Answer:
Step-by-step explanation:
this problem is on vector
given the vectors
a = 5i + j, and
b = i − 2j
1. summation of vector a + b
[tex]= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\[/tex]
collect like terms
[tex]=5i+i+j-2j\\\\=6i-j\\\\[/tex]
2. 2a + 3b
[tex]= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\[/tex]
collecting like terms we have
[tex]=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j[/tex]
(3) |a|, and |a − b|.
|a|= |5i+j|
[tex]=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1[/tex]
also,
[tex]|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\[/tex]
[tex]|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25[/tex]
the product of twenty and a number
The product of twenty and a number means; 20 * n
Whatever the number equals is what we have to multiply 20 too.
Best of Luck!
what is the nth term of 5,9,13,17....
Three times a number plus sixteen
Three times a number plus sixteen means; 3n + 16
We can solve this equation if any number equals n. Lets say n = 2.
3(2) + 16
6 + 16
22
Best of Luck!
Slide G
You can ride your bike 15 miles in 1 hour. At this rate, how
many miles can you ride your bike in 4 hours?
How many miles can you
ride your bike in 4 hours?
Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the first octant.
Answer:
I = 91.125
Step-by-step explanation:
Given that:
[tex]I = \int \int_E \int zdV[/tex] where E is bounded by the cylinder [tex]y^2 + z^2 = 81[/tex] and the planes x = 0 , y = 9x and z = 0 in the first octant.
The initial activity to carry out is to determine the limits of the region
since curve z = 0 and [tex]y^2 + z^2 = 81[/tex]
∴ [tex]z^2 = 81 - y^2[/tex]
[tex]z = \sqrt{81 - y^2}[/tex]
Thus, z lies between 0 to [tex]\sqrt{81 - y^2}[/tex]
GIven curve x = 0 and y = 9x
[tex]x =\dfrac{y}{9}[/tex]
As such,x lies between 0 to [tex]\dfrac{y}{9}[/tex]
Given curve x = 0 , [tex]x =\dfrac{y}{9}[/tex] and z = 0, [tex]y^2 + z^2 = 81[/tex]
y = 0 and
[tex]y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9[/tex]
∴ y lies between 0 and 9
Then [tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy[/tex]
[tex]I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}[/tex]
I = 91.125
what is the height of a trapezoid with one base equal to 20m, the other base equal to 7m, and an area of 135m^2
Answer:
The height is 10 mStep-by-step explanation:
Area of a trapezoid is given by
[tex]A = \frac{1}{2} (a + b)h[/tex]where
a and b are the bases
h is the height
From the question
A = 135 m²
a = 20m
b = 7 m
Substitute the values into the above formula and solve for the height
That's
[tex]135 = \frac{1}{2} (20 + 7)h \\ 135 = \frac{1}{2} \times 27h \\ 135 \times 2 = 2 \times \frac{1}{2} \times 27h \\ 270 = 27h[/tex]Divide both sides by 27
That's
[tex] \frac{27h}{27} = \frac{270}{27} [/tex]We have the final answer as
10 mHope this helps you
What is 64 186 300 in standard form
Answer:
Sixty-four , one eighty six, three hundred
Step-by-step explanation:
That’s it.-,
Answer:
sixty four million, one-hundred eighty-six thousand three hundred
Step-by-step explanation:
Which of the following quadratic functions has a graph that opens downward? A.y= 3/2x^2 -3x+15 B.y= 5/2x-3x^2 C.y= 3x^2-x-1 D.y= -(2x^2-1)
it says if
ax^2+bx+c=0
a<0
answer is D because, there is (-) near of x^2
x + 3 = -3 what is x
x = - 6
Step-by-step explanation:x + 3 = - 3
x = - 3 - 3
x = - 6
Answer:-6
Step-by-step explanation:
X+3=-3
X=-3-3
X= -6
Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects
Answer:
Area of triangle ADC is 54 square unit
Step-by-step explanation:
Here is the complete question:
Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .
Step-by-step explanation:
Please see the attachment below for an illustrative diagram
Considering the diagram,
BC = BD + DC = 14
Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]
and AD be [tex]y[/tex]
To, find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
= [tex]\frac{1}{2}(14-x)(y)[/tex]
We will have to determine [tex]x[/tex] and [tex]y[/tex]
First we will find the area of triangle ABC
The area of triangle ABC can be determined using the Heron's formula.
Given a triangle with a,b, and c
[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
For the given triangle ABC
Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA
Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]
∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]
Then,
Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]
Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]
Area of triangle ABC = 84 square unit
Now, considering the diagram
Area of triangle ABC = Area of triangle ADB + Area of triangle ADC
Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]
Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]
Hence,
Area of triangle ABC = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
84 = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]
[tex]84 = 7y\\y = \frac{84}{7}[/tex]
∴ [tex]y = 12[/tex]
Hence, [tex]y =[/tex] AD = 12
Now, we can find BD
Considering triangle ADB,
From Pythagorean theorem,
/AB/² = /AD/² + /BD/²
∴13² = 12² + /BD/²
/BD/² = 169 - 144
/BD/ = [tex]\sqrt{25}[/tex]
/BD/ = 5
But, BD + DC = 14
Then, DC = 14 - BD = 14 - 5
BD = 9
Now, we can find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
Area of triangle ADC = [tex]\frac{1}{2} (9)(12)[/tex]
Area of triangle ADC = 9 × 6
Area of triangle ADC = 54 square unit
Hence, Area of triangle ADC is 54 square unit.
mZFEG=6x - 7 and mZFED=2x +41 , find the mZDEG
Answer:
this might be the answer
Two of the sides of a triangle are 18 and 25. The length of the third side is also a positive integer. How many different possible values are there for the third side length? (Assume that the triangle is non-degenerate.)
If answered correctly in under 20 minutes. You shall be made brainliest. Thank you.
Answer:
35
Step-by-step explanation:
Third side = x
Any two sides of triangle is always greater than another one.
25+18>x, 43>x
25+x>18, x>-7
18+x>25, x>7
7<x<43
43-7-1=35
Taxi fare in Tampa costs a base fee of $4 plus an additional $0.85 for each mile traveled. How much would a person pay to take a taxi from work to home if the distance is 17 miles? Question 14 options: A) $18.45 B) $21 C) $14.45 D) $20.40
Answer:
A. $18.45
Step-by-step explanation:
17 miles * .85 = 14.45 + 4.00 = 18.45
A manufacturer has a monthly fixed cost of $750 and a production cost of $15 for each item x that is produced. The product sells for $37 per item.
Write the equation of the total cost function, C(x), in terms of x.
Write the equation of the total revenue function, R(x), in terms of x.
Write the equation of the profit function, P(x), in terms of x. Simplify P(x) completely.
Answer:
The cost function is C(x) = 14x + 100000,
the revenue function is R(x) = 20x,
the profit function is P(x) = R(x) − C(x) = 20x − 14x − 100000 = 6x − 100000.
Step-by-step explanation:
HELP!!!!!
k+a=500(1). 3k+10a=3,600(2)
Which equation has at least one of its variables with a 1 as a coefficient?
Answer:
eqn 1. ( k + a = 500 )
Step-by-step explanation:
In eqn. 1 , both 'k' & 'a' have co-efficient as 1. But in eqn. 2 , 'k' has co-efficient as 3 & 'a' has co-efficient as 10.
Prices of a certain item have a distribution that is skewed to the left with outliers in the left tail. Which of the measures of central tendency is the best to summarize this data set?a. Mode b. Median c. Mean
Answer: b. Median
Step-by-step explanation:
The most common measures of central tendency are :
a. Mode - It is used in nominal data.
b. Median - It is used as central tendency when data is skewed or having outliers in the data.
c. Mean - It is the best measure of central tendency when data does not have outliers because it affect mean badly.
Given, Prices of item have a skewed distribution with outliers in the left tail.
That means , the best measure of central tendency to summarize this data set is median.
So, the correct option is b.
Find the p-value using Excel (not Appendix D): (Round your answers to 4 decimal places.) p-value (a) Right-tailed test t = 1.465, d.f. = 11 (b) Two-tailed test t = 2.522, d.f. = 12 (c) Left-tailed test t = –1.952, d.f. = 22
Answer:
(a) 0.0855
(b) 0.0268
(c) 0.0319
Step-by-step explanation:
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or greater than what was truly observed.
A small p-value (typically p ≤ 0.05) specifies sturdy proof against the null hypothesis (H₀), so we discard H₀. A large p-value (p > 0.05) specifies fragile proof against the H₀, so we fail to discard H₀.
(a)
Use the Excel function "=T.DIST.RT(1.465,11)" to compute the right-tailed p-value for a test statistic of, t = 1.465 and s degrees of freedom of, df = 11.
p-value = 0.0855
(b)
Use the Excel function "=T.DIST.2T(2.522,12)" to compute the two-tailed p-value for a test statistic of, t = 2.522 and s degrees of freedom of, df = 12.
p-value = 0.0268
(c)
Use the Excel function "=T.DIST(-1.952,22,TRUE)" to compute the left-tailed p-value for a test statistic of, t = -1.952 and s degrees of freedom of, df = 22.
p-value = 0.0319
Adib is scheduled to work from 7:00 a.m. to
11:00 a.m. and from 12:00 p.m. to 3:30 p.m.
Monday through Friday at the local
television station. How many total hours
does he work in a week?
1. The ages of Sonal and Manoj are in the ratio of 7:5. Ten years hence, the ratio of their ages will be 9:7. Find the present age
Answer:
Ratio of present ages of Sonal and Manoj = 7:5
Let us consider the ages of Sonal and Manoj to be 7x yrs. and 5x yrs. respectively.
After 10 years, ratio of their ages = 9:7
A/q, 7x+10/5x+10 = 9/7
or 9 (5x+10) = 7 (7x+10)
or 45x + 90 = 49x + 70
or 49x - 45x = 90 - 70
or 4x = 20
or x = 20/4 = 5 .
Therefore, present age of Sonal = 7x yrs. = 7 x 5 yrs. = 35 yrs.
present age of Manoj = 5x yrs. = 5 x 5 yrs. = 25 yrs.
Step-by-step explanation:
You helped me before so thank you
Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 20 years and over at random. Define two events:
A= the person chosen is obese
B= the person chosen is overweight, but not obese.
According to the National Center for Health Statistics,
P(A)=0.38
P(B)=0.33
1. Explain why events A and B are disjoint.
a. Because event B rules out obese subjects.
b. Because an obese person is certainly overweight.
c. Because some people may be considered obese and overweight.
d. Because some people are not obese nor overweight.
2. Say in plain language what the event "A or B" is.
a. "A or B" is the event that the person chosen is overweight or obese.
b. "A or B" is the event that the person chosen is overweight and obese.
c. "A or B" is the event that the person chosen is overweight or obese or both.
d. "A or B" is the event that the person chosen is not obese or not over weight.
Answer:
a. Because event B rules out obese subjects.
b. "A or B" is the event that the person chosen is overweight and obese.
Step-by-step explanation:
1. Disjoint events are those events which do not have the same elements. Event A and event B can only be disjoint if they both have separate subjects that is event A contains obese persons and event B contains overweight persons.
Therefore they are only disjoint when set B rules out ( leaves out) obese people. So choice a is the best answer.
Disjoint events are also called mutually exclusive events
2. In statistics the symbol or means including. Event A or B would mean including both types of person obese and overweight. In mathematical expression it is written as
P (A or B) = P (A) + P (B) For mutually exclusive events. ( disjoint events)
HELP ME WITH THIS (a+5)(b-3)
Answer:
The answer is ab-3a+5b-15
Step-by-step explanation:
apply de disruptive property by multiplying each term a+5by each term b-3
Hope this helps :)
Answer:
here you go ab-3a+5b-15
please helppp
copying an angle
copy angle def to the line so that S is the vertex.
The tale with be complete when you have constructed and angle with vertex S that is congruent to angle def
Answer:
Step-by-step explanation:
To copy an angle we follow the following steps,
1). Draw a working line with the help of a straightedge.
2). Now we put a point S as the vertex of the angle.
3). Construct an arc with a radius 'r' (any length ) from vertex S which intersects the working line say at V.
4). With the same radius we draw an arc from point E which intersects the line ED and EF at G and H respectively.
5). Mark an arc from point G which intersects line EF at I.
6). Measure the distance between points G and I with compass and mark an arc from point V which intersects the previous arc say at U.
7). Now join the points S and U.
Hence we copy any angle.
767,074 to the nearesr hundred thousand
Answer:
800,00
Step-by-step explanation:
6 is grater than 5 so u round up
Answer:
800,000
Step-by-step explanation:
I remember learning this in 4th (so long ago) basically since the 7 is in the hundred thousand place you have to look to the left of it, since 6 is above 5 you have to round 7 up which is how you get 800,000
What are the amplitude and midline?
Amplitude: 2; midline: y = 3
Amplitude: 1; midline: y = 3
Amplitude: 2; midline: y = 1
Amplitude: 3; midline: y = 2
Answer:
Amplitude 3; midline y=2
Step-by-step explanation:
The midline is the mean of both ends of the function in the graph.
[tex]\frac{5-1}{2}=2[/tex]
The amplitude is the vertical distance between the midline and one of the end points.
[tex]5-2=3[/tex]
(sorry for the basic math, i just want to make sure you know where im getting the values from)
Evaluate each expression if a = 12, b = 9, and c = 4.
2c(a + b)
answers
312
336
45
168
Answer:
168
Step-by-step explanation:
2c(a+b) = 2 . 4 . (12 + 9) = 2 . 4 . 21 = 8 . 21 = 168
help pls!! 15 points!
Answer:
Third option choice
Step-by-step explanation:
Notice that the angle is in the second quadrant, where the cosine is negative, the sine is positive and the tangent negative. In particular given the value of the cosine you are located at the angle 150 degrees, which gives a sine of 1/2 and a tangent given by [tex]-\sqrt{3} /3[/tex]
Therefore the third option is the correct one.
Your friend and your cousin discuss measuring with a ruler. Your friend says that you must always line up objects at the zero on a ruler. Your cousin says it does not matter. Decide who is correct and explain your reasoning.
Answer:
Your friend is correct.
Step-by-step explanation:
It is given that your friend says that you must always line up objects at the zero on a ruler. Your cousin says it does not matter.
We need to decide who is correct.
When we measure the length of any object we have to line up objects at the zero on a ruler, so that mark on the rules along the other end of the object represents the length of the object.
Let we have a pencil of length 5 cm.
If we place the rules on 0, then 5 is the mark on the rules along the other end of the pencil. So, height of the pencil is 5 cm.
If we place the rules on 1, then 6 is the mark on the rules along the other end of the pencil. So, height of the pencil is 6 cm, which is not correct.
Therefore, your friend is correct.
Which point on the number line best represents -2/2
Answer:
B
Step-by-step explanation:
HELP PLEASE, BRAINLIEST AND 15 POINTS
Answer:
Step-by-step explanation:
MP, same thing
Answer:
MP
Step-by-step explanation:
PM is the same thing as MP just flipped around. So, they are equal to each other.
Hope This Helps :)
compute 17÷2 enter your answer using remainder notation
Answer:8.5
Step-by-step explanation: