To find the length of the parametric curve, we can use the formula:
L = ∫a^b √(dx/dt)² + (dy/dt)² dt
Substituting the given values, we get:
L = ∫0^1 √(6)² + (43/2, 03752)² dt
Simplifying:
L = ∫0^1 √(36 + (43/2, 03752)²) dt
Therefore, the length of the parametric curve is:
L = √(36 + (43/2, 03752)²)
In mathematics, substitution refers to the process of replacing a variable or expression in an equation or formula with another variable or expression that has the same value.
For example, if we have an equation: 2x + 3y = 7, and we want to substitute x with the value 4, we replace x with 4 to get:
2(4) + 3y = 7
8 + 3y = 7
We can then solve for y to find its value.
Substitution is a commonly used technique in algebra and calculus to simplify expressions, solve equations and evaluate functions.
Visit here to learn more about parametric curve brainly.com/question/15585522
#SPJ11
If john buys 8 jackets at x dollars a piece and 2 movie tickets at $11 a piece, whats the most he can spend on each jackets if his total budget is $200
Answer:
22.25
Step-by-step explanation:
8x+ (11*2)=200
first, multiply 11 and 2 =22
that leaves 8x+22=200
so now let's subtract the 22 from both sides
8x=178 now divide the 8
x= 22.25 so that is the most the jackets could have cost
1) Find the value of the k that makes the sequence arithmetic
-13,k,-3,2,...
A)5
B)-8
C)-5
D)-10
2) Which formula describes the arithmetic sequence?
-4/5, -3/5,-2/5,-1/5...
A)tn=-n/5
B)tn=n/5-1
C)tn=1+n/5
D)tn=-n/5-1
3)What're the next 4 terms in the series?
t1=3,tn=1/2,tn-1 -1
A)1/2, -3/4, -11/8, -27/10
B)3/2, 3/4, 3/8, 3/16
C)-1/2, 3/4, 5/8, 21/16
D)2, 0, -1, -3/2
4)Which formula describes the arithmetic sequence?
-3,-6,3,-6
A)tn=-tn-1+3
B)tn=-tn-1-1
C)tn=tn-1-1
D)-tn-1-3
If x = -3, then which inequality is true?
The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0
If x = -3, then which inequality is true?From the question, we have the following parameters that can be used in our computation:
The statement that x = -3
The above value implies that we substitute -3 for x in an inequality and solve for the variable y
Take for instance, we have
y < x + 3
Substitute the known values in the above equation, so, we have the following representation
y < -3 + 3
Evaluate
y < 0
This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0
Read mroe about inequailty at
https://brainly.com/question/25275758
#SPJ1
Your friend purchased a medium pizza for 10. 32 with a 30% off coupon what is the price of the pizza with out a coupon
The price of the medium pizza without the coupon is approximately $14.74.
To find the original price of the pizza without the coupon, we can use the following formula:
Original Price = Discounted Price / (1 - Discount Percentage)
In this case, the discounted price is $10.32 and the discount percentage is 30% or 0.3. Plugging the values into the formula:
Original Price = $10.32 / (1 - 0.3)
Original Price = $10.32 / 0.7
Original Price ≈ $14.74
So, the price of the medium pizza without the coupon is approximately $14.74.
To learn more about coupon, refer below:
https://brainly.com/question/30177801
#SPJ11
Dante has a tent shaped like a triangular prism. The tent has an equilateral base that measures 5 feet on each side. The tent is 8 feet long and 4. 3 feet tall.
101. 5ft
120 ft.
141. 5 ft.
184 ft
What is the surface area of the tent
The surface area of Dante's tent is approximately 180 square feet.
To find the surface area of Dante's tent, we need to find the area of each of its faces and then add them up. Since the tent is in the shape of a triangular prism, it has three rectangular faces and two triangular faces.
First, let's find the area of each rectangular face. We know that the tent is 8 feet long and 4.3 feet tall. To find the width of each face, we need to use the Pythagorean theorem since the base of the tent is equilateral. So, we can use a triangle with sides of 5 feet (the base of the tent) and 4.3 feet (the height of the triangular face) to find the width of each rectangular face.
a^2 + b^2 = c^2
5^2 + 4.3^2 = c^2
25 + 18.49 = c^2
43.49 = c^2
c = √43.49
c ≈ 6.6 feet
Now that we know the width of each rectangular face, we can find the area of each face:
Area of rectangular face = length x width
Area of rectangular face = 8 x 6.6
Area of rectangular face ≈ 52.8 square feet
Next, let's find the area of each triangular face. Since the base of the tent is equilateral, each triangular face has a base of 5 feet and a height of 4.3 feet. The area of each triangular face is:
Area of triangular face = (base x height) / 2
Area of triangular face = (5 x 4.3) / 2
Area of triangular face ≈ 10.8 square feet
Now we can add up the areas of all five faces to find the total surface area of the tent:
Surface area of tent = 3 x area of rectangular face + 2 x area of triangular face
Surface area of tent = 3 x 52.8 + 2 x 10.8
Surface area of tent = 158.4 + 21.6
Surface area of tent ≈ 180 square feet
Therefore, the surface area of Dante's tent is approximately 180 square feet.
To know more about surface area, visit:
https://brainly.com/question/29298005#
#SPJ11
Triangle XYZ undergoes a dilation to produce triangle X'Y'Z'. The coordinates of both triangles are shown.
X(8.2)→ X'(4,1)
Y(-10,4)→Y'(-5,2)
Z(-2,0) Z’(-1,0)
What is the scale factor of the dilation?
The scale factor used in the dilation of the triangles is 1/2
Determining the scale factor used.From the question, we have the following parameters that can be used in our computation:
XYZ with vertices at X(8, 2)X'Y'Z' with vertices at X'(4, 1)The scale factor is calculated as
Scale factor = X'/X
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (4, 1)/(8, 2)
Evaluate
Scale factor = 1/2
Hence, the scale factor is 1/2
Read more about scale factor at
brainly.com/question/29229124
#SPJ1
A video game player is creating a user identification to play a game. The identification must consist of one vowel (A, E, I, O, U) followed by any one number (2, 4, 6, 8). What is the probability that the user identification will contain both an E and an 8?
The probability that the user identification will contain both an E and an 8 is 1/20, or 5%.
To determine the probability of a user identification containing both an E and an 8, we will break down the problem step-by-step.
1. Identify the total number of possibilities:
There are 5 vowels (A, E, I, O, U) and 4 even numbers (2, 4, 6, 8). To calculate the total number of possible user identifications, multiply the number of vowels by the number of even numbers:
Total possibilities = 5 vowels × 4 even numbers = 20 combinations
2. Determine the desired outcome:
In this case, we are interested in the combination that has an E followed by an 8. There is only one such combination: E8.
3. Calculate the probability:
To find the probability of the desired outcome, divide the number of desired outcomes by the total number of possible outcomes:
Probability = Desired outcomes / Total possibilities
Probability = 1 / 20
You can read more about probability at https://brainly.com/question/13604758
#SPJ11
What is the probability of selecting an Ace, not replacing it, and then selecting a King?
The probability of selecting an Ace, not replacing it, and then selecting a King is 4/663 or approximately 0.006 or 0.6%.
The probability of selecting an Ace, not replacing it, and then selecting a King can be calculated using the rules of conditional probability.
First, we need to determine the probability of selecting an Ace from a standard deck of 52 cards. There are four Aces in the deck, so the probability of selecting an Ace is 4/52, which can be simplified to 1/13.
Next, we need to consider the fact that the Ace is not replaced before selecting the King. This means that the deck now contains 51 cards, with only three remaining Aces. Therefore, the probability of selecting a King after selecting an Ace without replacement is 4/51.
To determine the overall probability of selecting an Ace and then a King, we multiply the probability of selecting an Ace (1/13) by the probability of selecting a King after selecting an Ace without replacement (4/51).
The calculation is as follows:
(1/13) x (4/51) = 4/663
To know more about conditional probability, refer to the link below:
https://brainly.com/question/30144287#
#SPJ11
Nora signed up for a streaming music service that costs $5 per month. The service allows Nora to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0. 75 per song. How much total money would Nora have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?
cost of 30 songs:
cost of s songs:
Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.
The cost for downloading 30 songs would be:
$0.75 per song × 30 songs = $22.50
Therefore, Nora would have to pay a total of $5 + $22.50 = $27.50 in a month when she downloaded 30 songs.
If she downloaded "s" songs, the cost would be:
$0.75 per song × s songs = $0.75s
Therefore, Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.
To know more about cost calculations refer here:
https://brainly.com/question/14725550
#SPJ11
Cuánto interés ganará lesli si presta l 5000 a pagar en 3años? al:5%simple anual. 10%simple anual. 5%compuesto anual
The interest gained by Lesli is if she lends $5000 for 3 years at 5% simple interest annually is $750, 10% simple interest annually is $1500, and on 5% compound interest annually is $790
The simple interest is calculated by
I = P * r * t
where P is the principal
r is the rate of interest
t is the time
I is the simple interest
The compound interest is calculated by:
I = P[tex](1 +r)^t[/tex] - P
where I is the compound interest
P is the principal
r is the rate of interest
t is the time
According to the question,
P = $5000
t = 3 years
1. r = 5% simple interest
I = 5000 * 3 * 0.05
= $750
2. r = 10% simple interest
I = 5000 * 3 * 0.10
= $1500
3. r = 5% compounded annually
I = 5000 [tex](1+0.05)^3[/tex] - 5000
= 5000 * 1.158 - 5000
= $790
Learn more about Compound Interest:
https://brainly.com/question/30364118
#SPJ4
The question is in Spanish, and the question in English is:
How much interest will Lesli earn if she lends 15,000 to be paid in 3 years? at: 5% annual simple. 10% simple annual. 5% compounded annually
A snail moves about 0.013m each second. About how many hours would it take the snail to travel 174km?
Answer:
Step-by-step explanation:
A styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3. 14 for TT.
The volume of foam in the model is approximately 27,211.5 cubic centimeters
The radius of the circular base can be found by dividing the diameter by 2:
radius = diameter / 2 = 48 cm / 2 = 24 cm
The formula for the volume of a cone is:
V = (1/3) * π * r² * h
where π is approximately 3.14, r is the radius of the circular base, and h is the height of the cone.
Substituting the values we have:
V = (1/3) * 3.14 * 24² * 12
V = 27,211.52 cm³
Rounding this to the nearest tenth, we get:
V ≈ 27,211.5 cm³
Therefore, the volume of foam in the model is approximately 27,211.5 cubic centimeters
To learn more about volume here:
https://brainly.com/question/1578538
#SPJ4
Offering brainiest to whoever can give me the answer fastest, a nice explanation, and the correct answer!
Box C has the smallest volume, followed by Box A, and Box B has the largest volume.
Explanation on how to get the least volumeFirst, we need to find the volume of each box.
Recall that the formula for volume of a box is given as:
V = length x height x width
For Box A,
V = 3 cm x 2 cm x 4 1/2 cm = 27 cm³
For Box B,
V = 2 1/3 cm x 3 cm x 5 cm = 7/3 cm x 3 cm x 5 cm = 35 cm³
For Box C,
V = 4 cm x 3 cm x 1 1/4 cm = 4 cm x 3 cm x 5/4 cm = 15 cm³
So, the order of the boxes by volume from least to greatest is: Box C, Box A, and Box B.
Learn more about order here:
https://brainly.com/question/27864906
#SPJ1
HELP ASAP ! Given the rectangle in this example, and a scale factor of 3.5, what are the side lengths of the new rectangle?
Answer:
Length: 22 inches × 3.5 = 77 inches
Width: 10 inches × 3.5 = 35 inches
sum of 3 consecutive even numbers is 18
Answer:
Step-by-step explanation:
5 6 7
E
josh needs to find the measures of the
angles on a barn's trusses.
find the measure of abc if abd is a right angle and cbd is 60 degrees. write and solve a subtraction equation
The measure of angle ABC is 30 degrees.
How to find the measure of angle ABC?To find the measure of angle ABC, we need to use the fact that the sum of angles in a triangle is always 180 degrees. Since we know that angle ABD is a right angle (90 degrees) and angle CBD is 60 degrees, we can find the measure of angle ABC as follows:
angle ABD + angle CBD + angle ABC = 180 degrees
Substituting the given values, we get:
90 degrees + 60 degrees + angle ABC = 180 degrees
Simplifying, we get:
150 degrees + angle ABC = 180 degrees
Now we can solve for angle ABC by subtracting 150 degrees from both sides:
angle ABC = 180 degrees - 150 degrees
angle ABC = 30 degrees
Therefore, angle ABC measures 30 degrees.
Learn more about sum
brainly.com/question/31538098
#SPJ11
simplify
(2a² b c³) (-a² b⁵)
pls help asap!
Answer:
[tex]-2a^{4}b^{6} c^{3}[/tex]
Step-by-step explanation:
(2a² b c³) (-a² b⁵)
distribute amongst each other
-2a²bc³a²b⁵
rearrange
-2a²a²bb⁵c³
combine like terms
[tex]-2a^{4}b^{6} c^{3}[/tex]
Hope this helps!
Answer: -2[tex]a^{4}[/tex][tex]b^{6}[/tex]c³
Step-by-step explanation:
Given:
(2a² b c³) (-a² b⁵)
Rules:
>Multiply numbers first
>If a number with an exponent is multiplied to another, you can combine if the bases are the same(lower number)
>If they have the same base, you can add the exponents
Solution:
(2a² b c³) (-a² b⁵) >multiply the - and 2
-2(a² b c³) (a² b⁵) > combine the a's by adding the expnents 2+2
-2[tex]a^{4}[/tex]( b c³) ( b⁵) > combine b, there is an invisible 1 by the first b 1+5
-2[tex]a^{4}[/tex][tex]b^{6}[/tex]c³ >c stays as is because nothing to combine with
Redland Municipal Middle School offers the following girls sports:
Part A:
Regina wants to play one sport in each of the three seasons during her 8th grade year. Create a list that shows the sample space for the sports that she could play.
Part B:
What is the probability that Regina plays tennis and/or basketball during her 8th grade year?
probability that Regina plays tennis and/or basketball during her 8th grade year at Redland Municipal Middle School, we first need to know the total number of sports offered and the number of students participating in each sport. However, based on the information provided in your question, we do not have sufficient data to determine the probability.
In general, to determine the probability, we would follow these steps:
1. Determine the total number of sports offered at the school (let's call this S).
2. Find out the number of students participating in tennis (T) and basketball (B).
3. Calculate the probability of Regina playing tennis (P_T) by dividing T by S.
4. Calculate the probability of Regina playing basketball (P_B) by dividing B by S.
5. Use the formula P(T or B) = P_T + P_B - P(T and B) to calculate the probability that Regina plays tennis and/or basketball. Here, P(T and B) is the probability of her playing both sports.
Without the specific numbers, we cannot provide a precise probability. Please provide more details about the sports and participation at Redland Municipal Middle School to help us calculate the probability accurately.
To know more about Redland refer home
https://brainly.com/question/30294973#
#SPJ11
Mr. jackers was transporting a giraffe from one zoo to another. what is a reasonable amount of the weight of his cargo?
a. 200 lbs.
b. 400 lbs.
c. 1 ton
d. 2 tons
The reasonable amount of weight of his cargo Mr. Jackers while transporting a giraffe from one zoo to another is 1 ton and 2 tons. Options C and D are correct.
To arrive at a reasonable estimate, we can consider the average weight of a giraffe, which ranges between 2,600 lbs and 4,250 lbs for adult males and females, respectively.
Therefore, a reasonable amount for the weight of Mr. Jackers' cargo would be between 2,600 lbs and 4,250 lbs, which translates to either 1 ton or 2 tons.
Thus, options c and d are the only reasonable answers, with d (2 tons) being the safer choice.
Learn more about weight at
https://brainly.com/question/6904250
#SPJ4
PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST
Based on the information, statement (A) False is correct.
The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.
How to calculate the probabilityIt should be noted that since the proportion of females who work part-time only in the summer (84%) is greater than the overall proportion of students who work part-time only in the summer (80%), we can conclude that gender and working part-time only in the summer are dependent. This means that knowing someone's gender gives us information about the likelihood that they work part-time only in the summer.
Therefore, statement (A) False is correct.
The probability will be:
0.80 x 0.50 x 0.84 = 0.336
The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.
Learn more about probability on
https://brainly.com/question/24756209
#SPJ1
A cyclist went out for a solo ride but has become lost. He knows from his inexpensive cycletracker GPS the distance he has traveled and in which direction, but he has no idea how to get home short of retracing his path. The different legs of his trip are listed below.
Determine in which direction and how far he needs to ride to get back where he started in the shortest distance possible. (assume there are no obstacles in his way and he can travel in a straight line) (5 marks)
Leg #1-8 km [North]
Leg #2-10 km [East]
Leg #3-12 km [15 S of East]
Leg #4-14 km [South]
The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.
How to solve for the distanceWe can use trigonometry to find the x and y components.
x3 = 12 * cos(15°) ≈ 11.59 km (east)
y3 = -12 * sin(15°) ≈ -3.10 km (south, hence the negative sign)
Leg #4: 14 km [South]
x4 = 0 km (no east/west movement)
y4 = -14 km (south, hence the negative sign)
Now, let's find the total x and y displacements:
x_total = x1 + x2 + x3 + x4 ≈ 0 + 10 + 11.59 + 0 ≈ 21.59 km
y_total = y1 + y2 + y3 + y4 ≈ 8 + 0 - 3.10 - 14 ≈ -9.10 km
Now, we can find the distance and direction he needs to ride to get back to the starting point:
Distance=
[tex]\sqrt{21.59^2 + (-9.10)^2}[/tex])
23.21 km
Direction:
angle =
arctan(9.10 / 21.59)
= 23.13°
The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.
Read more on distance and direction here https://brainly.com/question/1326450
#SPJ1
(12.7)
2. A swimming pool is in the shape of a rectangular
prism with a horizontal cross-section 10 feet by 20
feet. The pool is 5 feet deep and filled to capacity.
Water has a density of approximately 60 pounds
per cubic foot
What is the approximate mass of water in the pool?
A. 8,000 lb.
B.
12,500 lb.
C
16,700 lb.
D. 60,000 lb.
Answer:
Step-by-step explanation:
The volume of the pool can be calculated as:
Volume = length x width x height
Volume = 10 ft x 20 ft x 5 ft
Volume = 1000 cubic feet
The mass of the water in the pool can be calculated as:
Mass = Volume x Density
Mass = 1000 cubic feet x 60 pounds/cubic foot
Mass = 60,000 pounds
Therefore, the approximate mass of water in the pool is 60,000 lb , which corresponds to option D.
Solutions of Two-Variable Linear Inequalities
-40
5
-5
40
X
Select all of the following ordered pairs that are in
the solution set of the inequality shown.
(-10,-10)
0
0
0
(0.
(0, 10)
(10,0)
(20, 0)
(100, 100)
Answer: -403
Step-by-step explanation:
Find an equation of the circle drawn below.
The equation of the circle in this problem is given as follows:
x² + y² = 49.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle. As this distance is of 7 units, it is then given as follows:
r = 7 -> r² = 49.
The center of the circle is at the origin, hence:
[tex](x_0, y_0) = (0,0)[/tex]
Thus the equation of the circle is given as follows:
x² + y² = 49.
More can be learned about the equation of a circle at https://brainly.com/question/1506955
#SPJ1
A particular fruits weight are normally disturbed, with a mean of 374 grams and a standard deviation of 20grams. the heaviest 20% of fruits weigh more than how many grams? answer to the nearest gram.
The weight of the heaviest 20% of fruits can be estimated using the z-score corresponding to the 80th percentile, which is 0.84.
The weight can be calculated by adding the z-score multiplied by the standard deviation to the mean weight. Therefore, the weight of the heaviest 20% of fruits is approximately 405 grams.
To calculate this, we first need to find the z-score for the 80th percentile, which is 0.84. Then, we can use the formula z = (x - mu) / sigma, where x is the weight we want to find, mu is the mean weight, and sigma is the standard deviation.
Rearranging this formula to solve for x, we get x = z * sigma + mu. Plugging in the values we have, we get x = 0.84 * 20 + 374 = 405.2 grams. Rounding this to the nearest gram, we get the answer of 405 grams.
For more questions like Z-score click the link below:
https://brainly.com/question/15016913
#SPJ11
Solve for x (2-3) 67
Over what interval is the function shown in the table increasing? Decreasing? Y=6x2
A rectangle has vertices located at the points: A(-1 1/4,3 1/2), B(2 2/3,3 1/2), C(2 2/3,-1 3/4), D(-1 1/4,-1 3/4). Find the length of BC
The length of BC is 5.25 units. when the rectangle has vertices located at the points: B is ( 2 2/3,3 1/2) and C is (2 2/3,-1 3/4).
We need to find the length of BC. The length of a line segment BC can be calculated using the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is given as :
d = √(x2−x1)²+(y2−y1)²
Given data:
A = (-1 1/4,3 1/2)
B = ( 2 2/3,3 1/2)
C = (2 2/3,-1 3/4)
D = (-1 1/4,-1 3/4)
We need to Convert the B and C mixed numbers to improper fractions, we get,
B = (2+2/3), (3 + 1/2)
= (8/3, 7/2)
C = (2+2/3) , (-1 + 3/4)
= (8/3, -7/4).
Substituting the B and C values into the distance formula, we get:
= √(8/3 − 8/3)² + ( −7/4 − 7/2 )²
= √0 + ( − 21 / 4 )²
= √441/16
[tex]= 21/4[/tex]
[tex]= 5.25[/tex]
Therefore, the length of BC is 5.25 units.
To learn more about the distance formula:
https://brainly.com/question/30395212
#SPJ4
The carpet for the office you completed cost $576. If you're using the same carpet in the new client's bedroom, how much will it cost? Round up to the nearest whole dollar. (Hint: You may want to find the area of each room and the cost of the carpet per square foot. )
The cost of a similar carpet in the client's bedroom is $225 when the area of the bedroom is 120 square feet.
Given Data:
Cost of Carpet = $576
length of office room = 16
Width of office room = 19.2
length of Bedroom = 12
Width of Bedroom = 10
We need to determine the area of the office and the bedroom. we can determine it by using the Area of a rectangle formula which is given as,
Area of a rectangle = length × width
Area of Office = length of office room × width of office room
= 16 × 19.2
= 307.2 square feet
Area of Bedroom = length of Bedroom × width of Bedroom
= 12 × 10
= 120 square feet
Therefore, the area of the office is 307.2 square feet, and the area of the Bedroom is 120 square feet.
From the above data, the area of the office is 307.2 square feet and the carpet will cost $576 for the office. we need to find the cost of the carpet for the 120 square feet bedroom, let's assume the cost as x, and cross multiply we get,
x = 120 × 576 / 307.2
x = 69120 / 307.2
x = $225
Therefore, the cost of the bedroom carpet is $225.
To learn more about the Area of a rectangle:
https://brainly.com/question/29604954
#SPJ4
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
The three equivalent equations are x+1=4, -5+x=-2, and 2+x=5. The x equals 3.
Step-by-step explanation: