Mrs kanja ,miss kanene and Mrs nyaga have to mark a form three contest for 160students .They take 5mins ,4mins and 12mins respectively to mark a script .If they all start to mark at 9.00am non-stop ,what is the shortest time they ca n take to complete the marking?

Hey there! I'm happy to help!

LENGTH OF CONVEYOR BELT

We are going to have to use some trigonometry. Let's think of this as a right triangle. The conveyor belt is the diagonal or the hypotenuse, while the ground is  and the height of the room make a right angle as the legs.

We have a sixty degree angle between the conveyor belt and the ground. This is means that the 21 foot height is the opposite side of our right triangle. So, we are dealing with the opposite and the hypotenuse, so we will use the sine. The sine of an angle is equal to the opposite length divided by the hypotenuse length.

We will set up the following equation and solve for the length of our conveyor belt (c).

[tex]sin60=\frac{21}{c}[/tex]

We multiply both sides by c.

[tex]c(sin60)=21[/tex]

We divide both sides by sin60.

[tex]c=\frac{21}{sin60}[/tex]

If we evaluate this with a calculator, we get that c is equal to 24.2487113..., or 24 when rounded to the nearest foot.

So, the supplies travel 24 feet from one end to the other.

DURATION OF TRAVEL

We want to find how long it takes the supplies to move across the conveyor belt. We see that every minute, it moves 75 feet. We want to see how many minutes it will take to move 24 feet, as that is the length of the conveyor belt as we previously solved. Let's set up a proportion.

[tex]\frac{feet}{minute} =\frac{75}{1} =\frac{24}{m}[/tex]

We cross multiply, giving us the following equation.

75m=24

We divide both sides by 75.

m=0.32

We want to round to the nearest tenth of a minute, so it will take 0.3 minutes for the supplies to move to the second floor.

Have a wonderful day! :D

Answer:

1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The joint equations of diagonals are;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Step-by-step explanation:

The equations are;

x² - 7·x + 6 = 0......................(1)

y² - 14·y + 40 = 0.................(2)

Factorizing equation (1) and equation (2) , we get

x² - 7·x + 6 = (x - 6)·(x - 1) = 0

Which are vertical lines at points x = 6 and x = 1

For equation (2) , we get

y² - 14·y + 40 = (y - 10)·(y - 4) = 0

Which are horizontal lines at point y = 4 and y = 10

The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The points of intersection of the equations are;

(1, 4), (1, 10), (6, 4), and (6, 10)

The end point of the diagonals are;

(1, 10), (6, 4) and  (1, 4), (6, 10)

The slope of the diagonals are;

(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5

The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)

y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5

5·y = 56 - 6·x

The other diagonal is therefore;

y - 4 = 6/5×(x - 1)

y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5

5·y = 6·x + 14.

The joint equations of diagonals are therefore;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Answer:  -1 < x < 3

Step-by-step explanation:

[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]

Step 1   The denominator cannot equal zero:

x + 2 ≠ 0    and     4 - x ≠ 0

     x ≠ -2                4 ≠ x

Place these restrictive values on the number line with an OPEN dot:

    <----------o-------------------o--------->

                -2                       4

Step 2   Find the zeros (subtract 1 from both sides and set equal to zero):

[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]

Add the zeros to the number line with an OPEN dot (since it is <):

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 3    Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):

Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive

Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive

Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative

Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive

Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive

          +         +        -          +       +

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 4  Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.

Negative values only occur between -1 and 3

So the solution is:     -1 < x < 3

Answer:

x-6/2=2x/7

7x-42=4x

7x-4x=42

3x= 42

X = 42/3

Answer:

number ten: x=5

number two: x=5³/5

Step-by-step explanation:

number ten:

4x + 3x - 9 = 26

4x + 3x = 26+9

7x = 35

x = 5

number two:

3x + 2x - 8 = 20

3x + 2x = 20+8

5x = 28

x = 5³/5

Answer:

ok so

faf

Step-by-step explanation:

Factor 20x2 + 25x – 12x – 15 by grouping.

1. Group terms with common factors.

2. Factor the GCF from each group.

3. Write the polynomial as a product of binomials.

(20x2 – 12x) + (25x– 15)

4x(5x – 3) + 5(5x – 3)

(5x – 3)(

x +  

)

Answer:

A. You can see which shape the bases are, how many bases there are, how many faces there are, and how many edges there are.

B. The bases are ABC and DEF, and I know because they are two congruent triangles on two opposite sides of the shape.

Answer: "B. [tex]12p^6q^5[/tex]

Step-by-step explanation:

The given monomial : [tex]6a^2b^8c[/tex]

Degree of this monomial = Sum of powers of variables=2+8+1= 11

Let's check all the options

A   [tex]18t^8[/tex]

Degree = 8

B [tex]12p^6q^5[/tex]

Degree = 6+5 =11

C [tex]9a^5b^3c^2[/tex]

Degree = 5+3+2=10

D [tex]6w^4x^2y^3z^3[/tex]

Degree =4+2+3+3=12

We can see that only option B has degree 11.

So, the monomial has the same degree as [tex]6a^2b^8c[/tex] is "B. [tex]12p^6q^5[/tex] "

Answer:

32

Step-by-step explanation:

If y is 2 times as much as x, then 1 = 2

5 x 3 = 15 + 1 = 16

10 x 3 = 30 + 2 = 32, or 16 x 2 = 32

Please tell me if I'm wrong.

Answer: D. The quadratic function has two distinct real zeros.

There are no complex roots as a quadratic's roots are maxed out at 2. The fundamental theorem of algebra says that if you have an nth degree polynomial, then the max number of real roots is n.

This quadratic's roots are distinct because the two x intercepts are in different places. Each x intercept is a root.

Answer:

500×4 =2400 I think would help u

Hey there! I'm happy to help!

The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).

So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.

We cannot divide by 2 because 47 is odd.

We cannot divide by 3 because it gives us 15.6666...

We can't divide by 4 because 47 is odd.

We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.

We can't divide by 6 because 47 is odd.

We can't divide by 7 because it gives us 6.714285....

We can't divide by 8 because 47 is odd.

We can't divide by 9 because it gives us 5.2222

And we obviously can't divide it by 10.

Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.

I hope that this helps! Have a wonderful day! :D

Answer: 47 is a prime number

The exponent of prime number 47 is 1 . Adding 1 to that exponent we get (1+1)=2

Factor of 47: 1, 47

Answer:

176m²

Step-by-step explanation:

When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.

Step 1

Find the Outer surface area of the cone

Outer / Lateral surface area of a cone =

πrl

Where l = √r² + h²

r = 4 m

h = 3m

Outer surface area = 22/7 ×√4² + 3²

= 22/7 × √16 + 9

= 22/7 × √25

= 22/7 × 5

= 62.83185m²

Step 2

Find the outer surface area of a cylinder

= 2πrh

π = 22/7

r = 4m

h = 4.5

π = 22/7

Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5

= 113.09734m²

Step 3

The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder

= 62.83185m² + 113.09734m²

= 175.92919m²

Approximately ≈ 176m²

Therefore, the outer surface area of the tent = 176m²

Answer:

17 quarters

Step-by-step explanation:

Let q = quarters

n = nickels

.25q + .05n = 5.90

we have 16 more nickels than quarters so add 16 quarters to make them equal

n = q+16

Substitute

.25q + .05( q+16) = 5.90

Distribute

.25q+.5q+.80=5.90

Combine like terms

.30q +.8 = 5.90

Subtract .8 from each side

.30q = 5.10

Divide each side by .3

.3q/.3 = 5.1/.3

q = 17

Answer:

Gisel have:

17

quarters

Step-by-step explanation:

1 nickel = 5 cents

1 quarter = 25 cents

1 dollar = 100 cents

5,90 dollars = 5,9*100 = 590 cents

then:

n = t + 16

5n + 25t = 590

n = quantity of nickels

t = quantity of quarters

5(t+16) + 25t = 590

5*t + 5*16 + 25t = 590

5t + 80 + 25t = 590

30 t = 590 - 80

30 t = 510

t = 510 / 30

t = 17

n = t + 16

n = 17 + 16

n = 33

Check:

5n + 25t = 590

5*33 + 25*17 = 590

165 + 425 = 590

Answer:

57 units^2

Step-by-step explanation:

First find the area of the triangle on the left

ABC

It has a base AC which is  9 units and a height of 3 units

A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5

Then find the area of the triangle on the right

DE

It has a base AC which is  6 units and a height of 1 units

A = 1/2 bh = 1/2 ( 6) *1  = 3

Then find the area of the triangle on the top

It has a base AC which is  3 units and a height of 3 units

A = 1/2 bh = 1/2 ( 3) *3  = 9/2 = 4.5

Then find the area of the rectangular region

A = lw = 6*6 = 36

Add them together

13.5+3+4.5+36 =57 units^2

Answer:

Total Area = 57 sq. units

Step-by-step explanation:

will make it simple and short

Total Area = A1 + A2 + A3

A1 = (7 + 6) * 6/2 = 39 sq. units  (area of a trapezoid)

A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)

A3 = 1/2 (3 * 3) = 4.5 sq. units  (area of a triangle)

Total Area = 39 + 13.5 + 4.5 = 57 sq. units

Answer:

6 grams

Step-by-step explanation:

(3/2)*4 = 12/2 = 6

Answer:

[tex]\boxed{\sf 6 \ grams \ of \ food}[/tex]

Step-by-step explanation:

1 week = [tex]\frac{3}{2} g\ of \ the \ food[/tex]

Multiplying both sides by 4

4 weeks = [tex]\frac{3}{2} * 4[/tex]

4 weeks = 3 * 2 g of the food

4 weeks = 6 g of food

Answer and Step-by-step explanation:

A) Probability of taken two odd numbered token without replacement:

P(3) = 2/5 = 0.4

P(7) = 1/4 = 0.25

Construct a probability distribution:

 X          3          7

p(X)      0.4      0.25

B) Mean of the probability distribution:

E(X) = ∑xp

E(X) = 3*0.4 + 7*0.25

E(X) = 2.95

Variance of the probability distribution:

V(X) = [tex]\Sigma X^{2}p - [E(X)]^{2}[/tex]

V(X) = [tex]3^{2}*0.4+7^{2}*0.25 - (2.95)^{2}[/tex]

V(X) = 7.1475

Mean and variance of the probability distribution are 2.95 and 7.145, respectively.

Answer:

100 minutes

Step-by-step explanation:

It takes each of the 3 cats about 1 minute to catch one mouse. If the same goes for the 100 cats, it will take them 100 minutes to catch 100 mice.

Hope that helps.

Answer:

3 min  

Step-by-step explanation:

These are all independent actions.

If you put 1 cat in a room with 1 mouse, it will take 3 min to catch the mouse.

If you put 2 cats in a room with 2 mice, they will act independently and it will take 3 min for each one to catch a mouse.

If you put 3 cats in a room with 3 mice, they will act independently and it will take 3 min for each one to catch a mouse.

If you put 100 cats in a room with 100 mice, they will act independently and it will take 3 min for each one to catch a mouse.

Each cat will finish at the same time — 3 min.

Answer:

area of polygon = 88 sq. units

Step-by-step explanation:

lets make it simple, short and accurate.

area of polygon = total area - total area of triangles

total area = 11 * 12 = 132

triangle 1 = 1/2 * 5 * 5 = 12.5

triangle 2 = 1/2 * 3 * 6 = 9

triangle 3 = 1/2 * 3 * 8 = 12

triangle 4 = 1/2 * 3 * 7 = 10.5

total area of triangle = 12.5 + 9 + 12 + 10.5 = 44

area of polygon = 132 - 44 = 88 sq. units

Answer:

The area of the irregular polygon:

88 units²

Step-by-step explanation:

The irregular polygon is insert in a rectangle

The strategy is:

1 - calculate the rectangle total area

2- calculate the area of each right triangle

3.- substracte the total area of the 4 right triangles from the area of the rectángule

then:

1.-

Ar = 12*11 = 132 units²

Ar = rectangle area

2.-

At₁ = (5*5)/2 = 25/2 = 12.5 units²

At₂ = (6*3)/2 = 18/2 = 9 units²

At₃ = (7*3)/2 = 21/2 = 10.5 units²

At₄ = (8*3)/2 = 24/2 = 12 units²

At total = 12.5 + 9 + 10.5 + 12 = 44 units²

At = right triangle areas

3.-

Ap = 132 - 44 = 88 units²

Answer:

Option (3)

Step-by-step explanation:

This question is not complete; here is the complete question.

Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?

Coordinates of the vertices of the triangle ABC are,

A(-3, 3), B(1, -3) and C(-3, -3)

When triangle ABC is reflected over y = -3

Coordinates of the image triangle A'B'C' will be.

A(-3, 3) → A'(-3, -9)

B(1, -3) → B'(1, -3)

C(-3, -3) → C'(-3, -3)

Further ΔA'B'C' is dilated by a scale factor of 2 about the origin then the new vertices of image triangle A"B"C" will be,

Rule for the dilation will be,

(x, y) → (kx, ky) [where 'k' is the scale factor]

A'(-3, -9) → A"(-6, -18)

B'(1, -3) → B"(2, -6)

C'(-3, -3) → C"(-6, -6)

Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                      = [tex]\sqrt{(-3-1)^2+(3+3)^2}[/tex]

                      = [tex]\sqrt{52}[/tex]

                      = [tex]2\sqrt{13}[/tex]

Length of A"B" = [tex]\sqrt{(-6-2)^2+(-18+6)^2}[/tex]

                         = [tex]\sqrt{64+144}[/tex]

                         = [tex]\sqrt{208}[/tex]

                         = [tex]4\sqrt{13}[/tex]

Therefore, [tex]\frac{\text{AB}}{\text{A"B"}}=\frac{2\sqrt{13}}{4\sqrt{13}}[/tex]

[tex]\frac{\text{AB}}{\text{A"B"}}=\frac{\sqrt{13}}{2\sqrt{13}}[/tex]

[tex]AB(2\sqrt{13})=A"B"(\sqrt{13})[/tex]

Option (3) is the answer.

Answer:

c(1) = -15

c(n) = c(n - 1) + 4

Step-by-step explanation:

Given arithmetic sequence is,

-15, -11, -7, -3...........

Common difference between each successive and previous term is,

d = -11 - (-15)

  = -11 + 15

  = 4

Since recursive formula of the arithmetic sequence is represented by,

a₁ = First term of the sequence

a(n) = a(n - 1) + d

where a(n) is the nth term and a(n-1) is the previous term of the nth term.

Form the given sequence,

c₁ = -15

c(n) = c(n - 1) + 4

Step-by-step explanation:

Multiplying the vertex matrix with the matrix gives us a reflection matrix. The most common matrix reflections are seen as reflection in the x - axis as well as reflection in the y - axis.  

It can also be reflect by  90 degree or by 180 degree.

So, one way to remember the elements is by multiplying the given matrix by a unit matrix. And on the other hand you can remember the elements remembering by what degree we are reflecting the matrix. This way makes it easier to remember the elements.

The explanation regarding the elements of the reflection is explained below:

The following information should be considered:

Learn more: https://brainly.com/question/17961582?referrer=searchResults

Answer:

[tex]\displaystyle \boxed{y = -1\frac{1}{3}x + 22}[/tex]

Step-by-step explanation:

Parallel Equations have SIMILAR RATE OF CHANGES [SLOPES], so keep [tex]\displaystyle -\frac{4}{3}[/tex]as is and do this:

14 = −4⁄3[6] + b

14 = −8 + b

+ 8 + 8

_________

[tex]\displaystyle 22 = b \\ \\ y = -1\frac{1}{3}x + 22[/tex]

I am joyous to assist you at any time.

Answer:

The correct option is;

Formal

Step-by-step explanation:

The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices

Formal diction is used when when communicating in a situation that is formal

Formal diction uses languages that is devoid of slang and grammatically correct

Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.

Answer:

7y - 2y² - 4

Step-by-step explanation:

5y - 5y² - 5 + 2 + 2y + 3y² - 1

5y + 2y - 5y² + 3y² - 5 + 2 - 1   (combine like terms)

7y - 2y² - 4

Answer:

29

Step-by-step explanation:

conjugate of a+ib=a-ib

conjugate of 2-5i=2+5i

(2+5i)(2-5i)=2²-(5i)²=4-25i²=4-25(-1)=4+25=29

Answer:

29

i had the same question and 29 was the right answer

Answer:

D

Step-by-step explanation:

This would be using the SSS.

Which means knowing three sides.

The other options do not relate to any of the SSS, SAS, ASA, RHS

Hope that helped!!! k

[tex]_{10}C_3=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot 3}=120[/tex]

Question :-

Answer :-

[tex] \rule{200pt}{3pt}[/tex]

Combinations refers to the number of ways of selecting from a set when the order is not important. The number of combinations of n objects taken r at a time is given by [tex]\sf C(n, r) = \dfrac{n!}{(n - r)!r!}, n \geqslant r[/tex].

Solution :-

As per the provided information in the given question, we have been given that the number of combinations of 10 students taken 3 at a time. We have been asked to calculate the ways that she can choose 3 of the 10 students.

To calculate the ways that she can choose 3 of the 10 students, we will apply the formula below :-

[tex] \qquad \bigstar \: \: \: \boxed{ \sf{ \: \: C(n, r) = \dfrac{n!}{(n - r)!r!} \: \: }}[/tex]

Substitute the given values into the above formula and solve for C:

[tex]\sf:\implies{ C(n, r) = \dfrac{n!}{(n - r)!r!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{(10 - 3)!3!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{7!3!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8 \cdot \cancel{7!}}{ \cancel{7!}3!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8}{3 \cdot 2}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{720}{6}}[/tex]

[tex]\sf:\implies \bold{ C(10, 3) = 120 \: ways}[/tex]

Therefore :-

[tex]\\[/tex]

Learn more about combinations at https://brainly.com/question/11955073

Have a great day! <33

Answer:

AB = 72°

Step-by-step explanation:

The inscribed angle ADC is half the measure of its intercepted arc, thus

56° = [tex]\frac{1}{2}[/tex] ( m ABC ) ← multiply both sides by 2

112° = ABC

ABC = AB + BC = AB + 40, so

AB + 40 = 112 ( subtract 40 from both sides )

AB = 72°