Answer:
The theoretical probability of rolling a 5 or 6 can be calculated by finding the sum of the probabilities of rolling a 5 and rolling a 6. Since the number cube has 6 equally likely outcomes, the probability of rolling a 5 or 6 is:
Theoretical probability = (probability of rolling a 5) + (probability of rolling a 6)
= 1/6 + 1/6
= 2/6
= 1/3
The experimental probability of rolling a 5 or 6 can be calculated by dividing the number of times a 5 or 6 was rolled by the total number of rolls. From the given data, the number of rolls for each outcome is:
Outcome | Number of Rolls
1 | 81
2 | 95
3 | 79
4 | 89
5 | 80
6 | 76
Experimental probability = (number of times a 5 or 6 was rolled) / (total number of rolls)
= (number of times a 5 was rolled + number of times a 6 was rolled) / 500
= (80 + 76) / 500
= 156 / 500
= 0.312
Therefore, the theoretical probability of rolling a 5 or 6 is 1/3, and the experimental probability is approximately 0.312.
Step-by-step explanation:
!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)
A) Inside the Square
B) Outside the Triangle
Answer:
A. 16.7%
B. 89.5%
Step-by-step explanation:
A) Inside the Square
length:4
The square has an area of 16 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being in the square is:
(area of square)/(area of rectangle)
= 16/96
= 0.16666666666666666
This is equal to 16.7%.
B) Outside the right angles Triangle
base:4 height 5
The triangle has an area of 10 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being outside the triangle is:
(area of rectangle - area of triangle)/(area of rectangle)
= (96 - 10)/96
= 0.8958333333
This is equal to 89.5%.
(09.01 LC)
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc
length s of the arc?
A)C=360°(s)(A)
B)C=360 degrees s over A
C)C=360 degrees(s+A)
D)C = 360°A over s
The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is
B) C=360 degrees s over A
How to find the relationshipThe relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:
s = A / 360 * C
Make C the subject of the formula
s = AC / 360
360s = AC
rearranging
AC = 360s
C = 360 degrees s / A
C = (s / A) * 360°
Learn more about arc length at
https://brainly.com/question/2005046
#SPJ1
Answer:
[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]
Step-by-step explanation:
In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.
This is because:
The circumference (C) represents the distance around the entire circle, and so an arc (s) is a fraction of the whole circumference. In a circle, there are 360° in total, and so a central angle (A) is a fraction of 360°.Therefore, this can be expressed as:
[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]
Cross multiply:
[tex]360^{\circ} \cdot s=C \cdot A[/tex]
Now, divide both sides by A to isolate C:
[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]
Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:
[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]
identify the initial amount a and growth/decay factor b.
y= -2(.5)^x
In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.
In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.
The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.
The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.
The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.
To summarize:
Initial amount (a) = -2
Growth/decay factor (b) = 0.5
for such more question on initial amount
https://brainly.com/question/22008756
#SPJ8
NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
The relationship between angles 8 and 7 is that they are supplementary. option B is correct.
Given that a quadrilateral, with three parallel lines, we need to find the relation between angles 8 and 7,
We know that the adjacent angles between the parallel lines are supplementary,
We know that,
Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures will always be 180 degrees.
So,
The relation between the angles is that they are Supplementary angles.
Hence the option B is correct.
Learn more about Supplementary angles click;
https://brainly.com/question/18362240
#SPJ1
HELP !!! URGENTTTTT PLS ANSWER!!!
Answer: z=3
Step-by-step explanation:
A right triangle has a hypotenuse of 9 and a leg of 2 to the square root of 6 what is the missing side
The missing side of the right triangle is √57
To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let's assume the missing side is represented by the variable x.
According to the Pythagorean theorem:
(2√6[tex])^2 + x^2 = 9^2[/tex]
Simplifying, we have:
[tex]4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57[/tex]
Taking the square root of both sides, we get:
x = √57
Thus, the missing side of the right triangle is √57
for such more question on right triangle
https://brainly.com/question/30678476
#SPJ8
You are asked to use the grouping method to factor x^2 - 12x + 13
How should the term -12x be rewritten?
A) 1x +35x
B)-5x -7x
C) 5x+7x
D) -1x-35x
The zeros of this expression are irrational, so it cannot be factored using integers.
When factoring a quadratic expression, we are trying to express it as the product of two binomial factors.
In some cases, such as when the quadratic has irrational zeros, it may not be possible to factor it using integers.
In the case of the quadratic expression x² - 12x + 13, the discriminant (b^2 - 4ac) is equal to (-12)² - 4(1)(13)
= 144 - 52
= 92.
Since the discriminant is positive and not a perfect square, the zeros of the quadratic are irrational.
This means that the expression cannot be factored into two binomial factors with integer coefficients.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
the headlights on a car are set so the light beam drops 2 in. for 26 ft measured horizontally. If the headlights are mounted 24 in. above the ground, how far ahead of the car will they hit the ground?>
Answer:
0.168 ft aprox
Step-by-step explanation:
To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).
According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:
2 inches / 26 feet = x inches / x + 26 feet
To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:
2 inches = 2/12 feet = 1/6 feet
1/6 feet / 26 feet = x feet / x + 26 feet
1/6 * (x + 26) = 26 * x
x/6 + 26/6 = 26x
x + 26 = 156x
156x - x = 26
155x = 26
x = 26 / 155 ≈ 0.168 ft
Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.
predict what will happen to the coordinates of a point (x,y) as the point reflects across a line to produce point (x1,y1)
The reflections are described below.
We know that,
There are two types of reflection:
Reflection with respect to X-axis:
The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.
As a result, the X-axis reflection of the point (x, y) is (x, -y).
Reflection with respect to Y- axis:
The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.
As a result, the Y-axis reflection of the point (x, y) is (-x, y).
Now the reflection is as following:
The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)
The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)
The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)
The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)
Learn more about the coordinate visit:
https://brainly.com/question/24394007
#SPJ1
I need help with this.
Answer:
Step-by-step explanation:
Area of parallelograph = bh
b=20 h =42
A=(20)(42) = 840 mm²
How do -3.8 and -4 1/2 compare
Answer:
-3.8 > -4.5
Step-by-step explanation:
Convert the fraction to decimal and then compare.
[tex]\sf -4\dfrac{1}{2}=\dfrac{-9}{2}[/tex]
= -4.5
Now compare (-3.8) & (-4.5)
-3.8 > -4.5
Write the quadratic equation in standard form that corresponds to the graph shown below.. Please help.
The quadratic equation in standard form that corresponds to the graph shown above is f(x) = x² + 2x - 8
What is the general form of a quadratic function?In Mathematics and Geometry, the standard form of a quadratic function can be modeled and represented by using the following mathematical expression;
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.In this scenario and exercise, we would write a quadratic function that represent f(x) in standard form and with a leading coefficient of 1 by using the roots (-4, 0) and (2, 0) as follows;
f(x) = (x + 4)(x - 2)
f(x) = x² - 2x + 4x - 8
f(x) = x² + 2x - 8
Read more on quadratic functions here: https://brainly.com/question/29499209
#SPJ1
Fred is buying A New
refrigerator for his
Apartment. His friend has A
4-year-old refrigerator that
he will sell to Fred for only
$200, but the refrigerator
Needs About $350 iN
repairs. The local Appliance
shop hAs A New model for
$615, plus 7% sales tax.
How much sales tax will Fred pay if he buys the new refrigerator?
Fred will pay $43.05 in sales tax if he buys the new refrigerator.
To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.
The cost of the new refrigerator is $615.
To calculate the sales tax, we multiply the cost by the tax rate of 7%:
So, Sales tax = 7% of $615
Sales tax = (7/100) x $615
Sales tax = $43.05
Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.
Learn more about Sales tax here:
https://brainly.com/question/29442509
#SPJ1
Which choice is a solution to this system of equations? -x=y-4 y=4x+9
The solution to the system of equations is x = 5.4 and y = -1.4
How to determine the solution to the system of equations?From the question, we have the following parameters that can be used in our computation:
-x=y-4 y=4x+9
So, we have
-x = y - 4
y = 4x + 9
Rewrite the equation as
x = -y + 4
y = 4x + 9
So, we have
y = 4(-y + 4) + 9
Open the bracket and evaluate
5y = 9 - 16
So, we have
y = -1.4
Recall that
x = -y + 4
So, we have
x = 1.4 + 4
Evaluate
x = 5.4
Hence, the solution is x = 5.4 and y = -1.4
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
give the rule in words of this pattern 10,13,17,238
Answer:
a set of numbers in order of least to greatest
PLEASE HELP AND SHOW WORK
The amount of fabric required is 400.551 ft².
We have,
CB= 8 feet
CF= 13 feet
AM = 8 feet
Using Pythagoras
AC² = AM² + CM²
AC = √64+16 = √80 = 4√5 feet
Now, the formula for Triangular prism is
= (Sum of three sides of triangle face)l + base area
= (4√5 + 4√5 + 8)13 + 8 x 8
= 104√5 + 104 + 64
= 104√5 + 168
= 232.551 + 168
= 400.551 ft²
Learn more about surface Area here:
https://brainly.com/question/29298005
#SPJ1
pleaseseee help
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable
pls help 100 points
Answer:
Step-by-step explanation:
Simplify. Write your answers without exponents. 4^ -5/2= (1/16)^-3/2=
Please look at photo for accuracy
The value of the given expression is,
[tex]4^{- 5/2[/tex] = 1/32
[tex](1/16) ^ {- 3/2[/tex] = 64
We have to given that,
Expressions to solve are,
⇒ [tex]4^{- 5/2[/tex]
And, [tex](1/16) ^ {- 3/2[/tex]
We know that,
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself
Now, We can simplify the given expression,
By using law of exponents
We get,
⇒ [tex]4^{- 5/2}[/tex]
⇒ [tex]2^{2(- 5/2)}[/tex]
⇒ 2⁻⁵
⇒ 1/2⁵
⇒ 1/32
Thus,
The value of [tex]4^{- 5/2[/tex] = 1/32
The given expression is,
⇒[tex](1/16) ^ {- 3/2[/tex]
By using law of exponents
We get,
⇒ [tex]16 ^{3/2}[/tex]
⇒ [tex](4^2)^{3/2}[/tex]
⇒ 4³
⇒ 64
The value of [tex](1/16) ^ {- 3/2[/tex] = 64
To learn more about exponent visit:
https://brainly.com/question/31242910
#SPJ1
Show your work show me how you got the answer HELP DUE TOMORROW!!
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
[a] 12 units
Step-by-step explanation:
The answer is (D) 44 units
Step-by-step explanation:1. The formula for the area of a rhombus is A= [tex]\frac{d_{1} d_{2}}{2}[/tex]
2. Fill in the information we know:
A = 264d1 = 123. Now work backward:
If A= [tex]\frac{d_{1} d_{2}}{2}[/tex] then that means 264 = [tex]\frac{12_ {} d_{2}}{2}[/tex] So 12 multiplied by a number divided by 2 is equal to 264That means that 264 multiplied by two and divided by 12 will give you the mystery number.4. Solve it:
264 multiplied by 2 is equal to 528 528 divided by 12 is equal to 44Hence 44 units (D) is your answer
A. How many combinations of the 5 white balls and 1 red ball are possible?
The number of combinations of the 5 white balls and 1 red ball are possible is 1.
We are given that;
White balls=5
Red ball=1
Now,
To find the number of combinations of 5 white balls and 1 red ball, we can use the combinations formula12:
[tex]nCr = n! / (r! (n-r)!)[/tex]
where n is the total number of objects, r is the number of objects to be selected, and ! is the factorial operator.
we can plug in these values into the formula:
[tex]6C6 = 6! / (6! (6-6)!) 6C6 = 6! / (6! 0!) 6C6 = 1 / (1 1) 6C6 = 1[/tex]
So, there is only one combination of 5 white balls and 1 red ball. This makes sense because the order of selection does not matter in a combination. No matter how we arrange the balls, we will always have the same group of 5 white balls and 1 red ball.
Therefore, by combinations and permutations the answer will be 1.
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
#SPJ1
What is the value of x?
NO SPAM OR I WILL REPORT YOU AND BAN YOU IMMEDIATELY
Using a trigonometric relation, we can see that the value of x is 10.39
How to find the value of x?Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.
Then to get the value of x, we can use the trigonometric relation:
sin(a) = (opposite cathetus)/hypotenuse.
Replacing the values that we know, we will get.
sin(60°) = x/12
solve that for x:
12*sin(60°) = x
10.39 = x
Learn more about right triangles at:
https://brainly.com/question/2217700
#SPJ1
What is the slope of the line that is perpendicular to the line of y=3x -8
The slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.
The given line has an equation in slope-intercept form, which is y = 3x - 8. In this form, the coefficient of x represents the slope of the line.
Therefore, the slope of the given line is 3.
To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope.
The negative reciprocal of 3 is -1/3.
Therefore, the slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.
Learn more about Slope here:
https://brainly.com/question/3605446
#SPJ1
Please help I have to get 100 in order to graduate to my next grade level please if you can help me do it I will give big points and there is more than 1 answer.
The solution of the given equations is: (3,-1).
Here, we have,
from the given graph we get,
1st line passes through ( 0,2 ) and (2,0)
so, equation: y = -x+2 .....1
2nd line passes through ( 0,-4 ) and (4,0)
so, equation: y = x-4 .....2
now, from 1 and 2 we get,
-x + 2 = x -4
or, 2x = 6
or, x = 3
so, we have, y = -1
so, the point of intersection is (3, -1)
Hence, The solution of the given equations is: (3,-1).
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ1
There are 840 learners and 17 teachers at Orefile Primary school.what is the learner to teacher ratio?
Answer: 49.4 thats the answer i devided it
4. The ratio of the length of the corresponding side of two
regular polygons is 3:4. The area of the larger polygon is
320 m². What is the area of the smaller polygon?
A-240 m²
B-427 m²
C-569 m²
D-180 m²
Write in exponential form. ln54.60=4
Step-by-step explanation:
ln 54.60 = 4 e^x both sides
e ^ (ln 54.60) = e^4
54.60 = e^4 Done.
simplify 9/14divided7/10
Answer:
45/49
Step-by-step explanation:
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
9/14 * 10/7 = 90/98
divide the numerator and the denominator by 2.
90 * 2 = 45
98 * 2 = 49
45/49
What is the solution to the proportion 2/3 m/9
What is the solution to this system?
3x+2y=6
-4x+ 5y = 15
4-3-2-1
1 2 3 4 5
-
S
Answer:
solution: (0,3)
Step-by-step explanation:
You can find the solution when the two lines intersect.