- A gardener wants to enclose his rectangular garden with fencing. The garden
is 20 feet long and 8 feet wide. How many feet of fencing does the gardener
need?

In 1st part expression there is a subtraction of 75% of 0.75d from orignal price and  in 2nd expression the discount of 75% of the orignal price.

In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, −, ×, ÷, etc.) that represent a quantity or a mathematical operation.

Expressions can be simple or complex, and they can involve variables, constants, and functions. Expressions can be evaluated or simplified to obtain a numerical or symbolic result.

d: This represents the original price of the video game in dollars.

0.75d: This represents the price of the video game after the 75% discount has been applied. It is equivalent to subtracting 75% of the original price (0.75 times d) from the original price (d).

0.25d: This represents the amount of the original price that is discounted by 75%. It is equivalent to subtracting the sale price (d - 0.75d) from the original price (d), since the discount is 75% or 0.75 of the original price (d).

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[tex]\cos( 50^o )=\cfrac{\stackrel{adjacent}{MN}}{\underset{hypotenuse}{MO}}[/tex]

keep in mind that the opposite side is the side "facing off" the angle, and the adjacent is the one "not" facing it off.

The angle of depression formed by the cable is approximately 41.4 degrees.

The angle of depression is the angle formed by the horizontal line and the line of sight from the observer to an object that is lower than the observer's position. In this case, the observer is at the top of the tower and the object is at the end of the cable that is stretched to a point 350 feet away from the base of the tower.

To find the angle of depression, we can draw a diagram as follows:

where h is the height of the tower, d is the horizontal distance from the base of the tower to the point where the cable is attached, and θ is the angle of depression that we want to find.

From the diagram, we can see that

tan(θ) = h / d

We know that the length of the cable is 500 feet and the horizontal distance from the base of the tower to the point where the cable is attached is 350 feet. We can use the Pythagorean theorem to find the height of the tower:

h^2 = 500^2 - 350^2

h = sqrt(500^2 - 350^2)

h = 300

Now we can substitute the values we have found into the equation for tan(θ) to get:

tan(θ) = 300 / 350

θ = tan^-1(300/350)

θ ≈ 41.4 degrees

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Yes, Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.

Sample

A subset of the population is known as a sample. A sample is a smaller group of individuals or things chosen from the population.

Error

The distinction between the estimated value of a population parameter and the true, but unknown, value of that parameter is referred to as an error. Sampling error is the difference between the sample statistic and the population parameter. Inference is less accurate if the sample is too small or if the sample is biased, and the resulting sample statistics may differ from the actual population parameters. 

Hence, from the above, we can conclude that yes the Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.

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The function representing the value of car is 10000 (1 - 0.045)[tex]^{(4t)}[/tex]. The percentage rate of change per quarter is 0.68%. The solution has been obtained by using the substitution method.

What is the substitution method?

The substitution approach is a widely used method in algebra for solving simultaneous linear equations. The name of the method implies that the value of one variable from one equation is changed in the second equation.

We are given that the value of car depreciates 18% every year.

Let f(t) represent the car's worth after t years.

So, we get the function as:

⇒ f(t) = 10000 (1 - 0.18/4)[tex]^{(4t)}[/tex]

⇒ f(t) = 10000 (1 - 0.045)[tex]^{(4t)}[/tex]

Now, the percentage rate of change per quarter is:

⇒ r = [tex](1-q)^{4}[/tex] - 1

Here, q = 0.045

On substituting the value, we get

⇒ r = [tex](1-0.045)^{4}[/tex] - 1

⇒ r = -0.68%

Hence, the required solutions have been obtained.

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Thus, the system of equation have no solution, solved by the elimination method.

To create an equation from one variable using the elimination approach, you can either add as well as subtract the equations.

To eliminate a variable, add the equations when the coefficients from one variable are in opposition, and subtract the equations when the coefficients from one variable are in equality.

Given system of equations are-

-3x - y = 10 ...eq 1

3x + y = -8  ... eq 2

Add both eq.

-3x - y + 3x + y = 10 - 8

0 = 2

As both value of x and y are getting cancelled.

But, 0 ≠ 2

Thus, the system of equation have no solution, solved by the elimination method.

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When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%

The variation between the real value and the predicted value, in relation to the theoretical value, is known as percentage error.

When compared to the real number and expressed in percent format, percentage error seems to be the gap between the anticipated amount and the actual number. The equation is as follows:

To put it another way, you divide the deviation between the true answer and the answer you guessed by the true answer to get the percent.

Amount paid by Fredrick for cup of coffee:  €1.65

Actual amount: €1.50.

percentage error = (amount paid - actual amount)/amount paid * 100 %

percentage error = (1.65 - 1.50)/1.65 * 100

percentage error = 9.09%

Thus, When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%

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The amount Sylvia should deposit today: P = A / (1 + r/n)^(nt)Where:P = P = $ ___The principal amount is $9,463. So, Sylvia has to deposit $9,463 today.

Sylvia wants to go on a cruise in 4 years. She could earn 7.3% compounded monthly in a bank account if she were to deposit the money today. She needs to have $14,000 in 4 years. To determine the amount Sylvia should deposit today to earn $14,000 in 4 years with a 7.3% interest rate compounded monthly,

we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:A = the amount of money at the end of the time periodP = the principal, or initial amount of moneyr = the annual interest raten = the number of times interest is compounded per yeart = the time period, in yearsWe need to solve for P.

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The values in the table represent a linear function with the function rule y = 3x + 6, where x is the input value and y is the output value.

To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the input and output values. This means that for every increase or decrease in the input value, there is a constant increase or decrease in the output value.

Looking at the input and output values in the table, we can see that for every increase of 1 in the input value, the output value increases by 3. This constant rate of change indicates that the values in the table represent a linear function.

To find the function rule, we can use the slope-intercept form of the equation for a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we can find the slope by dividing the change in output values by the change in input values:

slope = change in output / change in input = 3/1 = 3

Therefore, the slope of the function is 3. To find the y-intercept, we can use one of the points in the table. For example, we can use the first row, which gives an input value of 0 and an output value of 6:

y = mx + b

6 = 3(0) + b

b = 6

Therefore, the y-intercept of the function is 6. Combining the slope and y-intercept, we can write the function rule as:

y = 3x + 6

This means that for any input value x, the output value y is equal to three times x plus six.

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Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.

What is the range?

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.

Here, we have

Given: A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks for every unit up to 14.

We have to determine which measure of variability should be used for both sets of data to determine the location with the most consistent temperature.

We concluded that Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.

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A statement about the model that is true include the following: A. the number of customers visiting the bodega decrease by 25 for every inch of rainfall.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models the situation is given by;

y = 90 + (-25)x

y = 90 - 25x

By comparison of the two equations, we have:

mx = -25x

Slope, m = -25.

In conclusion, the rate of change is -25 customers per inch of rain.

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Answer:0.04

Step-by-step explanation:

Answer:

probability of getting a red ball= 6/11

Step-by-step explanation:

we know, to find a probability of a event

1st we have to get the total number of events that can occur,i.e

6+4=11

and

the total probability of getting a red ball is 6/11

which is the required answer..

Therefore, the answer is option 4: a reflection over the line y=-x-6.

In mathematics, a transformation is a process that changes the position, size, or shape of a geometric object in some way. Transformations are often used in geometry and other branches of mathematics to study the properties of shapes and their relationships to each other.

Here,

To determine which transformation carries the rhombus onto itself, we need to identify the symmetries of the rhombus. A rhombus has two types of symmetry: rotational symmetry and reflectional symmetry.

Option 1: a rotation of 180 degrees clockwise about (-2,-2)

This transformation takes each point of the rhombus and rotates it 180 degrees clockwise about the point (-2,-2). Since the rhombus has rotational symmetry of order 2 (i.e., a rotation of 180 degrees carries the rhombus onto itself), this transformation carries the rhombus onto itself.

Option 2: a rotation of 90 degrees counterclockwise about (-2,-2)

This transformation takes each point of the rhombus and rotates it 90 degrees counterclockwise about the point (-2,-2). Since the rhombus does not have rotational symmetry of order 4 (i.e., a rotation of 90 degrees does not carry the rhombus onto itself), this transformation does not carry the rhombus onto itself.

Option 3: a reflection over the line y=x+10

This transformation reflects each point of the rhombus over the line y=x+10. Since the rhombus does not have reflectional symmetry over this line, this transformation does not carry the rhombus onto itself.

Option 4: a reflection over the line y=-x-6

This transformation reflects each point of the rhombus over the line y=-x-6. Since the rhombus has reflectional symmetry over this line, this transformation carries the rhombus onto itself.

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Step-by-step explanation:

I added a photo of my solution

Answer:

3m+2L = 7

4m + L = 6

Step-by-step explanation:

Let m = cost of the muffins

Let L = cost of the lattes

3m+2L = 7

4m + L = 6

To solve

Multiply the second equation by -2 and add them together.

3m+2L = 7

-8m + -2L = -12

-------------------------

-5m  = -5

Divide by -5

-5m/-5 = -5/-5

m = 1

Then

4(1) +L = 6

L = 6-4

L =2

The solution is

muffins cost 1 dollar and lattes cost 2 dollars.

The approximate value of the home in 1987 is approximately $161,872.

The formula to calculate the approximate value of a home in 1987 is:

V1987 = 81600 x (1 + 0.12)^7

V1987 = 81600 x 1.987

V1987 = 161872

Therefore, the approximate value of the home in 1987 is approximately 161,872.

To arrive at this answer, we first started with the value of the home in 1980, which was 81,600. We then multiplied this value by 1.12, which is the 12% increase every year, to the seventh power. This resulted in a value of 1.987. We then multiplied this value by the original value of the home in 1980, which gave us the approximate value of the home in 1987. We then rounded the answer to the nearest hundred dollars, which resulted in the answer of 161,872.

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The scale of the map is 1:2, the distance from Averton to Charlbrough is 12 kilometers, and the distance in the map is 6.25 cm.

We know that 25 kilometers are represented in the map using only 12.5 centimeters. Now, let's simplify this:

25 kilometers / 12. 5 cm = 2

This can be expressed as a scale of 1:2 in which each centimeter represents 2 kilometers.

We know the distance on the map is 6 cm, let's now convert this to kilometers:

6cm x 2 = 12 kilometers

We know the distance is 12.5, using this information let's find out the distance on the map.

12.5/ 2 =6.25 cm.

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Answer:

Step-by-step explanation:

17y-12

11y+3(2y-4)

11y+6y-12

17y-12

I hope this helps!

As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as  the average rate of change of the function from x = 0 to x = 3.

A function is a rule in mathematics that links every element of one set, known as the domain, to a certain element of some other set, known as the range. A function is just a relationship between the values of the input and the output, where the outcome specifically depends on the input. A function can be depicted in a number of different ways, including as an equation, a chart, or a list of values. For instance, the function f(x) = 2x multiplies the input value x by two to get the output value f. (x). The range of this function is indeed the set of all real numbers, and its domain is any set of real numbers.

given

To determine (3, f(3)) on the function graph the average rate of change of the function from x = 0 to x = 3.

According to the graph, the point (0, f(0)) is on the y-axis and has a y-coordinate of 2, while the point (3, f(3)) is on the line that connects the points (2, 0) and (4, 6) and has a slope of m = 3. As a result, we have:

f(0) = 2 and f(3) = 6

We can determine the slope of the line connecting these two points using the slope formula:

m = (f(3) - f(0)) / (3 - 0) = (6 - 2) / 3 = 4/3

As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as  the average rate of change of the function from x = 0 to x = 3.

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The United States has a population of about 320 million, so if homicides were proportional to Honduras' rate of homicide, we would expect about 12,800 deaths due to homicides in the United States.

This is calculated by taking the population of the United States (320 million) and multiplying it by the Honduras' homicide rate of 40 per 100,000 people.


To calculate this, we first need to find Honduras' homicide rate. The World Bank has this information, which states that the rate is 40 per 100,000 people. We then need to take the population of the United States (320 million) and multiply it by the rate.

This equals 128 million homicides per 100,000 people in the United States. This comes out to 12,800 deaths due to homicides in the United States. Round this to the nearest person, and you get 12,800.

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The surface area of this rectangular prism is equal to 158 ft².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

SA = 2(WH + LW + LH)

Where:

By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;

SA = 2(8 × 3 + 5 × 8 + 5 × 3)

SA = 2(24 + 40 + 15)

SA = 2(79)

SA = 158 ft².

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The percentage of males who prefer football to baseball and basketball is 20%.

The percentage refers to the quotient or ratios between two values or quantities.

In this situation, the percentage of males who prefer football to baseball or basketball is expressed as the number of football fans over the total number of the three sports fans.

To compute the percentage, the quotient is multiplied by 100.

            Baseball    Basketball     Football     Total

Male         13                  15                 20          48

Female    23                  16                  13          52

Total        36                  31                 33        100

Percentage of males who prefer football = 20% (20/100 x 100)

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Answer: The equation x^2+3x+4 is a quadratic equation.

A quadratic equation is a second-degree polynomial equation in one variable (usually x), where the highest power of the variable is squared (x^2).

In this case, x^2+3x+4 is a second-degree polynomial with the variable x raised to the power of 2. Therefore, it is a quadratic equation.

Linear equations, on the other hand, are first-degree polynomial equations in one variable, where the variable is not raised to any power higher than 1.

Step-by-step explanation:

Ted's work to evaluate the expression 21 ÷ 3 + 5* 3 is incorrect, as he evaluated the division before the multiplication. He follow the wrong order of operations. The correct answer is 22, not 36.

Ted's work is incorrect. In step 1, he evaluated the division before the multiplication, which is incorrect according to the order of operations (PEMDAS). According to the order of operations, multiplication and division should be done before addition and subtraction. Therefore, the correct way to evaluate the expression is as follows:

21 ÷ 3 + 5 * 3

= 7 + 15 (evaluating multiplication before addition)

= 22

Thus, the correct answer is 22, not 36 as Ted calculated. It is important to follow the order of operations in order to arrive at the correct answer.

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_____The given question is incomplete, the complete question is given below:

Ted tried to evaluate the expression 21 ÷ 3 + 5* 3. Here, is his work:

21 ÷ 3 + 5* 3

= 7 + 5 * 3          step 1

= 12 * 3              step 2

= 36

Is his work correct?

The answer to the given problem is x = 3 and y = 1.

Simultaneous equations are a set of equations with multiple variables that must be solved at the same time. In other words, they are equations that have more than one unknown value, and their solutions must satisfy all the equations in the system. These equations are used to model many real-world situations, such as business and engineering problems.

Given equation;

x + y = 4 ...................... (1)

2x - 5y = 1 ..................... (2)

Multiplying by 5 equation (1) we get,

5(x + y = 4)

5x + 5y = 20 ................. (3)

Adding equation (2) and (3) we get,

2x - 5y = 1

5x + 5y = 20

7x = 21

x = 21/7

x = 3

Putting x=3 in equation(2), we get

2x - 5y = 1

2(3) - 5y = 1

6 -5y =-5y = 1 - 6

-5y = -5

y = -5/-5

y = 1

As a result, the equation's answer is x = 3 and y = 1.

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The complete question is:

x+ y = 4 ; 2x - 5y = 1 solve by simultaneous equation

so we can look at this as two triangles, one on the upper part, it has a base of 5+5 and a height of 5, and another triangle on the lower part, it has a base of 5+5 and a height of 12, let's get their area and sum them up.

[tex]\stackrel{ \textit{upper part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{5})}~~ + ~~\stackrel{ \textit{lower part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{12})}\implies25+60\implies \text{\LARGE 85}[/tex]

The length and the width of the rectangle are 1cm and 8/3cm

The formula that is used to calculate the area of a rectangle is expressed with the equation;

A = lw

Given that the parameters are;

From the information given, we have that;

Length = 3w - 7

Substitute the values, we have;

40 = (3w - 7)w

expand the bracket

40 = 3w² - 7w

3w² - 7w - 40 = 0

3w² + 15w - 8w - 40 = 0

3w(w + 5) - 8(w + 5) = 0

w = 8/3 or - 5

Length = 3(8/3) - 7 = 1

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Applying the linear pair theorem, the measures of the angles in degrees are:

m<ABD = 112°; m<DBC = 68°

The Linear Pair Theorem, also known as the Linear Pair Postulate, is a basic postulate in geometry that describes the relationship between two adjacent angles that form a straight line.

According to the Linear Pair Theorem, if two angles are adjacent and form a straight line, then they are supplementary. In other words, their measures add up to 180 degrees.

Therefore, according to the linear pair theorem, we have:

m<ABD + m<DBC = 180°

Substitute:

7x + 196 + 9x + 176 = 180

16x + 372 = 180

16x = 180 - 372

16x = -192

x = -192/16

x = -12

m<ABD = 7x + 196 = 7(-12) + 196 = 112°

m<DBC = 9x + 176 = 9(-12) + 176 = 68°

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