A family of 5 went to a matinee movie on a Saturday afternoon. The movie tickets for the matinee were a special
price for each person. The family spent a combined $25 at the concession stand on drinks and popcorn. Altogether,
the family spent $57.50 at the movies.
a. Draw a tape diagram to represent the situation above. Then write an equation.
b. How does the tape diagram help you understand how much the special price was?

The equation of line is y = ( -1/2 )x + 7/2 , where the slope is m = -1/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -1 , 4 )

Let the second point be Q ( -5 , 6 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 6 - 4 ) / ( -5 - ( - 1 ) )

Slope m = 2 / ( -5 + 1 )

Slope m = -2/4 = -1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = ( -1/2 ) ( x + 1 )

On simplifying the equation , we get

y - 4 = ( -1/2 )x - 1/2

Adding 4 on both sides of the equation , we get

y = ( -1/2 )x + 7/2

Hence , the equation of line is y = ( -1/2 )x + 7/2

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B is significantly more affordable and better than A, renting for $1.62 per square foot.

Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.

To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.

1 yard² = 9 feet²

A rents for $33 per yard squared

hence A rents $33 for 9 feet squared

hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared

Thus, as B is more economical, it is better.

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We can see that the exponential model is better

The main difference between a linear and an exponential function is the way they change as their input variable (usually denoted as x) increases.

In summary, linear functions have a constant rate of change, while exponential functions have an increasing rate of change.

For the linear function;

f(x) = 946(6) + 3349

= 9025

For the exponential function;

g(x) = 3866e^0.138(6)

g(x) = 8848

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Answer:

it is 3

Step-by-step explanation:

just subtract

If a line has two points with the same x-value, then the two points are on a vertical line.

So we know that we have some kind of a linear equation, such that in two points on the line we have the same x-value.

Then we can write these two points like (x₁, y₁) and (x₁, y₂). If the x-value is the same one, then we have a line of the form:

x = x₁

Which is a vertical line, then that is the correct answer.

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Answer:

15:18

Step-by-step explanation:

So, to say 9 more apples than pears means that 15-9 = 6. Now 3 times of 6 (pears) is 6*3= 18.

Write it in ratio is 15:18!

hope this helped!

Answer:

First side: 40in

Second side: 20in

Third side: 36in

Step-by-step explanation:

Let's call the triangle's first, second, and third sides a, b, and c respectively.

The perimeter of the triangle is 96in: a+b+c=96

The length of the first side is twice the second: a=2b

The third side is 16in more than the second: c=b+16

Now, consider the equation a+b+c=96 again, but sub '2b' in for a, and 'b+16' for c, in order to find the value of b:

a+b+c=96

2b+b+b+16=96

4b=80

b=20

Use this value for b to find a and c:

a=2b=2(20)=40

c=b+16=20+16=36

Answer:

Step-by-step explanation:

Let's call the length of the second side "x". Then, the length of the first side is 2x and the length of the third side is x + 16.

The perimeter of the triangle is the sum of the lengths of its sides, so we can set up an equation to solve for x:

x + 2x + (x + 16) = 96

Expanding the equation and solving for x, we get:

4x + 16 = 96

4x = 80

x = 20

So, the length of the second side is 20 inches, the length of the first side is 2 * 20 = 40 inches, and the length of the third side is 20 + 16 = 36 inches.

The amount of water used for each month and rounded off to the nearest 1000 is;

Amount of water used in May = 12567 litres

Amount of water used in June = 452 litres

Amount of water used in July = 15623 liters

Approximate amount of water used in May to the nearest 1000 = 13,000 liters

Approximate amount of water used in June to the nearest 1000 = 0 liters

Approximate amount of water used in July to the nearest 1000 = 16,000 liters

Therefore, the amount of water used each month rounded to the nearest 1000 are 13,000, 0, and 16,000 respectively.

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Answer:

Step-by-step explanation:

To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.

First, let's define the variables:

f(x) = 2x² - x - 6 is a quadratic function with x as the variable.

g(x) = x² - 4 is also a quadratic function with x as the variable.

Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:

2x² - x - 6 = x² - 4

Next, we simplify this equation by subtracting x² from both sides:

x² + x - 10 = 0

This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.

Let's try factoring:

x² + x - 10 = (x + 5)(x - 2) = 0

So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:

x = -5 or x = 2

These are the two values of x such that f(x) = g(x).

7.48 x 8.33 = 62.3664 pounds are the weight of one cubic foot of water. 1.8 x 62.3664 = 112.26 is the weight of one cubic foot of water. Therefore, 1.8 cubic feet of water weigh about 112.26 pounds.

3 dimensions: 3 by 3 by 3

A space that is 1 foot by 1 foot by 1 foot is called a cubic foot. Add the piece's length, breadth, and height together to get the cubic feet it will hold. For instance, the volume of a dresser that is 4 feet length, 2 feet wide, and 5 feet high is 40 cubic feet.

A Cubic Unit's Operation Each unit cube's dimension of a unit cube(length, width, and height) is one unit. So, one unit of length with one unit of width and one unit of height together make a volume of one cubic unit.

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There are 70 cars altogether in the lot.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of domestic cars to imported cars = 3 : 2,

Domestic cars = 42

Since, the number of domestic cars in the shop is 42,

Therefore,

3x = 42

x = 14

Therefore, the number of total cars = 14×5 = 70

Hence, there are 70 cars altogether in the lot.

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In this equation, the regular polygon's area is 72.5.

The area of a regular polygon is determined by multiplying its perimeter by its apex. The following is a common way to write the formula: An apothem's area is equal to 1/2(ap), where a denotes the length and p the circumference. Area of pentagon = 1/2 p an is the fundamental formula for computing the area of a regular pentagon, where p stands for the pentagon's perimeter and a for its apothem.

If a polygon has equal sides and angles, it is considered to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

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yearly multiplication growth factor is  (1+0.011) = 1.011.  the year 2017, seven years after 2010, the population will be  [tex]24800*2A1.011^7 = 26,774[/tex]

what is multiply ?

Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.

yearly multiplication growth factor is  (1+0.011) = 1.011.

the year 2017, seven years after 2010, the population will be  [tex]24800*2A1.011^7 = 26,774[/tex]

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On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4

The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.

By BODMAS

2.4of4.5-5.6/1.4+3.8*2

10.8-5.6/1.4+3.8*2

10.8-4+3.8*2

10.8-4+7.6

14.4

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We can presume that x is a positive number because we are aware of the widening of the roadways and the increase in Jonathan's speed. It takes three seconds for Jonathan's speed to change by 234.67 + 2x feet per second.

the definition of speed. a direction or speed at which an object's location changes. The distance travelled relative to the time it took to travel that distance is how fast something is moving.

In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity.

Let's first convert Jonathan's initial speed of 160 miles per hour to feet per second, since we're measuring the change in speed every three seconds.

160 miles per hour = 160 * 5280 feet per hour = 844800 ft/h

= 844800/3600  ft/s (since there are 3600 seconds in an hour)

= 234.67 ft/s (rounded to two decimal places)

Now, let's assume that Jonathan's speed increases by x feet per second every three seconds. After three seconds, his new speed will be 234.67 + x feet per second. After another three seconds, his speed will be 234.67 + 2x feet per second, and so on.

Since we know that the roads are getting wider and Jonathan's speed is increasing, we can assume that x is a positive number.

Therefore, the rate of change of Jonathan's speed is 234.67 + 2x feet per second every three seconds.

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The table of values is

X |f(x)

0 | 4

2 | 5.33

4 | 6.67

6 | 8

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

y = 2x/3 + 4

We have the x values to be

x = 0, 2 4 and 6

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

y = 2 * 0/3 + 4 = 4

y = 2 * 2/3 + 4 = 5.33

y = 2 * 4/3 + 4 = 6.67

y = 2 * 6/3 + 4 = 8

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(A) The angular speed of the wheel in radians per minute is 3.78 radians per minute.

(B) The linear speed of a passenger in miles per hour is 4.09 miles per hour.

Angular speed is the rate at which an object rotates, measured in radians per unit of time. The unit of radians is commonly used in circular motion problems because it allows us to express angles and rotational motion in a consistent way. Linear speed, on the other hand, is the rate at which an object moves in a straight line, measured in units of distance per unit of time.

(A) To find the angular speed of the Ferris wheel in radians per minute, we first need to convert the given rate of revolutions per hour to revolutions per minute. We can do this by dividing the rate by 60 since there are 60 minutes in an hour. Therefore, the wheel completes

=> 100/60 = 5/3 revolutions per minute.

Next, we need to find the angle that the wheel turns in one minute, which we can do by dividing a full rotation (360 degrees) by the number of revolutions per minute. In this case, the angle turned in one minute is

=> (360 degrees)/(5/3 revolutions per minute) = 216 degrees per minute.

To convert this angle to radians, we multiply by (π/180) since there are π/180 radians in one degree. This gives us an angular speed of

=> (216 * π/180) = 3.78 radians per minute.

(B) Using these values, we can calculate the linear speed of the passenger as follows:

Linear speed = (distance traveled)/(time taken) = (π * 72 feet)/(1/5 minutes) = (π * 72 * 5 feet/minute) = (360 * π feet/minute)

To convert this speed to miles per hour, we divide by the number of feet per mile (5280) and multiply by the number of minutes per hour (60), giving us:

Linear speed = (360 * π feet/minute)/(5280 feet/mile) * (60 minutes/hour) = 4.09 miles per hour (rounded to two decimal places).

Therefore, the linear speed of the passenger on the Ferris wheel is approximately 4.09 miles per hour.

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To prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.

What is the SSS Similarity Theorem?

The SSS Similarity Theorem states that two triangles are similar if the ratio of all three pairs of corresponding sides of two triangles are equivalent.

Given ΔUVW and ΔXYZ, where:

UV corresponds with XY, thus UV/XY = 50/40 = 1.25

WU corresponds with ZX, thus WU/ZX = 40/32 = 1.25

WV corresponds with ZY, thus WV/ZY = 60/48 = 1.25

Since all the ratio of all three corresponding sides of both triangles are equivalent, therefore both triangles can be proven to be similar by the SSS Similarity Theorem.

Therefore, to prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.

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The range and interquartile range is 11 and 2 respectively. The score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile is 7 and 4 respectively.

To calculate the range, we subtract the smallest value from the largest value:

Range = Largest Value - Smallest Value = 12 - 1 = 11

To calculate the interquartile range, we first need to find the first and third quartiles. We can do this by ordering the scores from lowest to highest and finding the median of the lower half and upper half of the scores, respectively:

1, 4, 5, 5, 6, 6, 7, 12

The median of the lower half (Q1) is the middle value of the numbers 1, 4, 5, and 5, which is 4.5 (the average of the two middle values).

The median of the upper half (Q3) is the middle value of the numbers 6, 6, 7, and 12, which is 6.5.

Interquartile Range = Q3 - Q1 = 6.5 - 4.5 = 2

To find the score that corresponds to the 75th percentile, we first need to find the index corresponding to the 75th percentile. We can do this by multiplying 0.75 by the total number of scores, which is 8. This gives us an index of 6, meaning the 75th percentile score is the 6th score in the ordered list:

1, 4, 5, 5, 6, 6, 7, 12

The score that corresponds to the 75th percentile is 7.

To find the score that corresponds to the 25th percentile, we can follow the same procedure. The index corresponding to the 25th percentile is 0.25 times the total number of scores, or 2. The 2nd score in the ordered list is 4.

The interquartile range is a better description of variability in the data than the range because the range is heavily influenced by outliers. In this case, the range is 11, which is largely driven by the outlier score of 12. The interquartile range, on the other hand, only considers the middle 50% of the scores and is therefore less affected by outliers. It gives a more accurate measure of the spread of the scores around the median.

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The standard error of a statistic or an estimate of a parameter is the standard deviation of its sampling distribution.

The standard deviation of the sample distribution is referred to as the standard error in statistics. In most cases, the sample mean of a data set differs from the actual population mean. SE is used to denote it. It is used to gauge how well a sample of a population represents that population. Data, samples and populations, means, medians and modes, dependent and independent variables, standard deviations, variance, and other concepts are all covered in the large field of statistics.

The standard error is one of the mathematical tools used in statistics to estimate variability. It is abbreviated as SE. The standard error of a statistic or an estimate of a parameter is the standard deviation of its sampling distribution. We can define it as an estimate of that standard deviation.

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The actual length of the house is 30 feet.

What is a scale factor?

A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.

It is given that:

Width of the kitchen = 4 inches.

Length of the kitchen= 6 inches.

It is also given that the actual width of the house is equal to 20 feet.

Now we have to find the length of the house:

The proportion will be:

[tex]\frac{4}{6} =\frac{20}{Length} \\Length=\frac{20*6}{4} \\Length=30feet[/tex]

Therefore the actual length of the house is 30 feet.

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Answer

D. 4.2794....

Step-by-step explanation:

A, B, and C all have repeating decimal numbers, meaning they are rational. D's decimals are not repeating but infinite, meaning it is an irrational number.

The sample variance and standard deviation are given as follows:

Variance = 87.22 %.

Standard deviation = 9.34%.

To obtain the variance and the standard deviation first, we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:

Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10

Mean = 75.85.

Then we must obtain the sum of the differences squared between each observation and the mean, as follows:

(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825

The sample variance is given by the above sum divided by one less than the sample size, hence:

Variance = 784.9825/9

Variance = 87.22 %.

The standard deviation is the square root of the variance, hence:

Standard deviation = sqrt(87.22)

Standard deviation = 9.34%.

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The following that are possible units for measuring mass in the metric system include the following below:

B. Kilogram

D. Gram.

This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.

Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.

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