The probability of rolling two trick number cubes with the numbers 5, 10, and 15 on them can be calculated using the formula P(A) = n(A) / n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.
In this case, the total number of possible outcomes is 6, since there are six possible combinations of two number cubes. The number of favorable outcomes for a sum of 10 is 2, since there are two possible combinations (5 and 5, and 10 and 15). Therefore, the probability of rolling a sum of 10 is 2/6, or one-third. The probability of rolling a sum of 15 is also one-third, since there is only one possible combination (10 and 5). The probability of rolling a sum of 20 is one-sixth, since there is only one possible combination (10 and 10). Therefore, the probability model for the sum of the two number cubes is a 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
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Determine the seating capacity of an auditorium with 35 rows of seats if there are 20 seats in the first row, 25 seats in the second row, 30 seats in the third row, 36 seats in the fourth row, and so on.
Total number of seats=_____.
The total number of seats in the auditorium is 3500.
What is the arithmetic series?
An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is always the same. It can also be defined as a sum of a finite number of terms of an arithmetic progression.
The seating capacity of the auditorium can be found by using the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
S = n/2 (2a + (n-1)d)
Where:
S is the sum of the series (total number of seats)
n is the number of terms in the series (number of rows of seats)
a is the first term in the series (number of seats in the first row)
d is the common difference between terms in the series (increase in number of seats per row)
In this case,
a = 20 (number of seats in the first row)
d = 25 - 20 = 5 (increase in number of seats per row)
n = 35 (number of rows of seats)
So,
S = 35/2 (2(20) + (35-1)(5))
S = 35/2 (40 + 160)
S = 35/2 (200)
S = 35*100
S = 3500
Hence, the total number of seats in the auditorium is 3500.
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Stefanie has 18 grams of 20% sugar syrup and John has 30 grams of 25% sugar syrup.
how many grams of sugar are in Stefanie's syrup?
how many grams of sugar are in John's syrup?
The grams of sugar that is in Stefanie's syrup = 3.60g
The grams of sugar that is in John's syrup = 7.50g
How to calculate the quantity of sugar?The quantity of sugar syrup that Stefanie has = 18grams
The percentage of sugar syrup that is sugar = 20%
That is, 20/100 × 18
= 360/100
= 3.60g
The quantity of sugar syrup that John has = 30 g
The percentage of sugar syrup that is sugar = 25%
That is;
= 25/100 × 30
= 750/100
= 7.50g
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regina takes yoga classes 2days a week at the community center
The option that will cost less money from Regina is $8 a class.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
Since the cost for the classes at the community center is $72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The amount will be:
= $72 + $12
= $84
The other cost at $8 a class for 2 weeks will be:
= $8 × 10 days
= $80
The second option is cheaper.
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Yoga classes are offered 2 days a week for 6 weeks
at both the community center and the local gym.
The cost for the classes at the community center is
$72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The cost at the
local gym is $8 a class. Regina wants to know which
class she can take for less money.
A certain blend of coffee sells for $15 per pound. Part 3 If a container has 31-x lb of coffee, write an expression that represents the cost.
The expression that represents the cost of coffee per container is (blank)
T = si is an expression that can be used to represent the party's projected cost.
How should the information be illustrated?T = si is an expression that can be used to represent the party's projected cost.
It should be remembered that expressions depict how variables relate to one another.
We can use the following phrase to obtain an estimated party cost:
T = s×i
where:
T is the ice cream party's overall budget.
s is the number of ninth-graders.
I = the ice cream unit price.
discover more on expressions;
All ninth graders are invited to an ice cream celebration as a prize for accomplishing their goals.
1) Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents.
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A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test?
The P-value of the test is the probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true.
This can be calculated using the formula P(X <= x) = Σ (n x) p^(x) q^(n-x), where n = 100, x = 80, p = 0.75 and q = 1-0.75. Following this formula, the P-value of the test is calculated to be 0.0009. This means that there is a 0.0009 probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true. Therefore, the data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%.The P-value of the test is the probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true.
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based on your calculated values, what can we say about the percentage of students using ipads in public school districts?
Relative to the mean, there are some school districts where many students are using ipads.
What is called the mean?
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is sometimes referred to as the "average" and is the most widely used central tendency metric.
Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
Mean: The "average" number; found by adding all data points and dividing by the number of data points. Example: The mean of 4, 1, and 7 is ( 4 + 1 + 7 ) / 3 = 12 / 3 = 4 (4+1+7)/3 = 12/3 = 4 (4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.
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Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below.
a) The first lefty is the fifth person chosen.
b) There are some lefties among the 5 people.
c) The first lefty is the second or third person.
d) There are exactly 3 lefties in the group.
e) There are at least 3 lefties in the group.
f) There are no more than 3 lefties in the group.
The first lefty is the fifth person chosen is7.45%
There are some lefties among the 5 people is, 50.16%
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.The first lefty is the fifth person chosen is
[tex](.87)^4(.13)=.07447=7.45 \%[/tex]
There are some lefties among the 5 people is,
[tex]$$1-(.87)^5=.50157=50.16 \%$$[/tex]
The first lefty is the second or third person.
[tex]$(.87)(.13)+(.87)^2(.13)=.211497=21.15 \%_0$[/tex]
There are exactly 3 lefties in the group.
[tex]$(5, .13,3)=.0166=1.66 \%$[/tex]
There are at least 3 lefties in the group,
[tex]1 \text { - binomadf }(5, .13,2)=.0179=1.79 \%[/tex]
There are no more than 3 lefties in the group
[tex]\text { binomcdf }(5, .13,3)=.9987=99.87 \%[/tex]
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Help please I think I’m not sure which one is the answer, confused!!!
a gallup poll utilizing a random sample of adults ages or older was conducted in april . the survey indicated a majority of americans () say driverless cars will be common in the next years (gallup,
A Gallup poll conducted in April found that 55% of Americans believe driverless cars will be common in the next 10 years, as presented in a histogram showing the percentage of responses in different time intervals.
A Gallup Poll was conducted in April that surveyed adults aged 18 or older to gauge their perceptions on when fully automated "driverless cars" will be commonly used in the United States.
The question asked was "how soon do you think driverless cars will be commonly used in the United States?" The survey indicated that 55% of Americans believe that driverless cars will be common in the next 10 years.
The results of the survey were presented in a histogram, showing the percentage of responses in different time intervals, which means it shows how many people responded within a certain time frame (e.g. within 5 years, within 10 years, etc.) when they think driverless cars will be commonly used.
This poll gives an insight into how people perceive the future of driverless cars and how soon they think it will become a common sight on the roads.
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The question is -
A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
write an equivalent expression for 4(w-5)
Answer:
4w - 20
Step-by-step explanation:
hope this help i guess
A recipe for soup calls for 6 tablespoons of lemon juice and cup of olive oil. The given recipe serves 4 people, but a cook wants to make a larger batch that serves 40
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
a) The chef needed
(Type a whole number,
cups of lemon juice for the larger batch.
proper fraction, or a mixed number.)
b) The chef needed
pints of olive oil for the larger batch.
(Type a whole number, proper fraction, or a mixed number.)
The chef needed a) 3¾ cups of lemon juice and b) 20 pints olive oil for the larger batch.
What is mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.
The recipe was for 4 person, but now here are 40
The scale multiple is = 40/4
= 10
a) As 1 cup = 16 tablespoon
The number of tablespoon of lemon required for 40 men = 6 × 10
= 60
Converting to cup = 60/16
= 3¾ cups
b) As 1 cup = 0.5 pints
The number of cups of olive oil required for 40 men = 1 × 10
= 10
Converting to pints = 10/0.5
= 20 pints
Thus, The chef needed 3¾ cups of lemon juice and 20 pints olive oil for the larger batch.
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A ball has a radius of 3 in how much air can the ball hold
Answer:
v = 113.04 [tex]units^{3}[/tex]
Step-by-step explanation:
v = 4/3[tex]\pi r^{3}[/tex]
v = 4/3[tex]\pi 3^{3}[/tex]
v = 113.04 [tex]units^{3}[/tex]
the radius of the wheelsof car is 35cm the car take 1 hour to cover 66 km find the number of revolution that the wheel of the car makes in one minute
The wheel of the car makes 500.5 revolution per minute
What is frequency?frequency is defined as the number of oscillation or revolution made in one seconds. It measured in Hertz. frequency is denoted as F. And it is expressed as :
F = w/2π
Where w = angular velocity and
2π = 360 which is also a revolution
to calculate w ;
v = wr
r = 35cm = 0.35m
v = 66km/h = 66×1000/60
v= 1100m/mins
therefore from the relation, v = wr
w = v/r
w = 1100/0.35
w = 3142.9rad/mins
therefore F = w/2π
F = 3142.9/ 2×3.14
F = 500.5 revolution per minute
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A dozen mangos and a pizza cost $2.70.
Half a dozen mangos and 2 pizzas cost $3.75.
What is the cost of a pizza?
Answer the question and show steps.
Please help me!! It is 5 questions
1. 80 people attended only the FSU-Butler game.
2. 165. Since it's not possible to have negative number of people, the answer is 0.
3. 210 people attended at least two of these games.
4. 340 people attended the Marist and Butler games, but not the North Carolina State game.
5. 365 people attended the North Carolina State or the Butler game
How do you calculate this vendiagram? We know that 215 people attended the FSU-Butler game, and that 70 of them also attended the NC State game and 65 of them also attended the Marist game. So, 215 - 70 - 65 = 80 people attended only the FSU-Butler game.We know that 460 people were surveyed in total, and 190, 215, and 220 attended the Marist, Butler and NC State games respectively. The number of people who attended at least one of these games is 190 + 215 + 220 = 625. Thus, 460 - 625 = -165. Since it's not possible to have negative number of people, the answer is 0.We know that 65 people attended the Marist and NC State games, 70 people attended the NC State and Butler games, and 65 people attended the Butler and Marist games. 10 people attended all three games. So, 65 + 70 + 65 + 10 = 210 people attended at least two of these games.We know that 190 people attended the Marist game, 215 people attended the Butler game, and 65 people attended both the Marist and Butler games. So, 190 + 215 - 65 = 340 people attended the Marist and Butler games, but not the North Carolina State game.We know that 220 people attended the North Carolina State game and 215 people attended the Butler game. 70 people attended both the North Carolina State and Butler game. So, 220 + 215 - 70 = 365 people attended the North Carolina State or the Butler game.To learn more about venn diagram refer
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I need help on getting an answer for "Y"
Answer: 50
Step-by-step explanation:
You can plug in 4 for any of the equations given.
y = 10 + 10(4)
y = 10 + 40
y = 50
OR
y = 30 + 5(4)
y = 30 + 20
y = 50
Answer:
y = 50
Step-by-step explanation:
Since x = 4, plug the value into either equation.
[tex]y =10+10x\\y = 10 + 10(4)\\y=10+40\\y=50[/tex]
Therefore, y equals 50.
Two factory outlets F_2 and F_2 in New York and Los Angeles sell sofas (S), chairs (C), and tables (T) with a profit of $35, $62, and $30, respectively. Let the sales in a certain week be given by the matrix A = [S 400 C 60 T 240] F_1 Introduce a "profit vector" such that the components of = give the total profits of F_1 and F_2
The total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.
The profit vector can be expressed as p = [35 62 30]. The total profit of F_1 and F_2 can be calculated by multiplying the matrix A by the vector p. The result, Ap, is a vector whose components give the total profits of the two stores in the week.
For example, the total profit of F_1 can be calculated as Ap_1 = [35 62 30] * [400 60 240] = [14000 3720 7200] = 25920.
Similarly, the total profit of F_2 can be calculated as Ap_2 = [35 62 30] * [0 0 0] = [0 0 0] = 0.
Therefore, the total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.
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Tell the percentage below:
Answer:
10%
Step-by-step explanation:
if the volume of the water increase by 10 when turns to
ice so it must be decrease by 10 if it changes to water again
1. Let there exist an antiderivative F such that the integral from 0 to x of e to the power of 4t dt period Find the value of x such that F(x) = 2. Justify your work.
The value of the variable x for the given f(x) = 2 by simplifying the antiderivative of the given function is given by x = 0.4865.
As given in the question,
Given anti derivative of f(x) :
For the limit 0 to x for the integration of e^4t with respect t
= [tex]\int\limits^x_0 {e^{4t} } \, dt[/tex]
= ( 1/4) e^4x + ( 1/4 )
Value of the function f (x) = 2
Now f(x) = 2
Substitute the value of the function f(x) we get,
( 1/4) e^4x + ( 1/4 ) = 2
⇒ e^4x + 1 = 8
⇒ e^4x = 7
⇒x = log7 / 4
⇒ x= 0.4865
Therefore, the value of the x by simplifying the antiderivative function f(x) for the given f(x) = 2 is equal to 0.4865.
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Three times a number minus 6 is equal to two times the sum of a number and 8.
Write as a equation
students will read word problems and decide if they are one or two steps. then students will work to solve. great for a formative assessment or math centers.
When working with word problems, students should first read the problem and decide if it is a one-step or two-step problem.
A one-step problem involves solving for a single unknown quantity, such as finding the total cost of 10 pencils at $0.50 each. The formula for this would be C = Pn, where C is the cost, P is the price, and n is the number of items. To solve this problem, the student would multiply the price and number of items, so C = 0.50 x 10 = $5.00. A two-step problem involves solving for two unknowns, such as finding the total cost of 10 pencils at a 10% discount. The formula for this would be C = Pn (1 - r), where r is the discount rate. To solve this problem, the student would first calculate the discount by multiplying the price and number of items by the discount rate, so C = 0.50 x 10 x 0.10 = $0.50. Then the student would subtract the discount from the total cost, so C = 0.50 x 10 - 0.50 = $4.50.
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Dr. Leona Williams, a well-known plastic surgeon, has a reputation for being one of the best surgeons for reconstructive nose surgery. Dr. Williams enjoys a rather substantial degree of market power in this market. She has estimated demand for her work to be: Q = 480 – 0.2P where Q is the number of nose operations performed monthly and P is the price of a nose operation. What is the inverse demand function for Dr. Williams’ services? What is the marginal revenue function?
The average variable cost function for reconstructive nose surgery is estimated to be:
AVC = 2Q2 – 15Q + 400
where AVC is the average variable cost (measured in dollars), and Q is the number of operations per month. The doctor’s fixed cost per month is $8,000. If the doctor wishes to maximize her profit, how many nose operations should she perform each month?
What price should Dr. Williams charge to perform a nose operation?
How much profit does she earn each month?
tysm! :)
The inverse demand function is P = 2400 + 5Q
The Marginal Revenue function is MR = 5QThe number of nose operations is 15The price per month is $2475Dr. Williams earns $19750 in profit each monthHow to determine the inverse demand functionGiven that
Q = 480 - 0.2P
We simply make P the subject of the formula
So, we have
0.2P = 480 - Q
Divide by 0.2
P = 2400 + 5Q
The marginal revenue functionTo find the marginal revenue function, we can use the inverse demand function P = 2400 + 5Q, and take the derivative of this function with respect to Q.
The derivative of P with respect to Q is dP/dQ = 5. This represents the change in price for a one unit change in the quantity of operations performed.
So the Marginal Revenue function is MR = dP/dQ * Q = 5Q
The number of nose operationsTo maximize profit, the doctor should equate marginal revenue to marginal cost, which is
MC = dAVC/dQ
So, we have
MC = d(2Q² - 15Q + 400)/dQ
Evaluate
MC = 4Q - 15.
So, we have
5Q = 4Q - 15
Q = -15
Take the absolute value
Q = 15
So, the number of operations is 15
The price for each operationWe have
P = 2400 + 5Q
This gives
P = 2400 + 5 * 15
Evaluate
P = 2475
The monthly profitTo find the profit, we need to subtract the total cost from the total revenue.
The total revenue is found by multiplying the price by the quantity of operations performed: TR = P * Q = 2475 * 15 = 37125
The total variable cost is found by multiplying the average variable cost by the quantity of operations performed: TVC = AVC * Q = (2Q^2 - 15Q + 400) * Q = 2Q^3 - 15Q^2 + 400Q
The total fixed cost is the fixed cost that doesn't change regardless of the level of output : TFC = $8000
The total cost is the sum of the total variable cost and total fixed cost: TC = TVC + TFC = 2Q^3 - 15Q^2 + 400Q + $8000
The profit is the difference between total revenue and total cost:
π = TR - TC = 37125 - (2Q^3 - 15Q^2 + 400Q + $8000)
When Q = 15,
profit is π = 37125 - (2(15)^3 - 15(15)^2 + 400(15) + $8000)
= 19750
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find the volume of the solid with semi-circular cross sections whose bases lie in the xy-plane on [0,9] and diameters run from y
The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy.
Step 1: Substitute the expression for the area of the semi-circular cross section into the equation for the volume of the solid:
V = π/2∫0,9r²dy
Step 2: Integrate the equation to find the volume of the solid:
V = π/2[y³/3]|0,9
Step 3: Evaluate the integral:
V = π/2(9³/3 - 0³/3)
step 4: Solve for the volume of the solid:
V = 7π/2
The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy. To calculate the volume, we must first substitute the expression for the area of the semi-circular cross sections into the equation for the volume of the solid: V = π/2∫0,9r²dy. Then, we must integrate the equation to find the volume of the solid: V = π/2[y³/3]|0,9. After that, we must evaluate the integral: V = π/2(9³/3 - 0³/3). Finally, we must solve for the volume of the solid: V = 7π/2. The answer is the volume of the solid is 7π/2.
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44+ 7/8r when r = -1/2
[tex]44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}[/tex]
Show that a quadrilateral with the given vertices is a parallelogram.
When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)
What is a Parallelogram ?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
A quadrilateral is a specific type of polygon known as a parallelogram if it contains two parallel opposed sides. A parallelogram has the following qualities:
The opposing sides are equal and parallel.Angles on either side are equal.The subsequent or neighboring angles are additional.All of the angles will be at right angles if any one of them is a right angle.The two diagonals are split in half.The parallelogram is divided into two congruent triangles by each diagonal.A parallelogram's total square sum and total square sum of its diagonals are equivalent. Also known as the parallelogram law.Each coordinate of the Parallelogram :
P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)
Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37
Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37
Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17
Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17
Here, PA = RT and PT = AR ,
so when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.
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Queen Laetitia is sorting her gem collection. She starts by placing some of her
diamonds into two boxes. In every box after the first two, the Queen puts as many
diamonds as in the previous two boxes combined. If there are 30 diamonds in the
fourth box, and 128 diamonds in the seventh box, how many diamonds did
Queen Laetitia place in the tenth box?
Answer:
Step-by-step explanation:
Let's represent the missing number with "---" -- so we have so far:
--- --- --- 30 --- --- 128 --- --- ?
Now, let's say 5th position number is x and 6th position number is y
So, we have 30 + x = y and x+ y = 128
Combining these 2 equation, we get: x + 30 + x = 128 or x = 49, so y = 79
thus from 4th position, the series can be written as
30, 49, 79, 128, 207, 335, 542....
Thus, at 10th position we will have 542 !!!
Procedure: Pick a number. Add 5 to the number and multiply the sum by 3. Subtract 7 and then decrease this difference by the triple of the original number.
Answer:
(3n +8) -3n = 8
Step-by-step explanation:
You have the difference (3n+15) -7, and you want its value when it is decreased by the triple of the original number (n).
Triple the numberThe phrase "triple the original number" will be translated to 3n. This is the value you want to subtract.
(3n +15) -7 = 3n +8 . . . . . "the difference"
(3n +8) -3n = 8 . . . . . . . . "decreased by triple the original number"
This simplifies to 8, which is the point of the exercise: showing the sequence of steps always gives a value of 8.
What is the sum of 3+3+
Answer:
0
Step-by-step explanation:
I believe this is correct. Since they don't have the same sign then you will just have to subtract them.
Answer: 6
Step-by-step explanation:
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
Answer: C. 25%
Step-by-step explanation: This is a basic probability problem. First, you must find the total which is in question. 400 grams is the total in this case. The Cs make up 100 grams of this. Next, you put the part over the whole, and divide. 100/400= 0.25. When you want to find the probability with the probability sign, you move the decimal place two points to the right and then add the sign. Hence, 25%.
1/4(x - 12) use your understanding of writing expressions to translate the expression
The expansion of 1/4(x - 12) is x/4 - 3
What is expansion of expression?In order to expand and simplify an expression, we need to multiply out the parentheses and then simplify the resulting expression by collecting the like terms. Expanding brackets (or multiplying out) is the process by which we remove parentheses. It is the reverse process of factorisation.
For example 4(3-y) can be expanded by multiplying the factor 4 by 3 and y = 12- 4y
Similarly the expression 1/4(x - 12) can be expanded by firstly multiply the factor ¼ by x and 12
therefore 1/4(x - 12) = 1/4×x -12×1/4
= x/4 - 3
Therefore the expansion of 1/4(x - 12) is x/4 -3
learn more about expansion of expression from
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