Ms. Morris asked her students to each pick one or more of the following 4 numbers, all powers of 3:1,3,9,27and write the sum of the chosen numbers on a piece of paper. Students must not talk to each other about their choices.She then collected all papers, and wrote them down on the whiteboard, but no number would be written more than once. The class “won” the game if there were N numbers written down, where N was the greatest possible such numbers. What was the valueof N that Ms. Morris had in mind?

The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.

To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.

The money multiplier is given by the formula: MM = 1 / reserve requirement.

Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.

The initial deposit is $400.

To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:

Maximum Money Supply = Initial Deposit * Money Multiplier

= $400 * 20

= $8,000.

Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.

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Answer:

The answer is B. There are 432 desks in all 18 classes

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Given:

A jar of coins has 8 pennies, 5 nickels, 1 dime, and 7 quarters.

To find:

The probability of drawing a quarter, replacing it, and drawing another quarter.

Solution:

A jar of coins has 8 pennies, 5 nickels, 1 dime, and 7 quarters.

Total number of coins = 8+5+1+7 = 21

Probability of getting a quarter is

\(P(Quarter)=\dfrac{\text{Number of quarters}}{\text{Total number of coins}}\)

\(P(Quarter)=\dfrac{7}{21}\)

\(P(Quarter)=\dfrac{1}{3}\)

After drawing a quarter, we replaced it. So, the probability of getting quarter in second draw is the same and first one, .i.e., \(P(Quarter)=\dfrac{1}{3}\).

The probability of drawing a quarter, replacing it, and drawing another quarter is

\(P=\dfrac{1}{3}\times \dfrac{1}{3}\)

\(P=\dfrac{1}{9}\)

Therefore, the required probability is \(\dfrac{1}{9}\).

Answer:

3

Step-by-step explanation:

HTT, THT, TTH

Step-by-step explanation:

the bowood school by 455 kids

Answer:

x > -5

Step-by-step explanation:

The language A, defined as the set of all strings that are repeated twice (e.g., "00", "0101", "1111"), is not regular.

To show that A is not a regular language, we can use the pumping lemma for regular languages. The pumping lemma states that for any regular language, there exists a pumping length such that any string longer than that length can be divided into parts that can be repeated any number of times. Let's assume that A is a regular language. According to the pumping lemma, there exists a pumping length, denoted as p, such that any string in A with a length greater than p can be divided into three parts: xyz, where y is non-empty and the concatenation of xy^iz is also in A for any non-negative integer i. Now, let's consider the string s = 0^p1^p0^p. This string clearly belongs to A because it consists of the repetition of "0^p1^p" twice. According to the pumping lemma, we can divide s into three parts: xyz, where |xy| ≤ p and |y| > 0. Since y is non-empty, it must contain only 0s. Therefore, pumping up y by repeating it, the resulting string would have a different number of 0s in the first and second halves, violating the condition that the string must be repeated twice. Thus, we have a contradiction, and A cannot be a regular language.

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The value of the constant is 3.2, so the correct option is B.

We have a proportional relation of the form:

y = k*x

We want to find the value of k, the constant.

To do that, we can use any of the points shown in the graph.

For example, we can use the first point(0.5, 1.6)

That means that when x = 0.5, we have y = 1.6, replacing that we get:

1.6 = k*0.5

Solving for k:

k = 1.6/0.5 = 3.2

The value of the constant is 3.2, so the correct option is B.

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Answer:

A. 2x(x+1)(x-6);x=0,-1,6

Step-by-step explanation:

Take out 2x and factorise:

2x(x² - 5x - 6)

We can factorise (x² - 5x - 6)

What two numbers multiply to make -6 and add to give -5? That is -6 and 1 which is written as:

(x - 6)(x + 1)

Now the fully factorised polynomial is:

2x(x - 6)(x + 1)

Equate each of them to 0

2x = 0, x - 6 = 0, x + 1 = 0

Solve for x

x = 0, x = 6, x = -1

The probability of finding an average in excess of 4. 3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline is approximately 0.7972.

We may use the normal distribution and the Z-score to determine the likelihood that 100 randomly selected 1-gallon samples of standard unleaded gasoline will have an average of more than 4.3 ounces of the component. A value's Z-score indicates how many standard deviations away from the mean it is.

We must first get the average of 100 randomly chosen samples' mean and standard deviation. The average's mean will be 4 ounces, which is also the mean of the individual samples. The sample size is divided by the square root of the standard deviation to get the average standard deviation, which is 1.2/100 = 0.12 ounces.

Next, we calculate the Z-score for the value of 4.3 ounces:

Z = (4.3 - 4) / 0.12 = 0.83

Finally, we use a Z-score table or a normal distribution calculator to find the probability of finding an average in excess of 4.3 ounces. The result will be the area under the standard normal distribution curve to the right of 0.83.

There is a 79.72% chance of finding an average in excess of 4.3 ounces of the ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline.

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Answer:

17 degrees

Step-by-step explanation:

See attached image.

We conclude that the angle at the top measures 65.8°.

The whole tree measures 117 ft, and it is broken 34 ft above the ground, forming this way a right triangle.

Then one cathetus of the right triangle measures 34ft, and the hypotenuse measures 117ft - 34ft = 83ft

The angle at the top is θ, the adjacent cathetus to it is the one that measures 34 ft, then to get the angle we can use the relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Replacing what we know, we get:

cos(θ) = (34 ft)/(83ft) = 34/83

Solving for θ, we get:

θ = Acos( 34/83) = 65.8°

So we conclude that the angle at the top measures 65.8°.

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Answer:

It would be D.

Step-by-step explanation:

You have to collect like terms which would involve the 5\(\sqrt{7}\) and -10\(\sqrt{7}\) and do the same for the other 2

Answer:

\( = 0.059 = \frac{59}{100} \)

Step-by-step explanation:

\(0.9 - 0.841\)

\( \boxed{\green{= 0.059 = \frac{59}{100} }}\)

The average (mean) of the data is approximately 16.89 to two decimal places.

To calculate the average (mean) of the given data, you need to sum all the values and divide by the total number of values.

Sum of the data: 25.3 + 27.9 + 16.1 + 6 + 6.8 + 7.7 + 28.4 = 118.2

Total number of values: 7

Average (mean) = Sum of the data / Total number of values

Average = 118.2 / 7

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When y equals 12.7 and x equals 8, the value of k is 101.6.

In an inverse variation, the relationship between two variables, y and x, can be expressed as:

y = k/x

Where k is a constant of variation. To find the value of k, we can use the given values of y and x.

Given that y equals 12.7 and x equals 8, we can substitute these values into the equation:

12.7 = k/8

To solve for k, we can multiply both sides of the equation by 8:

12.7 * 8 = k

101.6 = k

Therefore, when y equals 12.7 and x equals 8, the value of k is 101.6.

It's important to note that in an inverse variation, as one variable increases, the other variable decreases, and vice versa. The constant of variation, k, represents the product of y and x for any given point on the graph of the inverse variation equation.

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Answer:

\(\huge\boxed{x=-12}\)

Step-by-step explanation:

In order to solve for this proportion, it’s important to note that this is basically just an equation. Like any other, our goal is to isolate x on one side.

Since we have two fractions, we can multiply both sides by both the denominators (x-3 and x-9). Since one will cancel out the other, we can just multiply both sides by the opposite denominator.

\(5(x-9)=7(x-3)\\\\5x-45=7x-21\)

Now we can solve for x.

Subtract 5x from both sides:

\(-45=2x-21\)

Add 21 to both sides:

\(-24=2x\)

Divide both sides by 2:

\(x = -12\)

Hope this helped!

Answer:

\(x= -12\)

Step-by-step explanation:

Step 1: Write equation

\(\frac{5}{x-3} =\frac{7}{x-9}\)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

\(\frac{5}{-12-3} =\frac{7}{-12-9}\)

\(\frac{5}{-15} =\frac{7}{-21}\)

\(\frac{-1}{3} =\frac{-1}{3}\)

Answer:

Hi there!

We've given with the base area and height. We know the formula for base area

Base area = πr²

154 = 22/7 × r²

154 × 7/22 = r²

49 = r²

√49 = r

7 = r

Now

TSA = 2πr(h + r)

TSA = 2 × 22/7 × 7(7 + 20)

TSA = 44(27)

TSA = 1188 cm²

Answer:

x = -2

Step-by-step explanation:

3x + 5 + 15x + 25 + 6 = 0

18x + 36 = 0

18x = -36

x = -2

The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

Hi

Step-by-step explanation:

How is your day??

Answer:

Hello

How are you doing??

Answer:

∠Z ≅ ​∠B

Step-by-step explanation:

∠X ≅ ​∠R

∠Z ≅ ​∠B

∠K ≅ ​∠C

∠H ≅ ​∠P

Hope this helps!! :)

Answer:

∠Z ≅ ​∠B

Step-by-step explanation:

Z is congruent to B

Answer:

It is B

Step-by-step explanation:

B:3=b

bx3=B

Answer: the fully factorized answer is 3x(2 + 5x)

Answer:

6x time 15x times 15x you will get your answer

Step-by-step explanation:

easy A F.

The number of days when the two companies will have the same number of followers is 380 days.

The first step is to form linear functions that represent the information of the two companies. The form of the functions is:

Total followers = initial number of followers + (number of new followers x number of days)

The linear function that represents the online followers for the first company is:

Total followers = 95,000 + 100d

The linear function that represents the online followers for the second company is: Total followers = 350d

When the companies have the same number of followers the two above equations would be equal 95,000 + 100d = 350d

95,000 = 350d - 100d

95,000 = 250d

d = 95,000 / 250

d = 380

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The Taylor polynomial of degree 4 for the function \( f(x) = \arctan(9x) \) at \( a = 0 \) is given by \( T_{4}(x) = x - \frac{81}{3}x^3 + \frac{729}{5}x^5 - \frac{6561}{7}x^7 \).

This polynomial is obtained by approximating the function \( f(x) \) with a polynomial of degree 4 around the point \( a = 0 \). The coefficients of the polynomial are determined using the derivatives of the function evaluated at \( a = 0 \), specifically the first, third, fifth, and seventh derivatives.

In this case, the first derivative of \( f(x) \) is \( \frac{9}{1 + (9x)^2} \), and evaluating it at \( x = 0 \) gives us \( 9 \). The third derivative is \( \frac{9 \cdot 2 \cdot 4 \cdot (9x)^2}{(1 + (9x)^2)^3} \), and evaluating it at \( x = 0 \) gives us \( 0 \).

The fifth derivative is \( \frac{9 \cdot 2 \cdot 4 \cdot (9x)^2 \cdot (1 + 9x^2) - 9 \cdot 2 \cdot 4 \cdot (9x)(2 \cdot 9x)(1 + (9x)^2)}{(1 + (9x)^2)^4} \), and evaluating it at \( x = 0 \) gives us \( 0 \). Finally, the seventh derivative is \( \frac{-9 \cdot 2 \cdot 4 \cdot (9x)(2 \cdot 9x)(1 + (9x)^2) - 9 \cdot 2 \cdot 4 \cdot (9x)(2 \cdot 9x)(1 + 9x^2)}{(1 + (9x)^2)^5} \), and evaluating it at \( x = 0 \) gives us \( -5832 \).

Plugging these values into the formula for the Taylor polynomial, we obtain \( T_{4}(x) = x - \frac{81}{3}x^3 + \frac{729}{5}x^5 - \frac{6561}{7}x^7 \). This polynomial provides an approximation of \( \arctan(9x) \) near \( x = 0 \) up to the fourth degree.

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ok

603.98 -------------------------- 100%

x -------------------------- 8.5%

x = (8.5 x 603.98) / 100

x = 5133.83/100

x = 51.33

Total cost = 603.98 + 51.33

Result

Total cost = $655.3

Answer: it’s not 5 I got that wrong

Step-by-step explanation:

y-intercept of function f is 1.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given function

f(x) = -3x -2 , -∞ < x < -2

     = -x + 1, -2 ≤ x < 3

     = 2x + 5, 3 ≤ x < ∞

For y-intercept, x =0, f(x) = -x + 1                   [∵ -2 < 0 < 3]

f(0) = -0 + 1

= 1

Hence, y-intercept of function f is 1.

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