A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system.
The number of possible license plates that can be issued using this system is 67600000.
What is Combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Here, number plate contains 5 numbers and 2 letters
Total possible number (0-9) = 10
Total possible letters (A-Z) = 26
Possible number plates which contains 5 numbers and 2 letters are
¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ²⁶C₁ X ²⁶C₁
10 X 10 X 10 X 10 X 10 X 26 X 26
10⁵ X 26²
676 X 10⁵
67600000
Thus, the number of possible license plates that can be issued using this system is 67600000.
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The sides of a triangle are 5, 12 and 13 inches long. what is the angle between the 2 shortest sides?
a. 30
b. 45
c. 60
d. 90
e. 120
Answer: 90 degrees
Step-by-step explanation:
The hypotenuse is opposite the right angle, which is created by the two shortest sides.
Which shape(s) have 2 or more lines of symmetry?
Answer:
D is the answer for you.
(X^2-16)/(x^2)-x-12
I know the answer is x+4/x+3
but i don't understand how x^2 -x - 12 simplifies into (x+3) (x-4)
Round to the nearest hundredth
48.849
1/3 · (-3x + 4y - 5z)
(1/3 Is A Fraction)
(Write Explanation)
The value of expression is -(x- 4y/3 + 5z/3)
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
Given:
1/3 · (-3x + 4y - 5z)
= 1/3(-3x) + 1/3 *4y + 1/3* (-5z)
= -x +4/3*y -5/3 *z
=-(x- 4y/3 + 5z/3)
Hence, 1/3 · (-3x + 4y - 5z)= -(x- 4y/3 + 5z/3)
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Tutorial C
A 3-yard roll of aluminum foil costs $4.14. What is the price per
foot?
Answer:
$.46 or 46 cents per foot
Step-by-step explanation:
3 yards = 4.14
1 yard is 3 feet
3 yards is 9 feet
4.14 ÷ 9 = .46
What is the value of the expression (-5)-³?
1. Apply the negative exponents rule:
2. Expand the power:
3. Simplify:
What is the value of x?
X=
1
(-5)³
1
(-5)(-5)(-5)
XII
Answer:
-125 is the correct answer
Answer:
x = -125
Explanation:
[tex]\Longrightarrow \dfrac{1}{x} = (-5)^{-3}[/tex]
Apply the negative exponent rule: a⁻ᵇ = 1/aᵇ
[tex]\Longrightarrow \dfrac{1}{x} = \dfrac{1}{\left(-5\right)^3}[/tex]
Expand the power:
[tex]\Longrightarrow \dfrac{1}{x} = \dfrac{1}{\left(-5\right)\left(-5\right)\left(-5\right)}[/tex]
Simplify the following:
[tex]\Longrightarrow \dfrac{1}{x} =- \dfrac{1}{\left125}[/tex]
Flip the following:
[tex]\Longrightarrow x = -125[/tex]
if a/b and c/d are rational expressions, then: a/b / c/d = a*b/c*d
if a/b and c/d are rational expressions,a/b / c/d = a*b/c*d is false.
What is the definition of a fraction number?A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.
The given rational expression is;
a/b and c/d
Given relation;
[tex]\rm \frac{\frac{a}{b}}{\frac{c}{d}}\\\\ \frac{a d}{bc}[/tex]
When two fractions are divided the number got reversed and multiplied by the fraction.
Hence the given calculation is false.
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Answer: false
Step-by-step explanation: .
work out the size of angle x
Answer:
x =83
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
x+43 = 126
Subtract 43 from each side
x = 126 -43
x =83
Let's take this problem step by step:
For the angle adjacent to the exterior angle of 126°:
⇒ exterior angle plus the that angle is equal to 180 degrees
⇒ since it is on a straight line
[tex]126 + that_.angle=180\\\rm \hookrightarrow that.angle=180-126\\\rm \hookrightarrow that.angle=54[/tex]
The sum of all the angles in a triangle is: 180°
[tex]that.angle+43+x=180\\\rm \hookrightarrow 54+43+x=180\\\rm \hookrightarrow 97+x=180\\\rm \hookrightarrowx=83[/tex]
The size of angle x is 83°
Answer: 83°
Hope that helps!
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Martin uses of a gallon of paint to cover of a wall. What is the unit rate at which Martin paints in walls per gallon?
The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon
Unit rateUnit rate of paint per gallon = Quantity of wall / gallon of paint
= 4/5 ÷ 5/8
= 4/5 × 8/5
= (4 × 8) / (5 × 5)
= 32/25
= 1 7/25 walls per gallon
Complete question:
Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon
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Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x)=2^x-5
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x) = 2^(x-5)
As x approaches negative infinity, h(r) approaches negative infinity.
As x approaches positive infinity, h(t) approaches 0.
As x approaches positive Infinity, h(t) approaches positive infinity.
As x approaches negative infinity, h(a) approaches positive infinity.
The graph of the function is given below, as it can be observed that as x approaches positive Infinity, h(t) approaches positive infinity.
Hence, the correct option is C.
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The domain of the function
Step-by-step explanation:
[-5, 4] because it is an empty circle, meaning less than
if AB= 51, and AC = 120. find BC.
A
B
C
Answer:
Step-by-step explanation:
AB = 51
AC = 120
BC = AC - AB
BC = 120-51
BC = 69 units
Will bought a new skateboard that was on sale. The original price of the skateboard was $60. The store had marked it down by 20 percent, and Will had a 25 percent off coupon as well.
We conclude that after the discount and the coupon, Will paid $36 for the skateboard.
How much did Will pay for the skateboard?We know that the original price was $60, and two discounts were applied. One of 20% and other of 25%.
Then the amount that he paid is given by:
P = $60*(1 - 20%/100%)*(1 - 25%/100%)
P = $60*(0.8)*(0.75) = $36
We conclude that after the discount and the coupon, Will paid $36 for the skateboard.
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Find the Value of log10 (0.0001). Rescue me!
Let's see
[tex]\boxed{\sf log_aa=1}[/tex]
Now
[tex]\\ \rm\Rrightarrow log_{10}0.0001)[/tex]
[tex]\\ \rm\Rrightarrow log_{10}10^{-4}[/tex]
[tex]\\ \rm\Rrightarrow -4log_{10}10[/tex]
[tex]\\ \rm\Rrightarrow -4[/tex]
Answer:
This has already been answered correctly, but I'll add an additional perspective. The log of (0.0001 to the base 10 is -4.
Step-by-step explanation:
log(base 10) says give us an exponent, x, that would be required to make [tex]10^{x}[/tex] equal to a specified number, in this case 0.0001.
[tex]10^{0}[/tex] = 1
[tex]10^{1}[/tex] = 10
[tex]10^{-1}[/tex] = 0.1
[tex]10^{-2}[/tex] = 0.01
[tex]10^{-4}[/tex] = 0.0001
The log of (0.0001) to the base 10 is -4.
Which of the binomials below is a factor of this trinomial? x2+12x+31
A. x+4 B.x-2 C. x+2 D. x-4
(x+4) is a factor of this trinomial given , Option A is the right answer.
What is a Factor ?A factor is a number o expression that completely divides the number or the expression and the remainder is equal to zero.
The given trinomial is
x² +12x+32
x² + 8x +4x +32
x(x+8)+4 (x+8)
(x+8)(x+4)
From the given option Option A (x+4) is the right answer.
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If the degree of a polynomial function is even and the leading coefficient is negative, then the end behavior of the function is?
Answer:
Its the last option.
Step-by-step explanation:
The function will rise from the left and descend to the right.
f(x) ---> -∝ as x ---> -∝ and f(x) ---> -∝ as x ---> ∝
What is the range of the function y=-x² +1?
Oys-1
Oy2-1
Oyst
y21
The range of the function is
[tex]y \leqslant 1[/tex]
If the inequality contains < symbol, then graph the equation using a _______________ line.
Answer:
broken line
Step-by-step explanation:
for the graph of an inequality with < or > use a broken line
-----------------------------------
for the graph of an inequality with ≤ or ≥ use a solid line
Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
171 divided by 3.8
Jacob started by multiplying the divisor and the dividend by 10. This is the new problem:
1710 divided by 38
Use long division to find the quotient.
0.45
4.5
45
450
The answer is 45
------------------------------------------------------------
Angela is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. she uses the following formula to calculate voltage:
the circuit she tests has a current of 3 + j 4 amps and a resistance of 4 - j 6 ohms.
what is the voltage of the circuit?
The Voltage of the given Circuit is gotten as; V = 36 - 2j Volts
How to multiply Vectors?We are given;
Current; I = 3 + 4j amps
Resistance; R = 4 - 6j ohms
From ohms law, we know that;
V = IR
Thus;
V = (3 + 4j) * (4 - 6j)
V = 12 + 16j - 18j - 24j²
Now, in vector notation; j² = -1. Thus;
V = 12 - 2j + 24
V = 36 - 2j Volts
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Line A and Line B are perpendicular. The slope of line A is -0.5. What is
the gradient of line B? Give reasons.
Answer:
Step-by-step explanation:
When 2 lines are perpendicular, their slopes are negative reciprocals of one another. Here, if the slope of A is -1/2, the slope of B is +2/1, or just 2.
The probability of a drawing a blue marble from a box of 18 marbles is 2/3. How many green marbles should be added to the box in order to reduce the probability to 1/2?
Answer:
6 green marbles should be added.
Step-by-step explanation:
If the probability of drawing a blue marble from 18 marbles is 2/3 then there are 12 blue marbles because 18 times 2/3 is 12. This means that to reduce this probability to 1/2 you need to add 6 more marbles to the total amount to get it to 24. Now the probability of getting a blue marble is 12/24 which is 1/2.
A bag contains 4 red, 7 blue and 5 yellow marbles. Event A is defined as drawing a yellow marble on the first draw and event B is defined as drawing a blue marble on the second draw.
If two marbles are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 7/16
B. 7/15
C. 14/16
D. 14/15
Answer:
The answer is B. 7/15!!!
i just guessed and got it right, but i knew c. wasnt the answer.
)If 18th February, 2030 falls on Monday then what will be the day on 18th February, 2040
Who ever answers this quickly with explanation I will make then brainliest
The Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
18th February 2030 falls on Monday
To find what will be the day on 18th February 2040
Calculate the expression:
= Given date + Month code + (difference between years) + Numbe of leap year
Leap year = difference between years/4
= (2040-2030)/4
= 10/4 = 2.5 ≈2
= 18 + 3 + (2040-2030) + 2
= 33
Divide 33 by 7 the remainder will be 5
Day code = given day code + remainder
= 1 + 5
= 6 (saturday from the table attahced)
Thus, Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday.
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what is the explict formula for this sequence 5, 10, 20, 40, 80, 160, ...
Step-by-step explanation:
as we see in the sequence, each term is twice of the previous term.
we mark the Nth as a(N), then:
a(N)=2a(N-1)
Answer:
[tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2
this indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 5 and r = 2 , then
[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]
Laurel has an area in her yard that is in the shape of a parallelogram. It has a base of 30 feet and a height of 22 feet. She wants to cover this area with wildflower seeds. She finds out that 1 ounce of seeds covers 125 square feet of ground. How many ounces of seeds does she need to cover this area?
Answer:
Laurel has to cover this area with 2.64 ounces of seeds.
Step-by-step explanation:
Given
Base of Parallelogram = 30ft
Height of Parallelogram = 22ft
Area of Parallelogram = 1/2*base*height
Therefore, Area of Parallelogram = 1/2*30*22
= 330sq. ft
Given
One ounce of seed covers 125 sq. ft
Hence, No. of ounces needed to cover 330 sq. ft= 330/125
= 2.64
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Betty has the option of using three types of tables in her coffee shop:
square tables with a side length of 36 inches
rectangular tables 20 inches wide and 73 inches long
round (circular) tables with a diameter of 42 inches.
Which type of table has the largest area?
a.)
Square tables
b.)
Rectangular tables
c.)
Round tables
d.)
The tables all have the same area.
Answer:
The rectangular table
Step-by-step explanation:
Square table: 36*36=1296
Rectangular table: 20*42=1460 [tex]in^{2}[/tex]
Circular table: [tex]\pi * 21^{2}[/tex]≅1384
the number of sides of regular polygon if the measure of its interior angle is 150 degree
Answer:
12 sides
Explanation:
[tex]\sf interior \ angle = \dfrac{(n-2) \times 180}{n} \quad (where \ n \ denotes\ number \ of \ sides)[/tex]
Solving Steps:
[tex]\sf \dfrac{(n-2) \times 180}{n} = 150[/tex]
[tex]\sf (n-2) \times 180} = 150n[/tex]
[tex]\sf 180n-360 = 150n[/tex]
[tex]\sf 180n-150n = 360[/tex]
[tex]\sf 30n = 360[/tex]
[tex]\sf n = 12[/tex]