Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground.

Projectile motion formula:

h = -16t2 + vt + h0

t = time, in seconds, since the ball was thrown

h = height, in feet, above the ground

Which system models the height of the tennis ball and the height of the dog's mouth over time?

h = 4.5t + 18 and h = -16t2 + 1.5t + 21

h = 18t + 4.5 and h =-16t2 + 21t + 1.5

h = -16t2 + 4.5t + 18 and h = -16t2 + 1.5t + 14

h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5

Answer:

D

Step-by-step explanation:

The solid line is y = -x + 9, and everything below it is shaded, so the correct sign is less than or equal to.

Putting the two pieces of information together, the equation you get is:

D. y ≤ -x + 9

The answer is D) 0.99218

The probability that the person will not die in the next year is approximately 0.99218.

Option D is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability that a person will die in the next year is 782/100000.

To find the probability that the person will not die in the next year, we can subtract the probability of dying from 1, since the sum of the probabilities of dying and not dying is always 1.

1 - 782/100000 = 99218/100000

This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2:

99218/100000

= 49609/50000

This fraction can be converted to a decimal by dividing the numerator by the denominator:

= 49609/50000

= 0.99218

Therefore,

The probability that the person will not die in the next year is approximately 0.99218.

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By definition of linear independence, the vectors in the set {a, b, c} are independent if

[tex]k_1\vec a+k_2\vec b+k_3\vec c=\vec0[/tex]

can only be obtained with the choice of k₁ = k₂ = k₃ = 0.

This vector equation corresponds to the system of linear equations

[tex]\begin{cases}k_1 - 2k_3 = 0 \\ 2k_1 + k_2 = 0 \\ k_1 + 2k_3 = 0\end{cases}[/tex]

The first equation says k₁ = 2 k₃, while the third one says k₁ = -2 k₃. This can only be possible if k₁ = k₃ = 0, and from the second equation it follows that k₂ = 0. So the given set is linearly independent (and *not* dependent).

Answer:

15

Step-by-step explanation:

let the number=x

⅔x=18

2x=54

x=27

Now 5/9 of the number=5/9×27

=5×3=15

The total hours that Karen spent baby-sitting on the weekend is 7 hours.

a + b = 8 hours equation 1

6a + 13b = 55 equation 2

Where:

Multiply equation 1 by 13

13a + 13b = 104 equation 3

Subtract equation 2 from equation 3

7a = 49

a = 7 hours

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Step-by-step explanation:

Topic :- Percentage Increase

= Cost price × Rate/one hundred

⇒ 34.90 × 9/100

⇒ 314.1/100

⇒ 3.141

Therefore, the sale tax of the elephant would be $3.141

Answer:

3.15

Step-by-step explanation:

If you know what y = x², you can make the parabola more narrow by scaling this by some constant greater than 1 or smaller than -1. For example, y = 2x² or y = -5x². Note that if you pick a negative constant, you would end up reflecting the parabola across the horizontal axis.

To get a wider graph, you would instead scale by some constant between -1 and 1. For example, y = -1/2 x² (scaling by -1/2, or equivalently scaling by 1/2 and reflecting).

Taking the aformentioned details together, you can (1) reflect and (2) narrow the graph by multiplying y = 3x² by a negative constant larger than 1 in magnitude. For example, y = -15x², where we scale by -5.

Answer: 6/11

Step-by-step explanation:

28 - 7 = 21

16 + 11 - 21 = 6

11 - 6 = 5

16-6 = 10

10 + 5 15

P (a) = 16/28

p (b) = 11/28

A I B = 6/28/11/28 = 6/11

Answer:

each youth ticket costs $7

Explanation:

Let the cost of each youth ticket be "y"

Solve for y:

Answer:

t = 7

Step-by-step explanation:

total cost = 35

price per adult = 14x -> only 1 adult so 14(1) = 14

35 = 14(1) +3t

35-14 = 3t

21 = 3t

t=7

The pressure to the nearest tenth at the time of the first measurement  for this case was 1.82 atm approximately.

According to the Boyle's law, the pressure of a gas tends to drop as the capacity of the container increases. We can write it symbolically as:

[tex]P_1V_1 = P_2V_2[/tex]

where we have:

[tex]P_1[/tex] and [tex]V_1[/tex] are first pressure and first volume, and:

[tex]P_2[/tex] and [tex]V_2[/tex] are second pressure and second volume.

The complete question is:

" According to Boyle's law, PV = k, what was the pressure to the nearest tenth at the time of the first measurement given the following information?

V₁ = 7,450 mL, P₂ = 8.25 atm, V₂ = 1,645 mL"

So, using the Boyle's rule, we get:

[tex]P_1V_1 = P_2V_2\\\\P_1 = \dfrac{P_2V_2}{V_1}\\\\P_1 = \dfrac{8.25 \times 1645}{7450} \approx 1.82 \: \rm atm[/tex]

Thus, the pressure to the nearest tenth at the time of the first measurement  for this case was 1.82 atm approximately.

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Answer:

Step-by-step explanation:

(x+y)/2 - (x-y)/6 = 16

x/3 + (x+2y)/3 = 14

Multiply first equation by 6

3(x+y) - (x - y) = 96

2x + 4y = 96

x + 2y = 48       (A)

Multiply second equation by 3

x  + x + 2y = 42

x + y = 21         (B)

Subtract  A - B:-

y = 27

So:

x + 27 = 21

x = -6.

The quadratic relation

is f(x) = a(x - 27)(x + 6)

=   a(x^2 - 21x - 162)     where a is some constant

Vertex form:

f(x) = a[(x - 10.5)^2 - 110.25 - 162]  

f(x)  = a[(x - 10.5)^2 - 272.25]

f(x) = a[(x - 10.5)^2 -  272.25a.

Answer:

15 minutes.

Step-by-step explanation:

One hour is equal to 60 minutes. Since you're asking for 1/4, or a quarter, of that amount of time, we should divide 60 by four.

Using a calculator, you'd get 15 asap. Without one, if you can divide 60 in half (that equals 30), then divide that half in half again (that equals 15), you'll have divided it into quarters and gotten your answer.

Answer:

In the picture is how to solve it

Step-by-step explanation:

Answer:

We are multiplying sin theta by sec theta, so we first start with valuing sec theta. Re-evaluate sec theta as sec(theta), and get the reciprocal.

[tex]sin(theta) * \frac{1}{cos(theta)}[/tex] <-- reciprocal

Combine sin() with the reciprocal of sec theta.

[tex]\frac{sin(theta)}{cos(theta)}[/tex]

Rewrite this combination as tan(theta)

[tex]tan(theta)[/tex]

Since the sides are equal, they count as an identity.

[tex]sin(theta) * sec(theta) = tan(theta)[/tex]

That said, sin(theta) × sec(theta) = tan(theta) is an identity.

Answer:

~12 meters per second is your answer

Step-by-step explanation:

You need to do these specific things in order to convert.

Kilometers to meters - Multiply by 1000

Minutes to Seconds - Multiply by 60.

_______________________________________________________

First, do 20 kilometers multiplied by 1000

20 x 1000 = 20,000 meters

Do 29 minutes multiplied by 60.

29 x 60  = 1,740 seconds

_______________________________________________________

Now that we have everything converted, you need to divide it to find the speed.

Speed is Distance over Time.

20,000 meters / 1,740 seconds = Speed

Do 20,000 divided by 1,740

11.494252873563218390804597701149 That is your number.

You need to round that to the nearest whole number.

~12 meters per second is your answer

Th anwse is d) :B k .............

Answer:

X and 127 are co-interior angles and X and Y are straight angle

Answer:

Y=127°

X=53°

Step-by-step explanation:

Y is 127 bcs it is correspoding to the 127° it has given u in the question. But you know that half a circle is 180° now that you have 127 as y u minus 180- 127 which equals X that is 53 hope u understood

Answer:

  (a)  sec²(θ) -tan²(θ) = 1

Step-by-step explanation:

The identity relation between sec(θ) and tan(θ) is ...

  tan²(θ) +1 = sec²(θ)

__

When tan²(θ) is subtracted from both sides of this equation, the result matches the first choice:

  sec²(θ) -tan²(θ) = 1

_____

Additional comment

This is a variation of the "Pythagorean" relationship between sine and cosine. There is a similar relation between cot²(θ) and csc²(θ).

  [tex]\sin^2\theta+\cos^2\theta=1\\\\\dfrac{\sin^2\theta}{\cos^2\theta}+\dfrac{\cos^2\theta}{\cos^2\theta}=\dfrac{1}{\cos^2\theta}\qquad\text{divide by $\cos^2\theta$}\\\\\tan^2\theta+1=\sec^2\theta[/tex]

An equation is formed of two equal expressions. The equation of the new graph will be y=|1/(2x-4)|+3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation given is  [tex]y=\left|\dfrac{1}{2x-2}\right|+3[/tex], which is needed to be translated 1 unit to the right therefore, the value of x should be decreased by 1. Therefore, the equation of the new graph will be,

[tex]y=\left|\dfrac{1}{2(x-1)-2}\right|+3\\\\\\y=\left|\dfrac{1}{2x-2-2}\right|+3\\\\\\y=\left|\dfrac{1}{2x-4}\right|+3[/tex]

Hence, the equation of the new graph will be y=|1/(2x-4)|+3.

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Answer:

17.3

Step-by-step explanation:

area of paralellogram=base x height

height=sin(60) x 4= [tex]2\sqrt{3}[/tex]

area = 5 x [tex]2\sqrt{3}[/tex]

        = [tex]10\sqrt{3}[/tex] = 17.3(to nearest tenth)

A) y − 4

Four less than an unknown value

B) b + 4

Four more than some number

C) a^4

Some number to the power of four

D) 4x

Four times an unknown value

E) z ÷ 4 =

Quotient of a variable and four

Answer:B

Step-by-step explanation: Because the  science math Spanish and art. Science: MAD of 1.14, Math: of 1.6, Spanish: MAD of 1.2 Art: MAD of 1.93 In which class were his scores the closest together

Answer:

spanish

Step-by-step explanation:

Step-by-step explanation:

Let the number of phones sold in 1987 is k.

The rate of decrease is

The function to represent the number of phones P sold after x years after 1987 is

Answer:

[tex]f(x)=a(0.86)^x[/tex]

where:

Step-by-step explanation:

General form of an exponential function:

  [tex]f(x)=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given:

If the number of phones decreased by 14% each year, then each year the number of phones will be 86% of the previous year
(100% - 14% = 86%)

Therefore, b = 86% = 0.86

Substitute the given and found values into the general form of the function to create a function to represent the number of home phones sold:

   [tex]f(x)=a(0.86)^x[/tex]

where:

to get the LCD we should start by doing a quick prime factoring of each denominator, as you see in the picture below.

the factors in red are the common factors to all values, and they are used in the LCD only once, the other not common factors in blue, they're used in the LCD.

Answer:

The distance to the center of the earth from the equator is 6,378 km or 33,963 miles, whereas the distance to the center of the earth from a pole is 6,357km or 3,950 miles. Complete answer: The average distance from the surface of the earth to its center is 6,371 km or 3,959 miles.

The volume of the hopper bin is the amount of feed in it

The given parameters are:

Start by calculating the radius (r) of the cones.

r = D/2 -------- because the cones and the cylinder have equal diameters.

So, we have:

r = 36/2 = 18

The height (h) of the cones is:

tan(θ) = h/r

This gives

tan(52) = h/18

Make h the subject

h = 18 * tan(52)

Evaluate

h = 23.04

The volume is then calculated as:

Volume = Volume of cylinder + 2 * Volume of cone

This gives

Volume = πr^2H + 2 * 1/3πr^2h

Volume = πr^2H + 2/3πr^2h

Factor out πr^2

Volume = πr^2(H + 2/3h)

Substitute known values

Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)

Evaluate

Volume = 35973.85 cubic feet

Hence, the volume of the hopper bin is 35974 cubic feet

The given parameters are:

For a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:

Weight = 22 * 35974 pounds

Weight = 791428 pounds

At 85% full, the weight wuld be:

Weight = 85% * 791428 pounds

Weight = 672713.8 pounds

672713.8 pounds is greater than the weight limit of 500000 pounds.

Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit

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Answer:

It's X=3y = -9

Step-by-step explanation:

helping!!!

Step-by-step explanation:

11.

As all the exterior angles of a pentagon add up to 360, [ because exterior angle of a polygon = n(360/n) where n = no. Of sides, As the number of sides in a pentagon is 5, n=5. Thus, the sum of exterior angles of a pentagon = 5(360°/5) = 360°.]

THEN,

56 + 2x + 85 + 57 + 4x = 360

6x + 198 = 360

6x = 360 - 198

X = 162/6 = 27

Ans : x = 27

12.

Let the missing angle be x,

As we know that all exterior angles in a pentagon add up to 360 ( Write the same thing written above),

Then,

83 + 83 + 26 + 46 + x = 360

238 + x = 360

X= 360 - 238

X = 122

Answer : the fifth exterior angle = 122°

Hope this helps

Answer:

16

Step-by-step explanation:

3x - 12 = 36

3x = 48

x = 16