13.62

Round to the
nearest whole
number.

Answer: 1327.3 feet cubed\(V=\pi\cdot r^2\cdot h\\V=\pi\cdot(6.5)^2\cdot10\\V=\pi\cdot 42.25\cdot10\\V=422.5\pi ft^3\\or\\V\approx 1327.3 ft^3\)

Step-by-step explanation:

Volume of a cylinder:

The value of x and y which is on midsegment of the triangle is 1 and 11.

What is midsegment?

 A triangle's midsegment is the section of the triangle's shape that connects the midpoints of its two sides. a section of a line connecting the midpoints of two triangle's sides. There are three possible midsegments in a triangle. The section of a line between the midpoints of two triangle sides is known as a midsegment. Due to the fact that triangles have three sides, they also have three midsegments. A line drawn by joining the midpoints of any two of a triangle's sides is known as the midsegment.

let us assume triangle as ABC and DE is the midsegment .

Where  DE=2x+1 and BC = 8x-2 .

According to the midsegment theorem ,

=> DE = 1/2 BC

=> 2x+1 = 1/2(8x-2)

=> 2x+1=4x-1

=> 2x=2

=> x=1

Now AB divided intp AD=3z and DB=z+22

Then, AD=DB

=> 3z = z+22

=> 2z = 22

=> z = 11.

Hence the value of x=1 and z= 11.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Step-by-step explanation:

Given: A line is drawn between points \((x_2,x_1)\,,\,(y_2,y_1)\)

To find: distance between the two points

Solution:

A coordinate plane is a two-dimensional plane formed by the intersection of a  y-axis and x-axis. x-axis and y-axis are perpendicular lines that intersect each other at the origin.

Let d denotes distance between the two points \((x_2,x_1)\,,\,(y_2,y_1)\)

Use the formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The distance between the two points show on the coordinate plane is D = √[(x₂-x₁)²+(y₂-y₁)²]. Therefore, the correct answer is option C.

The given coordinate points are (x₁, y₁) and (x₂, y₂).

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula.

On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is

Distance = √[(x₂-x₁)²+(y₂-y₁)²].

Therefore, the correct answer is option C.

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Answer:

\(f(g(x))=x\)

\(g(f(x))=x\)

Step-by-step explanation:

Given functions:

   \(f(x)=\log_{10}(x)\)

   \(g(x)=10^x\)

The composite function f[g(x)] means to substitute the function g(x) in place of the x in function f(x):

\(\begin{aligned}f[g(x)]&=\log_{10}[g(x)]\\&=\log_{10}\left(10^x\right)\\&=x\log_{10}\left(10\right)\\&=x(1)\\&=x\end{aligned}\)

The composite function g[f(x)] means to substitute the function f(x) in place of the x in function g(x):

\(\begin{aligned}g[f(x)]&=10^{f(x)}\\&=10^{\log_{10}(x)}\\&=x\end{aligned}\)

Log rules used

\(\log_ax^n=n\log_ax\)

\(\log_aa=1\)

\(\:a^{\log _a\left(x\right)}=x\)

Answer:

A) 1/13

Step-by-step explanation:

In a deck of 52 cards, there are 13 clubs. Out of those 13 clubs, there is 1 ten.

Since a club was drawn, the probability of the card being a ten is:

1 ten out of 13 clubs = 1/13

Answer:

https://www.mathpapa.com/algebra-calculator.html

Step-by-step explanation:

Mathpapa is a pretty good and reliable algebra calculator would say to use it. It also has Inequalitys and system of equations calculators.

Answer: Symbolab, and this site are going to carry you through algebra.

Answer:

C

Step-by-step explanation:

When the whole number plus the exponent is being put to an exponent, you multiply the exponents

Selling price = $6.37 .

Selling price = $6.94

Selling price = $346.80

1)

Sales revenue = 6,000

Less:-Variable costs ($1.5 per unit 1,000) = 1,500

Less:- Fixed costs = (1,700)

Operating Income = 2,800

Variable costs and Fixed costs have increased.

Hence, in order to maintain the same Operating Income, the selling price should be higher than the current selling price .

Thus to maintain same operating income the selling price should be $6.37 .

2)

The computation is given below:

Sales price = ( Total sales revenue ÷ packages sold)

Total sales revenue = ( Total Cost + Operating income )

Total Cost = ( Variable Cost + Fixed cost)

Now

Variable cost = 1,000 packages × $1.90 per unit

= $1,900

Fixed cost = $1,700 × 120%

= $2040

Total cost = $1,900 + $2,040

= $3,940

Now  

Total sales revenue is

= $3,940 + $3,000

= $6,940

Now  

Sales price = $6,540 ÷ 1,000 packages

= $6.94

3)

-Fruit Computer Company has variable costs of $220 per unit and fixed costs of $32,000 per month.

- The company currently sells 500 units per month at a sales price of $300.

Net margin = $8000

- The company wants to increase its operating income by 30%.

- If the company upgrades the computer quality, the variable cost per unit will increase to $240 and the fixed costs will rise by 50%.

Thus the selling price per unit will be  $346.80 per unit.

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Answer:

Step-by-step explanation:

The area of the equilateral triangle is \(\frac{\sqrt{3}}{4}(6)^{2}=\boxed{9\sqrt{3}}\)

Answer: 5 ft

Step-by-step explanation:

Given

The path of the swimmer is given by

\(h=-0.1d^2+0.1d+3\)

The swimmer can go horizontally depends upon the depth

So, find the maximum depth by taking derivative w.r.t height

\(h'=-0.2d+0.1\)

Put derivative equal to 0

\(\Rightarrow -0.2d+1=0\\\\\Rightarrow d=\dfrac{1}{0.2}\\\\\Rightarrow d=5\ ft\)

thus, the swimmer can go up to a distance of 5 ft.

Answer: 52 seconds.

Step-by-step explanation:

|-3| + 23 = 26. 26 x 2 = 52.

To construct the first simplex tableau using the Big M method. The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

To construct the first simplex tableau using the Big M method, we first rewrite the problem in standard form as follows:

Maximize \(Z = 2x₁ + 5x₂ + 3x₃\)
subject to
\(x₁ - 2x₂ + x₃ + x₄ = 20\\2x₁ + 4x₂ + x₃ = 50\\x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0, x₄ ≥ 0.\)

To construct the initial simplex tableau, we introduce artificial variables x₅ and x₆ to the two equations.

The initial tableau is:

 Basis   |  x₁   |  x₂   |  x₃   |  x₄   |  x₅   |  x₆   |   RHS  
----------------------------------------------------------------------
    x₅    |   1    |   2    |   1    |   0    |   1    |   0    |   20    
    x₆    |   2    |   4    |   1    |   0    |   0    |   1    |   50    
----------------------------------------------------------------------
    -Z    |  -2    |  -5    |  -3    |   0    |   0    |   0    |   0    

The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

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Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │ s₁  │ s₂  │ a₁  │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│      Z      │  2   │   5   │   3   │  0  │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   x₁ - 2x₂  │  1   │  -2   │   1   │ -1  │  0  │  0  │     20      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   2x₁ + 4x₂ │  2   │   4   │   1   │  0  │ -1  │  0  │     50      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │ -M  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────┴─────────────┘

The initial (artificial) basic solution is x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, a₁ = 0. The initial entering basic variable is x₁, which has the most positive coefficient in the objective row. The leaving basic variable is s₁, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the second row (20/1) is the smallest, so s₁ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁, s₂) for the inequalities and an artificial variable (a₁) for the equality constraint. We assign a large positive value (M) to the coefficients of the artificial variables in the objective row.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₁₂₃ are taken directly from the given problem. The slack variables and the artificial variable (a₁) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial (artificial) basic solution is obtained by setting the decision variables to 0, the slack variables and the artificial variable to the right-hand side values. In this case, x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, and a₁ = 0.

The initial entering basic variable is determined by selecting the most positive coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the second row (20/1) is the smallest, s₁ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

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The words savage and savory are neither similar nor contradictory.

Contradiction is a term used to indicate mutually opposite things. It is commonly used in statements where both the statements cannot be true.

Savage is a word the meaning of which is wild or non cultivated in a context as an adjective. In another context, savage can be used as a noun to define an uncivilized or a brutal human.

On the other hand, savory is a completely different term which is used to define the taste of the dishes, typically in a positive way.

Hence the terms savage and savory are neither similar nor contradictory words.

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Using the Pythagorean theorem:

6^2 = 5^2 + x^2

Simplify:

36 = 25 +x^2

Subtract 25 from both sides:

11 = x^2

Square root of both sides:

x = sqrt(11) (exact) or 3.316625 as a decimal

Answer:

The Amount amount he pays each month is 298

Step-by-step explanation:

Given:

Total amount of new car (including interest) = 17,880

Payment is splited over 60 months i.e time = 60 months

Required:

How much will be paid each month

To find the amount to be paid each month use the formula:

Monthly payment = Total amount / time

\( = \frac{17880}{60} = 298 \)

Therefore, the amount William pays each month is 298

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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Answer:

Step-by-step explanation:

w = 5 cm

h = 6 cm

L = 7 cm

V = 5 * 6  7

V = 210 cm^3

1 L = 1000 cm^3

x L = 210 cm^3

1000 cm^3 *x = 210 cm^3

x = 0.210 L

11.392 grams = 11.392 kg/ 1000

mass = 0.011392 kg

density = mass / volume

density = 0.011392 / 0.210

density = 0.0367 kg/L to 3 places of accuracy.

Answer:

2, 5, 11, 23, 47, 95, 191

A, Z, B, Y, C, X, D, W, E, V

Step-by-step explanation:

1. 2, 5, 11, 23, 47, ...95, 191

5 - 2 = 3

12 - 5 = 6

23 - 11 = 12

47 - 23 = 24

Next

(24 × 2) + 47

= 48 + 47

= 95

Next

(48 × 2) + 95

96 + 95

= 191

Next

(96×2) + 191

192 + 191

= 383

The pattern follows (difference ×2) + previous number

That is,

(5 - 2) * 2 + 5

3*2 + 5

6 + 5

= 11

2, 5, 11, 23, 47, 95, 191

2. A, Z, B, Y, C, ...

First letter , 26th letter, 2nd letter, 25th letter, 3rd letter, 24th letter, 4th letter, 23rd letter, 5th letter, 22nd letter

A, Z, B, Y, C, X, D, W, E, V

The value of x in the figure is 3

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or \(\dfrac{a}{b}\)

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

\(a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3\)

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Given;

The ratio of line segment QP=2:6

The ratio of line segment RP=X:9

Now, to find x

2/6=x/9

x=9/3

x=3

Therefore, the value of x according to given ratio will be 3

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Answer:

32.7 degress

Step-by-step explanation:

In this question we are to find the value of the angle

The best way to do with the information given is the cosine rule

Mathematically that would be;

y^2 = x^2 + z^2 -2xzCosY

where x = 90 ft , y = 55ft and z = 50 ft

Plugging the values we have;

55^2 = 90^2 + 50^2-2(90)(50)CosY

-7575 = -9000cosY

cosY = 7575/9000

cosY = 0.841666666667

Y = cos^-1 0.841666666667

Y = 32.68 degrees which is 32.7 to the nearest tenth

Answer:

32.7

Step-by-step explanation:

Both functions decrease at (-1, 2)

The complete question is added as an attachment

The polynomial function f(x) is represented by the graph.

From the graph, the polynomial function decreases at (-2, 2)

The absolute function is given as;

f(x) = =5|x + 1| + 10

The vertex of the above function is

Vertex = (-1, 10)

Because a is negative (a= -5), the vertex is a maximum.

This means that the function decreases at (-1, ∞)

So, we have

(-2, 2) and (-1, ∞)

Combine both intervals

(-1, 2)

This means that both functions decrease at (-1, 2)

See attachment 2 for the number line that represents the interval where both functions are decreasing

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The probability that a bridge hand includes 4 acres and exactly 3 kings is 0.028%

To find the probability of getting exactly 4 aces and 3 kings in a bridge hand, we can use the following formula:

P(4 aces and 3 kings) = (number of ways to get 4 aces and 3 kings) / (number of ways to select 13 cards from a deck of 52)

To calculate the numerator, we can first find the number of ways to choose 4 aces from the 4 available in the deck, and then the number of ways to choose 3 kings from the 4 available in the deck. The remaining 6 cards can be any of the 44 non-ace, non-king cards. Therefore:

Number of ways to get 4 aces and 3 kings = (4 choose 4) x (4 choose 3) x (44 choose 6) = 1 x 4 x 44,380,776 = 177,523,104

To calculate the denominator, we can find the total number of ways to choose any 13 cards from the 52-card deck:

Number of ways to select 13 cards from a deck of 52 = (52 choose 13) = 635,013,559,600

Therefore, the probability of getting exactly 4 aces and 3 kings in a bridge hand is:

P(4 aces and 3 kings) = (number of ways to get 4 aces and 3 kings) / (number of ways to select 13 cards from a deck of 52) = 177,523,104 / 635,013,559,600 = 0.0002799 or approximately 0.028%.

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Answer

1242

Explanation

Given: 3% of 4.14 × 10⁴

3% of 4.14 × 10⁴ becomes

3 percent of the given number is 1242.

Given that, 3% of 4.14×10⁴.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, 3% of 4.14×10⁴ can be written as

3/100 ×4.14×10000

= (3×4.14×10000)/100

= 3×4.14×100

= 1242

Therefore, 3 percent of the given number is 1242.

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