Michelle has a 1 2/3 pound box of cereal. She wants to make equal servings that completely use all of the cereal. Which of these servings amounts would have no left over cereal?

A. 1/12 lb

B. 1/10 lb

C. 1/8 lb

D. 1/5 lb

Answer:

\(a_{n}\) = - \(\frac{1}{4}\) \(a_{n-1}\)

Step-by-step explanation:

The recursive formula lets us find a term in the sequence by multiplying the previous term by the common ratio r

Here r = \(\frac{20}{-80}\) = \(\frac{-5}{20}\) = - \(\frac{1}{4}\)

Then recursive formula is

\(a_{n}\) = - \(\frac{1}{4}\) \(a_{n-1}\)

Answer:

hope this helps 229 999 0523

117 /320 ≈ 0.366

Step-by-step explanation:

Step 1 of 1: Simplify.

Simplify

117 over 320

117

320

Step 1 of 1: Simplify, sub-step a: Reduce fraction to lowest terms.

Reduce fraction to lowest terms

1 is the greatest common divisor of 117 and 320. The result can't be further reduced.

Answer:

0.5087

Step-by-step explanation:

i just know it...

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

Step-by-step explanation:

Due to the '+1', the graoph of x^2 is shifted 1 unit to the left.  The '+9' results in the entire graph being shifted downward 9 units.

\(f(x)=x^2+4x-21\\f(x)=(x+7)(x-3)\)

These are x-intercepts form. So the answer is (x+7)(x-3).

Answer:  5.6 N/cm^2

============================================

Work Shown:

Pressure = (Force)/(Area)

P = F/A

P = (84 N)/(15 cm^2)

P = (84/15) (N/cm^2)

P = 5.6 N/cm^2

For every square cm, 5.6 newtons of force is applied.

-------------

Extra info:

If you wanted to convert this to pascals, then you would need to convert 15 cm^2 to 0.0015 square meters. Then apply the formula above to get 56,000 pascals. 1 pascal is equivalent to 1 N/m^2.

Answer:

Brad has been on the team for 8 years. Apply that and that means that Anderson has been on the soccer team for 2 years.

Step-by-step explanation:

I dont know how to explain lol i made an equation and figured it out

Step-by-step explanation:

let x be the number of years that Zach has been on the soccer team and y the number of years Anderson has been on the soccer team.

So, reading our problem it seems that

x=5y-2

x+y=10

replacing x on the second formula we take that 5y-2+y=10

6y-2=10

6y=12

y=2

so x=5y-2=5*2-2=10-2=8

Answer:

If both Kelsey and Jeana purchase 6 pairs of uniform pants then they would pay the same amount for their purchases.

Step-by-step explanation:

The information provided is as follows:

The variable x is the number of pairs of pants.

The total cost function for Kelsey will be:

\(TC_{K}=17.95\cdot x+24\)

The total cost function for Jeana will be:

\(TC_{J}=18.95\cdot x+18\)

Consider that both pay the same total cost for their purchases.

Compute the value of x as follows:

            \(TC_{K}=TC_{J}\)

\(17.95\cdot x+24=18.95\cdot x+18\\\\18.95\cdot x-17.95\cdot x=24-18\\\\x=6\)

Thus, if both Kelsey and Jeana purchase 6 pairs of uniform pants then they would pay the same amount for their purchases.

Answer:

win the lotto

Step-by-step explanation:

Answer:

i d k

Step-by-step explanation:

To solve the inequalities -2x + 4 < 8 and 3x + 4 ≤ -5, we will solve them individually and then represent the solutions on a number line.

For the first inequality, -2x + 4 < 8, we will isolate x:

-2x + 4 - 4 < 8 - 4

-2x < 4

Dividing both sides by -2 (remembering to reverse the inequality when multiplying/dividing by a negative number):

x > -2

For the second inequality, 3x + 4 ≤ -5, we isolate x:

3x + 4 - 4 ≤ -5 - 4

3x ≤ -9

Dividing both sides by 3:

x ≤ -3

Now we represent the solutions on a number line. We mark -2 with an open circle (since x > -2), and -3 with a closed circle (since x can be equal to -3). Then we shade the region to the right of -2 and include -3 to represent the solutions.

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Answer:

add 2 to each side of the equation

Step-by-step explanation:

x-2=10

To solve for x, we need to add 2 to each side of the equation

x-2+2 = 10+2

x = 12

Answer:

A. 9

Step-by-step explanation:

Answer:

It will take 4.84 hours for the drug to decay to 93​% of the original​ dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is: \(A = A_0 e^{kt}\)

Now, we know that A becomes half after 47 hours which means that;

\(A = 0.5 A_0\)

Using this in the above equation we get;

\(A = A_0 e^{kt}\)

\(0.5 A_0 = A_0 e^{(k\times 47)}\)  where t = 47 hours

\(\frac{0.5 A_0}{A_0} = e^{(47k)}\)

\(0.5 = e^{47k}\)

Taking log on both sides we get;

\(ln(0.5) = ln(e^{47k})\)

\(ln(0.5) =47k\)

\(k = \frac{ln(0.5)}{47}\)

k = -0.015

Now, the time it will take for the drug to decay to 93​% of the original​ dosage is given by;

\(0.93 = e^{kt}\)  where t is the required time

\(0.93 = e^{(-0.015 \times t)}\)

Taking log on both sides we get;

\(ln(0.93) = ln(e^{-0.015t})\)

\(ln(0.93) =-0.015t\)

\(t = \frac{ln(0.93)}{-0.015}\)

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93​% of the original​ dosage.

Answer:

130g

Step-by-step explanation:

Given:

The equation of a straight line is

\(y=20-x\)

The x value of a point on the line is 14.

To find:

The y value of this point.

Solution:

If a point (x,y) lines on line, then the equation of line must be stratified by that point.

We have, the equation of a straight line.

\(y=20-x\)

Putting x=14, we get

\(y=20-14\)

\(y=6\)

Therefore, the y-value is 6 when the x-value is 14.

Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

The painter would need to add 5 gallons of the mixture that is 40 percent blue pigment (Option B) to achieve a mixture that is 20 percent blue pigment.

To determine how many gallons of a mixture that is 40 percent blue pigment the painter needs to add to achieve a mixture that is 20 percent blue pigment, we can set up a proportion based on the amount of blue pigment in each mixture.

Let's assume the gallons of the 40 percent blue pigment mixture to be added is represented by x.

The amount of blue pigment in the initial mixture of 20 gallons at 15 percent concentration is:

20 gallons * 0.15 (15 percent) = 3 gallons of blue pigment.

The amount of blue pigment in the final mixture, after adding x gallons of the 40 percent blue pigment mixture, is:

(20 + x) gallons * 0.20 (20 percent).

Since the amount of blue pigment must remain the same, we can set up the proportion:

3 gallons of blue pigment = (20 + x) gallons * 0.20

Simplifying the equation:

3 = (20 + x) * 0.20

3 = 4 + 0.20x

0.20x = 3 - 4

0.20x = -1

x = -1 / 0.20

x = -5

Option B.

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Step-by-step explanation:

a =

\( \frac{1}{6} \)

A company conducts a survey to measure customer satisfaction on a scale of 1 to 10. The range of customer satisfaction scores is a. 4

To find the range of customer satisfaction scores, we need to calculate the difference between the highest and lowest scores.

The highest score in the given data set is 10, and the lowest score is 6. Therefore, the range is 10 - 6 = 4.

The range is a measure of variability and represents the spread of the data. In this case, the customer satisfaction scores range from 6 to 10, indicating a spread of 4 points on the scale.

It's important to note that the range only considers the highest and lowest scores and does not take into account the distribution of the remaining scores.

Therefore, it provides a limited understanding of the overall variability in customer satisfaction.

Other measures such as standard deviation or interquartile range may provide a more comprehensive analysis of the data distribution.

The correct option is: a. 4

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Complete question below :

A company conducts a survey to measure customer satisfaction on a scale of 1 to 10. The survey results for a sample of 50 customers are as follows: 8, 9, 7, 6, 9, 8, 10, 7, 8, 6, 7, 9, 10, 9, 8, 7, 6, 9, 8, 10, 7, 6, 7, 8, 9, 10, 8, 7, 9, 8, 6, 7, 9, 8, 10, 7, 8, 6, 9, 8, 7, 10, 9, 8, 6, 7, 9, 8, 10, 7, 8.

What is the range of customer satisfaction scores?

a. 4

b. 3

c. 5

d. 2

e. 1

Step-by-step explanation:

My z-score tables are set up to show the area to the LEFT
  so you will need to find the z-score that is   1-.10 = .90  

  which , by looking at the tables is z-score =  +1.28

Answer:

The sequence is not arithmetic.

Step-by-step explanation:

it goes 5,4,5,4 for the differences.

Answer:

Addition/Elimination

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(0,3)

Equation Form:

x=0,y=3

Answer:

19.2

Step-by-step explanation:

4.8 x-4 = 19.2 meters

Answer:

19.2

Step-by-step explanation:

4.8 x 4

The probability that the gambler has strictly more than $32 after playing the game five times is 68.75%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. In this problem, we are dealing with a gambler who is playing a game with equal probability of doubling or reducing their stake to half.

The gambler's initial stake is $32. Let us consider the possible outcomes after one play of the game. The stake can either double to $64 or reduce to $16, each with equal probability. If the stake doubles, the gambler has more than their initial stake. If the stake is reduced to half, the gambler has less than their initial stake.

Now, let us consider the possible outcomes after two plays of the game. There are four possible outcomes:

(1) the stake doubles twice and the gambler has

=> $64 * 2 = $128,

(2) the stake doubles then reduces to half and the gambler has

=> $32 * 2 * 0.5 = $32,

(3) the stake reduces to half then doubles and the gambler has

=> $32 * 0.5 * 2 = $32,

(4) the stake reduces to half twice and the gambler has

=> $32 * 0.5 * 0.5 = $8.

We can represent these outcomes using a tree diagram. Each branch represents a possible outcome, and the probability of that outcome is written next to the branch.

After five plays of the game, there are 32 possible outcomes.

We can calculate the probability of the gambler having more than their initial stake by adding up the probabilities of all the outcomes where the gambler has more than $32. This turns out to be 0.6875 or 68.75%.

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Answer:

-0.421875

Step-by-step explanation:

Answer:

\(-0.421875\)

Step-by-step explanation:

Turn the fraction to a decimal.

\(-\frac{3}{4}\) ⇒ \(-0.75\)

Solve the exponent.

\(-0.75^3\) ⇒ \(-0.421875\)

Thus, \(-0.421875\) is the answer.

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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By using Permutation, The number of ways in which 4 distinct prizes be awarded is 5,040.

Number of Contestants = 10

Number of distinct prizes = 4

We will use permutation to evaluate the number of ways in which 4 distinct prizes be awarded,

The first prize can be given in 10 ways

The second prize can be given in 9 ways

The third prize can be given in 8 ways

The fourth prize can be given in 7 ways

Now, Total number of ways 4 prizes can be awarded = 10 * 9 * 8* 7 = 5,040

Thus, the number of ways in which 4 distinct prizes be awarded is 5,040

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The sequence (nx/(1+nx)) converges uniformly on [a, ∞) for a > 0, but not uniformly on [0, ∞). To show that the sequence converges uniformly on [a, ∞), we need to prove two things: that the sequence converges and that the convergence is uniform.

Convergence on [a, ∞):

Let's denote the sequence by fn(x) = nx/(1+nx). Taking the limit as n approaches infinity, we have:

lim(n→∞) fn(x) = lim(n→∞) (nx/(1+nx)) = x.

This means that the sequence converges pointwise to x on [a, ∞) for any fixed x.

Uniform convergence on [a, ∞):

To prove uniform convergence, we need to show that for any ε > 0, there exists an N such that for all n > N and x ∈ [a, ∞), |fn(x) - x| < ε.

Consider the expression |fn(x) - x|:

|fn(x) - x| = |(nx/(1+nx)) - x| = |(nx - x(1+nx))/(1+nx)| = |(nx - x - x^2n)/(1+nx)|.

To simplify further, note that for x ≥ 0 and a > 0:

|x| ≤ a, and

|x^2n| ≤ a^2n.

Using these inequalities, we can bound the expression as:

|fn(x) - x| ≤ (n + 1)/(1 + nx) ≤ (n + 1)/(1 + a) ≤ (n + 1)/a.

Now, if we choose N = a/ε - 1, then for all n > N and x ∈ [a, ∞):

|fn(x) - x| ≤ (n + 1)/a < ε.

Therefore, the sequence converges uniformly on [a, ∞).

On the other hand, the sequence does not converge uniformly on [0, ∞) because the choice of x = 0 leads to fn(0) = 0 for all n, which does not converge to x = 0 uniformly on [0, ∞).

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Hope you could get an idea from here.

Doubt clarification - use comment section.

Note that the volume   of the cuboid is approximately  1,974.08 cm³.

To find the volume of a cuboid,you need to multiply its length (L),   height (H), and width (W) together.

In this case, the length (L) is given as 19 cm, the height (H) is given as 4 cm, and the diagonal represents  the hypotenuse of a right-angled triangle formed by the length, height,and width of the cuboid.

Using the Pythagorean theorem, we can determine the width (W) of the cuboid  -

Width (W) = √(Diagonal² - Height²)

          = √(21² - 4²)

          = √(441 - 16)

          = √425

          ≈ 20.62 cm

Now that we have the values for L, H, and W, we can calculate the volume (V) of the cuboid  -

Volume (V) = Length (L) * Height (H) * Width (W)

            = 19 cm * 4 cm * 20.62 cm

            ≈ 1,974.08 cm³

Therefore, the volume of the cuboid is approximately 1,974.08 cm³.

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