The total lemonade the two friends bring to the cookout when one brings 2.7 liters and the other brings 3.54 liters of lemonade is 6.24 liters of lemonade, computed using decimal addition.
The methods we use to add or subtract decimals are as follows:
Vertically align the decimal points. Any necessary zeros should be entered.Treat the integers as whole numbers when adding or subtracting them.Align the decimal point with the numbers being added or subtracted so that it sits vertically above the sum or difference.In the question, we are informed that two friends bring lemonade to the cookout. The first brings 2.7 liters and the second brings 3.54 liters.
We are asked to find the total lemonade brought by them to the cookout.
To find the total lemonade, we add both the decimal quantities following the steps discussed.
2.7
+ 3. 54
Step 1: Adding zeroes:
2.70
+ 3. 54
Step 2: Treating them as numbers and adding:
2.70
+ 3. 54
________
624
Step 3: Aligning decimal points:
2.70
+ 3. 54
________
6.24
Thus, the total lemonade the two friends bring to the cookout when one brings 2.7 liters and the other brings 3.54 liters of lemonade is 6.24 liters of lemonade, computed using decimal addition.
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During the sale, Carly pays $54 for a wheelbarrow. What was the original price?
The original price of the wheelbarrow is £75
How to determine the original price?Let the original price be x.
From the question, the amount paid is:
Amount paid = 54
The reduced price is calculated as:
Reduced = Original price * (1 - discount)
This gives
x * (1- 20%) = 54
Evaluate the difference
x * 0.8 = 54
Divide by 0.8
x = 67.5
Hence, the original price is $67.5
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Complete question
The price of a wheelbarrow is reduced by 20%. During the sale, Carly pays $54 for a wheelbarrow. What was the original price?
Use the Algebra Tiles to construct the algebraic expression for this situation:
What is this expression in simplified form?
`-4x -3 + 5x -2`
The given expression in simplified form is x - 5
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
-4x -3 + 5x -2
To simplify the expression, we collect like terms and then simplify
That is,
-4x + 5x -3 -2
= x - 5
Hence, the given expression in simplified form is x - 5
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Find the equivalent expression of the following: x3 (x2 + 5x + 7)
1. x5 + 5x3 + 7x2
2. x6 + 5x4 + 7x3
3. x5 + 4x4 + x4 + 8x3 – x3
4. x5 + 3x4 + x4 + 6x3 + x3
The product of the given function is x^5 + 5x^4 + 7x^3
Product of polynomial functionsThe leading degree of a polynomial function is always greater than or equal to 2.
Given the products below;
x^3 (x^2 + 5x + 7)
Expand
(x^3)(x^2) + 5x(x^3) + 7x^3
Simplify
x^5 + 5x^4 + 7x^3
Hence the product of the given function is x^5 + 5x^4 + 7x^3
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The equivalent expression of x³(x² + 5x + 7) is x⁵ + 5x⁴ + 7x³
How to find equivalent expression?The equivalent expression of the expression can be found as follows;
x³(x² + 5x + 7)
let's open the bracket by multiplying.
Therefore,
x³(x² + 5x + 7) = x⁵ + 5x⁴ + 7x³
Hence,
The equivalent expression of x³(x² + 5x + 7) is x⁵ + 5x⁴ + 7x³
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A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.
Which graph could represent the area of each rectangle in terms of the change in the length and width?
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.
The graph that can represent the area of each rectangle in terms of the change in the length and width is C. A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
How to illustrate the information?It should be noted that a graph gives a diagrammatic representation of an information.
Here, the rectangles are formed by decreasing the length and increasing the width, each by the same amount.
Thai can be illustrated by the third graph in the option as the line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
In conclusion, the correct option is C.
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Answer:
(っ◔◡◔)っ ♥ the answer is C ♥
Step-by-step explanation:
got it right on edge
P is a rectangle with a length of 40cm and width of x cm
Q is a rectangle with a width of y cm
the length of Q is 25% more than the length of P
the area of Q is 10% less than the area of P
work out the ratio of x:y
The ratio x:y as required in the task content is; 25:18.
What is the ratio x:y as required?It follows from the information given in the task content that;
The area of rectangle P is; 40x.
The area of rectangle Q is; y × (1.25 × 40) = 50y.
Hence, since the area of Q is 10% less than the area of P, it follows that A(q) = 0.9A(p).
And, A(p)/A(q) = 10/9
Hence, 10/9 = 40x/50y
x/y= 50/36 = 25/18
Hence, the required ratio is; 25: 18.
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AC is a tangent to the circle below at point B. Calculate the sizes of angle x, angle y and angle z. Justify each of your answers. .
[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)
[tex]x=78^{\circ}[/tex] (alternate segment theorem)
[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)
In constructing 98% confidence intervals for means, what do we expect will be true over the long run?
In constructing 98% confidence intervals for means, it is true that the statistic is good enough, and is less uncertain.
What is a confidence interval?A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.
Your level of confidence in your findings is shown by the confidence interval. You can never be certain that your results will hold for future surveys or experiments. In statistics, being 95% or 98.5% certain is typically seen as "good enough."
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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. Assume that the population standard deviation is 2.4 gallons. The mean water usage per family was found to be 19.5 gallons per day for a sample of 3034 families. Construct the 98% confidence interval for the mean usage of water. Round your answers to one decimal place.
The confidence interval for the mean usage of water is (18.7,20.5).
Given population standard deviation of 2.4, mean of 19.5 gallons per day and confidence interval of 98%.
We have to find the confidence interval for the mean usage of water.
To find out the confidence interval we have to first find margin of error.
μ=19.5
σ=2.4
α=0.98
α/2=0.49
We have to find the z value for the p value 0.49 which is z=2.33
Margin of error=z*μ/[tex]\sqrt{n}[/tex]
=2.33*19.5/[tex]\sqrt{3034}[/tex]
=0.82
lower level=mean -m
=19.5-0.82
=18.68
after rounding upto 1 decimal
=18.7
upper mean = mean+m
=19.5+0.82
=20.52
Hence the confidence interval for the usage of water is (18.7,20.52).
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prove it. this question is from trigonometry
Answer:
See below for step-by-step proof.
Step-by-step explanation:
[tex]\textsf{Given expression}:[/tex]
[tex]\cos^6 \theta+\sin^6 \theta[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3[/tex]
[tex]\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):[/tex]
[tex]\implies (\cos^2 \theta+\sin^2 \theta)^3-3 \cos^2 \theta\sin^2 \theta (\cos^2 \theta+\sin^2 \theta)[/tex]
[tex]\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:[/tex]
[tex]\implies (1)^3-3 \cos^2 \theta\sin^2 \theta (1)[/tex]
[tex]\implies 1-3 \cos^2 \theta\sin^2 \theta[/tex]
[tex]\implies 1-3 (\cos \theta\sin \theta)^2[/tex]
[tex]\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:[/tex]
[tex]\implies 1-3 \left( \dfrac{1}{2}\sin 2 \theta\right)^2[/tex]
[tex]\implies 1-\dfrac{3}{4} \sin^2 2 \theta[/tex]
[tex]\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta[/tex]
[tex]\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)[/tex]
[tex]\implies 1-\dfrac{3}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]
[tex]\implies \dfrac{1}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]
[tex]\textsf{Factor out }\dfrac{1}{4}:[/tex]
[tex]\implies \dfrac{1}{4}\left(1+3\cos^2 2 \theta\right)[/tex]
[tex]\textsf{Use the identity}\quad \cos (4 \theta)=2 \cos^2 2\theta - 1 \implies \cos^2 2 \theta=\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}:[/tex]
[tex]\implies \dfrac{1}{4}\left(1+3\left(\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}\right)\right)[/tex]
[tex]\implies \dfrac{1}{4}\left(1+\dfrac{3}{2}\cos 4 \theta+\dfrac{3}{2}\right)[/tex]
[tex]\implies \dfrac{1}{4}\left(\dfrac{5}{2}+\dfrac{3}{2}\cos 4 \theta\right)[/tex]
[tex]\implies \dfrac{1}{4} \cdot \dfrac{1}{2}\left(5+3\cos 4 \theta\right)[/tex]
[tex]\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)[/tex]
PLEASE REFER THE ATTACHMENT. THANK YOU
The solution is given below:
What is price index?An index number expressing the level of a group of commodity prices relative to the level of the prices of the same commodities during an arbitrarily chosen base period and used to indicate changes in the level of prices from one period to another.
Given:
Comm. p0 q0 p1 q1 p0q0 p1q0 p1q1 p0q1
A 25 750 30 960 18750 750 28800 24000
B 30 450 25 550 13500 750 13750 16500
C 5 250 6 360 1250 30 2160 1800
D 6 90 7 210 540 42 1470 1260
E 10 140 10 190 1400 100 1900 1900
F 4 48 5 65 192 240 365 260
Now,
[tex]\sum[/tex]p0q0 = 35632
[tex]\sum[/tex]p1q0 = 1912
[tex]\sum[/tex]p1q1 = 48445
[tex]\sum[/tex]p0q1= 45720
1) P01(L) = [tex]\sum[/tex]p1q0/[tex]\sum[/tex]p0q0 * 100
= 5.36
2) P01(L) = [tex]\sum[/tex]p1q1/[tex]\sum[/tex]p0q1 * 100
= 105.96
Dorbish- Bowley
= 5.36+ 105.96/2
=55.66
Marshall- Edgeworth
= 1912+ 48445/35632 + 45720
= 50357/ 81352
= 0.619 *100= 61.9
Fisher's price index
=( 5.36 * 105.96 )^ 0.5
=23.831
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A cylinder has a radius of 5x-1. Write a simplified expression for its volume where V= pi r^2 h
The volume of the cylinder whose radius is 5x-1 unit is 25x²πh + πh - 10xπh.
What is the volume of a right circular cylinder?
Suppose that the radius of the considered right circular cylinder is 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
The right circular cylinder is the cylinder in which the line joining centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given that the radius of the cylinder is (5x-1), while the height of the cylinder is h. Therefore, the volume of the cylinder is,
The volume of the cylinder = π × (5x-1)² × h
= (25x² + 1 - 10x)πh
= 25x²πh + πh - 10xπh
Hence, the volume of the cylinder is 25x²πh + πh - 10xπh.
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uuuuubhbjvykuhctkkhygtcykxmhfxg
The surface area of the spherical ball is given as follows:
[tex]635.04\pi[/tex] yd².
What is the surface area of a sphere?The surface area of a sphere of radius r is given as follows:
[tex]S = 4\pi r^2[/tex].
In this problem, the diameter is of 25.2 yd, hence the radius is given by:
r = 0.5 x 25.2 yd = 12.6 yd.
Then the surface area in yd² is:
[tex]S = 4\pi (12.6)^2 = 635.04\pi[/tex].
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Is Figure B a scale copy of Figure A?
Answer:
No.
Step-by-step explanation:
The ratio of the lengths of the vertical sides from A to B is 2/4 which equals 1/2.
The ratio of the lengths of the horizontal sides of A to B is 4/11.
Since 4/11 is not equal to 1/2, figure B is not a scale copy of figure A.
Which expression is equivalent to 54 · (5-2)3 ?
Jevon Noda's home has a market value of $72,000, the rate of assessment is 30%, and the tax rate is 85.
mills. Find the a) assessed value, b) tax rate as a decimal, and c) real estate tax.
The required a) assessed value = $21600,
b) tax rate = 0.0855,
c) real estate tax = $1836.
Cost price is that price for buyer which he pays to seller for an object or product.
a) assessed value = 72000 x 30/100
= $21600
b) tax rate = 85.5/1000
= 0.0855
c) real estate tax = 0.855 x 21600
= $ 1836
Thus, the required values of a) assessed value, b) tax rate as a decimal, and c) real estate tax is $21600, 0.085 and $1836 respectively.
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Whoever helps me with this problem will have brainlist.
By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number [tex]0.\overline{333}[/tex]
How to find the quotient of a fraction
The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.
[tex]\frac{1}{3} = 0.\overline{333}[/tex]
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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.
How to find the quotient of a fraction?
Quotient is described as the quantity produced by the division of two numbers.
Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;
0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.
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please help with sin question
Answer: A
Step-by-step explanation:
The cosine of an angle is equal to the sine of its complement, and vice versa.
What is the slope of a line that passes through the points ( -1, 9) and (3,6)?
Answer:
-¾
Step-by-step explanation:
Slope=m
(-1,9) (3,6)
m= Y2-Y1 / X2-X1
m=6-9/3-(-1)
m=-3/3+1
m=-3/4
Which of these tables represents a linear function?
Answer:
a
Step-by-step explanation:
a is the anwer because b/c it has a constant rate of change unlike the others
Can someone pls help with these geometry questions, it’s urgent.
Answer:
6. x + x + 14 = 90
2x + 14 = 90
2x = 76
x = 38
angle b = 38 + 14 = 52°
7. angles on a straight line add up to 180°
x + x - 32 = 180
2x = 212
x = 106°
angle d = 106 - 32 = 74°
8. vertically opposite angles are equal
7x - 80 = 3x
-80 = -4x
20 = x
angle 1 = 7(20) - 80 = 60°
angle 2 = 3(20) = 60°
3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.
Which inequality explains why these three segments cannot be used to construct a triangle?
EF + FD > DE
ED + EF < DF
ED + EF > DF
EF + FD < DE
The inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF
InequalitiesFrom the question, we are to determine which of the given inequalities explains why the three segments cannot be used to construct a triangle
From the given information,
Line DE is about half the length of line DF
That is,
ED = 1/2 DF
Also,
Line FE is about one-third of the length of line DF
That is,
EF = 1/3 DF
Then, we can write that
ED + EF = 1/2DF + 1/3DF
ED + EF = 5/6 DF
Since,
5/6 DF < DF
Then,
ED + EF < DF
Hence, the inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF
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Please help!
On a certain Saturday, the number of adult tickets sold was 1/3 (one third) of the children tickets sold. What was the greatest number of adult tickets sold if the box office receipts was not more than $3,190?
Adult admission fee: $8.50
Children admission fee: $5.50
The greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.
How to find the greatest number of adult tickets sold ?let
number of children tickets = x
number of adult ticket sold = 1 / 3 x
The greatest number of adult tickets sold if the box office receipts was not more than $3,190 can be calculated as follows:
The equations that represent the situation is as follows:
5.50x + 8.50 (1/3 x) = 3190
5.50x + 2.83333333333x = 3190
8.33333333333x = 3190
x = 3190 / 8.33333333333
x = 982.839313573
x ≈ 983
Therefore,
adult ticket = 983/3 = 328
Therefore, the greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.
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find the perimeter and area of a triangle whose sides are of length 2cm, 5cm and 5cm
Answer:
Perimeter:12cm
Area:5cm²
Step-by-step explanation:
Perimeter is the total distance around the figure ie sum of all sides of figure
∴Perimeter of triangle equals 2cm plus 5cm plus 5cm
∴The perimeter equals 12cm
Area of triangle equals 1/2×base×height,where base is 2cm & height is 5cm
(Inserting values)
∴Area of the triangle equals 1/2×2cm×5cm which equals 5cm²
Point A is the point of concurrency of the angle bisectors of ΔDEF.
Point A is the point of concurrency of triangle D E F. Lines are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Y, and A Z. The length of F A is 6 centimeters, the length of A D is 5 centimeters, the length of A X is 3 centimeters, and the length of Y D is 4 centimeters.
What is the length of ZA?
ZA = 3cm
ZA = 4cm
ZA = 5cm
ZA = 6cm
The correct answer is option A which is ZA = 3 cm
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
The triangle is shown below.
From the triangle, A is the concurrency point of angle bisectors of all vertices.
Consider ΔAYD,
Using the Pythagorean theorem,
AD² = AY² + YD²
5² = AY² + 4²
25 = AY² + 16
AY² = 25 - 16
AY² = 9
AY = √9 = 3 cm
Consider triangles ADY and ADZ.
∠AYD ≅∠AZD=90
∠ADY≅∠ADZ ( Angle bisector)
AD ≡ AD (common side)
The two triangles are congruent by the AAS postulate.
Therefore, by CPCTE, AY=ZA=3 cm
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Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3 hours and charged her $61 for parts. The total was $226. Write and solve an equation which can be used to determine x, the cost of the labor per hour
If the point P(-3/5,y) lies on the unit circle and P is in the 2nd quandrant, what does y equal
The value of y by virtue of the circle description above is; 0.8.
What is the value of y in the task?By definition, a unit circle is a circle whose radius is 1 and has its center at the origin (0,0).
On this note, the value of y can be evaluated as;
1² = (-3/5-0)² + (y-0)²
1 -0.36 = y²
0.64 = y²
±0.8 = y.
However, since point P is in the 2nd quadrant where y is positive, the value of y is 0.8.
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Is it possible to design a pair of nonstandard dice, with positive integers on the faces (not necessarily all distinct), so that the probability of rolling any given total on those two dice is the same as the probability of rolling that total on two standard dice
you can reduce it to factors of degree 2 or less).
The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.
Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).
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How many ways are there to fill either the pitcher or catcher field position (but not both) from among the 25 players (leaving the other field positions empty)
Using the permutation formula, it is found that there are 600 ways to fill the pitcher and catcher positions.
The order is important, as one player is the pitcher and the other is the catcher, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
2 players are taken from a set of 25, hence the number of ways is given by:
[tex]P_{(25,2)} = \frac{25!}{23!} = 600[/tex].
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What is EB and DY? DY, EY, and FY are bisectors, and the answers can be "can not be determined"
Based on Pythagoras' theorem, EB is equal to 38.7 and DY is 17.7.
What is the length of the sides EB and DY?The length of the sides EB and DY are obtained using Pythagoras theorem.
Since EY is a perpendicular bisector;
EB = √(64.2² - 51.2²)
EB = 38.7
Since, DY is a perpendicular bisector;
DY = √64.2² - 61.7²)
DY = 17.7
Therefore, EB is equal to 38.7 and DY is 17.7.
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1. Your friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns. If he gets paid $65 to detail a car
and $90 to detail an SUV, what linear inequality can be used to determine how many of each he must detail in order to earn at least $600?
A. 65c+90s > 600
B. 65c + 90s 2 600
C. 65c+90z ≤ 600
D. 65c+90z< 600
Answer:
I'm not sure if B. is incorrectly written but the answer would be
65c + 90s [tex]\geq[/tex]600
Step-by-step explanation:
since he needs AT LEAST 600$ then the sign should look like that. 65 dollars per car, and c represents the amount of cars, and 90 per SUV and s represents how many SUVS
B. 65c + 90s ≥ 600 is the correct option.
Our friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns.
What is inequality?Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
If he gets paid $65 to detail a car and $90 to detail an SUV
The inequality form for above condition so he can earn at least $600
= 65c + 90s ≥ 600, where c = cars and s = SUV
Thus, the required inequality is given by 65c + 90s ≥ 600.
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