Solve the expression one-half x (48 ÷ 6) – 2 + 5 using PEMDAS.

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If the cost to fill a gas tank in 1995 is $15 then the cost to fill a gas tank in 2015 is equals to the $31.25.

Price Index is a effective method of comparing relative change in the price of a quantity with respect to its price in a reference year. This year which we use as a reference is called the base year and price index is ratio of the price of a product in a year to its price in the base year ( expressed in percentage ).

The cost to fill a gas tank in 1995 = $15

Price index in 1995 = 100.8%

price index in 2015 = 210.0%

In this case we want to determine the cost to fill a gas tank in 2015. Let the required cost value be x dolars. Using the formula, price index in 1995/price index in 2015 = reference value/ value in 2015

=> 100.8% /210% = 15/x

=> 2015 cost value, x =( 15 × 210 )/100.8

=> x = 3150/100.8

=> x = 31.25

Hence, required value is $31.25.

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Complete question:

If it cost $15 to fill a gas tank in 1995, how much would it cost to fill the same tank in 2015. 1995 index is 100.8%

2015 index is 210.0% round your answer nearest cent.

Check the picture below.

so the center of the circle is the midpoint of that diameter, and its radius is half its length.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ r(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~4 - (-2)~~)^2 + (~~7 - (-1)~~)^2} \implies r=\sqrt{(4 +2)^2 + (7 +1)^2} \\\\\\ r=\sqrt{( 6 )^2 + ( 8 )^2} \implies r=\sqrt{ 36 + 64 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~10^2\implies {\large \begin{array}{llll} (x-1)^2+(y-3)=100 \end{array}}[/tex]

The calculated value of the surface area of the sphere is  676π

Given that

Radius, r = 13 inches

The formula for the surface area of a sphere is:

Surface area = 4πr^2

where r is the radius of the sphere

Substituting the given value of radius r = 13 inches, we get:

Surface area = 4π * 13^2

So, we have

Surface area = 676π

Hence, the surface area is 676π

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The value of the cosine of ∠L in triangle LMN is approximately 0.98 using Pythagorean Theorem.

To find the cosine of ∠L in triangle LMN, we first need to use the Pythagorean theorem to find the length of side LM, since only have the lengths of NM and LN:

[tex]LM^2 = LN^2 - NM^2\\LM^2 = 40^2 - 9^2\\LM^2 = 1521[/tex]

[tex]LM = \sqrt{1521}[/tex]

LM = 39

Now that we know the length of all three sides of the triangle, we can use the cosine rule to find the cosine of ∠L:

cos(L) = [tex](LM^2 + LN^2 - NM^2)[/tex] / (2 x LM x LN)

cos(L) = [tex](39^2 + 40^2 - 9^2)[/tex] / (2 x 39 x 40)

cos(L) = 0.975

Rounding to nearest hundredth:

cos(L) = 0.98

Therefore, the value of cosine of ∠L in triangle LMN is approximately 0.98.

The ratio of the neighbouring side to the hypotenuse is known as the cosine of an angle in a right triangle. As L is not a straight angle in this situation, its value must be determined using the cosine method. Whether a triangle is a right triangle or not, the cosine rule can be used to relate the lengths of its sides and angles.

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79 hours will it take for one person to harvest the entire strawberry patch.

The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.

Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.

The strawberry patch's measurements must first be changed from decameters (dam) to meters.

1 decameter (dam) = 10 meter

Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.

The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.

The strawberry patch's area is therefore:

Area of strawberry patch = length × width = 17 m × 14 m = 238 m²

We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:

[tex]\frac{Area of strawberry patch}{ Area picked per hour }[/tex] = a number of hours needed to harvest the complete patch.

The total harvesting time is [tex]\frac{238 m2 }{3 m2/hour}[/tex] = 79.33 hours nearly equal to 79

Therefore, it would take one person 79 hours to gather the complete strawberry patch.

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Answer:

A

Step-by-step explanation:

A has a positive slope

Option A is the answer. The system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:

8c + 6v ≤ 70

8c + 6v ≤ 7016c + 20v ≥ 150

The cost of c gallons of chocolate ice cream is $8c, and the cost of v containers of vanilla ice cream is $6v. Krystal wants to spend no more than $70 on ice cream, so the inequality for the total cost of ice cream is:

8c + 6v ≤ 70

Krystal needs at least 150 servings of ice cream, and each gallon of chocolate ice cream provides 16 servings, while each container of vanilla ice cream provides 20 servings. The inequality for the total number of servings of ice cream is:

16c + 20v ≥ 150

Therefore, the system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:

8c + 6v ≤ 70

16c + 20v ≥ 150

Option A is the correct answer.

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48% of the people polled like playing golf.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

The percentage of people polled who like playing golf can be calculated by dividing the number of people who like golf (3,360) by the total number of people polled (3,360 + 3,640 = 7,000) and then multiplying by 100 to express the answer as a percentage:

(3360 ÷ 7000) x 100% = 48%

Therefore, 48% of the people polled like playing golf.

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According to given information, the algebraic expression that represents the total number of quarters that Jake and Molly have is: 32 + q.

What is algebraic expression?

An algebraic expression is a mathematical phrase that contains numbers, variables, and arithmetic operations, such as addition, subtraction, multiplication, and division. It can also include exponents, roots, and other mathematical symbols.

The algebraic expression that represents the total number of quarters that Jake and Molly have is:

32 + q

where 32 represents the number of quarters that Jake has on his desk and q represents the number of quarters that Molly has in her purse.

Adding these two quantities together gives the total number of quarters that Jake and Molly have.

Therefore, the algebraic expression that represents the total number of quarters that Jake and Molly have is:

32 + q

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To get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies, you would use a proportional relationship.

Let's say x represents the number of eggs used to make a certain number of cookies, y represents the number of cookies made, and z represents the number of eggs needed to make some other number of cookies.

Then, we can set up the proportion:

x eggs / y cookies = z eggs / (some other number of cookies)

We can then solve for z by cross-multiplying:

z eggs = x eggs * (some other number of cookies) / y cookies

This formula tells us how many eggs are needed to make the specified number of cookies, based on the number of eggs used and the number of cookies originally made.

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Step-by-step explanation:

To find the percentage of a fraction you divide the top by the bottom and multiply by 100. So 3/4 = 0.75 then 0.75 x 100 = 75%. Now you need to find 3/4ths or 75 percent of 200. An easy way to do this is find 1/4 of 200. So 200/4 = 50. Now you need 3/4 of 200, not just one fourth so multiply 50 by 3 to get 150. The class has made 150 cranes.

Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.

A closed, 2D structure with a finite number of line segments is referred to as a polygon. A polygon's number of vertices and its number of line segments are always identical. The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides.

P = (Side length) x n

The apothem of each of the 9 isosceles triangles that make up the regular nonagon is 12 cm.

The angle at the circle's centre is 360/9 = 40º.

Hence, the sides of the regular nonagon, if the apothem of a isosceles triangles is 12 cm.

2*12 tan (40/2) = 8.73 cm

Then the perimeter:

P = 9 x 8.73

P = 78.57 units

Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.

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One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.

An arithmetic sequence is a sequence of numbers where each term is found by adding or subtracting a constant value from the previous term. The constant value is called the common difference and determines the rate at which the sequence increases or decreases.

One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.

Assuming that the initial cost of the service is $100 and the subscription fee increases by $25 every month, then the formula

=> f(n) = 100 + 25n

It can be used to calculate the cost of the subscription for any given month n.

For example, the cost of the subscription for the 5th month would be

f(5) = 100 + 25(5) = $225.

Similarly, the cost of the subscription for the 10th month would be

f(10) = 100 + 25(10) = $350.

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Answer:

3200

Step-by-step explanation:

If we know the fact that :
1GB = 1000MB
We can form an equation to show that 16000MB divided by 5MB should give you your answer.
The answer you get is 3200.
This means that you can fit 3200 5 MB files into a 16GB flash drive.
Hoped this helped,
thank you

The probability is unlikely.

What is probability ?

A probability is a number that expresses the possibility or liability that a specific event will take place. Chances can be stated as proportions with a range of 0 to 1, or as probabilities with a range of 0 to 100.

                              Probability is a measure of how likely or likely-possible commodity is to be. For case, there's only one system to admit a head and there are a aggregate of two possible issues, hence the chance of flipping a coin and entering heads is 1 in 2.( a head or tail). P( heads) = 12 is what we write.

The value of the probability and the notation is given as

P(true) = 0.2

As a general rule of probability, we have

Range of probability value = 0 to 1 (inclusive)

Unlikely = less than 0.5

Equally likely and unlikely = 0.5

Likely = greater than 0.5

Using the above as a guide, we have the following:

The value of P(true) = 0.2 is less than 0.5

This that the probability is unlikely.

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You can get a sense of what laptops are available, which brands are well-liked, and what specifications are shared by various models by looking through these three stores.

Amazon:

Go to Amazon's homepage and hover over the “Electronics” category in the top menu bar.

Click on “Computers & Accessories” in the dropdown menu.

Under “Laptops,” you can browse through the different categories such as “

2-in-1 Laptops," "Traditional Laptops," and "Gaming Laptops."

You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.

Best Buy:

Go to Best Buy's homepage and click on "Laptops & Computers" in the top menu bar.

You can browse through the different categories such as "Laptops," "Gaming PCs," and “Chromebooks.”

You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.

Dell:

Go to Dell's homepage and click on “Laptops & 2-in-1 PCs" in the top menu bar.

You can browse through the different categories such as "Consumer Laptops," "Gaming Laptops," and "Mobile Workstations.”

You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.

Therefore, By browsing through these three retailers, you can get an idea of what laptops are available, what brands are popular, and what features and specs are common across different models.

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Answer:

4÷2=2

12÷2=6

6÷3=3

45÷9 =5

Step-by-step explanation:

The probability of selecting three red balls or having three successes when drawing balls from the urn is 0.045, which is equivalent to 4.5%.

The probability of three successes can be calculated using the binomial probability distribution formula. Since there are only two outcomes for each ball drawn (success or failure), and the trials are independent, the binomial distribution applies.

The probability of drawing a red ball on the first attempt is 5/12. Since the ball is not replaced, the probability of drawing a red ball on the second attempt is 4/11. Similarly, the probability of drawing a red ball on the third attempt is 3/10.

To obtain the probability of three successes, we need to multiply these probabilities together:

P(three successes) = (5/12) x (4/11) x (3/10)

P(three successes) = 0.04545 or approximately 0.045

Therefore, the probability of drawing three red balls or three successes from the urn is 0.045 or 4.5%. This means that out of every 100 sets of three balls drawn, we can expect to get three red balls in approximately 4-5 sets.

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The percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%".

A decreased percentage refers to the amount or rate by which a quantity or value has decreased from its original or initial value, expressed as a percentage of the original value.

According to given information:

To find the percentage increase/decrease of the DJIA over the week, we need to calculate the overall change in the index and express it as a percentage of the initial value.

Let's assume that the DJIA started the week at a value of 100. Then, the following changes would occur:

On Monday, it went down by 3.2%, so its value decreased to 96.8.

On Tuesday, it went up by 11.2%, so its value increased by 11.2% of 96.8, or 10.82, to reach 107.62.

On Wednesday, it went up by 0.7%, so its value increased by 0.7% of 107.62, or 0.75, to reach 108.37.

On Thursday, it went down by 4.8%, so its value decreased by 4.8% of 108.37, or 5.20, to reach 103.17.

On Friday, it went down by 9.4%, so its value decreased by 9.4% of 103.17, or 9.70, to reach 93.47.

Therefore, over the week, the DJIA decreased by 6.53% (from 100 to 93.47).

Rounding this to the nearest hundredth of a percentage, we get a decrease of 6.53%.

So, the percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.

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The value of p in the equation shown is 0.3

An equatiοn in writing prοving the similarity οf twο phrases. It is made up οf a series οf characters divided intο left and right sectiοns and cοnnected by an equal sign.

Equatiοns are questiοns, and the search fοr methοdical sοlutiοns tο thοse questiοns has fueled the grοwth οf mathematics. Simple algebraic equatiοns with οnly additiοn οr multiplicatiοn tο differential equatiοns, expοnential equatiοns with expοnential fοrmulas, and integral equatiοns are examples οf variοus types οf equatiοns.

The equation that is in the question is given below

p³ = -0.027

or, p=-∛0.027

or, p = -0.3

Hence the value of the p is 0.3

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Answer:

5, 30, 180, 1080, 6480, 38880, 233280

The pattern is times 6.

Step-by-step explanation:

You're welcome.

The number of different ways in which no song is liked by all three and there is at least one song liked by those two girls but disliked by the third is (b) 132 ways.

Let the song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), be denoted as : AB, BJ, and AJ.

Similarly, let the letters "A, B, J, and N" denote the song that is liked by only Amy, only Beth, only Jo, and none of them, respectively.

We know that there is at least 1 AB, BJ, and AJ, there must be 3 songs out of 4 songs which Amy, Beth, and Jo listened to.

The fourth song can be of any type : N, A, B, J, AB, BJ, and AJ (there is no ABJ because "no-song" is liked by all three),

So, we must find the number of ways to rearrange AB, BJ, AJ and a song from the set {N, A, B, J, AB, BJ, AJ}.

⇒ Case 1: Fourth song choices = N, A, B, J

All the four of choices for fourth song are different from the first 3 songs.

⇒ Number of ways to rearrange = 4! × 4 choices = 96.

⇒ Case 2: Fourth song choices = AB, BJ, AJ

All 3 of choices for fourth song repeat in the first three songs.

So, Number of ways to rearrange = (4!/2!) × 3 = 36,

So, total number of ways = 96 + 36 = 132.

Therefore, the required number of ways of arrangement is 132 ways, the correct option is (b).

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The given question is incomplete, the complete question is

Amy, Beth, and Jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible?

(a) 108

(b) 132

(c) 671

(d) 846

(e) 1105

Based on the given frequency table, it takes between 150 and 160 minutes to fly from Denver to Atlanta on Delta Airlines for 25 out of 56 observations.

The table provides frequency data on flight times (in minutes) for the first week of March 2005 from Denver to Atlanta on Delta Airlines. The frequency table shows that there were 25 flights with a duration between 150 and 160 minutes, which is the most frequent flight duration. The flight times ranged from 140 to 190 minutes.

The frequency data can be used to construct a histogram that displays the distribution of flight times for the Denver to Atlanta route. The histogram can provide further insights into the distribution of flight times, such as whether the distribution is symmetric or skewed, and the location and spread of the data.

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--The complete question is, how long does it take to fly from denver to atlanta on delta airlines? the table below shows 56 observations on flight times (in minutes) for the first week of march 2005.

FROM      TO           FREQ

140         150            1

150         160            25

160         170            24

170         180            4

180         190            2--

The incidence of skin cancer over the two years in the high exposure group is 24.39%.

To calculate the incidence of skin cancer over the two years in the high exposure group, follow these steps:
1. Determine the number of workers in the high exposure group: 800 workers
2. Subtract the initial skin cancer cases in the high exposure group from the total number of workers in the group to find out the workers without skin cancer:

800 - 185 = 615 workers
3. Calculate the number of new skin cancer cases in the high exposure group by subtracting the new cases in the low-exposure group from the total new cases:

175 - 25 = 150 cases
4. Calculate the incidence rate by dividing the new cases in the high exposure group by the number of workers without skin cancer in the high exposure group:

150 / 615 ≈ 0.2439
5. Multiply the incidence rate by 100 to express it as a percentage:

0.2439 * 100 = 24.39%.

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The deviation of a measurement from the true value, while uncertainty quantifies the reliability of the measurement.

Systematic uncertainty can be estimated for a measured value by identifying and evaluating factors that may cause a consistent deviation in the measurements. These factors may include instrument calibration errors, environmental conditions, or personal bias. To estimate systematic uncertainty, follow these steps:
1. Identify potential sources of systematic error.
2. Quantify the magnitude of each error source.
3. Combine these errors, typically by adding them in quadrature (square root of the sum of squares).
Random uncertainty, on the other hand, arises from unpredictable variations in the measurement process. It can be estimated by performing multiple measurements and analyzing the data. The steps to estimate random uncertainty are:
1. Perform multiple measurements of the same quantity.
2. Calculate the mean (average) of the measurements.
3. Calculate the standard deviation, which represents the spread of the data around the mean.
The difference between error and uncertainty lies in their definitions and how they affect measurements. Error is the difference between the measured value and the true value of a quantity. It can be classified as systematic (consistent and predictable) or random (unpredictable and variable). Uncertainty, however, represents the level of confidence with which the measured value is known, considering the limitations of the measuring process. It is often expressed as a range or interval and encompasses both systematic and random uncertainties. In summary, error is the deviation of a measurement from the true value, while uncertainty quantifies the reliability of the measurement.

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Answer: 7>x< 10

Step-by-step explanation: