Answer:
f¹(12) = 20
Step-by-step explanation:
f(-2) = 24
f(-1) = 17
f(0) = 12
f(1) = 9
f¹(x) = 2x - 4
f¹(12) = 20
11 term of 7 -28 112
The 11th term of this geometric sequence 7 -28, 112, .... include the following: 7,340,032.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -28/7
Common ratio, r = -4
For the 11th term, we have:
a₁₁ = 7(-4)¹¹⁻¹
a₁₁ = 7,340,032.
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simplified ration of squares to total shapes is 6:16 for every 3 squares there are how many total shapes there fore the simplified ratio of squares to total shape is what
For every 3 squares, there are 5 total shapes. Therefore, the simplified ratio of squares to total shapes is 3 : 5.
What is the simplified ratio of squares to total shapes?If the unsimplified ratio of squares to total shapes is 6 : 16, then we can express this as 6/16, then,we can simplify this ratio by dividing both the numerator and denominator by 2, giving us 3/8.
This means that for every 3 squares, there are 5 total shapes. Therefore, the simplified ratio of squares to total shapes is 3 : 5.
Full question "Unsimplified ratio of squares to total shapes: 6 : 16. For every 3 squares, there are ____ total shapes; Therefore, the simplified ratio of squares to total shapes is __ : __.
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Can anyone help with this question on this picture
The distance it would take to travel across the river on the bridge than to take the ferry is 4√6 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance AC = √[(-4 - 0)² + (2 - 2)²]
Distance AC = √[(-4)² + (0)²]
Distance AC = √[16 + 0]
Distance AC = √16
Distance AC = 4 units.
Distance AB = √[(2 - 0)² + (0 + 2)²]
Distance AB = √[(2)² + (2)²]
Distance AB = √[4 + 4]
Distance AB = √8
Distance AC = 2√2 units.
From Pythagorean Theorem, the length of BC is given by;
BC² = (2√2)² + 4²
c² = 8 + 16
c = √24
c = 4√6 units.
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After reaching saturation, if the temperature of the room continues to decrease for one more hour, how many grams of water vapor (per kg of air) will have had to condense out of the air to maintain a relative humidity of 100%?
We can estimate that about 9 grams of water vapor per kg of air would have to condense out to maintain saturation and a relative humidity of 100%.
When air is saturated, it holds the maximum amount of water vapor it can at a given temperature and pressure. Any decrease in temperature leads to the condensation of water vapor out of the air, which can lead to the formation of dew or frost.
To maintain a relative humidity of 100%, the air must remain saturated. So, if the temperature of the room continues to decrease for one more hour, some of the water vapor in the air will condense out to maintain saturation. The amount of water vapor that condenses out depends on the initial temperature, the final temperature, and the amount of water vapor in the air.
To calculate the amount of water vapor that condenses out, we can use the concept of dew point temperature. The dew point temperature is the temperature at which the air becomes saturated and condensation begins to occur. If the temperature of the room reaches the dew point temperature, the air will be fully saturated, and any further decrease in temperature will lead to the condensation of water vapor.
Assuming that the initial temperature of the room was above the dew point temperature, we can estimate the amount of water vapor that would condense out after one hour of cooling by calculating the difference between the initial temperature and the dew point temperature, and then using a psychrometric chart or an online calculator to determine the corresponding amount of water vapor that would have to condense out.
For example, if the initial temperature of the room was 25°C and the dew point temperature was 20°C, and the room cooled to 19°C after one hour, then we can estimate that about 9 grams of water vapor per kg of air would have to condense out to maintain saturation and a relative humidity of 100%. However, this is just an estimate, and the actual amount of water vapor that condenses out depends on many factors, including the humidity and air circulation in the room.
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You get a part time job earning $12.50/hr. Tips are $4.60/hr average. Deductions are FICA (7.65%) and Federal Tax Withholding (10%). You work for 18 hours. What is your gross base pay?
If you are earning $12.50/hr in a part-time job, then your gross "base-pay" after deductions is $253.48.
Your base pay is $12.50/hr and you worked for 18 hours, so the base pay would be:
⇒ $12.50/hr × 18 hrs = $225;
The tips are $4.60/hr on average, so the "total-tips" earned would be:
⇒ $4.60/hr × 18 hrs = $82.80;
To calculate the "total-deductions", we first find the total percentage deducted, which is the sum of FICA and Federal Tax Withholding:
⇒ 7.65% + 10% = 17.65%,
To find the total amount deducted, we multiply the total percentage deducted by the "base-pay" + "tips";
⇒ 17.65% x ($225 + $82.80) = $54.32,
So the pay, before any deductions, is the sum of "base-pay" and "tips";
⇒ $225 + $82.80 = $307.80;
To find the "net-pay", we subtract "total-deductions" from pay;
We have,
⇒ $307.80 - $54.82 = $253.48,
Therefore, your gross base pay is $253.48.
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Answer:
add the tips and pay together , this equals 17.10
then multiply by the 18 hours and you’ll get 307.80
Step-by-step explanation:
What is the area of a triangle with vertices at (5,0), (-3,1) and (2,6)?
6 units squared
54 units squared
22. 5 units squared
36. 5 units squared
Answer:
To find the area of a triangle given its vertices, we can use the formula:
Area = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|
where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.
Using this formula, we can calculate the area of the triangle with vertices at (5,0), (-3,1), and (2,6) as follows:
Area = 1/2 * |(5*(1-6) + (-3)(6-0) + 2(0-1))|
= 1/2 * |-25 - 18 - 2|
= 1/2 * |-45|
= 22.5
Therefore, the area of the triangle is 22.5 units squared. So the answer is option C: 22.5 units squared.
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assume the data are three independent srss, one from each of the four populations of caffeine levels, and that the distribution of the yields is normal. a partial anova table produced by minitab follows, along with the means and standard deviation of the yields for the four groups. one-way anova: rest versus caffeine the null hypothesis for the anova f test is that group of answer choices the population mean minutes of sleep is the same for all four levels of caffeine. the population mean minutes of sleep is increasing as the caffeine level gets larger. the population mean minutes of sleep is decreasing as the caffeine level gets larger. the population mean minutes of sleep is largest for the high level of caffeine.
The statistics indicate that the assumption that the four populations have the same standard deviation has been broken.
a. This research was done via observation.
False, as this is a test. (unlike what Alex89 says). The response variable (minutes of rest) is then recorded because the researcher randomly assigns the fruit flies to one of the treatments, using a TREATMENT, and records the response variable.
b. The statistics indicate that the assumption that the four populations have the same standard deviation has been broken.
False: There is no deviation from the equality of standard deviations. We DO NOT need to test this assumption when the sample sizes are equal. Even if we did, 29.61/19.08 = 1.55 2 means that the greatest standard deviation is less than twice the lowest standard deviation. We are therefore okay.
c. Because ANOVA needs sample sizes, it may be applied to this data are equal.
False - The ANOVA does NOT require equal sample sizes.
3. The correct option is D, For this example, we notice that 3) None of the above
(4) The correct is option A, which states that 4) the population mean rest is the same for all four caffeine concentrations.
Statistics provides a framework for making informed decisions based on data by using methods such as probability theory, hypothesis testing, regression analysis, and statistical modeling. The importance of statistics lies in its ability to transform raw data into meaningful information that can be used to make decisions, develop policies, and solve problems in a wide range of fields, including business, healthcare, government, and social sciences.
Statisticians use various tools and techniques to summarize and describe data, identify patterns and relationships, and make predictions and inferences. They also play a critical role in designing experiments, surveys, and observational studies, ensuring that they are statistically sound and produce reliable results.
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Complete Question:-
An experiment to help determine if insects sleep gave caffeine to fruit flies to see if it affected their rest. The three treatments were a control, a low caffeine dose of 1 mg/ml of blood, a medium dose of 3 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest measured over a 24-hour period was recorded. The data follow.
Treatment Minutes of rest
Control 450 413 418
Low dose 466 422 435
Medium dose 421 453 419
High dose 364 330 389
Assume the data are three independent SRSs, one from each of the four populations of caffeine levels, and that the distribution of the yields is Normal.
A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups.
One-way ANOVA: Rest versus Caffeine
Source DF SS MS F P
Caffeine 11976
Error 538.75
Total
Level N Mean StDev
Control 3 427.00 20.07
Low 3 441.00 22.61
Medium 3 431.00 19.08
High 3 361.00 29.61
3. For this example, we notice that 3) __________
a. this is an observational study.
b. the data show evidence of a violation of the assumption that the four populations have the same standard deviation.
c. ANOVA can be used on these data because ANOVA requires the sample sizes are equal.
d. None of the above
4. The null hypothesis for the ANOVA F test is that 4) __________
a. the population mean rest is the same for all four levels of caffeine.
b. the population mean rest is increasing as the caffeine level gets larger.
c. the population mean rest is decreasing as the caffeine level gets larger.
d. the population mean rest is largest for the high level of caffeine.
Wanda's front porch is 7 feet wide and 13 feet long. Wanda wants to stain the wood on the porch next weekend. The stain costs $2. 00 per square foot. How much will it cost to buy enough stain for the whole porch?
The amount it will cost to buy enough stain for the whole porch is $182.
To determine the cost of staining Wanda's front porch, we'll first need to calculate the area of the porch, which is a rectangle in shape. The area of a rectangle can be found using the formula: Area = length × width.
In this case, the length of Wanda's porch is 13 feet, and the width is 7 feet. So, we'll multiply these two measurements to find the area:
Area = 13 ft × 7 ft = 91 square feet
Now that we know the area, we can calculate the cost of the stain. The stain costs $2.00 per square foot, so we'll multiply the area of the porch (91 square feet) by the cost per square foot:
Cost = 91 sq ft × $2.00/sq ft = $182
Therefore, it will cost Wanda $182 to buy enough stain for the whole porch.
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8. Brock placed a 20 foot ladder against the side of the house. The base of the ladder was 6 foot from the base of the house. How high does the ladder reach on the side of the house? Draw a picture and solve. (Round to tenth)
Step-by-step explanation:
1st i think u divide 20 and 6 and then round tht to the tenth place because we already know our answer is going to be a decimal bc 6 cant go into 20.
The monomial -3xy2z(-2x2yz) has degree of:
The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.
What is a monomialA monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.
Given the monomial:
-3xy²z(-2x²yz)
We can simplify it by multiplying the coefficients and adding the exponents of the variables:
-3(-2)x^(2+1) y^(2+1) z^(1+1)
= 6x³y³ z²
Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.
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Laura is currently paying off her four-year car financing. when she purchased her car, it had a list price of $19,858. laura traded in her previous car, a good-condition 2000 honda insight, for 85% of the trade-in value listed below, financing the rest of the cost at 9.5% interest, compounded monthly. she also had to pay 9.27% sales tax, a $988 vehicle registration fee, and a $77 documentation fee. however, because laura wants to pay off her loan more quickly, she makes a total payment of $550 every month. how much extra is she paying monthly? round all dollar values to the nearest cent.
Laura is paying each month:
extra payment = $550 - monthly payment
To calculate how much extra Laura is paying each month, we first need to calculate the total cost of her car financing. Here are the steps:
Calculate the trade-in value of Laura's old car. We don't have the exact value, but we know that she received 85% of the trade-in value listed below, so we can set up an equation:
0.85 * trade-in value = value Laura received
Solving for the trade-in value, we get:
trade-in value = value Laura received / 0.85
Add the trade-in value to the list price of the new car to get the total cost before taxes and fees:
total cost before taxes and fees = $19,858 + trade-in value
Add the sales tax, registration fee, and documentation fee to get the total cost of the car financing:
total cost = (1 + 0.0927) * total cost before taxes and fees + $988 + $77
Calculate the monthly payment using the formula for a loan with monthly compounding:
monthly payment = (principal * monthly interest rate) / (1 - (1 + monthly interest rate)^(-number of months))
We know that Laura is financing the rest of the cost after her trade-in value, so:
principal = total cost - value Laura received
monthly interest rate = 0.095 / 12
number of months = 48 (since it's a four-year financing)
Substituting these values into the formula, we get:
monthly payment = ($19,858 + trade-in value - value Laura received) * 0.007916 / [tex](1 - (1 + 0.007916)^{(-48)})[/tex]
Now that we have the total monthly payment, we can calculate how much extra Laura is paying each month:
extra payment = $550 - monthly payment
Note that this assumes that Laura doesn't have any other fees or interest charges on her car financing, such as late payment fees or penalties for paying off the loan early. If there are any additional fees or charges, the calculation may be different.
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describe the likelihood of the next elk caught being unmarked
The probability of the next elk caught being unmarked is 0.96 when the total number of elks is 5625 and the number of elks marked is 225.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Total number of elks = 5625
Number of elks marked = 225
We need to find the total number of elks not marked or unmarked we can find it by,
= 5625 - 225
= 5500
Therefore, the total number of elks unmarked is 5500.
We can determine determined the likelihood of the next elk caught being unmarked by using probability. The probability is given by:
P = 5500/5625
= 44 / 45
= 0.96
Therefore, The total number of elks unmarked is 0.96.
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The complete question is,
Describe the likelihood of the next elk caught being unmarked.
If $5,500 is invested at 1.55% interest, find the value (in dollars) of the investment at the end of 6 years if the interest is
compounded as follows. Roung vour answers to the nearest cent.
A. Annualy
B. quarterly
C. Monthly
The value of the investment at the end of 6 years is $6,359.77 if the interest is compounded annually, $6,416.52 if it is compounded quarterly, and $6,437.70 if it is compounded monthly.
What formula is used to for compound interest?
[tex]A = P(1 + r/n)^{nt}[/tex]
where A is the final amount, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
A. If the interest is compounded annually, we have:
A = [tex]5,500(1 + 0.0155/1)^{1*6}[/tex] = $6,359.77
B. If the interest is compounded quarterly, we have:
A = [tex]5,500(1 + 0.0155/4)^{4*6[/tex] = $6,416.52
C. If the interest is compounded monthly, we have:
A = [tex]5,500(1 + 0.0155/12)^{12*6[/tex] = $6,437.70
Therefore, the value of the investment at the end of 6 years is $6,359.77 if the interest is compounded annually, $6,416.52 if it is compounded quarterly, and $6,437.70 if it is compounded monthly.
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I need to know how to solve this equation
Answer:
3/y
Step-by-step explanation:
15x÷5xy
15x/5xy....you will cancel x by x and simplify by 5(GCF)
3/y ...... it is the simplify form of the given equetion.
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7
A graph of the axis of symmetry and the vertex for this function is shown below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function h(x) = (x - 5)² - 7 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -7.
In conclusion, the turning point and vertex is given by the ordered pair (5, -7).
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Find dy/dt at x = – 1 if y = – 2x^2 + 4 and dx/dt = 4. dy/dt =?
Derivative of y w.r.t t is dy/dt = 16 at x = -1.
How to find dy/dt?We need to find dy/dt at x = -1, given y = -2x² + 4 and dx/dt = 4.
Step 1: Differentiate y with respect to x.
Since y = -2x² + 4, we have:
dy/dx = -4x
Step 2: Substitute x = -1 into the dy/dx equation.
When x = -1, we get:
dy/dx = -4(-1) = 4
Step 3: Use the Chain Rule to find dy/dt.
The Chain Rule states that dy/dt = (dy/dx)(dx/dt). We know dy/dx = 4 and dx/dt = 4, so we have:
dy/dt = (4)(4) = 16
Thus, dy/dt = 16 at x = -1.
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Sketch a profit function P(q) satisfying the following: the domain is 0 ?q? 20,000; marginal profit is negative for 10,000 < q < 15,000 and nowhere else; P has an inflection point at q = 13,000; the break-even point is q = 2000; and marginal profit is constant for q > 17,000.
P(q) has a concave down inflection at q=13,000, negative marginal profit between q=10,000 to 15,000, constant marginal profit after q=17,000, and breaks even at q=2000.
One possible profit function that satisfies the given conditions is:
P(q) = -0.002(q-13,000)^3 + 20q - 40,000
The domain is 0 ≤ q ≤ 20,000, and the marginal profit is negative for 10,000 < q < 15,000, meaning that increasing production within this range will result in decreasing marginal profit. The inflection point at q = 13,000 indicates a change in the concavity of the profit function.
The break-even point is q = 2000, which means that the profit function crosses the x-axis at this point.
For q > 17,000, the marginal profit is constant, indicating that the profit function becomes linear beyond this point. This profit function satisfies all the given conditions and can be used to model the profit of a business or a product as a function of production quantity.
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Catering company provides packages for weddings and for showers. The cost per person for small groups is
pproximately Normally distributed for both weddings and showers. The mean cost for weddings is $82. 30 with a
andard deviation of $18. 20, while the mean cost for showers is $65 with a standard deviation of $17. 73. If 9
eddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than
e mean cost of the showers?
The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers is approximately 0.0207 or 2.07%.
The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers can be found using the Z-score and the difference between the means of two normally distributed variables.
1: Calculate the difference in means and standard deviations.
Δμ = μ_weddings - μ_showers = $82.30 - $65 = $17.30
Δσ = sqrt((σ_weddings²/n_weddings) + (σ_showers²/n_showers)) = sqrt((18.20²/9) + (17.73²/6)) = $8.47
2: Calculate the Z-score.
Z = (Δμ - 0) / Δσ = (17.30 - 0) / 8.47 ≈ 2.04
3: Determine the probability using a Z-table.
P(Z > 2.04) ≈ 0.0207
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Tara wants to prove that a second pair of corresponding angles from KJN and LJM are congruent.
Determine a second pair of corresponding angles from KJN and LJM that are congruent. Then explain how you know that the two angles are congruent
To determine a second pair of corresponding angles from KJN and LJM that are congruent, we can start by identifying the first pair of corresponding angles.
angle JKN is harmonious to angle LJM. thus, we need to find another brace of corresponding angles that involve these same two angles. One possibility is to look at the perpendicular angles formed by the crossroad of KJ and JM. Angle KJM is perpendicular to angle NJL. therefore, angle KJM in KJN corresponds to angle NJL in LJM. thus, these two angles are harmonious.
We can prove that these two angles are harmonious using the perpendicular angles theorem, which states that perpendicular angles are always harmonious. Since KJ and JM cross at point J, angles KJM and NJL are perpendicular angles and must be harmonious. thus, we've shown that the alternate brace of corresponding angles from KJN and LJM that are harmonious are angle KJM and angle NJL.
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(65 points) ASAP!!! Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)
Part B: Explain how you know the equation from Part A is correct. (1 point)
Part C: Solve the equation from Part A. Show every step of your work. (2 points)
Answer:
Total wood = 4.5 Left over wood = 0.7 let 1 piece of wood = x
hence we have 5x+0.7=4.5
5x=4.5 - 0.7
5x = 3.8 x= 3.8/5 = 0.76 ft
Step-by-step explanation:
Answer:
A: 5x + 0.7 = 4.5
B: You know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
C: 0.76 feet
Step-by-step explanation:
Part A:
Let x be the length of each of the five pieces of wood cut from the 4.5 feet long piece of wood. The equation that could be used to determine the length of each piece is:
5x + 0.7 = 4.5
Part B:
You know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
Part C:
5x + 0.7 = 4.5
5x = 4.5 - 0.7
5x = 3.8
x = 3.8/5
x = 0.76
Therefore, each of the five pieces of wood that Warren cut is 0.76 feet long.
The thickness of paper manufactured at a manufacturing company is roughly symmetrical with a mean of 0. 0039 inch and a standard deviation of about 0. 00001 inch. A marketing manager wants to divide the values of the thickness of paper by 0. 0001 to make the values easier to manage.
What are the mean and standard deviation of the thickness of paper after dividing by 0. 0001?
The mean is ?
inch.
The standard deviation is ?
inch
The mean of the thickness of paper is 39 inches, and the standard deviation is 0.1 inches.
To find the mean and standard deviation of the thickness of paper after dividing by 0.0001, you should follow these steps:
1. Divide the mean by 0.0001:
Mean after dividing = 0.0039 inches / 0.0001
Mean after dividing = 39 inches
2. Divide the standard deviation by 0.0001:
Standard deviation after dividing = 0.00001 inches / 0.0001
Standard deviation after dividing = 0.1 inches
The mean of the thickness of paper after dividing by 0.0001 is 39 inches, and the standard deviation is 0.1 inches.
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Which equation correctly describes the relationship between x and y in the table?
A. y = 2x - 5
B. y = x
C. y = x - 3
D. y = 1/2x + 1
It's "D"
It's self explanatory but y gets 1/2 of whatever x is and adds 1. So if x = 2, then it'll get half of two (which is one) and add one to it, getting two.
Find the solution and also verify your answer , under root 12 x 12 x - 4 is equals under root 4 x + 8
The solution to the given equation is x = -3/4 or x = 1.
What values of x satisfy the equation √(12x² - 4) = √(4x + 8)?In order to find the solution, we start by squaring both sides of the equation to eliminate the square roots:
12x² - 4 = 4x + 8
Next, we simplify the equation by moving all the terms to one side:
12x² - 4x - 12 = 0
Now we can factor the quadratic equation:
4x² - x - 3 = 0
By factoring or using the quadratic formula, we find that the equation can be written as:
(4x + 3)(x - 1) = 0
Setting each factor equal to zero gives us the solutions:
4x + 3 = 0 or x - 1 = 0
Solving for x in each equation yields:
x = -3/4 or x = 1
Therefore, the solution to the given equation is x = -3/4 or x = 1.
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Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard
deviation of 2. 9 in.
Find the z-score associated with the 96th percentile.
Find the height of a 16-year-old boy in the 96th percentile.
State your answer to the nearest inch
The height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.
Find out the height of a boy in the 96th percentile?To find the z-score associated with the 96th percentile, we need to find the z-score such that the area to the right of it under the standard normal distribution is 0.96. Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.75.
Next, we can use the z-score formula to find the height of a 16-year-old boy in the 96th percentile:
z = (x - μ) / σ
where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.
Plugging in the values we have:
1.75 = (x - 68.3) / 2.9
Multiplying both sides by 2.9, we get:
x - 68.3 = 5.075
Adding 68.3 to both sides, we get:
x = 73.375
So the height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.
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Type the correct answer in each box. use numerals instead of words.
lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. the doctors at the lab created the random data in the table using representative simulation. the letter e stands for "effective," and n stands for "not effective.
the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is ______. the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is ______.
To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we can use the geometric distribution. The probability of not curing the disease is 1 - 0.70 = 0.30.
Let X be the number of patients needed to find one patient on whom the medicine would not be effective. Then X follows a geometric distribution with p = 0.30. The probability that it will take at least five patients to find one patient on whom the medicine would not be effective is:
P(X ≥ 5) = (1 - p)^(5-1) = 0.7^4 ≈ 0.2401
Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is approximately 0.2401.
To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we can use the binomial distribution. Let X be the number of patients out of four who are cured by the medicine. Then X follows a binomial distribution with n = 4 and p = 0.70. The probability that the medicine will be effective on exactly three out of four randomly selected patients is:
P(X = 3) = (4 choose 3) * (0.70)^3 * (1 - 0.70)^(4-3) = 4 * 0.343 * 0.3^1 ≈ 0.4116
Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is approximately 0.4116.
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At a print shop reams of printer paper are stored in boxes in a closet. Each box contains 12 reams of printer paper. A worker uses 4 reams from 1 of the boxes. Which function shows the relationship between y, the total number of reams of printer paper remaining in the closet, and x, the number of boxes in the closet?
The function shows the relationship between y, the total number of reams of printer paper remaining in the closet, and x, the number of boxes in the closet is y = 12x - 4
Let's start by considering the initial amount of printer paper in the closet before any boxes are used. Since each box contains 12 reams of printer paper, if there are x boxes in the closet, then the total number of reams of paper is given by 12x.
Now, if a worker uses 4 reams from one of the boxes, then the total number of reams of paper remaining in the closet is (12x - 4). If we define y as the total number of reams of paper remaining in the closet, then we have:
y = 12x - 4
This function shows the relationship between y, the total number of reams of printer paper remaining in the closet, and x, the number of boxes in the closet.
As x increases, the total number of reams of paper in the closet increases as well. However, each time a worker uses 4 reams of paper from a box, the total number of reams of paper in the closet decreases by 4.
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Consider the expression 16 - y^2/square root of 49 + 12. What is the value of the expression when y=-5?
Answer:
Step-by-step explanation:
16 - (y^2/sqrt(49)) +12
at y = -5
16 - ( (-5)^2 / sqrt(49)) +12
16 - ( 25 / 7) + 12
28 - (25/7)
(28*7 - 5) / 7 (LCM)
(196 - 5) / 7
(191/7)
27.2857 = Ans
Use the rational expression below to match the variables on the left with their excluded value(s) on the right.
The value of b = 4
How to solveThe function becomes undefined when the denominator goes to 0
3x² - 48 = 0
3x² = 48
x² = 16
x = +/ 4
From the given choices, it's x = 4
Rational expressions that utilize ratios of polynomial expressions are referred to as rational expressions. These can be written in the format p(x)/q(x), where both p(x) and q(x) are polynomials with the constraint that q(x) cannot equal zero.
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Out of a sample of 760 people, 367 own their homes. Construct a 95% confidence interval for the population mean of people in the world that own their homes. CI = (45. 31%, 51. 27%) CI = (43. 62%, 52. 96%) CI = (44. 74%, 51. 84%) CI = (46. 87%, 52. 56%)
The correct confidence interval for the population mean of people in the world who own their homes is CI ≈ (45.3%, 51.3%).
To construct a confidence interval for the population mean of people in the world who own their homes, we can use the sample data and calculate the margin of error. The confidence interval will provide an estimated range within which the true population mean is likely to fall.
Given the sample size of 760 people and 367 individuals who own their homes, we can calculate the sample proportion of individuals who own their homes as follows:
Sample proportion (p-hat) = Number of individuals who own their homes / Sample size
p-hat = 367 / 760 ≈ 0.483
To construct the confidence interval, we can use the formula:
CI = p-hat ± Z * sqrt((p-hat * (1 - p-hat)) / n)
Where:
CI = Confidence Interval
p-hat = Sample proportion
Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)
n = Sample size
Plugging in the values, we get:
CI ≈ 0.483 ± 1.96 * sqrt((0.483 * (1 - 0.483)) / 760)
Calculating the expression inside the square root:
sqrt((0.483 * (1 - 0.483)) / 760) ≈ 0.0153
Substituting back into the confidence interval formula:
CI ≈ 0.483 ± 1.96 * 0.0153
CI ≈ (0.483 - 0.0300, 0.483 + 0.0300)
CI ≈ (0.453, 0.513)
Therefore, the correct confidence interval for the population mean of people in the world who own their homes is CI ≈ (45.3%, 51.3%). None of the provided answer choices match the correct confidence interval.
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There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 24 feet high, and the hook is 32 feet from its base. How long is the rope?
Answer:
Step-by-step explanation: