Answer:
Range of wages is £140 to £525.
Mean wage = £226
Step-by-step explanation:
Given:
Weekly wages paid to the staff are :
£245, £140, £525, £163, £195, £174 and £140.
To find:
Range of these wages = ?
Mean wage = ?
Solution:
First of all, let us learn about the range of wages and mean wage.
Range of wages has a minimum pay and a maximum pay.
Here, if we have a look £140 is the minimum pay and
£525 is the maximum pay.
So, range of wages is £140 to £525.
Mean wage means the average of all the wages given to the staff.
Mean is defined as the formula:
[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]
Here, Sum of all observations mean sum of the wages of all the staff members.
Number of observations mean the number of staff members i.e. 7 here.
Applying the formula:
[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]
So, the answer is:
Range of wages is £140 to £525.
Mean wage = £226
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]
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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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.
I need help asap please
Answer:
I think the answer is B, tell me if it is wrong.
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.
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
6th grade math help me, please :)
Answer:
B. 168 students
Step-by-step explanation:
Given that there are a total of 600 students.
28% of the students pack their lunch.
To find:
Total number of students who pack their lunch = ?
Solution:
Percentage of a given number is calculated using the following method.
[tex]y\%[/tex] of a number [tex]x[/tex] is given by:
[tex]x \times \dfrac{y}{100}[/tex]
i.e. multiply the number by percentage to be found and divide by 100.
So, we have to find 28% of 600 here, to find the answer to the question.
[tex]\therefore[/tex] Number of students who pack their lunch is given as: (Multiply the given number 600 with 28 and divide by 100.)
[tex]600 \times \dfrac{28}{100}\\\Rightarrow 6 \times 28\\\Rightarrow \bold{168}[/tex]
So, the correct answer is:
B. 168
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
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.
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].
objective: central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds is/are
Answer:
Sample size
Step-by-step explanation:
Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.
The CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
It is given that the objective that central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds.
It is required to describe the above theorem.
What is the central limit theorem?It is defined as the in statistics the assumption holds that the sample means distribution of arbitrary variables follows a normal distribution or close to normal distribution if the sample size is big.
We have an objective:
The CLT is the factor to be considered when assessing if the CLT holds a large sample size.
If we draw the random sample data and its measures, the Central limit theorem explains the distribution will explain the normal bell curve, the mean of the parameters and the distribution will be the same.
Thus, the CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
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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?
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
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!
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
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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.
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].
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°.
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]
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...
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.
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
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
Show all work for 135 points (90 points + brainliest = 135 pts)
Answer:
(a) 5/7 chance
(b) 2/7 chance
(c) 5/7 chance
Step-by-step explanation:
Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)
Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)
(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.
(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)
(c) The complement of Event Y is 1-4/7=5/7 chance.
Answer:
a) 5/7 chance
(b) 2/7 chance
(c) 5/7 chance
Step-by-step explanation:
Event X: There are 3 letters that come before "D". A, B, and C. There is a 3 out of 7 chance of picking one of those letters. (3/7)
Event Y: There are 4 letters in "C A G E". Those 4 letters are in the 7 first letters of the alphabet meaning that they are in our pile of tiles. There is a 4 out of 7 chance of picking one of those letters. (4/7)
(a) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 5/7 chance of either Event X or Event Y happening since tiles "A" and "C" are included in both events.
(b) Since there is a 3/7 chance of Event X happening and a 4/7 chance of Event Y happening, there is a 2/7 chance of both X and Y happening since there are only 2 tiles that are the same in both events, "A" and "C". (We are only allowed to pick one tile)
(c) The complement of Event Y is 1-4/7=5/7 chance.
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
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) 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
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
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.
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