find the values of the variables and the measures of the angles
To find variable values and angle measures, identify knowns, use appropriate equations for unknowns, calculate vector components, use trigonometric functions and the Pythagorean theorem for the resultant vector, and ensure angles are in radians.
Explanation:To find the values of the variables and the measures of the angles, you need to follow a systematic approach. Start by making a list of known variables and inferences from the problem. Once you've identified what is given, you can solve for the unknowns using the appropriate equations. If the problem involves vectors, you would identify the x- and y-axes before finding the vector components Ax = A cos and Ay = A sin, where A is the magnitude of the vector and cos and sin are the trigonometric functions corresponding to the angles the vectors make with the x-axis. After computing these, you can use the Pythagorean theorem to find the resultant vector length.
To verify your solutions, including the measures of the angles in radians, it's important to assess whether the answers are reasonable. This may involve checking the magnitude and direction of the resultant vector and ensuring that the angles are within the possible range (0 to 2π radians for a full circle).
Nadia started at 19.26 feet below sea level and then changed her altitude by climbing a total of 5,437.8 feet up from her initial position. What was Nadia’s altitude at the end of her climb?
A. 3,511.8 feet above sea level
B. 5,245.2 feet above sea level
C. 5,418.54 feet above sea level
D. 5,457.06 feet above sea level
Answer:
The correct option is:
C. 5,418.54 feet above sea level
Step-by-step explanation:
Nadia started at 19.26 feet below sea level.
She then changed her altitude by climbing a total of 5,437.8 feet up from her initial position.
Her new position would be 5437.8-19.26 feet above the sea level
i.e. 5,418.54 feet above sea level
Hence, the correct option is:
C. 5,418.54 feet above sea level
Answer:
5,418.54
Step-by-step explanation:
There are four cars entered into a pinewood derby race. In how many different orders can they cross the finish line?
To find out the different orders four cars can finish a race, we calculate the permutations, which is 4 factorial, resulting in 24 different orders.
The student is asking about the number of different ways that four cars can finish a pinewood derby race, which is a question of permutations in mathematics. In this case, we want to find out the number of possible arrangements for the four cars crossing the finish line. Since each car is distinct, the number of permutations of four items is given by 4! (4 factorial), which is calculated as 4 × 3 × 2 × 1.
Therefore, there are 24 different orders in which the cars can cross the finish line. Remember, factorial is a mathematical operation that involves multiplying a sequence of descending natural numbers.
How do you solve
x-3/(x-4) + 4= 3x/3
solve logx + log(x-3) = 1
Question 2:
Calculate the average rate of change for the function f(x) = −x^4 + 4x^3 − 2x^2 + x + 1, from x = 0 to x = 1.
A. 0
B. 1
C. 2
D. 7
Eric bought 300 t-shirts, which were sold in packs of 12. how many packs did eric buy?
Find the smallest positive angle θ in the third quadrant for which tan(θ) = 1.
...?
The polynomial given below has _____ root(s).
2x2 + 5x + 2
A. two complex
B. two positive
C. two negative
D. one positive and one negative
...?
Which transformation is not isometric?
4. A video game sells at Arnolds for $14.99. Arnold's marks the game up at 40% of the selling price. What is the cost of the game to Arnold?
A. $6.00 B. $9.10 C. $6.50 D. $8.99
Answer:
8.99
Step-by-step explanation:
Alice had 4 1/4 pounds of walnuts at the beginning of the week. At the end of the week, she had 2 3/4 pounds. How much has she used?
A. 1 3/4
B. 1 1/2
C. 2 1/2
D. 1 1/4
Step [tex]1[/tex]
Convert mixed numbers to improper fractions
we know that
[tex]4\frac{1}{4}=\frac{4*4+1}{4}=\frac{17}{4}[/tex]
[tex]2\frac{3}{4}=\frac{2*4+3}{4}=\frac{11}{4}[/tex]
Step [tex]2[/tex]
Find the difference of the numbers
[tex]\frac{17}{4}-\frac{11}{4}=\frac{6}{4}=\frac{3}{2}[/tex]
Step [tex]3[/tex]
Convert improper fraction to mixed number
[tex]\frac{3}{2}=1.5=1+0.5=1+\frac{1}{2} =1\frac{1}{2}[/tex]
therefore
the answer is the option B
[tex]1\frac{1}{2}[/tex]
1. Find the area of the given circle. Round to the nearest tenth. *theres a picture of a circle and the radius is 3.5*
A. 22.0 cm *squared* B.38.5 cm *squared* C. 11.0 cm *squared* D. 42.8 cm *squared* 2.Find the circumference of the given circle. Round to the nearest tenth.
*picture of a circle with the radius of 3.5* A. 11.0 B. 38.5 C.42.8 D. 22.0 Can you please check if I'm right? I think.. 1. B 2. D
The area and the circumference of the given circle are 38.5 cm² and 20 cm respectively.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given that, a circle with radius 3.5 cm, we are asked to find the circumference and the area of the given circle,
Area of a circle = π × radius²
Circumference of a circle = 2π × radius
1) Area =
π × 3.5²
= 3.14 × 12.25
= 38.465
≈ 38.5 cm²
2) Circumference =
2π × 3.5
= 2 × 3.14 × 3.5
= 21.98
≈ 20 cm
Hence, the area and the circumference of the given circle are 38.5 cm² and 20 cm respectively.
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wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. indetify the independent and dependent quanity in the situation. find reasonable domain and range values
- Independent quantity: Number of hours worked per week
- Dependent quantity: Earnings per week
- Domain: 20 ≤ hours ≤ 25
- Range: $180 ≤ earnings ≤ $225
In this situation:
- Independent quantity: The number of hours Wendy plans to work per week
- Dependent quantity: The amount of money she earns per week
Reasonable domain and range values:
- Domain: The reasonable range of values for the number of hours Wendy works per week is between 20 and 25 hours. This is because she plans to work between 20 and 25 hours per week.
- Range: The amount of money Wendy earns per week depends on the number of hours she works. The range of values for her earnings can be calculated by multiplying the number of hours worked by her hourly rate of $9. Therefore, the range of values for her earnings per week will be between $180 (20 hours * $9) and $225 (25 hours * $9).
To summarize:
- Independent quantity: Number of hours worked per week
- Dependent quantity: Earnings per week
- Domain: 20 ≤ hours ≤ 25
- Range: $180 ≤ earnings ≤ $225
Consider the basis B of R2 consisting of vectors
5
-6
and
-2
-2
Find x in R2 whose coordinate vector relative to the basis B is
[x]B = [-6]
[ 2 ]
The idea is to find a linear combination a_1(5, -6) + a_2(-2, -2) = (-6, 2) It boils down to a system of equations: Take the augmented matrix:
[5−6−2−2−62] Reduced form: [1001−8111311] -(8/11)*(5, -6) + (13/11)*(-2, -2) = (-6, 2)Answer: The required vector x is
[tex]x=\begin{bmatrix}-\dfrac{8}{11}\\ \dfrac{13}{11}\end{bmatrix}[/tex].
Step-by-step explanation: Given that a basis B of R² consists of vectors (5, -6) and (-2, -2).
We are to find the vector x in R² whose co-ordinate vector relative to the basis B is [tex]\begin{bmatrix}-6\\ 2\end{bmatrix}[/tex].
Let us consider that a, b are scalars such that
[tex]a(5,-6)+b(-2,-2)=(-6,2)\\\\\Rightarrow (5a-2b,-6a-2b)=(-6,2)\\\\\Rightarrow 5a-2b=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-6a-2b=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Subtracting equation (ii) from equation (i), we get
[tex](5a-2b)-(-6a-2b)=-6-2\\\\\Rightarrow 11a=-8\\\\\Rightarrow a=-\dfrac{8}{11}[/tex]
and from equation (i), we get
[tex]5\times\left(-\dfrac{8}{11}\right)-2b=-6\\\\\\\Rightarrow 2b=-\dfrac{40}{11}+6\\\\\\\Rightarrow 2b=\dfrac{26}{11}\\\\\\\Rightarrow b=\dfrac{13}{11}.[/tex]
Thus, the required vector x is
[tex]x=\begin{bmatrix}-\dfrac{8}{11}\\ \dfrac{13}{11}\end{bmatrix}[/tex].
Which of the following graphs represents the function f(x) = x4 - 2x3 - 3x2 + 4x + 1?
Answer: Graph D will be correct graph for the given function.
Explanation:
Given function [tex]f(x) = x^4-2x^3-3x^2+4x+1[/tex]
Since it is a bi-quadratic equation thus it must have 4 roots and (0,1) is one of its point.
Moreover, the degree of the function is even thus the end behavior of the function is[tex]f(x)\to+\infty[/tex], as [tex]x\to-\infty[/tex] and [tex]f(x)\to+\infty[/tex] as [tex]x\to+\infty[/tex]
In graph A, function has four root but it does not have the end behavior same as function f(x).( because in this graph [tex]f(x)\to-\infty[/tex], as [tex]x\to-\infty[/tex] and [tex]f(x)\to-\infty[/tex], as [tex]x\to+\infty[/tex].) so, it can not be the graph of given function.
In graph B, neither it has four root nor it has the end behavior same as function f(x).(because in this graph [tex]f(x)\to+\infty[/tex] as [tex]x\to-\infty[/tex] and [tex]f(x)\to-\infty[/tex] as [tex]x\to+\infty[/tex].) so, it can not be the graph of given function.
In graph C, neither it has four root nor it has the same end behavior as function f(x).(because in this graph [tex]f(x)\to-\infty[/tex] as [tex]x\to-\infty[/tex] and [tex]f(x)\to+\infty[/tex] as[tex]x\to\infty[/tex].) so, it also can not be the graph of given function.
In graph D it has four root as well as it has the same end behavior as the given function. Also it passes through the point (0,1).
Thus, graph D is the graph of given function.
Samantha and Luis are attempting to determine how many library books each seventh grade student checks out at the same time. Samantha surveys every other seventh grade student leaving the library. She samples a total of 40 of the 200 seventh graders. Luis samples 30 of the 200 seventh grade students at random in the school cafeteria. Whose sample is the most random? Luis because his sample is taken from the population of all seventh graders Luis because he samples fewer students Samantha because she samples more students Samantha because her sample is taken from the population of students who use the library
Answer:
Luis, because his sample is taken from the population of all seventh graders. However, Samanthan has the advantage of having a bigger sample, and that makes it more representative.
Step-by-step explanation:
Taking the sample of the library as Samantha did, is biased, because most of the students there is checking a book, and the aim of the study is not only the ones that use the library, but in general the seventh grade students.
If the sail of a ship is 10 feet long and has a diagonal length of 26 feet, what is the height of the sail in feet?
29
24
17
8
The height of the sail in feet is 24 feet.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Look at the triangle ABC below, where we have
BC² = AB² + AC².
The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.
Given:
Base = 10 feet
Hypotenuse = 26 feet
Using Pythagoras theorem
H² = P² + B²
P²= (24)² - (10)²
P² = 676 - 100
P² = 576
P=√576
P= 24 feet
hence, height of the sail in feet is 24 feet.
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there are 1176 students in central high school. there are 50 more girls than boys. how many boys are there.
Answer:
563
Step-by-step explanation:
Plato
If the purchase price for a house is $445,500, what is the monthly payment if you put 5% down for a 30 year loan with a fixed rate of 6.25%?
Answer:
The monthly payment is $2603.17
Step-by-step explanation:
The purchase price is = $445500
5% is down payment = [tex]0.05\times445500=22275[/tex]
Loan amount is = [tex]445500-22275=423225[/tex]
The EMI formula is = [tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
p = 423225
r = 6.25/12/100=0.0052
n = 30*12 = 360
Putting the values in the formula we get:
[tex]\frac{423225*0.0052*(1.0052)^{360} }{(1.0052)^{360}-1 }[/tex]
= $2603.17
The monthly payment is $2603.17 approx
Two angles are complementary. One contains 30' more than the other. Find both angles
A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross sectional area to allow the greatest amount of water to flow
To find the depth of the gutter that will maximize its cross sectional area, we can use optimization. We need to set up the area equation, differentiate it, find critical points, and determine the maximum area.
Explanation:To find the depth of the gutter that will maximize its cross sectional area, we need to use the concept of optimization. Let's assume the depth of the gutter is x inches. The width of the gutter would be 20 - 2x inches, as the edges are turned up to form right angles.
The cross-sectional area of the gutter would be x(20 - 2x) = 20x - 2x^2 square inches. To maximize this area, we can find the derivative of the area function with respect to x, set it equal to 0, and solve for x.
After finding the critical points, we can analyze which value of x gives the maximum area. Lastly, we can plug this value back into the area function to find the maximum area.
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A chicken soup recipe calls for 15cups of chicken stock how much is this in quarts
The question's topic is about converting volume from cups to quarts. In this particular case, 15 cups of chicken stock is equal to 3.75 quarts.
Explanation:The subject of this question is the conversion of volume from cups to quarts. In this case, the chicken soup recipe calling for 15 cups of chicken stock needs to be converted into quarts. We know that 1 quart is equal to 4 cups, so we can set up the equation:
4 cups/1 quart = 15 cups/x quarts
To solve for x, we multiply 15 (cups) by 1 (quart) and then divide by 4 (the number of cups in a quart).
Therefore, x = (15*1)/4 = 3.75 quarts. So, 15 cups of chicken stock is equal to 3.75 quarts.
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To set up long division of polynomials, you should make sure that each polynomial is written in _____ order and has no missing terms. ...?
I guess there should be an options to choose. But I'm pretty sure that the answer is: To set up long division of polynomials, you should make sure that each polynomial is written in descending order and has no missing terms.
Find the perimeter of the figure below. Notice that one side length is not given.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer
The perimeter of the figure is 58 feet if the missing side length is 10 feet.
What is perimeter?It is defined as the length of the circumference or outline of the geometry. It is the sum of the all side measures.
We have a two-dimensional geometry in the picture with dimensions.
The missing side length = 15 - 5 = 10 ft
The perimeter of the figure = 5+7+10+10+15+11
= 58 feet
Thus, the perimeter of the figure is 58 feet if the missing side length is 10 feet.
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What fraction is greater than 1/2. 4/6 3/8 1/3 2/5?
the ordered pair (0,0)(1,4)(2,16)(3,36)(4,64). write a rule that represents the function.
The ordered pairs (0,0), (1,4), (2,16), (3,36), and (4,64) can be represented by the function y = x^2.
Explanation:The question involves a list of ordered pairs that represent a mathematical function. Here, the ordered pairs are (0,0), (1,4), (2,16), (3,36), (4,64). Through these pairs, we can see a relationship between the x-values (first number in each ordered pair) and their respective y-values (second number in each pair). Specifically, each y-value appears to be the square of its respective x-value. By noticing this pattern, we can write a rule that represents this function: y = x^2. This means that for any given x-value, you just need to square it to get its corresponding y-value.
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You can run 3 3/5 miles in 40 minutes.
What is your unit rate?
The unit rate is calculated by dividing the distance run by the time taken. In this case, the unit rate is 5.4 miles per hour, indicating that the student runs 5.4 miles for every hour they run.
Explanation:To find the unit rate, we first convert the distance to a decimal. So, 3 3/5 miles becomes 3.6 miles. Unit rate is the ratio of the amount of a single unit of an item to its cost. In this case, your unit rate is the distance you run (in miles) per unit of time (in minutes).
Now, you should divide the total distance (3.6 miles) by the time (40 minutes). 3.6 miles / 40 minutes = 0.09 miles per minute.
If you want the unit rate per hour (commonly used), you should multiply this result by 60 (as there are 60 minutes in an hour). 0.09 miles per minute * 60 minutes/hour = 5.4 miles/hour.
So, your unit rate is 5.4 miles per hour, meaning you run 5.4 miles for every one hour of running.
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What times what equels 108
Abbreviate 375,000 using scientific notation is what eactly?