The null hypothesis states that there is no distinction between the mean shelf life of the rechargeable batteries marketed by Power+ and Electro. Whereas, the alternative suggestion maintains that the mean duration of the batteries sold by Power+ stands greater than that of Electro.
The test statistic is 2.24
How to explain the statisticsUtilizing a t-distribution with degrees of freedom akin to the entire sample size minus two (df = n1 + n2 - 2 = 104) alongside the derived test statistic, the p-value can be accessed via calculator or software as 0.014.
As the figure procured from the p-value is lower than the significance level α = 0.05, we invalidate the null positing. The evidence warrants corroborating the allegation that the rechargeable batteries proffered by Power+ remain usable for longer than those provided by Electro.
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help quick will give brainlist
The measure of angle or arc FDG is 285°.
What is an arc of circle?A circle's circumference may be divided up into arcs. It is described as the curved line that divides a circle into segments by joining two points on its circumference. An arc's length is inversely proportional to the angle it forms at the circle's centre.
The length of the arc increases with increasing central angle, and vice versa. In geometry, trigonometry, and physics, arcs are frequently employed to represent and compute measurements of circles and circular objects.
For given problem,
mGC = 105° and
mFDG= 360° - mGF (∵ Total arc or angle of circle is 360°)
(As, mGF=mFC-mGC)
= 360°-(180°-mGC) (Assuming FC is a diameter making mFC=180°)
= 360°-(180°-105°) (∵mGC = 105°)
= 360°-75° = 285°
Hence, arc or angle FDG= 285 degrees.
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Which has a higher exchange rate Euro or the U.S. dollar?
Answer:
Euro
Step-by-step explanation:
1 EUR = 1.07 USD
Answer:
hello i d k the answer but im pretty sure the other guy is correct
Step-by-step explanation:
You are on a fishing boat that leaves its pier and heads east. After traveling for 29 miles, there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of S35°W for 14.6 miles.
a. At this time, how far are you from the boat's pier?
b. What bearing could the boat have originally taken to arrive at this spot?
a. The boat is currently 60.5 miles from its pier.
b. The boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
a.How to determine the distance from the boat's pier?
To determine the distance from the boat's pier, we can use the Pythagorean theorem since we have a right triangle formed by the boat's original position, the current position, and the distance traveled to reach the current position.
Let's call the distance from the boat's pier to the current position "d", and let's call the distance traveled after the turn "x".
Using trigonometry, we can see that:
sin(35°) = x/d
Rearranging this equation, we get:
x = d×sin(35°)
Now we can use the Pythagorean theorem to solve for "d":
d² = 29²+ (d×sin(35°))²
d² = 841 + 0.77d²
0.23d² = 841
d² = 3661.74
d = 60.5 miles (rounded to one decimal place)
Therefore, the boat is currently 60.5 miles from its pier.
b. How to determine the original bearing?
To determine the original bearing, we can use trigonometry again. Let's call the original bearing "θ". Then we have,
cos(θ) = 29/d
Rearranging this equation,
d = 29/cos(θ)
Now we can substitute this expression for "d" into the equation we used to solve for "x" earlier:
x = d×sin(35°)
x = (29/cos(θ))×sin(35°)
We know that after traveling this distance, the boat is currently 14.6 miles away from its original position. So we can set up another equation:
cos(θ) = 14.6/(29/cos(θ))
Simplifying, we get:
cos²(θ) = 0.5
Taking the inverse cosine of both sides,
θ = 45° or θ = 315°
Therefore, the boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
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a. The boat is currently 60.5 miles from its pier.
b. The boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
a.How to determine the distance from the boat's pier?
To determine the distance from the boat's pier, we can use the Pythagorean theorem since we have a right triangle formed by the boat's original position, the current position, and the distance traveled to reach the current position.
Let's call the distance from the boat's pier to the current position "d", and let's call the distance traveled after the turn "x".
Using trigonometry, we can see that:
sin(35°) = x/d
Rearranging this equation, we get:
x = d×sin(35°)
Now we can use the Pythagorean theorem to solve for "d":
d² = 29²+ (d×sin(35°))²
d² = 841 + 0.77d²
0.23d² = 841
d² = 3661.74
d = 60.5 miles (rounded to one decimal place)
Therefore, the boat is currently 60.5 miles from its pier.
b. How to determine the original bearing?
To determine the original bearing, we can use trigonometry again. Let's call the original bearing "θ". Then we have,
cos(θ) = 29/d
Rearranging this equation,
d = 29/cos(θ)
Now we can substitute this expression for "d" into the equation we used to solve for "x" earlier:
x = d×sin(35°)
x = (29/cos(θ))×sin(35°)
We know that after traveling this distance, the boat is currently 14.6 miles away from its original position. So we can set up another equation:
cos(θ) = 14.6/(29/cos(θ))
Simplifying, we get:
cos²(θ) = 0.5
Taking the inverse cosine of both sides,
θ = 45° or θ = 315°
Therefore, the boat could have originally taken a bearing of either N45°E or S45°W to arrive at the current spot.
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Conditional probability 3. Anya travels to work by car or by bicycle. The probability that she travels by car is 0.35 If she travels to work by car, the probability that she will be late is 0.12 If she travels to work by bicycle, the probability that she will be late is 0.25 a) Draw a probability tree diagram to show all the possible outcomes. b) Work out the probability that Anya will not be late.
The probability that Anya will not be late is 0.7955.
How to solvea) Probability tree diagram:
Car (0.35) Bicycle (0.65)
/ \
/ \
Late (0.12) Late (0.25)
/ \ / \
Not Late (0.88) Not Late (0.75)
b. To determine the likelihood that Anya will not be late:
P(No Tardiness) = P(No Tardiness | Car) * P(Car) + P(No Tardiness | Bicycle) * P(Bicycle)
P(No Tardiness) = (0.88 * 0.35) + (0.75 * 0.65) = 0.308 + 0.4875 = 0.7955
The probability that Anya will not be late is 0.7955.
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Can anyone help me with this please?
The z-scores are given as follows:
Josh: Z = -1.79. -> more convincing.Rita: Z = -1.58.How to obtain the z-scores?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution. -> this means that the higher the absolute value of the z-score, the more convincing it is.Josh's z-score is given as follows:
Z = (185.16 - 185.81)/0.363
Z = -1.79.
Rita's z-score is given as follows:
Z = (109.89 - 110.1)/0.133
Z = -1.58.
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Please help!
Vector C is 3.5 units West and Vector D is 3.3 units South. Vector R is equal to Vector D - Vector C. Which of the following describes Vector R?..
8.3 units 54
South of East
8.3 units 54circ South of East
4.8 units 47
East of South
4.8 units 47circ East of South
6.2 units 32
West of South
6.2 units 32circ West of South
5.9 units 52
South of West
The corresponding to Vector R is 4.8 units 47 East of South 4.8 units 47circ East of South
How to solve for the vectorVector C comprises a magnitude of -3.5i
Vector D is established as –3.3j (South bearing is thought to be negative along the y-axis).
Vector R = Vector D - Vector C
= (-3.3j) - (-3.5i)
= 3.5i - 3.3j
To evaluate the strength of Vector R, we must first compute its magnitude:
Magnitude of R = √((3.5)^2 + (-3.3)^2) ≈ 4.8 units.
determine the direction,
we shall need to calculate the angle θ with respect to the South direction (the negative y-axis):
tan(θ) = (3.5) / (3.3);
θ = arctan(3.5 / 3.3) ≈ 47°
Hence the answer is option 2
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adam bought a skateboard that is on sale for 35% off the original cost is 150 what is the sale price
Answer:
$97.50
Step-by-step explanation:
To calculate the sale price of the skateboard, we need to apply a discount of 35% to the original cost of $150:
Discount amount = 35% x $150 = $52.50
The sale price is the original cost minus the discount amount:
Sale price = $150 - $52.50 = $97.50
Therefore, the sale price of the skateboard after a 35% discount is $97.5
The sale price of the skateboard is $97.50.
To calculate the sale price, we need to first determine the amount of the discount, and then subtract that discount from the original price.
The discount is 35% of the original price:
Discount = 0.35 x 150 = 52.50
So the sale price is the original price minus the discount:
Sale price = 150 - 52.50 = 97.50
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12(x-20)=-48 for 7th grade math equation algebra
Answer: 16
Step-by-step explanation:
1. Distribute the 12 to the x variable and the constant.
You will get 12x - 240 = -48
2. -48 + 240 = 192. You now have 12x = 192
3. solve for x. x = 192/12 -> x = 16
What is the system of inequalities shown in the graph?
A
B
C
D
x+y≥75
4x + 2y < 200
√x+y> 75
2x + 4y < 200
4x + 2y > 75
x+y≤ 200
√x+y > 75
4x + 2y ≥ 200
In order to determine a system of inequalities from a graph, these steps must be undertaken:
What are the steps?Initially, locate the boundary lines that form either solid or dashed sections of the graph. These lines serve as an illustration of the equations defining the bounds of the specified solution.
Next, it is important to identify which inequality symbol exists for each line on this graph. One can accomplish this by examining the shaded portion located within the region bounded by the particular line being considered.
Finally, once all relevant information has been gathered when assessing the inequality pairs against their respective graphical boundaries, you should study the resulting solution set closely. This collection represents the specific region depicted in the graph satisfying every provided inequality.
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A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.
Passed Failed
Male 33 8
Female 66 16
Since P(male)×P(fail) = and P(male and fail) = , the two results are___ so the events are___
Since, P(male)*P(fail)= 0.33 and P(male and fail) = 0.33 , the two results are equal and independent.
What is Probability?
The possibility of outcome of any event is found by probability. as for an example whenever we toss a coin in the air, then what is the possibility that we get a head? Only based on possible outcomes we can answer this question. It is that part of events which deals with the results of random events. We can basically call it as prediction of any event that is based on study of previous record or the type and no of possible outcome.
Probability of happening of an event= Total no of favorable outcomes/ Total no of outcomes
Here in this question;
P(male/fail)= P(male and fail)/P(fail)
= [tex]\frac{8/123}{(8+16)/123}[/tex]
=[tex]\frac{8}{24} = \frac{1}{3} = 0.33[/tex]
P(male) = [tex]\frac{33+8}{123} = \frac{41}{123} =\frac{1}{3} = 0.33[/tex]
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Brad Huxter rents a luxury coupe while on vacation. The vehicle rents for $200 per week or
$29.95 per day. Mileage is charged at a rate of $0.25 per mile with the first 500 miles free. He
rents the vehicle for 10 days, drives it 865 miles, and spends $62 on gasoline. What is the cost
per mile of renting the vehicle?
The cost of renting the vehicle per mile is $0.524.
How to determine the cost per mile of renting the vehicleTo get the cost per mile of renting a vehicle, multiply the total cost of renting the vehicle by the total number of miles driven.
The rental cost:
10 days multiplied by $29.95 per day equals $299.50.
The total rental cost is $299.50.
The mileage cost:
865 miles minus 500 free miles equals 365 miles.
365 miles multiplied by $0.25 each mile equals $91.25.
The total cost of miles is $91.25.
Finally, let's figure up the overall cost:
Total rental expense + total mileage expense + gasoline expense = $299.50 + $91.25 + $62 = $452.75
Let us now compute the cost per mile:
Cost per mile = total cost / total distance traveled = $452.75 / 865 miles = $0.524 per mile
Hence, the cost of renting the vehicle per mile is $0.524.
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Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years.
The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?
12
61
82
24
After 12 years, the environment can no longer support the population growth. (option a).
Population growth is a fundamental concept in ecology and biology. It refers to the increase in the number of organisms in a population over time.
The carrying capacity is the maximum number of individuals of a particular species that can be supported by the environment without degrading it. In this case, the carrying capacity of the environment is 600 organisms. When the population reaches this limit, the environment can no longer support the population, and the growth rate slows down until it reaches equilibrium.
The table provides the approximate number of organisms after y years. To determine when the environment can no longer support the population, we need to find the year when the population exceeds the carrying capacity of the environment. In other words, we need to find the year when the population reaches or exceeds 600 organisms.
Looking at the table, we can see that the population reaches 600 organisms in the year 12.
Hence the correct option is (a).
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Answer: The environment will no longer be able to support the population after 24 years
Step-by-step explanation:
The environment will no longer be able to support the population after 24 years
How to determine the number of years?
The proper representation of the table is given as:
y 1 2 3 4
n 55 60 67 75
An exponential function is represented as:
[tex]n=ab^y[/tex]
Where:
a represents the [tex]initial[/tex] [tex]value[/tex]b represents the [tex]rate[/tex]Next, we determine the function equation using a statistical calculator.
From the statistical calculator, we have:
[tex]a=49.19[/tex] [tex]and[/tex] [tex]b=1.11[/tex]
Substitute these values in [tex]n=ab^y[/tex] .
So, we have:
[tex]n=49.19*1.11^y[/tex]
From the question, the maximum is 600.
So, we have:
[tex]49.19*1.11^y=600[/tex]
Divide both sides by 49.19
[tex]1.11^y=12.20[/tex]
Take the logarithm of both sides
[tex]y log(1.11) = log(12.20)[/tex]
Divide both sides by log(1.11)
[tex]y=23.97[/tex]
Approximate
[tex]y=24[/tex]
Hence, the environment will no longer be able to support the population after a period of 24 years.
How many website graphics can be created?
I do not understand what do you mean
Given that log(x) = 14.11, log (y) = 5.43, and
log (r) = 12.97, find the following:
log(xy4)
Logarithm [tex]log(xy^{4})[/tex] is equal to 36.4.
We can use the properties of logarithms to simplify [tex]log(xy^{4})[/tex] :
[tex]log(xy^{4})[/tex] = [tex]log(x)[/tex] + [tex]log(y^{4} )[/tex] (by the product rule)
= [tex]log(x)+4log(y)[/tex] (by the power rule)
Substituting the given values:
[tex]log(xy^{4})[/tex] = [tex]log(x)+4log(y)[/tex]
= 14.11 + 4(5.43)
= 36.4
Therefore, [tex]log(xy^{4})[/tex] = 36.4. This means that [tex]xy^{4}[/tex] equals 10 to the power of 36.4. Using the inverse property of logarithms, we can find that:
[tex]xy^{4}[/tex] = [tex]10^{36.4}[/tex]
= 4.17 x [tex]10^{36}[/tex]
In summary, [tex]log(xy^{4})[/tex] equals 36.4 and [tex]xy^{4}[/tex] equals 4.17 x [tex]10^{36}[/tex].
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A composite figure is created using a rectangle and a semi circle. What is the area of the figure? Use 3.14 for Pi by the way.
Rectangle = 216 (12x18) ( already solved just need semi circle)
The value of the calculated area of the figure is 343.17 sq units
What is the area of the figure?From the question, we have the following parameters that can be used in our computation:
Composite figure
The shapes in the composite figure are
SemicircleRectangleThis means that
Area = Semicircle + Rectangle
Using the area formulas on the dimensions of the individual figures, we have
Area = 12 * 18 + 1/2 * 3.14 * (18/2)^2
Evaluate the sum of products
Area = 343.17
Hence, the area of the figure is 343.17 sq units
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12. A new software package is expected to improve productivity at X company. However, because of training and implementation costs, savings are not expected to occur until the third year of operation. At that time, savings of $10,000 are expected, increasing by $1,000 per year for the following five years. After this time (eight years from implementation), the software will be abandoned with no scrap value. How much is the software worth today, at 15% interest?
Okay, here are the steps to solve this problem:
1) Savings start in year 3 at $10,000.
2) Savings increase by $1,000 each year for 5 years, so years 4-8 savings are $11,000, $12,000, $13,000, $14,000, $15,000.
3) There are 8 years of savings total.
4) Interest rate is 15%.
To calculate the present value at year 0 (today), we use the following formula:
PV = FV / (1 + r)^n
Where FV is the future value, r is the interest rate, and n is the number of years.
So for year 3 savings of $10,000:
PV = $10,000 / (1 + 0.15)^3 = $8,562
For year 4 savings of $11,000:
PV = $11,000 / (1 + 0.15)^4 = $8,948
And so on...
Adding up the present values for years 3 to 8:
$8,562 + $8,948 + $9,371 + $9,820 + $10,298 + $10,796 + $11,310 + $11,842 = $80,847
Therefore, the total present value of the 8 years of savings is $80,847.
So the software is worth $80,847 today at a 15% interest rate.
Let me know if you have any other questions!
Find the radius of a cylinder or volume 45 cm3 and length of 4 cm
Using the given volume and the length of the cylinder we know that the radius is 1.89 cm approximately.
What is a cylinder?A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.
In elementary geometry, it is regarded as a prism with a circle as its basis.
A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.
So, the volume of the cylinder is 45 cm³.
The length is 4 cm.
Now, the formula for volume is: V=πr²h
Insert values and calculate r as follows:
V=πr²h
45=3.14r²4
45=12.56r²
45/12.56=r²
3.58 = r²
1.89 = r
Therefore, using the given volume and the length of the cylinder we know that the radius is 1.89 cm approximately.
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Complete question:
Find the radius of a cylinder or volume of 45 cm³ and length of 4 cm.
A furniture company makes bar stools, tables, and chairs. Each bar stool requires 1 hour of labor, 8 feet of wood, and 0.2 gallons of stain. Each chair requires 4 hours of labor, 16 feet of wood, and 0.4 gallons of stain. Each table requires 2 hours of labor, 32 feet of wood, and 0.5 gallons of stain. Each week, the company has 700 hours of labor, 3360 feet of wood, and 60 gallons of stain. The company makes $10 in profit per bar stool, $25 in profit per chair, and $35 in profit per table. In order to maximize their profit, the furniture company should make
In the given problem, the furniture company should produce 300 bar stools and 50 chairs to maximize their profit, and should not produce any tables.
How to solve the Problem?To maximize profit, the furniture company needs to determine how many units of each product (bar stools, chairs, and tables) they should produce. Let's use x, y, and z to represent the number of bar stools, chairs, and tables respectively.
The objective function to maximize profit is:
Profit = 10x + 25y + 35z
The company has constraints on the amount of labor, wood, and stain available. These constraints can be expressed as follows:
Labor: 1x + 4y + 2z ≤ 700 (the company has 700 hours of labor available each week)
Wood: 8x + 16y + 32z ≤ 3360 (the company has 3360 feet of wood available each week)
Stain: 0.2x + 0.4y + 0.5z ≤ 60 (the company has 60 gallons of stain available each week)
Also, since we cannot produce negative units of any product, we must add the constraint that x, y, and z are all non-negative.
x ≥ 0, y ≥ 0, z ≥ 0
We can now use linear programming techniques to solve this problem. One possible method is the simplex method, which involves converting the problem into an augmented matrix and applying row operations until we obtain the optimal solution.
The optimal solution is:
x = 300 (produce 300 bar stools)
y = 50 (produce 50 chairs)
z = 0 (do not produce any tables)
The maximum profit that the company can earn is:
Profit = 10x + 25y + 35z = 10(300) + 25(50) + 35(0) = $3,250
Therefore, the furniture company should produce 300 bar stools and 50 chairs to maximize their profit, and should not produce any tables.
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Tickets to concerts, sporting events, and other forms of entertainment should be taxed.
a. completely agree
b. mostly agree
c. mostly disagree
d. completely disagree
You have $4,500 on a credit card that charges a 19% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
What is the perimeter of ^PQR?
A. 4+√42
B. 14
C. 9+√17
D. 17
Please show work or give an explanation pleaseee
The perimeter of the triangle is
9 +√17 units How to ascertain the perimeterTo ascertain the perimeter of a triangle whose verticies reside at points P(-3, -2),Q(0, 2), and R(1, -2),calculate the distances between these points and then add them.
Using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance for PQ =√((0 - (-3))^2 + (2 - (-2))^2)
Distance for PQ =√(3^2 + 4^2)
Distance for PQ = √(9 + 16)
Distance for PQ = √25
Distance for PQ = 5
Distance for PR = (1 - (-3))
Distance for PR = 4
Distance for QR =√((1 - 0)^2 + ((-2) - 2)^2)
Distance for QR =√(1^2 + 4^2)
Distance for QR =√17
Perimeter
Perimeter = Distance PQ + Distance PR + Distance QR
Perimeter = 5 + 4 + √17
Perimeter = 9 +√17 units
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The perimeter of the triangle is
9 +√17 units How to ascertain the perimeterTo ascertain the perimeter of a triangle whose verticies reside at points P(-3, -2),Q(0, 2), and R(1, -2),calculate the distances between these points and then add them.
Using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance for PQ =√((0 - (-3))^2 + (2 - (-2))^2)
Distance for PQ =√(3^2 + 4^2)
Distance for PQ = √(9 + 16)
Distance for PQ = √25
Distance for PQ = 5
Distance for PR = (1 - (-3))
Distance for PR = 4
Distance for QR =√((1 - 0)^2 + ((-2) - 2)^2)
Distance for QR =√(1^2 + 4^2)
Distance for QR =√17
Perimeter
Perimeter = Distance PQ + Distance PR + Distance QR
Perimeter = 5 + 4 + √17
Perimeter = 9 +√17 units
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-1+2-3+4-5+6...-99+100
Can someone pls help
-1 +
2 -
3 +
4 -
5 +
6 -
...
-99 +
100
= -1 + 2 - 3 + 4 - 5 + 6 - ... - 99 + 100
= 1
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised appear in the table below. Price per Photo $56 $52 $24 Number of Photos Sold 4 5 12 Revenue $224 $260 $288 Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos are sold, and what price per photo will maximize her revenue?
Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size,
shape, and color. Five are jelly-filled, 9 are lemon-filled, and 10 are custard-filled. You randomly select
one donut, eat it, and select another donut. Find the probability of selecting a lemon-filled donut followed by a
custard-filled donut.
(Type an integer or a simplified fraction.)
The probability of selecting a lemon-filled donut followed by a custard-filled donut is given as follows:
p = 15/92
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The probability of each event is given as follows:
First donut is lemon: 9/24.Second donut is custard: 10/23. -> 23 total outcomes as one has been eaten.Hence the probability is obtained as follows:
p = 9/24 x 10/23
p = 9/12 x 5/23
p = 3/4 x 5/23
p = 15/92
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Please help mee
I'm struggling really hard on this I failed 2 times already
(the picture has the question)
Algebra II (2019) Sem 2 L 1.8.4 Quiz: More Than One Vertical Asymptote Question 2 of 10 Which of the following rational functions is graphed below? O A. F(x) = B. F(x) = x(x+3)(x-3) (x-3)(x+3) ○ C. F(x) = x(x-3) ○ D. F(x) = (x+3)
As per the given graph, the rational function that is graphed in the given image is option B: F(x) = x(x+3)(x-3) / (x-3)(x+3) as per the factors.
Based on the graph, we can see that the function has vertical asymptotes at x = -3 and x = 3.
Option A has only one factor of (x+3) and one factor of (x-3), so it would have only one vertical asymptote at x = 3 or x = -3, but not both.
Option B has two factors of (x-3) and two factors of (x+3), so it has two vertical asymptotes at x = 3 and x = -3, which matches the graph.
Option C has only one factor of (x-3) and no factor of (x+3), so it would have only one vertical asymptote at x = 3 or x = -3, but not both.
Option D has only one factor of (x+3) and no factor of (x-3), so it would have only one vertical asymptote at x = -3 or x = 3, but not both.
Therefore, the rational function that is graphed in the given image is option B: F(x) = x(x+3)(x-3) / (x-3)(x+3).
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An object launched directly in the air at a speed of 24 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=-16t^2+24t+16
The maximum height that the object will reach is 40 feet.
How to find the maximum height that the object will reach?For any quadratic equation of the form, f(t) = at² + bt + c,
where a, b and c are constants
The maximum value of f(t) is give by the formula:
f(t) = c - (b²/4a)
Since the position of the object can be modeled using the function:
f(t) = -16t² + 24t + 16
where a = -16, b = 24 and c = 16
Thus, the maximum height will be:
maximum height = 16 - (24² / 4(-6))
maximum height = 16 - 576/(-24)
maximum height = 16 + 24
maximum height = 40 feet
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Complete Question
An object launched directly in the air at a speed of 24 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=-16t^2+24t+16, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach? Do not include units in your answer.
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The probability that a student had blue eyes and wore glasses is 4% or 0.04.
B. The probability that a student's eye color is brown given that the student wears glasses is 42.9% or 0.429.
What is the probability?To find the probability of blue-eyed glasses-wearers, when you look where "Blue" intersects "Yes" in the table. The relative frequency is 0.04, or 4%, hence the probability of a student having blue eyes and wearing glasses 4%.
To find the probability that a student's eye color is brown since the fact is: that the student wears glasses, it can be calculated as:
P(A|B) = P(A and B)/P(B)
P(Brown and Yes) = 0.12
P(Yes) = 0.04 + 0.12 + 0.08 + 0.04
= 0.28
Hence, the probability that a student's eye color is brown since they wear glasses are:
P(Brown | Yes) = P(Brown and Yes) / P(Yes)
= 0.12 / 0.28
= 0.429 or 42.9%
So we can say that, Blank 1 is "0.04" while Blank 2 is "42.9%".
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See text below
Eye Color
Question 15 (2 points)
A high school class conducts a survey where students are asked about their eye color and whether or not they wear glasses. The two-way table below shows the results of the survey as relative frequencies.
Glasses?
Yes No
Blue 0.04 0.16
Brown 0.12 0.24
Green 0.08 0.12
Hazel 0.04 0.20
A. Based on thee results of the survey, what is the probability, rounded to the nearest tenth, that a student had blue eyes and wore glasses?
B. Based on the results of the survey, what is the probability, rounded to the nearest tenth, that a student's eye color is brown given that the student wears glasses?
Word Bank:
8% 4% 16% 20% 42.9%
24% 12%
Blank 1:
Blank 2:
What is 18% of 375.00
Answer:
[tex]375 \times .18 = 67.5[/tex]
I don't understand how you substituted the equation of this question noted the length,d m,of a rectangular field is 40m greater than the width. The perimeter of the field is 400m . Kindly simplify
The width of the rectangular field is 80 meters and the length is 120 meters for the given perimeter 400m.
What is the perimeter?Perimeter is a mathematical term that refers to the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
According to the given information:
Let's break down the information given in the question:
Length of the rectangular field is 40m greater than the width.
The perimeter of the field is 400m.
Let's denote the width of the rectangular field as 'w' meters. According to the first information, the length of the field would be 'w + 40' meters, as it is 40m greater than the width.
Now, let's use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (Length + Width)
Substituting the values we have:
Perimeter = 2 * (w + 40 + w)
Perimeter = 2 * (2w + 40)
Since the given perimeter is 400m, we can set up the equation:
400 = 2 * (2w + 40)
Now we can solve for 'w' by dividing both sides of the equation by 2:
400/2 = 2w + 40
200 = 2w + 40
Next, we subtract 40 from both sides of the equation to isolate the term with 'w':
200 - 40 = 2w
160 = 2w
Finally, we divide both sides of the equation by 2 to solve for 'w':
160/2 = w
80 = w
So, the width of the rectangular field is 80 meters. And since the length is 40 meters greater than the width, the length would be:
Length = Width + 40 = 80 + 40 = 120 meters.
So, the width of the rectangular field is 80 meters and the length is 120 meters.
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Margarita borrows $14,000 from her uncle and agrees to repay it in monthly installments of $400. Her uncle charges 0.9% interest per month on the balance.
(a) If her balance An in the nth month is given recursively by A0 = 14,000 and An = k · An − 1 − 400, what is k?
(b) Find her balance after two months. (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
(a) We know that the balance An in the nth month is given by:
An = k · An-1 - 400
where A0 = 14,000. Substituting n = 1, we get:
A1 = k · A0 - 400
A1 = k · 14,000 - 400
We also know that her uncle charges 0.9% interest per month on the balance. This means that the balance after one month should be:
A1' = A0 + 0.009 · A0 - 400
A1' = 14,000 + 0.009 · 14,000 - 400
A1' = 14,126
Setting A1 = A1', we can solve for k:
k · 14,000 - 400 = 14,126
k = 1.009
Therefore, k is approximately 1.009.
(b) To find her balance after two months, we can use the recursive formula with n = 2:
A2 = k · A1 - 400
A2 = 1.009 · 14,126 - 400
Using a calculator, we get:
A2 ≈ 14,272.34
Therefore, her balance after two months is approximately $14,272.34.