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The computation shows that the number of weeks that it take to repair this stretch of road will be 4 weeks.

From the information given, we are told that a thirteen kilometers stretch of road needs repairs and that the workers can repair three and half kilometers of road per week.

The question is simply for us to calculate the number or weeks that it will take to be able to repair the stretch of road.

Therefore, based on the information given, it should be noted that to get the number of weeks that will be used to repair the road, we simply have to divide the total distance or the road by the distance that is repaired every week.

Therefore, the number of weeks that it will take to be able to repair this stretch of road will be:

= 13/3.5

= 3.7

= 4 weeks approximately

Therefore, based on the information given, the number of weeks that's required is 4 weeks.

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3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

Answer: 2xy • (4x - 5y)

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

 ((8 • (x2)) • y) -  (2•5xy2)

STEP 2:

Equation at the end of step 2:

 (23x2 • y) -  (2•5xy2)

STEP 3:

STEP 4:

Pulling out like terms

4.1     Pull out like factors :

  8x2y - 10xy2  =   2xy • (4x - 5y)

Final result :

 2xy • (4x - 5y)

It's important to work through the problems yourself to improve your understanding and problem-solving skills.

For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.

To find the slope of a line given two points, you can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.

To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.

It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.

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Answer:

PR= 4.2  AC= 18

Step-by-step explanation:

1)divide by same sides

QP/GF

3/5=0.6

in order to get PR

7(GH) *0.6 =4.2

BA/ML

30/50=0.6

in order to get AC

30(LN) * 0.6= 18

Answer:

d

Step-by-step explanation:

Answer:

it should be 2/12 and 9/11

Step-by-step explanation:

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Step-by-step explanation:

sum=addition

3/10 +1/3

find the LCM of 10 and 3 Which is 30

9+10/30=19/30

I hope it helps ☺️

The solution must be inside the area in green

we have the next points

A. (-4, 2) point in yellow

B. (-1, -11) point in green

C. (4, 2) point in purple

D. (0, 0) point in red

E. (-4, -2)​ point in blue

as we can see the only points that are a solution

B. (-1, -11)

C. (4, 2)

D. (0, 0)

Answer:

(7,0)

Step-by-step explanation:

By Multiplying 4 and 7 (aka x), it will equal 28.

Multiplying 9 and y, (aka 0) , it will equal to 0

4(7)+9(0)=28

multiplying -4 by 7 will equal to -28 ,minus y which is 0, total will be -28

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

Answer:

420 = 4.2 x 100 = 4.2 × 102

Step-by-step explanation:

Answer:

do it like step by step down below

Step-by-step explanation:

123

+ 240

+ 300

= 663

With lining them up

Step-by-step explanation:

Say you have 357 + 872

You would position your numbers so that they line up then you add the numbers that line up with each other, if your number is 10 or more you need to carry the first didgit over above the next row if your number was 14 you would carry the 1 over above the next row then you would add that number to the multiplicated 2 other numbers.

       357

+      872

_________

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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Answer:

Step-by-step explanation:

-5y = -4x + 5

5y = 4x - 5

y = 4/5x - 1

perp. -5/4

y - 3 = -5/4(x - 5)

y - 3 = -5/4x + 25/4

y - 12/4 = -5/4x + 25/4

y = -5/4x + 37/4

The probability of losing the game is 0.9399. So, the answer is 0.9399.

The probability of losing the game is 0.9399. To determine the probability of losing, we must subtract the probability of winning from 1.

The probability of losing is equal to the complement of the probability of winning, and the complement of an event is the probability of the event not occurring.

Therefore, we will calculate the probability of the event not winning.  

We know that the probability of winning a two-spot Keno game is 0.0601.

This means that the probability of not winning is 1 - 0.0601 = 0.9399.

Therefore, the probability of losing the game is 0.9399. So, the answer is 0.9399.

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Answer:

20 for both

Step-by-step explanation:

hope this helps

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

\(\mathbf { \int _ c Fdr= - \dfrac{9 \pi ^2}{8} - \dfrac{3}{2} }\)

Step-by-step explanation:

GIven that:

\(r(t) = (sin \ t, cos \ t, t)\)

\(r' (t) = (cos \ t, -sin \ \ t, 1)\)

\(F(x, y, z) = ( -x, -2y , - z)\)

\(F(r(t)) = ( sin \ t , - 2 cos \ t, - 1 t)\)

\(F(r(t)) \times r'(t) = (sin \ t, - 2 \ cos \ t , -1 \ t)( cos \ t , - sin \ t , 1 )\)

\(= sin t \ cos t + 2 \ sin t \ cos t - 1t\)

\(= 3sint \ cost - 1 t\)

\(\int _ c Fdr = \int ^b_a f(r(t)) \times r'(t) \ dt\)

\(= \int^{3 \pi/2}_0 \ [3 sin \ t \ cos \ t - 1 \ t ] \ dt\)

\(= 3 \int ^{3 \pi/2} _0 \ cos \ t ( sin \ t \ dt ) - 1 \int ^{3 \pi/2}_0 \ (t) \ dt\)

Let   cos t = u   &

sint  dt = du

\(= 3 \int ^{3 \pi/2_} } _0 \ udu - 1 \int ^{3 \pi/2}_0 \ (t) \ dt\)

\(= 3 [ \dfrac{u^2}{2}]^{3 \pi/2}_0 - 1 [ \dfrac{t^2}{2}]^{3 \pi/2}_0\)

\(= \dfrac{3}{2} [ cos ^2 \ t ] ^{3 \pi/2} _0- \dfrac{1}{2} ( \dfrac{ 3 \pi }{2 })^2 - 0^2\)

\(= \dfrac{3}{2} [ cos ^2 \ \dfrac{3 \pi}{2} - cos ^2 \ 0 ] - \dfrac{1}{2}( \dfrac{9 \pi^2}{4})\)

\(= \dfrac{3}{2} ( 0 -1 ) - \dfrac{9 \pi^2}{8}\)

\(= - \dfrac{3}{2} - \dfrac{9 \pi ^2}{8}\)

\(\mathbf { \int _ c Fdr= - \dfrac{9 \pi ^2}{8} - \dfrac{3}{2} }\)

To answer this question, we apply:

∫CF×dr = ∫ c F (r(t)) × dr

Solution is:

( 1/2)  - (9/8)×π

We know  r(t) =  sint i + cost j + t k

Then  dr = ( cost i - sint j + k ) dt

And  F ( x , y , z ) = -x i - 2y j - z k

Then  F ( r(t)) =  - sint i - 2 × cost j - t × k

And F ( r(t)) × dr  = (- sint×cost + 2 ×sint ×cost - t ) dt

∫F (r(t)) × dr = ∫ (- sint×cost + 2 ×sint ×cost - t ) dt  

Integration limits 0≤  t  ≤ ( 3/2 ) π

∫ (- sint×cost + 2 ×sint ×cost - t ) dt  = ∫ ( sint ×cost - t ) dt

∫ sint ×cost × dt  - ∫ t ×  dt

∫F (r(t)) × dr = (1/2) sin²t  - ( 1/2) × t² | 0  y  (3/2) π

∫F (r(t)) × dr = (1/2)× ( -1)² - 0 - ( 9/8 ) × π - 0

∫F (r(t)) × dr = ( 1/2)  - (9/8)×π

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Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

Answer:

D

Step-by-step explanation:

I'm not 100% sure but since when you remove the square roots on a and b, you have to add it to X

Answer:

B

Step-by-step explanation:

\(\dfrac{\sqrt{a}}{\sqrt{b}}=x\\\\Take \ square \ both \ sides,\\\\(\dfrac{\sqrt{a}}{\sqrt{b}})^{2}=x^{2}\\\\x^{2}=\dfrac{a}{b}\)

The value of x is 14.

We know in an isosceles triangle an isosceles polygon is a polygon with at least two sides of equal length.

We have two sides measured 2x-9 and x+ 5.

From the figure the length of sides are equal then

2x-9 = x+ 5

2x- 9- x = 5

x-9 = 5

Add 9 to both sides of the equation:

x - 9 + 9 = 5 + 9

x= 14

Thus, the value of x is 14.

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To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

If 24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09: 51,960 is invested at 15%, and 22,823 is invested at 9%.

Let's x represent the amount invested at 15%

Let the  amount invested at 9% = 24,783 - x.

Interest earned at 15% is 0.15 * x

Interest earned at 9% is 0.09 * (24,783 - x)

We can set up the equation: 0.15x = 0.09 * 24,783 - 0.09x + 894.09

Solving for x:

0.06x = 24,783 * 0.09 + 894.09

0.06x = 2223.47 + 894.09

0.06x = 3117.56

x = 51,960

So,

(24,783 - x)

24,783 - 51,960

= 22,823

Therefore 51,960 is invested at 15%, and 22,823 is invested at 9%.

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Complete question :

The Venn diagram relating to the question can be found in the picture attached below :

Answer:

A.) 15 ; b.) 17 ; c.) 20 ; d.) 19 ; e.) 55 ; 67; 76 ;100 ; F.) 369

Step-by-step explanation:

Let :

Cars = C ; Motorcycle = M ; Tricycle = T ; Walking = W

a) How many students ride in a tricycle, motorcycle and car going to their school

Intersection of the 3 modes;

(C n M n T) = 15 ; it is the number which sits in between all the three circles.

B.) How many students ride in both a motorcycle and a tricycle?

(M n T) = 17 ; number in the middle of both circles representing motorcycle and tricycle

C.) How many students ride in both a motorcycle and a car?

(M n C) = 20 ; number in the middle of both circles representing motorcycle and Car

D) How many students ride in both a car and tricycle?

(C n T) = 19 ; number in the middle of both circles representing Car and tricycle

e.)How many students go to school

in a car only = 55

in a motorcycle only = 67

Tricycle only = 76

Walking = 100

F.) How many Grade Seven students of Koronadal National Comprehensive High School are there in all?​

(100 + 67 + 76 + 55 + 19 + 20 + 17 + 15) = 369

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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Answer:

Please find the complete question and its solution in the attached file.

Step-by-step explanation:

Shortest had survived after 6741 hours \(2.5\%\) of the lights burnt.

\(\to 0.15\% + 2.35\% = 2.50\%\)