Assuming that the order of the cities matters, the number of possible routes is 11! (11 factorial), which is 39916800.
The number of possible routes for an overnight express company that includes eleven cities on its route is 39916800. This is because when the order of the cities matters, the number of possible routes can be calculated by finding 11 factorial, which is:
11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.This calculation results in 39916800, which means that there are 39916800 potential routes for an overnight express company with eleven cities on its route.
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x + 2y² = 4
y=x-1
Solve system of equations step by step
Answer:
[tex]\displaystyle x_1=2,\,x_2=-\frac{1}{2}[/tex]
[tex]\displaystyle y_1=1,\,y_2=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle x+2y^2=4\\x+2(x-1)^2=4\\x+2(x^2-2x+1)=4\\x+2x^2-4x+2=4\\2x^2-3x-2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-3)\pm\sqrt{(-3)^2-4(2)(-2)}}{2(2)}\\ \\x=\frac{3\pm\sqrt{9+16}}{4}\\ \\x=\frac{3\pm\sqrt{25}}{4}\\ \\x=\frac{3\pm5}{4}\\\\x_1=\frac{3+5}{4}=\frac{8}{4}=2,\,x_2=\frac{3-5}{4}=\frac{-2}{4}=-\frac{1}{2}[/tex]
[tex]\displaystyle y_1=2-1=1, y_2=-\frac{1}{2}-1=-\frac{3}{2}[/tex]
Answer:
(2, 1) (-0.5, -1.5)
Step-by-step explanation:
[tex]\begin{cases}x + 2y^2 = 4\\y = x - 1\end{cases}[/tex]
From here, we can substitute [tex]y = 2x - 1[/tex] into the first equation.
[tex]x + 2(x - 1)^2 = 4\\x + 2(x^2 - 2x + 1) = 4\\x + 2x^2 - 4x + 2 = 4\\2x^2 - 3x + 2 = 4\\2x^2 - 3x - 2 = 0\\x = 2, -\frac12[/tex]
Substituting back into the second equation to find the corresponding y values:
[tex]y(x = 2) = 2 - 1 = 1\\y(x = -\frac12) = -\frac12 - 1 = -1.5[/tex]
Find the exact value of the logarithmic expression without a calculator. Show all work
log3 4√27
Answer:
3/4 or 0.75
----------------------
Given expression
[tex]log_3\ \sqrt[4]{27}[/tex]Find its value using logarithm rules:
[tex]log_3\ \sqrt[4]{27} =log_3\ \sqrt[4]{3^3} =log_3\ 3^{3/4}=3/4\ log_3\ 3=3/4[/tex]The rules used above:
[tex]log_a\ a=1,\ log_a\ b^c=c\ log_a\ b[/tex]multiply the following numbers -6 -2 -1
Answer: -12
Step-by-step explanation: -6*-2 = 12 and then 12*-1 = -12.
Answer: -12
Step-by-step explanation:
-6 x -2 x-1
12 x -1
-12
A lottery exists where balls numbered 1 to 16 are placed in an urn. To win, you must match the balls chosen in the correct order. How many possible outcomes are there for this game?
The number of possible outcomes will be 524160.
What are permutations and combinations?When an order or sequence of arrangement is required, permutations are used. Combinations are used when there are only a limited number of possible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of things, permutations are used. Combinations are employed for similar items.
Given that a lottery exists where balls numbered 1 to 16 are placed in an urn. To win, you must match the balls chosen in the correct order.
The arrangement can be calculated as:-
¹⁶C₅ = 16 x 15 x 14 x 13 x 12
¹⁶C₅ = 524160
Therefore, the number of possible outcomes will be 524160.
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©There is a bag with only milk and dark
chocolates.
The probability of randomly choosing a
dark chocolate is g
There are 18 dark chocolates in the bag
and each is equally likely to be chosen.
Work out how many milk chocolates
there must be.
Answer:
Step-by-step explanation:
We know that the bag has dark chocolates and milk chocolates, and the probability of randomly choosing a dark chocolate is g. And, we know that there are 18 dark chocolates in the bag and each is equally likely to be chosen.
Now, let's use this information to find the number of milk chocolates. If there are n total chocolates in the bag, then the probability of choosing a dark chocolate is g, and the probability of choosing a milk chocolate is 1-g. We can write these probabilities as:
g = 18/n
1-g = (n-18)/n
So, if we equate the two expressions, we get:
18/n = (n-18)/n
That means:
18 = n - 18
And finally:
n = 36
So, there must be 36 chocolates in the bag, and 18 of them are dark chocolates, which means there must be 18 milk chocolates!
YQ and XP are altitudes to the congruent sides of isosceles triangle △WXY.
Select all the true statements.
When YQ and XP are altitudes to the congruent sides of isosceles triangle, the true statement are:
WXY = WXY
PXY = QYX
How to illustrate the informationIsosceles triangle has three sides out of which two are equal. It has two congruent sides. The angle opposite to base is vertex. It should be noted that the two sides of the triangle are congruent and the angles opposite to these sides are also congruent
From the information WXY is an isosceles triangle.
WXY = WXY
XY = XY
QXY == PYX (property of congruent triangle}
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PLS HELP!!!!!!!!!!!!!!!!!
Problems 1-6
1.) Thalia is currently 104 cm tall, and the doctor tells her she can expect to grow at 2.2 cm per year for the foreseeable future. What is the function rule (equation) for this scenario?
2.) In the problem above, identify the linear function's parameters.
3.) The 2011 population of manatees in Florida was 5,067. The animal is thought to be experiencing annual exponential decay of 1.1%. What is the function rule for this scenario?
4.) In the problem above, identify the exponential function's parameters (the independent and dependent variables).
5.) Does problem 3 describe growth or decay? Why? Use a complete sentence.
6.) What is the growth or decay rate in problem 3?
Answer:The function rule for Thalia's height (h) in years (t) is h(t) = 104 + 2.2t.
The linear function's parameters are: h0 = 104 (initial height), and k = 2.2 (the rate of growth in cm per year).
The function rule for the population of manatees (P) in years (t) is P(t) = 5,067 * (1.011)^(-t), where t is the number of years passed since 2011.
The exponential function's parameters are: P0 = 5,067 (the initial population), t (the number of years passed since 2011), and k = 0.011 (the decay rate).
Problem 3 describes decay. The population of manatees is decreasing by a certain percentage each year, indicating a decrease in the number of animals over time.
The decay rate in problem 3 is 1.1% (or 0.011 in decimal form).
Step-by-step explanation:
1.) The function rule (equation) for Thalia's height over time can be modeled as h(t) = 104 + 2.2t, where h(t) is her height in cm at time t in years.
2.) In the equation for Thalia's height, 104 is the y-intercept and 2.2 is the slope.
3.) The function rule for the manatee population in Florida can be modeled as P(t) = P0 * 0.989^t, where P(t) is the population at time t in years and P0 is the initial population (5,067).
4.) In the equation for the manatee population, P0 is the initial population and 0.989 is the decay rate. The independent variable is t (time in years) and the dependent variable is P (population).
5.) Problem 3 describes decay. This is because the population of manatees in Florida is decreasing at a constant rate of 1.1% per year.
6.) The growth or decay rate in problem 3 is -1.1%.
Step-by-step explanation:
hope you appreciate it.
The probability that Dan wins in a raffle is given by the expression p. Write down an expression for the probability that Dan does not win
If the probability of Dan winning is 'p', then the probability that he does not win is ' 1-p' .
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. The probability of a event happening and the same event not happening is 1 or 100%.
Let Dan winning in a raffle is Event A.
Let Dan not winning in a raffle is Event B.
Probability of Dan winning + Probability of not winning = 1
p + P(B) = 1
P(B) = 1 - p
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It snowed 3.02 inches on Monday and 0.26 inches on Tuesday. How much did it snow on Monday and Tuesday combined?
Answer: 3.28
Step-by-step explanation: so on monday it snowed 3.02 plus 0.26 on tuesday, now add 3.02 + 0.26 = 3.28
hope it helps !!!
What percentage did you tip if your lunch was $5 and you left $1? Enter your answer with a "%"
Can anyone help me to answer this?
Supposed more data points were plotted on the scatterplot, shown above. Now with 50 data points, explain why there is no way to create the same linear module and the line of the best fit as before? Are there any other linear association on the scatterplot?
Addition of more points change the pattern on the plot
There is another linear association on the scatterplot
Why there is no way to create the same linear moduleFrom the question, we have the following parameters that can be used in our computation:
The scatterplot
When more points are added to the plot, the points may tend to change the relation on the scatterplot
Any other linear association on the scatterplot?Yes, there is.
This is represented by the set of points that form the negative linear relation
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0.5568 divided by 0.58
Answer:
Step-by-step explanation:
0.96!
0.5568 divided by 0.58 is approximately 0.9593.
Here, we have,
To divide 0.5568 by 0.58, you can follow these steps:
Step 1: Write down the dividend (the number being divided), which is 0.5568.
Step 2: Write down the divisor (the number you're dividing by), which is 0.58.
Step 3: To simplify the division, you can multiply both the dividend and divisor by a power of 10 to remove the decimal places. In this case, we can multiply both numbers by 100 to move the decimal point two places to the right.
0.5568 * 100 = 55.68 (new dividend)
0.58 * 100 = 58 (new divisor)
Step 4: Divide the new dividend by the new divisor:
55.68 / 58 ≈ 0.95931034
Step 5: Round the result to the desired number of decimal places. In this case, since the original dividend had four decimal places, we can round the result to four decimal places:
0.9593
Therefore, 0.5568 divided by 0.58 is approximately 0.9593.
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James invests £200 for 1 year in a bank account. This account pays simple interest at a rate of 3% per year. Work out the total amount of money in the account at the end of the year
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 200\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 200[1+(0.03)(1)] \implies A = 206[/tex]
Need help with figuring out this question
The translated function is g(x) = ∛(x + 4) + 3, so the correct option is C.
Which function is g(x)?We can see that function g(x) is a translation of f(x), which is the parent cubic root function:
f(x) = ∛x
We can see that g(x) is a translation of 3 units up, and 4 units to the left.
Then the function will be written as:
g(x) = f(x + 4) + 3
Replacing f(x) we will get:
g(x) = ∛(x + 4) + 3
Then the correct option is C.
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Please help only correct answers please
The length of line JM would be = 19.2.
How to determine the missing length of the given figure?To calculate the missing length of the given figure above, the following steps should be taken as follows:
The formula that should be used is given as;
= GJ/GM = HK/HN
where;
GJ = 16
GM = 16+X
HK = 15
HN = 15+18 = 33
That is;
16/16+x = 15/33
16×33 = 15(16+X)
528 = 240+15x
528-240 = 15x
15x = 288
X = 288/15
= 19.2
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Which expression has a solution of 36, if p = 4?
Answer:
9p, because 9x4=36
Step-by-step explanation:
Angle A is represented by the expression 3X + 2. Angle B is represented by the expression X + 10. Angles A and B are vertical angles. What is the sum in degrees of Angle A and Angle B?
The sum in degrees of Angle A and Angle B is 28 degrees
What is the sum in degrees of Angle A and Angle B?From the question, we have the following parameters that can be used in our computation:
Angle A is represented by the expression 3X + 2. Angle B is represented by the expression X + 10. Angles A and B are vertical angles.Using the above as a guide, we have the following:
3x + 2 = x + 10
This means that
2x = 8
Divide by 2
x = 4
S, we have
Sum = 3x + 2 + x+ 10
Evaluate
Sum = 3 * 4 + 2 + 4 + 10
Sum = 28
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Translate into an equation, then solve: The product of a number and 14 is 28.
Answer:
x = 2
Step-by-step explanation:
Product = muliplication
Let x represent the number
14x = 28
x = 2
E
Jean transformed a point by using the rule (x,y)(x-6,y+8). The image point is (-4, 1). Which point is the pre-image?
O (-10, 9)
O (2-7)
(-2,7)
(10,-9)
Mark this and return
Save and Exit
Next
Submit
By applying the transformation formula (x,y) -> (x-6,y+8) to the location (-4, 1), the pre-image would be (-4+6, 1-8) = (2,-7).
So the appropriate response is: (-2, -7).
What exactly are pre-image and image?Shifts and scaling are two common transformations used in geometry to create new shapes from figures in a plane. Images are the new (modified) shapes, and preimages are the original, unmodified shapes.
What does geometry's preimage mean?The preimage is the body of the object as it was originally, and the transformed shape of the object is termed the image.
The word "preimage" is plural (mathematics) The collection of all domain elements mapped onto a specific subset of the function's arguments.
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800(4)-{3(5)•5(2)-7(27)}-y
when y is 90
Answer:
3149
Step-by-step explanation:
800(4)-{3(5)•5(2)-7(27)}-y
800(4)-{3(5)•5(2)-7(27)} - 90
3200 -{15•10-189} - 90
3200 -{150-189} - 90
3200 -{-39} - 90
3200 + 39 - 90
3149
Write two different inequalities in which one of the solutions is the same as the solution x -23=191
This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.
1. x + 191 ≥ 214
2. x - 214 ≤ -23
1. To solve this inequality, we add 23 to both sides of the equation: x - 23 = 191.
x + 191 ≥ 214
2. To solve this inequality, we subtract 191 from both sides of the equation: x - 23 = 191.
x - 214 ≤ -23
1. x + 191 ≥ 214
This inequality can be expanded to x + 191 ≥ 214, which means that any value of x that is greater than or equal to 214 satisfies the inequality.
2. x - 214 ≤ -23
This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.
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Write the equation of the line that passes through (3,-4) and is parallel to the line y=-8x-5
Answer:
y = - 8x + 20
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 8x - 5 ← is in slope- intercept form
with slope m = - 8
• Parallel lines have equal slopes , then
y = - 8x + c ← is the partial equation of the parallel line
to find c substitute (3, - 4 ) into the partial equation
- 4 = - 8(3) + c = - 24 + c ( add 24 to both sides )
20 = c
y = - 8x + 20 ← equation of parallel line
The function f(x) = x + 3 represents the length of a rectangle, and the function g(x) = 6x − 5 represents the width of the rectangle. What is the area of the rectangle if x = 3?
−72
19
78
117
Answer: 78
Step-by-step explanation:
(3) + 3 = 6
6(3) - 5 = 13
13 x 6 = 78
:)
Ethan and Emily went shopping at a local farmers’ market. They both
bought the same type of apples and potatoes at the same stand. Ethan
paid $25.50 for 8 pounds of apples and 5 pounds of potatoes. Emily paid
$18.50 to buy 3 pounds of apples and 10 pounds of potatoes. Which
ordered pair represents the price per pound of apples, x, and potatoes,
y?
(3.66,0.76)
(2.50,1.10)
(1.71,2.36)
(0.62,4.11)
Let x be the price per pound of apples and y be the price per pound of potatoes.
For Ethan, the total cost for apples was $25.50 - 5y and the total cost for potatoes was $25.50 - 8x.
So, we have the following two equations:
8x + 5y = 25.5
3x + 10y = 18.5
Solving this system of linear equations, we get:
x = 1.71 and y = 2.36.
So, the ordered pair (x,y) = (1.71, 2.36) represents the price per pound of apples and potatoes.
Yesterday, Sam had 149 baseball cards. Today, he gave m away. Using m, write an expression for the number of cards Sam has left.
Answer: 149 - m
He gave some away so we subtract
Help me as fast as u can and get lost of points
the equation for the line will be y = -5x +11 .
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The given line is y = x/5 +3
the slope is m = 1/5
So the slope of the perpendicular line will be -5
So the equation of line will be y-3 = m1(x-1)+3
y-3 = -5x+5+3
y = -5x +11
Hence the equation for the line will be y = -5x +11 .
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Sunita creates a scale model of an
aeroplane.
The scale of the model is 4 cm to 13
m.
Sunita's model has a wingspan of 21
cm.
What is the wingspan of the real
aeroplane?
The wingspan of the real aeroplane is equal to 68.25 cm.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as aeroplanes, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):
Scale factor = 13/4
Scale factor = 3.25
For the wingspan of the real aeroplane, we have:
Real Wingspan = 3.25 × 21
Real Wingspan = 68.25 cm.
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Is x2 + 2bx - b? a perfect square trinomial? Explain. If not, what is an expression for the last term that will make it a perfect square trinomial?
The expression that will be a perfect square binomial is
x² + 2bx + b² = (x+b)²
What is meant by a perfect square trinomial?
By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similarly, trinomials are three-term algebraic expressions.
For example, if we take a binomial (x + 3)
The perfect square trinomial is (x + 3)² = x² + 6x + 9
Given equation is x² + 2bx - b
The general equation is ax² + bx +c
Comparing the expressions we get,
a = 1
b = 2b
c = -b
A trinomial is a perfect square if and only if it satisfies the condition
b² = 4ac
Substituting the above values,
(2b)² = 4 * 1 * -b
4b² = - 4b
The value of b² can never be a negative number. So the above relation is not true for the given expression.
For the expression to become a perfect square binomial, the last term should be b².
Therefore the expression that will be a perfect square binomial is
x² + 2bx + b² = (x+b)²
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Evaluate 8.3x + 7.5y when x = 3 and y = 4.
8.3( blank) + 7.5( blank) = blank + 30.0= Answer?
Answer:
54.9
Step-by-step explanation:
Substitute the provided values of x and y into the provided expression:
8.3(3) + 7.5(4)
= 24.9 + 30.0
= 54.9
Which expressions represent the length of side \overline{MN}
MN
start overline, M, N, end overline?
The length of side MN is approximately 4.43 for the right triangle MNO.
In a right triangle MNO, with side NO equivalent to 4 and MO equivalent to 1.9, and with points MNO equivalent to 25 degrees and MON equivalent to 90 degrees, the length of side MN can be tracked down utilizing the Pythagorean hypothesis.
The Pythagorean hypothesis expresses that in a right triangle, the square of the length of the hypotenuse (the longest side) is equivalent to the number of squares of the other different sides. Thus, for this situation:
MN² = NO² + MO²
MN² = 4² + 1.9²
MN² = 16 + 3.61
MN² = 19.61
Taking the square root of both sides:
MN = √(19.61)
MN = 4.43
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The question is -
Consider the right triangle MNO below. Which expressions represent the length of the side MN?