The amount of money Sam and Bethan share is $30 and $24 respectively.
Describe the term ratio of the number?The term "to" is used to convey ratios verbally; we phrase "the ratio of one thing to of something." Ratios can be expressed as a fraction, by using the word "to," or by using a colon. Let's study more about ratios using this example of a form.For the stated question-
Adding 5 and 4 results in 9.54 divided by 9 equals 6. This is because, for every five that Sam receives, Bethan receives four.You may calculate the entire cost of one share by adding those. When you increase the number of eros Sams by the fact that there are 6 shares, Bethan receives each share.Thus, Sam's share = 5 x 54 /9
Sam's share = $30
Similarly, Bethan's share = 4 x 54 /9
Bethan's share = $24
Thus, the amount of money Sam and Bethan share is $30 and $24 respectively.
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Min Kurata deposited $875 for 3 months at 4% and made no other deposits or withdrawals. How much simple interest did his money earn? What is the amount in the account?
Hello,
I hope you and your family are doing well!
To find the amount of simple interest earned by Min Kurata's money, we can use the formula:
I = P * r * t
Where I is the amount of interest earned, P is the principal (the initial amount deposited), r is the annual interest rate, and t is the time in years.
In this case, the principal is $875, the annual interest rate is 4%, and the time is 3 months. Since the time is given in months, we need to convert it to years by dividing it by the number of months in a year (12):
t = 3 months / 12 months/year = 0.25 years
Plugging these values into the formula gives:
I = $875 * 0.04 * 0.25 = $35
So Min Kurata's money earned $35 in simple interest.
To find the total amount in the account, we can add the amount of interest to the principal:
total amount = $875 + $35 = $910
So the total amount in the account after 3 months is $910.
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Happy Holidays!
{ ( 2 , 3 ) , ( − 2 , 5 ) , ( 4 , 4 ) , ( − 4 , 5 ) , ( x , y ) }
Answer:
Its gotta be (6, 5)
Step-by-step explanation:
If we look at the sequence, the x coordinates are 2, -2, 4, -4. In the first & third x coordinates, there is an increment of 2 i. e. first 2 and then 2+2=4 so the fifth x coordinate should be 4+2=6.
The y coordinates are 3, 5, 4, 5. In the first and third y coordinates, there is an increment of 1 i. e. first 3 and then 3+1=4 so the fifth y coordinate should be 4+1=5.
The sequence goes like this
(2, 3), (-2, 5), (4, 4), (-4, 5), (6, 5), (-6, 5), (8, 6), (-8, 5), and so on
Prove that tanx sinx + cosx = secx
The proof that tan(x) sin(x) + cos(x) = sec(x) is represented by the trigonometric equation sec(x) = sec(x)
How to prove the trigonometric equationFrom the question, we have the following parameters that can be used in our computation:
tan(x) sin(x) + cos(x) = sec(x)
Express tan(x) as sin(x)/cos(x)
So, we have the following representation
sin(x)/cos(x) * sin(x) + cos(x) = sec(x)
Evaluate the products
So, we have the following representation
sin²(x)/cos(x) + cos(x) = sec(x)
Take the LCM
[sin²(x) + cos²(x)]/cos(x) = sec(x)
Express sin²(x) + cos²(x) as 1
So, we have
1/cos(x) = sec(x)
Evaluate
sec(x) = sec(x)
Hence, the equation has been proved
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1. In linear equation with two variables "ax + by = c", a and b cannot be equal to
(a) One
(b) Zero
(c) Integer
(d) Rational number
In linear equation with two variables "ax + by = c", a and b cannot be equal to Zero. which is the correct answer would be an option (A).
In a linear equation with two variables "ax + by = c", a and b can be any real numbers, including zero and integers. They can also be irrational numbers or rational numbers.
There is no restriction on the values of a and b in this equation.
As per the question, the following are all valid linear equations :
x + 0y = 2 ⇒ x = 2
0x + y = 1 ⇒ y = 1
Here above linear equations having only one variable so a and b cannot be equal to zero.
Thus, in a two-variable linear equation, a and b cannot be equal to zero.
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1. $3.96 x 5
2. 0.023 x 40
3. 0.67 x 61
4. $19.99 x 6
5. 0.13 x 57
6. 0.041 x 15
Answer:
1. $19.80
2. 0.92
3. 40.87
4. 119.94
5. 7.41
6. 0.615
Step-by-step explanation:
1. $3.96 x 5 = $19.80
2. 0.023 x 40
⇒ 0.023 x 10 = 0.23
⇒ 0.23 x 4 = 0.92
3. 0.67 x 61
⇒ 0.67 x 1 = 0.67
⇒ 0.67 x 60 = 40.2
⇒ 0.67 + 40.2 = 40.87
4. $19.99 x 6
⇒ 19.99 x 6 = 119.94
5. 0.13 x 57
⇒ 0.13 x 50 = 6.5
⇒ 0.13 x 7 = 0.91
⇒ 6.5 + 0.91 = 7.41
6. 0.041 x 15
⇒ 0.041 x 10 = 0.41
⇒ 0.041 x 5 = 0.205
⇒ 0.41 + 0.205 = 0.615
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Which equation is equivalent to 1\5x-3-2\3
The equivalent equation of the equation given as 1/5x - 3 - 2/3 is 1/5x - 11/3
How to determine the equivalent equationFrom the question, we have the following parameters that can be used in our computation:
1\5x-3-2\3
The fractions can be properly expressed as
1/5x - 3 - 2/3
Next, we evaluate the difference between -3 and -2/3
So, we have the following representation
1/5x - 3 - 2/3 = 1/5x - (9 + 2)/3
Evaluate the like terms
So, we have the following representation
1/5x - 3 - 2/3 = 1/5x - (11)/3
Remove the brackets
This gives
1/5x - 3 - 2/3 = 1/5x - 11/3
Hence, the equivalent equation is 1/5x - 11/3
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Carlos graphed the system of equations that can be used to solve x cubed minus 2 x squared 5 x minus 6 = negative 4 x squared 14 x 12. On a coordinate plane, 2 functions are shown. The functions intersect at (negative 3, negative 66), (negative 2, negative 32), and (3, 18) What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66
Answer: A
Step-by-step explanation: the other guy is wrong
Percents, decimals, and fractions
Answer:
1.) 0.25
2.) 0.50
3.) 0.125
4.) 2.25
Step-by-step explanation:
When turning percentages into decimals, you move the decimal point two places to the left.
EX:
25%
25.0 (move the decimal point two places to the left)
2.5
.25
0.25 (add any zeros if necessary)
Hope this helps!!
Tip:It doesn't matter where the decimal point is in a percentage, as long as you move the point two places to the left, you are still turning it into a decimal.
Joseph bought a brand new car 6 years ago for $22,250. The table below shows v(n), the value of the car t years since it was purchased
What is the correlation coefficient between 1 and v(n), and what does the coefficient indicate?
The correlation coefficient is -0.955 and indicates a very weak linear association
The correlation coefficient is -0.913 and indicates a very weak linear association
The correlation coefficient is -0.913 and indicates a strong negative linear association
The correlation coefficient is -0.955 and indicates a strong negative linear association
F.
G
H.
J
t
0
1
2
3
4
5
6
v(t) $22,250 $16.200 $11.700 $8,100 $6,300 $4.950 $3.825
5
Answer:
Step-by-step explanation:
The correlation coefficient between 1 and v(n) is -0.913, and this coefficient indicates a strong negative linear association. The correlation coefficient is a measure of the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.913, which indicates a strong negative relationship between 1 and v(n). This means that as the value of 1 increases, the value of v(n) decreases, and vice versa. This relationship is linear, which means that it can be described by a straight line. Overall, the correlation coefficient indicates a strong negative linear association between 1 and v(n).
if lin and diego want to run a race where they will both finish when the timer hits 30 seconds exactly but diego runs 5.5 meters per 1 second and lin runs 4 meters per 1 second how long of a head start should lin get?
Lin needs a 45-meter head start as Lin will travel 120 meters in 30 seconds, and Diego will travel 165 meters in 30 seconds.
Time = 30 sec
Lin's speed = 4m/s
Diego's speed = 5.5m/s
Distance travelled by ,
Lin = speed * time = 4 * 30
= 120 m
Diego = 5.5 * 30
= 165
Therefore, Diego will travel 45 m more than Lin in 1 sec.
Therefore, the head start should be of 45m.
The most crucial scientific notion is measurement is speed . Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
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Alexis is `56` inches tall.
What is her height in centimeters?
the answer is 142.24 cm
Answer:
142.24 centimeters tall
Step-by-step explanation:
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Please factorize [tex]\ln ^2\left(4-x\right)+\ln \left(4-x\right)\ln \left(x+\frac{1}{2}\right)-2\ln ^2\left(x+\frac{1}{2}\right)=0[/tex]
Answer:
[ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)] = 0----------------------------------
Given equation:
ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0Substitute:
ln (4 - x) = p, ln (x + 1/2) = qThen we have:
p² + pq - 2q² = p² - q² + pq - q² = (p + q)(p - q) + q(p - q) = (p - q)(p + q + q) = 0(p - q)(p + 2q) = 0Substitute back:
ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0 [ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)] = 0Which of the following choices is not an example of a unit rate?
earnings per hour dollars per pound calories per serving $25.50 for 5 gallons
Examples of unit rates are Dollars per pound calories and earnings per hour. The rest is not the unit rate.
What is the unit rate?
An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.
Earnings per hour are a unit rate since it is calculated for an hour.
Dollars per pound calories is a unit rate.
Serving $25.50 for 5 gallons is not a unit rate, the cost is for 5 gallons. If the cost is for 1 gallon then it will unit rate.
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y is directly proportional to the cube of x. If y = 20 when x is 3 find y when x is 5
The solution is y = 2500/27
The value of y is 2500/27 when x = 5
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the proportionality constant be represented as = k
Now , the value of k is calculated by
y is directly proportional to the cube of x
Substituting the values in the equation , we get
y ∝ x³
On simplifying the equation , we get
y = kx³ where k is the proportionality constant
Now ,
when x = 3 , y = 20
Substituting the values in the equation , we get
20 = k ( 3 )³
20 = k x 27
Divide both sides by 27 , we get
k = 20/27
So , the proportionality constant k = 20/27
Now , when x = 5 ,
y = 20/27 ( 5 )³
y = ( 20 x 5 x 5 x 5 ) / 27
y = 2500/27
Therefore , the value of y is 2500/27
Hence ,
The value of y is 2500/27 and the proportionality constant is 20/27
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Suppose that the function y = f(x) is decreasing on the interval (2,4). What can be said about the graph of y = - f(x)?
Answer:
Good question
yes so the answer will be on your screen in
3
2
1
here it is
Step-by-step explanation:
did u get it
hamid is playing a trivia game with multiple choice questions. each question has 222 correct answers among 555 answer choices. hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random. what is the probability that hamid guesses both answers correctly? round your answer to two decimal places.
10 is the probability that hamid guesses both answers correctly .
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
the likelihood that Hamid will correctly guess both answers
= 2/5x1/4 = X
= 0.4x0.25 = X
= 0.1 = X
= 0.1x 100 = 10
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What are the significant digits?
2.6 × 10'-15'
( -15 is an exponent btw)
Therefore, the number of significant figures is 4.
What are Significant Figures?Significant figures are the digits of a number that are meaningful in terms of accuracy or precision. These digits indicate the precision of a calculation or measurement.
What are Significant Figures Rules?Non-zero digits are always significant.Zeros between non-zero digits are always significant.Leading zeros are never significant.if we have trailing zeros then they are only significant if the number contains a decimal point.Given:
exponential notification is,
2.6 ×[tex]10^{-15}[/tex]
=365500
(real number)
= 3.655 × [tex]10^{5}[/tex]
(scientific notation)
= 3.655e5
(scientific exponential notation)
Therefore, the number of significant figures is 4.
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a 52-foot ladder is leaning against a vertical wall. if the bottom of the ladder is being pulled away from the wall at the rate of 8 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall?
The rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.
Let's call the distance between the bottom of the ladder and the wall x. We can express the area of the triangle in terms of x as follows:
Area = (1/2) * 52 * x
The area of the triangle is changing at a rate of 8 square feet per second as x changes at a rate of 8 feet per second. We can find the rate of change of the area with respect to x by taking the derivative of the area expression with respect to x:
d(Area)/dx = (1/2) * 52 = 26
Therefore, the rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.
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Choose the expression that is equivalent to a fraction with five raised to the negative third power in the numerator and the quantity three raised to the negative second power times five squared end quantity in the denominator and the entire fraction is cubed.
three raised to the sixth power divided by five raised to the fifteenth power
three squared divided by five raised to the fifth power
negative three raised to the sixth power divided by five raised to the fifteenth power
negative three squared divided by five raised to the fifth power
The equivalent expression is three raised to the sixth power divided by five raised to the fifteenth power. Option A
What is an equivalent expression?An equivalent expression is simply described as an expression having the same solution as the original expression but have a different arrangement of its variables and numbers.
Equivalent expressions are also known as expressions that works the same even they look different.
From the information given, we have that;
[tex][\frac{5^-3}{3^-2 * 5^2} ]^3[/tex]
Now, find the exponential values, we have
[tex][\frac{5^-^3^-^2^)^}{3^-^2}]^3[/tex]
Subtract the exponents, we have;
[tex][\frac{5^-^5}{3^-^2} ]^3[/tex]
Multiply the exponents by the cube, we get;
[tex]\frac{5^-^5^*^3}{3^-^2^*^3}[/tex]
Now, multiply the values
5^-15/3^-6
Hence, the value is 5^-15/3^-6
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Roxanne drew an indigo line that was 11 4/5 inches long. Then she drew a white line that was 6 3/5 inches long. How much longer was the indigo line than the white line?
The indigo line is longer than the white line by 5.2 inches.
What is a line?A line is a one-dimensional figure that has length but no width.
The length of the indigo line can be represented as I and the length of the white line as W.
The length of the indigo line is 11 4/5, i.e., I = 11 4/5 = 11.8
The given length of the white line is 6 3/5, i.e. W = 6 3/5= 6.6
The difference in length between the indigo and white lines is given by
I-W = 11.8 - 6.6 = 5.2
Hence, the indigo line is 5.2 inches longer than the white line.
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Practice identifying solutions to linear equations.
This equation has one solution.
5(x – 1) + 3x = 7(x + 1)
What is the solution?
Answer: x=12
Step-by-step explanation: PEMDAS
first solve the parentheses. that would make the equation 5x-5+3x=7x+7. Since there are no exponents, we don't need to do the e. no multiplication or division. so now we add and subtract to get x. first ill subtract 3x from both sides. 5x-5=4x+7. now subtract 5x from both sides. -5=-x+7. after that, subtract 7 from both sides. -12=-x. then divide by -1 so we can get only x and not a negative x. 12=x. so, the answer is x=12.
Walmart is open Monday through Saturday from 8.00 AM to midnight and Sunday from 10.00 AM to 8:00 PM. How many hours is it open in one week? Show all work!
Please explain
The total number of hours that it opens in one week will be 104 hours.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Walmart is open Monday through Saturday from 8:00 AM to 12:00 AM and Sunday from 10:00 AM to 8:00 PM.
From 8:00 AM to 8:00 PM, there are 12 hours and from 8:00 AM to 12:00 AM there are 4 hours. Then the total hours from Monday to Saturday will be calculated as,
⇒ 6 x (12 + 4)
⇒ 6 x 16
⇒ 96 hours
From 10:00 AM to 8:00 PM, there are only 10 hours. Then the total number of hours that it opens in one week will be given as,
⇒ 96 + 8
⇒ 104 hours
The total number of hours that it opens in one week will be 104 hours.
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Find the missing values in the table below so that it represents a linear function.
The value of y₂, y₃ and y₄ in the linear function are -21, -26 and -31 respectively.
How to represent linear function?Linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, to find the missing values in the table we have to use the equation of the linear function.
y = mx + b
let's find m.
using (4, -16) and (8, -36)
m = slope = -36 + 16 / 8 - 4
m = -20 / 4
m = -5
Hence, let's find y-intercept using (4, -16).
y = -5x + b
-16 = -5(4) + b
-16 + 20 = b
b = 4
Therefore, the equation is y = -5x + 4.
Let's find y₂, y₃ and y₄
y₂ = -5(5) + 4 = -25 + 4 = - 21
y₃ = -5(6) + 4 = -30 + 4 = -26
y₄ = -5(7) + 4 = -35 + 4 = - 31
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Select the correct answer. If ( x + 4 ) is a factor of polynomial p, which statement must be true? A. p ( - 4 ) > 0 B. p ( 4 ) = 0 C. p ( - 4 ) = 0 D.
Only if (C) p(-4) = 0 will x + 4 be the polynomial p's factor.
What are the factors?A factor is a number that completely divides another number.
To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
There is therefore no residual after division.
The numbers you multiply together to obtain another number are called factors.
A factor is therefore another number's divisor.
So, this is only true if, and only if, x + 4 is a factor of the polynomial p.
x + 4 = 0
x = -4
Comply with the polynomial equation that is:
p(-4) = 0
Therefore, only if (C) p(-4) = 0 will x + 4 be the polynomial p's factor.
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Complete question:
If (x + 4) is a factor of polynomial p, which statement must be true?
A.p(4) = 0
B. p(-4) > 0
C. p(-4) = 0
D. p(4) < 0
*NEED HELP ASAP* See screenshot below.
The equation that gives the tree's height at any time in slope-intercept form is y = (9/2)x + 5. Select 2nd option
How to write equation in slope-intercept form the tree's height at any time?
The slope-intercept form equation of a line can be given as y = mx + c
where m is the slope and c is the y-intercept
Let y and x represent the height and time respectively
slope (m) = y2-y1 / x2-x1
where x1 = 2, y1 = 14 and x2 = 4, y2 = 23 (from table)
m = 23-14 / 4-2 = 9/2
y = mx + c
14 = (9/2 )×2 + c
14 = 9 + c
c = 14-9 = 5
put m = 9/2 and c = 5 into y = mx + c. Thus, the equation will be:
y = (9/2)x + 5
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The Tri-State Pick 3 lottery game offers a choice of several bets. You choose
a three-digit number. The lottery commission announces the winning three-digit number,
chosen at random, at the end of each day. The "box" pays $83.33 if the number you choose
has the same digits as the winning number, in any order. Find the expected payoff for a
$1 bet on the box. (Assume that you chose a number having three different digits.)
Answer: The Tri-State Pick 3 lottery game offers a choice of several bets, including a "box" bet where you choose a three-digit number and win if the number you choose has the same digits as the winning number, in any order. The expected payoff for a $1 bet on the box is $83.33.
To find this expected value, we need to consider all the possible ways that the winning number could be chosen and calculate the probability of each outcome. Since the winning number is chosen at random, each of the 10 possible digits (0 through 9) is equally likely to be chosen for each of the three positions in the winning number.
Since the box bet pays off if the digits of your chosen number match the digits of the winning number, regardless of their order, the number of winning combinations is equal to the number of ways to arrange the three digits of the winning number. This is equal to 3! (3 factorial), which is equal to 6.
Since there are a total of 10 possible digits for each position and the winning number has three positions, there are a total of 10 x 10 x 10 = 1000 possible winning numbers. Of these, 6 will pay off for a box bet, so the probability of winning a box bet is 6/1000 = 0.006.
Since the expected value of a bet is equal to the probability of winning multiplied by the payoff, the expected value of a $1 bet on the box is 0.006 x $83.33 = $0.05. Therefore, the expected payoff for a $1 bet on the box is $0.05.
What percent is equal to the part-to-whole ratio 9:80?
Solve for p: 3+ 10p - 8p = 17
s i have 24 vanilla wafer cookies to put in a bag how many bags can i fill if i put the same number in each
She can put it into 2, 4, and 8 bags such that wafer cookies will same number in each bag.
What is a number system?A way to express or represent numbers is through the number system.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
We often employ decimal numbers because they are so widely used.
The base of the decimal number system, which uses ten digits from 0 to 9, is 10.
A system of writing numbers is known as a number system. It is a mathematical notation that uses digits or other symbols to consistently express the numbers in a given set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Given,
Number of wafer cookies = 64
To put into 2 bags = 64/2 = 32 in each bag.
To put into 4 bags = 64/4 = 16 in each bag.
To put into 8bags = 64/8 = 8 in each bag.
The complete question is : Lindy has 64 vanilla wafer cookies to put in bags. How many bags can she fill if she puts the same number in each bag and uses them all? Find all the possibilities. Explain your reasoning.
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Write the equation for a line parallel to y=-x + 7 that
passes through (7,-2).
Pls help!! Asap
Answer:
the slope is same, so y=-x+5 (x=7, y=-2 insert)
