Step-by-step explanation:
22x + 2y = -14
2y = -22x - 14
y = -11x - 7
A Ferris wheel at a carnival has a diameter of 72 feet. Suppose a passenger is traveling at 100 revolutions per hour. (A) Find the angular speed of the wheel in radians per minute.(B) Find the linear speed of a passenger in miles per hour. (use the fact that 1 mile = 5280 feet)
(A) The angular speed of the wheel in radians per minute is 3.78 radians per minute.
(B) The linear speed of a passenger in miles per hour is 4.09 miles per hour.
Angular speed is the rate at which an object rotates, measured in radians per unit of time. The unit of radians is commonly used in circular motion problems because it allows us to express angles and rotational motion in a consistent way. Linear speed, on the other hand, is the rate at which an object moves in a straight line, measured in units of distance per unit of time.
(A) To find the angular speed of the Ferris wheel in radians per minute, we first need to convert the given rate of revolutions per hour to revolutions per minute. We can do this by dividing the rate by 60 since there are 60 minutes in an hour. Therefore, the wheel completes
=> 100/60 = 5/3 revolutions per minute.
Next, we need to find the angle that the wheel turns in one minute, which we can do by dividing a full rotation (360 degrees) by the number of revolutions per minute. In this case, the angle turned in one minute is
=> (360 degrees)/(5/3 revolutions per minute) = 216 degrees per minute.
To convert this angle to radians, we multiply by (π/180) since there are π/180 radians in one degree. This gives us an angular speed of
=> (216 * π/180) = 3.78 radians per minute.
(B) Using these values, we can calculate the linear speed of the passenger as follows:
Linear speed = (distance traveled)/(time taken) = (π * 72 feet)/(1/5 minutes) = (π * 72 * 5 feet/minute) = (360 * π feet/minute)
To convert this speed to miles per hour, we divide by the number of feet per mile (5280) and multiply by the number of minutes per hour (60), giving us:
Linear speed = (360 * π feet/minute)/(5280 feet/mile) * (60 minutes/hour) = 4.09 miles per hour (rounded to two decimal places).
Therefore, the linear speed of the passenger on the Ferris wheel is approximately 4.09 miles per hour.
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If $10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years? Round to the nearest dollar.
Mary is driving at 60 mph. She decreases her speed by 5 mph every second. Which signed number
represents the change in her speed after 5 seconds?
Answer:
35 mph
Step-by-step explanation:
5×5=25
60-25=35.
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The investments are $ 4000 and $ 3000 in the respective accounts
What is Algebra ?The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
In the given question,
x = amount invested at 10 %
( 7000 - x ) = amount invested at 11 %
The total interest was $730 :
.10 (x) + .11 (7000-x) = 730
0.1 x + 770 - 0.11 x = 730
0.01 x = 40
x = 4000
Therefore, the amount invested in an account that pays 10 % per year is $ 4000.
Hence , the amount invested in an account that pays 11 % per year is
= ( 7000 - x ) = 7000 - 4000 = $ 3000.
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Decide which of the two given prices is better and explain why. Storage locker A rents for $33/yd^2 per month. Storage locker B rents for $1.49/ft^2 per week. (Assume 1 month=4 weeks.)
B is significantly more affordable and better than A, renting for $1.62 per square foot.
Yard and feet conversion:Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.
To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.
1 yard² = 9 feet²
A rents for $33 per yard squared
hence A rents $33 for 9 feet squared
hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared
Thus, as B is more economical, it is better.
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If the x-values are equal for two points, then the two points are on a ____ line
If a line has two points with the same x-value, then the two points are on a vertical line.
What type of line we have here?So we know that we have some kind of a linear equation, such that in two points on the line we have the same x-value.
Then we can write these two points like (x₁, y₁) and (x₁, y₂). If the x-value is the same one, then we have a line of the form:
x = x₁
Which is a vertical line, then that is the correct answer.
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please help me with this!!
In this equation, the regular polygon's area is 72.5.
How is the area of a regular polygon determined?The area of a regular polygon is determined by multiplying its perimeter by its apex. The following is a common way to write the formula: An apothem's area is equal to 1/2(ap), where a denotes the length and p the circumference. Area of pentagon = 1/2 p an is the fundamental formula for computing the area of a regular pentagon, where p stands for the pentagon's perimeter and a for its apothem.
A regular polygon is exactly what?If a polygon has equal sides and angles, it is considered to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.
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HELP DUE TODY pls pls pls
Answer:
First side: 40in
Second side: 20in
Third side: 36in
Step-by-step explanation:
Let's call the triangle's first, second, and third sides a, b, and c respectively.
The perimeter of the triangle is 96in: a+b+c=96
The length of the first side is twice the second: a=2b
The third side is 16in more than the second: c=b+16
Now, consider the equation a+b+c=96 again, but sub '2b' in for a, and 'b+16' for c, in order to find the value of b:
a+b+c=96
2b+b+b+16=96
4b=80
b=20
Use this value for b to find a and c:
a=2b=2(20)=40
c=b+16=20+16=36
Answer:
Step-by-step explanation:
Let's call the length of the second side "x". Then, the length of the first side is 2x and the length of the third side is x + 16.
The perimeter of the triangle is the sum of the lengths of its sides, so we can set up an equation to solve for x:
x + 2x + (x + 16) = 96
Expanding the equation and solving for x, we get:
4x + 16 = 96
4x = 80
x = 20
So, the length of the second side is 20 inches, the length of the first side is 2 * 20 = 40 inches, and the length of the third side is 20 + 16 = 36 inches.
Find the dimensions for which the enclosed area is 1600 square feet. (View image)
Answer:
perimeter of rectangle = 2(length +breadth)
=2(20+80) m
=200 m
∴perimeter of rectangle is 200 m
If f(x) = 2x² - x - 6 and g(x) = x² - 4, find f(x) = g(x).
OA.
B.
C.
2x+3
2
2x-3
#+2
2x+3
#+2
O D. 22-2
Jhayq
Answer:
Step-by-step explanation:
To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.
First, let's define the variables:
f(x) = 2x² - x - 6 is a quadratic function with x as the variable.
g(x) = x² - 4 is also a quadratic function with x as the variable.
Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:
2x² - x - 6 = x² - 4
Next, we simplify this equation by subtracting x² from both sides:
x² + x - 10 = 0
This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.
Let's try factoring:
x² + x - 10 = (x + 5)(x - 2) = 0
So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:
x = -5 or x = 2
These are the two values of x such that f(x) = g(x).
Calculate the range and interquartile range for the following set of scores from a continuous variable: 5, 1, 6, 5, 4, 6, 7, 12. Identify the score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile. Why is the interquartile range a better description of variability in the data than the S range?
The range and interquartile range is 11 and 2 respectively. The score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile is 7 and 4 respectively.
To calculate the range, we subtract the smallest value from the largest value:
Range = Largest Value - Smallest Value = 12 - 1 = 11
To calculate the interquartile range, we first need to find the first and third quartiles. We can do this by ordering the scores from lowest to highest and finding the median of the lower half and upper half of the scores, respectively:
1, 4, 5, 5, 6, 6, 7, 12
The median of the lower half (Q1) is the middle value of the numbers 1, 4, 5, and 5, which is 4.5 (the average of the two middle values).
The median of the upper half (Q3) is the middle value of the numbers 6, 6, 7, and 12, which is 6.5.
Interquartile Range = Q3 - Q1 = 6.5 - 4.5 = 2
To find the score that corresponds to the 75th percentile, we first need to find the index corresponding to the 75th percentile. We can do this by multiplying 0.75 by the total number of scores, which is 8. This gives us an index of 6, meaning the 75th percentile score is the 6th score in the ordered list:
1, 4, 5, 5, 6, 6, 7, 12
The score that corresponds to the 75th percentile is 7.
To find the score that corresponds to the 25th percentile, we can follow the same procedure. The index corresponding to the 25th percentile is 0.25 times the total number of scores, or 2. The 2nd score in the ordered list is 4.
The interquartile range is a better description of variability in the data than the range because the range is heavily influenced by outliers. In this case, the range is 11, which is largely driven by the outlier score of 12. The interquartile range, on the other hand, only considers the middle 50% of the scores and is therefore less affected by outliers. It gives a more accurate measure of the spread of the scores around the median.
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check all of the following that are possible units for measuring mass in the metric system. A. Pound B. Kilogram C. Anagram D. Gram
The following that are possible units for measuring mass in the metric system include the following below:
B. Kilogram
D. Gram.
What is Mass?This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.
Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.
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A grocer has 15 apples some pears and some oranges.There are 9 more apples than pears and three times as many oranges as many pears .Find the ratio of the no. of apple to the no. of oranges he has?
Answer:
15:18
Step-by-step explanation:
So, to say 9 more apples than pears means that 15-9 = 6. Now 3 times of 6 (pears) is 6*3= 18.
Write it in ratio is 15:18!
hope this helped!
What is the x-coordinate of the image when M(4, −1) is reflected in y=3.
The image of the point M(4, -1) after reflection in the line y = 3 would have the x-coordinate of 4.
What is another way to say reflecting?When you reflect, you are giving something serious thought. [written] I continued my thoughtful stroll to the car while contemplating the unfortunate honeymooners. Synonyms: thoughtful, ponderous, contemplative, and pensive More reflective's opposites.
What other word for reflecting is there?Cogitate, deliberate, reason, conjecture, and think are a few words that frequently replace the word reflect. All of these terms indicate "to utilise one's faculties of imagination, reasoning, or inference," but reflect denotes thoughtful deliberation over a memory that has just come to mind.
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In May the Smith family used 12567 litres of water, In June they used 452 litres and in July they used 15623. Write down the amount of water used for each month and round off each to the nearest 1000
The amount of water used for each month and rounded off to the nearest 1000 is;
May = 13,000 litersJune = 0 litersJuly = 16,000 litersWhat is the approximate amount of water used?Amount of water used in May = 12567 litres
Amount of water used in June = 452 litres
Amount of water used in July = 15623 liters
Approximate amount of water used in May to the nearest 1000 = 13,000 liters
Approximate amount of water used in June to the nearest 1000 = 0 liters
Approximate amount of water used in July to the nearest 1000 = 16,000 liters
Therefore, the amount of water used each month rounded to the nearest 1000 are 13,000, 0, and 16,000 respectively.
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Find an equation for the line that passes through the points (-1, 4) and (-5, 6).
The equation of line is y = ( -1/2 )x + 7/2 , where the slope is m = -1/2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -1 , 4 )
Let the second point be Q ( -5 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - 4 ) / ( -5 - ( - 1 ) )
Slope m = 2 / ( -5 + 1 )
Slope m = -2/4 = -1/2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 4 = ( -1/2 ) ( x + 1 )
On simplifying the equation , we get
y - 4 = ( -1/2 )x - 1/2
Adding 4 on both sides of the equation , we get
y = ( -1/2 )x + 7/2
Hence , the equation of line is y = ( -1/2 )x + 7/2
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complete the remainder of the table for the given function rule: y=2x/3+4
The table of values is
X |f(x)
0 | 4
2 | 5.33
4 | 6.67
6 | 8
How to complete the table of valuesFrom the question, we have the following parameters that can be used in our computation:
y = 2x/3 + 4
We have the x values to be
x = 0, 2 4 and 6
Substitute the known values in the above equation, so, we have the following representation
y = 2 * 0/3 + 4 = 4
y = 2 * 2/3 + 4 = 5.33
y = 2 * 4/3 + 4 = 6.67
y = 2 * 6/3 + 4 = 8
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An architectural drawing of the kitchen of a house is 6 inches long by 4 inches wide. If the actual width of the house is 20 feet, what is the length?
The actual length of the house is 30 feet.
What is a scale factor?
A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.
It is given that:
Width of the kitchen = 4 inches.
Length of the kitchen= 6 inches.
It is also given that the actual width of the house is equal to 20 feet.
Now we have to find the length of the house:
The proportion will be:
[tex]\frac{4}{6} =\frac{20}{Length} \\Length=\frac{20*6}{4} \\Length=30feet[/tex]
Therefore the actual length of the house is 30 feet.
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graph the function f (x) = 3 cos (x) -4
Answer: DESMOS
Step-by-step explanation:
Your OHVA teacher reminded you in class to use DESMOS to see the graph and then sketch it on your test...
Point V is somewhere on the line segment . If UV = 8, then find the length of .
Answer:
it is 3
Step-by-step explanation:
just subtract
One cubic foot holds 7.48 gallons of water and one gallon of water weighs 8.33 pounds. How much does a 1.8 cubic foot of water weigh in pounds?
7.48 x 8.33 = 62.3664 pounds are the weight of one cubic foot of water. 1.8 x 62.3664 = 112.26 is the weight of one cubic foot of water. Therefore, 1.8 cubic feet of water weigh about 112.26 pounds.
What dimensions does a cubic foot have?3 dimensions: 3 by 3 by 3
A space that is 1 foot by 1 foot by 1 foot is called a cubic foot. Add the piece's length, breadth, and height together to get the cubic feet it will hold. For instance, the volume of a dresser that is 4 feet length, 2 feet wide, and 5 feet high is 40 cubic feet.
How big is one cubic?A Cubic Unit's Operation Each unit cube's dimension of a unit cube(length, width, and height) is one unit. So, one unit of length with one unit of width and one unit of height together make a volume of one cubic unit.
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Need assistance with this problem
We can see that the exponential model is better
What is the difference between a linear and an exponential function?The main difference between a linear and an exponential function is the way they change as their input variable (usually denoted as x) increases.
In summary, linear functions have a constant rate of change, while exponential functions have an increasing rate of change.
For the linear function;
f(x) = 946(6) + 3349
= 9025
For the exponential function;
g(x) = 3866e^0.138(6)
g(x) = 8848
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A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the (((volume of 15 bags in cubic yards.)))
Answer:
he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Step-by-step explanation:
To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:
1 pound = 0.453592 kilograms
So the weight of one bag in kilograms is:
42 pounds * 0.453592 kilograms/pound = 19.05 kilograms
The weight of 15 bags in kilograms is:
15 bags * 19.05 kilograms/bag = 285.75 kilograms
To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:
1 cubic yard = 27 cubic feet
So the volume of one bag in cubic yards is:
2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards
The volume of 15 bags in cubic yards is:
15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards
Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Complete the sentence below.
20.8 is ten times bigger than
4. Reginald created a mosaic from 6" square tiles.
If the completed mosaic was 2 feet by 3 feet, how
many square tiles did he use?
Reginald used 2 square tiles to make the mosaic
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The area is the product of the length and width. Hence:
Area = length * width
Reginald created a mosaic from 6" square tiles. Therefore:
Area of tiles = 6 in * 6 in = 36 in²
If the completed mosaic was 2 feet by 3 feet, Hence:
Area of mosaic = 2 feet * 3 feet = 6 feet
1 feet = 12 in
6 feet = 6 feet * 12 in per feet = 72 in²
Number of tiles = Area of mosaic / area of tiles = 72 in² / 36 in² = 2
Reginald used 2 tiles
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A boy contain 10 balls of which 6 are Red and the rest are White If a ball is pick at random find the probability of Either Red or White Not Red
Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
To prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.
What is the SSS Similarity Theorem?
The SSS Similarity Theorem states that two triangles are similar if the ratio of all three pairs of corresponding sides of two triangles are equivalent.
Given ΔUVW and ΔXYZ, where:
UV corresponds with XY, thus UV/XY = 50/40 = 1.25
WU corresponds with ZX, thus WU/ZX = 40/32 = 1.25
WV corresponds with ZY, thus WV/ZY = 60/48 = 1.25
Since all the ratio of all three corresponding sides of both triangles are equivalent, therefore both triangles can be proven to be similar by the SSS Similarity Theorem.
Therefore, to prove that ΔUVW and ΔXYZ are similar by the SSS Similarity Theorem: a. show that the ratios UV/XY, WU/ZX, and WV/ZY are equivalent.
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Convert the following quantities to the indicated units. 34 liters=to how many quarts
Answer:
Step-by-step explanation: 34 quarts
1 Liter = approximately 1.06 quarts
so 34 x 1.06 is about 36.04 quarts
Jonathan drove his motorcycle on the highway at 160 miles per hour. His speed increased every three seconds as the roads got wider. What is the rate of change?
We can presume that x is a positive number because we are aware of the widening of the roadways and the increase in Jonathan's speed. It takes three seconds for Jonathan's speed to change by 234.67 + 2x feet per second.
In plain English, what is speed?the definition of speed. a direction or speed at which an object's location changes. The distance travelled relative to the time it took to travel that distance is how fast something is moving.
What does science mean when it refers to speed?In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity.
Let's first convert Jonathan's initial speed of 160 miles per hour to feet per second, since we're measuring the change in speed every three seconds.
160 miles per hour = 160 * 5280 feet per hour = 844800 ft/h
= 844800/3600 ft/s (since there are 3600 seconds in an hour)
= 234.67 ft/s (rounded to two decimal places)
Now, let's assume that Jonathan's speed increases by x feet per second every three seconds. After three seconds, his new speed will be 234.67 + x feet per second. After another three seconds, his speed will be 234.67 + 2x feet per second, and so on.
Since we know that the roads are getting wider and Jonathan's speed is increasing, we can assume that x is a positive number.
Therefore, the rate of change of Jonathan's speed is 234.67 + 2x feet per second every three seconds.
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2x = 32 in y= mx +b form
