Which is the Better buy?
Regular Popcorn (8cups) ($4.00)
Large Popcorn (15cups) ($6.00)

Answer:

Step-by-step explanation:

Given the perimeter of a rectangle P = 80 inches

Let 'x' be the width of a rectangle.

i.e.

x = width

As the length of a rectangle is three times its width. Thus,

length = 3x

We know that perimeter is the sum of all the sides (width and length) of a rectangle. So,

The Perimeter of a rectangle = 2(width + length)

substituting P = 80, width = x, length = 3x

80 = 2(x + 3x)

80 = 2x + 6x

80 = 8x

divide both sides by 8

80/8 = 8x/8

10 = x

Thus, the value of x = 10

Therefore,

The width = x = 10 inches

The length = 3x = 3(10) = 30 inches

Thus,

Hello!

3x + 4 = 1

3x + 4 - 4 = 1 - 4

3x = -3

3x/3 = -3/3

x = -1

The solution of the equation 3x + 4 = 1 is -1.

The answer is:

C) x = -1

Work/explanation:

To solve this equation, I subtract 4 from each side:

\(\sf{3x+4=1}\)

Subtract :

\(\sf{3x=-3}\)

Divide each side by 3:

\(\sf{x=-1}\)

Hence, C is correct.

Accοrding tο the prοvided statement, there will be 21 favοrable results.

A cοmpοsite number is a pοsitive integer that can be fοrmed by multiplying twο smaller pοsitive integers. Equivalently, it is a pοsitive integer that has at least οne divisοr οther than 1 and itself.

A prime integer οnly has twο factοrs: οne and itself. A cοmpοund integer is made up οf at least three cοmpοnents, and οccasiοnally much mοre.

A prime number (οr a prime) is a natural number greater than 1 that is nοt a prοduct οf twο smaller natural numbers. A natural number greater than 1 that is nοt prime is called a cοmpοsite number. Fοr example, 5 is prime because the οnly ways οf writing it as a prοduct, 1 × 5 οr 5 × 1, invοlve 5 itself. Hοwever, 4 is cοmpοsite because it is a prοduct (2 × 2) in which bοth numbers are smaller than 4.

Primes are central in number theοry because οf the fundamental theοrem οf arithmetic: every natural number greater than 1 is either a prime itself οr can be factοrized as a prοduct οf primes that is unique up tο their οrder.

4, 6, 8, 9, 10, 12 - these are the cοmpοsite numbers pοssible as sum.

Favοurable number οf οutcοmes = 21 ans.

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

The price of the cost per quart of laundry detergent is A = $ 3.47

Given data ,

Let the unit cost rate be A

Now , There are 4 quarts in a gallon, so a 2-gallon container contains 8 quarts.

To find the price per quart, we can divide the total cost by the number of quarts:

Price per quart = Total cost / Number of quarts

Price per quart = $27.76 / 8 = $3.47

Hence , the price per quart of laundry detergent is $ 3.47

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The coordinates are ordered pairs with the x value listed first.

The change in x position is, 8-7=1

The change in y position is, 3-(-2)=5

Since the midpoint is halfway between A and B, the change will stay the same,

So, for B,

x is 7-1=6

y is -2-5=-7

The coordinnates of B is (6,-7)

Applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

When two secants intersect and form an angle outside the circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs.

Given the following:

m∠MEJ = 1/2(MJ - KL)

30 = 1/2(MJ - KL)

60 = MJ - KL

KL = MJ - 60

m∠MFJ = 1/2(MJ + KL)

50 = 1/2(MJ + MJ - 60)

100 = 2MJ - 60

2MJ = 100 + 60

2MJ = 160

MJ = 160/2

MJ = 80°

KL = MJ - 60 = 80 - 60

KL = 20°

Thus, applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

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Answer:

If solving for x, the answer is x = -2b - 4.

Step-by-step explanation:

If solving for b, the answer is b = -2 - \(\frac{x}{2}\).

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill\)

\(\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}\)

The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments

Degree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45

Mean squares between groups is calculated as follows:

Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58

Mean squares within groups is calculated as follows:

Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places

F ratio is calculated as follows:

F= Mean squares between groups/Mean squares within groups

= 58/8.89

= 6.524184477

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Given

Procedure

The natural log, or ln, is the inverse of e.

The answer would be option B. 2 = e^(3x+1)

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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Answer:

6 cubic feet

Step-by-step explanation:

Since each cube represents 1 cubic foot

volume of the prism = number of cubes * volume of 1 cube

Given

number of cubes = 6

volume of 1 cube = 1cubic foot

Substitute

volume of the prism = 6 * 1

volume of the prism = 6 cubic feet

Answer:

The value is  \(z = -2.5\)

Step-by-step explanation:

From the question we are told that

   The the random selected observation    \(x = 25\)

    The mean is  \(\mu = 50\)

    The standard deviation is  \(\sigma = 10\)

Generally z score is mathematically represented as

        \(z = \frac{x - \mu}{\sigma }\)

=>   \(z = \frac{25 - 50}{10 }\)

=>   \(z = -2.5\)

Answer:

1

Step-by-step explanation:

steps are in picture.Ignore hand writing

Therefore, the height of the rectangle and the radius of the semicircle should be 8 feet each in order for the Norman window to admit the most light.

The distance along the line defining a half circle's boundary is known as the semi circle's perimeter. It is made up of the diameter of the semi circle, which is a straight line that passes through the center of the circle, and the semi circle's curving arc. For example, he radius of the semicircle and the height of the rectangle such that the window will admit the most light. A semi circle's diameter must be determined before calculating the circumference. This may be accomplished by determining the radius of the semicircle, which is the separation between any two points on the circle and the circle's center. Simply said, the diameter is twice the radius.

How to solve?

If the perimeter of the Norman window is 32 feet, then each side of the rectangle must be 8 feet long. ( using 2(l+b))

The radius of the semicircle must also be 8 feet, as the perimeter of a semicircle is equal to 2 * pi * radius.

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The approximate volume of the solid generated when the region enclosed by the curves is rotated around the line y = -7 is 390.462 cubic units.

To find the volume of the solid generated by rotating the region enclosed by the curves around the line y = -7, we can use the method of cylindrical shells.

First, let's find the points of intersection between the curves x + 3 = y^2 and 3y = 6 - x. Solving these equations simultaneously, we have:

x + 3 = y^2

3y = 6 - x

Rearranging the second equation, we get:

x = 6 - 3y

Substituting this value of x into the first equation, we have:

6 - 3y + 3 = y^2

9 - 3y = y^2

Rearranging this equation, we get:

y^2 + 3y - 9 = 0

Using the quadratic formula, we can solve for y:

y = (-3 ± √(3^2 - 4(1)(-9))) / (2(1))

Simplifying this expression, we get:

y = (-3 ± √(9 + 36)) / 2

y = (-3 ± √45) / 2

Since we are interested in the region enclosed by the curves, we consider the positive value of y:

y = (-3 + √45) / 2

Next, we need to find the limits of integration for rotating the region. The lower limit is the y-coordinate of the point of intersection, and the upper limit is the y-coordinate of the line y = -7:

Lower limit: (-3 + √45) / 2

Upper limit: -7

Now, let's set up the integral to calculate the volume using the cylindrical shell method:

V = ∫[a,b] (2πy)(radius)(height) dy

The radius is the distance between the line y = -7 and the curve x + 3 = y^2:

radius = |-7 - y^2 - 3| = |-(y^2 + 10)| = y^2 + 10

The height is the differential dy, and the limits of integration are from the lower limit to the upper limit we found earlier.

V = ∫[(-3 + √45) / 2, -7] (2πy)(y^2 + 10) dy

Evaluating this integral will give us the volume of the solid generated when the region is rotated around the line y = -7.V ≈ ∫[-7,0.894] 2πy * (y^2 + 4) dy

Using numerical integration with the trapezoidal rule, the approximate volume is:

V ≈ 390.462 cubic units

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Answer:

15,659,568

Step-by-step explanation:

To calculate the expression 2308208 * 12 - 12038928, we can follow the order of operations (PEMDAS/BODMAS):

1. Multiply: 2308208 * 12 = 27698496

2. Subtract: 27698496 - 12038928 = 15659568

Therefore, 2308208 * 12 - 12038928 equals 15,659,568.

Answer:

w=25 degrees, x= 155 degrees, y= 155 degrees, z=155 degrees

Step-by-step explanation:

Angle W and angle I are equal because they are located on same line with PARALLEL lines A and C

Angle X and angle I need to add up to 180 degrees because they together are a strait line, so angle X is 155 because 155+25 =180

Angle Y and angle I are equal because they are exactly the same but lower on the line

Angle Z is same as angle X explenation just a different strait line

Answer:

W=25 degrees

X=155 degrees

Y =155 degrees

Z= 155 degrees

Step-by-step explanation:

Complete Question

Consider H0: μ=38 versus H1: μ>38. A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with σ=7.2.

Calculate the p-value. Round your answer to four decimal places.

Answer:

The   \(p-value = 0.030742\)

Step-by-step explanation:

From the question we are told that

  The population mean is  \(\mu = 38\)

   The sample size is  n = 35

   The sample mean is  \(\= x = 40.27\)

   The standard deviation is  \(\sigma = 7.2\)

The null  hypothesis is  \(H_o\): μ=38

The alternative hypothesis is H1: μ>38

Generally the test statistics is mathematically represented as

      \(t = \frac{ \= x -\mu }{\frac{\sigma }{ \sqrt{n} } }\)

=>    \(t = \frac{ 40.27 - 38 }{\frac{ 7.2 }{ \sqrt{ 35} } }\)

=>    \(t =1.87\)

Generally from the z table the p-value of  \((Z > 1.87 )\)  is  

    \(p-value = P(Z > 1.87) = 0.030742\)

Answer:

|6|-|1|=5

|6|=6

Step-by-step explanation:

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

c. 0.3974

Step-by-step explanation:

Given;

number of white balls, W = 17

number of red balls, R = 18

Total number of balls, T = 35

The number of ways the event will occur is given by

= P(2 whites) and P(2 reds)

= P(2whites) x P(2 reds)

= 17C2 x 18C2

= 136 x 153

= 20,808

The total number of possible outcome

= 35C4

= 52,360

The probability = 20,808 / 52,360

                          = 0.3974

The correct option is "C"

Probability that the sample contains two white balls and two red ones is equal to 0.3974.

So, option c. is correct.

Probability is a discipline of mathematics concerned with numerical explanations of the likelihood of an event occurring or the truth of a claim.

Number of white balls \(=\boldsymbol{17}\)

Number of red balls \(=\boldsymbol{18}\)

Total number of balls \(=\boldsymbol{35}\)

Probability that the sample contains two white balls and two red ones  

\(=\frac{\binom{17}{2}\binom{18}{2}}{\binom{35}{4}}\)

\(=\frac{\frac{17!}{15!2!}\frac{18!}{16!2!}}{\binom{35!}{31!4!}}\)

\(=\boldsymbol{0.3974}\)

So, option c. is correct.

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Answer:

225 calories

Step-by-step explanation:

1 recipe makes

12 standard sized pancakes

2 pancakes are 1/6 of the recipe

1/6 of the recipe has 150 calories

6 × 150 calories = 900 calories

The full recipe of 12 pancakes has 900 calories

1/2 recipe was made

1/2 recipe has 1/2 × 900 calories = 450 calories

1/2 recipe made 8 pancakes

4 pancakes are half of the half recipe or 1/4 recipe

1/4 × 900 calories = 225 calories

Answer:

i) Consecutive interior angles

ii) Supplementary angles

iii) The two oars are parallel by consecutive interior angles theorem

Step-by-step explanation:

i) m∠1  and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles

ii)x = 10

m∠1 = 6x + 18

= 6(10) + 18

= 60 + 18

= 78

m∠2 = 9x + 12

= 9(10) + 12

= 90 + 12

= 102

m∠1 + m∠2 = 72 + 108 = 180

Since m∠1 and m∠2 add to 180, they are supplementary angles.

iii) The two oars are parallel

consecutive interior angle theorem:

If  a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel