Two parachutists jump at the same time from two different planes as part of an aerial show. The height h1of the first parachutist in feet after t seconds is modeled by the function h1 = -16t2 + 5000. The height h2 of the second parachutist in feet after t seconds is modeled by the function h2 = -16t2 + 4000.
a. What is the parent function of the two functions given? b. Describe the transformations needed to obtain the graph of h1 from the parent
function.
c. Which parachutist will reach the ground first?

Answer:

Infinite many solutions

Step-by-step explanation:

9d − 8 = –8 + 9d

* add 8 to each side *

-8 + 8 cancels out

-8 + 8 cancels out

we're left with 9d = 9d

When the same number/variable is on each side of the equal sign there is an infinite amount of solutions

The coefficient of determination is 1.

Given

Total Sum of squares (SST) = 90

Sum of squares due to error (SSE) = 0

We have to find coefficient of determination.

The correlation of determination is the ratio of the explained variation to the total variation.

The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.

The coefficient of determination is also called r-squared or r-square.

Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.

Coefficient of determination can be found with the following formula:

Formula of coefficient of determination :

\(R^{2} = 1 - \frac{SSE}{SST}\)

= 1 - \(\frac{0}{90}\)

= 1 - 0

= 1

\(R^{2}\) = 1

Therefore,

The coefficient of determination is 1.

Find out more information about coefficient of determination here

https://brainly.com/question/28046641

#SPJ4

(2x–5)° + 45° = 180° (sum of consecutive interior angles

=> 2x + 40 = 180

=> 2x = 180– 40

=> x = 140 /2

=> x = 70

The required value of the x is 70 in the measures of the angle.

Given that Line m and n are parallel lines and intersect by a transversal line l.

When a transversal line intersects two other lines, it creates eight angles, four of which are called exterior angles and four are called interior angles.

From the sum of consecutive interior angles we have;

(2x–5)° + 45° = 180°

2x + 40 = 180

2x = 180– 40

x = 140 /2

x = 70

Learn more about lines here:

brainly.com/question/2696693

#SPJ4

In order to determine if a function is linear or exponential, you can observe the relationship between the function's input and output values.

For a linear function, the output values increase or decrease at a constant rate as the input values change. In other words, the function has a constant slope when graphed. You can check linearity by calculating the differences between consecutive output values and verifying if they remain the same. If the differences are constant, the function is linear.

On the other hand, an exponential function shows a constant ratio between the output values and the input values. This means that as the input values increase or decrease by a constant factor, the output values also increase or decrease by the same factor. You can check for exponential behavior by calculating the ratio between consecutive output values. If the ratios are constant, the function is exponential.

It is important to graph the function and analyze its behavior over a range of input values to confirm whether it is linear or exponential.

To know more about functions, refer here:

https://brainly.com/question/31215081#

#SPJ11

(a)2 sin 14° cos 14° = sin 28°

(b)2 sin 30° cos 36° = sin 72°

(c)2 tan 7° 1 - tan 7° = 2tan 14°

(d)2 tan 7° 1-tan2 7° = 2tan 14°

Trigonometric ratios of double angles (2θ) are expressed in terms of trigonometric ratios of single angles (θ) using double angle formulae. The Pythagorean identities are used to create certain alternative formulas, while the double angle formulas are special cases of (and are thus derived from) the sum formulas of trigonometry.

(a) Using the Double Angle Formula for sin 2θ:

2 sin 14° cos 14° = sin 28°

(b) Using the Double Angle Formula for cos 2θ:

2 sin 30° cos 36° = sin 72°

(c) Using the Double Angle Formula for tan 2θ:

2 tan 7° 1 - tan 7° = 2tan 14°

(d) Using the Double Angle Formula for tan 2θ:

2 tan 7° 1-tan2 7° = 2tan 14°

To learn more about half angle formula: https://brainly.com/question/14308845

#SPJ11

Using the cosine rule, the length of the hour hand is found to be 9cm, making the length of the minute hand 12cm.

Let's first determine the distance traveled by each hand, then we can set up an equation to solve for the length of the minute hand. At 9 o'clock, the hour hand is pointing directly at the 9, and the minute hand is pointing directly at the 12.

The minute hand travels a full circle (360 degrees) in 60 minutes or 1 hour, while the hour hand travels a full circle in 12 hours or 720 minutes. Therefore, the minute hand has traveled 90 degrees (1/4 of a full circle) from the 12 to the 9, and the hour hand has traveled 270 degrees (3/4 of a full circle) from the 12 to the 9.

Let's denote the length of the hour hand as "x". Then, the length of the minute hand is "x + 3" (since it is 3cm longer). We can use the cosine rule to find the distance between the tips of the hands:

\(d^2\) = \(x^2 + (x+3)^2 - 2x(x+3)*cos(270)\)

where d is the distance between the tips of the hands at 9 o'clock. Simplifying this expression, we get:

\(225 = 2x^2 + 6x + 9\)

\(2x^2 + 3x - 108 = 0\)

So, using the quadratic formula, we can find the value of "x":

\(x = (-3 + \sqrt{ (3^2 - 42(-108)})) / (2*2)\)

(We take the positive root because the length of a clock hand can't be negative)

x = 9

Therefore, the length of the minute hand is x + 3 = 12 cm.

Learn more about expresion here:

https://brainly.com/question/27856217

#SPJ4

The domain  -∞ ≤ x ≤ +∞ and range is -3≤ x ≤ 1.

All input values shown on the x-axis make up a graph's domain. The y-axis on a graph represents the possible output values, or range.

The domain would be determined by the set of all x-coordinates at all curve points, and the range would be determined by the set of all y-coordinates at all curve points. Both a set and an interval can be used to express each domain and range.

According to the domain is

from -∞ on left side and reaches to +∞ on the right side

So, domain is -∞ ≤ x ≤ +∞

Now, the range of the graph is -3 to 1

So, -3≤ x ≤ 1

Learn more about domain and range here:

https://brainly.com/question/28135761

#SPJ1

Answer:514 grams  of rice is in each of the 10 containers

Step-by-step explanation:

Amount of rice bought  =6 kilograms of rice.

6 kilograms =6000grams

Amount of rice reaming after filling 10 containers =860g

Amount used to fill up the containers ==6000grams-860grams =5140 grams

To get the amount filled inside the 10 containers since same amount is in each, we divide by 10

5140 grams/10=514 grams

Using  cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).

To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.

In cylindrical coordinates, the solid e can be defined as follows:

Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).

Angle: θ ranges from 0 to 2π (full revolution around the z-axis).

Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.

To convert the integral, we need to express x^2 in terms of cylindrical coordinates:

x^2 = (rcosθ)^2 = r^2cos^2θ

The integral in cylindrical coordinates becomes:

∫∫∫ (r^2cos^2θ) r dz dr dθ

Now we can determine the bounds for the variables:

r ranges from 0 to 2.

θ ranges from 0 to 2π.

z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.

Substituting the bounds and integrating, we can evaluate the integral to find the desired result.

To know more about cylindrical coordinates refer here:

https://brainly.com/question/30394340

#SPJ11

Answer:

The corresponding angles are congruent. The corresponding sides all have the same ratio.

Step-by-step explanation:

Congruent means the angles are equal to each other. There are three pairs of angles. "Matching angles" (not a mathematical term) will be the same/equal/congruent.

The sides would only be same/equal/congruent if the triangles were congruent. For similar triangles, you can find a ratio of sides like big/little or little/big and if you set up the ratios of the matching sides, the ratio will be the same for all three pairs of sides. See image for example.

The answer to the question is C, which is integers 4,5 or -4,-3.

Let's call the first integer x and the second integer x+1 (since they are consecutive).
According to the problem, we can set up the following equation:
x(x+1) = x + (x+1) + 19
We can simplify this equation by expanding the left side and combining like terms on the right side:
x^2 + x = 2x + 20
Now we can move all the terms to one side and get a quadratic equation:
x^2 - x - 20 = 0
We can factor this equation as (x-5)(x+4) = 0, which means the solutions for x are 5 and -4.
Therefore, the two consecutive integers are either 4,5 or -4,-3.
The long answer includes all the steps of solving the quadratic equation:
x^2 - x - 20 = 0
We can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a=1, b=-1, and c=-20.
x = (1 ± √(1 - 4(1)(-20))) / 2(1)
x = (1 ± √81) / 2
x = (1 ± 9) / 2

The two solutions for x are 5 and -4.
Therefore, the two consecutive integers are either 4,5 or -4,-3.
The product of two consecutive integers is 19 more than their sum. To find the integers, let's represent them as x and x+1.

To know more about integer visit:

https://brainly.com/question/15276410

#SPJ11

A. x is approximately a binomial random variable due to independent trials with two outcomes and a fixed probability of success.

b. p ≈ 0.59

c. μ ≈ 13.57, σ ≈ 2.23

d. P(x ≥ 1) ≈ 0.997.

A. The variable x is approximately a binomial random variable because the experiment consists of independent trials with two possible outcomes and a fixed probability of success.

b. The estimated probability (p) for the binomial random variable is 0.59.

c. The mean (μ) and standard deviation (σ) of x, the number of physicians who do not recommend medicine as a career in a sample of 23, are approximately 13.57 and 2.23, respectively.

d. The probability that at least one physician does not recommend medicine as a career in the sample is approximately 0.997.

learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

the complete question is:

Many primary care doctors feel overworked and burdened by potential lawsuits. In fact, a group of researchers reported that 59 % of all general practice physicians do not recommend medicine as a career. Let x represent the number of sampled general practice physicians who do not recommend medicine as a career. Complete parts a through d. a. Explain why x is approximately a binomial random variable. A. The experiment consists of n identical, dependent trials, with more than two possible outcomes. The probability that an event occurs varies from trial to trial. B. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S remains the same from trial to trial. The variable x is the number of S's in n trials. C. The experiment consists of n identical, dependent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). D. The experiment consists of n identical, independenttrials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S varies from trial to trial. The variable x is the number of F's in n trials. b. Use the researchers' report to estimate p for the binomial random variable. pequals nothing (Type an integer or a decimal.) c. Consider a random sample of 23 general practice physicians. Use p from part b to find the mean and standard deviation of x, the number who do not recommend medicine as a career. mu equalsnothing(Round to two decimal places as needed.) sigma equalsnothing(Round to three decimal places as needed.) d. For the sample of part c, find the probability that at least one general practice physician does not recommend medicine as a career. P(xgreater than or equals 1)equalsnothing (Round to three decimal places asneeded.)

Answer:

5 ft

Step-by-step explanation:

not sure what the wuestion is but using the formula. A^2 + B^2 = C^2 we find that 100 / 4 = 25 and the square root of 25 is 5

m=2

because in the other equation, the digit next to x is 2 so m must be 2

Functiοn mοdels the relatiοnship between the cοncentratiοn οf the medicatiοn in milligrams is P(t) = 25.5(0.838)ˣ and number οf hοurs since the medicatiοn was taken, t is 2 hοurs.

The cοncentratiοn οf the drug in the blοοdstream at t = 8 hοurs is 24 mg/L. Frοm t= 0 tο t= 2 hr, the cοncentratiοn is increasing and after 2 hrs the cοncentratiοn is decreasing. The level οf the drug in the blοοdstream reaches its maximum value at t=2 hrs , and  the cοncentratiοn in the blοοdstream at that time is 25.5 mg/L.

\After the drug reaches its maximum level in the blοοdstream, 8 additiοnal hοurs are required fοr the level tο drοp    tο 16 mg/L. As at t= 10 hrs, cοncentratiοn is 16 mg/L and maximum cοncentratiοn is at t=2hrs. Sο, additiοnal hοurs= 10-2=8 hrs

P(t) = 25.5( 1-16.2%)ˣ

= 25.5((100 - 16.2)/100)ˣ

= 25.5(83.8/100)ˣ

P(t) = 25.5(0.838)ˣ

Hence, functiοn mοdels the relatiοnship between the cοncentratiοn οf the medicatiοn in milligrams is P(t) = 25.5(0.838)ˣ and number οf hοurs since the medicatiοn was taken, t is 2 hοurs.

To know more about concentration check the below link:

https://brainly.com/question/29151650

#SPJ1

Complete question:

9. A patient has taken 25.5 mg of a prescribed medication. The concentration of the medication in the body decreases at a rate of 16.2% per hour.

Which function models the relationship between the concentration of the medication in milligrams, p(t), and the number of hours since the medication was taken, t?

So, the values of the trigonometric functions of t are sin(t) = 1/7, cos(t) = -√(1 - (1/7)^2) and tan(t) = -(1/7)/(-√(1 - (1/7)^2)).

Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.

csc(t) = 1/sin(t), so sin(t) = 1/7

Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the third quadrant.

Therefore, the values of the trigonometric functions of t are:

sin(t) = 1/7

cos(t) = -√(1 - sin^2(t)) = -√(1 - (1/7)^2)

tan(t) = sin(t)/cos(t) = -(1/7)/(-√(1 - (1/7)^2))

Note that the values of the other trigonometric functions, such as cot(t), sec(t), and csc(t), can be found using the definitions of these functions and the values of sin(t) and cos(t) that we have found.

To learn more about Trigonometric Functions

Visit; brainly.com/question/14746686

#SPJ4

So, the values of the trigonometric functions of t are  \(Sin(t)=\frac{1}{7}\), \(Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }\)  and  \(tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }\).

Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.

\(Cosec(t)=7\)

We known

⇒ \(Sin(t)=\frac{1}{Cosec(t)} =\frac{1}{7}\)

Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the second quadrant.

Therefore, the values of the trigonometric functions of t are:

⇒ \(Sin(t)=\frac{1}{7}\)

⇒ \(Cos(t)=-\sqrt{[1-(Sin^2t)]}\)

⇒ \(Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }\)

⇒ \(tan(t)=\frac{Sin(t)}{Cos(t)}\)

⇒ \(tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }\)

∴ Note that The definitions of the other trigonometric functions, along with the values of Sin(t) and Cos(t), can be used to determine the values of cot(t), Sec(t), and Cosec(t).

To learn more about trigonometric functions

brainly.com/question/14746686

#SPJ4

Answer:

42

Step-by-step explanation:

The order of PEMDAS is attached,

3³ + 6(2+½)​

3³ + 6(\(\frac{3}{2}\))​

27 + 6(\(\frac{3}{2}\))​

27 + 6(\(\frac{3}{2}\))​

27 + 15

42

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Answer:

The console was used 42,504 watt-hours of energy last year

Step-by-step explanation:

video game console uses 154 watt-hours of energy each hour

The console was used 276 hours last year.

How many watt-hours of energy did the console use?

Watt hours of energy used = 154 × 276

= 42,504 watt-hours of energy

The console was used 42,504 watt-hours of energy last year

Answer:

x=2<br/>y=1

Step-by-step explanation:

\left\{ \begin{array} { l } { 4 x + y = 9 } \\ { 3 x - 2 y = 4 } \end{array} \right.

4x+y=9,3x-2y=4

4x+y=9

4x=-y+9

x=\frac{1}{4}\left(-y+9\right)

x=-\frac{1}{4}y+\frac{9}{4}

3\left(-\frac{1}{4}y+\frac{9}{4}\right)-2y=4

-\frac{3}{4}y+\frac{27}{4}-2y=4

-\frac{11}{4}y+\frac{27}{4}=4

-\frac{11}{4}y=-\frac{11}{4}

y=1

x=\frac{-1+9}{4}

x=2

x=2,y=1

Answer: -(5x+6)

Step-by-step explanation:

To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

Using these rules, we can find the vertices of image U′V′W′ as follows:

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).

The correct answer is d. 56.

When computing a correlation coefficient, the degrees of freedom (df) is calculated as (n-2), where n is the sample size. In this case, we are given that df = 55.

Substituting df = 55 into the formula, we get:

55 = n - 2

Adding 2 to both sides, we get:

n = 57

Therefore, the sample size must be 57 in order to have 55 degrees of freedom when computing a correlation coefficient.
Hi! When computing a correlation coefficient with 55 degrees of freedom, your sample size must be 57 (Option c).

Here's the step-by-step explanation:
1. Recall that the formula to find degrees of freedom (df) in correlation is df = n - 2, where n is the sample size.
2. In this case, the degrees of freedom is given as 55.
3. To find the sample size (n), you'll need to rearrange the formula: n = df + 2.
4. Substitute the given degrees of freedom into the formula: n = 55 + 2.
5. Solve for n: n = 57.

Therefore, when computing a correlation coefficient with 55 degrees of freedom, your sample size must be 57.

To know more about coefficient visit:

https://brainly.com/question/1038771

#SPJ11

Answer:

Given the expression chase was asked to simplify as , lets first solve and compare our solution with chases's

Using the law of indices

Step-by-step explanation:I Know it is right

To obtain a feasible solution, you would need to revise the assignment limits or add additional constraints that do not violate the given constraint.

Based on the constraint you provided, x21 + x22 + x23 + x24 ≤ 3, it means that the sum of variables x21, x22, x23, and x24, representing the number of tasks assigned to agents 1, 2, 3, and 4 respectively, cannot exceed 3.

This constraint implies that agent 3 can be assigned to a maximum of 2 tasks (since x23 ≤ 2), and agent 2 can be assigned to a maximum of 3 tasks (since x22 ≤ 3).

However, there seems to be a contradiction with the statement that "agent 3 can be assigned to 2 tasks" and "agent 2 can be assigned to 3 tasks" because the sum of these maximum assignments would already exceed 3, which is not feasible according to the constraint.

Therefore, To obtain a feasible solution, you would need to revise the assignment limits or add additional constraints that do not violate the given constraint, such as reducing the maximum number of tasks that can be assigned to agent 2 or agent 3, or adjusting the total number of tasks available for assignment.

Learn more about Constraints

brainly.com/question/30703729

#SPJ11

Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

know more about consumer surplus click here;

https://brainly.com/question/14852681

#SPJ4