The 11th term in the arithmetic sequence 13, 19, 25, 31 is 73.
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed number called the common difference (d) to the preceding term.
According to given information:To find the 11th term in the arithmetic sequence 13, 19, 25, 31, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where:
an is the nth term
a1 is the first term
n is the number of the term we want to find
d is the common difference
In this sequence, the first term (a1) is 13 and the common difference (d) is 6 (we can see that by subtracting each term from the one before it). So we can plug in the values we know:
a11 = 13 + (11 - 1)6
a11 = 13 + 60
a11 = 73
Therefore, the 11th term in the sequence 13, 19, 25, 31 is 73.
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what is the probability that the sample mean for a sample of size 45 will be less than 34.5? use the results from above in your calculation and round your answer to the nearest percent.
To calculate the probability that the sample mean for a sample of size 45 will be less than 34.5, we can use the Central Limit Theorem (CLT).
The CLT states that, given a large enough sample size, the distribution of the sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Step 1: Identify the population mean (μ) and population standard deviation (σ) from the given information. Since it is not provided in the student question, I will assume that you have already calculated these values.
Step 2: Calculate the standard deviation of the sample mean (σ_sample_mean). This can be done using the formula:
σ_sample_mean = σ / √n
where n is the sample size (45 in this case).
Step 3: Convert the sample mean (34.5) into a z-score using the formula:
z = (x - μ) / σ_sample_mean
where x is the sample mean and μ is the population mean.
Step 4: Use the standard normal distribution table (also known as the z-table) or a calculator to find the probability associated with the calculated z-score. This probability represents the chance that the sample mean will be less than 34.5.
Step 5: Round the probability to the nearest percent.
Following these steps will give you the probability that the sample mean for a sample of size 45 will be less than 34.5, based on the information provided in the question.
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Express the trig ratios as fractions in simplest terms.
Help asap please!!!’
Step-by-step explanation:
In a right triangle such as this cos R will equal the other angle' s Sin
so cos R = sin S
= 24/51
the germination rate is the rate at which plants begin to grow after the seed is planted. a seed company claims that the germination rate for their seeds is 90 percent. concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. what are the
The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9
A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.
The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.
Complete Question:
The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.
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HELP ME PLEASEEE!!!
Answer:
3
Step-by-step explanation:
And also,PLEASE DONT YELL AT ME/US!!
simplify the square root 0.2 squr 25y^2 if y<0
b) squr 1/16x^2 if x greater then or equal to 0
The simplified expression for expression √0.2 × √25y² will be √5|y| and for 1/16x² if x is greater than or equal to 0 simplified expressions will be (1/4)x.
a) Simplifying the expression √0.2 × √25y² using the properties of square roots, we get:
= √0.2 × √25y²
= √(0.2 × 25 × y²)
= √(5y²)
= √5 × √y²
= √5 × |y|
Since y<0, we need to take the absolute value of y to ensure that the result is positive. Therefore, the simplified expression is √5|y|.
b) Simplifying the expression √(1/16 x²), we get:
= √(1/16 x²)
= (1/4) √(x²)
= (1/4) |x|
Since x≥0, we do not need to take the absolute value of x. Therefore, the simplified expression is (1/4)x.
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Find the area of the remaining pizza that has an angle of 7π/4
and a radius of 6 inches.
[tex]\textit{area of a sector of a circle}\\\\ A=\theta\cdot \cfrac{ r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{4}\\[1em] r=6 \end{cases}\implies A=\cfrac{7\pi }{4}\cdot \cfrac{6^2}{2} \\\\\\ A=\cfrac{63\pi }{2}\implies A\approx 98.96~in^2[/tex]
Look at the pattern below.
step 1 with 1 square
step 2 with 3 squares
step 3 with 6 squares
step 4 with 10 squares
How does the pattern grow at each step?
Choose 1 answer:
Answer: The pattern grows by adding the consecutive counting numbers starting from 1.
For example:
Step 1: 1 square
Step 2: 1 + 2 = 3 squares
Step 3: 1 + 2 + 3 = 6 squares
Step 4: 1 + 2 + 3 + 4 = 10 squares
So at each step, the number of squares increases by adding the next consecutive counting number.
Step-by-step explanation:
Multiply polynomials
HELP I NEED THIS ASAP
Answer:
6x^3-5x^2+9x+10
Step-by-step explanation:
Use the distributive property and multiply like terms.
Please Help if you can there’s this is 1 of 14 parts
By using the graph of the function shown above, the solution include the following:
f(-7) = -6.
f(-3) = 9.
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
This ultimately implies that, an input value (x-value) represents the value on the x-axis of a cartesian coordinate while an output value (y-value) represents the value on the y-axis of a cartesian coordinate.
Based on the information provided about this function, an ordered pair that models the situation is given by;
f(-7) = -6 ⇒ Ordered pair (-7, -6).
f(-3) = 9 ⇒ Ordered pair (-3, 9).
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A 6-inch candle burns down in 8 hours. how far has it burned after 7 1/2 hours?
Answer:
5.625 inches
Step-by-step explanation:
We Know
A 6-inch candle burns down in 8 hours.
6 / 8 = 0.75 inches burn down per hour
So, we know 0.75 inches burn down per hour
How far has it burned after 7 1/2 hours?
We take
0.75 x 7.5 = 5.625 inches
So, it burned 5.625 inches after 7 1/2 hours.
Please help, its urgent! its my practice test
The graph with all the solutions can be seen in the image at the end of the answer.
How to solve the quadratic equations?We want to solve the 3 quadratic equations and then graph them in a coordinate axis.
Remember that for a complex number z = a + bi, the real part a goes in the horizontal axis and the complex part b goes in the vertical axis.
a) We start with:
m² = 16
m = √16
m = ±4
b) x² = -9
x = ±√-9
x = ±3i
c) t² = -25
t = ±√-25
t = ±5i
The graph of all of these points can be seen in the image at the end.
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Please help me, only 20 points if answered !!
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ s=\pi \end{cases}\implies \pi =\cfrac{\theta \pi (4)}{180}\implies \cfrac{180}{4\pi }\cdot \pi =\theta\implies 45=\theta[/tex]
sketch the graph of each function in the interval from 0 to 2π y=cos θ
Answer:
The cosine curve is a type of periodic curve that is commonly used in mathematics and physics. It is defined by the equation y=cos(x). The cosine curve is a smooth wave-like curve that has the same shape as the sine wave, but shifted by a quarter of a period. The cosine curve is used to describe cyclical phenomena, such as sound waves and light waves. In addition, it is used in trigonometry and calculus to solve complex problems.
Marissa selects a card in a hat, notes which color it is, returns the card to the hat, and repeats. The results of 70 trials are 12 red cards, 38 green cards, and 20 purple cards. What are the experimental probabilities of selecting each color, based on these results?
Probability of selecting a red card=
Probability of selecting a green card=
Probability of selecting a purple card=
Answer:
Red=17.1%
Green=54.3%
Purple=28.6%
All of these answers are rounded.
Step-by-step explanation:
To solve for all, all you have to do is divide the number of trials of the specific color by the total number of trials. To get a percentage you then multiply by 100%.
Red:
12/70=0.171*100%=17.1%
Green:
38/70=0.543*100%=54.3%
Purple:
20/70=0.286*100%=28.6%
To check if you've rounded correctly, add all your values and they should add up to 100 exactly. If it is slightly over or below you may need to go back and check for a rounding error.
of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. how many of the students earned a c for the course?
Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.
To find the number of students who earned a C in the course, we'll follow these steps:
1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.
We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.
Now let's perform the calculations:
Step 1: We know that the total number of students is 180.
Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:
41 (A students) + 3 (B students) = 44 (A and B students)
Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):
180 (total students) - 44 (A and B students) = 136 (C students)
So, 136 students earned a C for the course.
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Nine students were asked how many minutes they worked on math homework each night the results are shown 20 60 50 30 40 35 30 75 20 what are the mean and the median number of minutes spent on math homework each night
Answer:
the median number of minutes spent on math homework each night is also 40.
the mean number of minutes spent on math homework each night is 40.
in 1960, there were 450,000 cases of measles reported in the u.s. in 1996, there were 500 cases reported. how many cases of measles would have been reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly?
We can estimate that around 205,313 cases of measles would have been reported in the U.S. in 1987 if the number of cases reported from 1960 to 1996 decreased linearly.
To estimate the number of measles cases reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly, we need to use a linear regression model. Linear regression is a statistical method that allows us to estimate the relationship between two variables by fitting a straight line to a set of data points.
In this case, we can use the number of reported measles cases as the dependent variable (y) and the year as the independent variable (x). We can then fit a linear regression line to the data from 1960 to 1996 and use this line to estimate the number of cases in 1987.
Assuming a linear relationship between the number of cases and the year, we can calculate the slope of the regression line as follows:
slope = (500 - 450,000) / (1996 - 1960) = -10,125
This means that the number of reported measles cases decreased by 10,125 per year, on average, between 1960 and 1996.
Using this slope and the known values for 1960 and 1996, we can estimate the number of cases in 1987 as follows:
y = mx + b
where y is the number of cases, m is the slope, x is the year (1987), and b is the y-intercept of the regression line.
We can solve for b as follows:
b = y - mx
where y is the number of cases in 1996, m is the slope, and x is the year (1996).
Substituting in the values, we get:
b = 500 - (-10,125) * 1996 = 20,503,500
Therefore, the equation of the regression line is:
y = -10,125x + 20,503,500
Substituting x = 1987, we get:
y = -10,125 * 1987 + 20,503,500 = 205,313
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Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?
WRONG ANSWER = REPORTED
Answer:
47/60
Step-by-step explanation:
You want to know the probability of a randomly selected student is on the honor roll or varsity team when 176 of 240 students are on the honor roll, 48 are on the varsity team, and 36 are on both.
One or the otherThe probability of A or B is ...
P(A+B) = P(A) +P(B) - P(A·B)
The probability of interest is ...
P(honor roll + varsity) = P(honor roll) + P(varsity) - P(honor roll & varsity)
P(honor roll + varsity) = 176/240 +48/240 -36/240 = (176 +48 -36)/240
= 188/240 = 47/60
The probability of interest is 47/60.
[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
The probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex][tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]
We can use the inclusion-exclusion principle to find the number of students who are on the honor roll or are members of the varsity team.
This principle states that:
[tex]\sf |A\cup B| = |A| + |B| − |A\cap B|[/tex]where:
A and B are sets,|A| is the cardinality (number of elements) of set A, andA∩B is the intersection of sets A and B.Using this principle, we can find that:
[tex]\begin{aligned}\sf |Honors\cup Varsity|& =\sf |Honors| + |Varsity| − |Honors\cap Varsity|\\& =\sf 176 + 48 - 36\\& =\sf\red{188}\end{aligned}[/tex]
Therefore, there are 188 students who are on the honor roll or are members of the varsity team.
The probability that a randomly selected student is on the honor roll or is a member of the varsity team is then:
[tex]\begin{aligned}\sf P(Honors\cup Varsity)& =\sf \dfrac{|Honors\cup Varsity|}{|Total|} \\ &=\sf \dfrac{188}{240} \\&=\boxed{\bold{\: \dfrac{47}{60}\:}}\end{aligned}[/tex]
Therefore, the probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex]
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]
These two maps show the same area at two different scales.
Columbus is not on Map A
Map B does not have a scale written on it.
Riverside and Gladville are 6.8 cm apart on Map A.
Riverside and Gladville are 3.4 cm apart on Map B.
Gladville and Columbus are 1.8 cm apart on Map B.
Determine the straight line distance, in miles, from Gladville to Columbus.
The distance from Gladville to Columbus is 144 miles.
How to calculate the distanceThe scale of map B is (3.4 cm) / (6.8 cm) = 1/2 that of map A.
Then the distance (d) between the cities is:
= (1.8 cm)/d = (1/2)·(1 cm) / (40 mi)
Multiplying by d·80 mi, we get
144 mi·cm = d cm
Dividing by cm, we have ...
144 mi = d
The distance from Gladville to Columbus is 144 miles.
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I NEED HELP YALL and the work
Variable x in the circle has a value of 9.
Define circleThe radius of a circle is the distance from any point on the circle to the centre, whereas the diameter is the distance across the circle passing through the centre. The area of a circle is the volume of space inside the circle, whereas the circumference of a circle is the distance around the circle. In geometry and mathematics, circles are frequently used to investigate features including area, circumference, and angles. They are also widely used in fields including physics, engineering, and architecture.
We know that the measure of the central angle of a circle is 360°
75°+13x+91°+x+68=360°
14x=360-68-91-75
x=9
the value of variable x in the circle is 9
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find the average values of prpblck and income in the sample, along with their standard deviations. what are the units of measurement of prpblck and income?
The units of measurement for prpblck are percentage points, while the units for income are typically a currency, like dollars or euros.
To find the average value of prpblck and income in the sample, you need to sum the values for each variable and then divide by the total number of observations. The average is also known as the mean. The standard deviation is a measure of dispersion that indicates how much the values vary from the mean. To calculate the standard deviation, you will need to find the difference between each value and the mean, square those differences, find the average of those squared differences, and then take the square root of that average.
The units of measurement for prpblck and income depend on the context and data source. Typically, prpblck is expressed as a proportion or percentage, representing the proportion of the population that is black. In this case, the unit of measurement for prpblck would be percentage points. On the other hand, income is usually measured in a currency, such as dollars or euros, and it can be presented as an individual's income or a household's income.
To summarize, to find the average values and standard deviations of prpblck and income in the sample, follow these steps:
1. Calculate the mean by summing the values and dividing by the number of observations.
2. Calculate the standard deviation by finding the square root of the average of the squared differences between each value and the mean.
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Which of the following is not a method for proving triangles congruent? Select one: O a. SSA O b. SSS O c. AAS O d. SAS O e. ASA
Answer:
The answer is A
Step-by-step explanation:
The answer is A, how I learned this was making sure that any combination of a and s would not spell out a bad word! With this in mind, we know that AS$ and SSA are not valid methods for proving triangles congruent!
Hope this helps!
(I had to use a $ symbol because there was an inappropriate word)
Find the inverse of the following function: f(x)=[tex]\sqrt[3]{4x+7}[/tex]
All functions have an inverse function, and for a function to have an inverse. The inverse of [tex]f(x) = 3\sqrt(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex]
What is the inverse function?The inverse function, often known as the "inverse mapping," is a function that "undoes" another function's operation. If a function f(x) translates an input x to an output y, the inverse function f(-1)(y) transfers the result y back to the input x.
To find the inverse of the function f(x) = 3√(4x + 7), we need to solve for x in terms of y.
Step 1: Replace f(x) with y
[tex]y = 3√(4x + 7)[/tex]
Step 2: Cube both sides to eliminate the cube root
[tex]y^3 = 27(4x + 7)[/tex]
Step 3: Simplify and solve for x
[tex]y^3 = 108x + 189[/tex]
[tex]x = (y^3 - 189)/108[/tex]
Step 4: Replace x with [tex]f^-1(x)[/tex]
[tex]f^-1(x) = (x^3 - 189)/108[/tex]
Therefore, the inverse of [tex]f(x) = 3√(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex] .
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when estimating a task, what values are you likely to use? choose all that apply.group of answer choices2 days2 hours2 minutes2 sprints2 weeks
However, depending on the project, other units of time, such as minutes or sprints, may also be used.
When estimating a task, the values that are likely to be used include 2 hours, 2 days, and 2 weeks. These values are commonly used in project management for estimating the time required to complete a task.
An estimation is an approximate calculation of the time, effort, or resources required to complete a particular task or project.
It is a critical aspect of project planning, and a good estimate can help ensure that the project is completed on time and within budget. The most common time values used when estimating a task are hours, days, and weeks.
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For what value(s) of x are the following Undefined
5x^2+x+1/x^2+4
Answer:
Undefined at x = 2 and x = -2
Step-by-step explanation:
(5x²+x+11)/(x²-4)
Function becomes undefined when the denominator goes to zero.
x² - 4 = 0
x = 2, -2
Answer:
In Real numbers: none (defined for all real numbers)
In Complex numbers: not defined for [tex]x = 2i, -2i[/tex]
Step-by-step explanation:
Fraction becomes undefined when the denominator = 0
[tex]x^2 + 4 = 0[/tex]
Has no real solutions
The fraction is defined for all real values of x
[tex]x^2 + 4 = 0[/tex]
[tex]x^2 = -4[/tex]
[tex]x = 2i, -2i[/tex]
The fraction is not defined for [tex]x = \dfrac{+}{-2i}[/tex] (in Complex Numbers)
events that occur in the extremes of the normal curve have a very small probability of occurring. group of answer choices true false
The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.
The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.
So, as one moves further from the mean, the probability of occurrence decreases exponentially.
So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.
Therefore, the statement is True.
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Given: m∠KAL=100°, m∠L=25°, and OA=25
Find: AK, AL, and KL
AK = AL ≈ 28.77, KL < 57.54. In summary, the values of AK = AL ≈ 28.77 and KL < 57.54 .
What is triangles?A closed triangle is a polygon with three sides and three angles in two dimensions.
We know that the radius of the circle, OA, is 25. Since OA is a radius of the circle and bisects triangle ΔKAL, we can conclude that AK = AL.
Let's call AK = AL = x.
Now we use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle K.
We know that angle L is 25 degrees, and since angle KAL is 100 degrees, angle K must be:
K = 180 - L - KAL
K = 180 - 25 - 100
K = 55 degrees
Now, we can use the law of sines to find x, which is the length of both AK and AL:
sin(K) / x = sin(L) / OA
sin(55) / x = sin(25) / 25
x = sin(55) * 25 / sin(25)
x ≈ 28.77
Therefore, AK = AL ≈ 28.77.
To find KL, we can use the fact that AK = AL = x and OA = 25 to find OK and OL:
OK = OA - AK
OK = 25 - 28.77
OK ≈ -3.77
OL = OA - AL
OL = 25 - 28.77
OL ≈ -3.77
Since OK and OL are both negative, we know that O must be located inside triangle ΔKAL. Therefore, we can use the triangle inequality to find KL:
KL < AK + AL
KL < 2x
KL < 2(28.77)
KL < 57.54
Therefore, KL < 57.54.
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After a blizzard the amount of snow on the ground melted by 3 inches one day and then another 8 inches the next day. write an expression that represents the total change in the amount of snow on the ground over the two days.
The expression that represents the total change in the amount of snow on the ground over the two days is -3 + (-8) = -11
The problem asks for the total change in the amount of snow on the ground over two days after a blizzard. The problem states that the snow melted by 3 inches one day and 8 inches the next day. The expression that represents the total change can be found by adding the two changes together. However, since the snow is melting, we need to use negative values to represent the change. Therefore, we can write the expression as:
-3 + (-8)
Simplifying this expression, we get:
-3 - 8 = -11
Therefore, the total change in the amount of snow on the ground over the two days is -11 inches.
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A sports store sells 92 pairs of swimming flippers per day for $50 each. The owner estimates that for each $3 increase in price, 3 fewer sales are made. What price should be charged to maximize profit?
Let's start by calculating the store's revenue at the current price of $50 per pair of swimming flippers:
Revenue = Price x Quantity Sold = $50 x 92 = $4,600 per day
Now, let's see how changes in the price affect the quantity sold. According to the problem, for each $3 increase in price, 3 fewer sales are made. This means that the demand function is:
Quantity Sold = 92 - 3/3 (Price - $50) = 92 - (Price - $50)
where Price is measured in dollars.
To calculate the store's profit, we need to subtract the cost of producing each pair of swimming flippers from the revenue:
Profit = (Price - Cost) x Quantity Sold
We don't have information about the cost of producing each pair of swimming flippers, so let's assume that it is a constant of $20 per pair. This means that the profit function is:
Profit = (Price - $20) x (92 - (Price - $50)) = (Price - $20) x (-Price + $142)
Expanding the brackets and simplifying, we get:
Profit = -$Price^2 + $122Price - $2840
To find the price that maximizes profit, we need to take the derivative of the profit function with respect to price, and set it equal to zero:
dProfit/dPrice = -$2Price + $122 = 0
Solving for Price, we get:
Price = $61
So, the store should charge $61 per pair of swimming flippers to maximize profit. To verify that this is indeed the maximum, we can take the second derivative of the profit function with respect to price:
d^2Profit/dPrice^2 = -$2
Since this is negative, we know that the profit function is concave down, which means that the critical point we found is indeed a maximum.
What is the standard form of the line that passes through the points (-4, 6) and (0, -7)?
This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation: [tex](\frac{13}{4} )x + y = -7[/tex]
How to find standard form?To find the standard form of the line that passes through the given points [tex](-4, 6)[/tex] and [tex](0, -7)[/tex], we need to first find the slope of the line using the slope formula:
[tex]\text{slope} = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of the two points.
Using the given points, we get:
[tex]\text{slope}=\dfrac{(-7-6)}{(0-(-4))}[/tex]
[tex]\text{slope}=-\dfrac{13}{4}[/tex]
Now that we have the slope of the line, we can use the point-slope form of the equation of a line:
[tex]y - y_1= m(x - x_1)[/tex]
where m is the slope and [tex](x_1, y_1)[/tex] is one of the points on the line. Using the point [tex](-4, 6)[/tex], we get:
[tex]y - 6 = \huge \text(-\dfrac{13}{4}\huge \text )(x - (-4))[/tex]
[tex]y - 6 = \huge \text(-\dfrac{13}{4}\huge \text )x-13[/tex]
[tex]y = \huge \text(-\dfrac{13}{4}\huge \text )x-7[/tex]
This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:
[tex]\huge \text(-\dfrac{13}{4}\huge \text )x+y=-7[/tex]
This is the standard form of the equation of the line that passes through the given points.
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