Answers
Die 1 Die 2 Sum
1) 1 1 2
2) 1 2 3
3) 1 3 4
4) 1 4 5
5) 1 5 6
6) 1 6 7
7) 2 1 3
8) 2 2 4
9) 2 3 5
10) 2 4 6
11) 2 5 7
12) 2 6 8
13) 3 1 4
14) 3 2 5
15) 3 3 6
16) 3 4 7
17) 3 5 8
18) 3 6 9
19) 4 1 5
20) 4 2 6
21) 4 3 7
22) 4 4 8
23) 4 5 9
24) 4 6 10
25) 5 1 6
26) 5 2 7
27) 5 3 8
28) 5 4 9
29) 5 5 10
30) 5 6 11
31) 6 1 7
32) 6 2 8
33) 6 3 9
34) 6 4 10
35) 6 5 11
36) 6 6 12
Probability the two numbers will have a sum of 5: P
P=(Number of favorable results)/(Number of possibe results)
Number of favorable results: 4
1) Dice 1: 1 and Dice 2: 4
2) Dice 1: 2 and Dice 2: 3
3) Dice 1: 3 and Dice 2: 2
4) Dice 1: 4 and Dice 2: 1
Number of possible results: 36
P=4/36
Simplifying, dividing the numerator and the denominator by 4:
P=(4/4)/(36/4)
P=1/9
Answer: Option B. 1/9
Related Questions
Two cable ferries start moving towards each other from shores A and B. When the pass each other for the first time the distance to shore B is 100 meters. Once they reach their destinations and start traveling back at the same time. When they meet for the second time, the distance to shore A is 50 meters. What is the distance between the shores Aand B?
Answers
The first meeting point of the ferries represents half of the total roundtrip, while the second meeting point represents a quarter of it. Knowing this proportion and the distances at which the meetings happen, we conclude that the distance between shores A and B is 200 meters.
Explanation:This problem can be solved using rates and proportions. Consider the total round trip of each ferry. The first meeting is at 100 meters from shore B and the second meeting is 50 meters from shore A.
Imagine a full roundtrip travel, from A to B and back to A. When the ferries meet for the first time, they have collectively completed one full round trip (distance A to B and B back to A). At their second meeting, they have collectively made two full round trips.
This means that the first meeting happened at 1/2 of the round trip distance and the second meeting happened at 1/4 of the round trip distance, meaning that the second meeting point was half the distance of the first meeting point. Based on where the second meeting point is (50 meters from shore A), we know that the first meeting point (100 meters from shore B) is twice the distance of the second meeting point from shore A.
Now, we understand the distances as follow: the total distance from shore A to shore B is the sum of the distance from the first meeting point to shore B (100 meters) and twice the distance from the second meeting point to shore A (2*50 meters), which sums up to 200 meters. Therefore, the distance between shores A and B is 200 meters.
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Hey can you please help me posted picture of question
Answers
Number of ways to select a letter = 26
So, number of ways to select 4 letters = 26 x 26 x 26 x 26 = 26⁴
Number of ways to select a number = 6
So, number of ways to select 3 numbers = 6³
Number of key code combinations = 26⁴ x 6³ = 98706816
So, option C is the correct answer
Solve the system of equations algebraically 5x - 3y = 6 6x - 4y = 2
Answers
Answer:
[tex]x=9[/tex] and [tex]y=13[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to solve our given system algebraically.
[tex]5x-3y=6...(1)[/tex]
[tex]6x-4y=2...(2)[/tex]
From equation (1), we will get:
[tex]x=\frac{6+3y}{5}[/tex]
Upon substituting this value in equation (2), we will get:
[tex]6(\frac{6+3y}{5})-4y=2[/tex]
[tex]\frac{36+18y}{5}-4y=2[/tex]
[tex]\frac{36+18y}{5}-\frac{5*4y}{5}=2[/tex]
[tex]\frac{36+18y-20y}{5}=2[/tex]
[tex]\frac{36-2y}{5}=2[/tex]
[tex]\frac{36-2y}{5}*5=2*5[/tex]
[tex]36-2y=10[/tex]
[tex]36-36-2y=10-36[/tex]
[tex]-2y=-26[/tex]
[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]
[tex]y=13[/tex]
Upon substituting [tex]y=13[/tex] in equation (1), we will get:
[tex]5x-3(13)=6[/tex]
[tex]5x-39=6[/tex]
[tex]5x-39+39=6+39[/tex]
[tex]5x=45[/tex]
[tex]\frac{5x}{5}=\frac{45}{5}[/tex]
[tex]x=9[/tex]
Peter makes $7,000 a month plus some extra commission he makes 6% of everything he sells if Peter sold $55,000 of jewelry this month what his salary this month
Answers
I'm taking this to mean that he does not have to sell above 7000 to start getting a commission. Furthermore, he makes 6% on the full 55000.
Formula
T = Base Salary + 6% Total Sales
T = Take home salary
Base Salary = 7000
Total Sales = 55000
Substitute and Solve
T = 7000 + 6% * 55000 Change the % to a decimal
T = 7000 + 6/100 * 55000
T = 7000 + 0.06 * 55000
T = 7000 + 3300
T = 10300 dollars.
Conclusion
His take home salary = 10300 dollars <<<< answer.
How many different ways can a family visit Philadelphia, Baltimore, and Washington? 3 6 12
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[tex]P\left(3,3\right)=3!=3\times 2\times 1=6[/tex]
There are 6 different ways.
Answer:
Answer is 6 ways
Step-by-step explanation:
Given that a family wants to visit three different places as Philadelphia, Baltimore, and Washington.
We have to find the number of ways these three can be visited.
Here this is a question of permutation since order matters.
There are 3 cities and these can be visited in 3P3 ways =3!
=3x2x1 =6 ways
There are in total 6 different ways that the family can visit three different places as Philadelphia, Baltimore, and Washington.
An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?
Answers
(5x4.8)x4 = 96 sq. in. x 2 = $192
5x5 = 25 sq. in. x 3 =$75
$192 + $75 = $267
A line passes through the ordered pairs (4,1) and (2,8) . What is the slope? Please help
Answers
Final answer:
The slope of the line that passes through the points (4,1) and (2,8) is calculated using the slope formula and results in a slope of -3.5.
Explanation:
To find the slope of a line passing through the ordered pairs (4,1) and (2,8), you can use the slope formula:
m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is the first point (4,1) and (x2, y2) is the second point (2,8).Plugging in the values, we get:
m = (8 - 1) / (2 - 4) = 7 / (-2) = -3.5Therefore, the slope of the line that passes through the points (4,1) and (2,8) is -3.5.
The slope of the line passing through the given points is -3.5.
Let’s find the slope of the line passing through the points (4, 1) and (2, 8).
The slope of a line can be calculated using the following formula:
[tex]\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where:
• [tex](x_1) and (y_1)[/tex] are the coordinates of the first point (in this case, (4, 1)).
• [tex](x_2) and (y_2)[/tex] are the coordinates of the second point (in this case, (2, 8)).
Let’s compute the slope:
1. Difference in (x)-coordinates: [tex](x_2 - x_1 = 2 - 4 = -2)[/tex]
2. Difference in (y)-coordinates:[tex](y_2 - y_1 = 8 - 1 = 7)[/tex]
Now, calculate the slope:
[tex]\text{slope} = \frac{7}{-2} = -3.5[/tex]
Therefore, the slope of the line passing through the given points is -3.5.
A 12 pack of soda is roughly $3.75. What is the cost per can of soda?
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That would be $3.75 / 12 = $0.3125
So answer is $0.3125 per can of soda or you can round it to approximately $0.31 per can of soda.
Hope this helps.
Find the area of a rectangle with a length of (4x^2) and a width of (x+6)
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area = length*width
area = (4x^2)*(x +6)
Use the distributive property to eliminate parentheses.
area = 4x^3 +24x^2
Find the sum of the first 10 terms for the sequence {21, 63, 189, . . . }.
5.2 × 1010
620,004
206,661
2730
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[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
You have a=21, r=3, so the sum of 10 terms is
[tex]S_{10}=21\cdot \dfrac{3^{10}-1}{3-1}=620004[/tex]
The appropriate choice is the 2nd one:
620,004
The sum of the first 10 terms for the sequence given is 620,004.
What is Geometric sequence?A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,
Sum of n terms of GP = aₙ = arⁿ-1 / r-1,
a₁ = 21
r = 3
So,
a₁₀ = 21 × 3¹⁰-1 / 3-1
a₁₀ = 21 × 29,524
a₁₀ = 620,004
Hence the sum is 620,004.
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The base of a triangular prism is an equilateral triangle with a perimeter of 15in. If the height of the prism is 4in, find the surface area.
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surface area=2*[area of the base]+perimeter of the base*height
find the area of the base
is an equilateral triangle
b=15/3----> 5 in
applying the law of sines to find the area
Area=(1/2)*b²*sin 60°------> area=(1/2)*5²*sin 60°----> 10.8253 in²
alternative method to find the area of the equilateral triangle
find the h value
applying the Pythagoras theorem
h²=5²-2.5²-----> h=√18.75-----> h=4.33 in
area=b*h/2----> area=5*4.33/2----> 10.8253 in²
surface area=2*[10.8253]+15*4-----> 81.65 in²
the answer is
81.65 in²
Mary has been $50 to spend on T-shirts from an online store. there is $10 shipping and handling fee and each t-shirt cost $5 which inequality represents the number of t-shirts s Mary can buy the answer choices are 5S + 10 greater than equal to 50, 5S + 10 less than equal to 50, 10s + 5 greater than equal to 50, 10s - 5 greater than equal to 50, 5S - 10 greater than equal to 50
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The inequality that represents this situation is 5S + 10 is less than or equal to 50.
The $10 is just a fee, and you don't have to multiply it by anything. However, when the problem says each it means that you have to multiply the given number.
Hope this helped!
1¼ gallons equals how many pints?
Answers
Answer:
10 pints
Step-by-step explanation:
There are 8 pints in a gallon, so ...
(1.25 gal) × (8 pt/gal) = 10 pt
i need help finding the perimeter of a rectangle
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L= length
W= width
Plug in the width and length into the formula above to solve for perimeter.
Hope this helps! :)
A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $41,949.00 each year, and $28,826.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,483,249.00. How many people does the company intend to employ next year?
Answers
Answer:
50
Step-by-step explanation:
Let
x = number of employees each yeary = labor costsThe relationship between x and y can be represented through a linear equation.
y = a . x + b
where,
a is the slope
b is the y-intercept
The slope represents the cost per each person employed, that is, a = $28,826.00/person.
Then,
y = ($28,826.00/person) . x + b
Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).
$41,949.00 = ($28,826.00/person) . 0 + b
b = $41,949.00
The final equation is
y = ($28,826.00/person) . x + $41,949.00
If the company will spend $1,483,249.00 (y = $1,483,249.00.),
$1,483,249.00 = ($28,826.00/person) . x + $41,949.00
1,441,300 = ($28,826.00/person) . x
x = 50 person (50 people)
The company intends to employ 50 people next year.
i need help with this
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B. The distribution is skewed left.
9. It seems likely the distribution has a number of low grades pulling the average down. There certainly exists the possibility that at least one of them qualifies as an outlier by being more than 1.5 times the IQR below the first quartile. That rule, however, only applies when the distribution is relatively symmetrical, which this one is not. There does not appear to be any recommended way to describe an outlier when the distribution is skewed and has a long tail.*
TRUE: The distribution likely has an outlier.
_____
* Math instruction these days rarely recognizes such subtleties. Since it is probable that at least one value is well below the bottom quartile, I've shown my guess at the expected answer as TRUE. In a real set of grades, I expect the tail of the distribution to have enough low grades that they cannot be considered to be outliers.
In a right triangle, if the measures of the other two angles are 2x – 5 and 3x + 10, what are the measures of these two angles?
A. 30° & 60°
B. 29° & 61°
C. 50° & 40°
D. 51° & 39°
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2x – 5 + 3x + 10 + 90 = 180
5x + 95 = 180
5x = 85
x = 17
2x – 5 = 2(17) - 5 = 29
3x + 10 = 3(17) + 10 = 61
Answer: 29° and 61° (Answer B)
Answer: B. 29° & 61°
Step-by-step explanation:
Hey can you please help me posted picture of question
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QM Q6.) Write the slope-intercept equation of the function f whose graph satisifies the given conditions.
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The equation of a line in slope-intercept form is:
y = mx + b
m is the slope
b is the y- intercept
What we need to do is to re-arrange 2x - 9y - 18 = 0. We wanna make it looks like y = mx + b
So, the equation is:
2x - 9y - 18 = 0
Subtract 2x - 18 from both sides
→ -9y = -2x + 18
Since we want y, we need to divide both sides by -9
[tex] \frac{-9y}{-9} = \frac{-2x + 18}{-9} [/tex]
Thus,
y = 2/9 x - 2 which is in the slope intercept form
Slope m = 2/9 and the y-intercept is = - 2
Given a line with slope m then the slope of a line perpendicular is:
[tex] m_{perpendicular} = - \frac{1}{m} [/tex]
[tex] m_{perpendicular} = - \frac{1}{2/9 } [/tex] = - 9/2
Thus,
The equation of the function is:
[tex]y = - \frac{9}{2} x - 2 [/tex]
Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!
When ordering a student desk priced at $69.00, the shipping charges are 6%. What is the total cost of the desk?
Answers
69*.06= 4.14
Your tax would be $4.14 so,
$4.14+$69.00= A total of $73.14
Total cost = $69 + $4.14 = $73.14
Answer: $73.14
Use technology to determine an appropriate model of the data. (0,0), (1,3), (2,4), (3,3), (4,0)
f(x) = – x2 + 4x
f(x) = x2 - 4x
f(x) = - x2 + 4x - 1
f(x) = x2 - 4x + 1
Answers
Each of the ordered pairs satisfies the expression.
Answer:
Option A.
Step-by-step explanation:
To determine an appropriate model of the data each data should satisfy the expression.
For function 1. f(x) = -x² + 4x
Now for each point
f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0
therefore the given points lie on the function.
For option 2
f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0
Therefore points do not lie on the function.
For Option 3.
f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1
Therefore the points do not satisfy the expression.
For option 4.
f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1
Therefore, the points do not satisfy the expression.
Option A. is the correct option.
The music teacher has a list if 128 students who have signed up for music classes. The music teacher can register 6 students in each class. What is the LEAST number of classes needed for all the students to be registered in a class?
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write (-5,2) and (-5,6) in standard form [if you can describe how to do this for the future]
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now, an undefined slope, simply means a vertical line, check the picture below.
£54 in the ratio 5:4
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divide the amount by 9:
54 / 9 = 6
multiply 6 by both 5 and 4
6 *5 = 30
6 * 4 = 24
30 and 24 are two amounts
The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground
Answers
At the time the object hits the ground, height h(t)=0. Substituting this value in the equation we get:
0=-12t²+36t
solving for t we obtain.
12t²=36t
12t=36
hence
t=4
thus the time taken for the object to hit the ground is 4 seconds
A sandwich shop offers the following toppings. How many two topping sandwiches can you make? -lettuce -tomato -bacon -cheese -mustard
A) 8
B) 10
C) 12
D) 20
Please include steps or explain how you got your answer! :)
Answers
The correct answer is: B) 10
Step 1:
To calculate the number of two-topping sandwiches you can make from the given toppings, you can use the combination formula:
[tex]\[C(n, k) = \frac{n!}{k!(n-k)!}\][/tex]
Where:
- [tex]\(n\)[/tex] is the total number of toppings available (5 in this case).
- [tex]\(k\)[/tex] is the number of toppings you want to choose (2 in this case).
- [tex]\(C(n, k)\)[/tex] represents the number of combinations.
Step 2:
Substituting the values:
[tex]\[C(5, 2) = \frac{5!}{2!(5-2)!}\][/tex]
[tex]\[C(5, 2) = \frac{5!}{2!3!}\][/tex]
[tex]\[C(5, 2) = \frac{5 × 4}{2 × 1}\][/tex]
[tex]\[C(5, 2) = \frac{20}{2}\][/tex]
[tex]\[C(5, 2) = 10\][/tex]
So, you can make [tex]\(10\)[/tex] two-topping sandwiches from the given toppings.
Identify the problem with the following poll.
A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.
correlation and causality
loaded questions
nonresponse
self interest
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I need help on this please
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(0, 1.5); (2, 1.5); (4, 1.5);(6,1.5),...
Explanation:
1) formula given:
h(t) = 0.5 sin (πt + π/2) + 1
2) You want the points (t, h) where h is maximum.
3) The mamimum of 0.5 sin (πt + π/2) + 1 is when 0.5 sin (πt + π/2) is maximum, and the maximum of 0.5 sin (πt + π/2) is when sin (πt + π/2) is maximum.
4) Now, the maximum of the sine function is 1, so you must solve this equation:
sin (πt + π/2) = 1.
5) As you know, sine function is equal to 1 when the argument is π/2 + 2nπ
So, find the first positive value of t doing
πt + π/2 = π/2
⇒ πt = 0 ⇒ t = 0
So, the first solution is t = 0.
Since the periodicity is 2π, the same value is obtained for t = 0, 2, 4, 6, ... 2n
6) The corresponding height is the same for all those t:
h(0) = 0.5 sin ( 0×t + π/2) + 1 = 0.5×1 + 1 = 1.5.
7) Therefore the points that you have to draw are: (0, 1.5); (2, 1.5); (4, 1.5);(6,1.5)...
I attach a figure just in case you need more help to visualize the answer.
Hey can you please help me posted picture of question
Answers
B. Empirical
The empirical probability is the one that is determined experimentally, repeating once many times under the same conditions.
When performing more repetitions, the empirical probability tends to establish a value that coincides with the theoretical probability of the event.
In this case, when the coin was tossed 10 times, it could be determined that the probability of occurrence of heads or tails was not 50%.
Therefore, the answer is:
B: Empirical
Solve for e.
9e^2f=49
e=±√7f/3
e=±7√f/3
e=±7√f/3f
e=±√7f/3f
Answers
Divide by the coefficient of e², multiply by f/f, then take the square root.
[tex]e^{2}=\dfrac{49}{9f}=\dfrac{49}{9f}\cdot \dfrac{f}{f}=\dfrac{49f}{9f^{2}}\\\\e=\pm \dfrac{\sqrt{7^{2}f}}{\sqrt{(3f)^{2}}}\\\\e=\pm \dfrac{7\sqrt{f}}{3f}[/tex]
The appropriate selection is ...
e = ±7√f/(3f)