One study suggests that from 1955 to 1970, the number of bachelor's degrees in mathematics awarded per year by Canadian universities grew exponentially, with growth constant k = 0.099. (a.) If exponential growth continues, how long will it take for the number of mathematics degrees awarded per year to increase 17-fold? Use yr for years. (Note on terminology: Here, by a 2-fold increase we mean the quantity doubles, by a 3-fold increase we mean the quantity triples, etc.) (b.) If 250 mathematics degrees were awarded in 1955, in which year did the number of degrees awarded reach 1000?

The dimensions of the tank with minimum weight are 24*24*12 ft

What is rectangular tank?

There is a benefit to employing vertical cylindrical stores that are put behind the double glass as in the Trombe wall system because a rectangular tank that extends from floor to ceiling is relatively expensive to construct and must be constructed to withstand quite high hydraulic pressures.

The tank with minimum weight is the one with minimum surface area.

Let x= base width and base height

     h= height of the tank

The volume of tank is :

  v=hx²

substitute v=6912 ft³

 6912=hx²

  h= 6912/x²............(1)

Formula for the tank surface area is:

A=x²+4xh

On substituting h value and simplifying,

A=x²+(27.648/x)

Differentiate with respect to x and equate to zero

2x-(27.648/x²)=0

On simplifying,

x³=27648/2 = \(\sqrt[^3]{13824}\)

x= 24

substitute x=24 into the equation 1

h= 6912/(24)²= 12 ft

So, the dimensions of the tank with minimum weight are 24*24*12 ft

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Answer:

9 lol

Step-by-step explanation:

comming from a highscholer its 12% of 12 =9

hope this helps

Answer:

.

Step-by-step explanation:

there has to be more to this question you csnt just guess the minutes

Answer:

What is the rate

Step-by-step explanation:

Answer:

m 7=129

Step-by-step explanation:

if 6 and 7 are right next to each other. it makes 180 degrees so you would take 180-51 to get your answer

Answer:

172

Step-by-step explanation:

I promise you that this is right!

The requried Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR. Option A is correct.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value.

Here,
Burger Quick is able to estimate its wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The smaller the IQR, the more consistent the data is around the median, which is represented by the line within the box in the box plot.

In this case, Burger Quick has a smaller IQR (8.0) compared to Super Fast Food (7.0), indicating that the wait times at Burger Quick are more consistent around the median. The range, which is the difference between the maximum and minimum values, is not a good measure of consistency as it is affected by outliers.

Therefore, based on the given information, Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR.

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According to the question For ( a ) The average velocity during this time

period is \(\[\text{Average velocity} = \frac{\Delta s}{\Delta t} = \frac{-4}{1} = -4 \, \text{cm/s}\]\). For ( b ) The estimated

instantaneous velocity of the particle when \(\( t = 1 \) is \( -5\pi \) cm/s.\)

a. Average velocity during each time period:

The equation of motion for the displacement of the particle is given by:

\(\[ s = 5\sin(\pi t) + 2\cos(\pi t) \]\)

To find the average velocity, we need to calculate the change in displacement divided by the change in time.

For the time period \(\( t = 0 \)\) to \(\( t = 2 \)\) :

\(\[\Delta t = 2 - 0 = 2\]\)

\(\[\Delta s = s(2) - s(0) = (5\sin(\pi(2)) + 2\cos(\pi(2))) - (5\sin(\pi(0)) + 2\cos(\pi(0)))\]\)

Using the values of \(\( \sin(2\pi) = 0 \)\) and \(\( \cos(2\pi) = 1 \)\), we can simplify the equation:

\(\[\Delta s = (5\sin(\pi(2))) + 2(1) - (5\sin(\pi(0)) + 2\cos(\pi(0))) = 0 + 2 - (0 + 2) = 2 - 2 = 0\]\)

The average velocity during this time period is:

\(\[\text{Average velocity} = \frac{\Delta s}{\Delta t} = \frac{0}{2} = 0 \, \text{cm/s}\]\)

For the time period \(\( t = 2 \)\) to  \(\( t = 3 \)\) :

\(\[\Delta t = 3 - 2 = 1\]\)

\(\[\Delta s = s(3) - s(2) = (5\sin(\pi(3)) + 2\cos(\pi(3))) - (5\sin(\pi(2)) + 2\cos(\pi(2)))\]\)

Using the values of  \(\( \sin(3\pi) = 0 \)\) and \(\( \cos(3\pi) = -1 \)\) , we can simplify the equation:

\(\[\Delta s = (5\sin(\pi(3))) + 2(-1) - (5\sin(\pi(2)) + 2\cos(\pi(2))) = 0 - 2 - (0 + 2) = -4\]\)

The average velocity during this time period is:

\(\[\text{Average velocity} = \frac{\Delta s}{\Delta t} = \frac{-4}{1} = -4 \, \text{cm/s}\]\)

b. To estimate the instantaneous velocity of the particle when \(\( t = 1 \)\) , we can use the velocity equation we obtained earlier:

\(\[v = 5\pi\cos(\pi t) - 2\pi\sin(\pi t)\]\)

Plugging in \(\( t = 1 \)\) :

\(\[v(1) = 5\pi\cos(\pi(1)) - 2\pi\sin(\pi(1))\]\)

Using the values of   \(\( \sin(\pi) = 0 \) and \( \cos(\pi) = -1 \)\) , we can simplify the equation:

\(\[v(1) = 5\pi(-1) - 2\pi(0) = -5\pi\]\)

The estimated instantaneous velocity of the particle when \(\( t = 1 \) is \( -5\pi \) cm/s.\)

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

The percentage of 4c that is each expression is:

1) 5%

2) 25%

3) 75%

4) 125%

5) (a/c)*50%

Here 4c represents the 100%, to get the percent of 4c that is each expression, we need to use the equation:

\(percentage = \frac{E}{4c}*100 \%\)

Where E is the expression.

Notice that if we use E = 4c we get the trivial percentage:

\(percentage = \frac{4c}{4c}*100 \% = 100 \%\)

Now we just need to evaluate the equation for all the given expressions:

1) E = 0.2c

\(percentage = \frac{0.2c}{4c}*100 \% = 5 \%\)

2) E = c

\(percentage = \frac{c}{4c}*100 \% = 25 \%\)

3) E = 3c

\(percentage = \frac{3c}{4c}*100 \% = 75 \%\)

4) E = 5c

\(percentage = \frac{5c}{4c}*100 \% = 125 \%\)

5) E = 2a

\(percentage = \frac{2a}{4c}*100 \% = \frac{a}{c}*50 \%\)

Here we can't give an exact percentage, because we don't know the relation between c and a.

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This is possible only when \(x = π/6 + 2nπ or x = 5π/6 + 2n\)π.

Substituting sin(x) = -1/3 in the equation, we get sin(x) = -1/3.

This is not possible over the domain 0 ≤ x ≤ 2π.

The given equation is 2sin²(x) - sin(x) - 1 = 0. This is a quadratic equation in sin(x).Let sin(x) = p, then the given equation becomes 2p² - p - 1 = 0.

Using the quadratic formula, we can find the value of p.p =\([1 ± √(1 + 8)]/4 = [1 ± 3]/4. Thus, p = 1 or p = -1/\)2.Substituting sin(x) = 1 in the equation, we get sin(x) = 1. This is possible only when x = nπ + (-1)ⁿ⁺¹π/2, where n is an integer.

Substituting sin(x) = -1/2 in the equation, we get sin(x) = -1/2.

This is possible only when\(x = 7π/6 + 2nπ or x = 11π/6 + 2\)nπ.

Therefore, the solutions of the equation 2sin²(x) - sin(x) - 1 = 0 over the domain \(0 ≤ x ≤ 2π are x = π/2 + 2nπ, 7π/6 + 2nπ, 11π/6 + 2nπ\) where n is an integer.

b)The given equation is 6sin²(x) - sin(x) - 1 = 0. This is a quadratic equation in sin(x).Let sin(x) = p, then the given equation becomes 6p² - p - 1 = 0. Using the quadratic formula, we can find the value of p.p = [1 ± √(1 + 24)]/12 = [1 ± 5]/12.

Thus, p = 1/2 or p = -1/3.

Substituting sin(x) = 1/2 in the equation, we get sin(x) = 1/2.

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l= 4.2 m = 4.2 * 100 = 420 cm

b = 1.4 m = 1.4*100 = 140 cm

h =1.2 m =1.2 *100 =120 cm

Volume of cuboid = l*b*h =  420 * 140 * 120  = 705600 cubic cm

Volume of cube = a*a*a = 20*20*20 = 8000 cubic cm

No.of cubes = Volume of cuboid / volume of cube

      = 705600 / 8000 = 882 cubes

or  420*140*120 / 20*20*20 = 42*14*12/2*2*2 = 21*7*6 = 882 cubes

Answer:

The algebraic equation for the given sentence is

3x - 8 = 25

Answer:

33 chocolates

Step-by-step explanation:

3 chocolates times 5 days = 15 chocolates

48 chocolates minus 15 chocolates = 33 chocolates

Answer

put 1 on top and exo on bottom

Step-by-step explanation:

The correct graph would be a straight line with a slope of 45 and passing through the origin (0, 0).

We have,

The graph that models the cost, y, in cents of making x minutes of international calls would be a linear graph, as the cost is directly proportional to the number of minutes.

The equation of the linear graph would be:

y = 45x

Here, y represents the cost in cents, and x represents the number of minutes.

Therefore,

The correct graph would be a straight line with a slope of 45 and passing through the origin (0, 0).

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Jim will have to pay $795 out-of-pocket if he has an accident that costs $3,000 in medical expenses. Option b is correct.

Let’s calculate the amount Jim has to pay out-of-pocket. Jim has an accident that costs $3,000 in medical expenses, so the total cost is $3000.Jim’s health insurance policy has the following provisions:

Deductible = $300

Co-pay = $50

Coinsurance = 70/30

Since the coinsurance provision is 70/30, this means that Jim's insurance will pay 70% of the remaining expenses after deductibles and co-pays and Jim will pay the remaining 30%.

Thus, Jim will pay 30% of the remaining expenses after deductibles and co-pays. Out of the total $3000 medical expenses, Jim has to pay the first $300 (deductible).

The remaining amount is $3000 – $300 = $2700.

He has a copay of $50, thus reducing the remaining amount to $2650.

So, Jim has to pay 30% of $2650 which is equal to:

$2650 × 0.3 = $795

Therefore, Jim has to pay out-of-pocket $795. The correct option is option B.

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The Answer:

The Cop= 4

The equivalent expression of the expression is 128x^5y^6/2x^7y^5

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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Complete question

Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Answer:

X=20-8

Step-by-step explanation:

Answer: she will have 12 dollars left

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the points be A and B

A ( 3 , 7 ) --------> (x1 , y1 )

B ( 2 , -1 ) --------> ( x2 , y2 )

Finding the midpoint:

\(( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )\)

\( = ( \frac{3 + 2}{2} , \: \frac{7 + ( - 1)}{2} )\)

\( = ( \frac{5}{2} , \: \frac{7 - 1}{2} )\)

\( = ( \frac{5}{2} ,\: \frac{6}{2} )\)

\( = (2.5 ,\: 3)\)

Hope this helps...

Good luck on your assignment ....

Answer:

(2,-1)

Step-by-step explanation:

Welol to find the line of (3,7) and (2,-1) we need to use the following formula,

\(\frac{y^2-y^1}{x^2-x^1}\)

So -1 is y2 7 is y1 so -1 - 7 = -8

2-3 = -1

Hence, the slope of the line is 8.

And graphing more points on the graph using the slope we can see the y intercept is -17.

So the equation is y = 8x - 17

And the mid point is at (2, -1)

Answer:

17.6

Step-by-step explanation:

The rate of the slower bus and faster bus is 135.5 miles per hour and 146.5 miles per hour respectively

Let

The train meets at a distance of 846 miles

The train meets in 3 hours

3(s) + 3(s + 11) = 846

3s + 3s + 33 = 846

6s = 846 - 33

6s = 813

divide both sides by 6

s = 813 / 6

s = 135.5

Therefore,

Speed of the slower train = s

= 135.5 miles per hour

Speed of the faster train = s + 11

= 135.5 + 11

= 146.5 miles per hour

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The central limit theorem (CLT) states that as sample size increases, "The correct answer is C - both A and B". The shape of the distribution of sample means tends to be normal if the population from which the samples are obtained is normal and the sample size is n-30 or more.

the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution, provided that the sample size is large enough. Therefore, the answer to this question involves both the conditions of the CLT and the nature of the population distribution.

Condition A states that the population from which the samples are obtained must be normal. This means that the population distribution is symmetrical and bell-shaped, with most of the observations clustered around the mean, and the tails of the distribution taper off towards plus and minus infinity. If the population is not normal, then the sample mean distribution may not be normal, regardless of sample size.

Condition B states that the sample size should be n-30 or more. The rule of thumb is that if the sample size is greater than or equal to 30, the distribution of sample means will be approximately normal, regardless of the population distribution. This is because as sample size increases, the sample means will tend to cluster around the population mean, and the standard error of the mean will decrease. This, in turn, will result in a narrower and more symmetrical distribution of sample means.

Therefore, both conditions A and B must be satisfied for the distribution of sample means to be normal. If either of these conditions is not met, the distribution of sample means may not be normal.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:if you are looking for the hypotenuse use Pythagoras theorem 17.2047

Step-by-step explanation:square both the base and height .Add their total then find the square root

Answer:

10

Step-by-step explanation:

k represents how many places the graph will be shifted. -k means that is being shifted to the right and positive means being shifted to the left.

So when moving 10 units to the right, k will equal 10

Answer:

its 10

Step-by-step explanation:

−2y + 2y + 3 = 3  this equation have infinite solution.

Equation with one variable that is linear. One solution exists for the linear equation with one variable, which is written as ax+b = 0, where a and b are two integers, and x is a variable. A linear equation with a single variable, for instance, is 2x+3=8.

The given equation is :

−2y + 2y + 3 = 3

rearranging the equation:

−2y + 2y = 3 - 3

the given equation is true for any value of y the the equation will be zero:

0 = 0

so,

this equation have infinite solution

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