1. Find the square root of each of the following numbers: (i) 152.7696
PLEASE HELP ME
I’LL GIVE YOU BRAINLIEST
The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.
How to explain the graphThe key features of the graph of the profit function are the following:
The degree of the polynomial function is 3, which means that the graph is a cubic curve.
The coefficient of the leading term is negative (-4), which means that the graph opens downwards.
The coefficient of the quadratic term is positive (32), which means that the graph is concave up.
The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.
It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:
P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78
Therefore, the maximum profit that the company can make is $23,780.
In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.
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Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
Step-by-step explanation:
+ 1.25
every new term is the previous term + 1.25.
with starting value -1.75
f(n) = 1.25n - 1.75
WILL MARK AS BRAINLEIST!!
Question in picture!!
Note: The graph above represents both functions “f” and “g” but is intentionally left unlabeled
Answer:
f(x) is the blue graph, g(x) is the red graph.
x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2
16 - x^2 = 0 when x = -4, 4
So the area between these two graphs is (using the TI-83 graphing calculator):
fnInt (16 - x^2, x, -4, 4) = 85 1/3
hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.
The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.
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ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:
P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)
where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.
Substituting the given probabilities into the formula, we get:
P(puncture or smashed corner) = 0.03 + 0.06 - 0.014
P(puncture or smashed corner) = 0.076
Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
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if x is a matrix of centered data with a column for each field in the data and a row for each sample, how can we use matrix operations to compute the covariance matrix of the variables in the data, up to a scalar multiple?
To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.
The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.
The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.
Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.
Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.
The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.
Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.
This step scales the sum of the products by 1/n, which is equivalent to taking the average.
So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.
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The given question is incomplete, the complete question is
Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 20 inches long. What is the side length of each piece?
1. 10√2
2. 20√2
3. 10√3
4. 20√3
Answer:
The correct answer is:
10√2
Explanation:
In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.
In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.
Let's denote the side length of each square as "s" inches.
According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
In this case, the hypotenuse is 20 inches, so we have:
20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)
400 = 2s^2
Dividing both sides by 2, we get:
200 = s^2
Taking the square root of both sides, we get:
s = √200
Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:
√200 = √(100 x 2) = 10√2
So, the side length of each quilt piece is 10√
The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.
This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).
[tex]h = \sqrt{p^2 + b^2}[/tex]
Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.
20 = √2p² (since p and b are equal, b can be taken as p)
On squaring both sides,
400 = 2p²
p² = 400/2
p² = 200
p = √200
p = 10√2 = b
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PLEASE HELP DUE TODAY!!!!!!!
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5
a. Without evaluating or graphing the functions, how do the ranges compare?
b. graph the 2 functions and describe each range over the given interval
Answer:
see the images and explanation
Step-by-step explanation:
for the graph:
the domain 0 < x < 5
the range for each functions:
g(x) = 2x + 1
g(x) = y , 1 < y < 11
h(x) = 2x + 2 , 2 < y < 12
which of the following is a correct statement regarding the null hypothesis? the null hypothesis is sometimes called the alternative hypothesis. the null hypothesis is the one the researcher cares the most about. the null hypothesis claims the opposite of what the researcher believes. the null hypothesis is usually more accurate than the research hypothesis.
The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.
The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The
null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative
relationship does not exist, hence the term "null".
In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative
hypothesis represents the effect or relationship the researcher is interested in demonstrating.
The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in
favor of the alternative hypothesis.
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how many intervals (or 'bins' or 'classes') should be chosen when creating a histogram? question 1 options: most often, about 8-10. eleven. it can vary - it really depends on the distribution of the variable. a minimum of 5.
"It can vary - it really depends on the distribution of the variable."
The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.
Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.
Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.
The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.
While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.
In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.
A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.
Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.
There is no established guideline, however 8–10 intervals are typically utilized.
A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.
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Please help me with this homework
Answer:
14
Step-by-step explanation:
c = 2[tex]\pi r[/tex]
c = 2[tex]\pi[/tex]7
x = 14[tex]\pi[/tex]
Helping in the name of Jesus.
three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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Find the nearest 10th the cylinder is 22 inches and 12.5 inches what is the lateral surface ?
Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².
What is surface area?Surface area is the total area of the exposed surfaces of a three-dimensional object. It is measured in square units such as square centimeters (cm2) or square meters (m2). Surface area is an important concept in mathematics, science, and engineering, as it is the total area that determines properties such as friction, heat transfer, and fluid dynamics. For example, a larger surface area can increase the rate of heat transfer and allow for more efficient cooling. Similarly, a larger surface area can increase the friction between two objects, allowing them to grip better. Surface area is also important in chemistry, as it affects the amount of gas or liquid that can be absorbed or released by a given object.
The cylinder has a radius of 11 inches and a height of 12.5 inches. To find the lateral surface area of a cylinder, the formula used is A = 2πrℎ, where r is the radius and h is the height of the cylinder. After plugging in the values, the lateral surface area of the cylinder is 821.75 inches². Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².
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brainlist
show all steps nd i will make u brainlist
Step-by-step explanation:
Again, using similar triangle ratios
7.2 m is to 2.4 m
as AB is to 12.0 m
7.2 / 2.4 = AB/12.0 Multiply both sides of the equation by 12
12 * 7.2 / 2.4 = AB = 36.0 meters
A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X:
EXPLANATION/ANSWER
The sample space is the set of all possible outcomes.
In this case, the sample space is , A, B, C, D, E, F, G.
The event X is "The letter selected is found in the word "BEAD". "
The outcomes in this event are A, B, D, and E.
The event Y is "The letter selected comes after "D". "
The outcomes in this event are E, F, and G.
(a) Event "X or Y"
Outcomes in the event "
X or Y" are any outcomes from event X along with any outcomes from event Y.
So the outcomes in the event "X or Y " are A, B, D, E, F, and G. Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y"
The outcomes in the event "X and Y" are the outcomes from event X that also occur in event Y.
So the outcome in the event "X and Y" is E. Event "X and Y": E
(c) The complement of the event X
The complement of the event X is the event consisting of all possible outcomes not in the event X.
So the outcomes in the complement of the event X are C, F, and G
The complement of the event X: , C, F, G
(a) Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y": E
(c) The complement of the event X: , C, F, G
My problem that I am having trouble with:
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is less than 4
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event"A or B":
(b) Event"A and B":
(c) The complement of the event B:
Event "X or Y": A, B, C, E, G. Event "X and Y": C. The complement of event X: D, E, F, G.
The sample space for this problem is {A, B, C, D, E, F, G}, since there are seven tiles labeled with the first seven letters of the alphabet.
Event X: The letter selected comes before "D". Outcomes in this event are A, B, and C.
Event Y: The letter selected is found in the word "CAGE". Outcomes in this event are A, C, E, and G.
Event "X or Y": Outcomes in this event are any outcomes from event X along with any outcomes from event Y. So the outcomes in the event "X or Y" are A, B, C, E, and G.
Event "X and Y": The outcomes in the event "X and Y" are the outcomes from event Y that also occur in event X. So the only outcome in the event "X and Y" is C.
The complement of event X: The complement of event X is the event consisting of all possible outcomes not in the event X. So the outcomes in the complement of event X are D, E, F, and G.
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--The given question is incomplete, the complete question is given
" A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X: "--
at a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). the remaining students do not win a prize. if 150 students play the game at the booth, how much money should the carnival committee expect to pay for prizes for that booth?: *
For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.
We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%
The percentage of students win a jump rope = 16%
The percentage of students win a t-shirt
= 6%
The winning amount for stuffed toy game = $ 3.60
The winning amount for jump rope game = $1.20
The winning amount for t-shirt game
= $7.90
The remaining students do not win a prize. Now, total number of students play the game at the booth = 150
So, number of students who win stuffed toy = 22% of 150 = 33
Number of students who win jump rope = 16% of 150 = 24
Number of students who win stuffed toy
= 6% of 150 = 9
For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6
= 218.7
Hence required value is $218.70.
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what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
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# 15) A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of
113 feet above the water. Jeriel measures an angle of depression to the boat at point A to be
8°. At some later time, Jeriel takes another measurement and finds the angle of depression to
the boat (now at point B) to be 52°. Find the distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.
the distance between point A and point B is approximately 777.9 feet.
what is distance ?
Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.
In the given question,
Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.
From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:
tan(8) = 113/x
x = 113/tan(8)
x =802.5
From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:
tan(52) = 113/y
y = 113/tan(52)
y =72.4
Now we can use the Law of Cosines to find d:
d² = x² + y² - 2xy cos(130)
where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:
d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)
d =777.9
Therefore, the distance between point A and point B is approximately 777.9 feet.
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A circle with center O and radius 5 has central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees, what is the length of chord XY?
The length of chord XY is 5√2.
What is the length of the chord?
It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.
Here, we have
Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees.
We have to find the length of chord XY.
∠XOY = 90°
OX = OY = 5
We draw a perpendicular from the center to chord XY bisect XY at D.
Now, since OD bisects ∠XOY
∠XOD = ∠YOD = 90°/2 = 45°
Now, in ΔXOD
sin45° = XD/OX
1/√2 = XD/5
5/√2 = XD...(1)
In ΔYOD
sin45° = YD/OY
5/√2 = YD...(2)
Adding (1) and (2), we get
XD + YD = 5/√2 + 5/√2
XY = 5√2
Hence, the length of chord XY is 5√2.
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Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
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julian rolled a normal 6-sided die 12 times. his rolls were as follows: 2, 4, 3, 3, 5, 1, 2, 6, 3, 1, 3, 5, 4. what is the probability that he will roll a 3 on the next roll?
The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.
Explanation
On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).
To find the probability, you can use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
In this case:
Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)
Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%
So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.
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Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and
wishes to earn the equivalent amount (same buying power) which she currently enjoys. Inflation is
expected to remain at 6% pa until retirement. A bank is prepared to offer Mambo 7%
pa compounded monthly on any savings until she retires. Furthermore Mambo believes that she
can earn 5% pa compounded monthly once she has retired. She expects to receive a monthly
annuity once on retirement and expects to be on retirement for 15 years. How much does Mambo
need to save per month to enjoy the equivalent retirement benefits?
Question 18
Mambo needs to save R2,322.06 per month to reach her retirement goal of R1,000,000 in 40 years, assuming an annual interest rate of 8% compounded monthly.
Using the formula for the future value of an annuity, we can solve for the monthly payment Mambo needs to make:
[tex]FV = P * [(1 + r/n)^{(nt)} - 1]/(r/n)[/tex]
where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Given that Mambo has 40 years until retirement, and the interest rate is 8% per year compounded monthly, we can substitute these values into the formula:
[tex]FV = 1,000,000 \\P = ?\\r = 0.08\\n = 12\\t = 40 \\1,000,000 = P * [(1 + 0.08/12)^(12*40) - 1]/(0.08/12)[/tex]
Solving for P, we get:
P = 2,322.06
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--The complete Question is, Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and wishes to have R1,000,000 by then. Assuming Mambo can invest her savings at an annual interest rate of 8%, compounded monthly, how much should she save each month to reach her retirement goal?--
2. when conducting a hypothesis test, the hypothesis that illustrates what we really think is going on in the population is called the hypothesis. an. analytical b. hypothetical c. null d. theoretical e. alternative
Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)