Answer:
The area is 196π, or 615.752160 when evaluated to 6 decimal places.
Step-by-step explanation:
There is an equation for the area of a circle:
A=π[tex]r^{2}[/tex], Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:
A=π([tex]14^{2}[/tex])
A=196π
If we write out π and evaluate with an (un)reasonable amount of decimal places:
π≅3.1415926536
A=196×(3.1415926536)
A≅615.752160
Answer:
A = [tex]\pi ^{2}[/tex]
Step-by-step explanation:
A≈615.75
the repair time for air conditioning units is believed to have a normal distribution with a mean of 38 minutes and a standard deviation of 12 minutes. find the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes.
The probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648
We are given:
u= 38,s = 12
We have to find P(29 < x< 44)
Using the z-score formula, we have:
P(29 <x <44) = P(-0.75 < z <0.5)
Using the standard normal table, we have:
P(29 <x<44) = P(-0.75 < z < 0.5) = 0.4648
Therefore, the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648
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Mr. Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long. If each DVD is 11⁄20 inches wide, how many DVDs can he put side-by-side on the shelf?
DVDs
The number of DVDs that he can put side-by-side on the shelf is 19.
How to calculate the value?From the information, Mr Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long and each DVD is 11⁄20 inches wide.
The number of DVDs that can be put will be the division of the numbers that are given. This will be:
= Length of shelf / Width of each DVD
= 10 2/3 ÷ 11/20
= 32/3 ÷ 11/20
= 32/3 × 20/11
= 640 / 33
= 19 13/33
= 19 approximately
He can put 19 DVD.
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Carmen participated in a walkathon to
raise money for the local library. Before the
hour-long event began, Carmen estimated
that she would walk 3.5 miles, but she
ended up walking 4 miles. What is the
percent error for Carmen's estimate?
Answer:
Step-by-step explanation:
12%
Answer:
12.5%
Step-by-step explanation:
xThe number of hours of daylight in a city in the Northern hemisphere shows periodic behavior over time.• The average number of daylight hours is 12.• The maximum number of daylight hours is 14.4.• The period is 365 days.• The day with the least sunlight is December 20.Which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year?
EXPLANATION
Since we know that the number of hours is represented by a periodic function, the appropriate model is the sine function.
As the average number of daylight hours is 12 with a maximum and minimum of 14.4 and 9.6 respectively.
Furthermore, the period is 365.
Thus, the period is as follows:
[tex]\frac{2\pi}{365}=0.017[/tex]The appropiate model is the following:
[tex]H(t)=a\sin(0.017t)+12[/tex]Now, we need to compute the value of a:
Since the sine function reaches its highest value at t=90° and is represented by 14.4, when t=90°, the value of the function is asin(0.017t) = 1
Therefore,
14.4 = a + 12
Subtracting -12 to both sides:
14.4 - 12 = a
Subtracting numbers:
2.4 = a
In conclusion, the final function is the following:
[tex]H(t)=2.4\sin(0.017t)+12[/tex]Since the minimum is at t=0, we want:
[tex]H\left(t\right)=-2.4cos\left(0.017t\right)+12[/tex]In conclusion, the solution is the OPTION C)
variables Review find r if 2r+10=22
EXPLANATION
If the equation is 2r+10=22
Subtracting -10 to both sides:
2r = 22 - 10
Subtracting numbers:
2r = 12
Dividing both sides by 2:
r = 12/2
Simplifying:
r=6
The answer is r=6
a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 140.9-cm and a standard deviation of 1-cm. for shipment, 22 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is less than 140.7-cm.
The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Steel rods are produced by a firm. The lengths of the steel rods have a mean of 140.9 cm and a standard deviation of 1 cm, and they are regularly distributed. 22 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.
mean is N (M) (109,1.6)
Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation
P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.
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5/7 of the teaching staff in a certain primary school are females, what fraction of the staff are males
Answer: 2/7
Step-by-step explanation:
Substract 7/7 AKA the whole, by 5/7 tp get 2/7
2/7 is the fraction of males.
The question is in the image. Answer question 13 only.
We need to convert 40 degrees to radians:
Then, we need to use the next equation:
[tex]40\ast\frac{\pi}{180}[/tex]Solve it:
[tex]40\ast\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Hence, 40 degrees is equal to 2/9π radians.
This question has two parts. First, answer Part A. Then, answer Part B.
part B :
The length of the incline of the ramp will be [h] = 12.0415 ft. The estimated length of the incline would be - 12ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
[A]
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
[B]
For estimating the length of the incline, we will round it off to the exact value. The rounding of length for zero digits after decimal will give the desired result as 12 ft
Therefore, the exact length of the incline of the ramp will be [h] = 12.0415 ft. The estimated length of the incline would be - 12ft
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[ This answer is the answer of part B of the question whose part A is attached with the answer.]
Answer the following. Where necessary, round your answers to 2 decimal places
In a work survey, it was found that:
28 employees preferred tea
45 employees preferred coffee
32 didn't like either
A) Express the number of employees that prefer coffee using a simplified fraction.
B) What percentage of employees don't like either tea or coffee?
C) Express the number of employees that preferred tea using a simplified fraction.
a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].
b) Percentage of employees don't like either tea or coffee is 30.4%
c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]
Define fraction.The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.
Given Data
In a work survey, it was found that:
28 employees preferred tea
45 employees preferred coffee
32 didn't like either
a) Number of employees that prefer coffee
= 45
Fraction:
= [tex]\frac{45}{105}[/tex]
= [tex]\frac{3}{7}[/tex]
b) Percentage of employees don't like either tea or coffee
= [tex]\frac{32}{105}[/tex] × 100
= 30.4%
c) Number of employees that prefer tea.
= 28
= [tex]\frac{28}{105}[/tex]
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A savings account increases from 250$ to 265$. What is the percent increase of the savings account?
when a grizzly bear hibernates, its heart rate drops to 101010 beats per minute, which is 20\ , percent of its normal value. what is a grizzly bear's normal heart rate when not hibernating? beats per minute
A grizzly bear's normal heart rate when not hibernating is 50 beats per minute.
What is a heart rate?
The number of heartbeats that occur in a specific amount of time, usually one minute. The wrist, side of the neck, back of the knees, top of the foot, groin, and other areas of the body where an artery is close to the skin can all detect the heartbeat.
Here,
We let his normal heart rate = h
and given in the question,
20% of h = 10
20/100 * h = 10
h = 10*5
= 50 beats/min
Hence, a grizzly bear's normal heart rate when not hibernating is 50 beats per minute.
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Helppppppppppppppoopppppppppppp
Answer:
-7, -6, -4, -2, 7
Step-by-step explanation:
f(-4) = -4 - 3
f(-4) = -7
f(-3) = -3 - 3
f(-3) = -6
f(-1) = -1 - 3
f(-1) = -4
f(1) = 1 - 3
f(1) = -2
f(10) = 10 - 3
f(10) = 7
8. The smaller of two numbers is five less than half the larger number. Their sum is 13. Find the numbers,
Larger number: 12
Smaller number: 1
Let Statements:
Let x = the larger number
Let 1/2x - 5 = the smaller number
Equation:
x + (1/2x - 5) = 13
1.5x - 5 = 13
1.5x = 18
x = 12
Solutions:
The larger number = x = 12
The smaller number = 1/2x - 5 = 1/2(12) - 5 = 6 - 5 = 1
Write an equation and solve.You bought a magazine for $5 and 4 erasers. You spent a total of $25. How much did each eraser cost?
Let the magazine be m and the eraser be e. Then the total cost is 25.
The equation can now be shown as follows;
[tex]\begin{gathered} 25=m+4e \\ 25=5+4e \\ Subtract\text{ 5 from both sides of the equation;} \\ 20=4e \\ \text{Divide both sides of the equation by 4} \\ 5=e \end{gathered}[/tex]Therefore each eraser cost $5
Use the frequency polygon to work out an estimate for the mean rounded to 1 DP
Considering the given frequency polygon, the mean of the distribution is of:
E(X) = 57.1.
Frequency polygonThe frequency polygon works similarly to an histogram, giving the number of times that each observation happens, with the dot being placed at the center of each interval.
Considering the given polygon, the absolute frequencies are given as follows:
X = 40: 10.X = 52.5: 7.X = 65: 8.X = 77.5: 2.X = 90: 3.The sum of the absolute frequencies is given as follows:
10 + 7 + 8 + 2 + 3 = 30.
Hence the relative frequencies = probabilities are given as follows:
P(X = 40) = 10/30 = 1/3 = 0.3333.P(X = 52.5) = 7/30 = 0.2333.P(X = 65) = 8/30 = 0.2667.P(X = 77.5) = 2/30 = 0.0667.P(X = 90) = 3/30 = 0.1.The mean is given by the sum of each outcome multiplied by it's probability, hence:
E(X) = 40 x 0.3333 + 52.5 x 0.2333 + 65 x 0.2667 + 77.5 x 0.0667 + 90 x 0.1 = 57.1.
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What do you call each part of an expression that is separated by a + or a -?
Please fully explain how to answer number 5 Thank you
Given: A right triangle with dimensions as shown in the figure
To Determine: The ratio for sin A and cos A
Solution
Given a right triangle ABC with a reference angle A, the trigonometry ratio is
[tex]\begin{gathered} sinA=\frac{opposite}{hypothenuse} \\ cosA=\frac{adjacent}{hypothenuse} \\ tanA=\frac{opposite}{adjacent} \end{gathered}[/tex]From the given right triangle with reference angle A, the hypothenuse is the side facing the right angle. The side facing angle A is the opposite, and the other side is adjacent. This is as shown below
Hence
[tex]\begin{gathered} sinA=\frac{24}{26} \\ cosA=\frac{10}{26} \end{gathered}[/tex]OPTION A is the correct option
Find the slope of the line that passes through (64, 94) and (48, -3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the points has a value of 97/16
How to determine the slope of the points?From the question, the line passes through the following points
(64, 94) and (48, -3).
The slope of the line that passes through the points is then calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are the coordinates above
Substitute the known values in the above equation
So, we have the following equation
Slope = (94 + 3)/(64 - 48)
Evaluate the difference and the sum
Slope = 97/16
Hence, the slope is 97/16
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Which statement about the location of √ 7 on a number line is true?
The location of √ 7 on a number line between 2 and 3.
What is a number line?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.
A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.
In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.
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oan, omb, apb and mpn are straight lines and an = 3oa. m is the midpoint of ob. oa = a ов = b ap = kab where k is a scalar quantity. express ab and mn in terms of a and b. express mp in terms of a, b and k. finally, find the value of k.
The values of the vectors of AB = b - a , MN = 29a - b/2 and MP = b/2 + (k + 1)( b - a)
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
We have been given that OB = b and OA = a
From ΔAOB we have;
OB + BA + AO = 0
b + (- AB ) -a = 0
AB = b - a
Now from ΔMNO we have;
MN + NO + OM = 0
MN + ( -ON) + OB/ 2 = 0
MN - (OA + AN ) + b/2 = 0
MN - ( a + 30a) + b/2 = 0
MN = 29a - b/2
Now from ΔMBP , we have;
MB + BP + PM = 0
OB/2 + (BA - PA) + PM = 0
b/2 + ( - AP/k + AP) + PM = 0
b/2 + ( -kAB /k + kAB) + PM = 0
b/2 + ( k AB + AB ) + PM ) = 0
PM = -b/2 - (k + 1) (b - a)
MP = b/2 + ( k+1) (b - a)
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17. A container is partially filled with 12 liters of whole milk containing 4% butterfat. How
much 1% milk must be added to get a mixture that is 2% butterfat? Construct a table,
then solve.
Step-by-step explanation:
a table ? why? what kind ?
it is relatively simple to solve :
x liters of 1% had to be mixed with 12 liters of 4% to get 12+x liters of 2%
x×0.01 + 12×0.04 = (12+x)×0.02 = 12×0.02 + x×0.02
12×0.02 = x×0.01
x = 12×0.02/0.01 = 12×2 = 24 liters
so, 24 liters of 1% had to be added to the 12 liters of 4% to get a 2% mixture (12 + 24 = 36 liters).
PLEASE HELP I NEED THIS ASAP PLEASE!!!!
Answer: Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04in²
Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04 in²
Radius (r) 0.999493 in
Diameter 1.998986 in
Circumference (c) 6.28 in
Area 3.13841 in²
Radius (r) 8.49569 in
Diameter 16.99138 in
Circumference (c) 53.38 in
Area 226.75 in²
Radius (r) 2.5 cm
Diameter 5 cm
Circumference (c) 15.70796 cm
Area 19.63495 cm²
Radius (r) 1.1 yd
Diameter 2.2 yd
Circumference (c) 6.9115 yd
Area 3.80133 yd²
Radius (r) 2 in
Diameter 4 in
Circumference (c) 12.56637 in
Area 12.56637 in²
Step-by-step explanation: I hope this helps.
Which of the following options results in a graph that shows exponential decay?
Group of answer choices
f(x) = 0.6(2)x
f(x) = 3(0.7)x
f(x) = 0.4(1.6)x
f(x) = 20(3)x
The equation of a function that results in a graph that shows exponential decay is f(x) = 3(0.7)ˣ
How to determine the function that represents an exponential decay?An exponential function is represented as
f(x) = abˣ
Where
Variable a represents the initial valueVariable b represents the rateA function that represents an exponential decay would have a rate less than 1
This is represented as b <1
From the list of options, we have
f(x) = 3(0.7)ˣ
By comparing f(x) = 3(0.7)ˣ and f(x) = abˣ, we have
b = 0.7
0.7 is less than 1
Hence, the exponential decay function is f(x) = 3(0.7)ˣ
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Tom’s car has 11 1/9 gallons of gas. If he uses 3/8 of the gas, how much gas does the car have left?
Answer:
10.736
Step-by-step explanation:
11 1/9 - 3/8 =10/53/72
= 10.736
You have a TV that is 30 inches tall and 40 inches wide. What is the length of the diagonal of the TV. (The measure from bottom left to top right of the TV) 2500 inches/ 1250 inches/ 50 inches/ 26.5 inches
The length of the diagonal of the TV is 2500 inches
Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner.
How do you measure the diagonal of a TV?TV that is 30 inches tall and 40 inches wide.
The length of the diagonal of the TV of the equation is
[tex]30^{2} + b^{2} =40^{2}[/tex]
Then
[tex]30^{2} +40^{2} =2500[/tex]
so
The length of the diagonal of the TV is 2500 inches
Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner. Most are expressed in inches.
The screen surface's diagonal length is calculated from one corner to the other corner (bottom left to top right or top left to bottom right)
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Write a simplified explession for the perimeter of the triangle.
[tex]p =( 1.5x - 3) + (1.5x - 3) + (0.75x - 1) \\ = 1.5x + 1.5x + 0.75x - 3 - 3 - 1 \\ p= 3.75x - 7[/tex]
ABOVE IS THE SIMPLIFIED PERIMETER OF THE TRIANGLE.
Triangle ABC is translated T(x,y) --> (x + 2, y - 3). What are the coordinates of the image of triangle ABC after this translation?
The coordinates of the image of triangle ABC would be A (-1, -1), B (3, 2), and C (4, -6) after translation, and if the original coordinates are A(-3,2) B(1,5) C(2,-3).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Let assume A(-3,2) B(1,5) and C (2,-3) are original coordinates
The following translation is being used: (x, y) ⇒ (x + 2, y - 3)
First, take your x-coordinates and add them by two because it is the translation utilized to solve for your x-coordinate.
You would receive the following for yours x's: A (-1, y ) B (3, y) C (4, y)
Next, remove three from each of your y-coordinates because it is the translation being utilized to solve for your y-coordinate.
You would receive the following for your y's: A (x, -1) B (x, 2) C (x, -6)
Finally, you would take each one and put it together, or piece it together.
Hence, the coordinates of the image of triangle ABC after translation would be A (-1, -1), B (3, 2), and C (4, -6).
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During two games, the number of points scored by a basketball team increased from 5 to 3 by what did the number of points scored increase?
EXPLANATION
Let's see the facts:
The increasing rate is:
[tex]Increa\sin g\text{ rate=}\frac{5}{3}=1.67[/tex]The increasing rate is 1.67
In percentage this is:
[tex]Increa\sin g=\frac{3}{5}\cdot100=\frac{3}{5}\cdot100=60[/tex]The percentage of increasing is of 60%.
£ represents a group of 20 people that visited paris for a weekend break. 8 of the group visited the eiffel tower (ET) 13 of the group visited the no tre-dame cathedral (NDC) 5 of the group did not visit either of these places a person is chosen at random from the group. what is the probability that this person only visited one of the two places?
The probability that this person choosen only visited one of the two places is 9/20
What is Probability?
Probability is a measure of the possibility that an event to occur.
The probability for an event to occur= Possible outcome /Total outcome
to get the possible out come we must Know the number of people that visited ET and NDC only.
using set theory;
if x is the no of people that visited both places then,
8-x =ET only
13-x= NDC only
5= none visited ET and NDC
x+13-x+8-x+5=20
collect like terms
26-x= 20
x =6
therefore ET only= 2
NDC only= 7
probability of ET = 2/20
probability of NDC= 7/20
therefore probability that the person chosen only visited one place = p(ET)+P(NDC)= 7/20+2/20
= 9/20
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