The system of equations has one unique solution.
The given system of equations consists of two equations:
4x - 5y = 5
-0.08x + 0.10y = 0.10
To determine the number of solutions, we can analyze the coefficients of the variables. In the first equation, the coefficient of x is 4, and in the second equation, the coefficient of x is -0.08. The coefficients are not proportional, indicating that the lines represented by the equations are not parallel. Since the lines intersect at a single point, the system of equations has one unique solution.
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2. In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language. If two Canadian households are selected at random, what is the probability that the first household speaks French, but the second household speaks English?
A. (0.23)(0.63) = 0.1449
B. 0.23 + 0.63 = 0.86
C. 0.23 + 0.63 – (0.23)(0.63) = 0.7451
D. 0.23/0.63=0.3650
The probability that the first household speaks French, but the second household speaks English is 0.1449
Let A be the event that the first household speaks French, and B be the event that the second household speaks English.
P(A) = probability that the first household speaks French
= 0.23
P(B|A) = probability that the second household speaks English given that the first household speaks French= 0.63
P(A and B) = probability that the first household speaks French and the second household speaks English
= P(A) × P(B|A)
= 0.23 × 0.63
= 0.1449
The correct option is (A) (0.23)(0.63) = 0.1449.
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Your bathtub holds 80 gallons of water. The cold faucet adds water to the tub at 2142 and 1 fourth gallons per minute. The hot water faucet adds water to the tub at 1121 and 1 half gallon per minute. The drain lets water out at a rate of 343 over 4 gallon per minute. You start the bath by turning both faucets on, but forget to close the drain. The tub fills in 27 minutes. How large is the bathtub?
How will you solve the question?
To determine the size of the bathtub, we can use the information provided about the fill rate of the cold and hot water faucets, the drain rate, and the time it takes to fill the tub. The size of the bathtub is 42,471 gallons.
To determine the size of the bathtub, we can use the information provided about the fill rate of the cold and hot water faucets, the drain rate, and the time it takes to fill the tub. By subtracting the drain rate from the combined fill rate of the faucets and multiplying it by the time, we can find the net fill rate. Dividing the total amount of water filled in the given time by the net fill rate will give us the size of the bathtub.
First, we calculate the net fill rate per minute: (2142 1/4 + 1121 1/2) - (343/4) = 2142 1/4 + 1121 1/2 - 343/4.
Next, we multiply the net fill rate per minute by the time in minutes (27) to find the total water filled in that time.
To compute the net fill rate per minute, we need to convert the mixed numbers to improper fractions and perform the necessary calculations:
2142 1/4 + 1121 1/2 - 343/4 = 2149/4 + 2243/2 - 343/4 = 2149/4 + 4486/4 - 343/4 = (2149 + 4486 - 343)/4 = 6292/4 = 1573/1 = 1573.
The net fill rate per minute is 1573 gallons.
Next, we calculate the total water filled in 27 minutes:
Total water filled = net fill rate per minute × time in minutes = 1573 × 27 = 42,471 gallons.
Therefore, the size of the bathtub is 42,471 gallons.
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Lynn had an opening balance of $179.30 in her checking account. She made deposits of $432 and had bank charges of $5.35. If her closing balance was $353.82, how much did she write in checks?
Lynn wrote checks for approximately $252.13.To find out how much Lynn wrote in checks, we need to calculate the total amount of money she added and subtracted from her opening balance.
Starting with an opening balance of $179.30, Lynn made deposits of $432. So far, her balance would be $179.30 + $432 = $611.30.
Next, we subtract the bank charges of $5.35 from the balance: $611.30 - $5.35 = $605.95.
Finally, we compare this balance to the closing balance of $353.82. Lynn must have written checks for the difference between the two balances: $605.95 - $353.82 = $252.13.
Therefore, Lynn wrote checks for approximately $252.13.
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Find the value of the power.5−5The value of the power is
The value of the given power, 5^(-5), can be found by calculating the reciprocal of 5 raised to the power of 5.
To find the value of 5^(-5), we need to calculate the reciprocal of 5 raised to the power of 5, which is equivalent to raising 5 to the power of -5.
Using the rule for negative exponents, we know that a negative exponent indicates the reciprocal of the base raised to the positive exponent. In this case, 5^(-5) is equal to 1/(5^5).
To simplify further, we can calculate 5^5, which is equal to 3125. Therefore, the reciprocal of 3125 is 1/3125.
Hence, the value of the power 5^(-5) is 1/3125.
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Find a number written in binary system that when read as a number in decimal system is five times
smaller than the same number read as a decimal (notice that any binary number can be also
interpret as a decimal, for example 111 can represent a binary number but also can be seen as one
hundred and eleven - a decimal).
Treat this question like a puzzle, just try different numbers and this way guess the answer.
Considering, the binary number to be represented is a two-digit number, the binary number to be represented is 0101.
Let us assume that the binary number to be represented is a two-digit number.
Therefore, it can be represented as xy where x and y are either 0 or 1.
We know that any binary number can also be interpreted as a decimal number.
For example, 111 can represent a binary number but also can be seen as one hundred and eleven - a decimal.
The number written in the binary system is thus 2x + y.
The number written in the decimal system is = x × 10 + y, which is 5 times greater than the binary number when the binary number is written in the decimal system.
5(2x + y) = x × 10 + y
10x - 9y = 0
y = 0, 10, 20, 30, ... are some solutions, but y cannot be greater than 10, as it is a two-digit number in the binary system.
As a result, the only feasible solution is y = 0.5(2x)
= 10x
x = 5
Therefore, the binary number to be represented is 0101.
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Describe the translation. Part a: first blank is the number, followed by left or right. Part b: first blank is the number, followed by up or down.
(-1, 4) —> (6, -2)
Translation is a term that defines a type of transformation in mathematics, specifically in geometry. It is defined as the movement of an object from one place to another in a two-dimensional coordinate plane without altering its shape, size, and orientation.
It is a type of rigid motion that is used in various fields of mathematics, especially in algebra and geometry. In the given (-1, 4) —> (6, -2) scenario, the translation is described below:
Part a: Since the value of x is increasing from -1 to 6, the first blank is filled with 7 (6 - (-1) = 7), which represents a right translation.
Part b: Since the value of y is decreasing from 4 to -2, the first blank is filled with 6 (4 - (-2) = 6), which represents a down translation.
Therefore, the translation can be described as (7, -6), i.e., the point is moved 7 units to the right and 6 units down.
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What is the value of q for which the lines qx−7y+10=20 and 4y+3x+9=0 are parallel to each other?
To determine the value of q for which the lines qx - 7y + 10 = 20 and 4y + 3x + 9 = 0 are parallel to each other, we need to compare their slopes.
First, we'll rewrite the equations in the standard form y = mx + b, where m represents the slope of the line:
For the line qx - 7y + 10 = 20, rearranging the equation gives us:
qx - 7y = 10
-7y = -qx + 10
y = (q/7)x - 10/7
For the line 4y + 3x + 9 = 0, rearranging the equation gives us:
4y = -3x - 9
y = (-3/4)x - 9/4
From the equations, we can see that the slopes are q/7 for the first line and -3/4 for the second line.
For two lines to be parallel, their slopes must be equal. Therefore, we can equate the slopes and solve for q:
q/7 = -3/4
Cross-multiplying, we have:
4q = -21
Dividing both sides by 4, we find:
q = -21/4
Therefore, the value of q for which the lines are parallel to each other is -21/4.
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Using the same trigonometric function, express the cos 115 degrees as a function of a positive acute angle
we can express cos 115 degrees as cos 25 degrees, which is a function of a positive acute angle
To express cos 115 degrees as a function of a positive acute angle, we can use the concept of reference angles.
The reference angle is the positive acute angle formed between the terminal side of an angle and the x-axis. It is the smallest angle between the terminal side and the x-axis.
To find the reference angle for 115 degrees, we subtract 90 degrees from 115 degrees:
Reference angle = 115 degrees - 90 degrees = 25 degrees
Since cosine is an even function, the cosine of the reference angle will be the same as the cosine of the original angle:
cos 115 degrees = cos 25 degrees
Therefore, we can express cos 115 degrees as cos 25 degrees, which is a function of a positive acute angle.
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In what order, from shortest to longest, will Sakura use the pieces of twine in the mobile? Drag the numbers into the correct order from shortest to longest.
The order from shortest to longest, in which Sakura will use the pieces of twine is :
0.75 foot 4/5 foot = 0.8 foot5/6 foot = 0.83 foot How to find the order ?Firstly, let's convert all lengths to a common format, decimals or fractions. Let's use decimals:
5/6 foot = 0.83 foot (approx.)
0.75 foot
4/5 foot = 0.8 foot
So, the order will be the piece of twine that is 0.75 foot, then the piece that is 0.8 foot (or 4/5 foot in fraction form), and finally the piece that is 0.83 foot (or 5/6 foot in fraction form).
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The full question is:
Sakura is making a mobile. She has a spool of twine that she cuts into
lengths of 5/6 foot, 0.75 foot, and 4/5 foot.
Drag the numbers into the correct order from shortest to longest.
A spinner is divided into six equal-sized sectors labeled 1 through 6. Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun. What are the mean and standard deviation of X? Mu Subscript x Baseline = 1, Sigma Subscript x Baseline = 1. 29 Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1. 29 Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1. 67 Mu Subscript x Baseline = 10, Sigma Subscript x Baseline = 2. 78.
Given that a spinner is divided into six equal-sized sectors labeled 1 through 6 and Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun.
We need to find the mean and standard deviation of X.Mean of X:Mean of a binomial distribution is given by the formula:μx = n * Pwhere n is the number of trials and P is the probability of success.Here, n = 12 and P = Probability of getting 1 on a single spin = 1/6.∴ μx = 12 × (1/6) = 2Standard Deviation of X:Standard deviation of a binomial distribution is given by the formula.
σx = √(n × P × Q)Where Q is the probability of failure and is given by:Q = 1 - PHere, n = 12, P = Probability of getting 1 on a single spin = 1/6 and Q = 1 - P = 5/6.∴ σx = √(12 × (1/6) × (5/6))= √1 = 1Hence, the mean and standard deviation of X are:Mean = 2Standard deviation = 1Therefore, the option that represents the correct values of mean and standard deviation of X is:Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1.
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If 8 is multiplied by a fraction greater than 1, which of the could be the product
A 5
-
2
B 8
(C) 7
(D) 16
If 8 is multiplied by a fraction greater than 1, the product could be 16. Therefore, the correct option is (D) 16.
Multiplying 8 by a fraction greater than 1 will result in a number greater than 8.The greater the value of the fraction, the greater the product will be. Thus, the product of 8 multiplied by a fraction greater than 1 could be 16, since 8 × 2 = 16.
Therefore, the correct answer is option (D) 16.
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What is the vertex of the absolute value function defined by f(x)=|x+9|+1?
The vertex of the absolute value function defined by f (x) = |x + 9 | + 1 = (-9, 1).
The modulus function is also called the absolute value of a function gives the magnitude or absolute value of a number irrespective of the number being positive or negative.
It always gives a non-negative value of any number or variable. (-9, 1).
The function given is
ƒ(x) = |x + 9| + 1
The vertex is denoted as (h, k)
h: |x + 9| = 0
x + 9 = 0
x = - 9
k can be found by substituting the x value in the given function.
ƒ(-9) = |-9 + 9| + 1
f(-9) = 0 + 1
f(-9) = 1
Therefore, the vertex of the absolute value given function (-9, 1).
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(m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (4)(m1)(23) + (1)(m0)(24)
Simplify each term to complete the expansion.
(m + 2)4 = m4 +
m3 +
m2 +
m +
The expanded form of (m + 2)4 is m4 + m3 + m2 + m + 16. To simplify each term, we can apply the binomial expansion formula.
The formula states that for any binomial expression (a + b)n, the expanded form can be written as the sum of the terms obtained by raising each term to the power of n and multiplying it by the corresponding coefficients. In this case, our binomial expression is (m + 2)4.
Expanding the binomial using the formula, we get:
(m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (4)(m1)(23) + (1)(m0)(24)
Simplifying each term, we have:
(m4)(20) = m4
(4)(m3)(21) = 4m3
(6)(m2)(22) = 12m2
(4)(m1)(23) = 8m
(1)(m0)(24) = 16
Combining all the simplified terms, we get:
m4 + 4m3 + 12m2 + 8m + 16
Therefore, the expansion of (m + 2)4 is m4 + m3 + m2 + m + 16.
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A bottle holds 1/5 L of water Sarah uses 10 bottles of water to make juice. How many liters of water does Sarah used to make juice?
Sarah uses 10 bottles of water to make juice, and each bottle holds 1/5 L of water. To find the total amount of water Sarah used, we multiply the number of bottles by the amount of water in each bottle. Therefore, Sarah used a total of 2 liters of water to make juice.
Given that each bottle holds 1/5 L of water, we can calculate the total amount of water used by multiplying the amount of water per bottle by the number of bottles.
Amount of water per bottle = 1/5 L
Number of bottles = 10
To find the total amount of water, we multiply:
Total water = (Amount of water per bottle) x (Number of bottles)
= (1/5 L) x (10 bottles)
= 2 L
Therefore, Sarah used a total of 2 liters of water to make juice.
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1. Determine p(3) if p(x) = 2x^3 - 6x^2- 36x - 36
To determine the value of p(3), we substitute 3 into the given polynomial p(x) = [tex]2x^3 - 6x^2 - 36x - 36[/tex]. After substituting, we find that p(3) = -36.
To evaluate p(3), we substitute 3 for x in the polynomial p(x) = [tex]2x^3 - 6x^2 - 36x - 36[/tex]. Plugging in 3, we get p(3) = [tex]2(3)^3 - 6(3)^2 - 36(3) - 36[/tex]. Simplifying this expression step by step, we find:
p(3) = 2(27) - 6(9) - 36(3) - 36
= 54 - 54 - 108 - 36
= -144.
Therefore, p(3) is equal to -144. By substituting the value of 3 into the polynomial expression, we can calculate the corresponding value of the polynomial at that point. In this case, the polynomial evaluates to -144 when x is equal to 3.
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The temperature of a certain liquid increases by 150 C in 3 minutes when it is heated. At this rate, what is the increase in temperature in 7 minutes?
The temperature of a certain liquid increases by 350 C in 7 minutes when it is heated. Determine the rate of temperature increase in the liquidRise in temperature / time taken = 150/3= 50C/min.
Given, The temperature of a certain liquid increases by 150 C in 3 minutes when it is heated.The rate of temperature increase in the liquid can be calculated as follows:Rise in temperature / time taken = 150/3= 50C/minTo find the increase in temperature in 7 minutes, the following formula can be used:Increase in temperature = Rate of temperature increase × time taken= 50 × 7= 350CTherefore, the temperature of a certain liquid increases by 350 C in 7 minutes when it is heated.
To find the increase in temperature in 7 minutes when the temperature of a certain liquid increases by 150 C in 3 minutes when it is heated, follow these steps:Step 1: Determine the rate of temperature increase in the liquidRise in temperature / time taken = 150/3= 50C/minTherefore, the rate of temperature increase in the liquid is 50C/min.Step 2: Calculate the increase in temperature in 7 minutesIncrease in temperature = Rate of temperature increase × time taken= 50 × 7= 350CTherefore, the temperature of a certain liquid increases by 350 C in 7 minutes when it is heated.
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y = 0.15x + 8.27 museum collected from 2007 to 2014. best fit line
The best fit line for the data collected from 2007 to 2014 is represented by the equation Y = 0.15x + 8.27.
To determine the best fit line, we utilize linear regression analysis, which aims to find the line that minimizes the overall distance between the line and the data points. In this case, the equation of the best fit line is in the form Y = mx + b, where "m" represents the slope and "b" represents the y-intercept.
Given the equation Y = 0.15x + 8.27, we can interpret it as follows:
The slope (m) of 0.15 indicates that for every unit increase in the independent variable (x), the dependent variable (Y) increases by 0.15 units.
The y-intercept (b) of 8.27 indicates that when x is zero (2007 in this case), the expected value of Y is 8.27.
Therefore, the equation Y = 0.15x + 8.27 represents the best fit line for the data collected from 2007 to 2014, where Y represents the dependent variable (museum collections) and x represents the independent variable (years).
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Adam’s credit card calculates finance charges using the adjusted balance method and a 30-day billing cycle. The table below shows his use of that credit card over three months. Date Amount ($) Transaction 4/1 626. 45 Beginning balance 4/10 37. 41 Purchase 4/12 44. 50 Purchase 5/3 65. 50 Payment 5/16 24. 89 Purchase 5/20 104. 77 Payment 6/6 23. 60 Payment 6/10 15. 00 Purchase 6/14 51. 85 Purchase If Adam’s credit card has an APR of 14. 63%, what is Adam’s balance at the end of June? a. $629. 42 b. $629. 66 c. $627. 27 d. $628. 40 Please select the best answer from the choices provided A B C D.
Adam's credit card uses the adjusted balance method and has a 30-day billing cycle. Given his credit card activity over three months and an APR of 14.63%, we need to determine Adam's balance at the end of June.
To calculate Adam's balance at the end of June, we need to consider his credit card activity and apply the adjusted balance method. The adjusted balance method takes into account the beginning balance, transactions during the billing cycle, and payments made.
Let's calculate Adam's balance step by step:
1. April:
- Beginning balance: $626.45
- Purchases: $37.41 and $44.50
- Ending balance: $626.45 + $37.41 + $44.50 = $708.36
2. May:
- Payments: $65.50 and $104.77
- Purchases: $24.89
- Ending balance: $708.36 - $65.50 - $104.77 + $24.89 = $563.98
3. June:
- Payments: $23.60
- Purchases: $15.00 and $51.85
- Ending balance: $563.98 - $23.60 + $15.00 + $51.85 = $607.23
To calculate the finance charges, we need to multiply the average daily balance by the daily periodic rate. The daily periodic rate can be calculated by dividing the APR by 365.
Average daily balance = (Beginning balance + Ending balance) / 2
= ($626.45 + $607.23) / 2
= $616.84
Daily periodic rate = 14.63% / 365 = 0.0004016
Finance charges = Average daily balance * Daily periodic rate * Billing cycle
= $616.84 * 0.0004016 * 30
= $7.41 (rounded to the nearest cent)
Finally, to find Adam's balance at the end of June, we add the finance charges to the ending balance:
Balance at the end of June = Ending balance + Finance charges
= $607.23 + $7.41
= $614.64
Therefore, Adam's balance at the end of June is approximately $614.64, which is not one of the options provided.
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Yaw spent 2/5 of his monthly salary on food, 1/2 of the remaining on the rent and 1/4 of what still remained on drinks. If he still had ¢80 left, a. find his salary per month. b. how much did he spend on food? C. how much did he spend on rent?
Therefore, Yaw spent approximately ¢142.22 on food and ¢53.34 on rent.
Let's solve the problem step by step:
a. To find Yaw's monthly salary, we need to reverse the calculations. We start with the remaining amount after all the expenses and work our way back.
Let's assume Yaw's salary per month is S.
Yaw spent 2/5 of his salary on food, which means he has 3/5 of his salary remaining.
Then, he spent 1/2 of the remaining amount on rent, leaving him with 1/2 * (3/5) = 3/10 of his salary.
Finally, he spent 1/4 of what still remained on drinks, leaving him with 3/10 * (3/4) = 9/40 of his salary.
We are given that Yaw still had ¢80 left, which represents 9/40 of his salary:
(9/40)S = ¢80
To find S, we can solve the equation:
S = (¢80 * 40) / 9
S ≈ ¢355.56
Therefore, Yaw's monthly salary is approximately ¢355.56.
b. Yaw spent 2/5 of his salary on food. Substituting the value of S we found in part a:
(2/5) * ¢355.56 = ¢142.22
Yaw spent approximately ¢142.22 on food.
c. Yaw spent 1/2 of the remaining amount on rent. Substituting the value of S we found in part a:
(1/2) * (3/10) * ¢355.56 = ¢53.34
Yaw spent approximately ¢53.34 on rent.
Therefore, Yaw spent approximately ¢142.22 on food and ¢53.34 on rent.
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When the Foresthill Wildfire band returned from a recent competition, 24 of the students attended school before realizing they had contracted a strong flu virus. The virus quickly spread and each day the number of students with the flu increased by an estimated 30%. How many people will have the flu after five days?
The number of people who have the flu after 5 days is A = 88 people
Given data,
To calculate the number of people who will have the flu after five days, we need to consider that the number of students with the flu increases by 30% each day.
Let's start with the initial number of students who contracted the flu, which is 24.
After the first day, the number of students with the flu will increase by 30% of 24:
30% of 24 = (30/100) * 24 = 7.2
The exponential equation is represented as
x ( t ) = x₀ × ( 1 + r )ⁿ
So, x ( 5 ) = 24 ( 1.3 )⁵
On simplifying , we get
x ( 5 ) = A = 88 people
Hence , after five days, approximately 88 students will have the flu.
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Sam’s brother is 4 years older than him. Their mother is 3 times older than Sam. Their ages together total 74 years. How old are the family members?
Let's assign variables to represent the ages of Sam, his brother, and their mother.
Let:
Sam's age = S
Brother's age = B
Mother's age = M
According to the given information, we can form the following equations:
1. Brother's age is 4 years older than Sam's age: B = S + 4
2. Mother's age is 3 times older than Sam's age: M = 3S
3. The sum of their ages is 74: S + B + M = 74
We can substitute the values from equations 1 and 2 into equation 3 to solve for the ages:
S + (S + 4) + 3S = 74
5S + 4 = 74
5S = 70
S = 14
Substituting the value of S back into equations 1 and 2:
B = S + 4 = 14 + 4 = 18
M = 3S = 3(14) = 42
Therefore, Sam is 14 years old, his brother is 18 years old, and their mother is 42 years old.
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In the study, palmitic acid was determined to be the most effective chemical, providing three times the protection of stearic acid and was ten percentage points higher in protection than linoleic acid. The effectiveness precentages of stearic acid plus linoleic acid together were five percentage points higher than palmitic acid. What is the effectiveness of stearic acid in repelling mosquitoes?
The effectiveness of stearic acid in repelling mosquitoes can be calculated by using the data given in the statement and the following formula.Effectiveness of Stearic Acid = (Effectiveness of stearic acid plus linoleic acid) - (Effectiveness of linoleic acid)
Substituting the given values, we get the effectiveness of stearic acid as: (Effectiveness of stearic acid + linoleic acid) - (Effectiveness of linoleic acid)=(5+10)−(Effectiveness of linoleic acid)=15 - Effectiveness of linoleic acidNow, it is given that palmitic acid was three times more effective than stearic acid.
Hence, the effectiveness of stearic acid can be written as: Effectiveness of stearic acid = 1/3 (Effectiveness of palmitic acid)Also, palmitic acid was 10% more effective than linoleic acid. Hence, the effectiveness of palmitic acid can be written as:Effectiveness of palmitic acid = 1.10
(Effectiveness of linoleic acid)Substituting the value of effectiveness of palmitic acid in the equation for effectiveness of stearic acid, we get:Effectiveness of stearic acid = 1/3 (Effectiveness of palmitic acid)= 1/3 x 1.10 (Effectiveness of linoleic acid)= 0.366 (Effectiveness of linoleic acid)
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Which statement correctly compares the values in the statement?
StartAbsoluteValue negative 0.45 EndAbsoluteValue blank box StartAbsoluteValue negative 0.0045 EndAbsoluteValue
The correct statement that compares the values is "The absolute value of -0.45 is greater than the absolute value of -0.0045."
Absolute value is a mathematical operation that yields the distance between a number and zero on the number line, regardless of its sign. In the given statement, we are comparing the absolute values of two negative numbers: -0.45 and -0.0045.
The absolute value of a negative number is always positive. In this case, the absolute value of -0.45 is greater than the absolute value of -0.0045. This is because -0.45 is closer to zero than -0.0045 on the number line, thus resulting in a larger absolute value. The absolute value of -0.45 is 0.45, while the absolute value of -0.0045 is 0.0045. Therefore, the statement correctly states that the absolute value of -0.45 is greater than the absolute value of -0.0045.
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the cuboid is then split apart into these smaller cuboids
If a cuboid is split apart into smaller cuboids, it means that the original cuboid is divided or partitioned into multiple smaller cuboids. Each smaller cuboid will have its own dimensions and volume.
To represent this visually, let's consider a cuboid with dimensions [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. When it is split apart, it can be divided into smaller cuboids with dimensions [tex]\(a_1\), \(b_1\), \(c_1\), \(a_2\), \(b_2\), \(c_2\),[/tex] and so on.
The original cuboid can be represented as:
[tex]\[\text{{Original Cuboid}} = a \times b \times c\][/tex]
And after splitting it into smaller cuboids, the total volume remains the same:
[tex]\[\text{{Total Volume}} = a \times b \times c = (a_1 \times b_1 \times c_1) + (a_2 \times b_2 \times c_2) + \ldots\][/tex]
Each smaller cuboid may have different dimensions, but their volumes add up to the volume of the original cuboid.
Note: The dimensions of the smaller cuboids may vary depending on how the original cuboid is split apart.
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If 980 = 2x X 5y X 7z, find the values of x, y and z... pls help with working
Answer:
x = 2, y = 1, z = 7-------------------------
We are given that, 980 = 2x × 5y × 7z
We need to find the values of x, y, and z.
Find the prime factorization of 980.
980 can be written as:
980 = 2 × 2 × 5 × 7 × 7Compare the given expression with the prime factorization of 980.
2 × 2 × 5 × 7 × 7 = 2x × 5y × 7zIt can be observed that:
2x = 2 × 2 ⇒ x = 25y = 5 ⇒ y = 17z = 7 × 7 ⇒ z = 7Hence, the values of x, y, and z are 2, 1, and 7 respectively.
Diego collected x kg of recycling. Lin collected 2/5 more than that
Lin collected 1.4 times that of Diego's recycling collection.
Let x be the amount Diego collected in kg of recycling.
Then, Lin collected 2/5 more than that is
x + 2/5x = 7/5x kg of recycling
.Let x be the amount of recycling Diego collected in kg.
Then, Lin collected 2/5 more than that, so Lin's collection is
x + 2/5x,
which is equivalent to 7/5x kg of recycling.
This means that Lin's recycling collection is 1.4 times that of Diego's.'
For example, if Diego collected 10 kg of recycling, then Lin collected
2/5 * 10 = 4 kg
more than that, which is a total of 14 kg.
Therefore, Lin collected 1.4 times that of Diego's recycling collection.
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Edgar owns 234 shares of Cawh Consolidated Bank, which he bought for $21. 38 apiece. Each share pays a yearly dividend of $3. 15. Edgar also owns two par value $1,000 bonds from Cawh Consolidated Bank. The bonds had a market value of 105. 166 when he bought them, and pay 8. 3% interest yearly. Which aspect of Edgar’s investment in Cawh Consolidated Bank offers a greater percent yield, and how much greater is it? a. The stocks have a yield 6. 43 percentage points greater than that of the bonds. B. The stocks have a yield 6. 84 percentage points greater than that of the bonds. C. The bonds have a yield 1. 05 percentage points greater than that of the stocks. D. The bonds have a yield 9. 13 percentage points higher than that of the stocks.
The stocks of Cawh Consolidated Bank offer a yield that is 6.84 percentage points greater than that of the bonds.
To compare the yields of Edgar's investment in Cawh Consolidated Bank stocks and bonds, we need to calculate the yields of both investments and then find the difference between them.
For the stocks, the yield can be calculated by dividing the annual dividend per share by the purchase price per share and multiplying by 100. In this case, the yield of the stocks is [tex][{\frac{3.15}{21.38}] *100= 14.71 \%.[/tex]
For the bonds, the yield is the annual interest payment divided by the market value of the bonds, multiplied by 100. The yield of the bonds is [tex][{\frac{8.3}{105.166}]* 100 = 7.89 \%[/tex] .
Now, to determine which aspect of Edgar's investment offers a greater percent yield, we find the difference between the yield of the stocks and the yield of the bonds. The difference is [tex]14.71 \% - 7.89 \% = 6.82 \%[/tex].
Therefore, the correct answer is option B: The stocks have a yield [tex]6.84[/tex]percentage points greater than that of the bonds.
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Janice works at a cell phone company. She wants to make a presentation to her team about the features of a new phone. She makes a scale drawing of the phone using a scale of 1 inch to 0. 5 centimeter. The length of the scaled drawing is 28 inches, and its width is 15 inches. What are the actual dimensions of the phone? A. The length is 14 inches, and the width is 7. 5 inches. B. The length is 56 inches, and the width is 30 inches. C. The length is 56 centimeters, and the width is 30 centimeters. D. The length is 14 centimeters, and the width is 7. 5 centimeters. E. The length is 12 centimeters, and the width is 5. 5 centimeters.
The actual dimensions of the phone are 14 inches in length and 7.5 inches in width, confirming option A as the correct answer.
Janice created a scale drawing of the phone using a scale of 1 inch to 0.5 centimeters. The length of the scaled drawing is given as 28 inches, and its width is 15 inches. To find the actual dimensions of the phone, we need to convert the scaled dimensions back to their actual values.
Since the scale is 1 inch to 0.5 centimeters, we can use this ratio to convert the scaled dimensions to actual dimensions. For the length, we have 28 inches in the scaled drawing, so the actual length would be 28 inches * 0.5 centimeters/inch = 14 centimeters. Similarly, for the width, we have 15 inches in the scaled drawing, so the actual width would be 15 inches * 0.5 centimeters/inch = 7.5 centimeters.
Therefore, the actual dimensions of the phone are 14 inches in length and 7.5 inches in width. Option A correctly represents these dimensions.
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Christine has 6 red scarves and 3 blue scarves.Each scarf has 2 stripes how many stripes does christine have on her scarves. Write an equation to represent and solve the problem
Let's denote the number of red scarves as 'r' and the number of blue scarves as 'b'. Each scarf has 2 stripes.
Therefore, the total number of stripes on the red scarves would be 2 * r, and the total number of stripes on the blue scarves would be 2 * b.
Given that Christine has 6 red scarves and 3 blue scarves, we can write the equation to represent the total number of stripes as:
Total number of stripes = 2 * r + 2 * b
Substituting the values, we get:
Total number of stripes = 2 * 6 + 2 * 3
Simplifying the equation:
Total number of stripes = 12 + 6
Total number of stripes = 18
Therefore, Christine has a total of 18 stripes on her scarves.
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Tamara likes to go hiking and tries to hike for at least 350 minutes every week. On Thursday she hiked for 1 mile in the morning and 3 miles in the evening. On Thursday, she hiked with a friend for 4 miles. On Saturday, she hiked for 5 miles. On Sunday, she hiked for 4 miles. If she hiked a total of 340 minutes all week and it takes her the same amount of time to hike each mile, how many minutes does it take her to hike each mile?
If Tamara hiked a total of 340 minutes and her goal is to hike for at least 350 minutes every week, it means she fell short by 10 minutes.
Since it takes her the same amount of time to hike each mile, we can calculate the time it takes her to hike each mile.
On Thursday, she hiked a total of 1 + 3 + 4 = 8 miles. On Saturday and Sunday, she hiked a total of 5 + 4 = 9 miles. So in total, she hiked 8 + 9 = 17 miles.
To find the time it takes her to hike each mile, we divide the total time she hiked (340 minutes) by the total distance she covered (17 miles). Therefore, it takes her 340/17 = 20 minutes to hike each mile.
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