The height in feet of a rocket launched into the air is modeled by the function (t)=-16t^2+160t+300 where t is time in seconds. Approximately how many seconds will the rocket exceed the height of 500 ft?

Answer: Choice A

Step-by-step explanation:

I'm bad at explaining things, sorry!

Answer:

Tomorrow is Thursday if today is Wednesday

Hypothesis: Today is Wednesday .

Conclusion: Tomorrow is Thursday.

Step-by-step explanation:

Given

1. If today is Wednesday , then tomorrow is Thursday.

Hypothesis p : Today is Wednesday .

Conclusion q : Tomorrow is Thursday .

Conditional statement:  [tex]p\implies q[/tex]

But given

Hypothesis : Tomorrow is Thursday .

Conclusion: Today is Wednesday .

Converse statement;  [tex]q\implies P[/tex]

Therefore, the given statement is converse not conditional.

2. If today is Wednesday , then tomorrow is Thursday.

Given

Hypothesis p: Tomorrow is Thursday.

Conclusion q: Today is not Wednesday.

Statement :[tex]q\implies \neg p[/tex]

Hence, it is not a true conditional statement.

3.Tomorrow is Friday if today is Wednesday.

Given

Hypothesis: Today is Wednesday.

Conclusion: Tomorrow is Friday.

It is not a true conditional statement.

4. Tomorrow is Thursday if today is Wednesday.

Given

Hypothesis p: Today is Wednesday.

Conclusion q: Tomorrow is Thursday.

Then the statement : [tex]p\implies q[/tex]

It is a true conditional statement.Because when hypothesis true and conclusion is true then the conditional is true.

Answer:

B. 330

Step-by-step explanation:

The question indicates the order doesn't matter, so it's a combination and not a permutation.

The combinations are calculated using this formula:

[tex]C(n,r) = \frac{n!}{r! (n-r)!}[/tex]

In this case we have a population of 11 (n = 11) and a selection of 4 (r=4), so...

[tex]C(11,4) = \frac{11!}{4! (11-4)!} = 330[/tex]

So, there are 330 different combinations that can be made of 4 paintings out of a selection of 11.

Answer:

The correct answer is option B.  330

Step-by-step explanation:

It is given that,There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window.

To find the possible ways

There are total 11 paintings.

We have to choose 4 of them

Possible number of ways = 11C₄

 = (11 * 10 * 9 )/(1 * 2* 3 * 4)

 = 330 ways

Therefore the  correct answer is option B.  330

Answer: 55.4

Step-by-step explanation:

The right triangle shown here is a 30-60-90 triangle. This means that its angles measure 30, 60, and 90 degrees. (I got the 30 degrees by subtracting the other two angles from 180 degrees, as the sum of the angle measures in a triangle is 180 degrees.)

The sides in such a triangle have the ratio of x:x[tex]\sqrt{3}[/tex]:2x

The x is across from the 30 degree angle, the x[tex]\sqrt{3}[/tex] is across from the 60 degree angle, and the 2x is across from the 90 degree angle.

The x in this triangle equals to 8 as the eight is across from the 30 degree angle.

This means that the x[tex]\sqrt{3}[/tex] side will equal 8[tex]\sqrt{3}[/tex].

That side is also the height of the triangle. The area of the triangle is then 1/2(8)(8[tex]\sqrt{3}[/tex]), or about 55.4.

Answer:

S = 13 - x

T = (18 + x) / 2

Step-by-step explanation:

S = 18

T= 18

Sue gives away x, so subtract it from 18. But Tony gets x, so add it to 18 in his expression.

S = 18 - x

T= 18 + x

Sue eats 5 so subtract 5 from her expression. Tony eats half, so divide his expression by 2.

S = 18 - x - 5

T = 18 + x / 2

Simplify 18-5.

S = 13 - x

T = (18 + x) / 2

Answer:

Step-by-step explanation:

The given function y=0.8^x is an exponential decay function. It's end behavior is defined such that as x grows significantly large, y approaches 0, and as x becomes significantly negative, y approaches infinity.

The function

represents exponential decay because the base (0.8) is between 0 and 1. When the base of the power function is in this range, it results in a decreasing or 'decay' function. This contrasts with an exponential growth function, where the base would be greater than 1.

Regarding the end behavior of this function, we can analyze it using the concept of limits. As x approaches positive infinity (x -> +∞), y will approach zero (y -> 0) because a fraction (0.8 in this case) to a large power tends to zero. This illustrates the decay aspect of the function. Conversely, as x approaches negative infinity (x -> -∞), y will approach positive infinity (y -> +∞).

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The function y = 0.8^x is an exponential decay function. As x increases, y decreases exponentially. The end behavior of the function is that it approaches 0 as x approaches positive and negative infinity.

The function y = 0.8^x is an exponential decay function. In an exponential decay function, the base is between 0 and 1, and as x increases, y decreases exponentially. This function represents the decay of a quantity over time, where the quantity is decreasing by 20% for each unit increase in x.

Regarding the end behavior and limits, as x approaches positive and negative infinity, the function approaches 0. This means that the y-values get closer and closer to 0 as x becomes larger and smaller. In other words, the function approaches the x-axis but never reaches it.

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Answer:

n=11 or n=-3

Step-by-step explanation:

Consider the quadratic equation [tex]n^2-8n-27=6.[/tex]

First, remind the formula

[tex](a-b)^2=a^2-2ab+b^2[/tex]

To complete the square, note that

[tex]8n=2\cdot n\cdot 4[/tex]

Hence, we need [tex]+4^2[/tex]

Add 16 to both sides of equation:

[tex]n^2-8n+16-27=6+16\\ \\(n-4)^2-27=22\\ \\(n-4)^2=49\\ \\n-4=7\text{ or }n-4=-7\\ \\n=11\text{ or }n=-3[/tex]

-The equation is actually

5x^2 -2x+1=0;

-The discriminant is b^2 -4ac=4-4•5•1=4-20=-16

-this means that the equation has no real number solutions

Answer:

The discriminant is equal to −16, which means the equation has no real number solutions.

Step-by-step explanation:

[tex]\text{Given the quadratic equation }-1=5x^2-2x[/tex]

we have to find the number of real number solutions the equation has.

The equation is

[tex]5x^2-2x+1=0[/tex]

[tex]\text{Comparing above equation }ax^2+bx+c=0[/tex]

a=5, b=-2, c=1

To find number of real solutions we have to find the discriminant

[tex]D=b^2-4ac[/tex]

[tex]D=(-2)^2-4(5)(1)[/tex]

[tex]D=4-20=-16[/tex]

The value of discriminant is -16<0

Hence, the equation has no real roots.

Hence, option 1 is correct

Answer: First option.

Step-by-step explanation:

You can use the inverse tangent function to find the value of the angle T:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

You can identify in the figure that:

[tex]\alpha=T\\opposite=RG=8\\adjacent=TR=15[/tex]

Then, knowing these values, you can substitute them into  [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex].

Therefore, you get that the value of the angle T rounded to the nearest degree is:

[tex]T=arctan(\frac{8}{15})\\\\T=28\°[/tex]

This matches with the first option.

H(t) = -16t² + vt + s

Where -16 is half of the gravitational constant of almost 32 ft/sec (downward, thus negative),

v is the initial velocity (90), and

s is the starting height (160)

so we have:

H(t) = -16t² + 90t + 160

How long before it hits the ground? Solve for h(t) = 0:

0 = -16t² + 90t + 160

Divide both sides by -2:

0 = 8t² - 45t - 80

Quadratic equation:

t = [ -b ± √(b² - 4ac)] / (2a)

t = [ -(-45) ± √((-45)² - 4(8)(-80))] / (2(8))

t = [ 45 ± √(2025 + 2560)] / 16

t = [ 45 ± √(4585)] / 16

throwing out the negative time:

t = (45 + √4585) / 16

t ≈ 7.04 seconds

Answer and Explanation: The results of the survey would not be accurate to the whole of springfield, as the sample was not a random sample. A random sample is where each person in a given area (Springfield in this case) has an equal chance of being surveyed. In this case, only walmart shoppers were surveyed. Therefor, the results can only apply to shoppers at walmart, not the whole of Springfield.

Answer:

Step-by-step explanation:

Given that a researcher interested in Springfield citizens' shopping habits surveys a randomly selected group of 200 Walmart shoppers. 76% of those surveyed indicated that price was more important to them than where an item was produced.

[tex]H_0: p=0.75\\H_a: p <0.75[/tex]

(One tailed test)

Sample proportion p = 0.76

p difference = 0.01

Std error = [tex]\sqrt{\frac{pq}{n} } =\sqrt{\frac{0.75(0.25)}{200} } \\=0.0433[/tex]

Test statistic z = p difference / std error = [tex]\frac{0.01}{0.0433} =0.23[/tex]

p value = 0.409

Since p >0.05 we accept null hypothesis.

There is no statistical evidence to prove that proportion >3/4 or 0.75

Answer:

  4.95 in

Step-by-step explanation:

The area is the same, no matter how you find it.

  (11 in)h = (9.9 in)(5.5 in) . . . . . area = base·height

  h = (9.9·5.5/11) in = 4.95 in . . . . divide by 11 in

The answer is:

It will take 18 hours for the return trip.

To calculate how long does it take for the return trip, we need to calculate the distance between it destination and the starting point.

We know that the ship sails at 15 miles per hour (mph) for 6 hours, so, calculating the distance we have:

[tex]x=x_o+v*t\\\\x=0+15mph*6hours=90miles[/tex]

We know that the distance between the destination and the starting point is 90 miles, now, to calculate how long does it take the return trip, we need to use the motor speed rate which is equal to 5 miles per hour (mph), so, calculating we have:

[tex]Distance=v*t\\\\t=\frac{Distance}{v}=\frac{90miles}{5mph}=18hours[/tex]

Therefore, we have that it will take 18 hours for the return trip.

Have a nice day!

The ship covers a distance of 90 miles to its destination at 15 mph, sailing for 6 hours. For the return trip motoring at 5 mph, it takes 18 hours.

The question asks how long it takes for a ship to return to its starting point at a slower speed than it originally traveled to its destination. To answer this question, first, we calculate the distance to the destination. Since the ship sails at 15 miles per hour for 6 hours, it covers a distance of 15 miles/hour × 6 hours = 90 miles. We use the same distance for the return trip. However, the ship will now motor back at 5 miles per hour, so the time taken to motor back will be the distance divided by the return speed: 90 miles ÷ 5 miles/hour = 18 hours. Therefore, it takes 18 hours for the return trip home.

Answer:

Answer: You could have an infinite amount of triangles with these measurements.

Unless, you are missing something in the problem, there is not enough information that would narrow it down to a single triangle. Angle A is fixed and the height is fixed. However, Angle B and C could be anything as long as they formed a triangle and had side a of 15 in between them.

Answer:

j

Step-by-step explanation:

i know this isnt anything that has to do with this question but i was wondering if you had the answers to the precal "lets dance! portfolio" i couldnt contact you through messaging so this is the only way lol i hope you see this

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

* lets revise the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are ( h ± a , k )  

- The coordinates of the co-vertices are ( h , k ± b )

- The coordinates of the foci are (h , k ± c), where c² = a² + b²

* Now lets solve the problem

∵ The equation of the hyperbola of vertex (h , k) is

    (y - k)²/a² - (x - h)²/b² = 1

∵ The equation is (y - 2)²/3² - (x - 2)²/4² = 1

∴ k = 2 , h = 2 , a = 3 , b = 4

∵ The foci of it are (h , k + c) and (h , k - c)

- Lets find c from the equation c² = a² + b²

∵ a = 3

∴ a² = 3² = 9

∵ b = 4

∴ b² = 4² = 16

∴ c² = 9 + 16 = 25

∴ c = √25 =  5

- Lets find the foci

∵ The foci are (h , k + c) and (h , k - c)

∵ h = 2 , k = 2 , c = 5

∴ The foci are (2 , 2 + 5) and (2 , 2 - 5)

∴ The foci are (2 , 7) and (2 , -3)

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

Answer:

  C.

Step-by-step explanation:

The mapping for 90° counterclockwise rotation is ...

  (x, y) ⇒ (-y, x)

If we consider how this applies to points X and Y, which both have a y-coordinate of 0 and a negative x-coordinate, (-a, 0), for example, we see it maps to ...

  (-a, 0) ⇒ (0, -a)

That is, both points X' and Y' will be on the negative y-axis. The only figure showing this is figure C.

______

Comment on the other answer choices

Figures A and D show clockwise rotation. In Figures A and B, the rotation is not about the origin, but is about a different point. (In Figure B, the points easy to consider are the ones on the -x axis, points X and Z. They should appear on the -y axis after rotation, but do not.)

Answer:c

Step-by-step explanation:

3m. The wall of the building is 3m far from the base of the ladder.

The key to solve this problem is use trigonometric ratios.

The cosine of the angle is the adjacent leg divided by the hypotenuse.

From the image attached we can modeling the problem as a right triangle, where we can see that the adjacent leg is the unknown, hypotenuse is 6m (long of the ladder), and the ladder make an angle of 60°  leans againts the building's wall, and x is the long of the adjacent leg. To calculate how far is the base of the ladder from the wall:

Cos 60° = adjacent leg/hypotenuse

adjacent leg = cos 60° x hypotenuse

x = cos 60° (6m) = (0.5)(6m) = 3m

-6b &gt; 36

Answer:

The answer is the second choice.

Step-by-step explanation:

The value of the domain which is not part of the function is x = -2.

Given data:

The domain of a function is the set of values that are allowed to plug into the function which are the inputs.

The domain of the three line segments is represented as:

Domain of line 1 ranges from [ -5 , -2 ).

Domain of line 2 ranges from ( -2 , 2 ).

Domain of line 3 ranges from [ 2 , 5 ].

So, the value -2 is not included in the domain values of the function.

Hence, x = -2 is not in the domain of function.

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Answer:

6 × 8

Step-by-step explanation:

Since the dilation factor is 4, and the image was ENLARGED, that means the original photo was smaller.  Smaller by a factor of 4.

So, we take the new dimensions (24x32) and we divide each side by the dilation factor of 4:

(24/4) x (32/4) = 6 x 8

It couldn't be the first answer choice (3x8) because  that doesn't maintain the ratio of the enlarge picture.  The other possible answers do match the right ratio... but only 6x8 is scaled by a factor of 4.

Answer:

6 x 8

Step-by-step explanation:

When you look at DQ,4 and you break it apart a little bit, you will realize that the dilation is 4 and in this case it will increase by 4.

(Don't mind the Q it is just there to tell you where the center point is)

So if you look at the options:

3 x 8  ---- that will not work because 3x4= 12 which is not 32 and not 24 so we should kick that one out.

6 x 8  ---- This is good because 6x4=24 and 8x4=32!

We don't have to go any further (you can if you want though)!

Again, 6 x 8 is your answer.

Answer:

  g(10) is undefined

Step-by-step explanation:

A vertical asymptote is a place where a function is literally undefined. That is commonly because the function is a rational function with a denominator of zero at that point (division by zero is undefined), but it can also be for any of a variety of other reasons.

43% = 'Piano'

28% = 'Guitar'

15% = 'Harmonica'

12% = 'Drums'

2% = ...Other Instruments

- '2' Does seems as to be the smallest but it could be a trick.

- '43' Is the largest percentage out of the whole group.

- '100' Is what you get when you add all of the percentages together.

- And if you try to evaluate the percentages together in either way it'll end up to be '0.00004334' so that executes '250' and '150' from out of the question.

I'm not sure exactly what the actual answer could be but I'm assuming since it said "What is the smallest number of people required for the sample to meet the conditions for performing inference" Then my assumption is '2'.

250

Remember there are 2 conditions to perform a goodness of fit chi-test:

Simple random sample: The data must come from a random sample or a randomized experiment.

Expected counts: All expected counts are at least five. You must state the expected counts.

To explain expected counts a bit better, imagine I surveyed 100 people about their ice cream preferences. Before beginning it is believed that 50% like chocolate, 47% like vanilla, and 3% like strawberry.

That means our expected counts are:

100(.50) = 50

100(.47) = 47

100(.03) = 3

This is a problem, because 3 < 5 and so we can not perform a goodness of fit chi-test.

So how do you find the minimum sample size? Use this formula:

sample size (n) * smallest proportion (p) = 5

In the context of ice cream:

n*.03 = 5

n = 5 / .03

n = 167 (because you can't interview 2/3s of a person)

In the context of the problem:

n* .02 = 5

n = 5 / 0.02

n = 250

This means we need to sample at least 250 people to meet our expected count condition.

Answer:

[tex]661.4\ rpm[/tex]

Step-by-step explanation:

we know that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

[tex]C=2\pi r[/tex]

we have

[tex]r=30/2=15\ in[/tex] -----> the radius is half the diameter

substitute

[tex]C=2\pi(15)[/tex]

[tex]C=30\pi\ in[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]C=30(3.14)=94.2\ in[/tex]

Remember that    

The circumference of the wheels represent one revolution

Convert 59 miles per hour to inches per minute

[tex]59\ mi/h=59*63,360/60=62,304\ in/min[/tex]

using proportion find the number of revolutions  

[tex]\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev[/tex]

therefore

substitute

[tex]62,304\ in/min=661.4\ rev/min=661.4\ rpm[/tex]

the angular velocity of the truck's wheels is approximately 661.03 rpm

We need to first convert 59 mph into in/h. For this we can use the conversion factor:

[tex]1\ mile = 63360\ in[/tex]

Thus, 59 mph in ft/h will be:

[tex]59 \times 63360 = 3738240\ in/h[/tex]

Now we need to convert this into in/min for which we can use the conversion factor:

[tex]1\ hour = 60\ minute[/tex]

So, on converting we get:

[tex]\frac{3738240}{60} = 62304\ in/min[/tex]

Radius of tire will be half of its diameter. Thus radius = 15 in

Circumference of tire can be calculated by using the formula:

[tex]circumference = 2 \pi r[/tex]

Putting in values we get:

[tex]Circumference = 2 \times \pi \times 15 \approx 94.25\ in[/tex]

To determine the number of rotations per minute we need to divide speed of tire by the circumference of tire as follows:

[tex]rpm = \frac{speed}{circumference}\\\\\\rpm = \frac{62304}{94.25} \approx 661.03\ rpm[/tex]

Therefore, the angular velocity of the truck's wheels is approximately 661.03 rpm

Final answer:

The minimum cost of production for the company is $260 for 70 dolls.

Explanation:

The minimum cost of production for the company can be determined by examining the options given. The correct statement is:
The minimum cost of production is $260 for 70 dolls.

In the given function, the cost of production is represented by the variable x. The equation cost = 50 + 10x describes the cost of producing x number of dolls. By substituting x with 70 in the equation, we can calculate the cost as follows:

Cost = 50 + 10 * 70 = 50 + 700 = $750

Therefore, the minimum cost of production for the company is $260 for 70 dolls.

939748.88 dollars is the answer

Answer:

$170,258.27

Step-by-step explanation:

Principal = $170,650

Interest = 5.5%

Term = 20 years

Monthly payment = $1,173.88

The interest on the first month is simply simple interest of 1 month on the principal.

I = prt = $170,650 * 0.055 * 1/12 = $782.15

Subtract the interest from the first months payment to find the amount of principal paid.

$1,173.88 - $782.15 = $391.73

Since the amount of principal paid on the first month is $391.73, the balance after paying the first month's payment is the original principal reduced by the amount of principal paid in the first month.

balance = $170,650 - $391.73 = $170,258.27

Answer:

-2

Step-by-step explanation:

hopefully this will help

Answer:

1/2x+y=-4

Step-by-step explanation:

Answer:

x + 3y = - 8

Step-by-step explanation:

Given

y = - [tex]\frac{1}{2}[/tex] x - 4

Multiply all terms by 2

2y = - x - 8 ( add y to both sides )

x + 2y = - 8 ← in standard form

Answer:

Step-by-step explanation:

Use the distance formula for coordinate geoemetry and the fact that x1 = 3, y1 = 5, x2 = 6 and y2 = 8 to fill in the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }[/tex]

fills in accordingly:

[tex]d=\sqrt{(6-3)^2+(8-5)^2}[/tex]

which simplifies a bit to

[tex]d=\sqrt{(3)^2+(3)^2}[/tex]

which is

[tex]d=\sqrt{18}[/tex]

The square root of 18 simplifies down to [tex]3\sqrt{2}[/tex], which is 4.2426 in decimal form

Answer:

4.24 units

Step-by-step explanation:

We can use the distance formula to solve this.

Distance formula: d = √((x₁ - x₂)² + (y₁ - y₂)²), where (x₁, y₁) and (x₂, y₂) are the two coordinates.

Plug in: d = √((3 - 6)² + (5 - 8)²)

Subtract: d = √((-3)² + (-3)²))

Square: d = √(9 + 9)

Add: d = √18

Square root: d = 4.24264... ≈ 4.24 units

Answer:

Step-by-step explanation:

Put the appropriate values of n in the formula and do the arithmetic.

  a(1) = 3·1 -7 = -4

  a(5) = 3·5 -7 = 8

The 1st and 5th terms are -4 and 8.

_____

The first few terms of the sequence are ...

  -4, -1, 2, 5, 8, 11, 14, ...

To find the sum of the 1st and 5th terms of the sequence defined by the function a(n) = 3n - 7, calculate each term using their respective n value and add the results together, resulting in a sum of 4.

When you are given the function a(n) = 3n - 7, which represents the value of the nth term in a sequence, the sum of the 1st and 5th terms of the sequence can be calculated by plugging in the values for n into the function for each term and adding the results.

For the 1st term (n = 1):

For the 5th term (n = 5):

The sum of the 1st and 5th terms is then:

-4 + 8 = 4

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Answer:

Step-by-step explanation:

There are three reasons here why randomization is not being applied.

First, the coach is only observing football players attending the meeting.  This is not representative of the entire team.

Second, there is no selection process.  The coach isn't using a random generator or using a similar method.

Third, the players are volunteering for the test.  The results will be biased because of this.

The sentence which is not used in the randomization situation

1. The coach is observing only football players attending the meeting.

3. The football players are volunteering for the test.

The sample is not biased. The members were selected at random from the gym's female population.

The question is biased. It described the weight lifting machines as "easy" and the free weights as "harder".

The meeting is not mandatory and only volunteers are participating in the task he wanted, this shows bias and doesn't correctly represent the whole team.

Therefore, the correct answer is options is 1 and 3.

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