Four gallons of paint are used to paint 20 chairs and 5 small tables. If each chair and table used the same amount of paint, how many gallons are used to pain each piece of furniture? between what two wholes numbers lie?

Answer:

1. 8liters

2.5

Step -by - step explaination:

8litres= 100

16litres=200

24litres=300

32litres=400

and so on

Answer:

1000=450 (1+ 0.06) y

                         4

Step-by-step explanation:

In the paranthesis where it says 0.06 and then 4 at the bottom its supposed to be a fraction btw

Answer: To apply the Ratio Test to the series

∞Σn=1 (-1)^n 2^(n) n / (5 · 8 · 11 · ... · (3n - 2))

we need to compute the limit of the ratio of successive terms:

|a_{n+1}| / |an| = [(2^(n+1))(n+1)] / [(3n+1)(3n+2)(3n+3)]

Simplifying this expression, we get:

|a_{n+1}| / |an| = [(2n+2)/3] / [(3n+1)(3n+2)/3]

|a_{n+1}| / |an| = (2n+2)/(9n^2 + 11n + 2)

Now, taking the limit as n approaches infinity:

lim n → ∞ |a_{n+1}| / |an| = lim n → ∞ (2n+2)/(9n^2 + 11n + 2)

Since the degree of the numerator and denominator are equal, we can apply L'Hopital's rule:

lim n → ∞ |a_{n+1}| / |an| = lim n → ∞ (2/(18n+11)) = 0

Since the limit of the ratio is less than 1, by the Ratio Test, the series is absolutely convergent. Therefore, the series converges.

Answer:

The answer is B.200

Step-by-step explanation:

145.93×1.37=199.9

We need to multiply because the second team takes the times as longer than the first team. The answer is 200 because we need to roundup 199.9 into 200

Hope it helps :)

Answer:

145.9 cubic inches

Step-by-step explanation:

The volume of a triangular prism is:

1/2 x length x width x height

Use the formula with the given dimensions:

1/2 x 5.27 x 8.13 x 6.81 = 145.8875655

Round it up to the nearest tenths:

145.8875655 —> 145.9

I hope this helps!

Answer:

145.9 cubic inches

Step-by-step explanation:

Therefore, the critical values for the test statistic Z₀ for a significance level of 0.08 are Z₀ = ±1.750.

To find the critical values for the test statistic Z₀ for a hypothesis test of a population mean with known variance σ, we need to determine the values that divide the upper and lower tails of the standard normal distribution, based on the given significance level.

For a two-tailed test at a significance level of α = 0.08, we need to split the significance level equally between the two tails, resulting in α/2 for each tail. In this case, α/2 = 0.08/2 = 0.04.

To find the critical value Z₀, we need to find the value of Z such that the area under the standard normal curve to the right of Z is equal to α/2 = 0.04.

Using a standard normal distribution table or a calculator, we can find that the critical value Z for an upper tail area of 0.04 is approximately Z = 1.750.

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Answer:

1/11

Step-by-step explanation:

First you have to times 1/3 and 1/2 and then you get 1/6. Then you add 1/3 and 1/2 and that's 1/5. then you add them both.

Answer:

7850

Step-by-step explanation:

Net worth: Assets-debt

The assets are:

car

investments

The debts:

credit cards

so we have

(3700+5400)-1250= 7850

If twice a certain number plus 4 is at the same number plus 10. Then the number is 6.

Let x = the number

According to the given statement, "Twice a certain number plus 4 is at the same number plus 10," we can form an equation:

2x + 4 = x + 10

Solve this equation to find the value of x.

2x - x + 4 = x - x + 10

x + 4 = 10

Next, subtracting 4 from both sides of the equation:

x + 4 - 4 = 10 - 4

Simplifying:

x = 6

Therefore, the number is 6.

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Answer:

sorry I could not help you but I wish you luck

Answer:

i think it is c

Step-by-step explanation:

The answer of this given question is ||u + v||^2 = ||u||^2 + ||v||^2.

Here are the steps involved in verifying the Pythagorean Theorem for the vectors u and v:

STEP 1: Compute u·v = (3, -1, -3) · (-1, -3, 0) = 3 · (-1) + (-1) · (-3) + (-3) · 0 = -3 + 3 + 0 = 0.                                                                           Since the dot product of u and v is zero, they are orthogonal.                                                                                                                STEP 2: Compute ||u||^2 and ||v||^2: ||u||^2 = 3^2 + (-1)^2 + (-3)^2 = 9 + 1 + 9 = 19||v||^2 = (-1)^2 + (-3)^2 + 0^2 = 1 + 9 + 0 = 10       STEP 3: Compute u + v and ||u + v||^2: u + v = (3, -1, -3) + (-1, -3, 0) = (2, -4, -3)||u + v||^2 = 2^2 + (-4)^2 + (-3)^2 = 4 + 16 + 9 = 29.                                                                                                                                                                                                               Now, we can verify the Pythagorean Theorem:  ||u + v||^2 = ||u||^2 + ||v||^2⇒ 29 = 19 + 10. This equation is true, so we have verified the Pythagorean Theorem for the vectors u and v. Therefore, the answer is:||u + v||^2 = ||u||^2 + ||v||^2.

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we have that

The fence around the garden is equal to

where

pi=3.14

D=25 ft

substitute

To find out the cost, multiply 64.25 ft by $8.00 per linear foot

so

64.25*8=$514

Answer:

a = -5

b = 2

Step-by-step explanation:

a + b = -3

a - b = -7    Add together

2a     = -10  Divide both sides by 2

a = -5

Use either of the two original equations to find b.

a + b = -3  Substitute -5 for a

-5 + b = -3  Add 5 to both sides

-5 + 5 +b = -3 + 5

b = 2

Check:

a + b = -3

-5 + 2 = -3

-3 = -3 Checks

a - b = -7

-5 - 2 = -7

-7 = -7 Checks

Answer:

C) 24

Step-by-step explanation:

Set x equal to the number of cousins Juan has:

5/8 = 15/x

Cross-multiply: 5x = 15 × 8

5x = 120

x = 24

Answer:

ta

Step-by-step explanation:

The equivalent expression is 1.4k - 1.16. Therefore, the numerical coefficient of k is 1.4.

The given expression is −0.4(−3.5k+2.9).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Now, simplify the given expression as follows:

−0.4(−3.5k+2.9)

= 1.4k - 1.16

So, numerical coefficient of k is 1.4

The equivalent expression is 1.4k - 1.16. Therefore, the numerical coefficient of k is 1.4.

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Using the combination formula, it is found that 4845 combinations of four students are possible.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, four students are taken from a set of 20, hence the number of combinations is given by:

\(C_{20,4} = \frac{20!}{4!16!} = 4845\)

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432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.

Here,

(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..

so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways

(2) Let us take the multiples of 2..

4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.

Thus 2*2*1=4

3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.

We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same

Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..

Total 2*2=4

Combined way of  integers = 27∗4∗4=432 ways

There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.

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Answer:

Step-by-step explanation:

26:45

Supercomputers are the most powerful computers at any given time, but are built especially for assignments that require arithmetic speed.

The supercomputers, which are the most advanced and high-performance computers available, are specifically constructed to handle assignments that demand rapid arithmetic processing.

These machines are optimized for executing complex mathematical operations and simulations, enabling them to tackle problems that require immense computational power.

By harnessing parallel processing, massive memory capacities, and specialized architectures, supercomputers excel in solving scientific, engineering, and research challenges that necessitate exceptional arithmetic speed.

Their capabilities contribute to advancements in various fields, including weather forecasting, molecular modeling, astrophysics, and cryptography.

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Answer:

It would be $281.60

Step-by-step explanation:

Answer: 34 units

Step-by-step explanation:

I took the test

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

The cost of the total fuel consumed can be determined by the conversion of the Euro into Dollars. The total cost of the fuel is 383 USD.

Significant Figure

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

Euro and Dollars:

The cost of the total fuel consumed can be determined by the conversion of the Euro into Dollars.

Given here,

Total distance = 5000 km

Average fuel consumption = 6 lit per 100 km = 0.06 lit / km

Average fuel cost = 1.063 EUR/lit

1 EUR  = 1.2 USD

So, Total fuel consumption,

⇒ 5000 km × 0.06 lit /km

⇒ 300 lit

Thus, Total fuel cost,

⇒ 300 lit × 1.063 EUR/lit

⇒ 318.9 EUR

⇒ 318.9 EUR × 1.2 USD

⇒ 383 USD

Therefore, the total cost of the fuel is 383 USD

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Answer:

Let m be the number of muffins.

a) 4m <= 30

b) m <= 7.5, so the maximum number of muffins to buy is 7.

c) $4 × 7 = $28, so $2 will be left over.

Answer:  see proof below

Step-by-step explanation:

Use the following Half-Angle Identities:

sin² A = (1 - cos 2A)/2

cos² A = (1 + cos 2A)/2

Proof LHS → RHS:

LHS:                          sin⁴ A

Expand:                     sin² A · sin² A

\(\text{Half-Angle:}\qquad \qquad \bigg(\dfrac{1-\cos (2A)}{2}\bigg)\bigg(\dfrac{1-\cos (2A)}{2}\bigg)\)

\(\text{Distribute:}\qquad \qquad \dfrac{1-2\cos (2A)+\cos^2 (2A)}{4}\)

\(\text{Half-Angle:}\qquad \qquad \dfrac{1-2\cos (2A)+\frac{1+\cos (2\cdot 2A)}{2}}{4}\)

\(\text{Simplify:}\qquad \qquad \dfrac{\frac{2}{2}[1-2\cos (2A)]+\frac{1+\cos (4A)}{2}}{4}\)

                         \(=\dfrac{2-4\cos (2A) + 1 + \cos (4A)}{8}\)

                         \(=\dfrac{1}{8}\bigg(3-4\cos (2A)+\cos (4A)\bigg)\)

LHS = RHS  \(\checkmark\)

Let's start from LHS...

LHS = sin^4A = sin^2A * sin^2A

We can apply a few formulas here;

cos 2A = 1 - 2sin^2A

sin^2A = (1 - cos2A) / 2

cos2A = 2cos^2A - 1

cos^2A = (1 + cos2A) / 2

According to the second formula, sin^2A * sin^2A = (1 - cos2A) / 2 * (1 - cos2A) / 2.

(1 - cos2A) / 2 * (1 - cos2A) / 2 = 1/4(1 - cos2A)^2

We can simplify "(1 - cos2A)^2." Remember that (a - b)^2 = a^2 - 2ab + b^2. Similarly (1 - cos2A)^2 = (1 - 2cos 2A + cos^2 2A);

1/4(1 - cos2A)^2 = 1/4(1 - 2cos 2A + cos^2 2A)

According to the fourth formula, cos^2 2A = (1 + cos4A) / 2;

1/4(1 - 2cos 2A + cos^2 2A) = 1/4(1 - 2cos 2A + (1 + cos4A) / 2)

= (taking LCM) 1/4( (2 - 4cos 2A + 1 + cos4A)/2 )

= (simplified) 1/8(3 - 4cos 2A + cos 4A)

Revenue: R(x) = x\(^2\) + 2x, Cost: C(x) = 500 + 24x, Profit: P(x) = x\(^2\)- 22x - 500, Marginal profit at x = 90 is 158 dollars.

(a). The revenue function in terms of x can be calculated by multiplying the price p by the quantity x:

R(x) = p * x

    = (x + 2) * x

    = x\(^2\) + 2x

(b). The cost function in terms of x can be determined by adding the fixed cost and the variable cost per unit:

C(x) = Fixed Cost + Variable Cost per unit * Quantity

    = 500 + 24x

(c). The profit function in terms of x can be obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(x)

    = (x\(^2\)+ 2x) - (500 + 24x)

    = x\(^2\) - 22x - 500

(d). To find the marginal profit when 90 memory sticks are produced and sold each week, we need to calculate the derivative of the profit function with respect to x and then substitute x = 90:

Marginal Profit = P'(x) = 2x - 22

                    = 2 * 90 - 22

                    = 158

Therefore, the marginal profit when 90 memory sticks are produced and sold each week is 158 dollars.

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Answer:  When you divide two integers with the same sign, the result is always positive. Just divide the absolute values and make the answer positive. When you divide two integers with different signs, the result is always negative.

Step-by-step explanation:

Answer:

positive

negative

Step-by-step explanation: