A water tank holds 36 gallons
of water. A new water tank holds
25% more water. How many
gallons of water can the new
water tank hold?

Answer:

he will have 29 nickles

Step-by-step explanation:

I just solved it on paper, hope it helps and if it's right

The distance between you and train 1 at time t is

20.6 km + (0.2 km/h) t

and the distance between you and train 2 at time t is

59.7 km - (2.1 km/h) t

The trains are an equal distance away from you when

20.6 km + (0.2 km/h) t = 59.7 km - (2.1 km/h) t

Solve for t :

(2.3 km/h) t = 39.1 km

t = 17 h

at which point they are

20.6 km + (0.2 km/h) (17 h) = 24 km

away from you.

Answer:

112 customers will pay cash next week

Step-by-step explanation:

1,100/138=7.97= approximately 8

Multiply the amount of customers who paid cash, 14 by 8.

Answer:

side lengths: 12 feet, 9 feet, 4 feet

Step-by-step explanation:

Conditions for unique triangles with 3 sides:

9 + 6 = 15

As 15 < 18 this is NOT a unique triangle

9 + 4 = 13

As 13 > 12 this IS a unique triangle

3 + 2 = 5

As 5 < 6 this is NOT a unique triangle

14 + 4 = 18

As 18 < 24 this is NOT a unique triangle

Answer:

25 and 49

Step-by-step explanation:

25 = 1, 5, 25

49 = 1, 7, 49

Hope this helps!

The statistical test at the 5% significance level shows that we fail to reject the null hypothesis.

From the information given, the level of significance is 0.05 and n is 600. The degree of freedom will be:

= 4 - 1 = 3

The test statistic will be:

= ∑(O - E)²/E

= 6.92

The critical value is also given as 7.815 from the table. Since the test statistic is lesser than the critical value, we fail to reject the null hypothesis.

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Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, [tex]\pm i, \pm 2i, \pm 3i[/tex], a sixth degree function with no real zeros is formed, so the answer is Yes.

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Answer:

297.99

Step-by-step explanation:

367.99-45-25=297.99

Answer:

20 cm²

Step-by-step explanation:

Look at the diagram attached.

If the height is 4cm, we will have two sides that are 4cm for our rectangle.

We can label the other sides as x.

They are both x since opposite sides of a rectangle are equal in length.

We can make an equation with our perimeter:

[tex]2(4) + 2(x) = 18\\8 + 2x = 18\\2x = 10\\x = 5[/tex]

Now that we know the length & height, we can calculate the area:

4 × 5 = 20 cm²

I assume the limit you're asked to copmute is supposed to be

[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5}[/tex]

Rationalize the numerator by multiplying it by its conjugate:

[tex]\dfrac{\sqrt{x+4}-3}{x-5} \times \dfrac{\sqrt{x+4}+3}{\sqrt{x+4}+3} = \dfrac{\left(\sqrt{x+4}\right)^2-3^2}{(x-5) \left(\sqrt{x+4}+3\right)} = \dfrac{x-5}{(x-5) \left(\sqrt{x+4}+3\right)}[/tex]

Since x is approaching 5, we have x ≠ 5 and can cancel the factors of x - 5 to remove the discontinuity.

Then

[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5} = \lim_{x\to5} \frac1{\sqrt{x+4}+3} = \frac1{\sqrt9+3} = \boxed{\frac16}[/tex]

because the simplified limand is continuous at x = 5.

Answer:

it is C. 1/6th

Step-by-step explanation:

When the bill came, she would need to pay Millersburg sales tax of 8% and would want to leave a 15% tip on the original $300. Including tax and tip, Camilla's meal cost $369.

Given that,

Original Meal Cost: $300

Sales Tax: 8% of the original meal cost

Tip: 15% of the original meal cost

Total Cost: Sum of the original meal cost, sales tax, and tip

Original Meal Cost = $300

Sales Tax = 8% of $300 = 0.08 * $300 = $24

Tip = 15% of $300 = 0.15 * $300 = $45

Total Cost = Original Meal Cost + Sales Tax + Tip

Total Cost = $300 + $24 + $45 = $369

Including tax and tip, Camilla's meal cost $369.

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Answer:

0.7.

Step-by-step explanation:

x^2 = 0.7x

x^2 - 0.7x = 0

x(x - 0.7) = 0

x = 0, 0.7.

After solving the quadratic equation x² = 0.7x , we get that the original number is 0.7

Quadratic equation is an equation which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the standard quadratic equation in x is given by

ax²+bx+c =0, where a, b, c are constants and a≠0

We can  solve this equation by factorizing ax²+bx+c and  putting those factors equal to zero to solve for x.

Let a non zero number be x, x≠0 and given that the square of a non zero number is equal to the 70% of the original number.

As 70 % of the original number = 70/100(x) = 0.7 x

⇒ x² = 0.7 x

⇒x²-0.7 x = 0

⇒ x(x -0.7)= 0

⇒ x =0 and x - 0.7 = 0

⇒  x = 0.7, as we have given that x is a non zero number

Therefore, the original number is 0.7

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Step-by-step explanation:

I guess you mean it is

12 cm long, 4cm wide and 5 cm high.

and the fabric goes outside on the box ? strange, but ok.

a box (like a die) has 6 sides in the form of 3 pairs of equal rectangles :

top-bottom, left-right, front-back

the surface area is the sum of all 6 rectangles.

top-bottom :

2 × 12×4 = 2 × 48 = 96 cm²

left-right :

2 × 4×5 = 2 × 20 = 40 cm²

front-back :

2 × 12×5 = 2 × 60 = 120 cm²

in total

120 + 40 + 96 = 256 cm²

Using it's concept, it is found that there is a [tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

Since the events are independent:

[tex]p = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]

[tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.

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Answer:

Below in bold.

Step-by-step explanation:

a) The volumes will be in the ratio of the cubes  of the edges.

So volume of A / volume B = 20^3 / 5^3

Volume A / 25 = 8000/125

Volume a = (25* 8000) / 125

= 8000/ 5

= 1600 cm^3.

b) ratio of the surface area of A to surface area of B

=  20^2 : 5^2

= 400:25

= 16:1.

c. The volume of pyramid B is 25 cm*3 so it' height is  25 / area of its base = 25/5^2

= 1 cm.

Now its slant height = √(1^2 + (2.5)^2)

= √7.25

= 2.6926 cm

So surface area = 25 + 4 * 1/2 * 5 * 2.6926

= 51.926

= 51.93 cm^2 to nearest hundredth.

and the surface area of pyramid B = 51.926 * 16

= 830.82 cm^2 to nearest hundredth.

Answer: A) -0.5 and -0.5

Step-by-step explanation:

Answer:

The answer is C. 2.94

Step-by-step explanation:

All you have to do is take 588 and divide it by 200 which gives you the answer of 2.94.

Answer:

312 divided by 24 = 13.

So the hourly rate is 13/hour

Answer:

$13.00. To find the hourly rate you need to divide the total amount Jackie earned by the amount of hours she worked in total. When you divide 312 by 24 you will get 13, therefore Jackie makes a total of $13.00 per hour.

Lets see

ATQ

Answer:

a = 3 cm

Step-by-step explanation:

The length of each side of a cube is 3 cm.

(Refer to the attachment)

Answer:

1. 9 6/12

2. 4 3/12

Step-by-step explanation:

I did the math on it.

Answer:

3. 9 (6/12)

4. 4 (3/12)

Step-by-step explanation:

Question 3:

6 (2/6) × 1 (1/2)

multiply the whole number by the denominator

6 x 6 = 36 + 2 (numerator) = 38/6

2 x 1 = 2 + 1 = 3/2

(38/6) x (3/2)

multiply (3/2) by 3

3 x 3 = 9

2 x 3 = 6

38/6 x 9/6

38 x 9 = 342

6 x 6 =  36

19/2 = 9 (1/2) or 9 (6/12)

Question 4:

5 (2/3) × (3/4)

15 + 2 = 17

17/3 x 3/4

17 x 4 = 68

3 x 4 = 12

3 x 3 = 9

4 x 3 = 12

(68/12) x (9/12)

68 x 9 = 612

12 x 12 = 144

612/144 = 4 (1/4) or 4 (3/12)

I hope this helps! I'm sorry if this is confusing.

Answer:

a₃₀ = 201

Step-by-step explanation:

there is a common difference between consecutive terms , that is

453 - 462 = 444 - 453 = - 9

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 462 and d = - 9 , then

a₃₀ = 462 + (29 × - 9 ) = 462 - 261 = 201

[tex]2 {ab}^{2} + {8a}^{2} b[/tex]

[tex]2ab(b + 4a)[/tex]

to factorise first, find the highest common factor of each of the terms in the expression then, write the highest common factor (HCF) in front of any brackets atlast, fill in each term in the brackets by multiplying out.

The value of the expression after factorization will be;

⇒ 2ab (b + 4a)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2ab² + 8a²b

Now,

Factorize the expression as;

⇒ 2ab² + 8a²b

⇒ 2ab × b + 2×2×2a×a×b

⇒ 2ab (b + 4a)

Thus, The value of the expression after factorization will be;

⇒ 2ab (b + 4a)

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Answer:

13

Step-by-step explanation:

First you would create a ratio.

Convert 3 1/4 gallons in a decimal -> 3.25 gallons

If 1 gallon = 4 quarts, then

[tex]\frac{3.25}{1} =\frac{x}{4}[/tex]

Now, solve for x via cross multiplying

[tex]x=13[/tex]

and sidenote ripp iready i feel your pain

Answer:

£28.8 Milllion

Step-by-step explanation:

£30,000,000 × 0.8 = £24,000,000 (Depreciates by 20%)

£24,000,000 × 1.2 = £28,800,000 (Appreciates by 20%)