1) coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 3 in / min . a) how fast is the level in the pot rising when the coffee in the cone is 5 in. deep? b) how fast is the level in the cone falling then?

Answer:

y = x + 5

Step-by-step explanation:

You can see that x is increasing at exactly the same rate as y. That rate is 1. This gives the graph a slope of 1. Now we can determine by subtracting 1 from y when x = 1 that the y intercept is 5. Slope intercept is y = mx+b. The y intercept is b which is five and the slope is m which is one.

Answer:

To answer this question, we need to use the properties of a normal distribution. So, the answer is b. 10,200

Step-by-step explanation:

The mean and standard deviation serve as the defining characteristics of a normal distribution, a form of probability distribution. The average tire lifespan in this situation is 50,000 miles, with a standard variation of 5,000 miles.

The number of tires that should last between 45,000 and 55,000 miles, or the region under the normal distribution curve between these two figures, is what we're looking for. The conventional normal table or a calculator using the inverse cumulative probability function can be used to find this region.

We can standardize the values by using the standard normal table, which is (X-mean)/standard deviation.

(45,000-50,000) / 5,000 = -1

(55,000-50,000) / 5,000 = 1

The area between -1 and 1 standard deviation from the mean is about 0.6826, which is the proportion of the tires that are expected to last between 45,000 and 55,000 miles.

To find the number of tires, we can multiply the proportion by the sample size (15,000)

0.6826 * 15,000 = 10,200

So, the answer is b. 10,200

Answer: C

Step-by-step explanation:

Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.

1. Constructing a t confidence interval requires that the sample size is greater than 30, so the first condition that must be met is that the sample size is greater than 30.

2. The second condition that must be met is that the sample is a random sample of the population of interest. In this case, the sample is a random sample of 10 deliveries from a large number of deliveries made.

Since both conditions are met, the conditions for constructing a t confidence interval are met.

Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.

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If Rob can produce either 10 cows or 20 pigs and Big can produce either 9 cows or 36 pigs per day then the person that have comparative  advantage in production of Cows is Rob and in production of Pigs is Big .

For Rob :

in 1 day , the number of cows produced is = 10 cows ,

the number of pigs produced is = 20 pigs ;

For Big :

in 1 day , the number of cows produced is = 9 cows ,

the number of pigs produced is = 36 pigs ;

On comparing ,we get that Rob produces more number of Cows than Big;

and also Big produces more number of Pigs than Rob .

Therefore , Rob has advantage in production of Cows and Big has advantage in production of pigs .

The given question is incomplete , the complete question is

Suppose that Rob and Big both raise animals and sell them. Because Rob and Big have different talents, they have varying abilities to raise these animals. In 1 day, Rob can produce either 10 cows or 20 pigs. In 1 day, Big can produce either 9 cows or 36 pigs.

Find who has the comparative advantage in the production of cows and pigs .

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The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.

In this case, the 4 is being multiplied by the formula, which makes it a coefficient.

A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.

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Answer: 226

Step-by-step explanation:

Substitute -8 into x. You will get,

4 (-8)² + 4(-8) + 2

4 x 64 - 32 + 2

256 - 30

226

Answer: 226

Step-by-step explanation:

So the question's asking you to solve for f(-8) which basically means to substitute the x in the equation of f(x) with -8 and solve.

It will then look like this:

f(-8)= 4(-8)^2+4(-8)+2

Then just put it in a calculator and solve.

Step-by-step explanation:

a0 = 0 ft (starting on the ground)

a1 = a0 + 3 - 1 = a0 + 2

an = an-1 + 3 - 1 if an-1 +3 < 15

an = an-1 + 3 if an-1 + 3 >= 15

so, we need to find the n, so that

an = an-1 + 2 >= 12

but by looking at the structure, we see that every step just adds 2 ft to the total height.

an = a0 + 2n = 0 + 2n = 2n

2n >= 12

n >= 6

so, with day 6 the bug reaches 12 ft height. in day 7 it gets up to 15 ft and reached its goal.

it will take 7 days for the bug to reach the top and get the food.

The types of polygons are different based on the number of sides they have and the sum of their interior angles.

The characteristics of different polygons are defined by the number of sides they have and the measure of their angles. Some polygons include:

There are other polygons and they change based on the number of sides they have.

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The possible values of x are values greater than 0.67

From the question, we have the following parameters that can be used in our computation:

0.6 < x > 67%

Express 67% as a decimal

So, we have the following representation

0.6 < x > 0.67

The above statement means that 0.6 is less than x and x is greater than 0.67

This implies that x is greater than 0.6 and x is greater than 0.67

The possible values in this case are values greater than 0.67

Take for instance, 0.7 is greater than 0.6 and 0.67

Hence, the value of x is 0.7

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Answer

212

because I added the 98,4,100,10

Answer:

This question is based on the concept of mean. Therefore, the scores for the four games were 97, 98, 98, 107.

Given:

Sue played four games of golf. For these games her modal score was 98 and her mean score was 100. Her range of scores was 10.

According to the question,

If the modal score is 98 then, there must be two games where she scored 98.

The mean is the total of all of her scores divided by the number of games,

We get,

98+98+x+y=400

x+y= 204

As it is given that, the range is 10 and x is the lowest and y is the highest we can say that:

As we know that, her range of scores was 10,

97+10= 107

Therefore, the scores for the four games were 97, 98, 98, 107.

No, it is not the same as receiving a 35% discount of all the $100 items.

A discount can be defined as the amount of money a seller deducts for their customers from the normal price of the products they are selling.

The percentage discount that is generally on products that are sold for the price of $100 = 35%

The additional discount Josh received were 25% and 10% which is a total of 35% which is different from the general discount.

Therefore, it is not the same as receiving a 35% discount of all the $100 items.

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Complete question:

Josh went into a store to buy a $100 item. There was a sale of 35% off all. The sales person gave Josh a 25% discount and then an additional merchandise.

10% discount. Is that the same as receiving a 35% discount? Prove your answer.

The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each).

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square $abcd$, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each). This can be solved by applying the concept of perimeter.

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square abcd, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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The solutions for the system of equations is the point (2, 2).

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given are two linear equations,

y = -x + 4 and

y = 2x - 2

First graph the lines.

For that, find two points on each equation and join them.

x = 0, then y = 4

y = 0, then x = 4

We have two points (0, 4) and (4, 0). Join these points to form the line.

x = 0, then y = -2

y = 0, then x = 1

We have two points (0, -2) and (1, 0). Join these points to form the line.

We have two equations, which are equal to each other.

-x + 4 = 2x - 2

-x - 2x = -2 - 4

-3x = -6

x = 2

y = -2 + 4 = 2

So the solution of the system of equations is the intersecting point of the two lines which is (2, 2).

Hence the solution of the system of equations is (2, 2).

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For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

By letting users know where they are while they use the keyboard to browse a page, keyboard focus aids keyboard accessibility. Even those who have trouble using a touchpad or mouse can use a computer thanks to keyboard navigation.

The sequence in which interactive objects acquire keyboard focus is crucial for keyboard users navigating the page. The order of the keyboard navigation must be reasonable and obvious by default. This typically means that it moves from left to right and from top to bottom of the page.

This typically means that the header appears first, followed by the main navigation, page navigation, and finally the footer. The web page's source code determines this navigation order as well as the reading order for screen readers.

For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

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From the given data, we said that this business is not profitable. This can be solved using addition method.

Mathematically, addition is the process of merging several numbers together. The numbers that are being added are known as addends, and the outcome of the addition process, or the answer we ultimately obtain, is known as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in many different contexts. In arithmetic sums, the plus sign (+) is used to indicate addition.

The combination of at least two integers constitutes basic addition. Once a student has mastered counting, they may begin to study basic addition. By locating the addend at the top of the chart and tracing down to the row of the second addend, they may utilize an addition chart as a learning tool.

Given that,

Jennifer makes cupcakes to sell at the local farmers market along with her own cookbook which she recently finished creating.

On a recent Saturday, Jennifer sold all 473 cupcakes she made at a cost of $2.50 each, so total amount = 473 × $2.50 = $1182.5

Now, the cost of all ingredients:

= $97.82 + (27 × $18) + $2,200 + $200

= $2983.82

Now, we said that this business is not profitable.

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Answer:

Step-by-step explanation:

y = x/(2+x²)

2y + yx² = x

yx² - x + 2y = 0

(1±√(1-8y²))/2y

Now, 1 - 8y² ≥ 0

8y²≤1

y² ≤ 1/8

y ∈ (-1/2√2, 1/2√2)
Thanks

the standard deviation for activity e is 6.8

What is the probability of finishing the project by the 24th day or less?

Recall that:

z = (Specified Time - Path's mean)/Path's Standard Deviation.

Hence for z₂₁

(21 − 20.5)/1.118   = 0.447 ≈ 0.45.

Hence the probability is:   P(Z<0.45) =0.6736

(21 − 21.5)/1.344 = −0.3721 ≈ −0.37

Hence the probability is:  P(Z<-.37) = 0.3557

(21 − 19.5)/.726 = 2.066 ≈ 2.07

Hence the probability is: P(Z<2.07) = 0.9808

Following through on the above, the project will be finished in less than 21 days is given as:

P = 0.23499920921

P ≈ 0.2350

the standard deviation for activity e is 6.8

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Step-by-step explanation:

complement angle means together they are 90°.

supplementary means together they are 180°.

x = the angle

90 - x = (180 - x)/3

270 - 3x = 180 - x

90 - 3x = -x

90 = 2x

x = 45°

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). The range of a function is the set of all possible output values (y-values) that the function can produce.

When working with inequalities, the domain and range can be found by analyzing the inequality and the context of the problem.

To find the domain of an inequality function, we need to identify any restrictions or limitations on the input values (x-values) that would make the inequality invalid.

For example, if the inequality contains a denominator that cannot be equal to zero, we need to exclude those values of x from the domain.

To find the range of an inequality function, we need to identify the set of all possible output values (y-values) that would make the inequality true.

For example, if the inequality is in the form y > x, we know that all values of y that are greater than x will satisfy the inequality.

In summary, finding the domain and range of inequalities of a function involves identifying any restrictions or limitations on input values and the set of possible output values that would make the inequality true.

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The following question can be solved using concepts of mathematical reasoning.

Mathematical reasoning is the process of using logical and systematic thinking to arrive at conclusions and make connections between mathematical concepts. It involves making logical deductions and inferences based on mathematical statements, definitions, postulates, and theorems.

Let p, q, and r be the propositions

p: Grizzly bears have been seen in the area.

q: Hiking is safe on the trail.

r: Berries are ripe along the trail.

a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.

Solution:

r ∧ ~p

b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.

Solution:

~p∧q∧r

c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area

Solution:

r → (q ↔ ~p)

d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe.

Solution:

~q ∧ ~p ∧ r

e) For hiking on the trail to be safe, it is necessary but not sufficient that berries were not ripe along the trail and for grizzly bears not to have been seen in the area.

Solution:

q → (~r ∧ ~p)

f) Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.

Solution:

(f) (p ∧ r) → ~q

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Answer: [tex]3:2[/tex]

Step-by-step explanation:

Using the zero-product property, we know that [tex]2x-3y=0[/tex] or [tex]x+5y=0[/tex]. We can rearrange these cases to yield [tex]x=\frac{3}{2}y[/tex] and [tex]x=-5y[/tex].

However, since [tex]x[/tex] and [tex]y[/tex] have the same sign, we neglect the case [tex]x=-5y[/tex]. This means [tex]x=\frac{3}{2}y[/tex].

[tex]x=\frac{3}{2}y \implies \frac{x}{y}=\frac{3}{2} \implies x:y=3:2[/tex]

Answer: We can use the distributive property to expand the left side of the equation:

2xx + 2x5y - 3yx - 3y5y = 0

Then, combine like terms:

2x^2 + 10xy - 3xy - 15y^2 = 0

Now we can add 3xy + 15y^2 on both sides of the equation to get:

2x^2 + 10xy = 0

We know that x and y are positive, so we can divide both sides by 2:

x^2 + 5xy = 0

and since x>0, we can divide both sides by x:

x + 5y = 0

So the ratio x:y = x/(-5y) = -x/5y.

To simplify we can divide x by -x and 5y by 5y and get the final answer as

x:y = -1:

Step-by-step explanation:

Answer:

f(6)=23

Step-by-step explanation:

f(n)=f(n-1)+3

f(1) becomes f(1-1)+3

f(1-1)+3 = 8

f(0) +3=8

f(0) = 5

=

f(2) = f(2-1)+3

f(2) = f(1)+3

f(2) = 8+3

f(2) = 11

f(3) = f(3-1)+3

f(3) = f(2) + 3

f(3) = 11+3

F(3) = 14

We can see that the sequence adds three to each prior value:

x  Result

 0     5

 1      8

 2     11

 3     14

 4     17

 5     20

 6     23

f(6) = 23

The length of each diagonal is of: 11 units.

The diagonal lengths are defined as follows:

As the figure is a rectangle, the diagonal lengths are the same, and thus the value of x is obtained as follows:

WY = XZ

6x - 7 = 3x + 2

3x = 9

x = 9/3

x = 3.

Hence the diagonal length is given as follows:

XZ = 3(3) + 2 = 9 + 2 = 11 units.

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Answer:

The value of b in the equation x^2+bx+c=0 can be found using the quadratic formula. The quadratic formula states that the roots of the equation are given by:

x = (-b ± √(b^2 - 4ac))/2a

Where a = 1, since the coefficient of x^2 is 1, b = b and c = c.

Step-by-step explanation:

Given that the roots of the equation are -4 and 2, we can substitute these values for x into the equation and solve for b.

For the first root of -4, we get:

1x^2 + bx + c = (1)(-4)^2 + b(-4) + c = 0

This simplifies to:

16 - 4b + c = 0

For the second root of 2, we get:

1x^2 + bx + c = (1)(2)^2 + b(2) + c = 0

This simplifies to:

4 + 2b + c = 0

Now we have two equations with two unknowns, we can use the substitution method to find the value of b.

By equating the two equation we get:

16 - 4b + c = 4 + 2b + c

We can simplify it as:

12 - 2b = 0

therefore b = 6

In summary, the value of b in the equation x^2+bx+c=0 is 6 when the roots of the equation are -4 and 2.

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When we alter an expressions form but not its value, then these expression are called Equivalent expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

We alter an expressions form but not its value.

Now, Let an expression is,

⇒ (x + 2)²

And, We can change its form as;

⇒ x² + 4x + 4

Clearly, Both expression are equal but its form are change.

Hence, These expressions are equivalent.

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Answer:

Step-by-step explanation:

It is unclear what is being asked in this question. The information provided does not make logical sense and it's hard to understand what is being asked. Could you please provide more information or rephrase the question?

Answer:

Step-by-step explanation:

You need to give more information. There is nothing you can tell from the information you gave. Nothing is fixed.

The ratio ( m :n ) of the line segment joining the given points is calculated by using the formula x = ( mx₂ + nx₁ ) /(m+ n) and y =   ( my₂ + ny₁ ) /(m+ n) provided all the three coordinates points should be given.

As given in the question,

Therefore, the ratio divides the given segment can be calculated by the formula x = ( mx₂ + nx₁ ) /(m+ n) and y =   ( my₂ + ny₁ ) /(m+ n) .

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The Partitions occur on the line segments that Partitions are referred or called  as directed line segments .

What are Directed Line Segments  ?

The Directed Line Segments are defined as the line segments that has distance (length) and direction .

A line segment can be partitioned into many smaller segments which are compared/called as ratios and the Partitions that occur on line segments  are referred to as Directed segments .

The Simple Definition of Partition means to separate or to divide .

let AB be any line segment and we Partition the line AB in the ratio a:b , it means that we are dividing it into (a + b) equal parts and then we find a  point C which is "a" equal parts from A and "b" equal parts from B .

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the probability of "heads" on the first flip of this coin will be 1/2.

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

"Heads" is the result of the latest flip and the preceding four flips. The total sample space for the heads.

P(A^B)=(1/2)^5

The preceding four flips in a row all resulted in "heads."

P(B)=(1/2)^4

The probability that the 5th flip lands head is;

⇒P(A^B)/p(B)= (1/2)⁵/(1/2)⁴

⇒P(A^B)/p(B)= 1/2

Hence, the probability of "heads" on the next (5th) flip of this coin will be 1/2.

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