The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units
The radius of the base = 4 units
The length of the side of the square = 2x
The area of the square = a^2
Where a is side of the square
The area of the square = (2x)^2
= 4x^2
The equation of the circle is
x^2 + y^2 = 16
x^2 = 16 - y^2
The area = 4(16 - y^2 )
= 64 - 4y^2
The volume of the square
V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]
= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]
= 64×4 - 4×(4^3/3)
= 256 - 256/3
= 512/3 cubic units
Therefore, the volume of the solid is 512/3 cubic units
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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 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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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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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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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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what is the least common denominator for 5/8, 7/20, and 7/13
Write down all of the options which are true of
similar shapes.
They must be the same shape
They can be different shapes
They must be the same size
They can be different sizes
All of the options which are true of similar shapes include the following:
A. They must be the same shape.
D. They can be different sizes.
What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied.
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ACTIVITY 2 1. Mr Nkomo lives in Three Rivers, in the Emfuleni municipality and uses prepaid electricity that is sold to customers at a VAT inclusive rate. The table below shows the cost of prepaid units of electricity. BLOCK UNITS (kWh) 2 3 4 0-50 51-350 351-600 >600 *Prepaid electricity: Paying for electricity before using it. *VAT = 15% *The municipality buys electricity from Eskom at an average VAT inclusive price of R1,33 per kWh. 1.1. State any two reasons why it is an advantage for the municipality to sell prepaid electricity. Verify, by showing ALL calculations, If his claim is VALID. You may use the formula: % Profit = (4) 1.2. Determine the number of units Mr Nkomo received when he bought prepaid electricity for R68,02. (3) 1.3. How much will Mr Nkomo pay if he wanted to buy 310 kWh of electricity? (3) 1.4. Mr Nkomo stated that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34%. RATE c/kWh (Including vat) sell price for the units-cost price for the units 144,72 186,06 261,87 308,37 ✓ 1000z IC) 2
Answer:
Step-by-step explanation:
1.1. Advantages of Selling Prepaid Electricity
Two advantages of selling prepaid electricity are:
a) Reduced costs for the municipality: Prepaid meters eliminate the need for the municipality to send meter readers to each property and manually read the meter. This can save the municipality time and money.
b) Improved cash flow: By receiving payment before the electricity is used, the municipality can improve its cash flow as it will have funds available to purchase more electricity.
1.2. Number of Units Mr Nkomo Received When He Bought Prepaid Electricity for R68,02
The rate per kWh including VAT is R1,33. To determine the number of units Mr Nkomo received, we can use the formula:
Units = Amount / Rate
Units = R68,02 / R1,33
Units = 51.04 kWh
So, Mr Nkomo received 51.04 kWh of electricity when he bought prepaid electricity for R68,02.
1.3. Cost of 310 kWh of Electricity
The rate per kWh including VAT is R1,33. To determine the cost of 310 kWh of electricity, we can use the formula:
Cost = Units * Rate
Cost = 310 kWh * R1,33
Cost = R411,30
So, Mr Nkomo will have to pay R411,30 for 310 kWh of electricity.
1.4. Percentage Profit the Municipality Makes When a Customer Buys 290 kWh of Electricity
To determine the percentage profit the municipality makes when a customer buys 290 kWh of electricity, we need to calculate the cost price and the selling price of the electricity. The cost price of electricity is R1,33 per kWh. The selling price is given in the table as R144,72 for 2-50 kWh, R186,06 for 51-350 kWh, R261,87 for 351-600 kWh, and R308,37 for over 600 kWh.
Since the cost price is R1,33 per kWh and the selling price is different for different ranges of units, we need to calculate the cost and selling price for each range of units and find the average.
For 2-50 kWh:
Cost = 2-50 kWh * R1,33
Cost = 50 kWh * R1,33
Cost = R66,50
Selling price = R144,72
Profit = Selling price - Cost
Profit = R144,72 - R66,50
Profit = R78,22
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R78,22 / R66,50) * 100
Percentage profit = 17.7%
For 51-350 kWh:
Cost = 51-350 kWh * R1,33
Cost = 350 kWh * R1,33
Cost = R466,50
Selling price = R186,06
Profit = Selling price - Cost
Profit = R186,06 - R466,50
Profit = R29,56
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R29,56 / R466,50) * 100
Percentage profit = 6.3%
For 351-600 kWh:
Cost = 351-600 kWh * R1,33
Cost = 600 kWh * R1,33
Cost = R798,00
Selling price = R261,87
Profit = Selling price - Cost
Profit = R261,87 - R798,00
Profit = -536,13
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-536,13 / R798,00) * 100
Percentage profit = -67.3%
For over 600 kWh:
Cost = over 600 kWh * R1,33
Cost = R1,33 * 1000
Cost = R1330,00
Selling price = R308,37
Profit = Selling price - Cost
Profit = R308,37 - R1330,00
Profit = -1021,63
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-1021,63 / R1330,00) * 100
Percentage profit = -76.7%
The average percentage profit for the municipality is calculated by finding the total profit and total cost for each range of units and then dividing the total profit by the total cost.
For the range 2-50 kWh, the total profit is R78,22 and the total cost is R66,50, so the average percentage profit is (R78,22 / R66,50) * 100 = 17.7%.
For the range 51-350 kWh, the total profit is R29,56 and the total cost is R466,50, so the average percentage profit is (R29,56 / R466,50) * 100 = 6.3%.
For the range 351-600 kWh, the total profit is -536,13 and the total cost is R798,00, so the average percentage profit is (-536,13 / R798,00) * 100 = -67.3%.
For the range over 600 kWh, the total profit is -1021,63 and the total cost is R1330,00, so the average percentage profit is (-1021,63 / R1330,00) * 100 = -76.7%.
The average percentage profit for the municipality for the four ranges of units is calculated as follows:
Average percentage profit = (17.7% + 6.3% - 67.3% - 76.7%) / 4
Average percentage profit = -34.05%
Therefore, Mr Nkomo's claim that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34% is NOT VALID.
In the diagram, RSTU~ ABCD. Find the ratio of their perimeters.
U
R
18 S
36
T
D
A
24
The ratio of their perimeters is
B
C
Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.
Since UR = 18 and DA = 24, k = 24/18 = 4/3.
So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.
Now that we have the lengths of all sides of ABCD, we can find its perimeter:
Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC
Perimeter of RSTU = 18 + 36 + 18 + 36 = 108
So the ratio of their perimeters is:
Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108
Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:
20/18 + BC/108 = 4/3
Solving for BC:
BC = (4/3 - 20/18) * 108 = 36
Step-by-step explanation:
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total is made up of Planes?
There are 33% of the total is made up of Planes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The table is given in the question, as follows:
Car Plane Train Total
Green: 120 250 500 870
Blue: 150 350 750 1250
Yellow: 170 200 450 820
Red: 200 300 300 800
Brown: 220 450 320 990
Total: 860 1550 2320 4730
Total number of planes = 1550
The total number of all vehicles = 4730
The percent of planes = (number of planes/number of all vehicles) x 100
The percent of planes = (1550/4730) x 100
The percent of planes = 0.3276 x 100
The percent of planes = 32.76
Round to the nearest percent, and we get
The percent of planes = 33%
Thus, 33% of the total is made up of Planes.
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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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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.
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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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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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:
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 . It goes through the point (5,189).
If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.
If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.
Based on the roots and multiplicity, we have:
P(x) = k · (x-2)^2 · (x-0) · (x - (-2))
P(x) = k · (x-2)^2 · (x-0) · (x+2)
We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).
To find "k", we plug in that point and solve for "k":
189 = k · (5-2)^2 · (5-0) · (5+2)
189 = k · (3)^2 · (5) · (7)
189 = k · 315
0.6 = k
So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)
What is the volume 
The volume of the composite figure is 12 cubic in.
How to calculate the Volume of Composite Shapes?
Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:
Step 1: Break down the compound shape into different components.
Step 2: Determine the volume of each basic shape.
Step 3: Combine the volumes of all the basic shapes.
Step 4: Write the solution in cubic units.
Firstly we can divide the figure into two rectangular prisms A and B. Then add these two to total volume the volumes of each prism.
The volume of prism A = length × width × height
V = 4 * 2 * 1
V = 8 cubic in.
The volume of prism B = length × width × height
V = 1 * 2 * 2
V = 4 cubic in.
Total volume = volume of prism A + volume of prism B
= 8 cubic in + 4 cubic in
= 12 cubic in
Hence, the volume of the composite figure is 12 cubic in.
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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
Costs of Starting Your Own Business
SHORT ANSWER
You are looking at a potential location to open your first spa. The rent is $21 per square
(annually), and the space is 1,800 square feet. How much rent would you pay each year? Each
foot
month?
The amount of money that would be paid for rent each year for the spa would be = $37,800
How to calculate the annual payment for the rent for spa?The area of the potential space for the opening of your first spa = 1,800 square feet.
The price for each square feet per year = $21
That is; = 1800× 21 = $37,800
Therefore, annual rent fees for the space which will be used for spa = $37,800.
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Swimming Pool On a certain hot summer's day, 507 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $761.75. How many children and how many adults swam at the public pool that day?
Answer:384 children and 123 adults swam at the public school.
Step-by-step explanation:
-17
ng
2
Zoom
Chapter 3: Probability (Add and Mult)
Score: 22.75/38 26/38 answered
Question 29
>
A bag contains 7 red marbles, 5 white marbles, and 6 blue marbles. You draw 3 marbles out at random,
without replacement. Find the following probabilities and round to 4 decimal places.
a. The probability that all the marbles are red is
b. The probability that none of the marbles are red is
a. The probability that all the marbles are red is calculated as follows:
(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429
So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.
b. The probability that none of the marbles are red is calculated as follows:
(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696
So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.
Solve for x !
[tex] \it \large {3x + 5 = 5( x + 3)}[/tex]
Thank You!:)
Answer:
[tex]\mathrm{x=-5}[/tex]Step-by-step explanation:
[tex]\mathrm{3x+5=5(x+3)}[/tex]
Expand:-
[tex]\mathrm{3x+5=5x+15}[/tex]
Subtract 5x from both sides:-
[tex]\mathrm{-2x+5=15}[/tex]
Subtract 5 from both sides:-
[tex]\mathrm{-2x=15-5}[/tex]
[tex]\mathrm{-2x=10}[/tex]
Divide both sides by -2:-
[tex]\mathrm{\cfrac{-2x}{-2}=\cfrac{10}{-2}}[/tex]
[tex]\mathrm{x=-5}[/tex]
___________________
Hope this helps!
Part D
What do the factors in the factored form represent?
BIUX² X₂ 15px
<
Space used (includes formatting): 0/ 15000
AV
The factors in the factored form represents the value of the function when x = 0.
What are Quadratic Functions?Quadratic functions are defined as the polynomial functions consisting of variables and exponents with the degree of the variable being 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
y = x² + 2x - 15
This can be factorized as (x + p)(x + q) such that p × q = -15 and p + q = 2.
Two such numbers are -3 and 5.
-3 × 5 = -15 and -3 + 5 = 2
y = x² + 2x - 15
y = (x - 3) (x + 5)
Factors are x - 3 and x + 5
Here, the numbers 3 and -5 represents the input values of the function when the output value or the value of the function equals 0 or they are the x intercepts of the function.
Hence the factors in the factored form are the x intercepts of the function.
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The complete question is as follows :
What do the factors in the factored form represent?
y = x² + 2x - 15
A verbal description of a linear function g is given. Express the function g in the form
g(x) = ax + b.
The linear function g has rate of change −12 and initial value 100.
g(x) =
G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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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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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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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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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.4 mmHg (millimeters of mercury) for a sample of size 686 and a sample standard deviation 5.5 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 90% confidence.
What is the 90% confidence interval to estimate the population mean? Round your answer to one decimal place.
Answer:
{30.1,30.7}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]
Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.
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.
solve for x, 11, 31°
The value of x is 21.4.
What is right-angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.
The sine of an angle is the ratio of height to the hypotenuse.
Therefore,
sin 31° = height/hypotenuse
sin 31° = 11/x
Multiply x with both sides:
x sin 31° = 11
Divide sin 31° with both sides:
x = 11/ sin 31°
x = 21.35
x ≈ 21.4 units
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