It takes Logan 3/10 of an hour to complete 1 lap.
How many laps will he complete 2/3 of an hour.

The reason is that the absolute value of a number discards the sign, so it can't be negative as the absolute value of a number is the distance of the number from zero.

Mean Absolute Error (MAE) is a measure of the difference between the predicted value and the actual value. It is calculated by taking the absolute value of the difference between each predicted value and the actual value, and then averaging the differences.

MAE is always positive because it is calculated using the absolute value of the errors, which always results in a positive value. The absolute value function removes the negative sign from any negative errors, so all errors are treated as positive. Therefore, the sum of all errors will always be positive regardless of whether the predicted values are greater or less than the actual values.

It's used in regression problems to measure how good the model is by comparing the actual value and the predicted value. Since MAE is a positive value, it gives a clear understanding of how far the predicted value is from the actual value, which helps to understand the model's performance.

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The volume of the ice cream cone is 100.48 in³.

The volume of the basketball is 267.95 in³.

The volume of the can of corn is 169.56 in³

To find the volume of the ice cream cone, use the formula for the volume of cone, which is given by:

V = (1/3)πr²h

r = 4 in and h = 6 in

V = 1/3 × 3.14 × 4² × 6 = 100.48 in³

To find the volume of the basketball, use the formula for the volume of sphere, which is given by:

V = (4/3)πr³, where r = 4 inches

V = (4/3) × 3.14 × 4³ = 267.95 in³

To find the volume of the can of corn, use the formula for the volume of cylinder, which is given by:

V = πr²h, where r = 3 in and h = 6 in

V =  3.14 × 3² × 6 = 169.56 in³

code: HG DA CF

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P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P [tex](\frac{9.85-10}{0.15} < \frac{X-10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P  [tex](\frac{9.85-10}{0.15} < \frac{X-10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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If blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle which is denoted as option C.

This refers to something which is used to transport people and goods from one place to another and examples include car, lorry etc. The lights are used at night for proper vision of the road so as to reduce the risk of accidents on the road.

here,

In a situation whereby an individual is blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle so as to prevent temporary vision impairment.

This helps to prevent accidents on the road and for the safety of the driver thereby making it the correct choice.

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The difference in the amount of interest paid the first month between the average and worst score is given as follows:

$94.58.

The average interest rate would allow you to do so while paying the least amount of money, due to the lower rate compared to the poor.

The equation to model the interest accrued after t years is given as follows:

I(t) = Prt

.

In which the parameters of the equation are explained as follows:

For the average score, the parameters are given as follows:

P = 25000, r = 0.0535, t = 1/12. (as one month = 1/12 of a year).

Hence the interest accrued is of:

I = 25000 x 0.0535 x 1/12

I = 111.46.

For the poor score, the parameters are given as follows:

P = 25000, r = 0,0989, t = 1/12. (as one month = 1/12 of a year).

Hence the interest accrued is of:

I = 25000 x 0.0989 x 1/12

I = 206.04.

Hence the difference is of:

206.04 - 111.46 = $94.58.

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Answer:$

94.58

Step-by-step explanation:

Answer: slope is 1 or m=1

Step-by-step explanation:

Answer:

4) is the least with 14.111°

1) is next with 17.9°

2) is next with 30.22°

5) is next with 65.84°

3) is the greatest with 86.82°

Step-by-step explanation:

1) csc θ = 3.2547

1/sinθ = 3.2547

sinθ = 1/3.2547

θ = [tex]sin^{-1}[/tex] 1/3.2547 or 17.9 ° ( I checked using a calculator here)

[tex]sin^{-1}[/tex]x is also known as arcsin.

Now, i will do the rest the same way.

2) θ = arccos(0.8641) = 30.22°

3) θ = arctan(17.9926) = 86.82°

4) θ = arcsin(0.2438) = 14.111°

5) θ = arctan(1/0.4485) = 65.844°

So, now u can tell the orders.

Pls mark as brainliest. This took a while. Cheers.

According to the Federal Emergency Management Agency (F.E.M.A.) , In case of emergency for two people , three days , number of gallons that should be packed is 6 gallons .

During Emergency Situations as we stock food, we need to take into account the family’s unique needs and tastes.

We try to include foods that require no refrigeration, water, special preparation, or cooking are best in case of emergency .

So , by FEMA , it states that we need to store at least one gallon per person per day .

Since there are two people , so , we need 2 gallons per day ;

and for three days , it would requires [tex]2 \times 3 = 6[/tex] gallons per day .

Therefore , 6 gallons of water should be packed .

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The monomial that completes the expression hence it is the square of a binomial is given as follows:

9p².

The square of a binomial is modeled as follows, considering that the binomial can be either a sum or a subtraction.

The expression for this problem is given as follows:

x - 42pq + 49q².

In which x is the monomial.

Hence the system of equations to obtain the values of the parameters a and b are given as follows:

Hence the parameter b is obtained as follows:

[tex]b = \sqrt{49q^2}[/tex]

b = 7q.

The parameter a is obtained as follows:

2ab = 42pq

14aq = 42pq

14a = 42p

a = 42p/14

a = 3p.

Hence monomial that makes the expression that square of a binomial is given as follows:

a² = (3p)² = 9p².

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After translating the sentence into an equation using n to represent the unknown number and solving the equation the unknown number is 5.5.

In the given question, we have to translate the sentence into an equation using n to represent the unknown number. Then solve the equation for n. the quotient of a number divided by 11 is 0.5.

Let the number is n. So

n/11 = 0.5

Now solving the expression to find the value of n.

Multiply the 11 on both side, we get

n = 0.5×11

n = 5.5

Hence, the unknown number is 5.5.

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Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.

The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.

Such data may come from a larger population, or from a data-generating process.

1 The correct option is B.

As the hypothesis testing helps to predict when certain certainty within which range the stock value will fluctuate.

The sampling is used to gather data from the population.

The sampling can be either random or systematic. The correct option is B.

2 The correct option is C

as the null hypothesis represents the current and present claim or knowledge.

The Alternate hypothesis is the assumption about the parameter need to be checked against the null hypothesis that is it is a new assumption to be proven. So the correct option is B.

3  The correct option is A.

As either there can be sufficient evidence to reject the null hypothesis or insufficient evidence to reject the null hypothesis.

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Based on the solution to a system of equations,  with John having four more than twice as many baseball cards as Caleb, and altogether the boys owning 286 baseball cards, Caleb alone has 94.

A system of equations or simultaneous equations is two or more equations solved simultaneously or concurrently.

Let the number of baseballs Caleb owns = c

Let the number of baseball John has = 2c + 4

The total number of baseball = 286

c + 2c + 4 = 286

3c = 282

c = 94

Thus, Caleb has 94 baseballs while John has 192 baseballs.

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The required graph has been attached below which represents the cube root function f(x) = ³√x.

The cube root function is given in the question, as follows:

f(x) = ³√x

We have to determine the graph of the given function.

The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

Thus, the required graph has been attached below which illustrates the cube root function f(x) = ³√x.

Hence, the correct answer would be an option (B).

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The consecutive integers for the two roots are:

17) 14 < √214 < 15

18) 7 < ∛441 < 8

17) First, we want to find two consecutive integers such that √214 lies between them.

To do so, we just need to find two consecutive integers such that when we square them, one is smaller than 214, and the other is larger than 214.

For example:

13*13 = 169

14*14 = 196

15*15 = 225

Now we can see that:

14² < 214 < 15²

If we apply the square root we get:

14 < √214 < 15

Thes are the two integers.

18) Now we want to do the same thing, but this time with:

∛441

This time we need to cube our numbers.

7*7*7 = 343

8*8*8 = 512

These are the two integers such that:

343 < 441 < 512

Now we can apply the cube root to get:

∛343 <∛ 441 < ∛512

7 < ∛441 < 8

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The volume of the figure is V = (1/2)xy*h.

The volume of an oblique prism can be found by multiplying the area of its base by its height.

Since the bases of the prism are right triangles, we can use the formula for the area of a right triangle, which is (1/2)base*height.

If we assume that the base is the right triangle with legs x and y, and the height of the prism is h. The volume of the prism can be calculated as:

V = (1/2)xy*h

Note that this formula is valid only if the prism is a right triangular prism and the bases are right triangles, otherwise we would need more information to calculate the volume.

Thus, The volume of the figure is V = (1/2)xy*h.

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Answer:

Step-by-step explanation:

2.73 (rounded)

The length and breadth of the rectangle are 10m and 6m respectively

The shorter side of a rectangle is called its breadth (width) and the longer side is the length.

The area of a rectangle = L×B

and the perimeter = 2(L+B)

where L is the length and B is the breadth

therefore 60 = LB, and B = 60/L

and 32 = 2(L+B)

substitute 60/L for B

32 = 2(L+60/L)

divide both sides by 2

16 = L+60/L

16 =( L²+60)/L

therefore L² +60 = 16L

L² -16L +60= 0

L²-10L-6L +60 = 0

L(L-10)-6(L-10) = 0

L-10 = 0 or L-6 = 0

therefore L = 10 or 6

when L is 10m then B = 60/10 = 6m

when L is 6m then B = 60/6 = 10m

Since the longer side is length then L = 10m and B = 6m

therefore the length and breadth of the rectangle are 10m and 6m respectively.

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The explicit formula for the arithmetic sequence 40, 37, 34, 31 is given as follows:

[tex]a_n = 40 - 3(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the explicit formula presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In the sequence, each term is the previous term subtracted by three, hence the common difference is given as follows:

d = -3.

The first term is of:

[tex]a_1 = 40[/tex]

Hence the explicit formula is given as follows:

[tex]a_n = 40 - 3(n - 1)[/tex]

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Answer:

37 and -18

Step-by-step explanation:

Answer:

let x and y be two numbers

There are many types of functions and each type of function has its own characteristics. This implies that their graph has also its own characteristics.

Based on the graph, the absolute value function has a "V-Shaped" graph.

Every absolute value graph makes a “V”-shaped figure. It consists of two parts: one with a negative slope and one with a positive slope. The point of their intersection is called the vertex. An absolute value graph is symmetrical, meaning that it can be folded in half on its line of symmetry.

An absolute value graph has a distinct V-shape. It is symmetric about the vertical line which passes through its vertex. The vertex of an absolute value function is the point at which the graph changes direction. Since the graph of y=|x-1|+1 changes direction at (1,1), this point is the vertex.

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The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.

Let a, b, c, and d are the zeroes of the polynomial.

Then the polynomial is given as,

⇒ (x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

Form a polynomial whose real zeros and degree are given.

Zeros: -1, 0, 6 and Degree: 3

Then the polynomial is given as,

⇒ (x + 1)(x + 0)(x - 6)

⇒ x(x + 1)(x - 6)

Information is given about a polynomial​ f(x) whose coefficients are real numbers.

Degree​ 4; ​ zeros: 7i, 2, -2

The last root will be opposite to the 7i and will be - 7i.

The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.

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The probability that at least two dice show 3 in the fraction form will be 1/9.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The total number of events is given as,

Total event = 6 x 6

Total event = 36

The favorable events are given as,

Favorable events = 4 {(1, 1), (1, 2), (2, 1), (2, 2)}

Then the probability that at least two dice show a 3 will be given as,

P = 4 / 36

P = 1/9

The probability that at least two dice show 3 in the fraction form will be 1/9.

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Answer:

Yes it’s functions, because for each input there is an output.

Answer: 3 more days

Step-by-step explanation:

8.75mi(has to run)-3.5mi(already ran)=5.25mi(left to run)

5.25mi(left to run)/1.75mi(how many she runs in a day)=3 more days (until she runs 8.75 mi)

The surface area per unit volume is increased by a factor of 1000.

1000

The surface area of a cube is 6 times the square of its side length, (A = 6s^2). Since the volume of a cube is the cube of its side length, (V = s^3), the surface area per unit volume is 6/s.

If the volume is increased by a factor of 10, the side length is increased by a factor of 10^(1/3), which is about 3.162. The surface area per unit volume is therefore increased by a factor of 6/3.162, which is about 1,000.

The surface area per unit volume is increased by a factor of 1000.

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The nonstop trip from Stein to Constance will take 48 minutes.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Let us suppose the distance between Stein to Constance as d:

Then according to the distance formula, we have:

Distance = Speed * Time

Now, let the velocity of boat be v, and the velocity of water be x.

To go from Stein to Schaffhausen it takes 40 minutes. This is represented as:

d = (v + x) (40) equation 1

To go from Schaffhausen to Stein it takes 60 minutes, this is represeted as:

d = (v - x)(60) equation 2.

Divide the equation 1 and equation 2 wegwt thw following:

3v - 3x = 2v + 2x

v = 5x

Substitute this value in the distance formula:

d = (5x + x) (40)

d = 240x

d/ x = 240

X can be written as v/5, substitute this value in the above equation we have:

d/ v = 48 minutes.

Hence, nonstop trip from Stein to Constance will take 48 minutes.

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Each piece of room or house length and width should be inverted to be scaled. For instance, a rectangle measuring 66" by 7" might be used to depict a dresser that is 5' by 2' at a scale of 14" = 1'.

A table that is 4' by 4' would also be 1" by 1" in size. [7] When measuring furniture that isn't square or rectangular, make the smallest square or rectangle the item might possibly fit and then use those dimensions. For instance, to represent a wingback chair that is 2' 6" wide and 2' deep, use a 5/8" by 1" rectangle.

Next, draw a rough outline of the chair inside the rectangle. On a piece of graph paper that is blank, draw the furnishings. Use graph paper without the room's floor plan drawn on it.

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Isolate the absolute value on one side of the equation, Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.

Piecewise Definition: with respect to a number of discrete intervals, sets, or pieces.

[tex]|a|=\left \{ {{a if a > =0} \atop {-aifa < =0}} \right.[/tex]

Square root definition:

|a|=√a²

There are a few Rules to define absolute value:

1.  |–a| = |a|

2.  |a| ≥ 0

3.  Products: |ab| = |a|*|b|

4.  Quotients: |a / b| = |a| / |b|

5.  Powers: |an| = |a|n

6.  Triangle Inequality: |a + b| ≤ |a| + |b|

7.  Alternate Triangle Inequality: |a – b| ≥ |a| – |b|

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When x=22 minutes, Amira was 9 blocks away from the house.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

From the given distance time graph,

At time x=22,

Corresponding y value is 9

Therefore, when x=22 minutes, Amira was 9 blocks away from the house.

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Answer:

An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).

Given the initial condition that there were 4 bacteria in the dish, we know that when x = 0, y = 4.

So we can set up the equation: 4 = a(b^0)

Given the condition that 5 hours later there were 972 bacteria in the dish, we know that when x = 5, y = 972.

So we can set up the equation: 972 = ab^5

We can now solve for b by dividing the two equations:

972/4 = ab^5/a(b^0) = b^5

b = (972/4)^(1/5)

With b calculated, we can substitute it into one of the equations to find a:

4 = a(b^0) = ab^0 = a

So the exponential function that satisfies the given conditions is:

y = ab^x = 4(b^x) = 4( (972/4)^(1/5)^x)

This function models the growth of bacteria in the Petri dish

I don't know exactly what the question was, but I'm guessing it's the bacteria growth rate.

You can use the formula

final amount of bacteria = (initial amount of bacteria)(bacteria growth rate)^number of hours

So,

972 = (4)(x)^5

then simplify this equation to solve for x

x=3

the amount of bacteria increased 3 times more every hour for 5 hours

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