(EMERGENCY) I need to know how exponents work

Answer:

32π cm³/sec

Step-by-step explanation:

List given information

[tex]\displaystyle V=\frac{4}{3}\pi r^3\\\\r=4\\\\\frac{dr}{dt}=\frac{2}{r}\\ \\\frac{dV}{dt}=\,\,?[/tex]

Solve for dV/dt

[tex]\displaystyle V=\frac{4}{3}\pi r^3\\\\\frac{dV}{dt}=4\pi r^2\biggr(\frac{dr}{dt}\biggr)\\\\\frac{dV}{dt}=4\pi r^2\biggr(\frac{2}{r} \biggr)\\\\\frac{dV}{dt}=4\pi (4)^2\biggr(\frac{2}{4} \biggr)\\\\\frac{dV}{dt}=4\pi(16)\biggr(\frac{1}{2} \biggr)\\\\\frac{dV}{dt}=4\pi(8)\\\\\frac{dV}{dt}=32\pi[/tex]

Hence, the volume of the balloon is increasing at a rate of 32π cm³/sec when the radius is 4 cm.

Step-by-step explanation:

the law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposing angles.

you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.

The probability the length of the display will exceed 154 inches is 0.1292

The probability that the length of the display shelf given to each bar of soap will exceed 154 inches when there are 50 bars of soap is 0.0062 or 0.62%. This is because the mean is 3 inches and the standard deviation is 0.5 inches, which means that the length of the display will have a normal distribution.

We can calculate this probability by using the following formula:

P(x > 154) = P (x > 154 - 50 × 3/√(50×0.5)) = P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.870 = 0.1292

The probability the length of the display will exceed 154 inches is 0.1292.

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a) Measurement of arcCD is 40°

b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD

We know the formula for external angle as per given diagram,

∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]

50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]

Simplify, arcCD = 140° - 100° = 40°

Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW

We know the formula for external angle as per given diagram,

∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]

36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]

Simplify, arcVW = 72° + 62° = 134°

Therefore, measurement of arcVW is 134°

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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°

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The cost of covering the wall with wall paper is 495.

the lengthe of the wall = 11 feet

the width of the wall = 15 feet

so, the area of the wall

A = the length of the wall x the width of the wall

A = 11 x15

A = 165 square foot

then, the total cost is

= 165 x 3

= 495

So, the cost of covering the wall with wall paper is 495.

The surface of a shape's area is measured. You must multiply the length and breadth of a rectangle or square in order to determine its area. A has an area of x time y.

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The probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 from a small hospital is 9/19, given 6 out of 19 are General Practitioners, 5 out of 19 are under 40, and 2 are both.

To find the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40, we need to add the probabilities of these two events and subtract the probability of selecting a doctor who is both a General Practitioner and under the age of 40, since we don't want to count that case twice:

P(General Practitioner or under 40) = P(General Practitioner) + P(Under 40) - P(General Practitioner and under 40)

we know 6 out of 19 doctors are General Practitioners, 5 out of 19 doctors are under the age of 40, 2 doctors are both General Practitioners and under the age of 40.

Therefore:

P(General Practitioner) = 6/19

P(Under 40) = 5/19

P(General Practitioner and under 40) = 2/19

Substituting these values into the formula:

P(General Practitioner or under 40) = 6/19 + 5/19 - 2/19

= 9/19

Therefore, the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 is 9/19.

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a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.

b) The mean salary of the given model by using the probability density function is approximately $270.86.

a) The cumulative distribution function of the given random variable is provided as follows:

F(x) = {1−kx^−3 if x>44000, and 0 otherwise

The cumulative distribution function is given as

F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)

We need to check the value of the cumulative distribution function at 44000

We have, F(44000) = 0

0 = 1−k(44000)^−3

⇒ 1 = k(44000)^−3

⇒ k = 1/(44000)^−3

⇒ 5.427 x 10^−12

Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)

Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68

b) The probability density function is given as,

f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise

The mean or expected value of the random variable is given as

E(X) = ∫[−∞,∞]xf(x)dx

= ∫[44000,∞]x(3kx^−4)dx

= 3k∫[44000,∞]x^−3dx

= 3k[(−1/2)x^−2] [∞,44000]

= (3k/2)(44000)^−2

= 270.86 (approx.)

Therefore, the mean salary given by the model is $270.86 (approx.)

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the equivalent closed form for the original rate function is

.[tex]S π/t 4tan (t) dt  = -4 ln |cos (t)| + C.[/tex]

a. [tex]S π / π /4 5t+4 / t² + 1 dt[/tex]We can write this rate function as a sum of two functions by expanding the denominator:

[tex]S π / π /4 5t+4 / (t² + 1) dt  = S π / π /4 5t+4 / (t² + 1) (t+1/t - 1/t) dt  = S π / π /4 5t+4 (t+1 - 1/t²) dt  = S π / π /4 5t+4 (t+1) dt - S π / π /4 5t+4 (1/t²) dt[/tex]

Now, integrating the two functions gives us the closed form:

[tex]S π / π /4 5t+4 (t+1) dt = 5/2 (t² + 2t + 2) + CS π / π /4 5t+4 (1/t²) dt = -5/2 (t + 1/t) + C[/tex]

Therefore, the equivalent closed form for the original rate function isS π / π /4 5t+4 / t² + 1 dt  = 5/2 (t² + 2t + 2) - 5/2 (t + 1/t) + C.

b. S π/t 4tan (t) dt
We can use a trig identity to change the form of this rate function:

S π/t 4tan (t) dt  = S π/t 4 (sin (t) / cos (t)) dt  = 4/cos (t) S π/t sin (t) dt

Integrating the rate function gives us the closed form:

S π/t 4tan (t) dt  = 4/cos (t) S π/t sin (t) dt = -4 ln |cos (t)| + C.

Therefore, the equivalent closed form for the original rate function is:

S π/t 4tan (t) dt  = -4 ln |cos (t)| + C.

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We have triangle ABC, the length of side AB is 16 inches and the length of side BC is 24 inches, the possible length of the side AC is less than 40 inches

To find the possible length of side AC, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side, that is, a + b > c, b + c > a, c + a > b.

Now, for the given triangle ABC:

a = AB = 16 inches

b = BC = 24 inches

c = AC

We know that a + b > c (using the triangle inequality theorem)

16 + 24 > cc < 40

Therefore, By using the triangle inequality theorem, the possible length of the side AC is less than 40 inches.

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Answer: 24000 g

Step-by-step explanation:

multiply together:

4 bags * 6 kg = 24 kg total

convert:

1 kg = 1000 g

24 kg * (1000 g / 1 kg) = 24000 g

To calculate the total mass of the box in grams, we need to first calculate the total mass of the 4 bags of sugar in kilograms, and then convert that to grams.

The mass of one bag of sugar is 6 kilograms.

The total mass of all 4 bags is:

4 bags x 6 kilograms/bag = 24 kilograms

To convert 24 kilograms to grams, we multiply by the conversion factor of 1000 grams/kilogram:

24 kilograms x 1000 grams/kilogram = 24,000 grams

Therefore, the total mass of the box, including all 4 bags of sugar, is 24,000 grams.

The correct answer is B) 24,000 grams.

Answer:

Step-by-step explanation:

Equivalent fractions are defined as fractions that are equal to the same value, regardless of their numerators and denominators.

Equivalent fractions can be defined as fractions that may have different numerators and denominators but represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both simplify to 3/4. 1/2, 2/4, 3/6 and 4/8 are equivalent fractions. Let's see how their values ​​are equal. We will represent each of these fractions with a shaded circle.

It can be seen that, seen as a whole, the hatched parts in all the figures represent the same parts.

Equivalent fractions can be written by multiplying or dividing the numerator and denominator by the same number. This is why these fractions reduce to the same number when they are simplified.

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Answer:

D

Step-by-step explanation:

The square root of 50 is approximately equal to 7.07

-7.1111… can be rounded to -7.11

23/3 is equal to approximately 7.67

-7 1/5 is equal to -7.2

The required distance the ship traveled from its starting point to its destination is approximately 44.8 miles.

To solve this problem, we can use the Pythagorean theorem to find the distance the ship traveled from its starting point to its destination.

We can see that the ship traveled 35 miles east and 28 miles south, forming a right triangle. The distance from the starting point to the destination is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]$\begin{align*}\text{distance} &= \sqrt{35^2 + 28^2}\&= \sqrt{1225 + 784}\&= \sqrt{2009}\&\approx 44.8 \text{ miles}\end{align*}[/tex]

Therefore, the distance the ship traveled from its starting point to its destination is approximately 44.8 miles.

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using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.

To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.

Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:

A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168

B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165

C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168

D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165

Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.

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Answer: £43.50

Step-by-step explanation:

each ticket from samuel is £12 if erica is spending £2.50 more per ticket that is £14.50 per ticket. £14.50 x 3 = £43.50

Answer:    

   False

   True

   False

   True

   False

   False

Step-by-step explanation:

From the plot, we can see that curve B is taller and more narrow than curve A, and it is shifted to the right relative to curve A. This tells us that curve B has a larger mean and smaller standard deviation than curve A. Therefore, statement 2 is true, and statements 1, 3, 5, and 6 are false. Finally, since curve A is more spread out than curve B, it has a larger standard deviation. Therefore, statement 4 is true.

0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.

0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.

2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.

2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.

Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.

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Answer: b

Step-by-step explanation: just took it on edge.

Answer:

A (-439)

Step-by-step explanation:

To find the value of (s•t)(-7), we need to first evaluate s(t(-7)) which means we substitute -7 for x in the function t, and then substitute the resulting value in the function s.

So, we have:

t(-7) = 3(-7) = -21

s(-21) = 2 - (-21)^2 = 2 - 441 = -439

Therefore, the value of (s•t)(-7) is -439, which corresponds to option A.

So, the correct answer is A(-439).

Answer:

A

Step-by-step explanation:

I believe you mean

(s ￮ t)(- 7)

to evaluate, first evaluate t(- 7) then substitute the value obtained into s(x)

t(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Answer:

1/5 and 25

5 and -1

Step-by-step explanation:

There are infinitely many pairs of rational numbers that have a product of -5. However, two possible pairs are:

1/5 and 25

5 and -1

In general, the product of two rational numbers can be negative if one of them is positive and the other is negative.

The explicit formula for the arithmetic sequence 12, 5, -2, -9,..is a(n) = -7n + 19.

To find the explicit formula for this arithmetic sequence, we first need to determine the common difference, which is the amount by which each term differs from the previous term.

d = 5 - 12 = -7

d = -2 - 5 = -7

d = -9 - (-2) = -7

Since the common difference is -7, we can use the formula for an arithmetic sequence:

a(n) = a (1) + (n - 1) d

where a(n) is the nth term of the sequence, a (1) is the first term, n is the term number, and d is the common difference.

Plugging in the given values, we get:

a(n) = 12 + (n - 1) (-7)

Simplifying, we get:

a(n) = -7n + 19

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The explicit formula for the arithmetic sequence will be f(n) = 19 -7n.

f(n) = a + (n - 1) d,

where an is the first term and is the explicit formula for an arithmetic series.

d = Common Difference

n = number of terms

The provided arithmetic series is = 12, 5, -2, -9.

First term: a = 12.

Common variation: d= 5-12= 7

[Difference between any two words that follow one another.]

When a = 12 and d = -7 are entered into equation (1), we obtain

f(n) = 12 + (n - 1) ( - 7 )

Thus, the explicit formula for the above arithmetic sequence is

f(n) = 12 = (n - 1). ( - 7 )

If we continue to solve it, we obtain

f(n) = 12 - 7n + 7

f(n) = 19 - 7n

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Answer:

37

Step-by-step explanation:

we know that:

C=?

c=17

b=26

a=14

using the law of cosine:

[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]

[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]

Check the picture below.

so if we just set h = 0, we'll get the "t" when that happened

[tex]\stackrel{h}{0}=-16t^2+29t+6\implies 0=-(16t^2-29t-6)\implies 0= 16t^2-29t-6 \\\\\\ 0=(t-2)(16t+3)\implies t= \begin{cases} ~~ ~ 2 ~~ \checkmark\\ -\frac{3}{16} ~~ \bigotimes \end{cases}[/tex]

now, let's notice that we get two valid values for "t", however the negative doesn't apply in this case, because we can't quite have negative seconds for the object in motion.

Answer:

2

Step-by-step explanation:

h(t) = -16t² + 29t + 6

h(2) = -16 * 2² + 29 * 2 + 6

h(2) = 0

t = 2 second's

Answer:

Since the lines are parallel, we know that alternate interior angles are congruent. Therefore, angles 1 and 5 are congruent, as they are alternate interior angles. So any angle that is congruent to angle 5 is also congruent to angle 1.

Looking at the answer choices, we see that angle 2 is adjacent to angle 5 and therefore also congruent to angles 1 and 5. So the correct answer is:

Therefore, the answer is "2".

a) If the number 646 from the ordered list changes to 639, c) the median stays the same.

b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.

The median is the middle value in an ordered list (descending or ascending).

The mean refers to the average value.

The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.

The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646

The total value (sum) = 3,472

The number of cards = 7

The median = 499

The mean = 496 (3,472/7)

If the number 646 changes too 639:

The total value (sum) = 3,465

The median = 499

The mean = 495 (3,465/7)

Difference in mean = 1 (496 - 495)

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Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.

Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.

We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.

Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.

Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.

Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.

Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.

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Step-by-step explanation:

Perimeter:

12m + 10m + 8m + (10 - 8)m + 9m + (12 - 9)m = 44m

or

12m * 2 + 10m * 2 = 44m

Area:

A = 9m * 8m + 12m * (10 - 8)m

A = 72m² + 24m² = 96m²

The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.

The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.

The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.

According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.

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Answer: 36.8

Step-by-step explanation:

First convert 7/19 to a decimal.

7/19 = 0.368421...

Then to convert a decimal a percent by multiplying by 100

0.3684... x 100 = 36.8