Answer:
0.3756
Step-by-step explanation:
I believe this is a combinatorics probability problem.
We first figure out in how many ways we can choose 3 cats out of 14 cats
Then we figure out how many ways we can choose 2 dogs out of 7 dogs
The total number of ways to select 3 cats and 2 dogs will be the product of these two
We then figure out in how many ways we can select 5 animals out of a total of 21 animals
The product we computed divided by the above number will give the probability
The number of ways we can choose k items out of n items is given by nCk i.e n Choose k
The formula is rather complicated but almost all calculators should be able to compute this given n and k
Let's deal with the selection of 3 cats from the population of 14 cats
This is given by 14C₃ which works out to 364
Number of ways for selecting 2 dogs from 7 dogs = 7C₂ = 21
Number of ways of selecting 5 animals from 21 = 21C₅ = 20349
The probability of selecting 3 cats and 2 dogs is therefore:
[tex]\dfrac{364 \times 21}{20349} = 0.3756[/tex]
That, I believe is the answer. Please let me know if it is correct and if you need more info.
order the fraction to least to greatest 2/3 3/7 4/8
Find the smallest length that can be divided exactly into equal sections of length 5m,8m and 12m
As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.
What is an LCM example?The acronym LCM stands for the least common multiple or factor of any two or more specified integers. The least common multiple for the numbers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.
What is the LCM of 4 and 8?8 is the LCM of 4 and 8. The LCM is the number that can be divided by the provided numbers equally. You can discover the least common multiple of 4 and 8 by looking at the common multiples. 4 is a multiple of 8, 12, 16, 20, 24, etc.
finding prime factors of the given numbers by repeated division method in order to find the LCM;
2 | 5,8,12
5 | 5,4,6
2 | 1,4,6
2 | 1,2,3
3 | 1,1,3
0 | 1,1,1
so we get 2x5x3x2=60
As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.
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The shortest length which can be split into equal segments of length 5 meters, 8 meters, or 12 meters is 120.
What does "section" signify in terms of forms and purposes?Your form may be divided into sections with the help of sections, as the name suggests. This enables your users to input responses that might be categorized. The fact that sections divide your form into distinct screens is another significant benefit. For instance, a first screen shows section 1. When concealed lines in external views cannot adequately represent a part's inner design, sections are employed. The internal components can be viewed more clearly by imagining cutting through the thing and removing a section of it.
Briefing:Finding the LCM by repeatedly dividing the supplied integers to get their prime components:
2 | 5,8,12
2 | 5,4,6
2 | 5,2,3
3 | 5,1,3
5 | 5,1,1
1 | 1,1,1
So we get 2*2*2*3*5*1 = 120
The lowest length that could be divided into precisely equal segments in lengths 5 m, 8 m, and 12 m is 120, which equals the LCM of 5, 8, & 12.
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4 7/8 + (2 1/6). It’s fractions by the way.
Answer:
7 and 1/24
Step-by-step explanation:
4 7/8 + 2 1/6
First when adding fractions, we want to have a common denominator. To do that, we must multiply the fractions until we get a desired denominator. We can find LCM.
The LCM of 6 and 8 is 24, so we must multiply accordingly.
We can put this into improper fraction form:
39/8 + 13/6
Then multiply accordingly. Multiply by 3 on both sides for the first fraction, and multiply by 4 on both sides for the second to get a denominator of 24.
117/24 + 52/24
Now, we can add the fractions.
169/24
Simplify
7 and 1/24
(04.06A) Which of the following does not describe slope?
The option that doesn't describe slope is A. A line joining points.
What is a slope?Slope is determined by dividing the vertical change by the horizontal change between two distinct points on a line.
It is defined as the difference in y coordinate divided by the difference in x coordinate between two distinct points on the line.
A line's slope is a number that describes both its direction and its steepness. Slope is a measure of change or a constant rate of change between two points.
As a result, from the options given, slope is not a line segment connecting two points, but rather the change in a line segment between two points.
It should be noted that the correct option is A.
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Complete question
Which of the following does not describe slope?
A. A line joining points.
B. A constant rate of change
C. A proportional relationship
D. A measure of change
"How do we transform System A into System B?
Equation [A1] → Equation [B1]
Equation [A2]→ Equation [B2]
Equation [A1]+Equation [A 2] → Equation [B 2]
Equation [A2]+ Equation [A 1] → Equation [B 1]"
The transformation of System A into System B is:
Equation [A2]+ Equation [A 1] → Equation [B 1]"
The correct answer choice is option D
How can we transform system A into System B ?To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].
System A:
-3x + 4y = -23 [A1]
7x - 2y = -5 [A2]
Multiply equation [A2] by 2
14x - 4y = -10
Add the equation to equation [A1]
14x - 4y = -10
-3x + 4y = -23 [A1]
11x = -33 [B1]
Multiply equation [A2] by 1
7x - 2y = -5 ....[B2]
So therefore, it can be deduced from the step by step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].
The complete image is attached.
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6,370 x 30 find the products
How do I show my thinking or ideas
Example
637•3 6370•30
=1911 =(6370•3)• (10•10)
Answer:
Product: 191,100
Step-by-step explanation:
Show your work:
(It should look something like this)
6370 x 30
First: 0 x 0 = 0 (so you put):
6370 x 30
0
(everything else times 0 just equals 0 so you'd get this):
6370 x 30
0000
Next: 3 x 0 = (so you put):
6370 x 30
0000
0
Next: 3 x 7 = 21 (so you put):
6370 x 30
0000
10
(carry the 2)
Next: 3 x 3 = 9 (so you put):
2
6370 x 30
0000
1 10
(add the number you carried to 9: giving you 11 so you also have to carry a 1 again)
(the first number: 0 of 110 goes under the third 0 of 0000)
(the spacing is just to make sure that the placement is correct: the first 1: of 110 goes under the first 0 of 0000)
Next: 3 x 6 = 18 (so you put):
1 2
6370 x 30
0000
191 10
(you add the 1 that you carried to 18 to give you 19)
(again: I only moved the zeros over so that the placement is correct)
Next: Now you add(this is why the placement of the numbers is important):
1 2
6370 x 30
0000
+ 191 10
191,100
(you will put imaginary zeros over 19 because you know that there is already nothing there. You will also add an imaginary zero under the last zero that is hanging there because you know there is nothing there either.)
(Hope this helps! I know its really confusing, if you have any further questions or if the way I explained confused you please tell me or ask me those questions.) :)
A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $22 . Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
The linear equation in the form p(n) = mn + b that gives the price p they can charge for n shirt is p(n) = - 1 / 250n + 34.
How to linear equation in slope intercept form?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p , it can charge per shirt. 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $22 .
Therefore,
using (1000, 30) and (3000, 22) let's find the slope.
m = 22 - 30 / 3000 - 1000
m = - 8 / 2000
m = - 1 / 250
Hence, let's find the y-intercept using (1000, 30)
p(n) = mn + b
where
p = pricen = number of shirtTherefore,
30 = - 1 / 250 (1000) + b
30 = - 4 + b
b = 30 + 4
b = 34
Hence, the linear equation is p(n) = - 1 / 250n + 34
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Jordan went swimming for 7/8 hour in the morning and 5/6 hour in the afternoon. What is the best estimate for the total time Jordan went swimming?
The total time for Jordan went swimming will be;
⇒ 41/24
What is Addition?
The process of combining two or more numbers is called the Addition.
Given that;
Jordan went swimming for 7/8 hour in the morning and 5/6 hour in the afternoon.
Now,
Since, Jordan went swimming for 7/8 hour in the morning and 5/6 hour in the afternoon.
Hence, The total time for Jordan went swimming will be;
⇒ 7/8 + 5/6
⇒ (21 + 20) / 24
⇒ 41/24
Thus, The total time for Jordan went swimming will be;
⇒ 41/24
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Solve for m.
m+15<−123
Responses
m>−11315
m is greater than negative 1 and 13 over 15
m>−1715
m is greater than negative 1 and 7 over 15
m<−1715
m is less than negative 1 and 7 over 15
m<−11315
help
The solution to the value of m in the inequality m + 1/5 < - 1 2/3 is "m is less than negative 1 and 13 over 15".
The correct answer option is option D
How to solve inequality?Inequality is a statement that is of two quantities I'm which one is specifically less than (or greater than) another. The symbols of inequality are;
Greater than >Less than <Equal to =Greater than or equal toLess than or equal tom + 1/5 < - 1 2/3
substract 1/5 from both sides
m < -5/3 - 1/5
m < (-25-3) / 15
m < -28/15
Therefore, from the inequality m + 1/5 < - 1 2/3, m is less than negative 1 and 13 over 15.
Complete question:
m + 1/5 < -1 2/3
Responses
A. m > −1 13/15
m is greater than negative 1 and 13 over 15
B. m > −1 7/15
m is greater than negative 1 and 7 over 15
C. m < −1 7/15
m is less than negative 1 and 7 over 15
D. m < −1 13/15
m is less than negative 1 and 7 over 15
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Write three and seven eighths as an improper fraction and as a mixed number.
A 17/8, 3 7/8
B 31/8, 3 7/8
C 31/8, 7 3/8
D 59/8, 7 3/8
Find the probability of exactly three
successes in six trials of a binomial
experiment in which the probability of
success is 50%.
The probability exactly three successes in six trials is 31.30%
What is Binomial Distribution?A binomial distribution can be defined as the probability of a success or failure outcome in an experiment or survey that is repeated multiple times.
The probability distribution of a binomial distribution is given by :
P(x = k) = n! /k!(n - k)! P^x(1 - P)^(n - k)
In our case :
n = 6
P = 50/100 = 0.5
Now we want the probability that:
x = 3
This is because the question states that we want the probability that the number of successes are exactly 3.
We do the substitution in the probability distribution function as follows :
P(x = 3) = 6!/3!(6 - 3)! × 0.5³ × (1 - 0.5)³
= 0.3125
= 31.25%
= 31.30%
Hence, the probability of exactly three successes in six trials of a binomial experiment in which the probability of success is 50 is 31.30%
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m/3 - 6 = 4
solve for m
Answer:
m=10
Step-by-step explanation:
m/3-6=4
30/3=10
10-6=4
3) A
a
Square with an area of 25m² and
perimeter of 20 is reflected across line
L, then translated 20m right, and then
rotated 20 degrees clockwise, what is
area and perimeter after these transformations?
the
Answer:
Area =25m²
Perimeter = 20m
Step-by-step explanation:
None of the transformations described change the size or shape of the original object, only position and orientation are changed
The temperature T°C of a cup a tea t minutes after being poured is modelled by the exponential decay function:
T=18+68e^-t/8, t>/= 0
a) What is the initial temperature of the tea the moment it was poured?
b) When will the temperature of the tea reach 35°C?
c) Explain why the tea will never reach an ambient temperature of 15°C.
Using the exponential function T = 18 + 68e^(-t/8), the initial temperature is 86°C, the time the temperature will reach 35°C is 11.1 minutes
Exponential FunctionAn exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form f(x) = aˣ
In the question given, the exponential function given shows an exponential decay
T = 18 + 68e^(-t/8)
a) The initial temperature when the tea was poured would be (t = 0)
T = 18 + 68e^(-0/8)
T = 16 + 68 = 86°C
b) The temperature of the tea at 35°C
35 = 18 + 68e^(-t / 8)
T = 11.1
c) The reason why the the tea will never reach 15°C is because there's no solution for the expression.
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The sales tax rate on a new vehicke is 6.5 percent. If the vehicle is priced at 12,000, how much will you be charged for sales tax?
If sales tax rate on a new vehicle is 6.5 percent. If the vehicle is priced at 12,000, then 780 will be charged for sales tax
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The sales tax rate on a new vehicle is 6.5 percent.
The price of the vehicle is 12000
We need to find the how much will you be charged for sales tax
Let us convert 6.5 percent to the decimal value by dividing it with 100
6.5/100×12000
0.065×12000
780
Hence, 780 will be charged for sales tax.
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Given m || n, find the value of x.
Answer:
x=11°
Step-by-step explanation:
Because line t is 180°, (9x-5)°+(6x+20)°=180°
Simplify:
(9x-5)°+(6x+20)°=180°
9x-5+6x+20=180
15x-5+20=180
15x+15=180
15x=165
x=11
PLEASE MARK AS BRAINLIEST!!Find the area of a shaded portion 10 km 20 km 20km
The area of the shaded region will be 150 square kilometers.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a 2- D figure as shown in the image.
The area of the shaded region will be -
A[shaded] = A [square] - {A [Δ1] + A [Δ2] + A [Δ3]}
A[shaded] = (20 X 20) - [{1/2 x 10 x 10} + {1/2 x 10 x 20} + {1/2 x 10 x 20}]
A[shaded] = 400 - [50 + 100 + 100]
A[shaded] = 400 - 250
A[shaded] = 150 square kilometers
Therefore, the area of the shaded region will be 150 square kilometers.
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find the greatest perfect square that is a factor of 495
Answer:
1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495 are the factors of 495. Additionally, the highest perfect square on this list is 9, and 3 is 9's square root. So, A is equal to 3.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The factors of 495 are:
1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495.
The greatest perfect square that is a factor of 495 is 9.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
495
The factors of 495 are:
1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495.
Now,
The perfect squares from the factors of 495 are 1 and 9.
9 is the greatest perfect square of 495.
Thus,
The greatest perfect square that is a factor of 495 is 9.
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Using division, what is the quotient (2x3 - 2x - 12) ÷ (x - 2)?
2x² + 4x-6 +
2x² - 4x + 6
1
X 2)
Answer: 2x²+4x+6
Step-by-step explanation:
[tex]\displaystyle\\\frac{2x^3-2x-12}{x-2} =\\\\\frac{2(x^3-x-6)}{x-2}=\\\\ \frac{2(x^2-8+8-x-6)}{x-2} =\\\\\frac{2(x^3-2^3-x+2)}{x-2} =\\\\\frac{2((x^3-2^3)-(x-2))}{x-2}=\\\\\frac{2((x-2)(x^2+2x+2^2)-(x-2))}{x-2} =\\\\\frac{2(x-2)(x^2+2x+4-1)}{x-2}=\\\\2(x^2+2x+3)=\\\\2x^2+4x+6[/tex]
There are approximately 123,000 people on the waiting list to get season tickets for the Green Bay Packers. This is about 14 times as many as are waiting for Bears tickets and 12 times the number of people waiting on lion's tickets. About how many people are waiting for chicago bears season tickets?
Answer:
8786
Step-by-step explanation:
123,000/14 = 8786 Since it is about, I rounded to the nearest whole number.
If 41 and 42 are complementary angles and if the measure of 41 is 50° more than the measure of 42, determine the measures of 41 and 42
Answer:
m∠1 = 70
m∠2 = 20
Step-by-step explanation:
41 and 42 are complementary angles: m∠1 + m∠2 = 90
measure of 41 is 50° more than the measure of 42: m∠1 = m∠2 + 50
substitute: (m∠2 + 50) + m∠2 = 90
simplify and solve: 2(m∠2) + 50 = 90
2(m∠2) = 40
m∠2 = 20
Which of the following choices is equivalent to the equation?
3(x−1) = 27
x – 1 = 9
x – 1 = 3
x – 1 = -3
Answer:
just finished a challenge
Step-by-step explanation:
Point P was rotated about the origin (0, 0) by - 15°.
Answer:
the answer is d.
Step-by-step explanation:
Write an equation of the line through (-4,0) and (6,-1). Write the equation in standard form.
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-1 -0}{6 +4} \implies \cfrac{ -1 }{ 10 } \implies - \cfrac{1 }{ 10}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{1 }{ 10}}(x-\stackrel{x_1}{(-4)}) \implies y -0 = - \cfrac{1 }{ 10} ( x +4) \\\\\\ y=- \cfrac{1 }{ 10}(x+4)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10(y)=10\left( - \cfrac{1 }{ 10} ( x +4) \right)}\implies 10y=-(x+4) \\\\\\ 10y=-x-4\implies {\Large \begin{array}{llll} x+10y=-4 \end{array}}[/tex]
3 + 5 to the power of 2 - 6 • 4
Answer: The correct answer is 4
Step-by-step explanation:
You welcome have a great day
Does the volume of a cone increase more when you double the height of the original or when you double its radius? Explain why.
The volume of a cone increase more when you double the height of the original or when you double its radius. This is true.
What is a cone?A cone is a shape formed by connecting a common point, known as the apex or vertex, to all the points of a circular base with a set of line segments. The height of the cone is the distance from the vertex to the base.
A cone always contains a right angle. To solve for the volume of a cone, we need to get the radius of the cone and its height. radius is the line from the center of the circle of the cone going to the edge of the circle. height is the measurement of the cone from its pointy tip going downward.
The volume of a cone is 1/3πr²h, so if you double the radius the volume would quadruple. So, when the height is doubled, the volume is also doubled.
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floor of a classroom is 38 feet in length and 34 feet in width. A scale drawing of the floor has a length of 19 inches.
Answer:
38 i think i hope this helps
What is the length of Line segment AC?
3 ft
4 ft
18 ft
12 ft
The function f(x) = 2x3 + 3x2 + 2x – 1 is divided by (x – 1) .
Step-by-step explanation:
here is your answer hope it helps you plaz mark me as brainlist
Evie just had her birthday. she got a $30 gift card for dunkin donuts and she can’t spend more than $30. the small coffees cost $2 and the large cost $4. she wants to buy at least 10 coffees. how many coffees can she buy using only her gift card?
Answer:
Step-by-step explanation:
30 dollars to spend she wants to buy at least ten which mean's since 2 times 5 is 10 and 4 times 5 is 20 and 10 plus 20 equals thirty which means she can buy 5 small coffee's and 5 large coffee's