3. a computer password consists of two lowercase letters followed by a capital letter and four digits. find the total number of possible passwords.

Given one point and a slope:

To graph the line plot the given point first.

Then find the second point, consider the slope by adding 1 to the x-coordinate and -5 to the y-coordinate, this gives us:

Next, plot the second point (-2, - 9).

Now connect the two pints and extend either side. This is the line you need.

Answer:

b = -66.

Step-by-step explanation:

[tex]18 = \frac{b}{ - 3} - 4 \\ = - 3(18) = - 3 \times \frac{b}{ - 3} - 4( - 3) \\ = - 54 = b + 12 \\ = - 54 - 12 = b \\ = - 66 = b[/tex]

attached is solution. please excuse handwriting.

break up summation into two smaller summation,

then use summation formula for E (x)

The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

An inequality response is defined?

An expression in mathematics where the sides are not equal is referred to as being inequal. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21.

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The value of t is 6.5. The value of the constant is 60

What varies directly?

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).

Given that  d varies directly as t.

The relation between d and t is

d = kt.

Given that d = 180 when t = 3.

Putting d = 180 and t = 3 in d = kt

180 = 3k

Divide both sides by 3:

k = 180/3

k = 60

Putting k = 60  in d = kt:

d = 60t

Now putting d = 390 in d = 60t:

390 = 60t

60t = 390

Divide both sides by 60

t = 6.5

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Answer: The two shaded parts of the wall have a combined area of 20m * 12m + 16m * 15m = 240 + 240 = 480 square meters.

Therefore, the volume of yellow paint required is 480 * 0.1 = 48 litres.

Step-by-step explanation:

The proof that AE = EF is done from the congruency theorem of triangles and the Pythagorean identity.

In order to prove that AE = EF, note that angle CEF is a right angle since EF is perpendicular to the diameter CD and intersects it at E.

Since AE = EB, triangles AEB and CED are congruent (SAS theorem)

Therefore, angle EAF is congruent to angle ECF.

Also, angle EAF is a right angle, since it is inscribed in a semicircle with a diameter CD.

Therefore, triangles EAF and ECF are similar by the Angle-Angle (AA) theorem.

Since they are similar, the ratio of corresponding side lengths is the same.

Since AE = EB, we have that:

AE / EF = EC / CF

But we also know that EC = ED + DC = ED + 2EF, since CD is the diameter of the semicircle and EF meets it at E perpendicularly.

Similarly, we have CF = CD + DF

CF = 2EF + DF, where DF is the other leg of the right triangle CDF.

Substituting these expressions for EC and CF in the above equation, we get:

AE / EF = (ED + 2EF) / (2EF + DF)

Simplifying this equation, we get:

AE / EF = (ED/EF) + 2 / (2 + DF/EF)

But ED/EF = sin(DEF) and DF/EF = sin(EFD) by the definition of sine in right triangle DEF. Since the angles DEF and EFD add up to 90 degrees, their sines are complementary.

Therefore, we have that:

ED/EF = cos(EFD) and DF/EF = sin(DEF)

Substituting these expressions in the above equation, we get:

AE / EF = cos(EFD) + 2 / (2 + sin(DEF))

But cos(EFD) + 2 = sin(DEF) (Pythagorean identity).

Therefore, we have:

AE / EF = sin(DEF) / (2 + sin(DEF))

Multiplying both sides by (2 + sin(DEF)), we get:

AE = EF

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This is a probability problem. To find the probability of removing two blue counters, we need to calculate the number of possible outcomes of removing two blue counters out of seven counters (3 blue and 4 yellow).

The number of possible outcomes of removing two blue counters is 3C2 = 3! / (2! * (3-2)!) = 3.

So, the probability of removing two blue counters is 3/7C2 = 3/21.

To find the probability of X being equal to 2, we need to calculate the probability of removing two blue counters.

Therefore, the probability of X being equal to 2 is 3/21.

Answer: Sure, I can help you with that!

Let's assume that the height of the cylinder is h and its radius is r. The volume of the cylinder can be calculated using the formula:

V = πr^2h

Similarly, let's assume that the length, width and height of the cuboid are l, w and h respectively. The volume of the cuboid can be calculated using the formula:

V = lwh

As the volume of the cylinder and the cuboid are the same, we can set the two expressions equal to each other:

πr^2h = lwh

Now, let's assume that the radius of the cylinder is equal to the length of the cuboid (r = l). This means that:

πl^2h = lwh

Solving for h, we get:

h = (πl^2)/w

Finally, substituting the value of h back into the original equation:

πr^2h = πl^2h = lwh

πr^2 = lwh/w = lw

r^2 = lw

r = sqrt(lw)

So, the value of x (the radius of the cylinder) can be found by knowing the length (l) and width (w) of the cuboid. To two decimal places, x = sqrt(lw).

Step-by-step explanation:

There are 56 servings in a 28 pound bag of dog food.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Each day Fei yen's dog eat dog food = 8 ounces

Fei yen bought a 28 pound bag of dog food.

And we know that 1 pound = 16 ounces

Then ,the food in ounces

= 28 x 16

= 448 ounces

Now, the number of 8 ounces servings are in a 28 pound bag of dog food

= 448 / 8

= 56

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The probability that Anthony is on time for work and takes the train is 0.76.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: the probability that Anthony is on time for work is 0.90. the probability that Anthony takes the train to work is 0.80. given that Anthony takes the train to work, the probability that he is on time is 0.95.

We let

A: Anthony being on time for work

B: Anthony will take the train to work

P(A) = 0.9

P(B) = 0.8

P(A/B) = 0.95

P(Anthony is on time for work and takes the train):

P(A∩B) = P(A/B). P(B)

P(A∩B) = 0.95×0.8

P(A∩B) = 0.76

Hence, the probability that Anthony is on time for work and takes the train is 0.76.

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There are 8.75 pounds of meat for 7 dogs

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.

Since 2.5 pounds of meat for 2 dogs x pounds of meat for 7 dogs. We can write:

2.5/2 = x/7

2*x = 2.5*7

2x = 17.5

x = 17.5/2

x = 8.75

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Step-by-step explanation:

Principal = $2,500

Rate = 3.8%

5A). The interest Yousuff make in one year

Therefore Time = 1 year.

Simple interest

[tex] = \frac{pincipal \times time \times rate}{100 \\ } \\ = \frac{2500 \times 1 \times 3.8}{100} \\ = 25 \times 1 \times 3.8 \\ = 95 .[/tex]

Therefore the interest Yousuff make in one year = $95.

5B). Interest Yousuff make in after 8 years

the time = 8 years

the interest

[tex] = \frac{pincipal \times time \times rate}{100} \\ = \frac{2500 \times 8 \times 3.8}{100} \\ = 25 \times 8 \times 3.8 \\ = 200 \times 3.8 \\ = 760 [/tex]

Therefore the interest Yousuff make after 8 years = $760.

5C). Principal - interest that Yousuff made after 8 years.

$2500 - $ 760

= $ 1,740.

Answer:

3

Step-by-step explanation:

1 loop around the block is 1/4 of a mile. multiply both sides by three. 3 loops is 3/4 of a mile.

The greatest number of 0.25 pound servings Becky can make is 18.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Becky has 1.84 pounds of strawberries and 2.62 pounds of cherries.

Now, number of pounds of salads

= 1.84+2.62

= 4.46 pounds

Becky mixes the two fruits together and then scoops out 0.25 pounds of fruit salad for each serving.

So, the number of servings = 4.46/0.25

= 17.84

≈ 18

Therefore, the greatest number of servings is 18.

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The measure of the angle x in the figure is 55 degrees

From the question, we have the following parameters that can be used in our computation:

The polygon and the external angles

The sum of the exterior angles of a polygon is 360°.

Using the above as a guide, we have the following:

5 * x + x + 30 = 360

Evaluate the like terms

So, we have

6x = 330

Divide by 6

x = 55

Hence, the value of x is 55

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Regular hexagon is a closed shape polygon having six equal sides and six equal angles.

A regular hexagon is defined as a closed 2D shape made up of six equal sides and six equal angles.

Each angle of the regular hexagon measures 120 degrees.

A hexagon has six angles and the sum of all six interior angles is 720 degrees. In a regular hexagon, each interior angle measures 120 degrees.

Polygon

A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices of a polygon.

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A correlation coefficient of 0.05 indicates a very weak positive correlation between the number of bedrooms and selling price.

When Bob calculates the correlation between the number of bedrooms in a home and its selling price and obtains a value of only 0.05, he can conclude that there is little to no linear relationship between the two variables.

Correlation is a statistical measure that indicates the degree to which two variables are related and the direction of the relationship. A correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

A correlation coefficient of 0.05 is very close to 0, indicating that there is almost no linear relationship between the number of bedrooms in a home and its selling price.

However, it is important to note that a low correlation coefficient does not necessarily mean that there is no relationship between the variables, as there could be a non-linear relationship or other types of relationships that cannot be captured by a correlation coefficient.

Therefore, Bob should further analyze the data set and explore other statistical measures or techniques to fully understand the relationship between the number of bedrooms in a home and its selling price.

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The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:

385.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is modeled as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence we consider that:

[tex]\pi = 0.5[/tex]

The minimum sample size is obtained as n when M = 0.05, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = 1.96 \times 10[/tex] (0.5/0.05 = 10).

[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]

n = 384.16

Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.

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Answer:

We can write an inequality to represent the weight that the truck can carry:

Weight of Refrigerators + Weight of Pianos <= 6500

Let x be the number of refrigerators and y be the number of pianos. Then we can write:

300x + 475y <= 6500

To determine if 10 refrigerators and 9 pianos would overload the truck, we can substitute the values into the inequality:

300 * 10 + 475 * 9 <= 6500

3000 + 4275 <= 6500

7275 <= 6500

Since 7275 is greater than 6500, this means that 10 refrigerators and 9 pianos would overload the truck.

Graphically, we can plot the points representing the weight of the refrigerators and pianos on the x-y plane, and shade the region below the line representing the inequality to show the combinations of refrigerators and pianos that would not overload the truck. Any point above the line would represent a combination of refrigerators and pianos that would overload the truck.

Answer:

7275lb

Step-by-step explanation:

Let R be the number of refrigerators and P be the number of pianos. The total weight of the load can be represented as:

Weight = 300R + 475P

The weight must be less than or equal to 6500lb, so we have the inequality:

300R + 475P <= 6500

To graph this inequality, we can first rewrite it in slope-intercept form:

475P <= 6500 - 300R

P <= (6500 - 300R) / 475

Next, we can plot the points (0, 13.68), (22, 0) on the coordinate plane, where (0, 13.68) corresponds to the y-intercept and (22, 0) corresponds to the x-intercept. The graph will be a line that starts at the y-intercept and goes down to the right, passing through (22, 0).

The truck could carry up to 22 refrigerators (when R = 22, P = 0), or up to 13.68 pianos (when R = 0, P = 13.68), or any combination of refrigerators and pianos that results in a weight of less than or equal to 6500lb.

As for the specific case of 10 refrigerators and 9 pianos, the weight can be calculated as:

Weight = 300 * 10 + 475 * 9 = 3000 + 4275 = 7275

This would overload the truck, as the weight of 7275lb is greater than the maximum allowed weight of 6500lb.

(i) none of these ailments, 26

(ii) arthritis but neither of the other two ailments, 17

(iii) exactly one of these ailments, 102

(iv) arteriosclerosis and loss of hearing but not arthritis, 16

We can use a Venn diagram to solve this problem.

Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:

A = 70

B = 60

C = 80

A ∩ B = 35

A ∩ C = 33

B ∩ C = 31

A ∩ B ∩ C = 15

Using these values, we can find the answers to the questions:

(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:

n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)

                      = 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)

                      = 26

Therefore, 26 senior citizens had none of these ailments.

(ii) The number of senior citizens with arthritis but neither of the other two ailments is:

n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15

                                                                   = 17

Therefore, 17 senior citizens had arthritis but neither of the other two ailments.

(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:

n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102

Therefore, 102 senior citizens had exactly one of these ailments.

(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:

n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16

Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.

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Answer:

The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)

Step-by-step explanation:

4x + 2y = 6 ....… (1)

x − y = 3 …..... (2)

Example, for equation 2 is:

x - y = 3

x = 3 + y

Put in equation 1:

4(y + 3) + 2y = 6

4y + 12 + 2y = 6

6y = -6

y = -6/6

y = -1

We have the value of y, then the value of x will be:

x = 3 + y

= 3 + (-1)

= 3 - 1

= 2

So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)

The expression 1000m ÷ 100n in the form of 10z is 10m/10n, which simplifies to m/10n.

What is an expression?

In mathematics, an expression is a combination of one or more numbers, variables, and operations such as addition, subtraction, multiplication, division, exponentiation, and so on.

We can simplify the expression 1000m ÷ 100n as follows:

1000m ÷ 100n = (1000 ÷ 100) × (m ÷ n)

= 10 × (m ÷ n)

= 10m/n

To write this in the form of 10z, we need to find a value of z that makes 10z equal to 10m/n. Since 10z is equal to 10 times z, we can set 10 times z equal to 10m/n and solve for z as follows:

10z = 10m/n

Dividing both sides by 10, we get:

z = m/10n

Therefore, the expression 1000m ÷ 100n in the form of 10z is 10m/10n, which simplifies to m/10n.

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The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line and m is the slope of the line. To use the formula, you need to know the coordinates of two points on the line. If you have the coordinates of two points, you can substitute them into the formula to find the slope.

Answer:

It's not a triangle

Step-by-step explanation:

What you do is add the two smallest numbers and hope it's smaller than the longer side

9 + 9 = 18

The longest side is 17, which is LESS than 18. That means it's not a triangle

Answer:

It isnt a triangle

Step-by-step explanation:

I did the quiz and this was the answer.

The amount in the account after 8 years will be $352.05.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P = $300

R= 2%

T = 8 years

We have to use the function

A = P[tex]e^{rt[/tex]

A = 300.00[tex](2.71828)^{(0.02)(8)[/tex]

A = $352.05

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The area of the region between line y =3x -6 and line y=-2x+8 and

the x-axis with the help of integration will be 2.88 sq units.

What exactly is integration?

The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).

Integral Fundamental

A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.

From a to b, use ∫f(x)dx

indefinite integral

Integrals are defined without upper and lower limits. It looks like this:

A indefinite Integral is written as:

∫f(x)dx = F(x) + C

Where C might be any constant and the function f(x) is referred to as the integrand.

Now,

As given in image

Area of the region will be  =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.

=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x)  from x=2.8 to 4.

=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2

=2.88 sq units.

Hence,

           The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.

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Answer:

He is correct.

Step-by-step explanation:

Shown in picture.

Hope its clear.

Answer:

[tex]x^{2}-4x-12[/tex]

Step-by-step explanation:

(x+2)(x-6)

STEP 1 - USE FOIL

(FOIL is a standard way of multiplying 2 fractions, just multiply in the following order):

Forward

Outside

Inside

Last

(x+2)(x-6) becomes this when you FOIL it:

[tex](x^{2} )(-6x)(2x)(-12)[/tex]

STEP 2 - COMBINE ALL THE TERMS

[tex]x^{2}[/tex] has to stay by itself because there are no other squares. [tex]-6x+2x=-4x[/tex] because you're adding two to -6 which effectively is 6 - 2 but you're adding a negative sign. And [tex]-12[/tex] stays the same because there are no x's  in it.

STEP 3 - WRITE THE SOLUTION

All in all, the final solution, once you put everything together, is:

[tex]x^{2} -4x-12[/tex]