a. The line equation is given by:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y intercep.
In this case y is the number of active pilots and x is the year.
In order to obtain the line equation of the function, you use the information about a pair of years in the given table, in order to calculate the slope of the line. You can select whichever two years with its number of active pilots.
For example, for years 1980 and 1990, you have that the pilots were 182,097 and 149,666 respectively.
To calculate the slope of the line, you use the following formula:
[tex]m=\frac{149,666-182,097}{1990-1980}=-3,243.1[/tex]Then, the slope of the line is negative.
If you consider the zero point of the year axis, as the year 1980, the y intercept of the function will the value of the active pilots in that years, which is 182,097.
Finally, the line equation is:
[tex]y=-3,243.1x+182,097[/tex]b. For the year 2003, you have that x is:
x = 2003 - 1980 =23
You replace this value of x into the linear equation:
[tex]y=-3,243.1(23)+182,097=107506[/tex]The number of active pilots for 2003 is 107,506
solve for t
275,000 = 300 1-(1 + .038/12 ) ^(-12t)/(.038/12)
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
What is meant by an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given: [tex]$275000=\frac{3001-\left(1+\frac{0.038}{12}\right)^{(-12 t)}}{\left(\frac{0.038}{12}\right)}$$[/tex]
Multiply both sides by 0.038 / 12, we get
[tex]$275000 \cdot \frac{0.038}{12}=\frac{3001-\left(1+\frac{0.038}{12}\right)^{-12 t}}{\frac{0.038}{12}} \cdot \frac{0.038}{12}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Add [tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}$[/tex] to both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}+\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001$$[/tex]
Subtract 5225 / 6 from both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}-\frac{5225}{6}=3001-\frac{5225}{6}$$[/tex]
Simplify
[tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}=\frac{12781}{6}$$[/tex]
By using exponent rules, we get
[tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right)$$[/tex]
Solve [tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right): \quad t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$[/tex]
[tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex]
Therefore, the value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
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Find the slope of the following equation. Simplify your answer.
5x + 2y = -10 And do not tell me it’s m= - 5/2 because clearly that’s not an option
The correct answer is: [D]: " [tex]m = \frac{-5}{2}[/tex] ".
______
Step-by-step explanation:
We are given:
" 5x + 2y = -10 " ; Find the slope of the equation.
______
Rewrite this equation in slope-intercept format ;
that is: " y = mx + b " ;
in which:
y remains as single value, as an 'output' ; or 'dependent
variable', on the 'y-axis' (if graphed);
isolated on the 'left-hand side' of the equation.
m is the coefficient of x in the equation; and represents the slope; for which we shall solve.
{If there is no slope, then "m = 0" ; and "[0 * x = 0]." };
And the "slope-intercept format" is: "y = b" }.
b represents the "y-intercept" ; i.e. when the line crosses the
"y-axis" when graphed; that is, the "y-value" of the "coordinate" of the "y-intercept" ; [i.e. the value of "y" when "x = 0" ; so; " (0, b) ".
{ Note: b can equal "0" ; in those cases: y = mx + 0 ; write as " y = mx "}.
{ If there is no slope, [i.e. "m = 0" ; and no "y-intercept" ; [i.e. "b = 0"];
Then: write the equation accordingly—e.g. " y = [whatever number the graph represents]." }.
Also, note that b can be a "negative number"; as well.
In that case, write an equation in "slope-intercept format" ; that is;
→" y = mx + b " ; as: " y = mx " .
______
Given: " 5x + 2y = -10 " ;
Let's rewrite: ↔ " 2y + 5x = -10 " ; to get the "y-value" a bit closer to the 'left-hand side' of the equation.
Then: Let's subtract 5x from Each Side of the equation;
2y + 5x − 5x = -10 − 5x ;
to get: " 2y = -10 − 5x " ;
______
Method 1):
We have: " 2y = -10 − 5x " ;
Divide Each Side by 2 ; to isolate y on the 'left-hand side' of the equation, and to rewrite as an equation in the slope-intercept format :
2y / 2 = (-10 − 5x)/2 ;
→ [tex]y =\frac{-10-5x}{2}= \frac{-10}{2}-\frac{5x}{2}[/tex] ;
→ [tex]\frac{-10}{2} =[/tex] -10 ÷ 2 = -5 ;
Rewrite the equation by replacing " [tex]\frac{-10}{2}[/tex] " ; with: -5 ;
→ [tex]y = -5 - \frac{5x}{2}[/tex] ;
Then, rewrite to get the equation in "slope-intercept format"
→ [tex]y = -5 - \frac{5x}{2}[/tex] ;
[tex]= -5 + (-\frac{5x}{2})[/tex] ; ↔ Rewrite:
[tex]= \frac{-5x}{2} + (-5)[/tex] ; ↔ Rewrite again:
[tex]=\frac{-5x}{2} -5[/tex] ;
→ [tex]y = \frac{-5x}{2} -5[/tex] .
Note: " [tex]\frac{-5x}{2} = \frac{-5}{2} x[/tex] " ;
→ [tex]y = \frac{-5}{2}x-5[/tex] ;
This is the equation written in "slope-intercept format" ;
that is: " y = mx + b " ;
in which:
y is isolated as a single variable on the 'left-hand side' of the equation;
m = [tex]\frac{-5}{2}[/tex] ; which is the slope; which is also the "coefficient" of x ;
b = -5 ; which is the 'y-coordinate' of the "y-intercept" of the graph;
So, the slope; "m = -5/2" ; is the correct answer; which corresponds to:
Answer choice: [D]: " m = [tex]\frac{-5}{2}[/tex] " .
______
Method 2):
Given: " 5x + 2y = -10" ; Find the slope of the line.
We want to rewrite the equation in the "slope-intercept format" ;
" y = mx + b " ; as explained above;
to get the correct answer for m, the slope of the line.
" 5x + 2y = -10 " ↔ Rewrite as:
2y + 5x = -10 ; since we want to isolate y as a single variable on the 'left-hand side' of the equation; and by rearranging & rewriting this equation, the 2y is closer to the 'left' of the equation.
Now, subtract 5x from Each Side of the equation:
2y + 5x − 5x = -10 − 5x ;
to get: 2y = -10 − 5x ;
Now, Let's multiply the entire equation (i.e. "Each Side") by -1 ;
to make the equation easier to handle;
-1(2y) = -1 (-10 − 5x) ;
For the 'left-hand side' of the equation:
-1*2y = -2y
For the 'right-hand side' of the equation:
Note the 'distributive property of multiplication'; as follows:
a(b + c) = ab + ac ;
Likewise:
-1(-10 − 5x) = (-1 *-10) + (-1 *-5x) ;
= (10) + (5x) = 10 + 5x ;
Now, rewrite the entire equation:
-2y = 10 + 5x ; ↔ Rewrite as;
-2y = 5x + 10 ;
Then, we divide Each Side of the equation by -2 ;
to isolate y as a "single variable" on the 'left-hand side' of the equation;
and to rewrite the equation in "slope-intercept format" ;
-2y / -2 = (5x + 10) /-2 ;
→ [tex]y=\frac{5x+10}{-2} =\frac{5x}{-2} +\frac{10}{-2} =\frac{5x}{-2}+(-5) =\frac{5x}{-2}-5[/tex] ;
→ [tex]y=\frac{5x}{-2} - 5[/tex] ;
which is written in "slope-intercept format" ; that is:
" y = mx + b " ;
in which:
y is isolated as a single variable on the 'left-hand side' of the equation;
m = [tex]\frac{5}{-2}[/tex] ; which does equal " [tex]-\frac{5}{2}[/tex] " ; which does equal " [tex]\frac{-5}{2}[/tex] " ;
which is the slope of the equation, as well as the 'coefficent of x' ;
b = -5 ; which is the 'y-coordinate' of the "y-intercept".
______
As such:
The correct answer choice is: [D]: " m = [tex]\frac{-5}{2}[/tex] " .
{Note: This is consistent with the answer choice from Method 1 above.}
______
Hope this answer and explanation is helpful.
Best of luck to you!
______
7) An amusement Park Charges a $50
admission free and $10 for each ride.
which equation can be used to determine
C, the total cost of a day at the amusement
Park, based on n, the humber of rides.?
Answer:
50+((10n) =
so 50 is how much it cost to walk in the park and 10 is how much each ride (n) cost soif you know how many rides your ride you times that by 10 the add 10 to 50 and you get how much it will cost you for the day
Simplify the equation. Show your work.[tex]-i^3^2[/tex]
[tex]{\Large \begin{array}{llll} i^4=1 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ -i^{32}\implies -i^{4\cdot 8}\implies -(i^4)^8\implies -(1)^8\implies \text{\LARGE -1}[/tex]
Levi is 5 feet, 9 inches tall. How many centimeters tall is Levi? (1 inch = 2.5 centimeters)
Answer:
175.259 cm
Step-by-step explanation:
Which statement describes the graph of the system of equations below?
1.5x + 0.2y = 2.68
1.6x + 0.3y = 2.98
The lines are parallel.
The lines overlap at all points.
The lines intersect at (1.6,1.4).
The lines intersect at (3.1,0.5).
Answer:
3rd answer option (1.6, 1.4)
Step-by-step explanation:
the slope of the lines is different.
to see we transform the equations to the regular slope-intercept form
y = ax + b
with "a" being the slope and "b" being the y-intercept (the y value when x = 0).
1.5x + 0.2y = 2.68
0.2y = -1.5x + 2.68
y = -1.5x/0.2 + 2.68/0.2 = -7.5x + 13.4
1.6x + 0.3y = 2.98
0.3y = -1.6x + 2.98
y = -1.6x/0.3 + 2.98/0.3 = -5.33333...x + 9.93333...
-7.5 is not -5.3333...
so, the lines are not parallel nor overlap at all points.
therefore, they intersect at a point.
(1.6, 1.4) ?
the equations must remain true when using the coordinates :
1.5×1.6 + 0.2×1.4 = 2.68
1.6×1.6 + 0.3×1.4 = 2.98
2.4 + 0.28 = 2.68
2.68 = 2.68 correct
2.56 + 0.42 = 2.98
2.98 = 2.98 correct
yes, they intersect at (1.6, 1.4).
for (3.1, 0.5) already the x coordinate is way too large.
1.5×3.1 or 1.6×3.1 are already by themselves much larger than 2.68 or 2.98.
Use Tools Telegraphs were used to send messages before the
telephone was invented. A telegraph operator could interpret about
40 words sent in Morse code per minute. Approximately how many words
sent in Morse code could the operator interpret in 12.5 seconds? State
what strategy and tool you will use to answer the question, explain your
choice, and then find the answer.
Answer:
stuff and more stuff
Step-by-step explanation:
When 6 times a number is increased by 11 the result is 16 less than 9 times the number. Find the number
Answer:
The number is 9
Step-by-step explanation:
6n + 11 = 9n -16 Subtract 6n from both sides of the equation
11 = 3x -16 Add 16 to both sides of the equation
27 = 3n Divide both sides of the equation by 3
9 = n
what is a four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners?
The four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners is a parallelogram.
What is a parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
The parallelogram is divided into two congruent triangles by each diagonal. The total of the squares of a parallelogram's sides equals the sum of the squares of its diagonals. It is also known as parallelogram law.
A parallelogram is a two-dimensional geometrical shape with two parallel sides. It is a four-sided polygon (sometimes known as a quadrilateral) with parallel sides that are equal in length. The sum of a parallelogram's neighboring angles equals 180 degrees.
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hopt shipping company charges a
flat fee of $9 Plus an additional
$0.18 per pound to ship a package.
Gespil shipping company
flat fee of $10 plus an additional
$0.10 per pound. How many pounds
would a package weigh
that cost the same at
both companines?
Answer:
Hopt: 10 Gesplil; 6
Step-by-step explanation:
At a carnival it costs $34.92 for 12 tickets. Write an equation that can be used to express the relationship between the total cost (t) and the number of tickets(n) you buy.
The equation that can be used to express the relationship between total cost and tickets is t = $2.91n.
What is the total cost?The first step is to determine the cost of one ticket. The cost of one ticket can be determined by dividing the total cost of the ticket by the total number of tickets. Division is the operation that is used to determine the quotient of two or more numbers.
Cost of one ticket = $34.92 / 12 = $2.91
The equation that can be used to determine the total cost would have this form:
Total cost = cost per ticket x number of tickets
t = $2.91 x n
t = $2.91n
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(9x-26) (4x+43) (2x-12)
The value of the expression given as (9x-26) (4x+43) (2x-12) is 72x³ + 134x² -5642x + 13416
How to evaluate the expression?From the question, the expression is given as
(9x-26) (4x+43) (2x-12)
Next, we evaluate the expression in pairs
So, we have
(9x-26) (4x+43) (2x-12) = (9x-26) (4x+43) (2x-12)
Evaluate the first two factors
So, we have
(9x-26) (4x+43) (2x-12) = (36x² + 387x - 104x - 1118) (2x-12)
Evaluate the like terms in the expression
So, we have
(9x-26) (4x+43) (2x-12) = (36x² + 283x - 1118) (2x-12)
Evaluate the first two factors
So, we have
(9x-26) (4x+43) (2x-12) = (72x³ - 432x² + 566x² - 3396x - 2246x + 13416)
Evaluate the like terms
So, we have
(9x-26) (4x+43) (2x-12) = (72x³ + 134x² -5642x + 13416)
Remove the bracket
(9x-26) (4x+43) (2x-12) = 72x³ + 134x² -5642x + 13416
Hence, the solution is 72x³ + 134x² -5642x + 13416
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What is -8.64 / -0.024?
Let's first write both numbers in their fraction form:
[tex]\begin{gathered} -8.64=-\frac{864}{100} \\ -0.024=-\frac{24}{1000} \end{gathered}[/tex]then, we can write the division like this:
[tex]-8.64\frac{\cdot}{\cdot}-0.024=-\frac{864}{100}\frac{\cdot}{\cdot}(-\frac{24}{1000})[/tex]Now, given the general rule for the division of fractions, we have:
[tex]\begin{gathered} \frac{a}{b}\frac{\cdot}{\cdot}\frac{c}{d}=\frac{a\cdot d}{b\cdot c} \\ b,d\ne0 \end{gathered}[/tex]also notice that we are dividing two negative numbers, then our final result will be positive according to the law of signs. Then, we have in this case:
[tex]-\frac{864}{100}\frac{\cdot}{\cdot}(-\frac{24}{1000})=\frac{864\cdot1000}{24\cdot100}=\frac{864\cdot10}{24}=\frac{8640}{24}=360[/tex]therefore the final result is 360
Exit ticket: Joehamster eats 12 muffin morsels every sixth day, 24 celery sticks every 8th oday, and 18 cookies every 10th day. After how many days will he eat all three food items on the same day?
In order to calculate after how many days all three food items will be eaten in the same day, we need to calculate the least common multiple (LCM) between the periods of 6 days, 8 days and 10 days.
First, let's factorize each number:
[tex]\begin{gathered} 6\to2\cdot3 \\ 8\to2\cdot2\cdot2 \\ 10\to2\cdot5 \end{gathered}[/tex]Then, let's multiply the factors using the maximum number of time they appear in a number, that is, number 2 three times, number 3 one time and number 5 one time:
[tex]2\cdot2\cdot2\cdot3\cdot5=120[/tex]So after 120 days all three food items will be eaten on the same day.
A box is in the shape of a right rectangular prism made from cardboard has dimensions of 18 inches, by 12 inches, by 8 inches, as shown in the diagram below. find the volume of the box and show your calculations and use appropriate units
Volume of the rectangular prism = 1,728 in³
Explanation:Volume of the rectangular prism = width × height × length
width = 12 in
length = 18 in
height = 8 in
Volume of the rectangular prism = 12 in × 8 in × 18 in
Volume of the rectangular prism = 1,728 in³
Percents
Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your and
Solve this problem, and identify the percent, amount, and base.
What percent of 60 is 45?
O Percent = 75, Amount = 60, Base = 45
O Percent = 45, Amount =27, Base = 60
O Percent = 75, Amount = 45, Base = 60
Percent 60, Amount = 27, Base = 45
Submit
Hold
The correct option is- Percent = 75, Amount = 45, Base = 60 for the movement of the progress bar.
What is termed as the progress bar?In math, bar notation is a simple method for expressing a repeating number by drawing a line over the number which repeats. Learn regarding infinity, when figures go on forever, and when to use bar notation by exploring the definition as well as examples of bar notion.For the given question,
The movement of the progress bar could be uneven due to questions can be worth more or less (including zero) due-
Type of problemThe individual capacityThe amount of something is stated in terms of a fraction of a hundred. The ratio can be expressed as a fraction of 100.
Base = 60 and the Amount is the 45.
Let the % will be x;
x% of 60 =45
60x =45
x=45/60
x=0.75
To obtain the percentage value, multiply it by 100 as follows:
% x = 0.75 × 100
% x = 75
Thus, the percentage of 60 is 45 will become 75%.
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Write the equation of the line that is perpendicular to y = 1 and goes through (4, −9).
FOR PERPENDICULAR LINES WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE -1
BUT IF WE ARE TO CHECK IN THE LJNE y=1 the gradient is 0
there is no number when multiplied with 0 that will give us -1 it means that the gradient of the line perpendicular to the given one will also be 0
when we substitute in the general equation y=mx+c together with the points
[tex] - 9 = (0)(4) + c \\ c = - 9[/tex]
IT MEANS THE EQUATION OF THE NEW EQUATION WILL BE
[tex]y = - 9[/tex]
HOPE THIS HELPS
HELP ME PLEASE!!! due tonight
Answer:
y=1x-5
Step-by-step explanation:
Use rise/run
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
Just look at the slope and the y-intercept.
The y-intercept is b, and it's -5. The slope is 1, so it is x.
Find the slope and y-intercept of the following equations :
3x-4y = 12
Kirsten bought a used car for $3,600. She made a $360 down payment on it. How much more does Kirsten owe on the car?
Answer:
Kirsten owes $3240 more on the car.
Step-by-step explanation:
$3600 - $360 = $3240
8. Find the value of x if xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰
The study of the correlations between triangles' side lengths and angles is known as trigonometry. x= 0.11
What is trigonometry?The study of the correlations between triangles' side lengths and angles is known as trigonometry. The field was created in Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.
Trigonometry has been used historically in the fields like geodesy, surveying, celestial mechanics, and navigation.
Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰
x0.7*0.70*1.73 =1*1-0.5*0.5
x = [tex]\frac{0.7*0.70*1.73}{1*1 - 0.5*0.5}[/tex] = 0.11
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The probability that Gavyn wins in a raffle is given by the expression
p. Write down an expression for the probability that Gavyn does not win.
Explanation:
Let's replace p with something like 0.72
Pick any number between 0 and 1.
This says he has a 72% chance to win
1-p = 1-0.72 = 0.28
and he has a 28% chance of not winning.
For more information, check out "probability complement".
help !
Select the correct answer.
What is the measure of an angle that is the complement of angle R? R 80
Answer: B: 10
Step-by-step explanation:
complementary angles are two angles that add up to 90 degrees
x = 8.27 rounded to the nearest tenth
Answer:
x = 8.3
Step-by-step explanation:
We look at the final place of the decimal to round, in this case the thousandths place (underlined)
8.27
If the final place of the decimal is greater than or equal to 5, we round up the decimal to the left, otherwise we round down.
Because 7 > 5, round 2 up to 3, therefore giving 8.3
Answer:
Your answer is 8.3!
Step-by-step explanation:
Step 1: Locate and underline the tenths place (2) then look at the digit to the right (7):
8.27
Step 2: In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tenth place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 8.3 as the answer.
In short: 8.27 rounded to the nearest tenth is 8.3.
suppose that a current recipe yields 30 servings (2 ounces each) and the desired recipe yields 30 servings (5 ounces each). what is the recipe conversion factor?\
Conversion factor [tex]= \frac{final serving}{initialserving}[/tex][tex]=\frac{5}{2} =2.5[/tex]
The recipe conversion factor is 2.5
Solve for v.
V =
Blank 1:
Answer:
v=60
Step-by-step explanation:
3v=180
v=60
:]
Solve the equation 3 sinx+3 = 1 for 0°
The value of x after solving the equation 3sinx+3 = 1 for 0° is -46.455.
First, take the equation 3sinx+3 = 1. This is a first order linear equation with a single variable, x. To solve this equation find the value of x.
First subtract three from both LHS and RHS part. The equation becomes
3sinx+3-3 = 1-3,
which is equal to,
3sinx = -2. now divide both LHS and RHS by 3 and the equation becomes, (3sinx)÷3 = -2÷3 solving this we get the equation as sinx = -2÷3.
now take the sine to the LHS we get the equation as,
x = [tex]sin^{-1}[/tex](-2÷3)
so by solving this, the final answer for x is,
x = -46.455
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A map ratio is 1:50 000. Two villages
are 8km apart. How far apart are they
on the map?
Answer: they should be 2cm apart
Step-by-step explanation: This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km). We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.
a computer password is required to be 8 characters long. how many passwords are possible if the password requires 1 letter(s) followed by 7 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
There will be 15724800 computer passwords possible with 1 letter followed by 7 digits without any repetition of letters or digits.
It is given to us that -
A computer password is required to be 8 characters long
The computer password requires 1 letter(s) followed by 7 digits
The 7 digits are from numbers 0-9.
It is also mentioned that there will be no repetition of any letter or digit
We know that,
The total number of English alphabets = 26 (from a-z)
The total number of digits = 10 (from 0-9)
Since it is given that the computer password has
1 letter followed by 7 digits without any repetition of any letters or digits
So, the number of computer passwords that are possible can be -
[tex]26*10*9*8*7*6*5*4\\= 15724800[/tex] (1 letter and 7 digits with no repetition)
Thus, 15724800 computer passwords are possible that contains 1 letter followed by 7 digits where no repetition of any letter or digit is allowed.
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Characterize the slope of the line in the graph
A. Positive
B. Negative
C. Zero
D. Undefined
The slope of the line in the graph is undefined.
The line in the graph is a straight vertical line whose slope can be found.
The characteristics of a vertical line can be used to find the slope of the vertical line given.
A vertical line has same x-co-ordinate but will have different y-co-ordinates.
Slope of a line is the change in y-co-ordinates divided by change in x-co-ordinates.
That is, slope = change in y-co-ordinates/ change in y-co-ordinates
But here, change in x-co-ordinates is zero since the x-co-ordinates are same for the vertical line given in the graph.
So slope = change in y-co-ordinates/ 0
This is undefined.
So the slope of the line in the graph is undefined.
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