❄ Hi there,
let us revise the two rounding rules before getting down to the actual process of rounding.
[tex]\sf{Rules:}[/tex]
If the number you ought to round to is followed by a number from 0 to 4, you round down, or in other words, just drop that number.If the number you ought to round to is followed by a number that's 5 or more, you add 1 to that number.Let's see these rules in action!
The number is – [tex]219.2[/tex].
Nearest whole number – [tex]219[/tex], which is followed by a number between 0 and 4, so we just drop that number :
[tex]\sf{219.2- > > 219}[/tex]
❄
400 people were surveyed for this grab how many more people prefer vanilla than do strawberry
Using proportions, it is found that 68 more people prefer vanilla than do strawberry.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that, out of 400 people:
35% preferred vanilla.18% preferred strawberry.Hence the amounts are:
V = 0.35 x 400 = 140.S = 0.18 x 400 = 72.The difference is:
140 - 72 = 68.
68 more people prefer vanilla than do strawberry.
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Find the dimensions of a rectangle with area 1,728 m2 whose perimeter is as small as possible
The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.
Let the dimension of the rectangle be x and y m.
According to the given question.
The area of the rectangle is 1728 square meter.
⇒ x × y = 1728
⇒ x = 1728/y
Since, the perimeter of the rectangle is the sum of the length of its boundary.
Therefore,
Perimeter of the recatngle with dimensions x and y is given by
Perimeter of the rectangle, P = 2(x + y)
⇒ P = 2(1728/y + y)
⇒ P = 3456/y + 2y
Differentiate the above equation with respect to y
⇒ [tex]P^{'} = -\frac{3456}{y^{2} } + 2[/tex]
For the minimum(small) perimeter equate the above equation to 0.
⇒ [tex]-\frac{3456}{y^{2} } + 2 = 0[/tex]
⇒ [tex]2y^{2} =3456[/tex]
⇒ [tex]y^{2} = \frac{3456}{2}[/tex]
⇒ y^2 = 1728
⇒ y = √1728
⇒ y = 41.56 m
Therefore,
x = 1728/41.56
⇒ x = 41.57 m
Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.
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Which of the following shows the simplified function of csc x sin(pi/2 -x)?
Answer:
cot x
Step-by-step explanation:
using the identities
csc x = [tex]\frac{1}{sinx}[/tex]
sin([tex]\frac{\pi }{2}[/tex] - x) = cos x
then
csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)
= [tex]\frac{1}{sinx}[/tex] × cosx
= [tex]\frac{cosx}{sinx}[/tex]
= cot x
How many lbs of peanuts must mike add to 9 lbs of mixed nuts containing 40% peanuts to make a mixture with 73% peanuts
The new mixture exists 56.5% peanuts.
How to estimate the total number of peanuts required for the mixture?The first batch of 9 lb of mixed nuts possesses 40% peanuts.
This means the quantity of peanuts exists:
9 [tex]*[/tex] 40/100 = 3.6 lb
The second batch of 9 lb of mixed nuts possesses 73% peanuts.
This means the quantity of peanuts exists:
9 [tex]*[/tex] 73/100 = 6.57 lb
The total quantity of peanuts in the mix exists
3.6 lb + 6.57 lb = 10.17 lb
There exist 9 lb + 9 lb = 18 lb of mix.
Therefore, the percent of peanuts in the mix exists:
10.17 / 18 [tex]*[/tex] 100 = 56.5%
The new mixture exists 56.5% peanuts.
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If $1= rs 115.4 ( buying rate ) and $1=rs116.20(selling rate). find the profit while selling and buying $6000.
The profit is Rs.4800.
What is profit?When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. It is calculated with the help of the formula: Profit = Selling price - Cost price.
Given that,
S.P =$6000
C.P = $6000
If, 1$ = Rs.115.4 (in cost price)
1$ = Rs.116.20 (in selling price)
Then,
C.P = Rs. 115.40×6000
S.P = Rs. 116.20×6000
Then,
Profit = S.P-C.P
= 116.20×6000 -115.40×6000
= (116.20-115.40)×6000
= 0.80×6000
= Rs.4800
Hence, The profit is Rs.4800.
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Graduate management aptitude test (gmat) scores are widely used by graduate schools of business as an entrance requirement. suppose that in one particular year, the mean score for the gmat was 473, with a standard deviation of 104. what values are three standard deviations within the mean?
The values that exist two standard deviations above and below the mean are 681 and 265.
How to determine the values?The given parameters exist:
Mean = 473
Standard deviation =104
The values above and below the mean exist calculated utilizing:
[tex]$x=\bar{x} \pm n \sigma$[/tex]
In this case n = 2.
So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]
The value above is:
x = 473 + 2 [tex]*[/tex] 104 = 681
The value below is:
x = 473 - 2 [tex]*[/tex] 104 = 265
Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.
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use the diagram to answer the question. what is the value of x
Answer:
2√(133)
Step-by-step explanation:
Triangle 1 = 8, 12, ?
triangle 2 = 18, x, ?
we have to find value of x which is a hypotenuse
a² + b² = c²
8² + 12² = 64 + 144 = √208 = 14.4222051019
x = 14.4222051019² + 18²
= 208 + 324
= 532
x = √532 = 2√(133)
Identify the two tables which represent quadratic relationships. x 0 1 2 3 y -4 -8 -10 -10 x 0 1 2 3 y 4 -4 -4 4 x 0 1 2 3 y -2 0 2 4 x 0 1 2 3 y 1 2 4 8 x 0 1 2 3 y -2 -4 -8 -16 x 0 1 2 3 y 3 4 5 6
To estimate that table given in Option (4) will define the quadratic relationship.
Therefore, the table of Option (5) will describe the quadratic relationship.
How to estimate the quadratic relationships between two tables?By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.
In the given option, we estimate that table given in Option (4) will define the quadratic relationship.
x y I st difference II nd difference
0 4 - -
1 -4 -4 - (4) = -8 -
2 -4 -4 - (-4) = 0 0 - (-8) = 8
3 4 4 - (-4) = 8 8 - 0 = 8
The second difference between the terms in y exists exactly as 8.
Therefore, the table of Option (4) means the quadratic relationship.
Similarly, in Option (5) we will estimate the second distinction of y terms.
x y I st difference II nd difference
0 -4 - -
1 -8 -8 - (-4) = -4 -
2 -10 -10 - (-8) = -2 -2 - (-4) = 2
3 -10 -10 - (-10) = 0 0 - (-2) = 2
Here the second difference exists identical to 2.
Therefore, the table of Option (5) will describe the quadratic relationship.
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If the mean on a test is 83 and the standard deviation is 6: What % has:
At least a 70% (passing with a C)
An 80 or above (a B)
Using the normal distribution, it is found that:
98.5% of students have at least a 70.69.15% of students have an 80 or above.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given, respectively, by:
[tex]\mu = 83, \sigma = 6[/tex]
The proportion of students, with a grade of at least 70 is one subtracted by the p-value of Z when X = 70, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 83}{6}[/tex]
Z = -2.17
Z = -2.17 has a p-value of 0.015.
1 - 0.015 = 0.985 = 98.5% of students have at least a 70.
The proportion of students, with a grade of at least 80 is one subtracted by the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 83}{6}[/tex]
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
1 - 0.3085 = 0.6915 = 69.15% of students have an 80 or above.
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Let x = a bi and y = c di and z = f gi. which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x × (y × z) x – y = y – x (x y) z = x (y z) (x – y) – z = x – (y – z)
The first one , the second one ,the fourth one are true.
What is a commutative property in math?
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.
1) x + y = y + x = a + c (b + d ) i true
2) ( xy )z = x (yz) = (a + bi)(c + di)( f + gi) true
3) x - y = a + bi - ( c - di ) = a - c + ( b- d )i
y - x = c + di - ( a+bi) = c-a +(d-b)i false
4) (x + y ) + z = x + ( y + z ) = a + c +f + (b +d + g)i true
5) (x - y ) - z = a + bi - ( c + di) - ( f + gi)
= a - c . f + ( b- d - g) i
x - ( y - z ) = a + bi - ( c + di - f - gi )
= a - c + f + ( b - d + g ) i
{ put the hypothesis into the equation and get the proof }
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solve the following system {y=x^2-3 and {y=3x-3 graphically and algebraicallyPLEASE HELP ME IM BEGGING
Answer:
There are two solutions:
x = 0, y = -3 Point (0, -3)
x = 3, y = -6 Point (3, 6)
The solutions are at the intersections of the two individual graphs corresponding to each of the two equations (see attached figure)
Step-by-step explanation:
Use a graphing calculator or tool to plot each equation. The point of intersection of the two is the solution to the system of equations. See attached image
Algebraically
The first equation must be equal to the second equation for a unique value of y and x
[tex]y = x^2 - 3 = 3x -3\\x^2 - 3 = 3x - 3[/tex]
Subtract 3x - 3 from both sides giving
[tex]x^2 - 3 - (3x -3) = 0\\x^2 -3 -3x + 3 = 0\\x^2 - 3x = 0\\[/tex]
Factoring out x we get
[tex]x(x-3) = 0[/tex]
This means that x = 0 and also
x -3 = 0, or x = 3
Substituting for x = 0 in y = 3x-3 gives
y = 3.0 - 3 = -3
So x= 0, y = -3 is one solution (0,-3)
Substituting for x = 3 in the same equation gives
y = 3(3) - 3 = 6
So x = 3, y = 6 is another solution (3, 6)
Bob's favorite restaurant were salmon filet and filet mignon. The restaurant served 70 specials in all, 80% of which were salmon filets. How many salmon filets did the restaurant serve?
By working with percentages, we will see that they served 56 salmon filets.
How many salmon filets did the restaurant serve?
Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.
So we just need to calculate what is the 80% of 70.
This is just given by:
70*(80%/100%) = 70*0.8 = 56
This means that they served 56 salmons filet.
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Robert wants to fence a rectangular plot of land of at least $500$ square feet while using the least amount of fencing possible. He wants the width of the plot to be $5$ ft longer than the length. What is the width of the plot
The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.
A rectangle is a plane shape with equal opposite sides. Its area can be determined by;
Area of a rectangle = length x width
Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;
w = l + 5
But,
Area of the plot = length x width
500 = l x (l + 5)
= [tex]l^{2}[/tex] + 5l
This implies that,
500 = [tex]l^{2}[/tex] + 5l
[tex]l^{2}[/tex] + 5l - 500 = 0
Applying the quadratic formula, we have;
l = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a
a = 1, b = 5, c = -500
= (-5 ± [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2
= (-5 ± 45) / 2
l = (40) / 2 OR l = (-50) / 2
l = 20 OR l = - 25.5
So that,
l = 20
Therefore, the length of the plot is 20 feet.
Thus the width of the plot can be determined as;
w = l + 5
= 20 + 5
w = 25
The width of the plot is 25 feet.
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Michael is constructing a circle circumscribed about a triangle. he has partially completed the construction. what should be his next step in the construction?
Answer:
Connect the arcs to make a perpendicular bisector
The chart below shows conversion between gallons and fluid ounces.
Conversion Chart
Gallons
Fluid Ounces
2
256
3
384
4
512
6
?
What is the missing value in the table?
======================================================
Explanation:
To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128
For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.
Another example: 3 gallons = 3*128 = 384 fl oz.
Therefore, 6 gallons would be 6*128 = 768 fl oz.
To go in reverse, from fl oz to gallons, we divide by 128.
4ln x -8=12 its giving me other equations
The solution of the given logarithmic equation is x = 28.1
How to solve the logarithmic equation?
Here we have the logarithmic equation:
4*ln(x - 8) = 12
And we want to solve this for x.
Remember the relations:
[tex]ln(e^x) = x\\e^{ln(x)} = x[/tex]
First, we divide both sides by 4:
[tex]ln(x - 8) = 12/4 = 3[/tex]
Then, if we apply the exponential equation to both sides of our equation, we get:
[tex]e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1[/tex]
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JUST NEED A BIT OF HELP PLS
Step-by-step explanation:
1st : Vector translation.
a vector -8j ( 0 , -8 ) helped translate (x , y) => (x , y - 8)
2nd : rotation.
The only rotation that results in (-x , -y) is pi rotation.
formula : (x , y -8) => ( xcos(pi) - ysin(pi) , xsin(pi) + ycos(pi) )
substitute x & y-8 into x & y respectively of the formula above.
If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)?
The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]
Therefore [tex](k o h)(x) = \frac{1}{5 + x}[/tex]
Given that the functions h is defined by h(x)=5+x
and k is defined by k (x) = [tex]\frac{1}{x}[/tex]
To find the composition of k and h that is: (k o h) (x)
Therefore
k (h(x)) = k (5+x)
k (h(x)) = [tex]\frac{1}{5+ x}[/tex]
The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.Expressions are syntactic devices. It must be properly constituted, which means that the permissible operators must have the right amount of inputs in the right places, legal characters for these inputs, a clearly defined order of operations, etc.The syntax requirements must be followed for a string of symbols to be considered a valid mathematical expression.To learn more about Expression with the given link
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Erin has developed a new lotion that will help children with sensitive skin. she invests $15,225 in equipment to manufacture and package her lotion. each bottle costs $3.25 to manufacture and sells for $12. how many bottles of lotion must she make and sell before her business breaks even? a. 998 bottles b. 1740 bottles c. 174 bottles d. 1269 bottles
Her business will break even when she contains sold 1740 bottles of her lotion.
How many bottles of lotion must she make and sell before her business breaks even?Given: She invests $15,225 in equipment to manufacture and package her lotion each bottle costs $3.25 to manufacture and sells for $12.
"Break even" occurs when Revenue = Costs.
($12/bottle)x = $15225 + ($3.25)x
Simplifying the above equation, we get
$8.75x = $15225
Diving both sides of the equation by 8.75, we get
$8.75x/8.75 = $15225/8.75
x = 1740 bottles
Therefore, the value of x = 1740 bottles.
Her business will break even when she contains sold 1740 bottles of her lotion.
Therefore, the correct answer is option b. 1740 bottles.
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how many lengths of strings measuring 0.8meters long can be cut from a piece of string measuring 0.5kilometers
0.0016
reduce expression if possible by canceling the common factors
90 times 2.5 divided by 3 +200,000?
Answer:
200,075
Step-by-step explanation:
90 times 2.5 = 225
225 divided by 3 = 75
75 + 200,000 = 200,075
Answer: 200075
Step-by-step explanation:
90 * 2.5 = 225
225 / 3 = 75
75 + 200,000 = 200,075
A planet orbiting a distant star has been observed to have an orbital period of 0.76 earth years at a distance of 1.2 au. what is the mass of the star the planet is orbiting? round your answer to the nearest whole number. solar masses
Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.
What is a solar mass?Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.
Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.
When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:
= Distance planet is rotating³ - Orbital period²
Solving gives:
= 1.2³ / 0.76²
= 2.99
= 3 solar masses
In conclusion the mass of the star is 3 solar masses
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Answer:
3 solar masses
Step-by-step explanation:
just did it and got it right
Students in Ms. Valendra’s science class planted 13 in different places around the school yard. After one month, they measured the heights of the conifers. They rounded each measurement to the nearest 1/4
Considering the dot plot, it is found that the tallest conifer is 3.25 inches taller than the shortest conifer.
What does a dot plot shows?It shows, with dots, the number of times that each of the measures appears in a data-set.
Researching this problem on the internet, and finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4 = 6.25 inches.The tallest conifer measures 9.5 inches.The difference is:
9.5 - 6.25 = 3.25 inches.
Hence the tallest conifer is 3.25 inches taller than the shortest conifer.
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Urve revolves around the x-axis. if you cannot evaluate the integral exactly, use your calculator to approximate it. (round your answer to four decimal places. ) y = 16 − x2 from x = −1 to x = 1
The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-[tex]x^{2}[/tex]
Find the integration of 16-[tex]x^{2}[/tex].
=16x-[tex]x^{3}/3[/tex]
Now find the value of integration from x=-1 to x=1.
=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
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The table above shows four numeric expressions. Which expression is an integer when it's evaluated?
Question 6 options:
A)
G
B)
F
C)
H
D)
E
Answer: H
Step-by-step explanation:
[tex]9(-3)=-27[/tex], which is an integer.
What is the value of y?
Z
Y
60 degrees
70 degrees
50 degrees
Using proportions, the value of y is of 100º.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:
y = 2 x 50º = 100º.
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The graph f(x) = (x + 2) ^ 2 - 7 is translated 3 units up, resulting in the graph g(x) . Which equation represents the new function, g(x) ?
Step-by-step explanation:
x^2 +4x +4 -7 is
y=x^2+4x-3
Answer: g(x)=(x+2)²-4.
Step-by-step explanation:
g(x)=f(x)+3
g(x)=(x+2)²-7+3
g(x)=(x+2)²-4.
Solve the system of equations by substitution.
3 /8 x +1/3y =17/24
x + 7y = 8
By substitution, the value of x and y are 1 and 1 respectively.
How to solve system of equation?3 / 8 x + 1 /3 y = 17 / 24
x + 7y = 8
x = 8 - 7y
Let's substitute the value of x in equation(ii)
3 / 8(8 - 7y) + 1 / 3 y = 17 / 24
3 - 21 / 8 y + 1 / 3 y = 17 / 24
1 / 3 y - 21 / 8 y = 17 / 24 - 3
8y - 63y/24 = 17 - 72/ 24
-55y / 24 = -55 / 24
cross multiply
-1320y = -1320
divide both sides by -1320
y = -1320 / -1320
y = 1
Hence,
x + 7(1) = 8
x = 8 - 7
x = 1
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You are on a jungle expedition and come to a raging river. You need to build a bridge across the river. You spot a tall tree directly across from you on the opposite bank (point ). You place a pole in the ground to mark the position directly across from the tree. From the spot you are standing, you walk directly downstream 16 feet and place another pole (point ). You keep walking down stream and mark a third spot with a pole that is 7 feet from your last pole (point ). Turning perpendicular from the last pole, you walk away from the river 9 feet to another position and place a fourth pole (point ).
a. Determine if the two triangles are similar. Explain which similarity theorem you used and why.
b. Use proportions to calculate the distance across the river.
A large tree is close to point and we could chop it down at an angle to reach point and safely cross the river.
c. How tall does the tree need to be to span the river from point to ?
does someone mind helping me with this question? Thank you!
Answer:
4/9
Step-by-step explanation:
.44444.. = 4/9
0.nnnnnnnn.... = n/9
0.mnmnmnmnmn.... = mn/99
and so on