solve the following initial-value problems starting from y0 = 6 . dy/d t = − 6y a. y = ____
at what time does y increase to 100 or drop to 1? round your answer to four decimal places.
b. t = ____

Answer:

720 square inches.

Step-by-step explanation:

To find the surface area of a triangular prism, we need to find the area of each face and add them together.

The triangular bases have base 12 in and height 15 in, so the area of each is:

(1/2) × 12 in × 15 in = 90 in²

The rectangular faces have dimensions 20 in × 15 in and 20 in × 12 in, so their areas are:

20 in × 15 in = 300 in²

20 in × 12 in = 240 in²

Adding these up, we get:

2 × 90 in² + 300 in² + 240 in² = 720 in²

the surface area of the triangular prism is 720 square inches.

The length of the boundary wall that needs to be raised to enclose the entire football stadium is 420 + 40 = 460 meters.

To determine the length of the boundary wall that needs to be raised, we need to know which part of the stadium the wall will enclose.

If the wall is to be raised along the length of the stadium (i.e., the longer side), then the length of the wall will be equal to the length of the stadium, which is 125 meters.

If the wall is to be raised along the width of the stadium (i.e., the shorter side), then the length of the wall will be equal to the width of the stadium, which is 85 meters.

If the wall is to enclose the entire stadium, then we need to find the perimeter of the stadium and add the length of the wall that will enclose the remaining side.

Perimeter of the stadium = 2 x (length + width)

Perimeter of the stadium = 2 x (125 + 85) = 420 meters

To enclose the remaining side, we need to add a wall of length 125 - 85 = 40 meters.

Therefore, the length of the boundary wall that needs to be raised to enclose the entire football stadium is 420 + 40 = 460 meters.

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1. The data show's a symmetric distribution

The second diagram is left skewed

2. The second shape would have a greater standard deviation because its skewness is more

3. √(2 + 5 + 0 + 3 + 4)²/17

= √(0.8235)²

= √0.6781

= 0.8234

using the same calculation the standard deviation is 1.1418

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The standard form for linear equations in two variables is Ax+By=C.

A group of two or more linear equations that you want to solve simultaneously is referred to as a system of linear equations. A combination of numbers that makes every equation true simultaneously is the solution to a system of linear equations.

Systems of linear equations can be solved using a variety of techniques, including substitution, elimination, and graphing.

For example, 2x+3y=5 is a linear equation in standard form.

Utilize it to determine the slope and y-intercept before writing the Slope-intercept form should be used to formulate the equation.

A linear equation can be used to represent a straight line on a graph.. There are several ways to write it, however one of the most used is the slope-intercept form:

y = mx + b

where m denotes the line's slope and b its y-intercept. The difference in y between any two points on a line, divided by the difference in x, is the slope of the line. The line's intersection with the y-axis is known as the y-intercept.

You need to know either two points on the line or the slope and one point on the line in order to form a linear equation. With this knowledge in hand, you may utilize it to determine the slope and y-intercept before writing the Slope-intercept form should be used to formulate the equation.

Complete question is below :

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How do you Writing Linear Equations Using the Slope and Intercept?

Answer:

Step-by-step explanation:

√4 - 3.14 ; -2/3 ;  √25 + √6 ; Зx3.14

Answer:

-8 - 1 - 2 = -9 - 3 is not an equal expression because when both sides are simplified you get -12 from -9-3 and -11 from -8-1-2.    (-11)≠(-12)

Step-by-step explanation:

If you are confused with subtracting negatives from negatives there is an equal trick which can make it seem a lot more easier. Basically instead of viewing it as -9-3, you can look at it was -9+(-3). Both of these problems are the same thing, but by just adding the + in the middle makes it seem a lot more easier to interpret. Hope this helps.

Answer:

the scale factor used to create the image is 3

Answer:

The answer is 3

Step-by-step explanation:

I took the test and got it right :)

The simplified expression is (7/4)a - 11.

What is simplification?

Exam scores are improved by simplifying mathematical problems, which is also used in everyday life to get discounts in malls of up to 35%, flat discounts, or 20% for purchases up to Rs. 100. In this section, you only need to use the basic simplification principles to solve equations.

Therefore, simplifying an expression entails using various techniques to transform it into a simpler variant. The actions needed to reduce things are carried out in a predetermined sequence known as BODMAS.

To simplify the expression, we can start by distributing the coefficients to the terms inside the parentheses:

3/4(5a - 16) - 1/3(6a - 3)

= (3/4 * 5a) - (3/4 * 16) - (1/3 * 6a) + (1/3 * 3)

= (15/4)a - 12 - 2a + 1

= (15/4)a - 2a - 11

= (7/4)a - 11

Therefore, the simplified expression is (7/4)a - 11.

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we know that

[tex]\text{[volume of a prism]}=\text{length}\times\text{width}\times\text{height}[/tex]

[tex]\text{length}=1 \dfrac{1}{4} \ \text{cm}\longrightarrow \dfrac{(1\times4+1)}{4} \longrightarrow \dfrac{5}{4} \ \text{cm}[/tex]

[tex]\text{width}=1 \dfrac{1}{2} \ \text{cm}\longrightarrow \dfrac{(1\times2+1)}{2} \longrightarrow \dfrac{3}{2} \ \text{cm}[/tex]

[tex]\text{height}=\dfrac{1}{6} \ \text{cm}[/tex]

[tex]\text{[volume of a prism]}=\huge \text(\dfrac{5}{4}\huge \text{)}\times\dfrac{3}{2} \times\dfrac{1}{6} \implies\dfrac{5}{16} \implies 0.3125 \ cm^3[/tex]

the answer is:

the volume is 0.3125 cm³ (5/16 cm³)

Answer:

To find the probability that on two consecutive mornings the person will miss the bus at least one morning, we can use the complement rule. The complement of missing the bus is catching the bus. Therefore, the probability of missing the bus on both mornings is (0.4) x (0.4) = 0.16. The probability of not missing the bus on both mornings is (1 - 0.4) x (1 - 0.4) = 0.36. To find the probability of missing the bus at least one morning, we can subtract the probability of not missing the bus on both mornings from 1: P(missing bus at least once) = 1 - P(not missing bus on both mornings) P(missing bus at least once) = 1 - 0.36 P(missing bus at least once) =

Here are the solutions for each situation, listed from least to greatest:

In mathematics, probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.

The probability of an event A is denoted by P(A) and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation.

For example, if we roll a fair six-sided die, the probability of rolling a 4 is 1/6 because there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling any number from 1 to 6).

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The correct statement is:

B. The gummy bear is more likely to be strawberry than orange or raspberry.

What are likely events?

In probability theory, an event is a set of outcomes of an experiment or a random phenomenon. A likely event is an event that has a high probability of occurring

To determine the probability of selecting a gummy bear of a particular flavor, we need to divide the number of gummy bears of that flavor by the total number of gummy bears in the package.

The total number of gummy bears is:

4 + 3 + 8 + 9 + 12 = 36

So the probabilities of selecting a gummy bear of each flavor are:

Pineapple: 4/36 = 1/9

Lemon: 3/36 = 1/12

Raspberry: 8/36 = 2/9

Orange: 9/36 = 1/4

Strawberry: 12/36 = 1/3

Therefore, the correct statement is:

B. The gummy bear is more likely to be strawberry than orange or raspberry.

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Answer:

any value of x that satisfies the given conditions (i.e., makes the mean of the marks equal to the given value) is a possible score for Esi in the test. For example, if we want the mean to be 80, we can substitute 80 for Mean in the expression above and solve for x.

Step-by-step explanation:

   Expression for the mean of the marks:

   The mean of the marks is the sum of all the marks divided by the number of students. So, for this problem, the expression for the mean is:

Mean = (92 + 85 + 65 + x) / 4

   Linear inequality for the mean being less than 80:

   We can find the mean of the marks using the expression above:

Mean = (92 + 85 + 65 + x) / 4

To write a linear inequality for the mean being less than 80, we can set up the inequality:

(92 + 85 + 65 + x) / 4 < 80

We can then solve for x:

92 + 85 + 65 + x < 320

x < 320 - 92 - 85 - 65

x < 78

Therefore, if Esi scored less than 78 in the test, the mean of the marks would be less than 80.

   Possible marks Esi scored in the test:

   We can use the expression for the mean of the marks to solve for Esi's score. We know that the mean of the marks is:

Mean = (92 + 85 + 65 + x) / 4

And we know that Esi's score is x. So, we can substitute x with Esi's score and solve for it:

(92 + 85 + 65 + Esi) / 4 = Mean

Multiplying both sides by 4:

92 + 85 + 65 + Esi = 4 x Mean

Simplifying:

242 + Esi = 4 x Mean

Substituting Mean with its value:

242 + Esi = 4 x ((92 + 85 + 65 + x) / 4)

Simplifying:

242 + Esi = 92 + 85 + 65 + x

242 + Esi = 242 + x

Subtracting 242 from both sides:

Esi = x

The map is scaled at 3 in. to 2 km. Therefore , 3 inches on the map correspond to 2 kilometres in actual distance between two tourist.

A scale is a group of figures—numbers, amounts, etc.—used to gauge or contrast an object's level. A scale in maps refers to the relationship between an object's actual size and its size on a map, model, or diagram.

We can use the following ratio to determine the real separation between the two tourist attractions:

"2 kilometers / 3 inches= kilometers /× 5  3/4 inches"

where x is the actual separation between the two attractions for tourists.

To find x, we can cross-multiply:

`3× x = (5 + 3/4× 2`)

`3x = 11.5`

`x = 11.5 / 3`

`x = 3.83 km`  

The actual distance between the two tourist destinations is 3.83 kilometers

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.

Answer: D3 friends equally share 7 peaches​

Step-by-step explanation:
there are 3 1/3 pieces meaning there are 3 friends. Each friend gets 2 so 2x3 = 6 and 1/3 times 3/1 = 1 so 6+1=7

If the total is 153, then the percentage would be of 107 be simply calculated by using the formula as 69.935.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is interpreted as "percent" or "percentage."

This percent sign may always be changed to a fraction or decimal equivalent by using "divided by 100."

We already have our first value 153 and the second value 107. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1

Y = 107 / 153

By multiplying both numerator and denominator by 100 we will get:

STEP 2

Y =  107 /153 × 100

= 69.935

STEP 3

Y = 69.935

Finally, we have found the value of Y which is 69.935 and that is our answer.

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Complete question;

If the total is 153, what would be the percentage of 107?

A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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Answer: 10 children

Step-by-step explanation:

Given:

First, let's find the cost "per child"

Notebook: 1 × 1.15

+

Pencils: 2 × 0.34

Equation for cost per child:

1(1.15) + 2(0.34)

Solve:

1.15 + 0.68

= 1.83$

We have $20. So, to find how many children can be provided with supplies, we divide 20 by 1.83 (which is the cost per child)

20 ÷ 1.83 = 10.928

(Gives us a terminating decimal)

Since we can't just give a child .928 of a set of supplies, we round down to 10.

Therefore,

10 children can be provided with supplies with $20.

The probability of 12 power failures occurring in a semester is approximately 0.065 or 6.5%.

To calculate the probability of 12 power failures occurring in a semester, we need to use the Poisson distribution, which models the number of events that occur in a fixed interval of time or space.

The Poisson distribution is appropriate when the events occur randomly and independently, and the rate of occurrence is constant.

The Poisson distribution has a single parameter, lambda (λ), which represents the mean and variance of the distribution. In this case, λ = 2 power failures per month * 6 months in a semester = 12 power failures per semester.

Using the Poisson probability mass function, we can calculate the probability of exactly 12 power failures in a semester:

P(X = 12) = (e^(-λ) * λ^12) / 12!

= (e^(-12) * 12^12) / 12!

≈ 0.065

This means that in a large number of semesters, we would expect to observe 12 power failures in about 6.5% of them.

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The value of x as required to be determined in the task content is; 10.7°.

It follows from the task content that the value of x is to be determined from the task content.

Since the given figure is such that the lines MN and MP are tangents to the circle; the assertion which holds is that <MLP and <MNP are supplementary angles.

On this note, it follows that;

73° + x° = 180°.

On this note;

x = 180 - 73

x = 107°.

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The strengthening of National Ambient Air Quality Standards for maximum daily concentration of PM2.5 from 65 micrograms to 35 micrograms is expected to have a positive impact on public health.

The PM2.5 is defined as a fine particulate matter which penetrate deep into the lungs and cause a range of health problems, including asthma attacks, heart disease, and lung cancer.

By lowering the maximum daily concentration of PM2.5, the EPA is aiming to reduce the amount of air-pollution that people are exposed to, which should lead to improvements in public health.

Therefore, the strengthening of the National Ambient Air Quality Standards for PM2.5 is a positive step towards protecting public health and reducing the burden on medical facilities.

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The grocer's gain percentage is 5% after he sells 40 liter of oil for the cost price of 42 liter.

In business and finance, profit is the amount of money earned by a company or an individual after deducting all the expenses and costs associated with producing and selling goods or services. It is essentially the difference between the revenue earned from selling goods or services and the costs incurred in producing and selling those goods or services.

Let's assume that the cost price of 1 liter of oil is $1 for simplicity.

According to the problem, the grocer is selling 40 liters of oil for the cost price of 42 liters. So, his total cost price for 40 liters of oil is 40 * $1 = $40.

However, he is selling 42 liters worth of oil, which means his selling price is 42 * $1 = $42.

Therefore, his profit in this case is $2 (selling price - cost price).

To find his gain percentage, we can use the following formula:

Gain percentage = (Profit / Cost price) x 100

Substituting the values, we get:

Gain percentage = ($2 / $40) x 100 = 5%

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The correct answers are:

C. The probability of being included in the sample is the same for all members of the population of interest.

D. Sampling must be done without replacement.

The correct answer is, "The probability of being included in the sample is the same for all members of the population of interest" and "sampling must be done without replacement."

An independent random sample is a subset of a population that is selected in such a way that each member of the population has an equal and independent chance of being included in the sample. This means that the probability of being included in the sample is the same for all members of the population, which is why the statement "the probability of being included in the sample is the same for all members of the population of interest" is correct.

In addition, sampling must be done without replacement, which means that once an individual has been selected for the sample, they cannot be selected again. This ensures that each member of the population has an equal chance of being selected and that the sample is not biased towards certain individuals.

The statement "sampling must be done with replacement" is incorrect because it implies that individuals can be selected multiple times, which would not result in an independent random sample. The statement "every time an individual is selected for the sample, each of the remaining individuals has a higher chance of being included" is also incorrect because it suggests that the sampling process is not independent, which would also result in a biased sample.

Therefore, The probability of being included in the sample is the same for all members of the population of interest and sampling must be done without replacement.

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The overall shape of the distribution is normal.

If the overall shape of the combined distribution for both the class samples and the simulation samples was normal, then it suggests that the individual distributions of the samples were either normally distributed or approximately normally distributed.

A normal distribution, also known as a Gaussian distribution or a bell curve, is a probability distribution that is symmetric and bell-shaped. The normal distribution is commonly used in statistical analysis and modeling because it is often observed in real-world data and has some desirable properties.

When the individual distributions of the samples are combined, their values are added up or averaged, resulting in a larger sample size and a more representative estimate of the underlying distribution. If the individual distributions are normally distributed, then the central limit theorem states that the combined distribution will tend towards normality as the sample size increases. This can explain why the overall shape of the combined distribution for both the class samples and the simulation samples was normal.

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Drawing a 10 from the bag      unlikely

Rolling a number less than 5   Likely

Drawing a red marble             equally likely and unlikely

Here is the completed frequency table:

Number       frequency

1                       9

2                    12

3                    10

4                    8

5                    5

6                     6

Hiro's prediction is likely.

Probability determines the odds that a random event would happen. If the probability value is 0.5, it is equally likely and unlikely that the event would happen. If it is less than 0.5, it is unlikely that the event would happen. If it is greater than 0.5, it is likely that the event would happen.

Probability of drawing a 10 = number of 10s in the bag / total number in the bag = 1/100 = 0.01

It is unlikely that you would draw a 10.

Probability of rolling a number less than 5 = numbers that are less than 5 / total number of sides =  4/6 = 0.67

It is likely that a number less than 5 would be rolled.

Probability of drawing a red marble = total number of red marbles / total number of marbles = 8 / 16 = 0.5

It is equally likely and unlikely that a red marble would be picked

In order to determine the frequency, if the denominator of the relative frequency of the number is equal to 50, then the numerator is equal to the frequency. In the case where the denominator is less than 50, divide 50 by the number, multiply the quotient by the numerator in order to determine the frequency.

The frequency of 2 = (50 / 25) x 6 = 12

Number       frequency

1                       9

2                    (6 x 2) 12

3                    (1 x 10) 10

4                    (4 x 2) = 8

5                    (1 x 5) 5

6                     (3 x 2) 6

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Answer:

438

Step-by-step explanation:

the rate of decay is 438 the decay factor is 999

the answer's translation.