For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy?

A) 64
B) 128
C) 8
D) 4

The differential equation of  the amount of a subject memorized in time t > 0 is k. a(t) + da(t)/dt = km, where k is a constant representing the rate  at which a subject is memorized.

Translate the given word problem into an algebraic expression.

Let m be the total amount of a subject to be memorized.

Let  a(t) be the amount memorized in time t > 0.

Let c(t) be the amount that is left to be memorized in time t > 0.

Then,

c(t) = m - a(t)

From the problem, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. It means:

da(t)/dt = k. c(t),  where k is a constant

da(t)/dt = k. (m - a(t))

k. a(t) + da(t)/dt = km

Hence, the differential equation is k. a(t) + da(t)/dt = km

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There are 10 centromeres if there are 20 chromatids in a cell in G1 phase.

A chromosome is a short DNA molecule that includes the entirety or a portion of an organism's genetic code. Packaging proteins can be found on the majority of eukaryotic organisms.

It is given that:

Number of chromatids = 20

There are 20 chromatids, replication has taken place, thus they should be in identical pairs of two (sister chromatids). Ten centromeres would therefore exist.

Thus, there are 10 centromeres if there are 20 chromatids in a cell in G1 phase.

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Answer:

y'all look fine ig

Step-by-step explanation:

The exact length of the curve y = ln(sec(x)), 0 ≤ x ≤ π/6 is given by \($\ln(\sqrt3+1)$\).

We are supposed to find the length of the curve y = ln(sec(x)), 0 ≤ x ≤ /6.

It is known that the formula to find the length of the curve y = f(x) between the limits a and b is given as

\(\[L = \int\limits_{a}^{b}{\sqrt {1 + {{[f'(x)]}^{2}}}} dx\]\)

Here, we have y = ln(sec(x)),

So, we need to find f(x) = ln(sec(x)) and then find f'(x) to substitute it in the above formula to get the length of the curve, y = ln(sec(x)), 0 ≤ x ≤ /6.So,

let's find f(x) and f'(x) as follows:

f(x) = ln(sec(x))

⇒f'(x) = d/dx[ln(sec(x))]

= d/dx[ln(1/cos(x))] (since sec(x)

= 1/cos(x))= d/dx[-ln(cos(x))] (using logarithmic differentiation)

= sin(x)/cos(x) (using quotient rule of differentiation and simplifying)

= tan(x)Now, we will substitute f'(x) = tan(x) in the formula

\(\[L = \int\limits_{a}^{b}{\sqrt {1 + {{[f'(x)]}^{2}}}} dx\]\)

and find the length of the curve.

0 ≤ x ≤ π/6

Thus, L is given by

\(\[L = \int\limits_{0}^{\frac{\pi }{6}}{\sqrt {1 + {{\tan }^{2}}(x)}} dx\]\[ = \int\limits_{0}^{\frac{\pi }{6}}{\sqrt {1 + {{\sec }^{2}}(x) - 1}} dx\]\)

(using identity

\(\[\tan ^2x + 1 = \sec ^2x\])\[ = \int\limits_{0}^{\frac{\pi }{6}}{\sqrt {{\sec }^{2}}(x)} dx\]\[ = \int\limits_{0}^{\frac{\pi }{6}}{\sec x} dx\]\)

Now, we know that

\(\[\int{\sec xdx} = \ln |\sec x + \tan x| + C\]So,\[L = \int\limits_{0}^{\frac{\pi }{6}}{\sec x} dx\]\[ = \ln |\sec (\frac{\pi }{6}) + \tan (\frac{\pi }{6})| - \ln |\sec 0 + \tan 0|\]\[ = \ln (\sqrt {3} + 1) - \ln (1)\]\[ = \ln (\sqrt {3} + 1)\]\)

Therefore, the exact length of the curve y = ln(sec(x)), 0 ≤ x ≤ π/6 is given by \($\ln(\sqrt3+1)$\).

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Answer:

3) 27.2 ft²

4) 115.5 in²

Step-by-step explanation:

the area of the triangle given two sides of the triangle and an angle between the two sides is caclulated as,

A = 1/2 * b  * c * sin ∅

where b and c are the given two sides and ∅ is the given angle between them.

thus substituting the values,

3)

area = 1/2 * 15 * 8 *sin27°

= 60 * sin27°

= 60 * .454 = 27.24

by rounding the answer to the nearest tenth,

area = 27.2 ft²

4)

Area = 1/2 * 16 * 14.5 * sin85°

= 116 * sin85° = 116 * .996 = 115.536

by rounding off to the nearest tenth,

area = 115.5 in²

the conversion, that one mile is 63360 inches.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

In daily life, people frequently utilize miles and inches as units of measurement. However, do you know how to convert miles to inches in the quickest method possible?

A standard definition of an inch states that it is equal to 1/12 of a foot or 1/36 of a yard. In use since the seventh century, this device. In 1066, when it was first used as a measurement, the length of three barleycorns was established as the standard definition of an inch.

The formula for miles to inches conversion is Inches = miles x 63360.

Hence the conversion, that one mile is 63360 inches.

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In the bag containing the combinations of coins, the number of ways in which the combination of two nickels, two dimes and a quarter can be obtained is 1960 ways.

The answer is Option (E).

For this question, we apply the concepts and principles of Combinations.

The main formula used in all combinatoric questions, which can also be used to obtain equations for special cases is:

If we want to choose 'x' objects from a total of 'n' objects in a bag, then the number of ways in which this can be done is denoted as ⁿCₓ. The expression for the above term is:

ⁿCₓ = n!/[ x! * (n - x)! ]

If we have more than one objects to be chosen, we just multiply the number of combinations of each object to obtain the totals.

We divide our question into three parts, Nickels, Dimes, and Quarters.

For Nickels:

We are asked to choose 2 nickels from the 5 in the bag.

So, the number of combinations will be:

⁵C₂ = 5!/2! (5 - 2)!

     = 5!/2!*3!

     = 120/2*6

     = 120/12

     = 10 possible combinations.

For Dimes:

We have to choose 2 dimes from the 8 dimes in the bag.

So, no. of combinations is

⁸C₂ = 8!/2!(8 - 2)!

      = 8!/2!*6!

      = 7*8/1*2

      = 56/2

      = 28 combinations

For Quarters:

We are supposed to choose a quarter from the 7 in the bag.

We can say even without writing the formula, that there 7 possible combinations.

So, finally, the total number of ways in which the selection can be made is simply the product of the values obtained.

T = 28*10*7

T = 1960 ways.

So, we can make the required selections in 1960 ways.

Question:

From a bag containing 5 nickels, 8 dimes, and 7 quarters, 5 Coins are drawn at random, and all at once. In how many ways can the desired selection be made such that we obtain 2 nickels, 2 dimes, and a quarter?

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Answer:

1. 286

2. 588

3.300

Answer:

this is the answer I came up with hope this helps

Answer:

E. The absolute value and square root function share an x-intercept.

Step-by-step explanation:

Pre-Calc on Edge 2022

The equation of tangent to a curve  corresponding to the given value of the parameter x = t⁵ + 1, y = t⁶ + t; t = 1 is y = 7x/5 - 4/5

The equation of tangent to a curve is the equation of the line that touches the curve at one point.

To find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

x = t⁵ + 1, y = t⁶ + t; t = 1, we proceed as follows.

We know that the tangent to the curve is the derivative dy/dx.

Now dy/dx = dy/dt ÷ dx/dt

x = t⁵ + 1

So, differntiating, we have

dx/dt = d(t⁵ + 1)/dt

= dt⁵/dt + d1/dt

= 5t⁴ + 0

= 5t⁴

Also, y = t⁶ + t

differentiating, we have that

dy/dt = d(t⁶ + t)/dt

= dt⁶/dt + dt/dt

= 6t⁵ + 1

= 6t⁵ + 1

Since dy/dx = dy/dt ÷ dx/dt, substituting the values of the variables into the equation, we have that

dy/dx = dy/dt ÷ dx/dt

dy/dx = (6t⁵ + 1) ÷ 5t⁴

At t = 1, we have that

dy/dx = (6t⁵ + 1) ÷ 5t⁴

dy/dx = (6(1)⁵ + 1) ÷ 5(1)⁴

dy/dx = (6(1) + 1) ÷ 5(1)

= (6 + 1) ÷ 5

= 7/5

Now, we know that the equation of the tangent is the equation of a straght line.

So, using the equation of a straight line in slope-point form, we have that

(y - y')/(x - x') = dy/dx

Now, y' = y at t = 1

So,y = t⁶ + t

y = 1⁶ + 1

= 1 + 1

= 2

Also, x' = x at t = 1

So,x =  t⁵ + 1

x =  1⁵ + 1

= 1 + 1

= 2

Since

Substituting the values of the variables into the equation, we have that

(y - y')/(x - x') = dy/dx

(y - 2)/(x - 2) = 7/5

Cross-multiplying,we have that

5(y - 2) = 7(x - 2)

5y - 10 = 7x - 14

5y = 7x - 14 + 10

5y = 7x - 4

y = 7x/5 - 4/5

So, the equation is y = 7x/5 - 4/5

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Answer:

20.8

Step-by-step explanation:

tan = opposite/ adjacent

opposite = tan * adjacent

opposite = 1,482561 * 14 = 20,755854

Answer:

20.8 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 56 = x/ 14

14 tan 56 =x

20.75585356 =x

To the nearest tenth

20.8 =x

The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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The critical point of f at z = 1 is a local minimum.

To find the critical points of the function f(z, 3) = 4z^2 - 8z + 1, we need to find the values of z where the first partial derivatives with respect to z are equal to zero. Let's solve it step by step.

Take the partial derivative of f with respect to z:

∂f/∂z = 8z - 8

Set the derivative equal to zero and solve for z:

8z - 8 = 0

8z = 8

z = 1

The critical point of f occurs when z = 1.

To determine whether the critical point is a local minimum, local maximum, or a saddle point, we can use the second partial derivative test. We need to calculate the second partial derivative ∂²f/∂z² and evaluate it at the critical point (z = 1).

Taking the second partial derivative of f with respect to z:

∂²f/∂z² = 8

Evaluate the second derivative at the critical point:

∂²f/∂z² at z = 1 is 8.

Analyzing the second derivative:

Since the second derivative ∂²f/∂z² = 8 is positive, the critical point (z = 1) corresponds to a local minimum.

Therefore, the critical point of f at z = 1 is a local minimum.

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Answer: y = 3x — 2

Step-by-step explanation:

Answer:

√74

Step-by-step explanation:

49 + 25

if brainly deletes this answer, i swear this community is going down in the dumps

Answer:

\(\sqrt{74}\) = 8.6

Step-by-step explanation:

use distance formula

points are (4,2) and (-3,-3)

d= \(\sqrt{(x_{2}-x_{1) ^{2} + (y_{2} -y_{1} )^{2} }\)

substitute points into formula

The final solution is x(t) = (−25/18)\(e^{3t}\) [ −4 −4 1 ] + (−25/18)\(e^{12t}\) [ −2 −2 1 ] + (25/18) \(e^{12t}\) [ 2 −2 1 ] + [ −4/9 −4/9 −5/9 ] + t[ −4/9 −4/9 −10/9 ].

We are given that;

x' = [ -8 -3 15 ] x

Now,

First need to find the eigenvalues and eigenvectors of A. The characteristic polynomial of A is

det(A − λI) = −(λ + 3)(λ2 + 9λ − 144) = 0

which has roots λ = −3, −12, and 12. The corresponding eigenvectors are

v1 = [ −4 −4 1 ] v2 = [ −2 −2 1 ] v3 = [ 2 −2 1 ]

The general solution of the homogeneous system x’ = Ax is then

\(xh(t) = c_1e-3tv_1 + c_2e-12tv_2 + c_3e12tv_3\)

where \(c_1, c_2, c_3\) are arbitrary constants. To find a particular solution of the nonhomogeneous system x’ = Ax + b, we can use the method of undetermined coefficients and guess a solution of the form

xp(t) = d + et

Ad + b = 0 Ae = d

Solving these equations, we get

d = [ −4/9 −4/9 −5/9 ] e = [ −4/9 −4/9 −10/9 ]

The general solution of the nonhomogeneous system is then

x(t) = xh(t) + xp(t)

To find the specific solution that satisfies the initial condition x(0) = c, we plug in t = 0 and get

\(c = x(0) = c_1v_1 + c_2v_2 + c_3v_3 + d\)

\(c_1 = -25/18\\\\ c_2 = -25/18 \\c_3 = 25/18\)

Therefore, by the equation answer will be x(t) = (−25/18)\(e^{3t}\) [ −4 −4 1 ] + (−25/18)\(e^{12t}\) [ −2 −2 1 ] + (25/18) \(e^{12t}\) [ 2 −2 1 ] + [ −4/9 −4/9 −5/9 ] + t[ −4/9 −4/9 −10/9 ].

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Answer:

x = 10

angle top = 118°

angle bottom = 62°

Step-by-step explanation:

6x + 2 + 11x + 8 = 180

17x + 10 = 180

17x = 170

divide both sides by 17.

x = 10

plug in the 10 to each equation to get the number for the angle

6(10) + 2 = 62°

11(10) + 8 = 118°

Using the sum of the sides of the triangle, it is found that the possibility that will form a triangle is:

Side = 14 cm, side 6 cm,side = 9 cm

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

In this problem:

Hence the correct option is:

Side = 14 cm, side 6 cm,side = 9 cm

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Answer:

It would take 26 day's

Step-by-step explanation:

hope this helps

Answer:

6/5

Step-by-step explanation:

We can use the slope formula to find the slope

Slope formula: \(m = \frac{y_2-y_1}{x_2-x_1}\), where the x and y values are derived from know points

The points chosen can vary as there are many given but the ones I chose were (6,9) and (11,15)

Now that we chose two points we want to define the variable ( the variables are x2, x1, y2 and y1 )

Define Variables

x1 = x value of first point which would be 6

x2 = x value of second point which would be 11

y1 = y value of first point which would be 9

y2 = y value of second point which would be 15

Now that we have defined our variables the next step is to plug in the variables into the slope formula

slope formula: \(m = \frac{y_2-y_1}{x_2-x_1}\)

y2 = 15, y1 = 9, x2 = 11 and x1 = 6

* plug in values *

\(m=\frac{15-9}{11-6}\)

subtract top numbers

\(m=\frac{6}{11-6}\)

subtract bottom numbers

\(m = \frac{6}{5}\)

there is no simplification needed meaning that the slope in simplest form is 6/5

Answer:

3/18

Step-by-step explanation:

3/18= 0.16

10/3= 3.33

Answer:

3/18

Step-by-step explanation:

3/18 , 10/3

Simplify it to the smallest size

3/18 , 10/3

1/6 , 10/3

1/6 = 3/18

Answer:

a)  Approximately 95% of healthy women in this group have blood platelet counts between 109.1 and 381.9 (1000 cells/μL).

b)  Approximately 99.7% of healthy women in this group have blood platelet counts between 40.9 and 450.1 (1000 cells/μL).

Step-by-step explanation:

The Empirical Rule (also known is the "68-95-99.7" rule) states that nearly all of the data within a normal distribution will fall within three standard deviations of the mean.

Given the blood platelet count of a group of women has a bell-shaped distribution with:

To determine the lower and upper bounds for blood platelet counts for 95% of the women, subtract and add two standard deviations to the mean:

\(\begin{aligned}\text{Lower bound}&= \mu - 2\sigma \\&= 245.5 - 2(68.2)\\&=245.5-136.4\\&=109.1\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 2\sigma \\&= 245.5 + 2(68.2)\\&=245.5+136.4\\&=381.9\end{aligned}\)

Therefore, approximately 95% of healthy women in this group have blood platelet counts between 109.1 and 381.9 (1000 cells/μL).

To determine the lower and upper bounds for blood platelet counts for 99.7% of the women, subtract and add three standard deviations to the mean:

\(\begin{aligned}\text{Lower bound}&= \mu - 3\sigma \\&= 245.5 - 3(68.2)\\&=245.5-204.6\\&=40.9\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 3\sigma \\&= 245.5 + 3(68.2)\\&=245.5+204.6\\&=450.1\end{aligned}\)

Therefore, approximately 99.7% of healthy women in this group have blood platelet counts between 40.9 and 450.1 (1000 cells/μL).

Answer:

a= one mile in 4 minutes

b =48 minutes

Step-by-step explanation:

A

t = 20 minutes

d = 5 miles

Average speed = distance ÷ time

5 miles÷ 20 minutes

= 1 mile in 4 minutes

= 0.25 miles in 1 minute

B

0.25 miles in 1 minute

12 miles in g minutes

12 miles in 48 minutes

we get this answer because 0.25 in one minute is 1 ÷4

12÷ 12 × 4

12÷ 48

= 12 miles In 48 minutes

Based on the provided question, it seems like you are asking about the most efficient evaluation method, either by hand or using a computer. To determine which method is the most suitable, you need to consider the complexity of the evaluation process and the number of alternatives.

Using a computer is generally faster and more accurate when dealing with large datasets or complex calculations. On the other hand, evaluating by hand may be more suitable for smaller datasets or simpler calculations. It can provide a more hands-on approach, allowing for a deeper understanding of the evaluation process. However, this method is generally more time-consuming and prone to human error.

To select the most appropriate evaluation method, consider the complexity of the task and the available resources. If the evaluation involves a large amount of data or complex calculations, using a computer would likely be the most efficient choice. However, if the task is relatively simple or involves a smaller dataset, evaluating by hand may suffice. In conclusion, the choice between evaluating by hand or using a computer depends on the complexity of the task and the available resources. Consider these factors to determine the most suitable method.

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A cell with a radius of 12 cm produces approximately 18.09 watts of power.

To find the power produced by a cell with a radius of 12 cm, we can substitute the given radius into the equation: r = √P / (0.02π)

12 = √P / (0.02π)

Squaring both sides of the equation to eliminate the square root:

12^2 = (√P / (0.02π))^2

144 = P / (0.04π)

Multiplying both sides by 0.04π to isolate P: 0.04π * 144 = P

Approximating the value of π as 3.14: 0.04 * 3.14 * 144 = P

18.0864 = P

Rounding to the nearest hundredth: P ≈ 18.09

Therefore, a cell with a radius of 12 cm produces approximately 18.09 watts of power.

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Answer:

The slope of the line is \(m=-\frac{7}{6}\)

Step-by-step explanation:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{11-4}{4-10}\)

\(m=\frac{7}{-6}\)

\(m=-\frac{7}{6}\)

Answer:

-7/6

Step-by-step explanation:

Given two points, we can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 11-4)/(4-10)

   = 7/-6

 = -7/6