Katie baked 215 cookies that she wants to divide equally among her 32 classmates. How many whole cookies will each student get, and how many will be leftover?
A) 5, r5
B) 6, r10
C) 6, r23
D) 7, r0​

1. Two lines that do not lie in the same plane and are parallel:

- Line 1: x = 2y + 3z

- Line 2: x = 2y + 3z + 5

In this case, both lines have the same direction vector, which is [2, 1, 0], but they do not lie in the same plane.

2. Two planes that have no point in common and are skew lines:

- Plane 1: x + 2y - z = 4

- Plane 2: 2x - 3y + z = 6

These two planes are skew because they do not intersect and have no common points.

3. Two lines that are in the same plane and have no points in common are not called parallel planes. In this case, they are referred to as coincident lines.

Parallel planes are planes that do not intersect and are always separated by a constant distance.

If you are looking for an example of parallel planes, here's one:

- Plane 1: x + 2y - z = 4

- Plane 2: x + 2y - z + 5 = 0

Both planes have the same normal vector [1, 2, -1], and they are parallel to each other.

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So, approximately 7.71 grams of radium will be present after 100 years.

To calculate the remaining amount of radium after 100 years, we will use the half-life formula:
Remaining Amount = Initial Amount * (1/2)^(time passed / half-life)
Here, the initial amount is 8 grams, the half-life is 1690 years, and the time passed is 100 years.
Step 1: Plug in the values
Remaining Amount = 8 * (1/2)^(100 / 1690)
Step 2: Calculate the exponent
Exponent = 100 / 1690 ≈ 0.05917
Step 3: Calculate the base raised to the exponent
(1/2)^0.05917 ≈ 0.9634
Step 4: Multiply the initial amount by the base raised to the exponent
Remaining Amount = 8 * 0.9634 ≈ 7.7072
So, approximately 7.71 grams of radium will be present after 100 years.
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Answer: He must save for 11 or more weeks.

Step-by-step explanation:

Using the inequality, we will solve for x to determine the number.

130 + 20x > 350    Subtract 130 from both sides

-130             -130

  20x > 220  

  x> 11

Since x is greater than 11, it means that if he saves for 11 weeks, then he will save the exact amount of $350, but since he wants to save more, he must save for 11 or more weeks.

Answer:

12 weeks hope helps

Step-by-step explanation:

Answer:

The number of batches of paving stones Eric needs is 5 batches

Step-by-step explanation:

Here we have the size of of one paving stone = 1 ft²

The dimensions, size, of one patio = 7 ft × 8 ft = 56 ft²

Therefore, the number of paving stones Eric needs per patio is given by the relation;

\(Number\, of\ paving\ stones \ required =\frac{size\, of \, one\, patio}{size \, of \, one\, paving\, stone} = \frac{56 \, ft^2}{1 ft^2/(paving \, stone)} = 56 \, paving \, stones\)

Since the paving stones are sold in batches of one dozen, we have ;

4 batches = 48 paving stones and 5 batches = 60 paving stones

Therefore, the number of batches of paving stones Eric needs = 5 batches.

Answer:

The no. are 11 and 12

Step-by-step explanation:

n(n+1)=17+5(2n+1)

n^2 +n=17+10n+5

n^2 -9n-22

Splitting the middle term

n^2 -11n+2n -22

n(n-11)+2(n-11)

(n-11)(n+2)

As n cannot ne negative,

n=11 and 12(consecutive no.)

Mark me brainliest!!

The two of the consecutive positive integers whose product is 17 more than 5 times their sum are 11 and 12.

An integer is a complete number, therefore, not including the decimals and fractions. And it that can be either positive, negative, or zero.

Integer examples include -5, 1, 5, 8, 97, and 3,043.

Non-integer numbers include: -1.43, 1 3/4, 3.14, and more.

Let the first of the two consecutive integers be represented by x. Then, the other number can be written as (x+1).

Now, the product and the sum of the two numbers can be written as,

Product = x(x+1) = x² + x

Sum = x + (x+1) = 2x + 1

Further, it is given that the product of two consecutive positive integers is 17 more than 5 times their sum. Therefore, we can write,

x² + x = 17 + 5(2x + 1)

x² + x = 17 + 10x + 5

x² + x - 17 - 10x - 5 = 0

x² - 9x - 22 = 0

x² - 11x + 2x - 22 = 0

x(x - 11) + 2(x - 11) = 0

(x - 11)(x + 2) = 0

x = -2, 11

Thus, there are two numbers that can fulfil the given condition but since it is mentioned that we only need two positive consecutive integers. Therefore, the two numbers are 11 and 12.

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Answer:

Screen shot the question and attach it and i will do it cus you making no sense

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The price p in dollars and demand x for wireless headphones are related by x = 6000 - 0.15p². If the current price of $110 is decreasing at a rate of $5 per week, then we need to find the rate of change of the demand.

Solution: Given, x = 6000 - 0.15p²

Differentiating both sides with respect to time, we get:$$\frac{dx}{dt} = \frac{d}{dt}(6000 - 0.15p^2)$$$$\frac{dx}{dt} = 0 - 0.15\frac{d}{dt}(p^2)$$$$\frac{dx}{dt} = -0.3p\frac{dp}{dt}$$We are given that the current price is $110 which is decreasing at a rate of $5 per week.

Therefore, the rate of change of the price of the wireless headphone is $\frac{dp}{dt} = -5$.Substitute the values of $\frac{dp}{dt}$ and $p$ into the above equation, we get:$$\frac{dx}{dt} = -0.3\times 110\times -5$$$$\frac{dx}{dt} = 165$$

Therefore, the rate of change of the demand for the wireless headphones is $165$ units per week.

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Answer: The rate of change of demand is approximately 33 units per week.

Step-by-step explanation: The given price and demand relationship is given by:

x = 6000 - 0.15p²

where x is the demand for wireless headphones in units, and p is the price of wireless headphones in dollars.

The rate at which the price is decreasing is given as -$5 per week.

Hence, the rate of change of price (dp/dt) is given by:

-5. Rate of change of demand (dx/dt) is to be calculated.

We have,

x = 6000 - 0.15p²

=> p² = 40000 - 6.67x

Differentiating both sides with respect to t, we get:

2p dp/dt = -6.67 dx/dt

=> dx/dt = (-2p/6.67) dp/dt

Substituting the given values, we get:

p = 110,

dp/dt = -5

dx/dt = (-2p/6.67) dp/dt

=> dx/dt = (-2 × 110/6.67) × (-5)

≈ 33 units/week.

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Answer:

The shadow of the windmill will be 24 yards long

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ A bell tower that is 60 yards tall casts a shadow 32 yards long

∴ The tall = 60 yards and the shadow = 32 yards

∵ A windmill is  45 yards tall

∴ The tall = 45 yards

→ By using the ratio method

→ Tall  :  Shadow

→  60   :  32

→  45   :  x

→ By using the cross multiplication

∵ x × 60 = 45 × 32

∴ 60x = 1440

→ Divide both sides by 60

∵ \(\frac{60x}{60}=\frac{1440}{60}\)

∴ x = 24

∴ The shadow of the windmill will be 24 yards long

Answer:

15

Step-by-step explanation:

Answer:

The smallest number is  

14

Explanation:

Let: x= the 1st con.even number

x+2=the 2nd con.even number

x+4=the 3rd con.even number

Add the terms and equate it with the total, 48

x + ( x + 2 ) + ( x + 4 ) = 48 , simplify

x + x + 2 + x + 4 = 48 , combine like terms

3 x + 6 = 48 , isolate x

x = 48 − 6 3 , find the value of x

x = 14

Answer:

57.15 cm

Step-by-step explanation:

FORMULA  

multiply the value by 2.54

Hope this helps! have a great day :)

Answer:

57.15 cm

Step-by-step explanation:

Use the appropriate conversion factor:

22.5 in     2.54 cm

----------- * -------------- = 57.15 cm

      1            1 in

The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are the true values that would be obtained if the entire population were measured.

The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are the true values that would be obtained if the entire population were measured. The y-intercept is the value of y when x equals 0, and it represents the starting point of the line. The slope represents the change in y for every one unit change in x, and it determines the steepness of the line. To estimate these population parameters, we use sample statistics such as the sample mean and sample standard deviation. The sample y-intercept and slope are calculated using regression analysis, which involves fitting a line to the data points in order to determine the relationship between x and y. It is important to note that the sample statistics may not be equal to the population parameters, as there is always some degree of error and variability in data. However, by using statistical inference techniques such as confidence intervals and hypothesis testing, we can make inferences about the population parameters based on the sample data. In summary, the population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are the true values that would be obtained if the entire population were measured. These parameters can be estimated using sample statistics and statistical inference techniques.

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Answer:

The answer for f(2) is 11. The answer for f(x+4) is f = 3x^2 - 4x + 7 / x + 4

Step-by-step explanation:

The vertex form of the given quadratic equation is

\(4(x-1)^{2} + 16 =0\).

According to the given question.

We have a quadratic equation

\(4x^{2} -8x + 20 = 0\)

Since, for the standard quadratic form is \(ax^{2} +bx + c = y\), the vertex form of a quadratic equation is \(y = a(x -h)^{2} + k\) where (h, k) is the vertex.    

And h and k can be calculated as

h = -b/2a and y = k

So, for the given equation \(4x^{2} -8x + 20 =0\) the vertex (h, k) is given by

h = -(-8)/2(4) = 8/8 = 1   (X coordinate of vertex)

and,

\(y =4x^{2} -8x+ 20\)

substitute x = 1 in the above equation for the value of k

Y = 4(1)(1) - 8(1) + 20

⇒ Y = 4 - 8 + 20

⇒ Y = -4 + 20

⇒ Y = 16

so, k = 16          (Y coordinate of vertex)

Now, substitute the value of a, k and h in \(y = a(x-h)^{2} + k\).

⇒  \(0 =4(x-1)^{2} + 16\)

Therefore, the vertex form of the given quadratic equation is

\(4(x-1)^{2} + 16 =0\).

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Comparing both given functions, we can state that: B. Function 1 has the greater rate of change; the slope is 2.

Another name for the rate of change of a function is the slope. It is calculated using the formula:

Slope / rate of change = change in y / change in x.

If the equation of a linear function is given in slope-intercept form as y = mx + b, the rate of change or the slope is represented by "m".

Given the first function as an equation, y = 2x - 6, the slope of this function is represented as 2. This means, the rate of change is m = 2.

To find the rate of change of function 2, use two points from the table, (1, -4) and (2, -5):

Rate of change / slope (m) = (-5 - (-4)) / (2 - 1) = -1/1

m = -1.

The slope value of 2 is greater than the slope value of -1, therefore, we can conclude that: B. Function 1 has the greater rate of change; the slope is 2.

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Answer:

D

Step-by-step explanation:

Piano: 2 hours

Cello: 4 hours

=============

Actual practice on the piano = 5 hours.

Actual practice on the cello = x

2/4 = 5/x

Notice the piano hours are on the top of the fractions on both the left and the right. All proportions work that way.

Cross multiply

2x = 4* 5

2x = 20               Divide by 2

x = 10

Answer:

4/5 is bigger than 7/10

Step-by-step explanation:

Just divide them each

4/5 = .8

7/10 = .7

Umm... your going to have to put those on the number line yourself sorry

Answer: 4/5. 4/5 can also mean 8/10. 8/10 is greater than 7/10. I do not know how to label the fraction on the number line if it is a picture so hopefully you can do that.

In order to determine the number of people in the sample for each age group, here are the steps:

1. Determine what proportion in the entire population the population of each group. To get the proportion, simply divide the population of each respective group by the entire population.

2. To get the number of samples for each group, multiply the proportion by 5,000 and round the answer to the nearest whole number.

Now, let's apply the steps above in each group.

Let's start with ages under 18.

Hence, we are expected to have 1,201 people aged under 18 in the sample.

For those aged 18 - 44,

Hence, we are expected to have 1,827 people aged 18-44 in the sample.

For those aged 45 - 64,

The expected number of samples for people aged 45-64 is 1,320.

Lastly, for aged 65 and over,

The expected number of samples for people aged 65 and over is 652.

To summarize, we have:

Age under 18 ⇒ 1,201 samples

18 - 44 ⇒ 1,827 samples

45 - 64 ⇒ 1,320 samples

65 and over ⇒ 652 samples

.

Answer:

I think 32

I'm not sure

Answer:

65

Step-by-step explanation:

you add all the numbers inside.

80+35= 115

You have to make sure it equals to 180 to find angle 1.

Therefore, 180-115=65.

Answer:

Step-by-step explanation:

cot²(3x)=y

y²-3y+2=0

y²-y-2y+2=0

y(y-1)-2(y-1)=0

(y-1)(y-2)=0

y=1,y=2

cot3x=1

tan 3x=1=tan (π/4)=tan (nπ+π/4)

3x=nπ+π/4=(4nπ+π)/4=(4n+1)π/4

x=(4nπ+1)π/12,n is an integer.

cot 3x=2

tan 3x=1/2

3x=tan^{-1}(1/2)≈26.57°+360n

x≈8.86°+120n

To write a logical expression that is true if and only if, for all natural numbers n and k, we can use the logical operator "and" and the quantifier "for all."

The logical expression can be written as follows:

∀n,k (expression)

In the expression, you would need to replace "expression" with the specific conditions or constraints that need to be satisfied for the statement to be true.

For example, if we want the expression to be true if and only if n is equal to k, we can write:

∀n,k (n = k)

To write a logical expression that is true if and only if, for all natural numbers n and k, we can use the logical operator "and" and the quantifier "for all." The logical expression can be written as ∀n,k (expression). In the expression, you would need to replace "expression" with the specific conditions or constraints that need to be satisfied for the statement to be true.

For example, if we want the expression to be true if and only if n is equal to k, we can write ∀n,k (n = k). This means that for every natural number n and k, the expression n = k must be true for the entire statement to be true. In other words, the logical expression will be true if and only if n and k have the same value. By using the quantifier "for all," we ensure that the statement holds true for every possible combination of natural numbers n and k.

A logical expression can be written to ensure that for all natural numbers n and k, the expression is true if and only if certain conditions or constraints are met. By using the logical operator "and" and the quantifier "for all," we can create a statement that encompasses all possible combinations of n and k. This allows us to define specific conditions or constraints within the expression. By using the quantifier "for all," we guarantee that the statement holds true for every natural number n and k.

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The two x-intercepts of the function f are 0 and -4.

The x-intercept of a function is a point on the x-axis where the graph of the function intersects the x-axis. In other words, it is a point where the y-value (or the function value) is equal to zero.

According to the given information:

To use Rolle's Theorem to find the x-intercepts of the function f(x) = x√(x+4) and show that f(x) = 0 at some point between the two x-intercepts, we need to follow these steps:

Step 1: Find the x-intercepts of the function f(x) by setting f(x) = 0 and solving for x.

Setting f(x) = x√(x+4) = 0, we get x = 0 as one x-intercept.

Step 2: Find the derivative of the function f'(x).

f'(x) = d/dx (x√(x+4)) (using the product rule of differentiation)

= √(x+4) + x * d/dx(√(x+4)) (applying the chain rule of differentiation)

= √(x+4) + x * (1/2√(x+4)) * d/dx(x+4) (simplifying)

= √(x+4) + x * (1/2√(x+4)) (simplifying)

Step 3: Check if f'(x) is continuous on the closed interval [a, b] where a and b are the x-intercepts of f(x).

In our case, the x-intercepts of f(x) are 0, so we check if f'(x) is continuous at x = 0.

f'(x) is continuous at x = 0, as it does not have any undefined or discontinuous points at x = 0.

Step 4: Check if f(x) is differentiable on the open interval (a, b) where a and b are the x-intercepts of f(x).

In our case, f(x) = x√(x+4) is differentiable on the open interval (-∞, ∞) as it is a polynomial multiplied by a radical function, which are both differentiable on their respective domains.

Step 5: Apply Rolle's Theorem.

Since f(x) satisfies the conditions of Rolle's Theorem (f(x) is continuous on the closed interval [0, 0] and differentiable on the open interval (0, 0)), we can conclude that there exists at least one point c in the open interval (0, 0) such that f'(c) = 0.

Step 6: Find the value of c.

To find the value of c, we set f'(c) = 0 and solve for c.

f'(c) = √(c+4) + c * (1/2√(c+4)) = 0

Multiplying both sides by 2√(c+4) to eliminate the denominator, we get:

2(c+4) + c = 0

Simplifying, we get:

3c + 8 = 0

c = -8/3

So, the point c at which f'(c) = 0 is c = -8/3.

Step 7: Verify that f(x) = 0 at some point between the two x-intercepts.

f(c) = f(-8/3) = (-8/3)√((-8/3)+4) = (-8/3)√(4/9) = (-8/3)(2/3) = -16/9

Since f(c) = -16/9, which is not equal to 0, we can conclude that f(x) = 0 at some point between the two x-intercepts.

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Answer:

Volume or amount to f water in a jug

The size of a plot of land.

Step-by-step explanation:

The volume of capacity which a certain container can hold such as ; The amount water which can be filled into a cylindrical jug will be measured in cubic units as it requires the multiplication of 3 measured sides of the container ; for a cylinder, radius is squared and multiplied by height. (radius * radius * height).

The size or area of rectangular garden is measured using in square units as it only takes into consideration 2 of the measured parts of a shape.

Answer: 10.92

Step-by-step explanation: Transforming the mixed fractions makes 4.2 and 2.6, which which when multiplied would give you 10.92.

The formula for profit is:

P = I - E

Where,

Income = I

Expenses = E

Profit = P

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,

Income = I

Expenses = E

Profit = P

Now,

Profit = Income - Expenses.

P = I - E

Thus,

The formula for profit is:

P = I - E

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Answer:

Use the formula C= 5/9 (F-32 degrees) to find the Celsius temperature that is equivalent to the 59 degrees Fahrenheit. Question 116085: Use the formula C= 5/9 (F-32 degrees) to find the Celsius temperature that is equivalent to the 59 degrees Fahrenheit. C=15 ANSWER.

Step-by-step explanation:

The formula C= 5/9 (F-32) gives the temperature in degrees celsius for a given temperature in degrees Fahrenheit, the temperature in degrees celsius would be 20° Celcius the temperature is 68 degrees Fahrenheit.

It is a scale of temperature used to measure the temperature, the kelvin scale of temperature is also known as the absolute scale of temperature.

The Standard International unit of thermodynamic temperature is the kelvin, often known less frequently as the degree Kelvin. The formal definition of one kelvin is 1/273.16  of the thermodynamic temperature of pure water's triple point.

It is impossible to have kelvin temperature in a negative value.

For the given problem for calculating the temperature in degrees Celcius

formula C= 5/9 (F-32) is used where C is the temperature in degrees Celcius and F is the temperature in degrees of Fahrenheit

As the given temperature in the fahrenheit scale is 68°

C= 5/9(68-32)

C= 20° Celcius

Thus, the temperature in degrees Celcius comes out to be 20°.

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