The license plate combinations with either three letters then three numbers or three numbers then three letters are 35152000.
The license plate combinations to be made are either three number followed by three letter or three letter followed by three number. we are here assuming that the repetition of the number and letter are allowed.
The number can be any three from 0-9. So, the total choices of number are 10.
The letter can be from A-Z. So, the total choices for letter are 26.
The total choices of the numbers possible are,
ΟΟΟ ΟΟΟ
1 2 3 4 5 6
The first three are the choices of letter and the last three are the choice of number. Two combinations are also possible by interchanging the position of the set of numbers and letters.
So, the possible combinations are,
2 x [26x26x26x10x10x10]
Hence,
The possible combinations for the license plate number are 35152000.
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a random sample of size 36 is taken from a population with mean 50 and standard deviation 5. what is (the mean of the sample mean)?
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
Calculate the z-score of 51.5 using the formula:We substitute From the standard normal distribution table, the area to the left of 1.80 is0.9641Therefore it is 0.9461learn more about standard deviation here:
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Pls help due tomorrow!!!!!!!
We have : (a+b)^2 = a^2 + 2ab + b^2.
So, we can see here : the first term (3x) is a, the second term (a) is b.
For it to be expanded as such, the second term in the bracket must be equal to a^2 when it is squared.
Therefore, the missing term is a.
Recheck : (3x + a)^2 = (3x)^2 + 2.3x.a + a^2 = 9x^2 + 6ax + a^2.
lupita rides a taxi that charges a flate rate of $6.75 plus $3.20 per mile . if the taxi charges lupita $40.03 in total for her trip , how many miles is her ride ?
50 miles because of the miles
a 3x3x3 cube is made of 27 small cubes of which one is blue and 26 are white. the surface of the cube is formed by 3x3 squares. the small cubes are arranged in such a way that the surface is as much white as possible. what fraction of the surface of the cube is white
The fraction of the surface of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-[tex]\frac{13}{27}[/tex]= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer
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The fraction of the surface area of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-(13/27)
= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer.
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simplify (-2b⁵)2 step by step
Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. Then, select the transversal that connects them.
∠1 and ∠14
corresponding
alternate interior
alternate exterior
consecutive interior angles
p
q
r
s
The identification of the missing angles and their congruency names are;
a. ∠4 and ∠7 = Consecutive interior
b. ∠2 and ∠11 = alternate exterior angles
c. ∠12 and ∠16 = corresponding angles
d. ∠8 and ∠13 = alternate interior angles
e. ∠11 and ∠15 = corresponding angles
f. ∠7 and∠10 = none
g. ∠1 and ∠14 = alternate exterior angles
h. ∠12 and ∠15 = Consecutive interior
i. ∠6 and ∠7 = none
j. ∠1 and ∠3 = corresponding angles
k. ∠12 and ∠16 = corresponding angles
l. ∠6 and ∠15 = alternate exterior angles
m. ∠5 and ∠10 = alternate interior angles
n. ∠8 and ∠14 = corresponding angles
How to classify congruent angles?Corresponding angles are defined as the angles which are formed in corresponding corners with the transversal in a case where two parallel lines are intersected by any other line.
Alternate interior angles are defined as the angles formed when a transversal intersects two coplanar lines.
Alternate exterior angles are defined as the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.
Therefore, the angles given can be classified similarly using the image as:
a. <4 and <7 are Consecutive interior angles
b. <2 and <11 are alternate exterior angles
c. <12 and <16 are corresponding angles
d. <8 and <13 are alternate interior angles
e. <11 and <15 are corresponding angles
f. <7 and <10 are none
g. <1 and <14 are alternate exterior angles
h. <12 and <15 are Consecutive interior
i. < 6 and <7 are none
j. <1 and <3 are corresponding angles
k. <12 and <16 are corresponding angles
l. <6 and <15 are alternate exterior angles
m. <5 and <10 are alternate interior angles
n. <8 and <14 are corresponding angles
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An aabbccddeeff individual is crossed with an individual with the genotype aabbccddeeff. What is the probability that their offspring will have the genotype aabbccddeeff?.
When an aabbccddeeff individual is crossed with an individual with the genotype aabbccddeeff, the probability that their offspring will have the genotype aabbccddeeff would be 1/64.
The genotype of an organism refers to the complete set of genetic material. An offspring's genotype is the result of the combination of genes from their parents. In order to obtain the overall probability, individual probabilities for each locus will be multiplied. The Parent cross would be AABbccDdEeFF x AaBBCCDdEeff and offspring would be AaBbCcddEEFf.
The A locus cross is AA x Aa, half of the offspring will be AA and half of the offspring will be Aa. Hence, the probability of Aa would be ½.The B locus cross is Bb x BB, half of the offspring will be BB and half of the offspring will be Bb. Hence, the probability of Bb is ½. The C locus cross is cc x CC. All of the offspring will be Cc. Hence, the probability of Cc is 1.The D locus cross is Dd x Dd. One-fourth of the offspring will be DD, one half of the offspring will be Dd, and one-fourth of the offspring will be dd. Hence, the probability of dd is ¼.The E locus cross is Ee x Ee. One-fourth of the offspring will be EE, half of the offspring will be Ee, and one-fourth of the offspring will be ee. Hence, the probability of EE is ¼.The F locus cross is FF x ff. All of the offspring will be Ff. Hence, the probability of Ff is 1.Multiplying all the probability:
½ * ½ * 1 * ¼ * ¼ * 1 = 1/64
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A satellite dish has the shape of a parabola when viewed from the side. the dish is 48 inches wide and 36 inches deep. how far is the receiver from the bottom of the dish if the receiver is placed at the focus?
If the receiver is placed at the focus, it is 4 inches from the bottom of the dish. The result is obtained by using the equation of parabola with the vertex is at (0,0).
What is the equation of a parabola?With the vertex at (0,0), the equation of a parabola can be expressed as
x² = 4ay
Where
x = half of the diameter of parabola a = the y-axis of the focus of parabolay = the depth of parabolaGiven
Diameter of the dish = 48 inchesy = 36 inchesHow far is the receiver from the bottom of the dish if it is placed at the focus?
Suppose that the vertex is at (0,0).
x = 1/2 × diameter
x = 1/2 × 48
x = 24
Now, we got two points (-24, 36) and (24,36). See the picture in the attachment!
By using the x and y value, the value of a is
x² = 4ay
24² = 4a(36)
576 = 144a
a = 576/144
a = 4 inches
Hence, the receiver is placed at 4 inches from the bottom of the dish.
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the freshman class of 63 students conducted a survey to compare how many students took spanish as opposed to french as a foreign language. the results are shown in the venn diagram. how many students studied neither spanish nor french?
With the help of sets we can conclude our answer.
What are sets?Simply put, a set in mathematics is a grouping of different items. Any group of objects, such as a collection of numbers, days of the week, different kinds of cars, etc., can be included in a set. An element of the set is any component of the set. When writing a set, curly brackets are utilized. An extremely basic set would look somewhat like this. Set A = {1,2,3,4,5}. The components of a set can be represented using a variety of notations. set is a well-defined collection of objects. Sets are named and represented using a capital letteracc to our qusetion-
Total students = 50Students taking french = 31Remaining Students= 50 - 31 = 19Students taking none = 10So remaining students have taken only spanish i.e. 19-10 = 9But total no of students taken spanish are 17So the students who had taken both are 17-9 = 8.Leran more about sets click here:
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true or false? the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.
It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.
What is Discrete uniform distribution?The Discrete uniform distribution is a symmetric probability distribution used in probability theory and statistics. It contains a finite number of values that are equally likely to be observed; each value has an equal chance of 1/n. "A known, finite number of outcomes equally likely to occur" is another approach to describe the discrete uniform distribution.
The perfect example of Discrete uniform distribution is throwing a die. Tossing a fair dice is an easy illustration of the discrete uniform distribution. The possible results are 1, 2, 3, 4, 5, and 6, and the likelihood of a certain result is 1/6 each time the die is thrown. Because not all sums have an equal chance, the distribution that results when two dice are thrown and their values are summed is no longer uniform.
From the above observation, we can say that the sum of the number of dots that show up when we roll three dice simultaneously will follow a discrete uniform distribution.
It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.
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it is given that I = PRT/100
express P in terms of I, R and T
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's express P (principle) in terms of I, R and T
[tex]\qquad \sf \dashrightarrow \: I= \dfrac{PRT}{100} [/tex]
[tex]\qquad \sf \dashrightarrow \: PRT = I \sdot 100[/tex]
[tex]\qquad \sf \dashrightarrow \: P = \dfrac{I \sdot 100}{RT} [/tex]
and that's it ~
P can be expressed in terms of I, R, T as P=100×I / (R×T)
Given equation
I=PRT/100
100 × I = PRT
100 × I / RT = P
P = 100 × I / RT
This formula is used to calculate Simple Interest, where P= Principal, I= Intrest to be Calculated. R= Annual rate of interest, T= Time (in years). Here one will shift the 100 from the denominator and multiply with the I next we will move the rate and time from the numerator to the denominator. The equation we now get will be in terms of I, R, and T and one can find the Principal using this equation.
I hope this answer helps.
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Part A: Timothy said that triangle KLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy correct? Explain your answer or show your work by listing the coordinates of the primage and image and showing the scale factor
Part B: Are the two triangles similar? Explain.
a. Timothy is correct, as each vertex of triangle KLM was multiplied by 1.5.
b. The two triangles are similar, as they have the same angle measures, since a dilation does not change the angle measures.
What is a dilation?A dilation occurs when each of the vertices of a image is multiplied by a constant, which is called scale factor.
The vertices of triangle KLM and given as follows:
K(-1,3), L(8,4) and M(10,-3).
The vertices of the triangle K'L'M', obtained after the dilation, are given as follows:
K'(-1.5, 4.5), L'(12, 6) and M'(15, -4.5).
Hence the scale factor is given by the multiplication of one the equivalent coordinates of the equivalent vertices, as follows:
-1.5/-1 = 1.5.
Meaning that Timothy is correct.
The two triangles are similar, as the dilation changes the side lengths but keep the angle measures constant, keeping the similarity of the triangles.
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help meeeeeeeeeeeeeee pleaseee
Answer:
Vertex: (2, -1)
Axis of Symmetry: x=2
Parabola: Downwards
Step-by-step explanation:
This shows a figure.
What is the value of x?
57
63
86
95
Answer:
57
Step-by-step explanation:
Straight line is 180 degrees
x+2x+9=180
3x=171
x=171/3
x=57
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Two congruent parallelograms are joined along their base
to make the shape below.
18 cm
Work out the total area of the shape.
11 cm
15 cm
The total area of the shape that is formed by the two congruent parallelograms is: 721 cm².
How to Find the Total Area of a Shape?To find the total area of the shape that is formed by the two congruent parallelograms, calculate the area of each face, then add all together.
The shape formed consist of:
2 identical parallelograms whose area = 2(base × height)2 identical right triangles = base × height1 rectangle = length × widthArea of the 2 identical parallelograms:
Base = 15 cm
Height = 11 cm
Area = 2(15 × 11) = 330 cm²
Area of the 2 identical right triangles:
Base = 11 cm
Height = 11 cm
Area = 11 × 11 = 121 cm²
Area of the rectangle = length × width = 18 × 15 = 270 cm²
Total area of the shape = 330 + 121 + 270
Total area of the shape = 721 cm²
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Evaluate the expression (3 • 2)^2
Answer:
36
Step-by-step explanation:
(3*2)^2
3*2=6
6^2=36
Answer:
36
Step-by-step explanation:
(3x2)^2
6^2
36
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Given that there are 100 centimeters in 1 meter, which of the following amounts is greater than 3 meters? Select all that apply.
A) 295 centimeters
B) 2 meters, 195 centimeters
C) 2 meters, 35 centimeters
D) 135 centimeters
E) 415 centimeters
Answer:
B, E
Step-by-step explanation:
3 meters is 300 centimeters so that eliminates A and D since they are lower and we know E is higher than 300
Now to find if B and C are higher since they both are 2 meters is we make 3 meters look like this it will be
2 meter 100 centimeters and b is the only one greater
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Between his 9th and 10th birthdays jimmy read one book each week there are 52 weeks in a year if each book at about 95 pages about how many pages did he read during the year?
Answer:
he read 4940 pages in a year
Step-by-step explanation:
Given data:
1 year= 52 weeks
1 book= 95pages (takes 1 week to complete)
for 1 year = 52x95
=4940
The Jackson family just bought 15-packs of Lacroix at Costco. On average, their family drinks about eight cans a week after how many weeks will there be only five cans left? Show how you figured it out.
If the Jackson family just bought 15 pack of Lacroix at Costco and the family drinks about eight cans a week, then after 1.25 weeks
Total number of packs they bought = 15 pack
The average cans they finish each week = 8
Number of cans left = 5 cans
Number of cans used = Total number of packs they bought - Number of cans left =
= 15 - 5
= 10 cans
After how many weeks will there be only five cans left = Number of cans used ÷ The average cans they finish each week
Here we have to use the division
Substitute the values in the equation
After how many weeks will there be only five cans left = 10 /8
= 1.25 weeks
Hence, if the Jackson family just bought 15 pack of Lacroix at Costco and the family drinks about eight cans a week, then after 1.25 weeks
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18^7 * 20^7 divided by 25^3 * 2^21 *27^4
Answer:
[tex]=45[/tex]
Step-by-step explanation:
1 ) Simplify
[tex]\frac{(18^7)(20^7)}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{612220032(20^7)}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{(612220032)(1280000000)}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{15625(2^2^1)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{(15625)(2097152)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{32768000000(27^4)}[/tex]
[tex]= \frac{783641640960000000}{(32768000000)(531441)}[/tex]
[tex]= \frac{783641640960000000}{17414258688000000}[/tex]
[tex]=45[/tex]
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qiang drives 15 miles at an average speed of 30 miles per hour. how many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
110 additional miles he will have to drive .
To calculate : additional miles qiang will have to drive
Let the additional no. of miles he has to drive be x .
⇒ Total Distance = 15 + x
Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )
The equation becomes ,
[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50
On simplification we get ,
15 + x = 25 + ( 10x / 11 )
x = 110
Therefore , 110 additional miles he will have to drive .
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find three consecutive integers such that 3 times the smallest is 18 more than the largest
The value of the three consecutive integers will be 10, 11, and 12.
What is Algebra?
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Three consecutive integers are such that three times the smallest is 18 more than the largest.
Let the three consecutive number be x, x + 1, and x + 2. Then the equation will be:
3x = (x + 2) + 18
Simplify the equation, then the value of the variable x will be:
3x = x + 2 + 182x = 20x = 20 / 2x = 10
Then the value of the integers will be:
x + 1 = 10 + 1 = 11x + 2 = 10 + 2 = 12
The value of the three consecutive integers will be 10, 11, and 12
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I need help like asap !!!
number and decimal points
Answer:
a = 5 cm
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (13)² = a² + (12)²
→ 169 = a² + 144
→ a² = 169 - 144
→ a = √25
→ [ a = 5 cm ]
Hence, value of a is 5 cm.
One bulldozer clears land twice as fast as another. Together they clear a large tract in 1.5 hours. How long would the larger bulldozer take?
The larger bulldozer would take about 30 minutes.
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how do you find proportional relationships? also, while answering this could you give me an example? Whoever CAN ANSWER THIS FIRST I WILL GIVE YPU 20 POINTs
Answer:
A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph.
Step-by-step explanation:
Answer:
simply just divide!
Step-by-step explanation:
okay, here is one example:
in 3 hours, you went 126 miles
In 4 hours, you went 168 miles
In 5 hours, you went 210 miles
So what is the unit rate of the miles(x) per hour(y).
The smallest number would be easier to divide. So you divide 126 and 3 and would be 42 miles.
Then find the quotient for the other ones.
168 divide 4 = 42
210 divide 5 = 42.
What is the same of all of them? 42 is the factor to all of the problems. So the proportional relationship (k) is 42. In a equation it would be y=42x (y=Kx)
To find the next number in the sequence you just multiply (x) with the factor.
Question 2 options:
Multiply the radicals.
What is the product in simplest form?
The product in simplest form is [tex]-250\sqrt[3]{50}[/tex] .
In the question,
It is given that,
[tex]5*\sqrt[3]{5} * (-10\sqrt[3]{50})[/tex]
By radical laws, [tex]\sqrt{a} * \sqrt{b} = \sqrt{ab}[/tex]
So,
The given question becomes:
[tex]-50*\sqrt[3]{50*5} = -50*\sqrt[3]{250} = -250\sqrt[3]{5} }[/tex]
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what is the equation of the linear graph
Answer: C
Step-by-step explanation:
All i used was a desmos graphing calculator
Explain how the distributive property cam be used to eliminate the fractions in the equation 1/5x +8 = 1/10x + 9
We will use the distributive property to take a common factor in the next step:
(1/5)*x - (1/10)*x = (1/5 - 1/10)*x
Using that we will see that the solution is x = 10.
How can we use the distributive property?The distributive property can be written as:
A*(B + C) = A*B + A*C
Now we have the equation:
(1/5)*x + 8 = (1/10)*x + 9
If we group like terms we get:
(1/5)*x - (1/10)*x = 9 - 8
Here we apply the property, we can rewrite the left side as:
(1/5)*x - (1/10)*x = (1/5 - 1/10)*x
Then we can write:
(1/5)*x - (1/10)*x = 9 - 8
(1/5 - 1/10)*x = 1
(1/10)*x = 1
x = 10*1
x = 10
And that is the solution.
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20 POINTS WILL MARK UR ANSWER THE BEST
Please help me solve this ASAP
can u also make sure there is a graph
Answer: The solution to this system is (1,3) as shown in the graph below.
Step-by-step explanation:
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NOTE: The red line is -x+y=2 and the blue line is y=3
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
Which rule describes rotating 90° counterclockwise?
(x,y)→(-y,x)
(x,y)→(y, -x)
(x,y)→(x,y)
(x,y)-(-x,-y)