Factor 18r+12s. Write your answer as a product with a whole number greater than 1.

Let x and y be the unit rates at which one large pump and one small pump works, respectively.

Two large/one small operate at a unit rate of

(1 pool)/(4 hours) = 0.25 pool/hour

so that

2x + y = 0.25

One large/three small operate at the same rate,

(1 pool)/(4 hours) = 0.25 pool/hour

x + 3y = 0.25

Solve for x and y. We have

y = 0.25 - 2x   ==>   x + 3 (0.25 - 2x) = 0.25

==>   x + 0.75 - 6x = 0.25

==>   5x = 0.5

==>   x = 0.1

==>   y = 0.25 - 2 (0.1) = 0.25 - 0.2 = 0.05

In other words, one large pump alone can fill a 1/10 of a pool in one hour, while one small pump alone can fill 1/20 of a pool in one hour.

Now, if you have four each of the large and small pumps, they will work at a rate of

4x + 4y = 4 (0.1) + 4 (0.05) = 0.6

meaning they can fill 3/5 of a pool in one hour. If it takes time t to fill one pool, we have

(3/5 pool/hour) (t hours) = 1 pool

==>   t = (1 pool) / (3/5 pool/hour) = 5/3 hours

So it would take 5/3 hours, or 100 minutes, for this arrangement of pumps to fill one pool.

Answer:

pi × 18cm^2

Or approximately,

56.52cm^2 (using 3.14 for pi)

or

56.5487cm^2 (using pi button on calculator)

Step-by-step explanation:

Area of a circle is pi times [radius squared].

All circles are 360°.

Problem can be solved by finding area of whole circle, and then using ratios.

Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2

80° / 360° = Area[shaded] / (pi × 81cm^2)

pi × 18cm^2 = Area[shaded]

((If you read my answer before the edit, I am sorry. I made a calculator error.))

A=16x²-8x+1

16x²-8x+1=l²

(16x²-4x)-(4x+1)=l²

4x(4x-1)-1(4x-1)=l²

x=1/4 or 1

Therefore

since x=1/4

l²=1/4=>l=>√(1/4)

l=1/2

since x=1

l²=1=>l=>√1

l=1

Therefore the length of each sides

1 or 1/2

Answer:

0.1294

Step-by-step explanation:

Number of chocolates in box = 38

Number of nuts = 8

Number of caramel = 16

Number of solid chocolate = 14

Since 2 are selected in a row and not replaced, then;

Probability of first being solid chocolate = 14/38

Probability of second being solid chocolate after first one = 13/37

Thus;

P(2 selected in a row being solid chocolate) = 14/38 × 13/37 = 0.1294

Answer:

The 19th term is 99.

Step-by-step explanation:

We can write a direct formula and use it to find the 19th term. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

Since the first term is 9 and the common difference is 5:

[tex]\displaystyle x _ n = 9+5(n-1)[/tex]

To find the 19th term, let n = 19. Thus:

[tex]x_{19} = 9+5(19-1)[/tex]

And evaluate:

[tex]\displaystyle \begin{aligned} x_{19} &= 9+5(18) \\ &= 9+90 \\ &= 99\end{aligned}[/tex]

The 19th term is 99.

Answer:

Step-by-step explanation:

Make g the subject means solve for g:

Answer: its going to be 3 dollars and 67 cents

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hypotenuse

cos x = 13/20

Taking the inverse cos of each side

arccos ( cos x ) = arccos( 13/20)

x = arccos ( 13/20)

x =49.45839

x = 49  to the nearest whole number

sin theta = opp/ hyp

sin y = 13/20

Taking the inverse sin of each side

arcsin ( sin y ) = arcsin( 13/20)

y = arcsin ( 13/20)

y=40.5416

y = 41 to the nearest whole number

Answer:

base = 3x - 1

height = x

area of triangle = (1/2)bh

22 = (1/2)(3x-1)(x)

44 = (3x-1)(x)

44 = 3x^2-x

0 = 3x^2-x-44

0 = 3x^2-12x+11x-44

0 = (3x^2-12x)+(11x-44)

0 = 3x(x-4)+11(x-4)

0 = (x-4)(3x+11)

x = {-11/3, 4}

throw out the negative solution (extraneous) leaving

x = 4 m (height)

.

Base:

3x - 1 = 3(4) - 1 = 12 - 1 = 11 

Step-by-step explanation:

I hope it will help you

Answer:

12/5

Step-by-step explanation:

Recall that trig function tan = opposite / adjacent

Find tan A

Opposite side of angle A = 24

Adjacent of A = 10

Tan (A) = 24/10

24/10 can be simplified to 12/5

Answer:

[tex]\frac{12}{5}[/tex]

Step-by-step explanation:

Tan is equal to [tex]\frac{opposite}{adjacent}[/tex]. The side opposite to angle A is BC while the side adjacent to it is AC. This means tan(A) is [tex]\frac{BC}{AC}[/tex]. It is given that BC is 24 and AC is 10, so we can substitute those values in and simplify:

tan(A) = [tex]\frac{24}{10} = \frac{12}{5}[/tex]

Answer:

Step-by-step explanation:

757 minutes = 12 hours 37 minutes

Answer:

120

Step-by-step explanation:

All the interior angles in a regular hexagon are 120 degrees.

Answer:

length of its each side is 786 cm

Step-by-step explanation:

l² = 617796cm²

l = √617796

l = 786cm

Answer:

[tex]area \: of \: square = {l}^{2} [/tex]

[tex]617796 = {l}^{2} [/tex]

[tex] \sqrt{617796 } = l[/tex]

[tex]786 = l[/tex]

therefore ,l=786cm

Answer:

a) Sinusoidal functions are y = a sin [b(x-h)] + k    (or)                                        

y = a cos [b(x-h)] + k

Where a is amplitude a= (max-min)/2=(16-2)/2=7

period p= 2π/b

            b=2π/30

            Horizontal transformation to 10 units right h=10

            k= (max+min)/2=(16+2)/2=9

h = 7 cos [π/15(t-10)]+ 9

b) t=10min=600 sec

substitue in the above equation

h=5.5m

The Euler's formula relates the vertices, faces and the edges of a polyhedron.

The correct option is (e) [tex]V = 6[/tex]    [tex]E = 10[/tex]    [tex]F = 6[/tex]     [tex]6- 10 + 6 = 2[/tex]

First, we count the number of faces. This is the flat parts of the shape.

The attached shape has 6 flat surfaces.

So:

[tex]F = 6[/tex]

Next, we count the number of edges. This is where two faces meet.

The attached shape has 10 edges;

So:

[tex]E = 10[/tex]

Lastly, we count the number of vertices. This is where two edges meet.

The attached shape has 6 vertices.

So:

[tex]V = 6[/tex]

Using Euler's formula, we have:

[tex]V - E + F = 2[/tex]

Substitute values for V, E and F

[tex]6- 10 + 6 = 2[/tex]

[tex]2 = 2[/tex]

Hence, the polyhedron has 6 vertices, 10 edges and 6 faces

Read more vertices, edges, and faces at:

https://brainly.com/question/23347978

Answer:

hello,

Step-by-step explanation:

[tex]cos(3\theta)+cos(4\theta)\\\\=2*cos(\dfrac{4\theta+3\theta}{2} )*cos(\dfrac{4\theta-3\theta}{2} )\\\\\boxed{=2*cos(\dfrac{7\theta}{2} )*cos(\dfrac{\theta}{2} )}[/tex]

we observe that this figure could be divided into a triangle and a rectangle.

for the area of the triangle, bxh/2, we have 15 x 12/2 = 90

and for the rectangle, we have 5 x 12 = 60

so, 90 + 60 = 150

hope it helps :)

Answer:

Last option= 30 minutes

Answer:

3.9

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 +b^2 =c^2 where a and b are the legs and c is the hypotenuse

7^2 + h^2 = 8^2

49 + h^2 = 64

h^2 = 64-49

h^2 = 15

Taking the square root of each side

sqrt(h^2) = sqrt(15)

h = 3.87298

To the nearest tenth

h = 3.9

Answer:

6

Step-by-step explanation:

4n - 12 < 2n + 2 is for n=6

4×6 -12 < 2×6 +2

24 - 12 < 12 + 2

12 < 14 correct

for n=7

4×7 - 12 < 2×7 + 2

16 < 16 incorrect

for n=8

4×8 - 12 < 2×8 + 2

20 < 18 incorrect

for n=9

4×9 - 12 < 2×9 + 2

24 < 20 incorrect

so, only for n=6 is the expression true.

Answer:

6

Step-by-step explanation:

4n - 12 < 2n + 2 is for n=6

4×6 -12 < 2×6 +2

24 - 12 < 12 + 2

12 < 14 correct

for n=7

4×7 - 12 < 2×7 + 2

16 < 16 incorrect

for n=8

4×8 - 12 < 2×8 + 2

20 < 18 incorrect

for n=9

4×9 - 12 < 2×9 + 2

24 < 20 incorrect

so, only for n=6 is the expression true.Step-by-step explanation:

Answer:

x =6

Step-by-step explanation:

5(x-2) = 14+x

Distribute

5x-10 = 14+x

Subtract x from each side

5x-x -10 = 14+x-x

4x-10 = 14

Add 10 to each side

4x-10+10 = 14+10

4x= 24

Divide by 4

4x/4 = 24/4

x =6

Answer:

5(×-2)=14+×

5x-10=14+x

5x-x=14+10

4x=24

x=6

Answer:

The correlation has no unit of measurement; it is just a number.

Correlation requires both variables to be quantitative.

Step-by-step explanation:

Correlation refers to the measure of the relationship between two variables. The correlation between two variables is measured using the correlation Coefficient which may take any value between - 1 and 1 ; the closer the correlation Coefficient is to either 1 or - 1, the greater the relationship with negative depicting a negative association and positive depicting a positive relationship between the variables. The correlation Coefficient requires that both variables are numeric (quantitative). The correlation Coefficient has no unit of measurement.

Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

it has all the properties matching with a rhombus

answer from gauthmath

=====================================================

Explanation:

We can rewrite 5 as 5s^0, since s^0 = 1 where s is nonzero.

Think of 2s as 2s^1

With those ideas in mind, the original polynomial turns into 5s^0 + 2s^1

Sorting the terms so that the largest exponent is first gets us the standard form 2s^1 + 5s^0

The largest exponent is the degree, so the degree is 1.

Side note: This trick only works for single variable polynomials.

Answer:

B: the accuracy rate of most people is barely above the 50% guessing level

Step-by-step explanation:

Bond and DePaul carried out a research and analysis on the accuracy of deception judgments in 2016.

This research involved synthesizing of results gotten from 206 research documents as well as a total of 24483 judges.

In this research and analysis, there were a couple of discoveries when people tried to discriminate lies from the truth and these discoveries include; average percentage of correct lie-truth judgments, percentage of those who correctly classified lies as deception and also percentage of those who classified truths as non-deceptive e.t.c. In conclusion, part of their discoveries was that the accuracy rate of most people is barely above the 50% guessing level.

This corresponds to option B.

Answer:

ab=9 and ac=12

Step-by-step explanation:

The fish's length will affect the mean because the new mean length will be less than 14.2 inches. That is option A.

Mean is defined as the sum of all the data values divided by the count of values in a data set.

What a new value is added to a data set such as the group of fishes, it will affect the fish mean by reducing it to less than its former mean value which is 14.2 inches.

Therefore, the fish's length will affect the mean because the new mean length will be less than 14.2 inches.

Learn more about mean here:

https://brainly.com/question/1136789

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Answer:

2=124  124/2

4=248 248/4

5=310 310/5

8=496 496/8

Step-by-step explanation:

40 + 22 = 62

62 x 2 = 124

62 x 4 = 248

62 x 5 = 310

62 x 8 = 496

i think