Find the value for sin θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form.
Answers
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
Related Questions
How many cubic units is a box that is 3 units high
Answers
Answer:
18 cubic units
Step-by-step explanation:
There are 18 cubic units in a box that is 3 units high.
3 x 3 = 6
6 x 2 = 18
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.
Is my answer I chose correct? I don't know how to determine if it doubled, tripled, or quadrupled...
Between 1965 and 1967, US troop strength
A) more than doubled.
B) more than tripled.
C) more than quadrupled.
Answers
Answer:
More than doubled
Step-by-step explanation:
The troop "strength" is basically just troop number. It went from about 200,000 to about 500,000.
US troop strength is more than doubled. The correct option is A.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
From the given data we can see that the troop "strength" is basically just troop number. It went from about 200,000 to about 500,000.
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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.
A 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
Based on sample results, a 90% confidence interval for the mean servings of fruit per day consumed by grade school children is (0.21, 2.45). What is the margin of error?
Answers
Answer: 1.12
Step-by-step explanation:
The confidence interval for the mean [tex]\mu[/tex] and margin of error E is given by :-
[tex](\mu-E,\ \mu+E)[/tex] --------------(1)
The given confidence interval : (0.21, 2.45) -------------(2)
From (1) and (2), we have
[tex]\mu-E=0.21-------(3)\\\\\mu+E=2.45--------(4)[/tex]
Subtract equation (3) from (4), we get
[tex]2E=2.45-0.21\\\\\Rightarrow\ 2E=2.24\\\\\Rightarrow\ E=\dfrac{2.24}{2}=1.12[/tex]
Hence, the margin of error is 1.12 .
The margin of error can be calculated as half the width of the confidence interval.
Explanation:The margin of error can be calculated by finding half the width of the confidence interval. In this case, the confidence interval is (0.21, 2.45), so the width is 2.45 - 0.21 = 2.24. Therefore, the margin of error is half of this width, which is 2.24/2 =
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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
There is $7 entrance fee and it costs $1.25 for every minute your on a trampoline.Your total was $43.25, write an equation to determine the number of minutes you were on the trampoline
Answers
Answer:
7 +1.25m = 43.25
Step-by-step explanation:
Let m represent the number of minutes on the trampoline. Then the charge (in dollars) for minutes you're on it is 1.25m. The entrance fee is added to that to give the total charges:
7 + 1.25m = 43.25
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.
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
Jorge has a credit card debt of $7,600.97. Jorge’s credit card has an APR of 23.99% and asks that Jorge makes a minimum payment of 3.5% of his balance. For Jorge’s current balance, what is the minimum payment he must make to the credit card company each month?
a.
$266.03
b.
$228.03
c.
$2,280.29
d.
$2,660.34
If Jorge (from #6) pays the minimum payment each month how many months will it take Jorge to pay off his balance, assuming he doesn’t make any more charges to his credit card? Assume the card compounds monthly. You may want to use the TVM solver
a.
About 43 months
b.
About 23 months
c.
About 29 months
d.
About 30 months
Answers
Answer:
a. $266.03 a. About 43 monthsStep-by-step explanation:
1. The calculation for the minimum payment is ...
0.035 × $7600.97 = $266.03
__
2. The answer choices assume that Jorge makes a payment of $266.03 each month. After the first month, the minimum payment due is less than that amount. If Jorge only pays the minimum payment each month the balance will decrease by about 1.5% each month, and it will take about 31 years before the minimum payment is below $1.
The TVM Solver says it will be about 43 months for the card to be paid off if Jorge pays $266.03 each month.
7. A 2600-pound truck is stopped at a red light on a hill with an incline of 25°. Ignoring the force of friction, what force is required to keep the truck from rolling down the hill? (Show work)
Answers
Answer:
about 75 percent of its force
Step-by-step explanation:
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.
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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
A figure formed by two rays that have the same endpoint
Answers
Answer:
That is known as a Vertex
A figure formed by two rays that share a common endpoint is known as an angle. The common endpoint is known as the vertex, while the rays are considered the sides of the angle.
Explanation:In mathematics, a figure formed by two rays that share a common endpoint is known as an angle. The common endpoint is referred to as the vertex and the rays are referred to as the sides of the angle.
Rays in the context of angles means a straight line that starts from a point (vertex) and extends indefinitely in a particular direction. For example, in a page of a book when it is half open, the two visible pages represent the rays, and where the pages meet (the spine) represents the vertex.
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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 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
What is the greatest common factor of 8x and 40y?
5
5xy
320
320xy
Answers
Answer:
8.
Step-by-step explanation:
It's none of those. It is 8, because 8 is a factor of 40 ( and of 8 of course).
Answer:
none of the above.
Step-by-step explanation:
when we talk about greatest common factor of 8 x and 40 y
8 x = 2× 2× 2 × x........................................(1)
40 y = 2 × 2 × 2 × 5 × y..............................(2)
when we see both equation (1) and (2 )
then we can clearly see
that the greatest common are 2 × 2 × 2
so, the greatest common will be 2 × 2 × 2 = 8
hence , the correct answer will be none of the above.
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 ....
I need to mix brown paint using red, blue, and, yellow in the ratio of 2:1:3. If I need to mix 18 fluid ounces of paint, hwo much yellow paint will I need?
Answers
hihi! so the ratio 2:1:3 can be rewritten as 2/6 (red) 1/6 (blue) and 3/6 (yellow).
this is because you have 2 floz of red, 1 floz of blue, and 3 floz of yellow, which adds up to 6 floz of paint total in your ratio.
since you have 18 fl. oz. of paint, you multiply the ratio 3/6 by 18 to get 9 fl. oz. of yellow paint.
hope this helps!
There would be of 9 ounces yellow paint needed.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The total quantity of fluid of paint= 18 ounces,
And the ratio of red, blue and yellow paint = 2:1:3
Let the multiplying factor in ratio is x,
So, total paint will be 6x,
According to given condition,
6x = 18 ounces,
x = 3 ounces
Since yellow paint is 3x,
So 3x = 9 ounces
9 ounces yellow paint is required,
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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.
sin4xcos2x =
1/2sin6x + 1/2sin2x
1/2sin6x - 1/2sin2x
1/2cos2x + 1/2cos6x
1/2cos2x - 1/2cos6x
Answers
Answer:
1/2sin(6x) + 1/2sin(2x)
Step-by-step explanation:
You can look up the formulas for the product identities for sine and cosine, or you can guess and check using a graphing calculator. I did the calculator solution first (see the first attachment), then looked up the identities so I can tell you what they are (see the second attachment).
__
These identities are based on the sum and difference angle identities:
sin(α+β) +sin(α-β) = (sin(α)cos(β) +sin(β)cos(α)) + (sin(α)cos(β) -sin(β)cos(α))
= 2sin(α)cos(β)
Dividing by 2 gives the identity of interest in this problem:
sin(4x)cos(2x) = (1/2)(sin(4x +2x) +sin(4x -2x))
sin(4x)cos(2x) = (1/2)(sin(6x) +sin(2x))
Answer: 1/2sin(6x) + 1/2sin(2x)
Step-by-step explanation:
took the test and got a 100
A shipping company must design a closed rectangular shipping crate with a square base. The volume is 3072ft3. The material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Find the dimensions of the crate that will minimize the total cost of material.
Answers
The dimensions that minimize the total cost of material for the shipping crate are:
- Length: 24 feet
- Width: 24 feet
- Height: 8 feet
To solve this problem, we can start by writing down the volume formula for a rectangular box with a square base:
Volume = Length × Width × Height
Given that the volume is 3072 ft³, we have:
3072 = L × W × H
We also know that the material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Let's denote the areas of the top, bottom, and sides as A_top, A_bottom, and A_sides, respectively.
A_top = L × W
A_bottom = L × W
A_sides = 2 × (L × H + W × H)
The total cost, C, can be expressed as:
C = 4 × (A_top + A_bottom) + 2 × A_sides
C = 4 × (L × W + L × W) + 2 × 2 × (L × H + W × H)
C = 8LW + 4LH + 4WH
We can substitute the volume equation into the cost equation to eliminate one variable. Let's express L in terms of W and H from the volume equation:
L = 3072 ÷ (W × H)
Now substitute L into the cost equation:
C = 8(3072 ÷ (WH))W + 4(3072 ÷ (WH))H + 4WH
C = 24576 ÷ H + 12288 ÷ W + 4WH
To minimize C, we take the derivative with respect to W and H, set them equal to zero, and solve for W and H:
∂C/∂W = -12288/W² + 4H = 0
∂C/∂H = -24576/H² + 4W = 0
Solving these equations gives us W = 24 and H = 8, which leads to L = 3072 ÷ (24 × 8) = 16.
So, the dimensions that minimize the total cost of material are Length: 24 feet, Width: 24 feet, and Height: 8 feet.
Complete Question:
A shipping company must design a closed rectangular shipping crate with a square base. The volume is 3072ft3. The material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Find the dimensions of the crate that will minimize the total cost of material.
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?
Answers
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.
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.
I've experiencing for a while but this is Finding missing angles. Please help me!!
Answers
Answer:
x=15
Step-by-step explanation:
165+x=180
x=180-165
x=15
Answer:
15° = x
Step-by-step explanation:
By the Supplementary Angles Theorem, you add m<x by 165, and set that equal to 180°, or π. Of course you have to do the inverse of addition in order to get this, so deduct 165 from 180 to end up with 15.
Please help with the attached question. Thanks
Answers
Answer:
Choice A) [tex]F(x) = 3\sqrt{x + 1}[/tex].
Step-by-step explanation:
What are the changes that would bring [tex]G(x)[/tex] to [tex]F(x)[/tex]?
Translate [tex]G(x)[/tex] to the left by [tex]1[/tex] unit, andStretch [tex]G(x)[/tex] vertically (by a factor greater than [tex]1[/tex].)[tex]G(x) = \sqrt{x}[/tex]. The choices of [tex]F(x)[/tex] listed here are related to [tex]G(x)[/tex]:
Choice A) [tex]F(x) = 3\;G(x+1)[/tex];Choice B) [tex]F(x) = 3\;G(x-1)[/tex];Choice C) [tex]F(x) = -3\;G(x+1)[/tex];Choice D) [tex]F(x) = -3\;G(x-1)[/tex].The expression in the braces (for example [tex]x[/tex] as in [tex]G(x)[/tex]) is the independent variable.
To shift a function on a cartesian plane to the left by [tex]a[/tex] units, add [tex]a[/tex] to its independent variable. Think about how [tex](x-a)[/tex], which is to the left of [tex]x[/tex], will yield the same function value.
Conversely, to shift a function on a cartesian plane to the right by [tex]a[/tex] units, subtract [tex]a[/tex] from its independent variable.
For example, [tex]G(x+1)[/tex] is [tex]1[/tex] unit to the left of [tex]G(x)[/tex]. Conversely, [tex]G(x-1)[/tex] is [tex]1[/tex] unit to the right of [tex]G(x)[/tex]. The new function is to the left of [tex]G(x)[/tex]. Meaning that [tex]F(x)[/tex] should should add [tex]1[/tex] to (rather than subtract [tex]1[/tex] from) the independent variable of [tex]G(x)[/tex]. That rules out choice B) and D).
Multiplying a function by a number that is greater than one will stretch its graph vertically. Multiplying a function by a number that is between zero and one will compress its graph vertically.Multiplying a function by a number that is between [tex]-1[/tex] and zero will flip its graph about the [tex]x[/tex]-axis. Doing so will also compress the graph vertically.Multiplying a function by a number that is less than [tex]-1[/tex] will flip its graph about the [tex]x[/tex]-axis. Doing so will also stretch the graph vertically.The graph of [tex]G(x)[/tex] is stretched vertically. However, similarly to the graph of this graph [tex]G(x)[/tex], the graph of [tex]F(x)[/tex] increases as [tex]x[/tex] increases. In other words, the graph of [tex]G(x)[/tex] isn't flipped about the [tex]x[/tex]-axis. [tex]G(x)[/tex] should have been multiplied by a number that is greater than one. That rules out choice C) and D).
Overall, only choice A) meets the requirements.
Since the plot in the question also came with a couple of gridlines, see if the points [tex](x, y)[/tex]'s that are on the graph of [tex]F(x)[/tex] fit into the expression [tex]y = F(x) = 3\sqrt{x - 1}[/tex].
Answer:
f(x) =3 sqrt(x+1)
Step-by-step explanation:
We notice two things about the graph, it has a shift to the left and is steeper
First the shift to the left
f(x) = g(x + C)
C > 0 moves it left
C < 0 moves it right
g(x) is 0 at x=0 f(x) is 0 at x=-1
We are moving it 1 unit to the left
This means our "c" is 1
f(x) = sqrt( x+1)
Now we need to deal with the graph getting steeper
f(x) = Cg(x)
C > 1 stretches it in the y-direction
0 < C < 1 compresses it
Since it is getting taller, "c" must be greater than 1
Remember the - sign means it is a reflection across the x axis, which we do not have
f(x) =3 sqrt(x+1)