A ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression -16t^2+40t+3. What is the meaning of the 3 in the expression?

Answer:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

10/1÷5/6

Applying the fractions formula for division,

  10×6  

= --------

    1×5

=60/5

Simplifying 60/5, the answer is

=12

Answer:

1.2

Step-by-step explanation:

5/6=8.333

10/8.3333

The volume of the wooden roller is approximately equal to 50.27 cm³ (when rounded to two decimal places).

To find the volume of the wooden roller, we can use the formula for the volume of a cylinder:

Volume = π x (radius)^2 x height

First, we need to find the radius of the wooden roller. The diameter is given as 8cm, so the radius is half of that, or 4cm.

Now, we have the following dimensions:

Radius = 4cm

Height = 1cm

Plugging these values into the formula for the volume of a cylinder, we get:

Volume = π x (4cm)^2 x 1cm

= 16π cm^3

Therefore, the volume of the wooden roller is approximately equal to 50.27 cm³ (when rounded to two decimal places).

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The probability that the jury makes the correct decision that the defendant is guilty is 0.7063.

In order to resolve this issue, we must determine the likelihood that the jury would find the defendant guilty. Let's divide the issue into more manageable components.

We are aware that there is a 0.80 chance that a single juror would choose correctly. If the defendant is found guilty, there is still an 80 percent chance that the jury will reach the right verdict. Consequently, if the defendant is found guilty, there is an 80 percent chance that one jury will reach the right verdict.

The likelihood that at least 10 out of 12 jurors will choose the right course of action may be calculated using the binomial distribution formula. The equation is:

\(P(X \geq k) = 1 - \sum (i=0, k-1) [\frac{i!}{(i!(n-i)!)} ]p^i*(1-p)^(^n^-^i^)\)

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Answer:

I wanna say in the year of 2018.

Step-by-step explanation:

In 2018 the population will reach 40 million.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let us consider x years later it would reach 40 million.

So, 39.1 + 0.35 x = 40

0.35x= 40- 39.1

0.35x= 0.9

x= 2.57

x= 3 years

Hence, In 2018 the population will reach 40 million.

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Answer:

If it walks like a duck and it talks like a duck, then it is a duck.

and

Either it does not walk like a duck or it does not talk like a duck, or it is a duck.

are logically equivalent to each other.

but neither of the two is logically equivalent to

If it does not walk like a duck and it does not talk like a duck, then it is not a duck.

Step-by-step explanation:

Given statements:

Statemen 1:

If it walks like a duck and it talks like a duck, then it is a duck.

Statement 2:

Either it does not walk like a duck or it does not talk like a duck, or it is a duck.  

Statement 3:

If it does not walk like a duck and it does not talk like a duck, then it is not a duck.

Let

Using p = it walks like a duck , q =it talks like a duck, r = it is a duck  the given statements can be written in symbolic form as:

Statement 1:  

p ∧ q → r

The ∧ symbol shows that if both p and q are true then, they imply r. This means both p and q together imply r

Statement 2:

~p ∨ ~q ∨ r

Here the statement p and q are negated and joined using or. So either negation p or negation of q or r (alternative)  

Statement 3:

~p ∧ ~q → ~r

The ∧ symbol shows that if both negation of p and negation of q are true then, they imply r. This means both negated p and negated q together imply negated r

Statement 1:

p ∧ q → r ≡ ~(p∨q) ∨ r               Using conditional equivalence p→q ≡ ~p ∨ q

              ≡ (~p ∧ ~q ) ∨ r          

You can see it is  equivalent to Statement 2 i.e. ~p ∧ ~q → ~r

Hence Statement 1 and Statement 2 are logically equivalent.

Now Statement 3:

~p ∧ ~q → ~r ≡ ~(~p ∧ ~q ) ∨ ~r   Using conditional equivalence p→q ≡ ~p ∨ q

                     ≡ ~(~p ) ∨ ~(~q ) ∨ ~r Using De Morgan's Law ~(p∧q) ≡ ~p ∨~q

                     ≡  p ∨ q ∨ ~r Using Double Negation Law ~(~p)≡p

This shows that Statement 3 is neither logically equivalent to Statement 1 nor logically equivalent to Statement 2.

Proof by truth table is attached. The table shows that the columns for Statement 1 and Statement 2 have same truth values.

Hence

"If it walks like a duck, and it talks like a duck, then it is a duck,"

and

"If it does not walk like a duck, and does not talk like a duck, then it is not a duck,"

are logically equivalent.

The table also shows that column for Statement 3 does not match with either of the columns for Statement 1 and Statement 2. So

If it does not walk like a duck and it does not talk like a duck, then it is not a duck.

is not logically equivalent to Statement 1 and Statement 2.

Answer:

duck walk

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

100 divided by 10 = 10

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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Answer:

D.

Step-by-step explanation:

pint slope form:

(y-y1)=m(x-x1)

do just olug in the point and the slope into the equation

(y-4)= -8/7 (x-4)

Answer: x=3

Step-by-step explanation:

4x-3y=18

4x-3(-2)=18

4x+6=18

(4x=12)/4

x=3

Answer:

z = 5*(1/2)

z = 5/10

---

time switching classes:

w = 7/10

---

y - 6x - z - w = 0

6x = y - z - w

x = (y - z - w)/6

x = (76/10 - 5/10 - 7/10)/6

x = (76 - 5 - 7)/(10*6)

x = (64)/(10*6)

x = (2*2*2*2*2*2)/(2*5*2*3)

x = (2*2*2*2)/(5*3)

x = 16/15

x = 1.0666666666

---

check:

y = 7 + 3/5

y = 7.6

z = 1/2

z = 0.5

w = 7/10

w = 0.7

y - 6x - z - w = 0

6x = y - z - w

x = (y - z - w)/6

x = (7.6 - 0.5 - 0.7)/6

x = 1.0666666666

---

answer:

z = 5*(1/2)

z = 5/10

---

time switching classes:

w = 7/10

---

y - 6x - z - w = 0

6x = y - z - w

x = (y - z - w)/6

x = (76/10 - 5/10 - 7/10)/6

x = (76 - 5 - 7)/(10*6)

x = (64)/(10*6)

x = (2*2*2*2*2*2)/(2*5*2*3)

x = (2*2*2*2)/(5*3)

x = 16/15

x = 1.0666666666

---

check:

y = 7 + 3/5

y = 7.6

z = 1/2

z = 0.5

w = 7/10

w = 0.7

y - 6x - z - w = 0

6x = y - z - w

x = (y - z - w)/6

x = (7.6 - 0.5 - 0.7)/6

x = 1.0666666666

---

answer:

each class is 1.07 hours

Step-by-step explanation:

a. Proportions in both the left-hand and right-hand tails tend to be relatively small.

The correct answer is: a. Proportions in both the left-hand and right-hand tails tend to be relatively small. This is because a normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean. As a result, the tails of the distribution have fewer data points and smaller proportions compared to the center. This is because a normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean.

So, a. Proportions in both the left-hand and right-hand tails tend to be relatively small.

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Answer: (-2, -4)

Step-by-step explanation:

When a point is reflected over the y-axis, multiply the x-coordinate by -1.

Answer:

(-2, -4)

Step-by-step explanation:

When we reflect a point over the y axis, all we do is change the sign of the x variable. As you see, that is what I did above.

Given

The data,

To find:

1) The equation of the line of best fit.

2) The time when the player can do 22 leg press repetitions.

Explanation:

It is given that,

That implies,

The equation of the line of best fit is given by,

Then,

Therefore,

Also,

Also,

Also,

That implies,

And,

Hence, the equation of the best line of fit is,

And, the time taken when L=22 is,

Hence, the time taken to complete 22 Leg press repetition is 11.6.

Answer: 138 women

Step-by-step explanation:

6 + 5 = 11

253/11 = 23

(men) 5 x 23 = 115

(women) 6 x 23 = 138

adds up to 253 so it is correct.

Answer:

it would cost 14 dollars

Step-by-step explanation:

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Answer:   You can set the equations equal to each other since they both equal Y, and then solve for x.

Or set the bottom equation equal to X (so x=y-1) and then substitute that for the x in the first equation.

Example:

Y=(Y-1)^2 - 2(Y-1) + 3

Y=(Y^2 -1Y -1Y + 1) - 2Y + 2 + 3

Y= Y^2 -2Y +1 -2Y +5

Y= Y^2 -4Y +6

0= Y^2 -5Y +6

And then factor:

0= Y^2 -3Y -2Y +6

0= Y(Y-3) + -2(Y-3)

0= (Y-2) (Y-3)

Y= 2 or 3

And then take those numbers and plug them into the bottom equation and solve for X. You should get something like (2,3) and (1,2) as answers.

This should be the way to do it. I might have made a multiplication or addition mistake on the way but the process should be the same. Please double check my work and let me know if I did indeed make a mistake.

Thank you, hope this helps :)

Answer:

y = (− 3 x/ 2 )− 1

Step-by-step explanation:

Answer:

3, 1, 2, 4, 5, 6

Step-by-step explanation:

i gave it to you in order from top to bottom

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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______________________________

 - When solving problems like these (One-Step Equations,) to get x alone you must do the opposite of what you see.

- In this situation we have a positive 3. So to get rid of both numbers you do the opposite: Opposite of +3 is -3. So you subtract 3 from each number.

______________________________

9514 1404 393

Answer:

  23.37 cm

Step-by-step explanation:

1 inch is 2.54 cm, so 9.2 inches is ...

  (9.2)(2.54 cm) = 23.368 cm ≈ 23.37 cm

Answer:

No solution

Step-by-step explanation:

It equals a negative so there is no solution

After approximately 113 minutes, there will be only 40 bacteria remaining.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, then

N₀ = 500, and N(t) = 350 when t = 16 minutes

Substitute the given values and solve for the half-life.

N(t) = N₀(1/2)^(t/T)

350 = 500(1/2)^(16/T)

T = 31.09 minutes

Using the formula, solve for t when n(t) = 40.

N(t) = N₀(1/2)^(t/T)

40 = 500(1/2)^(t/31.09)

t = 113.30 minutes

t ≅ 113 minutes

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The probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

Given data;

Five games are played. Each play has a probability of winning, P(W), of 0.4, and a probability of losing, P(L), of 0.6. The results of the plays are probabilistically independent.

To get the probability of the sequence W, W, L, L, W.

Now,

As the results are probabilistically independent,

The probability of the sequence is;

→ [(P(W)]³ + [(P(L)]²

→ (0.4)³ + (0.6)²

Hence, the probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

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h = 0.75m + 49.5 equation models Jeremy’s growth spurt, where h represents his height in inches, and m represents time in months.

Finding the product of two or more integers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

Jeremy was 49.5 inches tall when this picture was taken, and every month after then, his height has risen 0.75 inches.

h = 0.75m + 49.5, simulates Jeremy's growth spurt, where h represents his height in inches and m indicates time in months.

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The slope - intercept equation of a line that would pass through (1,-2) and has an undefined slope, is y = -2 x

The slope - intercept equation takes the form:

y = mx + b

m = slope

b = y - intercept

When the slope is undefined, it means that there is no y - intercept as the slope is a vertical line which crosses the x - axis alone. The slope would therefore be :

y = mx

- 2 = 1 x

m = - 2

The slope - intercept form is:

y = -2 x

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Answer:

3x(x + 3) = 0

Step-by-step explanation:

3x² + 9x = 0 ← factor out common factor of 3x from each term on the left

3x(x + 3) = 0 ← factored form

Answer:

Step-by-step explanation: