Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100. For(B) 8181 values of n is q + r divisible by 11.
5 digit Number:
A 5 digit number is a 5 digit number where the first digit is 1 or greater than 1 and the remaining digits can be any digit from 0 to 9. It starts at ten thousand (10,000) and goes up to 99,999 (99,999).
Given:
Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100.
When a five digit number is divided by 100, we get first three digits as quotient and last two digits as remainder. Therefore q can be any integer from 100 to 999 and r can be from 0 to 99
So for each value of 9 x 100 = 900 , possible value will be q = 100/11 = 9
Now,
q + r ≡ 0 (mod 11) will be possible values of r.
Since there is one extra , 900 / 11 = = 81
Hence, q + r ≡ 0 (mod 11)
So, possible values of n such that q + r = 0(mod 11) is 9 x 100 + 1 x 81
So, it will be 8100 + 81 = 8181
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6. A ferris wheel 250 feet across rotates once every 45 seconds.
rad
Find: a) angular velocity in
and
revolutions
hour
sec
b) velocity of the ferris wheel if it becomes disengaged from the motor and rolls away (ignoring friction....)
The angular velocity is 0.14 rad/sec.
The velocity of the Ferris wheel if it becomes disengaged from the motor and rolls away is 17.44 ft/sec.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Diameter of the Ferris wheel = 250 feet
The radius of the Ferris wheel = 125 feet
Now,
The linear velocity v = wr
Where w is the angular velocity.
The angular velocity.
w = v/r
The linear velocity v.
v = 2πr/T
v = (2 x 3.14 x 125) / 45
v = 17.44 ft/sec
The angular velocity.
w = v / r
w = 17.44/125
w = 0.14 rad/sec
Thus,
Angular velocity is 0.14 rad/sec.
The velocity of the Ferris wheel after disengaging from the motor is
17.44 ft/sec.
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Serenity is a waitress at a restaurant. Each day she works, Serenity will make a
guaranteed wage of $20, however the additional amount that Serenity earns from tips
depends on the number of tables she waits on that day. From past experience,
Serenity noticed that she will get about $13 in tips for each table she waits on. How
much would Serenity expect to earn in a day on which she waits on 19 tables? How
much would Serenity expect to make in a day when waiting on t tables?
Answer:
19 tables, f(19) = $280
1 table, f(1) = $33
Step-by-step explanation:
Let f(x) be the money Serenity makes each day, where x is the number of tables she serves.
Her saily income includes a fixed injcome of $20/day, plus $13/table in tips.
We can write f(x) = $20 + $13x
When x = 19, f(19) = $280
When x = 1, f(1) = $33
Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.
P(-2,1,0), Q(2,3,2), R(1,4,-1), S(3,6,1)
The volume of the parallelepiped with adjacent edges PQ, PR, and PS is V=4
Given three vectors, there is a product, called scalar triple product, that gives (the absolute value of it), the volume of the parallelepiped that has the three vectors as dimensions.
So
PQ=(-2-2,1-3,0-2)=(-4,-2,-2)
PR=(-2-1,-1-4,0+1)=(-3,-5,1)
PS=(-2-3,1-6,0-1)=(-5,-5,-1)
The scalar triple product is given by the determinant of the matrix (3×3)
that has in the rows the three components of the three vectors:
|-4 -2 -2|
|-3 -5 +1|
|-5 -5 -1|
and the determinant is given for example with the Laplace rule choosing the first row:
a(ad-bc)-b(ad-bc)+c(ad-bc)
=-4[(−5)(−1)−(1)(−5)]−(−2)[(−3)(−1)−(1)⋅(-5)]+(−2)[(−3)(−5)−(−5)(-5)]
=-4[5+5]+2[8]-2[-10]
-4(10)+16+20
=-40+36
V=-4
So the volume is: V=|−4|=4
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Is finding half of a number the same as dividing a number by ½ Why or why not?
No, finding half of a number is not the same as dividing a number by ½. When finding half of a number, the result is the number divided by 2. When dividing a number by ½, the result is the number multiplied by 2.
When finding half of a number, the result is the number divided by 2.
For example, if we want to find half of the number 8, we would divide 8 by 2 to get 4.
When dividing a number by ½, the result is the number multiplied by 2.
For example, if we want to divide the number 8 by ½, we would multiply 8 by 2 to get 16.
No, finding half of a number is not the same as dividing a number by ½. When finding half of a number, the result is the number divided by 2. When dividing a number by ½, the result is the number multiplied by 2.
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an airplane flies from one city in a straight line to another city, which is 360 kilometers north and 150 kilometers west of first city. how far does the plane fly?
Answer: 390 Km
Step-by-step explanation: Use the Pythagorean Theorem to solve this problem. We know that it is going north and west, forming a triangle. It says a straight line so we know it is the hypotenuse. 360^2 + 150^2 = x^2. X is 390.
The following data give the prices of seven textbooks randomly selected from a university bookstore. $93 $172 $109 $119 $54 $164 $143 a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero
The deviations of the data values as calculated form the data given in the question is found out to be as 1698.
The formula to calculate the mean is ,
mean = fixi / n
Therefore ,
mean = 93+172+109+119+54+164+143 / 7 = 861/7 = 731.42
Now, to calculate the standard deviation,
= √∑ (fx)²/ n
he value of y² as calculated is found out to be as ,
y² = 10190.
Therefore, SD = √(10190)²/ 7= 38.1
Now , variance is equal to the square of the standard deviation ,
or variance = ∑ ( y)² / n-1
= 10190 / ( 7-1)
= 10190 /6
= 1698.
The sum of these deviation thus , is not zero.
The variance is defined as the expectation of a random variable's squared departure from its mean value, and it is used to determine how far a set of values is spread out from its mean.
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A system of linear equations is shown in the graph. How many solutions does the system have?
a coordinate plane with one line that passes through the points 0 comma 3 and 3 comma 4 and another line that passes through the points 0 comma negative 2 and 3 comma negative 1
No solution
One solution at (0, 3)
One solution at (−2, 0)
Infinitely many solutions
The number of solutions which the system of equations has is: A. no solution.
How to determine the number of solutions?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (0, 3), a linear equation of the first line can be calculated in slope-intercept form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (4 - 3)/(3 - 0)(x - 0)
y = 1/3(x - 0) + 3
y = x/3 + 3
For the second line, we have:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y + 2 = (-1 + 2)/(3 - 0)(x - 0)
y + 2 = x/3
y = x/3 - 2
In conclusion, we can logically deduce that the given system of linear equations has no solution because it represents parallel lines.
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a rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. the length is increasing by 3 in/sec and the width is shrinking at 5 in/sec. what is the rate of change of the perimeter?
If the length of the given rectangle is increasing by 3 in/sec and the width is shrinking at 5 in/sec then the rate of change of its perimeter is 4 in/sec.
Length, L = 9 inches
Width, W = 5 inches
The perimeter of the rectangle is
P = 2L + 2W.
By Differentiating both sides with respect to time t, we get
dP ⁄ dt = 2 × dL ⁄ dt + 2 × dW ⁄ dt
From the given conditions,
dL ⁄ dt = 3 and dW ⁄ dt = -5
So at the moment when L = 9 and W = 5,
dP ⁄ dt = (2)(3) + 2(−5 )
= 6 - 10
= -4
Therefore, The perimeter of the rectangle is decreasing at a rate of 4 in ⁄ sec.
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a football field is 120 yd long and 50 yd wide. what is the area of the football field, in m2, if 1 yd
Consequently, a football field measuring 120 yards long and 50 yards wide has an area of 5016.76 m2.
what is area ?An object's surface area is a measurement of the total volume of space that it occupies. The entire region surrounding a three-dimensional shape is referred to as its surface area. Its surface area is the total area of a three-dimensional shape. By adding the surfaces of each of a cuboid's six rectangular sides, one may determine the cuboid's surface area. The box's dimensions could also be named using the following formula: Surface (SA) = 2lw + 2lh + 2hw. A three-dimensional shape's surface area is a measurement of the total area it occupies (a three-dimensional shape is a shape that has height, width, and depth).
given
You are required to bring the area in this instance in m2, however the length (120 yd) and breadth (50 yard) are given in yd.
The unit must then be changed into m2. The rectangle's area formula should be length * width.
So, the equation should be:
area = length * width= (50yd * 91.44cm/yd * 1m/100cm) * (120yd * 91.44cm/yd * 1m/100cm)
= 5016.76 m2
Consequently, a football field measuring 120 yards long and 50 yards wide has an area of 5016.76 m2.
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a backyard garden has an area of 6.59 square meters. how many square centimeters is this? express your answer in scientific notation and to three significant figures.
There are 65900 square centimetres present in a backyard garden that has an area of 6.59 square meters.
Scientific notation is the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number is between 1 and 10s, it is multiplied by a power of 10.
For example, 6,500,000,000,000 can be written as 6.5 × 10¹².
To calculate a square meter value to the related value in cm², just multiply the quantity in m² by 10000 (the conversion factor). Here is the formula for it:
Value in cm² = value in m² × 10000
We need to convert 6.59 m² into cm². Using the conversion formula above, we will get:
Value in cm² = 6.59 × 10000 = 65900 cm²
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how to find midline of sinusoidal functions from equation
A function's midline is the horizontal line positioned exactly halfway between its maximum and minimum values.
what is trigonometric ratios ?Trigonometric ratios are based on the side ratio of a right-angled triangle and consist of the values of all trigonometric functions. The ratios of the sides to any acute angle in a right-angled triangle are the trigonometric ratios of that angle. You can use trigonometric ratios to determine the lengths of one (or both) of the acute angles of a right triangle if you know the lengths of its two sides.
given
A function's midline is the horizontal line positioned exactly halfway between its maximum and minimum values.
The midline is the line y = 0 for y = sin (the horizontal axis). The difference between the highest and smallest values of a function is half its amplitude.
The amplitude of the y = sin function is 1.
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The table shows the inputs and corresponding outputs for the function f(x) = (1/8)(2)^x
Answer:
yes
Step-by-step explanation:
What are 2's factors?
1 and 2 are the factors of 2.
2 is a prime number, it has only two factors, 1 and 2. Also, we also know that the factors of 2 are the exact divisors of that number. There is another way to represent the factors of any number, by arranging the number of objects.
It is the only number when added and multiplied to itself brings the same result, 4. Factors of 2 can be positive and negative as well.
Prime factors of 2, and factors of 2 in pairs along with solved examples for a better understanding. Factors of 2 are all the numbers which on multiplying give the result of 2.
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The United States Coast Guard (USCG) is responsible for cruise ship safety. On some ships, USCG officers randomly select passengers for an extra security check before boarding. One such flight had 4300 passengers 1200 in balcony cabins and 2100 in ocean view rooms. USCG officers selected an SRS of 1000 passengers for screening. Let p be the proportion of passengers in balcony cabins in the sample. (c). What is the probability that no more than 75 of passengers in the sample have a balcony?
The probability that no more than 75 of passengers in the sample have a balcony is given as follows:
0%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given as follows:
n = 1000, p = 1200/(4300 + 1200 + 2100) = 0.158.
Hence the mean and the standard deviation for the normal approximation are given as follows:
[tex]\mu = 1000 \times 0.158 = 158[/tex][tex]\sigma = \sqrt{1000 \times 0.158 \times 0.842} = 11.5[/tex]Using continuity correction, the probability that no more than 75 of passengers in the sample have a balcony is P(X < 75.5), which is the p-value of Z when X = 75.5, hence:
Z = (75.5 - 158)/11.5
Z = -7.17
Z = -7.17 has a p-value of 0.
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please help me, i will mark brainliest for both answers.
Work out the size of angle x.
Answer: x = 83°
Step-by-step explanation:
First, a straight line is equal to 180°.
180° - 126° = 54°
Next, a triangle's internal angles add up to 180°.
54° + 43° + x = 180°
With this given equation, we can solve for x.
Given:
54° + 43° + x = 180°
Combine like terms:
97° + x = 180°
Subtract 97 degrees from both sides of the equation:
x = 83°
To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a side of the rectangle he draws. Which expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU
The expression which is to be subtracted as calculated from the data given is found out to be as , 0.22.
The coordinates of the parallelogram as mentioned in the question is , R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)
Therefore, the length of the sides as measured using distance formula is found out to be as,
RS = 4.1231, RT = 10 , ST = 9.2195 , SU = 10.198 ,TU = 4.1231 and UR = 9.2195.
Now as we know that 2 sides of a parallelogram are parallel , therefore,
RS || TU and ST || UR.
RS(slope) = (1 - (-3))/(-5 - (-4)) = -4
and the ,
ST(slope)= (3 - 1)/(4 - (-5)) = 2/9
Hence , to find the line perpendicular to ST is given by ,
y - 1 = -9/2×(x - (-5))
y = -9x/2 - 43/2
The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1
y = x/4 - 2
Their point of interaction is , -9x/2 - 43/2 = x/4 - 2
x = -78/19
y = -115/38
Side of rectangle = 4.1245
width of the rectangle = 0.1085
Therefore, the expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU = 1/2 × 4.1245 × 0.1085
= 0.22.
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For the equation: 2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7 , the right side of the equation can be simplified by combining like terms.
Simplify 9 - 3x + 6 + 8 + 3x + 7 :
2(x - 5) can be simplified using the Distributive Property.
Simplify 2(x - 5):
The value of the equation is x=20.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is
=> 2(x-5)=9-3x+6+8+3x+7
Now simplify the equation for x then
=> 2x-10 = 30-3x+3x
=> 2x-10=30
=> 2x=30+10
=> 2x=40
=> x=20
Hence the value of the equation is x=20.
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Two parallel lines are cut by a transversal as shown below.
Suppose m /_ 5 = 56 . Find m /_ 2 and m /_4.
When the parallel lines are cut by a transversal, the values for the measurement of ∠2 and ∠4 is 124° each.
What are parallel lines?
Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.
Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.
In the given diagram the parallel lines are cut by a transversal.
The measure of angle 5 is, m∠5 = 56°.
It is known that each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.
So, m∠5 + m∠2 = 180°
56° + m∠2 = 180°
m∠2 = 180° - 56°
m∠2 = 124°
Now, as it can be seen in the image ∠2 and ∠4 are vertically opposite angles.
So, they will be congruent or equal to each other.
So, it is obtained that -
m∠2 = m∠4
m∠4 = 124°
Therefore, the measures of angles are m∠2 = 99° and m∠4 = 99°.
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Is the absolute value always less than or equal to zero?
No, the absolute value of a number is always non-negative, meaning it is greater than or equal to zero, but it is not always equal to zero.
The absolute value of a number represents the distance of that number from 0 on the number line and a number can be positive or negative.
For example, the absolute value of 5 is 5, which is greater than zero. The absolute value of -5 is also 5, which is also greater than zero. The only time the absolute value of a number is equal to zero is when the number is zero, |0| = 0.
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Renee knows that there is 700 calories in 12 oz of chocolate. She wants to calculate how many calories would be in 30 oz of Chocolate. Below is her work. Did she calculate correctly? If not explain and correct her mistake.
Answer: 1750 calories
Step-by-step explanation:
[tex]\frac{700calories}{12oz} * 30 oz = 1750 calories[/tex]
What is an absolute value function called?
Answer:
An absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer: 2m+4
Step-by-step explanation:
To simplify, we need to combine "like terms", which means terms that are similar in that it is either just a number or a coefficient and variable. In this case, 3m and -m are like terms, and -6, 2, and 8 are like terms.
Now, we can combine.
-6 + 3m + 2 -m + 8
-4 + 3m - m + 8
4 + 3m - m
4 + 2m (also can be written as 2m + 4)
hope this helps!
to the nearest second, what is the first time between 4:00 and 5:00 that the minute and hour hands of the clock are perpendicular to each other?
So the first time between 4:00 and 5:00 that the minute and hour hands of the clock are perpendicular to each other to the nearest second is 4:06.
The minute hand of a clock moves 360 degrees in 60 minutes, or 6 degrees per minute.
The hour hand moves 360 degrees in 12 hours, or 30 degrees in 1 hour, or 30 degrees in 60 minutes, or 0.5 degrees per minute.
At 4:00, the minute hand is pointing straight up (12 o'clock), and the hour hand is pointing at 4 o'clock.
To find the first time that the hands are perpendicular, we need to find the first time that the difference between the angle of the minute hand and the angle of the hour hand is 90 degrees.
We know that the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute, so for every minute that passes, the angle between the hands increases by 5.5 degrees.
Each consecutive hour has 30 degrees in between, so angle between 12 and 4 is
4×30 = 120°
So,
At 4:00 the angle between the hands is
120°
At x minutes after 4, the angle is
120 - 5.5x
So to solve for x when angle is 90°
120 - 5.5x = 90
x = 30/ 5.5
x = 5.45 minutes
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Find the area of the composite figure.
Area =
8 ft
12ft
Answer:
Step-by-step explanation: the area of the shape is the length times width or base times height. It's our length is 12 Are with this eight. And when you multiply 12 times eight, we get 96 feet squared, which is the area of our rectangle. I think its a rectangle.
How many moles of KI are in 83 grams of KI?
Answer: 1 moles KI = 166.00277 gram using the molecular weight calculator and the molar mass of KI.
Step-by-step explanation
Answer was found by using the molecular weight calculator and the molar mass of KI.
Hope this helps :)
How is an inequality different from an equation? Give a real-world scenario in which you would write an inequality rather than an equation.
The main difference between an equation and an inequality is in an equation the elements are equal but in an inequality the elements are compared.
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
An equation has an answer that equals a number. An inequality has an answer that could be less than or more than or less than or equal to or more than or equal to.
For example: You have some money in your pocket. You want to buy some snacks for tonight's match, but your wife told you to buy one pizza on your way back to home that costs $10. That means that on snacks you can spend (y) :
y ≤ x - 10 where x represents money in your pocket.
This means that from money in your pocket you have to subtract $10 for pizza and out of the remaining money you can spend some part of it on snacks or all of it.
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the rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does. the total perimeter is fixed. find the proportions of the window that will admit the most light. neglect the thickness of the frame.
Assume that x represents the window's rectangular portion's width and y represents the window's rectangular portion's height. The width of the rectangular component of the window is equal to the diameter of the semicircle portion since the semicircle with diameter d is atop the window, or x = d.
x = circle diameter = window width
r = x/2 and y = window height
We'll now solve for the window's perimeter. The top section of the rectangular window is not included since it is continuous with the semicircular component of the window, therefore the perimeter of the rectangle portion is x + 2y, and the perimeter of the circular portion is x/2 (which is half the circumference of a circle).
hence:
P = x2y + πx/2 = 2r + 2y + πr
We will now find a solution for the light that passes through the window. Assuming that transparent glass transmits one light per square inch, tinted glass transmits just one light per square inch.
The area of the rectangle component multiplied by the clear glass light constant, or 1*2ry = 2ry, will determine the rectangular light. The semicircular component will be equal to (1/4)*r2/2, which is the tinted glass light constant multiplied by half the area of a circle. Hence,
L = 2ry + πr2/8
Isolating y from the perimeter equation now will allow us to enter that value of y into the light equation.
L = r(P - r(2 + )) + r2/8 y = (P - r(2 + ))/2
P is a constant, hence the only variables in the light equation are We can differentiate L with respect to r (i.e. dL/dr) and solve for when dL/dr = 0 to find the point at which the light transmitted is at a maximum.
dL/dr = P - 2r(2 + π) + πr/4
0 = P - 2r(2 + π) + πr/4
r = 4P/(16 + 7π)
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12.00 gram sample of brass (alloy of copper and zinc), is reported to
contain 4.21 grams of zinc, report percent mass composition of zinc and
copper.
Answer:
The percent mass composition of zinc in the brass sample is:
(mass of zinc / total mass of sample) x 100%
(4.21 g / 12.00 g) x 100% = 35.08% zinc
So the brass sample contains 35.08% zinc by mass.
To find the percent mass composition of copper in the sample, you can use the information that the sample is made of copper and zinc only, so you can use the difference between 100% and the percent zinc:
100% - 35.08% = 64.92% copper
So the brass sample contains 64.92% copper by mass.
who can help me plssssssssssssssssssssssssss
Answer:
Step-by-step explanation:
hi
Answer:
Step-by-step explanation:
hi
