Answer:
c 1 over 15
Step-by-step explanation:
To multiply fractions, you can multiply the numerators (top parts) and multiply the denominators (bottom parts) separately.
1/3 * 1/5 = (1 * 1) / (3 * 5) = 1/15
"double check answer"
Consider the vector function given below. r(t) = (9t, 4 cos(t), 4 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) N(t) = (b) Use this formula to find the curvature. k(t) = Consider the following vector function. r(t) = (2V2t, ezt, e-2t) (a) Find the unit tangent and unit normal vectors T(t) and N(t).
From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
(a) To find the unit tangent and unit normal vectors, we use the following formula:
T(t) = (1/|r'(t)|) * r'(t)
N(t) = (1/|r'(t)|) * (r'(t) x r"(t))
where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.
For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).
Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))
To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).
Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))
and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).
(b) To find the curvature, we use the following formula:
k(t) = |r'(t) x r"(t)| / |r'(t)|3
For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).
Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3
= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
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- At a bake sale, the Math Club raised $225 by selling 300 baked goods. If the amount
raised varies directly with the baked goods sold, how much money will be raised for
selling 450 baked goods?
Record your answer on the answer document.
5x3
The amount of money for selling 450 baked goods will be
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Now,
Let the amount of money for selling 450 baked goods = x
Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Hence, By definition of proportion we get;
⇒ $225/300 = x / 450
⇒ x = 225 × 450 / 300
⇒ x = $337.5
Thus, The amount of money for selling 450 baked goods = $337.5
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I need help with this please help me
The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).
What does a math translation mean?Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.
What does math formula translation mean?Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.
Briefing:The image of the translation is (9,-2).
The point is given as: P = (-6, -4)
The image of the point is: P' = (-2, 3)
The translation rule is calculated as:
T = x - 2 - (-6), y+3-(-4)
so, T = x + 4, y + 7
So, the image of (5, -1) is:
the Image of the translation = 5 + 4, -1 + 7
Hence, the image of the translation is (9, 6).
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Total students in a class are 120. 40% of them are female students. 70 male students passed with 100% pass rate. What is the pass rate of female students at 100 percent rate?
Answer:
Here is the answer
Step-by-step explanation:
If 40% of the students in the class are female, then there are 40/100 * 120 = 48 female students.
If 70 male students passed with a 100% pass rate, then the pass rate for male students is 100%.
If the pass rate for male students is 100%, then the pass rate for female students must also be 100%. This is because the pass rate is calculated as the number of students who pass divided by the total number of students, and if all the male students pass, then the pass rate for male students must be 100%.
Therefore, the pass rate for female students at a 100% rate is also 100%.
Can anyone help me ASAP?
Your iron works has contracted to design and build a 500-ft^3, square-based, open-top, rectangular steel holding tank for a paper company. The tank is made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weigh as little as possible. What dimensions do you tell the shop to use?
The dimensions for the base and height that will make the tank weigh as little as possible are 10 feet and 5 feet, respectively
How to determine the dimensions to use?From the question, we have the following parameters that can be used in our computation:
Volume = 500 cubic feet
Base = square base
This means that the volume can be calculated using
V = b²h
Where
b = base length
h = height
So, we have
b²h = 500
Make h the subject
h = 500/b²
The surface area is calculated as
A = 4bh + b²
Substitute h = 500/b² in A = 4bh + b²
A = 4b(500/b²) + b²
Evaluate
A = 2000/b + b²
Differentiate and set to 0
-2000/b² + 2b = 0
So, we have
2b = 2000/b²
Divide by 2
b = 1000/b²
Multiply by b²
b³ = 1000
So, we have
b = 10
Substitute b = 10 in h = 500/b²
h = 500/10²
Evaluate
h = 5
Hence, the height is 5 feet
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What is an equation of the parabola
Answer:
(c) x = -1/11(y -3)²
Step-by-step explanation:
You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).
EquationThe directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.
The vertex form of the equation is ...
x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)
ApplicationHere, we have ...
p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix
and
(h, k) = (0, 3)
so the equation is ...
x = 1/(4(-11/4))(y -3)² +0
x = -1/11(y -3)²
At a football game, a vender sold a combined total of 244 sodas and hot dogs. The number of hot dogs sold was 42 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
143 sodas101 hot dogsStep-by-step explanation:
Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.
SetupLet s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...
s +(s -42) = 244
SolutionAdd 42 and simplify
2s = 286
s = 143 . . . . . divide by 2
hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs
143 sodas and 101 hot dogs were sold.
8w-16 how do i answer this
The factor of the expression 8w - 16 will be 8 and (w - 2).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.
The expression is given below.
⇒ 8w - 16
The factor of each term in the expression, then we have
8w = 8 x w
16 = 8 x 2
Then the expression is written as,
⇒ 8w - 16
⇒ 8 × w - 8 × 2
⇒ 8 × (w - 2)
⇒ 8(w - 2)
The component of the articulation 8w - 16 will be 8 and (w - 2).
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which of the following is not a valid property of circles? a rotateangle b none of these c left d width
There is no property named 'left' for the circle. So the answer is 'c'.
What is Circle?Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.
The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.
Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.
Width is another term for diameter of the circle, although it is not commonly used.
Left is the only term which does not have any role in the properties of circles.
Hence, the term 'left' is not a valid property of circles.
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A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23
How to solve fraction word problems?We are given that;
The data by payment plans are;
Plan A: 27 texts, 21 Internet
Plan B: 13 texts, 10 Internet
Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.
The total number of observations for plan B is; 13 +10 = 23
The number of customers that are on payment plan B = 23 customers are on payment plan B.
The number of customers that are on plan B text is; 13
Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;
Probability = 13/23
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
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Which number is a solution of the inequality?
x(7-x) > 8
x(7 - x) > 8
Steps for calculationFirst solve x(7 - x) = 8
x^2 - 7x + 8 = 0
x = 5.56, 1.44
If we plug in these values into the original equation we can see that solution is
1.44 < x < 5.56
Meaning and definition of systems of inequality:The value of the variable(s) that transforms the inequality into a true statement is the solution. Think about the example (x+3>5). If we provide any real value bigger than (2) for this inequality, it will be true (x). (therefore) This inequality's answer is (x>2)A collection of two or more inequalities in one or more variables is referred to as a system of inequalities. Systems of inequalities are utilized when a scenario calls for several solutions but also places multiple restrictions on those answers.The best answer is often found by solving a set of linear inequalities. This response could be as simple as calculating the number of products that need be produced in order to maximize profit or as complex as selecting the ideal medication regimen for a patient. The different kinds of inequalities and how to solve them will be covered in this article.To learn more about Systems of inequalities refer https://brainly.com/question/26119697
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You are making several purchases from the I.B. Electric electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. Using this information and the information below, which way would you save the most money?
15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.
Which way would you save the most money?$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.
Let's say the entire amount spent was $100.
In a physical store, 100 times 15% equals 15 off.
100 - 15 = 85 is the item's reduced cost.
85 x 6% is 5.1 sales tax.
85 + 5.1 = 90.10 as a whole price
Internet shop:
Discounted cost of item: 100 - 5 = 95
95 plus 8.99 is 103.99 in total.
15% discount; 6% sales tax in-store.
Online retailer: $5 discount; $8.99 for delivery.
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An air traffic controller is tracking two planes. To start, plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitudes be when they’re at the same altitude?
44 seconds will pass before the planes are at the same altitude.
What do you mean by algebraic expression?
An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.
There are three main types of algebraic expressions:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression with only one term is called a monomial.
It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.
Let x seconds will pass before the planes are at the same altitude.
Plane A, 3500 + 45.5x
Plane B, 2609 + 65.75x
x is number of seconds of time
When altitudes equal
3500 + 45.5x = 2609 + 65.75x
3500 - 2609 = 65.75x - 45.5x
891 = 20.25x
891/20.25 = x
44 = x
Therefore, 44 seconds will pass before the planes are at the same altitude.
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a number has the same digit in its hundreds place and in its hundreds place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
A number has the same digit in its hundreds place and in its hundreds place. 10,000
What is the value of the digit?Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.
Let's say that the digit is a 1.
Therefore, the value of the hundreds position in a number is equal to 100.
The value of the hundredth position in a number is equal to 0.01%.
The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:
As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.
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CQ
A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
A. 100,00
B. 100
C. 1,000
D. 10,000
Write as a single fraction in its simplest form.
[tex] \frac{ {x}^{2} - 3x}{ {x}^{2} - 9 } [/tex]
Answer:
[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]
[tex]\frac{x}{x+3}[/tex]
You are given the figure below well as the following information.
Answer:
A. 110°
Step-by-step explanation:
according to the theorems,
m∠1=m∠6=m∠9=m∠14=110°;
m∠2=m∠5=m∠10=m∠13=70°;
m∠3=m∠8=m∠11=m∠16=70°;
m∠4=m∠7=m∠12=m∠15=110°.
all the details are in the attachment.
You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?
Find the angle round to the nearest degree. please help.
63 degrees is the angle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angle triangle.
The opposite side length is 85 and the adjacent side is 38.
Opposite side=85
Adjacent side=38.
Calculate Opposite/Adjacent
= 85/38= 2.236
Which is tanθ=2.236
Now tan inverse on both the sides
θ=tan⁻¹2.236
θ=tan⁻¹2
θ=63 degrees.
Hence, the angle is 63 degrees.
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Please help me with this question
Answer:
Point of intersection is (13.72, 660)
Step-by-step explanation:
You have to use your graphing tool to answer questions 2 and 3.
Then click on the point of intersection and note the coordinates.
That's it.
This can also be solved mathematically but since the question does not ask I have not given that solution process.
Graph attached
if you apply demorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))), you get:
Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).
DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).
Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).
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MP MODELING REAL LIFE You sell instruments at a
Caribbean music festival. You earn $326 by selling 12 sets
of maracas, 6 sets of claves, and x djembe drums. Find the
number of djembe drums you sold.
The number of djembe drums you sold is 8
How to determine the number of djembe drums you sold.From the question, we have the following parameters that can be used in our computation:
Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.
Earning = $326
Also, we have:
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
So, we have
12 * 14 + 6 * 5 + x * 16 = 326
Evaluate the products
198 + 16x = 326
Evaluate the iike terms
16x = 128
So, we have
x = 8
Hence, the number of djembe drums is 8
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Complete question
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
Find the number of djembe drums you sold.
Solve 0=sin1/2x+cosx−1
The value of x = 2nπ, (n ∈ Z) and
[tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex], (n ∈ Z)
What are Trigonometric Identities?
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions( similar as sine, cosine, tangent ) of one or further angles.
According to question
⇒ sin(x/2) + cos(x) - 1 = 0
⇒ sin(x/2) + cos(x) - 1 = 0
{ cos(2x) = 1 - 2sin²(x) }
cos(x) = 1 - 2sin²(x/2)
⇒ sin(x/2) + cos(x) - 1 = 0
⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0
⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0
⇒ - 2sin²(x/2) + sin(x/2) = 0
⇒ sin(x/2)(- 2sin(x/2) + 1) = 0
⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)
and
⇒ sin(x/2) = 1/2 , [tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex] (n ∈ Z)
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Help me! Can someone please
Answer:
13
Step-by-step explanation:
Divide both sides of the equation by 4.
Suppose X varies directly with YX equals 29 when Y equals -87 what is the constant variation and what is the value of x when y = -187
A. Constant variation -1/3, x= 63
B. constant variation -1/3, x= -63
C. Constant variation -3, x= 63
D. Constant variation -3, x = 567
The constant variation and the value of x are (a) Constant variation -1/3, x= 63
How to determine the constant variation and the value of xFrom the question, we have the following parameters that can be used in our computation:
X varies directly with Y
X equals 29 when Y equals -87
This means that
Constant of variation = X/Y
Substitute the known values in the above equation, so, we have the following representation
Constant of variation = 29/-87
Evaluate
Constant of variation = -1/3
From the question, we have
y = -187
This means that
Constant of variation = X/-187
So, we have
X = -187 * Constant of variation
This gives
X = -187 * -1/3
Evaluate
X = 63
Hence, the solution is (a)
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which are prime polynomials
-12f+21
f-36
-3f-23
5f+10
Answer:
f - 36
-3f - 23
are your prime polynomials.
NO LINKS!! Please help me with this problem. Part 3ff
Answer:
a) $48700, b) $305200------------------------------------
GivenStarting salary = $38500,Annual increase = $1700.Part AThe salary during the 7th year is:
38500 + 1700*(7 - 1) = 38500 + 1700*6 = 48700Part BTotal compensation through full 7 years is base salary for 7 years and total of the annual increase:
38500*7 + 1700*(1 + 2 + 3 + 4 + 5 + 6) = 269500 + 1700*6/2*(1 + 6) = 269500 + 1700*21 = 305200What are the domain and range of the function F(x) = 3/4 x + 5?
Domain (-infinite, infinite)
Range (-infinite, infinite)
Domain (3/4, infinite)
Range (-infinite, 5)
Domain (-infinite, 3/4)
Range (5, infinite)
Domain (3/4, infinite)
Range (5, infinite
The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.
What is function?A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
What is domain and range?The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).
Here,
f(x)=3/4x+5
Domain=(-infinite, 3/4)
Range=(5, infinite)
The domain for given function is (-infinite, 3/4) and range is (5, infinite).
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Five acres of land were divided into 4 lots of equal size. How many square feet did each lot measure? (1 acre = 43,560 sq ft)
The number of square feet each lot measure is 54, 450 square feet.
How to find the area in square feet of the lot?Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:
1 acre = 43,560 square ft
5 acres = ?
cross multiply
number of acres = 5 × 43,560
number of acres = 217800 square feet.
Therefore, the lots is divide into 4 equal lots.
Hence,
measure of each lot = 217800 / 4
measure of each lot = 54, 450 square feet.
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Can someone please explain step by step on how I solve this equation?
-1 - (-0.25) = ?
Answer: -1 - (-0.25) = -0.75
Step-by-step explanation:
The way you would do that is by first pretending as the negative sign (-), isn't present.
Then do "1 - 0.25".
1.00 - 0.25 = 0.75
After you solved the equation, then we can add the negative sign (-), back into the equation = -1 - (-0.25) = -0.75 ✅
