Final answer:
The probability of rolling factors of 3 on two six-sided dice is 13 out of 36 possible outcomes, which simplifies to approximately 0.361 or 36.1%.
Explanation:
Calculating the Probability of Rolling Factors of 3
To find the probability of rolling factors of 3 when tossing two dice, we must consider the combinations that result in multiplying to three or being a multiple of three. Each die has six faces, so there are a total of 6 x 6 = 36 possible outcomes when rolling two dice. The factors of 3 are 1 and 3. So we have to count the outcomes where at least one of the dice shows a 3 or both dice show 1, which are the relevant factors of 3. If we roll a 3 on one die, the other die can show any number from 1 to 6, giving us 6 outcomes. If we roll a 3 on the other die, we again have 6 different outcomes. However, this would double-count the scenario where both dice show 3, so we must subtract this outcome once.
Therefore, the number of favorable outcomes is (6 + 6 - 1 = 11). The probability can be computed as the number of favorable outcomes divided by the total number of possible outcomes, giving us a probability of 11/36.
If we want the probability of getting one 1 and one 3 in two tosses, we must add to this the probability of tossing a 3 first and a 1 second. The event of rolling a 1 and then a 3, or 3 and then a 1, each has a probability of 1/36. As there are two ways this can happen (1 then 3, or 3 then 1), the probability for this event is 1/36 + 1/36 = 2/36 or 1/18, which must be added to our initial 11/36.
Hence, the final probability of rolling factors of 3 on two dice is (11/36) + (1/18) = (11/36) + (2/36) = 13/36.
a square has an area of 25^2 what’s the length of each side??
Answer:
25
Step-by-step explanation:
Area is the square of the side length, so
s^2 = 25^2
Matching parts of this expression, we see ...
s = 25
The length of each side is 25.
Diameter =4 cm, height= 3.6cm
The lateral area of the cylinder is approximately [tex]45.24 \, \text{cm}^2\)[/tex] and the volume is approximately [tex]\(45.24 \, \text{cm}^3\)[/tex].
To find the lateral area and volume of a cylinder, you can use the following formulas:
1. Lateral Area [tex](\(A_{\text{Lateral}})\)[/tex]:
[tex]\[ A_{\text{Lateral}} = 2 \pi r h \][/tex]
where r is the radius of the base and h is the height.
2. Volume (V):
[tex]\[ V = \pi r^2 h \][/tex]
Given that the diameter (D) is 4 cm, the radius (r) is half of the diameter, so [tex]\( r = \frac{D}{2} = \frac{4}{2} = 2 \)[/tex] cm, and the height (h) is 3.6 cm.
Now, let's calculate:
1. Lateral Area:
[tex]\[ A_{\text{Lateral}} = 2 \pi \times 2 \times 3.6 \][/tex]
2. Volume:
[tex]\[ V = \pi \times 2^2 \times 3.6 \][/tex]
Calculating these values:
1. Lateral Area:
[tex]\[ A_{\text{Lateral}} \approx 45.24 \, \text{cm}^2 \][/tex]
2. Volume:
[tex]\[ V \approx 45.24 \, \text{cm}^3 \][/tex]
So, the lateral area of the cylinder is approximately [tex]45.24 \, \text{cm}^2\)[/tex] and the volume is approximately [tex]\(45.24 \, \text{cm}^3\)[/tex].
Complete Question: Find the lateral area and volume of the cylinder whose diameter is 4 cm and height= 3.6cm.
A train goes past you in 10 seconds and goes past a 100 meter long bridge in 30 seconds. What is the length (in meters) and the speed (in m/s) of the train?
To find the length of the train and its speed, we can use the formula Length = Speed x Time. By setting up and solving equations, we can find that the length of the train is 200 meters and the speed of the train is 20 m/s.
Explanation:To find the length of the train, we can use the formula:
Length = Speed x Time
Given that the train takes 10 seconds to pass you and 30 seconds to pass the bridge, we can calculate:
Length of train = Speed of train x Time taken to pass you = Speed x 10
Length of train + Length of bridge = Speed of train x Time taken to pass the bridge = Speed x 30
Substituting the values, we have:
Speed x 10 + 100 = Speed x 30
Simplifying the equation, we get:
Speed = 400/20 = 20 m/s
Substituting the value of speed back into the first equation, we have:
Length of train = 20 x 10 = 200 meters
Therefore, the length of the train is 200 meters and the speed of the train is 20 m/s.
Abby can buy an 8-pound bag of dog food for $7.40 or a 4-pound bag of the same dog food for $5.38 . Which is the better buy
Answer:
the eight pound bag is better because you would have to pay $10.76 if you buy two of the 4 pound bags so you are saving $3.36
Step-by-step explanation:
Answer:
the 8 pound buy
Step-by-step explanation:
Julie invested 3000 in a simple interest account for 2 years. At the end of the 2 years, she had earned $75 in interest. What was the simple interest rate of the account
The simple interest rate was: 1.25%
Step-by-step explanation:
Simple interest is given by:
[tex]A = Prt\\Here\\A => Interest\\P=>Principal\ Amount\\r => Rate\\t => Time\ in\ years[/tex]
Given
Principal amount =$3000
Time = t = 2 years
Interest amount = A = $75
putting the values in the formula
[tex]75 = 3000 * r * 2\\75 = 6000r[/tex]
Dividing both sides by 6000
[tex]\frac{6000r}{6000} = \frac{75}{6000}\\r = 0.0125\\[/tex]
So,
The rate is:
0.0125 * 100 = 1.25%
Hence,
the simple interest rate was: 1.25%
Keywords: Simple interest, percentage
Learn more about interest at:
brainly.com/question/5720422brainly.com/question/5565320#LearnwithBrainly
true or false a rectangle is never a rhombus
Answer:
Its true.A rectangle is never a rhombus.
Answer:
This is actually false according to most accepted definitions - a rectangle that has equal sides would be a square, and thus also a rhombus.
Step-by-step explanation:
The definition of a rhombus is that it has 4 equal sides.
Also, the definition of a rectangle is that it has two pairs or equal sides, and all angles are 90 degrees.
So a square is a special case of a rectangle. And a square is also a special case of a rhombus.
Meaning that a square is both a rhombus and a rectangle, so any rectangle with equal sides would also be a rhombus.
A teacher offers her students 5 fake dollars to spend in the class store, when they get a perfect score on their math tests. If one of her students gets a perfect score on 4 of the math tests and already has 25 fake dollars, how many fake dollars, in total, does this student have to spend in the class store?
Answer:
45 fake dollar.
Step-by-step explanation:
Given: teacher offer 5 fake dollar for each perfect score in Math test.
One of Student get perfect score on 4 maths test.
Student already have 25 fake dollor.
Now, solving to find total number of fake dollar teacher offered to student.
As given teacher offer 5 dollar for each perfect score in maths test and student got perfect score on 4 maths test.
Number of fake dollar offer to the student= [tex]Fake\ dollar\ offered\ for\ each\ perfect\ score\ \times\ number\ of\ maths\ test\ with\ perfect\ score[/tex]∴ Number of fake dollar offered to the student= [tex]5\times 4= 20\ fake\ dollar[/tex]
We know, student already have 25 fake dollar.
Next, finding total number of fake dollar student have.
Total fake dollar student have= [tex]fake\ dollar\ offered\ by\ teacher + fake\ dollar\ student\ already\ have[/tex].
Total fake dollar student have= [tex]20+25= 45\ fake\ dollar[/tex]
Hence, student have total 45 fake dollar to spend in the class store.
I need help please and thank you
Answer:30
Step-by-step explanation:
Answer:
I think the correct answer is
A- 40
B- 40
which is a better buy: 50 head of cattle for $24,500 or 37 head of cattle for $18,870?
Let us see...
50 head of cattle = 24,500
Divide everything by 50: 1 head of cattle = $490
37 head of cattle = 18,870
Divide the entire equation by 37: 1 head of cattle = $510
The second choice would cost a person $20 more than the first choice, so 50 head of cattle for $24,500 is a better buy.
42% of what number is 0.21?
Answer: 0.5
Step-by-step explanation:
Let the number be x , then
42% of x = 0.21
0.42x = 0.21
divide through by 0.42
x = 0.21/0.42
x = 0.5
Therefore : 42% of 0.5 = 0.21
Answer:
.5
Step-by-step explanation:
.42/1 * x = .21
x = .21/.42
x = .5 or 1/2
Write 1/10 and 1/10 as decimals to complete the expression.
Answer:0.2
Step-by-step explanation: 1/10 and 1/10
Simply means this in maths
1/10+1/10
0.1+0.1= 0.2
Determine the intercepts of the line.
-5x+9y=-18
y intersept-(0,_)
x intercept- (_,0)
The x intercept is [tex](\frac{18}{5} , 0)[/tex]
The y intercept is (0, -2)
Solution:
Given equation is:
-5x + 9y = -18
We have to find the y intercept and x intercept
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero
Finding x - intercept:To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.
Substitute y = 0 in given equation
[tex]-5x + 9(0) = -18\\\\-5x = -18\\\\x = \frac{18}{5}[/tex]
[tex]\text{Thus the x - intercept is } (\frac{18}{5}, 0)[/tex]
Finding y - intercept:To find the y-intercept, plug 0 in for 'x' and solve for 'y'
Substitute x = 0 in given equation
[tex]-5(0) + 9y = -18\\\\9y = -18\\\\y = -2[/tex]
Thus the y intercept is (0, -2)
Sneha is planning a 5-night vacation. It will cost $50 for transportation, $290 for food, and $95 per night for a hotel room. She has $143 in savings and can earn $48 per driveway shoveling driveways. How many driveways must she shovel to have enough money to pay for the trip?
Answer:
Step-by-step explanation:
Total cost for trip = 290 + 50 + 95*5 =290+50+ 475 = $ 815
Savings = $143
Money needed = 815 - 143 = $ 672
No. of driveways = 672/48 = 14
14 driveways must she shovel to have enough money to pay for the trip.
Sneha needs to calculate the total cost of her vacation which is $815. After taking into account her savings, she requires an additional $672. As she earns $48 shoveling each driveway, she would need to shovel 15 driveways.
Explanation:This is a question of basic algebra and problem solving. Sneha needs to calculate the total cost of her vacation first. She will spend $50 on transportation, $290 on food, and $95 per night for the hotel for 5 nights, or $475 ($95 x 5) for the hotel total.
Adding these amounts together, Sneha's vacation will cost $815 ($50 + $290 + $475). She currently has $143 in savings, meaning she needs $672 more dollars ($815 - $143).
As Sneha earns $48 for each driveway she shovels, we divide the total she needs by the earning for each driveway. That gives us 14 driveways. As Sneha can't shovel a fraction of a driveway, she will need to shovel 15 driveways in total.
Learn more about Problem Solving here:https://brainly.com/question/31606357
#SPJ2
This diagram shows the dimensions of a metal piece used in a machine.
What is the volume of the metal piece?
Enter your answer in the box.
____mm³
Answer:
Volume of metal piece = 3680 mm³
Step-by-step explanation:
volume of horizontal cuboid:
V = l * b * h
= 30 * 8 * 8 = 1920 mm³
Volume of vertical cuboid:
breadth = 10 mm
Length = 14+8 = 22 mm
Height = 8 mm
V = 22 * 10 * 8
= 1760 mm³
Volume of metal piece = 1920 + 1760
= 3680 mm³
Answer:
3680
i got 100 on test
2/3÷2⁴+(3/4+1/6)÷1/3
How do you figure this out
Answer: [tex]\frac{67}{24}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} /2^{4}+(\frac{3}{4} +\frac{1}{6})/\frac{1}{3} \\\\\frac{2}{3} /2^{4}+ \frac{11}{12} /\frac{1}{3} = \frac{2}{3} /16+ \frac{11}{12} /\frac{1}{3}[/tex]
Use the rule a÷b/c=a*c/b
[tex]\frac{2}{3} *\frac{1}{16}+ \frac{11}{12}/ \frac{1}{3}[/tex]
Use the rule a/b*c/d=ac/bd
[tex]\frac{2}{3*16}+ \frac{11}{12}/ \frac{1}{3} \\\\\frac{2}{48} +\frac{11}{12}/ \frac{1}{3} \\\\\frac{1}{24}+\frac{11}{12}/\frac{1}{3}[/tex]
Use the rule a÷b/c=a*c/b
[tex]\frac{1}{24} +\frac{11}{12} *3[/tex]
Use the rule a/b*c=ac/b
[tex]\frac{1}{24}+ \frac{11*3}{12}[/tex]
Simplify three times then you're done.
[tex]\frac{1}{24}+ \frac{33}{12}= \frac{1}{24}+ \frac{11}{4} =\frac{67}{24}[/tex]
Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! As well as a great Superbowl Weekend! :-)
- Cutiepatutie ☺❀❤
Arianna is saving money for college so she invests $1,000 into a savings account that earns interest every year. If the amount in the savings account is represented by the function
9x2+50x+1000, where x is the number of years. How much money does Arianna have in her account after 6 years?
Answer: $1,624
Step-by-step explanation:
The amount after x-years is given as :
9[tex]x^{2}[/tex] + 50x + 1000
Since x represents number of years , this means that after 6 years , the amount will be :
9([tex]6^{2}[/tex] ) + 50(6) + 1000
⇒9(36) + 300 + 1000
⇒324 + 300 + 1000 =
Therefore, the amount after 6 years will be $1,624
Which fraction is equivalent to 50%? (in simplest fraction form) A) 1 2 B) 1 4 C) 2 5 D) 4 5
Answer:
1/2 is equivalent to 50%
Step-by-step explanation:
In order to convert a fraction to a percentage you divide the numerator (Top number of a fraction) by the denominator (Bottom number of a fraction), multiply by 100, and add a percentage sign.
So lets try that with our first answer option A) 1/2:
1 divided by 2 = 0.5
0.5 x 100 = 50
50%
So we know that 1/2 is equivalent to 50%
10x — 12y = 6
5х – бу=3
Answer:
The equations system has multiple solutions for x, y.
Step-by-step explanation:
Let's solve for x and y this equations system:
We can observe that the second equation is a simplification of the first (divided by 2) and therefore, the system has multiple solutions for x and this way:
x y
-27/5 -5
-21/5 -4
-3 -3
-9/5 -2
-3/5 -1
3/5 0
9/5 1
3 2
21/5 3
27/5 4
33/5 5
PLZ help pic included
[tex]x = 4.82[/tex]
Step-by-step explanation:
Given equation is:
6.2 ÷ (2x+1) = 2 1/3 ÷4
Applying the division operation
[tex]\frac{6.2}{2x+1} = 2\frac{1}{3} * \frac{1}{4}\\\frac{6.2}{2x+1} = \frac{7}{3}*\frac{1}{4}\\\frac{6.2}{2x+1} =\frac{7}{12}\\[/tex]
Cross multiplication
[tex]6.2(12) = 7(2x+1)\\14x+7 = 74.4\\14x = 74.4-7\\14x = 67.4[/tex]
Dividing both sides by 14
[tex]\frac{14x}{14} = \frac{67.4}{14}\\x = 4.8142857....[/tex]
Rounding off to nearest hundredth
[tex]x = 4.82[/tex]
Keywords: Linear equation, variables
Learn more about linear equation at:
brainly.com/question/9969022brainly.com/question/9801816#learnwithBrainly
2x+y=1
9x + 3y = -3
The x-coordinate of the point of intersection is
-2
0
5
Answer:
The x-coordinate of the point of intersection is -2
Step-by-step explanation:
Here we have a typical system of linear equations whose solution will give us both the x- and the y- coordinates (i.e. the intersection point).
Let us solve the system and find which matches the available options, as follow. Given:
[tex]2x+y=1\\9x+3y=-3[/tex]
Taking the first expression and re arranging to solve for [tex]x[/tex] we have:
[tex]2x+y=1\\2x=1-y\\x=\frac{1-y}{2}[/tex] Eqn.(1)
Plugging in it, in the second expression we then have
[tex]9(\frac{1-y}{2} )+3y=-3\\\\\frac{9}{2}-\frac{9y}{2}+3y=-3\\ \\\frac{9}{2}-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}\\ \\-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}-\frac{9}{2}\\-3y=-15\\y=\frac{-15}{-3}\\ y=5[/tex]
So finally plugging in the y value in Eqn.(1) we have
[tex]x=\frac{1-5}{2} \\x=\frac{-4}{2}\\ x=-2[/tex]
The x-coordinate of the point of intersection is -2
The weight of an object on a particular scale is 145.2 lbs. The measured
weight may vary from the actual weight by at most 0.3 lbs. What is the range
of actual weights of the object?
Answer:
(144.9;145.5) so from 144.9 to 145.5lbs
Solve the below system of equations using the linear combination method. Show all your work, explaining each step in solving the system using the linear combination method.
2x + 3y = 1
y = -2x - 9
The solution of the system of equations is (-7 , 5)
Step-by-step explanation:
The steps of the linear combination method are:
Make the coefficients of one variable in the two equations same in values and different in signsAdd the two equations to eliminate that variable and make one equation of the other variableSolve the equation to find the other variableSubstitute its value in any one of the two equations to find the variable that eliminate before∵ 2x + 3y = 1 ⇒ (1)
∵ y = -2x - 9
- Add 2x to both sides
∴ 2x + y = -9 ⇒ (2)
Multiply equation (2) by -1 to make the coefficients of x opposites
∴ -2x - y = 9 ⇒ (3)
Add equations (1) and (3) to eliminate x
∴ 2y = 10
Divide both sides by 2
∴ y = 5
Substitute the value of y in equation (1) or (2) to find x
∵ 2x + 5 = -9
- Subtract 5 from both sides
∴ 2x = -14
- Divide both sides by 2
∴ x = -7
The solution of the system of equations is (-7 , 5)
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
#LearnwithBrainly
The table shows the times of the top six swimmers in the women’s 100 meter butterfly at the 2012 Olympic Games. A 2-column table with 6 rows. Column 1 is labeled Place with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Time (seconds) with entries 55.98, 56.87, 56.94, 57.17, 57.27, 57.35. Between which two places is the difference in finishing times the shortest? What is the difference in those times?
Answer:
The difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds.
Step-by-step explanation:
The first positioned swimmer took 55.98 seconds and the second positioned swimmer took 56.87 seconds to complete the race.
So, the difference is (56.87 - 55.98) = 0.89 seconds.
The second positioned swimmer took 56.87 seconds and the third positioned swimmer took 56.94 seconds to complete the race.
So, the difference is (56.94 - 56.87) = 0.07 seconds.
The third positioned swimmer took 56.94 seconds and the fourth positioned swimmer took 57.17 seconds to complete the race.
So, the difference is (57.17 - 56.94) = 0.23 seconds.
The fourth positioned swimmer took 57.17 seconds and the fifth positioned swimmer took 57.27 seconds to complete the race.
So, the difference is (57.27 - 57.17) = 0.10 seconds.
The fifth positioned swimmer took 57.27 seconds and the sixth positioned swimmer took 57.35 seconds to complete the race.
So, the difference is (57.27 - 57.35) = 0.08 seconds.
Therefore, the difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds. (Answer)
Answer:
Between which two places is the difference in finishing times the shortest?
2 & 3
What is the difference in those times?
0.07
Step-by-step explanation:
i do
A power regression equation for this data is: t = a^
Answer:
1.5
Step-by-step explanation:
Answer:
The person above is right.
Its: T = A^ 1.5
Step-by-step explanation:
Graph the planet data, shown right, using the regression calculator. When you are done, click “Resize window to fit data.”
Mercury and Venus are
✔ closer to
the sun than Earth is.
So, their orbital periods are
✔ shorter
than Earth's orbit.
The further a planet is from the sun, the
✔ longer
its orbit is.
A power regression equation for this data is:
T = A^
1.5
I took it and got it right.
20x^2+8x divided by 2
Answer:
[tex]10 {x}^{2} + 4x[/tex]
Step-by-step explanation:
[tex] \frac{20 {x}^{2} + 8x }{2} = \frac{20x}{2} + \frac{8x}{2} = 10 {x }^{2} + 4x[/tex]
What is the radius of my circle if it has a circumference of 154 cm give your answer to the nearest whole number
Answer: r ~= 24.50986
Step-by-step explanation:
This question is done by simply looking at the circumference formula for a circle (2pi r)
154= 2*pi*r
154/(2*pi) = r
r ~= 24.50986
Answer:
Step-by-step explanation:
[tex]circumference=2\pi*r\\\\2\pi*r=154\\\\2*\frac{22}{7}*r=154\\\\r=\frac{154*7}{2*22}\\\\r=\frac{49}{2}=24.5 cm[/tex]
The ratio of zinc to copper is 3 to 13 and a jar of the chemical contains 650 grams of copper. Can you please tell me the answer thanks :D
150 grams of zinc is present
Solution:
Given that, ratio of zinc to copper is 3 to 13
A jar of the chemical contains 650 grams of copper
From given information,
zinc : copper = 3 : 13
Let the zinc present be 3x
Let the copper present be 13x
Given that, jar contains 650 grams of copper
13x = 650
x = 50
Substitute x = 50 in 3x
Zinc present = 3x = 3(50) = 150
Thus it contains 150 grams of zinc
Find the sum 45+46+47+48...+135+136
Answer:
457
Step-by-step explanation:
I add all the numbers I could see and got 457.... i need more information hope this helps
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A.60
B.300
C.540
D.780
Answer:
540
Step-by-step explanation:
4×4×15×6×6=540
Explanation:
hope it helps
The volume of the solid rectangular prism with a hole is 444 mm³.
The correct answer is option A.
To find the volume of the solid rectangular prism with a hole, we calculate the volume of the outer rectangular prism and subtract the volume of the inner rectangular prism.
Volume of the Outer Rectangular Prism:
The outer rectangular prism has dimensions 15 mm (length) × 6 mm (width) × 6 mm (height). The volume (V_outer) is given by:
Volume_outer = length × width × height = 15 × 6 × 6 = 540 mm³.
Volume of the Inner Rectangular Prism:
The inner rectangular prism has dimensions 4 mm (length) × 4 mm (width) × the height of the outer prism (6 mm). The volume (V_inner) is given by:
Volume_inner = length × width × height = 4 × 4 × 6 = 96 mm³.
Volume of the Solid Rectangular Prism with Hole:
Subtracting the volume of the inner prism from the volume of the outer prism gives the volume of the solid:
Volume_solid = V_outer - V_inner = 540 - 96 = 444 mm³.
Therefore, the correct volume of the solid rectangular prism with a hole is 444 mm³.
The question probable may be:
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A. 444
B.300
C.540
D.780
Does anyone know this??
Answer:
z = 65°
y= 105°
Step-by-step explanation:
angle z is adjacent to 115° on a straight line, hence they are supplementary angles, i.e they add up to 180°
hence,
z + 115° = 180°
z = 180° - 115° = 65°
recall that the sum of angles inside a convex quadrilateral always adds up to 360°
i.e z + y + 102° + 88° = 360° (we know z from above)
65 + y +102+88=360
y = 360 -65-102-88 = 105°