What restriction should be applied to y = tanx for y = arctanx to be defined? (negative startfraction pi over 2 endfraction, startfraction pi over 2 endfraction) (negative startfraction pi over 2 endfraction, startfraction pi over 2 endfraction) left-bracket negative startfraction pi over 2 endfraction, startfraction pi over 2 endfraction right-bracket

Answer:

D

Step-by-step explanation:

since the inverse of the function is (4x+25)/(x+6), the inverse is simplified to 1/(x+6)+4 and x DOES NOT =-6

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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The equation of the line is y = -3x + 4.

The equation of a line can be represented in slope intercept form as follows:

y - mx + b

where

Hence, using (1, 1) and (0, 4)

Therefore,

m = 4 - 1 / 0 - 1

m = 3 / -1

m = -3

Hence, the y-intercept of the line is as follows:

y = -3x + b

4 = -3(0) + b

b = 4

Therefore, the equation of the line is y = -3x + 4

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Answer: Self Guidance. A slope of -3/4 and a y intercept doesn't look like any of them

Step-by-step explanation:

A slope of -3/4 and a y-intercept of 3/2 looks like this. After, maybe you can try it on your own. Hope this helps

Answer:

Estimated population of New Hampshire is

A. 35,000

The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2

How to calculate average rate?

The average rate is a measure of how quickly a quantity changes over a specific period of time. It can be calculated by dividing the change in the quantity by the change in time. The formula for calculating the average rate is:

Average rate = (final value - initial value) / (final time - initial time)

Given a function y, the average rate of change S of y = f(x)  in an interval (Xs, Xf)  will be given by the following equation:

In this problem, we have that:

Interval (1,5), so

Then

S = f(5) - f(1)/4

All options are compared to g(x).

g(5) = 1.8*(5)^2 = 45

g(1) = 1.8*(1)^2 = 1.8

An average rate of change greater than 10.8.

D.=k(x) = 2x^2

k(5) = 2*(5)^2 = 50

k(1) = 2*(1)^2 = 2

Greater than 10.8, this is the answer.

Hence, The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2

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Answer

The ratio of bananas to apples is 3 to 4

Step-by-step explanation:

2x + 3y = 1470

3y = -2x + 1470

y = -2/3 + 490

Price of each bag of cat food is $3 and the price of each bag of dog food is $2.75.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the cost of each small bag of cat food and y be the cost of each small bag of dog food.

Given that,

On Monday Carlos purchased 3 small bags of cat food and 5 small bags of dog food for $22.75.

3x + 5y = 22.75

On Thursday he buy 2 more small bags of cat food and 3 more small bags of dog food, which cost him $14.25.

2x + 3y = 14.25

So we have two linear equations.

3x + 5y = 22.75 and 2x + 3y = 14.25

Multiplying throughout the first equation with 2 and the second equation with 3, we get the two equations as,

6x + 10y = 45.5 and

6x + 9y = 42.75

Subtracting second from first,

y = 2.75

Substituting y = 2.75 in 2x + 3y = 14.25,

2x = 14.25 - 8.25

x = 3

Hence the the price of cat food and dog food are $3 and $2.75 respectively.

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Volume:-

\(\\ \rm\Rrightarrow V=\dfrac{4}{3}\pi r^3\)

\(\\ \rm\Rrightarrow V=\dfrac{4}{3}\pi (2)^3\)

\(\\ \rm\Rrightarrow V=\dfrac{32\pi}{3}in^3\)

Half volume:-

\(\\ \rm\Rrightarrow V=\dfrac{16\pi}{3}in^3\)

Answer:

16.8 in³ (nearest tenth)

Step-by-step explanation:

Volume of a sphere

\(V=\dfrac43 \pi r^3\)

(where V is volume and r is the radius)

Volume of a hemisphere

\(\textsf{Volume of a hemisphere}=\dfrac12 \ \textsf{Volume of a Sphere}\)

\(\implies V=\dfrac12 \cdot \dfrac43 \pi r^3=\dfrac23 \pi r^3\)

Given:

\(\begin{aligned}\implies V & =\dfrac23 \pi (2)^3\\\\ & =\dfrac{16}{3} \pi\\\\ & =16.8 \ \sf in^3 \ (nearest \ tenth)\end{aligned}\)

The rate at which the volume of the snowball is changing at the instant the radius is 4 cm is -(448*pi)/15 cubic cm/minute.

The volume of a sphere is given by the formula V = 4/3 * pi * r³, where r is the radius. To find the rate at which the volume of the snowball is changing, we need to take the derivative of this formula with respect to time.

V = (4/3) * pi * (r)³

dV/dr = 4pir²

r = 21 - (21-14)/30*t (Where t = time in minutes)

dV/dt = dV/dr * dr/dt

=> dV/dt = 4pi(21 - (21-14)/30*t)² * -(21-14)/30

=> dV/dt = -4pi(21 - (21-14)/30*t)² / 30

dV/dt = -4pi(21 - (21-14)/30t)² / 30 = -4pi*(21-7)² / 30 = -4pi(14)² / 30 = -(448*pi)/15 cubic cm/minute.

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Answer:

15

Step-by-step explanation:

Element that would be more effective in accepting electrons - Chlorine

Element that would be the  best insulator - As

Element that would combine with sulfur - Rb

We know that in a bonding situation, it is possible to have electrons closer to one of the bonding atoms than the other. In such case, the electron cloud is seen to be closer to a given atom. The atom to which the electron cloud is closer is said to be more electronegative.

In the periodic table electronegativity is a property that tends to increase from the left hand side to the right hand side of the periodic table.

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

The compound interest formula is given by the formula

Where A = Amount after t years

r = rate = 6

t = time = 5

p = $ 25000

For the first year

For the second year

P=26500+25000=51500

For the third year

P=54590 + 25000=79590

For the fourth year

P=84365.4 + 25000=109365.4

For the fifth year

P= 115927.324 + 25000 =140927.324

At the start of the 6th year

P= 149382.962+25000= 174382.96

Answer = $174382.96

Option B is correct

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The Number of small and large boxes shipped are 12 and 15 respectively.

Large boxes:

Volume = 18 cubic feets

Let number of large boxes = a

Small boxes :

Volume = 6 cubic feets

Number of small boxes = b

Total volume shipped = 342 cubic feet

Total boxes shipped = 27

Writing as a system of equation :

a + b = 27

18a + 6b = 342...........equation 1

6a + 6b = 162............equation 2

Subtracting equation 2 from equation 1

18a + 6b - (6a + 6b) = 342 - 162

18a 6a + 6b - 6b = 180

12a = 180

a = 180/12

a = 15

a + b = 27

b = 27 - 15

b = 12

Hence

Number of large boxes = 15 and Number of small boxes =12

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The probability that it will rain on exactly one of the seven days the Hiking Club is camping in the state park is approximately 0.293, rounded to the nearest thousandth.

The probability of rain on any given day is 0.66.

To find the probability that it will rain on exactly one of the seven days the Hiking Club is there, we can use the binomial probability formula.

The binomial probability formula is

\(P(x) = C(n, x) * p^x * (1-p)^{(n-x)}\),

where:

P(x) is the probability of exactly x successes,

C(n, x) is the combination formula, which calculates the number of ways to choose x successes from n trials,

p is the probability of success on a single trial, and

n is the total number of trials.

In this case, we want to find the probability of rain on exactly one day out of the seven days.

So, x = 1,

n = 7, and

p = 0.66.

Using the combination formula,

C(n, x) = n! / (x! * (n-x)!),

we can calculate

C(7, 1) = 7! / (1! * (7-1)!)

C(7, 1) = 7.

Plugging the values into the binomial probability formula, we get:

\(P(1) = C(7, 1) * 0.66^1 * (1-0.66)^{(7-1)}\)

\(= 7 * 0.66^1 * 0.34^6\)

Calculating this expression, we find that P(1) is approximately 0.293.

Therefore, the probability that it will rain on exactly one of the seven days the Hiking Club is camping in the state park is approximately 0.293, rounded to the nearest thousandth.

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Answer:

17s + 5t

Step-by-step explanation:

Simple. There are two variables that can be added. Also another that can't be added. Add the two variables and the other one and you've got the answer.

Answer:

the question is not complete

5s + 12s = 17s

Step-by-step explanation:

.7071 is the value to convert peak to RMS

If ten workers are randomly selected, the probability exactly nine of them say that their jobs were sometimes or always stressful is 0.268 or 26.8%

The result of the recent poll is

80% of respondents said that their jobs were sometimes or always stressful

The 10 workers are randomly selected

Then we have to find the probability exactly nine of them say that their jobs were sometimes or always stressful

The equation

P(X) = nCx × P^x × (1-P)^n-x

Here n = 10

r  = 9

P = 0.80

Substitute the values in the equation

P(9) = 10C9 × 0.80^9 × (1-0.80)^(10-9)

= 10 × 0.134 × 0.20

= 0.268

= 26.8%

Therefore, the probability exactly nine of them say that their jobs were sometimes or always stressful is 26.8%

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The rate of change of the divers elevation = 19.274

Given,

The depth to which the Scuba dove = -69 \(\frac{9}{10}\) feet

The rate at which he dove = -21.5 feet per min.

The time which he spent at the elevation = 12.5min.

The elevation the diver then ascended to -38 \(\frac{9}{10}\) feet

Thee total time for the dove = 19 \(\frac{1}{8}\) minutes.

Therefore, the time \(t_{d}\) with which the scuba diver descended to -69 \(\frac{9}{10}\) feet

is given as follows:
\(t_{d} = \frac{Distance}{speed}\) = \(= \frac{-69\frac{9}{10} }{-21.5}= \frac{-681}{-21.5}\) = 3.167 minutes

The time \(t_{e}\), it took the scuba diver to elevate to -38 \(\frac{9}{10}\) feet is given as follows:

\(t_{e}\) = 19 \(\frac{1}{8}\)minutes - (3.167 + 10.5) minutes = 5.458 minutes

The rate of change of the divers elevation = (Final elevation - Initial elevation)/(Time taken).

∴ The rate of change of the divers elevation

= (-38 \(\frac{9}{10}\) - (-69 \(\frac{9}{10}\) )) / 5.458 min

=(37.1 - (-68.1))/ 5.458 min

= 19.274 feet/minutes to the nearest hundredth.

Hence, The rate of change of the divers elevation = 19.274

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The equation of a plane that passes through a point and is parallel to the YZ plane can be written as:

x = constant

When a plane is parallel to the YZ plane, it means that its normal vector is perpendicular to the X-axis. Since the normal vector is perpendicular to the X-axis, the X-coordinate of any point on the plane remains constant.

To find the equation of the plane, we need a point that lies on the plane. Let's assume the point (a, b, c) lies on the plane.

Since the plane is parallel to the YZ plane, the X-coordinate of any point on the plane will remain constant. Therefore, we can say that x = a.

The equation of the plane becomes:

x = a

The equation of a plane that passes through a point and is parallel to the YZ plane is given by the equation x = a, where a is the constant X-coordinate of any point on the plane. This equation represents all points where the X-coordinate remains constant, while the Y and Z coordinates can vary freely.

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Listen In Excel we can use the RAND function inside an IF function to simulate whether some event occurs or does not occur  is True. because In Microsoft Excel, you can use the RAND function inside an IF function to simulate whether an event occurs or doesn't occur.

The RAND function generates a random number between 0 and 1. You can use this function in an IF statement to determine whether a certain condition is met, such as whether the generated number is greater than or equal to a certain probability.

For example, if you wanted to simulate a 50/50 chance of an event occurring, you could use the following formula: =IF(RAND() >= 0.5, "Event Occurs", "Event Doesn't Occur").

In this case, if the random number generated by the RAND function is greater than or equal to 0.5, the IF function will return "Event Occurs". If not, it will return "Event Doesn't Occur".

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Answer:

C) 4,0

Step-by-step explanation:

Basically to find zeros you set up the expression equal to zero.

First pair is (0,0) they derived this by setting the leftmost x to 0 so x=0, this meant that when x was plugged back into the equation y = x(x-4) the y value we got out was 0 because y = 0 (0-4) = 0, thus the pair (0,0).

For second pair, we set up x-4= 0, solve this to get x = 4 (add 4 to both sides). Now plug this back into full equation y= 4 (4-4)= 0, you get y=0 and your ordered pair is (4,0) which is the second pair of zero.

Zero are x-intercept where y is zero which is the main reason why we setup x=0 or x-4=0 to start with.

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The area of this circle is equal to 49π square meters.

Mathematically, the circumference of a circle can be calculated by using this formula:

C = 2πr

Where:

Next, we would determine the radius of this circle as follows:

Radius, r = C/2π

Substituting the given parameters into the formula, we have;

Radius, r = 14π/2π

Radius, r = 7 meters.

Mathematically, the area of a circle can be calculated by using this formula:

Area = πr²

Area = π × 7²

Area = π × 49

Area = 49π square meters.

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The statement "The equation ax=0 gives an explicit description of its solution set" is true.

When the equation ax=0 is given, the solution set is explicitly described as x = 0.

In other words, the only solution to the equation is x being equal to zero. This can be verified by dividing both sides of the equation by a (assuming a is non-zero), which yields x = 0/a = 0.

Therefore, the solution set is explicitly described as x = 0.

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