Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
What is the unit price?
In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.
According to given information
a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:
y - 0 = (-2/9)x
y = (-2/9)x
Substituting x = 18n, where n is the number of $18 price increases, we have:
y = (-2/9)(18n) = -4n
Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:
p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),
where q0 is the quantity of gaming systems sold at the original price of $180.
b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:
R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q
c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:
R'(q) = 9q - 9q0/2 = 0
q = q0/2
Substituting q = q0/2 into the revenue equation, we have:
R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)
R(q0/2) = (9/8)*q0^2 + (45/2)*q0
To find the corresponding price, we can use the expression for p(q) found in part (a):
p(q0/2) = 180 + (9/2)(q0/2 - q0)
p(q0/2) = 135
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
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There is a sale at khols, and tennis shoes are 30% off. How much are you saving if the shoes originally cost $62
Answer: $18.6
Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off
the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
7 and 31 it asks
the 3rd and 6th is
The 1st and 2nd terms of this Fibonacci sequence, given the 3rd and 6th terms would be 2 and 5.
How to find the Fibonacci sequence terms ?Let's denote the first and second terms of the Fibonacci sequence as F1 and F2. The Fibonacci sequence is defined by the recurrence relation:
F(n) = F(n-1) + F(n-2)
We are given that the 3rd term (F3) is 7 and the 6th term (F6) is 31. We can use this information to set up the following equations:
F3 = F2 + F1 = 7
F6 = F5 + F4 = 31
We can also express F4 and F5 in terms of F1 and F2:
F4 = F3 + F2 = (F2 + F1) + F2 = F1 + 2F2
F5 = F4 + F3 = (F1 + 2F2) + (F2 + F1) = 2F1 + 3F2
Now, let's substitute equation (4) into equation (2):
F6 = 2F1 + 3F2 + F1 + 2F2 = 31
3F1 + 5F2 = 31
By trial and error, we can find the possible values for F1 and F2 that satisfy this equation:
F1 = 1, F2 = 6: 3(1) + 5(6) = 3 + 30 = 33 (not a solution)
F1 = 2, F2 = 5: 3(2) + 5(5) = 6 + 25 = 31 (solution)
The solution is F1 = 2 and F2 = 5, so the first two terms of the Fibonacci sequence are 2 and 5.
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The manager of Tea for Us has been ordering stock based on the assumption that 51% of her customers prefer black teas. The following hypotheses are given:
H0: p = 0.51
H1: p ≠ 0.51
She sampled 158 of her customers and found that only 41% of those preferred black teas. At the 0.10 significance level, can the null hypothesis be rejected?
a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)
(Click to select)
H0
(Click to select)
H1 if z >
or z <
.
b. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round your answer to 2 decimal places.)
Value of the test statistic
-2.05
c. What is your decision regarding the null hypothesis?
The null hypothesis is
(Click to select)
.
a. The decision rule for this hypothesis test is: Reject H0 if the test statistic z is less than -1.645 or greater than 1.645. b. The test statistic for this hypothesis test is: -2.05.
What is hypothesis?In statistics, a hypothesis is an assumption or claim about a population parameter that can be tested by collecting and analyzing sample data.
According to given information:
a. The decision rule for this hypothesis test is:
Reject H0 if the test statistic z is less than -1.645 or greater than 1.645.
b. The sample proportion of customers who prefer black teas is:
= 0.41
The population proportion under the null hypothesis is:
p = 0.51
The sample size is:
n = 158
The test statistic for this hypothesis test is:
[tex]z = ( - p) / \sqrt(p * (1 - p) / n)[/tex]
[tex]= (0.41 - 0.51) / \sqrt(0.51 * 0.49 / 158)[/tex]
[tex]= -2.05[/tex]
c. The test statistic z of -2.05 is less than the critical value of -1.645, so we can reject the null hypothesis H0. At the 0.10 significance level, there is enough evidence to suggest that the proportion of customers who prefer black teas is not 0.51, and the manager of Tea for Us should consider adjusting their stock orders accordingly.
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answer these questions in detail
Answer:
5. x = 60
6. F' (1, 4)
Step-by-step explanation:
5. The angles shown are same side exterior angles, so they are supplementary (add to 180)
(x + 85) + 35 = 180
x + 120 = 180
x = 180 - 120 = 60
x = 60
6. The line x = 1 is a vertical line, passing through the x=axis at (1, 0). All x coordinates on this line equal 1.
The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)
If $r=9$ and $4r+3s=75$, what is the value of $s$? asap answer i only have like 1 hour to answer 50 questions
Answer:
the value of $s$ is 13.
Step-by-step explanation:
We are given that $r=9$ and $4r+3s=75$. We can use the value of $r$ to find $s$.
Substituting $r=9$ into the second equation, we get:
$4(9) + 3s = 75$
Simplifying the left-hand side, we get:
$36 + 3s = 75$
Subtracting 36 from both sides, we get:
$3s = 39$
Dividing both sides by 3, we get:
$s = 13$
Therefore, the value of $s$ is 13.
In ΔHIJ, i = 550 inches, h = 460 inches and ∠H=159°. Find all possible values of ∠I, to the nearest degree.
Write the absolute value equation that has the following solutions.
One solution: x = 15
The absolute value equation is:
|x - 15| = 0
How to write the absolute value equation?We want an absolute value equation that only has the solution x = 15.
So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)
So the equation will be something like:
|x - a| = 0
And the solution is 15, so:
|15 - a | = 0
then a = 15
The equation is:
|x - 15| = 0
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What is
22.50 x 15 Steph by step
Answer: 337.5.
Step-by-step explanation:
Answer:
337.5
Step-by-step explanation:
yara said that the vertical distance between two points is -5 units how do you know that yara's statement is incorrect
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
differentiate x^5(2x+1)^5
Answer:
[tex]5x^4(2x+1)^4(4x+1)[/tex]
Step-by-step explanation:
Okay so we have to use the product rule for this i.e.
d/dx[uv] = u'v + uv'
d/dx[x^5(2x+1)^5] =
[tex]5x^4(2x+1)^5 + x^5 * 2 * 5(2x+1)^4\\\\= 5x^4(2x+1)^5 + 10x^5(2x+1)^4\\\\= (2x+1)^4[5x^4(2x+1) + 10x^5]\\\\= (2x+1)^4[10x^5 + 5x^4 + 10x^5]\\\\= (2x+1)^4(20x^5+5x^4)\\\\=5x^4(2x+1)^4(4x+1)[/tex]
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A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot?
Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
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 constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.
The nth term of an arithmetic sequence can be found using the formula:
an = a1 + (n-1)d.
The merchant received 7/10 of a pound of diamonds and divided them into 7 equal lots. To find the weight of each lot, we need to divide 7/10 by 7:
(7/10) ÷ 7 = (7/10) × (1/7) = 1/10
Therefore, the weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
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Jackson has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $27.40? Round to the nearest cent.
Jackson's total cost after the discount and before tax would be $24.67.
Calculating discounted price :When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.
To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).
Here we have
Jackson has a 10% discount at his local hardware store.
Let 'x' be the cost before tax
After a 10% discount,
The amount that Jackson could pay 90% of the cost
Given that he wants to buy $ 27.40
The cost of items after discount = 90% of 27.40
= [ 90/100 ] × 27.40
= [ 0.9 ] × 27.40
= 24.66
Therefore,
Jackson's total cost after the discount and before tax would be $24.67.
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If $20,000 is invested at an interest rate of 2% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
6 years
12 years
18 years
Answer:
6 years = $22,536.50
12 years = $25,394.69
18 years = $28,615.38
Step-by-step explanation:
The find the value of the investment after the given number of years, first create an equation for A in terms of t using the compound interest formula.
Compound Interest Formula[tex]\boxed{\sf A=P\left(1+\frac{r}{n}\right)^{nt}}[/tex]
where:
A = Final amount.P = Principal investment.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $20,000r = 2% = 0.02n = 2 (semi-annually)Substitute the given values into the formula to create an equation for the value of the investment, A, in terms of time in years, t:
[tex]\implies \sf A=20000\left(1+\dfrac{0.02}{2}\right)^{2t}[/tex]
[tex]\implies \sf A=20000\left(1+0.01\right)^{2t}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{2t}[/tex]
[tex]\hrulefill[/tex]
To find the value of the investment after 6 years, substitute t = 6 into the equation:
[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 6}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{12}[/tex]
[tex]\implies \sf A=20000(1.12682503...)[/tex]
[tex]\implies \sf A=22536.5006026...[/tex]
Therefore, the value of the investment after 6 years is $22,536.50 rounded to the nearest cent.
[tex]\hrulefill[/tex]
To find the value of the investment after 12 years, substitute t = 12 into the equation:
[tex]\implies \sf A=20000\left(1.01\right)^{2 \cdot 12}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{24}[/tex]
[tex]\implies \sf A=20000\left(1.2697346...\right)[/tex]
[tex]\implies \sf A=25394.69297...[/tex]
Therefore, the value of the investment after 12 years is $25,394.69 rounded to the nearest cent.
[tex]\hrulefill[/tex]
To find the value of the investment after 18 years, substitute t = 18 into the equation:
[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 18}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{36}[/tex]
[tex]\implies \sf A=20000\left(1.43076878...\right)[/tex]
[tex]\implies \sf A=28615.37567...[/tex]
Therefore, the value of the investment after 18 years is $28,615.38 rounded to the nearest cent.
PLEASE HELP ME WITH THIS!!!!! I NEED HELP! A backyard pool is in the shape of a rectangle. The pool has a perimeter of 90 feet and and area of 500ft^2. which of the following could he the pools length and width? 1) 15 feet and 30 feet 2)10 feet and 35 feet 3) 50 feet and 10 feet 4) 25 feet and 20 feet.
Answer:3) 50 feet and 10 feet
Step-by-step explanation: Multiply every single choice
Answer:
4)
Step-by-step explanation:
Let x1 = length; x2 = width
+) x1 × x2 = 500
+) 2(x1 + x2) = 90 => x1 + x2 = 45
=> x1 and x2 are the roots of equation: [tex]x^2-45x+500=0[/tex]
=> x1 = 25; x2 = 20
Use the image to determine the line of reflection.
An image of polygon VWYZ with vertices V at negative 7, negative 2, W at negative 7, negative 4, Y at negative 1, negative 4, and Z at negative 1, negative 2. A second polygon V prime W prime Y prime Z prime with vertices V prime at 11, negative 2, W prime at 11, negative 4, Y prime at 5, negative 4, and Z prime at 5, negative 2.
Reflection across the x-axis
Reflection across the y-axis
Reflection across y = −2
Reflection across x = 2
An image of polygon VWYZ has a line of reflection across the x-axis. So option A is correct.
What is the line of reflection?In geometry, the line of reflection is the line over which a figure is reflected. When a point is reflected over a line, it moves the same distance on the opposite side of the line. The line of reflection is perpendicular to the figure at the point of reflection and is equidistant from the figure and its reflection.
What is a polygon?A polygon is a closed two-dimensional shape with straight sides. The sides are line segments that intersect only at their endpoints, called vertices. Polygons can have any number of sides, but they must have at least three. Common examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and octagons.
What is the formula for the line of reflection?The formula for the line of reflection in a Cartesian coordinate system is:
x = a
where a is the equation of the line of reflection.
This formula represents a vertical line that passes through the point (a, 0) and reflects points across the line of reflection to their corresponding images on the other side.
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Answer:
reflection across x=2
Step-by-step explanation:
the picture should be able to explain itself! :)))
i don't understand this question please help me answer it :)
What is 8% of 425 coins?
Answer: 34
Step-by-step explanation:
To find 8% of 425 coins, multiply 425 by 0.08 (which is the decimal equivalent of 8%).
425 * 0.08 = 34
So, 8% of 425 coins is 34 coins.
What fractions are close to 1 than to 0
The answer of the given question based on the fraction is , a value that is greater than 1/2.
What is Fraction?A fraction is mathematical expression that represents part of whole or ratio between the two numbers. It is expressed in the form of a ratio of two integers, with a numerator and a denominator separated by a horizontal or slanted line called a fraction bar.
Fractions that are closer to 1 than to 0 have a value that is greater than 1/2. This is because 1/2 is exactly halfway between 0 and 1 on the number line.
So, any fraction that has a numerator greater than its denominator is closer to 1 than to 0. For example:
2/3 is closer to 1 than to 0 because it is greater than 1/2
7/8 is closer to 1 than to 0 because it is greater than 1/2
3/4 is closer to 1 than to 0 because it is greater than 1/2
On the other hand, fractions that have a value less than 1/2 are closer to 0 than to 1. For example:
1/4 is closer to 0 than to 1 because it is less than 1/2
3/10 is closer to 0 than to 1 because it is less than 1/2
2/5 is closer to 0 than to 1 because it is less than 1/2
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Janna's health class measures the heart rates of students after they walked for five minutes. The heart rates, in beats
per minute, were as follows.
102, 74, 86, 74, 96, 95, 103, 102 Find the median of the data set. What does the median tell you? (Hint: If the data set has an even number of values,
the median is the mean of the two middle values.)
The median of the data set is: 95.5
What is median?
median is the number at the middle of the given data.
To find the median of the data set {102, 74, 86, 74, 96, 95, 103, 102}, we first need to arrange the values in order from lowest to highest:
74, 74, 86, 95, 96, 102, 102, 103
Since the data set has an even number of values, the median is the mean of the two middle values. In this case, the two middle values are 95 and 96.
Therefore, the median of the data set is: (95 + 96) / 2 = 95.5
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Pedro wants to grow tomatoes and herbs so he can make his own fresh pizza sauce. Pedro's planter box is seven feet long and four feet wide on the inside. Pedro fills the planter box with soil to a height of two feet. What is the volume of soil in Pedro's planter box?
According to the question the volume of soil in Pedro's planter box is 56 cubic feet (ft³).
What is volume?Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is measured in units of cubic centimeters (cm3), cubic meters (m3) or liters. Volume is an important concept in many areas of mathematics, including geometry, calculus and physics. It is also a key concept in many other disciplines, including engineering, architecture and the sciences. Volume is an important property of a solid object, and it is often used to quantify the size or capacity of an object. Volume can be calculated by multiplying the length, width and height of an object. It can also be calculated using the formula for the volume of a cylinder, cone, sphere or other shapes.
To calculate this, we need to multiply the length of the planter box (7 ft) by the width (4 ft) by the height of the soil (2 ft). This gives us the following equation: 7 ft x 4 ft x 2 ft
= 56 ft³.
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Leon is building a square picture frame. The side of the frame is 335 millimeters long. If a meter of wood costs $8, how much will the wood he needs cost?
Answer: $9.66
Step-by-step explanation: perimeter = 345mm + 345mm + 345mm + 345mm = 1380
We need 1380 millimeters which is equivalent to 1.38 meters.
We can multiply the number of meters by the cost of meters to find the total
Q6 : "Social media has become a ubiquitous part of modern life, allowing people to connect with friends, family, and strangers from all around the world. However, social media use has been linked to a number of negative mental health outcomes, including increased rates of depression, anxiety, and stress. This is due in part to the constant pressure to present a perfect image of oneself, leading to feelings of inadequacy and self-doubt. Additionally, the endless stream of news and information on social media can be overwhelming and lead to feelings of information overload and burnout. However, not all social media use is negative. Research has also shown that social media can be a valuable tool for promoting social support and connection, particularly among marginalized communities. It can also be a source of education and awareness, allowing people to learn about important issues and engage with social and political causes." What is one negative mental health outcome associated with social media use?"
Increased social support and connection
Greater awareness of social and political issues
Higher rates of depression and anxiety
Improved self-esteem and self-worth
Higher rates of depression and anxiety are one negative mental health outcome associated with social media use
Social media and modern life:The paragraph discusses the role of social media in modern life and its impact on mental health. It notes that social media has become a ubiquitous part of life that allows people to connect with others from around the world, including friends, family, and strangers.
However, the paragraph goes on to mention that social media use has been linked to negative mental health outcomes such as depression, anxiety, and stress.
These negative outcomes may be due to the pressure individuals feel to present a perfect image of themselves online, leading to feelings of inadequacy and self-doubt.
Despite these negative outcomes, the paragraph notes that social media can also be valuable for promoting social support and connection, especially among marginalized communities.
Furthermore, it can be a source of education and awareness, allowing people to learn about important social and political issues and engage with them.
Hence,
Higher rates of depression and anxiety are one negative mental health outcome associated with social media use
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which expression has a value between -4 and -3
One expression that has a value between -4 and -3 is (-7/2) - 3.
What is expression?Expression in math is a combination of numbers, symbols, and operations that represent a value, quantity, or an idea. Expressions can be used to represent equations, relationships between quantities, solutions to problems, and more. They can also be used to represent functions, which are a special type of expression that assign a unique output to a given input.
This expression can be simplified to (-1/2) - 3, which evaluates to -3.5. This value is between -4 and -3, as desired.
To confirm this, we can plug -3.5 into the original expression and see that it evaluates to -3.5: (-7/2) - 3 = -7/2 - 3 = -7/2 + (-3) = -7/2 - 3(-1/2) = -7/2 - (-3/2) = -7/2 + 3/2 = -7 + 3/2 = -7/2 + 3 = -4 + 3 = -1/2 = -3.5.
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Explain Why 387 is not a term of the sequence
Answer:
In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.
If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:
an = a1 + (n-1)d
where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.
If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:
a1 = 3
a2 = 8
a3 = 13
a4 = 18
and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:
a129 = a1 + (129-1)d
a129 = 3 + 128(5)
a129 = 643
Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
The answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).
(B) The right choice is Option B, which is Option II which is narrower.
What is a confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.
Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
So, let X represent the amount of time (in seconds) needed to complete a 100-meter race with Tom.
His population's mean 100-meter race finishing time falls within a 99% confidence interval of 12.8081 and 15.5919.
x = 14.2
s²= 0.9867
s= 0.9933
t α2, n-1 = 3.7074
The margin of error= 1.3919
lower bound= 12.8081
upper bound= 15.5919
Therefore, the answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).
(B) The right choice is Option B, which is Option II which is narrower.
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Correct question:
Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at 95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 18 , 27 , . . . Find the 8th term.
Answer: 205.031(nearest thousandth)
or 205.03125
Step-by-step explanation:
Suppose Fatima went to buy a $25,000 car and wanted to own it after 5 years. If she got a
4.7% interest rate, what is her monthly payment?
Therefore, Fatima's monthly payment would be $460.23.
What is interest?Interest is the amount of money that is charged by a lender to a borrower for the use of money or a loan. It is usually calculated as a percentage of the principal amount (the amount of money borrowed) and can be either simple or compound, depending on the type of loan. Interest is typically paid by the borrower to the lender over a set period of time, such as monthly, quarterly, or annually. The interest rate can be fixed or variable, and is determined by a variety of factors including the borrower's creditworthiness, the amount of the loan, and the length of the repayment period.
Here,
To calculate the monthly payment for a car loan, we need to use the formula:
M = P [ i(1 + i)ⁿ] / [ (1 + i)ⁿ – 1]
Where:
M = monthly payment
P = principal (the amount of the loan)
i = monthly interest rate (annual interest rate divided by 12)
n = number of months
First, we need to calculate the monthly interest rate:
i = 4.7% / 12
= 0.003917
Next, we need to calculate the number of months:
n = 5 years x 12 months/year
= 60 months
Now, we can plug in the values and solve for M:
M = 25,000 [ 0.003917(1 + 0.003917)⁶⁰ ] / [ (1 + 0.003917)⁶⁰ – 1]
M = $460.23 (rounded to the nearest cent)
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The number of deer on an island is given by D=200+100sin( 2 π x), where x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 150 ?
Therefore, the first Leap year after 2000 that the number of deer reaches 150 is 2000.1, or 2000 and 1/10 of a year.
What are a leap year and a year?If you sum up all the days on a calendar from January to December, there are 365 in a regular year. But about every four years, February has 29 days rather than 28. Therefore, a year has 366 days. There is a term for it: a leap year.
We must find x in the equation D=150 in order to determine the year that the number of deer exceeds 150 for the first time after 2000.
150=200+100sin(2πx)
Subtracting 200 from both sides, we get:
-50 = 100sin(2πx)
Dividing both sides by 100, we get:
-0.5 = sin(2πx)
To find the value of x that satisfies this equation, we can take the inverse sine of both sides:
sin⁻¹(-0.5) = 2πx
Using a calculator, we find that sin⁻¹(-0.5) = -π/6.
-π/6 = 2πx
Solving for x, we get:
x = -1/12
Since x is the number of years since 2000, we need to add 1/12 to find the first year after 2000 that the number of deer reaches 150:
2000 + 1/12 ≈ 2000.1
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721.60 divided by 80
Will mark brainliest if answer is correct
Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )
What is the points of intersection of both functionsWe are given two equations:
y = 4x² - 3x + 3
y = x³ + 7x² - 3x + d
and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:
y = 4(-4)² - 3(-4) + 3 = 49
y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d
So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:
49 = 60 + d
Solving for d, we get:
d = -11
Therefore, the two equations become:
y = 4x² - 3x + 3
y = x³ + 7x² - 3x - 11
We can now set them equal to each other:
4x² - 3x + 3 = x³ + 7x² - 3x - 11
Simplifying and rearranging, we get:
x³ + 3x² - 8x - 14 = 0
We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:
2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10
Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:
(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4
This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:
(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6
This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:
x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)
The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:
x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2
= [ -1 ± 3√(7) ] / 2
Therefore, the three intersection points are:
(-2, 0)
( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )
( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )
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