Please show all work and please do not use a
calculator, thank you.
3. A particle starts moving from the point (2,1,0) with velocity given by v(t) = (2t, 2t - 1,2 – 4t), where t > 0. (a) (3 points) Find the particle's position at any time t. (b) (4 points) What is t

Ive never been good at math, but I liked it because it challenged me. I remeber when I was in 8th grade I applied to take Algebra just to challenge myself. I did horrible in that class the first quarter but after that first quarter, I was excited for math class and to get assigned math work to do, because to me it was fun to be challenged. My first memories about math are when I was in 5th and I was so bad I asked for help every single day, but since that day I kept pushing myself harder and harder to do better and it paid off now I have A's and B's in my assignments for math and I could never be more proud with myself.

Answer:

i hate math its so boring so one day the teacher forgot homework and someone had to say hey teacher you forgot the homework and i was sooo mad like whyyyyyyyyyyyy

Step-by-step explanation:

The result of 297,060 divided by 0.0004839 is approximately 6.1429 x 10⁸ or 614,290,000 in standard notation.

To express 297,060 divided by 0.0004839 in scientific notation, we can represent it as:

297,060 / 0.0004839 = 6.1429 x 10⁸

In standard notation, the result is approximately:

614,290,000

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You are an scalene triangle.

You are a scalene triangle.

A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.

Here's a simple diagram of a scalene triangle to help illustrate:

    \

     \

      \

       \

        \

         \

In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.

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Answer:

  k = 7

Step-by-step explanation:

You want to know the value of k that transforms f(x) = 2/3x -3 to g(x) = f(x) +k, where g(x) is 2/3x +4.

The amount of vertical shift to get from f(x) to g(x) can be found by subtracting f(x) from g(x):

  g(x) = f(x) +k

  g(x) -f(x) = k

  (2/3x +4) -(2/3x -3) = k

  4 -(-3) = k = 7

Function f(x) is shifted upward by k = 7 to transform it to g(x).

__

Additional comment

We can read the equations from the graph by looking for the y-intercept (b) and the slope (m = rise/run) of each line. The slope is rise=-2 for run=3, so m=-2/3.

The +k means the transformation is a vertical shift. You don't need to know what the equations for f(x) and g(x) are; you only need to look at the difference between the y-intercepts. That difference is the amount by which g(x) is shifted upward.

Answer:

what-

Step-by-step explanation:

Rewrite the equation in expanded form:

(X+2)^2 -1 = x^2 + 4x + 3

The parabola parameters are : a = 1, b = 4, c = 3

The x vertex is -b/2a = -4/2(1) = -2

Replace x with -2 in the expanded equation to solve for the y vertex:

Y = -1

The vertex is (-2,-1)

x-value of the vertex:-2

Answer:

Solution given:

we have

f(x)=(x+2)²-1

y=x²+4x+3......(I)

parameters of parabola are:

a=1

b=4

c=3

we have

vertex=-b/2a=-4/(2*1)=-2

substitute value of x in equation 1.

y=4-8+3= -1

So

vertex(-2,1)

To arrange the books in the specified order (Mathematics, Science, and English), you need to determine the number of arrangements for each subject's books and then multiply them together.

For the 4 mathematics books, there are 4! (4 factorial) ways to arrange them, which is 4 × 3 × 2 × 1 = 24 ways.

For the 5 science books, there are 5! (5 factorial) ways to arrange them, which is 5 × 4 × 3 × 2 × 1 = 120 ways.

For the 3 English books, there are 3! (3 factorial) ways to arrange them, which is 3 × 2 × 1 = 6 ways.

To find the total number of ways to arrange all the books in the required order, multiply the arrangements for each subject together: 24 (Mathematics) × 120 (Science) × 6 (English) = 17,280 ways.

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Answer:

x=1

Step-by-step explanation:

The line that represents x=5 is vertical so the only equations that can parallel it must also be vertical. x=1 is the only vertical line on a graph that can pass through (1,4)

Answer: help is to make it easier for (someone) to do something by offering one's services or resources.

"they helped her with domestic chores"

Step-by-step explanation: hope this helps

See attachment for math work and answer.

Answer:

C

Step-by-step explanation:

The rate of charge is how often you are charged something.  If x represents miles than every ? miles you are charged 2.5. The 3 at the end is the y intercept or the point where you start so no matter how many miles you go you automatically owe 3 dollars

The height of the roof is 510.2 feet, rounded to one decimal place.The question is about finding the height of a building (roof) given the velocity of a stone dropped from its edge.

This is an example of free fall motion, which is a special type of motion that happens when an object falls freely due to the force of gravity acting upon it. The problem is asking for the height of the roof, which is the vertical distance the stone traveled from the roof to the ground. To solve for this, we can use the kinematic equation for free fall motion:d = vi*t + (1/2)*g*t^2where:d = distance traveled (in feet) vi = initial velocity (in feet per second)t = time (in seconds)g = acceleration due to gravity (32.2 feet per second squared)We are given that the stone hits the ground with a velocity of -100 feet per second. This is the initial velocity of the stone when it was dropped from the roof. We also know that the time it takes for the stone to hit the ground is the same as the time it takes for the stone to fall from the roof to the ground. So we can use the time it takes for the stone to fall to solve for the height of the roof.

We can use another kinematic equation for free fall motion to solve for time :t = (vf - vi)/g where:vf = final velocity (in feet per second)vi = initial velocity (in feet per second)g = acceleration due to gravity (32.2 feet per second squared)We are given that the final velocity of the stone is -100 feet per second, and the initial velocity of the stone is 0 feet per second (since it was dropped from rest). So we can plug in these values and solve for time :t = (-100 - 0)/32.2t ≈ 3.105 seconds Now we can use the first kinematic equation to solve for the height of the roof: d = vi*t + (1/2)*g*t^2d = 0*(3.105) + (1/2)*(32.2)*(3.105)^2d ≈ 510.2 feet Therefore, the height of the roof is approximately 510.2 feet.

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The rate of increase of the depth of the water is 6.67 ft/min.

First, calculate the volume of the water tank:

Volume = (1/3) πr²h

Volume = (1/3) × 3.14 × 10² × 24

Volume = 7,040 ft³

Now calculate the rate of increase of the depth of the water:

Rate of increase of the depth = (Flow rate of water into tank / Volume of tank)

Rate of increase of the depth = (20 ft³/min / 7,040 ft³)

Rate of increase of the depth = 0.0028 ft/min

Finally, calculate the rate of increase of the depth of the water when the water is 16 ft deep:

Rate of increase of the depth = (Flow rate of water into tank / Volume of water)

Rate of increase of the depth = (20 ft³/min / 4,096 ft³)

Rate of increase of the depth = 0.0049 ft/min

Therefore, the rate of increase of the depth of the water when the water is 16 ft deep is 0.0049 ft/min, which is equivalent to 6.67 ft/min.

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Answer:

Step-by-step explanation:

a) 1200≥25x+45y

b) YES, because:

1200≥25(15)+45(15)

1200≥375+675

1200≥1050

The correct option is c.Keep going.

Create a regression model and be able to optimize it, it is much better that all factors are on a scale. The answer is option c.Keep going.Regression analysis is an important statistical method that is commonly used in finance and other fields for prediction purposes. It is useful for finding the relationships between one dependent variable and one or more independent variables. In order to create an efficient regression model, the variables should be measured on a scale. Therefore, it is important to measure variables on a scale, as this makes it easier to create a regression model. If variables are categorical or binary, it becomes difficult to measure their relationship with the dependent variable using regression models as they are not measurable on a scale. This is why it is much better that all factors are on a scale while creating a regression model and optimizing it. Thus, the correct option is c.Keep going.

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The probability of Esteban winning the table game on his last turn is 1/3 or approximately 0.33.

To calculate the probability of Esteban winning the table game on his last turn, we need to find the probability of rolling a 5 or a number on a standard six-sided die.

There are a total of six possible outcomes when rolling a die, ranging from 1 to 6. Out of these six outcomes, two are favourable for Esteban to win: a 5 or any other number on the die.

Therefore, the probability of Esteban winning the game on his last turn is:

Probability = Favourable outcomes / Total outcomes

Probability = 2 / 6

Probability = 1 / 3

This means that there is a 33% chance of Esteban winning the game on his last turn by rolling a 5 or any other number on the die. The probability of winning is relatively low, so Esteban may need some good luck or strategy to increase his chances of winning the game.

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Answer:

X=15

Step-by-step explanation:

A +B + C = 180

2x +4x+ 6x = 180

12x =180

X= 15

The language paradigm that is based on the mathematical concept of a function is the functional programming paradigm.

In functional programming functions are treated as first-class citizens means that they can be passed as arguments to other functions returned as values from functions and assigned to variables.

This is similar to mathematical functions are used in algebra and calculus.

Functional programming emphasizes on the use of pure functions are functions that produce output only based on their input and do not have any side effects.

This helps in writing code that is easier to reason about and test.

Functional programming languages such as Haskell Lisp and OCaml are based on this paradigm and provide built-in support for functions as first-class citizens.

Object-oriented programming (OOP) is based on the concept of objects encapsulate data and behavior.

Imperative programming is based on a sequence of statements that change the state of the program declarative programming focuses on what the program should achieve rather than how to achieve it.

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Answer:

The answer is option B

f(x) = 4x + 8

g(x) = 9x + 7

(fg)(x) = (4x + 8)(9x + 7)

= 36x² + 28x + 72x + 56

= 36x² + 100x + 56

Hope this helps

Answer:

B

Step-by-step explanation:

Answer:

Area of smaller shape = 245 cm²

Step-by-step explanation:

Given:

Scale factor ration [Big shape to small shape] = 14:7

Area of bigger shape = 490 cm²

Find:

Area of smaller shape

Computation:

Area of smaller shape = Area of bigger shape[7 / 14]

Area of smaller shape = 490[7 / 14]

Area of smaller shape = 490[7 / 14]

Area of smaller shape = 35[7]

Area of smaller shape = 245 cm²

bisects x = -12AB / (2AB - 6BD)

m∠ABC = 6x

= 6 × (-12AB / (2AB - 6BD))

To solve for x and find the measure of angle ABC (m∠ABC), we will apply the angle bisector theorem and use the given information.

According to the angle bisector theorem, the ratio of the lengths of the segments created by an angle bisector is equal to the ratio of the measures of the angles formed by the bisector.

Let's set up the equation using the given information:

m∠ABD = 6x (angle ABD)

m∠DBC = 2x + 12 (angle DBC)

Using the angle bisector theorem, we have:

AB/BD = m∠ABD/m∠DBC

Since BD bisects ∠ABC, we can substitute the given measures into the equation:

AB/BD = (6x) / (2x + 12)

To solve for x, we can cross-multiply:

AB × (2x + 12) = BD × (6x)

Expanding both sides of the equation:

2ABx + 12AB = 6BDx

Rearranging the equation:

(2AB - 6BD)x = -12AB

Now we can isolate x:

x = -12AB / (2AB - 6BD)

The measure of angle ABC (m∠ABC), we substitute the value of x back into the expression:

Simplifying this expression further would require additional information about the lengths of AB and BD.

Without this information, we cannot find the exact value of m∠ABC.

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To test the hypothesis that population 1 has a mean that is exactly 2 less than the mean of population 2, we can use a two-sample t-test with unequal variances.

The test statistic for this hypothesis is given by:
t = (x1 - x2 - d) / sqrt[(s1^2/n1) + (s2^2/n2)]
where x1 and x2 are the sample means, s1 and s2 are the respective standard deviations, n1 and n2 are the sample sizes, and d is the hypothesized difference in means (in this case, d = 2).
Substituting the given values, we get:
t = (34.5 - 30 - 2) / sqrt[(5^2/33) + (9^2/42)]
t = 2.5 / 1.747
t = 1.43 (rounded to two decimal places)
Therefore, the test statistic for this hypothesis is 1.43.

You want to test the hypothesis that the mean of population 1 is exactly 2 less than the mean of population 2. Given that sample 1 has a mean of 34.5 and sample 2 has a mean of 30, the respective standard deviations are 5 and 9, and the sample sizes are 33 and 42. To find the test statistic, follow these steps:
1. State the null hypothesis (H0) and the alternative hypothesis (H1):
  H0: μ1 - μ2 = 2
  H1: μ1 - μ2 ≠ 2
2. Calculate the difference in sample means (M1 - M2):
  34.5 - 30 = 4.5
3. Calculate the standard error of the difference in means:
  SE = √[(s1²/n1) + (s2²/n2)] = √[(5²/33) + (9²/42)] = √[(25/33) + (81/42)] ≈ 1.595
4. Calculate the test statistic (t):
  t = (M1 - M2 - D) / SE = (4.5 - 2) / 1.595 ≈ 1.568
The test statistic for this hypothesis test is approximately 1.568.

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Answer:

morning - 40

afternoon - 85

Step-by-step explanation:

The bus traveled 40 miles in the morning and 85 miles in the afternoon.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The school bus traveled five miles more on a field trip in the afternoon than it did in the morning. If the journey was 125 kilometers long

Let x the distance traveled by bus in the morning.

As per the given condition, we can get the equation shown below:

⇒ x + 2x + 5 = 125

⇒ 3x + 5 = 125

⇒ 3x = 120

⇒ x = 40

In the afternoon, the bus traveled 2x + 5 miles.

Now substitute the value of x in the equation for the afternoon miles to include:

⇒ 2 × 40 +5 = 85

Therefore, the bus traveled 40 miles in the morning and 85 miles in the afternoon.

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Answer:

19 1/16

Step-by-step explanation:

Answer:

305/16

Step-by-step explanation:

Simplify the following:

(5 (30 + 1/2))/8

Hint: | Express (5 (30 + 1/2))/8 as a single fraction.

(5 (30 + 1/2))/8 = (5 (30 + 1/2))/8:

(5 (30 + 1/2))/8

Hint: | Put the fractions in 30 + 1/2 over a common denominator.

Put 30 + 1/2 over the common denominator 2. 30 + 1/2 = (2×30)/2 + 1/2:

(5 (2×30)/2 + 1/2)/8

Hint: | Multiply 2 and 30 together.

2×30 = 60:

(5 (60/2 + 1/2))/8

Hint: | Add the fractions over a common denominator to a single fraction.

60/2 + 1/2 = (60 + 1)/2:

(5 (60 + 1)/2)/8

Hint: | Evaluate 60 + 1.

60 + 1 = 61:

(5×61/2)/8

Hint: | Express 5×61/2 as a single fraction.

5×61/2 = (5×61)/2:

((5×61)/2)/8

Hint: | Express ((5×61)/2)/8 as a single fraction.

((5×61)/2)/8 = (5×61)/(2×8):

(5×61)/(2×8)

Hint: | Multiply 2 and 8 together.

2×8 = 16:

(5×61)/16

Hint: | Multiply 5 and 61 together.

5×61 = 305:

Answer:  305/16

Answer: 1.02

Step-by-step explanation:

Answer:

x= - 446428571 / 50000000000

Step-by-step explanation:

8(-7x+6)=-56x+49

-56x+48=56x+49

+56x      +56x

48=112x+49

-49        -49

-1=112x

/112  /112

x= - 446428571 / 50000000000

The correct statement is: b. The uncertainty will be larger in Study 1 than in Study 2.

This is because Study 2 used a larger random sample (100 cigarettes) compared to Study 1 (10 cigarettes), resulting in a more accurate estimate of the mean nicotine content and reduced uncertainty.

The uncertainty will be larger in study 1 than in study 2. This is because the sample size in study 1 is smaller than in study 2, which means there is more variability in the estimates due to the smaller sample size. In general, larger sample sizes lead to more precise estimates with less uncertainty.

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1 mile = 1.60934 km

58 x 1.60934 = 93.34 km/h

If on  Monday Tom work for 11 extra hours the total amount of money that tom made on Monday is £885.

As per the given data, the extra money he earns can be calculated as,

= [(11 - 7) × 15] × 13 + (7 × 15)]

= (4 × 15 × 13) + 105

= 780 + 105

= £885

Therefore, the amount of money  is £885.

Time and work are concerned with how long it takes a person or a group of people to finish a task and how well each of them completes it.

Indirect proportion is related to time and work. In both directions, when one quantity rises, the other falls, and vice versa. It takes less time to finish the same amount of work when people work more hours.

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The probability of rolling and odd number with both dice A and B is 1/4.

Probability simply means the likelihood that an event will occur on a scenario.

Since Dice A and dice B have ten sides,the numbers will be from 1 to 10. Therefore, there are 5 even numbers and 5 odd numbers.

Probability of odd number = 5/10 = 1/2

Probability of even number = 5/10 = 1/2

Probability of rolling both odd numbers will be:

= P(odd) × P(odd)

= 1/2 × 1/2

= 1/4

The probability is 1/4.

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Note that the rational numbers represented on points- P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3 respectively. See the explanation below.

A rational number is defined in mathematics as the proportion or fraction p/q of two integers, a numerator p, and a non-zero denominator q. 3/7, for example, is a rational number, as is every integer.

For the solution above:
Each section in between two numbers is broken into three sections.

Thus, we have a = (6/3), P = (7/3), Q = (8/3) and B = (9/3)

In the same way,

T = = -3/3,

R = -4/3

S = -5/3 and

U = -6/3

Therefore, the rational numbers represented - P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3.

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