Valeria drew a scale drawing of a house and its lot. The scale of the drawing was

12 centimeters : 7 meters. The actual length of the front patio is 21 meters. How long is the

patio in the drawing?

centimeters

Answer:

6

Your answer is correct, but since √1 = 1

we can simplify this as 6 · 1 = 6

Step-by-step explanation:

Since the given figure is a square, all four sides are equal.

Each side = 3√2

For a square of side a, the diagonal is given by

d = √(a²+a²) = √(2a²) = a√2

Here we have a = 3√2

So diagonal = x = 3√2 (√2) = 3 · 2 = 6

The margin of error to be 21.2

The formula for the margin of error for a simple random sample with a normal population and a known standard deviation is given by:

Margin of Error = z* (s / √n)

Where

z is the z-score that corresponds to the given confidence level. For a 99% confidence level, the z-score is 2.576.

Plugging in the given values, we get:

Margin of Error = 2.576 * (75 / √201) = 2.576 * (75 / 14.1) = 21.15

Rounding to one more decimal place than the sample standard deviation (which is 75), we get the margin of error to be 21.2.

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Answer:

Step-by-step explanation:

For the first question, the combinations of bananas and apples that Elena could buy for exactly $3.50 are:

2 bananas and 2 apples (A)

5 bananas and 1 apple (F)

For the second question, Andre's statement is incorrect. The first type of bus holds 50 people and the second type of bus holds 56 people. In total, 3 of the first type of bus and 3 of the second type of bus can only hold 3 * 50 + 3 * 56 = 318 people. However, there are 280 elementary school students and 40 adults, which is a total of 280 + 40 = 320 people. Hence, Andre's statement is incorrect.

For the third question, the reason why equations A and B are not equivalent is because the variables in Equation B are expressed in a different form than in Equation A. Equation A shows the relationship between the variable x and the constant value 13 and 48, while Equation B only shows the relationship between the variable x and the constant value 35. To determine if they are equivalent, we need to solve both equations for x and compare the solutions. Solving Equation A gives us x = (48 + 13) / -5 = 5.6. Solving Equation B gives us x = 35 / 5 = 7. Since the solutions are different, the equations are not equivalent.

Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.

The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.

When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.

Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.

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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.

The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.

When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.

Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.

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The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

The cones are given by the image presented at the end of the answer.

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Answer:

Angle W is 100 degrees

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

Angle W is the exterior angle of the given triangle.

We know that exterior angle is the sum of remote interior angles.

It gives us:

The abiotic factors are Sunlight, oxygen, Carbon Dioxide, Nitrogen, Clouds, Rain, Desert, Snow, Plastic, Dirt and Rock

Abiotic factors are non-living physical and chemical elements and conditions in the environment that influence the survival and growth of living organisms. The abiotic factors in the given list are:

Sunlight: The light energy from the sun that drives photosynthesis and provides energy to living organisms.

Oxygen: A colorless, odorless, tasteless gas essential for respiration in many organisms.

Carbon Dioxide: A colorless, odorless gas that is produced by respiration, combustion and decay of organic material and is used by plants during photosynthesis.

Nitrogen: An odorless, tasteless gas that makes up a major component of the Earth's atmosphere and is essential for plant growth as a component of amino acids and nucleic acids.

Clouds: A visible mass of water droplets or ice crystals suspended in the atmosphere.

Rain: Precipitation that falls from clouds as water droplets.

Desert: An area characterized by little rainfall and high temperature, often with limited vegetation.

Snow: Precipitation that falls from clouds as ice crystals.

Plastic: A synthetic or semi-synthetic material made from various organic polymers.

Dirt: The naturally occurring material that covers the surface of the earth, made up of organic and inorganic matter.

Rock: A naturally occurring solid composed of one or more minerals.

These are all abiotic factors, while the other items in the list are biotic factors, which are living or once-living elements in the environment.

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In FEM, nodal displacement is calculated using the matrix equation shown below: [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces.

A function is something that connects an input to an output.

Then, they are interpolated over entire elements using shape functions, which are essentially polynomials of different orders. Although quadratic shape functions, like a quadratic curve, are becoming common, linear shape functions, like a straight line used to approximate a distance between two locations, are the most fundamental. Even higher order shape functions (like cubic) exist, but they are rarely used in practical settings. The calculation of an element's stress uses Gauss Points rather than nodes. You can look up the GP locations for any given kind of element, but for the purposes of this discussion, let's just talk about singles.

Since [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces, the matrix equation presented below is used to determine nodal displacement.

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Complete question -

Given the tapered bar/axial element below, determine the exact displacement interpolation function and the associated exact shape functions. Show all intermediate steps.

Step-by-step explanation:

we need Pythagoras and a little bit of open mind.

Pythagoras is

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle), a and b being the legs.

the incenter means that it is the center point of the inscribed circle (being totally inside the triangle and touching every side at exactly one point).

that means that

GF = GB = GD

but GF we know : 22

so, GB = 22

now we can use the right-angled triangle ABG to find AG :

AG² = AB² + GB²

AG² = 32² + 22² = 1024 + 484 = 1508

AG = sqrt(1508) = sqrt(4×13×29) = 2×sqrt(377) =

= 38.83297568...

On solving the provided question, we can say that  Equivalent Fractions with the LCD 1/8 = 9/72 and 5/12= 30/72

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

LCD = 72

Equivalent Fractions with the LCD

1/8 = 9/72

5/12= 30/72

7/18 = 28/72

Rewriting input as fractions

1/8, 5/12, 7/18

For the denominators (8, 12, 18) the least common multiple (LCM) is 72.

LCM(8, 12, 18)

Therefore, the least common denominator (LCD) is 72.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/8 = 1/8 × 9/9 = 9/72

5/12 = 5/12 × 6/6 = 30/72

7/18 = 7/18 × 4/4 = 28/72

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The possible roots of the polynomial function f(x) is, 2/7

The polynomials are the algebraic expressions, which have multiple powers.

And based on powers of polynomials, we can categorize polynomials into following categories-

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

A polynomial function f(x) ,

Having a leading coefficient of 7 and a constant term of 2

The  possible roots of f(x) = ?

According to the Rational Root Theorem,  

Rational zero of polynomial = p/q

p  =  constant term of the polynomial

q  =  leading coefficient of the polynomial

Rational Zero =  a₀/aₙ

                       =  2/7

Hence, the rational zero is 2/7

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The magnitude of sum of the given two vectors is 5 .

A vector is an entity that possesses both magnitude and direction.

Ordinary quantities that are given with direction are called vectors; in other words, a vector quantity is any magnitude that is given with a direction. Scalar quantities refer to any quantity that is defined without any direction. In physics, vector quantities have a significant impact.

Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity.

Given vectors,

a = i + j

b = 2i + 3 j

sum of the vectors = a+ b

= i+j+2i+3j

= 3i+4j

So,

The magnitude of the sum of given vectors = √ (3 ^2 + 4 ^2 )

= √ (9 + 16 )

=   √25

= 5

Therefore, The magnitude of sum of the given two vectors is 5 .

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Answer:

Angle F i= 48 degrees

Step-by-step explanation:

Sum of angles in a triangle= 180°

8x -18+ 6x-4+5x-7= 180

Collect like terms

8x +6x +5x -18 -7-4=180

19x-29=180

19x = 180 +29

19x=209

x=209/19

x= 11

⇒Angle F= 5x-7

= 5(11)-7

= 55-7

=48 degrees

Answer:

48°

Step-by-step explanation:

A/C, 6x - 4 + 8x - 18 + 5x - 7 = 180°

or, 19x - 29 = 180°

or, x = 209 ÷ 19 = 11

So, x equals 11.

Now, Angle F = (5 × x) - 7 = (5 × 11) - 7 = 55 - 7 = 48°

Hence, Angle F measures 48°.

HOPE IT HELPED BUDDY!

There are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.

A standard deck of 52 cards contains 4 suits: spades, hearts, diamonds, and clubs.

(a) To find how many sequences have all cards of the same suit together, we need to find the number of sequences where all the cards of the same suit are together.

There are 4 possible suits, and each suit contains 13 cards.

So, the number of sequences where all the cards of the same suit are together is 13! x 4.

(b) To find how many sequences have all the clubs together, we need to find the number of sequences where all the clubs are together.

There are 13 clubs, and each club card can be placed in any order.

So, the number of sequences where all the clubs are together is 13!

Therefore, there are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.

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Rise divided by run gives you the slope. A line's rise and run can be used to calculate the slope of a line from its graph. A line's continuous slope is one of its defining characteristics. The slope is (-1,3).

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Answer:

False.

Step-by-step explanation:

8154 = eight thousand one hundred and five four

27 = Two seven.

Now we divide.

8154/27 = 302

Now you get 302 if you divide.

So therefore, its false.

Answer:

it is probably 70° of the triangle

∃x∀y(x ≤ y) We can write the negation by switching the existential and universal quantifiers, and inverting the inequality sign. The negation is therefore expressed as ∃x∀y(x ≤ y).

The negation of the statement “for all x, there exists a y such that x is greater than y” can be expressed as “there exists an x such that for all y, x is less than or equal to y”. This negation is written as ∃x∀y(x ≤ y). This is done by switching the existential and universal quantifiers, and inverting the inequality sign. By doing so, we can form an expression that is the logical opposite of the original statement, which is necessary in order to negate it.

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The possible measurements for the triangle are given as follows:

The three trigonometric ratios are defined as follows:

For this problem, we have an angle of 45º, which has the same value for sine and cosine, hence:

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True , a vector cannot have zero magnitude if one of its components is not zero.

If all of a vector's components are zero, is the vector's magnitude also 0?

A vector's magnitude cannot ever be smaller than any of its components' magnitudes. Only when all of a vector's components are 0 can the vector's magnitude be zero.

                       Their northward components are also equal, and the eastward component of vector A is equal to the westward component of vector B.

What is the vector's magnitude?

A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.

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The input values displayed on the x-axis make up the entirety of a graph's domain. The collection of potential output values that make up the range is represented by the y-axis.

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To calculate the area of a circle within a circle, you can use the following formula Area = πr^2 - πr1^2

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Answer:

3/10 or 0.3

Step-by-step explanation:

(9/15)(5/10)

= (3/5)(1/2)

  3x1=3 and 5x2=10

= 3/10 or 0.3

The probability of a couple having five children with no children being affected by the disorder is given by the formula (1 - 0.0025)⁵.

This formula calculates the probability of a certain event (in this case, having no children affected by the disorder) happening five times in a row. However, this does not give the probability of all five children being unaffected by the disorder.

To find the probability of all five children being unaffected, you would need to multiply the probability of each child being unaffected, which is (1 - 0.0025), five times:

This result is the correct probability of a couple having five children with no children being affected by the disorder.

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Answer:

-w - 4 is equivalent in the question you gave.

There are 100 degrees between the normal freezing and boiling points of water.

On the Celsius temperature scale, the difference between the normal freezing point (0°C) and the normal boiling point (100°C) of water is 100°C - 0°C = 100°C.

On the Kelvin temperature scale, the equivalent temperatures for the normal freezing and boiling points of water are 273.15 K and 373.15 K, respectively. The difference between these two temperatures on the Kelvin scale is 373.15 K - 273.15 K = 100 K.

So, in both Celsius and Kelvin scales, there are 100 degrees between the normal freezing and boiling points of water.

Therefore, there are 100 degrees between the normal freezing and boiling points of water.

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The definition that justifies the congruence of angle measures GJH and GJI is given as follows:

Definition of Angle Bisector.

A bisection is defined as a segment that splits an angle measure into two equal measures.

Hence an angle bisector means that an angle is divided into two angles of equal measure.

For this problem, we have that segment GJ is the angle bisector of angle G, meaning that the angle measures GJH and GJI are congruent.

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The parametric equations for the two circles are

A general parametric equation for a circle can be given as:

c(t) = R cos(t) i + R sin(t) j + k,

where

We can find two unit vectors perpendicular to the plane containing points p and q:

v1 = (1, 0, 0) and v2 = (0, 1, 1)/sqrt(2)

Thus, the two circles c1 and c2 with radius R and intersecting at p and q can be represented as:

c1(t) = R cos(t) i + R sin(t) (0, 1, 0) + (2, 1, 1),

c2(t) = R cos(t) (1, 0, 0) + R sin(t) (0, 1, 1)/√2 + (2, 1, 1).

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Linear equation for the relationship between flour and milk cups

y = 4x,

where x is number of milk cups

y is number of flour cups

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

A recipe requires 1 cup of milk for every 4 cups of flour.

Ratio between milk(x) and flour(y)

x/y = 1/4

y = 4x

where x number of cups of milk

y is number of cups of flour

Hence, y = 4x is the linear equation that defines the relationship.

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