The critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.
When finding a 98% confidence interval for a normally distributed population with a sample size of 32, you will need to use a critical value from the standard normal (z) distribution.
To find the critical value, you can refer to a z-table or use a calculator with statistical functions. For a 98% confidence interval, you will need the z-score that corresponds to the middle 98% of the data, leaving 1% in each tail. This z-score is approximately 2.33.
So, the critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
The dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
Let's start by finding the formula for the cost of the container in terms of its dimensions.
The volume of the cylinder is given as 600 cubic centimeters, so we have:
πr^2h = 600
where r is the radius of the cylinder and h is its height. Solving for h, we get:
h = 600 / (πr^2)
The surface area of the cylinder is given by:
A = 2πrh + 2πr^2
Substituting h in terms of r, we get:
A = 2πr(600/(πr^2)) + 2πr^2
= 1200/r + 2πr^2
The cost of the container is the sum of the cost of the styrofoam sides and bottom and the cost of the paper top. Let's call the radius of the paper top R, and assume that the height of the cylinder is greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Then the cost of the container is:
C = 0.04(2πrh + πr^2) + 0.05(πR^2)
Substituting h in terms of r, we get:
C = 0.08πr(600/(πr^2)) + 0.04πr^2 + 0.05πR^2
= 4.8/r + 0.04πr^2 + 0.05πR^2
To minimize the cost, we need to find the values of r and R that minimize the cost function C. To do this, we take the partial derivatives of C with respect to r and R, and set them equal to zero:
dC/dr = -4.8/r^2 + 0.08πr = 0
dC/dR = 0.1πR = 0
Solving for r and R, we get:
r = ∛(60/π) ≈ 2.78 cm
R = 2.5 cm
We can check that these values give us a minimum by checking the second derivatives:
d^2C/dr^2 = 9.6/r^3 + 0.08π > 0 (minimum)
d^2C/dR^2 = 0.1π > 0 (minimum)
Therefore, the dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
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Emma has a wooden sculpture in the shape of a cuboid.
The sculpture is 2. 2 m high, 1. 1 m wide and 0. 55 m thick.
Emma plans to paint all the faces of the sculpture with
three coats of wood varnish.
a How many tins of wood varnish does Emma
need to buy?
b What is the total cost of the wood varnish?
varnish
$ 3. 99
(Size of tin: 100 ml)
20 m2 per litre
a) To find the total surface area of the cuboid, we need to find the area of each face and then add them up.
Area of one face = length x width
Area of top and bottom faces = 1.1 m x 0.55 m = 0.605 m² (2 faces)
Area of front and back faces = 2.2 m x 0.55 m = 1.21 m² (2 faces)
Area of side faces = 2.2 m x 1.1 m = 2.42 m² (2 faces)
Total surface area = (2 x 0.605) + (2 x 1.21) + (2 x 2.42) = 7.7 m²
Each tin of varnish covers 20 m², so Emma needs:
Number of tins = (total surface area x number of coats) / coverage per tin
Number of tins = (7.7 x 3) / 0.02 = 1155
Emma needs to buy 1155 tins of wood varnish.
b) The cost of each tin of varnish is $3.99 for 100 ml. To find the cost of 1155 tins, we first need to convert the volume of varnish needed into liters.
Volume of varnish needed = (total surface area x number of coats) / coverage per litre
Volume of varnish needed = (7.7 x 3) / 20 = 1.155 liters
The number of tins required to make up 1.155 liters of varnish is:
Number of tins = (1.155 / 0.1) = 11.55
So Emma needs to buy 12 tins of varnish. The total cost is:
Total cost = cost per tin x number of tins
Total cost = $3.99 x 12 = $47.88
The total cost of the wood varnish is $47.88.
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Please help I need it ASAP, also needs to be rounded to the nearest 10th
Answer: AB = 16.4
Step-by-step explanation:
You can use tan x = opposite/adjacent
tan 38 = AB/21
21 tan 38 = AB
AB = 16.4
Let f(x) =x^2 + x + 9 and g(x)x = -4x - 3.
Find (fg) (x) and (f/g) (x)
Answer: First, we need to find the composite function (fg)(x):
(fg)(x) = f(g(x))
= f(-4x-3)
= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))
= 16x^2 + 24x + 18
Therefore, (fg)(x) = 16x^2 + 24x + 18.
Next, we need to find the quotient function (f/g)(x):
(f/g)(x) = f(x) / g(x)
= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))
To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:
-4 | 1 1 9
|_____-4__ 12
| 1 -3 21
Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)
Simplifying further, we get:
(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))
Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).
Step-by-step explanation:
The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?
O Use the distance formula to find the length of each side, and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
O Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicul
O Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
Answer:..
Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
the sample mean was 35 and the p -value for the test was 0.0627 . what would the p -value have been if the researcher had used
If the researcher had used H0 >= 38 as the alternative hypothesis instead of H1 < 38, the p-value would have been (1-0.0627) = 0.9373. This can be calculated using the complement rule for probabilities. So, the correct option is A).
The given hypothesis is
H0: µ = 38 (null hypothesis)
Ha: µ < 38 (alternative hypothesis)
Given: Sample mean = 35 and p-value = 0.0627
We need to find the p-value if the researcher had used Ha: µ > 38 instead of Ha: µ < 38.
The new alternative hypothesis is
Ha: µ > 38
We can find the new p-value as follows
p-value = P(Z ≤ z-score) [For a one-tailed test]
where z-score = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Here, hypothesized mean (µ) = 38, sample mean (X) = 35, standard deviation is not given, so we cannot calculate z-score directly.
But, we know that z-score is the number of standard deviations the sample mean is from the hypothesized mean.
Therefore, we can calculate the z-score indirectly using the formula
z-score = (X - µ) / (s / √n)
where s = sample standard deviation, n = sample size
We do not have the sample standard deviation, so we will assume it is equal to the population standard deviation or use a t-distribution if we have the sample size and degrees of freedom.
Assuming a standard normal distribution, the z-score can be calculated as
z-score = (35 - 38) / (σ / √(n))
where n = sample size
We do not have the value of σ, so we cannot calculate the z-score. However, we can still find the new p-value using the given p-value.
The p-value for the original test (Ha: µ < 38) is 0.0627.
For a one-tailed test, the p-value for the opposite direction (Ha: µ > 38) is:
p-value = 1 - 0.0627
p-value = 0.9373
Therefore, if the researcher had used Ha: µ > 38 instead of Ha: µ < 38, the new p-value would have been 0.9373. So, the correct answer is A).
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--The given question is incomplete, the complete question is given
" A researcher conducted a test of the hypotheses used H. <38 as the alternative hypothesis? 38 versus H. 38. The sample mean was 35 and the p value for the test was 0.0627 What would the pvalue have been if the researcher had A 1-0.0627 B) 1-2(0.0627) C 1-0) (0.0627) D) 2(0.0627) (E 0.0627)"--
Question Help
Kimo's Material Company hauls gravel to a construction site, using a small truck and a large truck. The
carrying capacity and operating cost per load are given in the accompanying table. Kimo must deliver a
minimum of 350 cubic yards per day to satisfy her
contract with the builder. The union contract with her drivers
requires that the total number of loads per day is a minimum of 9. How many loads should be made in each
truck per day to minimize the total cost?
Small Truck Large Truck
50
Capacity (yd)
70
Cost per Load
$87
$73
In order to minimize the total cost, the number of loads in a small truck that should be made is
number of loads in a large truck that should be made is
and the
Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
the total cost will be minimized when the loads are distributed in the following way:
5 loads in the small truck (total capacity of 5 * 50 = 250 cubic yards)
4 loads in the large truck (total capacity of 4 * 70 = 280 cubic yards)
This will result in a total of 9 loads and a total capacity of 530 cubic yards, which meets both the daily minimum delivery requirement of 350 cubic yards and the union contract requirement of 9 loads per day.
The total cost can be calculated as follows:
Cost of 5 loads in small truck = 5 * $87 = $435
Cost of 4 loads in large truck = 4 * $73 = $292
Total cost per day = $435 + $292 = $727
Therefore, Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.
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‼️WILL MARK BRAINLIEST‼️
The true statements are:
The range for the African-American outline is greater than the range for the Holocaust outline, so there is more variability in the data set for African-American outline.The mean for the Holocaust outline, 38.75, is greater than the mean for the African- American outline, 35, so a student working on the Holocaust project spent more time on the outline on average than a student working on the African-American project.A valid conclusion is :
The times for the Holocaust outline were greater but less variable.What is the range and mean of a data set?The range of a data set is the difference between the highest and lowest values in the set.
To calculate the range, you subtract the smallest value from the largest value.
The mean of a data set, also called the average, is the sum of all the values in the set divided by the total number of values in the set.
To calculate the mean, you add up all the values and divide by the total number of values.
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can someone help with this please
Answer:
shape a is 20 cm squared
Step-by-step explanation:
shape a is a parallogram, A =b×h. 5x4=20
shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.
area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units
(answer all for 15 points) 1) Chris went to Waffle House and his bill came out to $8. 23. He had a coupon for 40% off. How much did Leke pay for his meal?
2) To which set or sets does the number -5 belong?
3) Target bought a shirt for $4 from a factory. They mark it up 40%. How much does Target sell the shirt for? $_
1) Leke pay $4.938 for his meal after a 40% discount.
2) -5 belongs to integers, rational numbers, and real number sets.
3) Target sells the shirt for $5.6 after they mark it up for 40%
1) Bill = 8.23 , discount coupon = 40 %
The total amount paid by leke after the discount coupon = 8.23 - (40 % of 8.23)
Total amount = 8.23 - ( 8.23 × 40/100 )
Total amount = 8.23 - 3.292
The total amount paid by Leke is $4.938
2) -5 is an integer because it is a negative whole number.
-5 is a rational number because it can be written in the form of a fraction.
-5 is a real number because it is a rational number .
-5 belongs to integers, rational numbers, and real number sets.
3) Shirt price = $4 , price increased = 40%
selling price = 4 + (40% of 4)
selling price = 4 + (4 × 40/100)
selling price = 4 + 1.6
Target sell shirt for $5.6
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Nick is building a kaleidoscope by making a cylinder case with height of 11 inches and a diameter of 2 3/4 inches. What is the volume of the cylinder in cubic inches? Round to the nearest tenth. ( Use 3. 14 for pi ) Right Awnser will be marked brainliest!!
The volume 33.5 cubic inches
To calculate the volume of the cylinder, we need to use the formula:
V = π[tex]r^2[/tex]h
where V is the volume, π is the constant pi, r is the radius of the base (which is half the diameter), and h is the height.
First, we need to convert the diameter of the cylinder to inches:
2 3/4 inches = (2*4 + 3)/4 inches = 11/4 inches
The radius of the cylinder is half the diameter, so:
r = (11/4)/2 = 11/8 inches
Now we can plug in the values into the formula:
V = π[tex](11/8)^2[/tex](11) cubic inches
V ≈ 33.5 cubic inches (rounded to the nearest tenth)
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Im actually going to explode I hate geometry with a passion
Answer: B 28√15
Step-by-step explanation:
They want you to find the Area of the quadrilateral. But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.
We know the 2 triangles are congruent from the theorem (see diagram
We also know that QR=TR=SR They are all radius
Let's solve for triangle PRS
PR = hypotenuse = 10+7 =17
SR=7 radius
Use pythagorean to find PS
c²=a²+b²
17²=7²+b²
289 = 49 + b²
b²=289 -49
b² = 240
b=√240
b=[tex]\sqrt{16*15}[/tex]
b= 4√15 This is PS
Area of triangle = 1/2 bh b=PS h=7
Area of triangle = 1/2 (4√15)(7)
Area of triangle = (2√15)(7)
Area of triangle = 14√15
Area of quadrilateral = 2 (14√15) > 2 triangles make the quadrilateral
Area of quadrilateral = 28√15
PLEASE HELP ME WITH THIS MATH PROBLEM!!! WILL GIVE BRAINLIEST!!! 20 POINTS!!!
The average price of milk in 2018 was $6.45 per gallon.
The average price of milk in 2021 was $189.15 per gallon.
How to calculate the priceWhen x = 0 (which represents the year 2018), the function becomes:
3.55 + 2.90(1 + 0)³
= 3.55 + 2.90(1)³
= 3.55 + 2.90
= 6.45
The average price of milk in 2018 was $6.45 per gallon.
When x = 3 (which represents the year 2021), the function becomes:
3.55 + 2.90(1 + 3)³
= 3.55 + 2.90(4)³
= 3.55 + 2.90(64)
= 3.55 + 185.6
= 189.15
The average price of milk in 2021 was $189.15 per gallon.
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If the table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 2"
The relative frequency for the event of spin a 2 is P = 0.16
Given data ,
Let the total number of times the event occurs = 50
Now , the number of times the spin of 2 occurs = 8 times
So , the relative frequency is given by
Relative Frequency = Subgroup frequency / Total frequency
P = 8 / 50
P = 0.16
Hence , the relative frequency is 0.16
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The complete question is attached below :
If the table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 2"
someone PLSS helpi don’t know
The parts of this equilateral triangle ABC are as follows:
The length of side x is 3√3The length of segment DB is 3Angle C is 60 DegreesAngles B is 60 DegreesWhat is the length of side x of the equilateral triangle?The length of side x of the equilateral triangle is determined as follows:
AD = x
AB = 6
DB = 6/2 or 3
AB² = AD² + DB²
6² = x² + 3²
x² = 6² - 3²
x = 27
x = 3√3
Therefore, the length of the perpendicular bisector AD is 3√³ units
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Answer:
the length is 3√³ units
What is the quotient of 1. 892×10^8 and 4. 3×10^3
expressed in scientific notation? Please tell me the answer!
The quotient of 1.892×10^8 and 4.3×10^3 expressed in scientific notation is 4.4×10^4.
The quotient is determined by dividing any two numbers. In this case, the two numbers are 1.892×10^8 and 4.3×10^3. In order to calculate the quotient here, we will divide 1.892×10^8 by 4.3×10^3. Hence,
1. Divide the coefficients: 1.892 ÷ 4.3 = 0.44
2. Subtract the exponents: (10^8) ÷ (10^3) = 10^(8-3) = 10^5
3. Combine the results: 0.44 × 10^5
To express this answer in scientific notation, we need to move the decimal point one place to the left and adjust the exponent accordingly:
0.44 × 10^5 = 4.4×10^4
Therefore, the quotient expressed in scientific notation is 4.4×10^4.
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Regular quadrilateral prism has a height h = 11 cm and base edges b= 8cm. Find the sum of al edges
The sum of all edges of the regular quadrilateral prism is 108 cm.
To find the sum of all edges of a regular quadrilateral prism with height h = 11 cm and base edges b = 8 cm, follow these steps:
1. Determine the number of base edges: A quadrilateral has 4 edges, so there are 4 base edges for the top and 4 for the bottom, totaling 8 base edges.
2. Determine the number of height edges: There are 4 vertical edges connecting the top and bottom bases.
3. Add the number of base and height edges: 8 base edges + 4 height edges = 12 edges in total.
4. Calculate the sum of all edge lengths: (8 base edges (8 cm)) + (4 height edges (11 cm)) = 64 cm + 44 cm = 108 cm.
So, the sum of all edges of the regular quadrilateral prism is 108 cm.
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The volume of the cylinder displayed is approximately 9. 4 cubic feet. What is the approximate volume for a cone with the same height and radius? Whats the answer
The volume of the cone is approximately one-third the volume of the
cylinder
:V(cone) ≈ 1/3 V(cylinder) = 1/3 (9.4) ≈ 3.1 cubic feet.
The volume of a cone with the same height and radius as the given
cylinder, we can use the formula:
[tex]V = 1/3 πr²h[/tex]
where V is the volume, r is the radius, and h is the height.
Since the cylinder has a volume of approximately 9.4 cubic feet, we can
use the formula for the volume of a cylinder
:V = πr²hand solve for the radius:
[tex]r = √(V/πh) = √(9.4/πh)[/tex]
Now we can substitute this expression for the radius into the formula for
the volume of a cone:
[tex]V = 1/3 π(√(V/πh))²h[/tex]
Simplifying this expression gives:
[tex]V = 1/3 π(V/πh)hV = 1/3 V[/tex]
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Clarissa is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 10 inches × 14 1/2
inches. She needs to cut another rectangle that is 10 1/4
inches by 10 1/2 inches. How many total square inches of construction paper does Clarissa need for her project?
Clarissa needs a total of 251.25 square inches of construction paper for her project.
To find the total area of construction paper needed, we need to find the area of each rectangle and add them together.
The first rectangle has an area of 10 inches × 14.5 inches = 145 square inches.
The second rectangle has an area of 10.25 inches × 10.5 inches = 107.625 square inches.
Adding these two areas together, we get a total of 145 + 107.625 = 252.625 square inches.
Therefore, Clarissa needs a total of 251.25 square inches (rounded to two decimal places) of construction paper for her project.
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IVan charges an hourly rate for a moving team to load and unload a truck. The charge is a different
hourly rate for a team to pack and unpack boxes. For 8 hours of loading and unloading and 6 hours of
packing and unpacking the company charges $890. For 5 hours of loading and unloading and 3 hours of
packing and unpacking the company charges $515. Write a system of equations and then determine the
company's hourly rates?
Let's assume that the hourly rate for loading and unloading is $x and the hourly rate for packing and unpacking is $y.
From the given information, we can form the following two equations:
[tex]8x + 6y = 890[/tex] ...(1) (for 8 hours of loading and unloading and 6 hours of packing and unpacking)
[tex]5x + 3y = 515[/tex] ...(2) (for 5 hours of loading and unloading and 3 hours of packing and unpacking)
To solve for x and y, we can use the method of elimination.
Multiplying equation (2) by 2, we get:
[tex]10x + 6y = 1030[/tex] ...(3)
Now, subtracting equation (1) from equation (3), we get:
2x = 140
Therefore, x = $70 per hour.
Substituting the value of x in equation (2), we get:
5(70) + 3y = 515
Simplifying, we get:
3y = 165
Therefore, y = $55 per hour.
Hence, the company's hourly rates are $70 per hour for loading and unloading and $55 per hour for packing and unpacking.
In summary, we can set up a system of equations to solve for the hourly rates of a moving team.
From there, using the method of elimination, we can solve for the hourly rates for both loading and unloading as well as packing and unpacking.
In this case, the hourly rate for loading and unloading is $70 per hour, and the hourly rate for packing and unpacking is $55 per hour.
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You babysat your neighbor's children and they paid you $45 for 6 hours. Fill in the t-table for hours (x) and money (y)
The full t-table will be:
Hours (x) Money (y)
0 $0
1 $7.5
2 $15
3 $22.5
4 $30
5 $37.5
Given that the neighbors paid $45 for 6 hours to babysit their children.
So the rate to babysit is = $45/6 = $7.50 per hour.
So the function rule for the situation is given by,
y = 7.50x, where y is the total earning by babysitting neighbors' children and x is the number of hour to babysit.
when x = 0, y = 7.5*0 = $0
when x = 1, y = 7.5*1 = $7.5
when x =2, y = 7.5*2 = $15
when x = 3, y = 7.5*3 = $22.5
when x = 4, y = 7.5*4 = $30
when x = 5, y = 7.5*5 = $37.5
So the t-table will be:
Hours (x) Money (y)
0 $0
1 $7.5
2 $15
3 $22.5
4 $30
5 $37.5
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14
Find the limit of the rational function a. as x and b. as X-→ - 00 X + 6 f(x) = +3 + 20 X+6 a. lim x x² + 20 (Simplify your answer.) X + 6 b. lim x--00x2 + 20 = (Simplify your answer.) (
Both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0
Know more about rational function,
First, let's rewrite the rational function f(x) more clearly and identify the two limits we need to find: f(x) =[tex](x + 6) / (x^2 + 20)[/tex]
a. lim (x→∞) f(x) b. lim (x→-∞) f(x)
To find these limits, we can use the following steps:
Step 1: Divide both the numerator and the denominator by the highest power of x in the denominator.
In this case, it is x^2. f(x) = [tex][(x + 6) / x^2] / [(x^2 + 20) / x^2][/tex]
Step 2: Simplify the function. f(x) =[tex][(1/x) + (6/x^2)] / [1 + (20/x^2)][/tex]
Step 3: Evaluate the limits.
a. lim (x→∞) f(x)
= [(0) + (0)] / [1 + (0)]
= 0 / 1 = 0
b. lim (x→-∞) f(x)
= [(0) + (0)] / [1 + (0)]
= 0 / 1 = 0
So, both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0
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What is the perimeter of triangle abc? round answers to the nearest tenth.
a
145°
6 m
45°
b
oa.
20.5 meters
ob.
b. 22.4 meters
oc.
12 meters
od.
18 meters
The Perimeter of the Triangle is 20.5. when the AB value is 6 m and the angles are 45°. Option B is the correct answer
Given:
AB = 6 m
∠ACB = 45°
By using Trigonometry formulas,
We can determine the AC length by using the sin 45° formula and it is given as,
sin 45° = opposite / hypothesis
sin 45° = AB /AC
1/√2 = 6/ AC
AC = 6√2
We can determine the BC length by using the tan 45° formula which is given as,
tan 45° = opposite / adjacent
tan 45° =AB/ BC
1 = 6/ BC
BC= 6
Now we can determine the perimeter of the triangle by using the perimeter of the triangle formula which is given as,
[tex]P=a+b+√a²+b²[/tex]
Where:
a = opposite side = AC
b = adjacent side = BC
Substuting the a and b values in the above equation we get,
= 6 + 6 +√ 6²+ 6²
= 6 + 6 + 6√2
= 12 +6√2
= 6(2 + √2)
= 20.48 ≅ 20.5
Therefore, The perimeter of the triangle ABC is 20.5.
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Marlene wants to enclose her circular vegetable garden with fencing to keep rabbits from eating the vegetables. if the diameter of her garden is 14 feet, how much fencing will she need to buy if fencing is sold by the linear foot?
Marlene will need to buy approximately 44 feet of fencing to enclose her circular vegetable garden.
To determine the amount of fencing Marlene needs, we'll need to calculate the circumference of her circular vegetable garden. Here's a step-by-step explanation:
1. Given the diameter of the garden is 14 feet, we can find the radius by dividing the diameter by 2: Radius = Diameter / 2 = 14 feet / 2 = 7 feet.
2. Now, we will use the formula for the circumference of a circle, which is: Circumference = 2 * pi * radius.
3. Plug in the radius value we found in step 1: Circumference = 2 * pi * 7 feet.
4. Calculate the circumference: Circumference ≈ 2 * 3.1416 * 7 feet ≈ 43.98 feet.
5. Since fencing is sold by the linear foot, Marlene needs to buy approximately 44 linear feet of fencing to enclose her circular vegetable garden and keep the rabbits away.
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Consider the following. g(x) = 8e⁶·⁵x; h(x) = 8(6.5ˣ) (a) Write the product function. = f(x) = (b) Write the rate-of-change function. f'(x) = Consider the following. g(x) = 9e- ˣ + In(x); h(x) = 4x²·⁷(a) Write the product function. f(x) = (b) Write the rate-of-change function. f'(x) =
For the Following the product function is f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7} and rate of change of function is f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
For g(x) = 9e^{-x} + ln(x) and h(x) = 4x^{2.7}, we have:
(a) The product function is: f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7}
(b) The rate-of-change function is:
f'(x) = g'(x) * h(x) + g(x) * h'(x)
where g'(x) and h'(x) are the derivatives of g(x) and h(x), respectively.
Taking derivatives, we have:
g'(x) = -9e^{-x} + 1/x
h'(x) = 10.8x^{1.7}
Substituting into the formula for f'(x), we get:
f'(x) = (-9e^{-x} + 1/x) * 4x^2.7 + (9e^{-x} + ln(x)) * 10.8x^{1.7}
Simplifying, we get:
f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
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It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn. group of answer choices displacement sublimation projection rationalization regression
"It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn." refers projection (option c).
To understand projection in mathematical terms, we can think of it as a function f(x), where x represents the individual's own thoughts or emotions. The output of the function, f(x), represents the projection of these thoughts or emotions onto someone else.
In the case of arguments, the person who is most difficult to convince may have a high value of x, indicating that they are feeling stubborn. However, instead of accepting this feeling, they project it onto others, resulting in a high value of f(x) for those around them.
Projection is just one example of the many defense mechanisms that humans use to protect themselves from unpleasant thoughts or emotions. Understanding these mechanisms can help us to better navigate difficult situations, including arguments, and improve our communication skills.
Hence the correct option is (c).
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please help with the question in the image !!
Answer:
image dosent load
Step-by-step explanation:
Answer:
a = 80°, b = 100°, c = 80°, d = 100°
Step-by-step explanation:
You know a + b + c + d = 360°.
Plugging b + c + d = 280° into the formula above:
a + 280° = 360°.
a = 80°.
You know a + d = 180° because of angles on a straight line. Solve for d:
80° + d = 180°.
d = 100°.
For the same reason, you know a + b = 180°. b must be equal to d, which is 100°.
Lastly, c + d = 180° because they make up the second line. Solve for c:
c + 100° = 180°.
c = 80°.
a = 80°, b = 100°, c = 80°, d = 100°.
Qn in attachment . ..
The variance of first n even natural numbers is n²-1/12. So, the correct option is (a) .
The first n even natural numbers can be represented as 2, 4, 6, ..., 2n. The mean or expected value of this sequence is given by:
mean = (2 + 4 + 6 + ... + 2n) / n
= 2(1 + 2 + 3 + ... + n) / n
= 2n(n+1)/2n
= n+1
The variance of a sequence is the average of the squared differences from the mean, so we need to calculate:
Var = [(2- (n+1))² + (4- (n+1))² + (6- (n+1))² + ... + (2n- (n+1))²] / n
Simplifying the expression inside the brackets and using the formula for the sum of the first n integers, we get:
Var = [4(1² + 2² + 3² + ... + n²) - 4(n+1)(1 + 2 + 3 + ... + n) + n(n+1)²] / n
Substituting the formula for the sum of the first n squares and the sum of the first n integers, we get:
Var = [4n(n+1)(2n+1)/6 - 4(n+1)n(n+1)/2 + n(n+1)²] / n
Simplifying and factoring out (n+1), we get:
Var = (n+1)(n² - 1) / 3
Thus, the correct option is (a) n²-1/12.
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Can someone please help me ASAP? It’s due tomorrow. I will give brainliest if it’s correct. Show work.
The difference between the outcomes when selected with or without replacement is B. 10 outcomes.
How to find the number of outcomes ?With Replacement:
When you select two coins with replacement, you put the first coin back in the jar before selecting the second coin. This means that there are 10 possibilities for each selection. So, the number of outcomes for selecting two coins with replacement is 10 x 10 = 100 outcomes.
Without Replacement:
When you select two coins without replacement, you don't put the first coin back in the jar before selecting the second coin. This means that after selecting the first coin, there are 9 coins left in the jar for the second selection. So, the number of outcomes for selecting two coins without replacement is 10 x 9 = 90 outcomes.
Difference = 100 outcomes - 90 outcomes
Difference = 10 outcomes
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A bookmark has an area of 150 square centimeters and a perimeter of 62 centimeters. what are the dimensions of the bookmark
The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.
Let's denote the length of the bookmark as L and the width as W.
The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.
From the given information, we have two equations:
Equation 1: A = 150 square centimeters
Equation 2: P = 62 centimeters
Substituting the formulas for area and perimeter, we get:
Equation 1: L * W = 150
Equation 2: 2L + 2W = 62
To solve these equations, we can use substitution or elimination. Let's solve by substitution:
From Equation 1, we can express one variable in terms of the other:
L = 150 / W
Substituting this into Equation 2:
2(150 / W) + 2W = 62
300 / W + 2W = 62
300 + 2W^2 = 62W
2W^2 - 62W + 300 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
[tex]2W^2 - 62W + 300 = 0[/tex]
(W - 10)(2W - 30) = 0
This gives us two possible solutions:
W - 10 = 0 -> W = 10
2W - 30 = 0 -> W = 15
Since the width cannot be longer than the length, we discard the solution W = 15.
So, the width of the bookmark is W = 10 centimeters.
Now, we can substitute this value into Equation 1 to find the length:
L * 10 = 150
L = 150 / 10
L = 15
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