Answer:
Yes, this definition is valid. A regular polygon is a polygon where all sides are equal in length and all angles between the sides are also equal. Therefore, stating that a regular polygon has all sides of the same length is an accurate description of the defining characteristic of such a shape.
Write a sentence that describes the distribution of the data shown on the dot plot.
OFFERING 50 points HELP PLEASE
There's a picture too
The distribution of the data shown on the dot plot is Skewed.
We have to given that;
The data shown on the dot plot.
Now, We know that;
A graph is symmetric if the left and right side of the graph are mirror images of each other. A graph is skewed if it has more data on one side rather than the other.
Here, it has more data on one side rather than the other.
Hence, the distribution of the data shown on the dot plot is Skewed.
Thus, the distribution of the data shown on the dot plot is Skewed.
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the length of a rectangle is twice of its breadth if its perimeter is 48cm find the dimensions of the rectangle
The dimensions of the rectangle are 8cm by 16cm
How to find the dimensions of the rectangle?Remember that for a rectangle of length L and width W, the perimeter is.
P = 2*(L + W)
Here we know that:
L = 2*W
And that the perimeter is 48cm, so:
48cm = 2*(L + W)
So we have a system of equations:
L = 2*W
48cm = 2*(L + W)
Replacing the first equation in the second one, we will get:
48 cm = 2*(2W + W)
48cm = 6W
48cm/6 = W
8cm = W
And the length is:
L = 2W = 2*8cm = 16cm
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(solve for h) geometry
The value of h in the right triangle is 3 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find h in the right triangle as follows:
Let's find the angle.
cos ∅ = adjacent / hypotenuse
cos ∅ = 6 / 6.5
∅ = cos⁻¹ 0.92307692307
∅ = 22.6208962498
Therefore,
sin 22.62° = h / 7.8
cross multiply
h = 7.8 × sin 22.62°
h = 7.8 × 0.3846175604
h = 3.00001697112
h ≈ 3 units
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A device used to come in four models, each with nine colors to choose from. How many combinations were possible? (Select all that apply. )
n(A ⨯ B) = n(A)n(B)
n(A') = n(S) − n(A)
n(A) = number of elements in A
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
There are 36 possible combinations of the four models and nine colors to choose from.
To find the total number of combinations possible, we can use the formula: n(A ⨯ B) = n(A) x n(B), where n(A) is the number of models and n(B) is the number of colors to choose from.
In this case, there are four models and nine colors to choose from for each model. Therefore, the number of combinations possible would be:
n(A ⨯ B) = 4 x 9 = 36
So there are 36 possible combinations. This can also be calculated by using the formula n(A') = n(S) - n(A), where n(A') is the complement of the set A, n(S) is the total number of possible options, and n(A) is the number of options we are not interested in.
In this case, the complement of the set A (which represents all possible combinations) would be the empty set, since we are interested in all possible combinations. Therefore, n(A') = 0, and n(S) = 36.
We could also use the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B), where n(A ∪ B) represents the total number of options in both set A and set B, n(A) is the number of options in set A, n(B) is the number of options in set B, and n(A ∩ B) is the number of options that are common to both set A and set B.
In this case, we could consider set A to be the four models, and set B to be the nine colors for each model. The intersection of set A and set B would be the combinations where each model is paired with a specific color. Therefore, n(A ∩ B) = 4 x 9 = 36.
Using the formula, we can find the total number of options:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A ∪ B) = 4 + 9 x 4 - 36
n(A ∪ B) = 36
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Baseball Basketball Tennis Soccer
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Answer:
The second answer: histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
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Which is a diagonal through the interior of the cube?
C
G
O AH
EL-
Mark this and return
-
D
H
B
F
Save and Exit
Mext
Subm
AH is the diagonal of the cube through the interior.
Option A is the correct answer.
We have,
A diagonal through the interior of a cube refers to a straight line that passes through the interior of the cube and connects two opposite corners of the cube.
It does not lie on any of the faces of the cube but passes through the center of the cube.
From the cube,
The diagonal through the interior of the cube is:
AH, CF, BG, and DE.
Thus,
AH is the diagonal of the cube through the interior.
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Given two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.
How much more water can the second cone hold than the first cone? Round your
answer to the nearest hundredth.
603.19 in.3
753.98 in.3
1,357.17 in.3
1,960.36 in.3
Answer :
753.98 in³Step-by-step explanation:
According to the question It's given that :
Two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.
Here,
Radius of 1st cone = 8 inchesRadius of 2nd cone = 12 inchesSince, Both the cones are of the same height.
Height of 1st cone = 9 inchesHeight of 2nd cone = 9 inchesFormula of volume of cone = 1/3 πr²h
where,
π = 3.14 r = radius h = heightFor first cone,
[tex] \implies [/tex] Volume = 1/3 × 3.14 × (8)² × 9
[tex] \implies [/tex] 1/3 × 3.14 × 64 × 9
[tex] \implies [/tex] 1/3 × 3.14 × 576
[tex] \implies [/tex] 1/3 × 1808.64
[tex] \implies [/tex] 602.88 in³
For second cone,
[tex] \implies [/tex] Volume = 1/3 × 3.14 × (12)² × 9
[tex] \implies [/tex] 1/3 × 3.14 × 144 × 9
[tex] \implies [/tex] 1/3 × 3.14 × 1296
[tex] \implies [/tex] 1/3 × 4069.44
[tex] \implies [/tex] 1356.48 in³
Now, How much more water can the second cone hold than the first cone?
Volume of 2nd cone - Volume of 1st cone
[tex] \implies [/tex] 1356.48 - 602.88
[tex] \implies [/tex] 753 (approximately)
Therefore, 753.98 in³ is the answer .
So-hee and Ethan are at the arcade in the amusement park. They play a game in which they earn points by collecting coins and gems. So-hee collects 3 coins and 5 gems for a total of 70 points. Ethan collects 6 coins and 2 gems for a total of 52 points. How many points is 1 coin worth? How many points is 1 gem worth?
please help meee
The answer of the given question based on the equation problem is , one coin is worth 5 points and one gem is worth 11 points.
What is Equation?An equation is the mathematical statement that shows equality between the two expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain one or more variables, constants, mathematical operations, and functions.
Let's denote the value of one coin by x and the value of one gem by y. We can set up two equations based on the given information:
3x + 5y = 70 (equation 1)
6x + 2y = 52 (equation 2)
We can use these equations to solve for x and y. One way to do this is to multiply equation 2 by 5 and subtract it from equation 1 multiplied by 2:
6x + 10y = 140 (equation 1 multiplied by 2)
-30x - 10y = -260 (equation 2 multiplied by 5, with signs flipped)
-24x = -120
x = 5
Now that we know that one coin is worth 5 points, we can substitute this value into either of the original equations to solve for y. Let's use equation 1:
3(5) + 5y = 70
15 + 5y = 70
5y = 55
y = 11
Therefore, one gem is worth 11 points.
In summary, one coin is worth 5 points and one gem is worth 11 points.
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The volume of the prism is 90 cubic meters. Find the value of x.
x=
Answer: 5 meters
Step-by-step explanation:
volume of a rectangular prism: V=whl
90=6*h*3
h=90/(6*3)
h=90/18
h=5 meters
What is the radius of a sphere with a
volume of 384 ft3, to the nearest tenth of
a foot?
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=384 \end{cases}\implies 384=\cfrac{4\pi r^3}{3}\implies 384(3)=4\pi r^3 \\\\\\ \cfrac{384(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{384(3)}{4\pi }}=r\implies 4.5\approx r[/tex]
Answer:
[tex] \frac{4}{3} \pi {r}^{3} = 384[/tex]
[tex]r = 4.5 [/tex]
So the radius of this sphere is approximately 4.5 feet.
Determine if line AB is tangent to the circle.
10)
12
9
5
B
The value of r not equal to the radius of the circle, AB is not tangent to the circle.
What is tangent to the circle?A tangent to a circle is a straight line that precisely crosses the circle at the location where the tangency occurs. The tangent line must be perpendicular to the circle's radius in order to be at the point of tangency.
The circle's radius and the tangent line are related because at the point of tangency, the tangent line is always perpendicular to the radius. This indicates that at the point of tangency, the radius and tangent line make a right angle. In addition, the radius of the circle is equal to the length of the segment connecting the point of tangency and the centre of the circle. Tangent to circle difficulties can be resolved using these relationships.
In the given figure for AB to be the tangent we must determine whether the radius is perpendicular and has the same value of 9.
For the given triangle assume angle A is at 90 degree.
Thus,
12² + r² = 14²
144 + r² = 196
r² = 196 - 144
r = √52 = 7.2
Here, the given radius 9 is not equal to the calculated radius.
Hence, the value of r not equal to the radius of the circle, AB is not tangent to the circle.
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x^2+12x+35
work required
The solution or roots of this quadratic function are x = -7 and x = -5.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
x² + 12x + 35 = 0
x² + 7x + 5x + 35 = 0
x(x + 7) + 5(x + 7) = 0
(x + 7)(x + 5) = 0
x = -7 or x = -5.
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the volume of a large aquarium is 625 ft³ . It is 16[tex]\frac{2}{3}[/tex] wide and 3[tex]\frac{1}{3}[/tex] high. What is the length of the aquarium.
Length of the aquarium is 11.25 ft
We have,
Volume of the aquarium = 625 ft³
given by
Volume = length × width × height.
Width = 16 2/3 ft
= 50/3
and Height = 3 1/3 ft
= 10/3 ft
Length = Volume/Width × Height
= 625/ 50/3 × 10/3
= 625/ 500/9
= 11.25 ft
Hence, Length of the aquarium is 11.25 ft
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two sides of a right triangle measure 8 inches and 9 inches find the two possible lengths of the third side
c =
a
sin(α)
= 51.13963
b = √c2 - a2
= √51.1396257719972 - 82
= √2551.2613240999
= 50.51001
∠β = 90° - ∠α
= 81° = 1.41372 rad = 9/20π
area =
a × b
2
=
8 × 50.5100121174
2
= 202.04005
perimeter = a + b + c
= 8 + 50.5100121174 + 51.139625771997
= 109.64964
inradius =
a × b
a + b + c
=
404.0800969392
109.6496378894
= 3.68519
circumradius =
c
2
=
51.139625771997
2
= 25.56981
Find and use the x and y intercepts to draw the graphs and find the solution for the system of equations. Show your work to find the intercepts and the solution.
3x - 3y + 15 = 0
4x + 2y = 16
The solution for the given linear-pair of equations is (1,6) , and it has one number of solutions. The intercepts on x & y axis to plot the graph
i)3x - 3y + 15 = 0 : Point-1: (0,5) & Point-2:(-5,0)
ii)4x + 2y = 16 :Point-1:(0,8) & Point-2: (4,0)
What is linear-pair?
It is a system of continuous lines that looks like straight lines. The linear equation with two variables has a maximum degree of one. Ax+by+c=0 is the general form of a two-variable linear equation. A consistent pair of linear equations is a pair of linear equations in two variables that have a solution. To a pair of equivalent linear equations, there are countless possible common solutions. Such a pair is a dependent set of two-variable linear equations.
Given linear-pair :
3x - 3y + 15 = 0
3x - 3y = -15 ---- eqn-(i)
4x + 2y = 16 -----eqn-(ii)
Using elimination method: to equate the coefficient of x in both equations,
Multiplying equation -(i) by 4
(3x - 3y = -15 ) ⇒4(3x - 3y) = 4(-15)
⇒12x -12y = -60 ------eqn(iii)
Multiplying equation -(ii) by 3
4x + 2y = 16 ⇒ 3(4x + 2y = 16)
⇒3(4x + 2y ) = 3(16)
⇒12x + 6y = 48 ------eqn(iv)
Subtracting eqn-iv from eqn-iii
12x -12y - (12x + 6y) = -60 - 48
12x - 12y - 12x - 6y = -108
-12y - 6y = -108
-18y = -108
18y = 108
y = 6
Substituting y=6 in eqn-(i) 3x - 3y = -15
3x - 3(6) = -15
3x - 18 = -15
3x = -15 + 18
3x = 3
x = 1
The solution for the given pair of equations is (1,6)
Points to plot graph:
3x - 3y = -15 ---- eqn-(i)
Taking x=0,
3(0) - 3y = -15
3y=15
y=5
Point-1: (0,5)
Taking y=0;
3x - 3(0) = -15
3x = -15
x = -5
Point-2:(-5,0)
4x + 2y = 16 -----eqn-(ii)
Taking x=0
4(0) +2y=16
2y=16
y=8
Point-1:(0,8)
Taking y=0
4x + 2(0) = 16
4x = 16
x = 4
Point-2: (4,0)
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refer to attachment for graph.
Please help me with this homework
Answer:
36 cm²
Step-by-step explanation:
Area of a triangle = 1/2bh = 1/2(9)(8) = 36
A volume of a cone is 37.7 cubic inches, and its height is 4 inches. Find the diameter of the base of the cone.
Answer:
Approximately 5.988 inches
Step-by-Step Explanation:
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius of the base, h is the height, and π is the mathematical constant pi.
We are given that the volume of the cone is 37.7 cubic inches, and the height is 4 inches. We can plug these values into the formula and solve for the radius:
37.7 = (1/3)πr^2(4)
37.7 = (4/3)πr^2
r^2 = (37.7 x 3) / (4 x π)
r^2 = 8.9717
r ≈ 2.994 inches
Now that we know the radius of the base, we can find the diameter by doubling the radius:
d = 2r ≈ 5.988 inches
Therefore, the diameter of the base of the cone is approximately 5.988 inches.
Here's a box plot that summarizes the masses of Suika's watermelons. A horizontal boxplot is plotted along a horizontal axis marked from 2 to 10, in increments of 0. 5, labeled Mass (kilograms). A left whisker extends from 4. 5 to 6. The box extends from 6 to 8. 5 and is divided into 2 parts by a vertical line segment at 7. The right whisker extends from 8. 5 to 10. All values estimated. A horizontal boxplot is plotted along a horizontal axis marked from 2 to 10, in increments of 0. 5, labeled Mass (kilograms). A left whisker extends from 4. 5 to 6. The box extends from 6 to 8. 5 and is divided into 2 parts by a vertical line segment at 7. The right whisker extends from 8. 5 to 10. All values estimated. Find the interquartile range (IQR) of the data
The interquartile range (IQR) of the data is, 1.5, 2.5, 1.5 kilograms under the condition that a left whisker extends from 4. 5 to 6. The box extends from 6 to 8. 5 and is divided into 2 parts by a vertical line segment at 7.
Interquartile range (IQR) is the measurement of statistical dispersion based on splitting data and information, into four parts called quartiles.
To find the interquartile range (IQR), we have to evaluate the difference between the upper quartile (Q3) and lower quartile (Q1)
For the following case there are 3 cases, for the first case left whisker extends from 4. 5 to 6, for the second case it is given that the box extends from 6 to 8.5 and is divided into two parts by a vertical line segment at 7. and for the third case right whisker extends from 8. 5 to 10.
Therefore,
Q1 = 4.5
Q2 = 6
Q3 = 8.5
Q4 = 10
Then the evaluated IQR for first case is
Q2 - Q1
= 6 - 4.5
= 1.5 kilograms
for second case is
Q3 - Q2
= 8.5 - 6
= 2.5 kilograms
finally for the third case
Q4 - Q3
= 10 - 8.5
= 1.5 kilograms
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The complete question is
Here's a box plot that summarizes the masses of Suika's watermelons. A horizontal boxplot is plotted along a horizontal axis marked from 2 to 10, in increments of 0. 5, labeled Mass (kilograms). A left whisker extends from 4. 5 to 6. The box extends from 6 to 8. 5 and is divided into 2 parts by a vertical line segment at 7. The right whisker extends from 8. 5 to 10. All values estimated. Find the interquartile range (IQR) of the data
Rewrite the expression in the form a^na n a, start superscript, n, end superscript. \dfrac{1}{a^{^{\scriptsize -\dfrac56}}}= a − 6 5 1 =start fraction, 1, divided by, a, start superscript, start superscript, minus, start fraction, 5, divided by, 6, end fraction, end superscript, end superscript, end fraction, equals
The given expression is needed to be written in the the form a^n.
The required expression is a ^ -5/4
We have,
The given expression is
1/ a^5/4
We know,
the identity that a negative exponent means the reciprocal.
1/ a^b = a^-b
So, the given expression is
1/ a^5/4
=a ^-5/4
The required expression is a ^-5/4
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Find an equation in slope-intercept form for the line passing through each pair of points: (-4, 4), (-5, -3)
Answer:
y = 7x + 32
Step-by-step explanation:
The general equation of the slope-intercept form is
y = mx + b, where x and y are any point on the linem is the slope (change in y / change in x) and b is the y-intercept (point at which the line intersects the y-axis)Given two points which line on the same line, we can find the slope, m, using the slope formula, which is
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex],
where x1 and x2 are one of the points on the line and y1 and y2 are the other point.If we allow (-4, 4) to be our x1 and x2 point and (-5, -3) to be our y1 and y2 point, we can find the slope by plugging the points into the slope formula:
[tex]m=\frac{-3-4}{-5-(-4)}\\ \\m=\frac{-7}{-5+4}\\ \\m=\frac{-7}{-1}\\ \\m=7[/tex]
Since we now know the slope, we can b, the y-intercept by plugging in any of the two points for x and y and the slope (7) and solving for b:
Let's try the first point (-4, 4):
4 = 7(-4) + b
4 = -28 + b
32 = b
Thus, the equation of the line passing through the points (-4, 4) and (-5, -3) in slope-intercept form is y = 7x + 32
I do not understand what do I have to do here
Step-by-step explanation:
I think u have to find the degrees of x
The value of x in the figure is,
⇒ x = 65 degree
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Now, We can formulate;
The value of third angle in first triangle is,
180 - (50 + 62)
180 - 112
68 degree
And, The value of third angle in second triangle is,
180 - (53 + 80)
180 - 133
47 degree
Thus, The value of third angle in mid triangle is,
180 - (47 + 68)
180 - 115
65 degree
So, By definition of vertically opposite angle is,
⇒ x = 65 degree
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A spherical hot-air balloon has a diameter of 55 feet . When the balloon is inflated , the radius increases at a rate of 1.5 feet per minute .
The amount of time it would take to inflate the balloon to two-thirds of its maximum volume is 16 minutes.
How to calculate the volume of a sphere?In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):
Volume of a sphere = 4/3 × πr³
Where:
r represents the radius.
Note: Radius = diameter/2 = 55/2 = 27.5 feet.
For maximum volume, we have the following:
V ∝ R³
2/3V = v
2/3R³ = r³
r = 27.5 × ∛(2/3)
Radius, r = 24
Since the radius of this spherical hot-air balloon increases at a rate of 1.5 feet per minute, time to reach a radius of 24 feet can be calculated as follows;
Time = 24/1.5
Time = 16 minutes
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Complete Question:
A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to Two-thirds of its maximum volume? Use π = 3.14 and V = four-thirds pi r cubed.
Why does using the formula length × width to find the area of a rectangle give us the same answer as counting square units?
Because area calculations always involve multiplying two lengths somewhere in the formula. The lengths must be in the same units and that gives length times length or length^2 units.
A poll conducted by the UC Berkeley Institute of Governmental Studies in 2019 found that 51.7% of 4527 respondents said they considered moving out of the state. Complete parts a through c. a) Compute a 90% confidence interval for the proportion of all Californians who considered moving out of state. b) Int repret your interval in this context. Select the correct answer below and fill in the answer baxes to complete your choice: (Type integers or decimals rounded to one decimal place as needed.) A. One is 90% conficent that the probability a randomly sampled Casfornian who considered moving out of the state is between and B. One is 90% confident that the true proportion of Californans who considered moving out of the slate is between y and C. The percent of Calilomians who considered moving out of the state is between % and D. There is a 90se chance, based on this sample, that betreen … and % of Californians considered moving out of state c) Since high cost of housing has often been cited as a reason why residents move out, suppose thę state government wil consider investing in new aftordable housing initiatives if it can be reasonably sure that more than 50% of Californians would consider moving. What should the state government conclude, based on the data? Since the contidence interval _____50\%, the state government____consider investing in new atordabie housing initiatives.
Therefore, the state government should consider investing in new affordable housing initiatives.
a) To compute the 90% confidence interval, we can use the formula:
CI = p ± z*(√(p(1-p))/n)
where p is the sample proportion, z is the z-score corresponding to a 90% confidence level (which is 1.645), and n is the sample size.
Plugging in the values, we get:
CI = 0.517 ± 1.645*(√((0.517)(1-0.517))/4527)
CI = 0.505 to 0.529 (rounded to three decimal places)
b) The 90% confidence interval tells us that we are 90% confident that the true proportion of Californians who considered moving out of the state is between 0.505 and 0.529.
c) Since the confidence interval does not include the value of 0.5, which is the null hypothesis value, we can conclude that there is evidence to suggest that more than 50% of Californians would consider moving out of state due to high cost of housing.
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The function f(x) = 1.62x² models
the cost of a square carpet, where
x is the length in feet. Find the
average rate of change for f, to the
nearest tenth, over the interval
15 ≤ x ≤ 25. Explain your steps.
Answer:
Step-by-step explanation:
use integration
The shape shown is a right-angled triangle together with two-quarter circles of radius r cm.
a) Find the formulae for the area A and the perimeter P of the shape.
Can someone show me how to find the area and perimeter of the shape and explain why its the formulae, so I can understand please.
The formulas for the area and perimeter of the given shape are:
A = 1/2 x b x h + 1/2 x πr²
P = b + h + 1/2r
We
To find the area and perimeter of the given shape, we need to break it down into its constituent parts:
The right-angled triangle and the two-quarter circles.
Let's label the sides of the right-angled triangle as follows:
The side adjacent to the right angle (the base) has length b.
The side opposite the right angle (the height) has length h.
Now, let's find the area of the triangle.
The formula for the area of a triangle is:
A = 1/2 x base x height
So, in this case, we have:
A (triangle) = 1/2 x b x h
Next, let's find the perimeter of the shape.
The perimeter is the total length of the boundary of the shape.
To find the perimeter, we need to add up the lengths of all the sides of the triangle and the two-quarter circles.
The base and height of the triangle are already labeled as b and h, respectively.
The two-quarter circles each have a radius of r.
The formula for the circumference of a circle is:
C = 2πr
But since we only have quarter circles, we need to divide the circumference by 4:
C (quarter circle) = 1/4 x 2πr = 1/2πr
Therefore, the length of each quarter circle is:
L (quarter circle) = 1/2πr x π/2 = 1/4r
So the total perimeter of the shape is:
P = b + h + 2 L (quarter circle) = b + h + 1/2r
Now, to find the area of the entire shape, we need to add the area of the triangle and the two-quarter circles.
The area of each quarter circle is:
A (quarter circle) = 1/4 x πr²
So the total area of the two-quarter circles is:
A (circles) = 2 A (quarter circle) = 1/2 x πr²
Therefore, the total area of the shape is:
A = A(triangle) + A(circles) = 1/2 x b x h + 1/2 x πr²
Thus,
The formulas for the area and perimeter of the given shape are:
A = 1/2 x b x h + 1/2 x πr²
P = b + h + 1/2r
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You are surveying students to find out whir opinion of the quality of food served in the school cafeteria. You decide to poll only those students who buy hot lunch on a particular day. Is your sample random? Explain.
Answer:
The sample is not random because he only poll the person that bought a hot lunch on a particular day and not random people so the sample is not random.
If one dozen avocados the same size weigh 7. 2 lb then what does one avocado weigh?
If one dozen avocados the same size weigh 7. 2 lb then the weight of one avocado is 0.6lb.
Weight is a measurement of the force of gravity acting on an item. It is the result of the object's mass and acceleration brought on by gravity. Usually, weight is expressed in units like pounds (lb) or kilograms (kg). Weight may be defined more simply as the amount of pressure an object applies to a scale when it is placed there. The force produced by a person's body on a scale as a result of gravity, for instance, is equal to 150 lb if they weigh 150 lb.
One dozen avocados equals 12 avocados. If one dozen avocados weigh 7.2 lb, then we can find the weight of one avocado by dividing the total weight (7.2 lb) by the number of avocados (12):
Weight of one avocado = Total weight / Number of avocados
Weight of one avocado = 7.2 lb / 12
Weight of one avocado = 0.6 lb
Therefore, the weight of one avocado is 0.6lb.
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Is brainly freee for students the whole time they use it?
Answer:
there is brainly free and other options if you do not want to watch ads. but it is free if you do not want to upgrade.
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. The relationship between the elapsed time, t, in days, since an ocean sunfish is born, and its mass, M (t), in milligrams, is modeled by the following function: M(t) = (1.35)^t/6 +5 Complete the following sentence about the daily percent change in the mass of the sunfish. Round your answer to the nearest percent. Every day, there is a % addition to/ removal from the mass of the sunfish.
The sunfish adds around 2% to its present mass each day, which is the daily percent change in mass.
Based on the provided model, the daily percent change in the mass of the ocean sunfish is an addition of around 2% to its mass. By calculating the derivative of the function M(t) with respect to t, the following may be calculated:
[tex]M'(t) = \frac{ln(1.35)}6 * (1.35)^t[/tex]
This indicates that the constant factor is ln(1.35)/6, or around 0.02, and therefore the rate of change of the sunfish's mass with respect to time is proportionate to the sunfish's present mass.
As a result, the sunfish's daily percent change in mass is around a 2% increase over its present mass.
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