How many different regrestation codes are possible. And also what is the probability that all the first three digits of the code are not even numbers.
Answers
a) Consider the 7-digit registration code to be an arrangement of 7 cells to be filled using the given digits.
In the first cell, one can write any of the digits; on the other hand, there are only 6 digits available to fill the second cell (no number can be used more than once). Therefore, there are 5 digits that can be used in the third cell and so on; thus, there is a total of
[tex]7*6*5*4*3*2*1=7!=5040[/tex]5040 different registration codes.b) The 5040 different combinations found above are equally probable.
There are only 3 available even numbers (2, 4, and 6); therefore, we need to find the number of combinations such that none of the first three digits is equal to 2, 4, or, 6.
Thus, using a diagram,
There are 4 possible numbers that one can fit in the first cell (1,5,7, or 9), in the second cell, one can fit 3 numbers (any of the remaining ones from cell 1), and so on.
In the fourth cell (first cell in blue), one can fit any even number plus a remaining odd number from cell 3.
Therefore, the total number of codes such that their first three digits are not even are
[tex]4*3*2*4*3*2*1=576[/tex]Then, the corresponding probability is
[tex]P=\frac{576}{5040}=\frac{4}{35}[/tex]The answer to part b) is 4/35
Related Questions
What is the linear equation ( slope intercept equation ) for the line that passes through points (0,4) and (2,8) ?
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
Consideing the given points,
x1 = 0, y1 = 4
x2 = 2, y2 = 8
m = (8 - 4)/(2 - 0) = 4/2
m = 2
We would find the y intercept, c by substituting m = 2, x = 0 and y = 4 into the slope intercept equation. It becomes
4 = 2 * 0 + c
c = 4
Substituting m = 2 and c = 4 into the slope intercept equation, it becomes
y = 2x + 4
The last option is correct
69 is _________% more than 60
Answers
To find the solution we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 69\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{69\cdot100}{60} \\ x=115 \end{gathered}[/tex]This means that 69 is 115% of 60.
Therefore 69 is 15% more than 60.
Find a recursive rule for the nth term of the sequence.7, 28, 112, 448, ...
Answers
Solution
Given the sequence 7, 28, 112, 448, ...
The sequence is a Geometric sequence because it has a common ratio
[tex]Common\text{ ratio, r = }\frac{28}{7}=4[/tex]First term, a = 4
[tex]\begin{gathered} The\text{ nth term of a gp = ar}^{n-1} \\ Where\text{ n=number of terms} \\ a=\text{ first term } \\ r=common\text{ ratio} \end{gathered}[/tex][tex]T_n=7\text{ \lparen4\rparen}^{n-1}[/tex][tex]\begin{gathered} For\text{ recursive, } \\ T_n=r.T_{n-1} \\ T_n=4(T_{n-1}) \end{gathered}[/tex][tex]The\text{ recursive rule is 4\lparen T}_{n-1})[/tex]Solve the equation.56 = 13 + d
Answers
ANSWER
d = 43
EXPLANATION
We want to solve the equation for d.
The given equation is:
56 = 13 + d
To solve it, we collect like terms and simplify. That is:
56 - 13 = d
=> d = 43
That is the solution.
Convert the following measurement 19 quarts to cups
Answers
76 cups
Explanation:Note that:
1 quart = 4 cups
Therefore:
19 quarts = 4 x 19 cups
19 quarts = 76 cups
Summer earns 15% commission onsales for a software company. If inone week she makes three sales.one at $375, one at $1.200, and oneat $900. how much did Summerearn that week?
Answers
She made
[tex]375+1200+900=2475[/tex]in sales. Then, she earned
[tex]0.15(2475)=371.25[/tex]$371.25 that week.
I need help with geometry. I am supposed to solve for x in this diagram and assume lines marked with interior arrowheads are parallel :)
Answers
ANSWER:
40°
STEP-BY-STEP EXPLANATION:
We can make the following equality thanks to the properties of these angles:
[tex]\begin{gathered} 3x=120 \\ \text{ solving for x} \\ x=\frac{120}{3} \\ x=40\text{\degree} \end{gathered}[/tex]The value of x is 40°
How many solutions does the following system of equation have y = 2 x + 22y = 4x + 4
Answers
How many solutions does the following system of equation have
y = 2 x + 2
2y = 4x + 4
The answer is : Infinitely many solutions ( because they lie on each other ).
find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer to 22.5 in
Answers
Semicrcle area = π•Diameter^2 / 8
. = 3.14 • (2 R)^2/8
. = 3.14• (45)^2/8
. = 3.14• 2025/8= 794.81
Then answer is
Area of semicircle = 795 square inches
what is 4 2/3 + 7/9 as a fraction
Answers
The calculation is
[tex]4\cdot\frac{2}{3}+\frac{7}{9}[/tex]First step is to solve the multiplication.
4 means that there are four wholes, if you express in in thirds
[tex]\begin{gathered} 1\text{whole}=\frac{3}{3} \\ 4\text{wholes}=\frac{3\cdot4}{3}=\frac{12}{3} \end{gathered}[/tex]Then the multiplication you have to do is
[tex]\frac{12}{3}\cdot\frac{2}{3}=\frac{8}{3}[/tex]Now that the multiplication is done add 7/9
[tex]\frac{8}{3}+\frac{7}{9}=\frac{31}{9}[/tex]Please help me solve question 6 on my algebra homework
Answers
We have the following equation:
[tex]y-5=2(x-2)[/tex]First, we leave the equation in the slope-intercept form.
[tex]\begin{gathered} y=2x-4+5 \\ y=2x+1 \end{gathered}[/tex]First, we leave the equation in the slope-intercept form.
Domain
The domain of a function is the set of the existence of itself, that is, the values for which the function is defined.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Range
The range of the function is the set of all the values that the function takes in the existing interval of the domain.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Zero
The zeros of a function are the points where the graph cuts the x-axis.
To find this, we equate the function to zero.
[tex]\begin{gathered} 2x+1=0 \\ x=-\frac{1}{2}=-0.5 \end{gathered}[/tex]In this case, the zero is in -0.5.
Y-intercept
To find the y-axis intercept, we solve the equation when x=0.
[tex]\begin{gathered} y=2\cdot0+1 \\ y=1 \end{gathered}[/tex]In conclusion, the y-axis intercept is in the coordinate (0,1)
Slope
Looking at the equation of the form y = mx+b we can easily tell what the slope is, remembering that "k" is the slope of the function.
[tex]\begin{gathered} y=2x+1 \\ k=2 \end{gathered}[/tex]In conclusion, the slope is k=2
Type of slope
There are four different types of slopes: negative, zero, positive and undefined.
In this case, the slope is positive, because the angle of the slope is greater than zero and less than 90 degrees.
In conclusion, the slope is positive
f(3)
We will solve the function when x=3
[tex]\begin{gathered} f(3)=2x+1 \\ f(3)=2\cdot3+1 \\ f(3)=6+1 \\ f(3)=7 \end{gathered}[/tex]Value of x, where f(x)=7
We must equal the function to 7 and clear "x".
[tex]\begin{gathered} 2x+1=7 \\ x=\frac{7-1}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]In conclusion, the value of "x" is x=3
What lengths are possible for pieces cut from the 27-cm piece of string? Select all that apply. A. 2 cm B. 7 cm C. 5 cm D. 3 cm E. 9 cm F. 27 cm G. 18 cm H. 1 cm
Answers
Answer:
D, E, F, and H
Step-by-step explanation:
D. 27/3=9
E. 27/9=3
F. 27/27=1
H. 27/1=27
Answer: D,E,F, and H
Step-by-step explanation:
1, 3, 9, and 27 are the multiples of 27 itself
It can’t be 2 because it’s not an even number
It can’t be 7 because the closest number that is a multiple of 7 is 28 and it’s one over
It can’t be 5 because it doesn’t end in 5 or 0
it can’t be 18 because 18 + 18 equals 36 and that is 9 over the original number
how do you find 18.84 20.91 19.5 on a number line 14-22
Answers
In order to find the given numbers on a number line thats moves between 14 and 22, we shall illustrate with a number line.
The number line illustrated above shows the numbers arranged in order from 14 to 22.
The numbers indicated in the question are printed in blue.
The position of the numbers are also indicated with a black "stroke" in relation to the position of the numbers 14 to 22.
A vase can be modeled using x squared over 6 and twenty five hundredths minus quantity y minus 4 end quantity squared over 56 and 77 hundredths equals 1 and the x-axis, for 0 ≤ y ≤ 20, where the measurements are in inches. Using the graph, what is the distance across the base of the vase, and how does it relate to the hyperbola? Round the answer to the hundredths place.
Answers
We are given that a vase is modeled by the following hyperbola:
[tex]\frac{x^{2}}{6.25}-\frac{\left(y-4\right)^{2}}{56.77}=1[/tex]we are asked to determine the distance across the base. To do that we will first look at the graph of the equation:
Therefore, the base of the vase is the distance between the x-intercepts of the graph. To determine the x-intercepts we will set y = 0 in the equation. We get:
[tex]\frac{x^2}{6.25}-\frac{(0-4)^2}{56.77}=1[/tex]Solving the operation on the parenthesis we get:
[tex]\frac{x^2}{6.25}-\frac{16}{56.77}=1[/tex]Now we solve the fraction:
[tex]\frac{x^2}{6.25}-0.28=1[/tex]Now we add 0.28 to both sides:
[tex]\begin{gathered} \frac{x^2}{6.25}=1+0.25 \\ \\ \frac{x^2}{6.25}=1.25 \end{gathered}[/tex]Now we will multiply 6.25:
[tex]\begin{gathered} x^2=1.25(6.25) \\ x^2=7.81 \end{gathered}[/tex]Taking square root to both sides:
[tex]\begin{gathered} x=\sqrt[]{7.81} \\ x=\pm2.8 \end{gathered}[/tex]Therefore, the x-intercepts are -2.8 and 2.8.
Now we need to determine the distance between these two points. We will use the distance between two points in a line:
[tex]d=\lvert x_2-x_1\rvert[/tex]Substituting the points we get:
[tex]d=\lvert2.8-(-2.8)\rvert=\lvert2.8+2.8\rvert=5.6[/tex]Therefore, the distance is 5.6 inches and is related to the hyperbola in the sense that it is the distance between the x-intercepts.
7)Which table of values BEST represents a model of exponential decay?х012.34-12a(x)1a.251017-1012.34b.b(x)97531- 1х-101234cfx)346101834c.х-101234d.dx)191954723115
Answers
Answer:
the one that represents a model of experimental decay is d.
Step-by-step explanation:
In mathematics, exponential decay describes the process of REDUCING an amount by a consistent percentage rate over a period of time, it is different from linear decay because in linear decay factor relies on a percentage of the original amount, there is a constant rate of decay.
Therefore,
As we can see on the graphs, the only table of values that represent DECAYS is options b and d. But, notice option B is a linear decay since it has a constant rate of decay.
So, the one that represents a model of experimental decay is d.
Complete the following tables 1 and 3 only.
Answers
Answer:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
Explanation:
If two triangles are similar, their corresponding sides are proportional, so we can always use the following equation:
[tex]\frac{A}{B}=\frac{C}{D}[/tex]Therefore, for row (a), we can write the following equation:
[tex]\frac{5\frac{1}{2}}{1\frac{1}{4}}=\frac{2\frac{3}{4}}{D}[/tex]So, changing the mixed number by decimals and solving for D, we get:
[tex]\begin{gathered} \frac{5.5}{1.25}=\frac{2.75}{D} \\ 5.5D=2.75(1.25) \\ 5.5D=3.4375 \\ \frac{5.5D}{5.5}=\frac{3.4375}{5.5} \\ D=0.625 \end{gathered}[/tex]Then, for row (a), D = 0.625 = 5/8
In the same way, we can write and solve the following equation for row (b)
[tex]\begin{gathered} \frac{A}{23.4}=\frac{20.8}{15.6} \\ \frac{A}{23.4}\times23.4=\frac{20.8}{15.6}\times23.4 \\ A=31.2 \end{gathered}[/tex]For row (c), we get:
[tex]\begin{gathered} \frac{12}{B}=\frac{9}{6} \\ 12(6)=9(B) \\ 72=9B \\ \frac{72}{9}=\frac{9B}{9} \\ 8=B \end{gathered}[/tex]For row (d), we get:
[tex]\begin{gathered} \frac{4.5}{3.6}=\frac{C}{2.4} \\ \frac{4.5}{3.6}\times2.4=\frac{C}{2.4}\times2.4 \\ 3=C \end{gathered}[/tex]Therefore, the answers are:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
dominic is making meatballs. he uses 3/4 cup of breadcrumbs for every 1 1/4 pounds of ground beef. how many cups of bradecrumbs does he need when he uses 1 3/4 pounds of ground beef?
Answers
The number of cups of breadcrumbs he will need when he uses 3/4 pounds of ground beef would be = 1¹/20 cup.
What are breadcrumbs?Breadcrumbs is a type of food product that is produced from crumbling of dried bread which is used making dishes such as meatballs.
The number of cups of breadcrumbs for 1¼ of meat ball = ¾ cup
Therefore the number of cups of breadcrumbs for 1¾ = X cup.
That is ; 1¼ = ¾ cup
1¾ = X cup
Make X cup the subject of formula;
X cup = 1 ¾ × ¾ ÷ 1¼
X cup = 21/16 ÷ 5/4
X cup = 21/16 × 4/5
X cup = 21/20
X cup = 1 ¹/20 cup
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The portable basketball hoop shown is made so that BA = AS = AK. The measure of < BAK is 128 degrees. Calculate m < BSK.
Answers
The measure of ∠BSK is 64 degrees, that is the value of m∠BSK is 64 degrees.
We are given BA = AS = AK.
∠BAK = 128 degrees
From the linear pair concept:
∠BAK + ∠SAK = 180 degrees
128 degrees + ∠SAK = 180 degrees
∠SAK = 180 degrees - 128 degrees
∠SAK = 52 degrees
From the angle sum property of a triangle in triangle ASK, we will get;
∠SAK + ∠ASK + ∠AKS = 180 degrees
52 degrees + ∠ASK + ∠AKS = 180 degrees
2 ∠ASK = 180 degrees - 52 degrees (Since, AS = AK)
∠ASK = 128/2 degrees
∠ASK = 64 degrees
Thus, the measure of ∠BSK is 64 degrees, that is the value of m∠BSK is 64 degrees.
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Charnaie owns her own tutoring service. She charges new clients $20 for a placement test and then $10 per hour for every hour of tutoring.
Drag and drop the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
What is the independent variable in this real-world situation? Explain your reasoning.
The independent variable is the Response area because Response area.
What is the dependent variable in the real-world situation? Explain your reasoning.
The dependent variable is the Response area because Response area.
Answers
The correct equation for the given condition will be;
⇒ T = $20 + $10h
Where, T is the total cost and 'h' is the number of hours.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
She charges new clients $20 for a placement test and $10 per hour for every hour of tutoring.
Now,
Let total cost of charge = T
And, Number of hours = h
So, We can formulate by the given condition as;
⇒ T = $20 + $10h
Thus, The correct equation for the given condition will be;
⇒ T = $20 + $10h
Where, T is the total cost and 'h' is the number of hours.
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simplify (6r+5)(r-8)
Answers
To solve, first open the parenthesis
6r(r-8) + 5(r-8)
6r² - 48r + 5r - 40
Re-arrange
6r² + 5r -48r-40
6r² -43r - 40
solving absolute value inequalities[tex]8 - 9 |6x - 10| \ \textgreater \ - 82[/tex]please help with steps, I keep getting stuck on this one
Answers
For (1):
[tex]\begin{gathered} 6x-10<82 \\ \text{Add 10 to both sides:} \\ 6x<82+10 \\ 6x<92 \\ \text{Divide both sides by 6:} \\ x<\frac{92}{6} \\ x<\frac{46}{3} \\ \end{gathered}[/tex]For (2):
[tex]\begin{gathered} 6x-10>-82 \\ \text{Add 10 to both sides:} \\ 6x>-82+10 \\ 6x>-72 \\ \text{Divide both sides by 6:} \\ x>-\frac{72}{6} \\ x>-12 \end{gathered}[/tex]Therefore, the solution is:
[tex]-12Function A Function B Tell whether each function is linear or nonlinear. х y 4 0 1 3 5 24 8 2 3 13 0 1 2 3 4 5 Function A is a function. Function B is a function.
Answers
Function A is NOT LINEAR
Function B is LINEAR
The slope (change in y over change in x) does not follow a linear pattern in function A. That is the increase/decrease in the y coordinates is not at the same rate as that of the x coordinate. Whereas, for the other function, function B, the slope follows a linear pattern, that is the rate of change in y over the rate of change in x is the same rate, that is why function B has a straight line graph
Find the slope from the tableA. 3B. 2C. -3D. -1
Answers
Use 2 of the given ordered pairs to find the slope of the function. Use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where y2 and y1 are the y coordinates of the ordered pairs and x2 and x1 are the x coordinates. Replace for the given values:
[tex]m=\frac{2-5}{-2-(-3)}=-\frac{3}{1}=-3[/tex]The slope of the function is -3.
write 37,000,010 numbers using words
Answers
thirty-seven million ten
Explanation
Step 1
count the number of digits after 37
[tex]\begin{gathered} 37000010 \\ 6\text{ digits, it meas} \\ by\text{ now, we have} \end{gathered}[/tex]thirty-seven million
Step 2
the remaining number is
[tex]\begin{gathered} 000010 \\ it\text{ is , ten} \\ 10 \end{gathered}[/tex]ten
Step 3
combine
thirty-seven million ten
Find the radius of a circle on which a central angle measuring 5π/6 radians intercepts an arc on the circle with a length of 35π centimeters.A. 42 cmB. 37 cmC. 61 cmD. 44 cm
Answers
Solution:
the arc lenght s, of a circle of radius r, with central angle θ, is given by the following equation:
[tex]s\text{ = }r\theta[/tex]solving for r, we get the following equation:
[tex]r\text{ = }\frac{s}{\theta}[/tex]now, replacing in the previous equation the data given in the problem we get:
[tex]r\text{ = }\frac{s}{\theta}\text{ = }\frac{35\pi}{5\pi\text{ / 6}}\text{ = }\frac{(35\text{ }\pi)\text{ 6 }}{5\pi}\text{ = 42 }[/tex]so that, we can conclude that the correct answer is:
[tex]42\text{ cm}[/tex]Given:• 1 cm^3= 1 mL• 1 dm^3 = 1 L• 1L = 1,000 mLIf a health person's kidneys can filter 125 mL of blood per minute, then how long will it take for the kidneys to filter 4.5 L of blood?
Answers
Consider the function.f(x) = x2 − 1, x ≥ 1
Answers
t Given
[tex]f(x)=\sqrt{x^2-1}[/tex]Find
inverse of f(x)
domain and range of function and its inverse
Explanation
Let y = f(x)
[tex]y=\sqrt{x^2-1}[/tex]replace all x with y and y with x
[tex]x=\sqrt{y^2-1}[/tex]now solve for y
[tex]\begin{gathered} \sqrt{y^2-1}=x \\ y^2-1=x^2 \\ y^2=x^2+1 \\ y=\pm\sqrt{x^2+1} \end{gathered}[/tex]so, the inverse is
[tex]\pm\sqrt{x^2+1}[/tex]domain of f(x) is
[tex]x\epsilon R:x\leq-1\text{ or x}\ge1[/tex]range of f(x) is
[tex]y\epsilon R:y\ge0[/tex]domain of inverse is
[tex]R[/tex]range of inverse function is
[tex]y\epsilon R:y\ge1[/tex]Determine the scale factor of the dilation. Write your answer as a fraction if necessary.
Answers
The scale factor of the dilation is 1.5
Here, we want to determine the scale factor of the dialtion
From what we can see, we have the smaller, being moved to the bigger and thus, we expect a scale factor higher than 1
We can work with any of the side lengths to determine the scale factor
Let us look at the base
For the smaller shape, we have a length from (1,-2) to (-2,-2)
For the bigger shape, we have a length from (1.5,-3) to (-3,-3)
Calculating these distances, we have a unit of 3 units in the smaller and a unit of 4.5 units in the bigger
So, we have the scale factor as;
[tex]\frac{4.5}{3}\text{ = 1.5}[/tex]brainstorm some real-world applications where integration could be helpful, then describe your examples and explain how integration fits in
Answers
Given
Integration
Find
some real-world applications where integration could be helpful
Explanation
In real life , integrations are used in vaarious fields such as engineering , where engineers use integrals to find the slope of the building
In physics , it is used in the centre of gravity .
In field of graphical representation , where three- dimensional models are demonstrated.
Final Answer
Hence , above are the some real world applications.
-2. The sum of two cubes can be factored by using the formula o’ + b3 (a + b)(c? ab + b?).(a) Verify the formula by multiplying the right side of the equation.(b) Factor the expression 8x2 + 27.(C) One of the factors of q? - bºis a - b. Find a quadratic factor of q? - bº. Show your work.(d) Factor the expression x - 1.
Answers
Given that the sum of two cubes can be factored by using the formula
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]a) To verify the formula by multiplying the right side equation
[tex]\begin{gathered} (a+b)(a^2-ab+b^2) \\ =a(a^2-ab+b^2)+b(a^2-ab+b^2) \\ =a^3-a^2b+ab^2+a^2b-ab^2+b^3 \\ \text{Collect like terms} \\ =a^3-a^2b+a^2b+ab^2-ab^2+b^3 \\ \text{Simplify} \\ =a^3+b^3 \end{gathered}[/tex]Hence,
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]b) To factor
[tex]8x^3+27[/tex]Using the sum of two cubes formula, i.e
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (2x)^3+(3)^3=(2x+3)((2x)^2-(2x)(3)+(3)^2)_{} \\ (2x)^3+(3)^3=(2x+3)(4x^2-6x+9) \end{gathered}[/tex]Hence, the answer is
[tex](2x+3)(4x^2-6x+9)[/tex]c) Given that one of the factors of a³ - b³ is a- b, the quadratic factor of a³ - b³ can be deduced by applying the differences of cubes formula below
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)^{}_{}[/tex]Expanding the right side equations
[tex]\begin{gathered} (a-b)(a^2+ab+b^2)^{}_{}=a(a^2+ab+b^2)-b(a^2+ab+b^2) \\ =a^3+a^2b+ab^2-a^2b-ab^2-b^3 \\ \text{Collect like terms} \\ =a^3+a^2b-a^2b+ab^2-ab^2-b^3 \\ \text{Simplify} \\ =a^3-b^3 \end{gathered}[/tex]Hence, the quadratic factor is
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]d) To factor the expression
[tex]x^3-1[/tex]By applying the differences of cubes formula
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (x)^3-(1)^3=(x-1)(x^2+(x)(1)+1^2)^{}_{} \\ x^3-1^3=(x-1)(x^2+x+1) \end{gathered}[/tex]Hence, the answer is
[tex](x-1)(x^2+x+1)[/tex]