in a right triangle, what is the product of sin b and tan c and product of sin c and tan b
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Related Questions
1. An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line. How many different ways can they sit if the elf and the dwarf insist on sitting next to each other?
a. 6 ways
b. 48 ways
c. 36 ways
d. 12 ways
e. 24 ways
2. How many ways can you order a hamburger of you can order it with or without cheese, lettuce, tomatoes, pickles, or onions?
a. 10
b. 32
c. 64
d. 5
Answers
a. 6 ways
b. 48 ways
c. 36 ways
d. 12 ways
e. 24 ways
elf, dwarf, hobbit, wizar, man = 5 characters
Treat first elf and dwarf as one unique character, due to they will sit next to each other.
So, calculate the number of different ways 4 can sit, i.e permutations of 4 = 4! = 4*3*2*1 = 24 ways.
Given thath elf and dwarf can exchage their position between them, the above quantity has to be multiplied by 2:
24 * 2 = 48.
Answer: option b) 48 ways
2. How many ways can you order a hamburger if you can order it with or without cheese, lettuce, tomatoes, pickles, or onions?
a. 10
b. 32
c. 64
d. 5
with or without cheese => 2 options
with or without lettuce => 2 options
tomatoes => 2 options
pickles => 2 options
onions => 2 options
=> 2*2*2*2*2 = 32 ways.
answer: option b) 32
Final answer:
In this question, the arrangements of characters sitting together and the options for hamburger toppings are explored using permutations and combinations in Mathematics for High School.
Explanation:
(1) When the elf and the dwarf insist on sitting next to each other, treat them as one entity. Then, there are 4 entities: {elf & dwarf}, hobbit, wizard, man. This gives 4! ways to arrange them, and the elf and dwarf can be arranged within their entity in 2! ways.
So, the total ways are 4! x 2! = 48 ways.
(2) For the hamburger order, since you can choose to include/exclude each topping independently, there are 2 options for each topping (with or without).
Hence, the total ways to order the hamburger are 2⁵ = 32 ways.
FIND THE FOLLOWING USING THE GIVEN TRIANGLE...PLEASE HELP ME SUCK AT MATH...SOS!!! ASAP!!!!
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perimeter = 20 +20 +24 = 64 feet
area = 12^2 + x^2 = 20^2
144 + x^2 = 400
x^2 = 256
x = sqrt(256) = 16 feet
area = 1/2 x 16 x 24 = 192 square feet
cost = 192 x $2 = $384
Let g(x) = x - 3 and h(x) = x2 + 6. What is (h o g)(1)?
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which expression represents the distance between the two points x and y on the number line -4 and 3
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Answer with explanation:
The two points on the number line are
x = -4
y=3
The distance is a positive Quantity.
So, Distance between x and y can be written as:
=|x-y| or |y-x|
=|3-(-4)| or |-4-3|
=|3+4| or |-7|
=|7| or |-7|
=7 Units
The expression will be : =|x-y| or |y-x|
=|3-(-4)| or |-4-3|
In dogs, the drug carprofen has a half-life of 8 hours. If a veterinarian gives a dog an 80-milligram dose, how long will it take for the amount of carprofen in the dog to reach 10 milligrams?
Answers
N(t)=Ne^(-λt)
or
N(t)=N(1/2)^(t/τ)
where:
t=time
N=initial amount
N(t)=final amount
τ=half-life
thus the time taken for the drug to decay will be:
10=80(1/2)^(t/8)
1/8=(1/2)^(t/8)
introducing natural logs;
ln (1/8)=(t/8)ln (1/2)
thus;
[ln 1/8]/[ln 1/2]=t/8
3=t/8
t=3*8
t=24 hours
the answer is 24 hours
Final answer:
Using the half-life formula, it would take 24 hours for the amount of carprofen to reduce from an initial dose of 80 milligrams to 10 milligrams.
Explanation:
To calculate the time it will take for the amount of carprofen to decrease from 80 milligrams to 10 milligrams in a dog, given the half-life of 8 hours, the exponential decay formula can be used. The half-life formula is:
[tex]C = C0 \times (1/2)^{(t/T)[/tex]
C is the final concentration of the drug.C0 is the initial concentration of the drug.t is the time elapsed.T is the half-life of the drug.Let's set up the equation using the given values:
[tex]10 mg = 80 mg \times (1/2)^{(t/8 hours)[/tex]
Now, we solve for t:
[tex]10/80 = (1/2)^{(t/8)[/tex]
[tex]1/8 = (1/2)^{(t/8)[/tex]
To find the exponent t/8 that makes this equation true, we can use logarithms:
log2(1/8) = t/8
-3 = t/8
t = -3 * 8
t = -24 hours
The negative result is due to the fact that we are finding a factor by which the concentration is reduced. To get the actual time elapsed, we take the absolute value:
t = 24 hours
Therefore, it would take 24 hours for the amount of carprofen to reduce to 10 milligrams.
Andrew estimated the weight of his dog to be 60 lb. The dog’s actual weight was 68 lb. What was the percent error in Andrew’s estimate? Round your answer to the nearest tenth of a percent. __________ %
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[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 68&100\\ 8&x \end{array}\implies \cfrac{68}{8}=\cfrac{100}{x}[/tex]
Use the number 913,256. Write the name of the period that has the digits 913.
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Two standard number cubes are thrown, one after the other. What is the probability that the first cube lands showing a 1 and the second cube lands showing a number that is not 1? Round the answer to the nearest thousandth.
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Let B be the probability that you don't throw 1
A and B are independent events
P(A)= 1/6 and P(B)= 5/6
Because they are independent you multiply them: 1/6 x 5/6 = 0.138888...
Rounded to the nearest thousandth is 0.139
Answer:
B on edge
Step-by-step explanation:
A circular fountain has a circular walkway surrounding it with a width of 7 ft. The total area taken up by the walkway is 693π ft^2. Find the diameter of the pool.
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[tex]\bf A=2\pi pw\quad \begin{cases} w=7\\ A=693\pi \end{cases}\implies 693\pi =2\pi p7\implies \cfrac{693\pi }{14\pi }=p \\\\\\ 49.5=p\\\\ -------------------------------\\\\ r=p-\cfrac{w}{2}\implies r=49.5-3.5\implies r=46[/tex]
now, that's just the radius of the pool, the diameter would be twice as much, or 2r.
What are the values of a1 and r of the geometric series?
2 – 2 + 2 – 2 + 2
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Answer: For the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Step-by-step explanation: We are given to find the values of [tex]a_1[/tex] and [tex]r[/tex] of the following geometric series:
[tex]2-2+2-2+2-~.~.~..[/tex]
We know that
[tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
[tex]a_1=2.[/tex]
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio [tex]r[/tex] of the given geometric series is
[tex]r=\dfrac{-2}{2}=\dfrac{2}{-2}=~.~.~.~=-1.[/tex]
Thus, for the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Which measure of variability is the most appropriate for this set of values?
13, 42, 104, 36, 28, 6, 17
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Answer:
in other words that guy said E
Step-by-step explanation:
Write an appropriate inverse variation equation if y = 9 when x = 3.
Answers
y = k/x
so, 9 = k/3
k = 9x3
k = 27
then equation is, y = 27/x
The car salesman tells you that the car can go from a stop position to 60 mph in six seconds he's giving you the cars rate of
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Answer:
acceleration i think
Step-by-step explanation:
To keep heating costs down for a structure, architects want the ratio of surface area to volume as small as possible. An expression for the ratio of the surface area to volume for the square prism shown is . Find the ratio when b = 12 ft and h = 18 ft.
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Hope this helps!
"if z is a standard normal variable, find the probability. the probability that z lies between 0 and 3.01"
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P(0<z<3.01) = P(z<3.01) - P(z<0)
Reading from the z-table, we have
P(z<0) = 0.5
P(z<3.01) = 0.9987
Hence, P(0<z<3.01) = 0.9987 - 0.5 = 0.4987
The probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.
Given:
Probability between z = 0 and z = 3.01 is given by
As, P(0<z<3.01)
= P(z<3.01) - P(z<0)
So, the z score values are
P(z<0) = 0.5
and, P(z<3.01) = 0.9987
Hence, the probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.
Learn more about z- score here:
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What is the domain of y = sec(x)?
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The domain of y = sec(x) is all real numbers except for values where the cosine function is zero.
Explanation:The domain of y = sec(x) is all real numbers except for values where the cosine function is equal to zero. Since the secant function is the reciprocal of cosine, it is undefined when cosine is zero.
So, the domain of y = sec(x) is all real numbers except for values of x where cos(x) = 0.
For example, if we consider the unit circle, the cosine function is equal to zero at π/2 and 3π/2. Therefore, the domain of y = sec(x) would exclude these values.
The domain of [tex]\( y = \sec(x) \)[/tex] is all real numbers except [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex], [tex]\( n \)[/tex] integer.
Let's find the domain of [tex]\( y = \sec(x) \)[/tex].
The secant function, [tex]\( \sec(x) \)[/tex], is defined as the reciprocal of the cosine function, [tex]\( \cos(x) \)[/tex]. So, [tex]\( \sec(x) = \frac{1}{\cos(x)} \).[/tex]
The cosine function is defined for all real numbers, except where the denominator becomes zero, because division by zero is undefined.
So, to find the domain of [tex]\( \sec(x) \)[/tex], we need to find where [tex]\( \cos(x) \)[/tex] is not zero.
The cosine function has a range between -1 and 1. It equals zero at [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x = -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
So, the domain of [tex]\( \sec(x) \)[/tex] is all real numbers except where [tex]\( \cos(x) = 0 \)[/tex]. Therefore, the domain of [tex]\( \sec(x) \)[/tex] is [tex]\( x \neq \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x \neq -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
In interval notation, the domain of [tex]\( \sec(x) \)[/tex] is:
[tex]\[ (-\infty, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \infty) \][/tex]
Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?
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So for conjugate, you just flip the sign of the imaginary part:
2+8i will be the answer
The conjugate of the given complex number is:
[tex]2+8i[/tex]
Step-by-step explanation:We know that any complex number is written in the form of:
[tex]z=a+ib[/tex]
where a and b are real numbers.
The conjugate of the complex number is given by:
[tex]\bar z=\bar {a+ib}\\\\i.e.\\\\\bar z=a-ib[/tex]
Here we are given that:
We have a complex number such that the real part of a complex number is 2 and it's imaginary part is -8.
i.e.
a=2 and b= -8
i.e. the complex number is:
[tex]z=2+(-8)i[/tex]
Hence, the conjugate of this number is:
[tex]\bar z=2-(-8)i\\\\i.e.\\\\\bar z=2+8i[/tex]
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is negative and the value of b is zero. Where could point P be located on the coordinate plane?
Select one or more:
Quadrant I
Quadrant II
Quadrant IV
Quadrant III
x-axis
y-axis
Answers
Answer:
X-axis.Step-by-step explanation:
Givens
We have point which coordinates are (a,b)The value of a is negative.The value of b is zero.Now, remember that all coordinates with the form (a,0), represents points on the x-axis, because the y-coordinate is zero.
In this case, we have negative horizontal coordinates and a null vertical coordinate, like (-a,0).
This points is on the x-axis, because y-value is null. Actually, it's on the negative part of x-axis, because its horizontal coordinate is negative.
Therefore, the right answer is x-axis.
can anone help me please
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Area= 12
Cost= 84
a. The perimeter of the triangle is 18 cm. b. The area of the triangle is 24 cm². c. Tiling the triangle at $7 per square centimeter would cost $168.
a. Perimeter:
Perimeter} = 5 + 5 + 8 = 18 cm
b. Area:
Use Heron's formula since the sides are known:
[tex]\[ s = \frac{5 + 5 + 8}{2} = 9 \] \[ \text{Area} = \sqrt{s(s-5)(s-5)(s-8)} \] \[ \text{Area} = \sqrt{9 \times 4 \times 4 \times 1} = \sqrt{576} = 24 \, \text{cm}^2 \][/tex]
c. Cost to Tile:
If the cost is $7 per square centimeter:
[tex]\[ \text{Cost} = \text{Area} \times \text{Cost per square centimeter} \] \[ \text{Cost} = 24 \times 7 = 168 \][/tex]
Therefore,
a. Perimeter = 18 cm
b. Area = 24 cm²
c. Cost to Tile = $168
For more questions on perimeter :
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Choose the solution for the equation.
d3=284? need help asap
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Answer:
the answer is A
Step-by-step explanation:
ttm
Determine the angular velocity, in radians per second, of 4.3 revolutions in 9 seconds. Round the answer to the nearest tenth.
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simplify away.
A triangle has a perimeter of 10x+2. Two sides have lengths of 5x and 2x+9. What is the length of the 3rd side?
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Let the third side = a.
So we can write perimeter as = 5x + 2x + 9 + a
As given perimeter = 10x + 2
So we can write 10x + 2 = 7x + 9 + a
10x + 2 - 7x - 9 = a
3x - 7 = a
So third side = 3x - 7.
How long will it take a bird traveling at an average speed of 12 miles per hour to travel 202 miles while flying south for winter?
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Answer:
16 50 min
Step-by-step explanation:
During a sale, a dress decreased in price from $90 to &63. What was the percent of decrease?
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%change=100(63-90)/90
%change= -30%
So the price was decreased by 30%
Steps to solve y=3x + 8
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[tex]y-8=3x[/tex]
Step 2. Divide both sides by 3
[tex] \frac{y-8}{3} =x[/tex]
Step 3. Switch sides
[tex]x= \frac{y-8}{3} [/tex]
Done! :) Hope this helps!
Can two numbers have a GCF that is bigger than their LCM? Explain how you know?
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Greatest common factor biggest possible value is the number value itself. There is no factor that bigger than the number.
But the least common multiple smallest possible value is the number. There is no multiple that smaller than the number.
So it is not possible to have GCF bigger than LCM.
The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of the circles in inches?
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So basically N = 12r. You haven't given me any original radius, so I can't give you a constant for N, but if you do have that original radius you can just plug that into 12r.
Based on your comment, N = 12 * 9 = 108 inches
The value of n is 12 .
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
The circle will be dilated by a scale factor of 6 .
so,
New radius of the circle R = 6r
As is it dilated by a scale factor of 6
Now ,
The circumference of the new circles = 2πR
= 2.6π
= [tex]12\pi r[/tex] -------------------- (1)
and given circumference of the new circles = nπ ---------------------(2)
when we compare both n = 12
Hence, the value of n is 12 .
To know more about scale factor here:
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which expression is equivalent to (4h^7k^2)^4?
A: 16h^11k^6
B: 16h^28k^8
C; 256h^11k^6
D: 256h^28k^8
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The answer is D.
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex](4h^7k^2)^4[/tex]
We need to simplify this :
Here we go:
We will apply :
[tex](a^m)^n=a^{mn}[/tex]
[tex](4h^7k^2)^4\\\\=4^4\times (h^7)^4\times (k^2)^4\\\\=256h^{28}k^8[/tex]
Hence, option 'D' is correct.
what is the other measurement of the shape?
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for the length of the side that is not given:
look at it as part of a triangle with the legs being 4m tall by 6 m wide
so 4^2 + 6^2 = X62
16+36 = 52^2
square root(52) = 7.211 m
does it as to round of to nearest whole number? nearest tenth?
round off answer as needed
What is the value of a?
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Cross multiply and solve for 'a'
3/4 = 4/a
3*a = 4*4
3*a = 16
3*a/3 = 16/3
a = 16/3
a = (15+1)/3
a = (15/3)+(1/3)
a = 5+(1/3)
The answer is choice B)