The rectangular floor of a classroom is 20 feet in length and 30 feet in width.
A scale drawing of the floor has a length of 4 inches. What is the area, in
square inches, of the floor in the scale drawing?

Answer:1/6 barrels=1 batch

Step-by-step explanation:

4/.666666666666666=6 batch's came from one barrel

6 batch's came from one barrel

1/6= 1 batch

Answer:You consume 14 pounds of turkey annually. At a discount store, the price of turkey is $0.99 less per pound than at a supermarket. How much would you save annually, in dollars, if you bought all of your turkey at the discount store?

Step-by-step explanation:

The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°

According to the question,

A spring is attached at one end to support B and at the other end to collar A.

Part A: Given that : Reference angle (θ) = 28°

We have to find out the distance of point A to point B.

Adjacent = 3 ft (given)

To find AB, apply the trigonometry function which is:

cos θ = adj / hypotenuse

Substituting all the values ,

=> cos 28°= 3/AB

=> AB = 3/cos 28°

=>  AB = 3.4 ft (nearest tenth of a foot)

Part B:

It is given that Distance  from point A to point B is 5.2 feet

We have to calculate the Value of θ

adj = 3 ft

hypotenuse = AB = 5.2 ft

To find θ , We will again apply the trigonometry function

cos θ = adj/hypotenuse

Substituting all the given values

=> cos θ = 3/5.2

=> θ = cos⁻¹ ( 3 / 5.2)

=> θ = 54.8°

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The evaluation of the composite figures, distances and coordinates in the question indicates;

24. The volume of the figure is about c) 1440 cm³

25) The distance of the airport from the plane is about c) 41,043.6 feet

26) The coordinates of the vertex U are c) (-5, -7)

A composite figure is a figure that is composed of two regular figures.

24. The figure is a composite figure comprising of a cylinder and a cone.

Volume of the cylinder = π × 5² × 15 = 375·π

Volume of the cone = (1/3) × π × 5² × (25 - 15) = (83 1/3)·π

The volume of the figure is therefore; 375·π + (18 1/3)·π ≈ 1440

25) The height of the plane = 12,000 ft

The angle of elevation to the airplane = 17°

Let r represent the direct distance of the airport from the plane, we get;

sin(17°) = 12000/r

x = 12000/(sin(17°) ≈ 41,043.6

The direct distance from the plane to the airport which is the hypotenuse side of the right triangle in the figure is about; d) 41,036.6 feet

26) The coordinates of the vertices of the triangle are; R(-6, -3), S(3, 3), and T(4, -1)

The type of quadrilateral represented by quadrilateral RSTU = A parallelogram

The slope of the side ST = (-1 - 3)/(4 - 3) = -4

Equation of the side RU is therefore;

y - (-3) = (-4) × (x - (-6)) = -4·x - 24

y = -4·x - 24 - 3 = -4·x - 27

y = -4·x - 27

The slope of the side RS = (3 - (-3))/(3 - (-6)) = 2/3

Equation of the side TU = y - (-1) = (2/3)·(x - 4) = (2/3)·x - (8/3)

y = (2/3)·x - (8/3) - 1 = (2/3)·x - (11/3)

y = 0.2·x - 1.8

The x-coordinate of the point U can be therefore obtained from the equation;

-4·x - 27 = (2/3)·x - (11/3)

x = -5

y = -4×(-5) - 27 = -7

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The derivative of a whole number, like 1 is always zero as a whole number is constant.

In order to understand this answer, it is first necessary to realize that in calculus, a function's derivative is a formula that expresses the rate at which the function's value changes instantaneously in relation to x.

To get the derivative of a particular function, we can use specific rules like a whole number's derivative is always zero. To figure this out, we may apply the following calculus rule.

The derivative of f(x) is 0 if f(x) = a, where 'a' is any constant integer.

We can observe that the derivative of all constant functions is zero. This rule states that if f(x) = a, where 'a' is a whole number, then the derivative of f(x) equals 0, as 'a' whole number is a constant.

OR

We may infer from the graph below that for all values of x, the value of f(x) will stay constant (equal to 1). In light of the fact that f(x₂) = f(x₁), the derivative will be zero.

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Answer:

10 yrs old and 35 yrs old

Step-by-step explanation:

I figured it out by trial and error but here's the thinking process.

10 + 35= 45

Son becomes dad's age so 35-10=25, so plus 25 year to each age.

10+25=35

35+25= 60

35+60=95

I hope that makes enough sense!

The combined length for three shortest jumps is 43 feet. We can find out by analyzing the graph and its entities.

What are graph and entities ?

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Entity is any data or any existing object .

From the graph:

14*1/4 feet = by 2 students

14*1/2 feet = by 3 students

14*3/4 feet = by 1 student

15 feet = by 1 student

So the three shortest jumps are 14*1/4 , 14*1/4 , 14*1/2.

Total distance = 57/4 + 57/4 + 58/4

                        = 43 feet.

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The given statement that 'the batter's distance from the first base bag is a function of time.' is false.

If we need to call any quantity a function of any other quantity, we need to know what it means first. For this, we take the example of velocity. If we say that velocity is a function of time, what we mean is that the function is such that we input time and get velocity as the output. That quantity changes as the input increases or decreases.

We can deem distance as a function of time when it changes with respect to it. Here, it is evident that the distance between the batter and the first base is not going to change. Thus, it is not a function of time and the given statement is false.

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The average speed in mile per hour is  5.455  miles per hour    .

In the question ,

it is given that ,

the 1 mile distance is covered in 11 minutes ,

So , in 1 minute the distance covered is = 1/11 miles

So , the speed in miles per minute is 1/11 miles per minute .

To convert speed in miles per minute to miles per hour ,

we multiply it by 60 ,

So , we get ,

Average Speed in miles per hour  is = 60 * (1/11)

= 60/11

= 5.45454

≈ 5.455

Therefore , the average speed is 5.455  miles per hour .

The given question is incomplete , the complete question is

What is your average speed in mile per hour and in feet per second if you travel a mile in 11 minute ?

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

[tex]\boxed{8-2=6}\\\boxed{6/2=3}[/tex]

We are going to take that 25% and multiply it with 3 to get are final answer.

[tex]\boxed{25*3=75}\\\boxed{So,2=75}[/tex]

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume and length definitions are connected.

Here,

Cone has a radius of 4ft

A height of 2ft.

Thus,

The formula for volume of cone is used

V=π[tex]r^{2} \frac{h}{3}[/tex]

V=3.14*[tex]4^{2}[/tex]*2/3

V=50.24*2/3

V=100.48/3

V=33.51 [tex]ft^{3}[/tex]

Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

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The illustration based on the Gestalt principles of grouping are:

(A) Closure principle.

(B) Proximity principle.

(C) Continuity principle.

(E) Similarity principle.

The principles of grouping, also known as the Gestalt rules of grouping, are a collection of psychological concepts first put out by Gestalt psychologists to explain why people naturally perceive items as structured patterns and objects, or Prägnanz.

Gestalt psychologists asserted that these principles hold true because the mind is predisposed to recognize patterns in the stimulus based on predetermined rules.

Gestalt grouping guidelines include:

Continuity principle.

Similarity principle.

Proximity principle.

Closure principle.

Common region principle.

Figure-ground principle.

Focal point principle.

Therefore, the illustration based on the Gestalt principles of grouping are:

(A) Closure principle.

(B) Proximity principle.

(C) Continuity principle.

(E) Similarity principle.

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Answer:

sum = 196

Step-by-step explanation:

the sum to n terms of an arithmetic series, when the first and last terms are known is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first term + last term)

we require to find the number of terms in the series

the nth term of an arithmetic series is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = a₂ - a₁ = 3 - 1 = 2 , then

1 + 2(n - 1) = 27 ( subtract 1 from both sides )

2(n - 1) = 26 ( divide both sides by 2 )

n - 1 = 13 ( add 1 to both sides )

n = 14 ← number of terms in the series

Then

S₁₄ = [tex]\frac{14}{2}[/tex] (1 + 27) = 7 × 28 = 196

The inequality that represents the given statement is (C) f - 3 / 5 ≥ -4/7 or f plus 3 over 5 is greater than negative 4 over 7.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The equation-like form of the formula 5x − 4 > 2x + 3 has an arrowhead in place of the equals sign.

It is an illustration of inequity.

This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

Finding the x numbers for which the inequality holds true is what we are most interested in.

So, the answer to the query is:

A number's deviation from three-fifths is equal to f - 3/5.

The entire statement is at least four sevenths in the negative.

Therefore, the inequality that represents the given statement is (C) f - 3 / 5 ≥ -4/7 or f plus 3 over 5 is greater than negative 4 over 7.

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Complete question;
Write the inequality for the statement:

the difference between a number and three-fifths is a minimum of negative four sevenths

f minus 3 over 5 is greater than or equal to 4 over 7

f minus 3 over 5 is greater than or equal to negative 4 over 7

f plus 3 over 5 is greater than negative 4 over 7

f minus 3 over 5 is less than or equal to negative 4 over 7

The equation of a line that is perpendicular to the points will be equal to y = 1(x + 9) - 4.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given information in the question,

Supplied that the given line has a slope of 1, the perpendicular line will also have a slope of 1.

Then, the equation of the line which is perpendicular is written as,

y = 1 (x + 9) - 4

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The derivative of the function at P0 in the direction of A is,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

Given that,

The derivative of the function at P0 in the direction of A.

f(x, y, z) =

f(x, y, z) = (1,-1,-2)

x = 1

y = -1

z = -2

Derivative of f(x, y, z) = xy + yz + zx

[tex]\frac{df}{dx}[/tex] = y + z

[tex]\frac{df}{dy}[/tex] = x + z

[tex]\frac{df}{dz}[/tex] = x + y

We can substitute f(x, y, z) = (1,-1,-2) values,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = y + z

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -1 + (-2)

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = x + z

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1 + (-2)

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1-2

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = x + y

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1 + (-1)

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1-1

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

Therefore,

The derivative of the function at P0 in the direction of A is,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

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There is no such a number whose absolute value is -2. This is because the absolute value of any number is its distance from 0 irrespective of the direction.

An absolute value of a number is the distance of the number from 0 on a number line irrespective of the direction.

Consider the number "x".

Then its absolute value is written as

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

For example x = -9; then its absolute value is

|(-9)| = -(-9) = 9; (Since x = -9 < 0; we applied |x| = -x)

So, we can conclude that irrespective of the direction (positive or negative), the absolute value of any number remains positive.

We know that the absolute value of any number is calculated by

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

And the absolute value of any number irrespective of its direction on the number line remains positive.

So, no such number has a negative absolute value.

Hence, the answer is none for the given question.

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Answer:

  2378 m

Step-by-step explanation:

You want the ground distance from the takeoff point to an airplane that has flown 2500 m in the air at a takeoff angle of 18°.

The cosine relation tells you ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse · Cos

Here, the hypotenuse of the right triangle model is 2500 m, the angle is 18°, and we want to find the side of the triangle adjacent to the angle:

  AD = AP·cos(18°) = 2500·0.9510565 ≈ 2377.64 ≈ 2378 . . . . meters

The ground distance is about 2378 m.

Answer:

A) 14

Step-by-step explanation:

Nuts:

[tex]\frac{6}{\frac{1}{3} }[/tex] = [tex]\frac{6}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]  Get a common denominator of 3 and divide

[tex]\frac{18}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{\frac{18}{1} }{\frac{3}{3} }[/tex] = [tex]\frac{18}{1}[/tex] = 18

We can make 18 bags with the amount of nuts given.

Raisins:

[tex]\frac{8}{\frac{1}{4} }[/tex] = 8 ÷[tex]\frac{1}{4}[/tex]  Gert a common denominator of 4 and divide

[tex]\frac{32}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{\frac{32}{1} }{\frac{4}{4} }[/tex] = [tex]\frac{32}{1}[/tex] = 32

We can make 32 bags with the amount of raisins given.

32 - 18 = 14

14 more bags need nuts agged.

From the statistical point of view , the type I error was made , the correct option is (c) .

In the question ,

it is given that ,

the machine was working well, but on the basis of our statistical hypothesis test, it was concluded that the machine was under-filling or over-filling and hence it was shut down .

but after examination by the engineers , there was nothing wrong with the filling machine .

that means that the null hypothesis was rejected when it was actually true .

which refers to the type I error .

Therefore , the correct option is (c) A Type I error was made.  

The given question is incomplete , the complete question is

The result of a hypothesis test is used to prevent a machine from under-filling or overfilling quart size bottles of olive oil. on the basis of sample, the hypothesis is rejected and the machine is shut down for inspection. a thorough examination reveals to engineers there is nothing wrong with the filling machine. from a statistical point of view:

(a) correct decision was made.

(b) Both, a Type I and a Type II errors were made.

(c) A Type I error was made.

(d) A Type II error was made.

(e) None of these answers.

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Answer:

256

Step-by-step explanation:

((2*2)²)²

(((4)²)²)

(16)²

256

The answer is:

- 2x/(1+x^2)^2

Answer:

first option

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 , then the 2 roots are real and irrational

• If b² - 4ac > 0, and a perfect square, then 2 roots are real and rational

• If b² - 4ac = 0 , then 2 roots are real and equal

• If b² - 4ac < 0 , then 2 roots are not real

3x² + 4x - 2 = 0 ← is in standard form

with a = 3, b = 4 and c = - 2 , then

b² - 4ac = 4² - (4 × 3 × - 2) = 16 - (- 24) = 16 + 24 = 40

since b² - 4ac > 0 , then 2 real and irrational roots

Answer:

2. d = 40; 2 rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] is:

[tex]\boxed{\mathrm{d =} \ b^2 - 4ac}[/tex].

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation [tex]3x^2 + 4x - 2 = 0[/tex]. Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)

             = 16 - (-24)

             = 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.

The probability that it takes Emma more than 5 minutes to wait for the train is 0.8571.

Given :

the amount of time emma must wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes.

Let the random variable X denotes the amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes.

the distribution function of X is:

F ( x ) = x - 4 / 11 - 4

4 < x < 11

P ( X > 5 ) = 1 - P ( X < 5 )

= 1 - F ( 5 )

= 1 - 1 / 7

= 7 - 1 / 7

= 6/7

= 0.8571

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Answer:

D

Step-by-step explanation:

A Hyperbola looks like a Parabola and its reflection, each Parabola curving opposite directions.

Answer:

D.  Hyperbola

Step-by-step explanation:

A conic is the intersection of a plane and a right circular cone.

Formed when a cone is intersected by a plane so that the plane is parallel to the circular base.

Formed when a cone is intersected by a plane so that the plane is at an angle with respect to the circular base.

Formed when a cone is intersected by a plane so that the plane is parallel to an edge.

Formed when a double-cone is intersected by a plane so that the plane is perpendicular to the circular bases.

Length of wall = 10km

side of square= 10km

area of square= 10²= 100km²

radius of circle = 10/2 = 5km

area of circle = 3.14 × 5²

area of circle = 3.14 × 25

area of circla = 78.5 km²

area of square >>> area of circle

Answer:

Sqrt of 4²+ (-1)² = Sqrt. of 17

Step-by-step explanation:

2 points in a coordinate grid create a right-angled triangle.

the distance is the Hypotenuse (the side opposite of the 90° angle). and the x coordinate and y coordinate differences are the legs.

and with that we use Pythagoras

c² = a² + b²

with c being the Hypotenuse, and a and b being the legs.

so, in our case :

distance² = (1 - 2)² + (7 - 3)² = (-1)² + 4² = 1 + 16 = 17

distance = sqrt(17)

Answer: 24 cups of sugar

Step-by-step explanation: you multiple the orginal amount neede for one batch by 8

8*3=24