how many 3-letter passwords can be made using the letters a through z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?

The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.

In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

The given system of equations is

x + y = -1          ......(1)

3x - y = 21       ......(2)

Rewrite equation (1)

y = - x - 1        ......(3)

Put equation (4) in equation (3)

3x -(-x -1) = 21

3x + x + 1 = 21

4x = 20

x = 20/4

x = 5

Put x= 5 in equation (3)

y = - 5 - 1

y = - 6

So, both the options are correct, (5, -6) is the solution of both equations.

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Answer:

∠T

Step-by-step explanation:

∠T is the common angle found in both triangles.

In ΔPTS, ∠PTS represents ∠T.

In ΔQTR, ∠T is represented by ∠QTR.

Answer:

The angle T is common side.

Step-by-step explanation:

Given triangles,

→ ∆PTS & ∆QTR

Now we have to,

→ fInd common angle of both triangles.

The common angle is,

→ <T (angle T)

→ As it is present in both triangles.

Hence, the common part is angle T.

Finally, we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.

Given that;

A catering company needs 8.75 lbs of shrimp for a small party. they buy [tex]3\frac{2}{3}[/tex] lbs of jumbo shrimps, [tex]2\frac{5}{8}[/tex] lbs of medium-sized shrimps, and some mini-shrimps.

The total of 8.75th is changed as [tex]8\frac{3}{4}th\\[/tex]

Sum of  [tex]3\frac{2}{3}[/tex] +  [tex]2\frac{5}{8}[/tex] this is bought by the company.

So, to purchase the remaining  [tex]8\frac{3}{4}th\\[/tex] - [tex]3\frac{2}{3}[/tex] - [tex]2\frac{5}{8}[/tex]

We use a common denominator of 24 for the fraction parts.

Change [tex]8\frac{3}{4}[/tex] as [tex]8\frac{18}{24}[/tex]

Similarly, convert;

[tex]3\frac{2}{3}[/tex] as [tex]3\frac{16}{24}[/tex]

[tex]2\frac{5}{8}[/tex] as [tex]2\frac{15}{24}[/tex]

By solving all the above conversions, we get;

[tex]\frac{42-16-15}{24}[/tex] = 11/24

Considering all the factors together we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.

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Answer:

a

Step-by-step explanation:

The value of x will be; x = 14,000

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that  the equation 750 +0.05x = 1,100+ 0.025x

Here, we need to solve for x;

750 +0.05x = 1,100+ 0.025x

combine the like terms;

750 - 1,100= -0.05x + 0.025x

-350 = - 0.025x

x = 14,000

Therefore, the solution will be as;

x = 14,000

The value of x will be; x = 14,000

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Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.

See photo below. Comment for more clarification.

Answer:

t =2.45s

Step-by-step explanation:

H=-16t2+96t

then, -16t2= -96t

divide both sides by 16

-16t2/16 = -96t/16

-t2 = -6

t2=6

t=√6

t=2.45

The other leg has its length to be 11.49 units

To calculate the length of the other leg distance, we make use of the Pythagoras theorem

Mathematically, this theorem is represented by:

w² = y² + z²

Such that x = hypotenuse, y = leg and  z = other leg

From the question, we have the following parameters

w = 14, y = 8 and z = the other leg

Substituting these values in w² = y² + z²

14² = 8² + y²

Evaluate the exponents

196 = 64 + y²

Evaluate the like terms

y² = 132

Take the square roots of both sides

y = 11.49

Hence, the length of the other leg is 11.49 units

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Answer: 11 units

Step-by-step explanation: i took the test and got it right

0.1875 is  the probability of having a daughter .

Describe probability using an example?

Let X = No. of sons

n = 5 and p = 0.5, because probability of having son and daughter is same.

X follows Binomial distribution with parameter n and p. Then its pmf is,

P(X= x) = \binom{n}{x}p^xq^{(n-x)} \ \ \ \ \ x = 0,1,----5

Now,

P(X= 5) = \binom{5}{5}(0.5)^5 (0.5)^{(5-5)} \\ \\ \\ P(X= 5) = 0.03125

Probability of haveing at least four sons

P(X\ge4) = P(X=4) +P(X=5) \\\\ P(X\ge4) = 0.15625 + 0.03125 \\\\ P(X\ge4) = 0.1875

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Answer:7

Step-by-step explanation:

yabba dabba doo

the equation of the line passing through the given points is y = 3

What is an equation of the line?

An expression which is satisfied by every point on the line is known as equation of the line. generally it is given in y = mx + c form where m is the slope and c is the y-intercept

We are given two point (-7,3) and (5,3)

We first find the slope of the lines passing through the given points

Slope = [tex]\frac{3-3}{5+7}[/tex]

Slope = 0

Substituting the value in the equation we get

y = c

Now the value of y in both the cases is 3

Substituting that we get c = 3

Hence y = 3 is the required equation of the line

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The solution to the system of equations y = x − 5 and y = 5x − 17 is x = 3 and y = -2

The system of equations is given as

y = x − 5

y = 5x − 17

Substitute y = x − 5 in the equation y = 5x − 17

So, we have

x - 5 = 5x − 17

Evaluate the like terms

4x = 12

Divide both sides by 4

x = 3

Substitute x = 3 in y = x − 5

y = 3 − 5

So, we have

y = -2

Hence, the solution is x = 3 and y = -2

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The price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

Let the price of 1 kilogram of jelly bean cost be x

and the price of 1 kilograms of gummy worms be y

Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms

for $38

2x + 3y = 38......equation 1

Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms

for $45

3x + 3y = 45........equation 2

Subtracting equation 2 from equation 1

2x + 3y - (3x + 3y) = 38 - 45

2x - 3x + 3y - 3y = -7

-x = -7

x = 7

2(7) + 3y = 38

14 + 3y = 38

3y = 24

y = 8

Therefore, the price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

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1. The pairs of polygons are similar.

2. The pairs of polygons are not similar.

3. The missing measure is of x = 5.2.

4. The missing measure is of x = 16.

5. The value is AB = 6.

6. The perimeter of the yellow tile is of 240 cm.

7. The value is DF = 0.75.

Similar polygons are polygons that share these two following features:

Hence, for itens 1 and 2, we have that:

For item 3, the side lengths are proportional, hence:

x/2.6 = 8/4

x/2.6 = 2

x = 2 x 2.6

x = 5.2.

Same as item 4, hence:

x/10 = 9.6/6

x/10 = 1.6

x = 16.

For item 5, considering the equivalent side lengths, we have that:

AB/8 = 12/16

AB/8 = 3/4

AB = 24/4

AB = 6.

The perimeter of the yellow tile is of 240 cm in item 6, as the ratio between the side lengths is of 3, hence the ratio of the perimeters will also be of 3, then:

3 x 80 cm = 240 cm.

For item 7, we have that:

DF/3.4 = 2.25/9

DF = 3 x 2.25/9

DF = 0.75.

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Answer:

Step-by-step explanation:

from the area we find the side by taking the square root, having found the side we multiply it by 4 and we have the perimeter, we can solve it with a simple expression that summarizes what I wrote

4√81 =

4 × 9 =

36 mm

Answer: 45 minutes

Step-by-step explanation:

She rides 150/20 minutes per mile which is 7.5 minutes per mile. So it would take her 45 minutes to ride 6 miles because 6 × 7.5 = 45.

Answer: No

Step-by-step explanation: You want to find the unit rate for each bagel. 6/3 is 2 dollars, so each bagel is going to cost 2 dollars. If your getting 24 bagels for 9 dollars, 24/9 is 2 2/3 dollars for each bagel. 2 ≠ 2 2/3 so therefore, they're not the same.

Answer:

Step-by-step explanation:

To find the slope, subtract the y values, and divide it by subtracting the x values. The order matters!

(9-6)/(1-6)=-3/5

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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The number of yards of ribbon Isabel bought is 41 yards.

It is given in the question that:-

Money in prepaid debit card = $ 20

Price of ribbon = 7 cents per yard

Money left on the card after buying the ribbon = $ 17.13

We have to find the number of cards of ribbon Isabel bought.

Money used in buying the ribbon = 20 - 17.13 = $ 2.87

We know that,

$ 1 = 100 cents

Hence, according to the data given in the question, we can write,

$ 2.87 = 287 cents

Yards of ribbon bought = 287/7 = 41 yards.

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0.55 is the probability that a vacationer will visit at least one of these magnificent attractions.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

50% of the vacationers going to toronto visit the CN tower= 0.5

40% visit skydome= 0.4

35% visit both=0.35

P( At lease one) = P(Toronto) + P(Skydome) - P(Both)

P( At lease one) = 0.4 + 0.5 - 0.35

P( At lease one)  = 0.55

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An applicant needs 84.04 minutes to finish the test in order for 97 percent of them to pass.

An aptitude test is required of job candidates. Let's assume that the test's completion time has a mean of 69 minutes and a standard deviation of 8 minutes.

To get how much time an applicant should be given so that 97 percent of them will be able to complete the test.

Mean (μ) = 69

standard deviation (σ) =8

Hence, due to population standard deviation (σ) is known to use the normal distribution.

x_ Norm (μ,σ)

x_ Norm (69,8)

Therefore, x_ random variable that represents the time of applicant;

P(X<x) = 0.97

Corresponding to the left tail area of 0.97 lies in the z-table of z row of 1.8 and column 0.08.

P(z < 1.88) = 0.97

z < 1.88

(X - μ)/σ < 1.88

X < 1.88 (8) + 69

X < 84.04

The time taken by an applicant so that 97 percent of them will be able to complete the test is 84.04 minutes.

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Answer:

143.75

Step-by-step explanation:

11/4+110+15+16 1/2=143.75

[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]

[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]

[tex]{ \red{ \sf{7x = 14}}}[/tex]

[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]

[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]

The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15

General equation of quadratic is

f(x) = a[tex]x^{2}[/tex] + bx + c

and Standard form is

f(x) =a [tex](x-h)^{2}[/tex] + k

where h , k are coordinates of vertex

and x , y represent some point on the graph.

By replacing f(x) with y in standard equation we get

y = a[tex](x-h)^{2}[/tex] + k

Put value of x , y , h , k from the graph.

h = -2

k = 7

x = 0

y = 9

9 = a (4) + 7

a = 2

Now put value of a in standard equation

f(x) = 2 [tex](x + 2)^{2}[/tex] + 7

f(x) = 2[tex]x^{2}[/tex] + 4x + 15

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Answer:

m = -2

Step-by-step explanation:

slope of AB

(4-3)/(-1-2)= 1/-3 = -1/3

parallel lines have the same slope

slope of CD = -1/3

we can now find the line that passes through the point C

y-5= -1/3(x-4)

y = -1/3 x +4/3 +5

y = -1/3 x + (4+15)/3

y = -1/3 x + 19/3

this line must passes also through the point D

we know its y, so:

7 = -1/3 x + 19/3

(7 * 3) = (-1/3 x + 19/3) * 3

21 = - x + 19

x = 19 - 21

x = -2

Answer:

y = (2/3)y - 2

Step-by-step explanation:

Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).  

Line K

y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.  

Perpendicular Lines

Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to.  If, for example, we were ever asked  what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).

Line L

We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3).  That will be the slope of Line L that will make it perpendicular to Line K.

Line L will have the form y = (2/3)x + b

This line will be perpendicular to Line K, no matter the value of b.  But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.

The role b has in our equation is simply moving it up or down.  If b were 0, the line will go through the origin (0,0).  If b were 5, it would interect the y axis at 5 (0,5).  We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route:  Use the (x,y) value in the above equation and solve for b.  Its easy, and works great:

   y = (2/3)x + b for (6,2)

  2 = (2/3)(6) + b

   b = 2 - (2/3)*(6)

   b = 2 - 4

    b = -2

The equation for Line L is thus:  y = (2/3)y - 2

See the attached graph.  Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:

The Answers is 90

Step-by-step explanation: Imagion taking 4 DE and make a square out of it. All sides of a square is 90 degress so De is 90 degress

The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest.

To begin, change R from a percentage to a decimal, using the formula:

r = R/100 r = 14/100

r = 0.14 rate per year;

Next, find A by solving

A = P(1 + r/n)nt A = 12,000.00(1 + 0.14/12)(12). (5)

A = 12,000.00(1 + 0.011666666666667)(60) (60)

A = $24,067.32

Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.

The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest. You will then be left with the loan balance plus compound interest.

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