In the division example at the right A and B represent
different digits. What is the sum of A and B if the
remainder is zero?

The value of 'w' in the solution of the following system of linear equations is -[tex]\frac{1}{6}[/tex]

we can solve for a variable say 'v' then put the value of 'v' in the other equations and solve them for the value of 'w'

5v + 4w = 1

5v = 1 - 4w

v = [tex]\frac{1-4w}{5}[/tex]

now, when we put the value of 'v' in the second equation, we get:

3([tex]\frac{1-4w}{5}[/tex] ) - 6w = 2

3([tex]\frac{1-4w}{5}[/tex] ) = 2 + 6w

[tex]\frac{3-12w}{5}[/tex] = 2 + 6w

3 - 12w = 10 + 30w

-42w = 7

w = [tex]\frac{7}{-42}[/tex]

w = -[tex]\frac{1}{6}[/tex]

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The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

here, we have,

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value and b is the multiplicative factor.

Let y represent the amount of substance remaining after x hours. Hence:

a = 9375, at x = 4, y = 15:

15 = 9375(b)⁴

b = 0.2

y = 9375(0.2)ˣ

For the 7th hour, x = 7:

y = 9375(0.2)⁷

  = 0.12

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

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The congruence theorem that justifies the congruence of the two triangles is given as follows:

A. SSS.

The Side-Side-Side (SSS) congruence theorem states that three sides of a triangle are equivalent to the corresponding three sides of the another triangle, then the two triangles are said to be congruent by SSS rule.

In this problem, we have that:

Hence the triangles are congruent by the SSS postulate and the correct option is given by option A.

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The value of the network density is 0.9

Since the potential connections (PC) formula is n(n-1)/2 and number of nodes is 5 (i.e. n = 5). We have:

PC = n(n-1)/2

PC = 5(5-1)/2

PC = (5*4)/2

PC = 20/2

PC = 10

Actual connection (AC) = 9

Network Density = AC/PC

Network Density = 9/10

Network Density = 0.9

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Answer:

Step-by-step explanation:

The required value of x is equivalent to 30 units.

The state of likeness can be referred to as a similarity. When two elements, things, ideas, or people resemble one another, they are said to be similar. Example: In terms of the number of sides, a square and a rectangle are comparable ( four sides for each). The state of being different can be used to define a difference.

To find the value of x we will use the similarity which corresponding sides of similar triangle are Proportional.

So;

50/x = 75/45

2/x = 3/45

x = 30 units

Thus, required value of x is  30 units.

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The formula for compound interest is:

A = P(1 + r/n)^nt

where:

A is the total amount of money after t years,

P is the initial principal or deposit amount (in this case $1000),

r is the annual interest rate as a decimal (in this case 1.3% or 0.013),

n is the number of times interest is compounded per year (in this case, let's assume it's compounded annually), and

t is the number of years.

So, the function modeling the total amount of money Brigitte has over time, t, would be:

A = $1000(1 + 0.013)^t

This function shows how the amount of money in the savings account will increase as time goes on due to compound interest.

If a line has two points with the same x-value, then the two points are on a vertical line.

So we know that we have some kind of a linear equation, such that in two points on the line we have the same x-value.

Then we can write these two points like (x₁, y₁) and (x₁, y₂). If the x-value is the same one, then we have a line of the form:

x = x₁

Which is a vertical line, then that is the correct answer.

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1. the number ( of people without college degree ) = 125 - (24 +38)= 63

2. number of people without experience ) = 125- ( 41+38) = 46

3. number ( of applicants with college degree but no experience) = 24

4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

number of people that have previous work experience only) = 79-38 = 41

number ( of persons that have college degree only) = 62- 38 = 24

1. the n( of people without college degree ) = 125 - (24 +38)= 63

2. n( of people without experience ) = 125- ( 41+38) = 46

3. n( of applicants with college degree but no experience) = 24

4. n( of applicants with either college degree or experience) = 24+41 + 38 = 103

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This is a word problem and the value of the unknown number is equal to 25

Word problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.

Let us represent the unknown number with the letter x so that we derive the equation;

1 + 6x = 151

we subtract 1 from both sides of the equation

1 - 1 + 6x = 151 - 1

6x = 150

divide through by the coefficient of x which is 6

6x/6 = 150/6

x = 25

Therefore, the value of the unknown number for the word problem is equal to 25

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The measure of angle ABC in the figure of triangle attached is

In geometry, a perpendicular bisector is a line or line segment that divides another line segment into two equal parts and is perpendicular to it.

From the definition of perpendicular bisector, we have that

< A = < C

and using triangle ABD

< A + < ABD = 90

< A + 28 = 90

< A = 90 - 28

< A = 62

Using triangle ABC

< A + < ABC + < C = 180

62 + < ABC + 62 = 180

< ABC = 180 - 62 - 62

< ABC = 56

OR

< ABD = < DBC = 28 degrees

and < ABC = < ABD + < DBC adjacent angles

< ABC = < ABD + < DBC

< ABC = 28 + 28

< ABC = 56 degrees

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complete question

The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees

In this equation, the regular polygon's area is 72.5.

The area of a regular polygon is determined by multiplying its perimeter by its apex. The following is a common way to write the formula: An apothem's area is equal to 1/2(ap), where a denotes the length and p the circumference. Area of pentagon = 1/2 p an is the fundamental formula for computing the area of a regular pentagon, where p stands for the pentagon's perimeter and a for its apothem.

If a polygon has equal sides and angles, it is considered to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

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No, [tex]4^{3}[/tex]. 5 is not equal distance away from both [tex]4^{3}[/tex] and [tex]4^{4}[/tex]. However, when x is a perfect square, it is halfway between [tex]x^{3}[/tex] and [tex]x^{4}[/tex]. 5 is halfway between [tex]9^{3}[/tex] and [tex]9^{4}[/tex].

A perfect square is an integer that is the result of multiplying an integer by itself. In other words, it is a number that can be expressed as the product of two equal integers. For example, the number 16 is a perfect square because it can be written as 4 • 4.

Every perfect square has an ending of 1, 4, 5, 6, 9 or 00. (i.e. Even number of zeros). A number that finishes in 2, 3, or 7 is not a perfect square, and so is 8. In essence, a perfect square is the result of multiplying two equal numbers by one another. As a result of multiplying two equal integers (5 and 5) by one another, the number 25 is a perfect square.

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Answer:

a -3.9

Step-by-step explanation:

Subtract 13 from both sides which makes it -19 > 5x. then divide by 5 on both sides

18 points in 15 hour is greater than 45 points in 36 hours.

The unit rate compares a certain number of units of one quantity to units of another quantity. In other words, the second quantity in the comparison is always 1.

45 points in 36 hours and 18 points in 15 hours.

Points per hour

45 points in 36 hours is given by,

[tex]\frac{45}{60} =1.25[/tex] points.

18 points in 15 hours is given by,

[tex]\frac{18}{15}[/tex] = 1.2 points.

On comparing these points 1.2 > 1.25.

Hence, 18 points in 15 hour is greater than 45 points in 36 hours.

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Answer:

Step-by-step explanation:Base on the diagram, and the following question, the following are the answers to your question.

#1 Congruent Angle

#2 Congruent Sides

#3 Side Angle Side

I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification

Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

1) From Given output confidence level, is 95% level of significance = 1-0.95

10.05

2) null hypothesis : M = 150000

=

3) Alternative hypothesis Ha: [M> 150000]

4) since P value = 0.033 is less than d=0.05 Reject null hypothesis.

5) There is sufficient evidence to conclude that the mean life of transmissions is over 1500 comity

6) 95% CI = â ± E

-1519±1.129

=(151.2-1.129, 151.2+1.129)

=(150.071, 152.329)

7) Since M=150 fall out side of the C. We Shoul retect null hypothesis.

8) The null hypothesis value fall outside of the Confidence Interval.

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The probability that exactly 4 out of 7 seeds planted do not grow is 0.0007 (approximately), given that each seed has a 95% chance of growing into a healthy plant.

The probability that a seed doesn't grow is 1 - 0.95 = 0.05.

To calculate the probability that exactly 4 seeds don't grow out of 7, we need to use the binomial distribution formula, which is:

P(X=k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)}[/tex]

where:

X is the random variable representing the number of seeds that don't grow.

k is the specific number of seeds that don't grow (in this case, k=4)

n is the total number of seeds planted (n = 7)

p is the probability that a seed doesn't grow (p=0.05)

C(n,k) is the number of ways to choose k items out of n, also known as the binomial coefficient.

Plugging in the values, we get:

P(X=4) = C(7,4) * 0.05⁴ * 0.95³

          = 35 * 0.00000625 * 0.857375

          = 0.0006522

Rounding to four decimal places, the probability that exactly 4 seeds don't grow is 0.0007 (approximately).

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]9y=x-18\implies y=\cfrac{x-18}{9}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{9}}x-2\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{9}} ~\hfill \stackrel{reciprocal}{\cfrac{9}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{9}{1} \implies -9}}[/tex]

so we're really looking for the equation of a line whose slope is -9 and it passes through (5 , 1)

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 9 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- 9}(x-\stackrel{x_1}{5}) \\\\\\ y-1=-9x+45\implies {\Large \begin{array}{llll} y=-9x+46 \end{array}}[/tex]

The actual width and length of the bedroom are respectively; 9 ft and 12 ft

The parameters are given as;

Width of house = 30 feet = 360 inches

Length of house = 45 feet = 540 inches

Scale drawing width of house = 4 inches

Scale drawing length of house = 6 inches

Thus;

Scale factor width = 360/4 = 90

Scale factor length = 540/6 = 90

Scale drawing width of bedroom = 1.2 inches

Scale drawing length of bedroom = 1.6 inches

Thus;

Actual width of bedroom = 1.2 inches * 90 = 108 inches or 9 ft

Actual length of bedroom = 1.6 inches * 90 = 144 inches or  12 ft

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Answer:

Option A

Step-by-step explanation:

A = opposite/hypotenuse = 12/5

I don't really have anymore explanation I could give you because that just what I could think of!

Answer: I think D. Sin A…..

Step-by-step explanation: hope this helps:)

Answer:

  y = 1/8x +1/64

Step-by-step explanation:

You want the equation of the line that is tangent to the curve y = x³ -x⁴ in exactly two places.

Since the tangent line is not crossed, the difference between the line and the given curve is a 4th-degree polynomial with two roots, each of multiplicity 2. If those are 'a' and 'b', we can write for line y = mx +p, ...

  mx +p -(x³ -x⁴) = (x -a)²(x -b)² = 0

  x⁴ -x³ +0x² +mx +p = x⁴ -2(a+b)x³ +(a²+4ab+b²)x² -2ab(a+b)x +a²b²

Equating coefficients, we have ...

The coefficient of x³ tells us ...

  a +b = 1/2

The coefficient of x² tells us ...

  0 = (a +b)² +2ab

  0 = (1/2)² +2ab

  ab = -1/8

Using these value, we can find the equation of the line to be ...

  m = -2ab(a+b) = -2(-1/8)(1/2) = 1/8

  p = (ab)² = (-1/8)² = 1/64

The equation of the line is ...

  y = 1/8x +1/64

__

Additional comment

To find the line, we did not need the coordinates of the points of tangency. They are ((1-√3)/4, (3-2√3)/64) and ((1+√3)/4, (3+2√3)/64).

The slope of the line is equal to the slope of the quartic at the point of inflection of its derivative, at x=1/4.

The  fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.

One inch is equivalent to 25.4 millimeters internationally.

Expressing this relationship as a formula is as follows.

1 inch = 25.4mm

This official, standardized measurement has been used in international records since 1959.

Both inches and millimeters are units of measurement. Inches belong to the British system of units, and millimeters belong to the metric system of units.

Inches are used in the United States, but it is often necessary to convert this unit of measurement to a metric unit of measurement, such as "millimeters." for scientific purposes. Conversely, there are 0.0393700787402 inches in millimeters. 

Thus , the  fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.

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Answer: 32

Step-by-step explanation: divide 8 into 4/100

Kcf

Keep change flip

Keep the 4/100 change the division sign to multiplication then flip the 8 to 8/1 then just multiply across.

The tape diagram helped to understand by that we can subtract the combined $25 at the concession stand from the total and divide it by 5.

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication. It is also known as a divided bar model, fraction strip, length model or strip diagram.

Given that, a family of 5 went to a matinee movie on a Saturday afternoon. The movie tickets for the matinee were a special price for each person. The family spent a combined $25 at the concession stand on drinks and popcorn. Altogether, the family spent $57.50 at the movies.

By using the tape diagram we get an equation,

5x+25 = 57.50

5x = 32.5

x = 6.5

Therefore, the special price for each person was $6.5

The figure is attached

Hence, the tape diagram helped to understand by that we can subtract the combined $25 at the concession stand from the total and divide it by 5.

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The perimeter of each shape is obtained adding all of their outer side lengths.

The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.

Hence, for each polygon, you must identify the outer side lengths, and then add them.

The problem is incomplete, hence the standard procedure to find the polygon of a shape was presented.

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An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73

The formula for finding the equation of a circle is expressed as:

(x-a)^2 + (y - b)^2 = r^2

Determine the value of r^2 using the distance between two points

r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9

r^2 = 73

Given the centre (a, b) as (-3, 2), the equatio of the circle will be;

(x-(-3))^2 + (y - 2)^2 = 73

(x+3))^2 + (y - 2)^2 = 73

Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73

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Answer: 39%

Step-by-step explanation:

using calculator

1 seat = 0.058%
1700 - 1037 = 663 seats are taken.

0.058% x 663 seats = 39%