Simplify this expression 3x +2a +5x +4a

Answer:

[tex]D = 0.42m[/tex]

Step-by-step explanation:

Given

Force = 0.052 N when Distance = 1.6 m

Required

Find Force; when distance = 0.74 N

The question says force is inversely proportional to square of distance;

Let F represent Force and D represent Distance;

Mathematically;

[tex]F\alpha \frac{1}{D^2}[/tex]

Convert proportion to equation

[tex]F = \frac{k}{D^2}[/tex]

Where k is the proportionality constant; This means that k is always constant

Make k the subject of formula

[tex]F * D^2 = \frac{k}{D^2} * D^2[/tex]

[tex]FD^2 = k[/tex]

When F = 0.052 and D = 1.6; the value of k is as follows

[tex]0.052 * 1.6^2 = k[/tex]

[tex]0.13312 = k[/tex]

[tex]k = 0.13312[/tex]

When F = 0.74;

Recall that k is always constant; so [tex]k = 0.13312[/tex]

To solve for D, we'll make use of [tex]F = \frac{k}{D^2}[/tex]

Substitute [tex]k = 0.13312[/tex] and F = 0.74;

[tex]0.74 = \frac{0.13312}{D^2}[/tex]

Multiply both sides by D²

[tex]0.74 * D^2 = \frac{0.13312}{D^2} *D^2[/tex]

[tex]0.74 * D^2 = 0.13312[/tex]

Divide both sides by 0.74

[tex]\frac{0.74 * D^2}{0.74} = \frac{0.13312}{0.74}[/tex]

[tex]D^2 = \frac{0.13312}{0.74}[/tex]

[tex]D^2 = 0.17989189189[/tex]

Take square roots of both sides

[tex]D = \sqrt{0.17989189189}[/tex]

[tex]D = 0.42413664294[/tex]

[tex]D = 0.42m[/tex] (Approximated)

Answer:

r= 0.87

Step-by-step explanation:

It has the strongest correlation, which means it is closest to the line.

Answer:

work is shown and pictured

the volume of the cylinder is d)168 units

Answer:

Volume of a sphere = 4/3πr³

π = 3.14

r = radius which is 3in

Volume = 4/3 × 3.14 × 3²

= 37.68

= 38 cubic inches to the nearest hundredth

Hope this helps

Answer:

38 cubic inches

Step-by-step explanation:

Answer:

Primary source

Step-by-step explanation:

This is because it says "your" house, it means that you are the one looking and counting at the number of cars.

If this was not said "your", there is a higher chance that it is a secondary source, but in this case, it is a primary source.

Its Primary source

HOPE IT HELPS

Answer:

First one: true        Second one: true

Step-by-step explanation:

First Question: the lines will be parellel even though the shape grows or gets smaller

Second Question: the angle will stay the same even if it grows into a larger or smaller shape.

Answer:

the line of g(x) is steeper and has lower y intercept

Step-by-step explanation:

f(x)=1/4x-1

g(x)=1/2x-2

g(x) is steeper because the slope of gx is greater than f(x)

y intercept of gx=-2 and for f(x)=-1

the y intercept of g(x) is lower than the y intercept of f(x)

The steepness of a function is dependent on its slope.

The true statement is: (c) the line of g(x) is steeper and has lower y intercept

The equations are given as:

[tex]\mathbf{f(x)= \frac 14x-1}[/tex]

[tex]\mathbf{g(x)=\frac12x - 2}[/tex]

A linear function is represented as:

[tex]\mathbf{y = mx + b}[/tex]

Where:

For f(x)

[tex]\mathbf{m_1 = \frac{1}4}\\\mathbf{b = -1}[/tex]

For g(x)

[tex]\mathbf{m_1 = \frac{1}2}\\\mathbf{b = -2}[/tex]

By comparison:

This means that: the line of g(x) is steeper and has lower y intercept

Hence, the true option is: (c)

Read more about steep and intercepts at:

https://brainly.com/question/3309622

Answer: 1/3

the first answer choice

Step-by-step explanation:

Rate of increase is approximately 33%

Answer: 1/3

1st option

Step-by-step explanation:

Answer:

32.7 degress

Step-by-step explanation:

In this question we are to find the value of the angle

The best way to do with the information given is the cosine rule

Mathematically that would be;

y^2 = x^2 + z^2 -2xzCosY

where x = 90 ft , y = 55ft and z = 50 ft

Plugging the values we have;

55^2 = 90^2 + 50^2-2(90)(50)CosY

-7575 = -9000cosY

cosY = 7575/9000

cosY = 0.841666666667

Y = cos^-1 0.841666666667

Y = 32.68 degrees which is 32.7 to the nearest tenth

Answer:

32.7

Step-by-step explanation:

Answer:

5n = 1.75

Step-by-step explanation:

The 2 bars are equal thus lower equals upper, that is

5n = 1.75

Answer:

Coordinates of point P is [tex](-14,3)[/tex].

Step-by-step explanation:

Given that mid point of line segment [tex]\overline {PQ}[/tex] is at M(-9, 8.5).

Q is at (-4, 14).

Let coordinate of P be [tex](x,y)[/tex].

Using the ratio, we can say the following:

The coordinates of mid point [tex](X,Y)[/tex] of a line with endpoints [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:

[tex]X=\dfrac{(x_1+ x_2)}{2}[/tex]

[tex]Y=\dfrac{(y_1+ y_2)}{2}[/tex]

Using the formula for above given dimensions:

[tex]-9 =\dfrac{x+(-4)}{2}\\\Rightarrow x = -18+4 = -14[/tex]

[tex]8.5=\dfrac{(14+ y)}{2}\\\Rightarrow y = 17-14 =3[/tex]

So, the coordinates of point P are [tex](-14,3)[/tex].

Answer:

Step-by-step explanation:

measure of angles of a circle=360

angle ACB=360-82=278 degrees

Answer:

1463 : 5080

Step-by-step explanation:

There are 1463 cherry-flavored jelly beans.

There are 5080 non cherry-flavored jelly beans.

The ratio of cherry-flavored jelly beans to non-flavored jelly beans is:

1463 : 5080

Answer:

D. [tex]\sqrt{8}[/tex]

Step-by-step explanation:

We want to find the distance between (-6, 4) and (-8, 6).

First, we find the difference:

d = (-8 - (-6), 6 - 4)

d = (-8 + 6, 2)

d = (-2, 2)

We now find the magnitude:

[tex]|d| = \sqrt{x^2 + y^2}[/tex]

where x = x coordinate, y = y coordinate

[tex]|d| = \sqrt{(-2)^2 + (2)^2} \\\\|d| = \sqrt{4 + 4} = \sqrt{8}[/tex]

The answer is Choice D.

Answer:

D

Step-by-step explanation:

Khan said it was correct :)

Answer:

840 cm³

Step-by-step explanation:

To find it's volume , let's just divide the whole prism into two rectangular prisms.

Rectangular Prism 1:

Volume = [tex]Length * Width * Height[/tex]

Volume = 8 * 15 * 6

Volume = 720 cm³

Rectangular Prism 2:

Volume = [tex]Length * Width * Height[/tex]

Volume = 5 * 4 * 6

Volume = 120 cm³

Whole Prism:

Volume = 720+120

=> 840 cm³

Answer:

840 cm^3

Hope this helps :)

Answer:

The angle ZLK has a value of 75 degrees.

Step-by-step explanation:

We can calculate this as:

[tex]m\angle MLZ+m\angle ZLK=m\angle MLK\\\\(x+66)+(x+86)=130\\\\2x+152=130\\\\2x=130-152\\\\x=-22/2=-11\\\\\\m\angle ZLK=x+86=-11+86=75[/tex]

We replace the angles values in the equation, as both angles that are formed with Z (MLZ and ZLK), when added, gives as the angle MLK. This allows us to calculate x. The value for x is -11.

Then, with the value for x we can calculate any of both angles.

Answer:

Step-by-step explanation:

1050 flowers

3/10 of them are red=> 3/10 *1050=3*105=315 red flowers

2/5, (or 4/10),  are white =>4/10 * 1050=4*105=420 white flowers

=> 1050-(315+420)=1050-735=315 yellow flowers​

Answer:

2√6

Step-by-step explanation:

x + y = 6

xy = 3

Square the first equation.

x² + 2xy + y² = 36

Subtract 4xy from both sides.

x² − 2xy + y² = 36 − 4xy

Factor.

(x − y)² = 36 − 4xy

Substitute.

(x − y)² = 36 − 4(3)

(x − y)² = 24

Take square root.

x − y = ±√24

x − y = ±2√6

Take absolute value.

|x − y| = 2√6

Step-by-step explanation:

1/4 of the book = 66 pages

1/2 of the book = 132 pages

3/4 of the book = 132 + 66 = 198 pages

Answer:

Step-by-step explanation:

Total pages = 264

No of page read =[tex] \frac{3}{4} [/tex]( total pages)

[tex] = \frac{3}{4} \times 264[/tex]

Reduce the numbers with GCF 4

[tex] = 3 \times 66[/tex]

Calculate the product

[tex] = 198 \: pages[/tex]

Parul read 198 pages of the book till yesterday.

Again,

No.of pages to be read :

Total pages - No.of pages read

= 264 - 198

= 66 pages.

Thus, She has to read 66 pages more.

Hope this helps...

Good luck on your assignment..

Answer:

-1/16

-1/4

1

-4

16

Step-by-step explanation:

Put x as -4 and solve.

-4^-2 = 1/-4^2 = -1/16

-4^-1 = 1/-4 = -1/4

-4^0 = 1

-4^1 = -4

-4^2 = 16

Answer:

The mean salary for the 50 employees of the new company = $87

Step-by-step explanation:

Mean for any n set of number is \

mean = sum of n terms/ n

_________________________________

For company A

The mean salary for the 20 workers in company A is $90 per week,

mean = $90

n = 20

using above formula

90 = sum of salary of 20 workers/20

sum of salary of 20 workers = 90*20 = $1800

__________________________________________________

For company B

The mean salary for the 30 workers in company A is $85 per week,

mean = $85

n = 30

using above formula

85 = sum of salary of 30 workers/30

sum of salary of 30 workers = 85*30  = $2,550

____________________________________________

If two companies merge

Total salary for all the 50 workers for both the company =

sum of salary of 20 workers in company A + sum of salary of 30 workers in company B = $1800 + $2550 = $4350

Mean salary of 50 workers will be

n= 50

mean = Total salary of 50 workers/50

mean salary of 50 workers = 4350/50 = 87

The mean salary for the 50 employees of the new company = $87

Answer:

x =- 3 and y = -7

Step-by-step explanation:

2X-2Y=-8

X=2y + 11

We need to isolate both X and Y in both equations

so

2x-2y=-8

(add 2y to both sides)

2x=-8+ 2y

(divide both sides by 2)

x=-4+y and x=2y+11

because both of these equations are the same we can put them together

4+y=2y+11

(subtract y)

4=y+11

(subtract 11)

-7=y

so y = -7

then to find x you just need to plug in y to one of the equations

x=2(-7) + 11

x= -14 +11

x = -3

Answer:

x = - 19, y = - 15

Step-by-step explanation:

Given the 2 equations

2x - 2y = - 8 → (1)

x = 2y + 11 → (2)

Substitute x = 2y + 11 into (1)

2(2y + 11) - 2y = - 8 ← distribute and simplify left side

4y + 22 - 2y = - 8

2y + 22 = - 8 ( subtract 22 from both sides )

2y = - 30 ( divide both sides by 2 )

y = - 15

Substitute y = - 15 into (2) for corresponding value of x

x = 2(- 15) + 11 = - 30 + 11 = - 19

Solution is x = - 19, y = - 15

Answer:

(A)CPCTC

Step-by-step explanation:

Issa knows that ΔRED ≅ ΔTAN by the SSS theorem.

If two triangles are congruent, their corresponding parts will always be congruent. In fact, their corresponding angles will be equal.

Therefore, Issa concluded that ∠R ≅ ∠T by the fact that Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

The correct option is A.

Similarly, we can also conclude that:

Answer:

the 95th percentile for the sum of the rounding errors is 21.236

Step-by-step explanation:

Let consider X to be the rounding errors

Then; [tex]X \sim U (a,b)[/tex]

where;

a = -0.5 and b = 0.5

Also;

Since The error on each loss is independently and uniformly distributed

Then;

[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]

where;

n = 2000

Mean [tex]\mu = \dfrac{a+b}{2}[/tex]

[tex]\mu = \dfrac{-0.5+0.5}{2}[/tex]

[tex]\mu =0[/tex]

[tex]\sigma^2 = \dfrac{(b-a)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(0.5-(-0.5))^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(0.5+0.5)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(1.0)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{1}{12}[/tex]

Recall:

[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]

[tex]n\mu = 2000 \times 0 = 0[/tex]

[tex]n \sigma^2 = 2000 \times \dfrac{1}{12} = \dfrac{2000}{12}[/tex]

For 95th percentile or below

[tex]P(\overline X < 95}) = P(\dfrac{\overline X - \mu }{\sqrt{{n \sigma^2}}}< \dfrac{P_{95}- 0 } {\sqrt{\dfrac{2000}{12}}}) =0.95[/tex]

[tex]P(Z< \dfrac{P_{95} } {\sqrt{\dfrac{2000}{12}}}) = 0.95[/tex]

[tex]P(Z< \dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}}) = 0.95[/tex]

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1- 0.95[/tex]

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} = 0.05[/tex]

From Normal table; Z >   1.645 = 0.05

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1.645[/tex]

[tex]{P_{95}\sqrt{12} } = 1.645 \times {\sqrt{{2000}}}[/tex]

[tex]{P_{95} = \dfrac{1.645 \times {\sqrt{{2000}}} }{\sqrt{12} } }[/tex]

[tex]\mathbf{P_{95} = 21.236}[/tex]

the 95th percentile for the sum of the rounding errors is 21.236

The attached picture was omitted from the question.

Answer:

C = 41.88 feet

a = 33.1°

b = 56.9°

Step-by-step explanation:

From the diagram, we have a right angle triangle.

C = hypotenuse

C = sqrt(35^2 + 23^2)

C = sqrt(1225 + 529)

C = sqrt(1754)

C = 41.88 feet

The connecting Angles:

Angle 'a'

Using tan = opposite / Adjacent

Tan a = 23 / 35

tan a = 0.6571428

a = tan^-1 (0.6571428)

a = 33.1°

Angle 'b' :

Sum of angles in a triangle = 180

a + b + 90 = 180

33.1 + b + 90 = 180

b + 123.1 = 180

b = 180 - 123.1

b = 56.9°

Answer:

"Correct"

Triangles: Have three (3) sides

Quadriliaterals: QUAD being the key word means four (4)

"Incorrect"

Pentagons: Have five (5) sides

Hexagons: Have six (6) sides; key word being HEX

Heptagons: 7 sides (7)

Step-by-step explanation:

Answer:

3.38/6.21=54.428% (0.54428)

Step-by-step explanation:

biocapacity of grazing land of 0.85 ha/person+biocapacity of forest land of 2.53 ha/person

2.53+0.85=3.38

the percentage of biocapacity from grazing and forest land

3.38/6.21=54.428% (0.54428)

Answer:

Height = 3cm

Volume = 50.27cm^3

Step-by-step explanation:

Well to solve for the height with slant height and radius we can use the Pythagorean Theorem,

Which is [tex]a^2 + b^2 = c^2[/tex].

So we have c and a, so we have to fill those in.

(4)^2 + b^2 = (5)^2

16 + b^2 = 25

-16

b^2 = 9

[tex]\sqrt{b} \sqrt{9}[/tex]

b = 3cm

So to find the volume of a cone we use the following formula [tex]\pi r^2 \frac{h}{3}[/tex].

So we have the radius and height so we just fill those in.

(pi)(4)^2(3)/3

(pi)16(1)

pi*16

About 50.27cm^3