The product of six and a number is 108. What is the solution to the equation 1822, 102, 648

Answer:

A) 2,500 square yards

Step-by-step explanation:

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The area of the curve in the first quadrant is A = 2/7 units²

Given data ,

Let the region described is bounded by the curves y = x^(2/5) and y = 1 be in the first quadrant

Now , the point of intersection of these two curves is given by

x^(2/5) = 1

x = 1^5

So the two curves intersect at x = 1

Now , the area of the curve is given by y = x^(2/5) is the lower curve and y = 1 is the upper curve in the given interval [0, 1]

And , the , integral is used to find the area

∫[from 0 to 1] (1 - x^(2/5)) dx

∫(1 - x^(2/5)) dx = x - (5/7)x^(7/5) + C

Evaluated from 0 to 1, we get:

[(1 - (5/7)(1^(7/5))) - (0 - (5/7)(0^(7/5)))]

Simplifying further, we get:

[(1 - 5/7) - 0] = 2/7 units²

Hence , the area of the region bounded by the curves y = x^(2/5) and y = 1 in the first quadrant is 2/7 square units

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The missing side lengths in the triangles are c = 20 ft, b = 17.32 ft and x = y = 6√2

Triangle 1

The side length c is calculated as

sin(30) = 10/c

So, we have

c = 10/sin(30)

Evaluate

c = 20

This also means that the side length b is calculated as

b² = 20² - 10²

b² = 300

Take the square roots

b = 17.32

Triangle 2

Given that the acute angle in the right triangle is 45 degrees and the hypotenuse is 12 meters

The side lengths x and y are calculated as

x = y = 12/√2

Rationalise the expression

x = y = 6√2

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The amount of wax needed to make 288 candles is  41472 inches³.

A company makes wax candles in the shape of a rectangular prism. Each candle is 6 inches long, 3 inches wide, and 8 inches tall.

Therefore, the amount of wax to make 288 candles can be calculated as follows:

Hence,

volume of each rectangular prism = 6 × 3 × 8

volume of each rectangular prism = 18 × 8

volume of each rectangular prism = 144 inches cube

Therefore,

1 candle =  144 inches cube

288 candles = ?

cross multiply

volume of wax for 288 candles = 288 × 144

volume of wax for 288 candles = 41472 inches³

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Step-by-step explanation:

Use the Ratio Test since Ratio Test guarantee absolutely convergence.

[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]

This simplifes to

[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]

[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

Take the absolute value

[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

In order for this series to be convergent,

the limit as k approaches infinity must be less than 1.

In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.

Why

If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity

Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.

So one of the answer is 3.

The value of cost of the perimeter of the lid is, $32.625

Given that;

Dylan is putting a gold ribbon around the lid of a rectangular box. The lid ha a width of 6(1/4) inches and a length of 4(5/8) inches.

Hence, The value of perimeter of the lid is,

⇒ P = 2 (6 1/4 + 4 5/8)

⇒ P = 2 (25/4 + 37/8)

⇒ P = 2 (50/8 + 37/8)

⇒ P = 2 (87/8)

⇒ P =  87/4 inches

Since, The ribbon costs $1.50 per Inch.

Hence, Total cost for lid is,

⇒ 1.50 × 87/4

⇒ $32.625

Thus, The value of cost of the perimeter of the lid is, $32.625

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The measures of the angles are ∠1 = 35 and ∠2 = 30

From the question, we have the following parameters that can be used in our computation:

The figure

Using the sum of opposite internal angles in a triangle, we have

∠1 + 80 = 115

Subtract 80 from both sides

So, we have

∠1 = 35

Using the same theorem of sum of opposite internal angles in a triangle, we have

∠2 + 85 = 115

Subtract 85 from both sides

So, we have

∠2 = 30

Hence, the angles are ∠1 = 35 and ∠2 = 30

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The graph of the system of inequalities is on the image at the end.

Here we have the system of inequalities:

y > -2x + 9

y < 5x - 6

First we need to graph both of these lines with dashed lines (that is because the values on top of the lines are not solutions for the inequalities).

Then we need to shade the region above the first line, and the region below the second line.

Thenh the graph of the system is the one you can see in the image at the end.

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The simplified expression is 120x³ + 120x².

To simplify the expression 5x(2x+2)12x, we can use the distributive property of multiplication over addition and simplify the resulting terms.

First, we distribute 5x to the expression (2x+2), which gives us:

5x(2x+2) = 10x² + 10x

Next, we can multiply the result by 12x:

12x(10x² + 10x) = 120x³ + 120x²

Therefore, the simplified expression is 120x³ + 120x².

We can see that the original expression was a multiplication of three factors, and we used the distributive property to simplify it by expanding and multiplying the resulting terms. The final expression has a common factor of 120x², which we can factor out to get 120x²(x+1).

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Answer:

3. 504,875 shares

4. $10,829,568.75

5. $30,383,377.5

Step-by-step explanation:

1. For the first one, you just need to find 70% of 721,250, which we can do several ways:

If Allen owns 70% of Bull Corp, he owns 0.7 x 721,250 = 504,875 shares.

Therefore, Allen owns 504,875 shares of Bull Corp.

you can use cross-multiplication to solve this problem as well. Here's how:

Let X be the number of shares that Allen owns.

According to the problem, Allen owns 70% of the total number of shares, which is 721,250.
So we can write:

X/721,250 = 70/100

To solve for X, we can cross-multiply:

100X = 70 * 721,250

Simplifying the right-hand side:

100X = 50,487,500

Dividing both sides by 100:

X = 504,875

Therefore, Allen owns 504,875 shares of Bull Corp, which is the same answer we got earlier.

I added a picture below.

2. If Allen paid $21.45 PER share we just multiply that by he amount of shares, which is 504,875:

If Allen owns 504,875 shares of Bull Corp, and he paid $21.45 per share, his initial total investment would be:

Total investment = Number of shares * Price per share

Total investment = 504,875 * $21.45

Total investment = $10,829,568.75

Therefore, Allen's initial total investment was $10,830,093.75.
i added a picture for this too.

3. Just replace the 21.45 with 60.18:

If the shares are now worth $60.18, the total value of Allen's shares would be:

Total value = Number of shares * Current price per share

Total value = 504,875 * $60.18

Total value = $30,383,377.5

Therefore, the total value of Allen's shares now is $30,382,078.50.

Added a picture.

Answer:

6.4

Step-by-step explanation:

First add 10 to 22 to get 32

Then divide 32 by 5 to get x

The factor that one should consider when choosing a career is D. All of the above.

In choosing a career, a student should consider the required education and training involved, the work environment, and their potential earnings.

Other factors to consider include:

Thus, all the listed factors should be considered when choosing a career.

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The three equivalent numerical expressions are  1/32, 0.03125, 3.125 x 10^-2

Using the exponential rules, we can simplify the expressions as:

(2^-3)(2^5)/2^7)

= 2^(5-3)/2^7

= 2^2/2^7

= 1/2^(7-2)

= 1/2^5

= 1/32

Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2

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If the graphs of the linear equations in a system are parallel: A. There is no solution.

The general form for the equation of a line is:

y = mx + c

where:

m is slope

c is y-intercept

Usually, for two equations to have a solution, they must intersect each other.

However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.

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Answer:79

Step-by-step explanation:

The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1

From the question, we have the following parameters that can be used in our computation:

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

Evaluating the like terms, we have

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

Cancel out the common factors

So, we have

(x - 2) = 1

Add 2 to both sides

x = 3

Hence, the solution is 3

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The year in which the population of the town was 12,354 include the following: B. 1970.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

Based on the information provided about the population of this small town, a linear function that models the population as a function of time, t, in years past 1940 is given by;

P(t) = 1,854 + 350t

12,354 = 1,854 + 350t

12,354 - 1,854 = 350t

t = 10,500/350

t = 30

Since the years is past 1940, we have:

Year = 1940 + 30 = 1970.

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Complete Question:

The population of a small town, P, as a function of time, t, in years past 1940 is given below. P = 1,854 + 350t. For which of the following years was the population of the town 12,354?

A.1967

B. 1970

C. 1974

D. 1964

Answer:

a)

[tex] log_{9}(7) - log_{9}(8) = log_{9}( \frac{7}{8} ) [/tex]

b)

[tex] log_{5}(11) + log_{5}(4) = log_{5}(44) [/tex]

c)

[tex] log_{9}(81) = log_{9}( {3}^{4} ) = 4 log_{9}(3) [/tex]

Answer: The correct answer is option A. a reference point.

Step-by-step explanation:

An reference point is required to determine whether or not an object moves.

The missing terms in the logarithmic equation are solved

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

log₄ 11 + log₄ 5 = log₄ ( a )

Now , the value of a is

From the logarithmic properties , we get

log A + log B = log AB

So , a = 11 + 5 = 16

b)

log₅ 3 - log₅ ( a ) = log₅( 3/5 )

From the logarithmic properties , we get

log A − log B = log A/B

So , a = 5

c)

log₇ 8 = 3 log₇ ( a )

From the logarithmic properties , we get

log Aⁿ = n log A

8 = 2³

So , a = 3

Hence , the logarithmic equation is solved

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Answer:

Step-by-step explanation:

4992223553535

your in school ask a teacher

Answer:

If im not mistakeing

Step-by-step explanation:

(-15,2)

OR

2,15

or 2,-15

it's one of those three. im srry

Answer:

relation 1-function

relation 2-not a function

relation 3-function

relation 4-funtion

Solving the equation​ √(x - 3)³ - 64 = 0 for the variable x gives x = 19

From the question, we have the following parameters that can be used in our computation:

√(x - 3)³ - 64

Express as an equation

So, we have

√(x - 3)³ - 64 = 0

Add 64 to both sides of the equation

√(x - 3)³ = 64

Take the cube roots of both sides

So, we have

√(x - 3) = 4

Square both sides of the equation

This gives

x - 3 = 16

Add 3 to the equation

x = 19

Hence, the solution is x = 19

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If you invest $2,000 at the end of each year for the next 30 years and earn an annual rate of return of 13%, you would have a total of approximately $75,994.18 saved for retirement.

To calculate the future value of the investment, we can use the formula for the future value of an annuity:

[tex]FV = PMT \times \dfrac{((1 + r)^{n - 1})} { r}[/tex]

where PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

In this case, we have PMT = $2,000, r = 0.13 (since the stock market has earned 13% per year), and n = 30 (since we are investing for 30 years).

Plugging in the values, we get:

FV = $2,000 x ((1 + 0.13)³⁰ - 1) / 0.13

= $2,000 x (4,919.04) / 0.13

= $75,994.18

Therefore, a total of about $75,994.18 would be saved for retirement if you invested $2,000 at the end of each year for the next 30 years and saw a 13% annual return.

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Answer:

100 + 5f = 40

5f = -60

f = -12 feet per minute (decrease of 12 feet per minute)

Answer:height = 5 inches  and the base = 10 inches.

Step-by-step explanation:

The slope of the line that cuts through the points (1, -5) and (3, 5) is equal to 2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (5 - (-5))/(3 - 1)

Slope (m) = (5 + 5)/(2)

Slope (m) = 10/2

Slope (m) = 2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.

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Answer:

60.96 meters per hour.

Answer:

3658.53658537 meter per hour

Step-by-step explanation:

[tex]\frac{100ft}{30sec}[/tex] · [tex]\frac{1meter}{3.28feet}[/tex] · [tex]\frac{60sec}{1min}[/tex] ·[tex]\frac{60min}{hour}[/tex]  You can cross cancel works like you can numbers

[tex]\frac{100}{30}[/tex] · [tex]\frac{1meter}{3.28}[/tex] · [tex]\frac{60}{1}[/tex] · [tex]\frac{60}{1hour}[/tex]

[tex]\frac{360000meters}{98.4hours}[/tex]

3658.53658537 meter per hour