ANSWER
[tex]- \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j[/tex]
EXPLANATION
The given vector is v = −14.5i + 2.5 j.
The magnitude of this vector is
[tex] |v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} } [/tex]
[tex]v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} } [/tex]
[tex]v| = \sqrt{ 216.5} = \frac{ \sqrt{866} }{2} [/tex]
The unit vector in the direction of this vector is
[tex] = \frac{v}{ |v| } [/tex]
[tex] = - \frac{14.5}{ \frac{ \sqrt{866} }{2} } i + \frac{2.5}{ \frac{ \sqrt{866} }{2} } j[/tex]
[tex] = - \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j[/tex]
Pleaseeeeee help me!!
Answer:
118.3 m²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 13 ( or 18.2) and h = 18.2( or 13) ← sides perpendicular
A = 0.5 × 13 × 18.2 = 118.3 m²
How can the radian measure of an angle determine the arc length on the unit circle?
Step-by-step explanation:
Arc length is defined as:
s = rθ
where r is the radius and θ is the angle in radians
A unit circle has a radius of 1, so the arc length is equal to the radian measure of the angle.
The radian measure determines the arc length on the unit circle using the formula s = θ for a unit circle (radius = 1). Radians, being a ratio of arc length to radius, allow for direct conversion between angle and arc length, facilitating calculations and conversions between radians and degrees.
The radian measure of an angle can determine the arc length on the unit circle by using the formula arc length (s) = radius (r) × angle in radians (θ). Since the unit circle has a radius of 1, this simplifies to s = θ. The concept of radians is crucial here; a radian is defined as the ratio of the arc length to the radius of the circle, making it a dimensionless unit. This relationship remains constant regardless of the circle's size, meaning the radian measure directly gives the arc length on the unit circle.
For a full revolution of 2π radians (360 degrees), the arc length is equal to the circumference of the circle, which is 2πr. In the case of the unit circle, this equates to an arc length of 2π. This principle allows for the conversion between radians and degrees, and calculation of arc lengths for any given angle measured in radians.
The company president sets a goal that the percentage of working phones must increase from 30% to atleast 80% by the end of the day
a. 3/10+x/x>=8/10
b. 3/10+1/x>=8/10
c. 3x/10x>=8/10
d. 3x+x/10+x>=8/10
Answer:
D) 3+x/10+x > 8/10!
Answer:
the second part is a
Step-by-step explanation:
Find the cos of angle y
ANSWER
[tex]\cos(y) = \frac{4}{5} [/tex]
EXPLANATION
From the mnemonics SOH-CAH-TOA.
We want to find the cosine of y
CAH means cosine ratio involves adjacent over the hypotenuse.
[tex] \cos(y) = \frac{adjacent}{hypotenuse} [/tex]
From the right by triangle, the side ajacent to angle y is 64 units and the hypotenuse is 80 units.
[tex] \cos(y) = \frac{64}{80} [/tex]
[tex]\cos(y) = \frac{4}{5} [/tex]
Answer:4/5
Step-by-step explanation:
What is the surface area of the square pyramid below?
what pyramid???????
i think you forgot the pyramid
What is the value of x?
Enter your answer in the box.
x =
Answer:
4
Step-by-step explanation:
5 children have £23.09 three have between £5 and £6. 2 have between £3 and £4. How much could they each have.
Answer:
there are several possible answers child 1=5.50
child 2=5.03
child 3=5.06
child 4=3.99
child 5=3.51
Step-by-step explanation:
23.09 / 5 = £4.61 = 1 share
4.61 * 3 = 13.83
4.61 * 2 = £9.22
13.87 / 3 = 4.62
9.22 / 2 = 4.61
what is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4
Answer:
Required logarithmic function is :
[tex]f\left(x\right)=\log_3\left(x\right)[/tex]
Step-by-step explanation:
Given that table for the logarithmic function is:
x f(x)
9 2
27 3
81 4
which can be rewritten as:
x f(x)
3^2 2
3^3 3
3^4 4
Which are basically powers of 3
Hence required logarithmic function is :
[tex]f\left(x\right)=\log_3\left(x\right)[/tex]
A symbol used to represent an unknown value or quantity
Variables represent unknowns. They are often letters (like x) but can also be other symbols like Greek numerics.
Hope this helps!!
Answer: he is right it is variables that are the unknown
Step-by-step explanation:
A student solved this problem and said the answer is 81 2 pounds. Jill's club bought 42 5 pounds of hot dogs, 31 2 pounds of hamburger, and 23 10 pounds of chicken for the picnic. How much meat did they buy altogether? Is the student's answer reasonable? No, the answer is not reasonable. It should be about 12 pounds. No, the answer is not reasonable. It should be about 15 pounds. No, the answer is not reasonable. It should be about 10 pounds. Yes, the answer is reasonable.
Answer:
D. No the answer is not reasonable. it should be about 10 pounds.
I took the test.
Answer:
No, the answer is not reasonable. It should be about 10 pounds.
Step-by-step explanation:
Given,
The quantity of hot dog bought by Jill's club = [tex]4\frac{2}{5}[/tex] pounds,
Hot dog = [tex]3\frac{1}{2}[/tex] pounds
Hamburger = [tex]2\frac{3}{10}[/tex] pounds
So, the total quantity of meat they bought
[tex]=4\frac{2}{5}+3\frac{1}{2}+2\frac{3}{10}[/tex]
[tex]=\frac{22}{5}+\frac{7}{2}+\frac{23}{10}[/tex]
[tex]=\frac{44+35+23}{10}[/tex] ( Adding fractions ),
[tex]=\frac{102}{10}[/tex]
[tex]=10.2\text{ pounds}[/tex]
Since, [tex]8\frac{1}{2}=\frac{17}{2}=8.5[/tex]
[tex]\implies 8.5\neq 10.2[/tex]
Hence, the student's answer is not reasonable it should be about 10 pounds.
Third option is correct.
use formulas to find the lateral area and surface area of the given prism. round your answer to the nearest whole number.
11.21m , 5m ; 6m , 34m
A. 755 m^2; 815m^2
B. 755 m^2; 785m^2
C. 725 m^2; 815m^2
D. 725 m^2; 785m^2
will give brainliest but I need you to hurry!!!!
Answer:
OPTION A 755m^2;815m^2
Step-by-step explanation:
I hope it really helps I know everyone always needs help from time to time best of luck!
find the reference angle of -580?
a. 40
b. -60
c. 60
d. -40
Answer: The answer is a: 40
Step-by-step explanation:
PLEASE HELP! I been stuck on this assignment for over 2 weeks. My teacher gave me a simple explanation when I asked for help, but I still didn't understand it. I asked for more help and now they aren't responding anymore. I'm desperate. Nobody else I have asked understands it either. Here is the question:
Thomas wants to make a box with no lid out of a cardboard sheet to hold a marble collection. He plans to cut out four congruent squares from all corners of the sheet and then fold up the sides to make the box.
Thomas buys a cardboard sheet that is 8 by 12 inches. Let x be the side length of each cutout. Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
What is the size of the cutout he needs to make so that he can fit the most marbles in the box?
If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be? What would be the dimensions of this box?
This has to do with polynomials by factoring.
Please EXPLAIN IT so that I UNDERSTAND it. Don't just give me the answer. THANK YOU so much in advance. :)
Answer:
Question 1: x = 0,6,4
Step-by-step explanation:
#1. If we let x be the side of the cut-out square, the formula for the volume of the box is
[tex]\text{Volume} = (12 - 2x)(8 - 2x)(x).[/tex]
Expanding gives us
[tex]\text{Volume} = 4x^3 - 40x^2 + 96x. [/tex]
To find the zeros, we need to set the equation to 0, and the values of x that would result to zero would be:
[tex]x = 0, 6, 4[/tex]
As how it is told 'he' wanted to make a box with no lid for his marble connection, 'he' wants to cut out four "Identical" squares from all of the corners of the sheet (which I'm assuming is that there is four corners) and by doing so he then wants to fold all the sides...
So he buys one that is 8 by 12 inches, so you can draw a box that is (8, 12) put an 'x' at all four corners and 'cut' it the corners out.
Here's the formula that you can use... Which could be either one I guess..
-Cube = a 3
-- a is the side length
-Rectangular prism = a * b * c
-- a, b, c are the length, width, and height
The volume of a cube is side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed. If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches.
Once you found a function I think you should use the quadratic equation, which is- y=x2-20x+96
And you could use that equation to graph it out... But if they want it to be the volume of 12 cubic inches then er-... Yeah that's were i'm stumped at... My apologies..
Solve the following system of equations. Show your work
-3-3y=12x , -5-y=2x
solving simultaneously
let equation 1 be -3-3y=12x
let equation 2 be -5-y=2x
equation 2 make y subject of formula=> y=-5-2x
replace (y=-5-2x) in equation 1
-3-3(-5-2x)=12x
solve for x
x=2
replace x=2 in equation 2
y=-5-2(2)
y=-9
Therefore, x=2 y=-9
The area of the base of a rectangular prism is 36 cm2. The height of the prism is 3 5 6 cm. What is the volume of the prism?
Answer:
138 cm³
Step-by-step explanation:
Given in the question that base of the rectangular prism = 36 cm²
Height of the prism = 3 5/6 cm = 23/6
We know that the volume of a rectangular prism with base area B and height H is given by
Volume = B(H)Plug values in the formula above to find the volume of the prism
Volume = 36(23/6)
= 6(23)
= 138 cm³
So the volume of prism = 138 cm³
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule?
Enter your answer, as a decimal, in the box.
Answer:
0.22
Step-by-step explanation:
The point estimate is simply the middle of the confidence interval.
p = (0.195 + 0.245) / 2
p = 0.22
Please please help me out!!
Answer:
And step-by-step explanation
Answer:
x = 46°
Step-by-step explanation:
The angle 69° and z form a straight angle and are supplementary, thus
z = 180° - 69° = 111°
The sum of the 3 angles in a triangle = 180°, hence
x = 180° - (111 + 23)° = 180° - 134° = 46°
What is the probability of event B occurring given even A occurs if the probability of both evens are independent events
The probability of each event occurring does not affect the probability of the other event occurring
I am not sure about the numbers you are working with, but you can use this to help you out:
[tex]p(a \: and \: b) = p(a) \times p(b)[/tex]
Good luck!
Specify the domain for the function ƒ(x) = 2x4 + 4x3 + 2x2
Answer:
In interval notation it is ( -∞, ∞).
Step-by-step explanation:
All values of x can be input to this function.
The height in feet of a rocket launched into the air is modeled by the function (t)=-16t^2+160t+300 where t is time in seconds. Approximately how many seconds will the rocket exceed the height of 500 ft?
The rocket exceed the height of 500 ft in 1.46 seconds or 8.43 seconds.
what is quadratic equation?Standard form of the quadratic equation in the variable x is an equation of the form a[tex]x^{2}[/tex] + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Any equation of the form P(x) = 0, Where P(x) is a polynomial of degree 2, is a quadratic equation.
Given equation of height is:
h(t)= -[tex]16t^{2} +160t+300[/tex]
Now, the exceeded to 500 feet.
So,
-[tex]16t^{2} +160t+300[/tex]=500
16[tex]t^{2}[/tex] -160 t +200=0
Now, solve for t: a=16, b= -160, c= 200
D= [tex]\sqrt{b^{2}-4ac }[/tex]
= [tex]\sqrt{(-160)^{2}-4*16*200 }[/tex]
= [tex]\sqrt{12800 }[/tex]
= 80√2
As D>0 then,
x= [tex]\frac{-b\pm \sqrt{b^{2}-4ac }}{2a}[/tex]
x= (160 ±80√2)/32
x= (160 +80√2)/32 or x= (160 -80√2)/32
So, x= 8.43 and x=1.46
Learn more about quadratic equation here:
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A binomial experiment is conducted with 7
trials. Each trial has a probability of 0.75 for
success.
a) Which of these is a theoretical probability P(r)
for r trials
i. P(2) = 0.012 iv. P(5) = 0.015
ii. P(3) = 0.058 v. P(6) = 0.311
iii. P(4) = 0.005
b) What is the theoretical probability that at least
4 of the trials are successful, rounded to three
decimal places?
c) What is the theoretical probability that at most
2 of the trials are successful, rounded to three
decimal places?
Answer:
Step-by-step explanation:
To calculate the theoretical probability here, we need three inputs: 1) the number of trials (which here is 7); the probability of success (which here is 0.75); and an integer representing the particular outcome (which here would be r: {0, 1, 2, 3, 4, 5, 6, 7}.
(a) Most of today's calculators have probability distribution functions built in. I've used binompdf(n,p,r) here. i. P(2) = 0.012 is correct; it's the result of typing in binompdf(7,0.75,2). ii. P(3) = 0.058 is correct. iii. P(4) = 0.005 is false; this probability is 0.173. iv. P(5) = 0.015 is false. v. P(6) = 0.311 is correct.
(b) The probability that at least four trials are successful is equivalent to P(4) + P(5) + P(6) + P(7). Another way in which to calculate this would be to add up P(0) + P(1) + P(2) + P(3) and subtract the resulting sum from 1.00: That comes to: 1 - (0.000 + 0.001 + 0.012 + 0.058), or 1 - 0.071, or 0.929
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $45,920. The variable costs will be $11.25 per book. The publisher will sell the finished product to bookstores at a price of $21.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
The publisher should produce and sell approximately 4480 books in order to break even on the total costs of production.
Explanation:The problem requires figuring out when the revenues from selling the book will equal the total cost of production. This is a problem in algebra.
The one-time fixed costs total $45,920, and the variable costs per book are $11.25. The books will be sold for $21.50 each.
Step 1: Set up an equation
Let x be the number of books that need to be sold. The equation is then: 45920 + 11.25x = 21.50x.
Step 2: Solve for x
Subtract 11.25x from each side to isolate the variable on one side giving you: 10.25x = 45920. Then, divide both sides by 10.25 to derive x. So, the equation is x = 45920 / 10.25.
Step 3: Derive the solution
By doing the calculation, x approximately equals 4480. Thus the publisher needs to sell just about 4480 books to break even.
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The publisher must produce and sell 4,478 books to cover total production costs. They need to break even by equating total costs with total revenue, using the formula FC + (VC × N) = P × N, and solving for N after substituting the given fixed costs, variable costs per book, and price per book.
Explanation:To determine how many books a publisher must produce and sell to cover production costs, the following formula is used:
Total costs (TC) = Fixed costs (FC) + (Variable cost per book (VC) × Number of books (N))Total revenue (TR) = Price per book (P) × Number of books (N)To break even, TC must equal TR. This can be expressed as:
FC + (VC × N) = P × N
Now we substitute the given values:
$45,920 + ($11.25 × N) = $21.50 × N
To find N, we solve the equation for N:
$45,920 = ($21.50 - $11.25) × NN = $45,920 / $10.25N = 4,478Therefore, the publisher must produce and sell 4,478 books to cover total production costs.
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All matter is made up of both positive and negative charges and we can only rub off the charges
Answer:
true if that is the answer your looking for
Step-by-step explanation:
What is the volume of the sphere shown below?
Answer:
A. (4000/3) π cubic units
Step-by-step explanation:
The volume of a sphere is given by V = (4/3) π r³
Since this sphere has a radius of 10, we can find its volume by inserting the value of the radius in the formula:
[tex]V = \frac{4}{3} \pi 10^{3} = \frac{4}{3} * 1000 * \pi =\frac{4000}{3} \pi[/tex]
Since all the possible answers are given with π in them, we can stop the calculation there and say the volume is (4000/3) π cubic units.
Answer:
(4000/3)[tex]\pi[/tex] units³
Step-by-step explanation:
~apex
Using the side lengths determine whether the triangle is acute, obtuse or right 36, 45, 27
given sides,
a=36
b=45
c=27
From cosine law,
cosA=
[tex] \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} \\ = \frac{ {45}^{2} + {27}^{2} - {36}^{2} }{2 \times 45 \times 27} \\ = \frac{3}{5} = 0.6[/tex]
or, A= cos^-1(0.6)=53.13°
similarly, cosB=
[tex] \frac{ {a}^{2} + {c}^{2} - {b}^{2} }{2ac} \\ = \frac{ {36}^{2} + {27}^{2} - {45}^{2} }{2 \times 36 \times 27} \\ = 0[/tex]
or, B= cos^-1(0)=90°
Since, B=90, the given triangle is right angled triangle.
City park is a square piece of land with an area of 10,000 square yards. What is the length of the fence that encloses the park?
Answer:
400 yards
Step-by-step explanation:
(√A)4
(√10,000)4
(100)4
400
Hope This Helps! :D
A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter. 1
Answer:
1,005 cm³
Step-by-step explanation:
The volume of a cylinder can be calculated by multiplying the area of its base times the height. It is calculated as follows:
V = πr²h
V = π(8/2)²(20)
V = 1005.31 cm³
Answer:
1,005 cm³
Step-by-step explanation:
because im the goat
How do you round −248.0426206 dollars to the nearest cent?
Answer:
you multiply it by 100 since there are 100 cents in a dollar. so, 24804 cents. it stays at 4 because 2 is less than 5
Step-by-step explanation:
Answer:
$-248.04.
Step-by-step explanation:
This is the correct answer to your question.
Hope this helps!!!
Kyle.
In the equation y = 2(x + 5), if x is increased by 3, then y is increased by
6
3
5
11
Answer:
[tex]x = \frac{y}{2}- 5[/tex]
[tex]x = \frac{1}{2} y - 5[/tex]
Step-by-step explanation:
[tex]1. \: \frac{y}{2} = x + 5 \\ 2. \: \frac{y}{2} - 5 = x \\ 3. \: x = \frac{y}{2} - 5 \\ \\ or \\ \\ 1. \: 2x + 10 = y \\ 2. \: 2x = y - 10 \\ 3. \: \frac{2x}{2} = \frac{y - 10}{2} \\ x = \frac{1}{2} y - 5 [/tex]
Given: DR tangent to Circle O.
Ir DB=140, then A=
A)70
B)110
C)140
D)80
The quiz says 140 is wrong, but I don’t know if that’s a problem on the teacher’s end or not, because everyone here says it’s 140
Answer:
I believe the answer is 110.
Answer:
110°Step-by-step explanation:
In this problem we need to use the Inscribed Angle theorem, which states that an inscribed angle is one-half its subtended arc.
[tex]\angle C=\frac{1}{2}arc(DB)=70\°[/tex]
Then, we use the theorem about a cyclic quadrilateral, which is an inscribed quadrilateral: "the opposite angles in a cyclic quadrilateral are supplementary".
[tex]\angle C + \angle A = 180\°\\\angle A = 180\° - \angle C\\\angle A = 180\° - 70\° \\\angle A = 110\°[/tex]
Therefore, the answer is 110°