Final answer:
The probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12. There are 15 possible outcomes where the sum is less than 7 out of 36 total outcomes.
Explanation:
The question asks for the probability that the sum of the numbers shown by rolling a six-sided die twice is less than 7. To find this probability, we need to consider all the possible outcomes of rolling two dice.
Each die has 6 faces, so when you roll two dice, there are a total of 6 x 6 = 36 possible outcomes. To get the sum less than 7, we can have the following combinations:
(1,1) Sum = 2
(1,2) Sum = 3
(2,1) Sum = 3
(1,3) Sum = 4
(2,2) Sum = 4
(3,1) Sum = 4
(1,4) Sum = 5
(2,3) Sum = 5
(3,2) Sum = 5
(4,1) Sum = 5
(1,5) Sum = 6
(2,4) Sum = 6
(3,3) Sum = 6
(4,2) Sum = 6
(5,1) Sum = 6
Adding up the number of outcomes, there are 15 possibilities where the sum is less than 7. Therefore, the probability is 15 out of 36. This simplifies to 5/12 when reduced to its simplest form.
So, the probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12.
In ΔABC, ∡A is a right angle, and m∡B = 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer:
The length of BC is 11√2 ft.
Step-by-step explanation:
Given,
A right angled triangle ABC,
In which,
AC = 11 ft ( By diagram ),
∠A = 90°,
∠B = 45°,
By the law of sine,
[tex]\frac{sin B}{AC}=\frac{sin A}{BC}[/tex]
[tex]\implies BC\times sin B = AC\times sin A[/tex] ( By cross multiplication )
[tex]\implies BC = \frac{AC\times sin A}{sin B}[/tex]
By substituting the values,
[tex]BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}[/tex]
[tex]=\frac{11}{\frac{1}{\sqrt{2}}}[/tex]
[tex]=11\sqrt{2}[/tex]
Hence, the length of BC is 11√2 ft.
How many times larger is 4 x 1016 than 5 x 108?
Seven of the 10 children at art camp make an average of 8 paintings. The remaining children make an average of 12 paintings. What is the average number of paintings made by children at the art camp? Enter your answer in the box.
A football is selling for $35 off the original price. The original price was $60. What is the sale price of the football?
The volume of a right triangular prism is 72 cubic feet. The height of the prism is 9 feet. The triangular base is an isosceles right triangle.
Answer:
Step-by-step explanation:
What is the area of the triangular base? 8 square feet
What is the length of edge DF? 4 feet
Answer:
What is the area of the triangular base?
8 square feet
What is the length of edge DF?
4 feet
Step-by-step explanation:
just did the quiz on EDG
Which pair of points forms a vertical line segment that is 4 units long?
solve the equation
3x-3= -18
The solution of the equation 3x-3= -18 is -5.
The algebraic expressions which are separated by an equal symbol in between them and with the same value is called is an equation
Example = 5x + 5 = 12
here, x is a variable and 5 and 12 are constants.
Given equation;
3x-3= -18
To find the value of x add 3 to both side, we get
3x = -18 +3
we get
3x = -15
divide both side by 3 we get
[tex]x = \dfrac{-15}{3}[/tex]
Convert in into the lowest form we get,
x = -5
The solution of the equation 3x-3= -18 is -5
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What value of c makes the trinomial below a perfect square x2 + 7x + c?
Rewrite as perfect squares
(x+3.5)²+ c-3.5²Answer:49/4
Step-by-step explanation:
Find the diameter of a circle whose equation is x2+(y−2)2=100x2+(y−2)2=100.
400
20
10
100
What is true about side AB and side AD?
The lateral area of a cone is 555 \pi cm^2 and the radius is 15.1 what is the slant height?
What is the solution to the equation 1/square root of 8 = 4^(m + 2)?
m = −15/4
m = −11/4
m = 5/4
m = 9/4
Geometry question, will give brainiest
Which expression is equivalent to x3 – 7x – 6?
Anna and Ryelin together have 895 songs downloaded. Ryelin has 177 more songs downloaded than Anna. How many songs do each of them have?
A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer?
547.1 mm2
972.6 mm2
60.8 mm2
243.3 mm2
Answer: [tex]243.3\ mm^2[/tex]
Step-by-step explanation:
Given: The diameter of smaller circle = 13.2 mm
Then the radius of smaller circle r =[tex]\frac{13.2}{2}=6.6\ mm[/tex]
Also, the radius of larger circle R= [tex]6.6+4.4=11.0\ mm[/tex]
Now, the area of the washer is given by :-
[tex]\text{Area of washer=Area of larger circle-Area of smaller circle}\\\\\Rightarrow\\text{Area of washer}=\pi R^2-\p r^2\\\\\Rightarrow\\text{Area of washer}=\pi(R^2-r^2)\\\\\Rightarrow\\text{Area of washer}=(3.14159265359)((11.0)^2-(6.6)^2)\\\\\Rightarrow\\text{Area of washer}=243.284935094\approx243.3\ mm^2[/tex]
The area of the washer is 0 mm2.
Explanation:To find the area of the washer, we first need to find the area of the larger circle and the area of the smaller circle. The formula for the area of a circle is A = πr^2.
The larger circle has a diameter of 13.2 mm, so the radius is half of that, which is 6.6 mm. Plugging this value into the formula, the area of the larger circle is approximately 136.78 mm2.
The smaller circle has a diameter of 13.2 mm, so the radius is again 6.6 mm. Using the same formula, the area of the smaller circle is also approximately 136.78 mm2.
To find the area of the washer, we subtract the area of the smaller circle from the area of the larger circle: 136.78 mm2 - 136.78 mm2 = 0 mm2. Rounded to the nearest tenth, the area of the washer is 0 mm2.
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please help me figure out this probability problem!!!
Complete the area model to identify the factored form of the quadratic expression it represents. A) (x + 2)(x + 5) B) (x − 2)(x + 5) C) (x + 2)(x − 5) D) (x − 2)(x − 5)
The correct answer is D (x - 5)(x - 2)
You can tell this because in the picture, we are looking for all of the cross sections to multiply to their appropriate boxes. In the bottom right corner, we see the number 10. This means that the bottom number and the right number must multiply to 10. This only happens in A and D, whereas in B and C those equal -10.
To determine between A and D, you must find the ones that have negatives, since the two x values are both negatives. D is the only one with negative numbers out of the ones we are left working with. Therefore, D is the correct answer.
Answer:
its C i just did that question
Step-by-step explanation:
HELP ME PLEASE I DONT UNDERSTAND THIS PROBLEM!!!!! Worth 20PT
a ball is thrown with a slingshot at a velocity of 100 ft/sec at an angle 21 above the ground from a height of 5ft approximately how long does it take for the ball to hit the ground? acceleration due to gravity is 32 ft/s^2
Answer:
D) 2.37 seconds
Step-by-step explanation:
Took the test and got it wrong.
98 POINTS AND BRAINLIEST!!!!!!!!!!!
Hello!
I believe the answer is A) p(x) = 13x -20.
I hope it helps!
It takes 60 pounds of seed to completely plant a 10-acre field. How many acres can be planted per pound of seed
How to find the area of a triangle with a base of 32ft
Cindy and Giovanni plan to make spaghetti sauce. Cindy needs 4 3/4 pounds of tomatoes for her recipe. Giovanni needs 5 /34 pounds of tomatoes for his recipe. If they make both recipes, how many pounds of tomatoes do they need?
Answer:
[tex]10\frac{1}{2}\text{ pounds}[/tex]
Step-by-step explanation:
Given,
For a recipe,
Cindy needs tomatoes = [tex]4\frac{3}{4}[/tex] pounds,
While, Giovanni needs tomatoes = [tex]5\frac{3}{4}[/tex] pounds,
If they make both recipes,
Then, total tomatoes they need = [tex]4\frac{3}{4}+5\frac{3}{4}[/tex]
[tex]=\frac{19}{4}+\frac{23}{4}[/tex]
[tex]=\frac{42}{4}[/tex]
[tex]=10\frac{2}{4}[/tex]
[tex]=10\frac{1}{2}\text{ pounds}[/tex]
The outer edge of the dime is about 55mm. What is the approximate length of the radius?
A 3 inch wide border is wrapped around a rectangular prism. the length of the rectangular prism is 8 inches longer than its width. the surface area covered by the border is 383 square inches. what is the width of the rectangular prism? answer in units of inches.
The figure below shows a shaded circular region inside a larger circle:
Will insert pic below
What is the probability that a point chosen inside the larger circle is not in the shaded region?
24%
36%
50%
64%
Answer:
the answer is 64%
Step-by-step explanation:
what is the product? -9x(5-2x) 18x2 -45x -18x2-45x -18x-45 18-45x
Answer: A.
Step-by-step explanation:
The product of equation is 18x² - 45x.
What is linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given equation -9x(5 - 2x)
product = -9x(5) - (-9x)(2x)
= -45x + 18x²
= 18x² - 45x
Hence the product is 18x² - 45x.
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How do you complete the square of x^2-14x+33=0?
Final answer:
To complete the square for the equation x^2-14x+33=0, the constant 33 is moved to the other side, and the number needed to make the left side a perfect square trinomial, 49, is added to both sides, resulting in factoring and solving (x - 7)^2 = 16 to find x = 11 and x = 3.
Explanation:
To complete the square for the equation x^2-14x+33=0, you need to form a perfect square trinomial on the left side of the equation. First, you'll move the constant term to the right side:
x^2 - 14x = -33
Next, find the value that completes the square for the x-terms. This value is obtained by taking half of the coefficient of x (which is -14 in this case) and squaring it, giving us (-7)^2 = 49.
Add 49 to both sides of the equation:
x^2 - 14x + 49 = -33 + 49
x^2 - 14x + 49 = 16
Now, the left side of the equation is a perfect square trinomial, and can be factored into:
(x - 7)^2 = 16
To solve for x, take the square root of both sides:
x - 7 = [tex]\sqrt{16}[/tex]
x - 7 = +- 4
Finally, solve for x by adding 7 to both sides:
x = 7 +- 4
x = 11 or x = 3
Solve the equation using square roots. 3x2 – 27 = 0
The value of X are x = 3 and x = -3. using square root.
What is square root?A square root can be regarded as a factor of a number in the sense that when that number is multiplied by itself, it gives the original number.
3x²– 27 = 0
⇒3x²= 27
⇒x²= 27/3
⇒x² = 9
⇒x = sqrt(9)
⇒ x =±3
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Help me please & thank ya