Answer:
s = 3x - (1/2)y
Step-by-step explanation:
The perimeter of a square is 4s, where s is the side length. Here,
12x - 2y = 4s, and so s = 3x - (1/2)y
Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4?
Enter your answer, in simplest fraction form, in the box.
Answer:
7/18
Step-by-step explanation:
First we need to find what values of sum we can have.
The minimum value for a cube is 1, so the minimum value for the sum is 2.
The maximum value for a cube is 6, so the maximum value for the sum is 12.
Now, we find the multiples of 6 and the multiples of 4 between 2 and 12:
4, 6, 8, 12.
To have a sum of 4, we can have the pairs:
(1,3), (2,2), (3,1)
To have a sum of 6, we can have the pairs:
(1,5), (2,4), (3,3), (4,2), (5,1)
To have a sum of 8, we can have the pairs:
(2,6), (3,5), (4,4), (5,3), (6,2)
To have a sum of 12, we can have the pairs:
(6,6)
So we have 14 pairs among the 36 (6 possibilities of each cube, so 6*6=36) total possibilities of pairs, so the probability is P = 14/36 = 7/18
The probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4 is, [tex]P(E)=\frac{14}{36}=\frac{7}{18}[/tex]
The probability of any event is computed as divide number of favourable outcomes by total number of outcomes.
The sum that is a multiple of 6 or a sum that is a multiple of 4 are 4, 6, 8 and 12.
For sum of 4, we can have the pairs = (1,3), (2,2), (3,1)
For sum of 6, we can have the pairs: = (1,5), (2,4), (3,3), (4,2), (5,1)
For sum of 8, we can have the pairs = (2,6), (3,5), (4,4), (5,3), (6,2)
For sum of 12, we can have the pairs = (6,6)
Total number of favourable outcomes = 14
When two distinct number cubes are rolled. then,
Total number of outcomes [tex]=6^{2}=36[/tex]
The probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4,
[tex]P(E)=\frac{14}{36}=\frac{7}{18}[/tex]
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It took Beth 16 minutes to read 8 pages of a book. If she reads at a constant rate, how long did it take Beth to read 5 pages?
Answer:
Step-by-step explanation:
10 minutes
if it took her 16 minutes to read 8 pages then that means it takes her 2 minutes to read one page. 2 times 5 is 10
Answer:
Step-by-step explanation:
It would be ten. Because it took her 16 minutes to read 8 pages and 8 pages times 2 minutes each page = 16 minutes, so 5 pages times 2 minutes each page = 10
How many blocks with dimensions of 3 x1x1 can fit in a unit cube?
1
1
What is the answer to 50% of 480?
Answer:
240
Step-by-step explanation:
50% is the same as 50/100.
50/100=0.5
Then, multiply 0.5 by 480 (the same as dividing it by 2)
480*0.5= 240
What is the missing exponent in the equation 2? = 16?
Answer:
4
Step-by-step explanation:
2x2x2x2 = 16
Answer:
2^4 =16
Step-by-step explanation:
Rewriting 16
2^n = 2*2*2*2
2^n = 2^4
2^4 = 16
if the area of circle one is equal to the diameter of circle two what is the ratio of the area of circle two to the area of circle one
Answer:
0.7853981634
Step-by-step explanation:
it acually depends on the size of the circle. i asked google and they gave me that answer which is beloow "answer"
Consider rectangle ABCD with diagonals BD and AC
intersecting at
Which is true about the angle relationships in the
rectangle? Check all that apply.
BEA and 2 CED are vertical angles and equal
76
ZABE and 2 CBE are complementary angles,
BEC and CED are vertical angles,
-------
BEA and AED are supplementary angles
whose sum is 180°
O
BEC and
AED are adjacent angles,
Answer:
BEA and AED are supplementary angles whose sum is 180°
Step-by-step explanation:
complete question is:
Consider rectangle ABCD with diagonals BD and AC intersecting at E.
Which is true about the angle relationships in the rectangle? Check all that apply.
BEA and 2×CED are vertical angles and equal 76 ABE and 2×CBE are complementary angles, BEC and CED are vertical angles,BEA and AED are supplementary angles whose sum is 180° BEC and AED are adjacent angles,Answer:
it is abd
Step-by-step explanation:
1) Find the volume of the triangular prism.
5 yd
5 yd
3 yd
6 yd
8 yd
27 yd
72 yd
240 yd
360 yd
Answer:
I am not completely sure but I believe that it is C) 240 yd^3
Step-by-step explanation:
Find the mean, median, mode, and range of the data set.
23, 31, 26, 27, 25, 28, 23, 23, 25, 29, 29, 29, 25, 22, 30, 23
Answer:
Range: 9
Mode: 23
Median: 25.5
Mean: 26.1
Step-by-step explanation:
Arrange the data set from least to greatest.
22, 23, 23, 23, 23, 25, 25, 25, 26, 27, 28, 29, 29, 29, 30, 31
Range: Highest value - Lowest value =
Mode: The most number listed in the data set, or the listed numbers
Median: The middle number
Mean: finding the average of the data set
Range: 31 - 22 = 9
Mode: 23
Median: 25 + 26 = 51/2 = 25.5
Mean: 22 + 23 + 23 + 23 + 23 + 25 + 25 + 25 + 26 + 27 + 28 + 29 + 29 + 29 + 30 + 31 = 418/16 = 26.125 or 26.1
Which is equal
(please help asap!)
Answer:
B
Step-by-step explanation:
there
Eloise is designing a triangular flag. Is it possible to design more than one flag with side lengths of 27 inches and 40 inches and an included angle of50°? Explain. *
Answer:
Step-by-step explanation:
The given triangular flag has two given sides and an angle. Since the lengths of the sides and the size of the angle are known, it means that Eloise can design only one triangular flag. This is because the lengths cannot be altered. Also, the size of the angle is always the same. If the sizes of the three angles were known and the length of the sides were unknown, different sizes of the triangular flags can be produced with the angles remaining constant.
A cube with a volume of 64 cubic meters is scaled by factor of 5.what is the volume of cube in cubic meters?
Can you pleasee help me with the Screenshot Below its Overdue.
Answer:
what grade is this its and your answer is
Step-by-step explanation:
13/5 63/1 A = X
what is the volume of the solid
Answer:
204 cubic feet
Step-by-step explanation:
The formula for the volume of a rectangular prism is simply to multiply together the length, width, and height. In this case, 6*17*2=204 cubic feet. Hope this helps!
Answer:
do 16x17 divided by 2
Step-by-step explanation:
:)
a) -3 · x = -21
b) -7x + 16 = 2x - 20
help pls
The diagram below shows a shaded parallelogram drawn inside a rectangle. Using Pythagoras, find the hypotenuse of triangle A and the hypotenuse of triangle B to 1 decimal place.
Answer: 5.9 cm for both triangles.
Step-by-step explanation:
Hi, since the situation forms 2 right triangles we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of a triangle (the longest side of the triangle) and a and b are the other sides.
Replacing with the values given:
c^2 = 3^2 + 5^2
c^2 = 9+25
c^2 = 34
c = √34
c = 5.9 cm
Since both triangles are identical ( same side lengths) the hypotenuse is the same for both, 5.9 cm.
Feel free to ask for more if needed or if you did not understand something.
Unit 5. 8) Please help. Which of the two-dimensional cross sections listed below could be created by cutting a cube with a plane?
Select all that apply.
Answer:
hexagonrectanglesquaretrianglepentagonStep-by-step explanation:
Only a straight line can be formed at the intersection of a plane with another plane. The faces of a cube are planes, so a 2-dimensional (planar) cross section of a cube cannot be a curve. It cannot be an ellipse or circle.
What polygons are possible?The intersection of a plane with a cube can be a polygon with 3, 4, 5, or 6 sides. That is, the 2-D cross section of a cube can be ...
triangle, rectangle, square, pentagon, hexagon
__
The attachment shows some possibilities.
Answer
-5 < ___
A.-10
B.0
Answer:
B. 0
Step-by-step explanation:
The < sign means whatever is on the right side of the symbol should be greater than whatever is on the left side.
To solve this we need to understand that 0 is greater than -10. Then we need to make sure that 0 is greater than -5 and it is greater than -5.
Therefore the answer is 0
Hope this helps! If you have any more questions or need further clarification on anything please comment down below or message me! Good luck!
What
are the quotient and remainder of (5x^4+5x^2 +5)/(x^2-x+1)?
Answer:
Quotient is [tex]5(x^2+x+1)[/tex] and remainder is 0.
Step-by-step explanation:
Given: [tex]\frac{5x^4+5x^2+5}{x^2-x+1}[/tex]
To find: quotient and remainder
Solution:
In the given question,
Dividend = [tex]5x^4+5x^2+5[/tex]
Divisor = [tex]x^2-x+1[/tex]
[tex]\frac{5x^4+5x^2+5}{x^2-x+1}\\=\frac{5(x^4+x^2+1)}{x^2-x+1}\\=\frac{5[x^2(x^2+1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+x+1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x^3+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2-x+1+x-1)+1]}{x^2-x+1}\\=\frac{5[x^2(x^2-x+1)+x(x^2-x+1)+(x^2-x+1)]}{x^2-x+1}\\=\frac{5[(x^2-x+1)(x^2+x+1)}{x^2-x+1} \\=5(x^2+x+1)[/tex]
So, quotient is [tex]5(x^2+x+1)[/tex] and remainder is 0.
A store buys shirts from a distributor for $10 each and marks them up 50%. After selling them for 3 weeks, they put them on sale for 50% off. Is the discounted price $10?
Answer:
No, it’s 7.50
Step-by-step explanation:
The discounted price is 7.5, but according to question the discounted price is $10. Therefore given statement is wrong.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
Cost price of one shirt = $10.
Also, Shopkeeper marks up 50 % on shirts.
Marked up price = 10 x 50% = 10 x 50 / 100 = $15
Since, shopkeeper gives discount as put the shirts on sale for 50% off.
So the price after giving discount = 15 x 50 / 100 = 7.5
The discounted price of shirt is 7.5.
Hence, the given statement that is discount price is $10 is incorrect.
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Melanie earned $39 at her job when she worked for 3 hours. What was her hourly pay
rate in dollars per hour? Express your answer in simplest form.
Answer:
13
Step-by-step explanation:
To find the unit pay
you first had to do 39/3 (39 divided by 3) and then that answer you get is payment she receives in an hour
hour: 1 | 3
Pays: 13| 39
HOPE IT HELPS:)
Henry is standing on a catamaran at an elevation of 10 1010 feet relative to sea level. His friend Thomas is scuba diving at an elevation of − 12 1 2 −12 2 1 minus, 12, start fraction, 1, divided by, 2, end fraction feet relative to sea level. Which friend has greater elevation? Choose 1 answer: Choose 1 answer: (Choice A) A Henry (Choice B) B Thomas Which friend is farther from sea level? Choose 1 answer: Choose 1 answer: (Choice A) A Henry (Choice B) B Thomas
Answer:
A.) Henry
B.) Thomas
Step-by-step explanation:
Given the following :
Henry's elevation = 10feets relative to sea level
Thomas elevation = -12 1/2 that is (-25/2) feet relative to sea level
Person with greater elevation:
Elevation can be described as height, in this case, the sea level used as the reference point. Therefore, a positive distance denotes an elevation above the reference point (which is the sea level). Therefore, Henry has a greater elevation of 10 feet( a distance above 0).
B) Who is farther from sea level:
This can be calculated by comparing the absolute distance between the elevation of both Henry and Thomas relative to the reference point(sea level)
Take reference point as 0
Absolute distances relative to sea level:
Henry's distance | 10 - 0 | = 10
Thomas's distance | -(25/2)- 0 | = 12 1/2
Answer:
A then B
Step-by-step explanation:
PLEASE HELP!! Which diagram best models 2x3 + x2 + 3x + 4?
Answer:
O lol top right still
Step-by-step explanation:
Which account has the lowest minimum balance requirement? Bank Account Terms and Conditions Bank A has a $500 minimum balance, bank B has 250 dollars, bank C has 300 dollars, bank D has 100 dollars. Account A Account B Account C Account D
Answer:
The correct option is Account D
Step-by-step explanation:
Bank requires that $500 minimum balance,this is the highest minimum balance out of all the four banks.
Bank B's minimum required balance is $250 which is the third highest minimum balance.
Bank C requires account holder to have as minimum balance $300 which is second highest minimum balance.
Bank D only requires $100 that is the minimum among all the four banks
Bank D only requires $100 that is the minimum among all the four banks. Therefore, the correct answer is option D.
Bank requires that $500 minimum balance, this is the highest minimum balance out of all the four banks.
Bank B's minimum required balance is $250 which is the third highest minimum balance.
Bank C requires account holder to have as minimum balance $300 which is second highest minimum balance.
Bank D only requires $100 that is the minimum among all the four banks.
Therefore, the correct answer is option D.
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A researcher works on a study that has a population standard deviation of 0.73a sample mean of 84.5 and a sample size of 60 .What is the margin of error with a confidence level of 95%
Answer:
[tex] ME = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
The critical value can be founded in the normal standard distribution table using the value of [tex]\alpha/2 =0.025[/tex] and we got [tex] z_{\alpha/2}=1.96[/tex]. Replacing the info given we got:
[tex] ME = 1.96 \frac{0.73}{\sqrt{60}}= 0.185[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] \sigma = 0.73[/tex] represent the population deviation
[tex] \bar X = 84.5[/tex] represent the sample mean
[tex] n =60[/tex] represent the sample size
And we want to find the margin of error for a confidence level of 95%. So then the significance level would be [tex]\alpha=1-0.95 = 0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. The margin of error is given by:
[tex] ME = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
The critical value can be founded in the normal standard distribution table using the value of [tex]\alpha/2 =0.025[/tex] and we got [tex] z_{\alpha/2}=1.96[/tex]. Replacing the info given we got:
[tex] ME = 1.96 \frac{0.73}{\sqrt{60}}= 0.185[/tex]
A family has three children. The oldest child is 4 years older than the
middle child, and the youngest child is 2 years younger than the
middle child. The sum of the ages of the children is 26.
R
How many years old is the youngest child?
years old
Q
Answer:6 years
Step-by-step explanation:
Given
A family has 3 children
Suppose the age of middle child is [tex]x[/tex]
According to the question, Age of oldest child is [tex]=x+4[/tex]
Eldest child age [tex]=x-2[/tex]
Sum of the ages of children is [tex]26[/tex]
[tex]x+4+x+x-2=26[/tex]
[tex]3x+2=26[/tex]
[tex]3x=24[/tex]
[tex]x=8[/tex]
Therefore age of youngest child is [tex]x-2=8-2=6\ years[/tex]
If a circle has a diameter of 30 meters, which expression gives its area in
scuare meters
Answer:
A = pi (15)^2
Step-by-step explanation:
The diameter is 30
The radius is 1/2 of the diameter
r = d/2 =30/2 = 15
The area of a circle is
A = pi r^2
A = pi (15)^2
A = 225 pi
Answer:B
Step-by-step explanation: 30 is the diameter so we divide it by 2 to get 15 which is the radius. Radius to the power of 2 times pi is how you get area so 15^2 times pie equals area.
What is perimeter of rectangle JKLM?
Answer: 16 units
Step-by-step explanation:
Find the length of each of the four sides and add them all together. The short sides each measure 3 units and the long sides each measure 5 units. 3+3+ 5+5 = 16
What is the area of the base
A certain lot consisting of ten items has three defective items and seven nondefective items. How many possible subsets of 2 items can be chosen from this lot?
21
45
90
Answer:
45
Step-by-step explanation:
The order in which the items are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many possible subsets of 2 items can be chosen from this lot?
Combinations of 2 from a set of 10. So
[tex]C_{10,2} = \frac{10!}{2!(10-2)!} = 45[/tex]
Answer:
45
Step-by-step explanation:
