Experimental Probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.
Theoretical probability is equal to the number of favorable outcomes divided by the total number of possible outcomes.
In your case, when tossing a coin 15 times, you get the Pr(Heads)=2/5, this probability is experimental and the result is found by repeating an experiment.
Answer: correct option A.
Jack runs 3 miles in 27 minutes. at this constant rate how long will it take him to run 10 miles answer
A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°.What is the volume of the pyramid?2.4 cm33.6 cm34.8 cm37.2 cm3
Answer:4.8cm^3
Step-by-step explanation:I got it right on edge.
the height h of the equilateral triangle below is given by y= 5 cot theta where theta = 30 degrees
A) 2.9
B)4.3
C)7.1
D)8.7
Simplify the rational expression. state any excluded values. 4x - 4/ x - 1
Answer:
1 and 4 i believe
Step-by-step explanation:
In football, a field goal is worth 3 points, and the extra point after a touchdown is worth 1 point. During the 2006 season, John Kasay, of the Carolina Panthers scored a total of 100 points for his team by making a total of 52 field goals and extra points combined. How many 3 point field goals did he make?
Is my work correct?
Given: ABCD is an inscribed polygon.
Prove: ∠A and ∠C are supplementary angles.
Solution:
Given: A B CD is an inscribed polygon.
To Prove: ∠A and ∠C are supplementary angles.
Proof: Join AC and B D.
Angle in the same segment of a circle are equal.
∠ACB=∠ADB→→AB is a segment.
Also, ∠A B D=∠A CD→→AD is a Segment.
In Δ ABD
∠A+∠ABD+∠ADB=180°→→Angle sum property of triangle.
∠A+∠A CD+ ∠ACB=180°
∠A+∠C=180°
Hence proved, that is, ∠A and ∠C are supplementary angles.
The method Adopted by you
∠1=2 ∠A----(1)
and, ∠2=2 ∠C-------(2)
The theorem which has been used to prove 1 and 2, Angle subtended by an arc at the center is twice the angle subtended by it any point on the circle.→(Inscribed angle theorem)
Also, angle in a complete circle measures 360°.→→Chord arc theorem
∠1+∠2=360°→→Addition Property of Equality
2∠A+2∠C=360°→→[Using 1 and 2, Called Substitution Property]
Dividing both sides by 2→→Division Property of Equality
2∠A+2∠C=360°→→[Using 1 and 2]
∠A+∠C=180°
→→Correct work.
A two-column proof to prove that angles A and C are supplementary angles should be completed as follows;
Statement Reason______________
ABCD is an inscribed polygon Given
mBCD = 2(m∠A) Inscribed Angle Theorem
mDAB = 2(m∠C) Inscribed Angle Theorem
mBCD + mDAB = 360° The sum of arcs that make a circle is 360°
2(m∠A) + 2(m∠C) = 360° Substitution Property
m∠A + m∠C = 180° Division Property of Equality
∠A and∠C are supplementary angles Defintion of supplementary angles.
In Mathematics and Euclidean Geometry, the inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle or the inscribed angle of a circle is equal to half of the central angle of a circle.
Generally speaking, a supplementary angle refers to two angles or arc whose sum is equal to 180 degrees.
Based on the defintion of supplementary angles, we can logically deduce that angle A and angle C are supplementary angles.
What is grater 9km or 145cm
9km is greater than 145cm due to the conversion factor between kilometers and centimeters.
9km is greater than 145cm because when comparing the two, you need to ensure they are in the same unit. To compare, convert km to cm, 9km = 9,000,000cm. So, 9,000,000cm is greater than 145cm.
A cube has a side length of 120 cm, what is its volume in cubic meters? (100 cm = 1 m)
The value of volume of cube is,
⇒ V = 1.728 meter³
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
A cube has a side length of 120 cm.
Since, We know that;
1 m = 100 cm
Hence,
120 cm = 120 / 100 m
= 1.2 m
So, Volume of cube is,
⇒ V = side³
⇒ V = 1.2³
⇒ V = 1.728 meter³
Thus, volume of cube is,
⇒ V = 1.728 meter³
Learn more about the cuboid visit:
https://brainly.com/question/26403859
#SPJ3
how many terms are in the arithmetic sequence shown below?
15, 7, -1, -9...,-225
Final answer:
To determine the number of terms in the given arithmetic sequence, we calculate the common difference and apply the formula for the nth term. With a common difference of -8 and an nth term of -225, we find that there are 31 terms in the sequence.
Explanation:
To find out how many terms are in the arithmetic sequence 15, 7, -1, -9,..., -225, we need to determine the common difference and use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
In this sequence, the common difference d is 7 - 15 = -8. Now we use the formula with an = -225, a1 = 15, and d = -8 to find n.
Plugging these values into the formula, we get:
-225 = 15 + (n - 1)(-8)
-225 = 15 - 8n + 8
-225 = 23 - 8n
-248 = -8n
n = 31
Therefore, there are 31 terms in the arithmetic sequence.
What is the volume of a pyramid with slant height 17 feet and square base with edges of 16 feet?
The volume of the pyramid is 1280 cubic feet.
To find the volume of a pyramid, we can use the formula:
Volume = (1/3) * Base Area * Height
Given that the pyramid has a square base with edges of 16 feet, the base area (A) is calculated as:
[tex]Base Area (A) = side^2\\A = 16^2 = 256 square feet[/tex]
The height of the pyramid can be found using the Pythagorean theorem. The height, slant height, and half the length of a side form a right triangle. The half length of a side is 16/2 = 8 feet. The slant height is 17 feet. So, using the Pythagorean theorem:
[tex]Height^2 + (Half side length)^2 = Slant height^2\\Height^2 + 8^2 = 17^2\\Height^2 + 64 = 289\\Height^2 = 289 - 64\\Height^2 = 225\\Height = \sqrt{225}\\Height = 15 feet\\[/tex]
Now that we have the base area (A = 256 square feet) and the height (h = 15 feet), we can find the volume:
Volume = (1/3) * 256 * 15
Volume = (1/3) * 3840
Volume = 1280 cubic feet
Therefore, the volume of the pyramid is 1280 cubic feet.
To know more about volume:
https://brainly.com/question/15699665
#SPJ2
The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?
A)
v + 2b = 180; 2b - 20 = v
B)
v + 2b = 180; 2b + 20 = v
C)
v - 2b = 180; v + 2b = -20
D)
v - 2b = 180; -2b - 20 = v
The answer to the above question can be explained as under -
We know that, the sum of angles of triangle is 180°.
So, vertex angle plus base angles are equal are equal to 180°.
Let the vertex angle be represented by "v" and base angles be represented by "b".
Thus, v + b + b = 180°
So, v + 2b = 180°
Next, the question says, the vertex angle is 20° less than the sum of base angles.
Thus, 2b - 20° = v
Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v
The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.
The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:
The sum of the angles in a triangle is 180°, leading to the equation: v + 2b = 180.The vertex angle v is 20° less than the sum of the base angles, giving us the equation: 2b - 20 = v.To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.
In a 3-4-5 right triangle which expression would provide the measure of the smallest acute angle
If you buy a computer directly from the manufacturer for $ 2,469 and agree to repay it in 48 equal installments at 2.1 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
Final answer:
The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.
Explanation:
To calculate the monthly payments, you can use the formula for the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^-n)
Where:
P is the monthly paymentr is the monthly interest ratePV is the present value or the loan amountn is the total number of paymentsUsing the given values, we can calculate:
P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)
P ≈ $61.02
Therefore, the monthly payments would be approximately $61.02.
To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:
Total Interest = (P * n) - PV
Total Interest ≈ ($61.02 * 48) - $2469
Total Interest ≈ $1704.96 - $2469
Total Interest ≈ -$764.04
Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.
You hold $25 in a savings account and you deposit an equal amount into your account each week after 5 weeks the account holds $170 write an equation that represents the amount y in dollars of money in the account after x weeks
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+23x-15=0
David, Egil and Frances share money in the ratio 2:7:9. David gets £25. Work out how much Egil and Frances get.
Please help. Needed for tomorrow.
The base edge of the regular triangular pyramid is b=10 cm and altitude of the base hb ≈ 8.66 cm. The slant height of the pyramid is k=8 cm. Find:
Lateral area and Surface area of the pyramid
Answer:
Step-by-step explanation:
It is given that the base edge of the regular triangular pyramid is b=10 cm and altitude of the base h =8.66 cm. The slant height of the pyramid is k=8 cm.
Now, the lateral surface area of the pyramid is given as:
[tex]LSA={\frac{3}{2}}(b)(k)[/tex]
Substituting the given values, we have
[tex]LSA=\frac{3}{2}(10)(8)[/tex]
[tex]LSA=120cm^2[/tex]
Thus, the Lateral surface area of the pyramid is [tex]120cm^2[/tex].
Now, the surface area is given as:
[tex]SA=\frac{1}{2}bh+LSA[/tex]
[tex]SA=\frac{1}{2}bh+120[/tex]
[tex]SA=\frac{1}{2}(10)(8.66)+120[/tex]
[tex]SA=43.3+120[/tex]
[tex]SA=163.3cm^2[/tex]
Thus, the surface area of the pyramid will be [tex]163.3cm^2[/tex].
The Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
What is a pyramid?A polyhedron that has a polygonal base and triangles for sides, is a pyramid.
The lateral area of the pyramid is equal to the area of its three triangular lateral faces is;
[tex]\rm Lateral \ Area=3 \times \dfrac{1}{2}\times b \times k\\\\ Lateral \ Area=3 \times \dfrac{1}{2}\times 10 \times 8\\\\ Lateral \ Area=120[/tex]
The surface area of the pyramid is;
[tex]\rm Surface \ area=\dfrac{1}{2}bh + Lateral \ area\\\\Surface \ area=\dfrac{1}{2}\times 10 \times 8.66 +120\\\\Surface \ area=43.3+120\\\\Surface \ area=163.3 \ cm^3[/tex]
Hence, the Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
To know more about the pyramid click the link given below.
https://brainly.com/question/1318557
#SPJ3
Find the surface area 4cm 5cm 6cm 13cm
For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced
In mathematics, a conic section is
a curve obtained as the intersection of the surface of
a cone with a plane. The four types of conic section are
the hyperbola, the parabola, the circumference and the ellipse.
For the problem we have this parametric
equation:
(1) [tex]\left\{{{x=acost}\atop{y=bsint}}\right[/tex]
From geometry, we know that we can express a
circumference in terms of parameters like this:
(2) [tex]\left \{ {{x=rcost} \atop {y=rsint}}\right[/tex]
being r the radius of the circumference.
On the other hands, we know that a ellipse can
be expressed in terms of parameters like this:
(3) [tex]\left \{ {{x=acost} \atop {y=bsint}}\right[/tex]
Therefore, we will have three answers that are
the cases for the values a and b, namely.
Case 1:
Circumference
To the case of a circumference, the more simple
ordinary equation is given by:
(4) [tex]x^{2} + y^{2} = r^{2}[/tex]
Substituting (1) into (4):
[tex]a^{2}cos^{2}t+b^{2}cos^{2}t=r^{2}[/tex]
But because of the equation (2), necessarily:
[tex]a = b = r[/tex]
Case 2: Ellipse
(focal axis matches the x-axis)
In this case, the simple ordinary equation is
given by:
(5) [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]
being a and b semi-major axis and semi-minor
axis respectively.
Given that a an b are variables of the
parametrization, and a and b are variables of the ellipse as well, to avoid
confusion we will modify the equation (5) like this:
(6) [tex]\frac{x^{2}}{a'^{2}}+\frac{y^{2}}{b'^{2}}=1[/tex]
So, substituting (2) into (6):
[tex]\frac{a^{2}cos^{2}t}{a'^{2}}+\frac{b^{2}cos^{2}t}{b'^{2}}=1[/tex]
Necessarily:
[tex]a=a'[/tex] and [tex]b=b'[/tex]
and given that the focal axis matches the
x-axis, then:
[tex]a>b[/tex]
Case 3: Ellipse
(focal axis matches the y-axis)
In this case, applying the same previous
reasoning, the simple ordinary equation is given by:
(7) [tex]\frac{x^{2} }{b'^{2}}+\frac{y^{2}}{a'^{2}}=1[/tex]
being a' and b' semi-major axis and semi-minor
axis respectively.
So, substituting (2) into (7):
[tex]\frac{a^{2}cos^{2}t}{b'^{2}}+\frac{b^{2}cos^{2}t}{a'^{2}}=1[/tex]
Necessarily:
[tex]a = b'[/tex] and [tex]b = a'[/tex]
and given that the focal axis matches the y-axis, then:
[tex]a<b[/tex]
Finally, the conclusions are:
1. If [tex]a = b[/tex] then a circumference will be traced. (See Figure 1)
2. If [tex]a>b[/tex] then a ellipse will be traced with focal axis matching the x-axis. (See Figure 2)
3. If [tex]a<b[/tex] then a ellipse will be traced with focal axis matching the y-axis. (See Figure 3)
How the values of a and b determine which conic section will be traced was discussed thoroughly.
What is a conic section?A conic section is a curve obtained as the intersection of the surface of a cone with a plane.
The given parametric equations are:
[tex]x=acos t[/tex]
[tex]\frac{x}{a} =cost[/tex]....(1)
[tex]y=bsint[/tex]
[tex]\frac{y}{b} =sint[/tex]....(2)
Adding the squares of (1) and (2)
[tex](\frac{x}{a} )^2+(\frac{y}{b} )^2=cos^{2} t + sin^{2} t[/tex]
We know [tex]cos^{2} t + sin^{2} t=1[/tex]
So, [tex]\frac{x^{2} }{a^{2} } +\frac{y^2}{b^2} =1[/tex]........(3)
If [tex]a=b[/tex], (3) will be reduced into:
[tex]x^{2} +y^{2} =a^{2}[/tex] representing a circle.
If [tex]a > b[/tex], (3) will represent an ellipse with the length of the major axis > length of the minor axis.
if [tex]a < b,[/tex] (3) will represent an ellipse with the length of the major axis < length of the minor axis.
Thus, How the values of a and b determine which conic section will be traced was discussed thoroughly.
To get more about conics visit:
https://brainly.com/question/4017703
My coin collection had 27 coins. They are only quarters and half-dollars. If its worth $10.50. How many are there of each coin?
PLEASE SHOW WORK
On a coordinate plane, a shape is plotted with vertices of (3, 1), (0, 4), (3, 7), and (6, 4). what is the area of the shape if each grid unit equals one centimeter?
A number is chosen at random from 1 to 10. find the probabilty of not selecting a multiple of 3
Let f(x)=-4x+7 and g(x)=10x-6. Find f(g(x))
PLZZZZZZ HELPPPP MEEEE!!!!!!!!
Determine the number of real solutions for each system of equations.
Answer:
First box is 2, second box is 0, and the third box is 1.
Step-by-step explanation:
Geometry Problem (PIC)
A briefcase lock has 3 roating cylinders, each containing 10 digits. How many numerical codes are possible?
Step-by-step explanation:
If the numbers can be repeated, we have such numeric codes:
10 · 10 · 10 = 1,000
If the numbers can not be repeated, then we have such numeric codes:
10 · 9 · 8 = 720
The diagram below shows triangle MNR with ray NM.
-
What is the measure of MRN?
Answer:
The answer is 18
Step-by-step explanation:
Subtract 115 from 180
Add 65 and 97
Subtract 162 from 180
The measure of ∠MRN is 18°
What is sum of angles of a triangle?The sum of angles of a triangle equals the straight angle which is 180°.
According to ques
∠RNM= 97°
∠RMA = 115°
∠RMA +∠RMN = 180° ( sum of angles on straight line )
115° + ∠RMN = 180°
∠RMN = 180° - 115°
∠RMN = 65°
∠RMN + ∠MRN + ∠RNM = 180° ( Sum of angles of triangle )
65° + ∠MRN + 97° = 180°
162° + ∠MRN = 180°
∠MRN = 180° - 162°
∠MRN = 18°
Hence , measure of ∠MRN is 180°
To know more about Sum of angles of triangle click here
https://brainly.com/question/14780489
#SPJ2
On average, Carson spends $2 of his $20 monthly allowance on library fines. What percent of his allowance is spent on library fines?
T (2,10) is the midpoint of CD. The coordinates of D are (2,13). What are the coordinates of C?
A. (2, 16)
B. (2, 20)
C. (2, 11.5)
D. (2, 7)
What is 3X times 1/6X