The vertical support cable length that is 60 feet from the towers is 56.5 feet.
The given information:
Towers are 400 ft apart
The supporting cable is 100 ft high
The supporting cable runs 30 ft above the road
The shape of the cable is a parabola.
Find the length of the vertical support cables that are 60 feet from the towers.
First, let’s set up a coordinate system with the origin at the lowest point of the cable and the x-axis along the road. The towers are 400ft apart, so their x-coordinates will be -200 and 200.
The equation of a parabola is y = ax^2 + bx + c. Since the cable is 30ft above the road at its lowest point, c = 30.
The towers are 100ft tall, so when x = -200 and x = 200, y = 100. Substituting these values into the equation of the parabola gives us two equations: 100 = a(-200)^2 + b(-200) + 30 and 100 = a(200)^2 + b(200) + 30.
Solving these equations simultaneously for a and b gives us a = 0.001875 and b = 0.
So the equation of the parabola is y = 0.001875x^2 + 30.
The towers are 400ft apart, so their x-coordinates are -200 and 200. The vertical support cable that we want to find the length of is 60 feet from one of the towers. So if we move 60 feet from one of the towers along the x-axis towards the center of the bridge, we will reach the point where the vertical support cable is attached to the road. This point will have an x-coordinate of -200 + 60 = -140 or 200 - 60 = 140.
Now we can find the length of the vertical support cable that is 60 feet from one of the towers. When x = -140 or x = 140,
y = 0.001875(140)^2 + 30 ≈ 56.5.
So the length of the vertical support cable that is 60 feet from one of the towers is approximately 56.5 feet.
To know more about parabola: https://brainly.com/question/21191648
#SPJ11
Can someone PLEASE help me ASAP? It’s due today!! I will give you brainliest if it’s correct
Let's order them from most likely to least likely to occur:
Baseballs (0.3)Basketballs (0.24)Volleyballs (0.2)Soccer balls (0.16)Footballs (0.1)How to solveTo calculate the probability of selecting each type of ball, we need to find the total number of balls in the bin first.
Then, we will divide the number of each type of ball by the total number of balls.
Total number of balls = 15 baseballs + 12 basketballs + 8 soccer balls + 5 footballs + 10 volleyballs
Total number of balls = 50 balls
Now, let's calculate the probability of selecting each type of ball:
Baseballs: P(Baseballs) = (Number of baseballs) / (Total number of balls) = 15/50 = 0.3
Basketballs: P(Basketballs) = (Number of basketballs) / (Total number of balls) = 12/50 = 0.24
Soccer balls: P(Soccer balls) = (Number of soccer balls) / (Total number of balls) = 8/50 = 0.16
Footballs: P(Footballs) = (Number of footballs) / (Total number of balls) = 5/50 = 0.1
Volleyballs: P(Volleyballs) = (Number of volleyballs) / (Total number of balls) = 10/50 = 0.2
Now, let's order them from most likely to least likely to occur:
Baseballs (0.3)Basketballs (0.24)Volleyballs (0.2)Soccer balls (0.16)Footballs (0.1)Read more about probability here:
https://brainly.com/question/24756209
#SPJ1
Natalie uses a 50% off coupon when she buys a camera. The original price of the camera is
$46. 00
$46. 0. How much money does Natalie save by using the coupon?
Natalie saved amount $23 by using the coupon.
What is meant by the discount rate?
The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the present.
The data is available from the question is:
The discount through coupon is d = 50%.
The original price of camera is c = $46.00
The discount on the amount is:
[tex]d = (\frac{50}{100}) 46[/tex]
d = 23
Thus, the amount saved is $23.
Learn more about Discount rate at:
https://brainly.com/question/30392176
#SPJ4
Kevin ate 5/12 of a pizza. Which is a better estimate for the amount of pizza that he ate: about half of the pizza or almost all of the pizza?
Answer:
Step-by-step explanation:
answer: about half the pizza as 5/12 is closer to half(6/12) then the full pizza (12/12)
Tania is riding a train for $43.6$ miles to get to her destination. The train has $14.3$ more miles to travel before arriving at Tania's destination.
Which equation and solution correctly represent how many miles, $m$ , the train has already traveled?
Responses
Answer:
The answer to your problem is:
m +14.3 =43.6
m =29.3
Step-by-step explanation:
Miles to travel: 43.6
Miles left to travel: 14.3
To find the amount of miles that the train has already traveled (m), we know that the sum of that value (m) and the miles left to travel (14.3) is equal to the total miles (43.6)
m +14.3 = 43.6
m = 43.6-14.3= 29.9
Thus the answer to your problem is,
m +14.3 =43.6
m =29.3
The gcf of 18,36 and me is 2.
I am a multiple of 5
I am greater than 18 and less than 30
Based on the information provided, the only possible number that satisfies all the conditions is 20.
What is GCF?
GCF stands for "Greatest Common Factor". It is also sometimes referred to as the "Greatest Common Divisor" (GCD). The GCF of two or more numbers is the largest positive integer that divides evenly into each of the numbers. In other words, it is the largest factor that the numbers have in common.
The GCF (Greatest Common Factor) of 18, 36, and a number N is 2. Since 18 and 36 are both even numbers with a common factor of 2, any number that satisfies this condition must also be even and have a factor of 2.
The number N is a multiple of 5. Since the number is even and has a factor of 2, the only even multiple of 5 between 18 and 30 is 20.
Finally, we are given that N is greater than 18 and less than 30. The only number that satisfies all the given conditions is therefore 20.
To know more about GCF visit:
brainly.com/question/11154053
#SPJ1
Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?
A.
XY = 8 mm , YZ = 12 mm , XZ = 23 mm
B.
XY = 11 mm , YZ = 9 mm , XZ = 23 mm
C.
XY = 11 mm , YZ = 12 mm , XZ = 20 mm
D.
XY = 14 mm , YZ = 12 mm , XZ = 29 mm
The combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.
For a set of three side lengths to form a triangle, the sum of any two sides must be greater than the third side. Using this property, we can determine which of the given combinations of side lengths will form a triangle with vertices X, Y, and Z.
A. XY = 8 mm, YZ = 12 mm, XZ = 23 mm
Here, XY + YZ = 8 mm + 12 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.
B. XY = 11 mm, YZ = 9 mm, XZ = 23 mm
Here, XY + YZ = 11 mm + 9 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.
C. XY = 11 mm, YZ = 12 mm, XZ = 20 mm
Here, XY + YZ = 11 mm + 12 mm = 23 mm, which is greater than XZ = 20 mm. Therefore, this combination of side lengths will form a triangle.
D. XY = 14 mm, YZ = 12 mm, XZ = 29 mm
Here, XY + YZ = 14 mm + 12 mm = 26 mm, which is greater than XZ = 29 mm. Therefore, this combination of side lengths will form a triangle.
Therefore, the combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.
To learn more about combinations please click on below link.
https://brainly.com/question/30582704
#SPJ1
Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?
A.XY = 8 mm , YZ = 12 mm , XZ = 23 mm
B.XY = 11 mm , YZ = 9 mm , XZ = 23 mm
C.XY = 11 mm , YZ = 12 mm , XZ = 20 mm
D.XY = 14 mm , YZ = 12 mm , XZ = 29 mm
Please help VERY SOON
The person who has the fastest speed is given as follows:
Aubri and Tyler(tied).
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The constant for each person, representing the velocity, is given as follows:
Tyler: 6/4 = 3/2 = 1.5.Aubri: 3/2 = 1.5.Kyote: 5/4 = 1.25.Missing InformationThe problem asks for the person who has the fastest speed.
More can be learned about proportional relationships at https://brainly.com/question/7723640
#SPJ1
Find x. Please help I don't know
Probably 26 :P
Because its like almost double of 10 but it is not....
HOPE THAT MADE SENSE!
Answer: well imma said x=19
Step-by-step explanation:
because All the diameter of the circle is equal.
So 14+15=29
And X is
29-10=19
[tex]\frac{2}{3}a + 2 = \frac{1}{3}(4a + 1)[/tex]
solve for "a"
Answer:
a=5/2
Step-by-step explanation:
Answer:
a = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] a + 2 = [tex]\frac{1}{3}[/tex] (4a + 1)
multiply through by 3 to clear the fractions
2a + 6 = 4a + 1 ( subtract 4a from both sides )
- 2a + 6 = 1 ( subtract 6 from both sides )
- 2a = - 5 ( divide both sides by - 2 )
a = [tex]\frac{-5}{-2}[/tex] = [tex]\frac{5}{2}[/tex]
Let B and C be two ordered bases of Rº, and consider a linear transformation T:RR. Suppose that the change of base matrix Ic,B is given by 1-3 -1 1] -1 2 -1 -1 -3 -2] and the coordinate matrix Tc,c of T with respect to C is given by -2 -2 -27 |-1 -3 -1. | 2 0 -1] Use this to determine coordinate matrix TB,B of T with respect to B! TB,B =
The coordinate matrix TB,B of a linear transformation T with respect to bases B and C is found to be [2 5 4; 1 1 2; -1 -1 -1].
To find the coordinate matrix TB,B of T with respect to B, we can use the formula:
TB,B = Ic,B * Tc,c * Ib,c
where Ib,c is the change of basis matrix from basis B to basis C.
To find Ib,c, we can use the inverse of Ic,B:
Ib,c = (Ic,B)^(-1)
We can use a calculator to find the inverse of Ic,B:
Ib,c = [1/4 1/4 -1/4]
[ 0 1 1 ]
[-1/4 -3/4 3/4]
Now, we need to calculate Ic,B * Tc,c:
Ic,B * Tc,c = [ 1 -3 -1 ] [-2 -2 -27 ] [ 1/4 1/4 -1/4 ] = [ 23 29 68 ]
[-1 2 -1 ] [-1 -3 -1 ] [ 0 1 1 ] [-15 -23 -48]
[-1 -3 -2 ] [ 2 0 -1 ] [-1/4 -3/4 3/4 ] [ 3 11 25]
Finally, we can calculate TB,B:
TB,B = (Ic,B * Tc,c * Ib,c)^(-1)
We can use a calculator to find the inverse of Ic,B * Tc,c * Ib,c:
TB,B = [ 2 5 4 ]
[ 1 1 2 ]
[-1 -1 -1 ]
To know more about coordinate matrix:
https://brainly.com/question/31052618
#SPJ4
Tammy is planning to garden a plot of land in the shape of a right triangle.
The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches.
Answer: 7.5 square inches
Step-by-step explanation: the ratio is 1:2 meaning we cut the numbers in half, then we can find area normally
5/2=2.5
12/2=6
2.5x6=15
15/2=7.5
Gina was shopping and saw a t-shirt she really liked, but could not decide which color to buy. The clerk said she would reduce the price by $2.50 per shirt if Gina bought more than one. She purchased 5 shirts all in different colors, for a total of $47.50. Write an equation to find the original cost of one shirt.
Let x represent the original cost of one shirt. The equation is 5x - 47.50 = 0, which can be solved to find that x = $9.50.
Gina was shopping and saw a t-shirt she liked, but couldn't decide which color to buy. The clerk offered to reduce the price by $2.50 per shirt if Gina bought more than one. She decided to purchase 5 shirts in different colors and the total cost of all 5 shirts was $47.50. To find the original cost of one shirt before the discount, we can set up an equation. Let x represent the original cost of one shirt. The equation would be 5x - 47.50 = 0, since the total cost of the 5 shirts was $47.50. When this equation is solved, x = $9.50, which is the original cost of one shirt before the discount. Therefore, the total cost of all 5 shirts was reduced by $2.50 for each shirt, from $9.50 to $7.00.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ1
A raccoon consumes 500 calories of food. 50 of those
calories are converted to blomass. In other words:
50 calories turn into plant matter
50 calories leave the raccoon's body as waste
C
It uses 50 calorles of energy to keep warm, reproduce, and
move around
uses
50 calories of energy are stored In Its body
A raccoon consumes 500 calories of food. Of those calories, 50 are transformed into biomass. In other words, 50 calories of energy are stored In Its body. So, option D is correct.
When a raccoon eats 500 calories of food, some of those calories go towards its daily needs for warmth, movement, and reproduction. The raccoon's body does not store this energy; instead, it is transformed into other forms, including heat and movement. In addition, a portion of the energy in meals is expelled as waste rather of being absorbed. Nonetheless, 50 calories of the food's energy are transformed into biomass, which is then stored as fat or tissue in the raccoon's body. Thus, the right response is D) Its body stores 50 calories of energy.
Learn more about Calories:
brainly.com/question/29096838
#SPJ4
The actual question is:
A raccoon consumes 500 calories of food. Of those calories, 50 are transformed into biomass. In other words:
A) 50 calories turn into plant matter.
B) 50 calories leave the raccoon's body as waste.
C) In order to stay warm, reproduce, and move around, it needs 50 calories of energy.
D) 50 calories of energy are stored In Its body
What type of triangle is shown below?
Answer:
equalateral
Step-by-step explanation:
each side is equal to the next
Answer:
2. Equilateral
Step-by-step explanation:
Step 1: Process Of Elimination-
1. Right: No
This triangle is not a right triangle because it does not have a right triangle indicator nor does it equal 90°.
2. Equilateral: Yes
This triangle is an equilateral triangle because all 3 sides are equal and they add up to 180° meaning each side equal 60°.
3. Acute: No
A acute triangle is a triangle that is less then 90° but this triangle equals 180°.
4. Scalene: No
A scalene triangle is a triangle that has different side angles but they all add up to 180° but here we can see that the sides are equal.
What is the purpose of doing a multiple comparison? Choose the correct answer below. O A. O B. O C. ○ D. A multiple comparison is used to compare the results of a one-way ANOVA to the results of a two-way ANOVA. A multiple comparison is equivalent to a one-way ANOVA, except for more than two populations. When at least one of the variances is different, a multiple comparison shows the relationship between the variances. When the null hypothesis of an ANOVA test is rejected, a multiple comparison shows the relationship between the population means. Click to select vour answer
The purpose of doing a multiple comparison is to show the relationship between the population means when the null hypothesis of an ANOVA test is rejected.
What is meant by the multiple comparison?Multiple comparison is a statistical process that entails making a large number of comparisons, thus raising the chances of erroneously detecting false positives or type I errors.
When using multiple comparisons, there is a possibility that a statistical inference drawn for a single comparison is no longer valid.
Therefore, it is critical to adjust the p-values or confidence levels of these tests accordingly. As a result, multiple comparison methods have been devised.
The following are the purposes of doing multiple comparisons:
The relationship between the population means is shown when the null hypothesis of an ANOVA test is rejected.
A multiple comparison is used to compare the results of a one-way ANOVA to the results of a two-way ANOVA.
A multiple comparison is equivalent to a one-way ANOVA, except for more than two populations.When at least one of the variances is different, a multiple comparison shows the relationship between the variances.
The most important objective of multiple comparisons is to estimate, compare, and control the likelihood of making false conclusions.
Learn more about ANOVA test at
https://brainly.com/question/30127764
#SPJ11
Factor 12y−18 using the GCF.
Answer:
6(2y-3)
Step-by-step explanation:
Both 12 and 18 divide by 6.
12/6= 2 and 18/6 = 3
So we can take 6 out and put it outside the bracket and have 2y and 3 on the inside.
help asapp!!!!!!!!!!!!!
The total length of the cross-country course include the following: 16 miles.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;
P = 2(L + B)
Where:
P represent the perimeter of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;
P = 2(L + B)
P = 2(6 + 2)
P = 2(8)
P = 16 miles.
Read more on perimeter of a rectangle here: brainly.com/question/28695033
#SPJ1
Complete Question:
A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.
What is the total length of the cross-country course?
Answer: The total length of the cross-country course include the following: 16 miles.
How to calculate the perimeter of a rectangle?
In Mathematics and Geometry, the perimeter of a rectangular shape such as a parallelogram can be calculated by using this mathematical expression;
P = 2(L + B)
Where:
P represent the perimeter of a rectangle.
B represent the breadth of a rectangle.
L represent the length of a rectangle.
By substituting the given side lengths into the formula for the perimeter of a rectangular shape, we have the following;
P = 2(L + B)
P = 2(6 + 2)
P = 2(8)
P = 16 miles.
Read more on perimeter of a rectangle here: brainly.com/question/28695033
#SPJ1
Complete Question:
A cross-country course is in the shape of a parallelogram with a base of length 6 mi and a side of length 2 mi.
What is the total length of the cross-country course?
Step-by-step explanation:
HELP ASAP
This figure represents a planter
How much soil will it take to fill the planter?
Enter your answer in the box
the amount of soil needed is 27 cubic feet.
What is the value of x in the product of powers below
6 (to the power of 9) • 6 (to the power of X) = 6 (to the power of 2)
-11
-7
7
11
Pls help
Answer: 7
Step-by-step explanation:
Step 1: 6^9 * 6^x = 6^2
Step 2: 9 + x = 2
Step 3: x = 2 - 9
Step 4: x = -7
Step 5: Since the power of a number cannot be negative, x must be 7.
Algebraic expressions for geometry( just beginning geometry) please help this is 2 months late
We can see here:
4. Given: 6x + 7 = 8x - 17. Prove: x = 12
Statements Reasons
1. 6x + 7 = 8x - 17 Given
2. 7 = 2x - 17 Subtracted 6x from both sides
3. 24 = 2x Added 17 to both sides
4. 12 = x Divided both sides by 2
5. x = 12 Final answer proven
What is an algebraic expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It can represent a value, an equation, or a formula.
5. Given: -7(x + 2) + 4x = 6(2x - 4): Prove: x = 2/3
Statements Reasons
1. -7(x + 2) + 4x = 6(2x - 4) Given
2. -7x - 14 + 4x = 12x - 24 Opened the brackets by multiplying all
3. -3x - 14 = 12x - 24 Added -7x and 4x at LHS
4. -15x - 14 = -24 Subtracted 12x from both sides
5. -15x = -10 Added 14 to both sides
6. x = 2/3 Divided both sides by -5 to arrive to the result.
6. Given: 3x + 1 = -14: Prove: x = -5
Statements Reasons
1. 3x + 1 = -14 Given
2. 3x = -15 Subtracted 1 from both sides
3. x = -5 Divided both sides by 3. Final answer proven.
7. Given: 2(x - 9) = -10; Prove: x = 4
Statements Reasons
1. 2(x - 9) = -10 Given
2. 2x - 18 = -10 Opened the brackets.
3. 2x = 8 Added 18 to both sides
4. x = 4 Divided both sides by 2. Final answer proven.
Learn more about algebraic expression on https://brainly.com/question/4344214
#SPJ1
(Adding Integers MC) What is the value of 209 + −142 + −52? 15 −15 67 −194
The answer is positive 15 because the final result is 15 units to the right of zero on the number line.
To solve this problem, we simply need to add the three integers together.
Starting with 209, we add -142 to get 67. Then, we add -52 to get a final result of 15. Therefore, the answer is 15.
To understand why the answer is positive, negative, or zero, we can think of integers on a number line. Positive integers are to the right of zero, negative integers are to the left of zero, and zero is at the center.
Starting with 209, we move 209 units to the right of zero on the number line. Then, adding -142 means moving 142 units to the left of zero, resulting in a position of 67 units to the right of zero. Finally, adding -52 means moving 52 units to the left of 67, resulting in a position of 15 units to the right of zero.
Therefore, the answer is positive 15 because the final result is 15 units to the right of zero on the number line.
To learn more about number line:
https://brainly.com/question/16191404
#SPJ4
Upper & lower bounds
Brian weighs himself at 84kg to the nearest kg.
What is the most he could weigh?
Give the upper bound as your answer.
Thus, the most he could weigh that is the upper bound of the given condition is 84kg.
What about weigh?
The word "weigh" is not frequently used by itself in arithmetic. The notion of weight or mass, for example, can be used when measuring or comparing quantities. While mass is a measurement of the quantity of matter inside an object, weight is a measure of the gravitational force acting on it. Weight can be viewed as the force a standard gravitational field applies to an object in the setting of measurement. Weight or mass may be denoted in mathematical equations by variables such as "w" or "m," and the units used to measure them may change based on the situation.
Define upper bound:
In mathematics, an upper bound is a number that is greater than or equal to all the elements in a given set. More formally, let S be a set of real numbers. A number u is an upper bound for S if and only if for all x in S, we have x ≤ u.
For example, consider the set S = {2, 4, 6, 8}. The number 10 is an upper bound for S because 2 ≤ 10, 4 ≤ 10, 6 ≤ 10, and 8 ≤ 10. However, the number 7 is not an upper bound for S because 8 > 7.
Note that an upper bound need not be an element of the set S itself. For instance, the set of all negative real numbers does not have any upper bound among the negative real numbers, but 0 is an upper bound for this set.
It's worth noting that an upper bound may or may not be a member of the set S. If an upper bound is a member of S, then it is called a "maximum" or "greatest" element of S. However, if an upper bound is not a member of S, then S has no maximum element.
According to the given information:
Brain weigh himself at 84kg to the nearest kg as (given) , because uses the method of round off.
Thus, the range of weigh:
⇒ 83.5 ≤ Weigh ≤ 84.4.
Thus, the most he could weigh is 84.4kg.
To know more about upper bound visit:
https://brainly.com/question/22965427
#SPJ1
What is the term-to-term rule of the linear sequence below? 1 , 7 , 13 , 19 , 25
Answer:6n-5
Step-by-step explanation:
1,7,13,19,25
It goes up in 6 each time, so you will need to go back 6 back on the number one, so it will be -5 so the answer will be 6n-5.
6(2)-5 = 7
6(3)-5 =13
Carlos has scored 24, 19, 20, and 28 points in his four basketball games so far. How many points does he need to score in the next game so that his average (mean) is 24 points per game?
Carlos needs to score 29 points in the next game to have an average of 24 points per game.
What is the mean and standard deviation?The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
According to the given information:Let x be the number of points Carlos needs to score in the next game to have an average of 24 points per game.
To find the solution, we can use the formula for the mean of a set of numbers:
(mean) = (sum of numbers) / (number of numbers)
In this case, we want the mean to be 24, and we have 5 numbers (4 previous game scores and the score in the next game), so:
24 = (24 + 19 + 20 + 28 + x) / 5
Multiplying both sides by 5, we get:
120 = 91 + x
Subtracting 91 from both sides, we get:
x = 29
Therefore, Carlos needs to score 29 points in the next game to have an average of 24 points per game.
To learn more about the mean and standard deviation visit:
brainly.com/question/475676
#SPJ1
A recipe says that 6 spring rolls will serve 3 people. How many people will 1 spring roll serve
Answer:
Step-by-step explanation:
the answer will be 2
Answer:
2 people
Step-by-step explanation:
6/3 = 2
Helping in the name of Jesus.
Find n. Then find the area. Perimeter =60 2/4 in
The area of the rectangle is 220.5 square inches when the perimeter of the rectangle is 242/4 inch and one side of the rectangle is 49/4 inch.
Perimeter = [tex]60 \frac{2}{4}[/tex] inch = 242/4 inch
one side of rectangle = [tex]12\frac{1}{4}[/tex] inch = 49/4
The perimeter of a rectangle is the sum of all its sides. In this case, we know that the perimeter of the rectangle is 242/4 inch, which simplifies to 60.5 inch. We also know that one side of the rectangle is 49/4 inch.
Let's call the other side of the rectangle "n". Then, we can write the equation:
2(49/4 + n) = 60.5
Simplifying this equation, we get:
98/4 + 2n = 60.5
24.5 + 2n = 60.5
2n = 36
n = 18
Therefore, the other side of the rectangle is 18 inch.
To find the area of the rectangle, we can use the formula:
Area = length * width
In this case, the length is 49/4 inch and the width is 18 inch. So, we have:
Area = (49/4) * 18 = 220.5 square inches
Therefore, the area of the rectangle is 220.5 square inches.
Learn more about Perimeter :
https://brainly.com/question/6465134
#SPJ4
The complete question is :
Find n. Then find the area. Perimeter = [tex]60 \frac{2}{4}[/tex] inch . If one side of rectangle = [tex]12\frac{1}{4}[/tex] inch and other n inch.
five cores are removed from a new section of an asphalt highway. the following percentages of air voids were obtained from laboratory analyses: 3.7, 4.5, 4.1, 4.7, 3.9. past studies have suggested that the standard deviation of the air void content is 0.5%. compute the 95%, two-sided confidence interval on the mean
The two sided confidence interval on mean is 3.56 and 4.80.
What is confidence interval?
The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.
The given data is 3.7, 4.5, 4.1, 4.7, 3.9. Here n = 5
=> σ = 1- 95% = 5% = 0.05
We know that the confidence interval is
=> CI = [tex]\overline x {\displaystyle \pm }\frac{z(\sigma)}{\sqrt n}[/tex]
Here 95% confidence level so z= 1.96
Mean [tex]\overline x = \frac{3.7+4.5+4.1+3.9+4.7}{5} = 4.18[/tex] and σ = 0.5
Here n<30 so we can use t instead of z then t-value = 2.776.
Now confidence level CI = [tex]\ 4.18 {\displaystyle \pm }\frac{2.776\times0.5}{\sqrt 5}[/tex]
=> CI = 4.18 [tex]\display \pm[/tex] 0.62 = ( 3.56 , 4.80)
Hence the two sided confidence interval on mean is 3.56 and 4.80.
To learn more about confidence level refer the below link
https://brainly.com/question/29576113
#SPJ1
Write the equation of the parabola that has its vertex at (3,-12) and passes through the point (0,6)
Answer:
y=2(x-3)²-12
Step-by-step explanation:
Which of the following equations is the best model for a line of fit for the data?
An equation that is the best model for a line of best fit for the data include the following: C. y = 3/4x + 5.
How to write an equation of the line of best fit for the data set?In order to determine an equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).
Based on the scatter plot (see attachment) which models the relationship between the x-values and y-values, an equation for the line of best fit is given by
y = 3x/4 + 5
In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.
Read more on scatter plot here: https://brainly.com/question/28220792
#SPJ1
Complete Question:
Which of the following equations is the best model for a line of fit for the data?
y= 1/4x + 5.
y= -1/4x + 5.
y= 3/4x + 5.
y= -3/4x + 5.
what are the parameters of the relevant standard beta distribution?
The parameters of the relevant standard beta distribution are alpha and beta.
Determine the shape of the beta distributionThese are two parameters that determine the shape of the beta distribution
.The standard beta distribution is a continuous probability distribution that is defined on the interval [0, 1]. It is often used to model the probability of success or failure in a binary experiment.
The two parameters of the standard beta distribution determine the shape of the distribution. Alpha is the shape parameter that determines the slope of the distribution, while beta is the shape parameter that determines the height of the distribution.
The standard beta distribution is often used in Bayesian statistics to model the prior probability of a parameter. It is also used in applications such as modeling the proportion of a population that has a particular characteristic or modeling the probability of default on a loan.
Learn more about alpha and beta at
https://brainly.com/question/2264128
#SPJ11