A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The drawing has sides measuring 3 cm, 4 cm, and 5 cm, and angles measuring 37°, 53°, and 90°. To create the actual sign shown, the drawing must be dilated using a scale factor of 80.

The product of a, b, and c would be, 9/8

What is Expression?

An expression, often known as a mathematical expression, is a finite combination of symbols that is well-formed according to context-dependent principles.

First, let's simplify the expression:

              [tex]\frac{6 x^y^{-1} }{\sqrt[{4} ]{(16x^5y^2)}}\\\\\ = \frac{(6x^2y^{-1} )}{4x^{\frac{5}{4} } y^{\frac{1}{2} } } \\\\[/tex]

We can simplify further by dividing both the numerator and denominator by x²:

                       [tex]\frac{6x^{2} y^{-1} }{4x^{\frac{5}{4} } y^{\frac{1}{2} }} \\\\= \frac{6y^{-1} }{4x\frac{3}{4} y^{\frac{1}{2} } } \\\\= \frac{\frac{6}{4} *x^{2} y^{-1} }{x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\=\frac{3}{2x^{\frac{3}{4} }y^{\frac{1}{2} } } \\\\[/tex]

So, a = 3, b = -3/4, and c = -1/2.

The product of a, b, and c is 3 * -3/4 * -1/2 = 9/8.

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The sample space for pulling 2 marbles  to find the probability will be List 3.

Probability conveys how likely an event is to occur. The occurrence of a random event is the focus of this mathematical field of study. The value is in the zero to one range. Mathematicians use probability to predict the likelihood that certain events will take place.

The possibility of something happening is referred to as probability. The probability distribution also utilises this basic concept from probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event.

The proportion of favourable outcomes to all possible outcomes, or P(E), determines the likelihood that an event will take place.

Now,

Given that Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.

So no. of ways to pick first ball = 3

as there are three type of balls

and no. of ways to pick second ball= 3 as replacement is allowed.

Therefore total sample space = 3*3=9

Hence,

         The sample space for pulling 2 marbles will be List 3.

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Answer:

x[tex]\geq[/tex] 3

Step-by-step explanation:

-4x -2 ≤ -14
-4x ≤ -12
x ≥ 3

We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is  [tex]\mathrm{\dfrac{1}{m^4}}[/tex] .

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In language, a phrase by itself may contain an action, but it does not constitute a complete sentence.

The following are some examples of expressions and word phrases that they relate to:

Expression: 3 + 7

Given

⇒ [tex]\mathrm{(m)^6^{(-2/3)}}[/tex]

⇒ [tex]\mathrm{(m)^{(-12/3)}}[/tex]

⇒ [tex]\mathrm{(m)^{(-4)}}[/tex]

⇒ [tex]\mathrm{\dfrac{1}{m^4}}[/tex]

We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is  [tex]\mathrm{\dfrac{1}{m^4}}[/tex]

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The lowest values of x are;

1. x = 1/2, x = 2/4, x = 3/6

2. x = 14, 15, 16

From the information given, we have that;

10-3x > 8

collect the like terms, we get;

-3x > 8 - 10

subtract the values

-3x > -2

Make 'x' the subject

x > 2/3

5x-27 > 7x

collect the like terms

5x - 7x> 27

subtract the like terms

-2x> 27

Make 'x' the subject

x > -27/2

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If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9

Let the sets be

A =  {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {1, 2, 3, 4, 5}

C = {4, 5, 6, 7, 8, 9}

Then

B ∩ C = {4, 5}

Subsets of B ∩ C = {4}, {5}, {4,5}, {}

If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}

No. of elements in A = 9

No. of subsets of A = [tex]2^9[/tex]

No. of elements in B = 5

No. of subsets of B = [tex]2^5[/tex]

No. of elements in C = 6

No. of subsets of C = [tex]2^6[/tex]

If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C

But the null set will be subtracted twice

Also as the subsets of B ∩ C excluding null set will be subtracted twice

Therefore, total number of subsets of A not the subsets of B or C

[tex]k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414[/tex]

The sum of the digits of k=9

The complete question is-

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.

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From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.

Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.

Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.

Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.

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We can see here that simplifying, we have:

a. h²

b. h³

c. 1/(1 + h)

d. 3h

e. 3h/(64 + 4h)

f. h/(4h + 2h²)

Simplification is the process of reducing something to its most basic form or removing any unnecessary complexity.

In mathematics, simplification is often used to make equations or expressions easier to work with, solve, or understand. This can involve combining like terms, cancelling out common factors, or using rules of exponents and logarithms to simplify an expression.

We see here that the below gives us the workings:

a. (5 + h)³ - 125/ h = h³ +  5³ - 125/h = h²

b. [tex]\frac{(3 + h)^{4} - 81 }{h} =\frac{ 3^{4} + h^{4} - 81}{h} = \frac{ h^{4} + 81 - 81}{h} = h^{3}[/tex]

c. (1/1+h) - 1/h = 1/1+h - 1 ÷ h = 1/1+h

d. 3(1 + h)² -3/h = 3h² + 3 - 3/h = 3h²/h = 3h

e. [(3/4+h) - 3/4]/4 = (3/4+h - 3/4) ÷ 4 = 3h/64+4h

f. (-1 + 2 + h) + 1/2 ÷ h = h/4 + 2h × 1/h = h/4h + 2h²

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Answer:

Step-by-step explanation:

75 x 0.40= £30

The percentage change in the price is 15.78% decrease.

What is the percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.

Here are some percentage examples:

Now,

Initial price=4.1

Final price=3.5

Change=3.5-4.1= -0.6 , minus means decrease in price

final value + initial value=7.6

then

percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100

=0.6/3.8*100

=0.1578*100

=15.78%

hence,

         The percentage change in the price is 15.78% decrease.

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Answer:

∠ a = 30° , ∠ b = 90°

Step-by-step explanation:

∠ a and 150° are a linear pair and sum to 180° , that is

∠ a + 150° = 180° ( subtract 150° from both sides )

∠ a = 30°

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

the sum of the 3 angles in a triangle = 180° , that is

∠ b + ∠ a + 60° = 180°

∠ b + 30° + 60° = 180°

∠ b + 90° = 180° ( subtract 90° from both sides )

∠ b = 90°

Answer:

16x(1+2x^2)^3

Step-by-step explanation:

f(x)=(1+2x^2)^4

Use chain rule

4(1+2x^2)^3(4x)

There were 375 adult tickets sold and 316 student tickets for the school play.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the number of student tickets would be x and the number of adult tickets would be y

As per the question, we have a system of equations:

x + y = 691   ....(i)

x = y - 59     ....(ii)

Substitute the value of x = y - 59 in equation (i),

y - 59 + y = 691

2y = 691 + 59

2y = 750

y = 375

Substitute the value of y = 375 in equation (ii), and solve for x:

x = 375 - 59

x = 316

Thus, there were 375 adult tickets sold.

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The complete question would be as:

A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?

The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can use the formula for the margin of error for a 95% confidence interval:

margin of error = z× (standard deviation / √n)

where z is the z-score for a 95% confidence interval, which is 1.96.

a. The desired margin of error is $0.10:

0.10 = 1.96(0.25 /√n)

√n = 1.96×0.25 / 0.10

√n= 4.9

n = 4.9^2

n = 24.01

So the appropriate sample size for a margin of error of $0.10 is at least 25.

b. The desired margin of error is $0.07:

0.07 = 1.96 (0.25 / √n)

√n = 1.96 × 0.25 / 0.07

√n= 6.97

n = 6.97²

n = 48.53

So the appropriate sample size for a margin of error of $0.07 is at least 49.

c. The desired margin of error is $0.05:

0.05 = 1.96 (0.25 / √n)

√n= 1.96 × 0.25 / 0.05

√n= 9.8

n = 9.8²

n = 96.04

So the appropriate sample size for a margin of error of $0.05 is at least 97.

Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

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There will be a total of 741 greetings at the mother-daughter tea.

Two or more expressions with an Equal sign is called as Equation.

Let's start by counting the number of greetings between the host mother-daughter pair and the other 19 mother-daughter pairs.

Since each pair only greets once, the host pair will make 19 greetings.

Now we need to count the number of greetings between the 19 guest mothers and the other 19 mother-daughter pairs

Each of the 19 guest mothers will greet 18 other mother-daughter pairs, for a total of 19 x 18 = 342 greetings.

Finally, we need to count the number of greetings between the 19 guest daughters and the 20 mothers

Each of the 19 guest daughters will greet 20 mothers

Total is 19 x 20 = 380 greetings.

By adding all we get 741 greetings

Therefore, there will be a total of 741 greetings at the mother-daughter tea.

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Answer:

The correct answer is:

e = 0.25 t + 1.75 .

Answer:

44 in^2

Step-by-step explanation:

V = L×W×H

Bottom rectangle prism

L= 6 W= 4 H= 1

V = 6×4×1

V=24

Top rectangle prism

L= 2 W= 2 H= 5

V=2×2×5

V= 20

Add both of the rectangle prisms

24+25= 44

Answer:

18x+9

Step-by-step explanation:

Answer: 18x + 9

Step-by-step explanation:

1) Combine like terms 23x -5x to get a new equation of 18x + 9.

The average rate of change over each specified interval is 8/3 and -10.

The average rate shows the change in the function per unit, over an interval.

Given that, find the average rate of change over each specified interval.

The average rate of change is given by

f(b)-f(a) / b-a

a) [2, 5] :-

To find the average rate of change we will take the change in the function over the change in x,

f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3

Therefore, the average rate of change in interval [2, 5] is 8/3

b) [3.8, 4] :-

Similarly,

f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2

= -10

Therefore, the average rate of change in interval [3.8, 4] is -10

Hence, the average rate of change over each specified interval is 8/3 and -10.

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The quadrilateral is most specifically a square since all the sides of the quadrilateral are equal and have 90°

A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the quadrilateral be represented as ABCD

Now , the measures of the sides of the quadrilateral are

The measure of side AB = measure of side BC

And , the measure of side AB = measure of side AD

So , all the 4 sides of the quadrilateral are same so it is a square

And the measures of angles are 90° each

Therefore , the quadrilateral is a square

Hence , it is a square

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A. The firm's short-run total cost curve can be calculated as TC = 2K + 4L. The short-run average cost curve function will be SAC = TC/Q, where Q is the output.

B. The firm's short-run marginal cost function is MC = 4/Q. The short-run total cost (STC) at 25 and 200 levels of output will be 800 and 2400 respectively. The short-run average cost (SAC) at 25 and 200 levels of output will be 32 and 12 respectively. The short-run marginal cost (SMC) at 25 and 200 levels of output will be 16 and 8 respectively.

C. The graph of the SAC and SMC curves is shown below.

SAC and SMC Graph

D. The SMC curve intersects the SAC curve at its lowest or minimum point because at this point, the SAC curve is at its most cost-efficient level, meaning that the firm's costs are minimized. This is because at this point, the marginal cost is lower than the average cost, meaning that the firm can produce additional units of output with a decreasing cost.

Answer:

BEF

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.

There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).

Looking at the following answers provided, we can see that BEF is a proper angle, because it is made up of two rays in the proper order.

KGH on the other hand, is not. KGH would be a proper angle if it was in the correct order (GHK or KHG), but because it is not in the right order, it is not a proper angle. LEA is not a proper angle either. We know that an angle is made up of two rays, but LEA isn't, and it's the same with ADE.

Answer:

BEF and ADE

Step-by-step explanation:

These points when connected make and angle. The others do not as they sinply dont make sense or have the points in a way that makes the whole statement false.

The measurement closest to the area of the circle in meters is 379.94 sq. meters.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area. The majority of forms and things have corners and edges. When computing the area of a certain form, both the length and width of these edges are taken into account.

Given that,

diameter = 22m

radius = 22/2 = 11m

The area of the circle is:

A = πr²

Substituting the value of π = 3.14 and r = 11 we have:

A = (3.14)(11)²

A = 379.94

Hence, the measurement closest to the area of the circle in meters is 379.94 sq. meters.

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Answer:

15.40 ounces to 16.90 ounces.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sum of the exterior angles of a triangle is equal to 360 degrees, while the sum of the interior angles of a triangle is equal to 180 degrees.

When you combine the sum of the exterior angles and the sum of the interior angles of a triangle, you get:

360 degrees + 180 degrees = 540 degrees

So, the sum of the exterior angles and the sum of the interior angles of a triangle is equal to 540 degrees.

Answer:

Step-by-step explanation:

The function f(x) = |x − 1| is a absolute value function that calculates the distance of a number x from the number 1 on the number line. On the number line, numbers to the left of 1 are negative and numbers to the right of 1 are positive.

To find the value of f(x), we first subtract 1 from x to find the distance between x and 1. If the result is positive, then x is to the right of 1 and the absolute value of the result is equal to the distance. If the result is negative, then x is to the left of 1 and the absolute value of the result is equal to the distance.

For example, let's find f(-5):

f(-5) = |-5 - 1| = |-6| = 6

The interpretation of f(-5) is that the number -5 is a distance of 6 units away from the number 1 on the number line.

Now let's find f(3):

f(3) = |3 - 1| = |2| = 2

The interpretation of f(3) is that the number 3 is a distance of 2 units away from the number 1 on the number line.

The domain of the function is all real numbers. The range of the function is all non-negative real numbers.

After solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

The term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided.

Example of an algebraic expression: 3x + 9; 5x + 10.

So, we have the expression as follows:

(2/4x + 3) + (1/4x - 4)

Now, solve as follows:

(2/4x + 3) + (1/4x - 4)

2/4x + 3 + 1/4x - 4

2/4x +  1/4x + 3 - 4

3/4x - 1


Therefore, after solving the expression (2/4x + 3) + (1/4x - 4), the resultant answer is 3/4x - 1.

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find the length of the x

a^2 + b^2 = c^2

12x^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 25; x = 5

use the formula

a = (1/2)(24)(5)

a = (1/2)(120)

area = 60

Answer:Robert

Step-by-step explanation: 42/48 = 0.875,
43/50 = 0.86

0.875 > 0.86

Answer: d. Triangle with angle measures: 8·, 17·, and 152·

Step-by-step explanation: i did the test

The triangle not possible is option

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Let us find the sum of the angles for each triangle given.

(a) Triangle with angle measures: 26°, 19°, and 135°·

Sum = 26° + 19° + 135° = 180°

(b)Triangle with angle measures: 14°, 27°, and 139°·

Sum = 14° + 27° + 139° = 180°

(c) Triangle with angle measures: 9°, 18°, and 153°·

Sum = 9° + 18° + 153° = 180°

(d) Triangle with angle measures: 8°, 17°, and 152°·

Sum = 8° + 17° + 152° = 177°, which is not equal to 180°.

Hence the option (d) is not possible.

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