Evaluate the expression.

2
3
(
−
7
)
+
2
3
(
−
5
)
3
2
​
(−7)+
3
2
​
(−5)

The product of a, b and c is equal to 18.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is are the expression as -

[tex]$\frac{\sqrt[4]{81x^{4} y^{2} } }{x^{-1} 2y^{-1} }[/tex]

The given expression is -

[tex]$\frac{\sqrt[4]{81x^{4} y^{2} } }{x^{-1} 2y^{-1} }[/tex]

We can rewrite it as -

[tex]$\frac{(81x^{4} y^{2}) ^{\frac{1}{4} } }{x^{-1} (2y)^{-1} } = \frac{(3^{4} x^{4} y^{2})^{\frac{1}{4} } }{x^{-1} (2y)^{-1} } = 6xy^{\frac{1}{2} } xy[/tex]

Now, we can write -

[tex]6xy^{\frac{1}{2} } xy = 6x^{2} y^{(\frac{1}{2} + 1) } = 6x^{2} y^{(\frac{3}{2}) }[/tex]

On comparing, we get -

a = 6

b = 2

c = 3/2

So -

a x b x c = 6 x 2 x 3/2 = 18

a x b x c = 18

Therefore, the product of a, b and c is equal to 18.

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On solving the provided question, we can say that triangle BIG and triangle FUN are similar to each other and are congruent, so angle N is congruent to angle G.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have been provided with that

triangle BIG and triangle FUN are similar to each other and are congruent.

Angle N is congruent to angle G.

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Answer

9(r+6)

Step-by-step explanation:

9r + 54

Factor out 9.

9(x+6)

Answer:48 counters

Step-by-step explanation:8x3=2, 3x8=24, 24+24+48

Answer: c is correct

Answer:

c

Step-by-step explanation:

Yes , i agree with Rosa in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

3/4 is equal to 0.75 and 0.75 > 0.25

Or 0.25 is equal to 1/4,

and 1/4 < 3/4

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The required number line attached below shows the absolute value of the rational number 9/28 is from 0.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The rational number is given in the question, as follows:

98/28

We have to determine the graph of the rational number on a number line.

As per the question, we can write the simplest form of the fraction as:

⇒ 98/28 = 7/2

Thus, the number line attached below displays the distance of the fraction from 0.

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The concept given is Graphs. A graph is a chart showing the relationship between magnitudes of variables, usually two variables, each measured along a pair of orthogonal axes.

Charts and tables are powerful visual tools because they present information quickly and easily. that graphics are commonly used in print and electronic media.

Sometimes data is easier to understand in a chart than in a table because a chart can show a trend or comparison.

A) bar graph and pie chart.

B) histogram, stem plot, and box plot.

C) histogram, stem plot, and box plot.

D) time plot.

E) bar graph and pie chart.

F) normal quantile plot.

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Therefore , the solution of the given problem of parallel line comes out to be   MP =22.

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  PQ || MN

=> PQ =MP+2

=> PO = 12 , MN = 12

So,

=> PO + MN = 12 + 12

=> PQ = 24

=> PQ = MP +2

=>24 = MP +2

=> MP =22

Therefore , the solution of the given problem of parallel line comes out to be   MP =22.

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Answer: 204

Step-by-step explanation:

2 goes into 12 six times. 34x6=204

hence, your answer.

Answer:

Step-by-step explanation:

It would be -5 3-5=-2

The standard deviation of the sampling distribution is; Option A: 3.750

Standard deviation is defined as a measure of how spread out numbers usually are. It is further said to be the square root of the Variance, and then the variance is the average of the squared differences from the Mean.

Now, we are given;

Population standard deviation; σ = 15

Sample size; n = 16

Formula for sample standard deviation in this regards is;

s = σ/√n

Plugging in the relevant values gives;

s = 15/√16

s = 15/4

s = 3.750

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Therefore, the perimeter of a quadrilateral at the given vertices is 12.76 units.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

A face is a flat surface, an edge is a straight line connecting two faces, and a vertex is the corner of the form. Faces, edges, and vertices of three-dimensional forms are all unique. In the course of our daily activities, we come into contact with numerous things of all sizes and forms.

The length of each side:

CD: C(2,4) and D(1,1) = sqrt((1-2)^2 + (1-4)^2) = sqrt(1 + 9) = sqrt(10)

DE: D(1,1) and E(5,0) = sqrt((5-1)^2 + (0-1)^2) = sqrt(16+1) = sqrt(17)

EF: E(5,0) and F(3,4) = sqrt((3-5)^2 + (4-0)^2) = sqrt(4+16) = sqrt(20)

FC: F(3,4) and C(2,4) = sqrt((2-3)^2 + (4-4)^2) = sqrt(1) = 1

Perimeter of the quadrilateral = sum of the lengths of all four sides:

Perimeter = sqrt(10) + sqrt(17) + sqrt(20) + 1

Calculating, perimeter = 3.162+4.123+4.472+1 = 12.7557 and rounding to the nearest hundredth, it is 12.76

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Therefore . the solution of the given problem of distance comes out to be it follows that there are √17 units separating the two points.

Distance is a measure of an object's travels. Distance, put simply, is what an item travels over in a particular amount of time, or t. The shortest path an object can take while moving is displacement, nevertheless. We commonly incorporate the physical quantities of distance and displacement.

Here,

provided are (6, -3) & (2, -2)

Now, the separation between points (a, b) & (c, d) is

d= √(c-a)² + ( d- b) ²

Therefore, d= √(-3+2)² + (2-6)²

d= √ 1 + 16

d= √17

It follows that there are √17 units separating the two points.

Therefore . the solution of the given problem of distance comes out to be it follows that there are √17 units separating the two points.

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Graph G has 7 vertices. Graph C is isomorphic to graph G.

What are the vertices of a graph?

The term "vertex" refers to a node of a graph, which is one of the points on which the graph is constructed and which can be connected by graph edges.

The vertices of graph G are A, B, C, D, E, F, G

The number of vertices of graph G is 7.

The number of edges that are connected to a vertex that the degree of the vertex.

Vertex        degree

A                      4

B                      2

C                      3

D                      2

E                      3  

F                      3  

G                      3

The vertices of graph A are T, U, V, W, X,Y,Z

The number of vertices in graph A is 7.

Vertex        degree

T                      3

U                      3

V                      1

W                      3

X                      3  

Y                      3  

Z                      2

The degree of the vertices of graph A is not the same as the degree of graph G.

The vertices of graph B are T, U, V, W, X,Y,Z

The number of vertices in graph B is 7.

Vertex        degree

T                      2

U                      4

V                      2

W                      3

X                      3  

Y                      3  

Z                      3

The degree of the vertices of graph B is not the same as the degree of graph G.

The vertices of graph C are T, U, V, W, X,Y,Z

The number of vertices in graph C is 7.

Vertex        degree

T                      4

U                      2

V                      3

W                      3

X                      3  

Y                      3  

Z                      2

The degree of the vertices of graph C is the same as the degree of graph G.

Thus graph C is an isomorphism of graph G.

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The simplified expressions for (A), (B) and (C) are:

(A) [tex]f(x+h) = 4x + 4h - 6[/tex]

(B) [tex]f(x+h) * f(x) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]

(C) [tex]f(x+h) - f(x) / h = 4[/tex]

To simplify we use the given method.

A)

[tex]f(x+h) = 4(x+h) - 6 = 4x + 4h - 6[/tex]

B) [tex]f(x+h) * f(x) = (4x + 4h - 6) * (4x - 6) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]

C)

[tex]f(x+h) - f(x) / h = (4x + 4h - 6) - (4x - 6) / h = 4h / h = 4[/tex]

So the simplified expressions for (A), (B) and (C) are:

(A) [tex]f(x+h) = 4x + 4h - 6[/tex]

(B) [tex]f(x+h) * f(x) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]

(C) [tex]f(x+h) - f(x) / h = 4[/tex]

Please note that in (C) the difference of the functions is divided by h, not multiplied.

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Answer:

12 ft

Step-by-step explanation:

Assuming the triangle is a right triangle, we can use the Pythagorean theorem, a^2+b^2=c^2

Plugging our numbers in, we get 5^2+b^2=13^2

25+b^2=169

b^2=144

b=12

I also believe that this is a 5 12 13 triangle so if you remember those, you can automatically know the lengths!

99.4% chance that you are healthy if you receive a negative test. 67.9% chance that you are sick if you receive a positive test.

14% of population would test positive for the disease

Step 1. Give algebraic names to various events described:

Step-2: Model the given situation mathematically.

In other words, the conditional probability of the event that the diagnostic test gives a negative result (not A), given that the tested person does not have the disease (E2 = not E1) is given to be 90%

Thus P(not A/E2)=90%

Further, it is given that five percent of the population has the disease. In other words, the event that a person has the disease (E1) has the probability of 5% Thus P(E1)=5%

It is needed to find what percent of that population would test positive for the disease.

Thus, the probability that a person will have a positive result when tested, P(A) is to be determined.

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The area of a circle with a diameter of 6 is A=π(3)². Option C

It is important to note that the area of a circle is expressed with the formula;

A = πr² or πd²/4

Where;

From the information given, we have that the diameter is 6

Radius = diameter/2 = 6/ 2 = 3

Substitute the value into the formula for area

Area, A = π(3)²

Hence, the area of the circle is  π(3)²

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it is 57 understand the way is down there

Step-by-step explanation:

j

k

h

a

h

a

The height of the totem tree after solving the equation is 1/6 units

An equation is an expression that shows how numbers and variables relate with each other.

Mathematical operations include addition, subtraction, division and multiplication. Mathematical operations are used in equations

Let h represent the height of the totem pole.

Ronald carved 3/3/8 of a totem pole. he says that the totem pole is 3/4 completed. Hence:

(3/4)h = 3÷3÷8

(3/4)h = 3 * (1/3) * (1/8)

(3/4)h = 1/8

Cross multiplying gives:

h = (4 * 1)/(3 * 8)

h = 1/6

The height of the tree is 1/6 units

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Note that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.

A discrete variable is one that can only have particular, unique values and cannot have any other values in between. The number of students who increase their score is a whole number that can only take on specific values (e.g., 0, 1, 2, etc.), indicating that it is a discrete variable.

A quantitative variable in mathematics and statistics can be continuous or discrete depending on whether it is normally obtained by measuring or counting. The variable is continuous in that interval if it can take on two specific real values while simultaneously taking on all real values between them.

Thus, it is correct to state that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.

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Full Question:

Is the following variable best thought of as discrete or continuous?

The number of students, in a class of 35 , who improve their score from the first midterm to the second midterm

Therefore,  the solution of given problem of probability is there is a 0.397 percent chance that a randomly chosen male will have a systolic blood pressure below 100.

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A possibility is a number from 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages ranging from 0% to 100% and from 0 to 1.

Here,

Considering the query

In a particular municipality, men's systolic blood pressure has a median of 105 as well as a standard deviation = 9, which is considered to be regularly distributed.

Probability that the systolic blood pressure of a man chosen at random will be less than 100

P(x < 100)

Through the use of normalized normal distribution

=> N(100 -105)/9 \s=> N (-5/9)

We have a>0 and N(-a) = 1 - N(a).

=> 1 - N (-5/9)

=> 1 - N(0.556) (0.556)

=>1 - 0.6026

=> 0.3979

≈ 0.397 (nearest hundredths) (nearest thousandth)

Therefore, there is a 0.397 percent chance that a randomly chosen male will have a systolic blood pressure below 100.

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The answer is: 85870

Answer:

B

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{4}{5}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{4}{5}[/tex] and y- intercept c = 1

Answer: 30.48

Step-by-step explanation:

2.54x12=30.48

The volume of the cylindrical pipe in terms of π is 76π ft³.

The volume of the cylindrical pipe using ALEKS calculator is 238.76 ft³.

The radius of a cylindrical construction pipe is 2 ft, and its length is 19 ft. The exact volume of the cylindrical pipe can be found as follows:

The answer is in terms of π.

Therefore,

volume of a cylinder = πr²h

where

Therefore,

volume of the cylindrical pipe =  πr²h

where

volume of the cylindrical pipe =  π × 2² × 19

volume of the cylindrical pipe =  π × 4 × 19

volume of the cylindrical pipe =  76π ft³

Hence, let's approximate the volume of the cylindrical pipe using π in an ALEKS calculator.

Therefore,

volume of the cylindrical pipe = 76 × π = 238.761041673 = 238.76 ft³

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What is Constant of Proportionality?

The ratio between two proportional quantities' constant values is known as the constant of proportionality.

The formula for calculating slope is expressed as:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Given: the coordinate points (5,225) and (3, 135). The constant of proportionality is expressed as:

m =  [tex]\frac{135-225}{3-5}[/tex]

m = [tex]\frac{-90}{-2}[/tex]

m = 45

Hence, Constant of Proportionality is 45.

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