In a case whereby a right triangle, sin(7x+5)=cos(8x-5), the smaller of the triangles two acute angles is 43°.
How can the smaller of the triangles two acute angles be calculated?The concept that will be used is right triangle. An acute angle is one that is smaller than 90 degrees in length. The correct angle is larger than this angle (which is equal to 90 degrees).
We can see that sin(7x+5)=cos(8x-5)
An it implies that 7x+5 -8x-5 =90°
15x=90
x= 6
Then 7(6)+5= 47° 8(6)-5 = 43°
Hence the smaller of the triangles two acute angle is 43°
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should you give any discount to people who order two dozen cookies? if every customer orders 2 dozen, will your capacity increase? if yes, you may want to offer discount to encourage customers to order 2 dozen. you may assume the company operates 24/7 here.
Yes, it is possible to offer a discount to customers who order two dozen cookies.
What is Discount ?
The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
1 dozen=12 pieces
Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to consider the cost of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.
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Yes, it is possible to offer a discount to customers who order two dozen cookies.
What is Discount ?
The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
1 dozen=12 pieces
Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to cocost nsider the of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.
So ,Yes it is possible to offer a discount to customers who order two dozen cookies.
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PLEASE HELP ME!!! Complete the two-column proof.
The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
x/6 + 2 = 15
Subtract 2 on both sides. Then we have
x / 6 + 2 - 2 = 15 - 2
x / 6 = 13
Multiply the equation by 6, then we have
x/6 × 6 = 6 × 13
x = 78
The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.
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fill in the blank. in a certain company, the average salary for college graduates is $62,047 and the average salary for high school graduates is $40,626. the average salary for college graduates is ___% higher than that of high school graduates. (round your answer to the nearest whole percentage point, e.g., enter 14 if the answer is 14%.)
The average salary for college graduates is 53% higher than that of high school graduates.
How to calculate the percentage increase?Mathematically, percentage increase can be calculated by using this mathematical expression:
Percentage increase = [Final value - Initial value]/Initial value × 100
Substituting the given parameters into the percentage increase formula, we have the following;
Percentage increase = [62,047 - 40,626]/40,626 × 100
Percentage increase = 21,421/40,626 × 100
Percentage increase = 0.527 × 100
Percentage increase = 52.7 ≈ 53%.
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A diet is being prepared for WTAMU dorms. The varied diet is to be made of three foods: A, B and C. Food A costs $2.25 per pound and contains 500 calories. Food B costs $ 2 per pound and contains 700 calories. Food C costs $ 3 per pound and contains 600 calories No more than 0.75 pounds of food C can be used per resident. No less than 2 pounds of food B should be used per resident. The objective is to feed the students at the least cost, but the diet must have at least 1800 calories.
If we define the decision variables as A: pounds of food A, B: pounds of food B, and C pounds of food C, the object function is to minimize Blank 1. In addition to non-negative constraints, other constraints are Blank 2,Blank 3, and Blank 4.
(1. No need to use multiplication sign. For example, just write 10A not 10*A. For greater(less) than sign, just write it as >= (<=).
2. Also please leave no space in equation. For example, write A<=100, not A <= 100.
3. Please write decimal number for example as 0.32 not .32 when applicable. )
This problem is designed to minimize the cost of feeding students in the dorms while providing a minimum of 1800 calories. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost and adding them together. The constraints of the problem are that A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75.
1. 2.25A + 2B + 3C
2. A >= 0
3. B >= 2
4. C <= 0.75
The objective of this problem is to minimize the cost of feeding students in the dorms, while the diet must contain a minimum of 1800 calories. To achieve this, three decision variables were defined: A, B, and C, which represent the pounds of food A, B, and C respectively. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost, and adding them together. There are three constraints in the problem: A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75. These constraints ensure that the diet contains the desired amount of each food and that the total calories meet the minimum requirements.
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You get a personal loan of $5,000 with 12% simple interest to be paid over 30 months. What is your monthly payment?
Work Shown:
A = P*(1+r*t)
A = 5000*(1+0.12*30/12)
A = 6500
The amount $6500 is what you pay back
Divided over 30 months gives 6500/30 = 216.67 dollars per month.
Side note: The value t is in years, so 30 months = 30/12 years.
Several college students conduct a survey at their local community college. They find that 67% of the students live with their parents in the house they grew up in. Of the students who live with their parents 23% live within walking distance to campus. Of the students who do not live with their parents only
6% live within walking distance to campus. a) What is the probability of a student living within walking distance to campus? ( 1 point) b) What is the probability given a student lives within walking distance to campus they live with their parents? (1 point) c) Are living with parents and living within walking distance independent events? (2 points)
a) The probability of a student living within walking distance of campus is 0.1521.
To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:
P(A and B) = P(A) * P(B|A).
For this situation, An is "living within walking distance to campus" and B is "living with parents."
Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.
Hence, the probability of a student living within walking distance of campus is 0.1521.
b) The probability given a student living within walking distance of campus they experience with their parents is 0.67.
To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:
P(A|B) = P(A and B)/P(B).
In this situation, A is "living with parents" and B is "living within walking distance to campus."
Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.
Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.
c) Living with parents and living within walking distance are independent events.
To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).
On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.
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(2+v)^2
how do I rewrite with out parentheses
Answer:
v^2+4v+4
Step-by-step explanation:
To do this we have to know that (2+v)^2 is the same as (2+v) (2+v)
Next, use the distributive property and add like variables to get the final answer of v2+4v+4
I hope this was able to help you out :D
fill in the blank with a whole number with how many significant figures are in the following: a) 0.04550 b) 5.0003 c) 1.000 x 105 d) 0.00002 e) 1.01 x 10-2 f) 7
a) 0.04550 has four significant figures.
b) 5.0003 has four significant figures.
c) 1.000 x [tex]10^5[/tex] has four significant figures.
d) 0.00002 has one significant figure.
e) 1.01 x [tex]10^{-2}[/tex] has three significant figures.
f) 7 has one significant figure.
Significant figures are the digits in a number that are known with certainty, including one uncertain digit. In general, any non-zero digit is considered a significant figure, and zeros between non-zero digits are also significant figures.
Leading zeros before the first non-zero digit and trailing zeros after the last non-zero digit are not considered significant figures.
For example, in the given number 5.006, there is four significant number,
since all zeros between integers are always significant.
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In 2012, the population of a city was 5.89 million. The exponential growth rate was 3.42% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 8 million?
d) Find the doubling time.
The general form of exponential formula is y = a * b^x, the population of the city in 2018 6.058454 million.(c) the population of the city be 8 million19.38548963 years.
How to find the population?In this problem, a = 5.21 million and b = 1 + 2.86%/100 = 1.0286.
a is a constant.b is the basex is the exponent.In 2012, the population was 5.89 million.
In 2018, the population will be 5.89 * 1.0286 ^ (2018 - 2012) = 5.89 * 1.0286 ^ 6 = 6.058454 million.
To find when the population will be 9 million, your equation becomes:
9 = 5.21 * 1.0286 ^ x divide both sides of this formula by 5.21 to get:
9/5.21 = 1.0286 ^ x take the log of both sides of the equation to get:
log(9/5.21) = log(1.0286^x) since log(1.0286^x) = x * log(1.0286), the equation becomes:
log(9/5.21) = x * log(1.0286)
Divide both sides of this equation by log(1.0286) to get:
log(9/5.21) / log(1.0286) = x
Solve for x to get:
x = 19.38548963.
Confirm by replace x in the original equation to get:
9 = 5.21 * 1.0286 ^ 19.38548963 becomes 9 = 9.
This confirms the value of x is good.
The population will grow to 9 million in 19.38548963 years.
To find when the population will double, the equation becomes:
2 = 1 * 1.0286 ^ x
Simplify to get:
2 = 1.0286 ^ x
Take the log of both sides of this equation to get:
log(2) = log(1.0286 ^ x)
Since log(1.0286 ^ x) = x * log(1.0286), this equation becomes:
log(2) = x * log(1.0286)
solve for x to get:
x = log(2) / log(1.0286) = 24.5808602.
to confirm this is true, replace x in the original equation to get:
2 = 1.0286 ^ 24.5808602 which becomes 2 = 2.
This confirms the value of x is true.
The population will double in 24.5808602 years.
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A bicycle shop keeps the same ratio of wheels to bikes in stock. The ratio of wheels to bikes is always 4:1. How many wheels does the shop have if there are 18 bikes in stock?
Is it
4.5
42
72
76
Answer:
c (72)
Step-by-step explanation:
since there are four wheels to every bike, you just have to multiply the number of bikes to the amount of wheels per bike. given this, 18 * 4=72.
PLEASE HELP ASAP !! The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch???How many sec after launch did their rocket hit the ground???What was their rockets maximum height in meters??
The height in meters is 19.75 meters
The rocket hit the ground after 8.06 sec
The maximum height in seconds is 81 meters
What was their rocket's height in meters 0.5 seconds after launchwe would have to use 0.5 as the value for t in the formula
h(t) = -5t² + 40t + 1
h(0.5) = -5(0.5)² + 40(0.5) + 1
= -1.25 + 20 +1
= 19.75
How many sec after launch did their rocket hit the ground?To find when the rocket hit the ground, we need to find when the height of the rocket is equal to 0. So we will set h(t) = 0 and solve for t:
-5t² + 40t + 1 = 0
by using Quadratic equation formula we get t = (-b ± √(b²-4ac))/2a
we solve this using the calculator
so t1 = (40 + 40.6)/10 = 80.6/10 = 8.06 sec
Since the time of the rocket hit the ground should be positive, so the rocket hit the ground after 8.06 seconds after launch.
What was their rockets maximum height in meters?To find the rocket's maximum height, we need to find the vertex of the parabola. The vertex of the parabola can be found by using the formula x = -b/2a,
where x is time and a, b, c are from equation.
so, x = -b/2a
= -40/2*-5
= -40/ -10
= 4 sec
and by using the above formula of x, we get the
h(4) = -5(4)² + 40(4) + 1
= -80 + 160 + 1
= 81 meters
Therefore, the rocket's maximum height is 81 meters.
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What’s 23,760ft in miles
Answer:
So, there are 5,280 feet in a mile, so you will want to find out how many times 5, 280 will go into 23,760. To do this, you will divide.
23,760/5,280 = 4.5
There are 4.5 or 4 1/2 miles in 23,760 feet!
Step-by-step explanation:
Hope it helps! =D
which of these has a slope of -3
Answer:
Option 3. Look at my screenshot so you can see the circled one
Step-by-step explanation:
The reasoning behind this is slope is rise over run (rise/run)
Graph 3 goes down 3 so -3 and runs 1 over so (-3/1)
This is simplified as -3.
I hope this helps you out :D
There are 125 second graders amd 118 third graders at the museum. There are 249 more adults than students at the museum. Hire many adults are at the museum
Answer:
490 adults at the museum!
hope that helps :)
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Find an angle whose supplement is 30 degrees greater than 4 times the supplement.
Explanation needed
The angle whose supplement is 30 degrees greater than 4 times the supplement is 30°
What are supplementary angles?Two angles are called supplementary when their measures add up to 180 degrees.
For example:- 120° and 60°, 110° and 70°, 140° and 40°, 90° and 90°, 20° and 160°, 135° and 45° are some example of supplementary angles.
Given that, an angle whose supplement is 30 degrees greater than 4 times the supplement.
Let the angle asked be x,
Therefore, the supplement of x, will be = 180°-x
According to the question, Its supplement is 30 degrees greater than 4 times the supplement.
Therefore, establishing the equation,
So, for solving for x, we have,
180°-x = 30°+4x
4x+x = 180°- 30°
5x = 150°
5x/5 = 150°/5
x = 30°
As, we considered the angle asked be x,
Hence, the angle whose supplement is 30 degrees greater than 4 times the supplement is 30°
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12
75°
b
a
35°
Find all the unknow measures using the law of sines
Please help for math thank you!!!!!!!!
Answer:hie
hie
Step-by-step explanation:hie
Anything would be awesome
Answer:
I believe it's BC
Step-by-step explanation:
I can't really give an explanation but I've done this before and struggled but learned it, hope I'm right
A farmer is building a cylinder-shaped grain bin. The bin will be 10 feet tall and have a diameter of 12 feet. What is the surface area of the grain
bin in square feet? Use x = 3. 14. Round to the nearest hundredth if necessary.
Answer: 602.88 square feet
Equation for surface area of cylinder:
A = 2πrh+2πr^2
r = 6, because radius is half of the diameter
h = 10
A = 2(3.14)(6)(10) + 2(3.14)(6)^2
A = 376.8 + 226.08
A = 602.88 square feet
7th Grade Exit Ticket Lesson 5.5 "Dividing Fractions"
Answer: -1 7/20
Step-by-step explanation:
hope this helps
solve it to find the value of x. also find the actual length of each square
[tex]perimeter square[/tex]
The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.
What is the perimeter of the square?The sum of all the sides of the square or the product of the four and the edge length of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,
4(x + 2) = 40
Simplify the equation, then we have
4(x + 2) = 40
(x + 2) = 10
x = 10 - 2
x = 8
The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.
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The complete question is given below.
Solve it to find the value of x. Also, find the actual length of each square perimeter of the square is 40 cm and side length is (x + 2).
Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)
A solution of the first order IVP consisting of this differential equation is y = [tex]\frac{1}{x^2-5}[/tex] and the domain of y considered as a function over the reals is (-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).
We have to find the domain of y considered as a function over the reals.
The differential equation is y' + 2x[tex]y^2[/tex] = 0
The solution of the given differential equation is y = 1/([tex]x^2[/tex] + c)......(1)
The given initial value; y(-3) = 1/4
Replace the initial value in the first-order DE solution provided. To obtain the equation for y, locate the constant c and then re-substitute 'c'.
Now put x = -3 and y(-3) = 1/4 in equation 1
[tex]\frac{1}{4}=\frac{1}{(-3)^2+c}[/tex]
[tex]\frac{1}{4}=\frac{1}{9+c}[/tex]
9+c = 4
Subtract 9 on both side, we get
c = -5
Now substitute the value of c again in equation 1
y = [tex]\frac{1}{x^2-5}[/tex]
To find the domain of y we can write it as
y = [tex]\frac{1}{(x)^2-(\sqrt{5})^2}[/tex]
Now the simplified form is
y = [tex]\frac{1}{(x-\sqrt{5})(x+\sqrt{5})}[/tex]
Now the domain of y over R is
(-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).
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The complete question is:
y = 1/([tex]x^2[/tex] + c) is a one parameter family of solutions of the first order DE y' + 2x[tex]y^2[/tex] = 0. Find a solution of the first order IVP consisting of this differential equation and the given initial condition.
y(-3) = 1/4
Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)
Analyze the diagram below and complete the instructions that follow.
C
A
B
Given that
A. 10
B. 10.5
C. 11
D. 11.5
6
CB
CA
DE
DF'
find BA.
D
4
E
7
F
Save and Exit
Next
Submit
Analyze the diagram of the trapezoid gives BA = 10.5 units
How to find the side BA of the trapezoid the analyzing the diagram?A trapezoid (also known as a trapezium) is a four-sided geometric shape that has two parallel sides (the bases) and two non-parallel sides (the legs). The bases of a trapezoid can have different lengths, but the legs must be congruent and parallel to each other.
Let's analyze the diagram below and complete the instructions:
Since CB / CA = DE / DF
where CB = 6, DE = 4, EF = 7
We can say:
DF = DE + EF = 4 + 7 = 11
CA = CB + BA = 6 + BA
CB / CA = DE / DF
6/(6 + BA) = 4/11
6 × 11 = 4(6 + BA)
66 = 24 + 4BA
24 + 4BA = 66
4BA = 66 - 24
4BA = 42
BA = 42/4
BA = 10.5 units
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Find the equation of the line with slope = 7 and passing through (2,19)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{19}=\stackrel{m}{ 7}(x-\stackrel{x_1}{2}) \\\\\\ y-19=7x-14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]
Find the image of A(4, 2) after the following transformations
a. (1,4) ∘ (−) (4, 2)
b. (−) ∘ (1,4) (4, 2)
HELP PLEASE
POSSIBLE POINTS: 5 Your business borrowed 8 bitcoins on May 1, when 1 bitcoin was worth $1,418.86. On June 1, 1 bitcoin was worth $2,441.29. Not counting the 1 month of interest, what amount of profit would your business make buy selling the bitcoins June 1? $3,860.15 $11,350.88 $19,530.32 $8,179.44 $1,022.43 Shy
Answer:
$10,224.30
Step-by-step explanation:
Which set of ordered pairs is made up of points on the graph of the function below?
A.
(10,-1), (8,0), (1,6), (2,4)
B.
(10,-1), (8,0), (6,1), (4,2)
C.
(-1,10), (0,8), (1,6), (2,4)
D.
(-1,10), (8,0), (1,6), (4,2)
y=-2x+8
These points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.
What is the linear system?
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The linear function is given below.
y = 2x – 6
The points (-1,-8), (0,-6), (1,-4), and (2,-2) lies on the equation.
As when the put the given points in the equation , than it satisfies the given condition.
Hence, these points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.
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A figure is made up of an equilateral triangle and a square of side 7cm. The perimeter of the figure is in stepes
Which equation matches the hanger diagram 2x=5
The equation that matches the hanger diagram is 2x=5
How to determine the equation of the diagramFrom the question, we have the following parameters that can be used in our computation:
The hanger diagram added as an attachment
From the diagram, we hav
Left = x + x
Right = 1 + 1 + 1 + 1 + 1
This gives
Left = 2x
Right = 5
So, we have
2x = 5
hence, the equation is 2x = 5
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a bicycle has wheels 32 inches in diameter. a tachometer determines the weheels are rotating at 150 rpm(revolutions per minute). Find the speed the bicycle is traveling down the road.
The speed of the bicycle is 381 meters per minutes
we know that,
revolutions per minute = speed in meters per minute / circumference in meters.
Diameter = 32 inches
Circumference of the wheel = 2πr
r = Diameter/2 = 32/2 = 16
Circumference = 2 × π × 16
= 100.5714 inches
Approximately = 100 inches
we know that,
1 inch = 0.0254 meter
100 inches = x
x = 100 × 0.0254 meters
x = 2.54 meters
Hence:
Revolutions per minute = Speed in meters per minute / circumference in meters.
Speed = Revolutions per minute × circumference in meters.
Speed = 150 RPM × 2.54 meters
Speed = 381 meters per minutes
so, the speed of the bicycle is 381 meters per minutes.
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A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism. 1-2 in. 5 in. T 2 in. T 3 in. I -2 in. 2 in. t 3 in. What is the surface area, in square inches, of the container?
A 19
B 30
C 38
D 62
The surface area of the container is 62 square inches.
The correct option is D.
What is prism?In three-dimensional space,
a prism is a polyhedron where two ends are similar.
Given:
A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism.
We have H = 2 inches
L = 5 inches
W = 3 inches
Surface area of the rectangular prism,
A = 2(W×L + H×L + H×W)
A = 2(3×5+2×5+2×3)
A = 2(15+10+6)
A = 2(31)
A = 62 square inches
Therefore, the surface area is 62 square inches.
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