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
Combine like terms: 10 + 6y + 2x - 3
Answer:
6y +2x +7
Step-by-step explanation:
10 + 6y + 2x - 3
The only like terms are the constant
6y+2x +10-3
6y +2x +7
Answer:
2x + 6y + 7.
Step-by-step explanation:
10 + 6y + 2x - 3
= 2x + 6y - 3 + 10
= 2x + 6y + 7.
Hope this helps!
Which of the following pairs consists of equivalent fractions? 12/18 and 10/15 12/20 and 10/25 8/16 and 3/4 5/3 and 3/5
Answer:
12/18 and 10/15
Step-by-step explanation:
12/18 simplifies into 2/3
10/15 simplifies into 2/3
12/20 simplifies into 3/5
10/25 simplifies into 2/5
8/16 simplifies into 1/2
3/4 simplifies into 3/4
5/3 simplifies into 5/3
3/5 simplifies into 3/5
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
What is a fraction number?
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
Let's check all the options, then we have
A) 12/18 and 10/15
12/18 and 10/15
2/3 and 2/3
Yes, they are equivalent fraction numbers.
B) 12/20 and 10/25
12/20 and 10/25
3/5 and 2/5
They are not equivalent fraction numbers.
C) 8/16 and 3/4
8/16 and 3/4
1/2 and 3/4
They are not equivalent fraction numbers.
D) 5/3 and 3/5
5/3 and 3/5
They are not equivalent fraction numbers.
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
More about the fraction number link is given below.
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8.43 An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 45 minutes. a. What sample size is needed if the executive wants to be 90% confident of being correct to within {5 minutes
Answer:
a
The sample size is [tex]n = 219.2[/tex]
b
The sample size is [tex]n = 537.5[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 45 \minutes[/tex]
The Margin of Error is [tex]E = \pm 5 \ minutes[/tex]
Generally the margin of error is mathematically represented as
[tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]
Where n is the sample size
So
[tex]n = [\frac{z * \sigma }{E} ]^2[/tex]
Now at 90% confidence level the z value for the z-table is
z = 1.645
So
[tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]
[tex]n = 219.2[/tex]
The z-value at 99% confidence level is
[tex]z = 2.576[/tex]
This is obtained from the z-table
So the sample size is
[tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]
[tex]n = 537.5[/tex]
For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.
Given :
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily.From past studies, the standard deviation is estimated as 45 minutes.The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.
[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]
For the 90% confidence interval, the value of z is 1.645.
Now, substitute the values of all the known terms in the above formula.
[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex] --- (1)
[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]
n = 219.2
Now, for 99% confidence interval, the value of z is 2.576.
Again, substitute the values of all the known terms in the expression (1).
[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]
n = 537.5
For more information, refer to the link given below:
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What is the value of the expression below?
(-8)^4/3
Answer:
16
Step-by-step explanation:
(-8)^4/3
-(8^1/3)⁴
-(∛8)⁴
-(2)⁴
-2⁴
= 16
Answer: the ^^^^ right I check it
Step-by-step explanation:
if ade has 23hand bag and he sells one for 409$ and he sells 22 for toby what will be the amount
Step-by-step explanation:
Hello there!
Its simple,
Given that, Ade had 23 hand bags.
selling price of each bag=$409
total sold bags= 22.
now, total amount he got was = no.of sold bag×sp of each bag.
so, total amount = 22×$409
=$8998.
Therefore, he has $ 8998 now.
Hope it helps...
A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 years
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.
At the beginning the area is 2100
After one year the area will be
2100*(1-3.5%)=2100*0.965
After n years the area will be
[tex]2100\cdot0.965^n[/tex]
So after 5 years the area will be
[tex]2100\cdot0.965^5=1757.34027...[/tex]
So rounded to the nearest square kilometer is 1757
Hope this helps
Answer: 1757 km²
Step-by-step explanation:
Because 3.5% = 0.035, first do 1-.035 to get .965. Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.
2. Write as a complex number.
Answer:
Your answer is correct ✔️
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
2√3 + 3i is the answer
Step-by-step explanation:
Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?
Answer:
0.75x+15=2+0.5x-1
0.25x=1-15
0.25x=-14
x=-56
Step-by-step explanation:
Simplify 3 (2x + 1) - 2 (x + 1)
Let's simplify step-by-step.
3(2x+1)−2(x+1)
Distribute:
=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)
=6x+3+−2x+−2
Combine Like Terms:
=6x+3+−2x+−2
=(6x+−2x)+(3+−2)
=4x+1
4x+1 is the answer to the question
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answer:
b = sqrt(57)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
8^2 + b^2 = 11^2
64+ b^2 = 121
Subtract 64
b^2 = 121-64
b^2 =57
Take the square root of each side
b = sqrt(57)
Which expression is equivalent to 0.83¯ ?
Answer:
Hello There!!
Step-by-step explanation:
Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...
this graph shows the solution to which inequality?
Answer:
B. y > 2/3x + 1
Step-by-step explanation:
To find slope we'll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
(-3,-1) (3,3)
3 - -1 = 4
3 - -3 = 6
2/3x
The y intercept is 1,
we know this because that's the point the line touches the y axis.
Thus,
the answer is B. y > 1/3x + 1.
Hope this helps :)
The graph of the solution of an inequality is given .
The graph represents the inequality is [tex]y>\frac{2}{3} x+1[/tex]
Option B
Given :
The graph of an inequality. To find the inequality for the given graph we use linear equation [tex]y=mx+b[/tex]
where m is the slope and b is the y intercept
To find out slope , pick two points from the graph
(-3,-1) and (3,3)
[tex]slope =\frac{y_2-y_2}{x_2-x_1} =\frac{3+1}{3+3} =\frac{2}{3} \\m=\frac{2}{3}[/tex]
Now we find out y intercept b
The point where the graph crosses y axis is the y intercept
The graph crosses y axis at 1
so y intercept b=1
The linear equation for the given graph is
[tex]y=\frac{2}{3} x+1[/tex]
Now we frame the inequality . we use test point that lies inside shaded region
Lets take (4,5)
[tex]y=\frac{2}{3} x+1\\5=\frac{2}{3} (4)+1\\5=3.6\\5>3.6\\y>\frac{2}{3} x+1[/tex]
The inequality for the given graph is
[tex]y>\frac{2}{3} x+1[/tex]
Learn more : brainly.com/question/24649632
Which ordered pair is a solution of this equation 6x-y=-4 . -2,0 -1,-2 -2,-1 0, -2
Answer:
(-1,-2)
Step-by-step explanation:
[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]
so the only one is (-1,-2)
If sinθ = 12/13 and θ is an acute angle, find cotθ.
Answer:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \sin \theta = \frac{12}{13}[/tex]
Where θ is an acute angle, and we want to find cot(θ).
Recall that sine is the ratio of the opposite side over the hypotenuse. In other words, our opposite side is measures 12 units and our hypotenuse measures 13 units.
Find the adjacent side:
[tex]\displaystyle \begin{aligned} a^2 + b^2 & = c^2 \\ \\ (12)^2 + b^2 & = (13)^2 \\ \\ b & = 5\end{aligned}[/tex]
Hence, our adjacent side is 5, our opposite side is 12, and our hypotenuse is 13.
Recall that cotangent is the ratio of the adjacent side to the opposite side. Therefore:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
In conclusion:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
Answer:
-5/12
Step-by-step explanation:
I just completed Quiz 2: Evaluation of Functions. Of which, this was one of the questions.
The length, width and height are consecutive whole numbers. The volume is 120 cubic inches.
Answer:
4, 5 and 6
Step-by-step explanation:
Consecutive means right next to each other.
4 x 5 x 6 = 120 cubic inches.
4 X 5 = 20
20 X 6 = 120
The values of the consecutive numbers will be 4, 5, and 6.
Let the numbers be represented by a, a+1, and a+2.
Therefore, a(a+1)(a+2) = 120
a³ + 3a² + 2a = 120
a = 4
Therefore, a + 1 = 4+1 = 5
a + 2 = 4 + 2 = 6
Therefore, the values will be 4, 5, and 6.
Read related link on:
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Which statement is true about figures ABC D & ABCD
Answer:
it's option b that is the right answer
3
Easton mixed
kg of flour with
kg of sugar.
6
Determine a reasonable estimate for the amount of flour and sugar combined.
Choose 1 answer:
1
Less than
2
kg
B
More than
1
kg but less than 1 kg
2
More than 1 kg
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
Find the value of EB
Answer:
31Step-by-step explanation:
Given,
AD = 38
EB = 7x - 4
FC = 6x - 6
Now, we have to find the value of X
[tex]eb \: = \frac{1}{2} (ad \: + fc \: )[/tex] ( Mid segment Theorem )
Plug the values
[tex]7x - 4 = \frac{1}{2} (38 + 6x - 6)[/tex]
Calculate the difference
[tex]7x - 4 = \frac{1}{2} (32 + 6x)[/tex]
Remove the parentheses
[tex]7x - 4 = \frac{32}{2} + \frac{6x}{2} [/tex]
[tex]7x - 4 = 16 + 3x[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex]7x - 3x = 16 + 4[/tex]
Collect like terms
[tex]4x = 16 + 4[/tex]
Calculate the sum
[tex]4x = 20[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{20}{4} [/tex]
Calculate
[tex]x = 5[/tex]
The value of X is 5
Now, let's find the value of EB
EB = 7x - 4
Plug the value of X
[tex] = 7 \times 5 - 4[/tex]
Calculate the product
[tex] = 35 - 4[/tex]
Calculate the difference
[tex] = 31[/tex]
The value of EB is 31
Hope this helps..
Best regards!!
a food snack manufacturer samples 9 bags of pretzels off the assembly line and weights their contents. If the sample mean is 14.2 oz. and teh sample devision is 0.70 oz, find the 95% confidense interval of the true mean
Answer:
13.7≤[tex]\mu[/tex]≤14.7Step-by-step explanation:
The formula for calculating the confidence interval is expressed as shown;
CI = xbar ± Z(б/√n)
xbar is the sample mean
Z is the value at 95% confidence interval
б is the standard deviation of the sample
n is the number of samples
Given xbar = 14.2, Z at 95% CI = 1.96, б = 0.70 and n = 9
Substituting this values into the formula;
CI = 14.2 ± 1.96(0.70/√9)
CI = 14.2 ± 1.96(0.70/3)
CI = 14.2 ± 1.96(0.2333)
CI = 14.2 ± 0.4573
CI = (14.2-0.4573, 14.2+0.4573)
CI = (13.7427, 14.6537)
Hence, the 95% confidence interval of the true mean is within the range
13.7≤[tex]\mu[/tex]≤14.7 (to 1 decimal place).
which of the following descriptions represent the transformation shown in the image? Part 1d
Answer:
(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.
Step-by-step explanation:
Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.
In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).
Q is right now at (-3,-4) so we can translate this.
To get from -3 to -1 in the x-axis, we go right by 2 units.
To get from -4 to -3 in the y-axis, we go up one unit.
Now, if we reflect it, the triangles will be the same.
Hope this helped!
Answer:
C.
Step-by-step explanation:
When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.
Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.
All of these conditions match the ones put forth in option C, so that is your answer.
Hope this helps!
Can you help me with this.
Answer:
You would basically expand all the equations!
1. 7(4z+8b) is equal to 28z+56b.
2. 8(2x+3^2) is equal to 16x+72
3. 4(r+r+r+r) is equal to 4r+4r+4r+4r
4. 9(3+8x) is equal to 27+72x
5. 4^2(3+6f) is equal to 48+96t
6. (t+t+t)/4 is equal to t/4+t/4+t/4
7. 2(4s^3+2) is equal to 8s^3+4
8. 30(3x+4) is equal to 90x+120
9. 6(5a+9b) is equal to 30a+54b
10. 9(3x+5^4) is equal to 27x+5625
11. 7(c+c+c) is equal to 7c+7c+7c
12. 9(2+7f) is equal to 18+63f
13. 7^5(4g-8d) is equal to 67228g-134456d
Step-by-step explanation:
the numbers of students in the 10 schools in a district are given below. ( Note that these are already ordered from Least to Greatest) 198, 216, 220, 236, 246, 252, 253, 260, 290, 319. Suppose that the number 319 from this list changes to 369. Answer the following what happens to the median? what happens to the mean?
Answer:median:249
Step-by-step explanation:
median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369
246 +252=498
498/2=249
as for the mean i will give you that later
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2
Answer:
The answer is below
Step-by-step explanation:
a) y=3x-1
The standard equation of a line is given by:
y = mx + c
Where m is the slope of the line and c is the intercept on the y axis.
Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:
3 × d = -1
d = -1/3
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]
b) y=1/4 x+2
Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:
1/4 × f = -1
f = -4
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]
Here is a sample distribution of hourly earnings in Paul's Cookie Factory:
Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15
Frequency 16 42 10
The limits of the class with the smallest frequency are:_________
A) $6.00 and $9.00.
B) $12.00 and up to $14.00.
C) $11.75 and $14.25.
D) $12.00 and up to $15.00.
Answer:
The correct answer is:
$12.00 and up to $15.00 (D)
Step-by-step explanation:
Let us arrange the data properly in a tabular format.
Hourly Earnings($) 6 - 9 9 - 12 12 - 15
Frequency 16 42 10
The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.
From the frequency table above the following observations can be made:
Highest frequency = 42 (hourly earnings of $9 - $12)
smallest frequency = 10 ( hourly earnings of $12 - $15)
This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority
Find the value of x.
Answer:
[tex]\huge\boxed{y=\sqrt{55}}[/tex]
Step-by-step explanation:
ΔADC and ΔDBC are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AC}{CD}=\dfrac{CD}{BC}[/tex]
Substitute:
[tex]AC=6+5=11\\BC=5\\CD=y[/tex]
[tex]\dfrac{11}{y}=\dfrac{y}{5}[/tex] cross multiply
[tex](11)(5)=(y)(y)\\\\55=y^2\to y=\sqrt{55}[/tex]
Select the correct answer from each drop-down menu. The graph represents the piecewise function.
Answer:
1). f(x) = x² if ∞ < x < 2
2). f(x) = 5 if 2 ≤ x < 4
Step-by-step explanation:
The graph attached shows the function in two pieces.
1). Parabola
2). A straight line parallel to the x-axis.
Standard equation of a parabola is,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the given parabola is (0, 0).
Equation of the parabola will be,
y = a(x - 0)² + 0
Therefore, the function will be,
f(x) = ax²
Given parabola is passing through (-1, 1) also,
1 = a(-1)²
a = 1
Therefore, parabolic function will be represented by,
f(x) = x² if ∞ < x < 2
2). Straight line parallel to the x-axis,
y = 5 if 2 ≤ x < 4
Function representing the straight line will be,
f(x) = 5 if 2 ≤ x < 4
Answer:
Please mark me as Brainliest :)
Step-by-step explanation:
the answer choices are
sec y= b/6
sec y=6a
sec y=6b
sec y= 6/b
Answer:
sec y=6/b yw
Step-by-step explanation:
What are the solutions of the quadratic equation (x – 8)2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
Ox=-11 and x = -18
x= -2 and x = 5
x= 2 and x = -5
x= 11 and x = 18
Answer:
Its D
Step-by-step explanation:
x=11 and x=18
A test was marked out of 80. Aboy scored
60% of the marks on the test. How many
marks did he score?
(A)20
(B)48
(C)60
(D)75
Answer:
B
Step-by-step explanation:
To solve this you do 80/100=.8
You than do .8×60= 48