h(x) has the following formula: 9/2 cos[4/3 (x+/2)] + 1/2
What is a trigonometric function ?Trigonometry is a discipline of mathematics that examines certain functions of angles and how to use them in computations. There are six frequent uses for an angle in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant.
The graph is sent as
Two point (-π/2 , 5) , (π/4 , -4)
amplitude is A = 9/2
Period = π + π/2 = 3π/2
B = 2π/3π/2 = 4/3
Phase shift = - π/2 (π/2 to left)
midpoint y= 0.5
equation of cosine will be
9/2 cos[ 4/3 (x+π/2) ] + 1/2
Therefore h(x) = 9/2 cos[ 4/3 (x+π/2) ] + 1/2
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find the probability that the engineer has to test at least 5 computers in order to find 2 defective ones. g
The probability that the engineer has to test at least 5 computers in order to find 2 defective ones is 0.985.
Given :
A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.
So the probability of getting 0 defective computers out of 4 is :
= ( 1 - 0.05 )^4
= 0.95^4
= 0.814.
The probability of getting exactly 1 defective computer out of 4 is :
= 0.05 * ( 1 - 0.05 )^3 * 4! / ( 1! ( 4 - 1 )!)
= 0.05 * 0.95^3 * 24/ ( 1!3! )
= 0.05 * 0.857375 * 24/6
= 0.171.
So the probability of getting only 0 or 1 defective computers out of the 1st 4 is :
= 0.814 + 0.171
= 0.985
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PLEASE HELP ME OUT!!!!!!!!
GIVING BRAINLIEST
Fill in the blank with the correct response. If 24 is increased to 30, the percent of increase is %.
Answer:
there is a 25% increase from 24 to 30
Step-by-step explanation:
30-24/24 x 100
6/24x 100
0.25x100
25%
Answer:
[tex]\begin{align} \% \text{ Increase} &= \dfrac {\text{Final - Initial}}{\text{Initial}} \times 100 \\ \\ &= \dfrac {30 - 24}{24} \times 100 \\ \\ &= \dfrac {6}{24} \times 100 \\ \\ &= 0.25 \times 100 \\ \\ &= 25 \% \end{align} [/tex]
There is a 25 % increase from 24 to 30.
A small business produces soap and lotion gift baskets. Labor, utilities, and other fixed expenses
cost $6,000 a month. Each basket costs $8 to produce and sells for $20. How many baskets does
the company need to sell each month to break even?
•
Define n to be the number of gift baskets the company sells in a month
Cost Equation: C(n)= 6000 + 8n
Revenue Equation: R(n) = 20n
Cost
$
12000
11000-
10000+
9000
8000
7000-
6000
5000
4000+
3000
2000
1000-
C(n)
R(n)
100 200 300
400 500 600 700 800
TE
The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.
What is break even point?
In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total revenue are equal, or "even." Although opportunity costs have been paid and capital has received the risk-adjusted, expected return, there is no net loss or gain, and one has "broken even."
In this case we could probably solve the problem from the graph itself, but we can also solve it algebraically by setting the equations equal:
[tex]\begin{gathered}R(n)=C(n) \\20 n=6000+8 n\end{gathered}[/tex]
Subtract 8n from both sides:
[tex]12 n=6000[/tex]
Divide:[tex]n=\frac{6000}{12}=500[/tex]
Evaluate either function at this input: [tex]R(500)=C(500)=10,000[/tex]
The break even point is at 500 baskets. The company must sell 500 baskets a month, at which point their revenue of $10,000 will cover their total costs of $10,000.
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F(x)=2x-7
G(x)=3x²-5x-7
Find:f(g(x))
Express your answer as a polynomial in standard form.
The composition function for the given function f(x) and g(x) is,
f(g(x)) = 6x^2 - 10x - 21.
What is composition of function?
The mathematical operation known as "function composition" takes two functions, f and g, and creates a function, h = g o f, such that h(x) = g. This operation involves applying the function g to the outcome of applying the function f to x.
Given:
f(x) = 2x - 7
g(x) = 3x^2 - 5x - 7
We have to find the composition function f(g(x)).
[tex]f(g(x)) = f(3x^2- 5x - 7)[/tex]
Plug x = 3x^2 - 5x - 7 in f(x).
[tex]f(g(x)) = 2(3x^2 - 5x - 7) - 7\\f(g(x)) = 6x^2 - 10x - 14 - 7\\f(g(x)) = 6x^2 - 10x - 21[/tex]
Hence, the composition function for the given function f(x) and g(x) is, f(g(x)) = 6x^2 - 10x - 21.
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8. Which of the following is NOT preserved when a figure is dilated?
A. Betweenness
B.orientation
C. size
D. shape
C. size
because when things dilate they change in size but not shape, orientation or betweenness
1. Corey’s pay increases from £12.36 per hour to £14.11 per hour. Find the percentage increase to 1 decimal place.
2. Dele invests $6000 for 4 years at 3% per annum compound interest. Calculate the value of his investment at the end of 4 years.
3. The value of a car depreciates by 14% per annum. At the end of 2017 the car is worth $17500. How much is it worth at the end of 2020?
a) Corey's percentage increase in pay per hour is 14.2%.
b) When Dele invests $6,000 for 4 years at 3% per annum compound interest, the value of his investment (future value) at the end of 4 years is $15,757.12.
c) The worth of the car at the end of 2020 is $11,812.50, depreciating by 14% per annum.
a. Corey's original pay per hour = £12.36
Corey's new pay per hour = $14.11
Increase in pay = £1.75 (£14.11 - £12.36)
Percentage increase in pay = 14.2% (£1.75/£12.36 x 100)
b. Principal investment = $14,000
Investment period = 4 years
Compound interest rate = 3%
Compounding terms = Annually
The future value (FV) in 4 years:
N (# of periods) = 4 years
I/Y (Interest per year) = 3%
PV (Present Value) = $14,000
PMT (Periodic Payment) = $0
Results:
FV = $15,757.12
Total Interest = $1,757.12
c. Value of a car at the end of 2017 = $17,500
Depreciation rate per annum = 14%
Depreciation period = 3 years (Dec. 31, 2017 - Dece. 2020)
Value of the car at the end of 2020 = $11,812.50 ($17,500 x 1.14⁻³)
Thus, the car will reduce (depreciate) in value every year by 14%, making its value to be $11,812.50 at the end of 2020.
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A plane is flying at a speed of 425 miles per hour. How far will the plane travel in 0.75 hour.
Answer:
318.75 miles
Step-by-step explanation:
Jada has time on the weekends to earn some money. A local bookstore is looking for someone to help sort books and will pay $12.20 an hour. To get to and from the bookstore on a work day, however, Jada would have to spend $7.15 on bus fare.Write an equation that represents Jada’s take-home earnings in dollars, , if she works at the bookstore for hours in one day. One day, Jada takes home $90.45 after working hours and after paying the bus fare. Write an equation to represent this situation. Is 4 a solution to the last equation you wrote? What about 7? If so, be prepared to explain how you know one or both of them are solutions. If not, be prepared to explain why they are not solutions. Then, find the solution. In this situation, what does the solution to the equation tell us?
Equation that represents Jada’s take-home earnings in dollars E = 12.20(h)-7.15
The equation that represents the situation is h=6.82 hours.
What is equation?An equation, a formula that is express the equality of two expressions. The equation is representing direct proportion is , by the commenting them with in the equal sign .
As per the given question
Pay hour = $12.20 per hour
Bus fare = $7.15
1.Equation:
Assume that
She has work for "h" hours
Total earning = E
So, E = 12.20(h) - 7.15
If, Total earning = E = $90.45
So, E = 12.20(h) - 7.15
90.45 = 12.20(h) - 7.15
h = 6.82 hours
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pls help due now!!!!!!!!!!!
Answer:
B. For 5 students, the cost will be the same, and the cost will be $70
Step-by-step explanation:
Look at the graph and see where the two linear plots intersect.
This point of intersection is at the x value of 5 and y value of 70: (5, 70)
Since the x-axis represents the number of students and y axis the total cost, the answer is B
PLS HELP ME ASAP!! 30 points! Which triangle congruence theorem could be used to prove the following two triangles congruent? ASA, SAS, AAS, or not enough info
The best triangle congruent theorem for the image is Angle-Angle-Side (AAS)
How to prove congruency of Triangles?Two triangles are congruent if they have exactly the same three sides and exactly the same three angles.
From triangle ABC,
<BAC is given
<ABC=90⁰
<BCA is not given
Also, in triangle ACD,
<ACD is given
<CDA =90⁰
<DAC is not given
Therefore <BAC=<ACD (given)
<CDA=<ABC=90
<DAC=<BCA (not given)
Therefore, ΔABC=ΔACD (AAS)
In conclusion, The two triangles are congruent with SSA theorem.
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You want to prove a theorem in a two-column proof. You start with your given statement and list deductions in the left-hand column. What are the three main types of reasoning you will use for reasons in the right-hand column?
In an indirect proof, you prove an "if-then" statement is true by assuming the statement is false (stating the inverse or converse), and then disproving the false statement. You want to prove the statement shown below in an indirect proof. What statement should you prove is false? (1 point)
Statement to Prove True: If a figure has exactly three sides, then it is a triangle.
Statement to Prove False
Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.
What is a two column proof in math?A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.
Postulates, corollaries, and common notions are the three main types of reasoning we will use for reasons in the right- hand of column.
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12 less than twice a number.
help me please help help
Answer:
2x - 12
Hope this helps : )
Step-by-step explanation:
The equation for 12 less than twice a number is 2x-12. This is because "12 less than a number" means 12 is being subtracted from a number. The "number" is a variable which can be x. "Twice a number" is the variable being multiplied by 2. So the final equation would be 2x - 12.
please help! Need to get my math grade up
Answer: A.( 2,10) B.(4,6) C(5,4) D(6,2)
Step-by-step explanation:
b + ad/c = e. can anyone help me make C the subject
Answer:
[tex]\huge\boxed{\sf c=\frac{ad}{e-b}}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle b + \frac{ad}{c} = e[/tex]
Subtract b to both sides
[tex]\displaystyle \frac{ad}{c} = e-b[/tex]
Multiply c to both sides
[tex]ad=c(e-b)[/tex]
Divide (e - b) to both sides
[tex]\displaystyle \frac{ad}{e-b} = c\\\\\boxed{c=\frac{ad}{e-b} }[/tex]
[tex]\rule[225]{225}{2}[/tex]
a town has 10,000 two-child families.
Answer:
Step-by-step explanation:
if its asking how many people there are it would be 40,000
Mother, Father, 2 kids=4
4 x 10,000= 40,000
Select the correct answer.
Which function passes through points (2, 3) and (4, 4)?
Answer:
7
Step-by-step explanation:
Answer: y= 1/2x+2
Step-by-step explanation:
Using the y=mx+b formula you simply find the slope between the two points considered on a graph
Hope this helps you
B i the midpoint of AC. D i the midpoint of CE. DE=5 and AE=18. What i the length of BD?
The length of BD is 9 units when considering the idea of a line segment's midpoint.
What is midpoint of line segment ?A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line. The midpoint is the point on the middle of the line that is equally distant from the two points if a line is drawn connecting the two points. The midpoint is the point B that lies halfway between any two points, let's say A and C. As a result, measuring the length of the line segment and dividing it by two will yield the midway.
According to the given information :
AE = 18, DE = 5
However, D is the middle of CE
CE = 2 × 5 = 10
The line CE will become 10
But AE is the total length of the line segment and it is equal to 18
AE = AC + CE
AC = AE - CE
AC = 8
If AC = 8 , BC = 1/2AC
BC = [tex]\frac{8}{2}[/tex]
BC = 4
The BD becomes BC + CD
BD = 9 units
The length of BD is 9 units when considering the idea of a line segment's midpoint.
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Mr. Hill also teaches gym. He has 20 soccer balls and 3 teams of
students. He gives the same number of balls to each team.
Can Mr. Hill divide 20 balls into 3 equal groups?
»)
>>>
>>)
Yes
No
I am not sure.
Answer:No, because you cant divide 20 balls into 3 equal groups.
Step-by-step explanation:
i dont get this help
Answer:
x = 11
Explanation:
It looks like the total distance between points I and K is -3 + x. Since I to J and J to K is also the total distance, I to K is also equal to 6 + 2x - 20. You can represent this in an equation and solve for x.
-3 + x = 6 + 2x - 20
-3 + x = 2x - 14
- 3 = x - 14
11 = x
find an equation of a plane that contains the point (1, 2, 3) and is normal to the line . for what value of is on the plane?
Using the equation of the plane and the provided point (1,2,3) with the unit values perpendicular to the plane .The answer is [tex]\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1[/tex]
What do you mean by a plane?A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalization of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.
What are normal values to the plane?A normal in geometry is a piece of geometry that is perpendicular to another piece of geometry, such as a line, ray, or vector. For instance, the (infinite) line perpendicular to the tangent line to the curve at the point is the normal line to a plane curve at the point.
x1=1
y1=2
z1=3
[tex]\frac{x-x1}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{y-2}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{z-3}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} = 1[/tex]
[tex]\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1[/tex]
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)) Solve for
13 = r + 1
R =
Answer:
R = 12
Step-by-step explanation:
1 + 12/R = 13
Sixty one minus twenty nine
Answer:
Step-by-step explanation:
32
PLS HELP ASAP IM TAKING IT RN AND ITS TIMED
Days People
1 26
2 30
3 34
4 38
5 42
6 46
The chart shows how many people have signed up to go on a field trip each day. How many people would you expect to sign up on day 7?
Responses
A 49
B 48
C 47
D 50
Step-by-step explanation:
Using linear regression, you'd expect 50 people to sign up on day 7.
An author published a book which was being sold online. The first month the author sold 2500 books, but the sales were declining steadily at 12% each month. If this trend continues, how many total books would the author have sold over the first 18 months, to the nearest whole number?
An arithmetic sequence is a sequence where the difference between each consecutive term is the same.
The sum of an arithmetic sequence is given as,
S(n) = a + d(n - 1)
The total number of books sold over the first 18 months is 7600.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
In the first month, the author sold 2500 books, but the sales were declining steadily at 12% each month.
This means,
a = 2500
12% of 2500
12/100 x 2500
= 12 x 25
= 300
d = 300
Now,
The sum of an arithmetic sequence is given as,
S(n) = a + d(n - 1)
Now,
n = 18
a = 2500
d = 300
S(23):
= 2500 + 300(18 - 1)
= 2500 + 300 x 17
= 2500 + 5100
= 7600
Thus,
The total number of books sold over the first 18 months is 7600.
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4y=-3x+12 what is the answer
Adriano mixed 19/24 pound of butter with 3/16 pound of honey he ay that he ued 16/8 pound of butter than honey i hi tatement reaonable
The statements that Adriano mixed 19/24 pound of butter with 3/16 pound of honey he ay that he ued 16/8 pound of butter than honey is not reasonable.
what is mixture?A mixture is a substance made of two or more additional chemical compounds or substances that do not chemically combine. It is actually the physical blending of two or more substances so that they can still be distinguished from one another when combined as solutions, suspensions, or colloids. Physical means can be used to separate them. The different components in any mixture are not created through any sort of chemical transformation. As a result, each component's unique properties are unaltered.
A mixture's constituent parts also do not combine chemically to form new material, in contrast to a compound. Instead, they just combine while retaining their individual traits. because there are variable quantities of the components
Ratio 19/24 is nearby ¾
Ratio 3/16 is nearby ¼
And ratio 16/8 is nearby 2
So, that his statements is not reasonable.
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An investor invested a total of $2000 in two mutual funds. One fund earned a 9%
profit while the other earned a 2% profit. If the investor's total profit was $89,
how much was invested in each mutual fund?
$340 was invested in the 9% fund and 1660 was invested in the 2% profit fund.
Step-by-step explanation:
Let x be amount invested in 9% profit fund
let (2000-x) be the amount invested in the 2% profit fund
.09x+.02 times (2000-x)=89
.09x+40-.02x=89
0.07x=49
x=340
The amount invested in mutual fund A and mutual fund B is $700 and $1300 respectively.
what is profit margin?Profit margin is a measure of profitability. It is calculated by finding the profit as a percentage of the revenue. It is given by :
profit margin = (profit / revenue or return) × 100
Given here $ 2000 invested in two mutual funds
let the amount invested in A be x then the amount invested in B is $2000-x
now profit in dollars from the two mutual funds is equal to $89
therefore, 9% of x + 2% of $2000-x = $89
0.09x + 0.02×(2000-x) = 89
0.09x + 40 - 0.02x = 89
0.07x = 49
x = $700
Hence the amount invested in A is $700 and amount invested in B is $1300.
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Tony and ted went fishing. Tony caught 78. 29 pounds of fish, and ted caught 59. 36 pounds of fish. How many total pounds of fish did tony and ted catch?.
Together, Tony and Ted caught 78.29 pounds + 59.36 pounds = 137.65 pounds of fish when they went fishing.
What is meant by addition?Addition is a mathematical process that combines two or more numbers or units to form a sum. One of the four fundamental operations of mathematics, along with addition, subtraction, multiplication, and division, it is generally represented by the plus sign (+). The fundamental idea of addition is one that is taught to children at a young age and is utilized frequently in both mathematics and daily life. For instance, when shopping, one may tally up the costs of several goods to get the overall expense. In algebra, adding is used to solve problems and make statements simpler. Finding side lengths and shape areas are both important aspects of geometry. In general, adding is flexible. for example,Tony and ted went fishing. and we got to calculate the total fishes caught by them.
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7) What is the better deal? A 12 pack of gatorade for $25.20 or a 15 pack of gatorade for $33?
Answer: 12 pack.
Step-by-step explanation: 25.20 divided by 12 shows us that each gatorade costs 2.1 dollars. Now add the 3 gatorade worth to 25.2. You get 31.5 which is less than 33, showing that 12 pack is more worth as you pay less for 15 aswell.
Georgia want to end letter to 12 of her friend. Half of the letter will need 1 page each and the other half will need 2 page each. How many page will be needed altogether?
The total no: of pages needed are 18 pages
What is the unitary method?A fundamental idea behind the unitary method is using the value of one unit to determine the values of additional units. Study up on the unitary method. With an increase in units, the value of additional units rises.
What is unitary set?The general unitary group, also known as the group of unitary similitudes, is simply the product of the unitary group and the group of all positive multiples of the identity matrix. It includes all matrices A such that AA is a nonzero multiple of the identity matrix.
According to the question:-
The no: of pages needed for 6 letters = 6
The no: of pages needed for the other 6 letters= 6*2
=12
Total no: of pages are 18
Hence, the total no: of pages are 18
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