Let:
• A ,be the number of millilitres (mL) of solution A used.
,• B ,be the number of mL of solution B used.
We know that Dale uses four times as much solution A as solution B, meaning
[tex]A=4B[/tex]Now, we know that we will end up with 570 mL of pure alcohol in the final solution. Using the dilution of both A and B (20% means 0.2 and 15% is 0.15) we would have that:
[tex]0.2A+0.15B=570[/tex]We would have the following system of equations:
[tex]\begin{cases}A=4B \\ 0.2A+0.15B=570\end{cases}[/tex]Substituting equation 1 in equation 2 and solving for B :
[tex]\begin{gathered} 0.2A+0.15B=570 \\ \rightarrow0.2(4B)+0.15B=570 \\ \rightarrow0.8B+0.15B=570 \\ \rightarrow0.95B=570\rightarrow B=\frac{570}{0.95} \\ \Rightarrow B=600 \end{gathered}[/tex]Substituting in equation 1 and solving for A:
[tex]\begin{gathered} A=4B \\ \rightarrow A=4(600) \\ \Rightarrow A=2400 \end{gathered}[/tex]This way, we can conclude that 2400 mL of solution A and 600mL of solution B were used.
......................
Answer: x 0 1 2 3
p(x) 0.011 0.170 0.279 0.539
Given that the values of x =
Television 0 1 2 3
Household 30 443 727 1401
Let television be = x
Household = frequency = distribution
Firstly, we need to find the interval of x
The interval of x = Range between two numbers
1 - 0 = 1
2 -1 = 1
3 - 2 = 1
Hence, the interval is 1
[tex]p(x)\text{ = }\frac{frequency\text{ for x interval}}{N\text{ x w}}[/tex]Where N = total frequency
w = interval
Total frequency = 30 + 443 + 727 + 1401
Total frequency = 2601
[tex]\begin{gathered} \text{when x = 0} \\ p(x)\text{ = }\frac{30}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{30}{2601} \\ p(x)\text{ = }0.011 \end{gathered}[/tex]when x = 1
[tex]\begin{gathered} p(x)\text{ = }\frac{443}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{443}{2601} \\ p(x)\text{ = 0}.170 \end{gathered}[/tex]When x = 2
[tex]\begin{gathered} p(x)\text{ = }\frac{727}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{727}{2601} \\ p(x)\text{ = 0.279} \end{gathered}[/tex]when x = 3
[tex]\begin{gathered} p(x)\text{ = }\frac{1401}{1\text{ x 2601}} \\ p(x)\text{ = }\frac{1401}{2601} \\ p(x)\text{ = 0.539} \end{gathered}[/tex]Therefore,
x 0 1 2 3
p(x) 0.011 0.170 0.279 0.539
Solve the following expression when p = 15 p/3 + 4
So, our answer is 9!
LM is the midsegment of Trapeziod RSXY. may you please help me find what LM is?
Step 1: Problem
Mid-point of a Trapezoid
Step 2: Concept
[tex]LM\text{ = }\frac{RS+\text{ YX}}{2}[/tex]Step 3: Method
RS = 4.1
YX = 8.2
[tex]\begin{gathered} LM\text{ = }\frac{4.1\text{ + 8.2}}{2} \\ LM\text{ = }\frac{12.3}{2} \\ LM\text{ = 6.15} \end{gathered}[/tex]Step 4: Final answer
LM = 6.15
4)Describe the difference between a sampling error and non-sampling error .
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
sampling error and non-sampling error
Step 02:
statistics:
Sampling error:
It is the error that arises in a data collection process as a result of taking a sample from a population rather than using the whole population.
Non-sampling error:
It is the error that arises in a data collection process as a result of factors other than taking a sample.
non-response errors, coverage errors, interview errors, and processing errors
Given f(x)=6(1-x), what is the value of:a) f(-8)_____b) f(x) = -30 _____c) f(x) = 30____d) f(30)_____
Answer:
a) f(-8) = 54
b) f(x) = -30, x = 6
c) f(x) = 30, x = -4
d) f(30) = -174
Explanation:
Given the function:
f(x) = 6(1 - x)
To find f(-8), we replace x by -8 in the equation and then solve
f(-8) = 6[1 - (-8)8]
= 6(1 + 8)
= 6(9)
= 54
For f(x) = -30, we replace f(x) by -30 and solve for x
-30 = 6(1 - x)
Divide both sides by 6
1 - x = -30/6 = -5
Subtract 1 from both sides
-x = -6
Multiply both sides by -1
x = 6
For f(x) = 30, we replace f(x) by 30 and solve for x
30 = 6(1 - x)
Divide both sides by 6
1 - x = 30/6 = 5
Subtract 1 from both sides
-x = 4
Multiply both sides by -1
x = -4
f(30) = 6(1 - 30)
= 6(-29)
= -174
Which inequalities are shown on the graph?Find your inequalities in the grid below. Check the ONE box that pairs the two correct inequalitiesY-3-1 y>-**-172-**-1 y<-**-1<3+3y>+3y< <+3y2 ++3D D D DOOOO"OOOOPreviousPauseO Search for anything0-
From the graph we could see that y = x + 3 for the first line . The shaded line is where y is less than or equals to x + 3.
For the second line we can see that y = x - 1 . The shaded line is where y is greater than or equals to x - 1 . Therefore, the inequalities are as follows
[tex]\begin{gathered} y\leq x+3 \\ y\ge x-1 \end{gathered}[/tex]Tara makes and sells scarves for children and adults. She is able to sell the scarves for $18 per unit. Materials for the scarves cost $4 each. She has fixed cost per month of $280 and estimates that she can make and sell 80 scarves each month. How many scarves does Tara need to sell to break even?
Tara needs to sell 20 scarves to break even.
What is the break-even point?The break-even point is the sales level that the seller must attain to make the total revenue equal to the total costs (fixed and variable).
There is no profit or loss at the break-even point (either in units or dollar values).
Selling price per unit = $18
Product cost per unit = $4
Contribution margin per unit = $14
Fixed cost per month = $280
Estimated production and sales units per month = 80 scarves
Break-even sales units = fixed costs/contribution margin per unit
= 20 ($280/$14)
Check:
Total revenue at 20 units = $360 (20 x $18)
Total costs at 20 units = $360 ($280 + $4 x 20)
Thus, for Tara to break even, she needs to sell 20 scarves per month.
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Which of the following sampling methods would most likely have the smallest margin of erro?A. Roll a die 1000 times and estimate the proportion of 5's that result.OB. Sample 250 registered voters in a large city and ask them their political preference and use the results to estOC. Flip a coin 100 times and estimate the proportion of "heads" that resul.OD. Sample 10 adults and ask them if they support the current President's foreign policy and use this data to reReset SelectionMext
The sample methodology whose accuracy is better than another is the one with more approximation, this comes from the number of repetitions.
Therefore, option A is the one with more approximation, which mean the least error margin.
write a part to part and a part to whole ratio for each problem situationof the 250 students surveyed 142, prefer carrots and 97 prefer peas
Here, we want to write ratios in part to part and in part to whole ratio
For the part to part
Writing carrot to peas, we have;
[tex]142\colon97[/tex]For the parts to whole ratio, we have;
[tex]\begin{gathered} \text{Carrot} \\ \frac{142}{250}\text{ = 142:250} \\ \text{Peas} \\ \frac{97}{250}\text{ = 97:250} \end{gathered}[/tex]Which expression is equivalent to -(-r - 16)?
Answer: Hi that would be (r+16) since they are generally the same thing, hope this is what you are asking for!
Step-by-step explanation:
Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards
We would section the figure into two shapes as shown below
We can see a trapezium and a rectangle. We would find the area of each figure and add them.
For the trapezium,
Area = 1/2 * (a + b)h
a nd b are the opposite sides of the trapezium while h represents the height.
Thus,
a = 20, b = 24 and h = 9es of the trapezium while h represents the height.
Thu sid
why is height more specific measure than 'size'?
When you talk about height, it is a more precise value that require a vertical distance from a referenced point. While 'size' is not specific whatsoever and it's more like a form of range.
How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answer:
Step-by-step explanation:
64.528 is the decimal
find the value of XA. 11√ 41inB. 11 inC. 33 inD. 35 in
From the diagram provided, we have a right angled triangle with the hypotenuse (side facing the right angle) given as 55, while one of the other two sides is given as 44.
We shall apply the pythagoras' theorem as follows;
[tex]c^2=a^2+b^2[/tex]Where,
c = hypotenuse,
a and b = the other sides.
Therefore, we'll now have;
[tex]\begin{gathered} c^2=a^2+b^2 \\ 55^2=44^2+c^2 \\ 3025=1936+c^2 \end{gathered}[/tex]Next step, we'll subtract 1936 from both sides of the equation;
[tex]\begin{gathered} 3025-1936=1936-1936+c^2 \\ 1089=c^2 \end{gathered}[/tex]Add the square root sign to both sides of the equation;
[tex]\begin{gathered} \sqrt[]{1089}=\sqrt[]{c^2} \\ 33=c \end{gathered}[/tex]ANSWER
Therefore, the correct answer is option C, that is 33 inches.
Write an equation for the line through the point (x0,y0) with a slope of M in point slope form. Enter X0 and Y0 as y0. Use X and Y for variables names. Your equation should be of the form y=….
The equation of the line in point slope form is y = M(x - x₀) + y₀ .
The Point slope form of the line passing through the point (x₁,y₁) with slope m is given by the formula
(y - y₁) = m(x - x₁)
In the question ,
it is given that
the required line passes through the points (x₀ , y₀)
and the slope is M .
So, the point slope form equation of the line will be
( y - y₀) = M(x - x₀)
y - y₀ = M(x - x₀)
y = M(x - x₀) + y₀
Therefore , the equation of the line in point slope form is y = M(x - x₀) + y₀ .
The given question is incomplete , the complete question is
Write an equation for the line through the point (x₀,y₀) with a slope of M in point slope form. Your equation should be in the form of y = ... ?
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Solve the problems below as fast as you can because I’m trying to go to sleep but it’s not an assignment or graded or timed please
Given the inequality:
4m < 24
Let's solve for m.
To solve for m, divide both sides of the inequality by 4:
[tex]\begin{gathered} \frac{4m}{4}<\frac{24}{4} \\ \\ m<6 \end{gathered}[/tex]ANSWER:
m < 6
Seventeen percent of people say they've seen a ghost or felt its presence. If 10 people are asked, what is the probability that at least two have seen a ghost or felt its presence?Round your answer to at least three decimals.
Answer: the probability that at least two have seen a ghost or felt its presence is 0.527
Explanation:
In this scenario, it is either a person asked has seen seen a ghost or felt its presence or they have not. These outcomes are independent of each other. Thus, it's a binomial distribution. We would apply the formula for calculating binomial probability which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
p = probability of success
q = 1 - p = probability of failure
n = sample size
x = number of successes
From the information given, we are concerned with the people that say they've seen a ghost or felt its presence. Thus,
p = 17% = 17/100 = 0.17
q = 1 - 0.17 = 0.83
n = 10
x = 2
We want to find P(x ≥ 2)
P(x ≥ 2) = 1 - [P(x = 0) + P(x = 1)
P(x = 0) = 10C0 * 0,17^0 * 0.83^(10 - 0) = 0.1552
P(x = 1) = 10C1 * 0,17^1 * 0.83^(10 - 1) = 0.3178
P(x ≥ 2) = 1 - (0.1552 + 0.3178) = 1 - 0.473
P(x ≥ 2) = 0.527
the probability that at least two have seen a ghost or felt its presence is 0.527
a.a + 0 = 0Additive Identityb. Multiplicative IdentityCommutative Property of Additiond. Associative Property of AdditionC.
Answer:
a. Additive Identity
Explanation:
Given the equation:
[tex]a+0=a[/tex]When zero(0) is added to 'a', the result is still 'a'.
The number 0 is the additive identity of 'a'.
does (51, 58) make the equation y =x -7 true?
The objective is to verify whether the point (51,58) maes the equation y=x-7.
Substitute the values of x and y coordinate in the given equation.
[tex]\begin{gathered} y=x-7 \\ y-x=-7 \\ 58-51=-7 \\ 7=-7 \end{gathered}[/tex]Since, LHS is not equal to RHS.
Thus, the coordinate (51,58) does not make the equation y=x-7.
Hence the answer is NO.
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month
Megan sent 792 text messages in the month of October .
In the question ,
it is given that
Cost for first 600 messages = $15
additional text message charge = $0.05
Amount owed by Megan for the month of October = $24.60
Let the number of Additional messages be x.
So, according to the question
15 + 0.05x = 24.60
0.05x = 24.60-15
0.05x = 9.6
x = 9.6/0.05
x = 192
number of extra messages = 192
total messages = first 600 messages + extra messages
= 600+192
= 792
Therefore , Megan sent 792 text messages in the month of October .
The given question is incomplete , the complete question is
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?
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This is a graph of the motion of a small boat traveling at a constant speed. Total Distance Traveled 12 10 8 Distance (Kilometers) 6 0 2 4 6 8 1012 Time (Hours) How far will the boat travel in 15 hours? O A. 25 km O B. 30 km O C. 15 km O D. 10 km
The speed of the boat is given by the gradient of the line.
Given two points (x1,y1) and (x2,y2) on a graph, the gradient of the line that passes through the two points is given by
[tex]\text{ gradient = }\frac{y_2-y_1}{x_2-x_1}[/tex]In this case,
the line passes through the points (0,0) and (2,2).
We can set (x1,x2) = (0,0) and (y1,y2) = (2,2)
Therefore,
[tex]\begin{gathered} \text{ gradient = }\frac{2-0}{2-0}=\frac{2}{2}=1 \\ \text{therefore} \\ \text{the speed = 1km/h} \end{gathered}[/tex]Given that a body travels with speed, s, and in time, t, the distance travelled, d, is given by
[tex]d=st[/tex]In this case,
s = 1km/h, and t = 15hours
Therefore,
[tex]d=1\times15=15\operatorname{km}[/tex]Therefore, the boat travelled a distance of 15km
could you please help me answer this please and thank you it's about the rectangular prism....
ANSWER:
[tex]A_T=8+8+20+20+40+40[/tex]STEP-BY-STEP EXPLANATION:
In this case, what we must do is calculate the face area and then add each face, like this:
The area of each area is the product between its length and its width, therefore
[tex]\begin{gathered} A_1=2\cdot4=8 \\ A_2=10\cdot4=40 \\ A_3=10\cdot2=20_{} \\ A_4=10\cdot4=40 \\ A_5=10\cdot2=20_{} \\ A_6=2\cdot4=8 \end{gathered}[/tex]The total area would be the sum of all the areas, if we organize it would be like this:
[tex]A_T=8+8+20+20+40+40[/tex]Find an equation of line L. Write your answer using fractions or integers.The equation of line L is y =
Find slope m, in equation y= mx + b
m = Y/X =( y - y')/ (x - x')
m= (5 - -5 )/ (-3 -3) = 10/-6 = -5/3
Now find b
b = y - mx
= 5 - (-5/3)•-3
. = 5 - 5 = 0
b = 0
Then answer is, equation is
y = (-5/3)x
Find the x-intercept and y-intercept of the line.
5x-9y=-12
The x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
What is termed as the x and y intercepts?An intercept is a y-axis point that the slope of a line passes. It is the y-coordinate of the a point on the y-axis where a straight line or even a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope and c seems to be the y-intercept. There are two types of intercepts: x-intercept and y-intercept.For the given question,
The equation of the line is 5x-9y=-12.
For the x intercept, Put y = 0.
5x-9×0=-12.
x = 12/5
x intercept = (12/5, 0)
For y intercept, put x = 0.
5×0-9y=-12
y = -12/9
y = -4/3
y intercept = (0, -4/3)
Thus, the x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
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X + 2y = 3x = 5Enter your answer as a point using parenthesis and a comma. Do not use any spaces in youranswer.If there are no solutions, type "no solutions." If there are infinitely many solutions, type"infinitely many."Answer:
thats the explanation
answer is : (5, -1)
Boden's account has a principal of $300 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
formula for simple intrest
A= p(1+rt)
= 300(1+ 3.5 * 4)
=300( 15)
4500
after 4 years he has $4500
Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
1)
we have
100%-22%=78%=78/100=0.78
so
If is discounted 22%
the new price is 100,000*0.78=$78,000
2) If it is then marked up 22%
the new price is
100%+22%=122%=122/100=1.22
78,000*1.22=$95,160
therefore
The new price is not $100,000
the new price is $95,160
i need help with this question parts 3 - 7
Answer:
i also don't know
Step-by-step explanation:
i also don't know..,......
Tye mapping diagram below matches the points on the graph next to it.find the value of X
Given,
The coordinates of the points shown in the graph is:
[tex](-6,2),\text{ \lparen6,2\rparen, \lparen6,1\rparen and \lparen3,1\rparen}[/tex]Here, the given mapping is:
[tex](-6,2),\text{ \lparen6,2\rparen, \lparen x,1\rparen and \lparen3,1\rparen}[/tex]On comparing the coordinates then x = 6.
Hence, the value of x is 6.
May I please get help with this. For I have tried multiple times but still can’t get the right answer or the triangle after dilation?
Solution:
Given the triangle ABC as shown below:
To draw the image,
step 1: Determine the coordinates of the vertices of the triangle.
In the above graph,
[tex]\begin{gathered} A(6,7) \\ B(9,9) \\ C(8,6) \end{gathered}[/tex]step 2: Evaluate the new coordinates A'B'C' of the triangle after a dilation centered at the origin with a scale factor of 2.
After a dilation centered at the origin with a scale factor of 2, the iniatial coordinates of the vertices of the triangle are multiplid by 2.
Thus,
[tex]\begin{gathered} A(6,7)\to A^{\prime}(12,14) \\ B(9,9)\to B^{\prime}(18,18) \\ C(8,6)\to C^{\prime}(16,12) \end{gathered}[/tex]step 3: Draw the triangle A'B'C'.
The image of the triangle A'B'C' is as shown below:
