Answer:
Step-by-step explanation:
A car travels 32 km due north and then 46 km in a direction 40° west of north. Find the direction of the car's resultant vector. [?] Round to the nearest hundredth.
Answer:
Step-by-step explanation:
This requires some serious work before we even begin. First off, we will convert the km to meters:
32 km = .032 m
46 km = .046 m
And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:
40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.
[tex]A_x=.032cos90.0[/tex] so
[tex]A_x=0[/tex] (the 90 degrees comes from "due north")
[tex]B_x=.046cos130[/tex] so
[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:
[tex]C_x=-.030[/tex] And onto the y components:
[tex]A_y=.032sin90.0[/tex] so
[tex]A_y=.032[/tex]
[tex]B_y=.046sin130[/tex] so
[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:
[tex]C_y=.067[/tex] Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.
We find the magnitude of C:
[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]
We will round this after we take the square root to the thousandths place.
[tex]C_{mag}=.073m[/tex] and now for the angle:
[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:
The magnitude of the resultant vector is .073 m at 113°
how many letters in the english alphabet preeced the letter v?
Answer:
21 letters
Step-by-step explanation:
A, B, C, D, E, F, G, H, I, J, K, L, M, NO, P, Q, R, S, T, U
2x^2-4x+8 when factored is
Answer:
[tex]2(x^{2} -2x+4)[/tex]
Step-by-step explanation:
[tex]2x^{2} -4x+8[/tex]
= [tex]2x^{2} -2*2x+2*4[/tex]
= [tex]2(x^{2} -2x+4)[/tex]
Simplify the expressions by combining like terms.
30) 4x + 3-x =
Step-by-step explanation:
the answer is -1. I have a picture, take a lot at it
Answer: 3x+3
Step-by-step explanation:
4x+3-x
= (4x-x) + 3
= 3x+3
Solving just for X. Please help and thank you:)
Compare the functions shown below:
Which function has the greatest maximum y-value?
Answer:Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :)
Step-by-step explanation:
which algebraic expression represents this word description the quotient of six and the sum of a number and eight
work out the area of a semicircle take pi to be 3.142 11cm
Answer:
if the diameter is 11, them the answer is 47.52275cm
carly walks 30 feet in seven seconds. At this rate, how many minutes will it take for carly to walk a mile if there are 5,280 feet in one mile?
Answer:
20.53 minutes
Step-by-step explanation:
Speed = Distance/Time = 30/7
Time = Distance / Speed
= 5280/30/7
= 1232 seconds / 60 = 20.53 minutes
Answered by Gauthmath
The number 804 is divisible by what numbers?
Answer: 804 is divisible by 1, 2, 3, 4, 6, 12 ,67 ,134 ,201, 268, 402 ,804
Answer:
The factors of 804 are: 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402,804.
Step-by-step explanation:
WORKED EXAMPLES
Try Vertical Angle Problems
ZC and Dare vertical angles.
m_C=° and mZD=(-3x +80)°
What is mZC
Enter your answer in the box.
Answer:
M<C = 20°
Step-by-step explanation:
Because they’re vertical angles, that means they’re equal to each other so:
m<C = m<D
x = -3x + 80
x + 3x = 80
4x = 80
x = 20
Since m<C equals x, that means m<C is 20°
arrange0.2,¼,30%,10%in ascending and descending order
Answer:
Ascending- 10%, 0.2, 1/4, 30%
Descending- 30%, 1/4, 0.2, 10%
Step-by-step explanation:
0.2 = 2/10 = 4/20
1/4 = 5/20
30% = 30/100 = 6/20
10% = 10/100 = 2/20
Ascending
-2/20, 4/20, 5/20, 6/20
- 10%, 0.2, 1/4, 30%
Descending
- 6/20, 5/20, 4/20, 2/20
- 30%, 1/4, 0.2, 10%
Which is the graph of y = RootIndex 3 StartRoot x EndRoot?
Given:
The equation is:
[tex]y=\sqrt[3]{x}[/tex]
To find:
The graph of the given equation.
Solution:
We have,
[tex]y=\sqrt[3]{x}[/tex]
The table of values is:
x y
-8 -2
-1 -1
0 0
1 1
8 8
Plot these points on a coordinate plane and connect them by a free hand curve as shown in the below graph.
Answer:
D
Step-by-step explanation:
edge 2020
Solve for a.
-4a – 2a – 7 = 11
a =
[?]
Answer:
or, -4a - 2a -7 = 11
or, -4a -2a =11 +7
or, - 6a = 18
or, a= 18÷ -6
a= -3
The access code for a cars security system consists of 4 digits. The first digit cannot
be 0 and the last digit nust be even. How many different codes are available?
Answer:
4500
Step-by-step explanation:
The first digit can't be 0. so it will be a number from 1000 to 9999. That's a total of 9000 numbers (9999-1000+1=9000). Since the last digit must be an even number that is one half of the 9000 numbers which is 4500.
What are the solutions to the system of equations graphed below?
Answer:
The answer is B (4, 8) and (0, -8)
The probability of drawing a red candy at random from a bag of 25 candies is 2/5. After 5 candies are removed from tehe bag, what is the probability of randomly drawing a red candy from the bag?
Given:
The probability of drawing a red candy at random from a bag of 25 candies is [tex]\dfrac{2}{5}[/tex].
To find:
The probability of randomly drawing a red candy from the bag after removing 5 candies from the bag.
Solution:
Let n be the number of red candies in the bag. Then, the probability of getting a red candy is:
[tex]P(Red)=\dfrac{\text{Number of red candies}}{\text{Total candies}}[/tex]
[tex]\dfrac{2}{5}=\dfrac{n}{25}[/tex]
[tex]\dfrac{2}{5}\times 25=n[/tex]
[tex]10=n[/tex]
After removing the 5 candies from the bag, the number of remaining candies is [tex]25-5=20[/tex] and the number of remaining red candies is [tex]10-5=5[/tex].
Now, the probability of randomly drawing a red candy from the bag is:
[tex]P(Red)=\dfrac{5}{20}[/tex]
[tex]P(Red)=\dfrac{1}{4}[/tex]
Therefore, the required probability is [tex]\dfrac{1}{4}[/tex].
please help me!!! :)
Answer:
C
Step-by-step explanation:
f(x) = x-8 when x>3, f(7)=7-8=-1
If you apply the changes below to the absolute value parent function, 1(x) = 1X, what is the equation of the new function? Shift 8 units left. • Shift 3 units down. O A. g(x) = (x + 81 - 3 O B. g(x) B. g(x) = (x - 3| + 8 O c. g(x) = [X - 31- 8 D. g(x) = (x - 8 - 3
Answer:
A. g(x) = |x + 8| - 3Step-by-step explanation:
If the function is f(x), then shift 8 units left and 3 units down will result in:
g(x) = f(x + 8) - 3Apply to the given function to get:
g(x) = |x + 8| - 3Correct choice is A
Select the correct answer. Consider this system of equations, where function f is quadratic and function g is linear:
y = f(x)
y = g(x)
Which statement describes the number of possible solutions to the system?
A. The system may have no, 1, 2, or infinite solutions.
B. The system may have no, 1, or infinite solutions.
C. The system may have 1 or 2 solutions.
D. The system may have no, 1, or 2 solutions
Answer:
C is the answer
Step-by-step explanation:
Quadratic equations have at most 2 solution, and linear equations only have 1 solution, and since y is equal to both of them, it can only have 1 or 2 solutions.
The correct answer is option D. The system may have no, 1, or 2 solutions
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
f(x) is a quadratic function and g(x) is linear function
y=f(x)
y=g(x)
Quadratic equations have at most 2 solution
linear equations only have 1 solution,
f(x)=g(x)=y
y is equal to both of them, it can only have 1 or 2 solutions.
A line and a parabola can intersect zero, one, or two times
Therefore, a linear and quadratic system can have zero, one, or two solutions
Hence, the correct answer is option D. The system may have no, 1, or 2 solutions
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enter the repeating digit
[tex] \frac{9}{11} [/tex]
Answer:
Step-by-step explanation:
[tex]\frac{9}{11}=0 .818181....[/tex]
__
= 0.81
Simplify the following, leaving your answer with a positive exponent:
x^-12/ x^-7
Answer:
[tex]\frac{1}{x^{5} }[/tex]
Step-by-step explanation:
x^-12/ x^-7
= x^(-12-(-7))
= x^-5
= 1/x^5
Instructions: Find the value of the trigonometric ratio. Make sure to
simplify the fraction if needed.
Х
40
32
N
24
Y
Tan Z
Answer:
tan Z = 4/3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta= opp / adj
tan Z = 32/24
Divide top and bottom by 8
tan Z = 4/3
In a large midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 2001 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. The proportion of all entering freshmen in 1999 and 2001, who graduated in the bottom third of their high school class, are p1 and p2, respectively.Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999? To determine this, you test the hypothesesH0 : p1 = p2 , Ha : p1 > p2.The P-value of your test isA. 0.976.B. 0.024.C. 0.048.D. 0.001.
Answer:
B. 0.024
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
Of 100, 20 were in the bottom thid. So
[tex]p_B = \frac{20}{100} = 0.2[/tex]
[tex]s_B = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
Of 100, 10 were in the bottom third, so:
[tex]p_A = \frac{10}{100} = 0.1[/tex]
[tex]s_A = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.
Can also be rewritten as:
[tex]H_0: p_B - p_A = 0[/tex]
[tex]H_1: p_B - p_A > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample:
[tex]X = p_B - p_A = 0.2 - 0.1 = 0.1[/tex]
[tex]s_A = \sqrt{s_A^2+s_B^2} = \sqrt{0.03^2+0.04^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of proportions of at least 0.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.976.
1 - 0.976 = 0.024, so the p-value is given by option B.
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
a car can complete journey of 300 km with the average speed of 60 km per hour how long does it take to complete the journey what is the speed of the car if it covers only 200 km in the same interval of the time
please I need help urgent
Answer:
a. 5 hours
b. 40 kph
Step-by-step explanation:
300 km ÷ 60 km = 5 hours
200 km ÷ 5 hours = 40 kilometers per hour
Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 80 yd from B and 104 yd from A, with angle ACB
measuring 51.2º. How far apart are A and B (to the nearest yard)?
HURRYYY GIVING 20 POINTS!!
Answer:
Step-by-step explanation:
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The distance between A and B is 85.6 yds.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
The three points A, B, and C will form a triangle. Therefore, using the law of cosine the measure of the third side AB can be written as,
[tex]AB =\sqrt{(AC)^2 + (BC)^2 -2(AC)(BC)\cdot \cos(51.2^o)}\\\\AB =\sqrt{(80)^2 + (104)^2 -2(80)(104)\cdot \cos(51.2^o)}\\\\AB = \sqrt{6400+10816-16640\cos51.2^o}\\\\AB = \sqrt{7328.4}\\\\AB=85.6\rm\ yd[/tex]
Hence, the distance between A and B is 85.6 yds.
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Please help with this question
Answer:
-3.662rad × 180/π = -209.8°
Step-by-step explanation:
Answer:
1 degree = .01745329 radians
1 radian = 57.2957877856 degrees
-209.8 degrees = .01745329 * -209.8 =
-3.66170024200 radians
Step-by-step explanation:
Consider this equation. tan) 19 17 If 8 is an angle in quadrant II, what is the value of Cos() OA. 19 6 OB. 17 6 O c. V18 6 OD. 17
Using trigonometric identities, it is found that the value of [tex]\cos{\theta}[/tex] is given by:
B. [tex]\cos{\theta} = \frac{\sqrt{17}}{6}[/tex]
What is the tangent of an angle?It is given by the division of it's sine by it's cosine, that is:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
In this problem, the equation given is:
[tex]\tan{\theta} = -\sqrt{\frac{19}{17}}[/tex]
That is:
[tex]\frac{\sin{\theta}}{\cos{\theta}} = -\sqrt{\frac{19}{17}}[/tex]
[tex]\sin{\theta} = -\sqrt{\frac{19}{17}}\cos{\theta}[/tex]
The following identity is applied:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
Then:
[tex]\left(-\sqrt{\frac{19}{17}}\cos{\theta}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{36}{17}\cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{17}{36}[/tex]
[tex]\cos{\theta} = \frac{\sqrt{17}}{6}[/tex]
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Answer:
Hi sorry I just wanted to ask is it B or D? positive or negative?
Step-by-step explanation:
edmentum is the worst
I'll give brainliest :)
Are the lines y = –x – 4 and 5x + 5y = 20 perpendicular? Explain.
Yes; the product of their slopes is −1.
Yes; their slopes are equal.
No; their slopes are equal.
No; their slopes are not equal
Answer:
C
Step-by-step explanation:
In the equation y = -x - 4, the gradient is -1.
While in the second equation,
5x + 5y = 20
y = -x + 4
So the gradient is -1 too
Both sides are not perpendicular to each other because if you apply the formula, m1m2 = -1, and if substitute both gradient, (-1)(-1) = 1 ≠ -1
Therefore, no they are not perpendicular but parallel instead.
Answer: C
Step-by-step explanation:
Look above fool
Two friends are writing practice problems to study for a trigonometry test. Sam writes the following problem for his friend Anna to solve:
In right triangle ABC, the measure of angle C is 90 degrees, and the length of side c is 8 inches.
Solve the triangle.
Anna tells Sam that the triangle cannot be solved. Sam says that she is wrong.
Who is right? Explain your thinking
Answer:
Anna is right in her meaning concerning on triangle solvability.
Step-by-step explanation:
The side [tex]c[/tex] represents the hypotenuse of a right triangle as [tex]C = 90^{\circ}[/tex] and is opposite to that angle. There are two ways to solve this triangle trigonometrically:
i) Law of Sine
[tex]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}[/tex] (1)
ii) Law of Cosine
[tex]c^{2} = a^{2} + b^{2} - 2\cdot a\cdot b \cdot \cos C[/tex] (2)
The Pythagorean Theorem is a particular case of the Law of Cosine for [tex]C = 90^{\circ}[/tex]
The triangle cannot be solved as there is an input missing, either another side or another angle. If [tex]C = 90^{\circ}[/tex], then (2) is reduced into this form:
[tex]c^{2} = a^{2}+b^{2}[/tex] (2b)
In this case we need to know the measure of either [tex]a[/tex] or [tex]b[/tex] to determine its counterpart and the values of the missing angles by (1). In nutshell, Anna is right.
