponential function?In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the two bacteria cultures, we can logically deduce the following exponential functions;
[tex]y = 100(1.02)^x \\\\y = 80(1.05)^{2x}[/tex]
By equating the two exponential functions above, we have:
[tex]100(1.02)^x = 80(1.05)^{2x}\\\\\frac{1.02^x}{1.05^{2x}} =80/100\\\\\frac{1.02^x}{1.1025^{x}} =0.8\\\\0.9252^x = 0.8[/tex]
By taking the logarithm of both sides, we have:
[tex]Log_{0.9252}(0.9252^x) = Log_{0.9252}(0.8)[/tex]
x = 2.9 days.
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2 A fisherman catches 30 fish during a particular day.of the fish weigh more than 2 kg. He can sell each of these fish for £5.99. The remaining fish are sold to a pet food manufacturer at 75% of the price.
Answers
Let's say that the fisherman caught x fish that weigh more than 2 kg. Then, he caught 30 - x fish that weigh less than or equal to 2 kg.
The fisherman can sell each fish that weighs more than 2 kg for £5.99. Therefore, the total revenue from these fish would be:
£5.99 * x
The remaining fish, which weigh less than or equal to 2 kg, are sold to a pet food manufacturer at 75% of the price. This means that the fisherman will receive 75% of the original price for these fish, which is:
75% * £5.99 = £4.49
The total revenue from these fish would be:
£4.49 * (30 - x)
Therefore, the total revenue for the day would be:
£5.99x + £4.49(30 - x)
Simplifying this equation, we get:
£1.50x + £134.70
write the equation in standard form for the circle with center (0, -10) passing through (9/2, -16)
Answers
so we know the center and a point it passes through, so the distance from the center to that point on the circle is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{\frac{9}{2}}~,~\stackrel{y_2}{-16})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~\frac{9}{2} - 0~~)^2 + (~~-16 - (-10)~~)^2} \implies r=\sqrt{(\frac{9}{2} )^2 + (-16 +10)^2} \\\\\\ r=\sqrt{( \frac{9}{2} )^2 + ( -6 )^2} \implies r=\sqrt{ \frac{81}{4} + 36 } \implies r=\sqrt{ \cfrac{225}{4} }\implies r=\cfrac{15}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{0}{h}~~,~~\underset{-10}{k})}\qquad \stackrel{radius}{\underset{\frac{15}{2}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-(-10) ~~ )^2~~ = ~~\left( \frac{15}{2} \right)^2\implies x^2+(y+10)^2=\cfrac{225}{4}[/tex]
Answer:
x^2 + (y + 10)^2 = 225/4
Step-by-step explanation:
To find the standard form of a circle with center (h, k) and radius r, the equation is:
(x - h)^2 + (y - k)^2 = r^2
We are given the circle's center as (0, -10) and a point on the circle as (9/2, -16). We can use this information to find the radius of the circle.
Radius (r) = Distance between center and point on the circle
r = sqrt[(0 - 9/2)^2 + (-10 + 16)^2]
r = sqrt[(81/4) + 36]
r = sqrt[(81 + 144)/4]
r = sqrt(225)/2
r = 15/2
Now we can substitute the values of (h, k, and r) into the standard form equation to get:
(x - 0)^2 + (y - (-10))^2 = (15/2)^2
Simplifying and multiplying out the terms, we get:
x^2 + (y + 10)^2 = 225/4
Therefore, the standard form of the circle is:
x^2 + (y + 10)^2 = 225/4
Help me finish the table please!
Answers
The completion of the table comparing simple interest with compound interest for the amount (future value) of the investment of $1,000 for the different periods is as follows:
Simple Compound
Interest Interest
1 year $1,100.00 $1,100.00
2 years $1,200.00 $1,210.00
3 years $1,300.00 $1,331.00
4 years $1,400.00 $1,464.10
5 years $1,500.00 $1,610.51
What is the difference between simple interest and compound interest?Simple interest is computed on the principal only for each period.
Compound interest is computed on both the principal and accumulated interest to determine the future value.
For instance, at the end of the first year, there is no difference between the future value based on simple interest and the compound interest. However, differences exist from the second year because the accumulated interest is added to the principal before compound interest is determined.
The principal investment = $1,000
Interest rate = 10%
Simple Compound
Interest Interest
1 year $1,100.00 $1,100.00 ($1,000 x 1.1)
2 years $1,200.00 $1,210.00 ($1,000 x 1.21)
3 years $1,300.00 $1,331.00 ($1,000 x 1.331)
4 years $1,400.00 $1,464.10 ($1,000 x 1.4641
5 years $1,500.00 $1,610.51 ($1,000 x 1.61051)
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List two reason why do you think the given questionnaire i not suitable
Answers
Some of the general reason why questionnaire are often not suitable for a study includes:
being ambiguous or have unclear questions: being biased or have leading questionsWhat problems makes questionnaire unsuitable for a study?If the questions in the questionnaire are unclear or open to interpretation, then the results may not be accurate or useful. Respondents may answer questions differently based on their own interpretation, leading to inconsistent or unreliable data.
Also, if the questions in the questionnaire are biased, then, the results may be skewed towards a particular outcome or viewpoint. Respondents may feel pressured or influenced to answer questions in a certain way, rather than providing their honest opinion and this can lead to inaccurate or unrepresentative data.
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Suppose a standard six sided die is rolled 15 times. What is the probability of rolling 1 exactly 4 times? Round to four decimal places.
Answers
Therefore , the solution of the given problem of probability comes out to be rounded to four decimal places, is approximately 0.1041.
What precisely is probability?The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.
Here,
A typical six-sided die has a 1/6 chance of rolling a 1 on any particular roll.
We can describe this scenario using a binomial distribution with
=> n = 15 and p = 1/6 since we are rolling the die 15 times.
The binomial probability formula can be used to calculate the likelihood of rolling precisely four ones:
=> P(X = 4) = (15 choose 4) (15 choose 4) * (1/6)^4 * (5/6)^11
Calculating the answer, we obtain:
=> P(X = 4) ≈ 0.1041
The likelihood of rolling precisely four one-sided dice, rounded to four decimal places, is approximately 0.1041.
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write the equation of the line slope 4 and y intercept 1/2
Answers
Answer:
y = 4x + 1/2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 4
b = 1/2
So, the equation is y = 4x + 1/2
Simplify radical Write the solution as both a single power and a single
Answers
The solution written as both a single power and a single variable is y^4/3
What are index forms?
Index forms are defined as mathematical forms of presenting numbers too small or large in a more convenient form.
Other terms for index forms are;
Scientific notationsStandard forms.What are radicals?A radical is expressed with the symbol, '√' that is used to denote square root or nth roots.
From the information given, we have that;
[tex](\sqrt[3]{y^2} ) (\sqrt[6]{y^4} )[/tex]
expand the square root symbols, we have;
(y^2/3)(y^2/3)
expand the bracket and add the exponents, we have;
y^(2/3+2/3)
Add the values
y^ 4/3
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Total selling price $1,238.45; sales tax rate 8 1/2%. what is the sales tax?
Answers
Answer:
To find the sales tax, we need to first calculate the taxable amount.
Total selling price = $1,238.45
Sales tax rate = 8 1/2% = 8.5%
Let's assume that the sales tax is added to the selling price, which means the selling price includes the tax.
To find the taxable amount, we can divide the selling price by (1 + tax rate as a decimal):
Taxable amount = Selling price / (1 + tax rate as a decimal)
Taxable amount = $1,238.45 / (1 + 0.085)
Taxable amount = $1,238.45 / 1.085
Taxable amount = $1,140.00 (rounded to nearest dollar)
Now, to find the sales tax amount:
Sales tax = Taxable amount x tax rate as a decimal
Sales tax = $1,140.00 x 0.085
Sales tax = $97.00
Therefore, the sales tax is $97.00.
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One third of a birds eggs hatched. If 2 eggs hatched how many eggs did the bird lay
Answers
Answer:
The bird laid 6 eggs
Step-by-step explanation:
If [tex]\frac{1}{3}[/tex] of the birds egg has hatched; and if that one third is quantifiable as 2. We know that [tex]\frac{1}{3}\\[/tex] of the laid eggs (we can declare that as x) is 2.
So:
[tex]\frac{1}{3}x = 2[/tex]
Now multiply both sides by 3:
[tex]x=6[/tex]
Answer:
1 egg
Step-by-step explanation:
One third of a birds eggs hatched is the first egg. The sentence say if 2 eggs hatched how many eggs did the bird lay is the second egg. 3 eggs - 2 = 1 egg
HELP ASAP
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths
Answers
Answer:
(c) two hundred seventy-five and one-eighth cm² = 275 1/8 cm²
Step-by-step explanation:
You want the surface area of the rectangular prism represented by the given net.
Missing dimensionsThe first attachment shows the missing dimensions. The height of the vertical rectangle in the center of the net is a total of 2×(5 3/4 + 4) cm.
AreaThe area is the sum of the areas of the rectangular faces of the prism. It is the sum of the individual rectangles shown in the net diagram.
This area can be computed nicely by adding the vertical dimensions and multiplying by the width of the central rectangle. Then, added to that, is the area of the two "wings" on either side of that central rectangle.
In each case, the area of a rectangle is the product of its length and width.
The second attachment shows the calculation of the total area of the figure.
The surface area of the prism is 275 1/8 square centimeters.
Find the area of the figure below.
Answers
Answer:
348 in²
Step-by-step explanation:
[tex] \frac{ad \times (cd + ab)}{2} [/tex]
[tex] \frac{19.2(16 + 24)}{2} [/tex]
384 in²