Answer:
After 5 years of investment, Suzanne will have $ 4,400 in her account, while Derek will have $ 4,416.32 in his account.
Step-by-step explanation:
Since Suzanne deposits $ 4000 in an account that earns simple interest at an annual rate of 2%, and Derek deposits $ 4000 in an account that earns compound interest at an annual rate of 2% and is compounded annually., Both for a period of 5 years, to determine how much money each one will have in their account after 5 years, the following calculation must be made:
Suzanne:
((4,000 x 0.02) x 5) + 4,000 = X
(80 x 5) + 4,000 = X
400 + 4,000 = X
4,400 = X
Derek:
4,000 x (1 + 0.02 / 1) ^ 5x1 = X
4,000 x 1.02 ^ 5 = X
4,416.32 = X
Thus, after 5 years of investment, Suzanne will have $ 4,400 in her account, while Derek will have $ 4,416.32 in her account.
The venn Diagram represents the result of survey that asked participants wether they would want a bird or fish as a pet .
Match the box with the value that goes into the box to Conroe the way table
41. 1. Box 1
22. 2. Box . 2
3 . Box 3
32. Box 4
10. Box 5
19. Box 6
57. Box 7
16. Box 8
25. Box 9
6
The venn diagram has been created and solved in the table below
How to sdolve the venn diagramAs we can see the venn diagram:
number of bird+fish=6
number of bird+not fish= 10
number of fish+not bird=19
and number of not fish and not bird=22
Hence, we get the following table
Fish Not Fish Total
Bird 6 10 16
Not Bird 19 22 41
Total 25 32 57
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What is the total weight of the bags that weighed /8 pound each?
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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simplify using FOIL method (2x+3)•(2x-3)
Step-by-step explanation:
First 2x * 2x = 4x^2
Outer 2x * -3 = -6x
Inner 3 * 2x = 6x
Last 3 * - 3 = -9
4x^2 -6x + 6x - 9 = 4x^2 - 9
Answer
4x²-9
Step-by-step explanation:
Please mark brainliest
a system of equations is shown below
y = 3x - 1
y = - 2x + 4
what is the sum of X and Y in the solution to the system
Answer:
3
Step-by-step explanation:
You want the value of (x+y) as determined by the system of equations ...
y = 3x -1y = -2x +4SolutionWe can subtract the second equation from the first to get ...
(y) -(y) = (3x -1) -(-2x +4)
0 = 5x -5
0 = x -1
1 = x
Using the first equation to find y, we have ...
y = 3(1) -1 = 2
The sum of x and y is (x +y) = (1 +2) = 3.
Alternate solutionLet t = x+y. This means y = t -x.
Now, the equations become ...
t -x = 3x -1t -x = -2x +4Adding 4 times the second equation to the first gives ...
(t -x) +4(t -x) = (3x -1) +4(-2x +4)
5t -5x = -5x +15
Adding 5x and dividing by 5 gives ...
t = 3
The sum of x and y is 3.
__
Additional comment
Sometimes you can find the value of the objective function directly, as in the second solution here.
The reason we chose 4 as a multiplier in the alternate solution is that we observed the equations could be written as ...
t -4x = -1
t +x = 4
where the variable x has coefficients with a ratio of -4. Using 4 as the multiplier eliminates the x-variable, leaving t — the variable whose value we want.
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ITS DO TODAY HELPPPPPPP
The difference in the addition of both fractions is that they have different lowest common multiples.
How to solve Fraction Problems?We want to add the fraction expression given as:
¹/₂ + ¹/₄
Taking the Lowest common multiple of 8, we have:
(4 + 2)/8 = 6/8
However, for the second fraction expression, we have:
¹/₂ + ¹/₃
Taking the lowest common multiple which is 6, we have:
(3 + 2)/6 = 5/6
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At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 22 minutes and a standard deviation of 3 minutes. If you visit that restaurant 37 times this year, what is the expected number of times that you would expect to wait between 19 minutes and 23 minutes, to the nearest whole number?
To find the expected number of times you would wait between 19 and 23 minutes, we need to calculate the z-scores for these values and use them to find the area under the normal distribution curve between those values.
First, we calculate the z-score for 19 minutes:
z = (19 - 22) / 3 = -1
Next, we calculate the z-score for 23 minutes:
z = (23 - 22) / 3 = 0.33
Using a standard normal distribution table or calculator, we can find the area under the normal distribution curve between these z-scores:
P(-1 < z < 0.33) = 0.4082 - 0.3413 = 0.0669
This means that there is a probability of 0.0669 of waiting between 19 and 23 minutes for a single visit to the restaurant.
To find the expected number of times you would wait between 19 and 23 minutes over 37 visits, we multiply the probability for a single visit by the number of visits:
Expected number of times = 0.0669 x 37 ≈ 2.47
Rounding to the nearest whole number, we would expect to wait between 19 and 23 minutes about 2 times over 37 visits to the restaurant.
PLEASE ANSWER NOW I NEED THIS ASAP FOR 100 POINTS!!!!
[tex]1\frac{3}{4}[/tex] feet as a multiplication expression using the unit, 1 foot, as a factor is [tex]1\frac{3}{4}[/tex]×1.
The given fraction is [tex]1\frac{3}{4}[/tex].
[tex]1\frac{3}{4}[/tex] feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because [tex]1\frac{3}{4}[/tex] is the same as 1 + 3/4.
Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.
Therefore, the multiplication expression is 1 foot × [tex]1\frac{3}{4}[/tex] = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.
Therefore, [tex]1\frac{3}{4}[/tex] feet as a multiplication expression using the unit, 1 foot, as a factor is [tex]1\frac{3}{4}[/tex]×1.
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Step-by-step explanation:
1ft=12in
1¾ft=x
x=12×7/4=21in
1¾ft=1¾×1 ft
Determine two pairs of polar coordinates for (3,-3) when x^2-y^2=4 in polar coordinats
The two pairs of polar coordinates for the point (3, -3) when x² - y² = 4 in polar coordinates are (3√2, -45°) or (3√2, 315°) and (-3√2, 135°).
Given the Cartesian coordinate (3, -3), and the equation x² - y² = 4.To convert Cartesian coordinates to polar coordinates, we use the formula:r = sqrt(x² + y²)θ = tan⁻¹(y/x)
The first step is to substitute the given Cartesian coordinates into the formula:
r = sqrt(3² + (-3)²)r = sqrt(18)r = 3√2
To determine the angle θ, we first look at the sign of both the x and y coordinates. Since x is positive and y is negative, the angle θ is in the fourth quadrant.
To determine the angle θ, we use the formula:θ = tan⁻¹(y/x)θ = tan⁻¹(-3/3)θ = -45°Alternatively, we can add 360° to get the angle in the fourth quadrant:θ = 315°
Therefore, one pair of polar coordinates is (3√2, -45°) or (3√2, 315°).To determine the second pair of polar coordinates, we can add 180° to the angle and negate the radius,
since this will give us the same point but in the opposite direction.θ = -45° + 180° = 135°r = -3√2
Therefore, the second pair of polar coordinates is (-3√2, 135°).
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HURRY! The table shows the value of printing equipment for 3 years after it is purchased. The values form a geometric sequence. How much will the equipment be worth after 7 years?
Geometric sequence: a_n=〖a_1 r〗^(n-1)
Year Value $
1 $12,000
2 $9,600
3 $7,680
Find the common ratio, r, of the sequence
12 000 * r = 9600
r = 9600/12000 = 0.8
12000 ( 0.8)^6 = $ 3145.73 in year 7 ( I used '6' instead of '7' because 12 000 is listed as year '1' and not year '0' )
No do I solve this problem?
Using law of sine, the value of A is 54°, b is 4.4 units and c is 6.1 units
What is sine rule?The sine rule, also known as the law of sines, is a mathematical principle used in trigonometry to relate the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant for all sides and angles of the triangle.
The formula is given as;
a / sin A = b / sin B = c / sin C
To find the value of angle A
A + B + C = 180°
Reason: The sum of angles in a triangle is equal to 180°
46° + A + 80° = 180°
126° + A = 180°
A = 180° - 126°
A = 54°
Using this, we can apply sine rule;
a / sin A = b / sin B
5/ sin 54 = b / sin 46
b = 5sin46 / sin 54
b = 4.4 units
Using sine rule again;
a/ sin A = c / sin C
5/ sin 54 = c / sin80
c = 5sin80 / sin 54
c = 6.1 units
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kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answer:kkkkkkkkkkkkkkkkkkkkkkkkkkk mean ok 26 times
Please help me w this
The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q
How to solve Algebraic Expressions?We are given the algebraic expression as:
¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃
Combining Like terms gives us:
(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)
Solving both brackets individually gives us:
((11 - 4)/12) + ⁴/₆q
= ⁷/₁₂ + ⁴/₆q
Thus, we conclude that is the solution of the given algebraic expression problem
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Find the measurement of WX
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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For each pair of functions f and g below, find f(g(x)) and g (f(x)).
Then, determine whether fand g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
f(x) = x+4
g (x) = x+4
The Function f(g(x)) = g(f(x)) = x + 8.
The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).
f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8
Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8
Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,
which is x + 8.
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NO LINKS!! URGENT HELP PLEASE!!!!
Find the probability.
30. You flip a coin twice. The first flip lands heads-up and the second flip lands tails-up.
31. A cooler contains 10 bottles of sports drinks: 4 lemon-lime flavored, 3 orange-flavored, and 3 fruit-punch flavored. You randomly grab a bottle. Then you return the bottle to the cooler, mix up the bottles, and randomly select another bottle. Both times you get a lemon-lime drink.
Answer:
Flipping a coin twice and obtaining heads the first time and tails the second time has a probability of (1/2) * (1/2) = 1/4.
On the initial draw, there is a 4/10 chance that a drink with a lemon-lime flavor will be randomly chosen from the cooler. Because the bottle is put back in the cooler and mixed before the second draw, the likelihood of choosing a lemon-lime beverage at random is also 4/10. The likelihood of winning a lemon-lime drink on both draws is (4/10) * (4/10), which equals 16/100 or 4/25.
Step-by-step explanation:
Answer:
[tex]\textsf{30)} \quad \dfrac{1}{4}=25\%[/tex]
[tex]\textsf{31)} \quad \dfrac{4}{25}=16\%[/tex]
Step-by-step explanation:
Probability is a measure of the likelihood or chance of an event occurring. The basic formula for probability is:
[tex]\boxed{{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}}[/tex]
Question 30A fair coin has two possible outcomes: heads (H) or tails (T).
Each flip of the coin is independent, meaning the outcome of one flip does not affect the outcome of the other flip.
The probability of flipping a head is P(H) = 1/2.
The probability of filliping a tail is P(T) = 1/2.
To find the probability that the first flip lands heads-up and the second flip lands tails-up, we multiply the individual probabilities together:
[tex]\sf P(H)\;and\;P(T)=\dfrac{1}{2} \cdot \dfrac{1}{2}=\dfrac{1 \cdot 1}{2 \cdot 2}=\dfrac{1}{4}[/tex]
So the probability of flipping a coin twice and getting heads on the first flip and tails on the second flip is 1/4 or 25%.
[tex]\hrulefill[/tex]
Question 31There are 10 bottles in total, so there are 10 possible outcomes.
There are 4 lemon-lime drinks in the cooler, therefore the probability of selecting a lemon-lime bottle is:
[tex]\sf P(lemon$-$\sf lime)=\dfrac{4}{10}[/tex]
As you are randomly selecting two bottles with replacement, meaning you return the bottle to the cooler before selecting the next one, the probability of selecting a lemon-lime bottle each time is the same.
To find the probability of that both drinks are lemon-lime flavored, multiply the individual probabilities together:
[tex]\begin{aligned}\sf Probability &= \textsf{P(lemon-lime)} \cdot \textsf{P(lemon-lime)}\\\\&= \dfrac{4}{10} \cdot \dfrac{4}{10}\\\\&=\dfrac{4 \cdot 4}{10 \cdot 10}\\\\&=\dfrac{16}{100}\\\\&=\dfrac{4}{25}\end{aligned}[/tex]
Therefore, the probability of randomly selecting two drinks from the cooler and getting a lemon-lime drink both times is 4/25 or 16%.
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Solve each problem involving direct or inverse variation.
26. If y varies directly as x, and y = 15/4 when x = 15, find y when x = 11
27. If y varies inversely as x, and y = 4 when x = 9, find when x = 7
Answer:
see explanation
Step-by-step explanation:
26
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = [tex]\frac{15}{4}[/tex] when x = 15
[tex]\frac{15}{4}[/tex] = 15k ( divide both sides by 15 )
[tex]\frac{\frac{15}{4} }{15}[/tex] = k , then
k = [tex]\frac{15}{4}[/tex] × [tex]\frac{1}{15}[/tex] = [tex]\frac{1}{4}[/tex]
y = [tex]\frac{1}{4}[/tex] x ← equation of variation
when x = 11 , then
y = [tex]\frac{1}{4}[/tex] × 11 = [tex]\frac{11}{4}[/tex]
27
given y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 4 when x = 9
4 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
36 = k
y = [tex]\frac{36}{x}[/tex] ← equation of variation
when x = 7 , then
y = [tex]\frac{36}{7}[/tex]
Answer:
26) y = 11/4
27) y = 36/7
Step-by-step explanation:
Question 26Direct variation is a mathematical relationship between two variables where a change in one variable directly corresponds to a change in the other variable. It is represented by the equation y = kx, where y and x are the variables and k is the constant of variation.
To find the constant of variation, k, substitute the given values of y = 15/4 when x = 15 into the direct variation equation and solve for k:
[tex]\begin{aligned}y&=kx\\\\\dfrac{15}{4}&=15k\\\\k&=\dfrac{1}{4}\end{aligned}[/tex]
To find the value of y when x = 11, substitute the found value of k and x = 11 into the direct variation equation, and solve for y:
[tex]\begin{aligned}y&=kx\\\\y&=\dfrac{1}{4} \cdot 11\\\\y&=\dfrac{11}{4}\end{aligned}[/tex]
Therefore, if y varies directly as x, then y = 11/4 when x = 11.
[tex]\hrulefill[/tex]
Inverse variation is a mathematical relationship between two variables where an increase in one variable results in a corresponding decrease in the other variable, and vice versa, while their product remains constant. It is represented by the equation y = k/x, where y and x are the variables and k is the constant of variation.
To find the constant of variation, k, substitute the given values of y = 4 when x = 9 into the inverse variation equation and solve for k:
[tex]\begin{aligned}y&=\dfrac{k}{x}\\\\4&=\dfrac{k}{9}\\\\k&=36\end{aligned}[/tex]
To find the value of y when x = 7, substitute the found value of k and x = 7 into the inverse variation equation, and solve for y:
[tex]\begin{aligned}y&=\dfrac{k}{x}\\\\y&=\dfrac{36}{7}\end{aligned}[/tex]
Therefore, if y varies inversely as x, then y = 36/7 when x = 7.
decompose into partial fractions:
[tex]\frac{x^5-2x^4+x^3+x+5}{x^3-2x^2+x-2} \\ \\ \\ \frac{4x^2-14x+2}{4x^2-1}[/tex]
(1) (x + 1)/(x - 2) - (x + 1)/(x^2 + 1)
(2) -2/(2x - 1) + (3/2)/(2x + 1)
To decompose the rational expressions into partial fractions, we first need to factorize the denominators. Let's start with the first expression:
Factorizing the denominator:
x^3 - 2x^2 + x - 2 = (x - 2)(x^2 + 1)
Decomposing the fraction:
We have a linear factor and a quadratic factor, so the partial fraction decomposition will be of the form:
A/(x - 2) + (Bx + C)/(x^2 + 1)
Finding the values of A, B, and C:
Multiplying both sides of the equation by the common denominator (x - 2)(x^2 + 1) gives:
x^5 - 2x^4 + x^3 + x + 5 = A(x^2 + 1) + (Bx + C)(x - 2)
By equating coefficients of corresponding powers of x, we get:
A = 1
-2A + B = -2
A - 2B + C = 1
Solving this system of equations, we find A = 1, B = -1, and C = 0.
Therefore, the partial fraction decomposition is:
(x + 1)/(x - 2) - (x + 1)/(x^2 + 1)
Now let's move on to the second expression:
Factorizing the denominator:
4x^2 - 1 = (2x - 1)(2x + 1)
Decomposing the fraction:
Since we have two linear factors, the partial fraction decomposition will be of the form:
A/(2x - 1) + B/(2x + 1)
Finding the values of A and B:
Multiplying both sides of the equation by the common denominator (2x - 1)(2x + 1) gives:
4x^2 - 14x + 2 = A(2x + 1) + B(2x - 1)
By equating coefficients of corresponding powers of x, we get:
4A + 4B = 4 (coefficients of x^2)
A - B = -7 (coefficients of x)
A - B = 1 (constant term)
Solving this system of equations, we find A = -2 and B = 3/2.
Therefore, the partial fraction decomposition is:
-2/(2x - 1) + (3/2)/(2x + 1)
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Solve for |x + 4|= -8
If anyone helps thank u
Answer:
no solution!
Step-by-step explanation:
The absolute value of a quantity is always non-negative, meaning it cannot be negative. However, in this equation, we have the absolute value of x + 4 equaling -8, which is a negative value. Therefore, there is no solution to this equation.
Find the Perimeter of the figure below, composed of a square and four semicircles. Rounded to the nearest tenths place
The perimeter of the figure, rounded to the nearest tenths place, is 41.1 units.
To find the perimeter of the figure composed of a square and four semicircles, we need to determine the lengths of the square's sides and the semicircles' arcs.
Given that the side length of the square is 4 units, the perimeter of the square is simply the sum of all four sides, which is 4 + 4 + 4 + 4 = 16 units.
Now, let's focus on the semicircles. Each semicircle's diameter is equal to the side length of the square, which is 4 units. Therefore, the radius of each semicircle is half of the diameter, or 2 units.
The formula to find the arc length of a semicircle is given by θ/360 * 2πr, where θ is the angle of the arc and r is the radius. In this case, the angle of the arc is 180 degrees since we are dealing with semicircles.
Using the formula, the arc length of each semicircle is 180/360 * 2π * 2 = π * 2 = 2π units.
Since there are four semicircles in the figure, the total length of the arcs is 4 * 2π = 8π units.
Finally, we can calculate the perimeter by adding the length of the square's sides and the length of the semicircles' arcs:
Perimeter = Length of square's sides + Length of semicircles' arcs
= 16 units + 8π units
To round the perimeter to the nearest tenths place, we need to determine the approximate value of π. Taking π as approximately 3.14, we can calculate the approximate perimeter as:
Perimeter ≈ 16 + 8 * 3.14 ≈ 16 + 25.12 ≈ 41.12 units.
Therefore, the perimeter of the figure, rounded to the nearest tenths place, is approximately 41.1 units.
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a right triangle had side lengths d,e,and f as shown below. use these lengths to find sin x cos x and tan x
Geometry: Angle a) Draw a line segment AB. Mark a point O on AB and draw an angle BOC. Measure ZBOC and ZAOC. Verify that ZBOC + ZAOC = 180°.
The angles ZBOC + ZAOC = 180°.
In geometry, angles are two rays that share a common endpoint. The common endpoint is called a vertex, and the rays are known as sides.
In a plane, when two lines intersect, they form four angles at the point of intersection, and when a line segment intersects a line, they form two angles.Geometry: Anglea) Draw a line segment AB.
Mark a point O on AB and draw an angle BOC. Measure ZBOC and ZAOC. Verify that ZBOC + ZAOC = 180°.
To solve this problem, the following steps should be followed:
Step 1: Draw a line segment AB
Step 2: Mark point O on AB and draw an angle BOC
Step 3: Measure angles ZBOC and ZAOC
Step 4: Add angles ZBOC and ZAOCZBOC + ZAOC = 180°
The sum of angles ZBOC and ZAOC is 180°. It is because an angle is the amount of turn between two rays with a common endpoint.
When the rays of two angles form a straight line, the two angles are called supplementary angles.The sum of supplementary angles is always 180°.
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Joey is flying his Cesna due Northwest at 188mph. Unfortunately, a wind traveling.
60mph due 150 bearing. Find Joey's actual Speed and direction.
Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.
Given that Joey's aircraft speed: 188 mph
Wind speed: 60 mph
Wind direction: 150 degrees (measured clockwise from due north)
We can consider the wind as a vector, which has both magnitude (speed) and direction.
The wind vector can be represented as follows:
Wind vector = 60 mph at 150 degrees
We convert the wind direction from degrees to a compass bearing.
Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.
Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)
Wind vector = 60 mph at 210 degrees
To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.
Converting the wind vector into its x and y components:
Wind vector (x component) = 60 mph × cos(210 degrees)
= -48.98 mph (negative because it opposes the aircraft's motion)
Wind vector (y component) = 60 mph×sin(210 degrees)
= -31.18 mph (negative because it opposes the aircraft's motion)
Now, we can add the x and y components of the two vectors to find the resulting velocity vector:
Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph
Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph
Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)
= 143.59 mph
Direction = arctan((-31.18 mph) / 139.02 mph)
= -12.80 degrees
The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.
The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.
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the slope of the line is below -3. Which of the following is the point slope form if the line?
Answer: y=-3x+b
Step-by-step explanation:
You didn't give the answers, but it would look something like this:
y=-3x+b
Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
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Hi, I just needed some help with the question that is attached.
a. The total impedance, z is 6 Ohms
b. The modulus of the total impedance is 6 Ohms, which represents its magnitude or absolute value. The angle is not provided for the principal argument.
How to determine the impedanceFrom the information given, we have that;
z₁ = R₁ + Xₐ
z₂ = R₂ - Xₙ
We have that the values are;
R₁ = 3 OhmsXₐ = 3 OhmsR₂ = 4 OhmsXₙ = 4 OhmsNow, substitute the values, we have;
z₁ = 3 + 3
Add the values
z₁ = 6 Ohms
z₂ = 4 - 4
z₂ = 0 Ohms
To determine the total impedance, we have;
1/z = 1/z₁ + 1/z₂
Substitute the values
1/z = 1/6 + 1/0
1/z = 1/6
z = 6 Ohms
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Please answer the following question on linear algebra.
T satisfies both the additive and scalar multiplication properties, it can be concluded that T is a linear transformation.
To prove that T is a linear transformation, we need to show that it satisfies two properties: additive property and scalar multiplication property.
Additive property:
Let z = (x1, x2) be an arbitrary vector in R2. We want to confirm that T(z1 + z2) = T(z1) + T(z2).
Let z1 = (x1, x2) and z2 = (y1, y2) be arbitrary vectors in R2.
T(z1 + z2) = T((x1 + y1, x2 + y2)) = (x1 + y1, x2 + y2)
T(z1) + T(z2) = T(x1, x2) + T(y1, y2) = (x1, x2) + (y1, y2) = (x1 + y1, x2 + y2)
We can see that T(z1 + z2) = T(z1) + T(z2), thus satisfying the additive property.
Scalar multiplication property:
Let z = (x1, x2) be an arbitrary vector in R2 and k be an arbitrary scalar. We want to confirm that T(kz) = kT(z).
T(kz) = T(kx1, kx2) = (kx1, kx2)
kT(z) = kT(x1, x2) = k(x1, x2) = (kx1, kx2)
We can see that T(kz) = kT(z), thus satisfying the scalar multiplication property.
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A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
Statements Reasons
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared Take the square root of both sides of the equation
? Simplify the right side of the equation
The missing statement in the proof of the Quadratic Formula involves simplifying the right side of the equation by taking the square root of the numerator, resulting in x plus b over 2a equals plus or minus √((b^2 - 4ac)) all over 4a squared.
The missing statement in the proof of the Quadratic Formula, we need to simplify the right side of the equation:
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
To simplify the right side, we can take the square root of the numerator and denominator separately:
√(b squared minus 4 times a times c) = √((b^2 - 4ac))
Now, substituting the simplified expression into the equation, we have:
x plus b over 2 times a equals plus or minus √((b^2 - 4ac)) all over 4 times a squared
This completes the missing statement in the proof of the Quadratic Formula.
In conclusion, the missing statement in the proof of the Quadratic Formula involves simplifying the right side of the equation by taking the square root of the numerator, resulting in x plus b over 2a equals plus or minus √((b^2 - 4ac)) all over 4a squared.
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In APQR, m2 P = 60°, mz Q = 30°, and m2 R = 90°. Which of the following
statements about APQR are true?
Check all that apply.
A. PQ=2. PR
B. QR=
PQ
C. QR= 2 • PR
☐ D. PR = = 4. PQ
•
□E. QR=√√√3 PR
F. PQ=√√3 PR
The statements that are true about triangle PQR are QR = (sqrt(3))/2 * PQ and PR = (sqrt(3))/2 * PQ.The correct answer is option B and D.
Let's analyze the statements one by one:
A. PQ = 2PR:
This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x.
Therefore, PQ = x, and PR = x√3. Since √3 is not equal to 2, this statement is false.
B. QR = (sqrt(3))/2 * PQ:
This statement is true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x.
Therefore, QR = x√3/2 = (sqrt(3))/2 * x = (sqrt(3))/2 * PQ. This statement holds true.
C. OR = 2PR:
We don't have any information regarding the length of OR, so we cannot determine if this statement is true or false based on the given information.
D. PR = (sqrt(3))/2 * PQ:
This statement is true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, PR = x√3 = (sqrt(3))/2 * 2x = (sqrt(3))/2 * PQ. This statement is correct.
E. QR = sqrt(3) * PR:
This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, QR = x√3, and PR = x√3. So, QR = PR, but not QR = sqrt(3) * PR.
F. PQ = sqrt(3) * PR:
This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, PQ = x, and PR = x√3. So, PQ = PR/√3, but not PQ = sqrt(3) * PR.
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The probable question may be:
In triangle PQR , m angle P = 60 deg , m angle Q = 30 deg and m angle R = 90 deg Which of the following statements about triangle PQR are true?
Check all that apply
A. PQ = 2PR
B.QR = (sqrt(3))/2 * PQ
C. OR = 2PR
D.PR = (sqrt(3))/2 * PQ
E. QR = sqrt(3) * PR
F. PQ = sqrt(3) * PR
Cómo despejar an
Sn= (a1 + an)/2 n
Step-by-step explanation:
The formula:
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2
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S
n
=
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n
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is used to solve for the sum of the arithmetic sequence given the first term a₁, the number of terms n, and the last term in an.
Example:
3, 6, 9, 12, 15,...,123
The first term, a₁ = 3
The last term an = 123
Common difference, d = 3 (because the sequence are multiples of 3)
Number of terms, n= ?
Find the number of terms, n:
an = a₁ + (n-1) (d)
123 = 3 + (n-1) (3)
123 = 3 - 3 + 3n
123/3 = 3n/3
n = 41
To find the sum of the given sequence without adding 3 + 6 + 9, ... + 123, we use the formula:
S₄₁ = (41/2) (3 + 123)
S₄₁ = (41/2) (126)
S₄₁ = (41)(63)
S₄₁ = 2,583 ⇒ the sum of the given sequence
Determine the equation of a straight line that is parallel to the line 2x + 4y =1 and which passes through the point (1, 1).
The equation of the straight line parallel to 2x + 4y = 1 and passing through the point (1, 1) is y = (-1/2)x + 3/2.
To determine the equation of a straight line that is parallel to the line 2x + 4y = 1 and passes through the point (1, 1), we can use the fact that parallel lines have the same slope.
First, let's rearrange the given equation 2x + 4y = 1 into slope-intercept form, y = mx + b,
where m is the slope and b is the y-intercept.
2x + 4y = 1
4y = -2x + 1
y = (-2/4)x + 1/4
y = (-1/2)x + 1/4
From this equation, we can see that the slope of the given line is -1/2.
Since the parallel line we want to find has the same slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) is the given point.
Plugging in the values (1, 1) and the slope -1/2 into the equation, we have:
y - 1 = (-1/2)(x - 1)
To simplify, we distribute the -1/2:
y - 1 = (-1/2)x + 1/2
Next, we isolate y by adding 1 to both sides of the equation:
y = (-1/2)x + 1/2 + 1
y = (-1/2)x + 3/2.
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