For each function, graph the function and its inverse. If the inverse is a function, state the domain and range.
a. f(x)=2/(3x)-4
b. f(x)=2x²-1
c. f(x)=1/(x-1)

It will take approximately 11.62 years to reach a population of 7000 mice.

To solve this problem, we can use the formula for exponential growth:

[tex]\mathrm{N = N_0 \times e^{(r \times t)}}[/tex]

Where:

N = Final population size

N₀ = Initial population size

r = Growth rate

t = Time (in years)

Let's calculate the growth rate (r):

N₀ = 100

N = 4000

[tex]\mathrm{r = ln(N/N_0) / t}[/tex]

[tex]\mathrm {r = ln(4000/100) / 10}\\\\\mathrm {r = ln(40) / 10}\\\\\mathrm {r \approx 0.3688}[/tex]

Now, let's find the time required to reach 7000 mice:

[tex]\mathrm {N = 7000}\\\\\mathrm {t = ln(N/N_0) / r}[/tex]

[tex]\mathrm {t = ln(7000/100) / 0.3688}\\\\\mathrm {t \approx 11.52 \ years}[/tex]

Therefore, it will take approximately 11.62 years to reach a population of 7000 mice.

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The speed that will martin need to drive, if he wants to take the  512 hours is 0.537 mph.

Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.

Speed and travel time vary in opposite directions.,

So v ∝ 1/t.

speed = v

time = t

So

=> v = k/t,  k=constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph,

=>   v = 55mph and t = 5 hours.

=> 55 = k/5

by doing cross multiply

=> k = 55*5

=> k = 275

Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t  

=> v = 275/512

=> v = 0.537 mph

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(a) The statement about Bayesian model "For the Bayesian linear model, the priors for intercept and slope are independent" is  False  .

(b) The statement about posterior distribution "in posterior distribution, intercept and slope may be correlated" is  False  .

In the question ,

it is given that ,

Part(a) ,

the statement is given to be "In Bayesian linear model, the priors for the intercept and slope are independent" , we have to check whether the statement is True or False .

We have the linear model as [tex]y_{i}= \alpha +\beta x_{i} +A_{i}[/tex]   , where [tex]A_{i}[/tex]≈N(0,σ²) , α is the intercept and β is the slope .

we know that priors [tex](\hat{\alpha } , \hat{\beta })[/tex]   are not independent  ,

Cov [tex](\hat{\alpha } , \hat{\beta })[/tex] = [tex]\frac{-\bar{x}}{S_{xx} }[/tex] *σ² ,

So , the priors for the intercept and for the slope are independent ,

hence the statement is False .

Part(b) ,

the statement is given to be "In posterior distribution, intercept and the slope may be correlated" ,

For Posterior distribution , as  [tex]A_{i}[/tex]≈N(0,σ²)  ,

and 2 + [tex]\beta x_{i}[/tex] is a non random part of the model ,

and Cov([tex](A_{i} , A_{i} )[/tex] = 0 for i ≠ j .

hence , we can say that the intercept and slope are not Corelated ,

the statement is False .

Therefore , both the given statement are False .

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The remainder when x³ + 1 is divided by x + 1 is 0

Given,

The polynomial functions; x³ + 1 and x + 1

We have to find the remainder when x³ + 1 is divided by x + 1

Polynomial function;-

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Here,

p(x) = x³ + 1

g(x) = x + 1 = 0

          x = -1

Then,

p(x) = x³ + 1

p(-1) = -1³ + 1 = -1 + 1 = 0

That is,

The remainder when x³ + 1 is divided by x + 1 is 0

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consider ventilation of a well-mixed room, the differential equation for mass concentration in the room as a function of time is given as follow:

There are three characteristic parameters in such a situation:

L, a characteristic length scale of the room (assume L = V^1/3); V the volume flow rate of fresh air into the room, and [tex]c_{limit}[/tex], the maximum mass concentration that is not harmful.

Using these three characteristic parameters, define dimensionless forms of all the variables in the equation.  c* = c/[tex]c_{limit}[/tex].)

Rewrite the equation in dimensionless form, and identify any established dimensionless groups that may appear.

V = dc/dt = S - [tex]V_c[/tex] - c[tex]A_sk_w[/tex]

Although several models are available in legal contexts, the current implementations seem to be unable to correctly simulate concentration changes that actually occur in volatile mixtures and in particular in thin films.

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Full question:

Consider ventilation of a well-mixed room as in  The differential equation for mass concentration in the room as a function of time is given in  and is repeated here for convenience,

V = dc/dt = S - [tex]V_c[/tex] - c[tex]A_sk_w[/tex].

Answer:

3-7n

Step-by-step explanation:

Answer:6

Step-by-step explanation:

Three less than the product of 7 is 6

Just translate the sentence into a equation:7n-3=6

The equation of line that passes through the point (-8, 5) and perpendicular to y = 4x - 2 is, [tex]y=-\frac{1}{4}x+3[/tex].

What is point slope form of the line?

The general form of a linear equation is y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Consider the given equation of line

y = 4x - 2

And the point is (-8, 5).

We have to find the equation of line that passes through the given point and perpendicular to the given line.

First to find the slope of the line.

Since, slope of the perpendicular line is negative reciprocal of the slope of the given line.

Here, slope of the line is 4.

So, the slope of the perpendicular line is -1/4.

Now, consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (-8, 5), m = -\frac{1}{4}[/tex]

[tex]y-5=-\frac{1}{4}(x-(-8)) \\y-5=-\frac{1}{4}(x+8)\\ y-5=-\frac{1}{4}x-2\\y=-\frac{1}{4}-2+5\\ y=-\frac{1}{4}+3[/tex]

Hence, the equation of line perpendicular to the given line is, [tex]y=-\frac{1}{4}x+3[/tex].

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Answer:

180

Step-by-step explanation:

first we combine what Anthony and Tommy have by adding

40+50

90

And twice as many is multiplying by 2

2x90

180

Hopes this helps please mark brainliest

Answer:180

explanation:40+50=90

90x2=180

The rule to describe the translation is (x , y) ---> ( x + 3 , y + 5 )

Translation is Changing scale , shifting or reflection of a parent figure.

Scale means Changing  size and shape of figure

Shifting means moving the figure to new location this could be upwards downwards , left and right

Reflection means making a mirror image or figure to different quadrant or along different axis.

According to the question,

A rectangle on a coordinate plane whose coordinates are (x, y) is translated 5 units up and 3 units to left

Shifting a plane upwards means changing the y coordinates so ,

y +5

shifting towards left means shifting to left side of x - axis

so , x + 3

Hence , the rule to describe this translation is

(x , y) ---> ( x + 3 , y + 5 )

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Answer: 52.5

Step-by-step explanation: We can divide 50 by 20 to find what the number is. In this problem, the number is 2.5. Since we know this, we can multiply 2.5 and 21 to get 52.5.

hope this helps!

please give brainliest!

Answer:

21st term = 52.5

Step-by-step explanation:

Given that,

→ 20th term of a sequence is 50.

The common difference is,

→ 50 ÷ 20

→ 50/20

→ 2.5

Now the 21st term will be,

→ n × 2.5

→ 21 × 2.5

→ 52.5

Hence, the answer is 52.5.

Answer:

$770

$40,040

Step-by-step explanation:

Last week: 11% of $7,000

11% of $7000 = 11/100 × $7000 = $770

Full year is 52 weeks.

52 × $770 = $40,040

Answer:

No it is not irrational

Step-by-step explanation:

459.63 is a rational number.

Irrational numbers are numbers that can't be shown as simple fractions

Examples of irrational numbers are:

√2,  π(Pi), 0.45445544455544445555.. (because it doesn't end)

The solution to the inequality is solved as: x ≥ -10.

To solve an inequality means to find the possible values of the variable in the inequality that will make it true.

Given the inequality:

-4x + 14 ≤ 54

Subtract 14 from both sides of the inequality:

-4x + 14 - 14 ≤ 54 - 14 [Subtraction property of equality]

-4x ≤ 40

Divide both sides by -4 then change the inequality sign:

-4x/-4 ≥ 40/-4 [division property of equality]

x ≥ -10

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The value of k in k^3=1/125 is 1/5 (optionB)

Indices is the power or exponent which is raised to a number or a variable. For example, in number 2^5, 5is the index of 2 which means 2×2×2×2×2. The plural form of index is indices.

From the law of Indices,

a^-1= 1/a

similarly, 1/125= (125)^-1

from the expression, K^3= (125)^-1

K^3= (5^3)^-1

therefore K^3=(5)^-3

multiply the power of both sides by 1/3

=K^3×1/3= (5)^-3×1/3

therefore k= 5^-1=1/5

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The value of b in the equation [tex]b^{3}[/tex] = 125  will be 5. Option (b) is correct.

The question is about the system of equations. According to the question, we have the following equation:
b³ = 125.
We can find the value of b by simplifying and using the rules of equations.

First, we need to Factorize 125 on the right-Hand side, we get.

b³ = 5.5.5 = 5³

Hence we get,
b³ = 5³
We know that if there are two expressions that are equal and we add, subtract, multiply or divide into both sides of the equation, the resulting equation will also be equal. So, Multiply both sides by the cube root, and we get:

[tex]\sqrt[3]{b^{3}} = \sqrt[3]{5^{3}}[/tex]

[tex](b^{3})^{\frac{1}{3}} = (5^{3})^{\frac{1}{3}}[/tex]

[tex](b})^{\frac{3}{3}} = (5})^{\frac{3}{3}}[/tex]

[tex](b})^1 = (5})^1[/tex]

So we get the value of b = 5, hence the correction option will be (b).

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Answer:

I think it will be one eighth times the volume

Step-by-step explanation:

The required value of m is given as 25/4 as of the given proportionality.

Given that,

P is inversely proportional to the square root of m. P = 10 when m = 1/4 to work out the value of m when P = 2​.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,

According to the question,

P ∝ 1 / √m

Now,

P₁/P₂ = √m₂/√m₁

Substitute the value in the above equation,

10/2 = √m₂/√1/4

√m₂ = 5/2

m₂ = 25/4 researchers

Thus, the required value of m is given as 25/4 as of the given proportionality.

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Answer:

a) BC = 8.66

b) BC = 4.33

Step-by-step explanation:

a)

solution:

cos30°=BC/AC

or, BC=0.866*10

BC=8.66

b)

solution:

BC=5*0.866

BC=4.33

Every decision we make is followed by a series of related events. The magnitude of the decision will determine how drastically it will affect the person making it and those around them. There is always a result, whether the impact is positive or negative.

Step 1: Identification of the purpose of the decision

Step 2: Information gathering

Step 3: Principles for judging the alternatives

Step 4: Brainstorm and analyze the different choices

Step 5: Evaluation of alternatives

Step 6: Select the best alternative

Step 7: Execute the decision

Step 8: Evaluate the results

When making judgments, one should always balance the potential business benefits against the drawbacks, leaning toward the former.

By doing this, potential losses to the organisation are avoided, and sustainable growth is maintained within the business. When you have to make a difficult decision, it might often seem easier to postpone doing so, especially if you encounter a lot of conflict thereafter.

However, in order to maintain control over your work and time, decisions must be made and their implications accepted.

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Answer:

1818.9 mi

Step-by-step explanation:

If the num of miles is directly proportional, then we can find out that she drives 348.3/9 = 38.7 mi/gal (this also works for the other two pairs)

To find the distance with 47 gallons, you multiply 38.7 by 47, to get 1818.9 mi.

The value of the coordinate x in the point P(x, 3) s -2

From the question, we have the following coordinate points

Point P = (x, 3)

Point Q = (3, 5)

Point R = (-4, -2)

The point P is equidistant from the points Q and R

This means that

PQ = PR

These lengths can be calculated using the following distance formula

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, we have

PQ = √[(x - 3)² + (3 - 5)²]

PR = √[(x + 4)² + (3 + 2)²]

Recall that PQ = PR

So, we have

√[(x - 3)² + (3 - 5)²] = √[(x + 4)² + (3 + 2)²]

Square both sides

(x - 3)² + (3 - 5)² = (x + 4)² + (3 + 2)²

So, we have

(x - 3)² + 4 = (x + 4)² + 25

Open the brackets

x² - 6x + 9 + 4 = x² + 8x + 16 + 25

Evaluate the like terms

8x + 6x = 9 + 4 - 16- 25

Evaluate the like terms

14x = -28

This gives

x = -2

Hence, the value of x is -2

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Rigoberto invests $8,000, at 6% interest, compounded semiannually for 1 year the compound interest for his investment is 8487.2

A = P(1 + r/n)²

In the formula

A = Accrued amount (principal + interest)

P = Principal amount = 8000

r = Annual nominal interest rate as a decimal = 0.06

R = Annual nominal interest rate as a percent

r = R/100

n = number of compounding periods per unit of time

t = time in decimal years;

A = 8000(1 + 0.06/2)²

= 8000(1 + 0.03)²

= 8000(1.0609)

= 8487.2

Therefore, the compound interest for his investment is 8487.2

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The total possible number of points the team could score to earn pizzas is 700, using the inequality |x - 750| ≤ 50

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Based on the given conditions, formulate: 750 -50

Calculate the sum or difference will be 700

Hence, the inequality possible number of points the team could score to earn pizzas is 700

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Height and base of a triangle with given area 48 square meters is 12meters and 8 meters respectively.

As given ,

Area of the triangle = 48 square meters

Let 'y' meters represents the height of the triangle

Then 'y - 4' meters represents the base of a triangle.

Area of a triangle = ( 1/2 ) × base × height

Substitute the values we get

48 = ( 1 / 2) × ( y - 4 ) × y

⇒ 96 = y² - 4y

⇒ y² - 4y - 96 = 0

⇒ y² - 12y + 8y - 96 = 0

⇒ ( y - 12 ) ( y + 8 ) =0

⇒ y = 12 or y = -8

Height cannot be negative.

⇒y = 12meters

Base = 12 -4

        = 8 meters

Therefore, height and base of a triangle with given area is 12 meters and 8 meters respectively.

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The item that can be received at 45°F (7° C) is Milk , the correct option is (b) .

In the question ,

the receiving temperature of the items is given ,

we have to identify the item that can be received at  45°F (7° C) .

From the given options ,

we see that cold feed is received at 41°F (5° C) ,

Milk at 45°F (7° C) and Hot Food at 135°F (57° C) .

So , we can conclude that the option (b) Milk can be received at  45°F (7° C) .

Therefore , The item that can be received at 45°F (7° C) is Milk , the correct option is (b) .

The given question is incomplete , the complete question is

Temperature criteria for receiving items is given as follows ;

(a) Cold Food is received at 41°F (5° C) or lower ,

(b) Milk is received at  45°F (7° C) or lower ,

(c) Hot Food is received at 135°F (57° C) or lower .

Find the item that can be received at  45°F (7° C) ?

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Using Probability,

The probability that a randomly selected student in the class likes math or English is 11/26.

We have provided the following information,

total number of students in a class = 26

number of students who likes Math = 15

number of students who likes English = 13

number of students who does not likes English or Math = 9

let x be number of students who likes both of subjects .

firstly , we have to find out the value of x i.e total number of students who likes both subjects out of 26 students class .

For this , number of students who likes any one of subjects from both = 26- 9 = 17

but we have total 28 (i.e., 15 + 13 )students who likes Math and English.

so, number of students who likes only Math = 17-15 = 2

number of students who likes only English = 4

then, number of students who likes both subjects

(x) = 26 - 4- 2-9 = 11

randomly one student is selected from the Class,

The probability that a randomly selected student in the class likes math or English = 11/26

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Complete question:

In a class of 26 students: 15 like math, 13 like English, 9 does not like both. What is the probability that a randomly selected student in the class likes math or English?

The complementary event of rolling a die and getting a number less than three is that the six-sided die is rolled and the outcome is greater than three. Where P = n < 3  is the event and its complement is P' = n > 3.

The sample space of all outcomes that are not the event in question is the complement of an event. The inverse of "a flipped coin lands on heads" is "a flipped coin lands on tails."

If the chance of drawing a red marble from a bag is 26%, the chance of the complement (picking a non-red marble ) is 74%.

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