The quadratic equation y = - 1612 +40t +2 represents the height of a projectile, y ,in feet, at a particular time, 1, in seconds. For what interval or intervals of time will the projectile be above 18 feet?

Step-by-step explanation:

I'm thinking of a number, let's call it X, between 0 and 10 (inclusive). If I don't tell you anything else, what would you imagine is the probability that X=0? That X=4? Assuming that I don't have any preference for any particular number, you'd imagine that the probability of each of the eleven integers 0,1,2,…,10 is the same. Since all the probabilities must add up to 1, a logical conclusion is to assign a probability of 1/11 to each of the 11 options, i.e., you'd assume that the probability that X=i is 1/11 for any integer i from 0 to 10, which we write as

Pr(X=i)=111for i=0,1,2,…,10.

Implicit in this description is the assumption that the probability that X is any other number x is zero. (Here we make a distinction between the random number X and the variable x which can stand for any fixed number.) We can write this implicit assumption as

Pr(X=x)=0if x is not one of {0,1,2,…,10}.

What would change if instead I told you that I was thinking of a number X between 0 and 1 (inclusive)? You might assume that I was thinking of either the number 0 or the number 1, and you'd assign a probability 1/2 to both options. Or, you might guess that I had more than two options in mind. There was nothing in what I said that forces you to conclude that I was thinking of an integer. Maybe I was thinking of 1/2, or 1/4, or 7/8. Once you start going down that road, the possibilities are endless. I could be thinking of any fraction between 0 and 1. But who said I was limiting myself to rational numbers? I could even be thinking of irrational numbers like 1/2√ or π/5. If we allow the possibility that the number X could any real number in the interval [0,1], then there are clearly an infinite number of possibilities. (Of course, I could have been thinking of non-integers for the number betwen 0 and 10 as well, but most people would think I was referring to integers in that case.)

Since we don't want to assume that I am favoring any particular number, then we should insist that the probability is the same for each number. In other words, the probability that the random number X is any particular number x∈[0,1] (confused?) should be some constant value; let's use c to denote this probability of any single number. But, now we run into trouble due to the fact that there are an infinite number of possibilities. If each possibility has the same probability c and the probabilities must add up to 1 and there are an infinite number of possibilities, what could the individual probability c possibly be? If c were any finite number greater than zero, once we add up an infinite number of the c's, we must get to infinity, which is definitely larger than the required sum of 1. In order to prevent the sum from blowing up to infinity, we must have c be infinitesimally small, i.e., we must insist that c=0. The probability that I chose any particular number, such as the probability that X equals 1/2, must be equal to zero. We can write this as

Pr(X=x)=0for any real number x.

What went wrong here? We know all probabilities must not be zero, because we know that the total probability must add up to one. In fact, were know that, somehow, there must be something special for the probability of numbers 0≤x≤1. We know that X is somewhere in that interval with probability one, and the probability that X is outside that interval is zero.

Based on the direct variation relationship between x and y, where y is 33 when x is 11, we find that y is 36 when x is 12.

If x and y vary directly, it means that they have a constant ratio between them. We can express this relationship as:

y = kx,

where k is the constant of variation.

To find the value of k, we can use the given information that when x is 11, y is 33. Substituting these values into the equation, we have:

33 = k * 11.

Dividing both sides by 11, we find:

k = 3.

Now that we have determined the constant of variation, we can find y when x is 12 by substituting this value into the equation:

y = 3 * 12.

Evaluating this expression, we get:

y = 36.

Therefore, when x is 12, y will be 36.

Based on the direct variation relationship between x and y, where y is 33 when x is 11, we find that y is 36 when x is 12.

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1) The account balance in bank A is $320 after 1 month,  $540 after 1 year, $2700 after 10 years. The account balance in bank B is 130 after 1 month,  $460 after 1 year, $3700 after 10 years.

2) The model equation for bank A is y = 300 + 20x

The model equation for bank A is y = 100 + 30x

4)The account balances will be same after 20 months.

5) In bank A, $2400 grows in the account and in bank B $3600 grows in the account.

6) More important thing is saving rate.

What is the saving rate?

The savings rate, which can be calculated for an economy as a whole or at the individual level, is the proportion of personal savings to disposable personal income.

Given that, in bank A $20 deposit on each month.

Thus after 1 month the balance in bank A will be $(300 + 20) =$320.

After 1 year the balance in bank A will be $(300 + (12×20)) =$540.

After 10 years the balance in bank A will be $(300 + (10 × 12×20)) =$2700.

In bank B, $1 deposit on each day.

Thus after 1 month the balance in bank B will be $(100 + 30) =$130.

After 1 year the balance in bank A will be $(100 + (12×30)) =$460.

After 10 years the balance in bank A will be $(100 + (10 × 12×30)) =$3700.

The model equation of bank A will be:

y = 300 + 20x .....(i)

The model equation of bank B will be:

y = 100 + 30x ....(ii)

Where x is the number of months.

Equate equation (i) and (ii)

300 +20x = 100 + 30x

300 -100 = 30x - 20x

10x = 200

x = 20

Therefore the account balance will be equal after 20 months

The intersection point of both curves is (20,700).

After 20 months the balance will be equal.

The money grow in bank A is $(2700 - 300) = $2400 in 10 years

The money grow in bank A is $(3700 - 100) = $3600 in 10 years.

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The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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Given :

A triangle, ABC, has angle measures of 45°, 45°, and 90º and two congruent (equal) sides.

So, the triangle will be classified as : isosceles right triangle

Because, it has an angle = 90, so it will be a right triangle

And there are 2 congruent sides, so, it will be isosceles triangle

so, the answer is : Isosceles right triangle

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

Answer:

5

Step-by-step explanation:

since 5 is the only common factor of the three numbers

then that is our hcf

The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

  7.8 pounds

Step-by-step explanation:

The relation between pounds and kilograms is proportional:

  \(\dfrac{\text{books}}{3.5\text{ kg}}=\dfrac{1\text{ lb}}{0.45\text{ kg}}\qquad\text{pounds to kg proportion}\\\\\text{books}=\dfrac{(3.5\text{ kg})(1\text{ lb})}{0.45\text{ kg}}=\dfrac{3.5}{0.45}\text{ lb}\qquad\text{multiply by 3.5 kg}\\\\\boxed{\text{books}\approx7.8\text{ lb}}\)

The stack of books weighs about 7.8 pounds.

The inequality that represents p, the number of people the theater can seat is p ≤ 25

From the question, we have the following parameters that can be used in our computation:

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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Answer:

2 7/12

Step-by-step explanation:

5 1/3 − 2 3/4

=16/3 − 2 3/4

=16/3 − 11/4

=31/12

=2 7/12

Answer:

Step-by-step explanation:

double the amount of apples is greater than 8

Hope that helps!

Answer:

243 ft^3

Step-by-step explanation:

The volume of a triangular prism is the triangular base times the height.

To get the area of the triangle, multiply the base time height and divide by 2.

9*6/2=27

Now multiply by the height

27*9=243

Answer: 243 ft^3

Answer:

243ft^3

Step-by-step explanation:

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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In the given problem, approximately 20.03 gallons of coating  is required.

To find the area of the path between two concentric circles, we need to calculate the distinctness between the regions of the outer and central circles.

The formula for the area of a circle is A = πr², place A represents the region and r is the radius.

First, calculate the radii of the inner and external circles:

The inner width of the path is 14 yards, so the radii of the inner circle is half of that: r_central = 14/2 = 7 yards.

The outer width of the path is 20 yards, so the range of the outer circle is half of that: r_external = 20/2 = 10 yards.

Now we can calculate the area of the inner and external circles:

A_inner = π * (r_central)²

= π * 7²

≈ 153.94 square yards (rounded to two having ten of something places)

A_outer = π * (r_external)²

= π * 10²

≈ 314.16 square yards (rounded to two having ten of something places)

To find the area of punching competition-shaped course, we subtract the extent of the inner circle from the field of the outer circle:

A_course = A_outer - A_central

= 314.16 - 153.94

≈ 160.22 square yards (rounded to two having ten of something places)

Since one unit of capacity for liquids of coating can cover 8 square yards, we separate the area of the course by 8 to determine the number of gallons wanted:

Number of gallons = A_path / 8

≈ 160.22 / 8

≈ 20.03 gallons (curved to two decimal places)

Therefore, nearly 20.03 gallons of coating are wanted to cover the ring-formed path about the pool.

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Answer:

-4(5)+1(-2*-5+5*3)

Step-by-step explanation:

-20+1(10+15)

-19(25)

-475

Answer:

5

Step-by-step explanation:

Given :- a = -2 , b = 5 , c = -5 & d = 3

Solution :-

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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Answer:22 centimeters

Step-by-step explanation:

Answer:

The scale factor of AABC to ADEF is A). 1/6

The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.

To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.

Expanding the first term, we get 4x^2 + 4x.

Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.

Combining like terms, we obtain -3x^2 - 4x - 32.

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Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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Answer:

4x=0 x=0

Step-by-step explanation:

Answer:

$ 1,593.75

Step-by-step explanation:

this is the advanced sale calculation if you wan a simple one i can write that in the comments! hope this help you! :D

We have 4 students that read both genres, 8 that reads mysteries and 12 read science fiction. If we subtract those students that read both from the amount of students that reads mysteries, we're going to get the amount of students that ONLY read mysteries.

The same is valid to find those that ONLY read science fiction.

We have 4 students that read both genres, 4 that read only mysteries, and 8 that read only science fiction. The amount of students that read either of them is given by the sum of those 3 quatities.

The probability of taking one of them at random is given by the ratio between the amount of students that read either of them(16) by the total amount of students(30).

Option A is correct -- 19.9

from figure :

AB=\(5+\frac{9}{2}\)

    =9.5

From Pythagoras theorem:

\(x^{2} =(9.5)^2} +1\)

\(x^{2} =91.25\)

\(x=19.9\)

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as an equation:

\(a^{2} +b^{2}=c^{2}\)

where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The Pythagorean theorem is a very useful tool for solving problems involving right triangles, such as finding the distance between two points or the height of a ladder. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Answer:

Step-by-step explanation:

what is the sloution to this question x- 16=-8

x - 16 = -8

x = -8 + 16

x = 8

----------------

check

8 - 16 = -8

-8 = -8

the answer is good

The result of this equation is x = 8

-

To solve this equation - we will:

\( \\ \large \sf x- 16=-8\)

\( \large \sf x=-8 + 16\)

\( \green{ \boxed{ \large \sf x=8}}\)

So, the answer of this equation is x = 8