Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time t can be determined from the weight using the forumula: f'(t)=â5f(t)(3+f(t)). If there is 5 grams of solid at time t=2 estimate the amount of solid 1 second later.

I think niether I'm soooo sorry if I get it wrong

To represent a categorical variable with three possible levels in a regression study, you would need two dummy variables.

In general, when a categorical variable has k levels, you need to create k-1 dummy variables to represent the variable in a regression model. This is because you can represent any one level of the categorical variable as the reference category, and then use k-1 dummy variables to represent the other k-1 categories relative to the reference category.

In this case, since the categorical independent variable has three possible levels (level 1, level 2, and level 3), we would need to create two dummy variables. One dummy variable would represent the difference between level 2 and the reference level (level 1), and the other dummy variable would represent the difference between level 3 and the reference level (level 1).

For example, if we denote the dependent variable as Y, the quantitative independent variable as X, and the categorical independent variable as Z, the regression equation could be written as:

Y = β0 + β1X + β2D1 + β3D2

In this case, since the categorical independent variable has three possible levels (level 1, level 2, and level 3), we would need to create two dummy variables.

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Answer: The height of street sign = 15

Step-by-step explanation:

At the same time, the angle made by the light on each object is the same.

Pole and street sign both standing vertical to the ground.

So triangle made by both of them are similar

The sides of similar triangles are proportional,

\(\dfrac{\text{height of street sign}}{\text{height of pole}}=\dfrac{\text{Length of the shadow made by street sign}}{\text{Length of the shadow made by pole}}\\\\\dfrac{\text{height of street sign}}{40}=\dfrac{12}{32}\\\\\text{height of street sign}=\dfrac{12}{32}\times40=15\)

Hence, the height of street sign = 15

Answer:

a > 4

Step-by-step explanation:

\(6a > 20 + a \\ collect \: like \: terms \\ 6a - a > 20 \\ then \: add \\ 5a \: > 20 \\ divide \: both \: sides \: by \: 5 \\ \frac{5a}{5} > \frac{20}{5} \\ a > 4 \)

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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Answer:

\(a_{66}\) = 653

Explanation:

General formula: \(a_{n}\) = (\(a_{1}\) + ((term) - 1) · (common difference)

\(a_{66}\) = 3 + (66 - 1) · (10)

\(a_{66}\) = 653

Answer:

Y= -x-4

(-1,-3)

Step-by-step explanation:

Simply plot the point (-5,1) and draw in a line with a slope of -1. Take the slope of this line and the point it crosses the y-axis and use them to set up slope intercept form.

Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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Answer:

can't hwlp you without an image

Answer:

EF = 22 , AB = 1

Step-by-step explanation:

the midsegment of a trapezoid is equal to half the sum of the parallel bases

EF = \(\frac{1}{2}\) (AB + DC ) ← substitute values

x + 6 = \(\frac{1}{2}\) (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction

2x + 12 = 3x - 4 ( subtract 3x from both sides )

- x + 12 = - 4 ( subtract 12 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

Then

EF = x + 6 = 16 + 6 = 22

Similarly

EF = \(\frac{1}{2}\) (AB + DC ) , that is

x + 3 = \(\frac{1}{2}\) (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction

2x + 6 = 6x + 2 ( subtract 6x from both sides )

- 4x + 6 = 2 ( subtract 6 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

Then

AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1

Answer:

rise over run

the slope in the picture would be 3, because you rose six and ran two, which is 6/2=3

hope this helps

Answer:

kinda lol

Step-by-step explanation:

Answer: i have watched harry potter but never read the book. and for star wars i have never read or watched it so your good <3

Step-by-step explanation:

Answer:

14.5

Step-by-step explanation:

23.78 ÷ 1.64 = 14.5 meaning she bought 14.5 gallons of gas

Answer:

14.5

Step-by-step explanation:

If Elaine spent $1.64 per gallon for 14.5 gallons; she would have paid $23.78 for gas.

$23.78 ÷ $1.64 = 14.5

$1.64 • 14.5 = $23.78

I hope this helps

Answer: -842

Step-by-step explanation:

To find n95, we have to use the equation aₙ = d * n + a₁ - d

a₁ is the first term, which here is 4. d is the common difference, which we can find out but seeing what we can add pr subtract from 4 to -5 which also equals -5 to -14, in this equation, the common difference would be -9 as it goes down by 9 every term. Once we plug these into the equation, we get

a₉₅ = -9 * n + 4 - (-9)

We can solve this for - aₙ = -9n + 13

Now that we have our equation to find a term, we can plug in n for 95 for

-9(95) + 13

Which equals -842

1

Explanation:

7/7 - 2/5

Using compatible numbers:

7/7 = 1 as it is closer and equal to 1

so we have: 1 - 2/5

2/5 is approximately 0 as it is closer to 0 than 1

= 1 - 0 = 1

7/7 - 2/5 using compatible number = 1

To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:

The answer would be 3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

its the 2nd one

Step-by-step explanation:

The answer is 240.4cm^2

Or the second one

9514 1404 393

Answer:

  10.3 laps

Step-by-step explanation:

On each lap, Ashley runs two lengths of 100 m and the circumference of a 60 m circle. That circumference is ...

  C = πd

  C = π(60 m) ≈ 188.496 m

So, the length of one lap is ...

  2·100 m + 188.496 m = 388.496 m

The number of times around for 4000 m will be ...

  (4000 m)/(388.496 m/lap) = 10.30 laps

Ashley must run 10.3 times around in order to run a total distance of 4 km.

Answer:

6

Step-by-step explanation:

Step 1:

3 ( 2x - 5 ) - 4x + 8 = - 1

Step 2:

5x - 15 - 4x + 8 = - 1

Step 3:

x - 15 + 8 = - 1

Step 4:

x - 7 = - 1

Answer:

x = 6

Hope This Helps :)

The equivalent equation to ab=ac is b = c.

An equivalent equation to ab=ac using a−1 that simplifies to b=c is:

Simplifying the expression by canceling out a⁻¹a, we get:

b = c

Therefore, the correct option is b = c.

We can start with the equation ab = ac and multiply both sides by a−1, which is the inverse of a. This gives us:

a⁻¹(ab) = a⁻¹(ac)

Simplifying the left-hand side of the equation by using the associative property of multiplication, we get:

(a⁻¹a)b = (a⁻¹a)c

Since a⁻¹a is equal to 1, we can simplify the expression to:

1b = 1c

Which simplifies to b = c, as required.

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Answer:

3,7/6

Step-by-step explanation:

\((\sqrt{x^2-4x+3} )+(\sqrt{x^{2} -9} )-(\sqrt{4x^2-14x+6} )\\=(\sqrt{x^2-x-3x+3} )+(\sqrt{(x^2-3^2})-(\sqrt{4x^2-2x-12x+6})\\ =(\sqrt{x(x-1)-3(x-1)} )+\sqrt{(x+3)(x-3)}-\sqrt{2x(2x-1)-6(2x-1)} \\=\sqrt{(x-1)(x-3)}+\sqrt{(x+3)(x-3)} -\sqrt{2(2x-1)(x-3)} \\=\sqrt{x-3} (\sqrt{x-1} +\sqrt{x+3} -\sqrt{2(2x-1)} )\\\)

\(\sqrt{x-3} =0~gives~x=3\\or~\sqrt{x-1} +\sqrt{x+3} -\sqrt{2(2x-1)} =0\\or~ \sqrt{x-1} +\sqrt{x+3} =\sqrt{2(2x-1)} \\squaring\\x-1+x+3+2\sqrt{x-1} \sqrt{x+3} =2(2x-1)\\2x+2+2\sqrt{(x-1)(x+3)} =4x-2\\2\sqrt{x^2-x+3x-3} =2x-4\\\sqrt{x^2+2x-3} =x-2\\again ~squaring\\x^2+2x-3=x^2-4x+4\\\\2x+4x=4+3\\6x=7\\x=\frac{7}{6}\)

The equation of the unique function exists g(x) = -4(x-3)².

The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.

Given: F(x) = x²

The vertical stretch by a factor of 4 exists can be satisfied by (b)

if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.

Multiply 4 by f(x) which provides 4x².

As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².

Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.

Hence, the unique graph would be g(x) = -4(x-3)²

Therefore, the correct answer is option B. g(x) = -4(x-3)².

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There are 600 different combinations of 2 students that can be chosen from a class of 25, where the order of selection does not matter.

The number of different combinations of 2 students that can be chosen from a class of 25, where the order of selection does not matter, can be calculated using the concept of combinations.

The formula to calculate combinations is:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of students and r is the number of students to be chosen.

In this case, we have 25 students and we want to choose 2 students. Plugging these values into the formula:

C(25, 2) = 25! / (2!(25-2)!)

Simplifying further:

C(25, 2) = 25! / (2! * 23!)

Since 2! equals 2 and 23! equals 23 * 22 * 21 * ... * 2 * 1, many terms in the numerator and denominator will cancel out:

C(25, 2) = (25 * 24) / (2 * 1)

C(25, 2) = 600

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Answer:

x-2= Reese's age

Martin and Lee are the same age (12), and 2 years older than Reese. So, to know how old Reese is, you have to subtract 2 from the ages of Martin and Lee. Hence, the equation, 'x-2', because 'x' can be substituted with Martin or Lee's age.

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

Answer:

16.7 cm

Step-by-step explanation:

So B = 180 -A-C=180-58-75=47degree

sinB/AC = sinC/AB

sin47/AC=sin75/22

AC=16.65cm

Answer:

The opposite of -4:  4

The opposite of 5:  -5

The opposite of the opposite of -6:  -6