Suppose that the functions g and f are defined as follows.
g(x)=(x+6)(x+6)
f(x)=-6 x+7
(a) Find g/f
(b) Find all values that are NOT in the domain of g/f}. If there is more than one value, separate them with commas.

(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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Median won't change, however Mean will fall by 180.

By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.

African elephants total 555 in number.

Elephants had a 3800 kg average mass.

Elephants had a 3600 kg median mass.

Lola, the elephant that was the smallest, weighed 2700 kg.

Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.

What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.

now 2700 becomes 1800

so Median remains the same as 3600

No change in Median

The mean mass of the elephants was  3800 kg

=> total weight = 5 x 3800 = 19000 kg

2700 kg becomes 1800 kg

Hence new total mass = 19000 - 2700 + 1800 = 181000 kg

New Mean = 18100/5   = 3620  kg

Mean reduced by 3800 - 3620  = 180 kg

No change in Median weight

Mean reduced by 180 kg

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By using the concept of vector, it can be calculated that

28) First option is correct

29) Fourth option is correct

What is vector?

Anything that has both magnitude and direction and follow the vector addition law is called vector.

28) The vectors are

[tex]\vec{v} = -2i-5j,[/tex]

[tex]\vec{w} = -3i+j[/tex]

[tex]\vec{v}. \vec{w} = (-2i-5j).( -3i+j) = 6 - 5 = 1\\|\vec{w}|^2 = (-3)^2+(1)^2 = 9 + 1 = 10\\\vec{v_1} = \frac{1}{10}( -3i+j) = \frac{-3}{10}i+\frac{1}{10}j[/tex]

[tex]\vec{v_2} = (-2i-5j) - (-\frac{3}{10}i - \frac{1}{10}j)\\\vec{v_2}= (-2+\frac{3}{10})i+(-5 - \frac{1}{10}j)\\\vec{v_2}=-\frac{17}{10}i - \frac{51}{10}j\\[/tex]

First option is correct

29) P = (1, 2) and Q = (-6, -1)

Position vector = (-6-1)i + (-1-2)j = -7i - 3j

Fourth option is correct

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total = 15x + 30

EDIT: She has to mow 8 lawns. I didn't read the question

there you go its that simple

The first two columns of the table, considering logarithms, are completed as follows:

The table is completed in this problem applying the logarithms.

This is because on the first column we had that:

10^(0.3) = 2, which means that log10(2) = 0.3.

(log10(x) represents the logarithm of base 10 of x).

For the second row, the decimal approximation is found applying the power of 10^0.7, hence:

10^0.7 = 5.

For the third and fourth rows, to obtain the power of 10 expression, we need to calculate the logarithms of these numbers, as follows:

Hence the power of 10 expressions are given as follows:

For the fifth row, we just need to calculate the exponential expression, hence:

10^(0.4) = 2.51.

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}[/tex]

[tex]5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}[/tex]

Answer:

x = 8

y = 2

Step-by-step explanation:

To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.

We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:

y - (-1) = 4(x - (-2))

Simplifying this expression gives us:

y + 1 = 4(x + 2)

Which simplifies to:

y = 4x + 5

So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.

The difference between book value and the amount received is $2000

What was the difference between the book value and the amount received ?

van cost = $16000

Estimated life= 4 years

Residual value= $4000

using straight line method of depreciation

Depreciation per year= 16000-4000/4= 3000

Therefore book value after two years = $16000- 2*3000= $10000

Selling price of book after 2 years= $8000

hence the difference between book value and the amount received

10000-8000= $2000

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The circumference of the circle with the dimensions radius = 6 and π = 3.14 is 37.68

The circumference of a circle refers to the line that bounds a circle or other two-dimensional figure.

Circumference of a circle = 2πr

Where,

Circumference of a circle = 2πr

= 2 × 3.14 × 6

= 37.68

Therefore, the circumference of the circle is given by 37.68

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well, as you already know, to check if a function is EVEN, we simply check what's f( -x ), if f( -x ) = f( x ), then voila!!.  and if f( -x ) = -f( x ), then oddly enough, is an ODD function.

well, let's plug in " -x " to see what we get anyway

[tex]f(x)=-5x^2 + |2x|\implies \boxed{f(x)=-5x^2 + 2x} \\\\[-0.35em] ~\dotfill\\\\ f(-x)=-5(-x)^2 + |2(-x)|\implies f(-x)=-5(-x)(-x) + |-2x| \\\\\\ f(-x)=-5(+x^2) +2x\implies \boxed{f(-x)=-5x^2 + 2x}~\hfill \stackrel{\textit{\LARGE Even}}{f(-x)=f(x)}[/tex]

After solving the given equation, we know that the value of c is -11.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

Let's learn more about math equations in this tutorial.

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

Sc, we have the equation:

3c + 7 = c - 15

Now, calculate this equation for c as follows:

3c + 7 = c - 15

3c - c = -15 - 7

2c = -22

c = -22/2

c = -11

Therefore, after solving the given equation, we know that the value of c is -11.

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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15. What is c in this situation?

Olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%. The quiz average is 82%.

It is forming the outcome of multiplying the total of multiple quantities by their sum and then dividing this result by the number of quantities

Given,

She has test count = 55%,

quizzes count = 30%,

homework counts = 15%

If she had

test count = 92%

Homework counts = 100%

quizzes count = ?

Let x be the test count

x = (90 - (0.55(92) + 0.15(100)))/0.30x

  = 82

Olivia must have an 82 average on quizzes in order to have a 90 average in algebra.

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Answer:

Answer:  the correct option is(C) 3, -7.

Step-by-step explanation:

Answer:

[tex]y=x^2-8x+16[/tex]

Step-by-step explanation:

[tex]x=t+4 \implies t=x-4 \\ \\ y=(x-4)^2=x^2-8x+16[/tex]

Answer:

y=-1/2x+6

Step-by-step explanation:

slope: -5/10 = -1/2

y=mx+b

y=-1/2x+b

substitute points to find b: 8=-1/2(-4)+b

8=2+b

6=b

ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.

A rhombus is one type of parallelogram and has 4 sides and 4 vertices.

Every side is equal in length and opposite angles are equal.

Given that the side AE is congruent to EC of rhombus.

That means, AE ≅ EC.

And the diagonals of rhombus bisects each other.

Both the triangle AEB and triangle CEB share the same side which is BE.

That means BE ≅ BE, by the reflexive property.

And the sides AB and BC are the sides of rhombus.

So, AE ≅ BC.

Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.

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Answer:

86

Step-by-step explanation:

If you did 1,022 divided by 12, you would get something crazy like 85.16666666666. So round up.

It will take 12.91 years to earn $ 500 in interest  

Compound interest refers to the interest added to a loan or deposit. It is the concept that we employ every day on a regular basis. Amounts are based on both the principal amount and Rate of interest when calculating compound interest. 

The formula used for

P = Principal amount

r = Rate of interest  

n = Number of compounds in a year  

t = Time period in years

And the formula for

Here we have

Principal amount = 1700,

Rate of interest = 2% = 2/100  = 0.02 on decimals  

Given that compound interest gained = $ 500

Number of compounds = 4 times

Let a be the time period

By the given formula,

Amount, A = 1700(1+0.02/4)^4t  

= 1700(1+0.005)^4t    

= 1700 (1.005)^4t  

Compound interest = 1700 (1.005)^4t - 1700

From the given data,

Compound interest = $ 500

=> 1700 (1.005)^4t - 1700 = 500

=> 1700 (1.005)^4t = 2200

=> (1.005)^4t = 1.294

Take logs on both sides

=> log (1.005)^4t = log 1.294

=> 4t log (1.005) = log (1.294)

=> 4t = log(1.294)/log(1.005)

=> 4t = 0.111934276/ 0.00216606176      

[ Use calculator for log(1.294) and log(1.005) ]

=> 4t = 51.6764012

=>  t = 12.9191003  

=>  t = 12.91  

Therefore,

It will take 12.91 years to earn $ 500 in interest

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The given logarithmic expression can be evaluated as Logc1 = 0.

Logarithm function is defined as the inverse of the exponential function.

If a^(b) = c, then b = log(c) at the base of a.

Logarithm of any number is always positive.

For negative numbers, the logarithm are complex numbers.

The given expression is Logc1.

It implies that it is the logarithm of 1 with c as a base.

Sine, the logarithm of 1 to any base is equal to zero, the given expression can be evaluated as follows,

Logc1 = 0

Hence, the value of the given expression is 0.

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Answer:

see attachment

Step-by-step explanation:

The required anti derivative of given function is  -(ky^2)/2 + 77ky.

Anti-differentiation or integration is the converse interaction to separation. For instance, if f (x) = 2x, we realize that this is the subordinate of f(x) = x^2.

We have,

dy/dx +ky - 77k = 0

dy/dx = -ky + 77k

Integrate with respect to x

∫dy/dx =  ∫(-ky + 77k)

∫dy/dx = -∫ky +∫77k

y = -(ky^2)/2 + 77ky

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The required antiderivative is   [tex]y=e^{-(kx+c)} +77[/tex]

What is antiderivative?

In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.

[tex]\frac{dy}{dx} = 77k - ky\\\\dx=\frac{dy}{77k-ky} \\\\dx = \frac{dy}{77-y} \times \frac{1}{k} \\\\kdx = \frac{dy}{77-y} \\\\-\frac{dy}{y-77} =kdx\\\\log(y-77)=-(kx+c)\\\\y=e^{-(kx+c)} +77[/tex]

Hence, The required antiderivative is   [tex]y=e^{-(kx+c)} +77[/tex]

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Answer:

Step-by-step explanation:

The grams of coffee beans Diana uses when the company comes is:

                                              62.5 grams

Answer:

Step-by-step explanation:

X^-3=1/343

X^-3=1/7^3

X^-3=7^-3

Since the powers are equal, the bases should also be equal.

Therefore, X=7

it would be 1600 i hope this helps

26034 i hope this help man pls pls

Since the time is 0.24 hour. Yes, it takes less than a quarter of an hour to fill the container

Given: A container is a hemisphere of radius 30cm

Sand fills the container at a rate of 4000 cm³ per minute

A hemisphere is half a sphere. Thus:

The volume of a hemisphere = 1/2 × 4/3 πr³ = 2/3 πr³

The volume of a hemisphere = 2/3 × π × 30 = 56548.67 cm³

Rate = Volume / Time

Time = Volume/Rate

Time =  56548.67 /4000 = 14.14 minutes

In hours: Time = 14.14/60 = 0.24 hour

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The graph of the proportional relationship represented by the equation y = 7.5x is The graph is a line that goes through points (0, 0) and (1, 7.5)

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

considering the given equation y = 7.5x.

c = 0

hence the graph passed through (0, 0)

substituting x = 1 gives y = 7.5 hence (1, 7.5) is another point

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The top 18 percent of scores fall within two standard deviations of the mean.

Publicly recognized refers to something that is well-known or acknowledged by the public or by a large segment of the population. This could include a famous person, a popular business, or an important event or achievement. Public recognition is often seen as an indicator of success, as it shows that the person or thing being recognized has achieved something noteworthy or has had a positive influence on the public. Examples of publicly recognized things include awards, honors, and other achievements.

Assuming a normal distribution, a student needs to score at least two standard deviations above the mean to be publicly recognized. This is because the top 18 percent of scores fall within two standard deviations of the mean. This can be expressed mathematically as:
P(x > μ + 2σ) = 0.18
where μ is the mean and σ is the standard deviation.

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Answer:

Quotient: 66

Remainder: 1

Step-by-step explanation:

133/2 = 66.5

66.5 =

66 + 0.5 =

66 + 1/2 = 66 1/2

1/2 * 2 = 1  ==> Remainder: 1

Whole number : 66

Quotient: 66

Remainder: 1

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