The measure of the angle ∠S, obtained using the law of cosines is about 59.4°
What is the law of cosines?The law of cosines states that the square of the length of a side of a triangle is equivalent to the sum of the squares of the other two sides less the product of the length of the other two sides and the angle between them. Mathematically; a² = b² + c² - 2·b·c·cos(A)
Where;
a, b, and c = The length of the sides of the triangle
A = The angle between b and c
The lengths of the sides of the triangle, obtained from a similar triangle are;
s = 50 inches, t = 58 inches, and u = 27 inches
The measure of the angle ∠S is required
The angle ∠S is the angle facing TU or the side s
According to law of cosines, we get;
s² = t² + u² - 2·t·u·cos(∠S)
Therefore;
50² = 58² + 27² - 2 × 58 × 27 × cos(∠S)
2 × 58 × 27 × cos(∠S) = 58² + 27² - 50²
cos(∠S) = (58² + 27² - 50²)/(2 × 58 × 27)
∠S = cos((58² + 27² - 50²)/(2 × 58 × 27)) ≈ 59.4°
The measure of the angle ∠S is about 59.4°
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Casey bought an 100 pound bag of dog food . He gave his dogs the same amount of dog food each week. the dog food lasted eight weeks. How much dog food did Cassie give his dogs each week? give the answer as a fraction or a mixed number
In the addition problem shown, each letter represents a different digit. If GOD=605, what number does MOVED represent?
The number does MOVED represent 1110.
How determine what number does MOVED represent?Since GOD=605, we know that D=5. We can now substitute this value of D into the addition problem to get:
GOD+ DOG = MOVED
605+ 506 = 1111
Since M cannot be 0 (otherwise it wouldn't be a 4-digit number), we know that M=1.
We can now subtract 1 from both sides of the equation to get:
604+ 506 = 1110
Now we can see that E+4=10, so E=6. We can also see that O+0=0, so O=0. Finally, we can see that G+D=1, so G=6 and D=5.
Therefore, MOVED = 1110.
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Valerie is going to purchase a new car. the car she wants has a list price of $32,495. valerie is planning to make a down payment of $1,877. furthermore, she plans to trade in her current car, which is a 2006 hyundai sonata in good condition. she will finance the rest of the cost by making monthly payments over five years. she can finance the cost at a rate of 8.64%, compounded monthly. she will also have to pay 8.23% sales tax, a $2,243 vehicle registration fee, and a $314 documentation fee. if the dealer gives valerie 87.5% of the trade-in price on her car, listed below, approximately how much will valerie pay in total for her new car? (round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.) hyundai cars in good condition model/year 2004 2005 2006 2007 sonata $6,145 $6,520 $6,784 $7,066 tiburon $6,880 $7,144 $7,382 $7,785 elantra $4,211 $4,425 $4,598 $4,880 accent $5,676 $5,828 $6,005 $6,317 a. $37,385 b. $38,821 c. $38,287 d. $36,944
The approximate total amount Valerie will pay for her new car is $38,287.
How much will Valerie pay in total for her new car?
To calculate how much Valerie will pay in total for her new car, we need to consider several factors.
First, let's determine the trade-in value of her 2006 Hyundai Sonata. Since the car is in good condition, Valerie will receive 87.5% of the listed trade-in price for that year, which is $6,784. Therefore, the trade-in value is approximately $5,938.80 ($6,784 * 0.875).
Now, let's calculate the total cost of the new car. The list price is $32,495, and Valerie plans to make a down payment of $1,877. Thus, the remaining amount to be financed is $32,495 - $1,877 - $5,938.80 = $24,679.20.
Next, let's consider the interest on the financing. The interest rate is 8.64% per year, compounded monthly. Over five years, this amounts to 60 monthly payments. Using an amortization formula, we can determine that the monthly payment is approximately $516.27.
Additionally, Valerie will have to pay sales tax, vehicle registration fee, and documentation fee. The sales tax is 8.23% of the total cost, which is ($24,679.20 + $2,243) * 0.0823 = $2,329.48. The vehicle registration fee is $2,243, and the documentation fee is $314. The total additional fees amount to $2,329.48 + $2,243 + $314 = $4,886.48.
Finally, to calculate the total amount Valerie will pay, we add the down payment, monthly payments, trade-in value reduction, and additional fees: $1,877 + (60 * $516.27) + $5,938.80 + $4,886.48 = $38,285.88.
Rounding to the nearest cent, Valerie will pay approximately $38,286 for her new car. Thus, the correct answer is option c: $38,287.
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Calculate ∑ (-1)^k pi^2k/2k
To calculate ∑ (-1)^k pi^2k/2k, we can use the power series expansion for the cosine function:
cos(x) = ∑ (-1)^n x^(2n) / (2n)!
We can substitute pi^2 for x in this formula to get:
cos(pi^2) = ∑ (-1)^n (pi^2)^(2n) / (2n)!
= ∑ (-1)^n pi^(4n) / (2n)!
Now we can compare this to the original series we want to evaluate:
∑ (-1)^k pi^2k/2k = ∑ (-1)^n pi^(2n) / (2n)
We notice that the powers of pi in the two series match up, but the coefficients are different. However, we can use the identity cos(pi^2) = (-1)^n to rewrite the series we want to evaluate as:
∑ (-1)^n pi^(2n) / (2n) = ∑ (-1)^n pi^(4n) / (2n)! * (2n) / pi^2n
= pi^2 / 2 * ∑ (-1)^n pi^(4n) / (2n)!
Now we can substitute our expression for cos(pi^2) into this equation to get:
∑ (-1)^k pi^2k/2k = pi^2 / 2 * cos(pi^2)
= pi^2 / 2 * (-1)^n
Therefore, the value of the series is (-1)^n * pi^2 / 2.
To calculate the sum ∑ (-1)^k (pi^2k)/(2k), it is important to recognize that this is an alternating series with a general term given by a_k = (-1)^k (pi^2k)/(2k).
However, the question seems incomplete, as there is no specified range for the sum (i.e., the values of k). If you provide the range of k for which this sum is to be calculated, I would be glad to help you further.
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Choosing only among rectangle,rhoumbos,square, name all parallelograms that have the following property
Among rectangles, rhombuses, and squares, all three of these shapes are parallelograms that have specific properties.
A rectangle is a parallelogram with four right angles. Its opposite sides are equal and parallel, and it has diagonals that are equal in length and bisect each other.
A rhombus, on the other hand, is a parallelogram with all four sides being equal in length. Like a rectangle, its opposite sides are parallel, but it does not necessarily have right angles. The diagonals of a rhombus are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other into two equal parts.
Finally, a square is a special type of parallelogram that combines the properties of both rectangles and rhombuses. It has four equal sides and four right angles, making it a unique shape. The diagonals of a square are equal in length, bisect each other, and are also perpendicular bisectors.
In conclusion, rectangles, rhombuses, and squares are all parallelograms with distinct properties. Rectangles have right angles and equal opposite sides, rhombuses have equal sides and diagonals that are perpendicular bisectors, and squares possess all the properties of both rectangles and rhombuses.
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the life of light bulbs is distributed normally. the standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 580 hours. find the probability of a bulb lasting for at most 624 hours. round your answer to four decimal places.
The probability of a bulb lasting for at most 624 hours is 0.9861, rounded to four decimal places.
The standard deviation of the lifetime is a measure of how spread out the lifetimes are. In other words, it tells us how much the lifetimes of bulbs vary from the mean. In this case, the standard deviation of the lifetime is 20 hours.
Now, let's get to the question at hand. We want to find the probability of a bulb lasting for at most 624 hours. To do this, we need to use the properties of the normal distribution.
First, we need to calculate the z-score, which tells us how many standard deviations a value is from the mean. We can use the formula z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, and sigma is the standard deviation. In this case, x = 624, mu = 580, and sigma = 20.
Plugging these values into the formula, we get z = (624 - 580) / 20 = 2.2.
Next, we need to find the probability of a bulb lasting for at most 624 hours, which is the same as finding the area under the normal curve to the left of z = 2.2. We can use a standard normal distribution table or a calculator to find this probability.
Using a calculator, we can use the normal cdf function with the values -9999 (a very large negative number) and 2.2 to find the probability. This gives us a probability of 0.9861.
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Find the value of the variable.
(ill be needing an explanation along with the answer, ty!)
Thus, the value of the angle x for the given angles of value 100 and 112 is found as 36.
Define about the linear pair:An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees. As previously said, neighbouring angles are those that are close to one another.
An angle pair that forms a line is known as a "line-ar pair."
For the given triangle:
Using the triangle's angle sum property:
x + (180 - 100) + (180 - 112) = 180
(the other two angles except x are linear pair with the angles of value 100 and 112)
So,
x + 80 + 180 - 112 = 180
x = 112 - 80
x = 32
Thus, the value of the angle x for the given angles of value 100 and 112 is found as 36.
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A lean-to is a shelter where the roof slants down to the ground. The length of the roof of one lean-to is 17 feet. The width of the lean-to is 15 feet. How high is the lean-to on its vertical side?
The height of the lean-to on its vertical side is 8 feet.
What is the height of a lean-to on its vertical side?
To find the height of the lean-to on its vertical side, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the vertical side is the hypotenuse, and the length and width are the other two sides.
So, we have:
[tex]height^2 = hypotenuse^2 - width^2[/tex]
We know the length of the roof (the hypotenuse) is 17 feet, and the width is 15 feet. So we can plug these values into the equation and solve for the height:
[tex]height^2 = 17^2 - 15^2\\height^2 = 289 - 225\\height^2 = 64\\height = 8[/tex]
Therefore, the height of the lean-to on its vertical side is 8 feet.
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Construct the class boundaries for the following frequency distribution table. also construct less than cumulative and greater than cumulative frequency tables.
ages:- 1 - 3, 4-6, 7-9, 10-12, 13-15
no of children:- 10,12,15,13,9
The class boundaries are 0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5.
To find the class boundaries, we need to add and subtract 0.5 from the upper and lower limits of each class interval, respectively.
Using this formula, we get the following class boundaries:
Class Boundaries:
0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5
To construct the less than cumulative frequency table, we need to add up the frequencies of all the classes up to each class. For example:
Less than Cumulative Frequency Table:
Ages No. of Children Cumulative Frequency
1-3 10 10
4-6 12 22
7-9 15 37
10-12 13 50
13-15 9 59
To construct the greater than cumulative frequency table, we need to subtract the frequency of each class from the total frequency and then add the resulting values up to obtain the cumulative frequency. For example:
Greater than Cumulative Frequency Table:
Ages No. of Children Cumulative Frequency
13-15 9 59
10-12 13 50
7-9 15 37
4-6 12 22
1-3 10 10
Note that the last value of the greater than cumulative frequency table is always equal to the total frequency, which in this case is 59.
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SHOW YOUR W
(2x - 1)(3x + 4) = 0
Answer:
x = 1/2, -4/3
Step-by-step explanation:
(2x - 1)(3x + 4) = 0
We know any number multiplied by 0 will be equal 0.
2x - 1 = 0
2x = 1
x = 1/2
3x + 4 = 0
3x = -4
x = -4/3
So, x = 1/2, -4/3
[tex]2x(3x + 4) - 1(3x + 4) = 0[/tex]
[tex]6 {x}^{2} + 8x - 3x - 4 = 0[/tex]
[tex]6 {x}^{2} + 5x - 4 = 0[/tex]
[tex]6 {x}^{2} + 5x = 4[/tex]
"Bacteria in a culture can live for an average of two hours with a standard deviation of 15
minutes. How long can we expect at least 75% of the bacteria to live?"
75% of the bacteria to live for approximately 130.11 minutes
To answer your question, we'll be using the concept of standard deviation and the normal distribution.
Given that the average lifespan of bacteria in a culture is 2 hours (120 minutes) with a standard deviation of 15 minutes, we can expect at least 75% of the bacteria to live for a certain amount of time. Using the normal distribution, we can determine the corresponding z-score for the 75th percentile, which is approximately 0.674.
Now, we can apply the z-score formula:
z = (X - mean) / standard deviation
Rearrange the formula to solve for X (the time at which 75% of the bacteria will live):
X = mean + (z * standard deviation)
Plugging in the given values:
X = 120 + (0.674 * 15) ≈ 130.11 minutes
So, we can expect at least 75% of the bacteria to live for approximately 130.11 minutes.
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Write a note to your pen pal about the kinds of music you like best. In addition, write about any instruments you might play. Be sure you use at least 5-6 complete Spanish sentences in your response. Find the values of x, y, and z. Round answers to the nearest hundredths place, if necessary
Answer:
Querido/a [Pen pal's name],
¡Hola! Espero que estés bien. Quería escribirte sobre mis gustos musicales. Me encanta la música de todo tipo, pero mis géneros favoritos son el pop y el rock. Me gusta escuchar artistas como Taylor Swift, Ed Sheeran, Coldplay y Queen. También disfruto escuchar música latina como el reggaetón y la salsa.
Además de escuchar música, también me gusta tocar algunos instrumentos. Toco la guitarra y el piano desde hace algunos años y me encanta aprender nuevas canciones y melodías en ambos instrumentos.
Creo que la música es una forma maravillosa de expresión y me encanta poder hacer música yo mismo.
¿Y tú? ¿Qué tipo de música te gusta? ¿Tocas algún instrumento? Me encantaría saber más sobre tus gustos musicales y si tienes algún hobby musical.
Espero tu respuesta pronto. ¡Cuídate mucho!
Saludos cordiales,
[Your name]
x = 4.56
y = 8.24
z = 12.99
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Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot
The value of tanG is √3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
The value of KY
Tan 30 = 27/KY
1/√3 = 27/KY
KY = 27√3
Tan G = 27√3/27
tanG = √3
therefore the value of tanG is √3
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how could you use a number line to determine the number that is 7 more than -9? What is the number?
Answer:
Step-by-step explanation:
To use a number line to find the number that is 7 more than -9, we start by finding -9 on the number line. Then, we move 7 units to the right (because we want to find a number that is 7 more), staying on the number line.
Starting from -9 on a number line, we can count 7 units to the right, which brings us to:
-9 + 7 = -2
Therefore, the number that is 7 more than -9 is -2.
How many of the shapes below are trapeziums?
Answer:
2
Step-by-step explanation:
The K and N are the trapeziums and the two lines opposite to them go in a parallel line
Problem 68 An outdoor adventure club has 35 members, who are all either rock climbers or skiers. There are 3 more rock climbers than
there are skiers. How many climbers are there?
WHOEVER ANSWERS FIRST GETS BRAINLIEST AND ANSWER FAST FOR WHOEVER GOTS THE HIGHEST BRAILIEST I WILL GIVE THEM THE BRAINLIEST POINT
Answer: 14.5 climbers technically 14 because 1/2 a person is wrong
Step-by-step explanation:
Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2
The error in finding area of the sector is in formula applied the correct value is equal to 81.46 square feet.
Area of the sector with center Z is equal to 255 square feet.
Angle subtended in the center of the circle = 115 degrees
Let us consider 'r' be the radius of the circle.
And 'θ' be the angle subtended at the center of the circle.
Using the formula of a area of a sector we have,
Area of sector = θ/360 × πr²
Error in the calculation was made by applying wrong formula ,
Area of circle = 255 square feet
Center angle 'θ' = 115°
Substitute the value in the formula we have ,
⇒ Area of sector = (115°/360) × 255
⇒ Area of sector = 81.4583 square feet
⇒ Area of sector ≈ 81.46 square feet
From the attached figure the area of sector is 162.32ft².
Therefore, the error in finding area of the sector is in formula the correct answer is 81.46 square feet.
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The above question is incomplete, the complete question is:
Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet. Round to the nearest tenth. The area should equal ft2
Attached figure.
Kaylie put $900 in a savings account, earning 11% interest for 7 years. she did not make any additional deposits or withdrawals. what is the amount of interest kaylie earned?
Kaylie earned $693 in interest on her savings account.
What was the total amount of money Kaylie had in her savings account after 7 years of depositing $900 and earning 11% interest on it?Kaylie deposited $900 in a savings account and earned 11% interest on it for 7 years. After the 7-year period, Kaylie earned $693 in interest, which was compounded annually.
This brought the total amount of money in her savings account to $1,593. The power of compounding interest in savings accounts can help grow your money significantly over time.
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Considera el descuento indicado en cada tabla y calcula los diferentes porcentajes de descuento del mismo articulo
The 5% discount is 8.10, Namas divide 42 between the percentage follow me and give me crown.
A discount is a reduction in the price of a product or service offered to customers. It is a common marketing strategy used by businesses to attract customers and increase sales. Discounts can be offered in various forms, such as percentage off, dollar off, or buy-one-get-one-free deals.
Discounts are often used to clear out old inventory, promote new products or services, and to reward customer loyalty. They can be temporary or ongoing, and the amount of the discount can vary depending on the product, service, or promotion. Customers benefit from discounts as they can purchase products or services at a lower price, saving them money. Businesses benefit from discounts as they can increase sales volume, clear out inventory, and attract new customers.
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Complete Question:-
Consider the discount indicated in each table and calculate the different discount percentages for the same item.
A Texas House representative proposed placing solar panels on all public schools to increase green energy and reduce energy costs for districts. Suppose a manufacturer’s panels will be purchased only if real world results of the proposed panels show that more than 18% of the panels produce an efficiency rating greater than 20%. Of a random selection of 140 panels, 32 of the panels result in an efficiency rating greater than 20%. Is there sufficient evidence at the 5% significance level to purchase the proposed panels?
By null hypothesis there is sufficient evidence at the 5% significance level to purchase the proposed panels.
To determine if there is sufficient evidence to purchase the proposed panels, we can perform a hypothesis test. Let's define the following:
- p: the proportion of all panels that produce an efficiency rating greater than 20%
- p0: the proportion specified in the proposal, which is p0 = 0.18
- n: the sample size, which is n = 140
- x: the number of panels in the sample that produce an efficiency rating greater than 20%, which is x = 32
We want to test the null hypothesis H0: p <= p0 against the alternative hypothesis Ha: p > p0. The significance level is alpha = 0.05.
We can use the normal approximation to the binomial distribution since both np0 and n(1-p0) are greater than 10, where np0 is the expected number of panels that produce an efficiency rating greater than 20% under the null hypothesis.
Under the null hypothesis, the test statistic z is approximately:
z = (x - np0) / sqrt(np0(1-p0))
Plugging in the values, we get:
z = (32 - 140*0.18) / sqrt(140*0.18*0.82) ≈ 1.96
The critical value of z at alpha = 0.05 with a one-tailed test is 1.645. Since our calculated z value is greater than the critical value, we reject the null hypothesis.
Therefore, there is sufficient evidence at the 5% significance level to purchase the proposed panels.
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the expression x^2-8x+6 can be written in the form (x-p)^2+q
Answer:(x-4)^2-10
Step-by-step explanation:
50 POINTS ASAP Use the image to determine the type of transformation shown.
image of polygon ABCD and a second polygon A prime B prime C prime D prime above it
180° clockwise rotation
Horizontal translation
Reflection across the x-axis
Vertical translation
Since polygon A prime B prime C prime D prime above is above the image of polygon ABCD, the type of transformation shown is: D. vertical translation.
What is a transformation?In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
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Answer:
Vertical translation
Step-by-step explanation:
I am in the middle of taking the quiz and belive this is the correct answer!
WILL GIVE BRAINLYES, 5 STARS, AND A THANKS
Choose an amount between $50.00 and $60.00 to represent the cost of a meal for a family. Be sure to include dollars and cents.
Part A: If the family has a 15%-off coupon, calculate the new price of the meal. Show all work or explain your steps. (2 points)
Part B: Calculate a 20% tip using the new price. What is the final cost of the meal? Show all work or explain your steps. (2 points)
Answer:
The price of the meal after the discount was (A)$48.11 and the final price of the meal was (B)$57.73.
Step-by-step explanation:
Let us consider the amount of money $56.60 as the cost of the meal.
So the amount of money is 56 dollars and 60 cents.
A: The family has a 15% off coupon.
Discount = 15% of 56.60=0.15x56.60=8.49
Now we subtract the discount amount from the original amount.
Cost of the meal = 56.60-8.49=48.11
So the final price of the meal for the family is $48.11 or 48 dollars and 11 cents.
B: The family gave a tip of 20%.
Amount of money tipped= 20% of 48.11=0.20 x 48.11=9.622
To get the final amount we add the tip to the discounted price.
The final cost of the meal= 48.11+9.622=57.732=57.73
Therefore the family paid a total of 57 dollars and 73 cents for the final cost of the meal after the discount and tip.
Hope this helps :)
Pls help test which point (x,y) satisfies the given system of inequalities?
o a. (-1,-6)
ob. (3,-1)
o c. (-3,-1)
od. (1,-6)
reset
If the system includes the inequality y < 0, then the shaded region would be below the x-axis (in the third and fourth quadrants).
If we plot the system of inequalities on a graph, which quadrant(s) would the solutions lie in?The solutions to a system of linear inequalities can be graphed on a coordinate plane to form a shaded region.
The shaded region would be in the quadrant(s) that satisfies all the inequalities in the system. For example, if the system of inequalities includes the inequality x > 0, then the shaded region would be on the right-hand side of the y-axis (in the first and fourth quadrants).
If the system includes the inequality y < 0, then the shaded region would be below the x-axis (in the third and fourth quadrants).
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I know its not alot of point but please help me and no essay you will get brainliest if ur answer was first and correct
Will give brainliest for the answer no links
find the lateral surface area of this
cylinder. round to the nearest tenth.
8ft
4ft
[?] ft?
The lateral surface area of a cylinder is given by the formula:
Lateral surface area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
In this case, the height of the cylinder is 8 ft and the radius of the cylinder is 4 ft (half of the diameter). So, we can plug in these values to get:
Lateral surface area = 2π(4 ft)(8 ft)
Lateral surface area = 64π square feet
Rounding to the nearest tenth, we get:
Lateral surface area ≈ 201.1 square feet (rounded to one decimal place)
Therefore, the lateral surface area of the cylinder is approximately 201.1 square feet.
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Find the most important variable in the problem.
If a company hired an additional 12 employees, and every employee needed a
phone, it would require 8 more phones. How many phones does the company
have available now?
OA. the number of employees hired
OB. the money required to purchase phones
OC. the number of phones available
(co 4) market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.7 million. if this estimate was based on a sample of 10 customers, what would be the 90% confidence interval?
The 90% confidence interval of the new product has the potential to make the company an additional $3.8 million is (2.81, 4.79), option B.
Confidence intervals quantify how confident or uncertain a sampling technique is. They can take any number of probability thresholds, with a 95% or 99% confidence level being the most popular. The calculation of confidence intervals is done using statistical techniques like the t-test.
[tex]\bar x = $3.8[/tex]
sample standard deviation = s =1.7
sample size = n =10
Degrees of freedom = df = n - 1 = 10 - 1 = 9
At 90% confidence level
[tex]\alpha[/tex] = 1 - 90%
[tex]\alpha[/tex] =1 - 0.90 =0.1
[tex]\alpha/2[/tex] = 0.05
[tex]t\alpha/2[/tex] ,df = t0.05,9 =1.833
At 90% confidence level, the critical value is t = 1.833
The 90% confidence interval is:
[tex]\bar x \pm t*\frac{s}{\sqrt{n} }[/tex]
[tex]=3.8\pm 1.833*\frac{1.7}{\sqrt{10}}\\\\=3.8\pm 0.99[/tex]
=(2.81,4.79).
Therefore, 90% confidence interval estimate of the population mean is, (2.81,4.79).
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Complete question:
Market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.7 million. If this estimate was based on a sample of 10 customers, what would be the 90% confidence interval? (2.76, 4.84) O (2.81, 4.79) (2.11, 5.56) (3.06, 4.54)
In this problem you will only find the models. But make sure that you show all work to support
your answers. Use function notation in your final answers.
Suppose two types of wire will be used to form the edges of a rectangle. The wire used
for the width costs $2.50 per foot and the wire used for the height costs $4.25 per foot. Express the total cost of building the rectangle out of wire as a function of the with if the
enclosed area must be 500 square feet.
To start, let's call the width of the rectangle "w" and the height "h". We know that the area must be 500 square feet, so we can write an equation:
w*h = 500
We can solve this equation for h:
h = 500/w
Now we can express the total cost of the wire in terms of w. The cost of the wire for the width is $2.50 per foot, so the cost for that side is:
2.5w
The cost of the wire for the height is $4.25 per foot, so the cost for that side is:
4.25h = 4.25(500/w) = 2125/w
So the total cost of the wire is:
C(w) = 2.5w + 2125/w
This is our final answer expressed in function notation.
Let's denote the width of the rectangle as w and the height as h. We are given that the area of the rectangle must be 500 square feet, so we have:
w * h = 500
Now, we need to find the cost function based on the width. The cost of the wire for the width is $2.50 per foot and for the height is $4.25 per foot. Therefore, the total cost (C) can be expressed as:
C(w) = 2.50 * w + 4.25 * h
We need to express the height (h) in terms of the width (w) using the area equation:
h = 500 / w
Now, we can substitute this expression for h in the cost function:
C(w) = 2.50 * w + 4.25 * (500 / w)
This is the cost function for building the rectangle out of wire as a function of its width, given that the enclosed area must be 500 square feet.
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Find the curve in the xy plane that passes through the point (9,8) and whose slope at each point is 6 sqrt x
The equation of curve passing through the point (9,8) with slope [tex]6\sqrt{x}[/tex] is [tex]y = 4\times x^{(3/2)} -100[/tex] .
Slope of curve is given by [tex]6\sqrt{x}[/tex] and curve is passing through point (9,8) .
A curve can be represented in a graph using the standard form of equations. Equation will represent the slope of curve and point through which the curve is passing.
Equation of curve :
Differentiate the slope equation,
dy/dx = [tex]6\sqrt{x}[/tex]
dy = [tex]6\sqrt{x}[/tex] dx
Integrating both sides,
Integration rule : [tex]\int\ {x^n} \, dx = x^{n+1}/n+1 + c[/tex]
[tex]y = 6 \times (x^{3/2})/(3/2) +c[/tex]
[tex]y = 4 x^{(3/2)} + c[/tex]
Now substitute (9,8) in the equation of y,
[tex]8 = 4\times (9)^{3/2} + c[/tex]
[tex]c = -100[/tex]
Substitute the value to get the equation of curve,
The equation of curve is [tex]y = 4\times x^{(3/2)} -100[/tex] .
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