The price of the medium pizza without the coupon is approximately $14.74.
To find the original price of the pizza without the coupon, we can use the following formula:
Original Price = Discounted Price / (1 - Discount Percentage)
In this case, the discounted price is $10.32 and the discount percentage is 30% or 0.3. Plugging the values into the formula:
Original Price = $10.32 / (1 - 0.3)
Original Price = $10.32 / 0.7
Original Price ≈ $14.74
So, the price of the medium pizza without the coupon is approximately $14.74.
To learn more about coupon, refer below:
https://brainly.com/question/30177801
#SPJ11
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
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
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
If BA = 5x + 5 and AD = 10x - 20, find BD. It is a parallelogram by the way.
To find the length of BD in a parallelogram where BA = 5x + 5 and AD = 10x - 20, we use the fact that opposite sides of a parallelogram are equal in length. Therefore, BD = BA = 30.
Since it is a parallelogram, we know that opposite sides are equal. So, BD = BA = 5x + 5. To find the value of x, we can use the fact that AD is also equal to BD. So, we can set the two expressions for BD equal to each other
5x + 5 = 10x - 20
Simplifying and solving for x, we get
5x = 25
x = 5
Now we can substitute x back into the expression for BD to get the final answer
BD = 5x + 5 = 5(5) + 5 = 30
To know more about parallelogram:
https://brainly.com/question/29147156
#SPJ4
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
a laundromat has 5 washing machines. a typical machine breaks down once every 5 days. a repairer can repair a machine in an average of 2.5 days. currently, three repairers are on duty. the owner of the laundromat has the option of replacing them with a superworker, who can repair a machine in an average of 5 6 day. the salary of the superworker equals the pay of the three regular employees. breakdown and service times are exponential. should the laundromat replace the three repairers with the superworker?
Replacing three repairers with a superworker would be cost-effective for the laundromat as the expected repair time would increase and lead to more downtime for the machines.
To determine if the laundromat should replace the three repairers with the superworker, we need to compare the expected repair time under each scenario.
With three repairers, the expected time to repair a machine is the sum of the expected time until a machine breaks down and the expected time for a repairer to fix it
E(time with three repairers) = 5 + 2.5/3 = 6.167 days.
With the superworker, the expected time to repair a machine is
E(time with superworker) = 5/6 = 0.833 days.
Therefore, on average, it takes much less time to repair a machine with the superworker than with three repairers. Since the salary of the superworker is equal to that of three repairers, the laundromat should replace the three repairers with the superworker. It is also more cost-effective.
To know more about cost-effective:
https://brainly.com/question/28448166
#SPJ4
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
Which of the following are areas of sectors formed by Angle ABC?
B = 86.4º
AB=4.1cm
Answer:
about 12.67 cm²
Step-by-step explanation:
The area of a sector of a circle is given by:
A = (θ/360) x πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:
A = (86.4/360) x π(4.1)²
A ≈ 12.67 cm²
So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.
To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.
For the area "about 23.35 cm²":
23.35 = (θ/360) x π(4.1)²
θ ≈ 149.6 degrees
The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 3.09 cm²":
3.09 = (θ/360) x π(4.1)²
θ ≈ 19.16 degrees
The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 40.14 cm²":
40.14 = (θ/360) x π(4.1)²
θ ≈ 256.4 degrees
The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.
Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".
From a Word Problem
An online camera store charges $3 for every
8x10 picture that you order. The
shipping cost is $8. Write an equation to
model this situation. How much will it cost to
get 5 pictures printed?
Solve the system of equation and explain geometrically how you know that your answers are solutions to the system. x^2+y^2 =100 and 3x - y = 30 how you know
The solution of the system of equations is given by the ordered pairs [10, 0] and [8, -6].
How to graphically solve this system of equations?In order to graphically solve the given system of equations on a coordinate plane, we would use an online graphing calculator to create a plot of the system of equations and then determine their point of intersection;
x² + y² = 100 ......equation 1.
3x - y = 30 ......equation 2.
Based on the graph shown in the image attached above, we can reasonably infer and logically deduce that the solution to this system of equations lies in both Quadrant I and Quadrant IV, and it is represented by this ordered pairs (10, 0) and (8, -6).
Read more on solution and equation here: brainly.com/question/25858757
#SPJ1
The product of 58 and the quantity 8b plus 8.
Expression[tex]58(8b+8)[/tex]simplifies to[tex]464b+464.[/tex]
How to simplify quantity expressions?
Calculate the product of 58 and the quantity 8b + 8
The given expression is:
[tex]58(8b + 8)[/tex]
Multiplying 58 by 8b and 8, we get:
[tex]464b + 464[/tex]
Therefore, the answer is:
[tex]58(8b + 8) = 464b + 464[/tex]
To find the product of 58 and the quantity 8b + 8, we need to use the distributive property of multiplication over addition, which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can distribute 58 over 8b and 8, as follows:
[tex]58(8b + 8) = 58 × 8b + 58 × 8[/tex]
Multiplying 58 by 8b and 8 separately, we get:
[tex]58 × 8b = 464b[/tex]
[tex]58 × 8 = 464[/tex]
Adding the products, we get the final answer:
[tex]58(8b + 8) = 464b + 464[/tex]
Therefore, the expression [tex]58(8b + 8)[/tex]simplifies to[tex]464b + 464.[/tex]
Learn more about quantity
brainly.com/question/17957799
#SPJ11
2 x (2a x 7) PLEASE HELP ME PLEASE I WILL DO ANYTHING
A radar antenna is located on a ship that is 4 kilometres from a straight shore. It is rotating at 32 revolutions per minute. How fast does the radar beam sweep along the shore when the angle between the beam and the shortest distance to the shore is Pi/4 radians?
The radar beam moves at a pace of roughly 536.47 kilometers per hour as it scans the coastline.
Let A represent the location of the radar antenna and B represent the shoreline location that is closest to A. Let C represent the radar beam's current location on the coast and Ф represent the angle between the beam and the line AB. As a result, we obtain a right triangle ABC, where AB is equal to 4 km, and BC is the length at which the radar beam sweeps along the shore.
32 rev/min(2π/60 sec) = 3.36 radians/sec. BC = r(Ф) = (4 km)(π/4) = π km.
We may calculate the radar beam's speed down the shore by multiplying these two values:
(536.47 km/hr) = 10.54 km/sec or (3.36 rad/sec)(π km).
Hence, the of sweeping is 10.54 km/sec.
To know more about about Sweeping motion, visit,
https://brainly.com/question/29008714
#SPJ4
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
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.
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
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
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
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
Let L be the line of intersection between the planes x + y - 2z = 1, 4x + y + 3z = 4.
(a) Find a vector v parallel to L. V= (b) Find the cartesian equation of a plane through the point (2, -1, 3) and perpendicular to L.
(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1
(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.
In this case, the equations of the planes are:
x + y - 2z = 1
4x + y + 3z = 4
The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.
We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
Therefore, a vector v = <1, 1, -2>.
(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.
We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0
Simplifying, we get:
-7x + 10y - 3z = -1
Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.
To know more about cartesian equation, refer here:
https://brainly.com/question/11676110#
#SPJ11
A person completes 68 km in 50 minutes via Jeep. Starting 20 minutes, he travels by x km/hr and
next 25 minutes by 2x km/hr and rest time by 3x km/hr. What is the value of x ?
The value of x is 48 km/hr.
How to solve for X
Total distance = 68 km
Total time = 50 minutes
First part:
Duration = 20 minutes
Speed = x km/hr
Second part:
Duration = 25 minutes
Speed = 2x km/hr
Third part:
Duration = 50 - (20 + 25) = 5 minutes
Speed = 3x km/hr
We can calculate the distance traveled in each part using the formula:
distance = speed × time
For the first part:
distance1 = x × (20/60) = (1/3)x (because 20 minutes = 1/3 hour)
For the second part:
distance2 = 2x × (25/60) = (5/6)x (because 25 minutes = 5/12 hour)
For the third part:
distance3 = 3x × (5/60) = (1/4)x (because 5 minutes = 1/12 hour)
Now, we know that the total distance is 68 km, so:
distance1 + distance2 + distance3 = 68
(1/3)x + (5/6)x + (1/4)x = 68
To solve for x, we'll first find a common denominator for the fractions, which is 12:
(4/12)x + (10/12)x + (3/12)x = 68
Now, add the fractions:
(4+10+3)/12 * x = 68
17/12 * x = 68
To isolate x, we'll multiply both sides by the reciprocal of the fraction (12/17):
x = 68 * (12/17)
x = 4 * 12
x = 48
So, the value of x is 48 km/hr.
Read more on equations here:https://brainly.com/question/2972832
#SPJ1
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
Help with problem in photo pls
Check the picture below.
Please help me now Asapppp
So the angles that must be right angles are KER and ERI.
What is angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are usually denoted by the letters A and B, and the vertex is denoted by the letter V. The angle is denoted by the symbol ∠, followed by the letters of the rays with the vertex in between, such as ∠AVB. The measure of an angle is the amount of rotation needed to move one ray to coincide with the other ray, and is usually given in degrees or radians. Angles are used in many areas of mathematics and science, such as trigonometry, geometry, physics, and engineering. They are also used in everyday life, such as in navigation, construction, and design.
Here,
Since RE and RI are secants of the circle, we can use the Intersecting Secants Theorem to find the relationships between the angles in the diagram.
Angle ERK is half of the intercepted arc EIK, so we have m∠ERK = 1/2m(arc EIK).
Similarly, angle KRI is half of the intercepted arc KE, so we have m∠KRI = 1/2m(arc KE).
Angle REI is an exterior angle of triangle KIR, so we have m∠REI = m∠ERK + m∠KRI.
To determine which angles must be right angles, we need to look for cases where the intercepted arcs are semicircles, which have a measure of 180 degrees.
If arc EIK is a semicircle, then m(arc EIK) = 180 and m∠ERK = 1/2(180) = 90. Therefore, angle ERK is a right angle.
If arc KE is a semicircle, then m(arc KE) = 180 and m∠KRI = 1/2(180) = 90. Therefore, angle KRI is a right angle.
To know more about angle,
https://brainly.com/question/14569348
#SPJ1
Cîte numere de trei cifre se pot alcătui din cifrele 1, 2, 3, 4 încît:1) cifrele să nu se repete;2) cifrele să se repete.
There are 24 three-digit numbers without repeating digits, and 64 three-digit numbers with repeating digits.
How many three-digit numbers can be formed?1) Pentru a alcătui numere de trei cifre în care cifrele să nu se repete, putem utiliza principiul combinatoric al permutărilor. Având la dispoziție cifrele 1, 2, 3 și 4, vom avea 4 posibilități pentru a alege prima cifră, 3 posibilități pentru a alege a doua cifră și 2 posibilități pentru a alege a treia cifră. Prin înmulțirea acestor numere, obținem:
4 * 3 * 2 = 24
Există deci 24 de numere de trei cifre în care cifrele nu se repetă, utilizând cifrele 1, 2, 3 și 4.
2) Pentru a alcătui numere de trei cifre în care cifrele se repetă, vom avea 4 posibilități pentru a alege oricare dintre cele trei cifre și anume 1, 2, 3 și 4. Prin urmare, avem:
4 * 4 * 4 = 64
Există 64 de numere de trei cifre în care cifrele se pot repeta, utilizând cifrele 1, 2, 3 și 4.
learn more about numere
brainly.com/question/19427947
#SPJ11
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.
If f(x) = x2 + 4x + 6, find the following values. = 1. f(a) = 2. f(a - 1) = 3. f(a + 1) =
To find the values of f(a), f(a-1), and f(a+1) when f(x) = x^2 + 4x + 6, So, the values are: f(a) = a^2 + 4a + 6, f(a-1) = a^2 + 6a + 3, f(a+1) = a^2 + 6a + 11.
we simply substitute the given values of a into the function.
1. f(a) = a^2 + 4a + 6
2. f(a-1) = (a-1)^2 + 4(a-1) + 6 = a^2 + 2a + 1 + 4a - 4 + 6 = a^2 + 6a + 3
3. f(a+1) = (a+1)^2 + 4(a+1) + 6 = a^2 + 2a + 1 + 4a + 4 + 6 = a^2 + 6a + 11
So, the values are:
1. f(a) = a^2 + 4a + 6
2. f(a-1) = a^2 + 6a + 3
3. f(a+1) = a^2 + 6a + 11
Visit here to know more about values:
brainly.com/question/30145972
#SPJ11
What are the slopes and y-intercept of a graph?
The slopes and y-intercept of a graph are two key components of the equation that describes the relationship between two variables.
The slope of a graph is the measure of how steeply the line is rising or falling. It is calculated by dividing the change in the y-axis by the change in the x-axis between two points on the line. A positive slope indicates that the line is rising, while a negative slope indicates that the line is falling.
The y-intercept of a graph is the point where the line crosses the y-axis. It is the value of y when x=0. The y-intercept is a fixed point on the line and is used to help determine the equation of the line.
Together, the slope and y-intercept of a graph can be used to write an equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
The volume of the given cone is 402.1 cubic feet if the slant height is 10ft and the length is 6ft.
To calculate the volume of a cone, the formula used is :
V = (1/3) * π * [tex]r^2[/tex] * h
Here, the radius is the unknown term. we need to calculate the radius of the cone. We can use the Pythagorean theorem to find the radius of the cone.
[tex]l^2 = r^2 + h^2[/tex]
[tex]10^2 = r^2 + 6^2[/tex]
[tex]r = \sqrt{(10^2 - 6^2)}[/tex]
radius = 8 ft
V = (1/3) * π * [tex]r^2[/tex] * h
V = (1/3) * π *[tex]8^2[/tex] * 6
V = (1/3) * π * 384
V = 402.1 cubic feet
Therefore we can infer that the volume of the given cone is 402.1 cubic feet.
To learn more about the volume of a cone
https://brainly.com/question/29767724
#SPJ4
The complete question is:
'Find the volume of this cone. Round to the nearest tenth.
slant height = 10ft
length = 6ft
