You had some cookies and milk for breakfast this morning. The
total number of calories of your breakfast is 232. Each cookie
has 25 calories and a bottle of milk has 57 calories. How many
cookies did you have for breakfast?
cookies
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The forecasted sales in August 2021, using exponential smoothing with a smoothing constant of 0.31, is approximately 52.3251 units.

Exponential smoothing is a forecasting method that assigns weights to historical data points, giving more importance to recent observations. The forecasted value for a specific period is calculated by combining the actual value for that period with the forecasted value for the previous period. The formula for exponential smoothing is:

Ft = α * At-1 + (1 - α) * Ft-1

Where Ft is the forecasted value for period t, At-1 is the actual value for the previous period, Ft-1 is the forecasted value for the previous period, and α is the smoothing constant.

Given that the forecast in April 2021 was 39 units and the monthly sales data from April to September 2021 are 48, 55, 46, 54, 53, and 52 units, we can calculate the forecasted sales for each subsequent month using the exponential smoothing formula.

Using the given values and the formula, we can calculate the forecasted sales for August 2021 as follows:

Ft = 0.31 * 52 + (1 - 0.31) * 52.3251 = 52.3251

Therefore, the forecasted sales in August 2021, rounded to at least 4 decimals, is approximately 52.3251 units.

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Answer:

1 : 2.5

Step-by-step explanation:

All you have to do is 125/50 to get 2.5. So that means for every 2.5 eighth grader there is 1 eighth grader in summer school.

Hope this helped!!

The solutions to the equation x² + 10x + 22 = 13 are: x = -5 ± 4

To rewrite the equation by completing the square, we need to isolate the constant term on one side and group the x-terms together. Starting with:

x² + 10x + 22 = 13

Subtracting 13 from both sides:

x² + 10x + 9 = 0

Next, we add and subtract the square of half of the coefficient of x (which is 5 in this case) to complete the square:

x² + 10x + 25 - 25 + 9 = 0

x² + 10x + 25  - 16 = 0

Factor the perfect square trinomial:

(x + 5)² - 16 = 0

Now that we have rewritten the equation in the form (x + c)² = d, we can solve for x by taking the square root of both sides:

(x + 5)² - 16 = 0

Taking the square root of both sides and solving for x, we get:

x + 5 = ±4

So, we have

x = -5 ± 4

So the solutions to the equation are:

x = -5 + 4 = -1

x = -5 - 4 = -9

Therefore, the answer is x = -5 ± 4.

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Answer:

Y = 4

Step-by-step explanation:

The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

above beat me to it he is right

The volume of the rectangular prism given the length, width and height is 6 14/27 cubic feet.

The correct answer choice is option B

Volume of a rectangular prism= length × width × height

Length= 1 5/6 ft

Width = 1 1/3 ft

Height = 2 2/3 ft

Volume of a rectangular prism= length × width × height

= 1 5/6 × 1 1/3 × 2 2/3

= 11/6 × 4/3 × 8/3

= (11 × 4 × 8) / (6 × 3 × 3)

= 352 / 54

= 6 28/54

= 6 14/27 cubic feet

In conclusion, the volume of the rectangular prism is 6 14/27 cubic feet

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Answer:

1/4

Since there are 4 friends and 12 cookies, assuming they divide them equally, each friend gets 12/4=3 cookes and so the fraction would be 3/12 which would simplify to 1/4.

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\(\huge\textbf{Hey there!}\\\\\huge\boxed{\mathbf{Equation: \dfrac{4\ friends}{12\ friends}}}\\\\\\\huge\boxed{\mathbf{= \dfrac{12\ cookies}{4\ friends}}}\\\\\\\huge\boxed{\mathbf{= 4\ friends\div 12\ cookies}}\\\\\\\huge\boxed{\mathbf{= \dfrac{4\div4\leftarrow friends}{12\div4\leftarrow cookies}}}\\\\\\\huge\boxed{= \mathbf{\dfrac{1}{3}\ in\ all}}\\\\\huge\textbf{Thus, your answer is: \boxed{\mathsf{\dfrac{1}{3}}}}\huge\checkmark\)

\(\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{ your day!}\)

Answer:

x = -∛115

Step-by-step explanation:

x^3 - (-115) = 0

= x^3 + 115

Factoring

(a+b) • (a^2-ab+b^2) =

   a^3-a^2b+ab^2+ba^2-b^2a+b^3 =

   a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=

   a^3+0+0+b^3=

   a^3+b^3

(115 isn't a cube.)

Polynomial roots

P: -1, -5, -23, -115, 1, 5, 23, 115

Q: 1

P/Q: -1, -5, -23, -115, 1, 5, 23, 115

Divisor(s): None

In these sets of data, there are no rational roots shown.

Step-by-step explanation(part 2):

x^3 + 115 = 0

x^3 = -115

x  =  ∛-115

Negative numbers will always have real cube roots.

∛ -115 = ∛ -1 × 115  = ∛ -1 × ∛ 115 = (-1) × ∛ 115

Therefore,

x = -∛115

Step-by-step explanation:

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Answer:

what is the question tho you didn't post it

have a good day :)

Step-by-step explanation:

Answer:

part 1) BC is 17491 ft

part 2)  CD is 6499 ft

Step-by-step explanation:

Answer:

A. 150

Step-by-step explanation:

Calculate the probability of landing on an odd number: 1/2.

Multiply the probability by the number of trials: (1/2) * 300.

Simplify the expression: 150.

Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.

Answer:

To multiply square roots, we multiply the numbers inside the radical. Any numbers outside the radical are also multiplied.

Step-by-step explanation:

No, events a and b are not disjoint if if the p(a) = 0.25 and the p(b) = 0.5.

Two events are considered disjoint if they cannot occur at the same time, meaning their intersection is equal to zero. Mathematically, if A and B are disjoint events, then P(A ∩ B) = 0.

In this case, we do not know whether events a and b are independent or dependent. Therefore, we cannot determine whether they are disjoint based on the given probabilities alone.

To determine whether events a and b are disjoint, we need to know whether they share any common outcomes. If there are any outcomes that belong to both events, then the events are not disjoint.

Without further information, we cannot determine whether events a and b are disjoint.

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The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

\(Ax + By + C = 0\)

Equation of Straight Line or Slope:

\(y = mx+b\)

Point-slope form:

\(y-y_{1} = m(x-x_1)\)

Slope when 2 points are given:

\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)

Quadratic Equation:

\(Ax^2 + Bx +C = 0\)

When lines are parallel:

Slope of both lines are equal. \(m_1 = m_2\)

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).

Work Formula:

Total Work Done = Number of Days \(\times\) Efficiency

where Efficiency is inversely proportional to Time Taken.

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To find the probability that the mean salary of a person selected at random from Acme Corporation is less than 61,000, we can use the Z-score formula.

First, we need to calculate the Z-score, which measures the number of standard deviations a value is away from the mean. The formula for the Z-score is:

Z = (X - μ) / (σ / √n)

Where:
- X is the value we are interested in (in this case, $61,000)
- μ is the population mean annual salary for Acme Corporation ($63,500)
- σ is the population standard deviation (unknown in this case)
- n is the sample size (unknown in this case)

Since we don't have the population standard deviation or sample size, we cannot calculate the exact Z-score. Therefore, we cannot find the exact probability.

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Based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

The probability of a person selected at random having a salary less than $61,000 can be determined using the z-score and the standard normal distribution.

To calculate the z-score, we need to know the population standard deviation. Since it is not provided, we cannot calculate the exact probability. However, we can use the assumption that the population standard deviation is the same as the sample standard deviation.

Let's assume the sample standard deviation is $5,000.

First, we calculate the z-score:
    \(z = (x - \mu) / (\sigma / \sqrt n)\)
=> z = (61000 - 63500) / (5000 / √1)
=> z = -2500 / 5000
=> z = -0.5

Next, we find the corresponding area under the standard normal curve using a z-table or a calculator. The area to the left of -0.5 is approximately 0.3085.

Therefore, the probability that a person selected at random will have a salary less than $61,000 is approximately 0.3085 or 30.85%.

In conclusion, based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

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In the equation 12x+33=93, the value of x is 5.

The given equation is 12x+33=93.

Twelve times of x plus thirty three equal to ninety three.

x is the variable in the equation.

We need to solve for x:

Subtract 33 from both sides of the equation:

12x=93-33

12x=60

Divide both sides of the equation by 12:

x=60/12

x=5

Hence, the value of x in the equation is 5.

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Answer:

Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.

Step-by-step explanation:

After selling x pints of Boldly Buttered Popcorn icecream and y pints of Lovely Lavender Lemon on the charged of $10 for each, his profit equation is written as P = 6x + 6y = 6( x + y).

We have, Mr. McCoy's new ice cream shop. He sold two flavors of icecream. He sold his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. The quantity of sold Boldly Buttered Popcorn ice cream = x pints

The quantity of sold Lavender Lemon ice cream = y pints

Cost of each pint of ice cream = $4

Selling price of each pint of ice cream

= $10

First, total pints of icecream he sold

= pints of Boldly Buttered Popcorn ice cream+ pints of Lavender Lemon ice cream = ( x + y) pints

Now, Cost of (x + y) pints of ice cream

= $4 ( x + y)

Similarly, selling price of ( x + y ) pints of icecream = $ 10 ( x + y)

As we know, when selling price is greater than cost price then profit will occur. Equation for profit P = selling price - cost price = $ 10 ( x + y) - $4 ( x + y)

= 10 x + 10y - 4x - 4y

P = 6(x + y)

Hence, required equation is 6x + 6y.

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Complete question:

Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each. Write an equation for his profit or loss on ice cream selling.

Probability that at least two of them have the same number is 1 - 75! / (10! * (75-10)!) /\(75^{10}\).

Given,

A box contains 75 balls numbered from 1 to 75 .

Here,

The probability that at least two of the balls drawn have the same number is equivalent to the probability that there is at least one pair of matching numbers among the balls drawn, which is equal to 1 minus the probability that there are no pairs of matching numbers among the balls drawn.

We can calculate the probability that there are no pairs of matching numbers among the balls drawn by finding the number of ways that we can draw 10 balls without replacement from the set of 75 balls, and dividing that by the total number of ways to draw 10 balls with replacement.

The number of ways to draw 10 balls without replacement from a set of 75 balls is given by the binomial coefficient "75 choose 10", which can be calculated as:

75! / (10! * (75-10)!) = 828931106355

The total number of ways to draw 10 balls with replacement from a set of 75 balls is given by \(75^{10}\).

So the probability that there are no pairs of matching numbers among the balls drawn is:

75! / (10! * (75-10)!) /\(75^{10}\).

Therefore, the probability that at least two of the balls drawn have the same number is:

1 - 75! / (10! * (75-10)!) /\(75^{10}\).

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Answer:

3: 14

Step-by-step explanation:

we will divide 0.75m by 3.5

\( \frac{0.75 \\ }{3.5} \)

with the use of calculator we arrived at

\( \frac{3}{14} \)

so therefore the ratio og the width to the length is 3: 14

Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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Answer:

\(\dfrac{9}{35}\) is the fraction of 8th graders who are boys.

Step-by-step explanation:

Let total number of 8th graders = \(x\)

Given that, \(\frac{3}{7}\) of 8th graders play sports

\(\Rightarrow\) 8th graders who play sports = \(\frac{3}{7} \times x\)

Also, Given that, \(\frac{3}{5}\) of 8th graders that play sports are boys

Number of 8th graders that play sports, and are boys = \(\frac{3}{5} \times \text{Number of 8th graders who play sports}\)

\(\Rightarrow \dfrac{3}{5} \times \dfrac{3}{7} \times x\\\Rightarrow \dfrac{9}{35} \times x\)

Hence, the answer is:

\(\dfrac{9}{35}\) is the fraction of 8th graders who are boys.

Answer:

When we have a mean M and a standard deviation S, the values that are within the mean absolute deviation are all the values in the interval:

[M -S, M + S]

In this case, we have:

M = 782

S = 52

Then the interval is:

[782 - 52, 782 + 52]

[730, 834]

Then any number between 730 and 834 are possible answers to this question, for example, we can choose:

789 and 801

you would add up both of the other two measures and then subtract that by 180 since all triangles add up to 180 degrees

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k can be written as,

\(xy=k\\\\(7) \times (3 ) =k\\\\k= 21\)

Hence, the value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

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Answer:

D

Step-by-step explanation:

K=21

Given:

Nuts = $2.50

Cereal mixture = $1

Find -: How much each should be added.

Sol:

Obtain = 60 kg.

Let nuts = x kg

Cereal = y kg

To obtain 60 kg means:

Pricing at $1.90 per kg means:

Put the value of "y" then:

Then the value of "y" is:

So,

In the mixture 36 kg of nuts and 24 kg of cereal.

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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(a)  (1203)4 is equal to 99 in decimal and 12 in hexadecimal.

(b)  (5243)8 is equal to 2211 in decimal and 1523 in hexadecimal.

To convert numbers from different bases to decimal using the direct method, we multiply each digit of the number by the corresponding power of the base and sum the results. To convert to hexadecimal using the intermediary binary conversion method, we first convert the number to binary and then group the binary digits into groups of 4, starting from the rightmost digit, and convert each group to its hexadecimal equivalent.

(a) Converting (1203)4 to decimal:

(1203)4 = 1 * 4³ + 2 * 4² + 0 * 4¹ + 3 * 4⁰

= 64 + 32 + 0 + 3

= 99

Converting (1203)4 to hexadecimal:

First, convert (1203)4 to binary:

(1203)4 = (10010)2

Next, group the binary digits into groups of 4:

(10010)2 = (0001 0010)2

Finally, convert each group to its hexadecimal equivalent:

(0001 0010)2 = (12)16

Therefore, (1203)4 is equal to 99 in decimal and 12 in hexadecimal.

(b) Converting (5243)8 to decimal:

(5243)8 = 5 * 8³ + 2 * 8² + 4 * 8¹ + 3 * 8⁰

= 2048 + 128 + 32 + 3

= 2211

Converting (5243)8 to hexadecimal:

First, convert (5243)8 to binary:

(5243)8 = (101 010 100 011)2

Next, group the binary digits into groups of 4:

(101 010 100 011)2 = (0001 0101 0010 0011)2

Finally, convert each group to its hexadecimal equivalent:

(0001 0101 0010 0011)2 = (1523)16

Therefore, (5243)8 is equal to 2211 in decimal and 1523 in hexadecimal.

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