Yesenia placed bricks around her circular garden. It took 157 bricks to go all the way around the garden. If each brick was 4 inches long, what is the diameter of the garden?

Maria and Gabriella each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Maria spent $114 on 10 ft² of grass sod and 9 geraniums. Gabriella spent $90 on 5 ft² of grass sod and 10 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?

Answer:

$11/ft^2 of grass, $12/geranium

Step-by-step explanation:

Based on the properties of a rhombus, the measure of each numbered angle is:

m<1 = 36°

m<2 = 72°

m<3 = 72°

m<4 = 72°

m<5 = 36°

Using the properties mentioned above, we can solve for the numbered angles as explained below:

ED and FG are parallel, therefore, m<3 = 72° (alternate interior angles)

m<4 = 72° [bisected angles of a rhombus by the diagonal]

m<2 = m<4 (alternate interior angles)

m<2 = 72°

m<1 = 180 - m<2 + 72 [sum of a triangle]

Substitute:

m<1 = 180 - 72 + 72

m<1 = 36°

m<5 = m<1 [opposite angles are equal in a rhombus]

m<5 = 36°

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Answer:

  C. Exactly one solution

Step-by-step explanation:

You want to know the number of solutions of the system of equations shown in the graph.

A solution to a system of equations is the set of points on a graph where all of the equations are satisfied simultaneously. For a system of two linear equations, it will be the point(s) where the lines intersect.

Here, the lines intersect at one point, so there is exactly one solution.

Answer:

Step-by-step explanation:

a) The value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam, is 3/5. This is because out of the 5 students, 3 (Ashley, Brayden, and Carmen) got a 5 on the AP Statistics exam.

b) The 10 possible simple random samples of size n = 2 are:

Ashley, Brayden; P = 2/2 = 1

Ashley, Carmen; P = 2/2 = 1

Ashley, Dale; P = 1/2 = 0.5

Ashley, Eve; P = 1/2 = 0.5

Brayden, Carmen; P = 2/2 = 1

Brayden, Dale; P = 1/2 = 0.5

Brayden, Eve; P = 1/2 = 0.5

Carmen, Dale; P = 1/2 = 0.5

Carmen, Eve; P = 1/2 = 0.5

Dale, Eve; P = 0/2 = 0

c) To create the dotplot for the sampling distribution of p:

Label the number line with 0, 0.5, 1

For each sample proportion calculated, place a dot above the corresponding value on the number line

Repeat this process for all sample proportions

d) Yes, the sample proportion is an unbiased estimator of the population proportion. This means that on average, the sample proportion will equal the population proportion. In other words, the mean of the sampling distribution of the sample proportion will equal the population proportion.

Answer:

Δ = 20

Step-by-step explanation:

let triangle be Δ , then

32 - Δ = Δ - 8 ( subtract 32 from both sides )

- Δ = Δ - 40 ( subtract Δ from both sides )

- 2Δ = - 40 ( divide both sides by 2 )

Δ = 20

Answer:

1.8

Step-by-step explanation:

The equation we are given is [tex]\frac{n}{-1.5} = -1.2[/tex]. We can multiply both sides by -1.5 to get n = 1.8.

Answer:

N = 1.8

Step-by-step explanation:

You do cross multiplication

n*1 = -1.5 * -1.2

1n = 1.8

To check it, we plug in 1.8

1.8/-1.5 = -1.2

In 4 hours, and 30 minutes (or 4.5 hours), Wanda will catch up to the hector.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Hector competing in a 42-mile bicycle race he’s already completed 18 miles of the racing and is traveling at a constant speed of 12 mph.

Let x = the hours needed for Wanda to catch up to Hector.

Hector has already completed 18 miles. Hector travels at 12 miles per hour.

After x more hours, Hector will travel

18 + 12x miles

Wanda travels at 16 miles per hour. In x hours, she travels

16x miles

If Wanda catches up to Hector, then

16x = 18 + 12x

4x = 18

x = 4.5 hours

Therefore, Wanda will catch up to the hector at 4 hours, 30 minutes (or 4.5 hours).

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Complete question:

Answer:

1 1/15

Step-by-step explanation:

4 x 4/15 = 4/1 x 4/15 = 16/15 = 1 1/15

If sally has 20 water bottles and then he gives 10 to jerry, the number of water bottles he have left is 10.

According to the question, it is given that :

Total number of water bottles sally had = 20 water bottles

Number of water bottles, Sally gives to jerry = 10 water bottles

Number of water bottles sally have left are

Total number of water bottles sally had - Number of water bottles sally gives to jerry

Number of water bottles sally have left = 20 - 10

Number of water bottles sally have left = 10 water bottles

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On solving the provided question, we can say that value of the total surface area of the outside plus inside of the tube will be (1033+1143) = 2176 cubic cm

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Volume is 704cm3

Total Surface area is 2176

Cylinder volume is calculated as follows: cylinder volume = π * radius² * height.

Length of metallic tube, h = 35 c

Radius (R) =  5.2 cm

inner Radius (r) = 4.7cm

Volume of metal =

3.14*(27.04-22.09)*35

704 cm cubic

Surface area inside

2*22/7*4.7*35

1033 cubic cm

Surface area outside

2*22/7*5.3*35

1143 cubic cm

Value of the total surface area of the outside plus inside of the tube will be (1033+1143) = 2176 cubic cm

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I’m pretty sure it’s y = 0x+4

The diagram of the scatter plot is given in the attached image below.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

The data are shown in the table below:

x      y

4     1

5.5   2

7.5   3

9     4

11     5

14     6

From the given choices:

the last diagram of the scatter plot is given in the attached image.

Hence, the scatter plot is given below.

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The augmented matrix for the system of equations 7-6y+8x=0, 6x=-3-2y is:

| 7 -6 8 | 0 |

| 6 0 -2 | 3 |

This matrix represents the system of equations in a matrix form where the coefficients of the variables are on the left and the constant terms are on the right.

An augmented matrix is a rectangular array that is formed by appending the coefficients of variables and the constant terms of a system of linear equations in a single matrix. It is used as a tool in linear algebra to represent a system of linear equations in a compact form.

The augmented matrix is typically written as:

| a11  a12  a13 |  b1  |

| a21  a22  a23 |  b2  |

| a31  a32  a33 |  b3  |

where aij represents the coefficient of the i-th equation for the j-th variable, and bi represents the constant term for the i-th equation.

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The value of k depends on the specific functions f and g and their growth rates. The growth factor is a measure of how quickly a function grows relative to another function. To determine the value of k, you would need to compare the growth rates of f and g.

Here's how you can do to finding the value of k:

        n² = k * n

        n = k

This is just a simple example, and the specific value of k will depend on the growth rates of the specific functions you're comparing.

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The probability that a randomly chosen patient will be admitted for a reason other than coronary care is equal to one less than the likelihood that they will be admitted for that reason.

The likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 less than the likelihood that they will be admitted for that reason. For instance, if the chance of being admitted for coronary care is 0.25, the chance of being admitted for a different reason is 0.75. This is due to the requirement that the total number of outcomes must equal 1. Accordingly, if one outcome has a 0.25 probability, then the chance of every other outcome must equal 0.75. As a result, the likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 minus the likelihood that they will be admitted for that reason.

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Answer:

x=1°

Step-by-step explanation:

I gave my explanation in the previous question. Now, I can just solve:

(15x-30)°=45°

15x°=15°

x=1°

Answer:

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

Slope = (y2 - y1) / (x2 - x1)

Plugging in the given points, we get:

Slope = (9 - (-7)) / (7 - (-3))

= 16 / 10

= 1.6

So the slope of the line passing through (-3, -7) and (7, 9) is 1.6.

Answer:

m = 8/5

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

(-3,-7) and (7,9)

We see the y increase by 16 and the x increase by 10, so the slope is

m = 16/10 = 8/5

So, the slope is 8/5

If you draw five cards at random from a standard deck of 52 cards, the probability that there are at least 4 distinct characters (letters or numbers) is 0.8406.

This probability is calculated using the combination formula. The formula states that the number of possible outcomes when selecting r items from a set of n is equal to n!/(r! (n-r)!). consider a deck of 52 cards, each with a unique letter or number. When selecting 5 cards at random, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters.

This is because if there are 4 distinct characters, there must be a fifth card with a character that has already been drawn. Therefore, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters. Since there are 52 possible characters and we are selecting 5 cards, the probability can be calculated using the combination formula and is equal to 0.8406.

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Answer: To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the original line and use the point-slope form of a line.

The equation of the original line is 5y = 2x - 4, which we can rearrange to get y = (2/5)x - 4/5. The slope of this line is 2/5. The negative reciprocal of the slope is -5/2.

Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the slope -5/2 and the point (0, 7), we get:

y - 7 = -5/2 (x - 0)

y - 7 = -5/2 x

y = -5/2 x + 7

So the equation of the line perpendicular to 5y = 2x - 4 and passing through (0, 7) is y = -5/2 x + 7.

Step-by-step explanation:

The equation that shows the height of the tree is 42.5 = 15x + 5

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let y represent the height of the small tree and x represent the average number of feet the tree grew each month. Hence:

A small tree was planted at a height of 5 feet. Hence, b = 5.

The tree has been planted for 15 months, and is now 42.5 feet tall. This makes:

42.5 = 15x + 5

The equation is 42.5 = 15x + 5

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Answer:

see below

Step-by-step explanation:

4x^4 – 20x^2 + 25

= (2x-5)²

so the factor is 2x-5

Answer:

I'm not sure but it might be 8 42/167

Step-by-step explanation:

Answer:

4 terms

Step-by-step explanation:

-12x

15y

-17x

16y

This line represents the proportional relationship between x and y, as described by the given equation.

An equation is a physical and mathematical statement the describing physical phenomen or describe the relationship between different physical quantities. It typically consist of two or more variables which are symbol representing physical quantities and an equal sign the variable may be quantities such as force velocity your energy and the question describe how this quantities relate to each other.

To graph this relationship, I first plotted the origin (0,0) on the grid. Then, I made a table of values for x and y, using the given equation. I placed x values from 0 to 10 on the x-axis and the corresponding y values from 0 to 2.5 on the y-axis. Finally, I plotted each point on the graph to create a straight line. This line represents the proportional relationship between x and y, as described by the given equation.

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The expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.

Simplifying an expression means to write it in its simplest form by combining like terms and removing any redundant or unnecessary elements. There are several techniques you can use to simplify expressions, including:

Combining like terms: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms. To simplify an expression, you can add or subtract like terms.

Distributing: Distributing means multiplying a constant or variable by each term within a set of parentheses. For example, if you have the expression 2(x + 3), you can distribute the 2 to each term within the parentheses: 2x + 6.

Factoring: Factoring means finding a common factor among a set of terms and grouping them together. For example, if you have the expression [tex]x^{2}[/tex] + 4x, you can factor out the x: x(x + 4).

Simplifying rational expressions: Rational expressions are expressions that have one fractional term. To simplify a rational expression, you can cancel out common factors in the numerator and denominator.

Let's call the width of the portrait w and the height h. We know that the height of the portrait is 1.5 times its width, so h = 1.5w.

The area of the portrait is the product of its width and height: A = w * h = w * 1.5w =  [tex]1.5w^{2}[/tex].

The width of the frame is 4 inches all along its perimeter, so the total width of the framed portrait is w + 4 + 4 = w + 8.

The total height of the framed portrait is h + 4 + 4 = h + 8 = 1.5w + 8.

The area of the framed portrait is the product of its width and height: A = (w + 8) * (1.5w + 8) = (w + 8) * 1.5w + 8 * (w + 8) = 1.5w^2 + 12w + 64.

So, the expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.

This expression is already in standard form.

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There are 17,576,000 possible license plates consisting of 3 letters followed by 4 digits.

Fundamental Counting Principles:

The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation.

When something can be done m different ways and n different ways,

there are then [tex]m*n[/tex] ways to accomplish both.

Based on the given information, since the letters and digits may be repeated, there are:

26 ways to fill in the first letter

26 ways to fill in the second letter

26 ways to fill in the third letter

10 ways to fill in the first digit

10 ways to fill in the second digit

10 ways to fill in the third digit and

1 way to fill in the first digit (as the last digit end with 5)

Thus, by Fundamental Principle of Counting, there are 17,576,000 possible license plates.

26 x 26 x 26 x 10 x 10 x 10 x 1  = 17,576,000

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The volume of each marble in a 26 liter glass tank is 12.

The tank's volume is listed as 26.

The tank requires 20.9 liters of water to fill when 85 marbles are placed inside.

So the volume of 85 marble

= 26-20.9 = 5.1

So, volume of each marble

= 5.1/85 = 0.06

Therefore, the volume that will be covered if William wishes to use 200 marbles is:

200*0.6 = 12

Therefore, the volume of marbles in a 26 litre tank is equal to 12

Water will therefore be needed to fill the tank.

=  26 - 12 = 14

Therefore, The volume of each marble in a 26 liter glass tank is 12.

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Complete question:

William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? How much water is necessary if William uses 200 marbles?