i12 + 1 = 1 - i 1 + i 0 2

The expression x = ce−2t is a solution of the initial condition is x(0) = 100 and x (0) = −2x.

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0).

Differentiating the function x = ce−2t

x = ce−2t with respect to t ,

We have:

x ′ = d/dt (Ce−2t)

x ′ = C(−2e−2t)

x ′ = −2(Ce−2t)

x ′= −2x. x ′

x ′ = d / d t ( C e − 2 t )

x ′= C ( − 2 e − 2 t )

x ′= − 2 ( C e − 2 t )

x ′= − 2 x .

Therefore,

The expression x = ce−2t is a solution of the initial condition is x(0) = 100 and x (0) = −2x.

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The probability of getting at least one question wrong on a 6 question multiple-choice test is 0.9874

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(get one question right) = 1/2

P (get all questions right) = (1/2)^6

P(get one question wrong) = 1 - P (get all questions right)

P(get one question wrong) = 1 - (1/2)^6

P(get one question wrong) = 0.9874

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Logistic regression is a statistical method used for modeling the relationship between a dependent variable and one or more independent variables. Unlike multiple regression, which is used for continuous outcome variables, logistic regression is used for categorical outcome variables, such as yes/no or pass/fail. The key differences between logistic regression and multiple regression are as follows:

a) Logistic regression does not have "b" weights - Logistic regression models the relationship between the independent variables and the dependent variable by using the logit transformation. The logit transformation maps the continuous range of values of the dependent variable to a binary range of values, allowing the estimation of the probability of a specific event. Unlike multiple regression, which uses beta (b) coefficients to quantify the strength and direction of the relationship between the independent variables and the dependent variable, logistic regression models the relationship through the use of odds ratios.

b) Logistic regression is not immune to sources of bias - Like any statistical method, logistic regression is susceptible to sources of bias, such as omitted variable bias and measurement error. It is important to be aware of these potential sources of bias and to address them through appropriate data cleaning and variable selection procedures.

c) Logistic regression predicts a categorical outcome variable - As mentioned, logistic regression is specifically designed for categorical outcome variables, such as yes/no or pass/fail. The model predicts the probability of the dependent variable taking a specific value and uses a threshold value to convert the predicted probabilities into binary outcomes.

d) Logistic regression does not log-transform the predictor variables - Unlike some statistical methods, such as log-linear regression, logistic regression does not log-transform the predictor variables. This is because the logit transformation is already applied to the dependent variable in order to model its relationship with the independent variables.

In conclusion, logistic regression is a powerful tool for modeling the relationship between a dependent categorical variable and one or more independent variables. It is important to understand its key differences from multiple regression and to be aware of potential sources of bias in order to use this method effectively.

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Answer:

f(5)=21

Step-by-step explanation:

f(1) =5

f(2) =9

f(3)= 13

f(4)=17

there for f(5) =21 all added by four more

Using distributive property, each expressions are write in an appropriate form. The expression are shown below.

This characteristic states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend separately by the number and then combining the results collectively.

According to the property, the outcomes are the same whether the numbers in parenthesis are added before or after multiplication. In situations when the polynomial cannot be combined together before being multiplied, the distributive property is very helpful. Using this property the following expression are solved.

4(6 + 7) = 4.6 + 4.7

14.1 - (14 - 9) = 14 (1 - 9)

5 (z - 10) = 5.z - 5.10

8.6 + 8.2 = 8 (6 + 2)

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Answer:

see below

Step-by-step explanation:

road 1 100km/h x hrs

road 2 80km/hr y hrs

total 6hours

total 530 km

100x+80y=530

x+y=6

x=6-y

100(6-y) + 80y =530

600-100y+80y =530

20y=70

y=3.5

x =6-3.5 =2.5

Answer: x =2.5 y= 3.5

Step-by-step explanation:

The Walmart is 2.8 miles away from her home. The result is obtained by using the speed formula in constant motion.

Speed is the change in position per unit of time. It can be expressed as

v = d/t

Where

A student walked to Walmart, bought a bike, and rode it home.

Determine the distance between the Walmart and her home!

Let's say

The distance traveled when student walked and the riding a bike is the same. It is the distance between the Walmart and her home.

d₁ = d₂ = d

So, we get t.

d₁ = d₂

v₁t₁ = v₂t₂

3.5t = 14(1 - t)

3.5t = 14 - 14t

3.4t + 14t = 14

17.5t = 14

t = 17.5/14

t = 0.8 hour

Substitute t in the walking speed formula!

d₁ = v₁t₁

d₁ = 3.5(0.8)

d₁ = 2.8 miles

d = d₁ = 2.8 miles

Hence, the distance between the Walmart and her home is 2.8 miles.

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The percentage decrease is 19.4%

In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.

(Original Cost - New Cost) / Original Cost x 100 equals the percentage decrease.

In this case, the original cost is $36 and the new cost is $29, so we plug these values into the formula:

Percentage decrease = ($36 - $29) / $36 x 100 = $7 / $36 x 100 = 0.1944 x 100 = 19.44%

We can round the answer to the nearest tenth of a percent:

19.44% rounded to the nearest tenth is 19.4%

So the percentage decrease is 19.4%

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The combined perimeter and area of all three rectangular corrals can be represented algebraically as follows:

Total perimeter = 3 * (12x - 4) = 36x - 12

Total area = 3 * (5x^2 - 2x) = 15x^2 - 6x

Let x be the width of each rectangular corral.

L = 5x - 2

          P = 2(L + x)

             = 2(5x - 2 + x)

             = 2(6x - 2)

             = 12x - 4

         A = L * x

             = (5x - 2) * x

             = 5x^2 - 2x

So, the total perimeter and area of the three corrals can be represented algebraically as a function of x, the width of each corral.

Complete Question:

"A rancher has three rectangular corrals. They have the same dimensions. The length is five times the width minus two. How can the combined perimeter and area be represented algebraically? Let x be the variable."

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Answer:

c = 3n + 5

Step-by-step explanation:

The equation c = 3n + 5 fits the data in the table. When n = -7, c = -7 * 3 + 5 = -16. When n = -6, c = -6 * 3 + 5 = -13. When n = 3, c = 3 * 3 + 5 = 14. When n = 5, c = 5 * 3 + 5 = 20. And when n = 9, c = 9 * 3 + 5 = 32. All the values of c in the table match the values predicted by the equation c = 3n + 5. Therefore, c = 3n + 5 is the correct equation for the data.

Answer:

-25

Step-by-step explanation:

= (20-25)(16+4)/-8+(3×4)

= (-5×20)/(-8+12)

= -100/4

= -25

Answer:

w = 19

Step-by-step explanation:

w = 4 + 3p

w = 4 + (3 x 5) since p = 5

w = 4 + (15)

w = 19

Answer:

w = 19

If the equation is w = 4 + 3p, we can substitute the 'p' for five.

To solve for w, we need to first solve 3 times 5.

Now, just solve.

Therefore if p = 5, w = 19.

If in the survey of a survey of a community, 55%. The percentage of the people who don't like to listen to the radio as well as watch the television​ is 15%.

The number of people who like to listen to the radio as well as watch the television = 35%.

So,

The number of people who like to listen to the radio but don't like to watch the television

=  55% - 35%

= 20%

The number of people who like to watch television but don't like to listen to the radio =  65% - 35% = 30%.

The percentage of people who don't like to listen to the radio as well as watch the television

= 100% - (35% + 20% + 30%)

= 100% - 85%

= 15%

Therefore  15% of the people in the community don't like to listen to the radio or watch the television.

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The instantaneous voltage across the capacitor is 4/53 * (-cos (106 t - 25)) (volts).

The instantaneous voltage across a capacitor is given by v(t) = 1/C * integral(i(t)dt) where C is the capacitance of the capacitor.

For the current i(t) = 4 sin (106 t - 25), the voltage across the capacitor can be found using the following definite integral:

v(t) = 1/C * integral(4 sin (106 t - 25)dt) from 0 to t

v(t) = 4/106C * (-cos (106 t - 25)) from 0 to t

So, the instantaneous voltage across a 2-F capacitor for this current will be:

v(t) = 4/53 * (-cos (106 t - 25)) (volts)

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The correct answer of this expression is (b) g>-6.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

a formula expression with the first part signifying a mathematical item and the second part signifying a statement about mathematical objects

given that;

-3 (g + 5) > 3

divide both side by -3, we get

⇒ g + 5 > 3/-3

⇒ g + 5 > -1

subtract both side by 5

⇒ g > -1 -5

⇒ g > -6

so the correct answer is g > -6

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Therefore , the solution of the given problem of expression comes out to be 2x² (2x² - 1 ) / (x⁴ + 1 - 2x²) .

Mathematical operations including addition, subtraction, multiplication, and division are required. They result in the following when combined: An equation, some information, and an arithmetic operator Values, parameters, and operations like adds, omissions, multiplications, and divisions make up a statement of fact. Different phrases and words can be contrasted and compared.

Here,

Given :

=> 2x² / x² -1

=> 2x² / x² -1  *  x² -1 /x² -1

=> 2x²(x²-1) / (x² -1)²

=> 2x⁴ - 2x² / (x⁴ + 1 - 2x²)

=>  2x² (2x² - 1 ) / (x⁴ + 1 - 2x²)

Therefore , the solution of the given problem of expression comes out to be 2x² (2x² - 1 ) / (x⁴ + 1 - 2x²) .

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The kinetic energy of the object is 4 * π^2 * m * r^2 * n^2, which is option D.

The kinetic energy of an object with mass m and velocity v can be calculated as 1/2 * m * v^2.

In this case, the velocity of the object can be calculated as the circumference of the circle (2 * π * r) multiplied by the number of revolutions per second (n), so v = 2 * π * r * n.

Substituting this expression for v into the equation for kinetic energy, we get:

1/2 * m * (2 * π * r * n)^2 = 1/2 * m * (4 * π^2 * r^2 * n^2) = 4 * π^2 * m * r^2 * n^2.

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Answer:

768

Step-by-step explanation:

2 gallons is 32 cups. Times 32 by the servings which is 24. 32 times 24 equals 768

Answer: The actual selling price should be around $3472 and 22 cents.

Answer:

Step-by-step explanation:

elish as you know me lacey i will be glad to help you the correct awnser is 3472 dollars and 22 cents

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, it can be expressed as c² = a² + b² where c is the length of the hypotenuse and a and b are the lengths of the other two sides. The theorem can be proven using Euclidean geometry.

In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In short it is written as: a² + b² = c²

For example, if the sides are 6cm and 8cm, the hypothenuse will be:

c² = 6² + 8²

c² = 100

c = ✓100

c = 10cm

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Answer:

3 hours

Step-by-step explanation:

Given,
Distance = 180 miles
Speed = 60 miles per hour
Distance/Speed = Time
Thus, Time taken is 180/60
Which is 3 hours

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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As per the standard deviation the proportion of observations is in the interval between each pair of values is 190 and 310

The term in math known as standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the mean of a population is 250 and its standard deviation is 20.

Then the proportion of observations is in the interval between each pair of values is calculated as,

We have interval (190,310) and we can express this interval as:

=> (190,310) = (250−3⋅20, 250+3⋅20)

According to this interval , we have that k=3.

Based on the value of the constant the required percent of observations in interval(190,310) is at least 88.9%

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The area of rhombus KLMN is 287.3 in²

A rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.

Given that, a rhombus KLMN with diagonals KM and NL,

Since, the diagonals of a rhombus bisects each other at a right angle,

Let they bisect at O, so, KM = 2MO = 2KO = 2×11.4 = 22.8 in

Therefore, Δ KON is a right triangle,

Using Pythagoras theorem,

KN² = KO² + ON²

ON = √17²-11.4²

ON = 12.611 in

LN = 2×12.611

LN = 25.22 in

Area of a rhombus = 1/2 × diagonal 1 × diagonal 2

Area = 1/2 × 25.22 × 22.8

= 287.3 in²

Hence, the area of rhombus KLMN is 287.3 in²

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Zegen saves $1000 every month for their new house.

By definition, saving is income minus spending. Investment refers to physical investment, not financial investment. That saving equals investment follows from the national income equals national product identity.

Given here: Zegen's income is $6000 and the fixed expenses are $3000 with flexible expenses $2000

Thus we savings = Income-expenditure

Savings = 6000-5000

            =1000

Again it is given that the savings are put aside for the downpayment of a house

Hence, Zegen saves $1000 every month for their new house.

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The expression that irrational are:

B. 2–√. 3–√

C. 27−−√. 3–√

D. 57–√2−57–√

The square root of a non-perfect square is an irrational number, meaning that it cannot be expressed as a finite decimal or as a fraction of two integers.

In options B and C, the square root of 3 and the square root of 27 respectively are both irrational because 3 and 27 are not perfect squares.

In option D, both 57-√2 and 57-√ are irrational numbers because 57 is not a perfect square and the square roots of 2 and 3 are irrational.

Option A and E can be simplified to finite decimal or fraction, therefore they are rational numbers.

A fraction is not always expressed as a decimal. A fraction is a way of representing a number as a ratio of two integers, for example, 1/2 or 3/4. While a decimal is a way of expressing a number as a sum of powers of 10, for example, 0.5 or 0.75. A fraction can be converted to a decimal and vice versa, but they are not the same thing.

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Answer: D

Step-by-step explanation: y (Waffle cones) = 13 (Waffle cones sold during first hour) + x (Waffle cones sold during remaining hours.)

Answer:

Depreciation is the decrease in value of an asset over time. We know that the value of the equipment depreciates at a rate of 20% per year, and after 5 years the equipment is worth $98,304. We can use this information to set up an equation to find the original value of the equipment.

Let X be the original value of the equipment.

We know that:

X * (1 - 0.20)^5 = 98304

Where (1 - 0.20) is the depreciation rate, and the exponent 5 is the number of years.

We can solve for X by using the following steps:

X * (1 - 0.20)^5 = 98304

X * (0.8)^5 = 98304

X = 98304 / (0.8)^5

X = $143,680

So, the original value of the equipment was $143,680.

Step-by-step explanation: