Answer:
[tex] a.b = (1*0) + (-4*2) +(1*-2)= -10[/tex]
And replacing we got:
[tex] cos \theta = \frac{-10}{\sqrt{18} \sqrt{8}}= -\frac{10}{\sqrt{144}}= -\frac{10}{12}= -\frac{5}{6}[/tex]
And we can find the angle with the inverse cosine function and we got:
[tex]\theta =cos^{-1} (-\frac{5}{6})= 146.44°[/tex]
Step-by-step explanation:
for this case we can use the following identity:
[tex] cos \theta = \frac{a.b}{|a| |b|}[/tex]
We can begin finding the norm for each vector and we got:
[tex] |a| =\sqrt{(1)^2 +(-4)^2 +(1)^2}= \sqrt{18}[/tex]
[tex] |b| =\sqrt{(0)^2 +(2)^2 +(-2)^2}= \sqrt{8}[/tex]
Now we can find the dot product and we got:
[tex] a.b = (1*0) + (-4*2) +(1*-2)= -10[/tex]
And replacing we got:
[tex] cos \theta = \frac{-10}{\sqrt{18} \sqrt{8}}= -\frac{10}{\sqrt{144}}= -\frac{10}{12}= -\frac{5}{6}[/tex]
And we can find the angle with the inverse cosine function and we got:
[tex]\theta =cos^{-1} (-\frac{5}{6})= 146.44°[/tex]
A is any nonnegative real number and b is a square root of that number. Is a a function of b, b a function of a, both, or neither?
Answer:
B is a function of A
Step-by-step explanation:
If you do something to another thing, it is a function of that.
If y = x2 + 2x , find the value of y when x = 3
and
If y = x3 - 3 , find the value of y when x = 2 plsss help me
Answer:
y=15; y=5
Step-by-step explanation:
y=x2+2x
plug in x as 3:
y=3 2+ 2*3
y=9+6
y=15
Next problem:
y=x3-3
plug in x as 2:
y=2 3-3
y=8-3
y=5
WILL GIVE BRAINLIEST! EASY! Give detailed answer
11. What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? round to the nearest whole number.
O A. 746 67 m2
O B. 74 6 m2
O C.85 4 m2
O D. 8 54 m2
Answer:
85.4
Step-by-step explanation:
first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/
0.3y+ z y 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
Answer:
5
Step-by-step explanation:
Substitute the given values and do the arithmetic.
[tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]
Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.
Coefficients Standard Error
Constant 12.924 4.425
x1 -3.682 2.630
x2 45.216 12.560
Analysis of Variance
Source of Degrees of Sum of Mean
Variation Freedom Squares Square F
Regression 4853 2426.5
Error 485.3
We want to test whether the variable x1 is significant. The critical value obtained from ttable at the 1% level is:_______.
1. ±2.650.
2. ±2.921.
3. ± 2.977.
4. ± 3.012.
Answer:
4. ± 3.012
Step-by-step explanation:
Hello!
Assuming that for both variables X₁ and X₂ n₁= n₂ = 16
You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.
The hypotheses are:
H₀: β₁= 0
H₁: β₁≠ 0
α: 0.01
[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]
The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"
The rejection region for this test is two-tailed, the critical values are:
±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]
I hope this helps!
Two ships leave a port at the same time.
Ship A sails 12 knots on a bearing of 035°
Ship B sails 16 knots on a bearing of 270°
Calculate the distance between the ships after 2 hours
(1 knot = 1 nautical mile per hour)
Answer: 49.8 nautical miles
Step-by-step explanation:
Angle between routes = 125⁰
after 2 hours :-
d² = 24² + 32² - 2 x 24 x 32 cos 125⁰
d = 49•8 nautical miles
Which is greater 36÷(4×3) or 54-48-(16÷4
Step-by-step explanation:
36 ÷ (4 x 3)
36 ÷ 12
= 3
54 - 48 - (16 ÷ 4)
54 - 48 - 4
= 2
So first one is greater
how many are 4 x 4 ?
Use synthetic division to solve What is the quotient?
Answer:
[tex]3{x}^{3} + 2x + 5[/tex]
Step-by-step explanation:
Sorry if my notes weren't very clear.
Answer:B
Step-by-step explanation: got it right
Factor completely 2x⁴y³-12x³y²-8x²y
Given the sequence rn defined recursively below, find r3. r1rn=2=−rn−1+n−2
Answer:
[tex]r_3=3[/tex]
Step-by-step explanation:
Given:
[tex]r_1=2\\r_n=-r_{n-1}+n-2[/tex]
We want to find the value of [tex]r_3[/tex] .
[tex]\\r_2=-r_{2-1}+2-2\\r_2=-r_1\\r_2=-2\\\\r_3=-r_{3-1}+3-2\\r_3=-r_{2}+1\\r_3=-(-2)+1\\r_3=2+1\\r_3=3[/tex]
Suppose that 3 is a factor of a, a is a divisor of 12, and a is positive. What is the number of possible values of a?
Answer:
3
Step-by-step explanation:
12 is divisible by: 1, 2, 3, 4, 6, 12
Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.
Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis.
There food preferences among vole species are independent of one another. _____
There is a relationship between voles and food preference. ______
To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected:
meadow voles common voles
apple slices 26 32
peanut butter-oatmeal 35 25
When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated.
_____= expected meadow vole/apple slices
_____= expected common vole/apple slices
_____= expected meadow vole/peanut butter-oatmeal
_____= expected common vole/peanut butter-oatmeal
_____= chi-square value
_____= degrees of freedom (whole number only)
_____= using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of alpha=0.05?
_____= will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)
Answer:
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 28.983051
Chi-square value = χ² = 2.154239
Degree of freedom = 1
Critical value = 3.841
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Step-by-step explanation:
He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.
So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Data collected by Dr. Pagels:
meadow voles common voles Row Total
apple slices 26 32 58
peanut butter-oatmeal 35 25 60
Column Total 61 57 118
Where 118 is the grand total.
The expected number is given by
Expected = (row total)×(column total)/grand total
Expected meadow vole/apple slices = 58×61/118
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 58×57/118
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 60×61/118
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 60×57/118
Expected common vole/peanut butter-oatmeal = 28.983051
The chi-square statistic value is given by
χ² = Σ(Observed - Expected)²/Expected
χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051
χ² = 2.154239
The degrees of freedom is given by
DoF = (row - 1)×(col - 1)
For the given case, we have 2 rows and 2 columns
DoF = (2 - 1)×(2 - 1)
DoF = 1
The given level of significance = 0.05
The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be
Critical value = 3.841
Conclusion:
Reject H₀ If χ² > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
For the given case,
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Answer:
52.78% probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X greater than x is given by the following formula.
[tex]P(X > x) = \frac{b-x}{b-a}[/tex]
Uniformly distributed between 0 and 9 minutes.
This means that [tex]a = 0, b = 9[/tex]
Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
[tex]P(X > 4.25) = \frac{9 - 4.25}{9 - 0} = 0.5278[/tex]
52.78% probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these
Answer:
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
Step-by-step explanation:
13 − 01 + 1 = 13
34 − 14 + 1 = 21
56 − 35 + 1 = 22
99 − 57 + 1 + 1 = 44
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. (a) Determine the 30th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 98% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
(A) 1199.168
(B) 1503.372
(C) 159.17728
Step-by-step explanation:
(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.
Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524
The formula for finding X (the number of items in a given percentile) is:
X = M + Z(S.D.)
Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.
So for the 30th percentile,
X = 1261 + (-0.524)(118)
X = 1261 - 61.832 = 1199.168
(B) The number of chocolate chips that make up the middle 98% of chips in the bag is
X = 1261 + (2.054)(118)
X = 1261 + 242.372 = 1503.372
(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.
This is within 1.34896 standard deviations of the mean.
IQR = (1.34896)(118)
IQR = 159.17728
Questlon 3 of 10
2 Points
The volume of a cube depends on the length of its sides. This can be written
in function notation as (s). What is the best interpretation of (4) = 64?
O A. 4 sides of the cube have a total length of 64 feet.
B. A cube with side lengths of 4 feet has a volume of 64 cubic feet.
C. A cube with a volume of 4 cubic feet has side lengths of 64 feet.
O D. 4 of these cubes will have a total volume of 64 cubic feet.
SUBMIT
Answer:
b)A cube with side lengths of 4 feet has a volume of 64cubic feet
Step-by-step explanation:
volume=length×width×height
=4×4×4
=64feet³
The relation R is shown below as a list of ordered
pairs.
R={(1, 4), (1, 3), (-1,3), (2, 15)}
Which ordered pairs prevent this relation from
being a function?
0 (1, 4) and (1,3), because they have the same
X-value
(1, 3) and (-1, 3), because they have the
same y-value
Answer:
(1, 4) and (1,3), because they have the same x-value
Step-by-step explanation:
For a relation to be regarded as a function, there should be no two y-values assigned to an x-value. However, two different x-values can have the same y-values.
In the relation given in the equation, the ordered pairs (1,4) and (1,3), prevent the relation from being a function because, two y-values were assigned to the same x-value. x = 1, is having y = 4, and 3 respectively.
Therefore, the relation is not a function anymore if both ordered pairs are included.
The ordered pairs which make the relation not to be a function are: "(1, 4) and (1,3), because they have the same x-value".
y = 0.8x+ 7.2
20x + 32y = 48
Step-by-step explanation:
y = 0.8x+ 7.2 ..........(1)
20x + 32y = 48 .........(2)
Substitute (1) in (2)
20x +32*(0.8x+7.2) = 48 expand
20x + 25.6x+230.4 = 48 add
45.6x+230.4 = 48 transpose and simplify
45.6x = 48-230.4 = -182.4
x = -182.4 / 45.6
x = -4
Answer:
x=-4, Y=4
Step-by-step explanation:
20x+32(0.8x+7.2)=48
45.6x =48-230.4
x=-4
substitute x=-4 in y eqn
y=-3.2+7.2
y=4
The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12π cubic inches 36π cubic inches 64π cubic inches 81π cubic inches
Answer:
36pi
Step-by-step explanation:
Answer:
36pi
Step-by-step explanation:
i got it right on my test
Makayla is teaching Rodney how to construct a square inscribed in a circle.
I need help ...... Makayla says Rodney should draw diameter AB, and then use a compass and a straightedge to find chord CD that bisects diameter AB. Makayla also tells Rodney he should use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.
What error, if any, is Makayla making in her instructions to Rodney?
Answer:
A.) Chord CD must not only bisect but must also be perpendicular to diameter AB.
Step-by-step explanation:
The error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.
What is Geometric construction?Geometric construction is method todraw any sketch lines, angles, and other geometric forms and figures only using a compass and a straightedge. It generally is done without employing precise measurements of length, angle, etc.
Now the steps taken by Makayle are,
→draw diameter AB
→use a compass and a straightedge to find chord CD that bisects diameter AB.
→use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.
Now here the error she is making is that the required chords will be AB, BC, CD, and DA, not AC, AD, BC, and BD.
Hence,the error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.
To learn more about Geometry:
https://brainly.com/question/7558603
#SPJ2
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s) the degree of the function f(x) = -(x+1)^2(2x-3)(x+2)^2 is _ , and its y-intercept is ( _ , _ )
Answer:
Degree of the function = 5
y-intercept = (0, 12)
Step-by-step explanation:
Degree of a polynomial function is determined by the degree of the term having highest degree.
In the given function,
f(x) = -(x + 1)²(2x - 3)(x + 2)²
(x + 1)² → highest degree term = x²
(2x - 3) → highest degree term = x
(x + 2)² → highest degree term = x²
When we multiply these terms,
(x + 1)²(2x - 3)(x + 2)² highest degree term of the function will be,
[tex]x^{2} \times x \times x^{2} = x^{5}[/tex]
Therefore, degree of the function = 5
For y-intercept,
f(0) = -(0 + 1)²(0 - 3)(0 + 2)² = 12
Therefore, y-intercept of the function is (0, 12)
Solve this correctly for brainliest !!!!!! 3(7) + 2 • |7 - 8| - 12
Answer:
3(7) + 2* |7 - 8| - 12 = 11
Step-by-step explanation:
3(7) + 2* |7 - 8| - 12
21 + 2* |-1| - 12
21 + 2* 1 - 12
21 + 2 - 12
23 - 12 = 11
Hope this helps! :)
Find the length of AB. Leave
your answer in terms of 7.
A
20° AB = [ ? ]
27
1B
Enter
Answer:
AB = 3π
Step-by-step explanation:
See attachment for correct format of question.
Given
From the attachment, we have that
θ = 20°
Radius, r = 27
Required
Find length of AB
AB is an arc and it's length can be calculated using arc length formula.
[tex]Length = \frac{\theta}{360} * 2\pi r[/tex]
Substitute 20 for θ and 27 for r
[tex]Length = \frac{20}{360} * 2\pi *27[/tex]
[tex]Length = \frac{20 * 2\pi * 27}{360}[/tex]
[tex]Length = \frac{1080 \pi}{360}[/tex]
[tex]Length = 3\pi[/tex]
Hence, the length of arc AB is terms of π is 3π
which regression equation best fits these data
Answer:
D. y = 2.13x² +0.13x +6.39
Step-by-step explanation:
The quadratic regression function of a spreadsheet or graphing calculator will tell you the best choice is D.
Find the distance from R to S on the graph. Round to the nearest tenth.
Answer:
7.2
Step-by-step explanation
plug the values in in the distance formula
the points are -3,3 and 1, -3
sqrt((-3-1)^2+(3-(-3))^2)
sqrt(16)+(36)
sqrt(52)
approximately 7.2
1/9 − y2 when factored is:
Answer:
Step-by-step explanation:
hello
[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]
hope this helps
ASAP will give brainliest Which of the following formulas would find the surface area of a right cylinder where h is the height, r is the radius, LA is the lateral area, and BA is the base area?
Answer:
A. BA + 2πrh
C. 2πr² + 2πrh
Step-by-step explanation:
height of cylinder = h
Radius of cylinder = r
=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)
L.A of a cylinder = 2πrh
=>Base area = BA (this is the area of both circular bases of the cylinder)
Area of circle = πr²
Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²
=>Surface area of a right cylinder = B.A + L.A
= 2πr² + 2πrh
The formulas that can be used to find surface area of a right cylinder from the given options are:
A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)
C. 2πr² + 2πrh
A cash prize is randomly placed into certain cereal boxes that sell for $5. A $1 prize is placed in 10% of cereal boxes, a $5 prize is placed in 5% of cereal boxes, while 10% of boxes receive a $20 prize. The other boxes do not receive any cash prizes. What is the expected value of the cash prizes if you include the cost of purchasing the cereal in your calculations?
Answer:
-2.65 usd
Step-by-step explanation:
1. Note that 10%= probability 0.1 5%= 0.05 .
Lets find the average prize value :
1 usd *P(1 uzd)+5usd *P(5usd)+20,usd*P(20usd)=
= 1*0.1+5*0.05+20*0.1=2.35 USD is a value average prize brutto.
However for 1 turn the player has to pay 5 USD.
That means the net value is 2.35-5=-2.65 USD
Actually it means that every turn the player loses 2.65 USD averagly.