What is the value of sin 0 given that (5, -12) is a point on the terminal side of 0 ?
Answers
Answer:
The first choice is the one you want.
Step-by-step explanation:
If we plot the point (5, -12) we will be in QIV. Connecting the point to the origin and then drawing in an altitude to the positive x axis creates a right triangle with side adjacent to the angle being 5 units long, and the altitude being |-12|. To find the sin of theta, we need the side opposite (got it) over the hypotenuse (don't have it). We solve for the length of the hypotenuse using Pythagorean's Theorem:
[tex]c^2=12^2+5^2[/tex] and
[tex]c^2=169[/tex] so
c = 13.
Now we can find the sin of the angle in the side opposite the angle over the hypotenuse:
[tex]sin\theta=-\frac{12}{13}[/tex]
The first choice in your answers is the one you want.
To find the sine of an angle, we use the point given on its terminal side to represent a right triangle. The sine is calculated as the ratio of the opposite side to the hypotenuse. Using the point (5, -12), our calculation gives sin(θ) as -12/13.
Explanation:The question asks about the value of sin 0 where the point on the terminal side is (5, -12). However, in trigonometry, we more commonly write it as sin(θ) such that θ is the angle being referenced. Specifically, we are being asked to find the value of sin(θ) when a point on the terminal side of the angle is (5, -12).
To figure out what sin(θ) is, we use the mathematical definition of sine which states that sin(θ) = opposite/hypotenuse. In this context, we can treat the point (5,-12) as a representation of a right triangle. The x-coordinate is adjacent to the angle and the y-coordinate is opposite the angle. Accordingly, we can say that sin(θ) = -12/13.
This is because the hypotenuse can be calculated using Pythagoras' theorem, where hypotenuse = √[(x-coordinate)^2 + (y-coordinate)^2] which equals √[(5)^2 + (-12)^2] = √169 = 13. Hence, sin(θ) = (-12)/13.
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Related Questions
7x+8y=10 5x+y=−7 solve by elimination
Answers
Answer:
(-2,3)
Step-by-step explanation:
7x+8y=10
5x+y=-7
To solve this by elimination, we need both equations in the same form. There are. They are both in form ax+by=c.
Now we also need for one of the columns with the variables to be opposite or same terms.
I like the way the column with the y's are looking because if I multiply that second y by 8 or -8 I will have sames or opposites.
I'm going to multiply the second equation by -8.
This will give me:
7x+8y=10
-40x-8y=56
--------------------Add the equations!
-33x+0=66
-33x =66
x =66/-33
x =-2
Now we need to find the other variable. It doesn't matter which equation you use.
I'm going to use 5x+y=-7 where x=-2 to find y.
5(-2)+y=-7
-10+y=-7
Add 10 on both sides
y=3
The solution is (-2,3)
Answer:
The solution is x = -2, y = 3. As an ordered pair it is (-2, 3).
Step-by-step explanation:
7x + 8y = 10
5x + y = −7
Multiply the second equation by -8:
-40x - 8y = 56
Add this to the first equation, we get:
-33x = 66
x = -2
Now substitute for x in the second equation:
5(-2) + y = -7
y = -7 + 10
y = 3.
Check these results in the first equation:
7(-2) + 8(3) = -14 + 24 = 10 - so correct.
6.
Write the equation of the line in slope-intercept form that has the following points: (4, 5) (-1, 2)
A. y = 3/5x + 1
B. y = -x + 1
C. y = -x + 13/5
D. y = 3/5x + 13/5
Answers
Answer:
D. y = 3/5x + 13/5
Step-by-step explanation:
The slope of the desired line is the ratio of the difference in y-values to the difference in x-values:
m = Δy/Δx = (2 -5)/(-1 -4) = -3/-5 = 3/5 . . . . . . eliminates choices B and C
The slope-intercept equation will then be ...
y = mx + b . . . . . . . generic slope-intercept form
y = 3/5x + b . . . . . . put in m; true for some b that puts the given points on the line
Using the first point, we have ...
5 = 3/5×4 + b
25/5 = 12/5 + b
13/5 = b . . . . . . . . . subtract 12/5
Then the equation is ...
y = 3/5x + 13/5
_____
You know as soon as you consider putting a point value in the equation ...
y = 3/5x + b
that the equation of choice A cannot work. That only leaves choice D.
What is the quadratic function that is created with roots -10 and -4 and a vertex at (-7, -9)?
Answers
Answer:
In vertex form it's [tex]y=(x+7)^2-9[/tex]
In standard form it's [tex]y=x^2+14x+40[/tex]
Step-by-step explanation:
We can use the vertex form to solve for a in
[tex]y=a(x-h)^2+k[/tex]
"a" is the number out front that dictates the steepness, or lack thereof, in a parabola. That means that we need h and k (which we have in the vertex) and we need x and y (which we have in the form of one of the zeros). Filling in using a vertex of (-7, -9) and a coordinate point (-7, 0):
[tex]0=a(-4-(-7))^2-9[/tex] simplifies a bit to
[tex]0=a(-4+7)^2-9[/tex] simplifies a bit more to
[tex]0=a(3)^2-9[/tex] and
[tex]0=a(9)-9[/tex] so
[tex]0=9a-9[/tex],
[tex]9=9a[/tex] and finally,
a = 1
Phew! So there is the a value. Now we can simply fill in the formula completely, using the vertex as our guide:
[tex]y=(x+7)^2-9[/tex]
In standard ofrm that is
[tex]y=x^2+14x+40[/tex]
We can check ourselves for accuracy by factoring that standard polynomial using whatever method of factoring you like for quadratics and get that the roots are in fact x = -10, -4
The only reason we needed the zeros is to use one of them as the x and y to solve for a.
1) The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?
2)Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?
Answers
Answer:
1) 68%
2) 68%
Step-by-step explanation:
1) The ages of treesWe know the mean and the standard deviation.
The mean is:
[tex]\mu=25[/tex]
The standard deviation is:
[tex]\sigma=5[/tex]
The Z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=20 the Z-score is:
[tex]Z_{20}=\frac{20-25}{5}=-1[/tex]
For x=30 the Z-score is:
[tex]Z_{30}=\frac{30-25}{5}=1[/tex]
Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of the trees are between 20 and 30 years old
2) Pizza deliveryFirst we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:
[tex]\mu=27[/tex]
The standard deviation is:
[tex]\sigma=3[/tex]
The z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=24 the Z-score is:
[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]
For x=30 the Z-score is:
[tex]Z_{30}=\frac{30-27}{3}=1[/tex]
Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of pizzas are delivered between 24 and 30 minutes
I need help with these other quadratic story problems.
Answers
Answer:
1. 2.12 seconds
2. 10 feet
Step-by-step explanation:
1. "Pekka tosses a ball out of a window that is 40 feet in the air. Its initial velocity is 15 feet per second. The path of the ball is represented by:
h = -16t² + 15t + 40
How long does it take for the ball to hit the ground (in seconds) rounded to the nearest hundredth?"
When the ball hits the ground, its height is 0:
0 = -16t² + 15t + 40
0 = 16t² − 15t − 40
Solve with quadratic formula:
t = [ -b ± √(b² − 4ac) ] / 2a
t = [ 15 ± √(225 + 2560) ] / 32
t ≈ 2.12 or -1.18
t must be positive, so t = 2.12 seconds.
2. "Tricia bounces a ball in front of her feet. The path of the ball from the time it hits the ground until it lands on the floor is represented by:
f(x) = -2(x − 3)² + 10
Assuming that Tricia's feet are located at the origin (0, 0), what is the maximum height of the ball (in feet)?"
The function is a parabola. The vertex of this parabola is at (3, 10). So the maximum height is 10 feet.
Lisa owns a "Random Candy" vending machine, which is a machine that picks a candy out of an assortment in a random fashion. Lisa controls the probability of picking each candy. The machine has too much of the candy "Coffee Toffee," so Lisa wants to program it so that the probability of getting "Coffee Toffee" twice in a row is greater than \dfrac{4}{3} 3 4 start fraction, 4, divided by, 3, end fraction times the probability of getting a different candy in one try. Write an inequality that models the situation. Use ppp to represent the probability of getting "Coffee Toffee" in one try.
Answers
Answer:
p² > 4/3(1 -p)
Step-by-step explanation:
Assuming candy selections are independent from one to the next, the probability of getting Coffee Toffee twice in a row will be p². The probability of getting some other selection than Coffee Toffee will be 1-p.
Lisa wants ...
p² > (4/3)(1 -p)
_____
This has solution p > 2/3.
Answer:
Step-by-step explanation:
The value of Jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t +72t + 5000, where t is the time in months since she opened the account. After how many months will her portfolio be at a maximum? What is the maximum value of the portfolio?
Answers
Answer:
a) The portfolio will be at maximum after 12 months (1 year)
b) The maximum value of the portfolio is $5432
Step-by-step explanation:
The function that models Jennifer's stock portfolio (in dollars) is [tex]f(t)=-3t^2+72t+5000[/tex], where t is the time in months since she opened the account.
We complete the square to obtain this function in vertex form:
Factor -3 from the first two terms
[tex]f(t)=-3(t^2-24t)+5000[/tex].
Add the zero pairs -3(+144),-3(-144)
[tex]f(t)=-3(t^2-24t+144)+5000+-3(-144)[/tex].
Factor the perfect square trinomial and simplify.
[tex]f(t)=-3(t-12)^2+5432[/tex].
The vertex of this function is (h,k)=(12,5432)
a) The portfolio will be at maximum when t=12, the h-value of the vertex
b) The maximum value of the portfolio is the k-value of the vertex which is 5432
Jennifer's stock portfolio reaches its maximum value after 12 months, with the maximum value being $5432.
The given function is a quadratic equation in the form f(t) = -3t² + 72t + 5000. This function opens downwards because the coefficient of t2 is negative.
To find the time t when the portfolio is at its maximum, we use the vertex formula for a parabola
t = -b / (2a), where a = -3 and b = 72.
t = -72 / (2 * -3) = 72 / 6 = 12.
So, the portfolio reaches its maximum value at t = 12 months.
To find the maximum value of the portfolio, substitute t = 12 back into the function:
f(12) = -3(12)² + 72 * 12 + 5000.
f(12) = -432 + 864 + 5000 = 5432.
Therefore, Jennifer's stock portfolio will be at its maximum value after 12 months, and the maximum value of the portfolio will be $5432.
Complete Question:
The value of Jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t² +72t + 5000, where t is the time in months since she opened the account. After how many months will her portfolio be at a maximum? What is the maximum value of the portfolio?
select the graph of the equation below. y=1/2x^2+2x-6
Answers
Answer:
The correct graph is D (Compare to the graph above)
Answer:
D.
Step-by-step explanation:
You can see it calculating the vertex. the formula of the vertex is
[tex](\frac{-b}{2a}, y(\frac{-b}{2a}))[/tex]
where a = 1/2 and b=2.
[tex](\frac{-2}{1}, \frac{1}{2}(-2)^2+2(-2)-6)[/tex]
[tex](-2, \frac{1}{2}*4-4-6)[/tex]
[tex](-2, 2-4-6)[/tex]
[tex](-2, -8)[/tex]
The only option of graph that has vertex in (-2,-8) is option D.
two circles are externally tangent to each other. One circle has a diameter of 62 yards and the distance between the centers of the two circles is 85 yards. What is the diameter of the other crop circle
Answers
Answer:
108 yards
Step-by-step explanation:
Let circle A be the circle with the 62 yard diameter
Let circle B be the circle whose diameter we are trying to solve for.
Externally tangent circles are circles which touch each other and share a common external tangent.Circle A has a tangent of 62 yards and thus a radius ( half the diameter) of 31 yards.The distance between the centers of the 2 circles is 85 yards. If you subtract the radius ( distance from the center of the circle to its circumference) of circle A then we'll only be left with the radius of circle B.85 - 31= 54 yards which is the radius of circle BTo get the diameter: 54 x 2 = 108 yardsA committee consisting of
4
faculty members and
5
students is to be formed. Every committee position has the same duties and voting rights. There are
12
faculty members and
15
students eligible to serve on the committee. In how many ways can the committee be formed?
Answers
Answer:
Step-by-step explanation:
These are independent non-ordered events. The faculty members chosen don't affect the students and vice versa. There is no issue with replacement, and the only limitation is the number of people allowed to serve.
12C4*15C5
495*3003=1,486,485 ways
The equation represents Function A, and the graph represents Function B:
Function A: f(x) = x − 9
Which equation best compares the slopes of the two functions?
A.) Slope of Function B = 2 x Slope of Function A
B.) Slope of Function A = Slope of Function B
C.) Slope of Function A = 2 x Slope of Function B
D.) Slope of Function B = − Slope of Function A
Answers
Answer:
A.) Slope of function B = 2 * the slope of Function A.
Step-by-step explanation:
The slope of Function A is 1 ( because of the x ( = 1x) in the equation).
From the graph, the slope of Function B = 5 / 2.5 = 2.
Answer:
The correct option is A.
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (1)
where, m is slope and b is y-intercept.
The equation of Function A is
[tex]f(x)=x-9[/tex] .... (2)
From (1) and (2) we get
[tex]m=1[/tex]
It means slope of Function A is 1.
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that the line passes through two points (0,-1) and (1,1).
[tex]m=\frac{1-(-1)}{1-0}=2[/tex]
The slope of Function B is 2.
We can say that
Slope of Function B = 2 x Slope of Function A
Therefore the correct option is A.
Find the probability of drawing a green card, not replacing it, and then drawing another green card.
Answers
Answer:
The probability is 2 out of 9 chances to pull a green card.
Step-by-step explanation:
Because your original probability was 3/9 but you removed one so that makes it 2/9 chances to draw one.
If im right may i get brainliest?
Answer: 1/15
Step-by-step explanation:
The odds would be 1/15.
To find these odds, you first have to find the total number of cards.
2 + 3 + 1 + 4 = 10 cards
Then you can find the first set of odd for pulling a green card by placing the goal amount over the total amount.
3 green / 10 total = 3/10
Now, with that green card not being replaced, we have one less green and one less total. This gives us 2 green and 9 total, which helps us find the odds of pulling one again.
2 green / 9 total = 2/9
Now to find the odds of doing both, you need to multiply the two odds together.
3/10 * 2/9 = 6/90 or simplified 1/15
David was trying to sleep one night but there was too much noise around him? His clock ticked every 5 seconds , a tap was dripping every 7 seconds and his pet dog snored every 12 seconds he noticed n his clock that all three things happened together on the stroke of midnight (A) after how many second would all three things happen together again. (B) How many times would all three things happen together again between midnight and one o'clock
Answers
Answer:
A) 420 seconds = 7 minutes
B) 8 times
Step-by-step explanation:
A) After how many second would all three things happen together again?
Solution:
His clock ticked every 5 seconds , a tap was dripping every 7 seconds and his pet dog snored every 12 seconds. It all happens simultaneously = 5*7*12=420 seconds
B) How many times would all three things happen together again between midnight and one o'clock
Since all these events happen together after every 420 sec = 7 mins and there are 60 mins between midnight and 1 o'çlock , thus 60/7 = 8 times ....
A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is
Answers
Answer:
The probability that the sample mean will be between 80.54 and 88.9 is 0.951
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called M
- The standard deviation of the distribution of sample means is
called σM
- σM = σ/√n , where σ is the standard deviation and n is the sample size
- z-score = (M - μ)/σM, where μ is the mean of the population
* Lets solve the problem
∵ The sample size n = 36
∵ The sample mean M is between 80.54 and 88.9
∵ The mean of population μ = 84
∵ The standard deviation σ = 12
- Lets find σM to find z-score
∵ σM = σ/√n
∴ σM = 12/√36 = 12/6 = 2
- Lets find z-score
∵ z-score = (M - μ)/σM
∴ z-score = (80.54 - 84)/2 = -3.46/2 = -1.73
∴ z-score = (88.9 - 84)/2 = 4.9/2 = 2.45
- Use the normal distribution table to find the probability
∵ P(-1.73 < z < 2.45) = P(2.45) - P(-1.73)
∴ P(-1.73 < z < 2.45) = 0.99286 - 0.04182 = 0.95104
∴ P(-1.73 < z < 2.45) = 0.951
* The probability that the sample mean will be between 80.54 and 88.9
is 0.951
The probability that the sample mean lies between 80.54 and 88.9 is calculated using the Central Limit Theorem and z-scores. The standard error is calculated to convert the measure into a standard normal distribution where probability can be determined.
Explanation:In order to solve this problem, we use the concept of the Central Limit Theorem in statistics. According to the theorem, as the sample size increases, the sampling distribution tends towards a normal distribution. In this case, the population mean (μ) is 84 and the standard deviation (σ) is 12. If you take a sample of 36 observations, the mean of this sample should theoretically be close to the population mean. The standard deviation of the sampling distribution of the means (also known as Standard Error) is given by σ/√N (√36 in this case).
Now, to find the probability that the sample mean lies between 80.54 and 88.9, you'd first convert these into z-scores, using the formula z = (X - μ)/standard error. Thus, you get two z-scores corresponding to 80.54 and 88.9. The probability that the sample mean lies between these two points is the area under the standard normal distribution between these two z-values, which can be found using standard statistical tables or software.
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What is the greatest common factor of the terms of the polynomial below?
20x4 – 10x3 + 15x2
A. 5x3
B. 10x3
C. 10x2
D. 5x2
Answers
Answer:
D. 5x2 is the GCF
The greatest common factor of the terms of the given polynomial is 5x². So, option D is correct
How do find the GCF of a polynomial?To find the GCF of a polynomial,
find all the possible factors of each term in the polynomialpick out the common factors from all the terms ( the factor must be common for all the terms)multiply all the common factors to get the greatest common factor of the polynomial.Calculation:Given that,
the polynomial is [tex]20x^4-10x^3 + 15x^2[/tex]
Finding factors for all the terms:
[tex]20x^4[/tex] = 2 × 2 × 5 × x × x × x × x
[tex]10x^3[/tex] = 2 × 5 × x × x × x
[tex]15x^2[/tex] = 3 × 5 × x × x
So, from these three terms, the common factors are 5, x, x
On multiplying them,
⇒ 5 × x × x
∴ GCF = 5x²
Therefore, the greatest common factor of the given polynomial is 5x². So, option D is correct.
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A triangle with base b and height h is shown below. If the height of the triangle is 3 units more than the base, select the function that represents the area of the triangle. A. B. C. D.
Answers
Answer:
The area of a triangle is given by the formula:
A = bh/2
If the height of the triangle is 3 units more than the base we can say that:
h = b + 3
Therefore, the area of the triangle will be:
A= b(b+3)/2
Where 'b' comes to be the base of the triangle.
Answer:
A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]
Step-by-step explanation:
Given: Height of the triangle is 3 units more than the base.
Let "b" be the base of the triangle.
So, h = b + 3
Area of a triangle A = [tex]\frac{1}{2} base * height[/tex]
Now plug in h = b +3 in the above area of formula, we get
A(b) = [tex]\frac{1}{2} b*(b + 3)[/tex]
Now we can multiply b and (b + 3), we get
A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]
Therefore, the answer is A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]
Last year, 150 cases were reported of a new infectious disease. It has been predicted that the number will double every year. How many cases will be reported in the ninth year?
Answers
Answer:
76800 cases
Step-by-step explanation:
The number of cases of new infectious diseases reported last year= 150 cases
Number of cases are going to be double every year
Number of the cases in next or first year=150+150=300
Number of the cases in next or second year=300+300=600
Number of the cases in next or third year=600+600=1200
Number of the cases in next or fourth year=1200+1200=2400
Number of the cases in next or fifth year=2400+2400=4800
Number of the cases in next or sixth year=4800+4800=9600
Number of the cases in next or seventh year=9600+9600=19200
Number of the cases in next or eight year=19200+19200=38400
Number of the cases in next or ninth year=38400+38400=76800
Hence , the total number of cases are 76800 cases
Answer:
38,400
Step-by-step explanation:
The answer above me is wrong
Got it right on the test
The following table shows the amount of water leaking from an inflatable pool as a function of time:
x (time in minutes) f(x)
0 35
1 30
2 25
3 20
4 15
Find and interpret the meaning of the x‐intercept in this scenario.
A.) (7, 0); the time it takes to empty the water in the pool
B.) (5, 0); the time it takes to empty the water in the pool
C.) (5, 0); the time it takes to fill up the water in the pool
D.) (7, 0); the time it takes to fill up the water in the pool
Answers
Answer:
A). (7, 0) The time it takes to empty the water in the pool.
Step-by-step explanation:
If we extend the values we see that they are
x f(x)
5 10
5 5
7 0
So at time 7 minutes the pool is empty.
Answer:
(7, 0); the time it takes to empty the water in the pool
Step-by-step explanation:
The following table shows the amount of water leaking from an inflatable pool as a function of time:
x (time in minutes) f(x)
0 35
1 30
2 25
3 20
4 15
f(x) represents the amount of water in the pool. x intercept is the point where f(x) is 0 .At x intercept the amount of water in the pool is 0.
WE need to find out the point where f(x) becomes 0
F(x) is decreasing by 5. LEts extend the table till we get f(x) becomes 0
Decrease f(x) by 5
x (time in minutes) f(x)
3 20
4 15
5 15-5=10
6 10-5=5
7 5-5=0
When x=7, f(x)=0. (7,0) is the x intercept.
(7, 0); the time it takes to empty the water in the pool
Stephanie is making beef for a party the recipe uses 1 1/2 teaspoons of pepper, 3 2/4 teaspoons of garlic powder 1/8 teaspoons of thyme and 4 teaspoons of onion powder if she needs to double tap the recipe how many teaspoons will she use of each ingredient?
Answers
Answer:
She will use:
3 tablespoons of pepper
7 tablespoons of garlic powder
[tex]\frac{1}{4}[/tex] tablespoon of thyme
8 tablespoons of onion powder
Explanation:
To double the amount, Stephanie will need to double the amount of each ingredient used. This means that she will multiply each amount by 2
Therefore:
New amount of any ingredient = old amount of that ingredient x 2
This means that:
New amount of pepper = [tex]1\frac{1}{2}*2= 3[/tex] tablespoons
New amount of garlic powder = [tex]3\frac{2}{4}*2=7[/tex] tablespoons
New amount of thyme = [tex]\frac{1}{8}*2=\frac{1}{4}[/tex] tablespoons
New amount of onion powder = [tex]4*2=8[/tex] tablespoons
Hope this helps :)
Stephanie will need double the original amounts: 3 teaspoons of pepper, 7 1/2 teaspoons of garlic powder, 1/4 teaspoon of thyme, and 8 teaspoons of onion powder when doubling her recipe for the party.
When Stephanie needs to double the recipe for a party, the amount of each ingredient will be doubled as well. Here's the doubled amount for each ingredient:
Pepper: 1 1/2 teaspoons doubled is 3 teaspoons.
Garlic powder: 3 2/4 teaspoons doubled is 7 1/2 teaspoons (since 3 2/4 is equivalent to 3.75 and doubling it gives 7.5).
Thyme: 1/8 teaspoon doubled is 1/4 teaspoon.
Onion powder: 4 teaspoons doubled is 8 teaspoons.
To calculate this, each original amount is multiplied by two. For example, to double 3 2/4 teaspoons of garlic powder, you can first convert the mixed number to a decimal (3 + 2/4 = 3.75) and then multiply by 2 to find that you will need 7.5, which is the same as 7 1/2 teaspoons.
What is the first step in simplifying the expression
Answers
The first step in simplifying a mathematical expression, especially those with parentheses, is to eliminate and simplify terms within the parentheses. This involves combining like terms or performing operations according to the order of operations. Subsequent steps may involve factoring and applying algebraic rules to further simplify.
Explanation:The question is asking for the first step in simplifying a mathematical expression. To begin simplifying any expression, especially when involving parentheses, the first step typically involves eliminating terms within the parentheses wherever possible. This process often involves combining like terms or simplifying the algebraic expression by performing any operations inside the parentheses first, according to the order of operations (PEMDAS/BODMAS).
After simplifying the expression inside the parentheses, you can then apply other algebraic techniques, such as factoring, combining like terms outside the parentheses, and explicit multiplication of terms across the parentheses if needed. Always remember to check the answer to see if it is reasonable and to ensure that no simplification step has been missed.
If the expression involves complex denominators or numerators, applying algebraic rules such as the power rule or the chain rule can further simplify the expression. In cases involving equations, isolating the variable on one side can help in solving for the unknown value.
A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and will sell for $2.00 per pound. The other mixture will contain one-third cherries and two-thirds mints by weight and will sell for $1.25 per pound. How many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue?
Answers
Answer:
He should prepare 260 pounds of first mixture and 0 pounds of second mixture
Step-by-step explanation:
Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,
Since, first mixture will contain half cherries and half mints by weight,
That is, in first mixture,
Cherries = [tex]\frac{x}{2}[/tex]
Mints = [tex]\frac{x}{2}[/tex],
While, second mixture will contain one-third cherries and two-thirds mints by weight,
That is, in second mixture,
Cherries = [tex]\frac{y}{3}[/tex]
Mints = [tex]\frac{2y}{3}[/tex]
According to the question,
The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,
That is,
[tex]\frac{x}{2}+\frac{y}{3} \leq 130[/tex]
[tex]\frac{x}{2}+\frac{2y}{3}\leq 170[/tex]
Also, pounds can not be negative,
x ≥ 0, y ≥ 0,
Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,
Hence, the total revenue,
Z = 2.00x + 1.25y
Which is the function that have to maximise,
By plotting the above inequalities,
Vertex of feasible regions are,
(0,255), (180, 120) and (260, 0),
Also, at (260, 0), Z is maximum,
Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.
To maximize sales revenue, the candy manufacturer should prepare one-third cherries and two-thirds mints mixture.
Explanation:
To maximize sales revenue, the candy manufacturer should prepare a mixture that contains one-third cherries and two-thirds mints by weight. Let's assume that he prepares x pounds of this mixture. To calculate the amount of the other mixture, we subtract x from the total weight of the ingredients in stock. So, the amount of the other mixture will be (130 + 170) - x pounds. The candy manufacturer should prepare x pounds of the one-third cherries and two-thirds mints mixture and (130 + 170) - x pounds of the other mixture to maximize his sales revenue.
Learn more about Maximizing sales revenue here:https://brainly.com/question/30901146
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It took John 12 hours riding his bike to make the round trip to his uncle's. If he averaged 20 mph out and 30 mph back, how long did he travel each way? (Round answer to nearest tenth.)
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Answer:
Step-by-step explanation:
Let the time taken by the john to get to his uncle be x.
Let the time taken by the john to get back from his uncle be y.
So,
x+y=12 ------ equation 1
According to the given velocities:
20x=30y
x=3/2y
Put the value x=3/2y in equation 1
3/2y+y =12
3y+2y/2=12
3y+2y=12*2
5y=24
y=24/5
y=4.8h
Now put the value of y in x=3/2y
x=3/2*4.8
x=14.4/2
x=7.2h ....
DBA HELP!!!! FOR PRE-CALCULUS!!!
Whats are some super useful things I should know about Parabolas, Ellipses, Hyperbolas, Parametric Equations and Polar Coordinates? My teacher wants me to explain 3 topics to her tomorrow (7-20-19). I know that I should know this but I've been studying for over an hour and I still don't understand the module. Give me an actual answer, I will report if it's not useful to me.
Answers
Answer:
Step-by-step explanation:
Here are some facts you can mention:
1. Parabola.
The equation of a parabola is one where x^2 is the term of the highest degree. ( the degree being '2' in x^2). For example y = x^2, y = 2x^2 - 5x,
y = -x^2 + 1 are all parabolas. Also we have the type x = f(y) - for example
4x = y^2.
The graph looks like a U ( which maybe on its side or upside down The graph of a parabola where the term coefficient of x^2 is positive opens upwards while if it is negative it open downwards.
It is also a 'conic section' . A parabola is formed when we intersect a right cone with a plane surface through the side wall and through the base.
When a projectile is fired from a gun at an angle, the path it follows is close to a parabola. If fired in a vacuum the path we would be exactly parabolic.
2. Ellipse.
This is another conic section formed when we intersect the cone with a plane surface at an angle to the base ( not 90 degrees) and the plane passes through both sides walls of the cone.
It is oval shaped. The path of the planets around our sun form an ellipse.
You can draw an ellipse by fixing 2 pins at a distance apart on a sheet of paper, and tie the ends of a piece of string, longer in length than the distance between the pins, to each pin. We then press a pen or pencil to the string at some point and draw around the 2 pins.
3. Parametric equations.
A third variable is introduced in a parametric equation. Both x and y are written in terms of this third variable. This variable is called a parameter , hence the name parametric equation.
Many functions can be written in the form y = f(x) or x = f(y) but there are some that cannot be written this way. An example is the circle
x^2 + y^2 = r^2. There are many other such functions. By introducing another variable we are able to identify any point on the graph and it also makes the calculus work easier.
The variable used is usually t or the Greek letter theta (for angles). An example of parametric equations are the ones for a parabola: x= at^2, y = 2at,
which are the parametric equation for the parabola y^2 = 4ax.
I hope this helps.
Answer:
Step-by-step explanation:
I have the same problem. Do you still have the answers. I know I'm two years late but just checking.
Find the value for sin θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form.
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Answer:
sin θ = 4/5
Step-by-step explanation:
The Pythagorean theorem tells you the distance (h) from the origin to the terminal point:
h² = (-3)² +(4)² = 25
h = 5 . . . . . . . . take the square root
The mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse
For angles other than 1st-quadrant angles, it can sometimes be difficult to identify the relevant sides of the relevant triangle. If the angle were a 1st-quadrant angle, it would be clear that the side opposite the angle is the y-coordinate of the point on the terminal side. That remains the case for all angles. The hypotenuse is always the positive distance from the origin to the terminal point.
So, you have
sin θ = opposite/hypotenuse = 4/5
An acute angle θ is in a right triangle with sin θ = one half. What is the value of cot θ?
Answers
Answer:
√3
Step-by-step explanation:
cot²(θ) = csc²(θ) -1 . . . . . a relevant identity
= 1/sin²(θ) -1
= (1/(1/2))² -1 = 2² -1 = 3
Then ...
cot(θ) = √3 . . . . . . . . take the square root
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
It just is
In a survey of women in a certain country (ages 20minus29), the mean height was 64.3 inches with a standard deviation of 2.77 inches. Answer the following question about the specified normal distribution. (a) What height represents the 95th percentile
Answers
Answer: 68.86 inches
Step-by-step explanation:
Given : In a survey of women in a certain country having
Mean : [tex]\mu=64.3\text{ inches}[/tex]
Standard deviation : [tex]\sigma=2.77\text{ inches}[/tex]
The z-value corresponds to 0.095 is 1.645. [Using standard normal distribution table]
The height that represents the 95th percentile is given by :-
[tex]H=z\times\sigma+\mu\\\\=1.6449\times2.77+64.3=68.856373\approx68.86\text{ inches}[/tex]
Hence, the height represents the 95th percentile = 68.86 inches.
Answer:
95th percentile = 68.86 inches.
Step-by-step explanation:
Just took quiz :)
Suppose that the growth rate of children looks like a straight line if the height of a child is observed at the ages of 24 months, 28 months, 32 months, and 36 months. If you use the regression obtained from these ages and predict the height of the child at 21 years, you might find that the predicted height is 20 feet. What is wrong with the prediction and the process used?
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Answer:
The supposition is incorrect.
Step-by-step explanation:
The growth rate of a child is not constant, so height versus time does not look like a straight line. Nothing is wrong with the prediction made using the false assumption. You can conclude anything you like when you start with a false premise.
What is the solution to the system of equations shown below?
2x + 5y + 3z = 10
3x - y + 4z = 8
5x - 2y + 7z = 12
a(7, 1, -3)
b(7, -1, -3)
c(7, 1, 3)
d(-7, 1, -3)
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Answer:
Step-by-step explanation:
____
Good evening ,
_______________
2(7) + 5(1) + 3(-3) = 10
3(7) - (1) + 4(-3) = 8
5(7) - 2(1) + 7(-3) = 12
Then (7,1,-3) is a solution to system
____
:)
John sent a telegram of 44 words and he was charged shilling 25 for the first ten words and shilling 30 for each extra word .How much did the telegram cost?
Answers
Answer:
The cost of the telegram was 1,270 shilling
Step-by-step explanation:
we know that
The total words-----> 44
The first ten words ----> 10
Extra words----> 44-10=34
so
The total cost is equal to
25(10)+30(34)=1,270 shilling
For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . The population mean and the population standard deviation of the sampled population are, respectively, 55.7 and 3.8. n=256
(A) μ = 3.8; σ = 0.2
(B) μ= 14.1; σ = 1.1
(C) μ = 0.2; σ = 55.7
(D) μ = 55.7; σ = 3,8(E) μ = 55.7; σ = 0.2375.
Answers
Answer:
mean of sample is 55.7
sample standard deviation is 0.2375
Step-by-step explanation:
given data
population mean = 55.7
population standard deviation = 3.8
n = 256
to find out
the mean and standard deviation
solution
we know directly mean of sample is mean of population
i.e. mean of sample = 55.7
and standard deviation will be calculate by this formula
sample standard deviation = population standard deviation / [tex]\sqrt{n}[/tex]
sample standard deviation = 3.8 / [tex]\sqrt{256}[/tex]
sample standard deviation = 3.8/ 16
sample standard deviation = 0.2375
so last option is right
(E) μ = 55.7 , σ = 0.2375.