Situation
ion below. Then wr
1.
A rectangle is 4 times as long as it is wide. The
perimeter of a rectangle is 50 cm. What are the
dimensions of the rectangle?
Identify what you are looking
for and assign variables..
Write equations to model the
situation described in the
problem.

Check the picture below.

so the figure is really just a semi-circle, a rectangle and three triangles, let's simply get their area and sum them all up.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ semicircle }{\cfrac{1}{2}\pi (2)^2}~~ + ~~\stackrel{ rectangle }{(4)(5)}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{2})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{1})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{2})}} \\\\\\ 2\pi ~~ + ~~20~~ + ~~3~~ + ~~2~~ + ~~4 ~~ \approx ~~ \text{\LARGE 35.28}[/tex]

The cost of red grapes per pound is $2.8.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, cost of a large watermelon and 2.4 pounds of red grapes is $7.71.

Let the cost of red grapes be x.

So, the total cost = 7.71+2.4x

Cost of a platter of pre-cut fruit and 1.6 pounds of red grapes is $9.95.

The total cost = 9.95+1.6x

Person and his brother spent same amount of money.

So, 7.71+2.4x=9.95+1.6x

2.4x-1.6x=9.95-7.71

0.8x=2.24

x=2.24/0.8

x=$2.8

Therefore, the grapes cost per pound is $2.8.

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The measure of the missing angle α is 62 degrees.

The sum of angles on the straight line adds up to 180 degrees.

From the diagram;

Since the sum of angles on a straight line adds up to 180 degrees.

Angle 1 + Angle 2 + Angle 3 = 180

Plug in the values

118 + α = 180

Subtract 118 from both sides

118 - 118 + α = 180 - 118

α = 180 - 118

α = 62°

Therefore, the value of angle α is 62 degrees.

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The tables/graphs with their equations are

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

Tables, Graphs and equations

Table (a)

Here, we notice that:

The output is the 5 less than three times the input

This is represented as

y = 3x - 5

Table (b)

Here, we notice that:

The output is the 2 more than negative 12 times the input

This is represented as

y = -12x + 2

Graph (c)

Here, we have the following points

(4, 0) and (0, -5)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx - 5

Using the other point, we have

0 = 4m - 5

This gives

m = 5/4

So, we have

y = 5/4x - 5

Graph (d)

Here, we have the following points

(0.5, 0) and (0, 3)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the other point, we have

0 = 0.5m + 3

This gives

m = -6

So, we have

y = -6x + 3

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The function V(r) is representing the volume of basketball when the radius is r.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, the function V(r) =  4/3 πr³, can be used to find the volume of air inside a basketball given its radius (r).

We are asked to find that what does V(r) represents,

Here, V(r) is the function's output is r is the input, the only variable in the formula is r, that means the volume totally depends on the radius of the basket ball. & volume is changes with the radius.

Thus, this function represents the volume of the basketball when radius is r.

Hence, the function V(r) is representing the volume of basketball when the radius is r.

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The difference between rational algebraic expressions and fractions is discussed above.

In mathematics, an expression or mathematical expression is a combination of terms, both variables and constants.

For example → 2x + 3y + z

Given is to explain how is rational algebraic expressions different with fractions.

In a rational algebraic expressions, the expression function in the numerator and denominator both are non - zero polynomials. A fraction is of the form {x/y}, in which it is not necessary that {x} and {y} should be polynomials only. They can be numbers also.

Therefore, the difference between rational algebraic expressions and fractions is discussed above.

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first one is a

Step-by-step explanation:

Brand₂ has the highest impact on the price of a smartphone, increasing the price by $80 for each unit increase in that variable.

Regression analysis is a statistical method that helps us understand the relationship between two or more variables.

Based on the regression equation, we can determine which brand increases the price of a smartphone the most. The regression equation is as follows:

Price = 1100 + 50 (Brand₁) + 80 (Brand₂) + 30 (Brand₃) + 20 (Battery Life) + 10 (Camera Resolution)

In this equation, the intercept (1100) represents the average price of a smartphone with all other variables set to zero. The coefficients for each variable represent the change in the price of a smartphone for a one-unit increase in that variable, holding all other variables constant.

Brand₁ and Brand₂ have a lower impact on the price, increasing it by $50 and $30, respectively, for each unit increase in those variables. Battery life and camera resolution have the smallest impact on the price, increasing it by $20 and $10, respectively, for each unit increase in those variables.

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Complete Question:

Can brand, battery life, and camera resolution affect a smartphone's price? Use α= o.05 to perform a regression analysis for the Smartphones01BC dataset and answer the following questions. Solve this problem using Excel and Mega Stat, and write your complete answers in the Response Box so I know that you can interpret the output.

Based on your regression equation, which brand increases the price of a smartphone the most? Use the statistics from your output to explain your answer.

Answer:

(24) + (20) + (8) = 52 ft^2

Step-by-step explanation:

This figure is a compound of 3 rectangles that can be split up like in my attached picture.

The top, horizontal rectangle is 8x3 = 24 sq ft.

The bottom, almost square rectangle is 4x5 = 20 sq ft.

The middle rectangle has a height of 4 feet and a width of (8-6) = 2 feet.

So, its area is 4x2= 8 sq ft.

The compound figure is the sum of all of these areas:

24 + 20 + 8 = 52

The area of the compound figure is 52 sq ft.

Area of 1 = 8 * 3 = 24

Area of 2 = 4 * 2 = 8

Area of 3 = 5 * 4 = 20

Total area = 24 + 8 + 20 = 52

The graph that best models the exponential function is given as follows:

Graph A.

An exponential function is defined as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

y = 200000(1.06)^x.

The value of the home after 5 years is given as follows:

y = 200000(1.06)^5

y = $267,645.

Which is best approximated by the Graph A.

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There are 5,760 ways to arrange the books on the bookshelf.

A permutation is an ordered arrangement of objects, and it can be calculated as follows:

ⁿPₓ = n! / (n - x)!

where n is the total number of objects and r is the number of objects that we are arranging.

To determine the total number of ways in which we can arrange the books on a bookshelf, we need to first calculate the total number of possible arrangements. We can do this by using the fundamental principle of counting, which tells us that the total number of possible arrangements is equal to the product of the number of ways in which each book can be arranged.

Therefore, the total number of possible arrangements can be calculated as follows:

Total number of possible arrangements = Number of ways to arrange math books × Number of ways to arrange history books × Number of ways to arrange science books

In our case, we have 4 math books, 5 history books, and 2 science books, so we can calculate the number of permutations for each type of book as follows:

Number of ways to arrange math books = ⁴P₄ = 4! / (4-4)! = 4! / 0! = 24

Number of ways to arrange history books = ⁵P₅ = 5! / (5-5)! = 5! / 0! = 120

Number of ways to arrange science books = ²P₂ = 2! / (2-2)! = 2! / 0! = 2

Now, we can substitute these values in the formula for the total number of possible arrangements:

Total number of possible arrangements = 24 × 120 × 2 = 5,760

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a) The histogram of the data is illustrated below.

b) A cumulative percentage polygon is illustrated on histogram.

c) The cumulative percentage polygon shows us that approximately 66% of calls fall below 240 seconds.

Histograms are a way of representing data visually by dividing it into intervals or bins and plotting the frequency of data points in each bin. In this problem, we will be constructing a percentage histogram and polygon to analyze call duration data.

The call duration data is provided in seconds for 50 customers. To construct a percentage histogram, we need to first determine the bin size or interval. One way to do this is to use the square root rule, which states that the number of bins should be approximately equal to the square root of the sample size. In our case, the sample size is 50, so we can round the square root to 7 and use 7 bins.

Next, we need to determine the range of the data and set the limits for each bin. The range of the data is from 65 to 1141 seconds. We can set the limits for each bin as follows: 60-180, 181-300, 301-420, 421-540, 541-660, 661-780, 781-900, and 901-1020.

To construct the percentage histogram, we need to divide the frequency in each bin by the total sample size and multiply by 100. This gives us the percentage of data points in each bin. We can then plot these percentages as bars of equal width for each bin.

The percentage polygon is constructed by connecting the midpoints of the tops of each bar in the histogram with straight lines. This creates a polygon that represents the distribution of data in the histogram.

In this problem, we are asked to analyze call center performance if a call duration target of less than 240 seconds is set. From the percentage histogram and polygon, we can see that the majority of calls fall within the first three bins, which correspond to call durations of 60-180, 181-300, and 301-420 seconds. Only a small percentage of calls exceed 420 seconds.

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The statement that describes the conversion is To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound

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

The double number line

On the double number line, we have:

16 ounces = 1 pound

This means that

To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound

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The area of the composite figure is equal to 99 mm² square milimetresmetres.

The composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the bigger horizontal rectangle = 11 mm × 3 mm

area of the bigger horizontal rectangle = 33 mm²

area of the smaller horizontal rectangle = 5 mm × 2 mm

area of the smaller horizontal rectangle = 10 mm

area of the vertical rectangle = 14 mm × 4 mm

area of the vertical rectangle = 56 mm²

total area of the composite figure = 33 mm² + 10 mm² + 56 mm²

total area of the composite figure = 99 mm²

Therefore, the area of the composite figure is equal to 99 mm² square milimetres.

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Answer:

6

Step-by-step explanation:

12 is the full length. point E marks 1/2 of the line. 12-6=6

if it's asking the length of d-e, then the answer is (6) because the entire length of line is twelve and in the top line e-f in 6 and 6-12=6

The values and graph of the equation 3x - 2y = 6 is attached below while the slope is 3/2

The equation of a straight line can be represented in various forms. One of the most commonly used forms is the point-slope form, which is represented as:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line, which is the rate of change of y with respect to x.

Another common form of the equation of a line is the slope-intercept form, which is represented as:

y = mx + b

where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

In this problem, we need to write the table of values and the find the slope of the line.

3x - 2y = 6

rewriting this equation;

2y = 3x - 6

y = 3x/2 - 3

when y = 0

0 = 3x/2 - 3

3x/2 = 3

3x = 2 * 3

3x = 6

x = 2

when x = 0

y = 3(0)/2 - 3

y = 0 - 3

y = -3

The slope of the line can be calculated using the two points from above.

slope (m) = y₂ - y₁ / x₂ - x₁

m = -3 - 0 / 0 - 2

m = 3/2

The slope is 3/2

The graph of the equation is attached below

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Answer:

(X-3)5=575

5x-15=575

5x=575+15

5x=590

X= 590:5

X= 118

Answer: The two shaded parts of the wall have a combined area of 20m * 12m + 16m * 15m = 240 + 240 = 480 square meters.

Therefore, the volume of yellow paint required is 480 * 0.1 = 48 litres.

Step-by-step explanation:

Answer:

x = 4 twice.

Step-by-step explanation:

x^2-8x+ 16=0

Bring the constant to the other side.

x^2-8x=-16

Half the coefficient of x and square the result. Add to both sides.

x^2-8x+[-8/2]^2=-16+(-8/2)^2

x^2-8x+16= 16-16

x^2-8x+16=0

Now, whenever there's a perfect square constant, take the root of that constant. Since the coeff. of x is negative (-8),

(x-4)(x-4)=0  [-4^2=16 and -4+(-4)=-8]

Therefore, x-4=0 twice.

x=4 twice.

Hope this helps!  :]

List of perfect squares smaller than 10 are: {1, 4, 9}

Subtract 1 from each value to get a new list of {0, 3, 8}

None of these new values are a factor of 12.

The possible answers are: 0, 3, and 8

A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;

x = 0.258, y = 0.

x = 7.742, y = 0.

Vertex = (4, 14).

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Answer: 19

Step-by-step explanation: 15 x 19 = 285ft^2

The length of the radius of the circle is 7.5 inches.

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

Given that the diameter of the circle is 15 inches.

The radius of the circle is half the measure of the diameter.

That is,

R = d/2

R = 15/2

R = 7.5 inches

Hence, the length of the radius of the circle is 7.5 inches.

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Answer: 157.5

To find the volume of the smaller box, we use this equation:

Fitting the dimensions into the equation:

So, the volume of the smaller box is 262.5³.

If the height of the second box is %60 percent bigger, we can use this equation to figure out the new height.

10 × 1.6 = 16

Well, that's a good question! If we were to multiply by 0.6, the box would get smaller, instead of bigger. We add the 1.0 because we have to add the original height, not just the added height.

Now, the equation looks like this:

Now, the second boxes volume is 420³.

To find out the difference between the two volumes, we can subtract.

Therefore, the difference between the two volumes is 157.5.

The ratio tables based on the information will be:

12 16

3 4

36 48

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.

Since the ratio is 3:4. When the smaller number is 36, the larger number will be:

= 4/3 × 36.

= 48

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The probability that the orange has a mass of more than 80g is (y/x).

Given is that one of the oranges is chosen at random from the crate of oranges.

Assume that the total number of oranges are {x} and the oranges with a mass of greater than 80 are {y}. So, we can write -

P{E} = y/x

Therefore, the probability that the orange has a mass of more than 80g is (y/x).

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Answer:

48 residents

Step-by-step explanation:

Let's assume that there are 100 residents in the neighboring house. 64% of the residents subscribe to "Our Football" magazine, so there are 64 residents who subscribe to it. 84% of the residents subscribe to "Top Gear" magazine, so there are 84 residents who subscribe to it. The number of residents who subscribe to both magazines can be calculated by finding the intersection of the two sets, which is equal to the number of residents who belong to both sets. This can be found using the formula:

Number of residents subscribing to both magazines = 100 - (100 - 64) - (100 - 84)

= 100 - 36 - 16

= 48

Therefore, 48 residents of the neighboring house subscribe to both magazines.

Answer: 46ft

Step-by-step explanation:

Alright so for this you must reference the pythagorean theorem which is:

a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.

You can therefore set this up like this:

a^2+20^2=50^2 (where a is the side you are looking for- listed as x)

Solve:

a^2=50^2-20^2

a^2=2500-400

a^2=2100

sqrt(a^2)=sqrt(2100)

a= 45.8257569496

Round: a (or x)=46

The degree of the polynomial function represented by the graph is 4 and its leading coefficient is negative

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

The graph

The degree of the polynomial function is the number of times the curve tends to touch or intersect with the graph

In this case, we have

Degree = 4

For the leading coefficient, we have

leading coefficient = negative

This is because the graph opens down

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