The primary reason many present-day African nations struggled to unite their people is F. Because many African peoples have strong tribal ties.
The strong tribal identities and loyalties that exist among various ethnic groups inside African states today are one of the main causes of the effort to bring people together. Through colonisation, many African nations were developed, and many of them contained numerous groups with various cultural, linguistic, and ethnic origins.
Therefore, as a result, it has been challenging to forge a strong sense of national identity among many individuals who still identify primarily with their own tribe or ethnic group. This has occasionally resulted in disputes and hostilities amongst various diverse groups, impeding efforts to create a community that is more unified.
Read more about African nations on:
https://brainly.com/question/31148283
#SPJ4
Diego selling raffle tickets for $1.75 per ticket complete the table to show how much she earned for 50 tickets 20 tickets and r tickets
Diego selling raffle tickets for $1.75 per ticket and she earned for 50 tickets is $87.50.
When a purchase, appropriation, requisition, or direct engagement with the customer occurs at the point of sale, the seller or supplier of the products or services completes a transaction. Title (property or ownership) of the object is transferred, and a price is settled, meaning a price is agreed upon for which the ownership of the item will transfer.
We can calculate how much money Diego would make if he sold each quantity of raffle tickets for $1.75 each using Excel's multiplication function. It is possible to create a table with the number of tickets sold in one column and the money taken in the other.
Diego would receive $17.50, for instance, if he sold 10 tickets (10 x $1.75). If he sold 20 tickets, he would earn $35 (20 x $1.75), and so on. Using Excel's fill handle, you can quickly fill the table with the totals for each sold ticket.
The table would look like this:
Number of Tickets Sold | Amount of Money Earned
•----------------------------------|---------------------------------------•
10 | $17.50
20 | $35.00
30 | $52.50
40 | $70.00
50 | $87.50
By using the multiplication function in Excel, we can quickly calculate the amount of money Diego would earn for any number of raffle tickets sold at $1.75 per ticket.
Learn more about Tickets problems:
https://brainly.com/question/16746114
#SPJ4
2. Mandy is walking in the woods. She completes 70% of her walk in 3 hours. She continues walking at that same rate. How much time, in hours, will Mandy's entire walk take?
A 3 4\5
B. 5
C. 6
D. 6 1\2
Answer:
If Mandy completed 70% of her walk in 3 hours, then we can find her walking rate as follows:
Let's assume that the entire walk takes t hours. Then, 70% of the walk would take 0.7t hours. We know that Mandy completes 70% of her walk in 3 hours, so we can set up the following equation:
0.7t = 3
Solving for t, we get:
t = 3 ÷ 0.7 ≈ 4.29
So, the entire walk will take approximately 4.29 hours. Since Mandy has already walked for 3 hours, the remaining time she needs to complete her walk is:
4.29 - 3 = 1.29 hours
Therefore, the answer is closest to option A, 3 4/5 hours.
Learn more about Walking Rates here:
https://brainly.com/question/13790976
A person standing on the ground throws a rock upward with an initial velocity of 16 feet per second. The person’s hand is 12 feet above the ground when the rock is released. This is modeled by the equation h = -16^2 + 16t + 12. How long does it take for the rock to hit the ground?
It will take the rock 1.5 seconds to hit the ground
How to determine how long it take for the rock to hit the ground?Since the situation is modeled by the equation h = -16t² + 16t + 12
The rock will hit the ground when height is zero i.e. h = 0. Thus, we have:
-16t² + 16t + 12 = 0 and we can then solve for the time (t) .
-16t² + 16t + 12 = 0 (divide through by -16)
t² - t - 3/4 = 0
Using factorization method:
(t + 1/2) (t - 3/2) = 0
t = -1/2 or 3/2
Since t cannot be negative. Thus, t = 3/2 = 1.5.
Learn more about model equation on:
brainly.com/question/29130032
#SPJ1
One can of pumpkin pie mix will make a pie ofdiameter 8 in. if 2 cans 9f pie mix are used to make a larger pie of the same thickness, find the diameter use square root of 2 equals 1. 414
The diameter of the larger pie is 8 x sqrt(2) inches.
How to find the diameter?The area of a circle is proportional to the square of its diameter. If the diameter of a pie made with one can of pumpkin pie mix is 8 inches, then its area is (4 inches)^2 x pi = 16 pi square inches.
If two cans of pie mix are used to make a larger pie of the same thickness, the total area of the pie will be twice that of the smaller pie.
So, the area of the larger pie is 2 x 16 pi = 32 pi square inches.
To find the diameter of the larger pie, we need to solve for d in the equation:
Area of circle = (d/2)^2 x pi
32 pi = (d/2)^2 x pi
32 = (d/2)^2
Taking the square root of both sides, we get:
sqrt(32) = d/2 x sqrt(2)
d/2 = sqrt(32)/sqrt(2)
d/2 = 4 x sqrt(2)
d = 8 x sqrt(2)
Therefore, the diameter of the larger pie is 8 x sqrt(2) inches.
Learn more about Diameter
brainly.com/question/5501950
#SPJ11
The radius of a bade if a cone is 8 cm. The height is 15 cm. What is the volume of the cone?
Answer: 1,004.8 or 320[tex]\pi[/tex]
Step-by-step explanation:
[tex]\frac{1}{3} \pi 8^{2} 15=1,004.8[/tex]
Assume that a procedure yields a binomial distribution with n trials and a probability of success of p. use a binomial probability table to find the probability that the number of successes x is exactly .
To find the probability that the number of successes x is exactly a certain value in a binomial distribution with n trials and a probability of success of p, we can use a binomial probability table. The table will provide us with the probability of getting x successes out of n trials, given a specific value of p.
For example, let's say we want to find the probability of getting exactly 3 successes in a binomial distribution with 10 trials and a probability of success of 0.5. We can use a binomial probability table to find the probability of getting exactly 3 successes, which is 0.117.
It is important to note that the probability of getting a specific number of successes in a binomial distribution is dependent on both the number of trials and the probability of success. Therefore, if we change either of these values, the probability of getting a certain number of successes will also change.
To know more about binomial refer here
https://brainly.com/question/13870395#
#SPJ11
Find the volume of a hexagonal prism whose base
has area 30. 5 square centimeters and whose height is 6. 5 centimeters
The volume of the hexagonal prism is approximately 198.25 cubic centimeters.
To find the volume of a hexagonal prism, we need to know the area of the base and the height of the prism. In this case, we are given that the base has an area of 30.5 square centimeters and the height is 6.5 centimeters.
First, let's find the perimeter of the base. Since a hexagon has six sides, the perimeter will be six times the length of one side. To find the length of one side, we can use the formula for the area of a regular hexagon, which is:
Area = (3√3 / 2) × s²
where s is the length of one side.
30.5 = (3√3 / 2) × s²
s² = 30.5 × 2 / (3√3)
s² ≈ 11.13
s ≈ 3.34
So the perimeter of the base is 6 × 3.34 ≈ 20.04 centimeters.
Now we can use the formula for the volume of a prism, which is:
Volume = Base area × Height
Volume = 30.5 × 6.5 ≈ 198.25 cubic centimeters
Know more about volume here:
https://brainly.com/question/1578538
#SPJ11
Find the value of w. Round to the nearest tenth.
Answer:
w ≈ 68,3
Step-by-step explanation:
Use trigonometry:
[tex] \sin(42) = \frac{w}{102} [/tex]
Cross-multiply to find w:
[tex]w = 102 \times \sin(42°) ≈68.3[/tex]
A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week. If the business is open six days a week (Monday - Saturday) and a random sample of n = 200 customers is selected, the critical value for testing the hypothesis using a goodness-of-fit test is x2 = 9. 2363 if the alpha level for the test is set at. 10
The hypothesis to be tested here is that the number of cars arriving for service is the same for each day of the week.
The null hypothesis, denoted as H0, is that the observed frequency distribution of cars is the same as the expected frequency distribution.
The alternative hypothesis, denoted as H1, is that the observed frequency distribution of cars is not the same as the expected frequency distribution.
To test this hypothesis, we use a goodness-of-fit test with the chi-square distribution. The critical value for a chi-square distribution with 6 - 1 = 5 degrees of freedom (one for each day of the week) and alpha level of 0.10 is 9.2363.
If the computed chi-square statistic is greater than 9.2363, then we reject the null hypothesis and conclude that the observed frequency distribution is significantly different from the expected frequency distribution.
Thus, if the computed chi-square statistic is greater than 9.2363, we can conclude that the number of cars arriving for service is not the same for each day of the week, and there is evidence to support the alternative hypothesis.
If the computed chi-square statistic is less than or equal to 9.2363, then we fail to reject the null hypothesis, and there is not enough evidence to suggest that the observed frequency distribution is different from the expected frequency distribution.
To know more about hypothesis, refer here:
https://brainly.com/question/29519577#
#SPJ11
Given the following triangle, If Sin F = 3/5 , then find the Cos D: A) 4/5 B) 4/3 C) 3/4 D) 3/5
If Sin F = 3/5 , then the value of Cos D is 4/5 (option a)
Let us consider the triangle in the given question. Since we are given that Sin F = 3/5, we know that the side opposite angle F is 3 and the hypotenuse is 5. Using Pythagoras theorem, we can find the length of the adjacent side as follows:
Opposite² + Adjacent² = Hypotenuse²
3² + Adjacent² = 5²
9 + Adjacent² = 25
Adjacent² = 16
Adjacent = 4
So we have found that the length of the adjacent side is 4. Now we can use the definition of cosine to find Cos D.
Cosine is defined as the ratio of the adjacent side to the hypotenuse. Therefore,
Cos D = Adjacent/Hypotenuse = 4/5
Hence, the answer is option A) 4/5.
To know more about triangle here
https://brainly.com/question/8587906
#SPJ1
Express the function graphed on the axes below as a piecewise function.
Expressing this function as a piecewise function, we get;
y = -x + 1 for x< -5
y = -1/2x + 4 for x> 4
According to the question, we can see that the graph is a line for x < -5. We will find two points on this line to find out the slope.
( - 5,6) and ( -8,9)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 9-6)/(-8 - -5) = 3/ ( -8+5) = 3/-3
The slope is -1
Using point-slope form, we will find the general equation of this line
y-y1 = m(x-x1) and the point ( -8,9)
y -9 = -1(x - -8)
y -9 = -1(x +8)
y-9 = -x - 8
y = -x + 1 for x< -5
The graph is a line for x > 4
(4,2) and ( 6,1)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 1 - 2)/(6 - 4) = -1/ (2) = -1/2
The slope is -1/2
Using point-slope form
y-y1 = m(x-x1) and the point (6,1)
y -1 = -1/2(x - 6)
y-1 = -1/2 x + 3
y = -1/2x + 4 for x> 4
Therefore, expressing this function as a piecewise function, we get;
y = -x + 1 for x< -5
y = -1/2x + 4 for x> 4
To learn more about graphed functions;
https://brainly.com/question/18170083
#SPJ1
What is the equation of a circle whose center is at the origin and whose radius is 16?x 2 + y 2 = 256x 2 + y 2 = 4x 2 + y 2 = 16
The equation of the circle with center at the origin and radius 16 is x^2 + y^2 = 256.
To find the equation of a circle with center at the origin and radius 16, we can use the general equation of a circle:
x^2 + y^2 = r^2
where (x, y) are the coordinates of any point on the circle, and r is the radius.
In this case, the center is at the origin, so the coordinates (x, y) are both 0. The radius is given as 16. Plugging these values into the equation, we have:
0^2 + 0^2 = 16^2
0 + 0 = 256
Thus, the equation of the circle is:
x^2 + y^2 = 256
So, the equation of the circle with center at the origin and radius 16 is x^2 + y^2 = 256.
To know more about radius, refer here :
https://brainly.com/question/31831831#
#SPJ11
In triangle JK L, cos(K) = 21 and angle J is a right angle. What is the value of cos (L)?
solve in the simplest way possible
Prove the following two properties of the Huffman encoding scheme. (a) If some character occurs with frequency more than 2=5, then there is guaranteed to be a codeword of length 1. (b) If all characters occur with frequency less than 1=3, then there is guaranteed to be no codeword of length 1
(a) Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency. Therefore, there is guaranteed to be a codeword of length 1 for this character. (b) Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.
(a) Let's assume that some character occurs with frequency more than 2=5.
The two nodes with the lowest frequency are merged into a single node, with the sum of their frequencies as the frequency of the new node.
This process is repeated until all the nodes are merged into a single node, which becomes the root of the tree.
Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency.
Therefore, there is guaranteed to be a codeword of length 1 for this character.
(b) Let's assume that all characters occur with frequency less than 1=3.
Consider the binary tree created by the Huffman algorithm. The root of the tree corresponds to the least frequent symbol, which will be assigned the longest codeword.
Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3.
This means that the corresponding codeword for the root will be longer than 1 bit. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.
Know more about frequency here:
https://brainly.com/question/254161
#SPJ11
Please answer all three question
1. To the nearest tenth how many miles is alshleys house from Bridget house
2. To the nearest tenth how many miles is Ashley’s house from carlys house
3. Whose house does Ashley live the closet to and by how many miles
Please answer
The nearest tenth how many miles is alshleys house from Bridget house is AB = √[(xB-xA)² + (yB-yA)²]
The nearest tenth how many miles is Ashley’s house from carlys house is AC = √[(xC-xA)² + (yC-yA)²]
The distances from Ashley's house to both Bridget's house and Carly's house, we can compare them and see which one is shorter.
To find the distance between Ashley's house and Bridget's house, we need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Bridget's house is located at point B. We can use the distance formula to find the distance between A and B:
distance AB = √[(xB-xA)² + (yB-yA)²]
Here, xA and yA represent the coordinates of Ashley's house, and xB and yB represent the coordinates of Bridget's house. The formula calculates the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points.
To find the distance between Ashley's house and Carly's house, we again need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Carly's house is located at point C. We can use the same distance formula as before:
distance AC = √[(xC-xA)² + (yC-yA)²]
Here, xC and yC represent the coordinates of Carly's house. Plug in the values and calculate the distance to the nearest tenth of a mile.
To determine whose house Ashley lives closest to, we need to calculate the distances from Ashley's house to both Bridget's house and Carly's house. Whichever house has the shorter distance will be the closer one.
To find the difference between the two distances, we can subtract the smaller distance from the larger distance.
To know more about distance here
https://brainly.com/question/4199102
#SPJ4
PLEASE HELP THIS AN FRESHMAN QUESTION
Answer:
Sure, I can help you with that.
To find the area of the gazebo floor, we can think of the decagon as being composed of ten congruent triangles. Each triangle has a base of 10 feet and a height of 192 feet. The area of a triangle is equal to (1/2)bh, so the area of each triangle is (1/2)(10)(192) = 960 square feet. The area of the decagon is equal to 10 times the area of each triangle, or 960*10 = 9600 square feet.
Therefore, the area of the gazebo floor is 9600 square feet.
Here is a diagram of the decagon, with the ten congruent triangles labeled:
[Image of a decagon with ten congruent triangles labeled]
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
I'm so grateful for your help. I would be honored if you would give me a Brainlyness award."
Map of the city zoo a triangle with points zebras, monkeys, and lions. the distance from zebras to monkeys is 52 feet and from monkeys to lions is x feet. a triangle with points lions, tigers, elephants. the distance from lions to tigers is 96 feet and from tigers to elephants is 78 feet. the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants. what is the distance between the lions and monkeys? 1. proportion: 52 78 = x 96 2. cross-multiply: 4992 = 78x 3. solve: the distance between the lions and the monkeys is feet.
The distance between the lions and the monkeys is 64 feet.
We can set up a proportion to find the distance between the lions and monkeys. Here's the step-by-step explanation:
1. Proportion: Since the path from zebras to monkeys is parallel to the path from tigers to elephants, we can set up a proportion using the given distances: 52/78 = x/96.
2. Cross-multiply: To solve for x, we can cross-multiply: 52 * 96 = 78 * x, which simplifies to 4992 = 78x.
3. Solve: Now we just need to solve for x. Divide both sides of the equation by 78: x = 4992 / 78. This gives x ≈ 64.
So, the distance between the lions and the monkeys is approximately 64 feet.
Learn more about Proportion,
https://brainly.com/question/31188065
#SPJ11
When Bernard was as old as Hector is now, Bernard's age was 4 times Hector's age then. When Hector will be as old as Bernard is now, the sum of their ages will be 51. How old will Bernard be when Hector turns 18 years old?
Base on the word problem, Bernard is currently 21.25 years old. When Hector turns 18, he will be (18 - 17) = 1 year older than his current age. At that time, Bernard will be (21.25 + 1) = 22.25 years old.
Word problem calculation.Let's start by assigning variables to represent the current ages of Bernard and Hector. Let B be Bernard's current age and H be Hector's current age. Then we can write two equations based on the given information:
"When Bernard was as old as Hector is now, Bernard's age was 4 times Hector's age then." This means that Bernard is currently (B - H) years older than Hector, and that the age difference between them has remained constant over time. So, we can write: B - (B - H) = 4(H - (B - H)).
Simplifying this equation, we get: B - B + H = 4(2H - B)
Simplifying further, we get: 5H - 4B = 0, or B = (5/4)H.
"When Hector will be as old as Bernard is now, the sum of their ages will be 51." This means that when Hector is (B - H) years older than his current age, their sum of ages will be 51. So, we can write: B + (B - H + (B - H)) = 51.
Simplifying this equation, we get: 3B - 2H = 51.
Now we have two equations with two variables. We can substitute the expression for B from the first equation into the second equation, and solve for H:
3B - 2H = 51
3(5/4)H - 2H = 51
(15/4)H = 51
H = 17
So, Hector is currently 17 years old. To find out how old Bernard will be when Hector turns 18, we can use the expression we found earlier for B in terms of H:
B = (5/4)H
B = (5/4)(17)
B = 21.25
So, Bernard is currently 21.25 years old. When Hector turns 18, he will be (18 - 17) = 1 year older than his current age. At that time, Bernard will be (21.25 + 1) = 22.25 years old.
Learn more about word problem below.
https://brainly.com/question/21405634
#SPJ1
The Bayview community pool has a snack stand where Juan works part time he tracks his total sales during each shift last month this box plot shows the results what fraction of Juan’s shifts had a total sales of $225 or more
The fraction of Juan's shifts with a total sales of $225 or more can be found by looking at the box plot.
We can see that the top line of the box represents the third quartile (Q3) which is the value where 75% of the data falls below.
In this case, Q3 is at approximately $250. This means that 75% of Juan's shifts had total sales less than $250. To find the fraction of shifts with sales of $225 or more, we need to determine how many shifts fall within the range of $225 to $250.
Looking at the box plot, we can see that the distance between Q1 and Q3 (the interquartile range) is approximately $100. Therefore, the distance between Q1 and $225 is approximately one-third of the interquartile range or $33.33. So, any shift with total sales of $225 or more would fall within one-third of the distance between Q1 and Q3.
Therefore, the fraction of Juan's shifts with total sales of $225 or more is approximately one-third of 75%, which is 25%.
In summary, approximately 25% of Juan's shifts at the Bayview community pool had total sales of $225 or more, based on the box plot.
To know more about interquartile range click on below link:
https://brainly.com/question/29173399#
#SPJ11
Use differentials to estimate the value of ⁴√1.3 . Compare the answer to the exact value of ⁴√1.3 . Round your answers to six decimal places, if required. You can use a calculator, spreadsheet, browser, etc. to calculate the exact value. estimate= exact value=
Therefore, the estimate is quite close to the exact value, with an error of about 0.000450.
We can use differentials to estimate the value of ⁴√1.3 as follows:
Let y = ⁴√x, then we have:
dy/dx = 1/(4x^(3/4))
We want to estimate the value of y when x = 1.3, so we have:
Δy ≈ dy * Δx
where Δx = 0.3 - 1 = -0.7 (since we are approximating 1.3 as 1)
Substituting the values, we get:
Δy ≈ (1/(4(1)^3/4)) * (-0.7) ≈ -0.219
Hence, the estimate for ⁴√1.3 is:
y ≈ ⁴√1 + Δy ≈ 0.780
The exact value of ⁴√1.3 is approximately 0.780450255.
For more similar questions on estimation
brainly.com/question/22099020
#SPJ11
Can someone please help me ASAP? It’s due tomorrow.
The total number of outcomes for the compound event is m*n
option B.
What is the Counting Principle?The Fundamental Counting Principle states that if there are m ways to do one thing and n ways to do another thing, then there are m*n ways to do both things together.
This applies to compound events that consist of two or more independent events.
For example, suppose you have two dice and you want to know how many possible outcomes there are when you roll them. Each die has 6 possible outcomes, so by the Fundamental Counting Principle, the total number of outcomes for the compound event is 6*6 = 36.
So, for any two independent events with m and n outcomes, respectively, the total number of outcomes for the compound event is m*n.
Learn more about compound event here: https://brainly.com/question/12314211
#SPJ1
Ron is seeking a loan wi th a simple in teres t ra te o f 7 % per year . he wan ts to borrow $4,500.
If Ron were to borrow $4,500 at a simple interest rate of 7% per year, he would be charged $315 in interest each year.
How to find the interest rate?Ron is seeking a loan with a simple interest rate of 7% per year, which means that he will be charged 7% of the loan amount as interest each year. Ron wants to borrow $4,500, so to calculate the amount of interest he will be charged each year, we can use the following formula:
Interest = Principal x Rate x Time
In this formula, "Principal" refers to the loan amount, "Rate" refers to the interest rate as a decimal (so 7% would be 0.07), and "Time" refers to the length of time the loan will be outstanding, typically measured in years.
Since Ron is seeking a loan with a simple interest rate, we can assume that the interest will be calculated on an annual basis. So if Ron wants to borrow $4,500 at a simple interest rate of 7% per year, the amount of interest he will be charged each year would be:
Interest = $4,500 x 0.07 x 1
Interest = $315
Therefore, if Ron were to borrow $4,500 at a simple interest rate of 7% per year, he would be charged $315 in interest each year. It's important to note that this calculation assumes that Ron will not be making any payments on the loan during the year, and that the interest will be added to the principal amount at the end of the year. In practice, many loans are structured differently and may involve monthly payments or other terms.
Learn more about interest rate
brainly.com/question/28236069
#SPJ11
A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly. How much will the homeowner owe after 8 years? Group of answer choices $78,090 $65,023 $78,117 $67,300
A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly.
So we have to find 2.3% of 65,000 which is 1495
Now we have to multiply 1,495 by 8 because it is 8 years which is 11960. Now we add 11,960 to 65,000 and our answer is
Answer : 76960
(Choice 1)
Can someone please explain how to solve this question? Thanks!
The solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .
What is a polynomialA polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.
The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a)
For the polynomial; k²x³ - 6kx + 9 divided by x - 1, we shall evaluate for f(1) to solve k as follows:
k²(1)³ - 6k(1) + 9 = 1
k² - 6k + 9 - 1 = 0
k² - 6k + 8 = 0
by factorization;
(k - 4)(k - 2) = 0
k = 4 or k = 2
Therefore, solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .
Read more about polynomial here:https://brainly.com/question/24729294
#SPJ1
Ella makes a model of a log cabin that is 8 inches long at a scale of 1/2.5 feet. She makes a second model of the same building at a scale of 1/2.5 feet. How much longer is the second model than the first?
Answer: So the second model is 0.2667 feet longer than the first.
Step-by-step explanation: 8 inches * (1/12 feet per inch) * (1/2.5) = 0.1333 feet
So the length of the first model is 0.1333 feet.
The length of the second model is also at a scale of 1/2.5 feet, so its length can be found directly by multiplying the length of the actual building by the scale factor:
Length of second model = 1/2.5 * 1 foot = 0.4 feet
to make next step we can use difference between these numbers by their lengths: Length of second model - Length of first model = 0.4 feet - 0.1333 feet = 0.2667 feet
Question is attached.
Please show workings
When solved, the value of either a or b would be 0 such that we have a = 0 or b = 0. They could also both be zero.
How to solve the equation ?If the product of two numbers is zero, it necessitates that one or both of the values in question contain a value of zero. Similarly, when calculating the cross product of two given vectors and its resulting answer is equivalent to zero, then such vectors exist parallel with one another.
Alternatively, there is the possibility that only one vector holds a value of zero themselves:
( a × b ) = 0
This equation is true if either a = 0 or b = 0, or both a and b are zero.
Find out more on zero at https://brainly.com/question/1532651
#SPJ1
what's the solution?
Answer:
(1, 1.5)
Step-by-step explanation:
If x = 1, plug it into the other equation, y = 1/2x + 1, and y = 1.5.
Jon has 8 packets of soup in his cupboard, but all the labels are missing. he knows that there are 5 packets of tomato soup and 3 packets of mushroom soup. he opens three packets at random. work out the probability that all three packets are the same variety of soup.
Answer:
37.5%
Step-by-step explanation:
If all were the same from opening 3, it would all have to be mushroom soup. This would look like: desired outcome/total quantity: 3/8 = 0.375 = 37.5%
Reina’s greenhouse is shaped like a square pyramid with four congruent equilateral triangles for its sides. All of the edges are 6 feet long. What is the total surface area of the greenhouse including the floor? Round your answer to the nearest hundredth.
____ft2
With all of the edges 6 feet long, the total surface area of the greenhouse including the floor is approximately 98.39 ft².
To find the total surface area of Reina's greenhouse, we'll need to calculate the area of the equilateral triangular sides and the square base.
1. Equilateral triangular sides:
There are four congruent equilateral triangles with edges of 6 feet each. To find the area of one triangle, we can use the formula A = (s² * √3) / 4, where A is the area and s is the side length.
A = (6² * √3) / 4 = (36 * √3) / 4 = 9√3 square feet
Since there are four triangles, the total area of the triangular sides is 4 * 9√3 = 36√3 square feet.
2. Square base:
The base is a square with side lengths of 6 feet. To find the area, we can use the formula A = s².
A = 6² = 36 square feet
Now, let's add the area of the triangular sides and the square base
Total surface area = 36√3 + 36 ≈ 98.39 ft² (rounded to the nearest hundredth)
So, the total surface area of the greenhouse including the floor is approximately 98.39 ft².
More on area: https://brainly.com/question/14849668
#SPJ11
The table below shows the number of students in Mr. Jang's class that are taking 1, 2, 3, or 4 AP classes. After a new student joined the class (not shown in the table), the average (arithmetic mean) number of AP classes per student became equal to the median. How many AP classes is the new student taking?
A) 2
B) 3
C) 4
D) 5
Answer:
2
Step-by-step explanation:
To solve this problem, we need to first find the current average and median number of AP classes per student, and then use that information to determine the number of AP classes the new student is taking.
To find the current average number of AP classes per student, we can use the information in the table:
(1 AP class) x 6 students = 6 AP classes
(2 AP classes) x 9 students = 18 AP classes
(3 AP classes) x 5 students = 15 AP classes
(4 AP classes) x 4 students = 16 AP classes
Total number of AP classes = 6 + 18 + 15 + 16 = 55
Total number of students = 6 + 9 + 5 + 4 = 24
Average number of AP classes per student = Total number of AP classes / Total number of students
= 55 / 24
= 2.29 (rounded to two decimal places)
To find the current median number of AP classes per student, we need to order the number of AP classes per student from least to greatest:
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
The median is the middle value when the data is ordered in this way. Since there are 24 students, the median is the average of the 12th and 13th values:
Median = (2 + 2) / 2
= 2
Since we know that the current average and median are not equal, the new student must be taking a number of AP classes that will bring the average up to 2. We can set up an equation to represent this:
(55 + x) / (24 + 1) = 2
where x is the number of AP classes the new student is taking. Solving for x, we get:
55 + x = 50
x = -5
This is a nonsensical answer, as the number of AP classes taken by the new student cannot be negative. Therefore, our assumption that the new student is taking a number of AP classes greater than the current average is incorrect. Instead, the new student must be taking a number of AP classes less than the current average, which will bring the average down to 2.
Let y be the number of AP classes the new student is taking. We can set up a new equation to represent this:
(55 + y) / (24 + 1) = 2 - ((2.29 - 2) / 2)
where the term on the right-hand side represents the amount by which the average needs to decrease in order to reach 2. Solving for y, we get:
55 + y = 46.5
y = 46.5 - 55
y = 8.5
So the new student is taking 8.5 AP classes. However, since the number of AP classes must be a whole number, we need to round this value to the nearest integer. Since 8.5 is closer to 9 than to 8, we round up to 9. Therefore, the answer is:
The new student is taking 9 AP classes. Answer: None of the above (not given as an option).