Answer:
a) 9×2=18
b)16×2=32
c)14×9=126
d)20×10=200
e)10×3=30
Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what ws left in the afternoon. When he closes for the day, he has 4 liters left. How many liters of lemonade did he start the day with? math
Emil starts the day with 16 liters of lemonade if he is left with 4 liters by the end of the day. Computed using the fractional values given.
Let the initial quantity of lemonade with Emil be x liters.
Quantity sold by Emil in the morning = Half of his lemonade = (1/2)x liters, that is half fraction of x.
Quantity left with Emil = x - x/2 = x/2 liters, that is half fraction of x.
Quantity sold by Emil at lunchtime = Quarter of what was left = (1/4)(x/2) liters = x/8 liters, that is the one-eight fraction of x.
Quantity left with Emil = x/2 - x/8 = 3x/8 liters, that is the three-eight fraction of x.
Quantity sold by Emil in the afternoon = One-third of what was left = (1/3)(3x/8) liters = x/8 liters, that is the one-eight fraction of x.
Quantity left with Emil = 3x/8 - x/8 = x/4 liters, that is the quarter fraction of x.
Now, we are said that Emil closes for the day with 4 liters remaining.
Therefore, x/4 = 4, or, x = 4*4 = 16 liters.
Therefore, Emil started the day with 16 liters of lemonade.
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8 of 8
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The following are the temperatures in
°C for the first 12 days of January:
-5.5, 6, -1.5, 3, 4, -2.5,
0, 6.5, -3, 2.5, -1, 5.5
What is the median temperature for
those 12 days?
Give your answer as a decimal.
ABC Check
←
↑
X
Answer:
2.75 is the median
Answer:
1.25 is the median
Step-by-step explanation:
it is the middle of the number sequence.
to find the median, place the numbers in value order and find the middle
since there is an even amount of numbers, add 2.5 and 0 (the two middle numbers) and divide them by two
Yesterday, Jennifer walked several laps around a track. She made Graph 1 to describe the relationship between time and distance. Today, Jennifer alternated walking one lap and running one lap. She made Graph 2 to describe the relationship between time and distance.
Select True or False for each statement.
Graph 1. First quadrant of a coordinate plane with the X axis labeled Time and the Y axis labeled Distance. A line begins at 0, 0 and goes up and to the right. Graph 2. First quadrant of a coordinate plane with the X axis labeled Time and the Y axis labeled Distance. A graph made up of several line segments that vary in steepness begins at 0, 0 and goes up and to the right.
A
Graph 1 shows a proportional
relationship because the graph
is a line.
True False B
Graph 2 shows a proportional
relationship because the graph
passes through the origin.
True False C
Graph 2 does not show a
proportional relationship
because the graph is not a line.
True False D
Graph 1 shows a proportional
relationship because the graph
is a line that passes through the origin.
True False E
Graph 2 shows a proportional
relationship because the graph
is made up of lines.
True False F
Graph 2 shows a proportional
relationship because the graph
is increasing.
True False
The answers to the statements that have been made here are:
False falsetruetruefalsefalseHow to check for the answers.The first statement is false because the proportional relationship is not due to the fact that it is a line.The second is also false given that the graph is not proportional as it goes through the origin of the graph.True The graph in 2 does not show the proportional relationship given that it does not go by the origin.This is true. It passes through the origin.The lines contained in the graph would have to be similar first before it can show this relationship hence false.The graph is not increasing and cannot show the relationship hence false.Read more on graphs here:
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find x and y
can someone pls help
Answer:
x = 25, y = 10
Step-by-step explanation:
I'll add a drawing of my own so that it's easier for me to explain, and for you to understand.
Since line BC and line DE are parallel and line AE is being shared, angle ACB and angle CED will be the same. So the square will also be 3y.
Since line AB and line CD are parallel and line AE is being shared, angle CAB and angle ECD will be the same. So the heart will be 2x.
Now that we figured out two unknown angles, we can see that the two triangles share two angles with the same value. Since angles in a triangle add up to 180 (Added angles in every triangle are the same), the triangle shape (I drew) will be 4x.
We have a few clues to find the value of x and y.
1) 2x + 4x + 3y = 180 (all angles in a triangle add up to 180)
2) 3y + 2x = 180 - 100 (If you look near point C, we can see that 3y + 100 + 2x equals a flat line. A flat line equals 180)
We can use substitution. 3y + 2x can be replaced with 80.
So our new equation will be: 4x = 100
x = 25.
Now we can replace x with 25 in our second clue.
3y + 2(25) = 80
3y + 50 = 80
3y = 30
y = 10.
We can conclude that x = 25, and y = 10
Answer:
x = 25 and y = 10
Step-by-step explanation:
The arrows on the line segments mean the lines are parallel.
Therefore, the diagram shows two similar triangles, which means their interior angles are the same size. (Refer to the attached diagram).
Interior angles of a triangle sum to 180°:
⇒ 2x + 4x + 3y = 180
⇒ 6x + 3y = 180
⇒ 3(2x + y) = 180
⇒ 2x + y = 60
⇒ 2x = 60 - y
Angles on a straight line sum to 180°:
⇒ 3y + 100 + 2x = 180
⇒ 2x + 3y = 80
⇒ 2x = 80 - 3y
Substitute the first equation into the second equation, and solve for y:
⇒ 60 - y = 80 - 3y
⇒ 60 + 2y = 80
⇒ 2y = 20
⇒ y = 10
Substitute the found value of y into one of the equations and solve for x:
⇒ 2x = 60 - 10
⇒ 2x = 50
⇒ x = 25
Therefore, x = 25 and y = 10.
Find the integrals:
∫1÷(x(㏑x-π)^4)dx
Answer:
[tex]C-\frac{1}{3(lnx- \pi)^3}.[/tex]
Step-by-step explanation:
[tex]\int\ {\frac{1}{x(lnx- \pi)^4} } \, dx=\int\ {\frac{d(lnx- \pi)}{(lnx- \pi)^4}} \, dx=-\frac{1}{3(lnx- \pi)^3} +C.[/tex]
Rebecca earned $115 in simple interest for 8 months at an annual interest rate of 3%. How much money did she start with in her account?
Answer:
$5750
Step-by-step explanation:
For simple interest,
I = prt
115 = p × 0.03 × 8/12
p = 5750
Write the equation of the line in fully simplified slope-intercept form.
2H990 S4321
12
11
10
8
7
6
5
-12-11-10-9-8-7-6-5-4-3-2-1₁ 1 2 3 4 5 6 7 8 9 10 11 12
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-X
Answer:
what is the price of an article costing rs 2000 after levying 13 value added tax find it
what is a factor of x^4 + 8^x 3 + 17 x^2 − 2x − 24 ?
Answer:
factors are (x-1),(x+2),(x+4),(x+3)
Can someone help me
Step-by-step explanation:
1. Right angled triangle , scalene triangle
2. isosceles triangle, obtuse angled triangle
3. equilateral triangle
4. right angled triangle, isosceles triangle
5. scalene triangle, obtuse angled triangle
6. scalene triangle, acute angled triangle
Answer:
Step-by-step explanation:
Otto has some whipping cream that is 30%, butterfat, and some milk that is 2%, butterfat. He wants to make a 500 ML mixture of them that is 12%, percent butterfat.
What does point J represent in this context?
CORRECT (SELECTED)
The mixture has more than the intended volume and has the intended percent of butterfat.
Explanation: Point JJJ is on line aaa, so it represents a scenario where the mixture has 12\%12%12, percent butterfat. Also, point JJJ is above line bbb, so it represents a scenario where the mixture has a volume of more than 500 \,\text{mL}500mL500, start text, m, L, end text.
The point J connote that the mixture has more than the expected volume and has the optimal butterfat percentage.
What is the point implying?Note that in the question, it was supplied that Otto intended to make a mixture of 12% butter fat.
Since:
Milk = 2% butter fat
Whipping cream = 30% butter fat.
This implies that the milk contains the smallest of butter fat and it also implies that Otto would require a lot more milk than cream, to be able to attain the 12% mixture.
This is known to be when point J is said to meet, and by using that data from point J, Otto require more of milk than the cream to get what he wants.
Therefore, The point J connote that the mixture has more than the expected volume and has the optimal butterfat percentage.
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Complete the factorization of 3x2 – 5x 2. which two factors can be multiplied together to make this trinomial?
The two factors multiplied together to make a trinomial is (x-1)(3x-2).
Given equation is 3x²-5x+2.
An algebraic equation which of the second degree in x is known as quadratic equation. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
In the given equation,
Multiply the first coefficient 3 with the last coefficient 2 so we get 2×3=6
Use any two numbers which on multiply give 6 and on adding or subtracting give -5.
Such two numbers are -2 and -3
On multiplying, (-3)×(-2)=6
On Adding, -3-2=-5
So, break -5x into -3x and -2x and we get
3x²-3x-2x+2
Taking out 3x common from the first two terms and -2 from the last two terms as
3x(x-1)-2(x-1)
Taking out the common term (x-1) as common and get
(x-1)(3x-2)
Hence, the two factors of the equation 3x²-5x+2 that can be multiplied together to make this trinomial is (x-1)(3x-2).
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Help me please T^T
Solve for m.
m+1/3<-2 1/4
Answer:
B
Step-by-step explanation:
subtract 1/3 from both sides
m< -2 7/12
Translate the English phrase into an algebraic expression: the difference of f and the quotient of g and h.
Answer:
f-(g/h) is an algebraic expression of the difference of f and the quotient of g and h.
Step-by-step explanation:
[tex]f - ( \frac{g}{h} )[/tex]
I hope it was helpful for you..m
The requried algebraic expression of English phrase is given as f - g/h.
What is an algebraic expression?The algebraic expression consists of constants and variables. eg x, y, z, etc.
What is the equation?the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
The difference between f and the quotient of g and h.
The difference represents the subtraction of values, and the quotient can be obtained by division of g by h.
So,
Required algebraic expression,
= f - g/h
Thus, the required expression is given as f - g/h.
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JFDKGJNREITFHROIHTJFMNORHCTGJK,MV JIOKVMNTRH HTR OIMTGR
The multiples of 5 and 6 based on the information have been illustrated below.
How to illustrate the multiple?It should be noted that a multiple is a number that can be divided by another number without a remainder.
Here, the multiples of 5 will be:
5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
In this case, the multiples of the numbers have been illustrated.
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60 - 48 divided by 6 x 7 will equal to
Answer:
4
Step-by-step explanation:
i dont cap
The solution of the expression [tex]\dfrac{60-48}{6\times 7}[/tex] is [tex]\dfrac{2}{7}[/tex].
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expression is solved as,
[tex]\dfrac{60-48}{6\times 7}= \dfrac{12}{42}[/tex]
Solve the fraction [tex]\dfrac{12}{42}[/tex].
[tex]\dfrac{60-48}{6\times 7}= \dfrac{2}{7}[/tex]
Therefore, the solution of the expression [tex]\dfrac{60-48}{6\times 7}[/tex] is [tex]\dfrac{2}{7}[/tex].
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Which statements about the graph of the function f(x) = -x² - 4x + 2 are true? Select three options.
The domain is {x|x ≤-2}.
The range is {yly ≤ 6}
The function is increasing over the interval (-∞, -2).
The function is decreasing over the interval (-4,00).
The function has a positive y-intercept
Answer:
The range is {y l y ≤ 6}.The function is increasing over the interval (-∞, -2).The function has a positive y-intercept.Step-by-step explanation:
The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.
RangeThe range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.
The range is {y l y ≤ 6}.
IncreasingThe graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.
The function is increasing over the interval (-∞, -2).
Y-interceptThe y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.
The function has a positive y-intercept.
Mr. Capildeo's salary sfter a 5% increase was $6255 (a) calculage his salary if a 3% incrwae had been given instead (b) Calculate his original salry
Answer:
Original Salary: [tex]5,957.14[/tex]
Increase in 3%: [tex]6,135.85[/tex]
Step-by-step explanation:
So when something increases by x%, the new value is (100+x)% the original value. So 6255, is 105% the original value. This means to find the original value, we have to find the number that has 6255 as 105% of it's value. Whenever you try to find x% of a number, you multiply it by the decimal value of the percentage, which is found by dividing by 100. So to find x%, you do: [tex]o*\frac{x}{100}[/tex] where o = original value, x=percent. In this case the percent is 105%, which when divided by 100 is 1.05. So this gives us the equation: [tex]o*1.05=6255 \implies o = \frac{6255}{1.05} = 5,957.14[/tex]. This is his original salary. You need to do this process, do not make the mistake of subtracting 5% from 6255. This is because 5% of 6255 does not equal the 5% of the original value. 5% of 6255 should be greater than 5% of the original value, since the new value is an increase of 5%. So since we have his original salary, we can calculate the salary increase had it been 3%. to do this we multiply by 1.03 (103% divided by 100). This gives us the equation: [tex]5,957.14*1.03=6,135.85[/tex]
Suppose ABCD is a rectangle. Find AB and AD if point M is the midpoint of BC,
AM 1MD, and the perimeter of ABCD is 34 in.
Answer:
Step-by-step explanation:
Perform the calculation then round to the appropriate number of significant digits. 129 ÷ 3.332 Perform the calculation then round to the appropriate number of significant digits . 129 ÷ 3.332
The calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.
What is division of the two numbers?
Given that;
129 ÷ 3.332
First we convert 3.332 to fraction
3.332 = 3.332/1
3.332 = 3.332/1 × 1000/1000 = 3332/1000
3.332 = 833/250
Hence we have;
129 ÷ 833/250
This can be written as
= 129 × 250/833
= 32250/833
= 38.71549 ≈ 39
Therefore, the calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.
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what is the probability that the next person chosen will be in the 40-49 or 50-59 age groups
The probability that the next person chosen will be in the 40-49 or 50-59 age groups is 0.32
How to determine the probability?The frequency table is added as an attachment
From the attached image, we have:
40 - 49 or 50 - 59 = 6869 + 6323
40 - 49 or 50 - 59 = 13192
The probability that the next person chosen will be in the 40-49 or 50-59 age groups is then calculated as:
P = 13192/41557
Evaluate
P = 0.32
Hence, the probability that the next person chosen will be in the 40-49 or 50-59 age groups is 0.32
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OQ=4x+2,OQ=4x+2, PQ=4x-10,PQ=4x−10, and OP=3x-3,OP=3x−3, determine the numerical length of OQ
.
Answer:
22
Step-by-step explanation:
The segment addition theorem tells us the whole is the sum of the parts. We can use this to write an equation relating the expressions for segment length.
SetupOQ = OP +PQ . . . . . segment addition theorem
4x +2 = (3x -3) +(4x -10) . . . . substitute given expressions
Solution15 = 3x . . . . . . add 13 -4x to both sides
5 = x . . . . . . . divide by 3
OQ = 4x +2 = 4(5) +2 = 22
The length of OQ is 22 units.
Find n in this equation: 208P(n,2)=P(16,4)
Answer:
N=15
Step-by-step explanation:
Isabella uses the equation V = one-third (12) squared (9) pi to find the volume of the cone below.
A cone has a height of 9 centimeters and base of 12 pi centimeters squared.
What is Isabella’s error?
Isabella should have divided 12 by 2 before squaring to get V = one-third (6) squared (9) pi.
Isabella should have squared 9 instead of 12 to get V = one-third (9) squared (12) pi.
Isabella should have divided the product of 12 and 9 by 3 to get V = StartFraction 12 (9) Over 3 EndFraction.
Isabella should have divided the product of 12 pi and 9 by 3 to get V = StartFraction 12 pi (9) Over 3 EndFraction.
Isabella’s error is Isabella should have divided the product of 12π and 9 by 3 to get V = 12π(9)/3 option fourth is correct.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
Isabella equation:
[tex]\rm V = \dfrac{1}{3}(12)^2(9)\pi[/tex]
The area of the base = 12π square cm
[tex]\rm V = \dfrac{12\pi (9 )}{3}[/tex]
Thus, Isabella’s error is Isabella should have divided the product of 12π and 9 by 3 to get V = 12π(9)/3 option fourth is correct.
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Bonds have a maturity risk premium that can be modeled as the following:
MRP = (t-1) 0.3%
were t represents the years to maturity.
What is the Maturity risk premium of a bond that matures in 10 years?
answer in % without the symbol
Answer:
.
Step-by-step explanation:
Please help!!! If...........
Answer:
-1
Step-by-step explanation:
Simply plug in (-1) to both equations and add.
Equation 1:
2(-1)^2 = 2
3(-1) = -3
2 + -3 - 1 = -2
Equation 2:
-( - 1) = 1
Add both together:
-2 + 1 = -1
Answer:
The equation is 2x² + 3x - 1 and here f(x) is -1
Putting f(x) = -1.
[tex]f(x) = 2 {( - 1)}^{2} + 3( - 1) - 1[/tex]
[tex]f(x) = 2 (1) - 3 - 1[/tex]
[tex]f(x) = 2 - 3 - 1[/tex]
[tex]f(x) = - 1 - 1[/tex]
[tex]f(x) = - 2[/tex]
For g(x) put as -1
[tex]g(x) = - ( - 1)[/tex]
[tex]g(x) = 1[/tex]
Last step,
-2 + 1 = -1
So, option ( a) is correct
What is DC to the nearest tenth
Answer:
DC= 32.3 units
Step-by-step explanation:
Use Pythag theorem to find BC first
15 ^2 + BC ^2 = 22^2 then BC = sqrt 259
Then use the Pythagorean Theorem again to find DC
DC^2 = 28^2 + sqrt(259)^2
DC=32.3
Question 2 of 10
What is the point-slope form of a line with slope -4 that contains the point
(-2, 3)?
Replace the question mark with
either > or <.
y[? ]x and y[]-x
The complete inequality is y < x and y< -x
How to complete the inequality?The expressions are given as:
y[ ]x and y[ ]-x
From the graph, we can see that:
Only the lower regions are shaded
This represents the less than inequality sign
Hence, the complete inequality is y < x and y< -x
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W+3/5= 6 1/4
Solve W
Answer: W = 113/20
Explanation:What we know:
We need to find the value of W6 1/4 - 3/5 = WThe fractions need to be equivalent denominatorsProcess:
Set up equation W + 3/5 = 6 1/4
Expand W + 3/5 = 6*4+1 /4
Simplify W + 3/5 = 25/4
Common denominator W + 3*4/5*4 = 25*5 / 4*5
Simplify W + 12/20 = 125/20
Subtract -12/20 -12 /20
Solve W = 113/20
Answer: W = 113/20Check:
By converting our answers into decimals, we can see if the sides are equal:
113/20 = 5.65
3/5 = 0.6
5.65 + 0.6 = 6.25
Does 6.25 = 6 1/4?
1/4 = 0.25
6 + 0.25 = 6.25
6.25 = 6.25
Therefore, W = 113/20 is the correct answer.
(2a-x): ( b * 2x) be the sub-duplicate ratio of ab, then the value of x ^ 1 is
Answer:
x^2=ab
Step-by-step explanation:
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