20mnx^{2} \frac{x}{y} 50mx^{2} 4nx^{2} 9

Answer:

See below

Step-by-step explanation:

\(\textbf{Part A: } \text{ If }h(x) = f (x) + g(x) \text{, solve for } h(x) \text{ in simplest form.}\)

We have

\( f (x) = \log_3(x) + 3 \)

and

\(g(x) = \log_3(x^3) - 1\)

Thus

\(h(x) = f (x) + g(x) = (\log_3(x) + 3) + ( \log_3(x^3) - 1) = \log_3(x) + 3 + \log_3(x^3) - 1\)

\(= \log_3(x) + \log_3(x^3) + 2\)

Recall the property of logarithms:

\(\boxed{\log_b(n\cdot m) = \log_b(n) + \log_b(m)}\)

then,

\(\log_3(x) + \log_3(x^3) + 2 = \log_3(x\cdot x^3) +2 = \boxed{\log _3(x^4)+2}\)

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

\(\textbf{Part B: } \text{Determine the solution to the system of nonlinear equations of } f(x) \text{ and } g(x).\)

I am assuming that the system of equations is

\($\left \{ {{ f (x) = \log_3(x) + 3 } \atop {g(x) = \log_3(x^3) - 1}} \right$\)

and you probably want the solution when \(f(x)=g(x)\) I will name it \(y\), thus

\($\left \{ {{ f (x) = \log_3(x) + 3 } \atop {g(x) = \log_3(x^3) - 1}} \right \implies \left \{ {{y= \log_3(x) + 3 } \atop {y = \log_3(x^3) - 1}} \right$ \)

We should just solve

\(\log_3(x) + 3 = \log_3(x^3) - 1 \)

\(\log_3(x) - \log_3(x^3) = - 4\)

\(\log_3 \left(\dfrac{x}{x^3} \right) = - 4\)

\(\log_3 \left(\dfrac{1}{x^2} \right) = - 4\)

\(\log_3 (x^{-2}) = - 4\)

\(-2\log_3 (x) = - 4\)

\(\log_3 (x) = 2 \iff 3^2 = x \implies \boxed{x= 9} \)

The  9 x 10⁻¹¹ is greater number than 3 x 10⁻¹².

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

We have two numbers:

3 x 10⁻¹² or 9 x 10⁻¹¹.

To find the greater number;

Divide both numbers by 10⁻¹¹.

That means,

3 x 10⁻¹² becomes 3/10.

And 9 x 10⁻¹¹ becomes 9.

The absolute value,

9 > 3/10.

Therefore,  9 x 10⁻¹¹ is greater number.

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Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.

One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.

The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.

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Answer:

1 hour and 15 min

Step-by-step explanation:

I think this is right but look it up just to be sure

Step-by-step explanation:48miles in 60 min. 1/4 of 60 is 1so 60 +15 = 1hr 15 min.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{MN}\\ o=\stackrel{opposite}{18} \end{cases} \\\\\\ MN=\sqrt{ 30^2 - 18^2} \implies MN=\sqrt{ 576 }\implies MN=24 \\\\[-0.35em] ~\dotfill\\\\ \cos(M )=\cfrac{\stackrel{adjacent}{24}}{\underset{hypotenuse}{30}} \implies \cos(M)=\cfrac{4}{5}\)

The volume of the prisms are:

1. 432 yd³

2. 36in³

3. 252 m³

4. 240 ft³

5. 576 mm³

6. 144 cm³

7. 343 m³

8. 120 yd³

9. 150 in³

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

such that;

Now, substitute the value for each of the prisms, we have;

1. Volume = 6 × 6 ×12

Multiply

Volume = 432 yd³

2. Volume = 2 ×9 × 2

Multiply

Volume = 36in³

3. Volume = 9 × 4 × 7

Multiply

Volume = 252 m³

4. Volume = 10 × 8 × 3

Multiply

Volume = 240 ft³

5. Volume = 4 × 12 × 12

Multiply the values

Volume = 576 mm³

6. Volume = 6 × 8 × 3

Volume = 144 cm³

7. Volume = 7 × 7 ×7

Volume = 343 m³

8. Volume = 8 × 3 × 5

Volume = 120 yd³

9. Volume = 5 × 6 × 5

Volume = 150 in³

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Answer:

x = 0, -1, -3

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor to equal zero.

Answer:

the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.

Step-by-step explanation:

To find the semiannual simple interest payment, we need to divide the annual interest rate by 2, since there are 2 semiannual periods in a year:

Semiannual interest rate = Annual interest rate / 2

= 6.268% / 2

= 3.134%

To find the semiannual interest payment, we multiply the face value of the bond by the semiannual interest rate:

Semiannual interest payment = Face value x Semiannual interest rate

= $4900 x 3.134%

= $153.77 (rounded to two decimal places)

To find the total interest earned over the life of the bond, we need to multiply the semiannual interest payment by the number of semiannual periods in the bond's life. Since the bond has a 30-year term and 2 semiannual periods in a year, the bond has a total of 60 semiannual periods:

Total interest earned = Semiannual interest payment x Number of semiannual periods

= $153.77 x 60

= $9,226.20 (rounded to two decimal places)

Therefore, the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.

Answer:

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 109.0 inches, and a standard deviation of 12 inches.

This means that \(\mu = 109, \sigma = 12\)

Sample of 25.

This means that \(n = 25, s = \frac{12}{\sqrt{25}} = 2.4\)

What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches?

This is the p-value of Z when X = 112. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{112 - 109}{2.4}\)

\(Z = 1.25\)

\(Z = 1.25\) has a p-value of 0.8944.

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

15 units

because the y-coordinates are the same, simply take the absolute difference of the x-coordinates. |-8 - 7| = |-15| = 15

(we take the absolute difference because distance can never be negative)

hope this helps! <3

Answer:

6x+8=16

or,6x=16-8

or,6x=8

or,x=4 by 3

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

If the ml means miles than its 400

Step-by-step explanation:

Answer:

although it is true that could be -(1/4)^4

if you multiply the answer can also be -1/256

Heya!!

your answer is!

-1/256

Answer:

Step-by-step explanation:

Let x be the measure of the first angle.

According to the problem, we know that:

The sum of the angles of the triangle is 180: x + y + z = 180

The sum of the second and third angles is five times the measure of the first angle: y + z = 5x

The third angle is 16 more than the second: z = y + 16

We can substitute the third equation into the second equation to get:

y + (y + 16) = 5x

Simplifying this equation, we get:

2y + 16 = 5x

We can rearrange this equation to get:

y = (5/2)x - 8

Now we can substitute this equation and the equation z = y + 16 into the first equation to get:

x + (5/2)x - 8 + (5/2)x + 8 = 180

Simplifying this equation, we get:

6x = 360

Dividing both sides by 6, we get:

x = 60

Now we can use this value of x to find y and z:

y = (5/2)x - 8 = (5/2)(60) - 8 = 58

z = y + 16 = 58 + 16 = 74

Therefore, the measures of the three angles are x = 60, y = 58, and z = 74.

Answer: Your answer will be $240

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly

\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)

Answer:

  6.46

Step-by-step explanation:

To find the tax, multiply the amount by the tax rate

tax = 80.69 * 8%

     = 80.69*.08

      =6.4552

Rounding to the nearest cent

     6.46

Answer:

c,b,a

Step-by-step explanation:

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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Answer:

4/9

Step-by-step explanation:

Answer:

16x^2 - 64

Step-by-step explanation:

(4x − 8)(4x + 8)

We recognize that this is the difference of squares

(a-b) (a+b) = a^2 - b^2

                 =(4x)^2 - 8^2

                 =16x^2 - 64

Answer: 5x^11 * (−6x^7 − 9x^3 − 2)

Step-by-step explanation:

5x^6 * (−6x^12−9x^8−2x^5)=

5x^6 * x^5 * (−6x^(12-5) − 9x^(8-5) − 2x^(5-5))=

5x^6 * x^5 * (−6x^7 − 9x^3 − 2x^0)=

5x^(6+5) * (−6x^7 − 9x^3 − 2(1))=5x^11 * (−6x^7 − 9x^3 − 2)

Answer:

A. 266

Step-by-step explanation:

Answer:

266

Step-by-step explanation:

285+127-146=266

Answer:

3.36 cm

Step-by-step explanation:

24 - 5 1/2 = 18.5

To find the distance on the map, we can set up a proportion:

1 cm / 5.5 miles = x cm / 18.5 miles

5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).

Candice grows beets on 66 acres of farmland.

A ratio indicates the number of times one number contains another.

Given that, Candice has 88 acres of farmland and she grows beets on 3/4 of the land.

Candice grows beets on 3/4 of 88 acres of farmland,

3/4 of 88

= 3/4×88

= 66

Hence, Candice grows beets on 66 acres of farmland.

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Answer:

0.3968

Step-by-step explanation:

For exponential distribution :

P(A < x) = 1 - e^-x/m

Where m = mean of exponential distribution

Mean of distribution = 4

x = 3

P(A < 3) = 1 - e^-3/4

P(A < 3) = 1 - (0.4723665)

P(A < 3) = 0.5276335 =

Hence, p = 0.5276

(1 - p) = 1 - 0.5276 = 0.4724

Binomial distribution :

P(n, x) = nCx * p^x * (1 - p)^(n-x)

Served on atleast 4 of the next 6 days ;

P(4) + P(5) + P(6):

(6C4 * 0.5276^4 * 0.4724^2) + (6C5 * 0.5276^5 * 0.4724^1) + (6C6 * 0.5276^6 * 0.4724^0)

= (15 * 0.5276^4 * 0.4724^2) + (6 * 0.5276^5 * 0.4724^1) + (1 * 0.5276^6 * 0.4724^0)

= 0.3968

Using the exponential and the binomial distribution, it is found that there is a 0.3969 = 39.69% probability that a person is served in less than 3 minutes on at least 4 of the next 6 days.

First, we find the probability that a person is served in less than 3 minutes on a single day, using the exponential distribution.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:  

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:  

\(P(X \leq x) = 1 - e^{-\mu x}\)

In this problem, mean of 4 minutes, hence \(m = 4, \mu = \frac{1}{4} = 0.25\).

The probability that a person is served in less than 3 minutes on a single day is:

\(P(X \leq 3) = 1 - e^{-0.25(3)} = 0.5267\)

Now, for the 6 days, we use the binomial distribution.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

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

The parameters are:

In this problem:

The probability is:

\(P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6)\)

Hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 4) = C_{6,4}.(0.5276)^{4}.(0.4724)^{2} = 0.2594\)

\(P(X = 5) = C_{6,5}.(0.5276)^{5}.(0.4724)^{1} = 0.1159\)

\(P(X = 6) = C_{6,6}.(0.5276)^{6}.(0.4724)^{0} = 0.0216\)

Then:

\(P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2594 + 0.1159 + 0.0216 = 0.3969\)

0.3969 = 39.69% probability that a person is served in less than 3 minutes on at least 4 of the next 6 days.

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