Answer:
(a) (1,5)
(b) Every subset of a cartesian product is a relation, therefore this is a relation.
(c) The relation IS NOT a function.
Step-by-step explanation:
(a)
(1,5)
Notice that 3(1) +1 = 4 < 5 therefore (1,5) is an order pair that satisfies the equation.
(b)
Every subset of a cartesian product is a relation, therefore this is a relation.
(b)
A relation is a function of the following condition holds
if (a,b) and (c,b) belong to the relation then (a=c)
In this case, (1,5), (0,5) belong to the relation but 0 is different than 5, therefore the relation IS NOT a function.
There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. b How many ways can we choose a Senator from a chosen state? c How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Answer:
a) rCn = 1176
b) 2352
Step-by-step explanation:
a)Each committee should be formed with 3 members ( no two members could be of the same state) then
Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then
rCn = n! / (n - r )! *r!
rCn = 49!/ (49 - 2)!*2!
rCn = 49*48*47! / 47!*2!
rCn = 49*48 /2
rCn = 1176
So we can choose in 1176 different ways a senator for a given state
b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.
1176*2 = 2352
In the figure, find the value of x that makes a ∥ b. A. 50° B. 65° C. 75° D. 95°
Answer:
B
Step-by-step explanation:
Because alternate interior angles are congruent in parallel lines, the angle next to the 25° in the right triangle is 85 - 25 = 60° which makes the other angle in the right triangle 180 - 90 - 60 = 30°. Since they form a straight angle, we can write x + 30 + 85 = 180 → x + 115 = 180 → x = 65°.
Which of the following points is a solution of y > Ixl + 5?
A. (0, 5)
B. (1, 7)
C. (7, 1)
Answer:
B. (1,7)
Step-by-step explanation:
We can substitute the x and y values of each coordinate into the inequality and test if they work.
Let's start with A, 5 being y and 0 being x .
[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]
5 IS NOT greater than 5, they are the exact same, so A is out.
Let's try B, 1 being x and 7 being y.
[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]
7 IS greater than 6, so B. (1,7) does work for this inequality!
Let's do C for fun, when 7 is x and 1 is y.
[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]
1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.
Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].
Hope this helped!
24=3(n-5) solve for n
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
Help!! It’s much appreciated in this time
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
If 5e^x=300, x
I need help fast
Answer:
ln(60)
Step-by-step explanation:
We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].
Please help asap.
A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures $90$ degrees If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.) What is the degree measure of the fifth slice Larry eats?
Answer:
The answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Step-by-step explanation:
Given that pizza is divided into six unequal slices.
Largest slice has an angle of [tex]90^\circ[/tex].
He eats the pizza from largest to smallest.
Let the difference in angles in each slice = [tex]d^\circ[/tex]
1st angle = [tex]90^\circ[/tex]
2nd angle = 90-d
3rd angle = 90-d-d = 90 - 2d
4th angle = 90-2d-d = 90 - 3d
5th angle = 90-3d-d = 90 - 4d
6th angle = 90-4d -d = 90 - 5d
We know that the sum of all the angles will be equal to [tex]360^\circ[/tex] (The sum of all the angles subtended at the center).
i.e.
[tex]90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ[/tex]
So, the angles will be:
1st angle = [tex]90^\circ[/tex]
2nd angle = 90- 12 = 78
3rd angle = 78-12 = 66
4th angle = 66-12 = 54
5th angle = 54-12 = 42
6th angle = 42 -12 = 30
So, the answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Is this strong positive correlation or weak positive or strong negative or weak negative?
Answer:
Weak negative correlation
Step-by-step explanation:
The scatter plot shown in the graph above indicates a negative correlation between the x-variables and the y-variables, because, as the variables on the x-axis increases, the variables on the y-axis decreases.
Also, the if we are to draw a line of best fit to connect some of the data points on a straight line, we would see that a number of the data points would be far apart from each other away from the line. The data points are not much clustered around the line of best fit, therefore, this shows that the negative correlation between the variables is a weak one.
The data represented on the scatter plot show a weak negative correlation.
Enter a range of values of x
Answer:
[tex]-5<x<26[/tex].
Step-by-step explanation:
We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.
Angle opposite to larger side is larger.
Since, 14 < 15, therefore
[tex]2x+10<62[/tex]
[tex]2x<62-10[/tex]
[tex]2x<52[/tex]
[tex]x<26[/tex] ...(1)
We know that, angle can not not negative.
[tex]2x+10>0[/tex]
[tex]2x>-10[/tex]
[tex]x>-5[/tex] ...(2)
From (1) and (2), we get
[tex]-5<x<26[/tex]
Therefore, the range of values of x is [tex]-5<x<26[/tex].
The area of a circle is found using the formula A=\pi r^(2) , where r is the radius. If the area of a circle is 36π square feet, what is the radius, in feet? A. 6 B. 6π C. 18 D. 9π
Answer:
A. 6 feetStep-by-step explanation:
[tex]A=\pi r^2\\Area = 36\pi\\r = ?\\36\pi = \pi r^2\\Divide \:both \:sides \:of\: the \:equation\: by\: \pi\\\frac{36\pi}{\pi} = \frac{\pi r^2}{\pi} \\r^2 = 36\\Find\: the\: square\: root\: of\: both\: sides\: \\\sqrt{r^2} =\sqrt{36} \\\\r = 6\: feet\\[/tex]
A movie theater has a seating capacity of 179. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1284, How many children, students, and adults attended?
Answer:
31 adults, 62 children, and 86 students.
Step-by-step explanation:
The seating capacity of the movie theatre = 179
c+s+a=179Children's(c) Ticket = $5.00
Student's(s) Tickets = $7.00
Adult's(a) Tickets = $12.00
There are half as many adults as there are children.
[tex]a=c/2 \implies c=2a[/tex]The total ticket sales was $1284
5c+7s+12a=1284We then solve the three resulting equations simultaneously.
c+s+a=179
c=2a
5c+7s+12a=1284
We substitute c=2a into the first and third equation
[tex]2a+s+a=179 \implies s=179-3a\\5(2a)+7s+12a=1284 \implies 22a+7s=1284[/tex]
Substitute s=179-3a into 22a+7s=1284
[tex]22a+7(179-3a)=1284\\22a+1253-21a=1284\\a=1284-1253\\a=31[/tex]
Recall:
c=2a
c=2*31
c=62
Finally:
c+s+a=179
62+s+31=179
s=179-62-31
s=86.
Therefore:
31 adults, 62 children, and 86 students attended the movie theatre.
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
In △ABC, m∠A=19°, a=13, and b=14. Find c to the nearest tenth.
Answer:
c is either 25.4 or 1.1
Step-by-step explanation:
The Law of Sines is used to find sides and angles when you have a side and its opposite angle. Since the given angle is not opposite the longest given side, there are two possible solutions.
a) sin(B)/b = sin(A)/a
sin(B) = (b/a)sin(A) = 14/13·sin(19°) ≈ 0.350612
B = arcsin(0.350612) or 180° -arcsin(0.350612)
B = 20.525° or 159.475°
Then angle C is ...
C = 180° -A -B = 161° -B = 140.475° or 1.525°
__
Side c can be found from ...
c = sin(C)·a/sin(A)
For C = 140.475°, ...
c = sin(140.475°)·39.9302 ≈ 25.4
For C = 1.525°, ...
c = sin(1.525°)·39.9302 ≈ 1.1
The length of side c could be 25.4 or 1.1.
A coin is tossed and -sided die numbered 1 through is rolled. Find the probability of tossing a and then rolling a number greater than . The probability of tossing a and then rolling a number greater than is nothing.
Answer:
hello your question has some missing parts here is the complete question
A coin is tossed and an eight-sided die numbered 1 through 8 is rolled. Find the probability of tossing tail and then rolling a number greater than 6. The probability of tossing a tail and then rolling a number greater than 6 is? Round to three decimal places as needed
Answer : 0.5, 0.25, 0.125
Step-by-step explanation:
A coin when tossed has only two outcomes which are ( Head or tail )
a)Therefore the probability of tossing a tail = 1/2 = 0.5
A die having eight sides when tossed will have 8 outcomes
B) Therefore the probability of rolling a number greater than 6
p( x > 6) = p(7) + p(8) = 1/8 + 1/8 = 0.25
C) The probability of tossing a tail and then rolling a number greater than 6 is
= p( x > 6 ) * p( tail )
= 0.25 * 0.5 = 0.125
Can anyone help? I am stuck. Find m∠G.
Answer:
80
Step-by-step explanation:
The quadrilateral is a kite.
The angle opposite to angle H is equal to angle H.
Angle F = 110 degrees
Angles in a quadrilateral add up to 360 degrees.
60 + 110 + 110 + G = 360
280 + G = 360
G = 360 - 280
G = 80
The measure of angle G is 80 degrees.
Answer: 80 degrees.
Step-by-step explanation:
In a kite, the angles formed by noncongruent sides are congruent. Thus, <EFG is 110 degrees. Then, because a kite is a quadrilateral, all of the angles in it add up to 360. Thus, is <FGH = x, then 110+110+60+x=360. Thus, x = 80.
Hope it helps <3
a small business had a total revenue of $51600. If this is 29% more than their total revenue the previous year, what was their total revenue the previous year?
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green and 2 red marbles. Find probability that both marbles are white. Round to nearest thousandth
Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.
Answer:
23
Step-by-step explanation:
since the number is relatively prime to the product of the first 20 positive numbers
It number must not have factor of (1-20)
Therefore the smallest possible number is the next prime after 20
Answer is 23
The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).
Hence, The smallest possible number is the next prime after 20 is, 23
Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
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What is the vertex of the graph of the function f(x) = x2+8x-2?
Answer:
the answer is (-4,-18)
Answer:
The vertex is at (-4, -18).
Step-by-step explanation:
f(x) = x^2 + 8x - 2
Covert to vertex form:
f(x) = (x + 4)^2 - 16 - 2
f(x) = (x + 4)^2 - 18.
So the
vertex is (-4,18
How many different isosceles triangles have integer side lengths and perimeter 23?
Answer:
6 different isosceles triangles.
Step-by-step explanation:
This is a AMC 8 2005 question. (You can search up their solution)
There are 6 triangles:
6, 6, 11
7, 7, 9
8, 8, 7
9, 9, 5
10, 10, 3
11, 11, 1
There are only 6 because if there was an isosceles triangle with side lengths such as 5, 5, 13 the triangle would be impossible since the two smaller side lengths must sum up to be greater than the longest side length.
The number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
What is the isosceles triangle?In an isosceles triangle, two sides and angles are equal. The sum of the angle of the triangle is 180 degrees.
Given
Isosceles triangles have integer side lengths and a perimeter of 23.
Let x be the isosceles side and y be the other side. Then
[tex]\rm 2x + y = 23[/tex] ...1
And we know that the sum of the two sides of the triangle must be greater than the third side. Then
[tex]\rm 2x >y[/tex] ...2
From equations 1 and 2, we have
x > 5.75
But the value of x is an integer then x will be 6. Then
All possibilities are
[tex]6 + 6 > 11\\\\7 + 7 > 9\\\\8+8>7\\\\9+9>5\\\\10+10>3\\\\11+11>1[/tex]
Thus, the number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
More about the Isosceles triangle link is given below.
https://brainly.com/question/7915845
use the substitution method to solve the system of equation.s choose the correct ordered pair y=6x-4 y=x -7
Answer:
x=-3/5 and y=-38/5
Step-by-step explanation:
y=6x-4
y= x -7 substitute y=6x-4
6x-4=x-7
6x-x=-7+4
5x=-3
x=-3/5 ( substitute for x in y=6x-4)
y=6(-3/5)-4
y=-18/5-4
y=(-18-20)/5= -38/5
Solve for x. Answer as an integer or simplified fraction. Please include steps. Thanks!
Answer:
x=40 degreesStep-by-step explanation:
According to the angle sum theorem, the interior angles of a triangle add up to 180 degrees:
So, we can use the following equation to find x:
x+(x+10)+(210-3x)=180
now add like terms:
x+x+(-3x)+10+210=180
-x+220=180
now isolate the variable:
-x=180-220
-x=-40
x=-40/-1
x=40/1
x=40
The answer is that: the measure of x is 40 degrees
A certain medicine is given in an amount proportional to patient’s body weight. Suppose a patient weigh in 116 pounds requires 126 mg of medicine. What is the amount of medicine required by patient way and 174 pounds?
Answer: 189 mg.
Step-by-step explanation:
Let x be the weight of the body( in pounds) and y be the amount of medicine( in mg).
Given: A certain medicine is given in an amount proportional to patient’s body weight.
i.e. [tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Let [tex]x_1=116\ \ \ ,\ y_1=126[/tex] , [tex]x_2=174[/tex]
then,
[tex]\dfrac{116}{126}=\dfrac{174}{y_2}[/tex]
[tex]\Rightarrow\ y_2=\dfrac{174\times126}{116}\\\\\Rightarrow\ y_2=189[/tex]
Hence, he amount of medicine required by patient weighing 174 pounds = 189 mg.
What is the difference of the rational expressions below?
6/x - 5x/x+2
A.
5x + 6
2
O
B. 5x + 6x +12
** + 2x
O
c.
5x6
2x+2
D. 5x' +6x +12
2x + 2
The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
To find the difference of the rational expressions, we need to subtract the second expression from the first expression.
Let's simplify the expressions first:
The first expression is 6/x - 5x/(x+2).
To combine the terms, we need a common denominator, which is (x)(x+2).
Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).
Now, we can combine the terms:
[(6(x+2))/(x(x+2))] - [5x/(x+2)]
To subtract the fractions, we need to have a common denominator, which is (x)(x+2).
Expanding the numerators, we get:
[(6x + 12)/(x(x+2))] - [5x/(x+2)]
Now, we can subtract the fractions:
[(6x + 12 - 5x)/(x(x+2))]
Simplifying the numerator, we have:
(6x - 5x + 12)/(x(x+2))
Combining like terms, we get:
(x + 12)/(x(x+2))
Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
For similar question on rational expressions.
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PLEASE ANSWER QUICK A manufacturing facility pays its employees an average wage of $4.50 an hour with a standard deviation of 50cents. If the wages are normally distributed, what is the percentage of workers getting paid between #3.75 and $5.00 an hour? A. 80.4% B.77.4% C.70.5% D.65.4%
Answer:
B.77.4%
Step-by-step explanation:
Mean wage (μ) = $4.50
Standard deviation (σ) = $0.50
For nay given salary X, the z-score is given by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $3.75, the z-score is:
[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]
For X = $5.00, the z-score is:
[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]
A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:
[tex]P=84.13-6.68\\P=77.45\%[/tex]
The answer is alternative B.77.4%
I need help asap please
Answer:
I think the answer is B, tell me if it is wrong.
Someone help me please
Answer:
31Option D is the correct option.
Step-by-step explanation:
Given: 3 boxes with volumes 1331 , 1331 , 729
To find : Height of stacked boxes
[tex]h {1}^{3} = 1331 = h1 = \sqrt[3]{1331} = 11[/tex]
[tex]h {2}^{3} = 1331 = h2 = \sqrt[3]{1331} = 11[/tex]
[tex]h {3}^{3} = 729 = h3 = \sqrt[3]{729} = 9[/tex]
Now,
[tex]h = h1 + h2 + h3[/tex]
[tex] = 11 + 11 + 9[/tex]
[tex] = 31[/tex]
Hope this helps...
Good luck on your assignment...
(I NEED HELP) The data below shows the scores of some students on a test: 23, 27, 21, 20, 25, 31, 22 Which box-and-whisker plot represents the data?
Answer:
B
Step-by-step explanation:
Answer:
the 2nd one
Step-by-step explanation:
because the Minimum is 20
the Maximum is 31
the median is 23
20, 21, 22, 23, 25, 27, 31,
21, 22, 23, 25, 27
22, 23, 25,
23
If $y^2= 36$, what is the greatest possible value of $y^3$?
Answer:
The greatest possible value of [tex]y^3=216[/tex]
Step-by-step explanation:
We have the statement [tex]y^2=36[/tex], and we have to find the greatest possible value of [tex]y^3[/tex], first we need to find the value of y.
[tex]y^2=36[/tex], to get the y by itself on the left side, we need to take the square root of both sides. [tex]\sqrt{y^2} =\sqrt{36}[/tex] The square root of [tex]y^2[/tex] is y, because y*y = [tex]y^2[/tex], and the square root of 36 is 6 or -6.
We now need to find the greatest value of [tex]y^3[/tex]. When we plug in 6 to [tex]y^3[/tex], we get positive 216, and when we plug in -6, we get -216. We need to find the greatest possible value, so in this case we compare 216 and -216, 216 is greater than -216, so the answer would be positive 216.
Answer:
216
Step-by-step explanation:
If y² = 36, then y is 6 or -6. When y = 6, we have y³ = 6³ = 216. When y = -6, we have y³ = (-6)³ = -216. The greatest possible value of y³ is 216.
Alexandria ate at most two hundred fifty calories more than twice the number of calories her infant sister ate. Alexandria ate eighteen hundred calories. If i represents the number of calories eaten by the infant, which inequality represents the situation? A. 1,800 less-than-or-equal-to 250 + 2 i B. 1,800 less-than 250 + 2 i C. 1,800 + 250 greater-than 2 i D. 1,800 + 250 greater-than-or-equal-to 2 i
Hey there! I'm happy to help!
The words at most means that there is a maximum point that is included as a probability. This means that we will use the less than or equal sign (≤) in our inequality.
Let's write this all out as an inequality now. We will use i to represent how much the baby ate.
1,800≤2i+250
This inequality shows that Alexandria's 1,800 calories is at most 250 more than twice those of her baby sister. Therefore, the correct option is A. 1,800≤250+2i .
Have a wonderful day!
Answer:
The correct option is A. 1,800≤250+2i.