is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions? f is continuous on [ 2 , 5 ), minimum value f(5)=2, and no maximum value.
a. Yes
b. No

To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

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Answer:

\( \frac{73}{48} \)

Step-by-step explanation:

.......

To find the exact length of the polar curve r = θ^2, where 0 ≤ θ ≤ 2π, we can use the arc length formula for polar curves:

L = ∫[a, b] √(r^2 + (dr/dθ)^2) dθ

In this case, we have r = θ^2. Taking the derivative of r with respect to θ, we get dr/dθ = 2θ.

Substituting these values into the arc length formula, we have:

L = ∫[0, 2π] √(θ^4 + (2θ)^2) dθ

L = ∫[0, 2π] √(θ^4 + 4θ^2) dθ

To evaluate this integral, we can simplify the integrand:

L = ∫[0, 2π] √(θ^4 + 4θ^2) dθ

L = ∫[0, 2π] θ√(θ^2 + 4) dθ

Unfortunately, this integral does not have a simple closed-form solution. Therefore, we would need to use numerical methods or approximation techniques to find the exact length of the polar curve.

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Answer:

A =153.86 cm^2

Step-by-step explanation:

The diameter is 14 so the radius is d/2 = 14/2 = 7

A = pi r^2

A = (3.14) (7)^2

A =153.86 cm^2

Answer:

Step-by-step explanation:

First you take the diameter and cut it in half to find the radius. 14/2 = 7

Next you times the radius to the power of 2. 7^2= 49

Then you times your answer by 3.14. 49*3.14 = 153.86

153.86cm² is your answer

Answer:

Step-by-step explanation:

Given

When video is posted 5 people watched it

Next day number of viewers doubled

Suppose this trend continues i.e. No of viewers doubled each day

So on 2 nd day no of viewers is \(2\times 5\)

On 3rd day , viewers \(2^2\times 5\)

on n th day , viewers is \(2^{n-1}\times 5\)

So no of viewers in 1 year i.e. on 365 day

\(=2^{365-1}\times 5\)

\(=2^{364}\times 5\)

(ii)Day on which 640 people seen the video

\(2^{n-1}\times 5=640\)

\(2^{n-1}=128\)

\(2^{n-1}=2^7\)

Therefore

\(n-1=7\)

\(n=8\ days\)

Answer:

\(y\geq x\\x \geq -1\\y\leq \frac{1}{2} x+4\)

Hope it helps :) and let me know if you want me to elaborate/explain further.

Answer: 6 days and 18 hours

Step-by-step explanation: 9/4=1.25 1.25x3=6.75 and so on

Answer:

7 sqrt of 2

Step-by-step explanation:

Special triangles

45 45 90

X X. Xsqrt of2

Answer:7 \(\sqrt{2}\)

Step-by-step explanation: Khan academy

The average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.

What is average rate of change in stock?

We need to find the average rate of change of stock from 1 hour to 6 hours.

The value of stock was $11 in hour 1 and $10 in hour 6.

Average rate of change = Δy/ Δx

= $10 - $11 / 6-1

= - $1/5

= -$0.20 /hr

Hence, the average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.

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Answer:

12.566

12.6 (simplified to the tenths)

12.57(simplified to the hundredths)

Step-by-step explanation:

The diameter of a circle is always double of the radius

π is always ≈ 3.14

π * 2^2 = π * 4  ≈ 12.566

Answer:

3 is the slope of the line

Step-by-step explanation:

2 is the y-intercept:)

Hope I helped a little! I wish you lcuk with all my heart!

The two inequalities will be L>W-4 and (L x W) ≤ 32.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

It is given that:-

The length of the garden should be at least 4 ft shorter than the width

The distance around should be no more than 32 ft

The two inequalities will be as follows:-

a)The length of the garden should be at least 4 ft shorter than the width

L>W-4

b)The distance around should be no more than 32 ft

(L x W) ≤ 32.

Hence the two inequalities will be L>W-4 and (L x W) ≤ 32.

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Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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The z-score for a 34-minute wait time in the cpt-memorial distribution is 1.1.

The z-score is a measure of how many standard deviations away from the mean a particular value falls. It is calculated by subtracting the mean from the value of interest and then dividing by the standard deviation.
In this case, we want to find the z-score for a 34 minute wait when the mean is 23 minutes and the standard deviation is 10 minutes.
z = (34 - 23) / 10
z = 1.1
So the z-score for a 34 minute wait is 1.1. This means that a 34 minute wait is 1.1 standard deviations above the mean wait time for cpt-memorial.
We can use this z-score to determine the percentage of wait times that fall below or above 34 minutes by using a standard normal distribution table. For example, a z-score of 1.1 indicates that approximately 86.42% of wait times are below 34 minutes, while 13.58% of wait times are above 34 minutes.
Overall, the z-score is a useful tool for understanding how a particular value relates to the distribution of a dataset.

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The answer is g(f(x)) =(x+6)(x+2)

From the question, we have

f(x) = x + 3 and g(x) = x² + 2x - 3

g(f(x)) = g(x + 3)

=(x + 3)² + 2(x + 3) - 3

=x² + 9+6x+2x+6-3

=x² + 8x+12

=x² + 6x+2x+12

=(x+6)(x+2)

The answer is g(f(x)) =(x+6)(x+2)

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer: y = 3.75x + 2.50

Step-by-step explanation:

The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:

y = 3.75x + 2.50

Explanation:

Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:

The answer is A. PU(QU R) = {2, 4, 7, 8, 9, 11, 12, 13, 15}.

To find PU (QU R), we first need to find QU R, which means we need to take the union of Q and R and then find the union of that set with P.

Q U R = {2, 4, 7, 8, 11}

PU(QU R) = P U (Q U R) = {9, 12, 13, 15} U {2, 4, 7, 8, 11} = {2, 4, 7, 8, 9, 11, 12, 13, 15}

Therefore, the answer is A. PU(QU R) = {2, 4, 7, 8, 9, 11, 12, 13, 15}.

Note that the order of the sets does not matter when taking the union, and any repeated elements are counted only once in the final set.

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The null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.

A study has been carried out to determine the relationship between gratitude and prosocial attitudes. JASP is used to run a Pearson correlation test between gratitude and prosocial attitudes. The null hypothesis of this study is that there is no correlation between gratitude and prosocial attitudes.

In this investigation, the Pearson correlation is used. This research aims to identify the relationship between gratitude and prosocial attitudes. It can be difficult to determine whether or not there is a correlation between two variables. Pearson's correlation is a statistical method that can be used to examine the correlation between two variables.

This research is carried out with the hypothesis that there is a relationship between gratitude and prosocial attitudes. In this study, the null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.

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The value of a is 10 by solving the quadratic equation by completing the square method.

In this question,

Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. It is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)^2 + k.

The quadratic equation is

10x^2 + 40x - 13 = 0

Solving the quadratic equation by completing the square as

Step 1:

10x^2 + 40x = 13

Step 2:

10(x^2 + 4x) = 13

Thus on comparing the step 2 with the equation a(x^2 + 4x) = 13, the value of a is 10.

Hence we can conclude that the value of a is 10 by solving the quadratic equation by completing the square method.

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The total amount of snowfall on the two days combined is 4 3/8 cm

From the question, we are to determine the amount of snowfall on the two days combined

From the given information,

the amount of snowfall was 1/8 cm on Thursday

The amount of snowfall was 4 1/4 cm on Wednesday

Then,

The total amount of snowfall on the two days combined will be

\(\frac{1}{8}+4\frac{1}{4}\) cm

= \(\frac{1}{8}+\frac{17}{4}\)

= \(\frac{1+34}{8}\)

= \(\frac{35}{8}\)

= \(4\frac{3}{8} \ cm\)

Hence, the total amount of snowfall on the two days combined is 4 3/8 cm

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Answer:

6588 miles

Step-by-step explanation:

Here's what you have to do: multiply. 54.9×120= 6588 (you multiply it by 120 because that's how long two hours is) so if he traveled in the same speed for two hours the car would have traveled 6588 miles

The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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Answer:

A.

Step-by-step explanation:

   Factor out x^2-3x-40.  Know that the zeroes of a function multiply to be equal to the constant (-40) and add up to the coefficient of the x term (-3).  The two numbers that do that are -5 and 8.  Recall that to be zeroes, at least one of the x-values must make the equation equal 0.  So if x=-5, (x+5) is the term that would be 0.

You could also multiply the factored forms that are given to find the correct one.

9514 1404 393

Answer:

  Q ≈ 0.0314148930589 radians ≈ 1.79994078613°

Step-by-step explanation:

There is no algebraic solution for the set of equations with mixed polynomial and trig functions:

  x·sin(Q/2) = 5

  1/2x^2(Q -sin(Q)) = π/12

__

However, we can use the first equation to substitute for x in the second equation. This gives ...

  \(\displaystyle \frac{1}{2}\left(\frac{5}{\sin{\frac{Q}{2}}}\right)^2(Q-\sin{Q})=\frac{\pi}{12}\)

This can be simplified using the half-angle identity and recast as a function of Q:

  \(\displaystyle f(Q)=\frac{25(Q-\sin{Q})}{1-\cos{Q}}-\frac{\pi}{12}\)

This function will have a zero at the desired value of Q. It can be solved iteratively. A graph shows an approximate value of Q is 0.314 (radians). The value can be refined by Newton's method iteration to give the angle to full calculator precision:

  Q ≈ 0.0314148930589 radians ≈ 1.79994078613°

__

The corresponding value of x is about 318.333447755. In short, this is a very narrow sector/segment in a relatively large circle.

The height of the recycling bin is approximately 6.71 feet.

To find the height of the rectangular recycling bin, we'll use the given information of its length, width, and surface area.

Let's assume the height of the box is denoted by "h" (in feet).

The formula for the surface area of a rectangular box is given by:

Surface Area = 2lw + 2lh + 2wh

In this case, we have the following information:

Length (l) = 20 ft

Width (w) = 8 ft

Surface Area = 712 ft²

Plugging in these values into the surface area formula:

712 = 2(20)(8) + 2(20)h + 2(8)h

712 = 320 + 40h + 16h

712 = 336 + 56h

712 - 336 = 56h

376 = 56h

Dividing both sides by 56:

h = 376/56

h = 6.71 ft (rounded to two decimal places)

Therefore, the height of the recycling bin is approximately 6.71 feet.

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The question seems incomplete, the correct question is as follows:

A recycling bin is in the shape of a rectangular box find the height of the box if its length is 20 ft its width is 8 feet and its surface area is 712 ft squared.

Answer:

245/5 = 49 tickets per day

Answer:

245 / 5 = 49 so

49 tickets per day

Answer:

the answer is A

Step-by-step explanation:

\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 5.8\%\to \frac{5.8}{100}\dotfill &0.058\\ t=\textit{hours}\dotfill &2\\ \end{cases} \\\\\\ ~\hfill A=100(1 - 0.058)^{2} ~\hfill\)

The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour.

And, Time = 4 hours

Now,

Since, We know that;

Amount for Exponential Decay is,

⇒ \(C = P (1 - r)^t\)

Where, C is current amount, P is initial amount, r is rate and t is timeeee

Substitute all the values, we get;

The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

Thus, The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

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In this problem, and in general statistics, z represents the standard score of the data.

This standard score is the number of standard deviations that there are above or below a sample.

We have the mean: 173.38 cm

and the standard deviation: 8.78 cm

We first determined the standard score for the tallest living man:

We obtain the difference between this sample and the mean:

Then we calculate how many standard deviations are in this difference:

Then the standard score for the tallest living man is 9.87

We need to do the same to the shortest living man:

Remember that if the sample is minor than the mean we take the absolute value.

Then the standard score:

Then the standard score for the shortest living man is 7.38

The height that was more extreme is the height that has a standard score major, then we can conclude:

The standard score for the tallest living man is 9.87

The standard score for the shortest living man is 7.38

And the height that was more extreme is the tallest living man's height