The values of sec a - cosec a/sec a+cosec a is 4/25.
Trigonometric ratios:The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
In a right-angled triangle,
Sin θ = Opposite Side /HypotenuseCos θ = Adjacent Side /HypotenuseTan θ = Opposite Side/Adjacent Side Sec θ = 1/cos θCosec θ = 1/sin θHere we have
tan A = 21/29
As we know Tan θ = Opposite side/Adjacent side
=> Opposite side = 21
=> Adjacent side = 29
In a right-angle triangle,
=> Hypotenuse² = Opposite side² + Adjacent side²
=> Hypotenuse² = 21² +29²
=> Hypotenuse² = 441 + 841
=> Hypotenuse² = (35.8)²
Cos a = Adjacent side /Hyopenuse = 29/ 35.8
Sin a = Opposite side/Hypotenuse = 21/35.8
The given expression can be solved as follows
=> [tex]\frac{seca - coseca}{seca+coseca } = \frac{ \frac{1}{cos a}-\frac{1}{sina} }{\frac{1}{cos a }+\frac{1}{sin a} }[/tex]
=> [tex]\frac{ \frac{sin a - cosa}{cos a sn a} }{\frac{sin a + cos a}{cos a sin a} }[/tex]
=> [tex]\frac{sin a - cosa}{cos a+ sin a}[/tex]
=> [tex]\frac{ \frac{21}{35.8} - \frac{29}{35.6} }{\frac{29}{35.8} + \frac{21}{35.8} }[/tex]
=> [tex]\frac{21- 29}{29+21}[/tex]
=> [tex]\frac{8}{50}[/tex]
=> [tex]\frac{4}{25}[/tex]
Therefore,
The values of sec a - cosec a/sec a+cosec a is 4/25.
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the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers.
-17, -15 and -13 are the three consecutive odd integers.
Word problem involving linear equationLinear equation are equation that has a leading degree of 1
Let the smallest integer is '2x - 1'
The next two integers are 2x + 1 and 2x + 3
If the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers, hence;
2x - 1 + 2x + 1 + 2x + 3 = 2(2x-1) - 19
6x + 3 = 4x - 21
6x - 4x = -21 -3
3x = -24
x = -8
First number = 2(-8) - 1 = -17
Second number = 2(-8) + 1 = -15
Third number = 2(-8) + 3 = -13
Hence the 3 consecutive odd integers are -17, -15 and -13.
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Complete question
The sum of 3 consecutive odd integers is 19 less than twice the smallest of integers , what are the integers?
Determine the largest power of 10 that is a factor of the following numbers (equivalently, the number of terminal 0's, using ordinary base 10 representation):(a) 50!.
(b) 1000!.
The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.
(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.
There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.
Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.
(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:
⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249
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HELP!
The figure on the right is a scaled copy of the figure on the left, though it might have
also been rotated.
U
W
Η,
Which side in the figure on the right corresponds to segment UW?
What is the scale factor?
Answer:
HI
The scale fact from the smaller to the larger is 3. The scale factor from the larger to the smaller is 1/3
Step-by-step explanation:
X =
Evaluate.
-(-2)+√(-2)²-4(1)(-8)
2(1)
= 2 + (²)
X =
Enter the number that
belongs in the green box.
The value of the equation for x is 32
What is PEDMAS?PEDMAS is described as a mathematical acronym that represents the important operations during calculations.
The alphabets represents;
ParenthesesExponentsDivisionMultiplicationAdditionSubtractionFrom the information given, we have;
-(-2)+√(-2)²-4(1)(-8)
expand the brackets
2 + -2 -4(-8)
multiply the values
2 -2 + 32
Add the values
32
Hence, the value is 32
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please help me with math i’ll give you brainlist
Answer:we can’t help if it is barely readable
Step-by-step explanation:
Five students—the females Ann and Betty and the males Clint, Douglas, and Edward—are rated equally qualified for admission to law school, ahead of other applicants. However, all but two positions have been filled for the entering class. The admissions committee can admit only two more students, so it decides to randomly select two of these five candidates. For this strategy, let of females admitted. Using the first letter of the name to denote a student, the different combinations that could be admitted are (A, B), (A, C), (A, D), (A, E), (B, C), (B, D), (B, E), (C, D), (C, E), and (D, E).
(a)Construct the probability distribution for .
(b)Construct the sampling distribution of the sample proportion of the students selected who are female.
Answer:
(a) The probability distribution for the number of female students admitted can be calculated as follows:
P(0 female students) = (2C0) × (3C2) / (5C2) = (1) × (3) / (10) = 0.3
P(1 female student) = (2C1) × (3C1) / (5C2) = (2) × (3) / (10) = 0.6
P(2 female students) = (2C2) × (3C0) / (5C2) = (1) × (1) / (10) = 0.1
(b) The sampling distribution of the sample proportion of female students selected can be calculated as follows:
P(p = 0) = 0.3 (for 0 female students)
P(p = 1/2) = 0.6 (for 1 female student)
P(p = 1) = 0.1 (for 2 female students)
Note that the sampling distribution of the sample proportion is a discrete probability distribution with values of 0, 1/2, and 1, and corresponding probabilities 0.3, 0.6, and 0.1, respectively.
The weight of potato chips in a medium sized bag is stated to be 10 ounces. The amount that
the packaging machine puts in these bags is believed to be normally distributed with a mean of 10.2
ounces and a standard deviation of 0.12 ounces. Is it unusual for a bag to contain 9.8 ounces of
chips? Explain your answer.
Step-by-step explanation:
a normal distribution with mean m and standard deviation d gives us a few regular pieces of information.
for example, we know that 68.2% of all events are within the interval
m ± d
and 95.4% of all events are in the interval
m ± 2d
and 99.7% of all events are in the interval
m ± 3d
that means only 0.3% of all events are outside the interval
m ± 3d = 10.2 ± 3×0.12 = 10.2 ± 0.36
now, when a bag is filled with 9.8 ounces, it is 0.4 off the mean (10.2).
that means it is outside the 10.2 ± 0.36 interval and inside the 0.3% "exception" range.
you have to see it also that way : 0.3% means 3 out of 1000 bags are in that range.
so, yes, it is considered unusual.
Will your battery capacity go down if you update your iphone?
Unfortunately, a lot of software apps tend to use up battery life even if you aren't currently using the phone. This leads to the phone feeling more sluggish over time. To help combat this, it's helpful to clear out any unused apps and clear up the cache.
Even if software was perfectly written the most efficiently, and apps weren't intrusive, the physical nature of the battery itself has limitations. The capacity of the battery will slowly decay each time you charge or use your phone. Even just sitting idle it slowly loses capacity. This loss is very small that it's hard to detect. But add it up over time and the losses will get more noticeable. This is why you cannot simply charge a battery an infinite number of times. As with all things in life, there's a limit.
Summary: Yes the capacity will go down but ever so slightly. It depends how often the updates are done and what software is being updated. Ideally the updated software should be more efficient with the battery life. However, life isn't perfect and there will likely be flaws.
j is the midpoint of HI and GH. complete the proof that GHJ ≅ GIJ
4. Reflexive property
5. SSS
A quadratic function is shown on the graph
What is the range of the function?
The range is the set of all y-values used by the graph.
This graph's lowest y-value is 3 at the point (0,3).
The graph almost reaches as y-value of 12, but doesn't actually get there because of the closed circle at (-3,12).
The range is [3, 12) or { y | 3 ≤ y < 12}, depending on the notation needed.
Need help, got the answer as $10421.82 but it says it's wrong, I need the answer with steps please, thanks!
The balance in the account after 16 years, given interest rate and the compounding period, is $ 10, 421. 83.
How to find the balance in the account ?To find the balance after 16 years, the formula to be used is the compound interest formula which is:
= Amount invested x ( 1 + rate ) ^ number of periods
Rate :
= 6 % / 12 months per year
= 0. 5 %
The number of periods :
= 16 years x 12 months a year
= 192 periods
The value would be :
= 4, 000 x ( 1 + 0. 5% ) ¹⁹²
= $ 10, 421. 83
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11. Equipment for your salon will cost anywhere from $7,000 to $10,000. How much money will you spend over the course of the first year with rent and equipment?
You have to spend $26,500 over the course of the first year with rent and equipment.
What is the equipment cost about?To calculate how much money you will spend over the course of the first year with rent and equipment, you need to add the cost of rent to the cost of equipment.
In a hypothetical scenario, Let's assume that the cost of rent for the first year is $1,500 per month.
To calculate the total cost of rent for the first year, you can multiply the monthly rent by the number of months in a year:
$1,500/month x 12 months = $18,000
So the total cost of rent for the first year is $18,000.
To calculate the total cost of equipment, you can take the average cost of the equipment (i.e., the midpoint of the given range) and assume that you will spend that amount:
($7,000 + $10,000) / 2 = $8,500
So the total cost of equipment is $8,500.
To calculate the total cost of rent and equipment for the first year, you can add the two costs together:
$18,000 + $8,500 = $26,500
Therefore, you will spend $26,500 over the course of the first year with rent and equipment.
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Question 6 of 10
What is the length of the hypotenuse of the triangle below?
3√2
45°
90⁰
h
3√2
45°
Answer:
c) 6
Step-by-step explanation:
in a 45-45-90 degree triangle the hypotenuse is [tex]\sqrt{2}[/tex] times more than the length of the other sides
3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] is the same as 3(2) or 6
The length of the hypotenuse of the triangle is,
⇒ h = 6
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Base of triangle = 3√2
Length of triangle = 3√2
Now, We can formulate;
⇒ h² = (3√2)² + (3√2)²
⇒ h² = 18 + 18
⇒ h² = 36
⇒ h = 6
Thus, The length of the hypotenuse of the triangle is,
⇒ h = 6
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Solving right triangle
Answer:
[tex]BC= 2.23[/tex]
Step-by-step explanation:
We can solve this problem using the trigonometric identity of [tex]sin[/tex].
We know:
[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\sin(50 \textdegree) = \frac{?}{3}\\[/tex]
If we solve for [tex]?[/tex] we get:
[tex]3sin(50 \textdegree) \approx 2.23[/tex]
Use the formula V = ²h, where r is the radius and h is the height, to find the volume of the inside of this cylindrical pipe in terms of pi.
Answer:
Below
Step-by-step explanation:
r = 1/2 diameter = 4 x^2 y^2
Volume = pi r^2 h =
pi (4 x^2 y^2 )^2 * ( 12 x^2 y^2 ) =
16 x^4 y^4 * 12 x^2 y^2 * pi
= 192 x^(4+2) y^(4+2) pi
= 192 x^6 y^6 pi
Please help me !!! With this
Statistics: Suppose the population variance for a given
population is 36. If we select all possible samples of a certain size from this population, then, on average, what will be the value of the sample variance?
If we select all possible samples of a certain size from this population, then, on average, the value of the sample variance is 36.
What is a population?In Science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this context, we can reasonably infer and logically deduce that the sample variance on average would be equal to 36 because all possible samples of a certain size are selected from a population of 36 members.
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parallelogram has vertices at (–9, –6), (–3, 12), and (9, 12). What could be the coordinates of the fourth vertex? Use the coordinate plane below. .
The coordinates of the fourth vertex D = (3,−1.5).
What property this parallelogram has?A parallelogram has the following property AB=DC
AB=OB−OA=(3,3)−(1,5)=(2,−2)
DC=OC−OD=(8,3)−(a,b)=(2,−2)
OD=OC−DC=(8,3)−(2,−2)=(6,5)
Turn them into vectors. Position vector of point d
should be 6,5
To get the 2nd point, just do AD=BC
BC=OC−OB=(8,3)−(3,3)=(5,0)
AD=OD−OA=(a,b)−(1,5)=(5,0)
OD=OA−AD=(1,5)−(5,0)=(−4,5)
As long as the shape has four sides and two of them are parallel, and you know the length, this should work. For instance, a trapezium where AB=2DC/2CD:
A=(0,0),B=(2,0),C=(2,−1.5),D=(a,b)
AB=(2,0)DC=(2,−1.5)−(a,b)=12(2,0)(a,b)=(1,−1.5)
OR
AB=(2,0)CD=(a,b)−(2,−1.5)=12(2,0)(a,b)=(3,−1.5)
Thus, The coordinates of the fourth vertex D = (3,−1.5).
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What is the slope of line p? on a coordinate plane, a straight line goes through (negative 3, negative 2), (0, 0), and (3, 2).
Slope line formula is used for determining the slope of a line. Based on the given points, the slope of line is 2/3.
To find the slope of the line passing through the given points, we can use the slope formula, which states that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by the expression:
slope = (y2 - y1) / (x2 - x1)
Using this formula, we can calculate the slope of the line passing through the three given points as follows:
slope = (2 - (-2)) / (3 - (-3)) = 4/6 = 2/3
Therefore, the slope of the line passing through the given points is 2/3.
Alternatively, we can observe that the three points are collinear and lie on the same straight line. We can use this fact to find the slope of the line by computing the rise over run between any two of the points. For example, using the points (0,0) and (-3,-2), we have a rise of 2 and a run of 3, so the slope is 2/3. This confirms that the slope of the line passing through the given points is 2/3.
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At a recent Algebra lover's convention, 4 times as many people attended on Sunday as on Thursday. If a total of 2,910 people attended the convention on the two days combined, how many people attended on Thursday? How many people attended on Sunday?
people attended on Thursday.
people attended on Sunday.
the preimter of a rectangel measures 78 centimterers the measure of the with is 15 cenimeters what is the area of the rectangel
Answer:
360 cm^2
Step-by-step explanation:
The length of the rectangle can be found using the formula for perimeter:
Perimeter = 2 * (length + width)
Rearranging the equation, we can solve for the length:
length = (Perimeter - 2 * width) / 2
Plugging in the given values:
length = (78 - 2 * 15) / 2 = (78 - 30) / 2 = 48 / 2 = 24 cm
Next, the area of the rectangle can be found using the formula:
Area = length * width
Plugging in the given values:
Area = 24 * 15 = 360 cm^2
guys i swar this is the last one just this one and thats it <3
Answer:
Choice B is the closest
Step-by-step explanation:
A-lateral = 2πrh
r = D/2 = 16.5/2 = 8.25
h = 14
A = 2π(8.25)(14) = 725.7 in²
Which is stronger? 3 scoops of coffee for 4 cups of water, or 4 scoops of coffee for 6 cups of water? Show Your Work.
The stronger one is 4 scoops of coffee for 6 cups of water.
How strong coffee is made?Strong coffee is prepared by employing a greater coffee grounds-to-water ratio. Typically, 2 teaspoons of coffee grinds are used for every 6 ounces of water in a strong cup of coffee. To make a truly strong cup of coffee, use 3 teaspoons of ground coffee for every 6 ounces of water. If you use a French press, you need also increase the steeping time.
In the given question, it is stronger to use 4 scoops of coffee for 6 glasses of water. This is due to the fact that there are more coffee grounds in relation to the amount of water, resulting in a higher concentration of coffee in the combination.
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The red triangle is a dilation of the blue triangle, with a scale factor, of k=1.5
Use the hotspots to fill in the missing measurements and similarity statement
The measure of each angle and side is given above.
What is image dilation?An enlargement or reduction of a figure that preserves shape but not size.All dilations are similar to the original figure.Dilations have a center and a scale factor.Given is that the red triangle is a dilation of the blue triangle, with a scale factor of {k} = 1.5.
We can write -
57/RT = 1.5
RT = 57/1.5
RT = 38
LM/20 = 1.5
LM = 20 x 1.5
LM = 30
MN/26 = 1.5
MN = 26 x 1.5
MN = 39
∠2 = 15°
∠1 = 121°
Therefore, the measure of each angle and side is given above.
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Robert scored a 42 out of 48 on Quiz-1 and Julie scored a 43 out of 50 on Quiz-2.
Who received a higher percentage?
Answer:Robert
Step-by-step explanation: 42/48 = 0.875,
43/50 = 0.86
0.875 > 0.86
Question 30
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 4 digits
long, and that each digit could be a number between 0 and 4. Assume that the hacker makes random
guesses. What is the probability that the hacker guesses the password on his first try? Round to six decimal
places.
Probability:
The probability that the hacker guesses the password on his first try is, 0.001600.
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
The probability of a hacker guessing the correct password on their first try would be 1 in 10,000, since there are a total of 5⁴ possible combinations of 4 digits, each between 0 and 4, inclusive.
The probability can be calculated as:
= 1 / 5⁴
= 1 / 625
= 0.0016
Rounded to six decimal places, the probability is: 0.0016 = 0.001600.
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if an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s what is the value of V0y?
The value of the final velocity before striking the ground will be 9.899 meters per second.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
If an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s.
We know that if the object is projected horizontally, so initially the object has a vertical speed is zero. Then it increases due to acceleration due to gravity.
The speed of the object before striking the ground is given as,
v² - u²= 2gh
v² - 0² = 2 × (9.8) × (5)
v² = 98
v = 9.899 meters per second
The value of the final velocity before striking the ground will be 9.899 meters per second.
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Out of 1000 students who appeared for Cost accounting examinations,750 failed in maths,600 failed in accounts and 600 in costing,150 failed in both accounts and costing,450 failed in both maths and accounts,400 failed in both maths and costing.the students who failed all three subjects were 75.Prove that the above data is not correct
Answer: This data can be proven to be incorrect using the Principle of Inclusion-Exclusion.
The Principle of Inclusion-Exclusion states that for two events A and B, the number of elements in the union of A and B is equal to the sum of the number of elements in A and the number of elements in B minus the number of elements in their intersection.
Let's denote the number of students who failed in Maths as M, Accounts as A, and Costing as C.
From the information given, we have the following relationships:
M = 750
A = 600
C = 600
A ∩ C = 150
M ∩ A = 450
M ∩ C = 400
M ∩ A ∩ C = 75
Applying the Principle of Inclusion-Exclusion, the number of students who failed in at least one subject is:
M + A + C - (A ∩ C) - (M ∩ A) - (M ∩ C) + (M ∩ A ∩ C) = 750 + 600 + 600 - 150 - 450 - 400 + 75 = 925
However, the number of students who appeared for the exams is 1000, which means that the number of students who passed in all subjects should be 1000 - 925 = 75.
But we have already determined that the number of students who failed in all subjects is 75, which means that there are 75 students who are counted twice. This leads to a contradiction, and therefore the data given cannot be correct.
Step-by-step explanation:
NEEED HELPPO!!!!!!!!
Answer:
p = 23
Step-by-step explanation:
using the rules of exponents
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
then
[tex](x^3)^{5}[/tex] ([tex]x^{8}[/tex] )
= [tex]x^{3(5)}[/tex] × [tex]x^{8}[/tex]
= [tex]x^{15}[/tex] × [tex]x^{8}[/tex]
= [tex]x^{(15+8)}[/tex]
= [tex]x^{23}[/tex]
= [tex]x^{p}[/tex] ← with p = 23
TO determine which side of a linear inequality to shade in for its graph, you
should pick a point on one side of the dashed or solid line and plug its
coordinates into the original inequality. If the coordinates satisfy the
inequality, you should shade in that half of the plane.
• A. True
• B. False
The given statement about inequality is true.
What is inequality?The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.
The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.
The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.
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