A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what values of t is the particle moving to the right? responses the particle is moving to the right only if 0

Answer:

No

Step-by-step explanation:

1) Write out the inequality to get a better understanding

m ≤ -12

From this we can see that m can be any number less than -12!

2) Find out possible solutions

As -12 is a negative number, any number less than it would have a larger absolute value.

Some examples of numbers less than -12 would be -15, -13, -36 ect.

HINTS:

It may be easy to confuse which number is greater or smaller than a negative number.

To make sure that we don't make a mistake, we can always put the numbers on a number line!

Any number to the left of it, is smaller, and any number to the right, is larger!

Hope this helps, have a great day!

Answer:

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

This is a quadratic function and it can get maximum at vertex.

The x-coordinate of the vertex is determined by x = - b/(2a).

We have:

Find the value of x:

Correct choice is B.

11 cups of vinegar would Lorenzo use to make [tex]4\frac{2}{5}[/tex]  recipes.

Given that, Lorenzo uses [tex]2\frac{1}{2}[/tex] cups of vinegar in his salad dressing recipe.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Lorenzo use to make [tex]4\frac{2}{5}[/tex] recipes

Here, [tex]2\frac{1}{2}=\frac{5}{2}[/tex] and [tex]4\frac{2}{5}=\frac{22}{5}[/tex]

Now, 5/2 × 22/5

= 11

Hence, 11 cups of vinegar would Lorenzo use to make [tex]4\frac{2}{5}[/tex]  recipes.

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By using the concept of Probability, the result obtained is -

Probability of guessing the correct order = [tex]\frac{1}{720}[/tex]

What is Probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

There are 10 numbers from 1 to 10

Number of favourable outcomes = 10 [tex]\times[/tex] 9 [tex]\times[/tex] 8

                                                       = 720

There is only one correct order

So probability of guessing the correct order = [tex]\frac{1}{720}[/tex]

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Correct Question

To test Jake's abilities, Rosa chooses 3 different numbers

from 1 to 10. Rosa then asks Jake to identify which 3 of the 10 numbers she chose in the correct order.

Assume that Jake has no special abilities and is randomly guessing the numbers. What is the probability that Jake correctly identifies all 3 numbers in the correct order?.

Answer: no he is not correct because 5x5 is 25 and 10/5 is 2

Step-by-step explanation:

The expression n times d times q times in terms of number of nickels is n²(36-3n)/4 .

In the question ,

it is given that ,

there are n nickels , d dimes , q quarters .

Also given that there is  twice as many nickels as dimes ,

that means , n = 2d

So , d = n/2

also that total number of coins = 18 ,

So , n + d + q = 18

n + n/2 + q = 18

q = 18 - 3n/2

we need to find ,  n times d times q in terms of the number of nickels.

that means

= n × d × q

= n × n/2 × 18 - 3n/2

= n × n/2 × (36 - 3n)/2

= (n × n×(36 - 3n))/2×2

= n²(36-3n)/4

Therefore , The expression n times d times q times in terms of number of nickels is n²(36-3n)/4 .

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The number of tires that minimizes the cost is 800., And the cost for that number of tires is, $45.

What is parabola?

When the value of an is less than 0, a 0, the parabola's graph is downward (or opens down). When the value of an is more than zero, a > 0, the parabola's graph is upward (or expands). As a result, the direction of the parabola depends on the sign of the coefficient "a."

Consider, the equation

C = 0.002x^2 - 3.2x + 1325

Here, a = 0.002 > 0

Since, if a > 0 then parabola is open upward and having minimum value at it's vertex.

First, to  find the vertex of the quadratic equation.

Since,

V = (-b/2a, f(-b/2a))

Let, a = 0.002,  b = -3.2,   c = 1325

So,

-b/2a = 3.2/2(0.002) = 800

Therefore, the number of tires that minimizes the cost is 800.

Now to find the cost for that number of tires.

Plug x = 800 into the above quadratic equation

C = 0.002(800)^2 - 3.2(800) + 1325

C = 45

Hence, the cost for that number of tires is $45.

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final answer:

Hence, the simplest form of (64/25) -1/2 is 5/8

Answer:

Step-by-step explanation:

f(g(x)) = 6x^3 + 4 dollars/hour

Examining the figure the length of the side SU is calculated to be

6

Examining the figure, it can be deduced that

XW = VT = 2 (opposite side of a parallelogram)

XV = WT = 2 (opposite side of a parallelogram)

VT = SV, therefore ST = 2 + 2 = 4

UW = WT, therefore UT = 2 + 2 = 4

The figure form similar triangles and the ratios as written below are equal

SU / VW = ST / XW =  UT / XV

SU / VW = ST / XW

SU / 3 = 4 / 2

SU = 3 * 4 / 2

SU = 6

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Answer:

-1, 3, 7

Step-by-step explanation:

this is adding 4 every time

hopes this helps please mark brainliest

Answer: -1, 3, 7

Explanation: The pattern in this sequence, is that you add 4 for every new number in the sequence. So -5+4 is -1. Then the next one would be -1+4 is 3. And then finally, the next one would be 3+4, which is 7.

Answer:

Four consecutive odd integers are: 2n+1, 2n+3, 2n+5 and 2n+7

Three times the sum of the first and fourth then are 3(2n+1 + 2n+7)

80 less than 4 times the sum of the second and third then are 4(2n+3 + 2n+5) - 80

Since the two are equal:

3(2n+1 + 2n+7) = 4(2n+3 + 2n+5)-80

expanding the brackets:

6n+3 + 6n + 21 = 8n + 12 + 8n + 20 - 80

combining like terms

3 + 21 - 12 -20 + 80 = 8n + 8n - 6n - 6n

72 = 4n

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the book, they gave you the values of 'a', 'b', and 'c', and you're supposed to find the value of 'd'.

If you have two points on the line, then the slope of the line is

                      (the change in 'y') divided by (the change in 'x') .

If the two points are (a, b) and (c, d), then the slope of the line is

                      (d - b) divided by (c - a),

and you have to find the value of 'd' that makes that whole expression

equal to 1/2.

                                     (d - b) / (c - a) = 1/2

Multiply each side by  (c - a):     (d - b) = 1/2(c - a)

Add 'b' to each side:                    d        =  1/2(c - a)  +  b

If you know the values of 'a', 'b', and 'c', you can find the value of 'd'.

Different arrangements of candidates are possible is 210.

Given:

There are 7 students on a team. if they must elect a president, a vice president, and a treasurer.

Number of arrangements = [tex]7_p_{3}[/tex]

= 7!/(7-3)!

= 7!/4!

= 7*6*5*4! / 4!

= 7*6*5*1

= 42*5*1

= 42*5

= 210

Therefore Different arrangements of candidates are possible is 210.

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The total distance that Sylvie will have driven is, 459 miles.

What is distance?

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.

Let,  Sylvie is going on vacation. She has already driven 60 miles in one hour. She then travels for 7 hours at an average speed of 57 miles per hour.

In 7 hours Sylvie travel 7 x 57 = 399 miles.

So, the total distance is,

399 + 60 = 459 miles

Hence, the total distance that Sylvie will have driven is, 459 miles.

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By using the concept of Percentage, it is obtained that

New Salary of Vineeth = Rs. 15000

What is Percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means 2 is expressed as a fraction of 100.

Here, the concept of percentage has been used.

Original salary of Vineeth = Rs. 25000

Percentage decrease in salary = 40%

Decrease in salary = [tex]\frac{40}{100}\times 25000\\[/tex]

                               = Rs. 10000

New Salary of Vineeth = Rs.(25000 - 10000)

                                      = Rs. 15000

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Answer:

Step-by-step explanation:

V = (4/3) πR³

R = ³√(3V/(4π))

R = ³√(3*200/(4π)) = ³√(150/π) см

The percentage of the people polled who were in favor of the hotel is 44%.

From the information, Jackson's city took a telephone poll about a plan to build a new hotel downtown and 1,000 people took the poll whike.440 of them were in favor of the new hotel.

The percentage for those that were in favor will be:

= People in favor / Total survey × 100

= 440/1000 × 100

= 44%

The percent is 44%.

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Answer:c

Step-by-step explanation:

distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation is 0, 1, 2, ..................104000.

let, x denote the total number of hits,

y denotes the number of hits by a particle in a year or an individual,

one per week ⇒ 52 per year

therefore, rate = 52 per year

since it is very rare to hit all individuals, we can use Poisson distribution.

therefore by using the formula p (x = x) = (e^(-rate) × rateˣ) ÷ x! ; x = 0, 1, 2, ............( 2000 × 52)

p (x = 2) = (e⁻⁵² × 52ˣ) ÷ x! ; x = 0, 1, 2, ............104000

now each hit has a harm of probability 10⁻⁵.

so p(total no. of tumors produced over a one year period)

= {e⁻⁵² × 52ˣ} ÷ x! × 10⁻⁵ ; x = 0, 1, 2, ............104000

therefore total no. of tumors = 2000 × (e⁻⁵² × [tex]52^{x.10^{-5} }[/tex] ) ÷ x!  × xⁿ ; x = 0, 1, 2, ............104000

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(complete question)

Assume that each of the 2000 individuals living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. Suppose that each hit by a particle is harmless with a probability of 1 - 10⁻⁵, and produces a tumor with a probability of 10⁻⁵. Find the approximate distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation.

a) The conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home is of: 0.5714 = 57.14%.

b) There is a negative association between not attending college and living on their own.

The relative frequency of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For the conditional relative frequency of a student who does not plan to attend college, given that they plan to live at home, in item a, the outcomes are given as follows:

Hence the relative frequency is of:

p = 0.2/0.35 = 0.5714 = 57.14%.

Among people who plan to live on their own, the relative frequency of people who plan to attend college is of:

0.55/0.65 = 0.846 = 84.6%.

Hence there is a negative association between not attending college and living on their own, as people who live on their own are significantly more likely to attend college then people who do not live on their own.

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Answer:

6 Classes

Step-by-step explanation:

500 Students =25 Class

1 class= 500/25

=20

120 students = 120/20

=6

Hope it helps you

Answer:

6

Step-by-step explanation: i think its right

The value of cos 2x = -21/25.

Given:

cos x = -2/5

we know that,

cos 2x = [tex]2cos^{2}x -1[/tex]

= 1([tex](-2/5)^{2}[/tex] - 1

= 1[tex](2/5)^{2}[/tex] - 1

= 1*4/25 - 1

= 4/25 - 1

= 4 - 25 / 25

= -21/25.

Therefore the value of cos 2x = -21/25.

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Answer:

[tex] \huge{ \boxed{ \bold{g = - 2}}}[/tex]

Step-by-step explanation:

In order to find g we have to use the formula for finding the slope of the line passing through two points that's

[tex]m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are (g, -1) and (2, 5) and m = 3/2

We substitute it into the equation and find g

That's

[tex] \frac{3}{2} = \frac{5 - - 1}{2 - g} \\ \frac{3}{2} = \frac{5 + 1}{2 - g } \: \: \: \: \: \: \: \frac{3}{2} = \frac{6}{2 - g} \\ \\ 3(2 - g) = 6(2) \\ 6 - 3g = 12 \\ - 3g = 12 - 6 \\ - 3g = 6 \\ \\ \frac{ - 3g}{ - 3} = \frac{6}{ - 3} \\ \\ g = - 2[/tex]

We have the final answer as

Hope this helps you

Answer:

87,600 iPad are assembled in a year.

Step-by-step explanation:

You take the number of iPads assembled every day (240) and multiply it by the number of days in a year (365). 240 multiplied by 365 is 87,600.

Answer:

0.546 is greater than 0.056

If Sharifa's white ball rolled 143 centimeters in 4 seconds and her green ball rolled 112 centimeters in 3 seconds. The ball that rolled at a greater is: B: green ball.

Using this formula to find the fastest speed

White ball :

Speed for white ball = 143 centimeters /4 seconds

Speed for white ball = 34.75

Green ball:

Speed for green ball = 112 centimeters /3 seconds

Speed for green ball= 37.33

37.33 ≥ 34.75 which means that green ball is the fastest.

Therefore the correct option is B.

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El saco tiene un precio original de 400 soles.

En este problema tenemos el caso de un precio de compra (P'), en soles, que es resultado de aplicar dos descuentos consecutivos al precio original del saco (P), en soles. El precio es el resultado de multiplicar el precio original por los dos factores de porcentaje, descrito por la siguiente fórmula:

P' = P · (1 - r₁ / 100) · (1 - r₂ / 100), 0 ≤ r₁, r₂ ≤ 100.

Donde:

Si sabemos que P' = 224, r₁ = 30 y r₂ = 20, entonces el precio original del saco es:

224 = (1 - 30 / 100) · (1 - 20 / 100) · P

224 = 0.7 · 0.8 · P

P = 224 /(0.7 · 0.8)

P = 400

El precio original del saco es de 400 soles.

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Answer:

905789 x 9417 = 8529815013

Step-by-step explanation:

I hope this helps, friend :)