Ethan is saving money in his piggy bank for his upcoming trip to Disney world on the first day he put in $12 and plans to add seven more dollars each day write an explicit formula that can be used to find the amount of money saved on any given day

Final answer:

To find the approximate probability that the random sample of 200 candies will contain 26% or more orange candies, we can use the binomial distribution.

Explanation:

To find the approximate probability that the random sample of 200 candies will contain 26% or more orange candies, we need to use the binomial distribution.

The probability of selecting an orange candy is 24%. Let's define success as selecting an orange candy.

Using the binomial distribution formula, we can calculate the probability:

P(X ≥ k) = 1 - P(X < k)

where X is the random variable representing the number of orange candies in the sample, and k is the number of orange candies we want to have (26% of 200 is 52).

First, let's calculate P(X < 52). We can use a binomial probability table, or a binomial calculator to find this value. Once we have P(X < 52), we can find P(X ≥ 52) by subtracting it from 1.

Answer:

1/14

Step-by-step explanation:

Assuming you mean that there are 2 red, 2 green, and 4 blue marbles, there are a total of 8 marbles.

On the first draw, the probability the marble is red is 2/8.

On the second draw, there's one less marble, so the probability of selecting a green marble is 2/7.

The total probability is:

2/8 × 2/7 = 1/14

The probability that the first marble is red and the second is green is approximately 0.0626 or 6.26%.

To find the probability we need to follow these steps:

The probability of drawing a red marble first is:

P(Red) = Number of Red Marbles / Total Number of Marbles = 222 / 888 = 1/4 or 0.25.

The probability of drawing a green marble after a red one has been drawn is:

P(Green | Red) = Number of Green Marbles / Remaining Marbles = 222 / 887.

The overall probability is:

P(Red then Green) = P(Red) * P(Green | Red) = (222 / 888) * (222 / 887) = (1/4) * (222 / 887).

Therefore, the probability that the first marble is red and the second is green is approximately 0.0626 or 6.26%.

Answer:

Step-by-step explanation:

Given

speed of cyclist A is [tex]v_a=4 mi/hr[/tex]

speed of cyclist B is [tex]v_b=6 mi/hr[/tex]

At noon cyclist B is 9 mi away

after noon Cyclist B will travel a distance of 6 t and cyclist A travel 4 t miles in t hr

Now distance of cyclist B from intersection is 9-6t

Distance of cyclist A from intersection is 4 t

let distance between them be z

[tex]z^2=(9-6t)^2+(4t)^2[/tex]

Differentiate z w.r.t time

[tex]2z\frac{\mathrm{d} z}{\mathrm{d} t}=2\times (9-6t)\times (-6)+2\times (4t)\times 4[/tex]

[tex]z\frac{\mathrm{d} z}{\mathrm{d} t}=(-6)(9-6t)+4(4t)[/tex]

[tex]\frac{\mathrm{d} z}{\mathrm{d} t}=\frac{16t+36t-54}{z}[/tex]

Put [tex]\frac{\mathrm{d} z}{\mathrm{d} t}\ to\ get\ maximum\ value\ of\ z[/tex]

therefore [tex]52t-54=0[/tex]

[tex]t=\frac{54}{52}[/tex]

[tex]t=\frac{27}{26} hr [/tex]

Answer:

Alien does not take the sample because alien choose the data of a Government's congress and congress contain less women.

On the other hand general population contain women greater than congress

So as compared to general population confidence interval is not representative.

Answer: The sample is not a simple random sample

Step-by-step explanation:

Answer:

  (-4, 0)

Step-by-step explanation:

The scale factor of 1/2 means each "dilated" point is 1/2 the distance from the center of dilation that the original point is. That is, the dilated point is the midpoint between the original and the dilation center.

If O is the origin of the dilation, then ...

  (O + X)/2 = P . . . . . P is the dilation of point X

  O +X = 2P

  O = 2P -X = 2(0, 2) -(4, 4)

  O = (-4, 0)

The center of dilation is (-4, 0).

_____

Another way to find the center of dilation is to realize that dilation moves points along a radial line from the center. Hence the place where those radial lines converge will be the center of dilation. See the attachment for a solution that way.

Answer:

1. all real numbers

2. y ≥ -8

3. It is all of the possible values of a function

4. Domain:{-4,-2,0,2,4} and Range:{-2,0,1,2,3}

Step-by-step explanation:

Let f:A→B be a function. In general sets A and B can be any arbitary non-empty sets.

Values in set A are the input values to the function and values in set B are the output values

Hence Set A is called the domain of the function f.

Set B is called co-domain or range of function f.

Now coming back to problem,

In first picture,

Given function is a straight line ⇒it can take any real number as its input

and for each value it gives a unique output value.

Hence output value is set of all real numbers, i.e. range of the function represented by the graph is set of all real numbers.

In the second picture,

The graph is x values are extending from -∞ to ∞ but the y values is the set of values of real numbers greater than -8 since we can see that the graph has global minimum of -8

Therefore range of the graph is y≥-8

in the third picture,

as we have already discussed the range of a function is the set of all possible output values of the function

In the fourth picture,

Let the function be 'f'.

from question we can tell that we can take only -4,-2,0,2,4 as the values for x and for corresponding x values we get 1,3,2,-2,0 as y values which are the output values.

hence we can tell that domain, which is set of input values, is {-4,-2,0,2,4}

and range, which is the of possible output values, is {-2,0,1,2,3}

Answer:

B. [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Let x be the sum of the 21 numbers,

In which n is one of the numbers,

Since,

[tex]\text{Average}=\frac{\text{Sum of the observations}}{\text{Number of observations}}[/tex]

So, the average of 20 numbers excluded n = [tex]\frac{x-n}{20}[/tex]

According to the question,

[tex]n = 4\times \frac{x-n}{20}[/tex]

[tex]n = \frac{x-n}{5}[/tex]

[tex]5n = x - n[/tex]

[tex]6n = x[/tex]

[tex]\imples n = \frac{1}{6}x = \frac{1}{6}\text{ of the sum of the 21 numbers}[/tex]

Hence, OPTION 'B' is correct.

Answer:

  |h-13| ≤ 2

Step-by-step explanation:

The difference between the height of the plant (h) and show size (13 in) can be written as ...

  h - 13

This value is allowed to be positive or negative, but its absolute value must not exceed 2 inches. Thus, the desired inequality is ...

  |h -13| ≤ 2

To express the statement using an Inequality involving absolute value, use |height - 13| ≤ 2. This means the difference between the height of the plant and 13 inches must be less than or equal to 2 inches.

To express the statement using an inequality involving absolute value, we can use the inequality |height - 13| ≤ 2. This means that the difference between the height of the plant and 13 inches must be less than or equal to 2 inches.

For example, if the height of the plant is 12 inches, then |12 - 13| = |-1| = 1, which is less than 2, so it satisfies the inequality. However, if the height of the plant is 16 inches, then |16 - 13| = |3| = 3, which is not less than 2, so it does not satisfy the inequality.

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Answer: Choice A) 526 degrees,  -194 degrees

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

Work Shown:

A coterminal angle points in the same exact direction as the original angle.

Because there are 360 degrees in a circle, this means we can add 360 to the original angle to get 166+360 = 526, which is one positive coterminal angle to 166 degrees.

Subtract 360 from the original angle and we'll get a negative coterminal angle

166 - 360 = -194

Answer:

  $79.63

Step-by-step explanation:

You can figure this by estimating. 16% is a little less than 20%, which is 1/5. $497.69 is almost $500. So, 1/5 of that is almost $100, and a little less than that is about $80. The closest answer choice is $79.63.

__

If you want to figure it exactly, you can do the multiplication ...

  16% of $497.69 = 0.16 × $497.69 = $79.6304 ≈ $79.63

Answer:

8.25y-14

Step-by-step explanation:

The simplified expression is 8.25y - 14, which is obtained by combining the like terms 7y and 1.25y and adding the constant term -14.

Break down the expression step by step.

4(1.75y - 3.5): This is a product of a number and a sum. Distribute the 4 to get 4 × 1.75y + 4 × (-3.5).

4 × 1.75y: This is multiplication of a number and a variable. The product is 7y.

4 × (-3.5): This is multiplication of a number and a constant. The product is -14.

1.25y: This is a single term.

Now, combine the like terms. Like terms are terms that have the same variable and the same exponent. In this case, the like terms are 7y and 1.25y.

When combined, the like terms are, 7y + 1.25y = 8.25y.

Add the constant term, -14.

Therefore, the simplified expression is 8.25y - 14.

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I don't think that's correct

Step-by-step explanation:

Why are you splitting the $50? you'd end up paying more than the bill and he'd be getting back more money than he put in. Sounds like a rip off. If he had given you each $50 than maybe you'd each owe $140. I assume there is 3 friends, the original bill price would have been $110 for each of you. But then one friend gave $50 to help pay the bill, if you had split the $50 you'd still not be paying back that much. Also why are YOU paying so much more? Everyone else is paying $140 and you're paying $165? You would not be giving him that much, all of you would not be paying an extra $30 either. you'd be splitting it to where it equals $50 all around, so instead it'd be around $93.00. Not $140 or $165. $16.7 multipled by 3 = $50.1

But at the end of the day, just tell him to take his money back. He really didn't help pay the bill that much with his $50, he still owes you $60 if he too had participated in whatever you guys were doing. So instead of going through the trouble, just tell him to take back his money.

Answer:

5

Step-by-step explanation:

Plug x = 0 into f(x) to get

f(x) = 2^x

f(0) = 2^0

f(0) = 1

The y intercept (0,1) is on the graph of f(x).

The y intercept for the red curve shown is (0,3). It has been moved up two units compared to (0,1)

Therefore, g(x) = f(x)+2 where g(x) represents the red curve.

g(x) = f(x) + 2

[tex]g(x) = 2^x + 2[/tex] is the answer

The number of times the inner loop be iterated when the algorithm is implemented and run is 10.

We are given that;

i := 1 to 4, for j := 1

Now,

a. The inner loop will be iterated 10 times when the algorithm is implemented and run.

| i | j | Iterations |

|---|---|------------|

| 1 | 1 | 1          |

| 2 | 1 | 2          |

| 2 | 2 | 3          |

| 3 | 1 | 4          |

| 3 | 2 | 5          |

| 3 | 3 | 6          |

| 4 | 1 | 7          |

| 4 | 2 | 8          |

| 4 | 3 | 9          |

| 4 | 4 | 10         |

b. The number of iterations of the inner loop depends on the value of i. For each i, the inner loop runs from j = 1 to j = i.

So, the total number of iterations is the sum of i from i = 1 to i = n. This is a well-known arithmetic series, which can be written as:

[tex]$\sum_{i=1}^n i = \frac{n(n+1)}{2}$[/tex]

This is the formula for the number of iterations of the inner loop.

Therefore, by algorithm the answer will be 10.

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a. The inner loop will be iterated 10 times when the algorithm is implemented and run.

b. The total number of iterations for the inner loop when the algorithm is implemented and run will be (n^2 + n)/2.

a. In the given algorithm segment, we have two nested loops. The outer loop runs from 1 to 4, and the inner loop runs from 1 to i. Let's analyze how many times the inner loop will be iterated.

For i = 1, the inner loop will run once.

For i = 2, the inner loop will run twice.

For i = 3, the inner loop will run three times.

For i = 4, the inner loop will run four times.

Therefore, the total number of iterations for the inner loop can be calculated by summing the iterations for each value of i:

1 + 2 + 3 + 4 = 10

b. In this algorithm segment, we have the same nested loops as in part a, but the range of the outer loop is from 1 to n, where n is a positive integer.

The inner loop iterates from 1 to i, where i takes the values from 1 to n. So, for each value of i, the inner loop will run i times.

To determine the total number of iterations for the inner loop, we need to sum the iterations for each value of i from 1 to n:

1 + 2 + 3 + ... + n

This is an arithmetic series, and the sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is 1, and the last term is n. Substituting these values into the formula, we get:

Sum = (n/2)(1 + n) = (n^2 + n)/2

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Answer:

26 socks

Step-by-step explanation:

There are a total of 48 socks here. Let us assume you pulled out 24 socks at a go and all are red. Now, you would have exhausted the number of red socks here. You would be left with only blue socks which you can pull one after the other to give a total of  26 socks pulled out to have 2 blue socks at least.

Answer:

  On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6).

Step-by-step explanation:

Since you want a graph with a vertex of (0, 0), choose the one that is described as having a vertex of (0, 0).

Answer:

Option C.

Step-by-step explanation:

We need to find the graph which represents a quadratic function with vertex at (0,0).

The graph of quadratic function is a parabola (either upward or downward) and the extreme point of the parabola is know as vertex.

All graphs represent different parabolas.

Vertex of first parabola = (0,1)

Vertex of second parabola = (0,-1)

Vertex of third parabola = (0,0)

Vertex of fourth parabola = (3,0)

In option C, a parabola opens up on a coordinate plane. It goes through (-5, 6), has a vertex of (0, 0), and goes through (5, 6).

Only third graph represents a quadratic function with a vertex at (0, 0).

Therefore, the correct option is C.

Answer:

Let x be the time taken( in minutes ) by younger gardener,

So, the one minute work of younger gardener = [tex]\frac{1}{x}[/tex]

Also, the time taken by older gardener = (x+12) minutes ( given ),

So, the one minute work of older gardener = [tex]\frac{1}{x+12}[/tex]

Total work done in one minute = [tex]\frac{1}{x}+\frac{1}{x+12}[/tex]

Now, total time taken = 8 minutes,

Total work done in one minute = [tex]\frac{1}{8}[/tex]

Thus,

[tex]\frac{1}{x}+\frac{1}{x+12}=\frac{1}{8}[/tex]

[tex]\frac{x+12+x}{x^2+12x}=\frac{1}{8}[/tex]

[tex]\frac{2x+12}{x^2+12x}=\frac{1}{8}[/tex]

[tex]16x + 96 = x^2+12x[/tex]

[tex]x^2 -4x -96=0[/tex]

[tex]x^2 - 12x + 8x - 96=0[/tex]

[tex]x(x-12) + 8(x-12)=0[/tex]

[tex](x+8)(x-12)=0[/tex]

By zero product product property,

x + 8 =0 or x - 12 =0

⇒ x = -8 ( not possible ), x = 12

Hence, the time taken by younger gardener = 12 minutes,

And, the time taken by older gardener = 12 + 12 = 24 minutes.

Answer:

  4096

Step-by-step explanation:

The population doubles 12 times in that period, so is multiplied by 2^12 = 4096.

Answer:

Option A.

Step-by-step explanation:

Area of a square is

[tex]A=x^2[/tex]               .... (1)

where, x is side length.

The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.

[tex]\dfrac{dx}{dt}=2[/tex]

It is given that bob currently owns 250,000 square feet of land.

Fist find the length of each side.

[tex]A=250000[/tex]

[tex]x^2=250000[/tex]

Taking square root on both sides.

[tex]x=500[/tex]

Differentiate with respect to t.

[tex]\dfrac{dA}{dt}=2x\dfrac{dx}{dt}[/tex]

Substitute x=500 and [tex]\frac{dx}{dt}=2[/tex] in the above equation.

[tex]\dfrac{dA}{dt}=2(500)(2)[/tex]

[tex]\dfrac{dA}{dt}=2000[/tex]

Farmer bob is losing 2,000 square feet of land per year.

Therefore, the correct option is A.

Answer:

P ( z > 87 ) < 0,0015        

P ( z > 87 ) < 0,15 %

Step-by-step explanation:

Applying the simple rule that:

μ ± 3σ  , means that between

μ - 9  = 60   and

μ + 9 = 78

We will find 99,7 of the values

And given that  z(s) = 87 > 78  (the upper limit of the above mention interval ) we must conclude that the probability of find a value greater than 87 is smaller than 0.0015 ( 0r 0,15 %)

To determine the probability of a finish time greater than 87 seconds, we apply the Empirical Rule and find it equates to 3 standard deviations above mean, resulting in a probability of 0.15%.

The question revolves around the use of the Empirical Rule to determine the probability in a normal distribution. The mean time to complete an obstacle course is given as 69 seconds with a standard deviation of 6 seconds. According to the Empirical Rule:

To find out the probability of a finishing time being greater than 87 seconds, we first determine how many standard deviations above the mean this is:

(87 - 69) / 6 = 3

This indicates that 87 seconds is 3 standard deviations above the mean. Using the Empirical Rule, if 99.7% of the data falls within three standard deviations, this would leave 0.3% (or 0.003 in decimal form) of the data outside, which would be the tails of the distribution (both ends combined). Since we are looking for the area above 87 seconds, we only consider one tail, hence, we divide the 0.3% equally for each tail to get 0.15% (or 0.0015 in decimal form) for the probability that a randomly selected finish time is greater than 87 seconds.

Answer:

C. (1/2)acsinA

Step-by-step explanation:

Given is that, A, B, and C are the measures of the angles of a triangle and a, b, and c are the lengths of the sides opposite the corresponding​ angles.

So, the expression that does not represent the area of the​ triangle is :

C. (1/2)acsinA

For a 99% lower confidence bound, we use the Z-score of -2.33 with the formula for a confidence interval. The lower bound will be: 'Sample Mean - (-2.33) * (Sample Standard Deviation/√Sample Size).'

The solution to this problem involves using concepts of statistics, primarily regarding normal distribution and confidence intervals. Given that we're finding a 99% lower confidence bound, we're interested only in the lower range of the spectrum, not the upper.

We need to look at the Z-score associated with a 99% confidence interval in a standard normal distribution. The Z-score for 99% is approximately 2.33 (meaning it cuts off the lowest 0.5% and highest 0.5% of the curve). However, since we're only interested in the lower bound, we will be using a Z-score of -2.33.

The formula for a confidence interval is: µ = X ± Z(s/√n), where µ is the population mean, X is the sample mean, Z is the Z-score, s is the sample standard deviation, and n is the size of the sample. In our question, X is unspecified, s = 0.22, and n = 20. So, assuming 'Xbar' is your sample mean, your lower bound would be: Xbar - (-2.33) * (0.22/√20)

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To find a 99% lower confidence bound on the true Izod impact strength, use the formula: Lower Confidence Bound = Sample Mean - (Critical Value × (Sample Standard Deviation / √n)). Substitute the given values into the formula and perform the necessary calculations.

To find a 99% lower confidence bound on the true Izod impact strength, we can use the formula:

Lower Confidence Bound = Sample Mean - (Critical Value × (Sample Standard Deviation / √n))

Given that the sample mean is ______ and the sample standard deviation is s = 0.22, we need to calculate the critical value for a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576. Plug in the values into the formula, substituting n = 20:

Lower Confidence Bound = ______ - (2.576 × (0.22 / √20))

Perform the necessary calculations to find the lower confidence bound.

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Answer: b) [tex](0.035,\ 0.065)[/tex]

Step-by-step explanation:

The confidence interval for proportion (p) is given by :-

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

, where[tex]\hat{p}[/tex] = Sample proportion

n= sample size.

z* = Critical z-value.

Let p be the true proportion of defective manhole covers, based on this sample.

Given : The workers at Sandbachian, Inc. took a random sample of 800 manhole covers and found that 40 of them were defective.

Then , n= 800

[tex]\hat{p}=\dfrac{40}{800}=0.05[/tex]

Confidence interval = 95%

We know that the critical value for 95% Confidence interval : z*=1.96

Then, the 95% CI for p, the true proportion of defective manhole covers will be :-

[tex]0.05\pm (1.96)\sqrt{\dfrac{0.05(1-0.05)}{800}}\\\\=0.05\pm (1.96)(0.0077055)\\\\=0.05\pm0.01510278\\\\=(0.05-0.01510278,\ 0.05+0.01510278)\\\\=(0.03489722,\ 0.06510278)\approx(0.035,\ 0.065) [/tex]

Hence, the required confidence interval : b) [tex](0.035,\ 0.065)[/tex]

The probability of drawing two diet sodas is 0.0392, two regular sodas is 0.5948, and one of each is 0.3660. It would be unusual to select two diet sodas.

To answer this question, we will be using combinatorial probability. The pack contains 4 cans of diet soda and 14 cans of regular soda (18 in total).

Unusual results are typically those that have low probability. So in this context, it would be unusual to select two diet sodas (a).

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The probabilities of selecting two cans of diet soda, regular soda, and one of each (diest and regular) from an 18 pack are 0.0235, 0.5378, and 0.3878, respectively.

These types of calculations fall under the category of combinatorics, specifically combinations. We are interested in the number of ways we can select cans from a total of 18 where order does not matter.

a. The probability that both randomly selected cans are diet soda is calculated by the formula: (Number of ways to select diet soda) / (Total ways to select two cans). Here we have 4 cases in which we could select diet soda and 18 ways to select any two cans from the pack. Hence, we calculate the probability as:

(4/18) * (3/17) = 0.0235

b. In a similar manner, the probability that both randomly selected cans are non-diet soda (regular soda) is calculated as:

(14/18) * (13/17) = 0.5378

These results are not unusual as there are more regular soda cans in the pack, hence the probability of picking two regular soda cans is higher.

c. The probability that exactly one is diet and exactly one is regular, we have two cases: selecting diet soda first and then regular soda second or selecting regular soda first then diet soda. Hence we calculate the probability as:

(4/18) * (14/17) + (14/18) * (4/17) = 0.3878

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Answer:  The population of the country will be 106 millions in 2014.

Step-by-step explanation:

The exercise gives you the following exponential model, which describes the​ population "A" (in​ millions) of a country "t" years after 2003:

[tex]A=104.8 e^{0.001 t}[/tex]

In this case you must determine when the population of that country will be 106 millions, so you can identify that:

[tex]A=106[/tex]

Now you need to substitute this value into the exponential model given in the exercise:

[tex]106=104.8 e^{0.001 t}[/tex]

Finally, you must solve for "t", but first it is important to remember the following Properties of logarithms:

[tex]ln(a)^b=b*ln(a)\\\\ln(e)=1[/tex]

Then:

[tex]\frac{106}{104.8}=e^{0.001 t}\\\\ln(\frac{106}{104.8})=ln(e)^{0.001 t}\\\\ln(\frac{106}{104.8})=0.001 t(1)\\\\\frac{ln(\frac{106}{104.8})}{0.001}}=t\\\\t=11.38\\\\t\approx11[/tex]

Notice that in 11 years the population will be 106 millions, then the year will be:

[tex]2003+11=2014[/tex]

The population of the country will be 106 millions in 2014.

Answer:

The age of Noelle  =  20 years

Age of Noelle's dad   = 54 years

Step-by-step explanation:

Here, Let us assume:

The age of Noelle's age = m years

So, the age of Noelle's dad = 3 x ( Age of Noelle)  - 6    =  3(m)  - 6

Also, sum of both the ages = 74

So, sum of (Noelle's age  +  Noelle's dad's)  age = 74 years

⇒ m + ( 3 m  - 6)  = 74

or, 4 m =  74+ 6 = 80

or,m = 80 / 4  = 20

⇒ m  = 20

Hence, the age of Noelle =  m - 3   =   20 years

Age of Noelle's dad  = 3 m - 6 = 3(20) - 6 = 54 years

Answer: her call lasted for 22 minutes

Step-by-step explanation:

Rita purchased a prepaid phone card for $30. This means that the total credit on her card is $30. Long distance cost 16 cents a minute using the card. Converting to dollars, it costs 16/100 = $0.16

Rita used her card only once to make a long distance call. If the number of minutes if long distance call that she made is x, total cost of x minutes long distance calls will be 0.16 × x = $0.16x

The remaining credit on her card would be 30 - 0.16x

If the remaining credit on her card if $26.48, it means that

30 - 0.16x = 26.48

0.16x = 30 - 26.48 = 3.52

x = 3.52/0.16 = 22 minutes.

Given

[tex]a\sqrt{x+b}+c=d[/tex]

we have

[tex]\sqrt{x+b}=\dfrac{d-c}{a}[/tex]

Squaring both sides, we have

[tex]x+b=\dfrac{(d-c)^2}{a^2}[/tex]

And finally

[tex]x=\dfrac{(d-c)^2}{a^2}-b[/tex]

Note that, when we square both sides, we have to assume that

[tex]\dfrac{d-c}{a}>0[/tex]

because we're assuming that this fraction equals a square root, which is positive.

So, if that fraction is positive you'll actually have roots: choose

[tex]a=1,\ b=0,\ c=2,\ d=6[/tex]

and you'll have

[tex]\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16[/tex]

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

[tex]a=1,\ b=0,\ c=10,\ d=4[/tex]

and you'll have

[tex]\sqrt{x}+10=4 \iff \sqrt{x}=-6[/tex]

Squaring both sides (and here's the mistake!!) you'd have

[tex]x=36[/tex]

which is not a solution for the equation, if we plug it in we have

[tex]\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4[/tex]

Which is clearly false

Answer:

b(b/a)^2

Step-by-step explanation:

Given that the value of the car depreciates such that its value at the end of each year is p % less than its value at the end of the previous year and that car was worth a dollars on December 31, 2010 and was worth b dollars on December 31, 2011, then

b = a - (p% × a) = a(1-p%)

b/a = 1 - p%

p% = 1 - b/a = (a-b)/a

Let the worth of the car on December 31, 2012 be c

then

c = b - (b × p%) = b(1-p%)

Let the worth of the car on December 31, 2013 be d

then

d = c - (c × p%)

d = c(1-p%)

d = b(1-p%)(1-p%)

d = b(1-p%)^2

d = b(1- (a-b)/a)^2

d = b((a-a+b)/a)^2

d = b(b/a)^2 = b^3/a^2

The car's worth on December 31, 2013 =  b(b/a)^2 = b^3/a^2

Answer with Step-by-step explanation:

We are given that a matrix B .

The eigenvalues of matrix are 0, 1 and 2.

a.We know that

Rank of matrix B=Number of different eigenvalues

We have three different eigenvalues

Therefore, rank of matrix B=3

b.

We know that

Determinant of matrix= Product of eigenvalues

Product of eigenvalues=[tex]0\times 1\times 2=0[/tex]

After transpose , the value of determinant remain same.

[tex]\mid B^TB\mid=\mid B^T\mid \mid B\mid =0\times 0=0[/tex]

c.Let  

B=[tex]\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]

Transpose of matrix:Rows change into columns or columns change into rows.

After transpose of matrix B

[tex]B^T=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]

[tex]B^TB=\left[\begin{array}{ccc}0^2&-&-\\-&1^2&-\\-&-&2^2\end{array}\right][/tex]

[tex]B^TB=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&4\end{array}\right][/tex]

Hence, the eigenvalues of [tex]B^TB[/tex] are 0, 1 and 4.

d.Eigenvalue of Identity matrix are 1, 1 and 1.

Eigenvalues of [tex]B^2+I=(0+1),(1+1),(2^2+1)=1,2,5[/tex]

We know that if eigenvalue of A is [tex]\lambda[/tex]

Then , the eigenvalue of [tex]A^{-1}[/tex] is [tex]\frac{1}{\lambda}[/tex]

Therefore, the eigenvalues of [tex](B^2+I)^{-1}[/tex] are  

[tex]\frac{1}{1},\frac{1}{2},\frac{1}{5}[/tex]

The eigenvalues of [tex](B^2+I)^{-1}[/tex] are 1,[tex]\frac{1}{2}[/tex] and [tex]\frac{1}{5}[/tex]