For the given configuration, determine how many different licence plates are possible of (a) digits and letters can be repeated, and (b) digits and letters cannot be repeated. NO LINKS!!
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Answer:

7

Step-by-step explanation:

13 - [(3² x 4) - 30]

13 - [(9 x 4) - 30]

13 - (36 - 30)

13-6

7

Answer:

7

Step-by-step explanation:

I think the answer you're looking for is 7

Answer:

B. By personal experimentation and testing

Step-by-step explanation:

Answer:

[tex] \frac{8}{1} [/tex]

Step-by-step explanation:

[tex] \frac{ - 32}{ - 4} [/tex]

Reduce factor by 4

[tex] \frac{ - 8}{ - 1} [/tex]

A negative divided by a negative equal positve so

[tex] \frac{8}{1} [/tex]

the simplest form of 32/4 is 8/1

find the GCD ( or HCF) of numerator and denominator GCD of 32 4 is 4

divide both the numerator and denominator GCD

32/4 ÷ 4/4

reduce fraction: 8/1

therefore, 32/4 simplify to lowest terms is 8/1.

Answer:

5/64

Step-by-step explanation:

numerators 1 time 5 is 5 and denominators 8 times 8 is 64;  5/64

Question Completion:

The Worthington family has liquid assets of $10,000, use assets of $150,000 and investment assets of $34,000. They also have liabilities totaling $108,000. They need a loan from the bank and to qualify for the loan, they must have a net worth of $100,000.  They will incur additional $7,000 in liabilities.

Answer:

1. The Worthington Family's net worth is:

= $79,000.

2. No. They will not qualify for the loan, as their net worth fell short of the requirement by $21,000.

Step-by-step explanation:

a) Data and Calculations:

Worthington Family's net worth:

Liquid assets =                      $10,000

Use assets =                         150,000

Investment assets =              34,000

Total assets =                    $194,000

Liabilities =                            115,000

Net worth =                         $79,000

Required net worth =       $100,000

Shortfall in net worth =      $21,000

b) The Worthington Family's net worth is the difference between their assets (the things that they own) and their liabilities (the things that they owe others).  It is an important financial metric for calibrating the family's financial health.  Computing it provides a useful snapshot of the family's current financial position.  Financial institutions and other potential creditors use it to gauge if they might extend some credit facilities to the Worthington family.

Answer:

a.  71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

b.  23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

c. 99840π lb/ft-s²∫₀⁶rdr

Step-by-step explanation:

.(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.

The work done, W = ∫mgdy where m = mass of cylindrical tank = ρA([5 + 4] - y) where ρ = density of water = 62.4 lb/ft³, A = area of base of tank = πd²/4 where d = diameter of tank = 12 ft.( we add height of the tank + the height of point above the tank and subtract it from the vertical point above the base of the tank, y to get 5 + 4 - y) and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdy

W = ∫ρA([5 + 4] - y)gdy

W = ∫ρA(9 - y)gdy

W = ρgA∫(9 - y)dy

W = ρgπd²/4∫(9 - y)dy

we integrate W from  y from 0 to 5 which is the height of the tank

W = ρgπd²/4∫₀⁵(9 - y)dy

substituting the values of the other variables into the equation, we have

W = 62.4 lb/ft³π(12 ft)² (32 ft/s²)/4∫₀⁵(9 - y)dy

W = 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

.(b) Write down an integral for the fluid force on the side of the tank

Since force, F = ∫PdA where P = pressure = ρgh where h = (5 - y) since we are moving from h = 0 to h = 5. So, P = ρg(5 - y)

The differential area on the side of the tank is given by

dA = 2πrdy

So.  F = ∫PdA

F = ∫ρg(5 - y)2πrdy

Since we are integrating from y = 0 to y = 5, we have our integral as

F = ∫ρg2πr(5 - y)dy

F = ∫ρgπd(5 - y)dy    since d = 2r

substituting the values of the other variables into the equation, we have

F = ∫₀⁵62.4 lb/ft³π(12 ft) × 32 ft/s²(5 - y)dy

F = 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

.(c) How would your answer to part (a) change if the tank was on its side

The work done, W = ∫mgdr where m = mass of cylindrical tank = ρAh where ρ = density of water = 62.4 lb/ft³, A = curved surface area of cylindrical tank = 2πrh  where r = radius of tank, d = diameter of tank = 12 ft. and h =  height of the tank = 5 ft and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdr

W = ∫ρAhgdr

W = ∫ρ(2πrh)hgdr

W = ∫2ρπrh²gdr

W = 2ρπh²g∫rdr

we integrate from r = 0 to r = d/2 where d = diameter of cylindrical tank = 12 ft/2 = 6 ft

So,

W = 2ρπh²g∫₀⁶rdr

substituting the values of the other variables into the equation, we have

W = 2 × 62.4 lb/ft³π(5 ft)² × 32 ft/s²∫₀⁶rdr

W = 99840π lb/ft-s²∫₀⁶rdr

Answer:

Step-by-step explanation:

Segments AB and BC intersect each other at 90° at B.

Let the equation of the segment AB → y = mx + b

Here, m = Slope of the line

b = y-intercept

Slope of the line AB passing through A(14, -1) and B(2, 1)

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{1+1}{2-14}[/tex]

          = [tex]-\frac{2}{12}[/tex]

          = [tex]-\frac{1}{6}[/tex]

Equation of the line will be,

[tex]y=-\frac{1}{6}(x)+b[/tex]

Since, AB passes through (2, 1)

[tex]1=-\frac{1}{6}(2)+b[/tex]

[tex]b=1+\frac{1}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

Therefore, y-intercept of AB = [tex]\frac{4}{3}[/tex]

Equation of AB → [tex]y=-\frac{1}{6}(x)+\frac{4}{3}[/tex]

Since, line BC is perpendicular to AB,

By the property of perpendicular lines,

[tex]m_1\times m_2=-1[/tex]

Here, [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of line AB and BC respectively.

By this property,

[tex]-\frac{1}{6}\times m_2=-1[/tex]

[tex]m_2=6[/tex]

Equation of a line passing through a point (h, k) and slope 'm' is,

(y - k) = m(x - h)

Therefore, equation of line BC passing through B(2, 1) and slope = 6,

y - 1 = 6(x - 2)

y = 6x - 11

Since, line BC passes through C(x, 13),

13 = 6x - 11

6x = 24

x = 4

Therefore, x-coordinate of point C will be, x = 4

Answer:

2.8 liters

Step-by-step explanation:

6 - 3.20 = 2.8

Answer:

2 4/5

Step-by-step explanation:

6-3 1/5 = 2 4/5

Answer:

45/22

Step-by-step explanation:

Answer:

A. 175,760,000

B. 156,000,000

Step-by-step explanation:

For part A:

There are 26 letters in the alphabet.  Therefore, if there are 3 spots to use 26 letters, that is represented as [tex]26^3[/tex].  As for numbers, there are 10 digits from 0-9.  So if there are 4 spots for numbers, the total possible number of sequences is [tex]10^4[/tex].  So you simply multiply [tex]26^3[/tex] and [tex]10^4[/tex] to get 175,760,000 possible combinations.

For part B:

If the same letter can't be repeated, instead of using an exponent, we have to use a factorial, but only for the 3 digits required in the license plate.  These are called permutations and can be expressed as [tex]_2_6P_3[/tex], which is the same as saying 26 x 25 x 24.  Since there is no change to number of numbers, that remains the same.

[tex]_2_6P_3 * 10^4 =26*25*24*10^4=156,000,000[/tex]

Answer:

part a: she borrowed 3,700

part b: she would pay 555 interest

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

Answer:

As points, A and B move, the slope of the two lines change but remain equal to each other. As point C moves, the slope does not change but remains equal to each other since the line through C is drawn parallel to AB.

I can canclude that slope of any two parallel lines are equal

Step-by-step explanation:

Answer:

[tex]180x^4y^3z^2[/tex]

Step-by-step explanation:

Start by finding the LCM of the coefficients of each polynomial:

[tex]LCM(12,18,30)=180[/tex]

Next, to find the least common multiple of each of the following terms, we need to take the absolute minimum we can of each term ([tex]x[/tex], [tex]y[/tex], and [tex]z[/tex]). The largest term of [tex]x[/tex] is [tex]x^4[/tex] in the first polynomial, so we'll take exactly that for our [tex]x[/tex] term in the LCM, absolutely nothing more. Similarly, the largest term of [tex]y[/tex] in any of the three polynomials is [tex]y^3[/tex] (also in the first polynomial) and the largest [tex]z[/tex] term in any of the three polynomials is [tex]z^2[/tex] in the second polynomial. Thus, the LCM of all our polynomials is:

[tex]180\cdot x^4\cdot y^3\cdot z^2=\boxed{180x^4y^3z^2}[/tex]

Answer:

[tex]\mathrm{Factor\:}18x^4y^3z= 2\cdot \:3^2\cdot \:x^4\cdot \:y^3\cdot \:z\\\\\mathrm{Factor\:}30xy^2z^2= 2\cdot \:3\cdot \:5\cdot \:x\cdot \:y^2\cdot \:z^2\\\\\mathrm{Factor\:}12x^3y^2= 2^2\cdot \:3\cdot \:x^3\cdot \:y\\\\\mathrm{Multiply\:each\:factor\:with\:the\:highest\:power}= 2^2\cdot \:3^2\cdot \:5\cdot \:x^4\cdot \:y^3\cdot \:z^2\\\\180x^4y^3z^2[/tex]

Answer:

53 1/3 cups

Step-by-step explanation:

if there are 80 glasses and each glass has 2/3 of juice in it, there will be 53 1/3 cups in total because 80 x 2/3 = 53 1/3

Answer:

remy would be correct

Step-by-step explanation:

Answer:

484 students

Step-by-step explanation:

This is simple probability. Assuming 22/80 students walk to school within a small population, and there are 1760 students at the school, there should be (22/80)*1760 students that walk to school in total. (This is just theoretical). This is 484 students.

The number of students who usually walk to school will be 484 students.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Alexis surveys a random sample of 80 students at his school and finds that 22 of them usually walk to school.

Then the number of students who usually walk to school will be

⇒ 22 / 80

⇒ 11 / 40

We know that the ratio will remain the same.

There are 1,760 students at the school.

Let x be the number of students who usually walk to school.

Then the number of students who usually walk to school will be

x / 1760 = 11 / 40

x = 484 students

Thus, the number of students who usually walk to school will be 484 students.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

Answer:

Robert can read the books in 129,600 different ways.

Step-by-step explanation:

The order in which the book are read is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Top shelf:

4 books from a set of 6. So

[tex]P_{(6,4)} = \frac{6!}{2!} = 360[/tex]

Middle shelf:

2 books from a set of 3. So

[tex]P_{(3,2)} = \frac{3!}{2!} = 3[/tex]

Bottom shelf:

3 books from a set of 6. So

[tex]P_{(6,3)} = \frac{6!}{3!} = 120[/tex]

Total:

360*3*120 = 129,600

Robert can read the books in 129,600 different ways.

Answer:

y= -2/3x+9

Step-by-step explanation:

just do y=mx+b

Answer:

C) (0, -1) and ( [tex]\frac{1}{3}[/tex], 0)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

100 liters is 416.7 cups and 416.7 cups is 211.3 pints.

Answer:

10 times greater is the value of 5 in 3,590 than the value of 5 in 359.

Step-by-step explanation:

Answer:

soda = 10

burger = 5

fries = 2

5 + 2 x 10 = 25

Step-by-step explanation:

brainliest?

Answer:

D.

Step-by-step explanation:

The answer is 117

Answer: The answer is not listed

Step-by-step explanation:

Answer:

The height of the tree in 2020 was of 19.63 feet.

Step-by-step explanation:

Exponential equation for growth:

The exponential equation for the growth of an amount has the following format:

[tex]H(t) = H(0)(1+r)^t[/tex]

In which H(t) is the amount after t years, H(0) is the initial amount and r is the growth rate, as a decimal.

A 4 foot tree was planted in 2012 outside a high school.

This means that [tex]H(0) = 4[/tex]

The tree grew continuously by 22% each year from that point.

This means that [tex]r = 0.22[/tex]

Find out what the height of the tree was in 2020.

2020 is 2020 - 2012 = 8 years after 2012, so this is H(8).

[tex]H(t) = H(0)(1+r)^t[/tex]

[tex]H(t) = 4(1+0.22)^t[/tex]

[tex]H(4) = 4(1.22)^t[/tex]

[tex]H(4) = 4(1.22)^8 = 19.63[/tex]

The height of the tree in 2020 was of 19.63 feet.

Answer:

2200 cubic cm

Step-by-step explanation:

The volume of a rectangular prism is found using the formula:

V = l*w*h

V = 10 cm * 20 cm * 11 cm

V = 2200 cubic cm

Answer: 2200

Step-by-step explanation: