Answer:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160
Step-by-step explanation:
eight people are sitting around a circular table, each holding a fair coin. all eight people flip their coins and those who flip heads stand while those who flip tails remain seated. what is the probability that no two adjacent people will stand?
The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.
What is combination?A combination is a grouping of items where order does not matter. The formula of combination is
[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]
Where
C = number of combinationsn = number of total itemsr = number of choosing itemsGiven the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.
What is the probability that no two adjacent people will stand?
First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.
The number of arrangements according to the number of people standing.
Case 1: 0 people standing = 1 arrangement.
Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.
Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.
Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.
Case 5: 4 people standing but no two adjacent people = 2 arrangements.
The number of arrangements that no two adjacent people will stand.
n(A) = 1 + 8 + 20 + 16 + 2 = 47
The probability that no two adjacent people will stand is
P(A) = n(A)/n(S)
P(A) = 47/256
Hence, the probability that no two adjacent people will stand is 47/256.
Learn more about finding probability with combination here:
brainly.com/question/3901018
#SPJ4
which of the following quantitative research methods uses a relatively small group of people for testing and is most helpful in obtaining data that are representative of the whole population? a.) in-depth interviews b.) secondary data analysis c.) natural experiments d.) random sampling
In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.
Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.
An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.
Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.
For more information on quantitative research methods kindly visit to
https://brainly.com/question/29242901
#SPJ4
A triangle has vertices A(−1,2)
, B(2,5)
, and C(3,−4)
. If the image resulting from a rotation has vertices A'(−2,−1)
, B'(−5,2)
, and C'(4,3)
, write the rule that describes the rotation:
Answer: [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
90 degree counter-clockwise rotation around the origin.
===================================================
Explanation:
Focus on A(-1,2) and A'(-2,-1)
The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"
In other words, we've gone from (x,y) to (y,x) to (-y,x)
Representing this with arrows looks like:
[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]
or in short
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
which represents a 90 degree counter-clockwise rotation around the origin.
-----------------------------------
Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]
Sure enough, it works for point B.
Lastly, let's check if it works for point C.
We should go from C(3,-4) to C'(4,3).
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]
All points have been confirmed.
Can somone help me with this will mark u brainliest
Answer:
[tex] = 3 + \sqrt{25 } - \sqrt{12} \\ = 3 + 5 - \sqrt{12 \\ } \\ = 8 - \sqrt{12} [/tex]
[tex] = 8 - 2 \sqrt{3} [/tex]
option d is correct
You and 3 buddies take a job cleaning up your neighbor's garage and he pays you $220. How will you divvy it up so everyone gets an equal share? What percentage is that?
Answer:73.33
Step-by-step explanation:
The answer is 73.33 because 73.33 multiplied by 3 = 219.99
If g(x) = -2x² + 3x - 1, find g(x + 1)
The value of the equation g(x+1) is -2x²-x
Given equation,
g(x) = -2x²+3x-1
Replacing x in the equation by x+1
g(x+1) = -2(x+1)² +3(x+1) -1
g(x+1) = -2(x²+1+2x) +3x +3 -1
g(x+1) = -2x² -2 -4x +3x +3 -1
g(x+1) = -2x²- x
Hence the final answer is g(x+1) = -2x²-x
Since this, the question says to find the value g(x+1) we need to replace the value of x in the given equation g(x) by x+1 to find value. After replacing we get -2(x+1)² +3(x+1) -1. Next, we need to solve the bracket (x+1)² which will give us x²+1+2x. We will multiply this by -2, which will give us -2x² -2 - 4x. Next, we will solve 3(x+1) which will give us 3x+3. Finally, we need to solve the whole equation to get the answer -2x²- x
I hope this answer helps.
To learn more about composite functions,
https://brainly.com/question/20379727
The president of the Huerta Middle School science club suggested a field trip to the local
aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who
goes.
Write an equation showing how the total cost, y, depends on the number of students going,
X.
Do not include dollar signs in the equation.
►
y =
The equation that shows the total cost, depends on the number of students going is y = 21.25 + 14.75x
Equation:
An equation is made up of two expressions connected by an equal sign.
For example, y = 3x + 6 is an equation.
Given,
The president of the Huerta Middle School science club suggested a field trip to the local aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who goes.
Here we need to find the equation that shows the total cost depends on the number of students.
Let us consider x be the number of students and y be the cost for x number of students.
Here we know that, there is one club advisor whose ticket cost is $21.25 and the cost per student is $14.75.
So, based on these details, the equation for the total cost is calculated as,
=> y = 21.25 + 14.75x
To know more about Equation here.
https://brainly.com/question/10413253
#SPJ1
PLEASE HELP
Write the equation of a line that is perpendicular to y = 5 and that passes through the point
(-7, --5).
The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.
We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).
y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.
Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).
Hence, the line perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.
To learn more about equation, here:-
https://brainly.com/question/10413253
#SPJ1
The sum of two consecutive integers is less than -9. What is the smallest value that will make this true? Write and solve an inequality. Show your work using 3 or 4 steps.Use s as your variable. Round your initial answer to the nearest hundredth.
The value of the inequality when the sum of two consecutive integers is less than -9 is x < - 5.
How to calculate the value?It is vital to note that an inequality simply shows that the expressions aren't equal.
In this case, the sum of two consecutive integers is less than -9.
Let the integers be x and x + 1.
Therefore, x + x + 1 < -9
2x + 1 < -9
Collect like terms
2x < -9 - 1
2x < -10
Divide
x < - 10 / 2
x < - 5
The value is x < - 5.
Learn more about Inequalities on:
brainly.com/question/25275758
#SPJ1
When f(x) equals X -7/2, what is the value of (F•F^-1) (3)
The value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.
The given function is f(x)=x-7/2.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The inverse of the given function is
y=x-7/2
Replace y with x and x with y, we get
x=y-7/2
y=x+7/2
[tex]f^{-1}(x)[/tex]=x+7/2
When x=3
[tex]f^{-1}(3)=3+7/2[/tex]
=6.5
f(6.5)=6.5-7/2
=6.5-3.5
=3
Therefore, the value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1
Write 8433 in scientific notation.
I know the answer but can someone give me an explanation and steps.
Answer:
8.433 to the power of 4
Step-by-step explanation:
The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.
A C B D E Which statement cannot be assumed from the figure? OA A ZABD and ZDBE are supplementary OB BD bisects ZADE. Oc LCDA and ZADE are complementary. OD ZEDB and ZBDA are adjacent and are not complementary.
The statement that cannot be assumed from the figure is
B) BD bisects ∠ADE
What are Supplementary and Complementary Angles?
Supplementary angles are two angles that have a sum of 180°.
Complementary angles are two angles that have a sum of 90°.
Given data ,
From the figure we can arrive at each conclusions
A)
∠ABD and ∠DBE are supplementary
Now , from the figure we can see that point B lies on the line AE
And , ∠ABD + ∠DBE = 180°
Hence , ∠ABD and ∠DBE are supplementary and the statement is TRUE
B)
Bisecting a line means dividing the line into two equal parts
And from the figure BD does not bisect ∠ADE
Hence , BD does not bisect ∠ADE so the statement is FALSE
C)
∠CDA and ∠ADE are complementary
From the figure we can see that ∠EDC is 90°
And , ∠CDA + ∠ADE = ∠EDC
So , ∠CDA + ∠ADE = 90°
Hence , ∠CDA and ∠ADE are complementary and the statement is TRUE
D)
∠EDB and ∠BDA are adjacent and are not complementary
From the figure we can see that ∠EDB and ∠BDA are adjacent
∠EDB + ∠BDA ≠ 90°
Hence , they are not complementary and the statement is TRUE
To learn more about supplementary and complementary angles click :
https://brainly.com/question/14690981
#SPJ1
The side lengths of triangle ABC are written in terms of
the variable p, where p > 3.
A
p+4
C
4p-1
3p
B
Which is correct regarding the angles of the triangle?
Om/A> m2C> mzB
OmZB> mzA> mZC
Omzc>m mZB
O mzC> m2B> MZA
m∠C > m∠A > m∠B is correct regarding the angles of the triangle ABC.
What is the angle of the triangle?
While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.
Here, we have
In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.
AB=4p-1 , AC=p+4 , BC=3p
where p+4 < 3p [as p≥3]
3p < 4p-1 [as p≥3]
⇒ 4p-1> 3p > p+4
⇒AB > BC > AC
Angle opposite to AB, BC, and AC is m∠C,m∠A, and m∠B.
m∠C > m∠B > m∠A [∵Angle opposite to greater side is greater]
Hence, mC > mA > m∠B is correct regarding the angles of the triangle ABC.
To learn more about the angles of the triangle from the given link
https://brainly.com/question/20126678
#SPJ13
HELP MEEE PLEASEEEE
Answer:
5.8 cm
Step-by-step explanation:
the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:
4^2 + 4.2^2 = a^2
Simplify: 16 + 17.64=a^2
Simplify again: 33.64 = a^2
Square root both sides: 5.8 = a
write an equation of the line perpendicular to -4x+3y=12 and containing the point (6,8)
The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.
What is a perpendicular line?
Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.
Here,
The slope of ax + by = c is given by m = -a/b
m = -(-4)/3 = 4/3
m = 4/3 for this line.
A perpendicular line will have a slope -1/m = -3/4
The line through (6, 8) with slope -3/4
y = (-3/4)x + b
8 = (-3/4)(6) + b
b = 8 + 9/2 = 25/2
y = (-3/4)x + 25/2
4y = -3x + 50
3x + 4y = 50
Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.
To learn more about the perpendicular line from the given link
https://brainly.com/question/28028690
#SPJ13
-4 + (-1) - (-3)
Need HELP
Answer: The answer is -2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
-4 + (-1) - (-3) Distribute the + and - since they are outside the parenthesis
-4 - 1 + 3 Subtract 1 to -4
-5 +3 Add 3 to -5
-2
help meeeeeeeeeeeeeee pleaseee
Answer: See the image below for the table and graph
==========================================================
Explanation:
We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.
For instance, if x = -2, then...
[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]
If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.
We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.
Repeat for x values x = -1 through x = 2.
Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.
Please help me really fast
The equation of line parallel to the given line is found as y = -6x + 13.
What is meaning of the term parallel slopes?A line's slope is similar to the slopes of adjacent parallel lines, therefore m1 = m2. Additionally, the equations of a parallel line could be determined by applying the formulas; (y−y1)=m(x−x1) ( y − y 1 or by y = mx + c.The equation of the line is-
y = -6x + 1
The second line is parallel to the above line, thus the slopes of both the line are equal.
m1 = m2 = -6
The new line also passes from the point (1, 7)
(x1, y1) = (1,7)
Thus, the equation of the line will be calculated as-
y - y 1 = m2(x - x1)
y - 7 = -6(x - 1)
y - 7 = -6x + 6
y = -6x + 13
Thus, the equation of line parallel to the given line is found as y = -6x + 13.
To know more about the parallel slopes, here
https://brainly.com/question/28427398
#SPJ1
Write 12.4% as a decimal and a simplified fraction.
O 1.24 and 124
1,000
31
O 0.124 and 250
O 1.24 and 31
250
O 0.124 and
124
1,000
Answers:
decimal form = 0.124
simplified fraction = 31/250
=========================================================
Explanation:
To convert from percent to decimal, we move the decimal point 2 spots to the left.
12.4% converts to the decimal form 0.124
Optionally you could use your calculator to say 12.4/100 = 0.124
--------
To convert from a terminating decimal to a fraction, we write the decimal digits over some power of 10. In this case, we write the "124" over 10^3 aka 1000. We write it over 1000 since the '4' is in the thousandths place value. Then reduce as much as possible.
124/1000 = (31*4)/(250*4) = 31/250 is the simplified fraction form
Use your calculator to see that 31/250 = 0.124 to confirm the answer.
If a person spins a six-space spinner and then flips a coin, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the spinner outcomes and H, T for the coin outcomes.
The sample space is S={__}
(Use a comma to separate answers as needed.)
Answer:
Step-by-step explanation:
If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
As per the question statement, a person spins a six-space spinner and then flips a coin,
And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.
Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).
And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.
Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
To learn more about Outcomes and Samples Spaces, click on the link below.
https://brainly.com/question/16661472
#SPJ1
Jalen bought 4 bottles of water, 2 bags of chips, and a fruit salad. the cost of the fruit salad was $5. this expression was used to represent the amount jalen should pay. 4x +2x +5 based on the expression, the cost of each bottle of water is the cost of each bag of chips.
The cost of each bottle of water is equal to the cost of each bag of chips.
The expression:
The expression is defined as a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)
Here it is given that 4 bottles, 2 bags of chips, and a fruit salad.
The price of a fruit salad is $5.
The expression given is:
4x + 2x + 5
To find the relation between the price of a bottle and a bag of chips, we have:
Price of bottles = 4x/4 = x
Price of bag of chips = 2x/ 2 = x
Therefore we get that the cost of each bottle and each bag of chips is the same.
To know more about the expression refer to the link given below:
https://brainly.com/question/24734894
#SPJ4
The complete question is:
Jalen bought 4 bottles of water, 2 bags of chips, and a fruit salad. the cost of the fruit salad was $5. this expression was used to represent the amount Jalen should pay. 4x +2x +5 based on the expression, the cost of each bottle of water is ______the cost of each bag of chips.
Solve for x. (10x + 1) (12x-5)°
Please help me!!! I’m really trying…
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
x +
y
The equation in standard form is x - y = 9
How to determine the equation in standard form?From the question, we have the following parameters that can be used in our computation:
Points = (8, –1) and (2, –5)
Point-slope form is y + 1 = (x – 8).
Recall that the point-slope form is y + 1 = (x – 8).
So, we have
y + 1 = (x – 8)
Open the brackets
y + 1 = x – 8
Subtract 1 from both sides
y = x - 9
Rewrite as
-x + y = -9
Multiply through by -1
x - y = 9
Hence, the equation is x - y = 9
Read more about linear equations at
https://brainly.com/question/2030026
#SPJ1
An expression is shown.
4x+2(9−3x)
Select all that are equivalent to the given expression.
-18x+54
-2(x-9)
-18(x-3)
10x+18
2(5x+9)
-2x+18
Answer:
-2x+18, and -2(x-9)
Step-by-step explanation:
4x+18-6x
4x-6x+18
-2x+18
-2(x-9)
-2x+18
According to a report for veterinarians in the united states, 36. 5 percent of households in the united states own dogs and 30. 4 percent of households in the united states own cats. If one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?.
The probability of the selected household will own a dog or a cat can't be determined because there is not enough information to determine the probability
How to calculate probility?Probability is counted by dividing the event number with the total number of outcomes. In this case, the probability of the selected household will own a dog or a cat will have a formula like this:
P(A ∨ B)=P(A)+P(B)+P(A ∧ B)
Annotation:
P(A ∨ B) = probability own a dog or a cat
P(A) = probability own a dog
P(B) = probability own a cat
P(A ∧ B) = probability own a dog and a cat.
Based on question, we cant find value of the probability own a dog and a cat. Therefore, the best answer for this question there is not enough information to determine the probability
Learn more about probability https://brainly.com/question/24756209
#SPJ4
Write each ratio as a fraction in simplest form.
11 1/3 out of 50 2/3
Answer:
[tex]\frac{17}{76}[/tex]
Step-by-step explanation:
expressing the ratio in fractional form
[tex]\frac{11\frac{1}{3} }{50\frac{2}{3} }[/tex] ← change mixed number to improper fractions
= [tex]\frac{\frac{34}{3} }{\frac{152}{3} }[/tex] ( multiply numerator and denominator by 3 )
= [tex]\frac{34}{152}[/tex] ( divide numerator and denominator by 2 )
= [tex]\frac{17}{76}[/tex] ← in simplest form
When nineteen is subtracted
from three time a
number "X", the result is 110. Translate and find
the number.
Answer: x=43
Step-by-step explanation:
3x-19=110
3x-19+19=110+19
3x=129
3x/3=129/3
x=43
Please help!! 10 points
Answer:
y = - 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - 2x + 4 ← equation of line
60+16=x-16+16 x=? This math book hates me
Answer: 76
Step-by-step explanation: simplify equation
60+16=x-16+16 (cancel out 16 and add 60+16)
76=x
60+16=x-16+16
76=x
x=76
