The surface area of octagonal pyramid with height of 12 and a side length of 4.24 is 281.477 unit²
Height of octagonal pyramid = 12
Side length of octagonal pyramid = 4.14
The surface area of octagonal pyramid is
SA = 2s²( 1 + √2) + 4sh
Here, s is side length of the octagonal pyramid = 4.14
h is height of the octagonal pyramid = 12
putting the values in the equation we get
SA = 2 × 4.14 ( 1 + √2 ) + 4 × 4.14 × 12
SA = 82.757 + 198.72
SA = 281.477
The surface area of octagonal pyramid is 281.477
To know more about surface area click here :
https://brainly.com/question/29298005
#SPJ4
In the diagram shown, segments AE and CF are both perpendicular to DB.
DE=FB, AE=CF. Prove that ABCD is a parallelogram.
Answer:
Step-by-step explanation:
Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.
Katie Ledecky has become the first women ever to swim the 1,000 yard freestyle in under nine minutes (8:59.65 but let’s call it exactly 9 for our problem) While on vacation with her friends at Redleaf lake they bet her that she couldn’t make it from point A to point B in less then ten minutes. Assuming she can swim at her Olympic level pace should she take this bet? Justify your work.
Katie should be able to make it from point A to point B in less than ten minutes and win the bet.
What is minute?A minute is a unit of time equal to 60 seconds or one sixtieth of an hour. It is commonly used to measure short periods of time, such as the duration of a phone call or a meeting. The symbol for minute is "min".
According to given information:To determine whether Katie Ledecky can make it from point A to point B in less than ten minutes, we need to calculate the distance between the two points and compare it to her swimming speed.
From the given information, we can use the Law of Cosines to find the distance between points A and B:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
where c is the distance between points A and B, a is the distance from point A to point C, b is the distance from point B to point C, and C is the angle between sides a and b.
Plugging in the given values, we get:
[tex]c^2 = 620^2 + 455^2 - 2(620)(455) cos(150°)\\\\c^2 = 383,825[/tex]
c ≈ 619.5 yards
So the distance between points A and B is approximately 619.5 yards.
Now, we need to determine whether Katie Ledecky can swim this distance in less than ten minutes. We are given that she swam 1,000 yards in 8 minutes and 59.65 seconds, which is approximately 8.99 minutes. So her average speed for the 1,000 yard freestyle was:
speed = distance / time
speed = 1,000 yards / 8.99 minutes
speed ≈ 111.23 yards/minute
To swim the distance between points A and B in less than ten minutes, Katie would need to swim at an average speed of:
speed = distance / time
speed = 619.5 yards / 10 minutes
speed = 61.95 yards/minute
Katie's Olympic level swimming speed of 111.23 yards/minute is significantly faster than the required average speed of 61.95 yards/minute to swim from point A to point B in under ten minutes. Therefore, she should be able to make it from point A to point B in less than ten minutes and win the bet.
To know more about minute visit:
https://brainly.com/question/23365957
#SPJ1
so i need help with this question so please help
Answer:
I believe the answer is D.
Step-by-step explanation:
Her car tires need to be ATLEAST 28. So, the number will be 28 or above.
Volume question 5 of 5 the rectangle represents the base of a right rectangular prism. the height of the prism is 6 inches. what is the volume of the prism? 13 o a. 87.9 in o b. 105.8 in 3 3 in o c. 12.6 in 2 o d. 75.6 in 3 submit
The volume of prism is 75.6 [tex]in^3[/tex]. The correct answer is option d,
We are given that the rectangle represents the base of a right rectangular prism and the height of the prism is 6 inches. To find the volume of the prism, we need to multiply the area of the rectangle by the height.
The area of the rectangle can be found by multiplying its length and width. However, we are not given any specific values for the length and width of the rectangle. Therefore, we cannot directly calculate its area.
Since we are given answer choices, we can use them to check which option gives the correct volume of the prism. We can start by assuming that the length, width, and height of the prism are integers, and then calculate the volume for each option until we find the one that matches.
Option a: 87.9 in^3 - This is not an integer, so we can eliminate this option.
Option b: 105.8 in^3 - This is not an integer, so we can eliminate this option.
Option c: 12.6 in^3 - This is too small, so we can eliminate this option.
Option d: 75.6 in^3 - To check if this is the correct answer, we can calculate the area of the rectangle by dividing the volume by the height.
Volume of the prism = area of rectangle x height
75.6 in^3 = (length x width) x 6 in
Length x width = 12.6 in^2
Now, we need to find two integers whose product is 12.6 in^2 and whose sum is 16 in (since the rectangle represents the base of a right rectangular prism). After some trial and error, we find that 3.15 in and 4 in satisfy these conditions.
Therefore, the length of the rectangle is 4 inches and the width is 3.15 inches.
Now, we can calculate the area of the rectangle by multiplying its length and width:
Area of rectangle = length x width = 4 in x 3.15 in = 12.6 in^2
Finally, we can calculate the volume of the prism:
Volume of prism = area of rectangle x height = 12.6 in^2 x 6 in = 75.6 in^3
Therefore, the correct answer is option d, 75.6 [tex]in^3[/tex].
To learn more about Volume of prism refer here:
https://brainly.com/question/22023329
#SPJ11
2 x (2a x 7) PLEASE HELP ME PLEASE I WILL DO ANYTHING
HELPPPP!!!!!!
Based on this information, which function best models the number of game consoles sold in millions x years since 2010?
A) g(x) = 20(1. 5)
B) g(x) = 0. 15(20)*
C) g(x) - 0. 150. 2)*
D) g(x) = 2000. 15)
The function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20).
To answer this question, we need to identify the function that best models the number of game consoles sold in millions x years since 2010.
Option A can be simplified to g(x) = 30, which is a constant function. This means that it does not depend on the value of x and is not a good model for the number of game consoles sold over time.
Option B can be simplified to g(x) = 3x, which is a linear function. This means that the number of game consoles sold increases at a constant rate over time. This could be a good model for the number of game consoles sold, but we need to compare it to the other options.
Option C can be simplified to g(x) = 0.03x, which is also a linear function. However, the rate of increase is much slower than in option B. This is not a good model for the number of game consoles sold.
Option D can be simplified to g(x) = 300, which is a constant function like option A. Again, this is not a good model for the number of game consoles sold over time.
Therefore, the function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20). This is a linear function that represents a constant rate of increase in the number of game consoles sold over time.
Learn more about "function": https://brainly.com/question/2328150
#SPJ11
complete question:
Based on this information, which function best models the number of game consoles
sold in millions x years since 2010?
A- g(x) = 0.15(20)^x
B- g(x) = 20(0.15)^x
C- g(x) = 20(1.5)^x
D- g(x) = 0.15(.2)^x
Tom is considering opening a pool cleaning business as a summer job, he wants to determine the percentage of people in his town that own a pool. which is the best group of people for tom to survey?
The best group of people for Tom to survey would be homeowners in his town, as they are more likely to have a pool in their backyard.
To determine the percentage of people in his town that own a pool, Tom should survey a random sample of residents within the town. This will help him gather accurate and representative data about pool ownership in the area for his potential pool cleaning business.
Tom can also narrow down his survey to neighborhoods that are known to have a higher concentration of pool owners. This will give him a more accurate percentage of pool owners in his town and help him make an informed decision about opening a pool cleaning business.
More on survey: https://brainly.com/question/13283720
#SPJ11
Solve for the missing length and the other two angles in the triangle below.
By law of cosine, the triangle has a side of 1.348 units and two angles of 129.852° and 35.148°, respectively.
How to find missing lengths and angles in a triangle
In this problem we find the representation of a triangle, in which we must determine the value of a missing side and two missing angles. This can be done by law of cosine. First, find the missing side:
x = √(3² + 4² - 2 · 3 · 4 · cos 15°)
x = 1.348
Second, find the missing angles:
4² = 3² + 1.348² - 2 · 3 · 1.348 · cos α
cos α = - 0.641
α = 129.852°
β = 180° - 15° - 129.852°
β = 35.148°
To learn more on law of cosine: https://brainly.com/question/13098194
#SPJ1
How many 4-digit numbers have the second digit even and the fourth digit at least twice the second digit?
There are 1350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.
To form a 4-digit number, we have 10 choices for each digit, except the first digit, which can't be 0. Hence, there are 9 choices for the first digit.
For the second digit, there are 5 even digits (0, 2, 4, 6, 8) to choose from.
For the third digit, there are 10 choices.
For the fourth digit, we can choose any of the even digits we picked for the second digit, or any of the larger odd digits 4, 6, 8.
Hence, the number of 4-digit numbers that meet the given criteria is
9 × 5 × 10 × 3 = 1350.
Therefore, there are 1,350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.
To know more about 4-digit numbers:
https://brainly.com/question/679725
#SPJ4
If a point is randomly located on an interval (a, b) and if y denotes the location of the point, then y is assumed to have a uniform distribution over (a, b). a plant efficiency expert randomly selects a location along a 500-foot assembly line from which to observe the work habits of the workers on the line. what is the probability that the point she selects is:closer to the beginning of the line than to the end of the line
The probability that the point she selects is closer to the beginning of the line than to the end of the line is 0.5 or 50%.
If a point is randomly located on an interval (a, b), and y denotes the location of the point, then y is assumed to have a uniform distribution over (a, b). In this case, the interval is the assembly line of length 500 feet, where a is the beginning and b is the end of the line.
The question asks for the probability that the point she selects is closer to the beginning of the line than to the end of the line. For the point to be closer to the beginning, it must be located in the first half of the line, which is an interval of length 250 feet (500/2).
Since the point has a uniform distribution, the probability of the point being within any sub-interval is equal to the length of the sub-interval divided by the total length of the interval (500 feet).
So, the probability that the point she selects is closer to the beginning of the line than to the end of the line is the length of the first half (250 feet) divided by the total length (500 feet).
Probability = (Length of the first half) / (Total length)
Probability = (250 feet) / (500 feet)
Probability = 0.5 or 50%
There is a 50% chance that the place she chooses will be closer to the line's beginning than its finish.
Learn more about "probability": https://brainly.com/question/13604758
#SPJ11
Hannah has an offer from a credit card issuer for 0% APR for the first 30 days
and 12. 22% APR afterwards, compounded daily. What effective interest rate
is Hannah being offered?
To find the effective interest rate that Hannah is being offered, we need to take into account the compounding period, which is daily in this case. The effective annual interest rate (EAR) can be calculated using the formula:
EAR = (1 + APR/n)^n - 1
where APR is the annual percentage rate, and n is the number of compounding periods per year.
For the first 30 days, Hannah is offered a 0% APR, so the EAR for this period is simply 0.
After 30 days, Hannah is offered a 12.22% APR compounded daily, which means that there are 365 compounding periods per year. Therefore, the EAR for this period can be calculated as follows:
EAR = (1 + 0.1222/365)^365 - 1
≈ 0.1267
So the effective interest rate that Hannah is being offered is approximately 12.67%.
To know more about interest rate , refer here :
https://brainly.com/question/28236069#
#SPJ11
find the critical numbers of f(x)=4−5x/4 + x and classify any local extrema.
The function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.
To find the critical numbers of the function f(x) = 4 - 5x/4 + x, we first need to find its derivative:
f'(x) = -5/4 + 1
f'(x) = -1/4
To find the critical numbers, we set f'(x) equal to zero and solve for x:
-1/4 = 0
This is never true, so there are no critical numbers for f(x).
Since there are no critical numbers, there are no local maxima or minima for the function. Instead, we can analyze the behavior of the function to determine if it has any extrema.
One way to do this is to examine the end behavior of the function. As x approaches positive or negative infinity, the leading term of the function is -5x/4, which dominates the constant term. Therefore, as x becomes large in either direction, the function approaches negative infinity. This suggests that the function has a global maximum at its vertex.
To find the vertex, we can complete the square:
f(x) = 4 - 5x/4 + x
[tex]f(x) = -(5/4)x^2 + x + 4[/tex]
[tex]f(x) = -(5/4)(x^2 - (4/5)x) + 4[/tex]
[tex]f(x) = -(5/4)(x - 2/5)^2 + 4 + (5/4)(2/5)^2\\f(x) = -(5/4)(x - 2/5)^2 + 41/25[/tex]
Therefore, the function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.
For more such questions on global maximum :
https://brainly.com/question/29258664
#SPJ11
Which system of equations is equivalent to this system?
2 equations. 3 times (p minus q) = 2 times p + 11. 4 times p + q = p + 3. CLEAR CHECK
p−3q=113p+q=3
p−3q=333p+q=3
3p−q=113p+q=3
5p−3q=113p+q=3
The equivalent expressions are p−3q=11 and 3p+q=3. Option A
How to determine the equivalent equationsIt is important to note that equivalent equations are defined as equations that have the same solution but are different in the way with which the values are arranged.
From the information given, we have that;
3 times (p minus q) = 2 times p + 11
This equation is represented as;
3(p - q) = 2(p) + 11)
expand the bracket, we get;
3p - 3q = 2p + 11
collect the like terms
3p - 2p - 3q =11
Subtract the values
p - 3q = 11
Then,
4 times p + q = p + 3
4p + q = p + 3
collect like terms
4p - p + q = 3
3p = q = 3
Learn about equivalent expressions at: https://brainly.com/question/15775046
#SPJ4
What is the value of the h in the triangle below?
The value of h in the triangle shown above is calculated using proportion as: h = 4.
How to Find the Value of h in the Triangle?The two triangles shown are similar to each other based on the Angle-angle (AA) Similarity theorem. This implies that the length of their corresponding pair of sides would be proportional to each other.
Therefore, we have:
8/18 = h/9 [proportional sides of similar triangles]
Cross multiply:
h * 18 = 8 * 9
18h = 72
Divide both sides by 18:
18h/18 = 72/18 [Division property of equality]
h = 4
Therefore, the length of h in the given image is determined as: 4 units.
Learn more about similar triangles on:
https://brainly.com/question/21874653
#SPJ1
Compound Interest:
In March 2003, Natalie invested $800 in an account that earns 4. 8% interest compounded monthly. After 5 years, she withdrew all the money and reinvested it in a new account that earns 6% interest compounded semiannually. Assuming there were no other deposits or withdrawals, how much total interest will she have earned by March 2025?
I NEED HELP, CAN SOMEONE HELP ME, PLEASE?
Natalie will have earned a total of $488.97 in interest by March 2025.
"What is compound interest formula?To solve this problem, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^(nt)[/tex]
where A is the total amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
First, let's find out how much money Natalie will have in her first account after 5 years:
P = $800
r = 4.8% per year = 0.048
n = 12 (compounded monthly)
t = 5 years
A = [tex]800(1 + 0.048/12)^(12*5)[/tex]
A = $995.08
So after 5 years, Natalie will have $995.08 in her first account.
Next, let's find out how much money Natalie will have in her second account:
P = $995.08
r = 6% per year = 0.06
n = 2 (compounded semiannually)
t = 5 years
A = [tex]995.08(1 + 0.06/2)^(2*5)[/tex]
A = $1,288.97
So after reinvesting her money in the second account, Natalie will have $1,288.97 after 5 years.
Finally, let's calculate the total interest earned:
Total interest = A - P
Total interest = $1,288.97 - $800
Total interest = $488.97
Therefore, Natalie will have earned a total of $488.97 in interest by March 2025.
Learn more about compound interest
brainly.com/question/14295570
#SPJ11
FILL IN THE BLANK. Find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9. maximum value =_____ minimum value =_____
Maximum and Minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9.
The maximum value is 3
The minimum value is -3
To find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9, follow these steps:
how to find maximum and minimum value:1. Use the constraint equation (ellipse equation) to solve for one of the variables, either x or y.
Here, let's solve for y:
y² = 9 - 3x²
y = ±√(9 - 3x²)
2. Substitute y in the function f(x, y) with the expressions found in step 1:
f(x, y) = x(±√(9 - 3x²))
3. Differentiate f(x, y) with respect to x to find critical points (maximum or minimum):
f'(x, y) = ±(√(9 - 3x²) - (3x² / √(9 - 3x²)))
4. Set f'(x, y) = 0 and solve for x:
√(9 - 3x²) - (3x² / √(9 - 3x²)) = 0
5. Find the corresponding y values for the x values found in step 4 by substituting x back into the expressions found in step 1.
6. Evaluate f(x, y) at each critical point (x, y) found in steps 4 and 5 to determine the maximum and minimum values.
The maximum value of f(x, y) = xy on the ellipse 3x² + y² = 9 is 3, and the minimum value is -3.
To know more about Maximum values:
https://brainly.com/question/14316282
#SPJ11
Select all of the statements that are true.
Previous question
The 9.7-9.7 because the distance from -9.7 to 0 on the number line is 9.7 units.
Numbers with the same absolute value are opposites because they are the same distance from each other.
The 7.1 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units.
The -8.4 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units.
=
Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line.
The -12.5 12.5 because the distance from 12.5 to 0 on the number line is -12.5 units.
N
The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
To learn more about distance/absolute value click on,
https://brainly.com/question/16901376
#SPJ1
HELP!!!
Find the Area of a Rectengle with the base of 3x+1 in and a height of 2x-3 in.
A.5x^2-2 in^2
B.6x^2+7x-2 in^2
C.10x-4 in
D.6x^2-7x-3 in^2
The area of a rectangle with base of 3x+1 in and a height of 2x-3 in is given as follows:
D. A = 6x² - 7x - 3 in².
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:
A = lw.
The dimensions for this problem are given as follows:
w = 3x + 1.l = 2x - 3.Hence the expression for the area of the rectangle is given as follows:
A = (3x + 1)(2x - 3)
A = 6x² - 9x + 2x - 3
A = 6x² - 7x - 3 in².
More can be learned about the area of a rectangle at https://brainly.com/question/25292087
#SPJ1
Recent studies show that the number of three-legged frogs in a particular area is increasing due to exposure to chemical pollutants. The first set of data reported in 2000 estimates a population of 5000 three-legged frogs. Statistics show an annual increase of 15%. Let denote the number of three-legged frogs projected to inhabit this area in the year 2000N. How many three-legged frogs are projected to inhabit this area by 2009? Round to the nearest whole number
By 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area.
Recent studies have indicated a growing concern for the population of three-legged frogs in a specific area, as they have been exposed to chemical pollutants. In the year 2000, data estimated that there were about 5,000 three-legged frogs (N) in this area. With an annual increase of 15%, we can project the number of frogs in future years using the formula:
Future population = N * (1 + growth rate) ^ number of years
In this case, we want to determine the number of three-legged frogs in the area by 2009. To calculate this, we will use the given values:
Future population = 5,000 * (1 + 0.15) ^ (2009 - 2000)
Future population = 5,000 * (1.15)⁹
Future population ≈ 13,956
Therefore, by 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area, rounding to the nearest whole number. This increase in population highlights the potential ecological consequences of chemical pollutants on the environment and the need for further investigation and mitigation measures.
To know more about projection, refer to the link below:
https://brainly.com/question/15583437#
#SPJ11
In an effort to eat healthier, Bridget is tracking her food intake by using an application on her phone. She records what she eats, and then the
application indicates how many calories she has consumed. One Monday, Bridget eats 10 medium strawberries and 8 vanilla wafer cookies as an
after-school snack. The caloric intake from these items is 192 calories. The next day, she eats 20 medium strawberries and 1 vanilla wafer cookie as an after-school snack. The caloric intake from these items is 99 calories.
a. Write a system of equations for this problem situation. Let S represent the number of calories in one strawberry and let W represent the number of calories in one vanilla wafer cookie.
The equation _____ represents the calories Bridget ate on Monday and the equation _____ represents the calories she ate the next day.
b. Solve the system of equations using the substitution method. Check your work.
The number of calories in each strawberry is ____
And the number of calories in each vanilla wafer cookie is ____. The solution is ____.
PLEASE HELP ME
The equation 10S + 8W = 192 represents the calories Bridget ate on Monday and the equation 20S + 1W = 99 represents the calories she ate the next day.
The number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19.
a. We have two equations for the two days, using S for the number of calories in a strawberry and W for the number of calories in a vanilla wafer cookie:
On Monday:
10S + 8W = 192
On Tuesday:
20S + 1W = 99
b. To solve the system of equations using the substitution method, first solve one of the equations for one of the variables. We'll choose the second equation and solve for W:
W = 99 - 20S
Now substitute this expression for W in the first equation:
10S + 8(99 - 20S) = 192
Expand and simplify:
10S + 792 - 160S = 192
Combine like terms:
-150S = -600
Now divide by -150:
S = 4
Now that we have the value for S, substitute it back into the expression for W:
W = 99 - 20(4)
W = 99 - 80
W = 19
So the number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19. The solution is (S, W) = (4, 19).
To learn more about expression, refer below:
https://brainly.com/question/14083225
#SPJ11
Emily brought some homemade cookies for the school bake sale. The ingredients cost her $1.50 per cookie, but she sells them for a higher price at $3.00 per cookie. What is the percent markup per cookie?
The value of the calculated percent markup of the cookie is 100%
Finding the the percent markup per cookieFrom the question, we have the following parameters that can be used in our computation:
The ingredients cost her $1.50 per cookieShe sells them for a higher price at $3.00 per cookieThe percent markup of the cookie is then calculated as
Percentage = (Selling price - cost price)/cost price
substitute the known values in the above equation, so, we have the following representation
Percentage = (3 - 1.5)/1.5
Evaluate
Percentage = 100%
Hence, the percent markup of the cookie is 100%
Read more about percentage at
https://brainly.com/question/24877689
#SPJ1
Pedro is walking down the longest staircase ever, which contains 4000 steps. She
starts from the top and is walking down the staircase at 150 steps a minute. Hal is
walking up the staircase, starting at the bottom, at 80 steps a minute. After how
many minutes will they meet?
Pedro and Hal will walk 1800 steps staircase and meet after 25 minutes.
Pedro is walking down the longest staircase ever, which contains 4000 steps. She starts from the top and is walking down the staircase at 150 steps a minute. Hal is walking up the staircase, starting at the bottom, at 80 steps a minute. After how many minutes will they meet?
Let's assume that they will meet at point X, which is y steps away from the top and z steps away from the bottom. As Pedro is walking down the staircase, she will cover a distance of y steps, while Hal is walking up the staircase, he will cover a distance of (4000-z) steps.
The time taken by Pedro to cover a distance of y steps is y/150 minutes, while the time taken by Hal to cover a distance of (4000-z) steps is (4000-z)/80 minutes. Since they will meet at the same point X, we can set these two times equal to each other and solve for y and z.
y/150 = (4000-z)/80
Solving this equation, we get y = 1800 and z = 2200. This means that Pedro will have covered 1800 steps in y/150 = 12 minutes and Hal will have covered (4000-2200) = 1800 steps in (4000-2200)/80 = 25 minutes.
Know more about steps here:
https://brainly.com/question/1229805
#SPJ11
A line includes the points (0,-7) and (n, -8) has a slope of -1/6. What is the value of n?
Answer:
n = 6.
Step-by-step explanation:
The slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1) and (x2, y2).
So, (-8 - (-7)) / (n - 0) = -1/6
-1/n = -1/6
n = 6.
A dth tv connection provides channels in english and other languages in the ratio 7:13. what percentage of the channels are in english
A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.
Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:
(7/20) x 100 = 35%
Therefore, 35% of the channels on this DTH TV connection are in English.
To know more about TV connection refer here
https://brainly.com/question/30629673#
#SPJ11
An amusement park has 12 major attractions: four roller
coasters, two carousels, two drop towers, two gravity rides, and two dark ride
The park's app will randomly select attractions for you to visit in order. What
is the probability that the four roller coasters are the first four suggested
attractions?
Answer:
1/11880 or 0.00008417508
Step-by-step explanation:
The probability of this can be determined by 1/12 x 1/11 x 1/10 x 1/9
We subtract one from the denominator each time because that ride has already been used, and cannot appear again in the list.
Make a number line and mark all the points that represent the following values of x. X < -1 and x > 1
To make a number line for the values of x that are less than -1 and greater than 1, we can start by drawing a horizontal line and marking a point at 0. Then, we can label the left side of the line with negative numbers and the right side with positive numbers.
Next, we need to mark all the points that represent the values of x that satisfy the condition X < -1 and x > 1. This means we are looking for all the numbers that are less than -1 and greater than 1 at the same time. However, there are no numbers that satisfy this condition since a number cannot be both less than -1 and greater than 1 simultaneously.
Therefore, there are no points to mark on the number line for this condition.
To know more about number line:
https://brainly.com/question/24644930
#SPJ11
James says the fraction 3 4 has the same value as the expression 4 ÷ 3. Use the drop-down menus to state whether you agree or not, and why. James is Choose. . A fraction can be interpreted as division of the Choose. By the Choose.
James says the fraction 3/4 has the same value as the expression 4 ÷ 3. I disagree with James' statement.
The fraction 3/4 is not the same as the expression 4 ÷ 3. A fraction can be interpreted as division of the numerator (top number) by the denominator (bottom number). In this case, 3/4 represents the division of 3 by 4, whereas 4 ÷ 3 represents the division of 4 by 3. These two expressions have different values and are not equal.
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
More on fractions: https://brainly.com/question/12220774
#SPJ11
How many hours is 1,000,00 minutes
Answer:
16.6666 hours.
Step-by-step explanation:
This conversion of 1,000 minutes to hours has been calculated by multiplying 1,000 minutes by 0.0166 and the result is 16.6666 hours.
Answer:
16,666.67 hours
Step-by-step explanation:
A minute is a unit of time equal to 60 seconds.
what are the coefficients in the expression (2x+15)(9x-3) need it asap
Answer:
2x and 9x are the coefficients.
Step-by-step explanation:
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c ).
A company responsible for making gumballs found that their gumballs had an average diameter of 2. 21 cm and a standard deviation of 0. 01 cm. What is the percentage of gumballs that are within standard deviations of the mean?
Percentage of gumballs that are within standard deviations of the mean is 68% and have a diameter between 2.20 cm and 2.22 cm.
To find the percentage of gumballs that are within one standard deviation of the mean, we need to use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.Approximately 95% of the data falls within two standard deviations of the mean.Approximately 99.7% of the data falls within three standard deviations of the mean.Here we want to find the percentage of gumballs that are within one standard deviation of the mean. So we can use the first part of the empirical rule and say that approximately 68% of the gumballs have a diameter between:
Mean - Standard deviation = 2.21 - 0.01 = 2.20 cm and Mean + Standard deviation = 2.21 + 0.01 = 2.22 cm
Therefore, approximately 68% of the gumballs have a diameter between 2.20 cm and 2.22 cm.
To learn more about gumballs: https://brainly.com/question/30486855
#SPJ11
