[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]
circumference of a circle is 26.19. Find the diameter of the circle
35+6x-2=13x+12 solve for x
Answer:
x = 3
Step-by-step explanation:
Solve for x:
35 + 6x - 2 = 13x + 12
Simplifying on the left side:
33 + 6x = 13x + 12
Subtracting 33 on both sides:
6x = 13x - 21
Subtracting 13x on both sides:
-7x = -21
Dividing by -7 on both sides:
x = 3
the mass of a bag of flour is 7kg 500g. Joyce repacks the flour into 12 small packs of equal mass. What is the mass in kilograms of each small pack of flour
Answer:
I'm pretty sure it's 0.625kg
Step-by-step explanation:
There are 1000g in 1kg so 7kg would be 7000g plus 500g which is 7500g.
7500g divided by 12 is 625g. Divide by 1000 to get kg and you get 0.625kg.
Hope this helps!
a bowl contains 75 balls. of these, 10 are white, 11 are red, 12 are blue, 13 are green, 14 are yellow and 15 are black. what is the smallest number of balls that can be selected from the bowl to be certain that at least one ball of every color is chosen?
We have to use pigeonhole principle to find balls from bowl. From 75 balls at least one out of 31 balls will be of black color, out of 23 balls will be red, out of 25 will be blue, out of 27 balls will be green, out of 29 will be yellow.
out of 75 balls for each ball to be chosen at least once then we have to compute each color of ball separately,
By using the pigeonhole principle's formula n(r - 1) + 1
For red ball,
N=11, k=1, [N/2]≥3
= 11(3-1)+1
= 23
Hence, out of 23 balls from 75 balls at least one will be of red color
For, blue ball
N=12, k=1, [N/2]≥3
= 12(3-1)+1
= 25
Hence, out of 25 balls from 75 balls at least one will be of blue color
For green color,
N=13, k=1, [N/2]≥3
= 13(3-1)+1
= 27
Hence, out of 27 balls from 75 balls at least one will be of green color
For yellow ball,
N=14, k=1, [N/2]≥3
= 14(3-1)+1
= 29
Hence, out of 29 balls from 75 balls at least one will be of yellow color
For black ball,
N=15, k=1, [N/2]≥3
= 15(3-1)+1
= 31
Hence, out of 31 balls from 75 balls at least one will be of black color
The pigeonhole principle states that if n items are put into m containers, where n > m, at least one container must contain more than one item. If there are k+1 or more pigeons dispersed throughout the k pigeonholes, at least one pigeonhole will have two or more pigeons. Proof. The statement's converse is that there can only be a maximum of k pigeons if each slot can only accommodate one bird.
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
The no of student ticket, x = 30
The no of adult ticket, y = 37
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.
The drama club is selling tickets to their play to raise money for the show's expenses.
Let the student ticket be represented as x and adult ticket as y
Cost of student ticket,x = $7
Cost of adult ticket,y = $9
The total number of tickets, x + y = 67 ... (1)
There was a total of $543 in revenue from the sale of 67 total tickets.
7x + 9y = 543 ...(2)
Multiplying eq(1) by 7, we get
7x + 7y = 469 ...(3)
Subtract eq (3) from (2), we get
2y = 74
y = 37, sub in eq (1)
x = 30
The no of student ticket, x = 30
The no of adult ticket, y = 37
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Answer: Let s= the number of student tickets sold Let
Let a=the number of adult tickets sold
7s+9a=543
s+a=67
Step-by-step explanation:
A satellite flies 136640136640 miles in 17. 817. 08 hours. How many miles has it flown in 9. 879. 87 hours?.
If a satellite flies 136640 miles in 17.8 hours then in 9.87 hours the satellite flows down to 75766.6 miles
Given that:
A satellite flies 136640 miles in 17.8 hours
We will find the unit rate first,
Unit rate = 136640/17.8
Unit rate = 7676.40 miles per hour.
Miles flown in 9.87 hours,
Miles flown = 7676.40 × 9.87
Miles flown = 75766.6 miles
Hence Miles flown in 9.87 hours is 75766.6 miles
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The scatter plot shows the relationship between the average number of nightly customers and the number of months since a restaurant opened. The equation represents the linear model for this data. y = 5x + 120 What does the number 120 in the equation mean in this context? The restaurant has been open for 120 months. There were 120 customers per month after the restaurant was open 5 months. The number of customers per night increases by 120 each month. For every 5 months the restaurant has been open, there are 120 more customers per night. There were 120 customers per night when the restaurant opened. Number of Customers 300 270- 240- 210- L 180- ! 150- 120- Average nightly customers'
The number 120 in the equation of y = 5x + 120 mean is there were 120 customers per night when the restaurant opened.
How to read equation?For this case, the equation of y = 5x + 120 is for linear relationship.
Which is
y represent average number of nightly customer.
x represent number of months the restaurant opened.
For example for month 0 or for the first time restaurant open the nightly customer is,
y = 5(0) + 120
y = 0 + 120
y = 120
It mean the average number of nightly customer is 120 in the first time restaurant open. After month 0, in month 1 the nightly customer is increase by 5. So, total average nightly customer is 125, and so on.
Attached graph is for visualization and to make it easier to understand the equation mean.
Thus, number 120 in the equation is to represent there were 120 customers per night when restaurant opened.
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If I’m doing fractions on a number line how do I do thirds
Answer:
Step-by-step explanation:
it would be devided into 3 sections so the thing would look like this
the graph below shows the relationship between the number of hours cody works and the amount of money he earns at his job. Write a true statement about his relationship.
The true statement about his relationship is that the hours worked is directly proportional to the money earned.
What is the relationship shown in the graph?We know that a graph could be used to show the relationship between variables. This relationship can be shown by the use of the cartesian coordinates. The cartesian coordinates is directed in the x and the y plane as shown in the image in the question.
Now, we can see that the line of best fit that was drawn through the data points is point upwards. This would show us that as the number of hours worked is increasing, the money earned is also increasing.
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Erica has some stickers in her sticker album. Each week she plans to add 9 stickers. Erica had 50 stickers after 4 weeks. Assume the relationship is linear. Find the rate of change and initial value.
Rate of change: 9
Initial value: 14
explanation:
9 x 4 = 36 (she adds 9 stickers every week, it's 4 weeks)
50 - 36 = 14 (subtract what she added to find initial value)
A seasoning blend is 4\%4%4, percent onion powder, by mass. How much pure onion powder should they include in a 72\,\text{g}72g72, start text, g, end text bottle to make the final blend have 20\ , percent onion powder? khan academy
They need to put 14.4 grams of onion powder in each bottle.
Given,
The quantity of onion powder in a seasoning blend = 4%
We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;
How much is a percentage?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."
Here,
Let x be the seasoning blend.
Now, 4% of 72=20% of x
⇒ 0.04×72=0.2×x
⇒ 0.2x=2.88
⇒ x=2.88/0.2
⇒ x=14.4 g
Therefore, a container should contain 14.4 grams of onion powder.
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When 10 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
The positive solution is 5.
given,
When 10 is subtracted from a number's square, the result is three times the number.
let x be the number
according to given statement the quadratic equation will be
[tex]x^2-10=3x\\\\x^2-3x-10\\\\x^2+2x-5x-10=0\\\\x(x+2)-5(x+2)=0\\\\(x-5)(x+2)=0\\\\x=5\ or\ -2[/tex]
Thus, the positive solution is 5.
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Please help me with explanation
Answer:
[tex]5c+\frac{9-8c}{24}[/tex]
Step-by-step explanation:
Simplify
[tex]5c+\frac{1*(\frac{3}{4}-\frac{2c}{3} )}{2}[/tex]
[tex]5c+\frac{9-8c}{24}[/tex]
you toss a fair coin 9 times. find the probability of no more than 8 heads given that at least one toss resulted in heads.
The probability of no more than 8 heads given that at least one toss resulted in heads will be 511/512.
What is probability ?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
A coin has two possibility, either head or tail.
So, there will be 2 possible outcomes when a coin is tossed.
hence, Total no. of outcomes (T) = 2^9. = 512
Now, Probability of getting one tail = 1/2^9 = 1/512
and, Probability of getting at most 8 heads
= 1 - Probability of getting one tail
= 1 - 1/512
= 511/512.
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M is the midpoint of AC. A is (3, -9) and C is (-5, 16). Solve for the following
Answer:
[tex]M=\left(-1, \dfrac{7}{2} \right)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given endpoints:
A (3, -9)C (-5, 16)Substitute the given points in the midpoint formula:
[tex]\implies M=\left(\dfrac{x_C+x_A}{2}, \dfrac{y_C+y_A}{2} \right)[/tex]
[tex]\implies M=\left(\dfrac{-5+3}{2}, \dfrac{16+(-9)}{2} \right)[/tex]
[tex]\implies M=\left(\dfrac{-2}{2}, \dfrac{7}{2} \right)[/tex]
[tex]\implies M=\left(-1, \dfrac{7}{2} \right)[/tex]
Given two rectangular ducts with equal cross-sectional area but different aspect ratios (width/height) of 2 and 4 which will have the greater frictional losses? Explain your answer
The frictional loss will be greater for aspect ratio of 2 as friction will be more when the height of the duct is higher compared to the increase in width.
In a straight duct with constant cross sectional area , the velocity of the water is changed. The change in static pressure is the frictional loss .
In the duct the energy is constant. Therefore when water moves upwards with the increase in height the frictional loss or the pressure loss will be more more.
When width increases there will be less pressure, So frictional loss will be increased with height.
Let the width and height be a and b respectively.
now area = ab
and a\b =2
or, a = 2b
again a\b = 4 or, a = 4b
if ab is constant then the height for the aspect ratio of 4 is greater.
Therefore there will be more frictional loss for the increased height.
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which test should be used to determine if a difference exists between the proportion of all ucf and usf students who prefer to use hand sanitizer?
the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
When there are multiple alternatives accessible, hypothesis testing is utilised. To decide whether to accept or reject the null hypothesis, the z test is performed in the mean, which determines the t value. This value is then compared with the p value. The alternate explanation in this case is mu, which is represented. For P1 and P2, the 90% confidence interval is (- 0.0765, 0.02646).
Hence, the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%
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11. MARINE BIOLOGY Killer whales usually swim at a
rate of 3.2-9.7 kilometers per hour, though they can travel
up to 48.4 kilometers per hour. Suppose a migrating killer
whale is swimming at an average rate of 4.5 kilometers per
hour. The distance d the whale has traveled in t hours can
be predicted by the equation d = 4.5t.
a. Graph the equation.
b. Use the graph to predict the time it takes the killer
whale to travel 30 kilometers.
The graph of linear function d = 4.5t and the time to cover 30km is 6.67s
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here;
m = slopeb = y-interceptThe linear function given in the question is;
d = 4.5t
a) The graph of the function d = 4.5t is attached below.
b) The time it takes to cover 30km will be
d = 4.5t
30 = 4.5t
t = 30 / 4.5
t = 6.67 s
The time it takes to cover a distance of 30km is 6.67s
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Can someone help me with this??
Step-by-step explanation:
H is the plan
F is the side
A is the plan
hope it helps.. please mark brainliest
in a class of 45 student there are 12 girls what is the percentage of girls in the class?
The percentage of girls in a class are 26.67%.
What is percentage?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Given:
In a class of 45 student there are 12 girls.
We have to find the percentage of girls in the class.
Percentage of girls = (number of girls / Total number of students ) x 100
= (12 / 45) x 100
Percentage of girls = 26.6666
Percentage of girls ≈ 26.67
Hence, the percentage of girls in a class are 26.67%.
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consider the following binomial experiment: a study in a certain community showed that 6% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia?
Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is =24.21
What is binomial probability?
When an experiment or survey is repeated numerous times, the likelihood that the results will be SUCCESS or FAILURE is known as the binomial distribution. The prefix "bi" implies "two" or "twice," therefore the term "binomial" refers to a distribution type with two probable outcomes. A coin flip, for instance, can only result in one of two outcomes: heads or tails, and completing a test can result in either passing or failing.
standard deviation =[tex]\sqrt{n*p(1-p)}[/tex]
p = probability of success = 6% = 0.06
1 - p = 1 - 0.06 = 0.94
Sample size, n = 10400
Substituting the values into the equation :
[tex]\sqrt{10400*0.06(1-0.04)}[/tex]
[tex]\sqrt{10400*0.06(0.94)}[/tex]
[tex]\sqrt{10400*0.0564}[/tex]
[tex]\sqrt{586.56}[/tex]
= 24.21
Hence, the standard deviation is 24.21.
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how many 1/4 lbs are in 80 lbs
Answer:
640 1/4 lbs
Step-by-step explanation:
100x100x325x1773x3.44554x34444x6i78754x23324
Answer:
1.097174699×10^²⁶
Step-by-step explanation:
100×100×325×1773×3.44554×34444×6878755×23324=
1.097174699×10^²⁶
john drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. what was his average speed for the whole journey?
The average speed of John for the whole journey is 54km/h.
What is the average speed?Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.
Speed is the rate of movement of something at a specific time.
Average speed refers to the average speed over the course of a journey.
So, the average speed will be:
Distance = speed x time
d₁ = v₁ x t₁
d₁ = 50 x 3
d₁ = 150 km
d₂ = v₂ x t₂
d₂ = 60 x 2
d₂ = 120 km
So,
D = d₁ + d₂
D = 150 + 120
D = 270 km
Utilizing the S formula:
S = D/ T
S = 270 / 5
S = 54 km/hr
S = 54km/hr
Therefore, the average speed of John for the whole journey is 54km/h.
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Express the triple integral f(x, y, z)dV as an iterated integral in cylindrical coordinates for the given function f and solid region E
Evaluate the iterated integral.
f(x, y, z) = xy ZA 256-x-y? -y E == x + y ? 0
The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.
The iterated integral in cylindrical coordinates is given by:
∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz
Evaluating the integral yields:
∫∫∫f(ρ, θ, z)dV = 256π∫zdz
= 256πz²
= 256π(256 - x - y)²
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Find an expression that produces a quotation of 9 R15 . Write the expression in the box
Pls help me :,)
The numerical will be equal to 159 ÷ 16 and the polynomial will be (9x +15)/x.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
In comparison to the divisor, the dividend will be 15 times greater. It seems that you are free to select any divisor. It must be more than 15 if the divisor is totally numerical.
Numerical:
Divisor = 16,
so we have,
(9×16 +15) ÷ 16
= 159 ÷ 16
Polynomial:
The simplest divisor we can have is a single variable: x.
(9x +15)/x
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the faces of each of two fair dice are numbered 1, 2, 3, 5, 7, and 8. when the two dice are tossed, what is the probability that their sum will be an even number?
The probability that the sum will be an even number on the toss of two dice is 5/9 .
In the question ,
it is given that ,
the numbers on the faces of the dice are 1, 2, 3, 5, 7, and 8 .
the probability of getting an odd number first is = 4/6 = 2/3,
the probability of getting an even number first is = 2/6 = 1/3,
To get an even, we must get either 2 odds or 2 evens.
The probability of getting 2 odds is 4/6 × 4/6 = 16/36 .
The probability of getting 2 evens is 2/6 × 2/6 = 4/36.
If we add them together,
we get ,
= 16/36 + 4/36
= 20/36
= 10/18 = 5/9
Therefore , the required probability is 5/9 .
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What is the approximate speed of sound in the experimental medium ( speed = frequency X wavelength )
The speed will be calculated by the formula by the product of frequency and wavelength.
What is the speed of sound?The speed of sound is the distance travelled by a sound wave per unit of time as it propagates through an elastic medium. At 20 degrees Celsius, the speed of sound in air is approximately 343 metres per second or one kilometre in 2.91 seconds or one mile in 4.69 seconds.
Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
The speed of the sound will be calculated by the multiplication of frequency and wavelength.
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Bro please help and tell me how to do this with the steps!
For ΔDEF , Length of shorter side = 6, Length of medium side = 8 , Length of longer side = 12.
For ΔGHI , Length of shorter side = 9, Length of medium side = 12 , Length of longer side = 18.
For ΔJKL , Length of shorter side = 3/2, Length of medium side = 2 , Length of longer side = 3.
What are Similar Triangles ?
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.
In the given figure below, two triangles ΔABC and ΔXYZ are similar only if,
i) ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
ii) AB/XY = BC/YZ = AC/XZ (Similar triangles proportions)
Hence, if the above-mentioned conditions are satisfied, then we can say that ΔABC ~ ΔXYZ
It is interesting to know that if the corresponding angles of two triangles are equal, then such triangles are known as equiangular triangles. For two equiangular triangles we can state the Basic Proportionality Theorem (better known as Thales Theorem) as follows:
For two equiangular triangles, the ratio of any two corresponding sides is always the same
Given that ,
For ΔABC , Length of shorter side = 3, Length of medium side = 4 , Length of longer side = 6.
Now,
For ΔDEF ,
Scale Factor = 2
Length of shorter side = 2*3 = 6, Length of medium side =2*4 = 8 , Length of longer side =2*6 = 12.
For ΔGHI ,
Scale Factor = 3
Length of shorter side = 3*3 = 9, Length of medium side =3*4 = 12 , Length of longer side =3*6= 18.
For ΔJKL ,
Scale Factor = 1/2
Length of shorter side =3*1/2 = 3/2, Length of medium side =4*1/2= 2 , Length of longer side =6*1/2= 3.
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What is the value of x?
Enter your answer in the box.
x =[ ]
Answer:
(2x+2)=(3x-52)
2x+2=3x-52
2x-3x=-52-2
-x=-54
x=54