The length of the arc of the circle is 3.67 meters
What is an arc?The arc of a circle is a part of the circumference that makes up the circle
How to determine the length of the arc?From the question, we have the following parameters
Diameter, d = 14 meters
Central angle = π/6 radians
Start by calculating the radius of the circle using
Radius, r = Diameter/2
This is so because radius is half the diameter
So, we have
r = 14 meters/2
Evaluate the quotient of 14 meters and 2
r = 7 meters
The length of the arc of the circle is then calculated using
L = Radius * Central angle
Substitute known values in the above equation
L = 7 meters * π/6
Evaluate the product of 7 and π/6
L = 3.67 meters
Hence, the length of the arc of the circle is 3.67 meters
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11
A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively. Which sentence about the points is true?
OA
A, B, C, and D lle on the same line.
OB.
AB and CD are perpendicular lines.
OC. AB and CD are parallel lines.
OD. AB and CD are intersecting lines but are not perpendicular.
OE. AC and BD are parallel lines.
For the given coordinates of A, B, C, and D as (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively, OD, AB and CD are intersecting lines but are not perpendicular (third option) is the correct assertion.
Reasons for the Choice
Because parallel lines never intersect, the fact that lines AB and CD come to a point proves that they are not parallel. It indicates that they are intersecting lines. (Refer to the attached figure)The location where lines AB and CD intersect is not at a straight angle. As a result, lines AB and CD are not parallel.Because the distances separating the two lines differ, AC and BD are not parallel. As a result, lines AB and CD do indeed intersect, but not at a straight angle. Consequently, despite not being perpendicular, both lines intersect.Therefore, the lines OD, AB, and CD are intersecting lines but are not perpendicular.
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Calculate the volume of a sphere that has a radius of 4 meters
Answer:
268.08
Step-by-step explanation:
use the formula 4/3πr^3Answer:
803.84 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
radius ⇒ 4m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 4 )³
V = 4 π × 64
V = 4 π × 64
V = 12.56 × 64
V = 803.84 m³
Gia is participating in a jump-a-thon to raise money for her school. After completing
20 jumps, she raised $50. Gia wants to know how much money she raises per jump.
Which rate shows how much money Gia raises per jump?
50
20
20
50
jumps per dollar
dollars per jump
20
50
50
20
jumps per dollar
dollars per jump
Answer:
50/20
Step-by-step explanation:
Rate of money raised raises per jump is
money raised / jumps
$50/ 20 jumps
We can think that if we divide the $50 into 20 equal parts,
each part will represent 1 jump and will have 50/20 = $2.5 per 1 jump.
Question 1 Which number has the greatest value? O 0.095 O 1.24 1.215 O 0.365 Confident
Answer:
1.24
Step-by-step explanation:
because 1.24>1.215>0.365>0.095
WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
ACCOUNT IN HER NAME AT A SAVINGS AND LOAN ASSOCIATION (S&L). AT THE TIME,
THE S&L PAID 6% INTEREST COMPOUNDED SEMI-ANNUALLY. AFTER 10 YEARS, THE
S&L CHANGED TO A RATE OF 6% COMPOUNDED QUARTERLY. WHAT WAS THE
VALUE OF THE ACCOUNT AFTER 18 YEARS WHEN THE MONEY WAS WITHDRAWN TO
HELP PAY FOR HER COLLEGE EXPENSES
The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.
How are the future values determined?The future values of the savings account are calculated in two installments.
The first installment is for 10 years when the account earns 6% compounded semiannually.
Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.
Future values can be determined using the future value formula or an online finance calculator, as follows:
Data and Calculations:Investment of $2,000 for 10 years:N (# of periods) = 20 (10 years x 2)
I/Y (Interest per year) = 6%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $3,612.22
Total Interest $1,612.22
Investment of $3,612.22 for 8 years:N (# of periods) = 32 (8 years x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)
PMT (Periodic Payment) = $0
Results:
FV = $5,816.85
Total Interest $2,204.63
Thus, the value of the account after 18 years was $5,816.85.
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What is the value of 2 + (- 2/3)^2 ÷ 1/3 ?
16
3
-2
0
Answer:
3
Step-by-step explanation:
2+ (-2/3)^2 ÷ 1/3
make -2/3 postive because its being raised by an even exponent
you never divide by fractors so make 1/3 into 3 and make it multiplication
2+ (2/3)^2 × 3
raise the fraction to the power of 2
2+ (4/9)× 3
cancel out the GCF
2+ 4/3
add
10/3
simplify
3.3 ≅ 3
Graph the line y+3x=-3
Answer: y = -3x-3 (Choose values for x)
Step-by-step explanation:
1st change the equation to y = mx+b form
In order to change the equation to y = mx+b form subtract the 3x to both sides.
The equation now becomes y = -3x-3
2nd we can either choose values for x such has (-2,-1,0,1,2) and plug in those values into our equation y = -3x-3
For example, if we plug in x= -2 we get y= -3(-2)-3 which becomes y =3. We then plot the point (-2,3) because -2 is our x coordinate and 3 is our y coordinate.
Or we can plug the equation into a calculator that will graph the equation for you.
Find the area of rhombus JKLM given the coordinates of the vertices. Round to the nearest tenth if necessary.
J(-2, -4), K(2, 2), L(6, -4), M(2, -10)
Answer:
The area of rhombus JKLM is 48 units²=====================================
Given Rhombus JKLM,Vertices at J(-2, -4), K(2, 2), L(6, -4), M(2, -10).To find The area of rhombus JKLMSolutionWe know that diagonals of rhombus are perpendicular to each other.
Hence its area is half the product of diagonals.
The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.
Let's find the length of diagonals, using the difference of coordinates:
JL = 6 - (-2) = 8 units,KM = 2 - (-10) = 12 units.Now find the area:
A = JL*KM /2 = 8*12 / 2 = 48 units²A random sample of 80 tires showed that the mean mileage per tire was 41,400mi, with a standard deviation of 4700mi
Question 14
Part (a)
[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]
Part (b)
[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]
Which statement best reflects the solution(s) of the equation? ASAP
The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Given the equation:
1 / (x - 1) + 2/x = x / (x - 1)
Multiplying through the equation by x(x - 1):
x + 2(x - 1) = x(x)
x² - 3x + 2 = 0
x² - 2x - x + 2 = 0
(x - 2)(x - 1) = 0
x = 2; and x = 1
The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1
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The hypotenuse of an isosceles right triangle is 14 centimeters longer than either of its legs. Find the exact length of each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.)
The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]
a and b are two legs of a right trianglec is the hypotenuseThe Quadratic Formula[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Solving the QuestionLet a represent the length of one leg.
Because the hypotenuse is 14 cm longer than a leg, we can say that the hypotenuse's length is 14 + a.
Plug these into the Pythagorean theorem:
[tex]a^2+b^2=c^2\\a^2+a^2=(14+a)^2\\2a^2=14^2+2(14)a+a^2\\2a^2=196+28a+a^2\\a^2=196+28a\\a^2-196-28a=0\\a^2-28a-196=0[/tex]
Factor using the quadratic formula:
[tex]a=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]a=\dfrac{-(-28)\pm \sqrt{(-28)^2-4(1)(-196)}}{2(1)}\\\\a=14\pm14\sqrt{2}\\\\a=14+14\sqrt{2}[/tex]
We know that it's plus because subtracting results in a negative value, and length cannot be negative.
This is the length of each side.
Because the hypotenuse is 14 cm longer, we can say that the hypotenuse is [tex]28+14\sqrt{2}[/tex].
AnswerLeg length = [tex]14+14\sqrt{2}[/tex]
Hypotenuse length = [tex]28+14\sqrt{2}[/tex]
Decimals, fractions, and percents can all represent the same values.
True
False
The given statement that, decimal, fraction, and percent can all represent the same values is True.
Verification of the True Statement:
The ratio of two numbers results in a fraction which are often rational numbers (often integers). As an illustration, 11/59 is a fraction. Typically, absolute values for fractions should be larger than 0 and less than 1. A mixed fraction equivalent to 1 3/4 is 7/4.
A fraction stated in tenths are known as a decimal (or tenths of tenths, etc.). The decimal equivalent of one fourth, or 1/4 as a fraction, is 0.25 (which equals 25/100). (Remember that 1/100 is just a tenth of a tenth.)
Percentage (percent) is a decimal fraction multiplied by 100. Therefore, 0.25 is equivalent to 25 percent, for instance. The ratio of two numbers results in fractions, which are often rational numbers (often integers).
Let us take a number 3/5, this is a fraction.
Now, if we further divide, 3 by 5, we will get 0.6
This 0.6 is a decimal number, but it still represents the number 3/5
Similarly, it is equivalent to 60 percent which again represent the fraction 3/5 or decimal 0.6.
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Compute (x4 - 5x3+4x² - 15x + 3) = (x² + 3).
Check the attached file.
Drag the tiles to the correct boxes to complete the reasoning of the proof. Not all tiles will be used.
May this help other people in the near future!!!!!
The missing reasons for each of the given statements are respectively;
1) Substitution
2) Definition of a Straight angle because a straight angle is 180°.
3) Congruent Angles have equal measures
How to prove angles in a triangle?
We are given that;
m∠1 = 90°
m∠1 + m∠2 = m∠5
∠3 ≅ ∠4
Statement 1; 90° + m∠2 + m∠4 = 180°
Reason 1; Substitution
Statement 2; m∠1 + m∠2 + m∠3 = 180°
Reason 2; Definition of a Straight angle because a straight angle is 180°.
Statement 3; m∠3 = m∠4
Reason 3; Congruent Angles have equal measures
Thus, the missing reasons for each of the given statements are respectively;
1) Substitution
2) Definition of a Straight angle because a straight angle is 180°.
3) Congruent Angles have equal measures
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Someone please help me with this question thank youuu
Answer: 148 degrees
Step-by-step explanation:
The total measure of all exterior angles of a convex pentagon is 360 degrees.
If four of them equal 53 degrees then all those together is 212 degrees
53 times 4 = 212
Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!
Hope this helps :)
Part of the arena is being turned into a public darkroom. The floor needs covering in rubber tiles before work can begin on the dark room. The tiles are 20 cm by 30 cm. The dark room floor is 6 metres by 3 metres. Are 280 tiles enough? How many more/less tiles are needed?
The number of tiles used is 300 tiles.
According to the statement
We have given that:
The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.
And we have to find that the number of tiles used to prepare the dark room.
So, For this purpose we have to find the area of the room floor.
The area of the floor is 6 *3.
The area of the floor is 18 meter per square.
The area of the tile is 0.2*0.3
The area of the tile is 0.06 meter per square.
Now,
The number of tiles used is 18/0.06
The number of tiles used is 300.
So, The number of tiles used is 300 tiles.
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When the equation a-bx=cx
+d is solved for x, the result is
Answer:
x=a-d/c+b
Step-by-step explanation:
a-bx =cx+d
collect like terms
a-d=cx+bx
a-d=x(c+b)
x=a-d/c+b
Take 4x + 2 from 8x + 5.
4x + 3
4x - 3
-4x - 3
Answer:
4x + 3 just take away rhe values
Solve the differential equation. (x^2 + 11)y' = xy
Separate the variables.
[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]
Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].
[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]
[tex]\ln|y| = \frac12 \ln|u| + C[/tex]
[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]
[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]
[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]
Using separation of variables, the solution to the differential equation is:
y = ksqrt(x² + 11)
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
(x² + 11)y' = xy
Applying separation of variables, we have that:
y'/y = x/(x² + 11)
[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]
[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]
[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]
[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]
Hence the solution is:
y = ksqrt(x² + 11)
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4/7=×/6 what does × =
Answer:
3.42857143
Step-by-step explanation:
You multiply 4/7 by 6 to isolate the variable
Answer:
3 3/7 or 24/7
As a decimal: 3.42857143
Step-by-step explanation:
Rewrite the proportion:
4/7 = x/6
Multiply both sides by 6 to isolate x:
(4/7) * 6 = x
Multiply 4 and 6, 7 is multiplied by 1 since 6 = 6/1:
x = 24/7
Rewrite as mixed number:
7 * 3 = 21
24 - 21 = 3
x = 3 3/7
Brainliest, please :) (Hoping to become a genius)
how is the e - lambda figured out as 0.00248?
Answer:
Step-by-step explanation:
e^-6 = 1/e^6 = about 0.00248
Express each of the following in metres.
(iii) 10,000cm
Answer:
100m
Step-by-step explanation:
How much are 10000 centimeters in meters?
10000 centimeters equal 100.0 meters (10000cm = 100.0m). Converting 10000 cm to m is easy. Simply use our calculator above, or apply the formula to change the length 10000 cm to m.
Answer:
100m
Because- 1m=100cm
10m=1000cm
100m=10,000cm
Suppose you want to have $300,000 for retirement in 25 years. Your account earns 8% interest. How much would you need to deposit in the account each month?
Using the future value formula, it is found that you would need to deposit $272.95 in the account each month.
What is the future value formula?It is given by:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
In which:
P is the payment.n is the number of payments.r is the interest rate.For this problem, considering that there are monthly compoundings, the parameters are:
r = 0.08/12 = 0.0067, V(n) = 300000, n = 25 x 12 = 300.
Hence we solve for P to find the monthly payment.
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
[tex]300000 = P\left[\frac{(1.0067)^{299}}{0.0067}\right][/tex]
1099.12P = 300000
P = 300000/1099.12
P = $272.95.
You would need to deposit $272.95 in the account each month.
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Assume the graph is derivative f(x). Answer for f(x)
The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
How to determine the intervals which the original function f(x) concave down?The information that completes the question are added as an attachment
The question requires that we determine the intervals which the original function f(x) concave down
From the attached graph, we have the following turning points
(-2, -4) and (3, 2)
From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)
So, we have:
(-5, 0), (-2, -4), (3, 2) and (5, 0)
Remove the y coordinates
x = -5, -2, 3 and 5
Express as intervals
(-5, -2) and (3, 5)
Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)
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According to a recent poll at a university,70.7 % of high school seniors in a certain region had a driver's license. A sociologist thinks this rate has declined. The sociologist surveys randomly selected high school seniors and finds that have a driver's license. a. Pick the correct null hypothesis. b. Pick the correct alternative hypothesis. c. In this context, what does the symbol p represent?
your mother i swear
Step-by-step explanation:
ask yo mom
Which of the following is NOT part of a scatter plot graph?
Key
Source
Labels
Scale
Which of the following is the scale on each axis based on?
Averages
Percents
Data
Number of data poin
The first step in the area method to estimate the line of best fit is to ______.
divide the data points equally with a horizontal line
draw a line around all of the data points
place two x's centered in each half of the data points
divide the data points equally with a vertical line
The complete statements are:
The Key is not part of a scatter plotThe scale on the axes of a scatter plot is based on the number of data pointsThe first step in the area method to estimate the line of best fit is to draw a line around all of the data pointsHow to complete the statementsPart of a scatter plot
The parts of a scatter plot are
LabelSourceScaleThe dataThe axesThis means that the Key is not part of a scatter plot
The scale on the axes
Here, the scale is determined by the number of data points that exists on the scatter plot
This means that scatter plots that have 10 and 100 data points might not be represented on the same scale
The line of best fit
This is determined by drawing a line through the data points on the scatter plot.
The line is know as the line of best fit
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Tyson uploaded 500 videos to the Internet. Sarita uploaded fewer videos than Tyson. Write an inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded.
→WILL MARK BRAINLIEST←
The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
Inequalitynumber of videos Sarita uploaded = vnumber of videos Tyson uploaded = 500Total videos updated = yInequality for number of videos Sarita uploaded:
v - 500 < y
Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
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Answer:
- v < 500
Step-by-step explanation:
Ronaldo specializes in creating sewing patterns for dresses, and wants to set up his own website to sell electronic copies. He pays $120 for a domain name and web hosting services for the first year. Ronaldo makes $14.25 for each electronic pattern that he sells. How many patterns must he sell to cover the cost of the website for the first year? Round your answer to a whole number.
Answer:
8
Step-by-step explanation:
120/14.25=8.4 rounded off to a whole number is 8
Please Help!!!
Type the correct answer in the box. Use numerals instead of words.
The surface area of a cone is square units. The height of the cone is times greater than the radius.
What is the length of the radius of the cone to the nearest foot?
The radius is about
feet.
Answer:
Step-by-step explanation:
9.05737
The length of the radius of the cone to the nearest foot is 5 feet.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The surface area of a cone is 216π sq units and the height of the cone is (5/3) times of the radius.
∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.
∴ πrl = 216π.
√{(34/9)r³ = 216.
1.9r³ = 216.
r³ = 113.7.
r = 4.8 feet Or 5 feet.
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A large hall has a capacity of 3481 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row
Answer:
59
Step-by-step explanation:
Suppose, The number of seats in each row = z
Number of rows = number of seats in each row 7 z
So, the total plants = z×z=z^2
As per question,
z^2=3481
z=59
So the seats in each row = 59.
