Using the Fundamental Counting Theorem, it is found that there are 1024 ways of delivering the letters.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, each house has a correct letter, however the letter cannot be used for the house, hence the parameters are given as follows:
n1 = n2 = n3 = n4 = n5 = 5 - 1 = 4.
Thus the number of ways is:
N = 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.
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The total volume of a tree increases 6% each year. what will its volume be after 7 years if its volume is 5 cubic meters now?
Answer:
7.52 m^3
Step-by-step explanation:
This is like compound interest in a banking calculation
Future volume = 5 (1 + .06)^7 = 7.52 m^3
When a number increases by 10 % it become 22, Find the number.
pls help with math!!!
A softball player throws a ball into the air with an initial velocity of 32 feet per second. The ball is released at a height of 5 feet. The function h(t) = [tex]-16t^{2}[/tex]+32t+5 models the height h (in feet) of the ball as a function of the time t (in seconds) after it is thrown. Use the equation to find the time that the ball is in the air if the player lets the ball drop
The time that the ball is in the air if the player lets the ball drop is 2.145 sec
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
-16t²+32t+5
by comparing this equation to the standard form of the quadratic equation we get
a=-16 b=32 c=5
the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:
the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)
t = -32/2×-16
t=1sec
by putting h(t) to zero and determining the time (t) when the ball hits the ground:
-16t²+32t+5=0
-16(t²+2t+5/16)=0
t²-2t-5/16=0
(t)²-2×1×t+(1)²-5/16=1
(t-1)²=21/16
t-1=√21/√16
t=1+4.58/4
t=1+1.145
t=2.245sec
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A bucket contains exactly 3 marbles, one red, one blue and one green. a person arbitrarily pulls out each marble one at a time. What is the probability that the last marble removed is non-red?
The probability that the last marble removed is non-red is 2/3.
According to the given question.
Total number of marbles in a bucket = 3
And, a person arbitary pulls out each marble one at a time.
So, there are 6 possible sequences of removing 3 marbles.
Let R be the red marble, B be the blue marble and G be the green marble.
The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.
Let A denotes the event of removing the non-red marbles at the last.
The favorable cases for event A are: RBG, RGB, BRG and GRB.
As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.
Thereofre,
The probability that the last marble removed is non-red
= 4/6
= 2/3
The probability that the last marble removed is non-red is 2/3.
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Hich number is not in scientific notation? (5 points) group of answer choices 9 ⋅ 1019 7.8 ⋅ 106 1.45 ⋅ 10−7 0.33 ⋅ 10−15
Answer:
0.33 ⋅ 10^−15
Step-by-step explanation:
Scientific notation requires exactly one non-zero digit to the left of the decimal point.
The number ...
0.33 ⋅ 10^−15
has no non-zero digits to the left of the decimal point. It is not in "scientific notation."
__
Additional comment
Expressed in scientific notation, it would be ...
3.3 ⋅ 10^−16
3. Ying Yu turned 22 this year. In 8 years, she will be three times as old as her little brother will be then. How old is her little brother now? Answer
Answer:
He is 2 years old.
Step-by-step explanation:
She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.
If you must show algebra work:
x = brother's age now.
x+8=brother's age in 8 years.
YingYu's age in 8 years = 3 × brother's age in 8 years
22+8 = 3(x+8)
30 = 3x +24
6 = 3x
2 = x
A team plays 93 games in a season. The team won 15
more than twice as many games as they lost.
How many wins and losses did the team have?
PLS HELPPPP THE WORDING IS CONFUSING
Answer:67 wins, 26 losses
Step-by-step explanation: They played 93 games. Let L = their losses and w = their wins. They won 15 more than twice as many games they lost so w = 2L + 15. So, 93 = 3L + 15. 93 - 15 = 78. 78 divided by 3 is 26 so they lost 26 games and won the rest of them or 93-26 = 67 wins and 26 losses.
What is the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3?
The value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is 16.94%
How to solve for the mean absolute percentage errorThe equation is given as
∝At + (1-∝) Ft
The value for Alpha = 0.7
1 - ∝ = 1 - 0.7
= 0.3
Forecast in match = 62
Ft = 51. 5
the difference = 62 - 51.5
= 10.5
The error = 10.5/62 * 100
= 16.94%
Hence the value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is 16.94%
Complete question
The past demand data shown below can be regarded as stationary.
Month Demand
January
50
February
55
March
62
April
45
What is the mean absolute percentage error of the forecast for March found by the exponential smoothing method with a smoothing constant of 0.3?
O a. 14.68%
Ob. 16.94%
O c. 12.57%
Od. 11.33%
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The two rectangles are similar. which is the correct proportion for corresponding sides?
Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.
According to the statement
we have given that the two rectangle which are similar to each other and we have to find the correct proportion for corresponding sides of rectangles.
So, we know that the
For the two rectangles to be similar, it means the ratio of their corresponding sides must be the same.
Looking at the two rectangles, the corresponding sides are pf the rectangles are:
4 m side corresponds to 8 m side in rectangle A
12m side corresponds to the 24 m side in rectangle B.
Then
The ratios of the both rectangles are:
In rectangle A is 8/4 = 2
In rectangle B is 24/12 = 2
From this it is clear that the ratios are equal.
Thus, the scale factor is 2
Since 8/4 = 24/12, we can rearrange to get;
12/4 = 24/8.
So, Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
The two rectangles are similar with sides 4 m side corresponds to 8 m side in rectangle A and 12m side corresponds to the 24 m side in rectangle B.which is the correct proportion for corresponding sides?
A. 12/3 = 24/12.
B. 12/2 = 27/8.
C. 11/4 = 23/8.
D. 12/4 = 24/8.
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A sales team estimates that the number of new phones it will sell is a function of the price that it sets. It estimates that if it
sets the price at.x dollars, it will sell f(x) = 2,712 - 3x phones. Therefore, the company's revenue is x (2,712 - 3x). Find
the price x that will maximize the company's revenue.
The price x which will maximize the company's revenue is 904
How to determine the priceThe price x which will maximize the company's revenue is 240
Let
Price of the good = x
Number of goods sold = 2712- 3x
The formula for revenue is given as;
Revenue = Price × Quantity
= x( 2712 - 3x)
Expand the bracket
2712x - 3x^2
Therefore, the price x which will maximize the company's revenue will be:
2712x - 3x^2 =0
Collect like terms
3x² = 2712x
3x = 2712
Divide both side by 3
3x/3 = 2712/3
x = 904
Hence, the price x which will maximize the company's revenue is 904
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Can the mixed number 7 and 13/100 be simplified?
Step-by-step explanation:
Reduce 13/100 to lowest terms
13
100
is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 13 and 100 is 1
Divide both the numerator and denominator by the GCD
13 ÷ 1
100 ÷ 1
Reduced fraction:
13
100
Therefore, 13/100 simplified to lowest terms is 13/100.
The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.
A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.
Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.
Given that
[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]
[tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]
Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].
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–4.9(–7.3 + 3.6n) =
Simplify the expression please :)
What are the y-intercept and the asymptote of g(x) = 3x – 5? (0, –5); y = 3 (0, –2); y = 5 (0, –4); y = –5 (0, 5); y = –3
The y-intercept of the equation g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation g(x) = 3^x - 5 is y = -5
How to determine the y-intercept?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The y-intercept is a point on the graph where the value of x is 0
This is represented by x= 0 or (0, y)
This means that we substitute 0 for x in the above equation
So, we have:
g(0) = 3^0 - 5
Evaluate the exponent 3^0
g(0) = 1 - 5
Evaluate the difference of 1 and 5
g(0) = -4
Rewrite this point as
(0, -4)
This means that the y-intercept of the equation g(x) = 3^x - 5 is (0, -4)
How to determine the asymptote?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The asymptote is a point on the graph where that is parallel to the graph
In the above equation, we have:
g(x) = 3^x - 5
Express the radical as 0
y = 0 - 5
Evaluate the difference of 0 and 5
y = -5
This means that the asymptote of the equation g(x) = 3^x - 5 is y = -5
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G(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
Answer:
-7
Step-by-step explanation:
[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]
Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. Length of Time (in minutes) Number 1 up to 4 4 4 up to 7 8 7 up to 10 14 10 up to 13 9 13 up to 16 5 16 up to 19 2 What is the mean (in minutes)
The mean in minutes of the length of time given= 9.1
Calculation of mean when frequency table is givenThe formula used for the determination of mean when a frequency table is given is
= total/n
Where total = frequency×midpoint
n = 42
To calculate the total, the mid point of each length of time is determined as follows;
1+4/2 = 2.5 × 4 = 10
4+7/2= 5.5 × 8 = 44
7+10/2 = 8.5 × 14= 119
10+13/2 = 11.5× 9 = 103.5
13+16/2= 14.5×5 = 72.5
16+19/2= 17.5× 2= 35
Total= 10+44+119+103.5+72.5+35 = 384
Therefore mean = 384/42= 9.1
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In a simple bivariate regression with 60 observations, there will be _____ residuals.
There will be 60 residuals for simple bivariate regression's 60 observations.
According to the statement
We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.
So, For the solution of this problem,
We know that the
A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.
And we know that the it is always same for the number as the number of given observations.
That's why there is 60 residuals.
So, There will be 60 residuals for simple bivariate regression's 60 observations.
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If two 6-sided dice are rolled what is the probability that both numbers will be even?
June and Angad have played 30 tennis matches.
June has won 14 times.
Angad won the rest.
a) Estimate the probability that June wins.
b) Estimate the probability that Angad wins
Answer:
The file contains the solution to the question
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
x²+x+
X+
a
X+
2a
b
2a
Statements
2a
2a
= ±₁
==
4ac b²
+
4a² 4a²
b²-4ac
4a²
b²-4ac
4a²
b²-4ac
4a²
?
Reasons
Find a common denominator on the right side of the equation
Add the fractions together on the right side of the equation
Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
Take the square root of both sides of the equation
Simplify the right side of the equation
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 -4ac}}{2a}[/tex]
Match each correlation coefficient to its corresponding description.
Urgent!!!!!!!!!!!!!!!!!!
PLEASE ITS MY LAST QUESTION
Answer:
[tex]y = - \frac{1}{4} x - 10[/tex]
Step-by-step explanation:
The negative reciprocal of 4 is -1/4.
Let's substitute in our values, to find the y-intercept:
[tex]y = - \frac{1}{4} x + c[/tex]
[tex] - 11 = - 1 + c[/tex]
[tex]c = - 10[/tex]
Finally, our full equation is:
[tex]y = - \frac{1}{4} x - 10[/tex]
In the regular pentagon below, if AP = 4 m and BC = 10 m, find it's area.
First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)
Then find the area of one of the triangles:
Area of Triangle = [tex]\frac{1}{2} bh[/tex]
A = [tex]\frac{1}{2}[/tex] × 4 × 10
A = 20 m²
To find the area of the whole pentagon shape:
A = 20 × 5 = 100 m²
Hope it helps!
Two linear equations are shown.
A coordinate grid with 2 lines. The first line is labeled y equals StartFraction one-third EndFraction x plus 2 and passes through (negative 6, 0) and (0, 2). The second line is labeled y equals StartFraction 4 over 3 EndFraction minus 5.
What is the solution to the system of equations?
Answer:
x = 7; y = 4 1/3
Step-by-step explanation:
The solution is the point of intersection of the lines.
Read the point of intersection.
You can also solve the system using algebra.
y = 1/3 x + 2
y = 4/3 x - 5
1/3 x + 2 = 4/3 x - 5
x + 6 = 4x - 15
-3x = -21
x = 7
y = 1/3 x + 2
y = 1/3 × 7 + 2
y = 2 1/3 + 2
y = 4 1/3
Answer: x = 7; y = 4 1/3
Which of the following graphs has a zero correlation?
What is the slope of the line that passes through the points (10, 3) and
(7,0)? Write your answer in simplest form.
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )
m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1
xy =8 inches wy =24 and xz=48 inches height from the ground to the base of the window is?
The height of the ground from the base of the window is 144 inches.
How to find the side of a right angle triangle?One angle of a right angle triangle is equals to 90 degrees.
Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.
tan x = WY / XY
tan x = opposite / adjacent
tan x = 24 / 8
x = tan⁻¹ 3
x = tan⁻¹ 3
x = 71.5650511771
x = 71.60°
tan 71.60 = h / 48
cross multiply
h = 48 tan 71.60
h = 48 × 3
h = 144 inches
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When rolling two dice what is the probability of rolling a sum of six or two even numbers.
The probability of rolling a sum of six or two even numbers.
is P = 1/3
How to find the probability?
Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:
6*6 = 36
Now, the outcomes that given a sum of 6 are:
dice 1 dice 2.
1 5
5 1
2 4
4 2
3 3
We have 5 outcomes there.
The outcomes where both numbers are even are:
dice 1 dice 2.
2 2
2 4
4 2
4 4
4 6
6 2
6 4
6 6
We have 8 outcomes here (such that 2 are in the ones we counted before).
Then the total number of outcomes that either add to 6 or have both even numbers are:
5 + 8 - 2 = 12
Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:
P = 12/36 = 1/3
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A small manufacturer constructs refrigerators. the fixed monthly cost is $200,000, and it costs $450 to produce one refrigerator. the average cost function to produce x refrigerators is represented by: what is the horizontal asymptote of c(x)? y =
Horizontal asymptote of c(x) is 450.
What is Horizontal asymptote?A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.
According to the information:Since we have given that
Cost to produce one refrigerator = $450
Fixed monthly cost = $200,000
Thus, the following formula represents the average cost to produce x refrigerators:
C(x) = (200000 + 450x)/x
Horizontal asymptote of c(x) would be
= 450x/x
= 450
Hence, Horizontal asymptote of c(x) is 450
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