The ratio of teachers to assistants to children at a day care center is 2: 1: 9. Of the 96 people at the center, how many of them are children?

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.

Let's assume the job takes x hours for Bruce to complete alone, y hours for Bryce to complete alone, and z hours for Marty to complete alone.

From the first piece of information, we can create the following equation based on the work completed in 1 hour and 20 minutes (4/3 hours):

1/x + 1/y = 3/4

From the second piece of information, we can create the following equation based on the work completed in 1 hour and 36 minutes (8/5 hours):

1/y + 1/z = 5/8

From the third piece of information, we can create the following equation based on the work completed in 2 hours and 40 minutes (8/3 hours):

1/x + 1/z = 3/8

Solving these equations simultaneously, we can find that x = 5, y = 8, and z = 10.

Therefore, Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.

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the interval of convergence for the given power series is:

from x = 3, left end included (Y),

to x = ∞, right end not included (N).

What is interval of convergence?

The interval of convergence is a concept in calculus that refers to the range of values for which a power series converges. For a given power series \(∑(n=0 to ∞) cn(x-a)^n\), the interval of convergence represents the set of x-values for which the series converges.

To find the interval of convergence for the given power series ∑n=1 to [infinity] \((x−3)^n/(n(−6)^n)\), we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Let's apply the ratio test to the given series:

\(|((x - 3)^(n+1)/(n+1)(-6)^(n+1)) / ((x - 3)^n / (n(-6)^n))|= |(x - 3)/(n+1)(-6)|\)

To ensure convergence, we need the absolute value of the ratio to be less than 1:

|(x - 3)/(n+1)(-6)| < 1

Now, let's consider the numerator:

If (x - 3) > 0, then we have:

(x - 3)/(n+1)(-6) < 1

(x - 3) < -(n+1)(-6)

(x - 3) < 6(n+1)

x < 6(n+1) + 3

x < 6n + 9

If (x - 3) < 0, then we have:

-(x - 3)/(n+1)(-6) < 1

(x - 3) > (n+1)(-6)

(x - 3) > -6(n+1)

x > -6(n+1) + 3

x > -6n - 3

In summary, for the series to converge, x must satisfy the following inequalities:

If (x - 3) > 0, then x < 6n + 9

If (x - 3) < 0, then x > -6n - 3

Now, let's determine the left and right ends of the interval of convergence:

Left end:

When (x - 3) = 0, we have x = 3. Thus, the left end of the interval of convergence is x = 3.

Right end:

Considering the case where (x - 3) > 0, for convergence, x < 6n + 9. As n approaches infinity, 6n + 9 also approaches infinity. Therefore, there is no finite right end to the interval of convergence.

In conclusion, the interval of convergence for the given power series is:

from x = 3, left end included (Y),

to x = ∞, right end not included (N).

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The number of students who registered for both robotics and app development is 70.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total members = 280

The number of members who registered for the robotics class.

= 75% of 280

= 3/4 x 280

= 3 x 70

= 210

The number of members who registered for the app development class

= 50% of 280

= 1/2 x 280

= 140

We see that,

210 + 140 = 350

But we have 280 members.

So,

The number of students who registered for both robotics and app development.

= 350 - 280

= 70

Thus,

The number of students who registered for both robotics and app development is 70.

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

(-1,3)

Step-by-step explanation:

\( - x + 2 = 3x + 6\)

\( - x - 3x = 6 - 2\)

\( - 4x = 4\)

\(x = - 1\)

\(y = - ( - 1) + 2 = 3\)

Answer:

1= 1/6, 2= 1/6, 3= 4/6

Step-by-step explanation:

'1' and '2' are equal and only take up 1/6 of the "circle" each, leaving '3' with 4/6 of it.

Therefore, '1' and '2' would be placed 1/6 along the line, and '3' would be placed 4/6 along the line.

a. Own Price Elasticity of Demand = (-30) / (0) = undefined. Since the own price elasticity of demand is undefined, we cannot determine if the demand is elastic, inelastic, or unitary elastic based on this information.

b. Cross-Price Elasticity of Demand = (12/7) / 0 = undefined. Since the cross-price elasticity of demand is undefined, we cannot determine if goods X and Y are substitutes or complements based on this information.

c. Income Elasticity of Demand = (-2860.71) / (0) = undefined. Since the income elasticity of demand is undefined, we cannot determine if good X is a normal or inferior good based on this information.

d. We cannot calculate the own advertising elasticity of demand with the provided data.

a. To determine the own price elasticity of demand, we need to use the formula:

Own Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

Given the demand equation OX​d​ = 7−15PX​+2Py​+0.5M+A, we can calculate the derivative of demand with respect to price:

d(OX​d​) / d(PX​) = -15

Now, let's plug in the values:

% Change in Quantity Demanded = (d(OX​d​) / d(PX​)) * (PX​ / OX​d​) = (-15) * (15 / 7) = -30

% Change in Price = (ΔPX​ / PX​) = (15 - 15) / 15 = 0

b. To determine the cross-price elasticity of demand between goods X and Y, we use the formula:

Cross-Price Elasticity of Demand = (% Change in Quantity Demanded of Good X) / (% Change in Price of Good Y)

Using the same demand equation, we calculate the derivative of demand with respect to the price of good Y:

d(OX​d​) / d(Py​) = 2

Now, let's plug in the values:

% Change in Quantity Demanded of Good X = (d(OX​d​) / d(Py​)) * (Py​ / OX​d​) = (2) * (6 / 7) = 12/7

% Change in Price of Good Y = (ΔPy​ / Py​) = (6 - 6) / 6 = 0

c. To determine the income elasticity of demand, we use the formula:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

Using the same demand equation, we calculate the derivative of demand with respect to income:

d(OX​d​) / d(M) = 0.5

Now, let's plug in the values:

% Change in Quantity Demanded = (d(OX​d​) / d(M)) * (M / OX​d​) = (0.5) * (-40000 / 7) = -2860.71

% Change in Income = (ΔM / M) = (-40000 - (-40000)) / (-40000) = 0

d. The own advertising elasticity of demand measures the responsiveness of quantity demanded to changes in advertising expenditure. Unfortunately, the given demand equation does not provide any information about advertising expenditure or its impact on quantity demanded.

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To find the area enclosed by the curves y = tan(9x) and y = 2 sin(9x) for -π/27 ≤ x ≤ π/27, we need to calculate the definite integral of the difference between the two functions over that interval.

The area can be found using the formula:

A = ∫[a,b] (f(x) - g(x)) dx

Where f(x) is the upper curve (in this case, f(x) = 2 sin(9x)) and g(x) is the lower curve (in this case, g(x) = tan(9x)).

Therefore, the area can be calculated as:

A = ∫[-π/27, π/27] (2 sin(9x) - tan(9x)) dx

To find the exact numerical value of the area, you would need to evaluate this integral.

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Answer:

its 4, but give the other guy brainliest he answered first :D

Step-by-step explanation:

Answer:

9.1 units

Step-by-step explanation:

formula of a distance of two points:

\(\sqrt{(x1-x2)^2+(y1-y2)^2}\) where x and y indicate the coordinates of the points

\(\sqrt{(4+5)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} = 9.1 units\)

Answer:it is 40! :D

Step-by-step explanation:

Answer:

The answer is 40 no problem please mark me brainlyest

Step-by-step explanation:

20x2=40

its like counting by 2s

You need to adjust the tube of the microscope to 6.83cm in order to view the sample in focus with a completely relaxed eye

Given, Focal length of the eyepiece,  = 2.50 cm

The focal length of the converging lens, f = 1.00 cm

The distance of the object, p = 1.30 cm

Lens equation, \(\frac{1}{f} = \frac{1}{p} + \frac{1}{q}\)

Substitute the values in the above equation

\(\frac{1}{1.00} = \frac{1}{1.30} + \frac{1}{q}\)

q = 4.33 cm

now, the image is formed at the focal point of the eyepiece,

therefore, the distance between the objective and the eyepiece, d =  + q = 2.50 cm + 4.33 cm

d = 6.83 cm

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Answer:

x = 7

Step-by-step explanation:

23 - 2 = 21

21 / 3 = 7

x = 7

Answer:

x = 7

Step-by-step explanation:

3x + 2 = 23

3x = 23 - 2

3x = 21

x = 21/3

x = 7

I hope you understand...

This is Right answer...

From the information provided the measure of the angles are given as, m∠EFH = 71; and m∠EFG = 142°. See the explanation below.

It is to be noted that

m∠GFH = m∠EFH

m∠EFH = 71°

m∠EFG = m∠GFH + mEFH

Hence,

m∠EFG = 71 + 71

= 142°

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Answer:

The answer is 21.2in² when it is rounded.

After graphing  x⁵ – 4x³ + x² + 2, we have

x-intercepts : x ≈ 2.16, x = 1, x ≈ 1.75

local maximums : (-1.63, 10.47)

local minimums : (1.46, -1.68)

increasing : 1.46 < x < -1.63

decreasing : -1.63 < x < 1.46

In discrete mathematics, and mοre specifically in graph theοry, a graph is a structure amοunting tο a set οf οbjects in which sοme pairs οf the οbjects are in sοme sense "related". The οbjects cοrrespοnd tο mathematical abstractiοns called vertices (alsο called nοdes οr pοints) and each οf the related pairs οf vertices is called an edge (alsο called link οr line).

Typically, a graph is depicted in diagrammatic fοrm as a set οf dοts οr circles fοr the vertices, jοined by lines οr curves fοr the edges. Graphs are οne οf the οbjects οf study in discrete mathematics.

After graphing  x⁵ – 4x³ + x² + 2, we have

x-intercepts : x ≈ 2.16, x = 1, x ≈ 1.75

local maximums : (-1.63, 10.47)

local minimums : (1.46, -1.68)

increasing : 1.46 < x < -1.63

decreasing : -1.63 < x < 1.46

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Complete correct question:

The final value of the given expressions are:

1) 12√(33)c

2) 8√5 (3√2 + 8√3)

3) 3

4) -12√6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1)

√99c . √48c

√(9 x 11)x . √(16 x 3)c

3√11c . 4√3c

12√(11 x 3)c²

12√(33)c

2)

2√(80) ( √18 + 4√12 )

2 √(16 x 5) ( √(9 x 2) + 4√(4 x 3) )

2 x 4√5 ( 3√2 + 8√3 )

8√5 (3√2 + 8√3)

3)

(√2 - √5) . (-√2 - √5)

= -2 - √10 + √10 + 5

= 3

4)

√(48) x -√18

= √(16 x 3) x -√(2 x 9)

= 4√3 x -3√2

= -12√6

Thus,

The value of each of the expresssion is given above.

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That slope appears to be 4/6 or 2/3.

The perpendicular slope will have the opposite sign and be the reciprocal.

The perpedicular slope is –3/2.

Therefore:

Answer:

your answer will be A)719 units²

Step-by-step explanation:

hope it helps ^_^

$QS$ and $PR$ are parallel sides of the square, they have the same length, which is $10$. Therefore, we can conclude that $XM = NY = 10$.

Given the square $PQRS$ with side length $10$, the points $X$ and $Y$ are located outside the square such that $XQ < XS$ and $YR < YS$. We need to determine the relationship between the lengths of the segments $XY$, $QS$, and $PR$.

Since $XQ < XS$, we can conclude that $X$ lies between $Q$ and $S$. Similarly, since $YR < YS$, we can conclude that $Y$ lies between $R$ and $S$. Therefore, the segment $XY$ intersects the segments $QS$ and $PR$.

Let $M$ be the point of intersection between $XY$ and $QS$, and let $N$ be the point of intersection between $XY$ and $PR$. We can observe that $QS$ and $PR$ divide $XY$ into three segments: $XM$, $MN$, and $NY$.

Since $QS$ and $PR$ are parallel sides of the square, they have the same length, which is $10$. Therefore, we can conclude that $XM = NY = 10$.

In summary, we have $XM = 10$, $MN$, and $NY = 10$.

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Step-by-step explanation:

2,250 was made in a month

Answer:

14 miles

Step-by-step explanation:

make it into an equation 1.50x+3=24 then solve

Main Answer: The dot plots for tasks A+ and D show the mean time is approximately equal to the median time.

Supporting Question and Answer:

How do we determine if the mean time is approximately equal to the median time based on a dot plot?

To determine if the mean time is approximately equal to the median time based on a dot plot, we need to look at the distribution of the data and see if it is symmetric or skewed. If the data is roughly symmetric, with values distributed evenly on both sides of the median, then the mean and median will be close to each other, and the mean time will be approximately equal to the median time. Conversely, if the data is skewed, with more values on one side of the median than the other, then the mean and median will be further apart, and the mean time will not be approximately equal to the median time.

Body of the Solution:The dot plots of tasks for which the mean time is approximately equal to the median time are:

Dot plot A+: The median is around 25 minutes, and the mean is also around 25 minutes.

Dot plot D: The median is around 20 minutes, and the mean is slightly above 20 minutes.

Therefore, dot plots A+ and D have approximately equal mean and median times.

Final Answer:Thus, dot plots A+ and D have approximately equal mean and median times.

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The dot plots for tasks A+ and D show the mean time is approximately equal to the median time.

To determine if the mean time is approximately equal to the median time based on a dot plot, we need to look at the distribution of the data and see if it is symmetric or skewed. If the data is roughly symmetric, with values distributed evenly on both sides of the median, then the mean and median will be close to each other, and the mean time will be approximately equal to the median time. Conversely, if the data is skewed, with more values on one side of the median than the other, then the mean and median will be further apart, and the mean time will not be approximately equal to the median time.

Body of the Solution: The dot plots of tasks for which the mean time is approximately equal to the median time are:

Dot plot A+: The median is around 25 minutes, and the mean is also around 25 minutes.

Dot plot D: The median is around 20 minutes, and the mean is slightly above 20 minutes.

Therefore, dot plots A+ and D have approximately equal mean and median times.

Thus, dot plots A+ and D have approximately equal mean and median times.

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Answer:

4 2/3 gallons of gas

Step-by-step explanation:

Step 1

Suppose a car gas tank holds 21 gallons of gas.

On a trip it uses 2/3 of a tank of gas on a trip.

= 2/3 × 21 gallons of gas

= 14 gallons of gas

Step 2

Then it uses 1/3 of what is left in the tank.

The number of gallons of gas left =

21 gallons of gas - 14 gallons of gas

= 7 gallons of gas

Hence, this is calculated as:

1/3 × 7 gallons of gas

= 2 1/3 gallons of gas

Step 3

How many gallons of gas are left in the tank?

This is calculated as:

7 gallons of gas - 2 1/3 gallons of gas

= 7/1 - 7/3

Lowest common denominator =

= 21 - 7/3

= 14/3

= 4 2/3 gallons of gas is left

Therefore, 4 2/3 gallons of gas is left.

The value of x for the given expression is found as 2189/3.

The stated expression is-

3x − 2 = 3^7

Obtain the value of 3^7 by solving its power.

3x − 2 = 2187

(3x − 2) + 2  = 2187 + 2

3x − 2 + 2  = 2189

3x  = 2189

3x / 3  = 2189 / 3

x = 2189/3

Thus, the value of x for the given expression is found as 2189/3.

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The correct question is-

Solve 3x − 2 = 3^7 and find the value of x.

The probability of the complement of this event occurring is  5/6.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

Sample space: {1,2,3,4,5,6}

Total number of outcomes=6

Complement of an Event: All outcomes that are NOT the event

In this case:

So, possible outcomes in the complement event:{1,2,4,5,6}

Number of possible outcomes=5

Formula:

Probability = (Number of possible outcomes)/(Total number of outcomes)

                  = 5/6

So, the probability of the complement of this event occurring is  5/6.

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