Answer: 120
Step-by-step explanation:
Given: A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles.
The total number of marbles in the bag : 2+2+1+5+6=16
Now, the number of ways of selecting sets of four marbles include one of each color other than lavender is
[tex]\( C(2,1) \times C(2,1) \times C(5,1) \times C(6,1)=2 \times 2 \times 5 \times 6\)=120[/tex] [[tex]\because\ C(n,1)=n[/tex]]
Hence, the number of sets of four marbles include one of each color other than lavender = 120
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
i need both answers pls !!
Instructions: Find the missing length indicated.
225
144
X=
Answer:
108
Step-by-step explanation:
To find x, you need the geometric mean. First, find the second part of 225 by doing 225 - 144 = 81. Now, to find geometric mean, do 81 x 144 = 11,664; [tex]\sqrt{11,664} = 108[/tex].
The missing length in the right triangle as given in the task content is; 108.
What is the missing length indicated?It follows from the complete question that the triangle given is a right triangle and the missing length can be calculated as;
First, find the second part of 225 by
225 - 144 = 81.
Now, to find geometric mean,
81 × 144 = x²
11,664 = x²
x = 108
Thus, The missing length in the right triangle as given in the task content is; 108.
Read more on missing length;
https://brainly.com/question/28040679
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Given $m\geq 2$, denote by $b^{-1}$ the inverse of $b\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\equiv 1\pmod{m}$. Sadie wonders if $(a+b)^{-1}$ is always congruent to $a^{-1}+b^{-1}$ (modulo $m$). She tries the example $a=2$, $b=3$, and $m=7$. Let $L$ be the residue of $(2+3)^{-1}\pmod{7}$, and let $R$ be the residue of $2^{-1}+3^{-1}\pmod{7}$, where $L$ and $R$ are integers from $0$ to $6$ (inclusive). Find $L-R$.
[tex](2+3)^{-1}\equiv5^{-1}\pmod7[/tex] is the number L such that
[tex]5L\equiv1\pmod7[/tex]
Consider the first 7 multiples of 5:
5, 10, 15, 20, 25, 30, 35
Taken mod 7, these are equivalent to
5, 3, 1, 6, 4, 2, 0
This tells us that 3 is the inverse of 5 mod 7, so L = 3.
Similarly, compute the inverses modulo 7 of 2 and 3:
[tex]2a\equiv1\pmod7\implies a\equiv4\pmod7[/tex]
since 2*4 = 8, whose residue is 1 mod 7;
[tex]3b\equiv1\pmod7\implies b\equiv5\pmod7[/tex]
which we got for free by finding the inverse of 5 earlier. So
[tex]2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7[/tex]
and so R = 2.
Then L - R = 1.
Can someone please help me?
Answer:
B
Step-by-step explanation:
When you plug it in, another form could be y=-3x+2
Answer:
y=-3x+2
Step-by-step explanation:
y=-3x+7
parallel lines have the same slope but different y intercept which is b in the equation y=mx+b
since it passes through (2,-4) then x=2 and y=-4, m(slope)=-3
y=mx+b
-4=-3(2)+b
b=-4+6
b=2
y=-3x+2
It is 64º F at the 5000-foot level of a mountain, and 48º F at the 10,000-foot level of the mountain. Write a linear equation, in slope-intercept form, to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.
Answer:
T = - 3.2e + 80
Step-by-step explanation:
Given the following :
e = elevation in thousands of feets
T = temperature (°F)
e1 = 5 ; e2 = 10 (in thousands of feet)
T1 = 64° ; T2 = 48°
y = mx + c ; T = me + c
y = ; m = slope, c = intercept
64 = m5 + c - - - - (1)
48 = m10 + c - - - - (2)
From (1)
c = 64 - m5
Substitute c = 64 - m5 into (2)
48 = m10 + c - - - - (2)
48 = m10 + 64 - m5
48 - 64 = 10m - 5m
-16 = 5m
m = - 16 / 5
m = - 3.2
Substitute the value of m into c = 64 - m5
c = 64 - 5(-3.2)
c = 64 - (-16)
c = 64 + 16
c = 80
Inserting our c and m values into T = me + c
T = - 3.2e + 80
Where e is in thousands of feet
T is in °F
We have 9 balls, numbered 1 through 9, and 27 bins. How many different ways are there to distribute these 9 balls among the 27 bins? Assume the bins are distinguishable (e.g., numbered 1 through 27).
Answer:
7625597484987 ways
Step-by-step explanation:
Given the following :
Number of ball(k) = 9
Number of bins (n) = 27
How many different ways are there to distribute these 9 balls among the 27 bins.
Here, the balls have different labels (1 to 9)
The bins are also distinguishable, therefore each ball can go into any of the 27 distinct bins.
Therefore, the different ways are there to distribute these 9 balls among the 27 bins equals = n^k
27^9 = 7625597484987 ways.
Tapiwa raked %5, percent more leaves than Adam raked. Tapiwa raked 357 liters of leaves. How many liters of leaves did Adam rake?
HELP!! DUE SOON
Answer:
340 liters
Step-by-step explanation:
357/1.05=340
What is the product of the complex numbers below? (3-9i) (6-i)
[tex](3-9i)(6-i)=18-3i-54i+9i^2=18-57i-9=\boxed{9-57i}[/tex].
Hope this helps.
The number of bacteria in a petri dish on the first day was 113 cells. If the number of bacteria increase at a rate of 82% per day, how many bacteria cells will there be after 7 days?
Answer:
4107 cells
Step-by-step explanation:
From the question, we have the following values:
Day 1 : 113 cells
Number of cells increases by day by 82%
Hence,
Day 2
113 × 82% = 92.66cells
Hence, Total number of bacteria cells for Day 2 = 113 + 92.66 = 205.66cells
Day 3
205.66 × 82% = 168.6412 cells
Hence, Total number of bacteria cells for Day 3 = 168.6412 + 205.66 = 374.3012 cells
Day 4
374.3012 × 82% = 306.926984 cells
Hence, Total number of bacteria cells for Day 4 = 306.926984 + 374.3012 = 681.228184 cells
Day 5
681.228184 × 82% = 558.60711088 cells
Hence, Total number of bacteria cells for Day 5 = 558.60711088 + 681.228184 = 1239.8352949 cells
Day 6
1239.8352949 × 82% = 1016.6649418 cells
Hence, Total number of bacteria cells for Day 5 = 1016.6649418 + 1239.8352949 = 2256.5002367 cells
Day 7
2256.5002367 × 82% = 1850.3301941 cells
Hence, Total number of bacteria cells for Day 7 = 1850.3301941 + 2256.5002367 = 4106.8304308 cells
Approximately to nearest whole number, the total number of bacteria cells that would be present after 7 days = 4107 cells
You measure the sides of a pool and find that it is 20 yards wide and 50 yards long. Approximately, how far would it be diagonally between corners of the pool?
A. 54 yards
B. 58 yards
C. 62 yards
D. 66 yards
Answer:
[tex]\boxed{d = 54 yards}[/tex]
Step-by-step explanation:
Formula for diagonal is as follows:
[tex]d = \sqrt{l^2+w^2}[/tex]
Where d is diagonal, l is length (50 yards) and w is width (20 yards)
[tex]d = \sqrt{(50)^2+(20)^2}[/tex]
[tex]d = \sqrt{2500+400}[/tex]
[tex]d = \sqrt{2900}[/tex]
d = 53.85 yards
d ≈ 54 yards
Answer:
[tex]\boxed{\mathrm{54 \: yards}}[/tex]
Step-by-step explanation:
The shape of the pool is a rectangle.
The diagonal of a rectangle can be found through a formula by using Pythagorean theorem.
[tex]d^2=l^2 +w^2[/tex]
[tex]d=diagonal\\l=length\\w=width[/tex]
The length is given 50 yards, and width is given 20 yards. Find the diagonal.
[tex]d^2 =50^2 +20^2[/tex]
[tex]d^2 =2500+400[/tex]
[tex]d^2 =2900[/tex]
[tex]d=\sqrt{2900}[/tex]
[tex]d \approx 53.851648[/tex]
[tex]d \approx 54[/tex]
A square has diagonals of length 10 cm. Find the sides of the square
Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The diagonal divides the square into 2 right triangles.
let s be the side of the square with the diagonal being the hypotenuse.
Applying Pythagoras' identity to one right triangle, gives
s² + s² = 10² , that is
2s² = 100 ( divide both sides by 2 )
s² = 50 ( take the square root of both sides )
s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]
In a standard normal distribution, what is the probability of a z-score being less than 2.55?
Answer:
The probability is 0.0053861
Step-by-step explanation:
To answer this question, the best thing to do is to put the wordings in a mathematical expression.
Thus what we have is;
P(z < 2.55)
Now since we have the mathematical expression, the next thing to do here is to use the standard normal distribution table.
From the standard normal distribution table, we can get the probability value that equals the given z-score value
Mathematically this is;
P(z<2.55) = 0.0053861
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that
costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30
before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50.
Let S represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Answer:
[tex]\bold {3.25+5.50S \le 30}[/tex] is the correct answer.
Step-by-step explanation:
Given that
Chocolate milk already ordered for the cost of $3.25.
Maximum bill that Benjamin wants = $30
Cost of a stack pancake = $5.50
Number of stacks of pancakes bought = S
It is given that all the money available is to be spent on 1 chocolate milk and S number of stacks of pancakes.
Cost of 1 pancake = $5.50
Cost of S number of stacks of pancakes = [tex]\text{Number of stacks of pancakes} \times \text{Cost of each pancake}[/tex]
i.e. [tex]S \times 5.50 = 5.50S[/tex]
So, total money spent = $3.25+5.50S
Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.
So, the inequality can be written as:
[tex]\bold{3.25+5.50S \le 30}[/tex]
Find the measure of b.
Please help
Answer:
125 degrees
Step-by-step explanation:
Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.
Hope this is helpful! :)
A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 12 members and any member can be elected to each position? No person can hold more than one office.
Answer:
1320 setsStep-by-step explanation:
This problem brothers on selection without repetition, so we will be using permutation to solve this problem.
Given
n= 12 ,which is the number we are choosing from
r= 3, which is the number of committee(president, vice-president, and secretary-treasurer.)
[tex]= \frac{n!}{(n-r)!}[/tex]
Substituting we have
[tex]= \frac{12!}{(12-3)!}\\\\ = \frac{12!}{(9)!}\\\\= \frac{12*11*10*9!}{9!}[/tex]
[tex]= 12*11*10= 1320[/tex]
30 - 7p = -7 (p+6) -5
Answer:
I think it doesnt have solution.
Select the correct answer.
Which table shows a proportional relationship between x and y?
x y
1
5
2
6
3
7
x y
2
3
4
6
6
9
x y
4
16
8
64
12
144
x y
1
3
2
9
3
27
Answer:
I think
x y
2
3
4
6
6
9
Step-by-step explanation:
but i don't see any table
Which is the definition of a rhombus?
a. A quadrilateral with four right angles
b. A quadrilateral with four congruent sides
c. A quadrilateral with interior angles that sum to 360°
d. A quadrilateral with two pairs of opposite congruent sides
Answer:
a) A quadrilateral with 4 right angles
Answer:
I think the answer is b
I'm sorry if I'm not correct
A waffle cone has a height of 7 inches and a diameter of 3 inches. What is the volume of ice cream that can be contained within the cone? Use 3.14 to for pi. Round your answer to the nearest hundredth.
15.43 in^3
16.49 in^3
17.86 in^3
18.89 in^3
Hey there! I'm happy to help!
To find the volume of a cone, we multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find a circle, you square the radius and then multiply by pi (or 3.14 in our case).
Radius is half of the diameter.
3/2=1.5
We square this.
1.5²=2.25
We multiply by 3.14
2.25×3.14=7.065
Now, we multiply this base area by the height.
7.065×7=49.455
We divide by 3.
49.455/3=16.485
Therefore, if we round this, our answer is 16.49 in³.
Now you can find the volume of a cone! Have a wonderful day! :D
Answer:
16.49
Step-by-step explanation:
How do you solve this? Please provide a step-by-step explanation
The residual value is the distance between where the line is and the dot is.
At x = 2, the line crosses at y = 2, and the dot is at y = 1
The difference is: 2-1 = 1
BeUse the dot is below the line it becomes a negative value.
The answer would be -1
Pls hellppp
Jennifer wants to visit 4 different cities A,B,C and D on her vacation. If she will visit them one at a time, and completly random, what is thr probabitly that she will visit them in the exact order ABCD or DCBA?
Answer: The probability that she will visit them in the exact order ABCD or DCBA = [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Jennifer wants to visit 4 different cities A,B,C and D on her vacation.
If she visits in an order , total such orders will be [tex]4![/tex] = 4 x 2 x 3 x 1 =24.
Since probability = [tex]\dfrac{\text{Favourable outcomes}}{\text{total outcomes}}[/tex]
In this case favorable outcomes ( ABCD , DCBA)= 2
Total outcomes = 24
Required probability = [tex]\dfrac{2}{24}=\dfrac{1}{12}[/tex]
Hence, the probability that she will visit them in the exact order ABCD or DCBA = [tex]\dfrac{1}{12}[/tex]
HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
x= 24, y= 33°
Step-by-step explanation:
MJ is part of the diameter of the circle and there is right angle between the diameter and HK
As the diameter and HK are perpendicular, HM=MK and mHJ= mJK
So,
x= 24and
y= 66°/2= 33°A rectangle has a height of 2 and a width of 5x^2-2x+3x
Express the area of the entire rectangle.
Expression should be expanded.
how would I do this?^^ if you can break down the steps for me that'd be amazing!
Answer:
[tex] area = 10x^2 - 4x + 6 [/tex]
Step-by-step explanation:
Given that the rectangle has a height = 2, and width of [tex] 5x^2 - 2x + 3 [/tex]
Area of the whole rectangle can be calculated as:
[tex] area = 2(5x^2 - 2x + 3) [/tex]
Use the distributive property of multiplication by using 2 to multiply each term in the expression, [tex] (5x^2 - 2x + 3) [/tex]
[tex]area =2(5x^2) +2 (-2x) + 2(3)[/tex]
[tex] area = 10x^2 - 4x + 6 [/tex]
PLEASE help me with this question with solutions
Answer:
D
Step-by-step explanation:
the inscribed angle intersects an arc that twice the measure of the arc interested by the central angle. The inscribed angle's arc measures 144° and the central angle's arc measures 72°
>central angle and the arc the intersected arc are equal i.e they are both 72°
>the inscribed angle is half of the measure of the intersected arc i.e since the inscribed angle is 72° the arc interested is 144°
MATH HELP ME ASAP!!!!
Answer:
You get 12$ per B and 15$ per A. Thus, the answer is A) $282
Step-by-step explanation:
4A+4B=108
Divide by 4
A+B=27
Subtract B
A = 27 - B
3A+5B=105
Substitution
3(27-B)+5B = 105
Distribute
81-3B+5B=105
Combine like terms
81+2B=105
Subtract 81
2B=24
Divide by 2
B = 12
A = 15
14(15)+6(12)=x
210+72=x
282=x
Hope it helps <3
John has 9 boxes of apples. Each box holds 16 apples. If 7 boxes are full, and 2 of the boxes are half full, how many apples does john have?
Answer:
128 Apples
Step-by-step explanation:
Answer:
128 apples
Elaborated:
Your first multiple 16 and 7 which is 112. Your than multiply 2 and 8 since the remaining boxes are half full which is 16. 112+16 is 128. Hope this helps!
A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug remains in the body. (a) How much of the drug is in the body just after the sec- ond tablet is taken
Answer:
120 mg
Step-by-step explanation:
20% of 100 is 20 so that would be 20mg plus the 100mg they just took
100+20=120mg
i hope this helps you!
Simplify. Your answer should contain only positive exponents.
9) 3^-1 • 3^0
Answer:
1 / 3^1
Step-by-step explanation:
3^-1 • 3^0
When multiplying exponents with the same base, we add the exponents
3^ (-1+0)
3 ^-1
We know that a^ - b = 1/a^b
3 ^ -1 = 1/3^1
Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?
Complete question :
The table shows the total number of student applications to universities in a particular state over a period of 12 semesters. States base their decisions on data like this. Suppose they decide that if fewer than 200,000 students apply during 6 or more semesters, the state will make a special effort to promote university education. Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?
Semester Student Applications (in thousands)
1 106
2 137
3 285
4 120
5 202
6 195
7 327
8 139
9 307
10 318
11 212
12 217
Answer:
42%
Step-by-step explanation:
Given the above data in thousand :
Proportion of students
1 - - - - 106, 000
2 - - - -137, 000
3 - - - - 285, 000
4 - - - 120, 000
5 - - - 202, 000
6 - - - 195, 000
7 - - - 327, 000
8 - - - 139, 000
9 - - - 307, 000
10 - - - 318, 000
11 - - -212, 000
12 - - - 217, 000
Therefore, proportion of semesters with student application below 200,000
= (Number of semesters below 200,000 / total number of semesters)
Semesters below 200,000 :
(106000, 137000, 120000, 195000, 139000) = 5
(5 / 12) = 0.416666
= 0.42
In terms of percentage :
0.42 * 100 = 42%