Use the information provided to write the equation of the circle Center (-8, 11) Radius is 2 is equal to (x + 8)² + (y - 11)² = 4.
What is equation of the circle?
To write the equation of a circle, we need to know its center and radius. If we have the center at point (a, b) and the radius is r, the equation of the circle is:
(x - a)² + (y - b)² = r²
If you have the specific values of a, b, and r, you can plug them into this equation to get the equation of the circle.
The general equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)²= r²
Using the given information, we can substitute the values into the equation:
(x - (-8))² + (y - 11)² = 2²
Simplifying, we get:
(x + 8)² + (y - 11)² = 4
Therefore, the equation of the circle with center (-8, 11) and radius 2 is:
(x + 8)² + (y - 11)² = 4
This equation represents all the points that are 2 units away from the center (-8, 11).
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On a road trip to central Florida, you average 35 miles per hour while driving within city
borders and 60 miles per hour while driving on the highway (not in the city.) The trip was 995 miles long. You were in city borders for 4 hours longer than on the highway. Let C be the time, in hours, you spent driving in the city. Let H be the time, in hours, you spent driving on the highway. Find the sum C + H
The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.
What is distance?Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.
Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.
Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation
Distance = Speed × Time
to solve for the time spent in both city and highway.
For time spent in city:
35 mph × C = 995 miles
C = 995 miles/35 mph = 28.43 hours
For time spent in highway:
60 mph × H = 995 miles
H = 995 miles/60 mph = 16.58 hours
Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.
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Find the volume of the irregular figure. 1 cm 5 cm 1 cm 6 cm 4 cm 10 cm 12 cm [?] cm ³ Enter
The volume of the irregular figure is solved to be
78 cubic centimetersHow to find the volume of the irregular figureThe volume of the irregular figure is solved by the formula
= area of the figure * thickness
The area of the figure is solved by dividing the firue into regular shapes and this will result to two rectangles
Area of the first rectangle
= length x width
= 4 * (12 - 5)
= 4 * 7
= 28 square centimeters
Area of the second rectangle
= 10 * 5
= 50 square centimeters
Total area = 50 + 28 = 78
volume = 78 * 1 = 78 cubic centimeters
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I need help math asap algebra 2
Answer:
c = 8
Step-by-step explanation:
4x³ + cx² + x + 2 ÷ x + 2 = ...
first we divide
4x³ + cx² by x + 2
and that is by doing 4x³/x = 4x².
4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...
now we need to find the remainder, as with regular number divisions :
4x² × (x + 2) = 4x³ + 8x²
which we need to subtract from the left side
4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...
- 4x³ + 8x²
----------------
0 cx² - 8x²
now we pull down the next position (x) and divide that by x + 2
4x³ + cx² + x + 2 ÷ x + 2 = 4x² + 1
- 4x³ + 8x²
----------------
0 cx² - 8x² + x
and the same again, to find the remainder, we have to subtract 1×(x + 2) = x + 2 from the left side
4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...
- 4x³ + 8x²
----------------
0 cx² - 8x² + x
- x + 2
-----------------------------
cx² - 8x² 0 0
the polynomial is divisible by x + 2, if the remainder is 0.
so,
cx² - 8x² = 0
cx² = 8x²
c = 8
CIRCLES DRAG & DROP ACTIVITY 1: Drag & Drop the correct values to fill in each table below.
HELP ASAP WILL GIVE BRAINLIST!!!!!!!!!!
The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.
What are the radius, diameter, area and circumference of each of the given circle?The diameter of a circle is 2 times the radius of the circle.
The area of a circle is expressed as: A = πr²
The circumference of a circle is expressed as: 2πr
For question 1)
Radius r = 2
Diameter = 2 × radius = 2 × 2 = 4
Area = πr² = π( 2 )² = 4π
Circumference = 2πr = 2 × π × 2 = 4π
For question 2)
Radius r = 4
Diameter = 2 × radius = 2 × 4 = 8
Area = πr² = π( 4 )² = 16π
Circumference = 2πr = 2 × π × 4 = 8π
For question 3)
Diameter d = 2
Radius = diameter / 2 = 2/2 = 1
Area = πr² = π( 1 )² = 1π
Circumference = 2πr = 2 × π × 1 = 2π
For question 4)
Diameter d = 16
Radius = diameter / 2 = 16/2 = 8
Area = πr² = π( 8 )² = 64π
Circumference = 2πr = 2 × π × 8 = 16π
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Find the surface area of the prism.
in. 2
To find the area of the prism we must identify the area of each of the faces of the prism and then add them. So, the surface would be: 312 ft²
How to find the surface of the prism?To find the surface of the prism we must find the area of each of the faces and then add them as shown below:
3 * 8 = 2424 * 2 = 4812 * 3 = 3636 * 2 = 7212 * 8 = 9696 * 2 = 192192 + 72 + 48 = 312
Based on the above, the correct answer would be 312 ft² is the total area of this prism.
Note: This question is incomplete. Here is the complete information:
Image attached.
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Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $
3.00 for rolling a 1 or a 3, nothing otherwise. What is your expected net winnings?
for
lingun?
Answer:
21.7% to win $3, thats ~1/5
Step-by-step explanation:
100/6 = 10.(6) % to roll for each number (let it be just ~10.7)
for rolling a 3 or a 1 u will get $3
10.7 + 10.7 = 21.7% to win $3, thats 1/5
Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
The distance between the point P and the plane through the points Q, R, and S is 60/23.
How did we get the value?The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:
d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|
Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:
n = (Q-R) x (Q-S)
The coefficients of the normal vector can be found using the following equations:
A = n1
B = n2
C = n3
D = -(A * x2 + B * y2 + C * z2)
Substituting the values of Q, R, and S, we have:
Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)
Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)
The cross product of Q-R and Q-S is:
n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)
So,
A = -23
B = 29
C = 17
D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109
Finally, substituting the values of x1, y1, and z1:
d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|
= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|
= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|
= |60 / √(-23^2 + 29^2 + 17^2)|
= |60 / √(529)|
= 60 / 23
So the distance between the point P and the plane through the points Q, R, and S is 60/23.
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Find the equation of any line parallel to the line 2x-3y=6
Answer:
The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.
Step-by-step explanation:
what is the least common denominator for 5/8, 7/20, and 7/13
A researcher establishes that a patient reaction time R in minutes to a dose of particular drug is R(d)=d3+3d2-8where d is the amount of drug in milliliters that absorbed in the patients blood. find the patients reaction time when d=3
On solving the provided question, we can say that quadratic equation is 46.
What is quadratic equation?A quadratic equation is x ax² +bx +c = 0, which is a quadratic polynοmial in a single variable. a 0. The Fundamental Theοrem of Algebra ensures that it has at least οne solution since this polynomial is of second οrder. Solutions may be simple or cοmplicated.
An equation that is quadratic is a quadratic equatiοn. This indicates that it has at least οne word that has to be squared. The fοrmula "ax² + bx + c = 0" is one of the often used solutions for quadratic equatiοns. where are numerical cοefficients or constants a, b, and c. where the variable "X" is unidentified.
Quadratic equatiοn is
R(d) = d³ +3d² -8
R(3) = (3)³ +3(3)² - 8
R(3) = 27 + 27 - 8
R(3) = 46
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PLEASE HELP (image attached)
Find the perimeter of the figure
Add up all the sides:
-x^2+2x+3x-4+2x^2+5
x^2+5x+1
Solve the formula A=1/2h (a+b) for b 
Ten thousand marbles were produced on a production line. The first 100 marbles off the line were taken and tested for roundness. Does this sampling result in a simple random sample? Yes, because each group of n items has an equal chance of being selected. No, because each group of n items does not have an equal chance of being selected. Yes, because each item has an equal chance of being selected. No, because each item does not have an equal chance of being selected.
No, because each item does not have an equal chance of being selected. That is option D.
What is a simple random sample?A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.
The simple random sampling method which is used by researchers has the following disadvantages such as:
It relies on the quality of the researchers performing the work.It can require a sample size that is too large.It must have a significant population or demographic at the beginning of the process.It does not provide a guarantee that the data conclusions will be accurate because not all the data have equal chance to be selected.Learn more about random sampling here:
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You rent an apartment that costs \$900$900 per month during the first year, but the rent is set to go up \$120$120 per year. What would be the monthly rent during the 11th year of living in the apartment?
Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.
The total increase in rent over 10 years is $120 per year * 10 years = $1200.
So, the monthly rent during the 11th year would be $900 + $1200 = $2100.
Therefore, the monthly rent during the 11th year would be $2100.
Step-by-step explanation:
hilary was examining the differences between perfect squares of numbers separated by 5. She made the following conjecture the differences always have the digit 5 in the ones place. for example: 17^2 - 12^2 = 289 -144 = 145
State another example that supports hilary's cpnjecture?
The another example that supports Hilary's conjecture are, 26² - 21²
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Given that,
Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.
Another example that supports Hilary's conjecture is:
= 26² - 21²
= 676 - 441
= 235
As we can see, the difference between the perfect squares of 26 and 21 is 235,
which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.
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Construction each spatial figures
Blue pyramid
Black cown
Yellow cube
Green rectangular prism
Red silendar
Violet sphere
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.
How to explain the shapesA cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.
A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.
A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
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a ferris wheel at a carnival has a diameter of 62 feet. suppose a passenger is traveling 6 miles per hour. Find the angular speed in radians per minute. Find the number of revolutions the wheel makes per hour.
On solving the provided question, we can say that relation between tangential speed and angular speed, v = r * w; v: tangential speed; r: radius; w: angular speed
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.
relation between tangential speed and angular speed
v = r * w
v: tangential speed
r: radius
w: angular speed
the radius is
r = d/2
d is the diameter
[tex]v = (d * w)/2\\w = 2*v/d\\w = (2*9 mile/h)/(58 feet)\\w = (2*9 mile/h)/(0.011 miles) = 1636 rad/h\\w = 1636/60 = 27.2 rad/min\\[/tex]
the angular speed is in radians,
[tex]n = v/(π*d)[/tex]
n = (9 mile/h)/(π*0.011 mile) = 260 rev/h
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There are 7 1/5 groups of 2/5 in 3 do you agree with this statement show reasoning
The statement made by Diego is correct.
In order to determine the number of groups of 5/6 that are in 1, 1 would be divided by 5/6.
1 ÷ 5/6
= 1 x 6/5 = 6/5
6/5 is called an improper fraction because the numerator is greater than the denominator.
6/5 can also be rewritten as a mixed fraction. If it is rewritten as a mixed fraction, it becomes 1 1/5.
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Given question is incomplete , the complete question is given below:
Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.
Refrigerator a uses 500 watts per hour when the motor is operating. The motor needs to run an average of 12 hours per day, every day, to stay at a constant, cold temperature. This model of refrigerator lasts an average of 20 years before it needs to be replaced and costs $1,000. Each kwh of electricity costs $0. 12.
To determine the total energy consumption of refrigerator A in a day, we need to first convert the power usage from watts to kilowatts.
500 watts/hour * 1 kilowatt/1000 watts = 0.5 kilowatts/hour
Next, we can calculate the energy consumption in kilowatt-hours (kWh) per day:
0.5 kilowatts/hour * 12 hours/day = 6 kilowatt-hours/day
To find the daily cost of running the refrigerator, we can multiply the energy consumption by the cost per kWh:
6 kWh/day * $0.12/kWh = $0.72/day
To calculate the yearly cost of running the refrigerator, we can multiply the daily cost by 365 days:
$0.72/day * 365 days = $262.80/year
To calculate the total cost of running the refrigerator for 20 years, we can multiply the yearly cost by 20:
$262.80/year * 20 years = $5,256.00
In addition to the cost of running the refrigerator, there is also the cost of purchasing the unit itself. In this case, the cost is $1,000.
Therefore, the total cost of owning and operating Refrigerator A for 20 years is:
$5,256.00 (operating cost) + $1,000.00 (purchase cost) = $6,256.00
It's worth noting that this calculation assumes that the cost of electricity remains constant over the 20-year lifespan of the refrigerator. In reality, the cost of electricity may increase over time, which would increase the overall cost of running the refrigerator.
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Suppose you deposit $1,000 into a
savings account that earns simple
interest. After 4 years, the savings
account balance is $1,200. Determine
the annual interest rate.
100
1000
The annual interest rate on the saving account is 5%.
What does an annual interest rate refers to?Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.
To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.
Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:
$200 = $1,000 * r * 4
r = $200 / ($1,000 * 4)
r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.
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BIL
K-7 ft-X-8 ft-
K
-20 ft-
✈
The simplified expression of K-7 ft-X-8 ft-K-20 ft is -35ft-X
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is K-7 ft-X-8 ft-K-20 ft
We need to simplify the given expression.
Add the like terms
-7 ft-X-8 ft-20 ft
-27ft-X-8 ft
-35ft-X
Hence, -35ft-X is the simplified expression of K-7 ft-X-8 ft-K-20 ft
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What proportion of U.S. residents receive a jury summons each year? A polling organization plans to survey a random sample of 500 U.S. residents to find out. Let § be the proportion of residents in the sample who received a jury summons in the previous 12 months. According to the National Center for State Courts, 15% of U.S. residents receive a jury summons each
year. Suppose that this claim is true.
a) Calculate the mean and standard deviation of the sampling distribution.
b) Interpret the standard deviation
c) Justify that the sampling distribution is approximately normal.
Answer: a) Mean and standard deviation of the sampling distribution:
The mean of the sampling distribution, also known as the expected value or the population mean, is equal to the proportion of U.S. residents who receive a jury summons each year, which is 15%. So, the mean of the sampling distribution is:
µ = 0.15
The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:
σ = √(p(1 - p) / n)
where p is the population proportion of U.S. residents who receive a jury summons each year (0.15), and n is the sample size (500).
σ = √(0.15 * (1 - 0.15) / 500)
σ ≈ 0.03
So, the standard deviation of the sampling distribution is approximately equal to 0.03.
b) Interpretation of the standard deviation:
The standard deviation measures the spread of the sampling distribution, or how much the sample proportions deviate from the population proportion. A smaller standard deviation indicates that the sample proportions are more likely to be close to the population proportion, while a larger standard deviation indicates that the sample proportions are more likely to be further from the population proportion.
In this case, the standard deviation of 0.03 indicates that the sample proportions are expected to be within 0.03 of the population proportion (0.15) about 68% of the time.
c) Justification for the approximate normality of the sampling distribution:
According to the central limit theorem, the distribution of the sample proportions will be approximately normal as long as the sample size is large enough. In this case, with a sample size of 500, we can assume that the sampling distribution is approximately normal.
Step-by-step explanation:
The temperature in a certain location was recorded each day for two months. The mean temperature was 28.8°F with a standard deviation 7.4°F. What can you determine about these data by using Chebyshev's Inequality with =K3?
Using Chebyshev's Theorem, it is found that at least 89% of days have a high temperature between 6.6ºF and 51ºF.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].Considering k = 3, the percentage is of at least 89% and the bounds are given as follows:
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Question 2 Part A:
An industrial copy machine has the ability to edit image dimensions by reducing it by a certain percentage
each time it copies. A design began with a length of 24 inches, represented by the point (0,24). After going
through the copy machine once, the length is 18, represented by the point (1,18).
Double click and enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)*
In the function, f(x) = a(b)ˣ the value of a and b is
a = 24b = 0.75How to find the value of a and bThe function defined by f(x) = a(b)ˣ is a exponential function
Where
a is the starting function
b is the base function
The starting function from (0,24)
24 = a(b)ˣ
a = 24
using (1, 18), we solve for the base
18 = 24(b)
b = 0.75
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One snowy day 3/4 Ms staples class was late to school 1/3 of the late students brought notes what fraction of Mrs. Stanford class bra late notes that day
The fraction of Mrs. Stanford's class that came late and brought notes that day was 1 / 4
How to find the fraction of students ?To find the fraction of Mrs. Stanford's class that came late and brought notes that day, the relevant formula would be:
= Fraction of students who came late x Fraction of late students who brought notes
Fraction of students who came late = 3 / 4
Fraction of students who were late and brought notes = 1 / 3
The fraction of total students who were late and brought notes were ;
= 3 / 4 x 1 / 3
= 3 / 12
= 1 / 4
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Solve the quadratic equation by the square root method and write the solution in radical form. simplify the solution. 4y^2=80
Answer:
[tex]y=\pm2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4y^2=80\\y^2=20\\y=\pm\sqrt{20}\\y=\pm2\sqrt{5}[/tex]
The square root method for solving a quadratic equation involves isolating the squared term, and then taking the square root of both sides of the equation.
Starting with the equation 4y^2 = 80, we can isolate the squared term by dividing both sides of the equation by 4:
y^2 = 20
Next, we take the square root of both sides of the equation:
y = ±√20
The solution in radical form is y = ±√20. To simplify the radical, we can factor 20 into 2 * 10. Then, we can simplify the square root as follows:
y = ±√2 * √10 = ±2√10
So, the simplified solution is y = ±2√10.
In country A, there were 131,000 foreign students from country B. This number is 23% more than the number from country C. How many foreign students were from country C
There were a total of 95,082 students from country C.
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.
To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
x represents the number οf students from cοuntry C.
then 122percent of x = 116,000
122/100 * x = 116000
x = 116000 * 100/122 = 95,082 students
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Carole is paid a monthly salary of $2011.10. Her regular workweek is 35 hours.
(a) What is Carole's hourly rate of pay?
(b) What is Carole's gross pay for May if she worked 73/4 hours overtime during
the month at time-and-a-half regular pay?
What is a inequality on a number line
Answer:
add wtwo numbers x by 3? I am sorry don't understand question
Step-by-step explanation:
Jade and Juliette are riding their bikes across the country to promote autism awareness. They rode their bikes 45.4 miles on the first day and 56.3 miles on the second day. From now on, Jade and Juliette plan to ride their bikes 62 miles per day. If the entire trip is 2,878 miles, how many more days do they need to ride?
Write a short script that could be used to make a video about this cross-country bike trip. Provide a short character description, dialogue (conversation between characters), and directions for the actors, but keep the script simple
Jade and Juliette 44.7days more days to complete their trip.
How to calculate the number of days to complete the tripTo calculate how many more days Jade and Juliette need to ride, we can use the equation:
Total distance = Distance on first day + Distance on second day + Distance on remaining days
We know the first and second day distances, and the daily distance for the remaining days, so we can substitute those values in the equation:
2878 = 45.4 + 56.3 + 62x
where x is the number of remaining days they need to ride.
Simplifying the equation:
2878 - 101.7 = 62x
2776.3 = 62x
Dividing both sides of the equation by 62
x = 44.7
hence, Jade and Juliette need to ride for 44.7 more days to complete their trip.
