a standard pair of six-sided dice is rolled. what is the probability of rolling a sum less than or equal to 6 ? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778.
To calculate the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice, we need to find the number of ways the dice can be rolled to get a sum less than or equal to 6 and divide it by the total number of possible outcomes.
There are 6 x 6 = 36 possible outcomes when rolling a pair of dice, since there are 6 possible outcomes for each die. To get a sum less than or equal to 6, the only possible outcomes are:
1+1 = 2
1+2 = 3
1+3 = 4
1+4 = 5
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
4+1 = 5
There are 10 possible outcomes that result in a sum less than or equal to 6. Therefore, the probability of rolling a sum less than or equal to 6 is:
P(sum less than or equal to 6) = number of favorable outcomes / total number of possible outcomes
P(sum less than or equal to 6) = 10 / 36
Simplifying this fraction, we get:
P(sum less than or equal to 6) = 5 / 18
Therefore, the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778 when rounded to four decimal places.
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A large cheese pizza costs
$
18
$18dollar sign, 18. Each topping you add on costs
$
1.50 dollar sign, 1, point, 50.
How much would it cost to get a large cheese pizza with
cc toppings added?
Write your answer as an expression.
Answer:
A
=
1.50c + 18
where
A
is amount and
c
is toppings added
Step-by-step explanation:
The constant price is
18
dollars, which never changes and for every topping you get, it costs
$
1.50
. If you got no toppings, sub in
0
for
c
to get
$
18
.
1. Laquan is hosting a brunch and buying pastries for himself and each of his 12 guests. If each pastry costs $3.50, how much will he spend?
Answer:
$45.5
Step-by-step explanation:
12 guests and himself : 13×3.50=45.5
college gpa and salary. do students with higher college grade point averages (gpas) earn more than those graduates with lower gpas (civicscience)? consider the college gpa and salary data (10 years after graduation) provided in the file gpasalary. a. develop a scatter diagram for these data with college gpa as the independent variable. what does the scatter diagram indicate about the relationship between the two variables? b. use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college gpa. c. at the .05 level of significance, does there appear to be a significant statistical relationship between the two variables?
The scatter diagram for the data with college GPA as the independent variable is illustrated as follows.
In this case, we have a dataset that includes the GPA and salary of graduates ten years after graduation. We can use GPA as the independent variable (or x-axis) and salary as the dependent variable (or y-axis). We can then plot each data point on the graph, where the x-coordinate represents the GPA and the y-coordinate represents the salary.
To create the scatter plot, we first need to organize the data into pairs of GPA and salary values. For example, the first pair is (2.22, 72,000), where 2.22 is the GPA and 72,000 is the salary. We can then plot this point on the graph by locating 2.22 on the x-axis and 72,000 on the y-axis.
We repeat this process for each data point, and then connect the points with a line or a curve. The resulting scatter plot shows us the overall pattern of the relationship between GPA and salary. If there is a positive relationship between the two variables, we would expect to see the points cluster around a line that slopes upwards from left to right.
Overall, the scatter plot provides a useful visual tool for exploring the relationship between college GPA and salary. While it suggests that there is a positive relationship between the two variables, it also reminds us that there are many other factors that contribute to earnings.
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Complete Question:
Do students with higher college grade point averages (GPs) earn more than those graduates with lower GPAs?
Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary (S)
72,000 2.22
48,000 2.29
72,000 2.57
64,000 2.59
86,000 2.77
98,000 3.12
133,000 3.35
130,000 2.85
157,000 3.66
162,000 3.68
Develop a scatter diagram for these data with college GPA as the independent variable
FLIPPING COINS There are 2³
possible outcomes for flipping a
penny three times. There are 2⁹
possible outcomes for flipping a
penny nine times. How many times
more possible outcomes are there for
flipping a penny 9 times than flipping a
penny three times?
Answer:
504
Step-by-step explanation:
2 to the power of 9 is 512 2 to the power of 3 is 8 so 512-8 is 504 (hope w this helps!)
Answer:
504
Step-by-step explanation:
2^9 = 512
2^3= 8
512-8=504
14. Refer to the figure. Prove that AC is perpendicular to BC.
Answer:
∴Sum of interior angles in ΔABC = 180°
∠A + ∠B + ∠C = 180°
2x° + 4x° + 6x° = 180°
12x° = 180°
= x =
∴x = 15
∴∠C = (6)×(15)
= 90°
This means AC makes a 90° angle (i.e. ∠C) with BC.
∴AC is perpendicular to BC (Proved)
Also ΔABC is a right-angled triangle
A 7meter flog poce costs a shadow of 5meter. Calculate height of an electric pole that will cost a shadow of 10m under the same condition
The height of the electric pole in order to cast a shadow of 10 m in the same condition as to be 14 m.
The flog poce cast a shadow of 5 metre and itself as a height of 7 m.
Now we have to find the height of an electric pole that will cast the shadow of length 10 m under the same conditions.
The word under the same condition means that the angle of elevation will be same in both the cases, so, we can use the tan theta here,
Tan A = perpendicular/base
Tan A will be equal for both.
Tan A = 7/5
Tan A = H/10
H is the height of the electric pole.
7/5 = H/10
H = 14m
The height of the electric pole will be 14 m.
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A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?
Answer:
=3y - x =0
Step-by-step explanation:
[tex] \frac{y - y1}{x - x1} = m[/tex]
Therefore the gradient ( m ) is not given
from the question point =(-9,-3) and (-12,-4).
Gradient (m) =
[tex] \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 4 - ( - 3)}{ - 12 - ( - 9)} \\ = \frac{ - 4 + 3}{ - 12 + 9} \\ = \frac{ - 1}{ - 3} \\ = \frac{1}{3} [/tex]
therefore m = 1/3.
The equation
[tex] = \frac{y - y1}{x - x1} = m \\ \frac{y - ( - 3)}{x - ( - 9)} = \frac{1}{3} \\ \frac{y + 3}{x + 9} = \frac{1}{3} \\ 3(y + 3) = 1(x + 9) \\ 3y + 9 = x + 9 \\ 3y = x + 9 - 9 \\ 3y = x + 0 \\ 3y - x = 0[/tex]
therefore the equation of the line = 3y-x=0
Select the correct answer. Newspaper Advertisement on Front Page ABC 89. 4% JKL 86. 3% PQR 80. 5% TUV 88. 7% XYZ 89. 1% Total 82. 4% The probabilities of different newspapers having an advertisement on the front page are given in the table. What is the chance of seeing an advertisement on the front page if the newspaper is JKL? A. 82. 4% B. 86. 3% C. 88. 7% D. Insufficient data
The chance of seeing an advertisement on the front page if the newspaper is JKL is 86.3%.
Probabilities:
In science, the probability of an event is a number representing the probability that an event will occur. It is expressed as a number ranging from 0 to 1, or as a number ranging from 0% to 100% using percentage display. The more likely an event is to happen, the more likely it is to happen. The probability of an impossible event is zero. The probability of an event that must happen is 1. The probabilities of two complementary events A and B (A or B) add up to 1.
A simple example is a fair (unbiased) coin toss. When the coin is fair, the two possible outcomes (heads and tails) are equally likely. Since the two outcomes are complementary and the probability of heads is equal to the probability of tails, the probability of each of the two outcomes is 1/2.
Therefore,
After looking at the table, the percentage that represents JKL and a front page advertisement is 86.3%.
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Two similar triangles, ∆ABC and ∆JKL are shown.
What is the length of side JL? Show all work solving for segment JL.
- show the proportion you set up to solve.
- show all work solving for JL
The solution is, the value of JL = 15.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Two similar triangles, ∆ABC and ∆JKL are shown.
so, from the diagram we get,
BC/KL = AB/JK = AC/JL
so, 1/3 = AC/JL
or, JL = 3 * 5
or, JL = 15
Hence, The solution is, the value of JL = 15.
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See had some cherries. Every day he ate 10 cherries and gave 5 away. After he gave that last 5 cherries away he had eaten 40 cherries altogether. How many cherries did Seb have at the start?
50 must have been his starting number of cherries.
Seb had 50 cherries at the start. This can be determined by solving the equation 10x + 5 = 40, where x is the number of days he ate 10 cherries and gave 5 away. When you solve the equation, you get x = 5, meaning he did this 5 times. Since 10x is 50, and 5 is added to that, the total is 50. Therefore, Seb had 50 cherries at the start.
To solve the equation, you first need to subtract 5 from both sides to get 10x = 35. Then, divide both sides by 10 to get x = 3.5. Since Seb could not have eaten 3.5 days worth of cherries, it means that he did the 10 and 5 activity 4 times, giving him 40 cherries before giving away the last 5. So 40 + 5 = 45 and 10x = 50, so 50 must have been his starting number of cherries.
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A researcher found that for the years 2011 to 2017, the equation y = -0. 25(x - 2)^2 + 16, models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. During what year was the average of couches sold in Germany the greatest?
The vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
The equation y = -0.25(x - 2)² + 16 models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. We can find the year when the average of couches sold in Germany was the greatest by finding the maximum value of the equation.
To find the maximum value, we can first rewrite the equation in vertex form: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
y = -0.25(x - 2)² + 16
y = -0.25(x² - 4x + 4) + 16
y = -0.25x² + x + 15
To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h), where f(h) is the value of y at the vertex.
h = -b/2a = -1/(2*(-0.25)) = 2
k = f(h) = -0.25(2)² + 2 + 15 = 16
Therefore, the vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
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Hello guys. If you could help me with this one question you shall get 80 whole points!
The solution to the given problem is 25/88. The solution has been obtained by applying BODMAS rule.
What is the BODMAS rule?
The letters BODMAS stand for Bracket, Of, Division, Multiplication, Addition, and Subtraction. An explanation of a mathematical expression's execution sequence is provided by the BODMAS. According to the BODMAS rule, brackets must be answered first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction.
We are given an expression as (3/11 + 2/11) * 5/8
Now, as per the BODMAS rule, we will first solve the brackets.
On solving the brackets, we get
5/11 * 5/8
Now, on solving it further, we get
5/11 * 5/8 = 25/88
Hence, the solution to the given problem is 25/88.
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Question
You work with a carpenter who asks you to cut 4 boards to the following lengths: 7½ inches, 10½ inches, 9 inches, and 5½ inches. What is the total length, in inches, of the cut boards?
The total length, in inches, of the four cut boards is 130 inches.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.
We have to find the total length of the board.
Total length of the board is found by adding each length.
Total length = 7½ + 10½ + 9 + 5½
Mixed fraction can be converted to improper fraction by cross multiplication.
7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2
Total length = 15/2 + 21/2 + 9 + 11/2
= (15/2 + 21/2 + 11/2) + 9
= 47/2 + 9
= 65/2
Again improper fraction can be converted to mixed fraction.
Total length of a board = 32 1/2 inches
But there are 4 boards.
Total length of the 4 boards = 4 × 65/2 = 130 inches
Hence the total length is 130 inches.
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Estimate the depth d of the crater to the nearest tenth.
The depth d of the crater is 714 m. The solution has been obtained by using trigonometry.
What is trigonometry?
The area of mathematics known as trigonometry is concerned with the study of the sides, angles, and connections of the right-angle triangle.
We are given a figure which shows that the sun's rays are falling at an angle of 55° and the base is given as 500 m.
Using trigonometry,
We know that tan theta = opposite side/ adjacent side
So,
⇒tan θ = d/500
Here, θ = 55°
So,
⇒tan 55° = d/500
⇒x = 500 tan 55°
⇒x = 500 * 1.428148
⇒x ≈ 714.074
⇒x ≈ 714 m
Hence, the depth d of the crater is 714 m.
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6. 56% of
_ is 3.92 *
Answer:
60
Step-by-step explanation:
3.92 = (6.56/100) * _
To solve for _, we can multiply both sides by 100:
100 * 3.92 = (6.56/100) * _
100 * 3.92 = 6.56 * _
_ = (100 * 3.92) / 6.56
Therefore, _ = 60.
Answer: 60
Step-by-step explanation:
Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 204 square meters. Solve for the dimensions (length and width) of the field
The dimension of rectangular piece of land is 17 x 12 square units in size.
The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.
The space occupied by a flat shape or an object's surface can be referred to as the area.
What is the rectangular area formula?
Rectangle area equals length x width
Let the rectangle plot's length and breadth be x and y, respectively.
Juliet has a 58-meter fence.
The rectangular piece of land's perimeter is 58 meters.
2(length + width) = 58
x + y = 58\2
⇒ x + y = 29
Moreover, the plot's total area is 204 square units.
x × y = 204
⇒ x × (29 - x) = 204
[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]
(x-12) (x-17) = 0
x = 12, x = 17
When, x= 17
y = 29 - 17 = 12m
when x = 12
y = 29 - 12 = 17m
As a result, the rectangular land parcel has dimensions of 17 x 12 square units.
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WILL MARK BRAINLIST PLS HELP
Answer:
56.549=56.5
Step-by-step explanation:
A = πr²/2 = 18 * π [in²] ≈ 56.549 [in²]
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $45 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $250, how many hours did the plumber work?
The equation to the context is 50x + 45 = 250 and the plumber worked for 4.1 hours.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let, 'x' represents the number of hours worked by the plumber.
Therefore, The equation can be represented as,
50x + 45 = 250.
50x = 205.
5x = 20.5.
x = 20.5/5.
x = 4.1 hours.
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What shape do u expect the graph of the function described by 3x + 7y =8
Answer: A linear function with a line heading toward negative infinity as x approaches infinity and with a y-int at (0,8/7)
Step-by-step explanation:
The line will be linear as you rearrange the function to be y=
You would do this by moving the 3x over to the right side by subtracting both sides by 3x, giving you 7y=-3x+8. From here, you get y by itself by dividing both sides by 7. Giving a final function of [tex]y=-\frac{3}{7} x+\frac{8}{7}[/tex]
Given ƒ (z) — 5(x − 6)³ + 4, classify each statement about ƒ-¹ (z) as true or false. The point of symmetry on f-¹(x) is (4,6). The domain of f-¹(x) is (-∞,4). The graphs of f¹(x) and f(x) are reflections across the x axis. The range of f¹(x) is (-∞,∞). True False OO O
The correct classification of the statements is: False, True, False, True.
What is Function ?
Function can be defined in which it relates an input to output.
The point of symmetry on f-¹(x) is (4,6).
False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.
The domain of f-¹(x) is (-∞,4).
True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].
The graphs of f¹(x) and f(x) are reflections across the x-axis.
False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.
The range of f¹(x) is (-∞,∞).
True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).
Therefore, the correct classification of the statements is: False, True, False, True.
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the superstone patio company designed these patios.Calculate the area of each. Determine the total cost of each at 23 dollars / m
1.
2.
1. The area of the marble is 6.6m² and the cost is
$3491.4
2. The area of the marble is 42.84m² and the cost is $22662.36
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
1. The area of the marble is
A=( 3.7 × 1.2 ) + 0.9 × 2.4
A= 4.44 + 2.16
A= 6.6m²
if the cost is 23 dollars /meter
per meter square = 23² = $ 529 / meter square
1 meter square = 529
6.6 meter square = 529 × 6.6 = $3491.4
2. The area of the marble is obtained by cutting it into rectangle and trapezium
A= ½(8.8+4.8) 3.9 + 4.8 × 3.4
A= ½(13.6× 3.9) + 16.32
A= 26.52+ 16.32
A= 42.84 m²
The cost will be 529 × 42.84
= $22662.36
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If you borrow $1,100 for 9 years at an annual interest rate of 4% , what is the total amount of money you will pay back?
HELPPPPPPPPPPPPPPPPPPPPP
Answer: look at the image for the answer and solution
Step-by-step explanation:
Find the volume of the composite solid. Round your answer to the nearest tenth. The volume is about cubic centimeters
The volume of the composite solid with cube and hemisphere is equal to 646.0 cubic centimeters ( nearest tenth ).
In the attached figure:
Composite figure consists of two figures:
Cube and hemisphere
Side length of the cube = 8cm
Diameter of the hemisphere = 8cm
Radius of the hemisphere 'r' = 8cm / 2
= 4cm
Volume of the cube = ( side length )³
⇒ Volume of the cube = (8)³
⇒ Volume of the cube = 512 cubic centimeters
Volume of the hemisphere = ( 2/3 )πr³
⇒ Volume of the hemisphere = ( 2/3 ) × 3.14 × ( 4 )³
⇒ Volume of the hemisphere = 133.97 cubic centimeters
Volume of the composite figure
= Volume of the cube + volume of the hemisphere
= 512 + 133.97
= 645.97 cubic centimeters
= 646.0cubic centimeters
Therefore, the volume of the composite solid is equal to 646.0cubic centimeters ( nearest tenth ).
The above question is incomplete, the complete question is:
Find the volume of the composite solid. Round your answer to the nearest tenth. The volume is about cubic centimeters.
Figure is attached.
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How do you find the slope intercept in a table
Answer:
To find a slope intercept in a table look what x is like this. ( 2,9) 2 is the x-intercept and 9 is the y-intercept. Furthermore, if you get a slope like 0,0 which is the origin put a dot on there.
Answer:
Step-by-step explanation:
use this equation
(y1-y2)/(x1-x2)
Question 6 of 10
The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
a(b)=12.b+9
2
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
OA. b(a)=2-9
6
OB. b(a)=+9
6
O C. b(a)=8-6
O
D. b(a)= +6
Answer:96
Step-by-step explanation:
uwu yay
The required equation represents the inverse function b(a), which takes the trapezoid's area is B(a) = a/6 - 9.
What is a trapezoid?A trapezoid is a quadrilateral having two parallel bases and one set of other sides called as legs.
We have been given that the trapezoid's base is nine and its height is twelve.
As an outcome, 'b' is the base's parallel side.
The function that represents the trapezoid's area is given by:
A(b) = [12(b + 9)]/2
Let's consider A(b) = a
Then, a = [12(b + 9)]/2
Now solving for b, we get
2a = 12(b + 9)
a = 6(b + 9)/2
a = 6b + 54
6b = a - 54
b = (a - 54)/6
b = a/6 - 9
Assuming that the length of the side parallel to the base 'b' = B(a), the equation will be:
B(a) = a/6 - 9
Thus, the correct answer would be option A. B(a) = a/6 - 9.
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What is the average rate of change of the function -4≤x≤-3
Check the picture below.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}[/tex]
Answer:
-2
[tex]\hrulefill[/tex]
Step-by-step explanation:
The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
The given interval is -4 ≤ x ≤ -3, so:
[tex]a=-4[/tex][tex]b=-3[/tex]From observation of the given graph, the values of f(a) and f(b) are:
[tex]f(a)=f(-4)=-4[/tex]
[tex]f(b)=f(-3)=-6[/tex]
Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:
[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}[/tex]
Therefore, the average rate of change of the function f(x) on the given interval is -2.
round 224.91 to the nearest whole number
PLEASE HELP!!!
Write a linear equation given slop is -1/3 and the point (-9,-1)
The equation of a line is y = -1/3x - 4
How to determine the equation of the lineThe general formula for the equation of a line is expressed as;
y = mx + c
Given that the parameters are;
y is a point on the y-axis of the linem is the slope of the linex is a point on the x-axis of the linec is the intercept of the line on the y -axisFrom the information given, we have that;
Slope, m = -1/3
Substitute the values
-1 = -1/3(-9) + c
expand the bracket
-1 = 3 + c
collect like terms
= -4
Hence, the equation is y = -1/3x - 4
Learn about equation of a line at:
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