In linear equation , 240 liters of 90% solutions will be used.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,
Since, the total quantity of the mixture = 360,
⇒ x + y = 360 ----- (1),
Also, the resultant solution is of 85% antifreeze solution,
⇒ 75 % of x + 90% of y = 85% of 360
0.75x + 0.90y = 0.85 × 360
0.75x + 0.90y = 306
75x + 90y = 30600 -----(2),
Equation (2) - 75 × equation (1),
We get,
15y = 3600
⇒ y = 240
Hence, 240 liters of 90% solutions will be used.
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The probability of each two occurring given that event he has happened is called wha
Answer:
Conditional Probability
Step-by-step explanation:
Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening
NO LINKS! Please help me with these problems
Answers in bold:
Problem 4) Shift 6 units left, 1 unit down
Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.
The graphs are below.
==========================================================
Explanation:
In problem 4, the parent function is y = x^2
Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.
Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.
So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.
I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.
---------------------------------
For problem 5, the parent function is y = |x|
Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.
The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).
Answer:
4. Translated 6 units left and 1 unit down.
5. Translated 3 units right and stretched vertically by a factor of 2.
Step-by-step explanation:
Transformations
[tex]\textsf{For $a > 0$}[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Question 4Parent function:
[tex]f(x)=x^2[/tex]
Translated 6 units left:
Add 6 to the x-variable of the function:
[tex]\implies f(x+6)=(x+6)^2[/tex]
Translated 1 unit down:
Subtract 1 from the function:
[tex]\implies f(x+6)-1=(x+6)^2-1[/tex]
Question 5Parent function:
[tex]f(x)=|x|[/tex]
Translated 3 units right:
Subtract 3 from the x-variable of the function:
[tex]\implies f(x-3)=|x-3|[/tex]
Stretched vertically by a factor of 2:
Multiply the function by 2:
[tex]\implies 2f(x-3)=2|x-3|[/tex]
On a recycling drive, Janet collected 2 1/8 pounds of canned goods and Steve collected 3 4/8 pounds of canned goods. How many total pounds of canned goods did Janet and Steve collect together?
A.
B.
C.
D.
Answer:
5 5/8 pounds
Step-by-step explanation:
I added the fractions and got that
Determine the point that is 1/3 of the distance from (-4.5, 0) to (0, 9)
The point that is 1/3rd of the distance from (-4.5,0) to (0,9) is (-3,3).We use a formula similar to the midpoint formula for finding the point.
We have been given two points (-4.5,0) and (0,9), we have to find the point is on the line formed by these two points and is 1/3rd away. We don't need to find the distance between these two points to find the asked point. We have to use a formula that is similar to finding the midpoint of a line. For two points (a,b) and (x,y) the midpoint is ([tex]\frac{a+x}{2} ,\frac{b+y}{2}[/tex]).We used equal parts of the two points to find the midpoint, for 1/3rd we will be using uneven parts of the two points.
[tex]x_{1} =\frac{2}{3} (-4.5)+\frac{1}{3} (0)=-3[/tex]
[tex]y_{1} =\frac{2}{3} (0)+\frac{1}{3} (9)=3[/tex]
Therefore the point that lies 1/3rd of the distance from (-4.5,0) and (0,9) is (-3,3).
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(a)The area of a rectangular garden is 8613 m^2 .
If the length of the garden is 99m, what is its width?
(b)The perimeter of a rectangular window is 350 cm.
If the width of the window is 82 cm, what is its length?
Answer:
Step-by-step explanation:
Find the measure of the smaller angle formed by the hands of a clock at the following time. 4:25
The minute hand has moved 25 times out of a possible 60 from the top of the clock as of 4:25. 150 degrees is 25 multiplied by 6 degrees. Simply subtracting those degrees from the above calculation, the angle from the minute hand to the hour hand is equal to 360 degrees. 342.5 degrees is 360 minus 17.5.
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex. Using a protractor, angles are measured in degrees (°).
An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.
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In an addition equation, when one addend is positive and the other is negative. How do you determine whether the sum will be positive or negative?
If a > b then;
a + -b = a positive number
If b > a then;
a + -b = a negative number
If both addends are positive or if the positive addend has a greater absolute value than the negative addend, the sum will be positive. If both addends are negative or if the negative addend has a greater absolute value than the positive addend, the sum will be negative.
Y equals X² + 8X + 12show in a graph
Answer:
Step-by-step explanation:
[(1.7×10^6)÷(2.63×10^5)]+7.33
i’ll give brainliest and about 15 points (i’m talking about the 2-80 ones)
Here are the values of the expressions :
a. 3(4) = 12
b. 4 + 11 + (-4) = 11
c. 3.2(2) = 6.4
d. | (-2) + (-2) + (-2) | = 6
e. |2 (-7.5) | = 15
f. 10 1/5(-5) = -51
a. 9(410) = 3690
b. 6(592) = 3552
What are the values of the expressions?Take not of the following rules:
When a term is in bracket, it means that the values should be multiplied : 2 (3) = 2 x 3 = 6
When numbers are between this sings | |, it means that the answer should be an absolute value. e.g. | - 5 - 5 | = 10
When a negative sign is multiplied by a positive sign, the result would be a negative sign. -1 x + 1 = -1
a. 3(4) = 3 x 4 = 12
b. 4 + 11 + (-4)
= 4 + 11 - 4 = 11
c. 3.2(2) = 3.2 x 2 = 6.4
d. | (-2) + (-2) + (-2) |
|- 2 - 2 - 2| = 6
e. |2 (-7.5) |
|2 x -7.5| = 15
f. 10 1/5(-5)
10 1/5 x - 5
51/5 x - 5 = -51
a. 9(410)
= (9 x 400) + (10 x 9)
3600 + 90 = 3690
b. 6(592)
= (6 x 500) + (92 x 6)
3000 + 552
3552
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Two triangles are similar. First triangle has sides of length 6, 8, and 14. The shortest
side of the other has length 12.
a) What is the scale factor going from first to the second triangle?
b) Determine the length of the longest side of the second triangle.
The scale factor going from the first to the second triangle according to the task content is; 2.
The length of the longest side of.the triangle as required in the task content is; 24.
What is the scale factor going from the first to the second triangle?According to the task content, it follows that the two triangles are similar.
Therefore, the corresponding sides of such triangles must be in proportion.
Therefore the scale factor from the first to the second triangle as required is;
Scale factor = 12/6; since the shortest sides are corresponding sides.
Scale factor = 2.
Hence, since the length of the longest side in the first triangle is 14, the length of the longest side in the second triangle is;
L = 2 × 14
L = 28
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Rearrange this equation to isolate c.
a=b (1/c-1/d)
Answer:
[tex]c=\frac{bd}{ad+b}[/tex]
Step-by-step explanation:
By isolating the term c, we are trying to arrive at the equation c= ____.
[tex]a=b(\frac{1}{c}-\frac{1}{d} )[/tex]
Divide both sides by b:
[tex]\frac{a}{b}= \frac{1}{c}-\frac{1}{d}[/tex]
Add [tex]\bf{\frac{1}{d}[/tex] to both sides:
[tex]\frac{1}{c} =\frac{a}{b} +\frac{1}{d}[/tex]
Rewriting the right-hand side as a single fraction:
[tex]\frac{1}{c} =\frac{a(d)}{b(d)} +\frac{1(b)}{d(b)}[/tex]
[tex]\frac{1}{c} =\frac{ad+b}{bd}[/tex]
Find the expression of c:
[tex]1\div\frac{1}{c} =1\div\frac{ad+b}{bd}[/tex]
[tex]\bf{c=\frac{bd}{ad+b}[/tex]
Additional:
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Answer:
[tex]c=\dfrac{bd}{ad+b}[/tex]
Step-by-step explanation:
Given equation:
[tex]a=b\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]
Divide both sides by b:
[tex]\implies \dfrac{a}{b}=\dfrac{b}{b}\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]
[tex]\implies \dfrac{a}{b}=\dfrac{1}{c}-\dfrac{1}{d}[/tex]
Add 1/d to both sides:
[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}-\dfrac{1}{d}+\dfrac{1}{d}[/tex]
[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}[/tex]
[tex]\textsf{Simplify the left side by applying the fraction rule} \quad \dfrac{p}{q}+\dfrac{r}{s}=\dfrac{ps+qr}{qs}:[/tex]
[tex]\implies \dfrac{ad+b}{bd}=\dfrac{1}{c}[/tex]
Cross multiply:
[tex]\implies c(ad+b)=bd[/tex]
Divide both sides by (ad + b):
[tex]\implies \dfrac{c(ad+b)}{ad+b}=\dfrac{bd}{ad+b}[/tex]
[tex]\implies c=\dfrac{bd}{ad+b}[/tex]
Given
F(x)=3x+9
And
g(x) =1/3x-3
verify by composition that f(x) and g(x) are inverse functions.
Step-by-step explanation:
use fog
3(1/3x-3)+9
=x
use gof
1/3(3x+9)-3
=x
we can see that both results give us x hence they are inverse
What is the greatest common factor of 41 and 48?
Answer:
the gcf of 41 and 48 would be 1
Answer: 1
Step-by-step explanation:
41 48
/\ /\
1 * 41 1 * 48
A company has found that the demand for its product varies inversely as the price of the product. When the price x is 3.5 dollars, the demand is 400 units. Find a mathematical model that gives the demand y in terms of the price x in dollars.
I don't understand how to make this into an equation. Do I have enough variables?
A mathematical model that gives the demand y in terms of the price x in dollars.
y = 1400/ x
This is further explained below.
What is a mathematical model that gives the demand y in terms of the price x in dollars.?Generally, The following formula would apply in the situation when there is an inverse link between y and x:
y = k/x
where k is constant.
In a relationship with an inverse connection, one variable will tend to decrease as the other variable grows.
y denotes the amount of demand.
x is equivalent to the cost.
400 = k/3.5
k = 400 * 3.5
k = 1,400
The following is the formula for the mathematical model that calculates the demand y based on the price x in dollars:
y = 1400/ x
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35/456 long division
The quotient after the long division of 35/456 is 0.076.
What do we mean by long division?The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations. The division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains when no further full chunk of the size of the second number can be allocated during the quotient computation. Long division is a standard division algorithm that is simple enough to perform by hand for dividing multi-digit Hindu-Arabic numerals (Positional notation).So, after the long division:
(Refer to the image given below)Quotient: 0.076(Calculated to 3 decimal places)Therefore, the quotient after the long division of 35/456 is 0.076.
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Question 6 (1 point) Mrs. Sullivan wants to make a square tablecloth for her dining room table. She has 400 ft? of fabric. What are the possible side lengths of the tablecloth? A. 11 ft x 11 ft B. 11 ft x 2 ft C. 60.5 ft x 2 ft D. 60.5 ft x 60.5 ft
The required possible side length of the tablecloth is 11ft x 11ft.
What is the square?
A square is for sided regular polygon, where the length of all sides is identical and the angle between the adjacent side is 90°.
Given the following parameters
Area of fabric =121 ft² of fabric.
She wants to make a square tablecloth for her dining room table.\
Area of the square = a²
121 = a²
a = √121
a = 11 ft
Thus, the required possible side length of the tablecloth is 11ft x 11ft.
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HELPPPPPPP MEEEEEEEEEEEE AHHHHH
Answer:
Question have problem.
An advertiser goes to a printer and is charged $38 for 100 copies of one flyer and $50 for 208 copies of another flyer. The
printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost
of a printing job, if x is the number of copies made. C(x) =
4.
Answer:
C(x) = (1/9)x + 242/9
Step-by-step explanation:
Let x = number of pages.
Let y = cost.
We are given two ordered pairs, (x, y):
(100, 38) and (208, 50)
We must find the equation of the line that passes through these two points.
y = mx + b
m = (y_2 - y_1)/(x_2 - x_1) = (50 - 38)/(208 - 100) = 12/108 = 1/9
y = (1/9)x + b
Use point (100, 38) as x and y to find b.
38 = (1/9)(100) + b
38 × 9 = 100 + 9b
9b + 100 = 342
9b = 242
b = 242/9
The equation is:
y = (1/9)x + 242/9
Answer: C(x) = (1/9)x + 242/9
About what percent of the data are greater than 20?
About what percent of the data are less than 15?
Describe and correct the error in interpreting the box-and-whisker plot.
please answer questions 8-10.
About 25 percent of the data are greater than 20.(option a)
About 50 percent of the data are less than 15. (option b)
20 is wrongly interpreted as the median. 20 is the third quartile. The data between 11 and 20 is 50%.
How can a box-and-whisker plot be interpreted?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
The box plot consists of two whiskers and a box. The first whisker represent the minimum value. The second whisker represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.
20 is the third quartile. Score greater than 20 is 25% (100% - 75%)
15 is the median. Scores less than 15 is 50% (100 - 50%),
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Find the quotient the problem below.
⅝ × ¾
Answer: 5/8 + 3/4 = 11/8 = 1 3/8 = 1.375
Step-by-step explanation:5/8+ 3/4= 5/8+ 3 · 2/4 · 2 = 5/8+ 6/8= 5 + 6/8 = 11/8
Answer: Incorect answer
Step-by-step explanation:
5/8X3/4 =11/8 =1 3/8=1.375
a circle has a diameter of 18 ft what is it's circumference
Step-by-step explanation:
The formula for circumference when the diameter is given is C = π • d
C = circumference
π = pi
d = diameter
So to find the circumference plug in the number (18 - diameter).
C = π • 18
C = 56.5486677646
If needed to round to nearest ...
tenth = 56.5
hundredth = 56.55
However, if the directions say to use 3.14 for π (pi) then the answer would be different.
C = 3.14 • 18
C = 56.52
Hope this helps :)
simplify 3 • 3^2 + 8 divided by 2 - (4 + 3)
[tex]3 \cdot 3^2 + 8 : 2 - (4+3) =[/tex]
[tex]3 \cdot 3^2 + 4 - 7=[/tex]
[tex]3 \cdot 9 +4 -7=[/tex]
[tex]27 + 4 - 7 = 24[/tex]
==axel134==
I didn’t know what I did wrong please help thank u
Answer: -4/7
Step-by-step explanation:
the formula for the slope is rise/run
or (y-y1)/(x-x1)
we can apply this concept like this:
7-(-7)=7+7=14
-4-4=-8
since -8 is the rise and 14 is the run, the slope is -8/14
simplify to -4/7
How is the word term used to describe a ratio relationship and in the context of an expression?
It should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.
How to illustrate the information?It should be noted that it's important to understand ratio and use ratio language to describe the relationship between two quantities.
For example, it van be stated that the ratio of wings to beaks in the bird house at the zoo is 2:1, this implies that b for every 2 wings there is 1 beak.
Therefore, it should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.
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In a random sample of 144 observations, begin mathsize 15px style p with bar on top end style = .7. The 95% confidence interval for p is
The 95% confidence interval for p is (0.333, 0.480).
What is the confidence interval?If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
The formula for calculating the confidence interval is expressed as shown below;
CI = p±Z * √p(1-p)/n±0.5/n
Where Z is the z-score at 95% confidence
p is the sample proportion
n is the sample size
Given that n = 144, p = 0.7 and z-score at 95%
CI = 1.645 (from z table)
Now Substituting this values;
CI = p ± 1.645*√0.7(1-0.4)/144 ±0.5/n
CI = 0.4 ± 1.645*√0.7(0.6)/144 ± 0.5/144
CI = 0.4 ±1.645 * √0.24/144 ± 0.00347
CI = 0.4 ±1.645 * 0.04087± 0.00347
CI = 0.4±0.06723±0.00347
CI =(0.333, 0.480)
Hence, The 95% confidence interval for p is (0.333, 0.480).
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2. Given K is the midpoint of GH, GK = 5x - 3,
and GH = 2x + 24, find the value of x.
NEED HELP ASAP
The value of the x in the linear equation of the midpoint is a 3.85.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
Midpoint is the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.
From the given information:
Given K is the midpoint of GH, GK = 5x - 3,and GH = 2x + 24
As the midpoint the both equation are equal to the each other.
Then
GK = GH
5x - 3 = 2x + 24
5x+2x = 24+3
7x = 27
x = 27/7
x = 3.85.
So, The value of the x in the linear equation of the midpoint is a 3.85.
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HOW MUCH TICKETS DID THE MOVIE SELL?
Movie a costs 4 dollars
Movie b costs 5 dollars
Movie theater got 200 dollars and sold 47 tickets
How many tickets did movie a sell
PLS ANSWER ILL GIVE BRAINLIEST
Taking into account the definition of a system of linear equations, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Number of tickets soldIn this case, a system of linear equations must be proposed taking into account that:
xa: number of tickets sold for Movie Axb: number of tickets sold for Movie BOn the other hand, you know:
Movie A costs 4 dollars.Movie B costs 5 dollars.Movie theater got 200 dollars.Movie theater sold 47 tickets.So, the system of equations to be solved is
[tex]\left \{ {{xa + xb=47} \atop {4xa + 5xb=200}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable xa from the first equation, you obtain:
xa= 47 - xb
Substituting this expression in the second equation you get:
4×(47 -xb) + 5xb= 200
Solving:
4×47 - 4xb + 5xb= 200
188 - 4xb + 5xb= 200
- 4xb + 5xb= 200 - 188
xb= 12
Remembering that xa= 47 - xb. you get: xa=47 - 12 → xa= 35
Finally, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.
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Why do you multiply by a power of 10 when writing a repeating decimal as a rational number?
Answer: So that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.
Step-by-step explanation:
What is the distance between −9 and 3 on a number line ,in why ?
Answer:a
a
Step-by-step explanation:
Answer:
12
Step-by-step explanation: