a. The data provided enough evidence at a = 0.05 level that the true mean pH of water from this source differs from 7
b. A 95% confidence interval for the true mean pH level of the water is (6.21, 6.59) means about 95% of those intervals would contain the true mean pH level.
c. The estimated mean pH level of seven is not included in the interval in section (b). This is consistent with the result of the test in part (a), which also rejects the null hypothesis that the true mean pH level is 7.
(a) To test whether the true mean pH of water from this source differs from 7, we can perform a one-sample t-test. The null hypothesis is that the true mean pH is equal to 7, and the alternative hypothesis is that the true mean pH is not equal to 7.
The test statistic can be calculated as follows:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
t = (6.4 - 7) / (0.5 / sqrt(30))
t = -3.07
Using a t-table with 29 degrees of freedom at a significance level of 0.05 (two-tailed test), the critical t-value is ±2.045. Since the calculated t-value (-3.07) is outside of the critical t-value range, we can reject the null hypothesis and conclude that there is enough evidence at a = 0.05 level to suggest that the true mean pH of water from this source differs from 7.
(b) A 95% confidence interval for the true mean pH level of the water is (6.21, 6.59). This means that if we were to take many random samples of size 30 from this water source, and construct a 95% confidence interval for each sample mean pH level, then about 95% of those intervals would contain the true mean pH level.
(c) The interval in part (b) does not include the hypothesized mean pH level of 7. This is consistent with the result of the test in part (a), which also rejects the null hypothesis that the true mean pH level is 7.
The confidence interval provides additional information by giving a range of plausible values for the true mean pH level, and we can see that all of the values in this range are below 7, indicating that the water is indeed slightly acidic.
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Can someone please help I'm stuck at this
Answer:
Step-by-step explanation:
6.48x1.0e5=x
x/0.35
HELP PLEASE
I have no idea what to do anything I try fails.
Answer:
The distance between these parallel lines is 2 - (-7) = 9 units.
Madison swims 2/5 mile in an hour. Declan swims 7/10 mine in 1/5 hour. Who swims faster?
Declan swims faster than Madison, with a speed of 7/2 miles per hour compared to Madison's speed of 2/5 miles per hour.
How to compare swimming speed?Declan swims faster than Madison. While Madison swims 2/5 mile in an hour, which means her speed is 2/5 miles per hour, Declan swims 7/10 mile in 1/5 hour, which means his speed is 7/2 miles per hour. This indicates that Declan's speed is greater than Madison's speed.
In fact, we can see that Declan's speed is almost 4 times faster than Madison's speed. This means that Declan can cover a greater distance in the same amount of time compared to Madison.
Therefore, based on the given information, we can confidently say that Declan swims faster than Madison.
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Gray made a $3,500 tax-deductible contribution to his individual retirement account (IRA). Assuming he is in a 28 percent tax bracket, how much will this contribution save him on his taxes?
Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes.
When Gray contributes $3,500 to his individual retirement account (IRA), it is considered a tax-deductible contribution. This means that the amount contributed is deducted from his taxable income, reducing the amount of taxes he owes.
Since Gray is in the 28 percent tax bracket, this means that for every dollar of taxable income, he pays 28 cents in taxes. To calculate the tax savings from his $3,500 IRA contribution, we need to multiply the contribution amount by his tax rate:
$3,500 (contribution) x 0.28 (tax rate) = $980 (tax savings)
In this case, Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes. By contributing to his IRA, Gray not only invests in his future retirement but also takes advantage of the tax benefits associated with these accounts. In the end, he reduces his taxable income and, consequently, the amount of taxes he needs to pay.
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If the probability that the Islanders will beat the Rangers in a game is 0.88, what is the probability that the Islanders will win at least three out of four games in a series against the Rangers? Round your answer to the nearest thousandth.
Which pair of transformations moves quadrilateral 1 to quadrilateral 2?
o a. reflect it over the line y = -3, then rotate it 90° counterclockwise about the origin
o b. reflect it over the x-axis, then rotate it 180° about the origin
o c. rotate it 90° counterclockwise about point (-3,-3), then translate it 8 units to the right
o d translate it 8 units to the right, then reflect it over the line y=-3
c. rotate it 90° counterclockwise about point (-3,-3), then translate it 8 units to the right
How does quadrilateral 1 move to quadrilateral 2?The correct pair of transformations that moves quadrilateral 1 to quadrilateral 2 is option d: translate it 8 units to the right, then reflect it over the line y = -3.
First, by translating it 8 units to the right, all points of quadrilateral 1 will shift horizontally to the right by 8 units, maintaining their relative positions.
Next, reflecting it over the line y = -3 will result in a vertical flip of the shape. This reflection will change the orientation of the quadrilateral while keeping the translated positions intact.
Together, these two transformations will precisely move quadrilateral 1 to quadrilateral 2. Therefore, option d is the correct choice.
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Which of the following show a geometric series? select all that apply. 2 3 4.5 6.75 … 2 2.5 3 3.5 … 6 7 9 12 … 4 8 16 20 … 8 4 2 1 …
The first and fourth sequences show a geometric series.
2, 3, 4.5, 6.75, … is a geometric series with a common ratio of 3/2. Each term is received through multiplying the preceding term through the common ratio 3/2.2, 2.5, 3, 3.5, … is not a geometrical series since the common distinction among consecutive terms isn't always constant.6, 7, 9, 12, … isn't a geometrical collection since the ratio among consecutive terms isn't always steady.4, 8, 16, 32, … is not geometrical series with a common ratio of 2, Each term is obtained by means of multiplying the previous term through the common ratio 2.8, 4, 2, 1, … is a geometric series with a common ratio of 1\/2.Each term is acquired by means of multiplying the preceding time period with the aid of the common ratio 1\/2.Consequently, the sequences 2, 3, 4.5, 6.75, … and 4, 8, 16, 32, … are the geometric series.
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Complete Question:-
Which of the following show a geometric series? select all that apply.
1) 2 3 4.5 6.75 …
2) 2 2.5 3 3.5 …
3) 6 7 9 12 …
4) 4 8 16 20 …
5) 8 4 2 1 …
Answer:
Step-by-step explanation:
Find the necessary sample size.
A population is normal with a variance of 99. Suppose you wish to estimate the population mean μ. Find the sample size needed to assure with 68. 26 percent confidence that the sample mean will not differ from the population mean by more than 4 units.
A. 9
B. 7
C. 613
D. 25
If a population is normal with a variance of 99, the necessary sample size is 7 (Option B).
To find the necessary sample size for a given confidence level and margin of error, we can use the formula:
n = (Z² * σ²) / E²
where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ² is the population variance, and E is the margin of error.
In this case, the population variance (σ²) is 99, the desired confidence level is 68.26%, and the margin of error (E) is 4 units. The Z-score corresponding to a 68.26% confidence level is approximately 1, as it is close to one standard deviation from the mean in a normal distribution.
Now, we can plug the values into the formula:
n = (1² * 99) / 4²
n = (1 * 99) / 16
n = 99 / 16
n ≈ 6.19
Since we cannot have a fraction of a sample, we round up to the nearest whole number, which is 7. So, the necessary sample size is 7 (Option B).
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3. Un negociante tiene un capital de 40 000 soles y piensa guardarlo por un periodo de 2 años. Tiene dos propuestas de bancos. Banco A: 1,5 % bimestral. Banco B: 0,5% mensual. ¿Cuál de las dos propuestas le conviene?, ¿Cuánto interés recibirá en la entidad más conveniente? (7 puntos) Alternativas
Answer:
Para comparar las propuestas de los bancos, debemos llevar las tasas de interés a una misma unidad de tiempo. Podemos convertir la tasa del Banco A de bimestral a mensual multiplicándola por 2 (ya que hay 6 bimestres en 1 año):
Tasa del Banco A: 1,5% * 2 = 3% mensual
Tasa del Banco B: 0,5% mensual
Para calcular los intereses que se obtendrán en cada banco, podemos utilizar la fórmula del interés compuesto:
I = C * ((1 + r/n)^(n*t) - 1)
Donde:
I es el interés
C es el capital inicial
r es la tasa de interés en forma decimal
n es el número de veces que se capitaliza al año
t es el tiempo en años
Para el Banco A, como la tasa está en meses, capitalizaremos mensualmente (n=12):
I = 40 000 * ((1 + 0,03/12)^(12*2) - 1) = 4 896,18 soles
Para el Banco B, como la tasa ya está en meses, capitalizaremos mensualmente (n=12):
I = 40 000 * ((1 + 0,005)^(12*2) - 1) = 4 225,48 soles
Por lo tanto, la propuesta más conveniente es la del Banco A, ya que ofrece una tasa de interés mayor y genera un interés total de 4 896,18 soles. En cambio, el Banco B genera un interés total de 4 225,48 soles.
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Given the differential equation dy/dx = x-3/y, find the particular solution, y = f(x) with initial condition f(6) = -2
The particular solution of the given differential equation with the initial condition f(6) = -2.
To find the particular solution of the given differential equation dy/dx = (x-3)/y with the initial condition f(6) = -2, we first need to solve the differential equation. This is a first-order separable equation, so we can rewrite it as:
y dy = (x - 3) dx
Now, integrate both sides:
∫y dy = ∫(x - 3) dx
(1/2)y^2 = (1/2)x^2 - 3x + C
Now, apply the initial condition f(6) = -2:
(1/2)(-2)^2 = (1/2)(6)^2 - 3(6) + C
(1/2)(4) = (1/2)(36) - 18 + C
2 = 18 - 18 + C
C = 2
So the particular solution is:
(1/2)y^2 = (1/2)x^2 - 3x + 2
This is the particular solution of the given differential equation with the initial condition f(6) = -2.
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how to calculate the length of ED AND BE
With regard to the similar triangles,
The length of ED is 6.5cm.The length of BE is 14.4 cm.How is this so?In ΔACD
BE ∥ CD
In ΔACD and ΔABE
BE ∥ CD
∠ACD =∠ABE (corresponding angles)
∠ADC = ∠AEB (corresponding angles)
∠A = ∠A (common angle)
ACD ∼ ΔABE
So, The corresponding sides are in proportion.
Now, find ED
AB/BC = AE/ED
ED = AE (BC/AB)
ED = 26(5/20)
ED = 6.5cm
For BE
AB/AC = BE/CD
BE = CD (AB/AC)
BE = 18 (20/25)
BE = 14.4cm
Now, find BE
Therefore, the length of ED is 6.5cm and the length of BE is 14.4 cm.
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HELP MARKING BRAINLEIST IF CORRECT
Answer:
21.5
Step-by-step explanation:
First we can solve for c using the pythagoreom theorem. (probably didn't spell that right)
A squared + B squared = C squared
9 squared + 3 squared = c squared
81+9= c squared
90=c squared
90 square root is (rounded to the nearest tenth) 9.5
c=9.5
Then we can add 9.5+9+3= 21.5
The school assembly is being held over the lunch hour in the school gym. All the teachers and students are there by noon and the assembly begins. About 45 minutes after the assembly begins, the temperature within the gym remains a steady 77 degrees Fahrenheit for a few minutes. As the students leave after the assembly ends at the end of the hour, the gym begins to slowly cool down
1 hour =60 minutes
Step-by-step explanation:
Let M be the time in minutes . T be temperature in Farhenheit. From 45th min to end of the hour there remains a steady temperature. after that gyms starts to cools down . For time 45≤M≤60, Temperature T=77oF.To find a) Is M a function of T ? we know that Temperature changes with respect to time . So M is independent variable and T is dependent variable . so M cannot be a function of T .
A company manufactures computers. Function N represents the number of components that a new employee can assemble per day. Function E
represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours
worked in one day.
50€
1+4
N (t) =
E (t)
Which function describes the difference of the number of components assembled per day by the experienced and new employees?
=
O A D (t):
=
OB.
D (t)
O C.
OD.
D (t)
D (t)
=
=
10(2-13)
10(2-13)
(+3)(+4)
100 (21+13)
1+3
10e(2+13)
(+3)(+4)
Consider the function f(x) = 3x^2 +4x - 5 on the closed interval [ - 1,2). Find the exact value of the slope of the secant line connecting ( - 1, f( - 1)) and (2, f(2)). m = ?
The slope of the secant line connecting two points on a curve can be calculated using the formula: slope of secant line = (change in y) / (change in x).
For this problem, the two points are (-1, f(-1)) and (2, f(2)), and we need to find the slope of the secant line connecting them. To do this, we first need to find the y-coordinates of these points by plugging the given x-values into the function f(x) = 3x^2 + 4x - 5. Then we can use the formula for the slope of a secant line to find the slope of the line connecting these two points. The slope of the secant line is an important concept in calculus and is used to approximate the instantaneous rate of change of a function at a particular point.
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Will upvote if answer is correct.
Find the surface area of revolution about the x-axis of y = 4x + 2 over the interval 2
The surface area of revolution about the x-axis of y=4x+2 over the interval 2 is approximately 88.99 square units.
How to find the surface area of revolutionTo find the surface area of revolution about the x-axis of y=4x+2 over the interval 2, we first need to express the equation in terms of x.
Rearranging the equation, we get x = (y-2)/4.
Next, we need to determine the limits of integration.
Since we are rotating about the x-axis, the limits of integration are the x-values, which in this case are 0 and 2.
Using the formula for the surface area of revolution, S = 2π∫(y√(1+(dy/dx)^2))dx, we can plug in the values we have found.
dy/dx for y=4x+2 is simply 4, so we get:
S = 2π∫(4x+2)√(1+16)dx from 0 to 2
Simplifying this, we get:
S = 2π∫(4x+2)√17 dx from 0 to 2
Evaluating this integral using calculus, we get:
S = 32π√17/3
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WILL MARK BRAINLIEST QUESTION IS IN THE PHOTO
Based on the inscribed angle theorem, the measure of angle JKL in the circle is: m<JKL = 121°.
What is the Inscribed Angle Theorem?Where an inscribed angle is subtended by an arc it intercepts, the measure of the inscribed angle is equal to half of the the measure of the intercepted arc in the circle, based on the inscribed angle theorem.
Angle JKL is the inscribed angle that is subtended by arc JML. Find the measure of arc JML.
Measure of arc JML = 360 - 53 - 65
Measure of arc JML = 242°
m<JKL = 1/2(measure of arc JML) [inscribed angle theorem]
Substitute:
m<JKL = 1/2(242)
m<JKL = 121°
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Please help and solve this! Have a blessed day!
Answer: 8
Step-by-step explanation:
CF looks like the radius of the circle.
ED looks like the diameter.
.: ED = 2 x CF = 2 x 4 = 8
.: ED = 8
Answer:
The length of ED, or the diameter, is 8
Step-by-step explanation:
As the other person explained, CF is the radius, as the radius is from the centermost point to the edge. I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point. Therefore, since the diameter is double the radius, we can solve this with the following equation:
2 * r = d, where r is radius and d is diameter.
2 * 4 = d
8 = d
Pls help me it’s due tmrw
Answer:
Problem 8:
Option C) DE = √21
Problem 9:
Option C) Perimeter = 30 cm
Step-by-step explanation:
1. Problem 8
Draw a line segment connecting the center of the circle, X, to A. This is the radius of the circle
The points ABX form a right triangle with AX as the hypotenuse and AB, BX as the legs of the right triangle
By the Pythagorean theorem
hypotenuse² = sum of the squares of the two legs
Plugging in line segment references
AX² = AB² + BX²
We are given AC = 8, BX = 3
Since the segment BX intersects AC at right angles, AB = BC = AC/2
So AB = 8/2= 4
Plugging these values into the Pythagorean formula
AX² = AB² + BX²
AX² = 4² +3²
AX² = 16 + 9
AX² = 25
Draw a line connecting X and D
The points DEX form a right triangle with DX as the hypotenuse and EX and DE as the legs
Again, by the Pythagorean theorem
DX² = DE² + EX²
But DX is the radius of the circle so it must be the same as AX
Substitute for DX in terms of AX
DX² = DE² + EX²
=> AX² = DE² + EX²
But AX² = 25 and EX = 2 giving EX² = 4
Therefore
AX² = DE² + EX² becomes
25 = DE² + 4
DE² = 25 - 4
DE² = 21
DE = √21
This is choice C
Problem 9
To find the perimeter, just add up the individual side lengths:
Perimeter = 10 + 8 + 7 + 5 = 30 cm
Option C
Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x) and C(x) are in dollars. R(x) = 60x – 0.5x², C(x) = 2x+ 10, when x = 35 and dx/dt = 20 units per day = The rate of change of total revenue is $ per day. The rate of change of total cost is $ per day. The rate of change of total profit is $ per day.
The rate of change of:
total revenue is $500 per day
total cost is $40 per day
total profit is $460 per day
To find the rate of change of total revenue, cost, and profit with respect to time, we need to take the derivative of the given functions with respect to x and then multiply by the rate of change of x with respect to time (dx/dt).
Total revenue (R) = 60x – 0.5x²
dR/dx = 60 – x
When x = 35, dR/dx = 60 – 35 = 25
Rate of change of total revenue = (dR/dx) * (dx/dt) = 25 * 20 = $500 per day
Total cost (C) = 2x+ 10
dC/dx = 2
When x = 35, dC/dx = 2
Rate of change of total cost = (dC/dx) * (dx/dt) = 2 * 20 = $40 per day
Total profit (P) = R - C
dP/dx = (dR/dx) - (dC/dx)
When x = 35, dP/dx = 25 - 2 = 23
Rate of change of total profit = (dP/dx) * (dx/dt) = 23 * 20 = $460 per day
Therefore, the rate of change of total revenue is $500 per day, the rate of change of total cost is $40 per day, and the rate of change of total profit is $460 per day.
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Consider the function.
f(x) =1/x - 8
Identify the domain of f. (Give your answer as an interval in the form (*, #). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parentheses "(".")", "I*, or "J" depending on whether the interval is open or closed.
Find f = _____
The domain of the function f(x) = 1/x - 8 is (-∞, 0) U (0, +∞), and f = 1/x - 8.
The function f(x) is defined as 1/x - 8. The domain of the function is the set of all possible values of x for which the function is defined. Since the function involves division by x, x cannot be equal to zero. Therefore, the domain of f(x) is (-∞, 0) U (0, +∞), which means that x can take any value except 0.
To find f(x), we simply substitute the expression for f(x) in the definition of the function. Therefore, we have:
f(x) = 1/x - 8
This is the final answer. We cannot simplify it any further. The function f(x) represents a hyperbola with a vertical asymptote at x = 0 and a horizontal asymptote at y = -8.
As x approaches 0 from the left, f(x) goes to negative infinity, and as x approaches 0 from the right, f(x) goes to positive infinity. Similarly, as x approaches positive or negative infinity, f(x) approaches 0.
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traveling 60 mhp in the car after 3 hours how long would that be
Answer:
Step-by-step explanation:
60 x 3 = 180
180 miles
The graph below shows the relationship between temperature in degrees Fahrenheit and degrees Celsius.
What is the meaning of the y-intercept?
A the change in degrees Fahrenheit for each change of one degree Celsius
Bel change in degrees Celsius for each change of one degree Fahrenheit
the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius
D the temperature in degrees Celsius when the temperature is zero degrees Fahrenheit
The y-intercept of the graph is: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."
What is the Meaning of the Y-intercept of a Situation?In mathematical terms, the y-intercept is the point where a line or curve intersects the y-axis on a coordinate plane.
In practical terms, the y-intercept of a situation often represents the starting point or initial value of a variable or function.
In the graph given above that shows the relationship between temperature in degrees Fahrenheit and degrees Celsius, the y-intercept is 32 degrees Fahrenheit, which means: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."
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7. Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, four-year loan at an APR of 10%. A. What is the monthly payment? b. What is the total amount of the monthly payments? c. What is the finance charge?
A. Melissa's monthly payment is approximately $146.89.
B. The total amount of the monthly payments over the four-year period is approximately $7,052.72.
C. The finance charge on the loan is approximately $1,052.72.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.
To calculate the monthly payment, we can use the formula:
Monthly payment = [P x r x (1 + r)ⁿ] / [(1 + r)ⁿ⁻¹]
where P is the principal (the amount of the loan), r is the monthly interest rate, and n is the number of monthly payments.
A. To find the monthly payment, we first need to calculate the values of r and n.
Since the APR is 10%, the monthly interest rate is 10% / 12 = 0.00833 (rounded to 5 decimal places).
The number of monthly payments over four years is 4 x 12 = 48.
Using these values, we can calculate the monthly payment:
Monthly payment = [6000 x 0.00833 x (1 + 0.00833)⁴⁸] / [(1 + 0.00833)⁴⁸⁻¹]
Monthly payment ≈ $146.89
So Melissa's monthly payment is approximately $146.89.
B. To find the total amount of the monthly payments, we can multiply the monthly payment by the number of payments:
Total amount of monthly payments = Monthly payment x Number of payments
Total amount of monthly payments = $146.89 x 48
Total amount of monthly payments ≈ $7,052.72
So the total amount of the monthly payments over the four-year period is approximately $7,052.72.
C. To find the finance charge, we can subtract the original principal from the total amount of the monthly payments:
Finance charge = Total amount of monthly payments - Principal
Finance charge = $7,052.72 - $6,000
Finance charge ≈ $1,052.72
So the finance charge on the loan is approximately $1,052.72.
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A shoe store orders shoes from the manufacturer and sells them at a mall. Storing shoes at the store costs $6 per shoe pair for a year. When reordering shoes from the manufacturer, there is a fixed cost of $14 per order as well as $7 per shoe pair. The retail store sells 1750 shoe pairs each year. Find a function that models the total inventory costs as a function of x x the number of shoe pairs in each order from the manufacturer
The total inventory costs consist of two parts: the cost of storing the shoes and the cost of reordering the shoes. The cost of storing the shoes is given by the formula:
Cost of storing = $6 per shoe pair per year x number of shoe pairs
Since the shoes are stored for a year, this cost is incurred annually. The cost of reordering the shoes is given by the formula:
Cost of reordering = $14 per order + $7 per shoe pair x number of shoe pairs
This cost is incurred each time the store places an order with the manufacturer.
Let x be the number of shoe pairs in each order from the manufacturer. The number of orders needed to sell 1750 shoe pairs each year is given by:
Number of orders = 1750 shoe pairs / x shoe pairs per order
The total inventory costs can be expressed as:
Total cost = Cost of storing + Cost of reordering
Substituting the formulas for the two costs and the expression for the number of orders, we get:
Total cost = $6 per shoe pair per year x 1750 shoe pairs + ($14 per order + $7 per shoe pair x x shoe pairs) x (1750 shoe pairs / x shoe pairs per order)
Simplifying this expression, we get:
Total cost = $10,500 + $14(1750/x) + $7(1750)
Total cost = $10,500 + $24,500/x
Therefore, the function that models the total inventory costs as a function of x is:
Total cost(x) = $10,500 + $24,500/x
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The end points of five lines are shown below. Which line is parallel to the line in the diagram? A (1, 1) and (4,4) B (4, 1) and (4,4) C (2, 2) and (5,5) D (5,2) and (2,5) E (4,1) and (6,3)
D (5,2) and (2,5)
This is correct indeed
According to researchers one of the primary reasons relationship sour is that people stop listening to one other assumed that the relative frequency distribution for the length of time couples in conflict listen to each other has a mean of eight seconds and standard deviation of five seconds in sample of 37 couples in conflict let X represent the main of length of time the couples listen to each other what is the sample distribution of X
The square root of the sample size (n=37), which is approximately 0.820 seconds:
X ~ N(8, 5/√37)
The sample distribution of the mean, denoted as X, is the distribution of all possible sample means of a certain sample size taken from a population. In this case, we have a population of couples in conflict, and we have a sample size of 37. The mean length of time couples in conflict listen to each other is known to be 8 seconds with a standard deviation of 5 seconds.
Since we have a large enough sample size (n=37), we can assume that the sample mean follows a normal distribution according to the Central Limit Theorem. The Central Limit Theorem states that the sample means from a large enough sample size will be approximately normally distributed regardless of the population distribution, given that the samples are independent and randomly selected.
Thus, the sample distribution of X can be represented by a normal distribution with a mean of 8 seconds (same as the population mean) and a standard deviation of 5 seconds divided by the square root of the sample size (n=37), which is approximately 0.820 seconds:
X ~ N(8, 5/√37)
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Kendrick wants to build a slide for his sons. The height of the stairs is 5 feet. The base of the slide will be 6 feet from the bottom of the stairs. If he wants to build two slides so that each of his sons has their own, how many feet of plastic will he need? Round to the nearest tenth.
Answer:
Step-by-step explanation:
5^2 + x^2 = 8^2
25 + x^2 = 64
x = 6.2
Use the equation, 8^2x = 32^x+3 , to complete the following problems.
(a) rewrite the equation using the same base.
(b) solve for x. write your answer in the simplest form.
side note: don't respond with a link because your answer is deleted immediately, and i therefore i have no way of accessing the answer, also please show your work!
The solution to the equation is x = 15.
(a)How to rewrite the exponential equation?To rewrite the exponential equation using the same base, we need to express both 8 and 32 as powers of the same base. Since both 8 and 32 are powers of 2, we can rewrite the equation as:
[tex](2^3)^(2x) = (2^5)^(x+3)[/tex]
Here, we used the fact that[tex](a^b)^c = a^(b*c)[/tex]to simplify the exponents. We also used the property that 8 is equal to 2 raised to the power of 3, and 32 is equal to 2 raised to the power of 5.
(b)How to solve for x?Now that we have rewritten the equation with the same base, we can equate the exponents on both sides of the equation to solve for x:
[tex]2^(6x) = 2^(5x + 15)[/tex]
Since the bases on both sides of the equation are equal, we can equate the exponents and solve for x:
6x = 5x + 15
Subtracting 5x from both sides, we get:
x = 15
Therefore, the solution to the equation is x = 15.
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Find the sum of first seven terms of 5+11+17......
Step-by-step explanation:
d = a2 - a1
d = 11 - 5
d = 6
[tex]Sn \: = \frac{n}{2} (2a1 + (n - 1)d) \\ S7 = \frac{7}{2} (2 \times 11 + (7 - 1)6) \\ S7 = \frac{7}{2} (22 + 36) \\ S7 = \frac{7}{2} \times 58 \\ S7 = 7 \times 29 \\ S7 = 203[/tex]
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