Bill Casler bought a $1000, 9-month certificate of deposit (CD) that would earn 8% annual simple interest. Three months before the CD was due to mature, Bill needed his CD money, so a friend agreed to lend him money and receive the value of the CD when it matured.

(a) What is the value of the CD when it matures?
value = ? $
(b) If their agreement allowed the friend to earn a 10% annual simple interest return on his loan to Bill, how much did Bill receive from his friend? (Round your answer to the nearest cent.) value = ?

Answer:

  4096

Step-by-step explanation:

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

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]

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:

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: it will take 2.7 hours to get to the surface

Step-by-step explanation:

A submarine was stationed 700 feet below sea level. It means that the height of the submarine from the surface is 700 feet.

It ascends 259 feet every hour.

If the submarine continues to ascend at the same rate, the time it will take for it to get to the surface will be the distance from the surface divided by its constant speed.

Time taken to get to the surface

700/259 = 2.7 hours

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:

  $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:

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:

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

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:

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

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:

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: 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:

25% would be the answer

Step-by-step explanation:

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]

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.

Using related rates and the Pythagorean theorem, we can find that dy/dt, the rate of change of the y-coordinate, is 0 ft/s.

To find dy/dt, we need to determine the rate of change of the y-coordinate of the jogger. Since the jogger is running on a circular track, we can use the concept of related rates to solve this problem.

Let's assume that the jogger completes a full lap around the track in a time interval of Δt. During this time interval, the x-coordinate of the jogger changes by Δx, the y-coordinate changes by Δy, and the distance traveled along the track is Δs.

Since the jogger is running at a constant speed, the distance Δs is equal to the distance traveled in a straight line, which is the hypotenuse of a right triangle with legs Δx and Δy. Using the Pythagorean theorem, we have:

Δs^2 = Δx^2 + Δy^2

Taking the derivative with respect to time, we have:

2Δs(dΔs/dt) = 2Δx(dΔx/dt) + 2Δy(dΔy/dt)

Substituting the given values, Δx is 15 ft/s, Δy is 0 (since the y-coordinate is not changing), and Δs is the distance around the circular track, which is equal to the circumference of the circle:

2π(55ft) = 2(15ft)(dΔx/dt) + 2(0)(dΔy/dt)

Simplifying, we have:

dΔx/dt = π(55ft)/15s = 11π/3 ft/s

Therefore, dy/dt = dΔy/dt = 0 ft/s, since the y-coordinate is not changing.

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:

[tex]P=M(1-e^{-kt})[/tex]

Step-by-step explanation:

The relation between the variables is given by

[tex]\frac{dP}{dt} = k(M- P)[/tex]

This is a separable differential equation. Rearranging terms:

[tex]\frac{dP}{(M- P)} = kdt[/tex]

Multiplying by -1

[tex]\frac{dP}{(P- M)} = -kdt[/tex]

Integrating

[tex]ln(P-M)=-kt+D[/tex]

Where D is a constant. Applying expoentials

[tex]P-M=e^{-kt+D}=Ce^{-kt}[/tex]

Where [tex]C=e^{D}[/tex], another constant

Solving for P

[tex]P=M+Ce^{-kt}[/tex]

With the initial condition P=0 when t=0

[tex]0=M+Ce^{-k(0)}[/tex]

We get C=-M. The final expression for P is

[tex]P=M-Me^{-kt}[/tex]

[tex]P=M(1-e^{-kt})[/tex]

Keywords: performance , learning , skill , training , differential equation

The differential equation dp/dt = k(M - P) can be solved via separating variables, integrating and applying the initial condition. Result provides the equation for performance over time: P(t) = M(1 - e-kt).

The subject of the question is around a differential equation. Firstly, you will rewrite the given equation dp/dt = k(M - P) in the form necessary for separation of variables: dp/(M - P) = k dt. Then, integrate both sides: ∫dp/(M - P) = ∫k dt. The left-hand side integral results in -ln|M - P|, and the right side is k*t + C, where C is the constant of integration. Finally, solve for P(t) by taking the exponential of both sides, and rearranging. The procedure results in the performance level equation.

P(t) = M - Ce-kt

Since we're given P(0) = 0, we can determine that C = M. Hence, we finally have the solution:

P(t) = M(1 - e-kt)

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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:

  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:

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: 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.

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:

  (-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.

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:

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:

  |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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