Graph the piece wise function. See image below for problem.

Answer:

[tex] \sqrt{ \frac{13}{16} } [/tex]

Step-by-step explanation:

[tex]cos \: theta = \frac{ \sqrt{3} }{4} \\ sin \: theta = \sqrt{1 - {cos}^{2} theta} \\ = \sqrt{1 - {( \frac{ \sqrt{3} }{4} ) }^{2}} \\ = \sqrt{1 - \frac{3}{16}} \\ = \sqrt{ \frac{13}{16} } [/tex]

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

• sin²x + cos²x = 1 ⇒ sin x = ± [tex]\sqrt{1-cos^2x}[/tex]

Since sinΘ < 0 , then

sinΘ = - [tex]\sqrt{1-(\frac{\sqrt{3} }{4})^2 }[/tex]

       = - [tex]\sqrt{1-\frac{3}{16} }[/tex]

      = - [tex]\sqrt{\frac{13}{16} }[/tex] = - [tex]\frac{\sqrt{13} }{4}[/tex]

Answer:

[tex]\boxed{\text{C. }{f(x) =3(x + 2)^{2} - 1}}[/tex]

Step-by-step explanation:

The vertex form of a quadratic function

ƒ(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

You convert ƒ(x) = 3x² + 12x + 11 to the vertex form by completing the square.

Step 1.  Move the constant term to the other side of the equation

y - 11 =3x² + 12x

Step 2. Factor out the leading coefficient

y - 11 =3(x² + 4x)

Step 3. Complete the square on the right-hand side

Take half the coefficient of x, square it, and add it to each side of the equation.

4/2 = 2; 2² = 4

y – 11 + 12 =3(x² + 4x  + 4)

Note that when you completed the square by adding 4 inside the parentheses, you were adding 3×4 to the right-hand side, so you had to add 12 to the left-hand side.

Step 4. Simplify and write the right-hand side as a perfect square

y + 1 = 3(x + 2)²

Step 5. Isolate the y term

Subtract 1 from each side

y = 3(x + 2)² -1

[tex]\text{The vertex form of the equation is }\boxed{\mathbf{f(x) =3(x + 2)^{2} - 1}}[/tex]

If you compare this equation with the general vertex form and with the graph, you will find that h = -2 and k = -1, so the vertex is at (-2, -1).  

The quadratic equation f(x) = 3x^2 + 12x + 11 can be rewritten in vertex form as C. f(x) = 3(x + 2)^2 - 1 after completing the square.

The function f(x) = 3x2 + 12x + 11 can be rewritten in vertex form, which is y = a(x - h)2 + k, where (h, k) represents the vertex of the parabola. To convert the given quadratic to vertex form, we need to complete the square:

So, the correct vertex form of the equation is C. f(x) = 3(x + 2)2 - 1.

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=64\\ b=8 \end{cases}\implies 64=\cfrac{1}{2}(8)h\implies 64=4h \\\\\\ \cfrac{64}{4}=h\implies 16=h[/tex]

Answer:

[tex]\large\boxed{A.\ -10x^2-33x+1}[/tex]

Step-by-step explanation:

[tex]6x(x-4)-16x^2-(9x-1)\qquad\text{use the distributive property}\\\\=(6x)(x)+(6x)(-4)-16x^2-9x-(-1)\\\\=6x^2-24x-16x^2-9x+1\qquad\text{combine like terms}\\\\=(6x^2-16x^2)+(-24x-9x)+1\\\\=-10x^2-33x+1[/tex]

The expression simplifies to -10x^2 - 33x +1, following the distribution and combination of like terms.

The given question asks to simplify the expression 6x(x − 4) − 16x2 − (9x − 1). To solve, we follow these steps:

Therefore, the correct option is A. -10x2 − 33x + 1.

Answer:

D) 5985

Step-by-step explanation:

Total area: 150×100 = 15000

Area for stars: 6×6 = 36

Total area - area for stars = area for fans

15000-36= 14964

14964ft² for fans, each takes up 2.5 ft²

14964 ÷2.5 = 5985.6 fans

Since we can't have 0.6 of a person, we round down to 5985 fans

Answer:

5,985 fans

Step-by-step explanation:

First you will need to get the floor area of the store

The dimensions are:

150' by 100'

This is 150 ft by 100 ft

Area would be:

Side x side (Assuming that the floor area is a quadrilateral)

150 ft x 100 ft = 15000 ft²

Next we solve for the area of the stars only:

6' by 6'

Side x side

6 ft x 6 ft = 36 ft²

So here we subtract the stars only area from the total floor area:

15,000 ft² - 36 ft² = 14,964 ft²

This is the floor area that the fans can occupy.

Next since the fire marshal said 1 person must occupy an area no less than 2.5ft², we divide the floor area for fans by the requirement.

14,964 ft²  = 5,985.6 fans

   2.5ft²

Since we cannot have a decimal for people, we need to round it down. If it goes beyond 5,985.6 that means we do not meet the minimum requirement of 2.5 ft² per person. So we need to round it down, to the nearest whole number, the answer would be:

5,985 fans.

Answer:

Find the attached

Step-by-step explanation:

We are given the following linear equation;

-3y = 2x - 7

In order to graph it, we need to determine at least 3 pairs of points that lie on the line;

we first solve for y by dividing both sides of the equation by -3;

y = (-2/3)x + 7/3

let x be 3;

y = (-2/3)*3 + 7/3

y = 1/3

(3, 1/3)

let x be 6;

y = (-2/3)*6 + 7/3

y = -5/3

(6, -5/3)

let x be 9;

y = (-2/3)*9 + 7/3

y = -11/3

(9, -11/3)

Using the three set of points we graph our linear function. Find the attached;

The football, kicked by a football player during a practice, is in the air for approximately 3.79 seconds based on the model h = -4(4t - 11)^2.

The question asks for the duration that the football is in the air. This problem involves solving a quadratic function to determine the time when the height of the ball is zero, i.e., when it hits the ground again. The mentioned equation and given information form a quadratic equation.

The equation h = -4(4t - 11)^2 models the height of the football at any given time. The football is on the ground when h = 0. If we substitute h = 0, the equation becomes -4(4t - 11)² = 0. Using the quadratic formula, we find two solutions t = 0.54 s and t = 3.79 s.

As we are looking for the total time that the football is in the air, we are interested in when it falls back to the ground which corresponds to the larger solution. Therefore, the football is in the air for approximately 3.79 seconds.

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The football is in the air for 2.75 seconds.

The given function h = -4(4t-11) models the height h of the ball t seconds after it is kicked. To find how long the football is in the air, we need to find the time when the ball reaches the ground. This occurs when the height h is equal to 0. So, we can set the equation -4(4t-11) = 0 and solve for t.

-4(4t-11) = 0

4t-11 = 0

4t = 11

t = 11/4

Hence, the football is in the air for 11/4 seconds or 2.75 seconds.

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Answer:

The midpoint is (9,6)

Step-by-step explanation:

The midpoint is just the average of the two end points.

x: (5 + 13)/2 = 18/2 = 9

y: (1 + 11)/2 = 12/2 = 6

The midpoint is (9,6)

Answer: 544 ft²

Step-by-step explanation: 17*32=544 and ft*ft=ft² so it is 544 ft²

Answer:

We can use this knowledge in planning of cities

Step-by-step explanation:

The transversal is a line that intersects two or more parallel lines.Angles with similar characteristics are formed when this occurs.

In city planning, streets can be designed to resemble parallel lines with roads that do not meet.However, other roads can be constructed to allow people on the other street to cross to neighboring streets.Such roads allowing this access can be viewed as transversal.

The areas where street roads meet the transversal roads have similar angle characteristics thus could be used for CCTV cameras for surveillance and traffic lights positioning.

A rectangle is a 4-sided flat shape with straight lines where all interior angles are rights angles (90°)

A shape that has two long sides &’ two short sides .

Answer:

99.87% of cans have less than 362 grams of lemonade mix

Step-by-step explanation:

Let the the random variable X denote the amounts of lemonade mix in cans of lemonade mix . The X is normally distributed with a mean of 350 and a standard deviation of 4. We are required to determine the percent of cans that have less than 362 grams of lemonade mix;

We first determine the probability that the amounts of lemonade mix in a can is less than 362 grams;

Pr(X<362)

We calculate the z-score by standardizing the random variable X;

Pr(X<362) = [tex]Pr(Z<\frac{362-350}{4})=Pr(Z<3)[/tex]

This probability is equivalent to the area to the left of 3 in a standard normal curve. From the standard normal tables;

Pr(Z<3) = 0.9987

Therefore, 99.87% of cans have less than 362 grams of lemonade mix

2/3 - Red

4/21 - Blue

Change the red fraction so both fractions will have the same denominator

2/3 change to 14/21

Add blue and red together

14/21 + 4/21 = 18/21

Then subtract it from the total to get the white beads

21/21 - 18/21 = 3/21

Simplify it to get 1/7

Ans : 1/7

Fraction of white beads used is 1/7.

A number expressed as a quotient, in which a numerator is divided by a denominator.

Given:

red beads used = 2/3 = /1

blue beads used = 4/21

Total beads other than white

=14/21 + 4/21

= 18/21

N/ow, fraction of the beads should be white

=1- 18/21

=21/21 - 18/21

=3/21

=1/7

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Answer:

P(A)= 21/36

P(B)=1/2

Step-by-step explanation:

Given:

An ordinary Fair die is a cube with the numbers 1 through 6 on the sides represented by painted spots imagine that such a die is rolled twice

So the sample space of rolling two dices is:

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Total number of sets=36

1)Now Finding probability of

Event A: The sum is greater than 6

From the above sample space sets that have the sum >6 are

(6,1)

(5,2) (6,2)

(4,3) (5,3) (6,3)

(3,4) (4,4) (5,4) (6,4)

(2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

there are 21 sets

hence probability of Event A= 21/36

P(A)= 21/36

2) Now Finding probability of

Event B: The sum is an odd number

From the above sample space sets that have the sum an odd number are

(2,1)(4,1) (6,1)

(1,2)(3,2) (5,2)

(2,3) (4,3)(6,3)

(1,4) (3,4) (5,4)

(2,5) (4,5) (6,5)

(1,6) (3,6) (5,6)

there are 18 sets

hence the probability of Event B = 18/36

         P(B)= 1/2 !

Answer:

19.5

Step-by-step explanation:

just look at the equation like this

1 1/2 - 1/4

???? - 3 1/4

divide 3 1/4 by 1/4 and multiply the result by 1 1/2

or just treat it as a ratio

1.5/x=.25/3.25

Answer:

29000, with the margin of error of ±5000

Step-by-step explanation:

Margin of error is the amount of error that can be caused due to variation, change of circumstances or any miscalculation.

In given case value of college student's debt can be between

24000 and 34000

Finding mid-point

(24000+34000)/2

29000

Now finding deviation of 29000 from 24000 and 34000

24000-29000= -5000

34000-29000= 5000

Hence

29000, with the margin of error of ±5000 !

Answer:

x = i and x = i[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + 6x² + 5 = 0

Using the substitution u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Convert solutions back into terms of x

x² = - 1 ⇒ x = [tex]\sqrt{-1}[/tex] = i

x² = - 5 ⇒ x = [tex]\sqrt{-5}[/tex] = i[tex]\sqrt{5}[/tex]

Answer:

t = (f - v)/a

Step-by-step explanation:

We have been given that;

The equation f = v + at represents the final velocity of an  object, f, with an initial velocity, v, and an acceleration rate,  a, over time, t.

The question requires us to solve for t;

The first step is to subtract v on both sides of the equation,

f - v = v + at - v

f - v = at

The next step is to divide both sides by a,

(f - v)/a = t

which is our required equation solved for t.

Answer:

i) P(A) ; The probability that event A occurs

ii) P(AB) ; The probability that both event A  and event B occur

iii) P(AUB) ; The probability that either event A  or event B occurs

iv) 1 - P(ANB) ; The probability that both events A  and B do not occur                                 together, but either  may occur by itself

v) 1- P(AUB) ; The probability that neither event A  or event B occurs

vi) P(AIB) ; The probability that event A occurs  given the fact that event B occurs

Step-by-step explanation:

i)

P(A) simply represents the probability that an event A will occur. This event could be passing an examination, having snow in summer, arriving to work on time and so forth.

ii)

P(AB) is simply the probability that both event A  and event B do occur. This is usually given by the product of the individual probabilities. Event A could be rolling a 6 in one throw of a fair die while B could be the event that a fair coin lands heads in a single toss.

iii)

P(AUB) refers to the probability that either event A  or event B occurs. This is read out as the probability of A union B. This is usually given by the sum of the individual probabilities.

iv)

1 - P(ANB) is the probability that both events A  and B do not occur                                 together, but either  may occur by itself. P(ANB) is the probability that both events A  and B occur together. This is read out as the probability of A intersection B. Therefore implying that 1 - P(ANB) is simply the probability that either event A or B occurs but A and B can not occur together.

v)

1- P(AUB) refers to the probability that neither event A  or event B occurs. Earlier we defined P(AUB) as the probability that either event A  or event B occurs. 1- P(AUB) simply the complement of P(AUB).

vi)

P(AIB) refers to the probability that event A occurs  given the fact that event B occurs. This is a conditional probability event which evaluates the likelihood of an event A occurring given that an associated event B has already occurred

Answer:

x=-5   x=-4

Step-by-step explanation:

y=x^2 + 9x + 20

We need to factor the equation

What 2 numbers multiply to 20 and add to 9

4*5 = 20

4+5 =9

y=(x+5) (x+4)

To find the zero's we set the equation equal to zero

0= (x+5) (x+4)

Using the zero product property

x+5 = 0   x+4=0

x=-5   x=-4

Answer:

8 laps

Step-by-step explanation:

Assuming in the equation given than n represents the number of laps run and t represents the time in minutes, when we plug in 16 in for t and simplify we get:

n=5/10*16

n=1/2*16 (Simplify the fraction by dividing top and bottom by 5)

n=16/2 (Multiply the fractions together by writing 16 as 16/1 and multiplying straight across)

n=8

Answer:

8

Step-by-step explanation:

This question is a bit of a guess. You have to assume that n is in laps and that t  is in minutes.

n = (5/10) * t Reduce 5/10 to 1/2

n = 1/2 * 16

n = 8

So if the assumptions are correct, he should be able to do 8 laps.

Answer:

Linear Positive Association

Step-by-step explanation:

Answer:

A. [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

The given equation is

[tex]3x-7y=14[/tex]

We solve for y by  subtracting 3x from both sides to obtain;

[tex]-7y=14-3x[/tex]

We now divide through by -7 to get;

[tex]y=\frac{-3}{-7}x+\frac{14}{-7}[/tex]

This simplifies to;

[tex]y=\frac{3}{7}x-2[/tex]

This equation is now in the form y=mx +c, where [tex]m=\frac{3}{7}[/tex] is the slope.

Answer:

(5 1/2, 1), ( 5 1/2, 2) and (5 1/2, 3).

Step-by-step explanation:

The x coordinates will all be 5 1/2 so we could have 3 points with coordinates:

(5 1/2, 1), ( 5 1/2, 2) and (5 1/2, 3).

Answer:

The answers are already in order, so it makes this more simple to solve. To find the mean of all those numbers, you must add all the numbers up, then divide by the numbers that is given. In which this problem, it gives 6 numbers. 

So, 1+35+36+37+37+38= 184. Then, divide it 184/6= 30.6. The mode is the number that occurs the most in that set of numbers. In this case, it would be 37. The median is basically the number in the middle when the set of numbers is ordered from least to greatest. 1,35,36,37,37,38 (here's a hint: cross it off on each side) If there is no obvious middle number, in this case because we have an even set of numbers, we can calculate the median by taking the mean of the 2 middlemost terms and: 36, 37. 

36+37= 73

After that, divide by 2. 

73/2= 36.5

Answer:

Mean=30[tex]\frac{2}{3}[/tex]    Median= 36.5     Mode= 37

Step-by-step explanation:

Mean= You add up all of the numbers and then divide by 6.

Median= You go in from the right and the left till you are in the middle (for an even number of data points you add the two data points together and then divide by 2).

Mode= It is the most common number.

Since you're looking for the volume of each...

Circle: you want to find the area (πr^2) times height

Rectangle: l×w×h

Answer:

3x-15

Step-by-step explanation:

(x-10)+(x-5)+(x)=3x-15

3x - 15

Simply add the different container sizes together. The first container holds x - 10 liters, the second holds x - 5 liters, and the third holds x liters.

(x - 10) + (x - 5) + x

Because of the associative property of Addition, we can remove the parentheses.

x - 10 + x - 5 + x

Because of the communicative property of addition, we can reorder the terms so that the like terms are next to each other.

x + x + x - 10 - 5

Now, combine the x’s.

3x - 10 - 5

Finally, subtract -10 minus - 5.

3x - 15

Answer:

False

Step-by-step explanation:

EU and the US are very good friends and they often trade with them.

Answer:

The answer to your question is True

Step-by-step explanation: Because The EU is largely viewed as a cornerstone of European stability and prosperity. For much of the last decade, however, many EU countries have faced considerable economic difficulties.

Hope this helps :)

And please mark my answer as the brainliest  

Answer:

Step-by-step explanation:

So, carmen has 54 golf balls. He wants to put the same number of balls into each of 9 buckets.So, 54 divided by 9 is 6

the answer is 6

Answer:

9*6=54

Step-by-step explanation:

54÷9=6. You must reverse the equation to make it multiplication. There will be 6 balls in each bucket.

Subtract the 30 feet from the overall height:

325 - 30 = 295

The height of the drop is 295 feet.

Answer:

295 hope this helps!!

Step-by-step explanation: