Explain the meaning of the following A scale on a map is 1mm:20 miles

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

e = 5h

$100

Step-by-step explanation:

Let e = earnings

e = 5h

For h = 20,

e = 5h = 5(20) = 100

Answer:

$ 100

Step-by-step explanation:

1 hour = $ 5

h (hours worked in a week) = 20 hrs

EXPRESSION: amount of money earned in a week = h × 5

EVALUATION: amount of money earned in a week = 20 × 5

amount of money earned in a week = $ 100 ... answer

hope that helps...

The end behavior of the function f(n) = 3(n + 2)²(n - 3)(n - 2) is given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

The function for this problem is given as follows:

f(n) = 3(n + 2)²(n - 3)(n - 2).

Considering the degree, the function can be interpreted as follows:

\(3n^4\)

(for the limit when the input goes to infinity we consider only the term with the highest degree).

The leading coefficient is positive and the exponent is even, hence the end behavior is given as follows:

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Answer:

3(n-9)-2(n+4)=6n

3n-27-2n-8=6n

n-35=6n

-35=5n

n= -7

Step-by-step explanation:

3(n-9)-2(n+4)=6n

open the brackets by multiplication

3n-27-2n-8= 6n

n-35=6n

n=-7

Answer: A IS CORRECT

Step-by-step explanation:

The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Answer:

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sofiapenaloza

05/31/2023

Mathematics

College

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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66; The line of best fit overpredicts the temperature change.

2.66; The line of best fit underpredicts the temperature change.

1.94; The line of best fit underpredicts the temperature change.

−1.94; The line of best fit overpredicts the temperature change.

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The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Step-by-step explanation:

The equation of the lines parallel or perpendicular to another line and that pass through a point are listed below:

Case 7: y = (7 / 4) · x + 3

Case 8: y = 2 · x + 1

Case 9: y = (3 / 2) · x + 2

Case 10: y = (6 / 5) · x - 1

Case 11: y = - (2 / 5) · x

Case 12: y = - (5 / 2) · x - 19 / 2

Case 13: y = - x + 3

Case 14: y = - (5 / 4) · x - 5

In this problem we have eight cases of line equations parallel or perpendicular to a line and that pass through a point. The equation of a line is an expression of the form:

y = m · x + b

Where:

There are the following relationships between two lines:

Now we proceed to determine the line equations:

Case 7

Slope

m = 7 / 4

m' = 7 / 4

Intercept

b = y - m · x

b = - 4 - (7 / 4) · (- 4)

b = - 4 + 7

b = 3

Equation of the line

y = (7 / 4) · x + 3

Case 8

Slope

m = 2

m' = 2

Intercept

b = 1 - 2 · 0

b = 1

Equation of the line

y = 2 · x + 1

Case 9

Slope

m = 3 / 2

m' = 3 / 2

Intercept

b = - 4 - (3 / 2) · (- 4)

b = - 4 + 6

b = 2

Equation of the line

y = (3 / 2) · x + 2

Case 10

Slope

m = - 5 / 6

m' = 6 / 5

Intercept

b = 5 - (6 / 5) · 5

b = 5 - 6

b = - 1

Equation of the line

y = (6 / 5) · x - 1

Case 11

Slope

m = 5 / 2

m' = - 2 / 5

Intercept

b = - 2 - (- 2 / 5) · 5

b = 0

Equation of the line

y = - (2 / 5) · x

Case 12

Slope

m = 2 / 5

m' = - 5 / 2

Intercept

b = - 2 + (- 5 / 2) · 3

b = - 2 - 15 / 2

b = - 4 / 2 - 15 / 2

b = - 19 / 2

Equation of the line

y = - (5 / 2) · x - 19 / 2

Case 13

Slope

m = 1

m' = - 1

Intercept

b = 5 - (- 1) · (- 2)

b = 3

Equation of the line

y = - x + 3

Case 14

Slope

m = 4 / 5

m' = - 5 / 4

Intercept

b = 0 - (- 5 / 4) · (- 4)

b = 0 - 5

b = - 5

Equation of the line

y = - (5 / 4) · x - 5

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Answer:

x=3

(26x+50degreese) = 134 degreese

Step-by-step explanation:

Given:

ground to building top is 30 degrees.

Distance = 400 feet

The angle of elevation at is top of the building = 52 degrees.

Find-: Height of the building.

Sol:

For the triangle ABC

Perpendicular = Height

Base = x

Angle = 52

Use trigonometric formula:

For the triangle ABD is:

Perpendicular = Height

Base = x+400

Angle = 32

Put the value of "x" is:

So the height of the building is: 488.407 feet

Answer: x=68° because this triangle is a isoscele triangle which means that it haves 2 sides that are congruent and equivalent which means they have the same value and sides and are Congruent just means In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The value of angle [x] is equivalent to 44°.

We have a triangle as shown.

We know, the angles opposite to equal sides are equal.

So, we can write -

x + 68° + 68° = 180°

x = 180° - (136°)

x = 44°

Therefore, the value of angle [x] is equivalent to 44°.

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Step-by-step explanation:

hope it helps you see the attachment for further information

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Step-by-step explanation:

yes it is very simple question for me Kida

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer: the Nswer for this is 30 people

Step-by-step explanation:

Answer:

10n=40    n=4

Step-by-step explanation:

10n=40  divide each side by 10

n=40/10   simplify

n=4

Answer:

Step-by-step explanation:

For all Plato users.

We have to find the sum of the series has been given as.

\(\sum_{k=1}^{8}5(\frac{4}{3} )^{k-1}\) -----(1)

If the series has been given as,

\(\sum_{n=1}^{k}a(r)^{n-1}\) -------(2)

It's a geometric series with first term 'a' and common ratio 'r'.

Comparing both the expressions (1) and (2),

\(a=\) 5

\(r=\frac{4}{3}\)

Number of terms 'n' = 8

Sum of the k terms of this series is given by,

Sum = \(\frac{a(r^k-1)}{r-1}\)

       = \(\frac{5[(\frac{4}{3})^8-1)]}{\frac{4}{3}-1 }\)

       = \(\frac{5(9.98872-1)}{\frac{1}{3}}\)

       = \(\frac{44.9436}{\frac{1}{3} }\)

      = 134.83

Therefore, Option (B) is the correct option.

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The bar diagram could describe the following real-world problem:

"Peter has an amount of $12 in a piggy bank. If he spends two-thirds of his piggy bank, what does he have now?"

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have to give that;

A bar diagram is shown in the figure.

Now, We can make a real-world problem that could represent the bar diagram.

So, We get;

"Peter has an amount of $12 in a piggy bank. If he spends two-thirds of his piggy bank, what does he have now?"

Hence, the above question represents the bar diagram shown.

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The question seems incomplete, the missing graph has been attached below.

The length of FG chord is 5 units.

What bout chord?

A chord is a line segment that joins two points on the circumference of a circle. More specifically, a chord is a straight line that intersects a circle at two points, and the segment of the line between these two points is called a chord.

The length of a chord can be calculated using the Pythagorean theorem, given the radius of the circle and the distance between the two points on the circumference. The length of a chord is always less than or equal to the diameter of the circle.

Chords have various applications in geometry, trigonometry, and calculus. For example, in trigonometry, the chord function is defined as the ratio of the length of a chord to the radius of the circle. In calculus, chords are used in the definition of the derivative, which is the slope of the tangent line to a curve at a given point.

According to the given information:

2(x + 2 )=  ( 5 x - 5 )

2x + 4 = 5x -5

9 = 3x

3 = x

The length of FG is = x+2 = 3+2 = 5 units

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The length of FG chord is 5 units.

What bout chord?

A chord is a line segment that joins two points on the circumference of a circle. More specifically, a chord is a straight line that intersects a circle at two points, and the segment of the line between these two points is called a chord.

The length of a chord can be calculated using the Pythagorean theorem, given the radius of the circle and the distance between the two points on the circumference. The length of a chord is always less than or equal to the diameter of the circle.

Chords have various applications in geometry, trigonometry, and calculus. For example, in trigonometry, the chord function is defined as the ratio of the length of a chord to the radius of the circle. In calculus, chords are used in the definition of the derivative, which is the slope of the tangent line to a curve at a given point.

According to the given information:

2(x + 2 )=  ( 5 x - 5 )

2x + 4 = 5x -5

9 = 3x

3 = x

The length of FG is = x+2 = 3+2 = 5 units

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9514 1404 393

Answer:

Step-by-step explanation:

In early primary education, when you're learning your arithmetic facts, you were probably exposed to math problems that looked like this:

  ___ + 4 = 5

In algebra problems, we give a name to the blank, and we call that name a "variable." In this problem, we have have named the blank "y". The variable in the equation is y.

  y + 4 = 5

__

To answer the math question above, we fill in the blank with the numerical value that makes the statement true. To solve the algebraic equation, we find the value of y that makes the equation true.

__

1 goes in the blank to make the original statement true:

   1   + 4 = 5

1 is a solution to the equation because replacing y with 1 makes 1+4=5 a true statement.

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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9514 1404 393

Answer:

  (c)  1/(36·a^4·b^10)

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

  a^-1 = 1/a

__

  \(\left(\dfrac{(2a^{-3}b^4)^2}{(3a^5b)^{-2}}\right)^{-1}=\dfrac{(3a^5b)^{-2}}{(2a^{-3}b^4)^2}=\dfrac{3^{-2}a^{-10}b^{-2}}{2^2a^{-6}b^8}=\dfrac{1}{3^22^2}a^{-10-(-6)}b^{-2-8}\\\\=\boxed{\dfrac{1}{36a^4b^{10}}}\)

Answer:

dont know

Step-by-step explanation:

sorry

Answer: B) 2000

Step-by-step explanation:

Sale Price: The cost following a discount applied to the initial cost.

Cost Price: The cost price is what we pay to purchase a good.

Discount Price : A price that is lower than the usual price.

Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).

So, The sale price is Rs 1600 after discount.

Discount =20%

Selling price of the skates = Rs 1600

Discount price = 100/80 × 1600= Rs 2000

Discount price = Rs 2000

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Answer:

I think it's C

Step-by-step explanation:

I just rotated point K 180 degrees and C was the only one with the coordinate points I got for K'

Given:

The recursive formula of a geometric sequence is

\(a_n=a_{n-1}\cdot (\dfrac{1}{8})\)

\(a_1=-3\)

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is \(a_1=-3\).

Recursive formula of a geometric sequence is

\(a_n=a_{n-1}\times r\)      ...(i)

where, r is common ratio.

We have,

\(a_n=a_{n-1}\cdot (\dfrac{1}{8})\)    ...(ii)

On comparing (i) and (ii), we get

\(r=\dfrac{1}{8}\)

The explicit formula of a geometric sequence is

\(a_n=a_1r^{n-1}\)

Putting \(a_1=-3\) and \(r=\dfrac{1}{8}\), we get

\(a_n=-3\left(\dfrac{1}{8}\right)^{n-1}\)

Therefore, the correct option is D.

Answer:

139.5 cm²

Step-by-step explanation:

12 · 9

108 cm²

7 · 9

63

63 ÷ 2

31.5 cm²

108 cm² + 31.5 cm²

139.5 cm²

His total monthly cash inflow is $2073.6 which is the correct answer would be option (D).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

We have been given that Tyrone’s hourly wage is $18

And he spends about $1,800 on his monthly expenses

Since Tyrone works 40 hours per week

So Monthly hours worked would be: 40 × 4 = 160

To determine the total wage

We have multiplied the hours worked by the wage rate  

So total wage = hours worked × wage rate  

Total Wage = 160 × 18 = 2880

Tyrone's net salary is 72% of his total income, as determined by the formula below:

Tyrone's net salary = 72% of the total Wage

Tyrone's net salary = 0.72× 2880

Tyrone's net salary = 2073.6

Therefore, His total monthly cash inflow is $2073.6 which is the correct answer would be an option (D).

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The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

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Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Answer:

720 Minutes

An analogue clock is split up evenly in two ways. Minutes are sixty equal parts and hours are 12 equal parts. That means that for every hour maker from 12 there are also five minute markers.

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