Select all of the following statements that are true:
A. Random samples only generate unbiased estimates of long-run proportions, not long-run means.
B. You shouldnt take a random sample of more than 5% of the population size.
C. There is no way that a random sample of 100 people can be representative of all adults living in the United States.
D. If this question is voted out, the alternate option is "larger samples are always better than smaller samples, regardless of how the sample was collected."
E. Nonrandom samples are always poor representations of the population

The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

It is known that,

Cos(A + B) = cosAcosB - sinAsinB

Cost(A - B) = cosAcosB + sinAsinB

As per the given,

cos(θ + π/4) - cos(θ - π/4)

(cosθ cos π/4 - sinθ sin π/4) - (cosθ cos π/4 + sinθ sin π/4)

-2 sinθ sin π/4

-2 sinθ (1/√2)

-√2 sinθ

Hence "The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ".

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h: The domain

-5 ≤ x ≤ 5

Answer:

22cm

Step-by-step explanation:

Start by writing down what you know:

Area of rectangle = length x width = L · W = 20

Since decreasing the length by 2.5 and increasing the width by 3 results in a square, we also know: L - 2.5 = W + 3

Solve the above for L: L = W+5.5

Substitute W+5.5 in for L in A = (W+5.5)·W = 20

Distribute on the left, subtract 20 from both sides, and solve the resulting quadratic. NOTE: Remember that we're dealing in length, so only the positive solution counts!

One side of the square = either W+3 or L-2.5, and perimeter of a square is 4s.

Answer:

9

Step-by-step explanation:

1. mean = sum of all data values divided by total number of data values

\(\frac{3+6+9+12+15}{5}\) = \(\frac{45}{5}\) = 9

Answer:

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

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

We are 95% confident that the true population proportion is between 71.6% and 80.4%

The 95% confidence interval for the proportion of all U.S. grown people who would include those  on their list of 10 historic events can be constructed using the formula:

Where:

\(pi\) = sample proportion (76%)

SE = standard error (square root of \(pi(1-pi)/n\))

z = the critical value for a 95% confidence level (1.96)

n = sample size (2025)

Plugging in the values, we get:

\(SE =\sqrt{(0.76(1-0.76)/2025)} = 0.0240\\CI = 0.76 ± (1.96)(0.0240) = (0.716, 0.804)\)

The 95% confidence interval can be interpreted as follows: If we repeated this study many times, 95% of the intervals constructed would contain the true population proportion of all U.S. grown persons who would include on their list of 10 historic events. Based on this sample, we are 95% confident that the true population proportion is between 71.6% and 80.4%.

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The excluded values are the ones that make the denominator equal to zero, these are x = 4 and x = 5.

Remember that we can´t divide by zero, then we need to remove all the values of x that make the denominator equal to zero, so we need to solve:

x² - 9x + 20  =0

Using the quadratic formula we will get:

\(x = \frac{9 \pm \sqrt{(-9)^2 - 4*20} }{2} \\\\x = \frac{9 \pm 1}{2}\)

So the two values are:

x = (9 + 1)/2 = 5

x = (9 - 1)/2 = 4

Now, the numerator is not zero in neither of these two values, so these are the excluded values.

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Answer:

Area of the circle is 6.25π sq.unit

Step-by-step explanation:

The centre of the circle is at the mid point of a diameter. Th mid point of the diameter is at (5+22,5+12)or(72,3),which is centre. Radius is the distance from end point (5,5)to centre (72,3)∴r=√(5−72)2+(5−3)2=√1.52+4=√6.25=2.5∴

Area of the circle is Ac=π⋅r2=π⋅2.52=6.25π sq.unit[Ans]

The Area of Circle whose endpoints of a diameter of a circle are A (2,1) and B(5,5) is 6.25 sq unit.

If there are two points in the coordinates plane as P(a, b) and Q(c, d) then the distance between these two points are

PQ = √(c- a)² + (d-b)²

We have the endpoints of a diameter of a circle are A (2,1) and B(5,5).

Now, using Distance Formula

d= √{(x2 - x1)² + (y2 - y1)²}

Here, x1 = 2; y1 = 1; x2 = 5; y2 = 5

d = √{(5 - 2)² + (5 - 1)²}

d = √{(3)² + (4)²}

d = √{9 + 16}

d = √25

d = 5 unit

Now, Area of Circle

= πr²

= 3.14 x 2.5 x 2.5

= 6.25π sq units

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Answer:

35 failed and 140 passed

Step-by-step explanation:

Let  p = number who passed

f = number who failed

p+f = 175

4 times the number of students passed as failed, so we need to balance this to set it equal

4f = p

Substitute this into the first equation

4r+f = 175

5f = 175

5f/5 =175/5

f = 35

Now find the number who passed

p = 4f

p = 4*35

p =140

Answer:

Dang I forgot how to do that

The probabiltiy that when a marble is chosen from the bag at random then choosen marble is blue is 1/2.

Given that the bag has 6 red marble and 6 blue marbles. Now, a marble is chosen from the bag at random. Therefore, the probabiltiy that choosen marble is blue is:

Probability(Blue Marble)

= Number of blue marbles / Total number of marbles in the bag

= 6/ 12

= 1/ 2

Hence, the probability is 1/2.

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The complete question must be:

A bag with 6 red marbles has 6 blue marbles. A marble is chosen from the bag at random. What is the probability that it is blue? Write your answer as a fraction in simplest form.

Answer:

n = 2; the number equals two

Step-by-step explanation:

n/2 = 2n - 3

2/2 = 2(2) - 3

1 = 4 - 3

1 = 1

n = 2

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer:

$54.87

Step-by-step explanation:

The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.

The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.

The total area to be covered with mulch is 108 - 15 = 93 square feet.

The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.

Therefore, the total cost of the mulch will be $54.87.

Answer:  

b=2A/h-a

Step-by-step explanation:  

A=1/2h(a+b)

Multiplying by 2

2A=h(a+b)

Dividing by h  

2A/h=a+b

Subtracting a  

2A/h-a =b

b=2A/h-a

Answer:

2 ⋅ A /h -   a = b

Explanation:

Multiplying by  2 :

2 A  =  h  ( a + b )

dividing by  h

2 A /h =  a  +  b

substracting  a

2  ⋅  A /h  −  a  = b

Answer: yes anazing splenddi

Step-by-step explanation:

Answer:

B. Seraphina is not correct. The sum of the squares of the two legs of the triangle is not equal to the square of the hypotenuse.

Step-by-step explanation:

If KLM is a right triangle, then 12^2+16^2=19^2,

144+256 = 361

400 = 361 false

so, KLM is not a right triangle as the sum of the squares of the two legs are not equal to the square of the hypotenuse.

The sum of the squares of the two legs of the triangle is not equal to the square of the hypotenuse. Seraphina is incorrect.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

Seraphina says that ΔKLM is a right triangle.

Let us check whether triangle ΔKLM is a right triangle or not.

By the Pythagoras theorem, we have

19² = 16² + 12²

361 = 256 + 144

361 ≠ 400

Thus, the triangle is not a right triangle.

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Answer:

Step-by-step explanation:

28 x 14 equals 392 so the answer is 392

Answer:

Call the number of pizzas x;They buy pizzas from the supplier at:4x+100They sell at:7xWhen these two expressions match they will start to make a profit; so:4x+100=7xRearranging:3x=100x=1003=33.3So after the 33rd pizza they will start to make a profit.For example at the 34th they have payed:34%C3%974+100=236$ to the supplier;Selling they will get: 7%C3%9734=238$. sorry if this is complex

Answer:

n = -24/7

Step-by-step explanation:

3 -7n = 27

-7n = 24         Subtract 3 from both sides

n = -24/7        Divided by -7 both sides

So, the answer is n = -24/7

Answer:

Below

Step-by-step explanation:

Subtract 3 from both sides of the equation THEN divide both sides of the equation by  - 7

Answer:

80 miles per day

Step-by-step explanation:

Let the unit rate be x miles per day for humpback whale

It means that in one day humpback whale travels x miles

Given that it traveled for 25 days

in 1 day humpback whale traveled = x miles

in 1*25 days humpback whale traveled = x*25 miles

Thus, in 25 days humpback whale traveled 25x miles

given that humpback whale traveled 2000 mile sin 25 days

thus,

25x = 2000

x = 2000/25 = 80

Thus, unit rate for humpback whale is 80 miles per day

Answer:

c = 8

Step-by-step explanation:

4x³ + cx² + x + 2 ÷ x + 2 = ...

first we divide

4x³ + cx² by x + 2

and that is by doing 4x³/x = 4x².

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

now we need to find the remainder, as with regular number divisions :

4x² × (x + 2) = 4x³ + 8x²

which we need to subtract from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

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

0 cx² - 8x²

now we pull down the next position (x) and divide that by x + 2

4x³ + cx² + x + 2 ÷ x + 2 = 4x² + 1

- 4x³ + 8x²

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

0 cx² - 8x² + x

and the same again, to find the remainder, we have to subtract 1×(x + 2) = x + 2 from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

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

0 cx² - 8x² + x

- x + 2

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

cx² - 8x² 0 0

the polynomial is divisible by x + 2, if the remainder is 0.

so,

cx² - 8x² = 0

cx² = 8x²

c = 8

Answer:

2nd option bro

Step-by-step explanation:

answer

= amount to be paid by kylee to repair her car = $ 400

And this loss is claimed under comprehensive deductible worth $375

So the extra amount which is to be paid to insurance company is =$ 25

= $ 25

Kylee receive from her insurance company when she files her claim for $25.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Kylee's car was broken into, and her stereo and GPS system worth $425 total were stolen.

The amount to be paid by Kylee to repair her car is $400

And this loss is claimed under a comprehensive deductible worth $375.

So the extra amount which is to be paid to an insurance company will be

⇒ $400 - $375

⇒ $25

Kylee receive from her insurance company when she files her claim for $25.

The complete question is...

Kylee's car was broken into, and her stereo and GPS system worth $425 total were stolen. If Kylee's insurance policy summary is given below.

The amount to be paid by Kylee to repair her car is $400

And this loss is claimed under a comprehensive deductible worth $375.

How much will Kylee receive from her insurance company when she files her claim?

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Hi there!

Answer:

\(\boxed{-12m -3 }\)

Step-by-step explanation:

\(-\frac{3}{4} ( 16 m + 4 )\)

\(= ( - \frac{3}{4} ) ( 16m + 4)\)

\(= ( -\frac{3}{4} ) ( 16 m) + ( - \frac{3}{4} ) (4)\)

\(= -12m - 3\)

Have a great day!

Answer:

- 12m - 3

Step-by-step explanation:

\( - \frac{3}{4} (16m + 4) \\ \\ = - \frac{3}{4} \times 16m - \frac{3}{4} \times 4 \\ \\ = - 3 \times 4m - 3 \\ \\ = - 12m - 3\)

Answer:

The width and length of the rectangle are \(22\) and \(16+x\), for \(x > -16\), respectively.

Step-by-step explanation:

From Geometry, we remember that area of the rectangle (\(A\)) is defined by:

\(A = w\cdot l\) (1)

Where:

\(w\) - Width.

\(l\) - Length.

In addition, we know that area is described by a first-order polynomial:

\(A = 352+22\cdot x\) (2)

Meaning that is the product of another first-order polynomial and a constant. That is:

\(A = a\cdot (b+c\cdot x)\)  (3)

Now we determine the Great Common Divisor of 352 and 22:

\(352 = 2\times 2\times 2 \times 2 \times 2 \times 11\)

\(22 = 2\times 11\)

The Great Common Divisor is 22.

Then, the area of the rectangle can be expressed by this expression:

\(A = 22\cdot (16+x)\) (3b)

According to this, the width and length of the rectangle are \(22\) and \(16+x\), for \(x > -16\), respectively.

Answer:

After applying the distributive property, Ezra's expression was 8y + 16

After he used the commutative property, his expression was 16 + 8y

Step-by-step explanation:

Distributive property rule: a(x+y) = ax + ay
   Not much to explain here

Commutative property rule: a + b = b + a   or  xy = yx
   We use addition rule in this case, simply place 16 in front of 8y