The value of a carpet increases by 6% to $78.56. find the original value.​

The cost of plowing the roads after 24 inches have fallen is increasing at a rate of $0.4 million per inch.

Evaluate this expression, we need to break this into two pieces. First, we have the value of c(15), so thankfully, we don't need to run any calculations to find it. This means that we just need to evaluate this definite integral, which is the integral of the derivative of c(n) from 15 to 24.

The Fundamental Theorem of Calculus relates a function to its antiderivative as a way to find the value of the integral of that function. Since the antiderivative of  , which we have the value for at the endpoints of this integral, we can evaluate this integral as follows.

[tex]\int\limits^a_b {c'(n)} \, dn = c(24 ) - c(15) = 0.4 - 0.6 = -0.2[/tex]

We can now find the value of this entire expression as follows.

[tex]c(15) +\int\limits^a_b {c'(n)} \, dn = 0.6 + (-0.2) = 0.4[/tex]

Since this represents the derivative of C(n), the cost for plowing the roads, this tells us that the cost of plowing the roads after 24 inches have fallen is increasing at a rate of $0.4 million per inch.

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The probability that there are no more than 3 cars in the system is 0.50

Probability:

In math, the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is referred as probability.

Given,

Because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to have no more than three cars in the system at any time.

Here we need to find the probability that there are no more than 3 cars in the system.

Here we know that the present level of service for three or fewer cars is the probability that there are 0, 1, 2, or 3 cars in the system.

As per the Model 1, Exhibit 8A.8, the probability of having more than three cars in the system is 1.0 minus the probability of three or fewer cars => 1.0 − 0.685 = 31.5 percent

And the 95 percent service level of three or fewer cars, this states that

=> P0 + P1 + P2 + P3 = 95 percent.

When we can solve this by trial and error for values of λ/μ.

Therefore, the value of λ/μ = 0.50

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Answer:just solve it

Step-by-step explanation:

it is super easy

F(x)= -ln(-x3+3x-1) is a particular solution to the differential equation that passes through (1, 0).  An equation for the tangent line to the graph of f at the point (1,0) = -3.

b.[tex]\frac{dy}{e^y} = (3x^2-6x)dx\\[/tex]

∫[tex]e^{-y} dy =[/tex] ∫[tex](3x^2-6x)dx[/tex]

[tex]-1e^{-y} = x^3-3x^2+C\\e^{-y} = -x^3+3x^2+C_{2}\\ -y= ln(-x^3+3x^2+C_{2}) \\y=-ln(-x^3+3x^2+C_{2}[/tex]

Given (1,0)

[tex]0= -ln (-1+3+C)\\0=ln_{c} (2+C)\\e^{0} = 2+C\\-1=C\\so f(x)= -ln(-x^3+3x^2-1)\\[/tex]

f(1.2)=-.465 as the actual value.

c. tangent line slope at (1,0).[tex]= e^0 (3(1)^2-6(1))\\[/tex]

[tex]=-3[/tex]

Line equation: y= 3(x-1) or y= 3x + 3

with f(1,2)=-3(1.2)+3 =-.6

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Answer: -5/4

Step-by-step explanation:

The slope is rise/run or y2 - y1/ x2 - x1

The two points are (-6,-3) (-2, -8)

The y decreases by 5 and the x increase by 4

So the slope is -5/4

Order of Operations: BPEMDAS

Substitution

Functions

Let's see what the problem as given us.

[tex]\displaystyle\begin{aligned}& b(x) = 6x^2 \\& x = 16\end{aligned}[/tex]

We can easily see that we can substitute in x as 16.

∴ our final answer to the question is b(16) = 1536.

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Topic: Algebra I

Unit: Functions

Three identically sized sectors make up a spinner. Two sectors are colored blue, while one sector is labeled red. Kathryn turns the spinning while recording the outcomes. Kathryn comes to the conclusion that there is a problem with her experiment after running several trials for it.

The object's sample space affects theoretical probability. For instance, the likelihood of rolling a 3 when using a fair die is 1/6. This is so because, when a fair die is rolled, the number 3 indicates one of the six possible results.

Divide the total number of trials by the number of times the desired result has occurred to determine the experimental probability.Every time, one fourth of the time, the spinner will land on a different color. The likelihood of rolling each number on the die in Experiment 2 is always one sixth. The results are equally likely to occur in both of these tests. Let's examine a test in which the results are not equally likely.

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Answer:

7.20cm I think

........

Answer:

Step-by-step explanation:

52%

The expression for the volume of the pyramid is V = 2/9s^3

Volume of a pyramid

To find the volume of a pyramid, we multiply the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V=(1/3)×B×H, where B is the area of the base of the pyramid, and H is its height.

The volume of a pyramid is:

V=1/3(B)(H)

Where

B:Base = s^2

H:Height = 2/3s

Then:

V=1/3(B)(H) = 1/3(s^2)(2/3s) = 2/9s^3

Hence, the expression for the volume of the pyramid is V = 2/9s^3

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Answer: b) 7

Step-by-step explanation:

mean = average of the data

[tex]mean = \frac{sum of all terms}{total number of terms}[/tex]

[tex]5 = \frac{5+10+2+1+x}{5}\\ 25 = 18+x\\\\25 - 18 = x\\\\7= x[/tex]

The value of angle x in the triangle is 130 degrees

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

Lines = parallel lines

Shapes = Triangles

By the alternate interior angle, the third angle in the bottom triangle has the  same measure as 60 degrees

This means that

x = 70 + 60 -- by the alternate exterior angle throrem

Evaluate the sum

x = 130

Hence, the value of x is 130

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Sarah needs 7 and three-fourths of pounds of clay to make 31 small vases. By using the proportion of pounds of clay to the number of small vases, the required value is calculated.

Proportions are equations in which two ratios are made equal to each other. By using these we can relate a part to a whole. The formula for the proportions is written as

a : b = c : d or a/b = c/d or ad = bc

Here the variables a and d are said to be the extreme terms and the variables b and c are the mean terms.

Mostly used proportions are inverse proportion, direct proportion, compound proportion, etc.

Given that,

Sarah uses 3 and 1/2 pounds of clay to make 14 small vases.

And x pounds of clay to make 31 small vases.

So, applying the proportions formula for finding the x value as

[tex]3\frac{1}{2}:x=14:31[/tex]

Then, we can write them as

bc = ad ⇒ 14x = 7/2 × 31

⇒ 14x = 217/2

⇒ x = 217/28

⇒ x = 7.75 = [tex]7\frac{3}{4}[/tex]

Therefore, Sarah needs 7 and three-fourths pounds of clay to make 31 small vases. So, option C is correct.

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Between 10:00 and 10:30, there is a 0.333 percent chance that the switchboard will field more than 9 calls but fewer than 18 calls.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Time = 30 min (as 10:00 to 10:30)

Total calls = 9+18 =27

Probability receive more than 9 calls but fewer than 18 calls

p(9 < x > 18) = { 10, 11, 12, 13, 14, 15, 16, 17, 18}  = 9 (all possibilities)

Total Probability = (likely event / total outcomes)

p(9 < x > 18) = (9/27)

p(9 < x > 18) = 1/3

p(9 < x > 18) = 0.333

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Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.

Jogging, riding, swimming, and brisk walking are among examples. Exercises that build muscle strength are known as resistance training. Using a resistance band and lifting weights are two examples. Walking on uneven ground can be made simpler with balance exercises, which can also assist prevent falls.

Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.

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The number of applicants that were not accepted are calculated to be 1260.

The number of applicants that were not accepted can be determined as follows;

Since 2 out of every 9 applicants are accepted; therefore the total number of applicants out of which 360 applicants were accepted can be calculated as follows;

360 × 9 / 2 = 3240 / 2 = 1620

Therefore the total number of applicants is calculated to be 1620, out of these 1620 applicants, 360 were accepted therefore the number of applicants that were not accepted can be determined by subtraction.

The number of applicants that were not accepted can be determined by subtracting the accepted applicants from the total number of applicants as follows;

Applicants not accepted = 1620 - 360

Applicants not accepted = 1260

Therefore 1260 applicants were not accepted by the program.

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For the given conditions convention B attendance is decreasing at a greater rate.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, the number of people attending convention A can be modeled by the function as,

f(x) = 1200 • 0.95ˣ

where x is the number of years that the convention has been occurring.

The number of people attending convention A in year 1,

f(x) = 1200 × 0.95¹

f(x) = 1140

The number of people attending convention A in year 2,

f(x) = 1200 × 0.95²

f(x) = 1083

The number of people decreasing in the Convention A,

=1140 - 1083

=57

If the number of people attending Convention B was 2200 in year 1 and 2100 in year 2. The number of people decreasing in the Convention B,

=2200-2100

=100

Thus, for the given conditions convention B attendance is decreasing at a greater rate.

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Answer: P is 1 and q is 11, making your answer 12.

Step-by-step explanation:

If the chart is displaying prime numbers in order from 1 to 13, list all of the prime numbers. We would start with '1' because '1' is a prime and the first one on the list, thus followed by 3, then 5, then 7, then 11 because the only prime number between 7 and 13 is 11.

Then, add your P and q together, 1 and 11 in this example, to get your final answer of 12.

Answer:

log_20(35)= 1.5372435736805

Step-by-step explanation:

(A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

A polynomial is a mathematical equation made up of coefficients and indeterminates that exclusively uses the operations of addition, subtraction, multiplication, or powers of positive numbers of the variables.

x² - 4x + 7 is an illustration of a quadratic with a solitary indeterminate x.

(A) 4x² - 3x + 7:

'x' is the only variable in the provided polynomial.

As a result, the polynomial 4x² - 3x + 7 has one variable.

(B) y² + √2:

'Y' is the only variable in the provided polynomial.

y² + √2 is a polynomial in one variable as a result.

(C) 3√t + t√2:

Since the power of the variable in the first term is 1/2, which is not a whole integer, 3√t + t√2 is not a polynomial.

(D) y + (2/y):

Because the power of the variable in the second term is -1, which is not a whole number, y + 2y⁻¹ is not a polynomial.

(E) x¹⁰ + y³ + t⁵⁰

Due to the fact that x, y, and t are all three variables, x¹⁰ + y³ + t⁵⁰ is not a polynomial in one variable.

Therefore, (A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

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No, the line passing through  (-4, 26) and (-2, 0) is  not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.

Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.

We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.

Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)

So, for first line we have (x₁, y₁)=(-4,26)

and (x₂, y₂)=(-2,0)

So, slope(m₁) of first line is =(0-26)/(-2 - (-4))

                  =>m₁ = -26/2

                   =>m₁ = -13     ----(eq1)

Similarly, for second line, we have (x₁, y₁)=(10,18)

and (x₂, y₂)=(5,3)

So, slope(m₂) of second line is =(3-18) / (5-10)

                =>m₂ = -15/-5

                 =>m₂=     3   -------(eq2)

On comparing eq1 and eq2,we get

 =>m₁≠m₂.

Hence, the given lines are not parallel.

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(Complete question) is:

Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?

The product of a and b is 140. Hence option B is the correct option.

What is an exponential function?

The formula for an exponential function is f (x) = a^xx, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given exponential equations are

x^8 • x^a = x^64 .....(i)

(x^2) ^b = x ^ 5 .....(ii)

Solve the equation (i) to calculate the value of a:

x^8 • x^a = x^64

Applying the formula of product of two exponents with same base a^b • a^c = a^(b+c):

x^(8+a) = x^64

Now compare the exponent of the above equation:

8 + a = 64

Subtract 8 from both sides:

a = 64 - 8

a = 56

Solve the equation (ii) to calculate the value of b:

(x^2) ^b = x ^ 5

Now applying the formual (a^b)^c = a^ (bc)

x^(2b) = x^5

Now compare the power of x of the above equation:

2b = 5

divide both sides by 2

b = 5/2

The product of a and b is 56 • (5/2) = 140.

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By using graphical method, it can be seen that-

(-4, 8) satisfies the system of inequality

So third option is correct

What is linear inequation?

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by  >, <, ≥, ≤.

A one degree inequation is known as linear inequation.

The system of linear inequation is to be solved graphically

For y  ≥ -3x-4

The line passes through (0, -4) and ([tex]-\frac{4}{3}, 0[/tex])

Since (0, 0) satisfies the line, shaded region is towards the origin

Now, as equality is maintained, line is a solid line

The above line is plotted by a red line

For [tex]y \geq \frac{1}{2}x-6[/tex]

The line passes through (0, -6) and (12, 0)

Since (0, 0) satisfies the line, shaded region is towards the origin

Now, as equality is not maintained, line is a dotted line

The above line is plotted by a blue line

From the intersection of two shaded regions, it can be seen that (-4, 8) satisfies the system of inequality

So third option is correct

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The volume of rectangular prism A will be 48 cm³

How to find area of Rectangular Prism?

The volume of a rectangular prism is given by the formula:

A = lwh

Where:

l = length

w = width

h = height.

Since the surface ratio of rectangular prism A to rectangular prism B is 4:1, the ratio of the linear dimensions of A to B must also be 4:1.

This means that if one linear dimension of rectangular prism A is 4 times the size of the corresponding dimension of rectangular prism B, then all of the linear dimensions of A will be 4 times the size of the corresponding dimensions of B.

Since the volume of a rectangular prism is given by the product of its linear dimensions.

The volume of rectangular prism A will be 4 times the volume of rectangular prism B.

Therefore, if the volume of rectangular prism B is 12 cm³, the volume of rectangular prism A will be 4 * 12 cm³ = 48 cm³.

Hence, The volume of rectangular prism A will be 48 cm³.

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413 bricks are needed to build a wall whose area is equivalent to 10.32 m².

Given is that a brick wall of dimension 4.3 m by 2.4 m is to be built. There are 40 bricks per m².

The area of the wall will be -

[A] = 4.3 x 2.4 = 10.32 m²

[A] = 10.32 m²

Now, for the area of 1 m², 40 bricks are needed. So, for 10.32 m², we can say that -

10.32 x 40

412.8

413 bricks.

Therefore, for the area of 10.32 m², to only 413 bricks are needed to build it.

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The temperature of the mixture when it cools is; -10.7°C

A change in temperature is defined as the difference in the initial and final temperatures.

Now, we are told that the chemist has a mixture with a temperature of 3.5°C.

We are also told that the temperature changes by -14.2 °C

Let the initial temperature be T₁ and the final temperature be T₂ and as such,  the change in temperature will be;

ΔT = T₂ - T₁

Plugging in the relevant values gives;

-14.2 = T₂  - 3.5

T₂  = -14.2 + 3.5

T₂ = - 10.7°C

This is the temperature of the mixture after it cools.

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Answer:

a.  Area of rectangle: Length x Width or Base x height

b. The length of the base is 6

c. The height is 3

d. Area of the rectangle is 18

Step-by-step explanation:

a. Area of the rectangle formula is: L x W

b. We find the Length, which means we find the distance of the x; we see that to get from point A to point B the x change is 6, so the base is 6

c. We find the height, which means we find the distance of the y; we see that get from point B to point C, the y change by 3, so the height is 3

d. To find the area we take 6 times 3 = 18

In each case, for a) f has local maximum at (1,1) and for b) f has saddle point at (1,1).

a) f_{xx}f_{yy}-(f_{xy})2

=(-4)(-2)-(1)2

=8-1

=7>0

f_{xx}=-4<0

Therefore, f has local maximum at  (1,1)

b) f_{xx}f_{yy}-(f_{xy})2

=(-4)(-2)-(3)2

=8-9

=-1<0

Therefore, f has saddle point at  (1,1)

A factor at which a feature of  variables has partial derivatives identical to 0 however at which the feature has neither a most nor a minimal value.

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Complete question:

Suppose (1, 1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f?a) f_{xx}f_{yy}-(f_{xy})2 and b) f_{xx}f_{yy}-(f_{xy})2

Answer:

g(0) = 3

Step-by-step explanation:

x=0 fits perfectly in the range -1<x<2:  -1<0<2 √

Hence:

g(x)=3 when x=0

Since x=0:

g(x) = g(0) = 3

Answer:

x = 2

Step-by-step explanation:

⭐What is the solution of an equation?

Thus, we need to solve for x, the variable.

Given:

3x - 7 = 7 - 4x

To solve for x, we need to have all the variables on the LHS (or RHS), and all the constants on the RHS (or LHS).

To do so, first add 4x to the LHS and RHS. This "moves" -4x to the LHS:

3x +4x - 7 = 7 +4x -4x

Add like terms (terms with the same variable) to simplify:

7x - 7 = 7

Next, add 7 to the LHS and RHS. This "moves" -7 to the RHS:

7x +7 -7 = 7 +7

7x = 14

Finally, divide the LHS and RHS by 7 to isolate the variable:

[tex]\frac{7x}{7} = \frac{14}{7}[/tex]

∴ x = 2

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