Please help me understand? I don't get it.​

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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To find the height the ladder reaches on the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder in this case) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the height the ladder reaches on the wall "h." Then we have a right triangle with sides h, 7 (the distance from the wall), and 12 (the length of the ladder).

Using the Pythagorean theorem, we have:

h^2 + 7^2 = 12^2

Solving for h:

h = sqrt(12^2 - 7^2) = sqrt(144 - 49) = sqrt(95) = 9.746781

Rounding to two decimal places, the ladder's height on the wall is 9.75 feet.

The Pythagorean theorem is a mathematical principle named after the ancient Greek mathematician Pythagoras. It 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 lengths of the other two sides.

The theorem can be written as an equation:

a^2 + b^2 = c^2,

Where c is the hypotenuse length, and a and b are the lengths of the other two sides.

The Pythagorean theorem has numerous applications in mathematics, physics, engineering, and other fields and is considered one of the most important theorems in mathematics.

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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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Value of d = -8/3

The slope of a line is defined as the change in vertical coordinate with respect to the change in horizontal coordinate of that line.

Given,

Slopes of perpendicular lines are 3/4 and d/2

When two lines are perpendicular, product of their slopes = -1

3/4 × d/2 = -1

3d/8 = -1

d = -8/3

Hence, -8/3 is the value of d.

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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.)

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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Answer:

768

Step-by-step explanation:

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

How quickly a disease spreads through a population is shown by its incidence rate. So this measurement represent incidence type of rate. So the option A is correct.

How quickly a disease spreads through a population is shown by its incidence rate. It has a few benefits over an occurrence ratio because it is based on person-time. Person-time may account for people entering and exiting the research because it is calculated for each participant.

Incidence is the percentage or rate of people who develop a condition within a specific time period, as opposed to prevalence, which refers to the proportion of people who have a condition at or during a specific time period.

The total number of event occurrences within a given time period are represented by the COUNT metric submission type.

The mortality rate, often known as the death rate, is a measurement of the number of fatalities (generally speaking, or those caused by a particular cause) in a given population, scaled to that population's size, per unit of time.

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The complete question is:

A public health nurse is developing an educational program on the Zika virus for a community based on the information found on the county health website and comparing the number of persons (1,237) in the community. The nurse found there were 6 new cases in the past month in the country. The rate was computed as 0.005%. What type of rate does this measurement represent?

a. incidence

b. prevalence

c. count

d. mortality

Answer:

Sqrt92

9.6 or rounded to the nearest whole #, 10

Step-by-step explanation:

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

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: x = g - c

Step-by-step explanation:

Isolate the variable: g-c = c-c + x

Rearrange the terms: g - c = x

x = -c + g

Answer:

B C F

Step-by-step explanation:

Total flour =   5  * 3/8

  and this is divided by 7 loaves

this becomes

5 *  3/8  /  7         then you just to look for the equivalent expressions

B      C    and F   are the same thing

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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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.

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 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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For per unit scoops of powdered 2 cups of Water is Needed.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given,  Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.

We have to find how many cups of water should he use with 6 scoops of fruit mix

Let "n" be the number of cups required for 6 scoops of fruit mix

3 cups of water ⇒ 1.5 scoops of fruit mix.

Then, n cups of water ⇒ 6 scoops of fruit mi

So, by cross multiplication,

6 * 3 = n *1.5

n = 12

Ryan has to use 12 cups of water for 6 scoops.

thus,

For per unit scoops of powdered 2 cups of Water is Needed.

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When the curve with equation y = f(x) is reflected and squared, the transformed function of f(x) is -1/2f(y).

Transformations are a catch all term for four different kinds of changing the location and/or shape of a circle, line, or geometric figure. The words used are the Pre-Image, which describes the shape of the object at first, and the Image, it describes the final shape and location of the object following alteration. Translations, mirrors, and dilations are the three different types of transformations. A function can be transformed in two different ways: vertically (which affects the y-values) and horizontally (affects the x-values). The equations of a function illustrated below includes the four conversion variables (a, b, h, and k). altering the log Consider the record of each observation as an illustration. multiplying by the square root each term's square root .

given

Initial Reflection Axis = ( -5 , -2 )

the axis of the x coordinate contracts to 1/2 (y )

= -1/2f ( y )

When the curve with equation y = f(x) is reflected and squared, the transformed function of f(x) is -1/2f(y).

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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 average velocity of a hiker that climb 0.9 km in 45 minutes is 1,2 km/hour.

Velocity is a derived quantity derived from the principal quantities of length and time, where the formula for speed is distance divided by time. Velocity is a vector quantity that indicates how fast an object is moving. Average velocity is the ratio between the displacement that occurs in an object with the time it takes to make the move.

Given,

Distance traveled = [tex]\frac{9}{10}[/tex] of 1 kilometer = 0.9 km

Time = [tex]\frac{3}{4}[/tex] of 1 hour = 0.75 hours

Velocity = [tex]\frac{distance}{time}[/tex]

Velocity =  [tex]\frac{0,9 km}{0,75 hours}[/tex]

Velocity = 1,2 kph

So that the velocity taken by the hiker is 1,2 kph.

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The probability of grabbing 2 consecutive orange pieces is approximately 0.101.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of grabbing 2 consecutive orange pieces without replacement is calculated as:

[tex]\frac{30}{100}[/tex] × [tex]\frac{29}{99}[/tex] = 0.090/0.9 = 0.101010101...

Therefore, the probability of grabbing 2 consecutive orange pieces is approximately 0.101.

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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:

-25

Step-by-step explanation:

= (20-25)(16+4)/-8+(3×4)

= (-5×20)/(-8+12)

= -100/4

= -25

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:

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:

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