Part 3: Hitting the baseball over the lights


Meanwhile at the ballpark Juan was practicing his hitting while talking to some friends. He started telling them how he hit the ball over the 50 foot light tower yesterday.



The formula for this hit is h(x) = -16xsquared + 60x + 4 , where h is the height of the ball and x is the number of seconds the ball is in the air.



How can Juan provide proof to the friends that he actually hit the ball over the tower?








How high did Juan actually hit the ball? Is Juan able to mathematically back up how high he says he hit the ball?

9514 1404 393

Answer:

  A'(-4, 6)

Step-by-step explanation:

When dilation is about the origin, the image points are the preimage points multiplied by the scale factor.

  A' = (2/3)A = (2/3)(-6, 9)

  A' = (-4, 6)

Answer:

(-4, 6)

Step-by-step explanation:

The acceleration of the particle at 4 seconds is approximately 3.97 ft/sec^2.  "None of these".

To find the acceleration of the particle at 4 seconds, we need to take the second derivative of the position equation with respect to time. The first derivative gives us the velocity, and the second derivative gives us the acceleration.

So, first we find the first derivative of the position equation:

s'(t) = 4t + 1/(2*sqrt(t))

Then, we find the second derivative:

s''(t) = 4 - 1/(4*t^(3/2))

Now we can evaluate the acceleration at t = 4 seconds:

s''(4) = 4 - 1/(4*4^(3/2))

s''(4) = 4 - 1/32

s''(4) = 127/32

s''(4) = 3.96875 ft/sec^2 (rounded to the nearest hundredth)

Therefore, the acceleration of the particle at 4 seconds is approximately 3.97 ft/sec^2.

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The acceleration of the particle at 4 seconds is 15.75 ft/sec2 which is option B.

To find the acceleration, we need to take the second derivative of the position equation with respect to time:

s(t) = 2t^2 + √t

v(t) = s'(t) = 4t + 1/(2√t)

a(t) = v'(t) = 4 - 1/(4t^(3/2))

Substituting t = 4, we get:

a(4) = 4 - 1/(4(4)^(3/2)) = 16 - 1/32 = 511/32 ≈ 15.97 ft/sec^2

Therefore, the answer is approximately 15.97 ft/sec^2, which is closest to option (b) 15.75 ft/sec^2.

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Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Answer: 571.11111...(Fraction: 9/28)

Step-by-step explanation:

5,140÷9 = 571.11111...

A) horizontal asymptote: y = 7 B) vertical asymptote: x = -4, 5 is the required answers for horizontal and vertical asymptotes of the curve.

The horizontal asymptote of a curve is a horizontal line that the curve approaches as x approaches infinity or negative infinity. The vertical asymptote of a curve is a vertical line that the curve approaches but never crosses as x approaches a certain value. In this case, the horizontal asymptote is found by letting x approach infinity in the fraction and observing what the value of y approaches. In the limit as x approaches infinity, the x^2 term dominates and thus y approaches 7, which is the horizontal asymptote. To find the vertical asymptote, we find the values of x where the denominator equals 0 and the numerator is not equal to 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5. Thus, the vertical asymptotes are x = -4 and x = 5. To find the vertical asymptotes, we look for the values of x where the denominator of the function equals 0 and the numerator does not equal 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5, which means that x = -4 and x = 5 are the vertical asymptotes of the function. These values of x represent the values at which the function is undefined, and as x approaches these values from either side, the value of the function approaches positive or negative infinity.

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Answer:

825 miles

Step-by-step explanation:

Divide starting number by nine to get 55. Then multiply 55 by 15 to get 825 miles

Answer:

A 825

Step-by-step explanation:

Answer: $ 251.93

Step-by-step explanation:

Answer:

x ≥ -2

Step-by-step explanation:

The elements in order of greatest mass are hydrogen, carbon, oxygen, silver, and gold.

List the elements in ascending order of mass per atom, from least to most.) of Element Weight per atom Carbon 1.995 X 10-23 0 Gold 3.272 X 10-22 0 Hydrogen 1.674 X 10-24 6 2.658 x 10-23 6 oxygen Silver 1.792 X 10-22 0

Scientific notation is used to write the mass. Large numbers are expressed in smaller quantities using scientific notation.

For instance:

The elements in order of greatest mass are hydrogen, carbon, oxygen, silver, and gold.

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

The probability that a randomly

selected point within the circle falls in the

red-shaded square is 63.7%.

A figure is shown, in which a square is inscribed in a circle. To find the probability that a randomly selected point within the circle falls in the red shaded area (Square).

radius  = 7cm

side of square = 7√2 cm

Area of the circle = πr²

                             = 3.14 * 7²

                             = 153.86 cm²

Area of the square = side * side

                               =  7√2 * 7√2

                               = 98 cm²

= Area of square / Area of the circle

= 98 / 153.86

=  63.7%

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Answer:

63.7

Step-by-step explanation:

I entered that and got it right

-2(-3)+18=24

6+18 = 24

24 = 24

6(-3) +9=-13

-18+9 = -13

-9 ≠ - 13

4(-3)-9=-21

-12 -9 =-21

-21 = -21

Answer:

1.35 square miles I think

Step-by-step explanation:

Answer:

Julie travels 1.35 miles on the same path every day.

Area = 1.35 miles

Step-by-step explanation:

What we know so far:

- It takes 2.4 miles to walk from house to school.

- The distance from the park to school is 2.1 miles.

- It takes 1.5 miles to walk from your house to the park.

The area of a triangle is 0.5 or 1/2 x base x height.

As a result, 1.5 x 1.8 divided by two equals 1.35.

So, Julie walks 1.35 miles every day on the same route.

Area = 1.35 miles

Hope this helps! :D Brainliest?

Step-by-step explanation:

6b x>=1

6c y>7

7a x>3

7b -2<=2x<6

-1<=x<3

answer:-1,0,1,2,3

Statistical inference is the process of using data from a sample to make generalizations or draw conclusions about a larger population.

Based on the sample data, assumptions are made about the fundamental traits of the population, and the uncertainty in those assumptions is quantified using statistical techniques.

Because it enables us to forecast the future and make judgements based on incomplete data, statistical inference is crucial. For instance, with a sample of data, it enables us to confidently estimate population parameters such as averages and proportions. This can be helpful in a variety of contexts, including marketing analysis, surveys of public opinion, clinical trials, and manufacturing quality control.

By comparing the results of several groups or treatments, statistical inference also enables us to assess the efficacy of interventions or treatments.This can inform decisions about which treatments are most effective or which interventions should be implemented.

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Answer:

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

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

The given drug experiment is an example of observation.

There are three major types of statistical studies :

Given is that a doctor gives 10 patients Drug A and 10 patients Drug B and records the differences.

Giving 10 patients Drug A and 10 patients Drug B and then recording the differences is an example of observation.

Therefore, the given drug experiment is an example of observation.

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Answer:

we cant see the picture

Step-by-step explanation:

Answer:25.3

Step-by-step explanation:

Because your adding 25 to 0 and leaving the decimal point and taking away 0 from 30

Answer:

Step-by-step explanation:

A plane can be named by a capital letter, often written in script, or by the letters naming three non-collinear points in the plane. For example, the plane in the diagram below could be named either plane ABC or plane P .

P(A and B) is equal to 6.

To find P(A and B), we can use the formula:

P(A and B) = P(A) + P(B) - P(A U B)

Given the information:

P(A U B) = 32 (the probability of either event A or event B occurring)

Universal set contains 52 elements (total number of possible outcomes)

P(A intersection B) = 6 (the probability of both event A and event B occurring)

P(A) = 12 (the probability of event A occurring)

P(B) = 26 (the probability of event B occurring)

We can substitute the known values into the formula:

P(A and B) = P(A) + P(B) - P(A U B)

P(A and B) = 12 + 26 - 32

Simplifying the expression:

P(A and B) = 38 - 32

P(A and B) = 6

Therefore, P(A and B) is equal to 6.

The result indicates that the probability of both event A and event B occurring simultaneously is 6 out of the total number of possible outcomes in the universal set. It means that out of the 52 elements in the universal set, 6 of them satisfy the conditions of both A and B.

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done

plz mark me brainliest ok

plz follow me

Part A: The measures of center in Mountain View School, mean = 4.75, median = 4.5 and Bay Side School, mean = 5.5, median = 4.5

Part B: The measures of variability: Mountain View School, Range= 9 IQR= 4,  Bay Side School, Range= 10 IQR= 3

Part C: Bay Side School would be the better choice.

Part A: Measures of Center

To calculate the measures of center, we will determine the mean and median for each school.

Mountain View School:

Mean = (0 + 5 + 6 + 8 + 9 + 8 + 2 + 0) / 8 = 38 / 8 = 4.75

Median = (4 + 5) / 2 = 4.5

Bay Side School:

Mean = (10 + 2 + 4 + 5 + 6 + 8 + 8 + 7 + 6 + 5 + 5 + 4 + 4 + 3 + 1 + 0) / 16 = 88 / 16 = 5.5

Median = (4 + 5) / 2 = 4.5

Part B: Measures of Variability

To calculate the measures of variability, we will determine the range and interquartile range (IQR) for each school.

Mountain View School:

Range = 9 - 0 = 9

IQR = (6 - 2) = 4

Bay Side School:

Range = 10 - 0 = 10

IQR = (6 - 3) = 3

Part C: Choice based on Class Size

If you are interested in a larger class size, Bay Side School would be the better choice. The mean class size at Bay Side School is 5.5, while at Mountain View School it is 4.75. The range of class sizes at Bay Side School is also larger (10) compared to Mountain View School (9). This indicates that there is a greater variation in class sizes at Bay Side School, providing a higher likelihood of finding larger class sizes. However, it's important to consider other factors such as teaching quality, resources, and overall educational environment before making a final decision.

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Answer:

Induction

Step-by-step explanation:

Induction reasoning refers to conjectures which is what you will need for this

The Inductive reasoning allows to use observation to find the next three

values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

For given example,

We have been given the number pattern 1, 4, 7, 10, . . .

Here, 4 - 1 = 3                             ..................(i)

7 - 4 = 3                                       ..................(ii)

10 - 7 = 3                                      ..................(iii)

From (i), (ii) and (iii),

the common difference between consecutive terms is 3.

The next three values would be,

10 + 3 = 13

13 + 3 = 16

16 + 3 = 19

So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .

Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

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Answer:

$383,500.68  

Step-by-step explanation:

The amount needed is the present value of the $30,000 that Anna will withdraw for 25 years compounded at 6% annually

=pv(rate,nper,pmt,fv)

rate is the annual rate of 6%

nper is the number of years of withdrawal which is 95-70=25

pmt is the amount of annual withdrawal which is $30,000

fv is the amount of withdrawals which is unknown

=pv(6%,25,-30000,0)=$383,500.68  

The amount of she required at 70 is $$383,500.68   which gives her the benefit of withdrawing $30,000 per year at retirement

Answer:

The answer is t=8

Step-by-step explanation:

simplify both sides or the equation, then isolate the variables

Answer:

t = 8

Step-by-step explanation:

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 6 to both sides of the equation:

1/4t + (-6) = -4

1/4t - 6 = -4

1/4t - 6 (+6) = -4 (+6)

1/4t = -4 + 6

1/4t = 2

Next, multiply 4 to both sides of the equation to isolate the variable, t:

4 * (1/4)t = (2) * 4

t = 2 * 4

t = 8

t = 8 is your answer.

~

Step-by-step explanation:

\(\qquad\quad {:}\leadsto\sf \dfrac {2x (x+7)}{\cancel{(x-3)}}\times {\dfrac {(x-9)\cancel{(x-3)}}{8x^2 (x+7)}}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {2x\cancel{(x+7)}}{x-3}\times {\dfrac {x-9}{8x^2 \cancel{(x+7)}}}\)

\(\qquad\quad {:}\leadsto\sf \dfrac{2x (x-9)}{8x^2}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {\cancel{2x}^2-18x}{\cancel{8x}^2}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {18x}{4}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {9x}{2}\)

\(\qquad\quad {:}\leadsto\sf 4.5x \)

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2