The unit vector with the same direction as the given vector is (−0.45i, 0.9j, −1k). This vector has been normalized so that the magnitude is equal to 1, while still preserving the direction of the original vector.
To find the unit vector with the same direction as the given vector, we need to normalize the vector. This means we need to divide each component of the vector by its magnitude. The magnitude of the vector is the square root of the sum of the squares of its components, which in this case is the square root of (9^2 + 2^2 + 1^2), or 9.64. Dividing each component of the vector by its magnitude gives us the unit vector (−0.45i, 0.9j, −1k). The magnitude of this vector is equal to 1, and the direction is the same as the original vector.
Learn more about vector here
https://brainly.com/question/29740341
#SPJ4
Question 41 of 53
Which of the following exponential equations is equivalent to the logarithmic
equation below?
x = In 9.45
The exponential equation that is equivalent to the logarithmic equation is e^x = 9.45
How to determine the equivalent equationFrom the question, we have the following parameters that can be used in our computation:
x = In 9.45
Take the exponent of both sides
e^x = 9.45
Hence, the equivalent equation is e^x = 9.45
Read more about exponential equation at
https://brainly.com/question/2456547
#SPJ1
9. What is the length of QR?
Answer:
48
Step-by-step explanation:
definition of very similar triangles hope the answer is correct
In the figure below, AABC AYXZ.
Find sin X, tan X, and cosX.
Round your answers to the nearest hundredth.
B
12
17.4
12.6
Y
N
X
sin X = 0.72, cos X = 0.69, tan X = 1.05
What do you mean by Pythagorean Theorem?The Pythagorean Theorem is a fundamental mathematical principle named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The theorem can be expressed mathematically as c² = a² + b², where a and b are the lengths of the two shorter sides of the triangle and c is the length of the hypotenuse. The theorem can be used to find the length of a missing side of a right triangle if the lengths of the other two sides are known.
To find sin X, cos X, and tan X in triangle ABC, we need to first find the measures of the other angles in the triangle. Since angle C is a right angle, we can use the Pythagorean theorem to find the lengths of the sides adjacent to angle X (i.e., sides AC and BC).
AC² + BC² = AB²
(12.6)² + (12)² = (17.4)²
159.36 + 144 = 304.76
303.36 = 304.76
Since AC² + BC² = AB², we can conclude that triangle ABC is a right triangle, with angle X as the acute angle opposite side AC.
Using the definitions of sine, cosine, and tangent, we can find the values of sin X, cos X, and tan X:
sin X = [tex]\frac{AC}{AB}[/tex] = 12.6 / 17.4 = 0.72
cos X = [tex]\frac{BC}{AB}[/tex] = 12 / 17.4 = 0.69
tan X = [tex]\frac{AC}{BC}[/tex]= 12.6 / 12 = 1.05
Rounding to the nearest hundredth, the values are:
sin X = 0.72
cos X = 0.69
tan X = 1.05
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
5 students are choose at random and there is 4 options (A, B, C and D)
1. What is the probability none choose option B
2. What is the probability all choose option A
3. What is the probability 3 students choose option C
The probability none choose option is [tex]\frac{243}{1024}[/tex] , the probability all choose option A is [tex]\frac{1}{1024}[/tex] , the probability 3 students choose option C is [tex]\frac{15}{256}[/tex]
What do you mean by Probability?Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.
Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.
Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
To find the probability that none of the 5 students choose option B, we need to find the probability that each student chooses one of the other 3 options (A, C, or D) and then multiply these probabilities. Since each student has the same choices, the probability that each student chooses one of the other options is 3/4. So, the probability that none of the 5 students choose option B is (3/4)^5 = 243/1024.To find the probability that all 5 students choose option A, we need to find the probability that each student chooses option A and then multiply these probabilities. The probability that each student chooses option A is 1/4. So, the probability that all 5 students choose option A is (1/4)^5 = 1/1024.To find the probability that 3 students choose option C, we can use combinations. There are C(5,3) = 10 ways to choose 3 students out of 5. For each of these combinations, the probability that the chosen 3 students choose option C is (1/4)^3, and the probability that the remaining 2 students choose options other than C is (3/4)^2. So, the total probability is 10 * (1/4)^3 * (3/4)^2 = 15/256.To know more about outcomes visit:
https://brainly.com/question/19916581
#SPJ1
I can't find the answer PLEASE HELP! Find 42% of 175
Answer:
73.5
Step-by-step explanation:
This is a percentage question.
To solve it we need to first divide the amount by 100 then multiply it with 42:
175 ÷ 100 × 42 = 73.5
Ms. Jackson wants to rent an oversized truck for a week. It will cost the weekly fee plus $0.20 per mile driven. Let m=the number of miles Ms. Jackson drives during the week.
Answer:
ms Jackson let m=the number of miles ms
The distance traveled (in feet) is proportional
to the number of seconds. Find the values of
x, y, and z.
Answer:
te56
Step-by-step explanation:
y8888888755555555555555578
If the cone’s radius is 1/2 what is its height
The term "directrix" refers to the circumference of a cone's base, and "generatrix" or "generating line" refers to each line segment between the directrix and apex.
What is the parameter for cone radius calculation?(For a relationship between the directrix of a conic section and the name "directrix" in this sense, see Dandelin spheres.
A cone's volume is equal to one-third of the sum of the base's area and the cone's height. Cubic units are used to measure volume.
A cone's radius affects how tall it is. A cone with a radius of 1 /2 has a height of 0.26. Volume is the amount of space that is occupied by a three-dimensional object.
A cone's volume (V) is determined by:
V = (1/3)πr²h
Where r is the radius and h is the height.
For a radius of 1/2:
=(1/3)π*(1/2)²*h
=(1/3)(22/77)(1/4)h
=0.26
Therefore, its height is 0.26.
Learn more about cone radius here:
https://brainly.com/question/1351159
#SPJ1
In your own words, describe four ways in which errors in statistical data occur.
Four ways errors can occur in statistical data are:
Measurement errorSampling errorData entry errorModel error.How Errors Can Occur in Statistical Data?Errors in statistical data can occur in several ways, including:
Measurement error: This happens when the data collected is not accurate, such as using an incorrect instrument or using the instrument improperly.
Sampling error: This occurs when a sample of the population is used to represent the entire population, and the sample is not representative or randomly selected.
Data entry error: This happens when data is recorded incorrectly or transcribed inaccurately, such as mistyping a number or mixing up entries.
Model error: This occurs when the model used to analyze the data is incorrect or does not fit the data well, leading to incorrect or misleading results.
Learn more about errors in statistical data on:
https://brainly.com/question/12600423
#SPJ1
the outbound trip of a bus was made at 24mi/h, while the return trip was made at 30mi/h. find the one way distance fi the total running time was 4.5 hour.
With a running time of 4.5 hours and speeds of 24 mph and 30 mph, respectively, the bus covered a one-way distance of 72 miles.
With a running time of 4.5 hours and speeds of 24 mph outgoing and 30 mph inbound, the bus covered a one-way distance of 72 miles.
As the outgoing and inbound timings were equal, the computation was performed by multiplying the outbound trip's speed by the entire running time, and then dividing the result by two. Therefore, 108 miles are equal to 24 mph times 4.5 hours. The one-way distance is equal to 72 miles when you divide this result in half. When both directions' speeds are known, this calculation can be used to determine the overall distance of a round trip.
Learn more about distance here
https://brainly.com/question/28956738
#SPJ4
Mary is planning to buy a new pair of jeans. They are on sale. The total cost of the jeans including tax is $17.00 Her mother gave her $14.50. How much more money does Martia need to purchase the jeans?
Mary need $2.5 more money to buy her jeans.
What is subtraction?Subtraction is simply the process of taking one quantity and removing part of it to work out what is left. It is the opposite of addition, because we are reducing the value of the number rather than increasing it by adding more numbers.
Given that, Mary is to buy a new pair of jeans, whose price including tax is $17.00, her mother gave her $14.50,
We need to find how much more money do Mary need,
Here, we will use a simple rule of subtraction, since, total price is $17, and she has $14.50,
Therefore, extra money she need = $17 - $14.50
= $2.5
Hence, Mary need $2.5 more money to buy her jeans.
Learn more about subtraction, click;
https://brainly.com/question/2346316
#SPJ1
(3x^3 y^0/x^-2)^4*(y^2 x^-4 5xy^-8)^3
The expression evaluates to 3x⁹y⁻¹⁸.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
{(3x³ y⁰)/(x⁻²)}⁴ × (y² x⁻⁴ 5xy⁻⁸)³
The given expression is -
{(3x³ y⁰)/(x⁻²)}⁴ × (y² x⁻⁴ 5xy⁻⁸)³
{3x³/x⁻²}⁴ × (y⁶x⁻¹²5xy⁻²⁴)
(3x¹²/x⁻⁸) × (y⁶x⁻¹²5xy⁻²⁴)
3x²⁰ × (y⁶x⁻¹²5xy⁻²⁴)
3x²⁰y⁶x⁻¹²5xy⁻²⁴
3x²⁰ ⁻¹² ⁺¹y⁶ ⁻ ²⁴
3x⁹y⁻¹⁸
Therefore, the expression evaluates to 3x⁹y⁻¹⁸.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
What is 9/51 simplified.
Answer: 9/51 simplified would be 3/17
perform the indicated operations, given c = −4, a = 1 6 2 0 1 −1 , and b = 1 2 −1 6 . c(ba)
The value of give operation is =[[0,-4,-28][20.4.-32]]
A rectangular or square array of numbers or variables that are arranged in rows and columns is known as a matrix in mathematics. Elements or entries are the names for individual things in a matrix.
The application of matrix plays a major role in Mathematics, as well as in other fields. It helps in solving linear equations. Matrices are extremely valuable objects that can be found in a wide range of applications. The application of matrices in mathematics is used in a wide range of scientific fields as well as mathematical areas. Engineering mathematics is used in almost every aspect of our lives. In this article, we are going to learn what is a matrix, different matrix operations and the application of matrices in detail.
Some of the matrix's rows and columns define how big it is. A matrix of "m" rows and "n" columns is written as "m*n," where "m" and "n" are the dimensions of the matrix.
We have, c=-4
[tex]A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right][/tex]
first, compute the cA.
[tex]=(-4)\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\cA=\left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\Now, BcA=\left[\begin{array}{ccc}1&2\\-1&3\\\end{array}\right] \left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\\\=\left[\begin{array}{ccc}0&-4&-28\\20&4&-32\\\end{array}\right][/tex]
The complete question is-
Perform the indicated operation,c=-4,
[tex]A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right][/tex]
B(cA)=?
learn more about Matrices,
https://brainly.com/question/11367104
#SPJ4
Mary i going to divide her ticker collection among four friend he ha five pack of 20 ticker how many ticker will each friend receive
Each friend will receive 25 sticker from Mary's collection
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Number of friends = 4Number of stickers per pack = 20Number of pack = 5Sticker per friend = ?Calculating the number of sticker per friend:
Sticker per friend = (Number of stickers per pack * Number of pack) / Number of friends
Sticker per friend = (20*5)/4
Sticker per friend = 100/4
Sticker per friend = 25
Learn more about algebraic operations at: brainly.com/question/3927786
#SPJ4
Correctly written question:
Mary is going to divide her sticker collection among four friends she has five packs of 20 sticker how many stickers will each friend receive?
PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!
Describe exactly what type of transformation has been applied to triangle QRS to triangle Q'R'S'
What is (14x-2)-(11x-21) as a simplified expression
Answer: (14) x (-2)- (11) x (-21)
Step-by-step explanation: Hope I was I right!
I need help solving this absolute value equation
3|x-4|=33
Answer: x = 15 or x = -7
Step-by-step explanation:
Step 1: Divide both sides by 3.
Step 2: Solve Absolute Value.
|x−4|=11 We know either x − 4 = 11 or x − 4 = −11
x−4=11(Possibility 1)
x−4+4=11+4(Add 4 to both sides)
x=15
x−4=−11(Possibility 2)
x−4+4=−11+4(Add 4 to both sides)
x=−7
Which is the approximate measure of angle acb? 31.0° 36.9° 53.1° 59.0°
Answer: the answer is
53.1
The angle on f depression between a bird and its prey is 70%. If the bird is 18 feet off the ground, what is the distance between the bird and its prey? Round your answer to the nearest foot.
The distance between the bird and its prey is 19 feet. The solution has been obtained by using trigonometry.
What is trigonometry?
The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry."
We are given that the angle on f depression between a bird and its prey is 70%.
This means that Theta = 70°
Also, the height of the bird from the ground is 18 feet.
Using trigonometry, we get
⇒sin theta = perpendicular side/hypotenuse
⇒sin 70 = 18/hypotenuse
⇒Hypotenuse = 18/sin 70
⇒Hypotenuse = 19.1 ≈ 19 feet
Hence, the distance between the bird and its prey is 19 feet.
Learn more about trigonometry from the given link
https://brainly.com/question/13729598
#SPJ1
Your scores on the last 3 bowling games are 99,92, and 115. Write and solve an inequality to find the score you need in the next game to have a mean score of at least 100.
Answer:
Score in 4th game = 94
Step-by-step explanation:
The mean is the average of all the data points, which means we divide the sum of all the points by the total number of points.
Letting s represent the score in the 4th game, we can use the following equation to find the score needed to end up with a mean score of 100:
[tex]\frac{99+92+115+s}{4}=100\\ \frac{306+s}{4}=100\\ 306+s=400\\s=94[/tex]
together, a piece of pie plus ice cream costs $2.20 in total. the pie costs $2 more than the ice cream. how much does the ice cream cost?
The ice cream costs $0.10 and the pie costs $2.10.
Let's call the cost of the ice cream "x".
According to the problem,
The pie costs $2 more than the ice cream, so the pie costs x + $2.
And, together, the pie and ice cream cost $2.20, so:
x + (x + $2) = $2.20
Expanding and solving for x:
2x + $2 = $2.20
2x = $0.20
x = $0.10
A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept.
The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
Ax+By=C is the typical form for linear equations in two variables.
2x+3y=5, for example, is a simple linear equation.
It is rather simple to get both intercepts when an equation is stated in this way (x and y).
For more questions on Linear Equation
https://brainly.com/question/2030026
#SPJ4
The surface area of a cylinder is 48π m². the distance around the base of the cylinder is 5π meters and the diameter of a base of the cylinder is 8 meters. what is the height of the cylinder? enter your answer, as a simplified fraction, in the box. m
The height of the cylinder is 2 m.
The surface area of a cylinder is [tex]48 \pi m^{2}[/tex]
The distance around the base of the cylinder is 5π m and the diameter of a base of the cylinder is 8 meters.
The total surface area of a cylinder is equal to the sum of the areas of all its faces. The total surface area with radius ‘r’, and height ‘h’ is equal to the sum of the curved area and circular areas of the cylinder.
Let's call the height of the cylinder "h". The surface area of a cylinder can be calculated as
[tex]2 \pi rh + 2 \pi r^{2}[/tex]Since the diameter of the base is 8 meters, the radius is 8/2 = 4 meters.
We know the surface area of the cylinder is 48π m², so we can use this information to find h:
⇒[tex]48 \pi = 2 \pi(4)h + 2 \pi(4)^{2}[/tex]
Expanding and simplifying the equation:
⇒48π = 8πh + 32π
Subtracting 32π from both sides:
⇒16π = 8πh
Dividing both sides by 8π:
⇒h = 2
So the height of the cylinder is 2 meters, expressed as a simplified fraction, h = 2 m
Therefore, the height of the cylinder is 2 m.
For more such questions on TSA of cylinder
https://brainly.com/question/30295407
#SPJ4
1
*
Name the angle pa: 27 and 25
vertical angles
alternate exterior angles
same side interior angles
linear pair
alternate interior angles
same side exterior angles
corresponding angles
Vertical angles are opposite angles formed by intersecting lines.
Alternate exterior angles are angles on the same side of the transversal and outside of the two lines being intersected.
What are the angles about?Same side interior angles are angles on the same side of the transversal and inside of the two lines being intersected.
A linear pair is two angles that add up to 180 degrees and are adjacent to each other.
Alternate interior angles are angles on opposite sides of the transversal and inside of the two lines being intersected.
Same side exterior angles are angles on the same side of the transversal and outside of the two lines being intersected.
Corresponding angles are angles that have the same relative position and orientation in two similar figures.
An overview was given as your information is incomplete.
Learn more about angles on:
https://brainly.com/question/25716982
#SPJ1
Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets marked down. During the sale, rashguards sell for $5 less than full price. Miguel purchases 3 rashguards and pays a total of $60.
Which equation can you use to find how much money, f, each rashguard costs at full price?
The cost of each rashguard is $25, the equation is 3 (x - 5) = 60.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Given;
During the sale, rashguards sell for $5 less than full price
Miguel purchases 3 rashguards and pays a total of $60
Now,
Let the full price of each rashguard be x,
Rashguards sell for $5 less than full price.
x - 5
Miguel purchases 3 rashguards and pays a total of $60.
3 (x - 5) = 60
On solving;
x-5=60/3
x-5=20
x=25
Therefore, the answer of arithmetic problem will be $25.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ1
Translate this sentence into an equation.
The product of Goran's age and 3 is 36.
Use the variable g to represent Goran's age.
Answer:
3 x g = 36
Step-by-step explanation:
3 multiplied by Gordon's age equals 36.
There are 14 sixth graders, 29 seventh graders,
and 37 eighth graders in the musical at
Canon Middle School. If 65% of the students
in the musical are girls, how many are girls?
Answer:
52 girls
Step-by-step explanation:
You have to find the total number of students first which is 80. Then you figure out 65% of 80. You can write a proportion which is 65/100 = x/80, you then solve for x by using the butterfly method.
So,
65/100 = x/80
5200 = 100x
divide by 100 to isolate x
52 out of the 80 students are girls
Find x and y.
PLEASE HELP
Answer:
Step-by-step explanation:
If a line is parallel to a side of a triangle, then the intersected sides are divided proportionally
4/2=y/3
2=y/3
y=2*3 = 6
next,
If the angles of one triangle are equal to the angles of another triangle, then the triangles are said to be equiangular.
(4+2)/4=6/x
6/4=6/x
x=4
With carbon dioxide, what phase change takes place when the temperature
increases from -40°C to 0°C at 10 atm?
Pressure (atm)
20-
15-
10-
5-
0-
Carbon Dioxide Phase Diagram
Melting
point
Solid
-100
Boiling
point
Liquid
Gas-
887
Temperature (°C)
20
The phase change takes place when the temperature increases from -40°C to 0°C at 10 atm is solid-liquid change phase(melting).
What is Phase- change?Phase change refers to the process of a substance changing from one physical state to another, such as solid to liquid, liquid to gas, or solid to gas. These changes occur as a result of changes in temperature or pressure, and are characterized by changes in the physical properties of the substance, such as its volume, density, and viscosity.
Phase changes are classified into two types: physical and chemical. Physical phase changes involve a change in the physical state of a substance without any change in its chemical composition, such as the melting of ice to liquid water or the boiling of water to steam. Chemical phase changes, on the other hand, involve a change in the chemical composition of a substance, such as the formation of a chemical compound through a reaction.
The diagram you provided shows the phase diagram of carbon dioxide at a pressure of 10 atm. It shows that the melting point of solid carbon dioxide is -100°C and the boiling point of liquid carbon dioxide is -87°C.
When the temperature increases from -40°C to 0°C, the carbon dioxide is in the solid state at -40°C. As the temperature increases, it will reach the melting point of -100°C, causing a phase change from solid to liquid.
Therefore, the phase change that takes place when the temperature increases from -40°C to 0°C at 10 atm is a solid-liquid phase change, also known as melting.
To know more about melting visit:
https://brainly.com/question/29138757
#SPJ1
Given the arithmetic sequence 10, 15, 20, 25,... find the a15.
Answer
a15 is equal to 75
