If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.
Answers
Radius of the circle : Radius is the distance from the center outwards.
With the help of radius we can determine the following terms:
1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :
[tex]\text{ Diameter= 2}\times Radius[/tex]2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:
[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:
[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :
[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :
[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]In the given figure the radius is AO & BO
Related Questions
between 1993 and 1996 there were 6545 injured during horse races find the ratio of injured per year
Answers
First, we have to calculate the years passed between 1993 and 1996:
1996-1993 = 3 years
Now divide the number of injured during horse races (6545) by the number of years (3)
6545 /3
2,182 injured per year
The Connecticut River flows at a rate of 6 km / hour for the length of a popular scenic route. If a cruiser to travels 3 hours with the current to reach a drop-off point, but the return trip against the same current took 7 hours. Find the speed of the boat without a current?The speed of the boat without a current is ____ km/hour. (if needed, round to 2 decimal places).
Answers
Given:
Speed of current (y)= 6 km/hour
Distance = d km
Speed of boat in still water = x km/hour
Speed of the cruiser with the current= (x+6) km/hour
Speed of the cruiser against the current= (x-6) km/hour
[tex]\text{Time to travel with the stream=}\frac{d}{x+6}[/tex][tex]3=\frac{d}{x+6}[/tex][tex]3\mleft(x+6\mright)=d[/tex][tex]d=3x+18\ldots.\text{ (1)}[/tex][tex]\text{Time to travel }against\text{ the stream=}\frac{d}{x-6}[/tex][tex]7=\frac{d}{x-6}[/tex][tex]d=7x-42\ldots.\text{ (2)}[/tex]From equation (1) and (2)
[tex]7x-42=3x+18[/tex][tex]7x-3x=18+42[/tex][tex]4x=60[/tex][tex]x=15[/tex]Therefore the speed of the without a current is 15km/hour.
Convert each angle in radians to degrees 3π/4
Answers
we have only to change pi by 180, and solve the multiplication
[tex]\frac{3\pi}{4}\rightarrow3\cdot\frac{180}{4}=135^{\circ}[/tex]Solve the inequality: 3x + 4 < 5
Answer in interval notation.
Answers
Answer:
0.3 recurring
Step-by-step explanation:
3x+4<5. -4
3x<1. ÷3
×<0.333
1. A table is 2 feet wide. It is 6 times as long as it is wide. Table= A-Label the diagram with the dimensions of the table.B-find the perimeter of the table
Answers
Width(w) = 2 feet
Length (L)= 6w = 6(2) = 12 feet
a. Table = 2 x 12
b: Perimeter of a rectangle:
P = 2w+ 2L = 2(2)+2(12) = 4+24 = 28 feet
Hello could you please help me with question number five?
Answers
Question #5
Given:
The number of people who own computers has increased 23.2% annually since 1990
In 1990: the number of people who own computers = half a million
We will predict the number of people in 2015
We will use the following formula:
[tex]P(t)=P_o\cdot(1+r)^t[/tex]Where: (r) is the ratio of increasing = 23.2% = 0.232
And (t) the number of years after 1990
And P₀ is the initial value of the number of people
P(t) will be the number of people after (t) years
To predict the number of people in 2015
t = 2015 - 1990 = 25 years
so,
[tex]\begin{gathered} P=0.5\cdot(1+0.232)^{15} \\ P=0.5\cdot1.232^{15}\approx11.43\text{ millions} \end{gathered}[/tex]So, the answer will be:
The estimated number of people = 11.43 million
Simplify and give answer as positive exponentkoa) x4. x-7xb)k4
Answers
To simplify the expression, we need to use an exponent propertie
[tex]a^n\cdot a^m=a^{n+m}[/tex]Then, we can see that in this case a = x, n = 4 and m = -7
So now we must replace the values
[tex]x^4\cdot x^{-7}=x^{4-7}=x^{-3}[/tex]Please help solve thank you
Answers
a) 2711/7576
b) 43
=================================================
Explanation:
a) 2711 are e-bikes and there are 3277+2711+1588 = 7576 total bikes. Divide the values to get 2711/7576 . This fraction cannot be reduced because the GCF of 2711 and 7576 is 1.
---------
b) There are 3277 bikes with fat tires out of 7576 total. Use a calculator to get 3277/7576 = 0.43255 approximately. This converts to 43.255% and then rounds to 43%
The percent sign is already typed in, so you just need to type in the whole number 43 for this box.
This is due tomorrow! Smart people help me, please!!
Answers
Two wheelchair ramps, each 10 feet long, lead to the two ends of the entrance porch of Mr. Bell's restaurant. The two ends of the porch are at the same height from the ground, and the start of each ramp is the same distance from the base of the porch. The angle of the first ramp to the ground is 24°.Which statement must be true about the angle of the second ramp to the ground?A. It could have any angle less than or equal to 24°.B. It must have an angle of exactly 24°.C. It could have any angle greater than or equal to 24°.D. Nothing is known about the angle of the second ramp.
Answers
Given statement
The ramps have
- the same height
- the same angle measure relative to the ground
- the two ends of the porch are at the same height from the ground
- the start of each ramp is the same distance from the base of the porch
A pictorial description of the problem is shown below:
Since the two ramps have similar descriptions, the angle measure of the second ramp to the ground would be exactly 24 degrees
Answer: Option B
option b your welcome
simplify the following expression:7^-6 × 7^3
Answers
To solve this question, we will apply the knowledge of exponents and indices
The values have the same bases (7) but different powers and they are separated by a multiplication sign.
So we can use the law:
[tex]a^{x\text{ }}\text{ x a}^{y\text{ }}=a^{x\text{ + y}}[/tex]so that
[tex]7^{-6}\text{ x 7}^3=7^{-6\text{ + 3}}[/tex]on simplifying will give
[tex]7^{-3}[/tex]=>
[tex]7^{-3}\text{ =}\frac{1}{7^3}[/tex]How4 x 8 sheet ofmanyply wood do you need tocover a 24 x 24 deck?
Answers
Given
Dimensions of deck = 24 by 24
dimensions of ply wood = 4 by 8
Find
Number of sheets of ply wood needed to cover the deck
Explanation
number of sheets = area of deck divided by area of 1 ply wood
so ,
area of deck =
[tex]\begin{gathered} 24\times24 \\ 576 \end{gathered}[/tex]and
area of ply wood =
[tex]\begin{gathered} 4\times8 \\ 32 \end{gathered}[/tex]so ,
number of sheets needed =
[tex]\begin{gathered} \frac{576}{32} \\ \\ 18 \end{gathered}[/tex]Final Answer
Hence , the required number of sheets of ply wood is 18
Which ordered pair represent points on the graph of this exponential function?f(x) = 2^x+1A(1, 3)B(-4, -7)C(-2, -3)D(4, 9)
Answers
Answer:
[tex]A(1,3)[/tex]Step-by-step explanation:
To determine which of the given ordered pairs belongs to the given function, substitute each x-value and see if the y-value is correct.
[tex]\begin{gathered} f(1)=2^1+1 \\ f(1)=3 \\ \\ f(-4)=2^{-4}+1 \\ f(-4)=\frac{17}{16} \end{gathered}[/tex][tex]\begin{gathered} f(-2)=2^{-2}+1 \\ f(-2)=\frac{5}{4} \\ \\ f(4)=2^4+1 \\ f(4)=17 \end{gathered}[/tex]Therefore, the only point that represents points on the given function is A(1,3)
Im confused on how to make the table and plug the dots while also describing both behaviors on this equation.
Answers
Here, we want to complete the table
To do this, we consider points on the plot
From what we have;
We are told that a graph of an exponential function does not cross the x-axis and thus, y cannot be zero
When x =0, y = 1
When x = 1, y = 2
when x = 2, y = 4
The y-intercept is the value of y when x = 0; it is the point at which the graph crosses the y-axis
What we have here is that wehn x = 0, y = 1
Hence, 1 is the y-intercept
Now, let us take a look at the end behavior
We can obtain this from the graph;
As x moves towards infinity, the y value moves towards infinity too as evident from the upward curve of the graph
As x moves toward negative infinity, y moves closer to zero
Timothy ran a lemonade stand for 6 days. on the first day he made $5. Each day after that he made $2 more than the previous day. How much money did Marcus make, , after the 6 days?A) $60B) $15C) $12D) $30
Answers
Step `1;
Total number of days = 6
Step 2:
First day = $5
Second day = $5 + $2 = $7
Third day = $7 + $2 = $9
Fourth day + $9 + $2 = $11
Fifth day = $11 + $2 = $13
Sixth day = $13 + $2 = $15
Step 3:
Marcus made = $5 + $7 + $9 + $11 + $13 + $15
= $60
Second method
Use the sum of nth terms of arithmetic progression.
first term a = $5
Common difference = 2
n = 6
[tex]\begin{gathered} S\text{um of the 6 terms = }\frac{n}{2}(\text{ 2a + (n-1)d)} \\ =\text{ }\frac{6}{2}\text{ ( 2}\times5\text{ + (6 -1) }\times\text{ 2)} \\ =\text{ 3( 10 + 5}\times2\text{ )} \\ =\text{ 3( 10 + 10 )} \\ =\text{ 3 }\times\text{ 20} \\ =\text{ \$60} \end{gathered}[/tex]Final answer
Marcus made = $60 Option A
Find the equation for the line that passes through the point (1,0), and that is perpendicular to the line with the
Answers
step 1
Find out the slope of the given line
we have
-(4/3)x+2y=4/3
isolate the variable y
2y=(4/3)x+(4/3)
Divide both sides by 2
y=(4/6)x+(4/6)
simplify
y=(2/3)x+(2/3)
the slope is m=2/3
Remember that
If two lines are perpendicular, then their slopes are negative reciprocal
that means
the slope of the perpendicular line to the given line is
m=-3/2
step 2
Find out the equation in slope-intercept form of the perpendicular line
y=mx+b
we have
m=-3/2
point ( 1,0)
substitute and solve for b
0=-(3/2)(1)+b
0=-(3/2)+b
b=3/2
therefore
the equation is
y=-(3/2)x+(3/2)ory=-1.5x+1.5Betsy has $400 in a personal bank account, and then withdraws $14 perweek. Carlos has $25 in a personal bank account, and then deposits $61earned from babysitting each week. After how many weeks will they have thesame amount of money in the bank?
Answers
Given:
Betsy has $400 in a personal bank account, and then withdraws $14 per
week.
Carlos has $25 in a personal bank account, and then deposits $61
earned from babysitting each week.
Required:
The same amount will they have in the bank after how many week.
Explanation:
After 5 weeks Betsy will have $330 in her account.
Since
[tex]\begin{gathered} 14\times5=70 \\ \Rightarrow400-70=330 \end{gathered}[/tex]After 5 weeks Carlos will have $330 in her account.
Since
[tex]\begin{gathered} 61\times5=305 \\ \Rightarrow305+25=330 \end{gathered}[/tex]Hence, after 5 weeks they will have the same amount of money $330 in the bank.
Final Answer:
After 5 weeks they will have the same amount of money $330 in the bank.
A committee of five members is to be randomly selectedfrom a group of nine freshman and seven sophomores.Which expression represents the number of different committeesof three freshman and two sophomores that can be chosen?
Answers
The answer would be the product of the number of 3 freshman groups by 2 sophomores groups.
The number of 3 freshman groups is given by
[tex]C^9_3=\frac{9\times8\times7}{3\times2\times1}=84[/tex]The number of 2 sophomore groups is given by
[tex]C^7_2=\frac{7\times6}{2\times1}=21[/tex]Now, doing their product
[tex]21\times84=1764[/tex]We have 1764 different committees of three freshman and two sophomores.
Calculate the area of the right triangle that has the following coordinates:
A: (-2,-1)
B: (1, 1)
C: (3,-2)
You must show all calculations to earn any credit. I suggest that you sketch this
triangle on graph paper so that the visual can help you.
Answers
The area of right triangle is [tex]\frac{1}{15}[/tex].
The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].
We have to find the area of right triangle.
To find the area we first draw the graph using that coordinate.
The graph of the coordinate is
To find the area we use the formula
[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]
We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].
e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].
The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]
The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]
The slope of [tex](|AB|)=\frac{2}{3}[/tex]
The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].
The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]
The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]
The slope of [tex](|AC|)=-\frac{1}{5}[/tex]
Now finding the area of right triangle by putting the values.
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]
Area can't be negative so
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]
Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].
To learn more about area of right triangle here link
https://brainly.com/question/27694270
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Julie has a total of 16 chickens. If she has 4 times as many chickens as dogs, write and solve an equation to determine the number of dogs she has.
Answers
The equation that can be used to determine the number of dogs that Julie has =
4× (number of chicken) = 64
What is an equation?An equation is defined as the expression that shows a connection between two variables that are connected with an 'equal to' sign.
The number of chicken owned by Julie = 16 chickens
The number of dogs = X
But she has 4× (number of chicken) = X
That is 4 × 16 = X
X= 64
Therefore the number of dogs that Julie has = 64 dogs.
Learn more about addition here:
https://brainly.com/question/25421984
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for the polyhedron, find the missing numberneed a whole number of faces
Answers
The Euler's polyhedron formula states that, for a polyhedron with F faces, E edges and V vertices, we have:
F + V - E = 2
For E = 12 and V = 6, then we have:
F + 6 - 12 = 2
F = 2 + 12 - 6
F = 8
Graph the line with the given slope m and y-intercept b
Answers
Answer:
draw a line from the top left to the bottom right going through the centre
Step-by-step explanation:
because m=-1 (gradient)
and b=0 (y intercept)
I wonder what I’m doing wrong ?
P^2-10p+16=1+6p
Answer is (15,1)
But I can’t seem to figure it out.
Answers
Steps to Solve:
1. Collect like terms
2. Factor quadratic
3. solve for p
Factoring a Quadratic where a = 1
1. find two numbers that are the product of ac and the sum of b
2. set up the two linear terms with the variable associated with a
2. insert the values found in step 1 into parentheses
1. collect like terms
[tex]p^2-10p-6p+15-1=0[/tex]
[tex]p^2-16p+15 = 0[/tex]
2. Factor quadratic
ac = 15 and b =-16, two numbers that multply to ac and are the sum of b are -15 and 1[tex](p-15)(p-1)=0[/tex]
2 solutions can be found[tex]p-15=0[/tex] OR [tex]p-1=0[/tex]
[tex]p= 15[/tex] [tex]p=1[/tex]
7. Martha baked 332 muffins. She packed them in boxes of twelve muffins and sold each full box for S6How much money did she make?
Answers
• Given that Martha baked 332 muffins,
,• 332 / 12 = 27.67 boxes
,• If she sold each box for $ 6 ; it will be
27*6 = $162
0.67 * 6 = 4.02
Total 162+4.02 = 166.02≈ $166
• She will make $166, ,
Is the ratio 11/15 the same as 15/11 Choose the correct answer below A,B,C or D
Answers
Given,
The ratios are,
[tex]\frac{11}{15},\frac{15}{11}[/tex]The value of 11/15 is,
[tex]\frac{11}{15}=0.7333[/tex]The value of 15/11 is,
[tex]\frac{15}{11}=1.3636[/tex]Hence, option B is correct.
lan is working two summer jobs, making $19 per hour lifeguarding and making $9per hour clearing tables. In a given week, he can work no more than 14 total hoursand must earn a minimum of $180. If x represents the number of hours lifeguardingand y represents the number of hours clearing tables, write and solve a system ofinequalities graphically and determine one possible solution.Inequality 1: y 24plot switch shadeInequality 2: y 24plotswitch shade2019181716151413121110Yes
Answers
Given:
Lan is working two jobs:
1) $19 per hour life guarding
2) $9 per hour clearing tables
The total hours per week = 14
He must earn a minimum of $180
Let x represents the number of hours life guarding and y represents the number of hours clearing tables
So, we have the following inequalities
[tex]\begin{gathered} x+y\le14 \\ 19x+9y\ge180 \end{gathered}[/tex]We need to solve the inequalities by graph
So, we will graph the lines: x + y = 14 and 19x + 9y = 180
The shaded area represents the solution of the system of inequalities
The following figure represents the solution of the system of inequalities
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 500 contains 100 green, one-headed Jolos; 125 purple, two-headed Jolos; and 270 one headed-jolos.How many green Jolos are there in Balan's colony?A. 105B. 170C. 205D. 230
Answers
According to the table, there are 270 one-headed in total, and there are 500 Jolos, we just have to subtract to find the total of two-headed Jolos
[tex]500-270=230[/tex]There are 230 two-headed Jolos.
Now, we subtract the total of two-headed Jolos and the two-headed purple Jolos to find the total green.
[tex]230-125=105[/tex]There are 105 two-headed green Jolos.
At last, we have to sum the number of one-headed green Jolos and the two-headed green Jolos,
[tex]100+105=205[/tex]Hence, there are 205 green Jolos in total.The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 8lb stretches a certain spring 9in., how far will the spring stretch if the weight is increased to 37lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)
Answers
ANSWER
L = 42in
EXPLANATION
The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 433 ft long and 4 mm in diameter has a resistance of 1.22 ohms, find the length of a wire of the same material whose resistance is 1.43 ohms and whose diameter is 5 mm.
Answers
Given:
The resistance
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. The equation that give the height (h) of the ball at any time (t) is: h(t)= -16t^2 + 40t + 1.5. Find the maximum height attained by the ball. I need a clear explanation because I have to expose this
Answers
The height of the ball at any time t is given by
[tex]h(t)=-16t^2+40t+1.5[/tex]This is a quadratic equation, which attains its maximum value at time:
[tex]t=\frac{-b}{2a}[/tex]In the given equation, a = -16 and b = 40. substitute these values in the formula:
[tex]t=\frac{-40}{-16\times2}=\frac{-40}{-32}=\frac{5}{4}[/tex]Therefore, the ball attains its maximum height at t=5/4 seconds which is given below:
[tex]\begin{gathered} h(\frac{5}{4})=-16(\frac{5}{4})^2+40(\frac{5}{4})+1.5 \\ =-25+50+1.5 \\ =26.5 \end{gathered}[/tex]Thus, the maximum height attained by the ball is 26.5 feet.
