in a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system to a semester-system. how many students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval? no information is available concerning an approximate value of p.

Answer:

Step-by-step explanation:

a d c

The area of the circle is increasing at a rate of 126π sq. inches per second

What are Derivatives?

The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.

Solution:

Area of Circle = πr²

To find the rate of change we need to use Derivatives

dA/dt = 2πr * dr/dt

we know that the radius is increasing at a rate of 3 inches per second so,

dr/dt = 3 inches per second

Rate of Change = 2π*21*3 inches per second

The area of the circle is increasing at a rate of 126π sq. inches per second

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The probability that they will each win a game = 0.24

Given,

The probability that Trevor will win the game p = is 0.6

The formula we will use for calculating Trevor losing the game

⇒ q = 1 - p

Now the probability of Trevor losing the game ⇒ q = 1 - 0.6

= 0.4

Now the probability that Brian wins = 0.4 when Trevor loses and the probability that Trevor wins = 0.6 when Brian loses the game.

Now the four possibilities that will decide the outcome for 2 ping pong games-

Total probability = 0.36 + 0.24 + 0.24 + 0.16

= 1

Therefore, the probability that they each win one of the games = is 0.24

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There is a total of 2520 ways to create an injective function.

What is an injective function?

A function f called an injective function (sometimes called an injection, or one-to-one function) translates different elements of its domain into different elements.

Now, we can create an injective function from a set of 5 elements to a set of 7 elements

Based on the definition of an injective function,

For 1st element, we have a total of 7 choices

For 2nd element, we have a total of 6 choices and so on.

So, total ways = 7*6*5*4*3 = 2520

Hence, 2520 ways are there to create an injective function.

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The remainder when the number 464 is divided by 60 is 44.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number 464 is divided by 60. The remainder will be calculated as,

Divide the number 464 by the basic operation of long division.

60 ) 464 ( 7

      -420

     _______

         44

When 464 is divided by 60, the remainder is 44.

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Answer: 58 degrees

Step-by-step explanation: add the 2 angles that you know together, then subtract that number from 180. This is using the triangle sum theorem.

Answer:

b is the correct answer

Step-by-step explanation:

92 degree +30 degree +angle 1 = 180 (Since, Sum of angles of triangle is 180 degree)

Therefore, angle 1 is 58 degree .

Splitting a verb represents the meaning to divide lengthwise basically by layers or along a grain.

Explanation:

Splitting a verb represents the meaning as follow :

Therefore, splitting a verb represents to divide lengthwise basically layer wise or along a grain.

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The value of the length of side DE is 6.3 units

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and DBE

From the question, we can see that the following corresponding sides on the triangles:

Sides AD and DB

Sides CE and EB

This implies that these sides are congruent sides

This is evident by the marks on these sides

Also from the figure, we have that:

The endpoints of the line DE is at the midpoint of lines AB and BC

This means that we have the following equation

DE = 1/2 * AB

Substitute the known values in the above equation, so, we have the following representation

DE = 1/2 * 12.6

Evaluate the products

DE = 6.3

Hence, the length DE is 6.3 units

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A kind of evolution through artificial selection is the practice of choosing creatures with desired features over several generations.

The mix of alleles found in an organism is known as its genotype. A phenotype is also the culmination of all the organism's discernible traits. In artificial selection, people choose animals or plants with favored phenotypic features for reproduction.

Since the phenotype is impacted by the genotype, the process of artificial selection alters allele frequencies throughout generations, resulting in the evolution of desirable features in offspring.

In conclusion, a kind of evolution through artificial selection is the practice of selecting creatures with desired qualities over several generations.

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Using percentages we know that the total price of the book that Tommy will pay is $131.04.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the price of the book is 180.

Sales tax is 4%. So, the total price:

180/100 * 4 = 7.2$ ⇒ $187.2

Now, there is a 30% discount:

187.2/100 * 30 = $56.16

⇒ 187.2 - 56.16 = $131.04

Therefore, using percentages we know that the total price of the book that Tommy will pay is $131.04.

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Answer:

4*2=8

8+1=9

Step-by-step explanation:

The shortest total length of the fence is 808 m.

What is a rectangle?

A rectangle is a quadrilateral with all four interior angles 90°.

Given that the area of the rectangular field is 800 m².

Let the length and the width of the rectangle be x and y.

Then, the area of the rectangle is:

A= xy

Or, xy = 800

x = 800/y     (1)

The perimeter of the triangle is:

2x +2y

Since the triangle is divided into three equal parts by fence, the total length of the fence is equal to the sum of the perimeter of the triangle and two times the length or width of the triangle.

Therefore, the total length of the fence is:

L = 2x + 2y + 2x

L = 4x +2y

Substitute x = 800/y into the above equation:

L = 4(800/y) + 2y

L = 3200/y +2y         (2)

Differentiate the equation with respect to y:

L' = -3200/y² +2

Substitute L'= 0 into the above equation:

0 = -3200/y² + 2

y² = 3200/2

y² = 1600

y = 400

Substitute y = 400 into equation (2):

L = 3200/400 + 2(400)

L = 8 + 800

L = 808

Hence, the shortest total length of the fence is 808 m.

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Answer:

x=21.

Step-by-step explanation:

x=21.

Answer: i need the answer

Step-by-step explanation:

HE LP

If the p-value less than the significance level then we have a type i error.

We know that if your P-value is less than the chosen significance level then you reject the null hypothesis i,e. accept that your sample gives reasonable evidence to support the alternative hypothesis.

Im statistics, a type i error means rejecting the null hypothesis when it's actually true, while type ii error means failing to reject the null hypothesis when it's actually false.

The chance that you commit type i errors is known as the type i error rate or significance level (p-value). This number is conventionally and arbitrarily set to o.o5 or 5%. Type ii errors are like "false negatives", an incorrect rejection that a variation in a test has made no statistically significant difference.

The probability of making a type i error is represented by alpha level, which is the p-value below which you reject the null hypothesis.

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The approximation of the area of the region R is 182.8125

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

The area using the Right Endpoint approximation is 182.8125.

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Answer: 42

Step-by-step explanation:

Answer: m = 4

hope thats right .

Step-by-step explanation:

Answer:

Let

Step-by-step explanation:

Let, (8,12) be (x1 and y1)

(10,20) be (x2 and y2)

We know that,

Slope = y2-y1

-----------.

x2-x1

= 20-12

-----------

10-8

= 8

-------

2

= 4 ans

so, the slope between twoo points is 4

Answer:-3

Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry

Answer: Neither.

Step-by-step explanation: I believe it's neither because I plotted the given points below and it gave me this for the result:

Hope this helps! :)

Answer:

Domain: [-3,100] if continuous. {x|x=-3,-2,0,1,4,100} if discrete.

Range: [0,100] if continuous. {y|y=0,10,19,77,100} if discrete.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

we find how many people are every square mile by dividing

397,546/387

1027 people per square mile

Town B: 264,108/261

             1012 people per square mile

1027-1012

15

Town A is bigger by 15 people so A is correct

hopes this helps

The population density of Town A is 15 more than the of Town B so, option A is correct.

It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

Town A: 397,546 people within 387 square miles,

Town B: 264,108 people within 261 square miles,

Calculate the density in Town A as shown below,

The density in Town A = Total number of people/total area

The density in Town A = 397546 / 387

The density in Town A = 1027.25

Calculate the density in Town B as shown below,

The density in Town B = Total number of people/total area

The density in Town B = 264108 / 261

The density in Town B = 1011.9

Thus, find the difference as shown below,

The density in Town A - The density in Town B

1027.25 - 1011.9

15.3 or 15

Therefore, the greater population density, is of Town A, by about 15 people per square mile.

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Answer:

x = 5

Step-by-step explanation:

[tex]\frac{45}{27}[/tex] = [tex]\frac{x}{3}[/tex] ( cross- multiply )

27x = 3 × 45 = 135 ( divide both sides by 27 )

x = 5

Answer:X=5

Step-by-step explanation:

1st. divide the numbers

2nd. Multiply all terms by the same value to eliminate fraction denominators

3rd.Cancel multiplied terms that are in the denominator

4thMove the variable to the left

which gets: x=5

The value of x is 9°

What do you mean by degree?

A unit of measure is used to measure the magnitude of an angle.

1 degree equals 1/360 of a complete revolution in magnitude.

Given that:

ΔUVW with side UW extended to X

m ∠UVW = (3x + 4)°

m ∠VWX = (8x -12)°

m ∠WUV = (x + 20)°

We know that ,

Sum of angles of triangle = 180°

m ∠UVW + m ∠WUV  + m ∠VWU = 180°

m ∠VWU = 180° - (m ∠UVW + m ∠WUV)

Also we know that sum of angles on a straight line

m ∠VWX and m ∠VWU are supplementary angles

m ∠VWX + m ∠VWU = 180°

m ∠VWU = 180° - m ∠VWX

m ∠VWX = (m ∠UVW + m ∠WUV)

Substituting the given values , we get

(8x -12)° = (3x + 4)° + (x + 20)°

8x - 3x - x = 4 + 20 + 12

           4x = 36

             x = 36/4 = 9

             x = 9°.

Therefore , The value of x is 9°

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Answer:

Step-by-step explanation:

pemdas - parenthesis , exponet, multiply, divide, add, subtract. your answer is 3.5

If m∠AOB = (3x − 6)° and m∠BOD = (5x + 14)° in this pizza, the value of x is equal to: B. 21.5.

In Mathematics, a supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.

Mathematically, a supplementary angle can be calculated by using this formula:

X + Y = 180

Where:

X and Y are measure of the angles subtended.

Generally speaking, we know that an entire pizza is circular in shape with an angular measure of 360°. This ultimately implies that, one-half of an entire pizza is equal to 180°, which means m∠AOB and m∠BOD are supplementary angles.

Substituting the given parameters into the formula, we have;

m∠AOB + m∠BOD = 180

3x − 6 + 5x + 14 = 180

8x + 8 = 180

8x = 180 - 8

8x = 172

x = 172/8

x = 21.5.

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Answer:

Step-by-step explanation:

B) 21.5

Answer:

C

Step-by-step explanation:

Working on the perimeter of the hoop, The rotation by the hoop to reach the end of 15 foot is about 1.59.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

The required formula is:

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

radius = 18 inches = 1.5 foot

Perimeter = 2 * 3.14 * 1.5

=9.42

Number of rotations = 15 / 9.42

=1.59

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Answer:

The number of cakes Sophia can make is 10.

Step-by-step explanation:

The bag of flour contains 152 quarter-cup servings. So, the quantity in t he bag has to be divided by four.

Number of cups = 152 / 4 = 38 cups

In order to determine the number of cakes she can make, divide the number of cups in the bag by the cups needed to make one cake.

38 ÷ 3 3/4

38 ÷ 15/4

38 × 4/15 = 10.1 cakes