antti entered a 10 kilometer race. his goal is to finish in one hour. he starts off sprinting, and completes the first 2 kilometers of the race at an average speed of 12 kilometers per hour. to achieve his goal of a one-hour finish time, what average speed must antti maintain for the last 8 kilometers of the race?

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:

37 and -18

Step-by-step explanation:

Answer:

let x and y be two numbers

The number of hot cocoas the Ai Mi would be expected to sell with a high temperature of 64 ºF is given as follows:

60.

As the graph of the linear function is given, the most practical way to define the function is using the slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

From the graph, when x = 0, y = 111, hence the intercept b is given as follows:

b = 111.

When x increases by 5, from 0 to 5, y decays by four, from 111 to 107, hence the slope m is obtained as follows:

m = -4/5

m = -0.8.

Hence the function that predicts the amount of hot cocoa sold for a high temperature of x ºF is given as follows:

y = -0.8x + 111.

The prediction for a high temperature of x = 64 is given as follows:

y = -0.8(64) + 111

y = 60 hot cocoas, rounded.

The graph is given by the image presented at the end of the answer.

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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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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:

Step-by-step explanation:

2.73 (rounded)

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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No, the absolute value of equations does not always have two answers

Understanding the absolute value is crucial for mathematicians. We place vertical bars on either side of a number to show its absolute value. On a number line, absolute value refers to distance from zero. A negative number's absolute value is a positive number. A positive number has the same absolute value as another positive number.

There are not always two solutions to an equation's absolute value. An equation involving fundamental values may have one or more solutions, depending on the equation's overall structure and the values that are being entered. For example, whereas the equation |x| = 2x has no solutions, but the equation |x| = 1 has two solutions (x = 1 and x = -1).

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Answer:

  a ≠ 0

Step-by-step explanation:

You want to know the restriction applicable to 2(y+a)/a(x-3).

A rational expression is undefined when its denominator is zero. The restrictions are applied so that no denominator is zero.

Here, the expression is ...

  [tex]\dfrac{2(y+a)}{a}(x-3)[/tex]

The only denominator is 'a'. It cannot be zero.

The restriction is a ≠ 0.

__

Additional comment

If we assume this is a relation in which x- and y- are the only variables, there is no restriction on the relation as written.

Perhaps you intend that (x-3) be a denominator factor. Then the relation would have the restriction x≠3. Such an expression would need to be written as ...

  2(y+a)/(a(x-3)) . . . . . . using parentheses around the denominator

<95141404393>

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 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 system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.

Let x be the number of square feet of carpet and y be the number of square feet of hardwood.

The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:

x + y <= 2000

The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:

4.50x + 8.25y <= 10000

So the system of inequalities is:

x + y <= 2000

4.50x + 8.25y <= 10000

This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.

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To complete the given statement, we have;

i. SM > DM

ii. <PQS < <RQS

iii. AS > RM

iv. m<1 = m<2

Any given shape which is bounded by straight side is referred to as a plane shape. Examples include: triangles, rectangle, trapezium, parallelogram etc.

It can be observed in the given question that the shapes have different properties regarding their length of sides and measure of internal angles. Each of the statement can be completed as thus;

1. From triangle SJD,

m<SJM > m<DJM

Then, it can be deduced that;

SM > DM

2. From quadrilateral PQRS,

RS > PS

It can be deduced that;

<PQS < <RQS

3. From triangle AMS, it can be deduced that AS > RM.

4. From quadrilateral ABCD,

AD II BC

Then,

m<1 = m<2             (by alternate angle property)

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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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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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Answer:

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

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 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:

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.

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)

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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Answer: slope is 1 or m=1

Step-by-step explanation:

Answer:

A [tex]180^{\circ}[/tex] rotation about the origin, then a dilation by a scale factor of [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The preimage is larger than the image.

Also, the orientiation of the triangle didn't change.

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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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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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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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 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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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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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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