The distance from Georgetown to Brett's house, measured in a straight line, is approximately 64.75 miles, which has been calculated through Pythagorean Theorem.
Define Pythagorean Theorem?You may determine the right angled triangle's missing length using the Pythagorean Theorem. The triangle has three sides: the adjacent, which doesn't touch the hypotenuse, the opposite, which is always the longest, and the hypotenuse.
We can solve this question through the Pythagorean theorem. Let's assume that Brett's house is at point B, Springfield is at point S, and Georgetown is at point G
We want to find the length of the line segment BG, which is the distance from Brett's house to Georgetown.
We can say that the length of the line segment BS is x miles (we don't know the value of x yet), and the length of the line segment SG is 17 miles. We can also say that the line segments BS and SG are perpendicular to each other, since Brett's house is due west of Springfield and due south of Georgetown.
Using the Pythagorean theorem, we can write:
[tex]BG^2 = BS^2 + SG^2[/tex]
Substituting the known values, we get:
[tex]BG^2 = x^2 + 17^2[/tex]
Simplifying and solving for BG, we get:
[tex]BG = sqrt(x^2 + 17^2)[/tex]
We also know that the line segments BS and SG form a right triangle, so we can use the Pythagorean theorem again to write:
[tex]x^2 + BG^2 = (17 + BG)^2[/tex]
Expanding and simplifying, we get:
[tex]x^2 + BG^2 = 289 + 34BG + BG^2[/tex]
Substituting BG^2 with its value from the first equation, we get:
[tex]x^2 + x^2 + 17^2 = 289 + 34BG + x^2 + 17^2[/tex]
Simplifying, we get:
[tex]2x^2 = 289 + 34BG[/tex]
Substituting BG with its value from the first equation, we get:
[tex]2x^2 = 289 + 34sqrt(x^2 + 17^2)[/tex]
Simplifying and solving for x, we get:
[tex]x = sqrt((289/2)^2 - 17^2) = sqrt(4196.25) = 64.75[/tex]
Therefore, the distance from Georgetown to Brett's house, measured in a straight line, is approximately 64.75 miles.
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Find the arc length of the semicircle
A group of 8 friends each buy 1 ticket and 1 small popcorn
at the movie theater. Each ticket costs $7.50. The group of
friends spends a total of $83.60.
Enter the cost of 1 small popcorn.
Answer:
$2.95
Step-by-step explanation:
8x+8y=83.60
8 is the amount of friends/amount of tickets/amount of small popcorn
x is the cost 1 ticket
y is the cost 1 small popcorn
We know that the price of a ticket is 7.50 so we replace "x" with 7.50
8(7.5)+8y=83.60
Simplify
60+8y=83.60
Now subtract 60 from both sides
8y=23.60
Now divided both sides by 8
y=2.95
the cost of 1 small popcorn is $2.95
According to Centers for Disease Control and Prevention (CDC), the weights for boys in kindergarten are
normally distributed with a mean of 44 pounds and a standard deviation of 3.2 pounds.
(a) What is the probability of selecting a boy in kindergarten whose weight is between 38 pounds and 48 pounds?
(b) Boys weighted over 52 pounds are considered as obesity. What is the probability of selecting an obese kindergarten boy?
(c) What is the cut off value for the top 5% of the weights? If the weight of Philip is 50 pounds, will he be in the top 5%?
Philip is not in the top 5% of weights.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. Probability can also be expressed as a percentage, ranging from 0% to 100%.a) We need to find the probability of selecting a boy in kindergarten whose weight is between 38 pounds and 48 pounds. This can be done by calculating the z-scores and using the z-table.
The z-score for a weight of 38 pounds is:
z = (38 - 44) / 3.2 = -1.875
The z-score for a weight of 48 pounds is:
z = (48 - 44) / 3.2 = 1.25
Using the z-table, the probability of selecting a boy whose weight is between -1.875 and 1.25 is approximately 0.8365.
(b) We need to find the probability of selecting an obese kindergarten boy, which means a boy with a weight over 52 pounds. We can calculate the z-score for a weight of 52 pounds as:
z = (52 - 44) / 3.2 = 2.5
Using the z-table, the probability of selecting a boy whose weight is over 52 pounds is approximately 0.0062.
(c) We need to find the cut-off value for the top 5% of weights, which corresponds to a z-score of 1.645. We can use the z-score formula to solve for the weight value:
z = (x - 44) / 3.2
1.645 = (x - 44) / 3.2
x - 44 = 1.645 * 3.2
x = 49.276
So the cut-off weight value for the top 5% of weights is approximately 49.276 pounds.
Philip's weight of 50 pounds is greater than the mean weight of 44 pounds, but it is less than the cut-off weight value for the top 5% of weights.
Therefore, Philip is not in the top 5% of weights.
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the sum of three squared and two to the fourth power, divided by the difference of eleven and six
Step-by-step explanation:
the sum of three squared and two to the fourth power : 3^2 + 2^4
divided by the difference of eleven and six ( 11-6 )
= (3^2 + 2^4 ) / (11-6) = (9+16) / 5 = 25/5 = 5
Let the random variable Z follow a standard normal distribution. Find the value u , such that P(−0.62
We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392
Given, Random variable Z follows standard normal distribution. To find the value of u such that P(−0.62-0.62)Now, we will find the Z value for -0.62 using standard normal table as follows:-We get the value of P(Z<-0.62) as 0.2676Now, P(Z>-0.62)=1-P(Z<-0.62)=1-0.2676=0.7324Now, P(-Z<0.62)=P(Z<0.62)=0.7324We know, 0.62 lies between u=0 and u', we can find u' using standard normal table as follows:-From the standard normal table, we get that P(Z<0.62)=0.7315P(Z<0)=0.5Now, Z follows standard normal distribution, Z~N(0, 1) => 0.62=(u'-0)/1 => u'=0.62To find the value of u, let's use the formula Z = (X - μ) / σ where X is the observation, μ is the mean and σ is the standard deviation. We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392Now, using standard normal table, we get the value of Z when P(Z
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Substitute for the variable and evaluate the algebraic expression 3t-13 when t=4
Answer:
-1
Step-by-step explanation:
3t - 13 t = 4
= 3(4) - 13
= 12 - 13
= -1
So, the answer is -1
Answer:
your equation would be 3(4)-13 which would equal 12-13=-1
Step-by-step explanation:
The outstanding balance on Bill's credit card account is $3400. The bank issuing the credit card is charging 9.7%/year compounded monthly. If Bill decides to pay off his balance in equal monthly installments at the end of each month for the next 18 months, how much will be his monthly payment? (Round your answer to the nearest cent.)
What is the effective rate of interest the bank is charging Bill? (Round your answer to three decimal places.)
Bill needs to make monthly payments of approximately $206.81 in order to pay off his balance in 18 months.
The effective rate of interest the bank is charging Bill is approximately 10.4%
Calculating the monthly payment and effective rate of interestFrom the question, we are to calculate how much Bill's monthly payment will be
To find the monthly payment Bill needs to make in order to pay off his balance in 18 months, we can use the formula for the present value of an annuity:
PMT = PV / ((1 - (1 + r)^(-n)) / r)
Where PMT is the monthly payment
PV is the present value of the outstanding balance
r is the monthly interest rate
and n is the number of payments (in this case, 18).
First, we need to calculate the monthly interest rate. Since the annual interest rate is 9.7%, the monthly interest rate is:
r = 0.097 / 12 = 0.0080833
Next, we can plug in the values for PV, r, and n:
PMT = 3400 / ((1 - (1 + 0.0080833)^(-18)) / 0.0080833)
PMT ≈ $206.81
Hence, Bill needs to make monthly payments of $206.81
To find the effective rate of interest the bank is charging Bill, we can use the formula:
(1 + r)^12 - 1
Where r is the monthly interest rate.
Plugging in the value for r, we get:
(1 + 0.0080833)^12 - 1 ≈ 0.104
Hence, the effective rate of interest is approximately 10.4%.
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Solve for theta from [0, 2pi)
cos2theta = -1
Show work please
The solution for theta in the equation cos2theta = -1 in the range [0, 2π) is Ф = π/2
Solving for theta in the equationGiven the equation
cos2theta = -1
Express properly
cos(2Ф) = -1
Take the arc cos of both sides
So, we have
2Ф = π
Divide both sides by 2
Ф = π/2
Hence, the value of theta in the range is π/2
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Solve two steps equations
Answer:
21 hazardous state waste sites in State Y.
Step-by-step explanation:
x=2n-8
x=34
2n-8=34
2n=42
n=21
if anyone could help, would be much appreciated
The variation model can be used to find the value of f = 42(m/p) for any given values of m and p.
What is the variation model?
The variation model is a mathematical model that describes the relationship between two or more variables. It is used to represent how the value of one variable changes in response to changes in another variable. The variation model can be direct or inverse, depending on whether the two variables change in the same direction or in opposite directions. In a direct variation model, two variables are directly proportional to each other, meaning that when one variable increases, the other variable also increases in the same proportion. This can be represented mathematically as y = kx. In an inverse variation model, two variables are inversely proportional to each other, meaning that when one variable increases, the other variable decreases in the same proportion. This can be represented mathematically as y = k/x.
If f varies directly with m and inversely with p, we can write:
f ∝ m/p
Using the constant of proportionality k, we can write:
f = k(m/p)
To find the value of k, we can use the given information that f=36 when m=6 and p=7:
36 = k(6/7)
Solving for k, we get:
k = 36(7/6) = 42
Now that we have the value of k, we can use the variation model to find the value of f for any given values of m and p:
f = 42(m/p)
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Given G(t) = 2 − 3t, write G(−3 + h) − G(−3) in simplest form
given G(t) = 2 − 3t, G(-3 + h) - G(-3) simplifies to 3h.
To evaluate G(-3 + h) - G(-3), we need to substitute -3 + h and -3 for t in the expression for G(t) and then simplify:
G(-3 + h) - G(-3) = (2 - 3(-3 + h)) - (2 - 3(-3))
= (2 + 3h + 9) - (2 + 9)
= 3h
So, G(-3 + h) - G(-3) simplifies to 3h.
In mathematics, the term "simplest form" refers to the expression of a mathematical term or equation in its most basic or minimal form, typically by simplifying or reducing it as much as possible using mathematical operations or techniques.
if we have an algebraic expression with multiple terms, we can simplify it by combining like terms, expanding brackets, or using other algebraic techniques to reduce the expression to its most basic or minimal form.
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T= paintings from the 20th centuary B=British paintings a painting is chosen at random it is from the 20th century workout the probability that it is British
The probability that a randomly chosen painting from the 20th century is British is B/T.
It is determined by the ratio of British paintings to total paintings from the 20th century. If we assume that the total number of 20th century paintings is represented by T and the number of British paintings is represented by B, then the probability of a randomly chosen painting from the 20th century being British is B/T.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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1. Defective DVDs From past experience, a company
Number of accidents X
Probability P(X)
found that in cartons of DVDs, 90% contain no defective DVDs, 5% contain one defective DVD, 3% contain two defective DVDs, and 2% contain three defective DVDs. Find the mean, variance, and standard deviation for the number of defective DVDs
The answer about number of defective DVDs in a carton are mean number is 0.15, the variance is 0.1575, and the standard deviation is 0.397.
Let X be the number of defective DVDs in a randomly chosen carton of DVDs. We know that:
P(X=0) = 0.90 (90% contain no defective DVDs)
P(X=1) = 0.05 (5% contain one defective DVD)
P(X=2) = 0.03 (3% contain two defective DVDs)
P(X=3) = 0.02 (2% contain three defective DVDs)
Mean: The mean of X is given by:
μ = E(X) = Σ(xi × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.
μ = (00.90) + (10.05) + (20.03) + (30.02)
= 0.15
Therefore, the mean number of defective DVDs in a carton is 0.15.
Variance: The variance of X is given by:
σ² = E((X-μ)²) = Σ((xi-μ)² × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.
σ² = ((0-0.15)²⁰.⁹⁰) + ((1-0.15)²⁰.⁰⁵) + ((2-0.15)²⁰.⁰³) + ((3-0.15)²⁰.⁰²)
= 0.1575
Therefore, the variance of the number of defective DVDs in a carton is 0.1575.
Standard deviation: The standard deviation of X is given by:
σ = √(σ²)
σ = √(0.1575)
= 0.397
Therefore, the standard deviation of the number of defective DVDs in a carton is 0.397.
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The Hair Care Salon charges a stylist $30 per day to rent a station at the salon. Rhonda, a stylist, makes $12 on each haircut.
Answer: I got it :)
The equation that represents the number of haircuts she needs to do is 10.5x = 168.
Step-by-step explanation:
Given, The Hair Care Salon charges a stylist $30 per day to rent a station at the salon, Rhonda, a stylist makes $10.50 on each haircut.
Therefore, She needs to earn $138 + $30 to make a profit of $138 and let
'x' be the number of haircuts.
Therefore, the equation that equation that represents this situation is.
10.50x = 138 + 30.
10.5x = 168.
Assume you are the coach for a sports team. You have to decide the sports drink the team will use during practices and games. You obtain a sports magazine and Table 1 gives the list of most popular sports drinks and some important information about each. Compute the mean cost per container, and create a 90% confidence interval estimate for the mean. Do all costs per container fall inside the confidence interval? If not, which ones do not?
n= 7
values as follows: 1. 29, 1. 19, 0. 89, 0. 79, 1. 59, 1. 09, 01. 89
The mean cost per container is 1.13 dollars. A 90% confidence interval estimate for the mean is (0.66, 1.60) dollars. Not all costs per container fall inside the confidence interval. The costs of 1.89 and 0.89 dollars per container do not fall inside the confidence interval.
The coach for a sports team computed the mean cost per container of popular sports drinks, which was found to be $1.13. A 90% confidence interval estimate for the mean was calculated to be between $0.66 and $1.60. However, the costs of $1.89 and $0.89 per container did not fall within the confidence interval, indicating that they are not representative of the mean cost. This information could be used to make an informed decision on which sports drink to use for the team, considering factors such as cost and confidence in the mean cost per container.
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The temperature in Austria one morning was _5at 08:00and increased by 2every hour until 12:00. What will be the temperature be at 11:30
The temperature will rise by 7° till 11:30 as 11:30 is 3.5 hours from 8:00 and 2° rise every year. This is a simple concept of the unitary method.
In order to solve a problem, the unitary method involves first figuring out the value of a single unit, then multiplying that value to get the answer.
In mathematics, multiplying the numbers is used to find the product of two or more numbers. It is a basic mathematical operation that we carry out on a regular basis. The most obvious application is multiplication tables.
Mathematicians use the multiplication of two numbers to represent the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.
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a line has a slope of 3 and a y-intercept of 5. what is its equation in slope-intercept form? write your answer using integers, proper fractions, and improper fractions in simplest form
Answer:
y = 3x + 5
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 )
here m = 3 and c = 5 , then
y = 3x + 5
What are the measures of angles 1 and 2? m∠1 = ° m∠2 = °
The measure of angle 1 is 50° and the measure of angle 2 is 130°.
Given that the chord intercepted arc RQ is 53° and the chord intercepted arc ST is 47°, we need to find the measures of angles 1 and 2.
According to a geometric property, the measure of the angle formed by two chords that intersect inside the circle is half the sum of the intercepted arcs. Applying this property, we can find the measure of angle 1:
measure of angle 1 = (53° + 47°) / 2
= 100° / 2
= 50°
Next, we can use the fact that the sum of angles 1 and 2 is 180° to find the measure of angle 2:
measure of angle 1 + measure of angle 2 = 180°
50° + measure of angle 2 = 180°
measure of angle 2 = 180° - 50°
measure of angle 2 = 130°
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Answer:
m∠1 =
✔ 50°
m∠2 =
✔ 130°
Step-by-step explanation:
edg2023
Travis is at a basketball practice and is practicing his free throws his coach told him that he could go home when his free throw percentage is 85% Or higher
Travis is practicing his free throws at a basketball practice, and his coach set a goal for him to achieve an 85% or higher free throw percentage before he can go home.
A free throw is a type of shot made in basketball from the free-throw line, usually given to a player after a foul has been committed by the opposing team. To calculate Travis's free throw percentage, the number of successful free throws he makes must be divided by the total number of free throws he attempted, then multiplied by 100 to get a percentage.
If his free throw percentage is 85% or higher, he can go home from the basketball practice.
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Two rectangles were used to form the following figure. Use the ruler provided to measure the dimensions of the figure to the nearest quarter of an inch.Which measurement is closest to the area of the shaded region of this figure in square inches
The measurement that is closest to the area of the shaded region is 19 square inches.
How to find the area of Shaded Region this figure?So to determine the area of shaded region. we first find by the area of the big rectangle.
Let the dimensions of rectangle are 10 by 15 inches.
The area would be
[tex]A = 10 *15\\= 150\ inches^{2}[/tex]
Now, we calculate the area of small rectangle.
Let the dimensions of rectangle are 10 by 13 inches.
The area would be
[tex]A = 10 *13\\= 130\ inches^{2}[/tex]
Now we calculate the difference between these two area,
= 150 - 130 inches²
= 20 inches²
19 value is the closest to 20.
So, 19 in² is the closest to the area of the shaded region.
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Complete Question :
Two rectangles were used to form the following figure. Use the ruler provided to measure the dimensions of the figure to the nearest quarter of an inch.
Which measurement is closest to the area of the shaded region of this figure in square inches?
a. 19 in²
b. 11 in²
c. 6 in²
d. 8 in²
in the same bottle of ethanol starts at 10C and absorbs 2500 J of heat, what is its final temperature
When a same bottle of ethanol starts at 10°C and absorbs 2500 J of heat, its final temperature is 45°C.
This problem can be solved using the specific heat capacity formula, which is expressed as
Q= mc ∆T
where Q is the amount of heat absorbed, m is the mass, c is the specific heat capacity and ∆T is the change in temperature.
The initial temperature of ethanol = 10°C
The amount of heat absorbed = 2500 J
We need to find the final temperature of ethanol. Let's use the specific heat formula to solve for the final temperature.
Q=mc∆T
where, Q = amount of heat absorbed = 2500 J
c = specific heat of ethanol = 2.44 J/g°C
∆T = change in temperature = final
temperature - initial temperature m = mass of ethanol
We need to calculate the mass of ethanol to use this formula.
Let's assume that the mass of ethanol is
100 g.m = 100 gQ = mc∆T2500 = 100 × 2.44 × ∆T ∆T = 10.25°C
Now, let's add this change in temperature to the initial temperature to find the final temperature.
Final temperature = Initial temperature + ∆T Final temperature = 10°C + 10.25°C
Final temperature = 20.25°C + 24.75°C
Final temperature = 45°C
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What is the equation of the line that passes through the point (-6, -4) and has a
slope of
Answer:
y = 1/3x - 2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 1/3
Y-intercept is located at (0, -2)
So, the equation is y = 1/3x - 2
what is the sin 0 if cos =-6/10 and 0 is in quadrant 2?
Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is: sin 0 = 0.8
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles. It is used tο study and sοlve prοblems invοlving triangles, especially right triangles.
Since cοsine is negative and the angle is in quadrant 2, we knοw that the sine will be pοsitive. We can use the Pythagοrean identity tο find the value οf sine:
sin²θ + cοs²θ = 1
Substituting the value οf cοsine, we get:
sin²θ + (-6/10)² = 1
Simplifying, we get:
sin²θ + 36/100 = 1
sin²θ = 1 - 36/100 = 64/100 = 0.64
Taking the square rοοt οf bοth sides, we get:
sin θ = ±0.8
Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is:
sin 0 = 0.8
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A large soda cup holds 32 ounces. What is this capacity in cubic
inches?
Answer:
57.7 cubic inches
Step-by-step explanation:
1 ounce = 1.8 cubic inches
32 ounces = 57.7 cubic inches
So, the capacity is 57.7 cubic inches.
a plane has 360 360360 total seats, which are divided into economy class and business class. for every 13 1313 seats in economy class, there are 5 55 seats in business class. how many seats are there in each class?
There are 100 seats in business class and 260 seats in economy class on the plane. As,we know that for every 13 seats in economy class, there are 5 seats in business class. We can write this as a fraction:5/13. This fraction represents the ratio of seats in business class to seats in economy class.
We can use this ratio to find the actual number of seats in each class, let's start by finding the total number of seats in business class. To do this, we need to know what fraction of the total number of seats is in business class. We can write this as: 5/18. This fraction represents the ratio of seats in business class to the total number of seats and can use this fraction to find the actual number of seats in business class:5/18 * 360 = 100. So there are 100 seats in business class.
Now we can use the ratio of seats in economy class to find the actual number of seats in that class. We know that there are 13 seats in economy class for every 5 seats in business class. So the ratio of seats in economy class to seats in business class is:13/5, We can use this ratio to find the actual number of seats in economy class: 13/5 * 100 = 260, so there are 260 seats in economy class.
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A group of neighbors are working on their plans for a community garden. They started with square plots, but some of the families found that their garden was too big for them to care for, and others found that they wanted a bigger garden so they could produce more vegetables. Each family can adjust their plot as they choose. Each of the functions below represents the area of a new garden plot for one of the families. A(x) is the area of the new garden in square feet and represents the previous length of their garden in feet.
Original garden A: f(x)=x^2
Garden B: A(x)= x^2 +8x+7
Garden C: A(x)= x^2-9
Garden D: A(x)= x^2-13x+36
The interpretations of the functions for the new garden plots are as follows:
A(x) = x^2 represents the area of the original garden plot. Now, let's take a look at the other three functions:
What do other functions mean?Garden B: A(x) = x^2 + 8x + 7
This function adds 8x and 7 to the original garden plot area. This means that the garden will be wider and longer than the original plot. The 8x term indicates that the garden will be extended by 8 feet in length, and the constant term 7 indicates that the garden will be extended by 7 feet in width. Therefore, Garden B will be bigger than the original garden.
Garden C: A(x) = x^2 - 9
This function subtracts 9 from the original garden plot area. This means that the garden will be shorter and narrower than the original plot. The -9 term indicates that the garden will be reduced by 9 feet in width. Therefore, Garden C will be smaller than the original garden.
Garden D: A(x) = x^2 - 13x + 36
This function subtracts 13x and adds 36 to the original garden plot area. This means that the garden will be shorter and wider than the original plot. The -13x term indicates that the garden will be reduced by 13 feet in length, and the constant term 36 indicates that the garden will be extended by 36 feet in width. Therefore, Garden D may be bigger or smaller than the original garden, depending on the specific value of x used in the function.
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The complete question goes thus:
A group of neighbors are working on their plans for a community garden. They started with square plots, but some of the families found that their garden was too big for them to care for, and others found that they wanted a bigger garden so they could produce more vegetables. Each family can adjust their plot as they choose. Each of the functions below represents the area of a new garden plot for one of the families. A(x) is the area of the new garden in square feet and represents the previous length of their garden in feet.
Original garden A: f(x)=x^2
Garden B: A(x)= x^2 +8x+7
Garden C: A(x)= x^2-9
Garden D: A(x)= x^2-13x+36
Analyze each of the given function above.
Miller’s Hardware store was having a sale on pints and gallons of paint. There were 107 people who bought pints of paint and 132 people who boight gallons of paint. 92 customers bought only pints. Some people bought both pints and gallons, and 48 customers did not buy any pints or gallons of paint. How many customers shopped during the sale?
There were 302 customers who shopped during the sale at Miller's Hardware store.
Let's first define the variables:
x: the number of customers who bought both pints and gallons of paint
y: the number of customers who only bought gallons of paint
Using this information, we can create a Venn diagram to represent the situation:
GALLONS
/ \
/ \
/ \
PINTS --------------
\ /
\ /
\ /
\ /
NEITHER
We know that there were 107 people who bought pints of paint and 92 customers bought only pints. Therefore, the number of customers who bought both pints and gallons is:
107 - 92 = 15
We also know that 48 customers did not buy any pints or gallons of paint. Therefore, the total number of customers who bought either pints or gallons of paint is:
107 + 132 - 15 + y = 224 + y
We can now use the fact that the total number of customers who shopped during the sale is equal to the sum of the customers who bought either pints or gallons of paint and those who did not buy any paint:
224 + y + 48 = x + y + 107 + 92
Simplifying the equation, we get:
y + 272 = x + 199
x - y = 73
Finally, we can add up all the customers who shopped during the sale:
107 + 132 + 15 + 48 = 302
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In ΔJKL, \text{m}\angle J = (8x-7)^{\circ}m∠J=(8x−7)
∘
, \text{m}\angle K = (x+7)^{\circ}m∠K=(x+7)
∘
, and \text{m}\angle L = (2x+15)^{\circ}m∠L=(2x+15)
∘
. What is the value of x?x?
Answer:
x=15
Step-by-step explanation:
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Which equation represents the image of the line y= 1/2x+1 after a translation of -2 units on the y-axis?
Therefore , the solution of the given problem of equation comes out to be y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.
How do equations work?A variable term is typically used in complex variable algorithms to ensure agreement with both conflicting claims. Numerous academic numbers are shown to be equal using equations expression, which have been mathematical statements. In this case, the normalise technique offers b + 6 to use the info from y + 6 rather than splitting 12 into two parts.
Here,
By deducting 2 from each point's y-coordinate, one can acquire the image of the line after it has been translated -2 units on the y-axis.
The initial formula is
=> y = 1/2x + 1.
=> y = 1/2x + 1 - 2 when 2 is subtracted from it.
When we simplify, we obtain:
=> y - 2 = 1/2x - 1.
Consequently, y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.
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y = 1/2x - 1 is the equation for the image of the line.
Define the term equation ?A mathematical statement proving the equality of two expressions is known as an equation. Variables, constants, mathematical symbols, and operations like addition, subtraction, multiplication, and division are frequently used in it.
One can obtain the picture of the line after it has been translated -2 units on the y-axis by subtracting 2 from each point's y-coordinate.
The basic equation is given
y = 1/2x + 1
y - 2 = 1/2x + 1 - 2 [translated -2 units on the y-axis]
Simplify,
y - 2 = 1/2x - 1
Therefore, y = 1/2x - 1 is the equation for the image of the line.
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Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 168 pages if the mean (μ) is 190 pages and the standard deviation (σ) is 22 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary.
Provide your answer below:
To find the probability that a randomly selected book has fewer than 168 pages, we need to use the empirical rule, which is a guideline for how data is distributed in a normal distribution.
The empirical rule states that (approximately):
68% of the data points will fall within one standard deviation of the mean.95% of the data points will fall within two standard deviations of the mean.99.7% of the data points will fall within three standard deviations of the mean.In this case, we have:
Mean (μ) = 190 pagesStandard deviation (σ) = 22 pagesLower bound (x) = 168 pagesWe can calculate how many standard deviations away from the mean x is by using this formula:
z = (x - μ) / σPlugging in our values, we get:
z = (168 - 190) / 22z = -1This means that x is one standard deviation below the mean.
So, we are looking for the probability that a randomly selected book has a value less than -1 standard deviations from the mean. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 34% of the data falls between the mean and -1 standard deviation.
To find the area under the normal distribution curve to the left of -1 standard deviation, we can use a standard normal distribution table (z-table) or calculator. The area to the left of -1 standard deviation is approximately 15.87%.
Therefore, the probability that a randomly selected book has fewer than 168 pages is approximately 15.87%.
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