Find
(1) a + b,
(2) 2a + 3b,
(3) |a|, and |a − b|.
a = 5i + j, b = i − 2j

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:

Answer:

B

Step-by-step explanation:

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.

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.

Answer:

A. $18.45

Step-by-step explanation:

17 miles * .85 = 14.45 + 4.00 = 18.45

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.

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.

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.

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

x = - 6

x + 3 = - 3

x = - 3 - 3

x = - 6

Answer:-6

Step-by-step explanation:

X+3=-3

X=-3-3

X= -6

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!

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)

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

Answer:

Step-by-step explanation:

Area of a trapezoid is given by

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

Divide both sides by 27

That's

We have the final answer as

Hope this helps you

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.

Answer:

168

Step-by-step explanation:

2c(a+b) = 2 . 4 . (12 + 9) = 2 . 4 . 21 = 8 . 21 = 168

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)

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

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

Answer:

this might be the answer

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

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:

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!

it says if

ax^2+bx+c=0

a<0

answer is D because, there is (-) near of x^2

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

Answer:8.5

Step-by-step explanation:

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 :)