The values of x after the statement are:
b) If x=1, then the statement P(1)="1>1" is false, and thus the value of x is equal to 1 after the statement "P(x) then x := 1".c) If x=2, then the statement P(2)="2>1" is true, and thus the value of x is equal to 1 after the statement "if P(x) then x := 1".What is Discrete Mathematics?This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.
Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false
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General admission tickets to a play cost $18 each. Reserved seats cost $22 each. There were 20 reserved seats sold. There were 28 more general admission tickets sold than reserved seats. How much money was paid for all of the tickets put together? Complete the chart and answer the question:
Answer:
$22 * (20) + $18 * (48) = $1304
Step-by-step explanation:
There are 20 reserved seats so it would be: $22 * 20 = $440 for all reserved seats
There are 28 general admission tickets more than reserved seats ticket so number of general admission tickets is: 20 + 28 = 48 (tickets)
Each general admission tickets cost $18, so: $18 * 48 = $864 for all general admission tickets
So the total money was paid for all of the tickets is: $440 + $864 = $1304
On a recent trip to the convenience store, you picked up 3 gallons of milk, 6 bottles of water, and 6 snack-size bags of chips. Your total bill (before tax) was $29.10. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.70 more than a bottle of water, how much does each item cost?
Hi
the trick is to define price by referring only to one item.
Here the bootle of water is you reference.
there is 3 gallons of milk
6 bottles of water
6 bags of chips
let's call bottle of water " X"
water cost = X
milk = X+1.7
chips = X/2
So we have :
3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1
3X+ 5.1 + 6X + 6X/2 = 29.1
3X +6X + 3X + 5.1 = 29.1
12X +5.1 = 29.1
12X = 29.1 - 5.1
12 X = 24
X = 24/12
X = 2
price of bottle is 2 dollars
then milk is 2 + 1.7 = 3.7
chips = 2/2 = 1
let's check = 3*3.7 + 6*2 + 6*1 = 11.1+12+ 6 = 29.1
answer this please only the ones that are blank
Answer:
#3 5(2a+4)
#4 5(a+2+4)
#5 5a+5(2+4)
Step-by-step explanation:
I think so, I am probably wrong
Find the measure of the ndicaited angle to the nearest degree 35 and 38
The measure of the indicated angle to the nearest degrees is 23 degrees.
How to find angle of a right angle triangle?The angle of a right angle triangle can be found as follows:
Therefore, the angle can be found using trigonometric ratios as follows;
cos ∅ = adjacent / hypotenuse
Therefore,
adjacent side = 35 units
hypotenuse side = 38 units
Hence,
cos ∅ = 35 / 38
∅ = cos⁻¹ 0.92105263157
∅ = 22.9272842944
∅ ≈ 23 degrees.
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Determine the interval(s) on which the given function is decreasing?
Answer:
(-∞, -1) U (0, ∞)
Step-by-step explanation:
To figure out which parts of the function are decreasing, we need to read the graph left to right.
Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.
How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.
The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).
Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).
Therefore, our final answer is (-∞, -1) U (0, ∞).
Suppose you are looking to purchase a new TV. You are placing it in an opening that is 136 cm wide but want to leave at least 2 cm of room on either side of the TV. If the TV screen measures 86 cm high, what is the largest size TVin inches, that you can purchase? TV's are measured based on the diagonal measure. (1inch = 2.54cm) Write your answer as an integer.
Answer:
62 inches
Step-by-step explanation:
Since we need to leave 2 cm of room on both sides, the maximum width of TV is 136 - 2 - 2 = 132 cm. Next, use the Pythagorean Theorem, a^2 + b^2 = c^2, to find the diagonal.
132^2 + 86^2 = c^2
c^2 = 17424 + 7396
c^2 = 24820
c = 157.543644746 cm
Finally, convert the value to inches using the given conversion factor.
157.543644746/2.54 = 62.0250569868 inches
Robert can mow a 600 square lawn in 1 hour and 20 minutes. How many lawns in the same size's can he mow in 8 hours?
define cultural identity in your own words
Cultural identity component of an individual which makes him identifiable with a given group. For example, British Asian is a cultural identity.
What is the Meaning of Cultural Identity?Cultural identity can be described as a component of an individual which makes him identifiable with a given group that share the same characteristics.
Examples of cultural identities may include the following:
ReligionEthnic backgroundTraditionNationalityFoodI can state that I am a British Asian. British Asian is my cultural identity.
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define cultural identity in your own words
Simply put, cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.
What is Cultural Identity?Cultural identity can be defined as the self-perception of an individual which gives them a sense of belonging to an identical group that shares same qualities which may included music, food, traditions, social class, beliefs, ethnicity, among others.
In summary, we can say that cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.
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Name the type of angle relationship. Set up the equation and solve for x.
Equation:
Solve: x :
Answer:
Same side interior angles
x=10
Step-by-step explanation:
The angles are same side interior angles
The add to 180 degrees
6x+10 + 110 = 180
Combine like terms
6x+120 =180
Subtract 120 from each side
6x = 180-120
6x= 60
Divide by 6
6x/6 = 60/6
x = 10
Answer:
Same-Side Interior Angles
Equation: 6x + 10 + 110 = 180
x = 10
Step-by-step explanation:
Hello!
The sum of the two given angles is 180°, as they are same-side interior angles.
Equation: 6x + 10 + 110 = 180
Solve for x6x + 10 + 110 = 1806x + 120 = 1806x = 60x = 10The value of x is 10°.
solve the equation 13Z/Z+1 =11-3i, Z£C where Z=X+yi X&Y£R?
Presumably you mean the equation
[tex]\dfrac{13z}{z+1} = 11-3i[/tex]
Observe that for [tex]z\neq-1[/tex],
[tex]\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}[/tex]
so we can simplify the equation to
[tex]13 - \dfrac{13}{z+1} = 11 - 3i \implies \dfrac{13}{z+1} = 13 - (11 - 3i) = 2+3i[/tex]
Multiply both sides by [tex]\frac{z+1}{2+3i}[/tex].
[tex]\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1[/tex]
Rationalize the denominator by introducing its complex conjugate.
[tex]z = \dfrac{13(2-3i)}{(2+3i)(2-3i)} - 1 = \dfrac{26-39i}{2^2+3^2} - 1 = \boxed{1 - 3i}[/tex]
Which of the following functions has a vertical asymptote at x=−1, a horizontal asymptote at f(x)=5, and a root at x=−3?
Answer:
Step-by-step explanation:
B :10/(x+1) +5
Does this graph show a function? Explain how you know. O A. No, the graph fails the vertical line test. OB. No; there are y-values that have more than one xvalue. OC. Yes; the graph passes the vertical line test. OD. Yes; there are no y-values that have more than one x-value.
The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.
What is a function in the graph?The collection of all points in the plane with the form (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.Use the vertical line test to establish if a graph reflects a function. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line crosses it at more than one location.First-order variables are present in linear functions, and the graph's placement is determined by two constants. These operations graph into a line in every case. The slope of the line is determined by the constant m. The slope of the line will slope up if it is positive and down if it is negative.
The graph represents a parabola.
The graph can be a function if it passes the vertical line test.
The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.
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PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.
The piece-wise linear functions can be written as follows:
[tex]f(x) = -0.5x + 3, x < 5[/tex].[tex]f(x) = -5, x = 5[/tex][tex]f(x) = -x + 9, x > 5[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
[tex]f(x) = -0.5x + 3, x < 5[/tex].
When x = 5, the function is constant at -5, hence:
[tex]f(x) = -5, x = 5[/tex]
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
[tex]f(x) = -x + 9, x > 5[/tex].
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Off the production line, there is a 2.2% chance that a candle is defective. If the company selected 40 candles off the line, what is the standard deviation of the number of defective candles in the group?
The standard deviation of the number of defective candles in the group is 0.9277.
When a random variable X follows a binomial distribution, with the sample size n, and the proportion of success is p, then the standard deviation is calculated as:
σ = √{np(1-p)}.
In the question, we are given that off the production line, there is a 2.2% chance that a candle is defective.
We are asked if the company selected 40 candles off the line, then what is the standard deviation of the number of defective candles in the group.
Assuming the occurrence of a defective bulb as success, we get the proportion of success, p = 2.2% or 0.022, and the sample size, n = 40.
Thus, we can calculate the standard deviation of the number of defective candles in the group as:
σ = √{np(1-p),
or, σ = √{40*0.022*(1 - 0.022)} = √0.86064 = 0.9277.
Thus, the standard deviation of the number of defective candles in the group is 0.9277.
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how do I find the value of x?
Answer: x = 15
Step-by-step explanation:
The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.
sum of angles = (n - 2) × 180
sum of angles = (7 - 2) × 180
sum of angles = 5 × 180
sum of angles = 900°
Now to find the value of x, we have to set each of the interior angles, added up, equal to 900°:
7x + 1 + 10x + 6x + 7 + 10x - 9 + 9x + 4 + 8x + 10 + 9x + 2 = 900
Combine like terms:
(7x + 10x + 6x + 10x + 9x + 8x + 9x) + (1 + 7 - 9 + 4 + 10 + 2) = 900
59x + 15 = 900
59x + 15 - 15 = 900 - 15 subtract 15 from both sides
59x = 885
59x/59 = 885/59 divide by 59 on both sides
x = 15
adjoint of [1 0 2 -1] is
The adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
How to determine the adjoint?The matrix is given as:
[tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex]
For a matrix A be represented as:
[tex]A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
The adjoint is:
[tex]Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
Using the above format, we have:
[tex]Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
Hence, the adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
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necesito ayuda con estas operaciones
3x=12
3x= -5=0
x+4=17
9y+3=21
5(x-2)=20
x÷2=4
2x÷=4
5÷x=2
4x+5=3x-6
3(x-2) =0
x÷3-4=0
5(7-x) =31-x
3(2x-2) =2(3x+9)
The expressions are illustrated below.
How to compute the expression?3x = 12
x = 12/3
x = 4
x + 4 = 17
x = 17 - 4
x = 13
9y + 3 = 21
9y = 21 - 3
9y = 18
y = 18/9
y = 2
x ÷ 2 = 4
x = 4 × 2
x = 8
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Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9 dimes and 15 quarters. What is the total amount of the deposit?
The total amount of the deposit is $592.92.
What is the total amount of the deposit?The total amount of the deposit can be determined by adding all the money deposited together.
(47 x 1) + (22 x 5) + (9 x 10) + (17 x 20) + (67 x 0.01) + (0.05 x 12) + (9 x 0.1) + (15 x 0.25)
47 + 110 + 90 + 340 + 0.67 + 0.60 + 0.9 + 3.75 = $592.92
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The population of a city is modeled by the equation P(t)=232012e0.23t where t is measure in years. If the city continues to grow at this rate, approximately how many years will it take for the population to reach one million? Round your answer to two decimal places
In around 6.35 years, the population will be 1 million.
how many years will it take for the population to reach one million?
The population is modeled by the exponential equation:
[tex]P(t) = 232,012*e^{0.23*t}[/tex]
Then we just need to solve the equation for t:
[tex]P(t) = 232,012*e^{0.23*t} = 1,000,000[/tex]
Let's solve that:
[tex]232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\[/tex]
If we apply the natural logarithm to both sides:
[tex]ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35[/tex]
So in around 6.35 years, the population will be 1 million.
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At the movie theater child admission is $5.20 and adult admission is $9.90.. On Friday 163 tickets were sold for a total sales of $1303.50. How many adult tickets were sold that day?
The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of children and y represent the number of adult, hence:
5.2x + 9.9y = 1303.5 (1)
Also:
x + y = 163 (2)
From both equations:
x = 66, y = 97
The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.
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The box plot below shows the total amount of time, in minutes, the students of a class surf the Internet every day: Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)
Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)
Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)
The pieces of information that is provided by the box plots are the median and first quartile.
The piece of information that is not provided by the box plots is the mean.
The interquartile range is 22.50.
An outlier would distort the values of the median and the quartiles.
What is a box plot?
A box plot is used to study the distribution and level of a set of scores. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the quartiles is the interquartile range.
Interquartile range = 60 - 37.50 = 22.50
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23 gram put into milligrams
Answer:
Step-by-step explanation: 23000 milligrams
Cual es el valor de A si 900 es el 130% de A
El valor del número A es 692.31.
PercentageThe percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:
[tex]\frac{50}{100} =0.5*100=50%[/tex]
The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks etc.
The exercise asks you the value of A and it gives you the value (900) that represents 130%A. Thus, you should write an equality between the division the percentage and the variable A by 100 with the value 900.
You should follow the steps below.
[tex]\frac{130*A}{100}=900\\ \\ 130A=90000\\ \\ A=\frac{90000}{130} =692.31[/tex]
You can check the result : [tex]\frac{692.31*130}{100} =\frac{90000.3}{100} =900.003=900[/tex]
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two vertices are 3x+10 and x+60 find x
The value of x such that the vertices 3x + 10 and x + 60 are equal is 25
What are vertices?Vertices are the endpoints or corners of a shape (such as triangle, square, rectangle and related shapes)
How to determine the value of x?The two vertices are given as:
3x + 10 and x + 60
The condition on the two vertices are not given.
So, we assume that the vertices are equal (as in the base angles of an isosceles triangle)
So, we have the following equation
3x + 10 = x + 60
Subtract x from both sides of the equation
2x + 10 = 60
Subtract 10 from both sides of the equation
2x = 50
Divide both sides of the equation by 2
x = 50/2
Evaluate the quotient
x = 25
Hence, the value of x such that the vertices 3x + 10 and x + 60 are equal is 25
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6x+2y=8
9x+3y=14
Skew
Neither
Perpendicular
Parallel
Which is the equation of the given line?
x = 4
y = 3
y=−2x
y = x
Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points (four, three) and (four, negative two).
Since the x-coordinates are equal, hence the equation of the line will be x =4
Equation of a lineThe equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the intercept
From the given coordinate points (four, three) and (four, negative two), we can see that the x-coordinates are equal, hence the equation of the line will be x =4
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) Explain why the expression x2 + (p + q )x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x2 + bx + c.
The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique
How to factorize Quadratic Equations?We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.
Now, using the FOIL Technique we can say that the factors are;
(x + p)(x + q)
Expanding this gives;
x² + px + qx + pq
⇒ x² + (p + q)x + pq
Now, applying that to the trinomial; x² + 6x + 8, we can say that;
p + q = 6, and pq = 8
Thus, solving simultaneously gives;
p = 2 and q = 6.
Thus;
x² + 6x + 8 = (x + 2)(x + 6)
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Need help on these trig homework
8. The length of the support is 7. 9 m
9. The length of the conveyer is 12m
3. a = 59m
A = 44°
B = 52°
4. c = 88. 6 mm
b = 49. 1 m
B = 34°
How to solve the trigonometry
8. We have the angle to be 20 degrees
Opposite side = x
hypotenuse = 23m
Using the sine ratio
sin θ = opposite/ hypotenuse
[tex]sin 20 = \frac{x}{23}[/tex]
Cross multiply
[tex]sin 20[/tex] × [tex]23 = x[/tex]
[tex]x = 0. 3420[/tex] × [tex]23[/tex]
x = 7. 9 m
The length of the support is 7. 9 m
9. The angle of elevation is 37. 3 degrees
Hypotenuse = 19 . 0m
Opposite = x
Using the sine ratio
sin θ = opposite/ hypotenuse
[tex]sin 37. 3 = \frac{x}{19}[/tex]
cross multiply
[tex]x = 0. 6059[/tex] × [tex]19[/tex]
x = 11.5
x = 12 m in 2 significant figures
The length of the conveyer is 12m
3. To determine the sides and angles, we use the sine rule;
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
For side a, we use the Pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
[tex]85^2 = a^2 + 67^2[/tex]
[tex]a = \sqrt{89^2-67^2}[/tex]
[tex]a = \sqrt{3432}[/tex]
a = 58. 58, a = 59m
To find angle A and B, use the sine rule
[tex]\frac{59}{sin A } = \frac{85}{sin 90}[/tex]
cross multiply
[tex]sin A[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]59[/tex]
make sin A subject of formula
[tex]sin A = \frac{59}{85}[/tex]
[tex]sin A = 0. 6941[/tex]
A = [tex]sin^-^1(0. 6941)[/tex]
A = 44°
[tex]\frac{67}{sin B} = \frac{85}{sin 90}[/tex]
cross multiply
[tex]sin B[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]67[/tex]
make sin b subject of formula
[tex]sin B = \frac{67}{85}[/tex]
[tex]sin B = 0. 7882[/tex]
B = [tex]sin^-^1( 0. 7882)[/tex]
B = 52°
4. To find the sides, we use the sine rule;
[tex]\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}[/tex]
Cross multiply
[tex]sin 56. 6[/tex] × [tex]c = sin 90[/tex] × [tex]74[/tex]
make 'c' subject of formula
[tex]c = \frac{74}{0. 8348}[/tex]
c = 88. 6 mm
To find length b, we use the Pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
[tex]b^2 = c^2 - a^2[/tex]
[tex]b^2 = 88. 8^2 - 74^2[/tex]
[tex]b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}[/tex]
b = 49. 1 m
[tex]\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}[/tex]
cross multiply
[tex]sin B = \frac{40. 99}{74. 0}[/tex]
B = [tex]sin^-^1(0. 5539)[/tex]
B = 34°
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Imogen buys some sandwiches costing £3.50.
She has a 20% off coupon.
How much discount will Imogen receive?
K
4