Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability of selecting an orange marble is 0.33.
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads is 49%.
The theoretical probability of a fair coin landing on heads is 0.5.
How to calculate the probability?It should be noted that a coin has a head and tail. Therefore, the probability of getting either will be:
= 1/2 = 0.5
Therefore, Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The statement that compares the theoretical and experimental probability of landing on orange is that the theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability will be:
= 4/(6+3+7+4)
= 4/20 = 1/5
Based on the given frequency, the experimental probability of selecting an orange marble will be:
= 5/(4+6+5)
= 5/15
= 0.33
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads will be:
= 98/(98 + 102)
= 98/200
= 49%
The theoretical probability of a fair coin landing on heads will be:
= 1/2 = 0.5
Flip a coin 14 times and record the frequency of each outcome gives:
Head, Tail, Head, Head, Head, Tail, Tail, Head, Tail, Tail, Tail, Tail, Head, Head. The theoretical and experimental probability are 0.5.
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Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Answer:
9/41
Step-by-step explanation:
Cosine represents adjacent / hypotenuse.
When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).
9/41 is already simplified.
please explain how to do this
The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.
Find the length of the arc AB:Formula used for finding arc length:
If the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,⇒ L = 2 π r (θ/360°)
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
If the angle made by the arc at the center of the circle is in radians, the formula to find the length of the arc is,⇒ L = r × θ
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
Here in the question it is given that,
r = 27 units
θ = 20°
Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,
⇒ L = 2 π r (θ/360°)
L = 2 π (27) (20°/360°)
L = π (27) (20°/180°)
⇒ L = 3 π
Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.
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Find the area of the shape
3.14 for pi
[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]
[tex]a = 78.5[/tex]
Solve each of the following systems of equation.
(b.) 3x + y = 1
6x^2 - y^2 - 2y - 3 = 0
(a) The solution to the given system of equations is x = 1, y = 2, z = -3
(b) The solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
x + y + z = 0 ----------- (1)
2x + z = -1 ----------- (2)
x - y - z = 2 ----------- (3)
Add equations (1) and (3)
x + y + z = 0 ----------- (1)
x - y - z = 2 ----------- (3)
__________
2x = 2
x = 2/2
x = 1
Substitute the value of x into equation (2) to find z
2x + z = -1
2(1) + z = -1
2 + z = -1
z = -1 -2
z = -3
Substitute the values of x and z into equation (1) to determine the value of y
x + y + z = 0
1 + y + -3 = 0
1 + y - 3 = 0
y = 3 -1
y = 2
Hence, the solution to the given system of equations is x = 1, y = 2, z = -3
b.
The given system of equations is
3x + y = 1 --------- (1)
6x² - y² - 2y -3 = 0 --------- (2)
From equation (1)
3x + y = 1
y = 1 - 3x -------- (3)
Substitute into equation (2)
6x² - y² - 2y -3 = 0
6x² - (1 -3x)² -2(1 -3x) -3 = 0
6x² - (1 -3x)(1 -3x) -2 + 6x -3 = 0
6x² - (1 -3x -3x +9x²) -2 +6x -3 = 0
6x² - (1 -6x + 9x²) +6x -5 = 0
6x² -1 +6x -9x² +6x -5 = 0
-3x² +12x -6 = 0
3x² -12x +6 = 0
x² -4x + 2 = 0
Solve the quadratic equation by the formula method,
x = [-b±√(b²-4ac)]/2a
a = 1, b = -4 and c = 2
Thus,
x = [-(-4)±√((-4)²-4(1)(2))]/2(1)
x = [4±√(16-8)]/2
x = (4±√8)/2
x = (4+√8)/2 OR (4 - √8)/2
x = 3.4142 OR x = 0.5858
Substitute the values of x into equation (3)
y = 1 - 3x
When x = 3.4142
y = 1 - 3(3.4142)
y = -9.2426
When x = 0.5858
y = 1 - 3(0.5858)
y = -0.7574
Hence, the solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
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bennett was visiting five cities that lie on a coordinate grid at A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1). What is the midpoint between A and E
The midpoint between A and E is (0,1)
How to determine the midpoint between A and E?The coordinates of the cities are given as:
A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).
From the above, we have:
A = (-2,3)
E = (2,-1)
The midpoint between A and E is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
Substitute the known values in the above equation
Midpoint = 1/2 * (-2 + 2, 3 - 1)
This gives
Midpoint = 1/2 * (0, 2)
Evaluate the product
Midpoint = (0, 1)
Hence, the midpoint between A and E is (0,1)
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How many different integers are there such that the square of the square of the integer is a two-digit integer
The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.
How many integers satisfy the given condition?According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.
The numbers in discuss, x must satisfy;
x⁴ < 99.
The numbers in this regard are therefore, -2, -3, 2, 3.
Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.
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There are 12 marbles in a box. 8 are purple, and 4 are green. What is the probability of picking a purple marble and then a green marble, without replacing the first marble?
Answer: 8/33
Step-by-step explanation:
So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box
Now the probability of picking a green marble without placing the first marble back is 4/11
So the probability of doing both is 8/12 x 4/11 = 8/33
(a 2n - a n - 6) (a n + 8)
If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center are the foci located? a. 4 units b. 2 units c. units d. units e. 5 units
The distance from the center to where the foci are located exists 8 units.
How to determine the distance from the center?The formula associated with the focus of an ellipse exists given as;
c² = a² − b²
Where c exists the distance from the focus to the center.
a exists the distance from the center to a vertex,
the major axis exists 10 units.
b exists the distance from the center to a co-vertex, the minor axis exists 6 units
c² = a² − b²
c² = 10² - 6²
c² = 100 - 36
c² = 64
[tex]c = \sqrt{64}[/tex]
c = 8
Therefore, the distance from the center to where the foci are located exists 8 units.
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The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.03) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2012?
Answer:
343.608 million to nearest thousand.
Step-by-step explanation:
Projected annual percent of growth = 3% ( from the values 1.03 in the equation)
Worth is 2012 ( 12 years after 2000) is:
241(1.03)^12
= 343.608 million
(-2a²) (36³)
What’s do I simply using the properties of exponents
Answer:
-93312a²
Step-by-step explanation:
1) Simplify 36³ to 46656.
-2a² × 46656
2) Simplify 2a² × 46656 to 93312a².
-93312a²
Find the total surface area of the square pyramid in the figure.
each base side is 8 yds, vertex to centr of base is 3 yds, vertex to center of one side of base is 5 yds. 9Cannot send picture, only link)
The total surface area of the square pyramid (SA) = 144 yd².
What is a Square Pyramid?A square pyramid is a solid shape that has a square base and four rectangular lateral faces.
How to Find the Total Surface Area of a Square Pyramid?The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:
Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:
Area of base = APerimeter of base = PSlant height of pyramid = lGiven the following:
Area of base (A) = 8² = 64 yd²
Perimeter of base (P) = 4(8) = 32 yds
Slant height of pyramid (l) = 5 yds
Plug in the values
Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)
Total surface area of a square pyramid (SA) = 64 + 80
Total surface area of a square pyramid (SA) = 144 yd².
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An interior designer is sketching a rough outline of a
corner room of an office building, as shown above.
If the area of the triangular-shaped room is 1,728
square feet, what is the value of sin(x)?
The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The area of triangle A = 1728 square feet
The base length of the triangle b = 72 feet
Let h be the height of the triangle
Area = (1/2)b×h
1728 = (1/2)72×h
h = 48 feet
Half of the 72 is 72/2 = 36
As we know,
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Applying trigonometric ratio:
tan(x) = 48/36
tan(x) = 1.333
x = 53.13 degrees
Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
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what is 3x+4=8 please answer quick
Hello,
[tex]3x + 4 = 8[/tex]
[tex]3x + 4 - 4 = 8 - 4[/tex]
[tex]3x = 4[/tex]
[tex] \frac{3x}{3 } = \frac{4}{3} [/tex]
[tex]x = \frac{4}{3} [/tex]
Determine which of the following graphs does not represent a function.
Answer:
Graph b.
Step-by-step explanation:
B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.
help math related pleaseee
[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]
[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]
If a girl lifts a load of 60N to a height of 3m, find work.
Let the mass of the object exists at 60 N and the height exists at 3m then work
exists in 1764.
What is work?
The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.
Work can be estimated by multiplying Force and Distance in the direction of force as follows.
W = F × d. Unit.
Given data:
m = mass of the object = 60 N
h = height = 3 m
Work = Fh = mgh
g = gravity = 9.8 m/s²
work = Fh = mgh
[tex]= 60*3*9.8[/tex]
= 1764
Therefore, the work exists in 1764.
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If tan A 3/4 find the value of: sin2A
Answer:
24/25
Step-by-step explanation:
use tan^-1 to find the angle
tan^-1(3/4)=36.86989765°
A =36.86989765°
2A= 2×36.86989765
=73.73979529°
sin2A>>>>sin(73.73979529°)
=24/25 or 0.96
Answer:
sin2A = [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
using the identity
sin2A = 2sinAcosA
given
tan2A = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
then this is a 3- 4- 5 right triangle with
hypotenuse = 5, opposite = 3 , adjacent = 4 , then
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] and cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
Then
sin2A = 2 × [tex]\frac{3}{5}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{2(3)(4)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]
What is the point-slope form of a line with slope 4/5 that contains the point (-2,1)?
Answer: [tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]
Step-by-step explanation:
Given the requirement for function
Point-slope form : y - y₁ = m (x - x₁)
m = slope(x₁, y₁) = Any points on the lineGiven information
m = 4/5
Point = (x₁, y₁) = (-2, 1)
Substitute values into the function form
y - y₁ = m (x - x₁)
y - (1) = (4/5) (x - (-2))
Simplify the function
[tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
If f(x) = 5x, what is f¹(x)?
Answer:
C
Step-by-step explanation:
For any function x, inverse will = 1/x. so the answer is C
Answer:
C. [tex]f^{-1}(x) = \frac{1}{5} x[/tex]
Step-by-step explanation:
The question is asking to find [tex]f^{-1}(x)[/tex] of f(x)=5x, which is the same as finding the inverse of the function.
To find the inverse of a function, we first need to replace f(x) with y.
The function will therefore be:
y = 5x
Now, we solve the equation for x.
So divide both sides by 5.
y = 5x
÷5 ÷5
_________
[tex]\frac{y}{5} = x[/tex]
Now, we replace x with y and y with x.
[tex]\frac{x}{5} = y[/tex]
Finally, we replace y with [tex]f^{-1}(x)[/tex].
[tex]\frac{x}{5} = f^{-1}(x)[/tex]
We can re-write this though, to make it easier to read.
We can write [tex]f^{-1}(x)[/tex] first, and rewrite [tex]\frac{x}{5}[/tex] as [tex]\frac{1}{5}x[/tex].
[tex]f^{-1}(x) = \frac{1}{5} x[/tex]
Therefore, the answer is C.
A satellite orbits the earth at a height of 343 kilometers. if the satellite makes 8 revolutions around the earth, how many kilometers does it travel? (earth's diameter is 6371 kilometers.) use 3.14 as the approximate value of pi.
The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
How many kilometers does the satellite make 8 revolutions around the earth?
The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.
The satellite rotates around the earth to form a circle,
diameter of circle = Diameter of earth + 2(Height)
d = 6714 + 2(343)
d = 6714+ 686
d = 7057
Perimeter = πd
Perimeter = 3.14 (7057)
Perimeter = 22158.98
Total Revolution exists 8
Therefore, 8πd = 8(22158.98)
= 177272 kilometers.
Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
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Find the value of each variable.
one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°
So in this case to get x we= 180°-105°=285°
therefore x is 285°
Based on these segment lengths, which group of segments cannot form a triangle? a. 12, 7, 8 b. 8, 7, 13 c. 1, 2, 3 d. 80, 140, 70
(D) 80°, 140°, and 70° group of segments cannot form a triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC represents a triangle with vertices A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. In other words, the triangle is contained in just one plane, and every triangle is contained in some plane. There is just one plane and all triangles are enclosed in it if the entire geometry is merely the Euclidean plane; but, in higher-dimensional Euclidean spaces, this is no longer true.To find which group of segments cannot form a triangle:
80°, 140°, and 70° cannot form a triangle because the sum of the three angles is 290°, whereas the sum of the angles in a triangle is 180°.Therefore, (D) 80°, 140°, and 70° group of segments cannot form a triangle.
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Answer:
80, 140, 70
Step-by-step explanation:
Draw an area model to represent 4x^2+12x+9 = (2x+3)^2. Label the length and width of the whole square and label each individual small square and rectangle.
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
What are area models?Area models are shapes used to model or illustrate products, multiplications, divisions and quotients
How to draw the area model?The equation is given as:
4x^2+12x+9 = (2x+3)^2
Express (2x+3)^2 as the product of (2x+3) and (2x+3)
4x^2+12x+9 = (2x+3) * (2x+3)
The above means that the area model is a square.
So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9
See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2
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Can someone help me with this? I cannot figure it out
Answer:
Step-by-step explanation:
To graph by hand I would first convert both equations into y=mx+b.
We start with:
[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]
Solve for y for 2x-2y=4
[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]
Solve for y for x+2y=8
[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]
Giving the new but equal system of equations:
[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]
From this point on you can graph the two functions to find where the two lines intersect, thats your solution.
I've gone ahead and graphed it on desmos for you
Which of the
following satisfies
this graph?
Answer:
C
Step-by-step explanation:
y is greater or equal to 0
x is also greater or equal to 0
you can see that only one answer choice can be the answer
the line is x-y = 2
the upper side is x-y <= 2
proves that c is the answer
x-y ≤ 2
y ≥ 0
x ≥ 0 satisfies this graph. Thus option C is correct.
What is a graph?A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.
When y is bigger than 0 and x is also.
The equation is 2x-y.
x-y ≤ 2 on the upper side of the graph is represented in this same way.
x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.
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I need help here’s a picture can somone explain what I need to do??
The total area of the composite figure is 176 ft
How to find the area of a composite figure?The area of a composite figure can be found as follows;
Therefore,
Total area = area of rectangle + area of triangle
area of rectangle = lw
where
l = lengthw = widthTherefore,
area of a rectangle = 16 × 8
area of a rectangle = 128 ft²
area of triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of triangle = 1 / 2 × 12 × 8
area of triangle = 48 ft²
Total area of the composite figure = 48 + 128 = 176 ft
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Sea World's dining card offers a choice of a three main entrees, a choice from five sides and a choice from four desserts. How many different meals can be selected?
Part III: Is x+1 a factor of the polynomial 12x+5x+3x²-5? Explain your answer. (2 points)
Answer:
no
Step-by-step explanation:
So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.
x + 1 = 0
x = -1
The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.
Original Equation:
[tex]12x+5x+3x^2-5[/tex]
Plug in -1 as x
[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]
Multiply values
[tex]-12-5+3(1)-5[/tex]
Simplify:
[tex]-17+3-5\\-14-5\\-19[/tex]
Since the value of the polynomial is not 0, this means x+1 is not a factor
You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic
Remainder Theorem:
If a polynomial P(x) is divided by x-a, the remainder is P(a)
Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states
Factor Theorem:
The expression "x-a" is a factor of P(x) if and only if P(a) = 0
Indicate the equation of the line meeting the given conditions. Put the equation in standard form.
Containing E(4, 3) and A(6, 1)
Answer:
x + y = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = E (4, 3 ) and (x₂, y₂ ) = A (6, 1 )
m = [tex]\frac{1-3}{6-4}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then
y = - x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, 3 )
3 = - 4 + c ⇒ c = 3 + 4 = 7
y = - x + 7 ← equation in slope- intercept form ( add x to both sides )
x + y = 7 ← equation in standard form