If dy/dt= -10e^-t/2 and y(0)= 20, what is the value of y(6)?
A. 20e^-6
B. 20e^-3
C. 20e^-2
D. 10e^-3
E. 5e^-3

1. The length of the two legs are 5 and 9

2. The length of the hypotenuse is 10.3( nearest tenth)

Distance between two points is the length of the line segment that connects the two points in a plane.

D = √ x2-x1)²+(y2-y1)²

The length of the horizontal leg is

= 8-3 = 5

The length of the vertical leg is

= 8-(-1) = 9

Alternatively, we can use Pythagoras theorem to solve for the hypotenuse.

c² = a²+b²

c² = 9²+5²

c² = 81+25

c² = 106

c = √106

c = 10.3( nearest tenth)

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The cups of flour required for 2 cups of cashew is 2.6667

Here, we have,

to find the proportion for 2 cups of cashews

The proportion given in the problem is 3 cups of cashews for 4 cups of flour.

From the given proportion we calculate for the quantity of flours required for 2 cups of cashew

3 cups of cashew = 4 cups of flours

2 cups of cashew = ?

cross multiplying

3 * ? = 4 * 2

? = 4 * 2 / 3

? = 8 / 3

? = 2.6667

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complete question:

3 cups of cashews for 4 cups of flour how many cups of flour for 2 cups of cashews

The toolbox's width, that is 1.5 inches and has the shape of a rectangular prism.

A rectangular prism's volume can be calculated:

V = lwh

where, l denotes the length, w the width, h the height, and V the volume.

We have dimensions: length of the toolbox is 3 feet, and the width of the toolbox is 1 foot.

we can calculate the width:

V = lwh

4.5 = 3 (1)w .....(7)

4.5 = 3w

w = 1.5

As a result, the toolbox has a 1.5 inch width.

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Answer:

Step-by-step explanation:

30

The relation y = -x + 2 is a function because (a) yes, because it passes the vertical line test.

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

y = -x + 2

The above equation is a linear function

As a general rule of functions and relations

All linear functions are functions

This is because they pass the vertical line test

So, the true statement is (a)

Hence, the relation y = -x + 2 is a function because (a) yes, because it passes the vertical line test.

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The total amount of screen Alice will need to cover the habitat is 3.04 m².

Alice plans to cover all sides of the habitat with screen so the caterpillars get plenty of fresh air.

The habitat is a rectangular prism. Therefore, the total amount of screen to cover the habitat is as follows:

surface area of the prism = 2(lw + hw + lh)

Hence,

l = 1 m

w = 0.4 m

h = 0.8 m

Therefore,

surface area of the prism = 2(1 × 0.4 + 0.8 × 0.4 + 1 × 0.8)

surface area of the prism = 2(0.4 + 0.32 + 0.8)

surface area of the prism = 2(1.52)

surface area of the prism = 3.04 metres²

Hence,

amount of screen needed to cover the habitat = 3.04 m²

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Cutting each x-value in half and subtracting 0.04 from each y-value does not affect the correlation between x and y, as linear transformations do not change the correlation coefficient.

If each x-value is cut in half and 0.04 is subtracted from each y-value, the correlation between the two variables (x, y) will not change.

This is because linear transformations, such as subtracting a constant from each data point or multiplying each data point by a constant (as in the case of cutting each x-value in half), do not affect the correlation between two variables.

To see why this is the case, consider the formula for the correlation coefficient:

r = (n * Σxy - Σx * Σy) /√[(n * Σx² - (Σx)²) * (n * Σy² - (Σy)²)]

where n is the sample size, Σxy is the sum of the products of the x and y values, Σx and Σy are the sums of the x and y values, and Σx² and Σy² are the sums of the squared x and y values.

If we apply a linear transformation to the x or y values, the values of Σx, Σy, Σx², Σy², and Σxy will change accordingly, but the formula for r will remain the same.

Therefore, the correlation between x and y will not change when we cut each x-value in half and subtract 0.04 from each y-value.

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If r is < 0, then lambda must be:  Less than 0, Less than 1, Greater than 1  and Greater than 0. The correct answers are: A), B), C), and D).

Recall that the exponential growth or decay model is given by the function:

[tex]y = y0 * e^(rt)[/tex]

where y0 is the initial value of the function, r is the rate of change (growth or decay), t is the time, and e is the mathematical constant approximately equal to 2.71828.

If r < 0, then the function represents exponential decay, and we have:

[tex]y = y0 * e^(rt)[/tex]

y/y0 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(y/y0) = rt

r = (1/t) * ln(y/y0)

Since ln(y/y0) is the natural logarithm of a ratio, it can take any real value. Therefore, r can take any negative value, and there is no restriction on the value of lambda (which is[tex]e^r[/tex]).

So, the correct answers are: A), B), C), and D).

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The concept of mean to guide our understanding of the typical values in these distributions.

Without any specific information about the distributions of dogs and cats, it is difficult to say anything definitive about the means of these distributions. However, we can make some general observations about the concept of mean.

The mean, also known as the average, is a measure of central tendency that represents the typical value in a set of data. It is calculated by adding up all the values in the data set and dividing by the total number of values. In other words, the mean is the sum of all values divided by the count of values.

If a distribution is roughly symmetric and bell-shaped, the mean will be close to the center of the distribution. In this case, the mean represents a typical or average value in the data set. However, if a distribution is skewed, the mean may be pulled in the direction of the skew. For example, if a distribution has a long tail to the right, the mean will be greater than the median and may not be a good representative of the center of the distribution.

It is also important to note that the mean can be influenced by outliers, or extreme values that are much larger or smaller than the other values in the data set. In this case, the mean may not be a good representative of the typical value in the data set.

Therefore, without knowing specific information about the distributions of dogs and cats, we cannot say anything definitive about the means of these distributions. However, we can use general principles about the concept of mean to guide our understanding of the typical values in these distributions.

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What can be said about the mean of each distribution of dogs and cats?

The solutions to the inequality are:

C) 5.6

D) 5.75

E) 6

To solve the inequality y + (-8) > -2.5, we can isolate the variable y by adding 8 to both sides:

y + (-8) + 8 > -2.5 + 8

y > 5.5

Therefore, any value of y that is greater than 5.5 will satisfy the inequality.

From the options given:

A) 5.25 is not greater than 5.5, so it is not a solution.

B) 5.5 is equal to 5.5, and we need values greater than 5.5, so it is not a solution.

C) 5.6 is greater than 5.5, so it is a solution.

D) 5.75 is greater than 5.5, so it is a solution.

E) 6 is greater than 5.5, so it is a solution.

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The speed of the boat using the distance and time form the graph would be = 26 miles per hour. That is option B.

To calculate the speed of the boat, the formula that should be used is given as follows. That is;

Speed of boat = Distance/time

Distance = y2-y1= 117-13 = 104

Time = X2-X1 = 4-0 = 4

Speed = 104/4 = 26 miles/hr

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The y-intercept of the given function is (0,-7) and the horizontal asymptote is y=−3.

The given function is f(x)=-(2)ˣ⁺²-3.

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: (-∞,-3),{y|y<-3}

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): None

y-intercept(s): (0,-7)

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=−3.

Therefore, the y-intercept of the given function is (0,-7) and the horizontal asymptote is y=−3.

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The number of boxes required to ship n units of the product can be expressed using the floor notation as [tex]$\left\lfloor\frac{n}{36}\right\rfloor$[/tex] and using the ceiling notation as [tex]$\left\lceil\frac{n}{36}\right\rceil$[/tex].

The floor notation gives the largest integer less than or equal to the quotient of n divided by 36. It is appropriate to use the floor notation when we want to round down to the nearest integer value. For example, if we have 100 units of the product, we would need [tex]$\left\lfloor\frac{100}{36}\right\rfloor=2$[/tex] boxes, meaning we would need to ship the product in two boxes.

The ceiling notation gives the smallest integer greater than or equal to the quotient of n divided by 36. It is appropriate to use the ceiling notation when we want to round up to the nearest integer value. For example, if we have 38 units of the product, we would need [tex]$\left\lceil\frac{38}{36}\right\rceil=2$[/tex] boxes, meaning we would need to ship the product in two boxes.

In most cases, it is appropriate to use the ceiling notation since it ensures that we always have enough boxes to ship the product. However, in some cases, such as when we want to minimize shipping costs, it may be more appropriate to use the floor notation to reduce the number of boxes needed.

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The final temperature of the liquid is 4°C.

Remember that two real numbers are called opposites if their sum is equal to zero, so, A and B are opposites if:

A + B = 0

And neither A or B are zero.

Here the initial tempreatuire is -4°C and the final temperature is T, and it is the opposite of the initial one, then we can write:

-4°C + T = 0

T = 4°C

That is the final temperature.

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The average rate of change during those 6 hours was 12/6 = 2 inches per hour.

To find the constant rate of change, we need to determine how much the water level increased per hour.

From noon to 1:00 pm, the water level rose by 2 inches, so the rate of change during that hour was 2 inches. From 1:00 pm to 7:00 pm, or over a period of 6 hours, the water level rose by 14 - 2 = 12 inches. So, the average rate of change during those 6 hours was 12/6 = 2 inches per hour.

We can conclude that the constant rate of change for the water level of the pond was 2 inches per hour, which means that the water level was rising at a steady pace throughout the period from noon to 7:00 pm.

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Rounded to one decimal place, the volume of the prism is approximately 0.0 liters.

To find the volume of the prism, we multiply the length (l), width (b), and height (h) together.

Given:

l = 0.15

b = 40 mm

h = 20 cm

First, let's convert the measurements to the same unit for consistency. We'll convert mm to cm for the width.

b = 40 mm = 4 cm

Now, we can calculate the volume:

Volume = l * b * h

Volume = 0.15 cm * 4 cm * 20 cm

Volume = 12 cm³

To convert the volume to liters, we divide by 1000 since there are 1000 cm³ in 1 liter:

Volume = 12 cm³ / 1000 = 0.012 liters

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Theorem 4.4.3 is the transitivity of divisibility theorem, which states that for all integers a, b, and c, if a divides b and b divides c, then a divides c. In other words, if a is a factor of b and b is a factor of c, then a is also a factor of c.

To prove this theorem, we can use the definition of divisibility, which states that if a and b are integers, then a divides b if and only if there exists an integer k such that b = ak. Suppose that a divides b and b divides c. Then, we can write b = am and c = bn, where m and n are integers.

Substituting b = am into the expression for c, we get c = anm. Since n and m are integers, their product nm is also an integer, which means that c = a(nm) is a multiple of a. Therefore, a divides c, which proves the transitivity of divisibility theorem.

This theorem is a fundamental property of divisibility and is often used in number theory and other mathematical areas. It allows us to establish relationships between divisors and can be used to simplify calculations involving factors and multiples of integers.

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The Minimum number of lines needed to cover all zeroes is 2.

To determine the minimum number of lines needed to cover all the zeroes after row and column reductions, we must first perform the reductions on the given matrix. The matrix is not provided in a standard format, but I will assume it is a 3x3 matrix based on the 9 given numbers:
Initial matrix:
4 7 6
6 6 9
6 9 6
Row reduction - Subtract the minimum value of each row from all elements in that row.
Row 1: 4 - 4 = 0, 7 - 4 = 3, 6 - 4 = 2
Row 2: 6 - 6 = 0, 6 - 6 = 0, 9 - 6 = 3
Row 3: 6 - 6 = 0, 9 - 6 = 3, 6 - 6 = 0
Row-reduced matrix:
0 3 2
0 0 3
0 3 0
Column reduction - Subtract the minimum value of each column from all elements in that column.
Column 1: 0 - 0 = 0, 0 - 0 = 0, 0 - 0 = 0
Column 2: 3 - 0 = 3, 0 - 0 = 0, 3 - 0 = 3
Column 3: 2 - 2 = 0, 3 - 2 = 1, 0 - 0 = 0
Row- and column-reduced matrix:
0 3 0
0 0 1
0 3 0
Draw the minimum number of lines needed to cover all zeroes.
1. Draw a line through the first row, covering one zero.
2. Draw a line through the second column, covering the two remaining zeroes.
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Thus, for random samples of 50 students taken from the population, the sampling distribution of the sample mean completion time will be approximately normally distributed, with a mean of 70 minutes and a standard error of 3.75 minutes.

The sampling distribution of the sample mean completion time for random samples of 50 students from the high school can be described using the Central Limit Theorem.

In this case, the original population has a mean completion time of 70 minutes and a standard deviation of 26.5 minutes.

So, the standard error would be 26.5 / √50 ≈ 3.75 minutes.

In summary, for random samples of 50 students taken from the population, the sampling distribution of the sample mean completion time will be approximately normally distributed, with a mean of 70 minutes and a standard error of 3.75 minutes.

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Answer:

cos(L) = √73/11 = 0.776

Step-by-step explanation:

i explaind every thing on the image

Answer:

-2(-6+3y-1) = -6y+14

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/5, 4/20/ 3/15, are three fractions equilvent to 2/10.

The value of the composite function g(-1) - h(1) is -7.

We have,

Functions:

h(t) = 16t - 4 and g(t) = 3 - 2t

Now,

We subtract the function g(t) from h(t).

g(-1) - h(1)

= (3 - 2(-1)) - (16(1) - 4)

= 5 - 12

= -7

Therefore,

The composite function g(-1) - h(1) is -7.

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Answer:

In the mathematical expression 2πn, "n" typically represents an integer variable, which can take on any whole number value (positive, negative, or zero). In this case, it's positive.

When used in this context, 2πn represents a sequence of values that are evenly spaced at intervals of 2π, and infinitely repeats every 2π. For example, if n takes on the values of 0, 1, 2, 3, 4, 5, ..., then the corresponding values of 2πn would be 0, 2π, 4π, 6π, 8π, 10π, ..., respectively.

Answer:

Step-by-step explanation:

It's like saying there are infinite solutions

(n) is number of times going around

Ex.

pi/6 is a solution   also,

pi/6 +2pi     still brings you back to same position, but also

pi/6 +2pi + 2 pi   or   pi/6 + 2pi (2)   going around twice

pi/6 +  2pi (3)    going around 3 times.

It's saying you have pi/6 as a solution + everytime you go around the circle 2pi , n times.

The price for a measurement of per fluid ounce for the carton of sour cream is $0.11.

Given that,

A 6-cup carton of sour cream costs $5.28.

Total cups of sour cream = 6 cups

We have the conversion factor,

1 cup = 8 fluid ounces

6 cups = 48 fluid ounces

Price for 48 fluid ounces of sour cream = $5.28.

Price for 1 fluid ounces of sour cream = 5.28 / 48

                                                              = 0.11

Hence the price per fluid ounce is $0.11.

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The conditional value probability is solved and P ( A/B ) = 0.947

Given data ,

The Bayes theorem of conditional probability to calculate P(A/B):

P(A/B) = P(AnB) / P(B)

We are given that P(AnB) = 0.72 and P(B) = 0.76, so we can substitute these values into the formula:

P(A/B) = 0.72 / 0.76

Simplifying this expression, we get:

P(A/B) = 0.947

Hence , the probability P(A/B) is approximately 0.947

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We are given to select the correct expression that gives the volume of a sphere with radius 11 units.

We know that the Volume of a sphere with radius 'r' units is given by

[tex]\text{V}=\dfrac{4}{3}\pi \text{r}^3[/tex]

Here, the radius of the given sphere is

Therefore, the volume of the sphere will be

[tex]\text{V}=\dfrac{4}{3}\pi \text{r}^3[/tex]

[tex]\rightarrow\text{V}=\dfrac{4}{3}\pi (11)^3[/tex]

Thus, the required expression is:

[tex]\boxed{\bold{\rightarrow V=\dfrac{4}{3}\pi (11)^3}}[/tex]

Answer: y = 2x - 3

Step-by-step explanation:

   To solve, we will isolate the y variable.

Given:

   2x - y = 3

Subtract 2x from both sides of the equation:

   - y = -2x + 3

Divide both sides of the equation by -1:

   y = 2x - 3