Approximate 4/9 as a percent?

The differential equation representing the model of the number of words memorized by the students is equal to option C. dL/dt = k(100 - L).

Let us consider function 'L' represents the number of words memorized at time 't'

Total number of words students asked to memorized = 100 words

Rate of change of number of words with time 't' is equal to ( dL/dt )

Number of words left to memorized by the students = 100 - L

Differential equation representing the situation is

= Rate of change of number of words memorized ∝ number of words left to memorized

= dL/dt ∝ ( 100 - L )

⇒ dL/dt = k( 100 - L )

Where 'k' is the constant of proportionality .

k is a positive number.

Therefore, the differential equation representing the situation of memorizing word is given by option c. dL/dt = k( 100 - L ).

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The above question is incomplete, the complete question is:

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memorized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized.

1. Which of the following differential equations could be used to model this situation, where k is a positive constant?

A. dL/dt = kL

B. dL/dt = 100 - kL

C. dL/dt = k(100 - L)

D. dL/dt = kL - 100

Answer:

19-x

the expression that show how many bacon pancakes Mackenzie is 19 - x

Answer:

823.2

Step-by-step explanation:

Interest = 700 × 4.4/100 × 4 = 123.2

Balance = Principle + interest

700 + 123.2 = 823.2

Answer - 823.2

Hope this helps!!!

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

simplified: 4x−28

Step-by-step explanation:

The product of 4 and the difference of a number and 7 can be written as 4(x-7) where x is the number you are looking for.

The x-intercept and the y-intercept are ±3 and 9 respectively

The x-intercept of a function is the point where y = 0
Given the function y = 9 - x^2

0 = 9 -x^2
x^2 = ±9
x = -3 and 3

The y-intercept of a function is the point where x = 0
Given the function y = 9 - x^2

y = 9 -0^2
y = 9

Hence the x-intercept and the y-intercept are ±3 and 9 respectively

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Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 13, \sigma = 0.2\)

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{13.36 - 13}{0.2}\)

\(Z = 1.8\)

\(Z = 1.8\) has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

The distance between Ray-Ann and Steve, using the law of cosines, is given as follows:

11.5 feet.

The law of cosines states that we can find the length of the missing side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

The parameters of the equation are given as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the distance between Ray-Ann and Steve is obtained as follows:

c² = 6²+ 7² - 2 x 6 x 7 x cos(124)º

c² = 132

c = square root of 132

c = 11.5 feet.

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Answer:

need help too

Step-by-step explanation:

There ar 4persons so each will pay

\(\\ \sf\longmapsto \dfrac{83.90}{4}=20.975\)

Only two persons have spent more money than everyone average i.e mia and Jasmin.

Now

Mia left more money so she saved most money.

Mia saved the most money.

An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given that, the total amount each person spent Mia: 28.47, Jolene: 19.47, Jasmin: 20.99, Chloe: 14.97 and The total amount is 83.90

We will the find the average that how much each paid, = 83.90 / 4 = 20.98

There are two persons who are spending more than the average, Mia and Jolene.

Mia has $28.47, since she is left with more money than every one has.

Hence, Mia saved the most money.

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Answer:

  76 units

Step-by-step explanation:

You want the length of AC in the given triangular pyramid.

The Pythagorean theorem can be used to find the lengths of AD and CD.

  AD² + 40² = 41²

  AD² = 41² -40² = 81 . . . . . = 9²

and

  CD² +40² = 85²

  CD² = 85² -40² = 5625 . . . . . = 75²

It can also be used to find AC:

  AD² + CD² = AC²

  81 + 5625 = AC²

  AC = √5706 = 3√634 ≈ 76

The length of side AC is about 76 units.

__

Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.

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Using either shell method, the volume of the solid generated by revolving the region bounded by y = \(x^{3}\) and y = 0 around the lines x = 2 (a), x = 0 (b), and x = 9 (c) can be determined to be 8π, 0, and 54π, respectively.

To solve this problem using the disk method, we first need to determine the area of the region bounded by the two equations. This can be done by integrating y = \(x^{3}\) from x = 0 to x = 2, which gives us A = 8/4 = 2. We then need to determine the radius of the disk, which is the distance from the line of rotation to the point of intersection of the two equations.

For (a), this is the distance from x = 2 to y = 2, which is 2. For (b), this is the distance from x = 0 to y = 0, which is 0. For (c), this is the distance from x = 9 to y = 27, which is 27/3. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:

(a) V = π(2)2 × 2 = 8π

(b) V = π(0)2 × 2 = 0

(c) V = π(27/3)2 × 2 = 54π

To solve this problem using the shell method, we first need to determine the limits of integration, which is the same as for the disk method. We then need to determine the radius of the shell, which is the distance from the line of rotation to the point of intersection of the two equations.

This is the same as for the disk method. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:

(a) V = 2π ∫(2) (\(x^{3}\)) dx = 8π

(b) V = 2π ∫(0) (\(x^{3}\)) dx = 0

(c) V = 2π ∫(27/3) (\(x^{3}\)) dx = 54π

The disk and shell methods are two methods used to find the volume of a solid generated by revolving a region bounded by the graphs of two equations around a given line.

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Answer: 45

Step-by-step explanation:

The total profit in all was \(1040-900=\$ 140\).

The total profit per pizza was \((0.50)(8)=\$4\).

This means they sold \(\frac{140}{4}=35\) pizzas.

Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.

No,  a continuous function  function f(x) exits in (0 , 2 ) .

What does continuous function mean?

In mathematics, a continuous function is a function without discontinuities, i.e. without unexpected changes in value.

                        A function is continuous if it can be guaranteed for arbitrarily small changes by limiting the changes in the input to be small enough. 

A function f(x) such that

        f(0) = 10,   f(2) = 2

f'(x) ≤ 1   ∀  in (0,2)

If f'(x) ≤ 0

then f(x) decreasing on (0, 2 )

But her  f'(x) ≤ 1

So,  f(x) is not continuous  (0, 2 )

So, No continuous function f(x) exits in (0 , 2 ) .

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Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

Answer:

Marie earns more per hour

Step-by-step explanation:

Carlos earns $10.06 per hour

Marie earns $11.00 per hour

46-20=26

Marie earns more money per hour

A) There are 330 possible ways to form the committee if any EE and any CE can be included.

B) There are 210 possible ways to form the committee if one particular CE must be in the committee.

C) The total number of ways to form the committee with two particular CE excluded is 205

In this case, we are given a scenario where a committee is to be formed from a group of chemical and electrical engineers. Let's dive into the details of the problem and explore how probability can be used to solve it.

(a) If any EE and any CE can be included, we need to find the number of ways to form a committee of 7 members from a group of 6 CE and 5 EE. In this case, the order in which the committee members are selected does not matter, so we can use the formula for combinations.

The total number of ways to select 7 members from a group of 11 engineers is given by:

C(11,7) = 11! / (7! * 4!) = 330

(b) If one particular CE must be in the committee, we can first select that CE and then form the rest of the committee from the remaining engineers. The probability of selecting that particular CE is 1/6, since there are 6 CE in total.

Once we have selected that particular CE, we need to select 6 more members from a group of 5 EE and 5 CE (excluding the one we have already selected). The total number of ways to do this is given by:

C(10,6) = 10! / (6! * 4!) = 210

(c) If two particular CE cannot be in the same committee, we can use the principle of inclusion-exclusion to find the total number of ways to form the committee.

First, we find the total number of ways to form the committee without any restrictions. This is given by:

C(11,7) = 330

Next, we find the number of ways to form the committee with both particular CE included. This is given by:

C(9,5) = 126

We subtract this from the total number of ways to form the committee to get the number of ways with at least one of the particular CE excluded:

330 - 126 = 204

However, we have counted the case where both particular CE are excluded twice, so we need to add this back in:

C(7,7) = 1

Therefore, the total number of ways to form the committee with two particular CE excluded is:

204 + 1 = 205

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To round the given number to the nearest ten thousand, we would count four digits to the left of the last digit. If the value of the 4th digit is greater than or equal to 5, the first digit before it increases by 1. If it is lesser than 5, there would be no change.

Looking at the given figure, the 4th digit to the left is 7 which is greater than 5. Therefore, by rounding up to the nearest ten thousand,

it becomes 40000

Direct Materials Purchases Budget  is given by,

Rubber Steel

Expected production 3,718,000 lb. 590,000 lb.

Desired ending inventory 62,000 lb. 13,000 lb.

Total required 3,780,000 lb. 603,000 lb.

Less: Beginning inventory (73,000 lb.) (11,000 lb.)

Total to be purchased 3,707,000 lb. 592,000 lb.

Unit price $2.90/lb. $3.80/lb.

Total cost $10,749,300 $2,249,600

To prepare a direct materials purchases budget for Solid Grip Company,

The amount of rubber and steel belts needed for the production of 66,000 passenger car tires and 20,000 truck tires.

The desired ending inventories and estimated beginning inventories for each material.

First, let us calculate the amount of rubber and steel belts required for the production of passenger car and truck tires.

Passenger car tires,

Rubber,

66,000 tires x 33 lb. per unit = 2,178,000 lb.

Steel belts,

66,000 tires x 5 lb. per unit = 330,000 lb.

Truck tires,

Rubber,

20,000 tires x 77 lb. per unit = 1,540,000 lb.

Steel belts,

20,000 tires x 13 lb. per unit = 260,000 lb.

Next, let us calculate the total amount of rubber and steel belts needed for production.

Rubber,

2,178,000 lb. + 1,540,000 lb. = 3,718,000 lb.

Steel belts,

330,000 lb. + 260,000 lb. = 590,000 lb.

To calculate the total amount of rubber and steel belts required for purchase,

Add the desired ending inventories and subtract the estimated beginning inventories,

Rubber,

3,718,000 lb. + 62,000 lb. - 73,000 lb. = 3,707,000 lb.

Steel belts,

590,000 lb. + 13,000 lb. - 11,000 lb. = 592,000 lb.

Finally, calculate the total cost of rubber and steel belt purchases.

Rubber,

3,707,000 lb. x $2.90 per pound = $10,749,300

Steel belts,

592,000 lb. x $3.80 per pound = $2,249,600

Therefore, the direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8 is as follows,

Direct Materials Purchases Budget

Rubber Steel

Expected production 3,718,000 lb. 590,000 lb.

Desired ending inventory 62,000 lb. 13,000 lb.

Total required 3,780,000 lb. 603,000 lb.

Less: Beginning inventory (73,000 lb.) (11,000 lb.)

Total to be purchased 3,707,000 lb. 592,000 lb.

Unit price $2.90/lb. $3.80/lb.

Total cost $10,749,300 $2,249,600

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Answer:

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

\(P(t) = P(0)e^{-kt}\)

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that \(P(300) = 0.694P(0)\). We use this to find k.

\(P(t) = P(0)e^{-kt}\)

\(0.694 = P(0)e^{-300k}\)

\(e^{-300k} = 0.694\)

\(\ln{e^{-300k}} = \ln{0.694}\)

\(-300k = \ln{0.694}\)

\(k = -\frac{\ln{0.694}}{300}\)

\(k = 0.0012\)

So

\(P(t) = P(0)e^{-0.0012t}\)

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

\(0.5P(0) = P(0)e^{-0.0012t}\)

\(e^{-0.0012t} = 0.5\)

\(\ln{e^{-0.0012t}} = \ln{0.5}\)

\(-0.0012t = \ln{0.5}\)

\(t = -\frac{\ln{0.5}}{0.0012}\)

\(t = 569.27\)

The half-life of this substance is of 569.27 days.

Answer:

C

Step-by-step explanation:

The graph of the absolute value function y = | x | has its vertex at the origin and has the shape V

The graph here is the absolute value translated vertically 3 units down, so

y = | x | - 3 → C

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(c) |x| - 3\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

Option C should be the correct answer.  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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la surface de l'écharpe est de 1 1 56 cm² car la formule pour calculer l'air d'un carré est A= coté * coté soit coté²

donc :  Aécharpe=34²=1156

The volume of the circular cylinder be,

⇒ 62.8 mm³

Given that,

For a circular cylinder,

Height = 5 mm

Radius = 2 mm

Then we have to find the volume of this circular cylinder

Since we know that,

The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centers of the cylinder's two bases.

This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.

volume of circular cylinder = πr²h

Here we have,

r = 2 mm

h = 5 mm

Now put the values into the formula we get,

Volume = π x 2² x 5

             = 62.8 mm³

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Answer:

Answer is ¼

Step-by-step explanation:

\({ \tt{25\% = \frac{25}{100} }} \\ \\ { \tt{ \frac{25}{100} = \frac{1}{4} }}\)

Answer:

6/10

Step-by-step explanation:

6/10

Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

The inverse operation would be to cube both sides.

The missing value is -64. The correct option is a.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given equation:

-4 = ∛?

The equation shown has a missing value.

Let x be the missing value.

To find the missing value:

-4 = ∛x

Take cube of both sides,

(-4)³ = x

x = -64.

Therefore, the missing value is -64.

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