The specified scalar or vector 5u(3v - 4w) is equal to -420i + 250j.
We can begin by distributing the scalar 5 to the vector 3v - 4w:
5u(3v - 4w) = 5u(3v) - 5u(4w)
Next, we can find the scalar multiples:
5u(3v) = 5(-4i + 2j)(3(3i - j)) = 5(-36i + 10j)
5u(4w) = 5(-4i + 2j)(4(-6j)) = 5(48i - 40j)
Now we can substitute these values back into the original expression:
5u(3v - 4w) = 5(-36i + 10j) - 5(48i - 40j)
Simplifying:
5u(3v - 4w) = -420i + 250j
Therefore, 5u(3v - 4w) = -420i + 250j.
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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What linear function equation is represented by this graph?
ANSWER: 1
3
x−4 just took the test
Answer:
The linear function is y = (1/3)x - 4.
Step-by-step explanation:
The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is
y = (1/3)x - 4.
scheduled payment of $1010 due five months ago and $1280 due today are to be repaid by a payment of $615 in four month and the balance in seven months. If money is worth 7.75% p.a , and the focal date is in seven months, what is the amount of the final payment?
The amount of the final payment is $1,004.99.
To solve the given problem, we will use the concept of present value. We need to find the present value of the two payments due in the past, and then find the future value of the remaining payments due in the future.
Let's first find the present value of the two past payments:
PV1 = $1010 / (1 + 0.0775/12)⁵ = $868.15
PV2 = $1280 / (1 + 0.0775/12)⁰ = $1280
Next, we can find the future value of the remaining payments due in the future
FV1 = $615 x (1 + 0.0775/12)⁴ = $664.69
FV2 = X
Now we can set up an equation to solve for X, the final payment:
PV1 + PV2 = FV1 + FV2 / (1 + 0.0775/12)⁷
Substituting the values we have calculated:
$868.15 + $1280 = $664.69 + X / (1 + 0.0775/12)⁷
Simplifying and solving for X
X = ($868.15 + $1280 - $664.69) x (1 + 0.0775/12)⁷ = $1,004.99
Therefore, the amount of the final payment is $1,004.99.
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N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Heracio used the computer 2 more hours to do homework than to shop online.
To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:
Videos: 10% of 40 hours = 4 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Shopping: 15% of 40 hours = 6 hours
To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 6 hours (shopping) = 2 hours
Therefore, Heracio used the computer 2 more hours to do homework than to shop online.
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A salesman earns $60,000 in commission in his first year and then has his commission reduced by 20% the second year. What percent increase in commission over the second year will give him $57,600 in the third year?
first off, let's find out how much he's making on the 2nd year, so since he's getting slashed by 20%, that means his new commission is 100% - 20% = 80%, so 80% of 60000, how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 60000}}{\left( \cfrac{80}{100} \right)60000}\implies 48000[/tex]
now, if we want to go up to 57600, that means we need to increase his commission by 57600 - 48000 = 9600.
So, if we take 48000(origin amount) to be the 100%, what's 9600 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 48000 & 100\\ 9600& x \end{array} \implies \cfrac{48000}{9600}~~=~~\cfrac{100}{x} \\\\\\ 5 ~~=~~ \cfrac{ 100 }{ x }\implies 5x=100\implies x=\cfrac{100}{5}\implies \boxed{x=20}[/tex]
Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.
Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag
Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.
The system of equations where the combination of the candies gives you a total of 22 points are:
x + y = 9
2x + 3y = 22
How can we create system of equations?To create the equations, we shall first define the variables:
x = the number of purple candies
y = the number of yellow candies
Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.
Then, we would make sure that the total number of candies selected is 9.
The first equation represents the total number of candies selected:
x + y = 9
The second equation represents the total number of points obtained:
2x + 3y = 22
Therefore, the system of equations is:
x + y = 9
2x + 3y = 22
This is a system of linear equations.
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Consider the graph of function f below. A diagonal curve declines through (negative 6, 7), (negative 5, 5), (negative 4, 3), (negative 3, 1), (3, negative 1, negative 3), (0, negative 5) and (1, negative 7) on the x y coordinate plane. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g? A. g(x) = f(x) - 1 B. g(x) = f(x + 4) C. g(x) = f(x - 1) D. g(x) = f(x) + 4
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The y-intercept for each function is given as follows:
f(x): y = -5.g(x): y = -1.Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
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Answer: D
Step-by-step explanation:
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?
A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).
Translation right a units: f(x - a).
Translation up a units: f(x) + a.
Translation down a units: f(x) - a.
The y-intercept for each function is given as follows:
f(x): y = -5.
g(x): y = -1.
Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
Two points on the path of a planet are A and B. The points A and B have coordinates (1, 4, 2) and (2, –1, 3) respectively.
The line l has equation r= (2i-j+3k)+µ(i-j+k)
(a) Calculate the distance between the points A and B .
(b) The line AB makes an acute angle θ with l. Calculate θ.
(c) The point P on the line l is where λ = p.
(i) for the vector AP how that :
AP. (i-j+k)=7+3p
(ii) Hence find the coordinates of the foot of the perpendicular from the point
A to the line l.
(c) Determine the cartesian equation of line l.
(d) Determine the cartesian equation of line A
Answer:
Step-by-step explanation:
(a) The distance between two points A(x1, y1, z1) and B(x2, y2, z2) is given by the formula: AB = √((x2-x1)² + (y2-y1)² + (z2-z1)²). Substituting the coordinates of points A and B into this formula gives: AB = √((2-1)² + (-1-4)² + (3-2)²) = √(14).
(b) The direction vector of line l is given by the vector (i-j+k). The direction vector of line AB is given by the vector AB = (2-1)i + (-1-4)j + (3-2)k = i - 5j + k. The cosine of the angle between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. Therefore, cos(θ) = (AB.(i-j+k)) / (|AB|.|i-j+k|) = ((i - 5j + k).(i-j+k)) / (√14.√3) = -3/√42. Hence θ = cos⁻¹(-3/√42).
©(i) Let P be the point on line l where λ = p. Then P has position vector r = (2i-j+3k)+p(i-j+k) = (2+p)i + (-1-p)j + (3+p)k. The vector AP is given by AP = r - a = ((2+p)i + (-1-p)j + (3+p)k) - (i+4j+2k) = pi - (5+p)j + pk. Taking the dot product of AP with (i-j+k), we get AP.(i-j+k)=7+3p.
©(ii) The foot of the perpendicular from point A to line l is the point on line l that is closest to point A. This point is obtained when AP is perpendicular to the direction vector of line l, which is (i-j+k). Therefore, AP.(i-j+k)=0. Substituting the expression for AP.(i-j+k), we get 7+3p=0, so p=-7/3. Substituting this value of p into the expression for r, we get r = (2-7/3)i - 8/3j + 2k. Hence, the coordinates of the foot of the perpendicular from point A to line l are (1/3,-8/3,2).
(d) The cartesian equation of a line with direction vector d and passing through a point with position vector a is given by r=a+λd. For line l, d=(i-j+k), a=(2i-j+3k), so its cartesian equation is r=(2i-j+3k)+λ(i-j+k).
Baristas at Hot Cocoa Coffee Shop tested their new hot chocolate machine. The following table shows the number of seconds the machine was turned on and the amount of hot chocolate that filled up the cup. Time (seconds) 4 8 12 16 20 24 Hot Chocolate Amount (fluid ounces) 5 7.5 9 11 13 16 Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time? scatter plot titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 5 comma 4, 7 and a half comma 8, 9 comma 12, 11 comma 16, 13 comma 20, and 16 comma 24 line graph titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 5 comma 4, 7 and a half comma 8, 9 comma 12, 11 comma 16, 13 comma 20, and 16 comma 24, with line segments connecting each point to the next scatter plot titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16 line graph titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16, with line segments connecting each point to the next
The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine.
Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?
The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine with the x-axis labeled time in seconds going from 0 to 28 and the y-axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16.
A scatter plot is a useful way to show the relationship between two variables, in this case, the amount of hot chocolate and time. Each point on the scatter plot represents a pair of values for time and hot chocolate amount. A line graph with line segments connecting each point to the next would not be appropriate because the data is not continuous, and there is no reason to assume that the relationship between time and hot chocolate amount is linear.
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34 Points! Multiple choice algebra question. Photo attached. Solve e^x>2.7. Thank you!
Answer:
B
Step-by-step explanation:
not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa
To reach escape velocity, a rocket must travel at the rate of 2.2×106 feet per minute. Express this number in standard notation.
The rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.
Expressing this number in standard notation.2.2×10^6 feet per minute is in its scientific notation.
In scientific notation, a number is written as the product of a coefficient and a power of 10.
So, 2.2×10^6 is already in scientific notation, where the coefficient is 2.2 and the power of 10 is 6.
If you want to convert it to standard notation, you can multiply the coefficient by the power of 10:
2.2×10^6 = 2.2 x 1,000,000 = 2,200,000
Therefore, the rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.
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what is the solution to
-15x=90
Answer:
option c) x=-6
Step-by-step explanation:
-15x = 90
= x = 90/-15
= x = (-6)
I arrived home to discover that my 50-foot by 40-foot basement has 18 inches of water in it! There are about 7.5 gallons in 1 cubic foot of water. How much water is in the basement?
Calculate using the most appropriate units to describe the amount of water, and state your answer in a meaningful sentence.
The amount of water in the basement is V = 22,500 gallons
Given data ,
To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.
First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:
50 feet x 40 feet x 1.5 feet = 3,000 cubic feet
There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:
3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons
Hence , there are 22,500 gallons of water in the basement
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Please help me with this
Answer:
a) y = 5.2727x + 32.5276
b) y = 5.2727(6) + 32.5276
= 64.1638 inches
c) y = 5.2727(7.153) + 32.5276
= 70.2432 inches
Someone help i really need help with this
Step-by-step explanation:
step A is incorrect.
-40/5 does not equal to -40/-5.
-40/-5 is equal to 40/5 as we can simplify the negative 1 out.
Answer:
The correct answer is step A
PLEASE ANSWER FAST!!!! NEED TO UNDERSTAND!!!
Step-by-step explanation:
X component = 4.5 - 2.1 = 2.4
Y component = 7.8 - 2.1 = 5.7
Find magnitude using Pythagorean theorem
m^2 = 2.4^2 + 5.7^2
magnitude = 6.18 units
Remember for a right triangle tangent Φ = opposite leg / adjacent leg
angle = arctan ( 5.7 / 2.4 ) = 67.2 degrees
I need help finding the answer to this question
Answer: I believe it would be 2/5.
Step-by-step explanation:
Reduction means the fraction is reduced to it's simplest form.
7/7=1
2/5=2/5
15/13=1 2/13
See as the '2/5' does not change in reduction.
So, '2/5' would be your answer.
Hope this helps! :)
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
A. The 51st note on a piano keyboard corresponds to a pitch of 440 cycles per second.
B. The pitch that is 73 notes higher on the keyboard has a frequency of about 1760 cycles per second.
How to determine frequency?A. Use the formula to find how many notes up the piano keyboard the pitch of 440 cycles per second corresponds to:
440 = 27.5 × 2⁽ⁿ⁻¹⁾/12
Dividing both sides by 27.5 and taking the logarithm with base 2 gives:
log₂(440/27.5) = (n-1)/12
n-1 = 12 × log₂(440/27.5)
n-1 = 12 × 4.1702 ≈ 50.042
n ≈ 51.042
Therefore, the pitch of 440 cycles per second is the 51st note up the piano keyboard.
B. Use the same formula to find the frequency of the pitch that is 73 notes up the keyboard:
73 = 1 + 12 log₂(f/27.5)
72 = 12 log₂(f/27.5)
6 = log₂(f/27.5)
f/27.5 = 2⁶
f = 27.5 × 2⁶
f ≈ 1760
Therefore, the frequency of the pitch that is 73 notes up the keyboard is approximately 1760 cycles per second.
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How many triangles exist with the given side lengths?
3in , 4in , 2in
Step-by-step explanation:
Only ONE .....there are three sides to a triangle and you supplied 3 sides.
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.
How to solveThe interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.
For groups of 15 students, we have that:
The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.
The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.
The quartiles for Bus 14 are given as follows:
Q1 = 12.
Q3 = 18.'
Hence the IQR is of:
IQR = Q3 - Q1 = 18 - 12 = 6.
The quartiles for Bus 18 are given as follows:
Q1 = 9.
Q3 = 16.
Hence the IQR is of:
IQR = Q3 - Q1 = 16 - 9 = 7.
Hence Bus 14 is the more consistent bus, due to the lower IQR.
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Four data sets are shown below. Set 1: {10, 19, 38, 50, 51} Set 2: {5, 21, 26, 39, 51} Set 3: {9, 38, 50, 50, 51} Set 4: {5, 28, 28, 28, 51} Which data set has the largest standard deviation? * Set 1 Set 2 Set 3 Set 4
Answer:
Set 1: {10, 19, 38, 50, 51}
Step-by-step explanation:
To calculate the standard deviation of a data set, we first find the mean of the data set. The mean is simply the sum of all the values in the data set divided by the number of values. For example, the mean of Set 1 is:
(10+19+38+50+51)/5=33.6
Next, we find the variance of the data set. The variance is the average of the squared differences between each value in the data set and the mean. For example, the variance of Set 1 is:
((10−33.6)^2+(19−33.6)^2+(38−33.6)^2+(50−33.6)^2+(51−33.6)^2)/5=323.84
Finally, we take the square root of the variance to get the standard deviation. For example, the standard deviation of Set 1 is:
[tex]\sqrt{323.84}[/tex]=17.99
We can repeat this process for each of the four data sets and find that Set 1 has the largest standard deviation.
hi I need help on questions 10-17 on this paper. if you are a expert (know what to do) of vertical angles and angle relationships in a triangle then please help me.
Answer:
10) 73
11) 107
12) 107
13) x = 23
14) 135
15) 45
16) 123, 28 29
17) 180 - 72 - 28 = 80
Angle K is 80
Step-by-step explanation:
10:
Vertical angels are congruent. The same measurement.
11:
Supplements angles add to 180
180 - 73 = 107
12:
Same as 11
13:
135
Vertical angles are congruent
5x + 20 = 3x + 66 Subtract 3x from both sides
2x + 20 = 66 Subtract 20 from both sides
2x = 46 Divide both sides by 2
x = 23
14:
5x + 20 Substitute 23 for x
5(23) + 20
115 + 20
135
15:
This angle is supplemental to ABC
180 - 135 = 45
16:
The sum of the interior angles of a triangle is 180
123 + x-2 + x -3 = 180 Combine like terms
118 +2x = 180 Subtract 118 from both sides
2x = 62 Divide both sides by 2
x = 31
x- 2
31 - 2 = 29
x - 3
31 - 3 = 28
Three angles 123, 29, 28
17:
The sum of the interior angles is 180
180 - 72 - 28 = 80
Helping in the name of Jesus.
Suppose that the function g is defined, for all real numbers, as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 106, and the sample
standard deviation, s, is found to be 10.
(a) Construct a 95% confidence interval about u if the sample size, n, is 16.
(b) Construct a 95% confidence interval about u if the sample size, n, is 11.
(c) Construct a 90% confidence interval about μ if the sample size, n, is 16.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
what is standard deviation ?A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.
given
(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :
x ± tα/2 * (s/√n)
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.
When we enter the values, we obtain:
106 ± 2.131 * (10/√16)
which is equivalent to:
106 ± 5.33
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
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Can anyone help me on this
can someone please helppp
Answer:
6 presents / minute
Step-by-step explanation:
We can represent the given information in a ratio:
amount of present wrapped : minutes it took to wrap
2/3 : 1/9
Then, we can multiply both sides by 9 (the reciprocal of 1/9) so that the right side of the ratio is 1 minute.
presents : minutes
2/3 : 1/9
× 9 × 9
6 : 1
So, Patricia can wrap 6 presents in 1 minute.
Caroline fills 3 quarts pint glasses with grape juice they grape juice container si too heavy so she uses a smaller 1 quart pint pitcher yo pour the juice how many times does she have to full the smaller pitcher un order to fill 3 of the glasses with grape juice?
Caroline needs to fill the 1-quart pitcher four and a half times in order to fill all 3 pint glasses.
Calculating how to fill a container rightSince Caroline has 3 pint glasses to fill, she needs to use the 1-quart pitcher multiple times. Each time she fills the pitcher, she can pour it into 2 pint glasses
From this, we can say that Caroline needs to pour a total of 3 x 1.5 = 4.5 quarts of juice.
What is a Pitcher
Pitcher is a container with a spout and handle, used for holding and pouring liquids. It is typically used for serving beverages such as water, juice, milk, or iced tea. Pitchers can be made from a variety of materials, including glass, ceramic, metal, or plastic.
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Find the missing value on the table below:
x y
2 4
? 6
4 8
Select the statement that is true a.16.7-8=2.9×3 b. 4×3.2=17.8-5 c.10.5÷5+1=8.8÷4 d.
Answer:
b
4 x 3.2 = 12.8
17.8 - 5 =12.8
so,
4 x 3.2 = 17.8-5
12.8=12.8
Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below.
The composition of functions is solved and the expressions are
a) ( g o f ) ( -1 ) = 1
b) ( g o f ) ( 0 ) = 4
c) ( f o g ) ( -1 ) = -2
d) ( f o g ) ( 4 ) = -1
Given data ,
Let the composition of function be represented as A
Now , the value of A is
a)
( g o f ) ( -1 ) = g ( f ( -1 ) )
On simplifying the function , we get
when x = -1 , f ( -1 ) = 2
g ( 2 ) = 1
So , ( g o f ) ( -1 ) = 1
b)
( g o f ) ( 0 ) = g ( f ( 0 ) )
On simplifying the function , we get
when x = 0 , f ( 0 ) = 0
g ( 0 ) = 4
So , ( g o f ) ( 0 ) = 4
c)
( f o g ) ( -1 ) = f ( g ( -1 ) )
On simplifying the function , we get
when x = -1 , g ( -1 ) = 2
f ( 2 ) = -2
So , ( f o g ) ( -1 ) = -2
d)
( f o g ) ( 4 ) = f ( g ( 4 ) )
On simplifying the function , we get
when x = 4 , g ( 4 ) = 1
f ( 1 ) = -1
So , ( f o g ) ( 4 ) = -1
Hence , the composition of function is solved
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