when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.
How to find large cake pieces ?
Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]
So original large cake weight is
[tex]w=120*3\\\\w=360[/tex]
So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece
[tex]pieces=\frac{360}{2}\\=180[/tex]
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given that 4x-y=5 4y-z=7 and 4z-x=18 what is the value of x+y+z
Answer:
x + y +z= 10
Step-by-step explanation:
4x - y = 5 ---------(I)
4y - z = 7 ---------(II)
4z - x = 18 ---------(III)
Add all the three equations,
4x - y + 4y - z + 4z - x = 5 + 7 + 18
4x - x -y + 4y -z + 4z = 30
3x + 3y + 3z = 30
Divide the entire equation by 3
[tex]\sf \dfrac{3x}{3}+\dfrac{3y}{3}+\dfrac{3z}{3} = \dfrac{30}{3}[/tex]
x + y + z = 10
Given: mAngleTRV = 60°
mAngleTRS = (4x)°
Prove: x = 30
3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees.
What is the missing reason in step 3?
A 2-column table with 6 rows is shown. Column 1 is labeled Statements with entries measure of angle T R V = 60 degrees and measure of angle T R X = (4 x) degrees, angle T R S and angle T R V are a linear pair, measure of angle T R S + measure of angle T R V = 180, 60 + 4 x + 180, 4 x =120, x = 30. Column 2 is labeled Reasons with entries given, definition of a linear pair, question mark, substitution property of equality, subtraction property of equality, division property of equality.
substitution property of equality
angle addition postulate
subtraction property of equality
addition property of equality
Mark this and return
https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.
Therefore, the required proof and answer to the question are stated below:
a) m< TRV = 60° (given)
m<TRS = 4x° (given)
Thus, it can be concluded from the diagram that:
<TRV ≅ m<BRW (vertically opposite angle property)
Also,
m<TRS ≅ m<VRW (vertically opposite angle property)
But,
m<VRW = m<VRZ + m<ZRW
Thus,
m<TRV ≅ m<BRW = 60°
m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]
60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]
m<TRS + m<VRW = [tex]360^{o}[/tex] - [tex]120^{o}[/tex]
= [tex]240^{o}[/tex]
2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )
m<TRS = 120
4x = 120
x = [tex]\frac{120}{4}[/tex]
= [tex]30^{o}[/tex]
Thus, x = [tex]30^{o}[/tex]
b) The missing reason in step 3 is the angle addition postulate.
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If 4 is the solution set of the equation x² -4 = 0 and B is
the solution set of the equation x²-3x+2=0, how many
elements are in the union of the two sets?
A. 1
C. 3
B. 2
D. 4
Answer:
3 elements
Step-by-step explanation:
Let A = solution set of x²-4
B = solution set of x²-3x+2
First, find the solution of each sets:
[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]
Set B:
[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]
Now we can write new set as:
A = {2, -2}
B = {1, 2}
The union of A and B means combine both sets together:
A ∪ B = {2, -2, 1, 2}
However, in a set, we do not write duplicate elements, so the union set will be:
A ∪ B = {2, -2, 1}
Hence, there are 3 elements in A ∪ B.
Which function is negative for the interval [-1, 1]?
ty
3
2
-3-2-11
-3
ty
O
Intro
123
x
3
2
1
-3-2-1₁
-3
O
x
23
2,
-3-2-1
2 of 11
O
x
123
321
-3-2-11
-2
MAR
-3
ty
x
23
Done
O
Answer:
Graph number 2
Step-by-step explanation:
See attached image.
Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 x + 2 B. y ≥ 2 x + 2 C. y < 2 x + 2 D.
Considering the given linear function, the inequality graphed is:
B. [tex]y \geq 2x + 2[/tex].
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:
m = (4 - 2)/(2 - 1) = 2.
Thus the equation of the line is:
y = 2x + 2.
The left-side of the line is the values above the line, hence the inequality is:
B. [tex]y \geq 2x + 2[/tex].
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If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?
The value of the ratio a:b is 2:1
What is a surd?Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.
Example of some surds are the square root of prime numbers.
Analysis:
a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]
Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]
[tex]\frac{1}{2 - \sqrt{3} }[/tex] x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Equating,
a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Comparing the variables,
a = 2, b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1
The ratio, a: b = 2:1
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6x^2-19xy-7y^2 HELP ME PLS??
Answer:
(3x+y) (2x-7y)
Step-by-step explanation:
first write -19xy as a difference and you get 6x^2+2xy-21xy-7y^2
and then take the factor 2x from the expression that is 2x(3x+y) and do the same with the -7 that is = -7(3x+y). So this is you answer= (3x+y)(2x-7)
Out of 500 people in a room, 200 of them are wearing red shirts. Of the people wearing red shirts, 15% are wearing red pants. What percentage of the people in the room are wearing both red shirts and red pants?
write the equation of a line this is parallel to y=0.5x-4 and that passes through the point (9,-6).
Answer:
[tex]y=0.5x-10.5[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 0.5.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y+6=0.5(x-9) \\ \\ y+6=0.5x-4.5 \\ \\ y=0.5x-10.5[/tex]
A triangle on a coordinate plane has three vertices A(2 , 3), B(5, 4), and C(3, 6). Use this description to do the following transformations (if needed, draw this triangle on a sheet of paper):
a. Dilation 1: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the origin? How did you determine these points?
b. Dilation 2: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the point (6, 8)? How did you determine these points?
c. What series of transformations would carry dilation 1 onto dilation 2? Compare Dilation 1 to Dilation 2. Explain what conclusions you can draw about the scale factor, difference in area, and center of dilation.
d. What is the proportion of the side lengths from Dilation 1 to Dilation 2? What is the proportion of their angle measures? Explain your answer.
The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;
a. A'(4, 6), B'(10, 8), C'(6, 12)
b. A'(-2, -2), B'(4, 0), C'(0, 4)
c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)
The area of dilation 1 and 2 are the sameThe center of dilation does not change the aread. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1
The angle measures are the sameHow can the new coordinates be found?The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;
[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]
Where;
(a, b) = The center of dilation
k = The scale factor of dilation
(x, y) = The coordinate of the pre-image
The given points are;
A(2, 3), B(5, 4), C(3, 6)
a. The scale factor of dilation = 2
The center of dilation = The origin (0, 0)
Therefore;
[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]
Therefore dilation about the origin, with a scale factor of 2 gives;
A(2, 3) → A'(4, 6)Similarly
B(5, 4) → B'(10, 8)C(3, 6) → C'(6, 12)b. With the center of dilation at (6, 8), we have;
[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]
A(2, 3) → A'(-2, -2)[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]
B(5, 4) → B'(4, 0)[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]
C(3, 6) → C'(0, 4)c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places
Using notation, we have;
Dilation 1 T(-6, -8) → Dilation 2The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.
The location of the center of dilation does not change the area of the imaged. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;
The proportion of the side lengths is 1Given that the side lengths are the same, by AAA congruency postulate, we have;
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Answer:
The angle measures are the same.
Step-by-step explanation:
The KM values for the reaction of chymotrypsin with 2 substrates are given below. Which substrate is likely to give a higher value for Vmax
N-acetyltyrosine ethyl ester may likely have a higher Vmax.
How are the Km and Vmax of an enzyme and substrate related?Km is inversely proportional enzyme affinity for substrate. The lower the Km, the higher the enzyme affinity for substrate and vice versa.
Vmax is the maximum velocity of the reaction when the enzyme is fully saturated with substrate.
Based on the Km values, chymotrypsin has higher affinity for N-acetyltyrosine ethyl ester, thus, N-acetyltyrosine ethyl ester may likely have a higher Vmax.
In conclusion, the Vmax is the maximum velocity of an enzyme-catalyzed reaction.
Note that the complete question is given below:
The Km for the reaction of chymotrypsin with N-acetylvaline ethyl ester is 8.8 x 10-2 M, and the Km for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is 6.6 x 10-4 M.
Which of the following substrates is likely to give a higher value for Vmax?
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Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The five-number summary are as follows:
Minimum = 58Lower quartile(Q₁) = 67Median = 79Upper quartile(Q₃) = 82Maximum = 87Interquartile range = 15How to solve for five-number summary?The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.
Therefore,
Given:
58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87
Therefore,
Minimum = 58
Lower quartile(Q₁) = 67
Median = 79 + 79 / 2 = 79
Upper quartile(Q₃) = 82
Maximum = 87
Interquartile range = Q₃ - Q₁ = 82 - 67 = 15
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id love some help!!!
Answer:
Circle:circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
[tex] \sf{formula \: to \: find \: the \: area \: is}[/tex][tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]
[tex] \sf{formula \: to \: find \: perimeter \: of \: circle \: is}[/tex][tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]
Continue to Question.If the radius is 2 inches and
Use 3,14 for π So:
[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]
[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]
[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]
So, The Area of circle is 12.56inches²Need help with number 3 inequalities with variables on both sides
Answer:
x ≤ 2
Step-by-step explanation:
We are given the inequality:
[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]
First, get rid of the denominator by multiplying both sides by 2:
[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]
Add both sides by 6 then subtract both sides by x:
[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]
Then divide both sides by 3:
[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]
Therefore, the answer is x ≤ 2
Answer: [tex]x \leq 2[/tex]
Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)
We then get [tex]4x - 6 \leq x[/tex].
Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].
Subtracting x from both sides, we get [tex]3x \leq 6[/tex]
Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]
Hope this helped!
The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.) Mutarazi - Zimbabwe 24.99 x 102 Gocta Cataracts - Peru 2.532 x 103 Utigord - Norway 2,625 x 100 Angel - Venezuela .3212 x 104 Espelands - Norway 2.307 x 103 Yosemite - California (USA) 2,425 Monge - Norway 25.4 x 102 Tugela - South Africa 3.11 x 103 **Heights are approximations** [Part 1] List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning. [Part 2] What is the difference between the tallest and shortest heights? Show your work.
The difference between the tallest and shortest heights is 0.787 × 10
StatisticsMutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³From tallest to shortest:
Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425Difference between tallest and shortest heights =
3.212 x 10⁴ - 2,425
= 3.212 x 10⁴ - 2.425 × 10³
= (3.212 - 2.425) × 10^4 - 3
= 0.787 × 10
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help me w this pls thanks
Answer:
Perimeter: 4+[tex]\pi \\[/tex] mm
Area: [tex]\pi[/tex] mm^2
Step-by-step explanation:
Perimeter:
90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]
Area:
90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]
Answer: 7.14 mm and 3.14 mm²
Step-by-step explanation:
The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.
Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is
[tex]\frac{1}{2} \pi*2=\pi[/tex]
However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is
[tex]2+2=4[/tex]
By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.
The area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.
[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]
Hence, the area is [tex]\pi[/tex], or around 3.14 mm².
A grocery store sells a bad of 4 oranges for $1.04. how much would it cost for 11 oranges?
If a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.
Given that a grocery store sells a bag of 4 oranges for $1.04 means revenue is $1.04 with no profits.
We have to find the cost of 11 oranges. We have assumed that there are no profits as we are require to find cost. But there is huge difference between cost and profits.
We know that average cost is total cost divided by number of items.
Cost of 4 oranges=$1.04
cost of 1 orange=1.04/4
=$0.26 per orange
Cost of 11 oranges=0.26*11
=$2,86.
Hence if a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.
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which statemennt is false?
Answer:
B. Every integer is also an irrational number.
visualize "4.298" on the number line
Answer:
Step-by-step explanation:
The visualization of "4.298" on the number line is attached below.
How does the dot plot work?Suppose we're measuring something whose values are numeric.
For each value of that thing we observe, we plot a dot above that value in the number line.
Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
We know that 4.298 is greater than 4 but less than 5.
The visualization of "4.298" on the number line is attached below.
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Simplify the expression using trigonometric identities:
The simplified expression is the one in option B.
How to simplify the expression?Remember that:
[tex]sec(x) = 1/cos(x)\\\\cos(x) = cos(-x)[/tex]
With these two, we can rewrite the numerator as:
[tex]sec(x)*sin(-x) + tan(-x)\\\\\frac{1}{cos(x)}*sin(-x) + tan(x)\\\\\frac{1}{cos(-x)}*sin(-x) + tan(-x)\\\\2*tan(-x)[/tex]
Replacing that in the given expression, we have:
[tex]\frac{2*tan(-x)}{1 + sec(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}[/tex]
Now, if we multiply and divide by cos(-x), we get:
[tex]\frac{2*tan(-x)}{1 + 1/cos(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}*\frac{cos(-x)}{cos(-x)} \\\\= \frac{2*sin(-x)}{1 + cos(-x)}[/tex]
Now remember that:
[tex]cos(x) = cos(-x)\\sin(-x) = -sin(x)[/tex]
With these two properties:
[tex]\frac{2*sin(-x)}{1 + cos(-x)} = \frac{-2*sin(x)}{1 + cos(x)}[/tex]
Then the correct option is B.
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Suppose the shipping weight of your cheese shop's customized gift baskets is asymmetrically distributed with unknown mean and standard deviation. For a sample of 70 orders, the mean weight is 57 ounces and the standard deviation is 7.1 ounces. What is the lower bound of the 90 percent confidence interval for the gift basket's average shipping weight
The lower bound of the 90% confidence interval for the gift basket's average shipping weight is 55.605.
Given mean weight of 57 ounces ,sample size 70 ,confidence level 90% and standard deviation of 7.1 ounces.
We have to find the lower bound of the confidence interval for the gift's basket's avrage shipping weight.
We can easily find the confidence interval and its lower bound through theformula of margin of error.
Margin of error is the difference between real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of confidence level
σ is standard deviation,
n is the sample size
We have to first find the z value for 90% confidence level which is 1.645.
Margin of error=1.645*7.1/[tex]\sqrt{70}[/tex]
=11.6795/8.3666
=1.395
Lower bound of the confidence interval = Mean - margin of error
=57-1.395
=55.605.
Hence the lower bound of the confidence interval for the gift basket's average shipping weight is 55.605.
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Find the missing length of the triangle (Side AC)
Answer: 17.3 cm
Step-by-step explanation:
[tex]\tan 68^{\circ}=\frac{AC}{7}\\\\AC=7\tan 68^{\circ}\\\\AC \approx 17.3[/tex]
1.rani was selling flowers. each day she made 7 bouquets by arranging 8 roses and 6 marigolds in each bouquet. each bouquet was sold for rs.85. a) find the number of marigolds used in a day. b) find the total number of flowers used by using suitable property of whole numbers. c) if she sold 42 bouquets in a whole week, find the amount she earned. 2. by suitable rearrangement, find the value of a) 819 + 364 + 181 + 436 b) 20 x 348 x 50 3. using suitable property find the value of 492 x 13 + 492 x 37 4. a) name the property 86 + 65 = 65 + 83 b) the multiplicative identity of whole numbers is ______ 5. find the next two numbers in the pattern 1,1,2, 3,5,8, ______, ________
1.(a) The number of marigolds used in a day is 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98.
(c) She earned Rs. 3570
2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.
(b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.
3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.
4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.
(b) The multiplicative identity of whole numbers is 1.
5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.
1. (a) The number of marigolds used in a day is 42.
Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.
What is distributive property of whole numbers?
The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.
Distributive property = a×(b+c) = a×b+a×c
Total number of flowers = 7×(8+6) = 7×14 = 98.
(c) If she sold 42 bouquets in a whole week, find the amount she earned is rs.3570.
Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.
2. (a) By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.
Rearrangement of the given numbers = (819+181)+(364+436)
= 1000+800
= 1800
(b) By suitable rearrangement, the value of 20 x 348 x 50 is 348000.
Rearrangement of the given numbers = 348×(50×20)
= 348×1000
= 348000
3. Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.
By using distributive property = 492 x 13 + 492 x 37
= 492×(13+37)
= 492×50
= 24600
4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.
What is commutative property?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.
By using commutative property, a+b = b+a
86 + 65 = 65 + 86
151 = 151
(b) The multiplicative identity of whole numbers is 1.
Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.
5. The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.
Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0
1+0=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
Hence, The next two numbers for the given series are 13 and 21.
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Jane takes out a loan for $100,000.00 over 10 years
and agrees to pay interest only at an annual rate of
8%. What will her monthly payment be?
$1799.10
Step-by-step explanation:Each year, the amount of money in the account is increased by 8%. This is the same as multiplying by 1.08 each year.
For 10 years, you multiply the original $100,000 by 1.08 a total of 10 times.
This tends to be simplified to:
[tex]100,000 * 1.08^{10}[/tex]
This gives $215892.4997.
This is paid back over 10 years, which is 10 x 12 months, or 120 months.
Divide the $215892.4997 by 120 to get the monthly payment of:
$1799.10 (round to 2 decimal places as it is a currency)
5/8 of the students in siena's class have brown eyes. 2/3 of the students with brown eyes are girl. what fraction of the students in siena's class are girls with brown eyes? *
The fraction of the students in Siena's class are girls with brown eyes is 5/12.
Let the fraction of students in Siena's class with brown eyes be a=5/8.
And the fraction of students in Siena's class with brown eyes are girls be b=2/3.
Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b
Therefore, by substituting the fraction values, we get
z=(5/8)×(2/3)
z=5/12.
Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.
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Consider the series one-fourth, startfraction 1 over 16 endfraction startfraction 1 over 64 endfraction startfraction 1 over 256 endfraction ellipsis which expression defines sn? limit of (one-fourth) superscript n baseline as n approaches infinity limit of (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (one-fourth) superscript n baseline as n approaches infinity
The sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)
How to evaluate the sum of the series?The complete question is added as an attachment
The given series is a geometric series. So, we first calculate the common ratio (r) using:
r = T2/T1
From the series, we have:
T1 = 1/4 and T2 = 1/16
Substitute the known values in the above equation
r = (1/16)/(1/4)
So, the equation becomes
T = 1/16 / 1/4
Rewrite as product
T = 1/16 * 4
Evaluate the product
r = 1/4
The formula to calculate the sum of a geometric series of is:
Sn = a(1 - r^n)/(1 - r)
Where
a = 1/4 -- the first term
r = 1/4 --- the common ratio
Substitute the known values in the above equation
Sn = 1/4 * (1 - (1/4)^n)/(1 - 1/4)
Simplify the denominator
Sn = 1/4 * (1 - (1/4)^n)/(3/4)
Divide 1/4 by 3/4
Sn = 1/3 * (1 - (1/4)^n)
Take the limit to infinity of the series
Sn = lim n⇒∝ 1/3(1 - (1/4)^n)
We can conclude that, the sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)
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Answer:
Step-by-step explanation:
B
Suppose you are saving your money to pay for a vacation for your family. so far, you have saved. you plan on saving more each month so you can pay for the vacation at the end of the year. assume that you save more each month than the previous month.
part a: write a formula that would show the amount you will have saved after year.
part b: if the vacation costs a total of , will you be able to pay for it after year?
part c: explain why or why not. show your work to support your answer.
440 repeat 11 more times.
400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.
Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.
Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.
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(pls help me with this)
4. The points C and D are (4, 5) and (p, q) respectively,
a) Write down, in terms of p and q, the coordinates of the midpoint of CD.
b) Given that the midpoint of CD is (7, 1), find the coordinates of D.
A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
A. How to determine the mid pointCoordinate of C = (4, 5)Coordinate of D = (p, q)Mid point =?Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
B. How to determine the coordinates of DMid point = (7, 1)Coordinates of D =?Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
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Which bag has more fruit? Use the ratios to justify your answer.
The bag that has more fruits is the second bag, because the ratio is greater.
Which bag has more fruits?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
Number of fruits in the first bag : (3/8) x 60 = 22.50
Number of fruits in the second bag :(7/17) x 60 = 24.71
Here is the complete question:
Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts. Ratio of fruit to nuts in the first bag:3 5 Ratio of fruit to nuts in the second bag:7 10 Which bag has more fruit? Use the ratios to justify your answer. The first bag, because the ratio is greater. The first bag, because the ratio is smaller. The second bag, because the ratio is greater. The second bag, because the ratio is smaller.
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How much does a $5.40 lunch cost if it is discounted by 10%
Answer:
$4.86
Step-by-step explanation:
Original price: $5.40
Discount: 10%
Discount amount:
10% of $5.40 = 0.1 × $5.40 = $0.54
Discounted price:
$5.40 - $0.54 = $4.86
Answer:
$4.86
Step-by-step explanation:
There are two approaches to this problem.
1:
You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.
2:
You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.