Answer:
-270
Step-by-step explanation:
120 down to -150= 270 decrease=(-270)
If y varies directly with x and y=-16 when x=8, find y when x=2
Answer:
y=-4
Step-by-step explanation:
The answer is going to be -4 as when y=-16 x=8.
The number 21x09 is equal to 22 00, correct to 2 significant figures. find the value of x if 21x09 is a perfect square
No, the number 21x09 is not equal to 22 00, correct to 2 significant figures. To determine the value of x if 21x09 is a perfect square, we need to consider its prime factorization.
The prime factorization of 21x09 is 3^2 * 7 * x * 13. For a number to be a perfect square, each prime factor must have an even exponent. Since 13 is the only prime factor with an odd exponent, we need to choose a value of x that cancels out the odd exponent of 13.
To achieve this, x must be a multiple of 13. Therefore, any value of x that is a multiple of 13 will make 21x09 a perfect square.
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Jack had m math problems to complete during his vacation. He solved the same
number of problems every day and finished them all in 5 days.
Suppose Jack was solving 15 problems per day. Use this information and the answer
to part (a) to build an equation.
Answer:
M/5 =15
Step-by-step explanation:
The answer to part a was m/5. m/5 is the amount of questions Jack does per day. If 15 is supposedly the number of question he does per day, then m/5 and 15 are equal. Making m/5=15. Good luck fellow RSM student.
A triangle has sides with lengths of 6 meters, 8 meters, and 10 meters. Is it a right triangle?
Answer:
No
Step-by-step explanation:
becuase no
Zaboca Printing Limited (ZPL) has only one working printer. Eight (8) customers submitted their orders today Monday 6th June 2022. The schedule of delivery of these orders are as follows:
Jobs (in order of arrival) Processing Time (Days) Date Due
A 4 Monday 13th June 2022
B 10 Monday 20th June 2022
C 7 Friday 17th June 2022
D 2 Friday 10th June 2022
E 5 Wednesday 15th June 2022
F 3 Tuesday 14th June 2022
G 8 Thursday 16th June 2022
H 9 Saturday 18th June 2022
All jobs require the use of the only printer available; You must decide on the processing sequence for the eight (8) orders. The evaluation criterion is minimum flow time.
i. FCFS
ii. SOT
iii. EDD
iv. CR
v. From the list (i to iv above) recommend the best rule to sequence the jobs
The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.
The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.
In this case, applying the EDD rule, the sequence of jobs would be as follows:
D (Due on Friday 10th June)
F (Due on Tuesday 14th June)
E (Due on Wednesday 15th June)
C (Due on Friday 17th June)
G (Due on Thursday 16th June)
H (Due on Saturday 18th June)
A (Due on Monday 13th June)
B (Due on Monday 20th June)
By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.
Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.
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Consider a signal represented by the function ƒ (t) = { ={& −1 < t < 0 0 < t < 1 where f(t) = f(t+2). (a) Sketch f(t) for -2 ≤ t ≤ 2. (b) Obtain a general Fourier series representation for f. (c) Use MATLAB to plot both f(t) and the partial sum of the Fourier series f5(t) on the same set of axes for -1 ≤ t ≤ 1, where 5 f5 (t) = ao +(an cos(nwt) + b₁ sin(nwt)). n=1
Part (a): Part (b): Part (c): The signal is given by ƒ(t) = { ={& −1 < t < 0 0 < t < 1 where ƒ(t) = ƒ(t + 2).
The signal can be represented graphically by plotting ƒ(t) versus t. The sketch of the function ƒ(t) can be shown as follows:Using the trigonometric Fourier series formula we can write the general form of the Fourier series as follows: where wn is the frequency of the Fourier series and n is the harmonic number.
For this function, we can use the Fourier series formula for the square wave of amplitude one and period 2 as follows: where n is the harmonic number and wn = 2π/T = π.
the general Fourier series representation for ƒ(t) is given by;We can use MATLAB to plot both ƒ(t) and the partial sum of the Fourier series f5(t) on the same set of axes for -1 ≤ t ≤ 1, where 5 f5(t) = ao + (an cos(nwt) + b1 sin(nwt)). n=1.The following is the MATLAB code:The graphical representation of the function ƒ(t) and the partial sum of the Fourier series f5(t) can be shown as follows:In conclusion, the signal is represented by the function
ƒ(t) = { ={& −1 < t < 0 0 < t < 1 where ƒ(t) = ƒ(t + 2).
The sketch of the function ƒ(t) was plotted and the Fourier series representation was obtained by using the Fourier series formula for the square wave of amplitude one and period 2. Finally, MATLAB was used to plot both ƒ(t) and the partial sum of the Fourier series f5(t) on the same set of axes for -1 ≤ t ≤ 1, where 5 f5(t) = ao + (an cos(nwt) + b1 sin(nwt))
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Analyze the polynomial function f(x) = (x+4)-(3 - x) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph off behaves like y= for large values of Ixl. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is :
The y-intercept is (0, 1). a. the end behavior of the graph is that it behaves like y = 2x + 1 for large values of |x|. b. the y-intercept of the graph of the function is y = 1.
(a) The end behavior of the graph of the function is that it behaves like y = 2x + 1 for large values of |x|.
To determine the end behavior, we look at the highest degree term in the polynomial function, which is x. The coefficient of this term is 2, which is positive. This tells us that as x becomes very large in either the positive or negative direction, the function will also become very large in the positive direction. Therefore, the end behavior of the graph is that it behaves like y = 2x + 1 for large values of |x|.
(b) To find the x-intercepts of the graph of the function, we set f(x) = 0 and solve for x:
(x+4)-(3-x) = 0
2x + 1 = 0
x = -1/2
Therefore, the x-intercept of the graph of the function is x = -1/2.
To find the y-intercept of the graph of the function, we set x = 0 and evaluate f(x):
f(0) = (0+4)-(3-0) = 1
Therefore, the y-intercept of the graph of the function is y = 1.
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solve for x pleaseeeeeee
do all square numbers have an odd number of factors
No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.
A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.
When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.
However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.
In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.
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What is the first step to solving the quadratic equation x2=9over 16
Answer:
divide both sides by 2
Step-by-step explanation:
divide both sides by 2 then simplify and get x = 9 over 32
Answer:
Transposing square to rhs,it becomes root
Step-by-step explanation:
\(x^{2} =9/16\)
\(x=\)\(\sqrt{9}/\sqrt{16\\\) (transposing square to rhs,it becomes root)
\(x= 3/4\)
Hope it helps...Pls mark as Brainliest!!!
11. The data are the number of text messages you send a day.
Find the mean, median, and mode of the data.
10, 12, 20, 8, 6, 10, 18
Answer:
mean= 12
median= 10
mode= 10
Step-by-step explanation:
mean: add up all values, then divide by how many values you have(84/7=12)
median: when sorted, value in middle(See pic)
mode: value that appears most
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
The probability of selecting an orange marble is 0.33.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of times each marble is selected.
Green = 4
Black = 6
Orange = 5
Total number of times all marbles are selected.
= 4 + 6 + 5
= 15
Now,
The probability of selecting an orange marble.
= 5/15
= 1/3
= 0.33
Thus,
The probability of selecting an orange marble is 0.33.
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The diameter of a hydrogen atom is about 1.05 cross times 10 to the power of negative 10 end exponentmeters. a protein molecule has an overall length of 3000 times (or 3 cross times 10 cubed times) the diameter of a hydrogen atom. what is the length of the protein molecule, in meters, if it were written in scientific notation?
The length of the protein molecule, in meters, is 208 × 10⁻⁹m.
What is an atom?An atom is a matter particle that defines a chemical element uniquely. An atom is made up of a central nucleus and one or more negatively charged electrons. The nucleus is positively charged and contains one or more protons and neutrons, which are relatively heavy particles.To find the length of the protein molecule:
Diameter of hydrogen atom = 104 × 10⁻¹⁰m
We are given that A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom.
Length of protein molecule = 2000 × Diameter of the hydrogen atomLength of protein molecule = 2 × 10⁺³ × 1.04 × 10⁻¹⁰Length of protein molecule = 2 × 1.04 × 10⁻¹⁰⁺³Length of protein molecule = 2 × 1.04 × 10⁻⁷Length of protein molecule = 2.08 × 10⁻⁷Length of protein molecule = 208 × 10⁻⁷⁻²Length of protein molecule = 208 × 10⁻⁹mTherefore, the length of the protein molecule, in meters, is 208 × 10⁻⁹m.
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The correct question is given below:
The diameter of a hydrogen atom is about 1.04 cross times 10 to the power of negative 10 end exponent meters. A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation?
About 1/10 of the bones in your body are in your skull. Your hands have about 1/4 of the bones in your body . Write and solve an equation to find the fraction of the bones in your body that are in your hands or skull.
Answer:
Step-by-step explanation:
so to get the answer, we just add the number of bones in your hands and bones in your skull1/4 (bones in hands) + 1/10 (bones in skull)we can only add fractions that have the same denominator (bottom number in a fraction) so we change the numbers to have a common denominator:5/20 + 2/20 = 7/20so 7/20 of your bones are in your hands or skull
how many ways can Aileen choose 2 pizza toppings from a menu of 19 toppings if each topping can only be chosen one
Answer:
There are 342 different combinations.
Step-by-step explanation:
Ok, Aileen is choosing toppings for a pizza.
She can choose two.
There are 19 options that can be chosen once.
The first thing we need to do, is find all the "selections".
Here we have two selections:
Topping number 1
Topping number 2.
Now we need to find the number of options for each one of these selections:
Topping number 1: Here we have 19 options.
Topping number 2: Here we have 18 options (because one was already taken in the previous selection)
The total number of combinations is equal to the product between the numbers of options.
C = 19*18 = 342
There are 342 different combinations.
Find the linearization of the function f(x,y) = √x^2 + 16y^2 at the point (3,1), and use it to approximate f(2.9.1.1)
The linearization of the function f(x,y) = √(x² + 16y²) is L(x,y) = 5 + 3(x-3)/5 + 16(x-1)/5 and the approximation of f(2.9.1.1) is 5.26.
The linearization of a function f(x,y) at the point (a,b) is given by,
L(x,y) = f(a,b) + fₓ(a,b)*(x - a) + fᵧ(a,b)*(y - b)
where fₓ and fᵧ are the partial derivatives of function 'f' with respect to 'x' and 'y' respectively.
Given the function is,
f(x,y) = √(x² + 16y²)
Now partially differentiate the above function firstly with respect to 'x' and then by 'y' we get,
fₓ(x,y) = (1/(2√(x² + 16y²)))*(2x) = x/√(x² + 16y²)
fᵧ(x,y) = (1/(2√(x² + 16y²)))*(32y) = 16y/√(x² + 16y²)
Given the point (a,b) = (3,1).
So substituting we get,
fₓ(3,1) = 3/√(9+16) = 3/√25 = 3/5
fᵧ(3,1) = 16/√(9+16) = 16/√25 = 16/5
f(3,1) = √(9 + 16) = √25 = 5
Then the linearization of the function f(x,y) = √(x² + 16y²) at the point (3,1) we get,
L(x,y) = f(a,b) + fₓ(a,b)*(x - a) + fᵧ(a,b)*(y - b)
L(x,y) = 5 + 3(x-3)/5 + 16(x-1)/5
Now approximating by this linear equation we get,
L(2.9, 1.1) = 5 + 3(2.9 - 3)/5 + 16(1.1 - 1)/5 = 5 - 0.3/5 + 1.6/5 = (25-0.3+1.6)/5 = 26.3/5 = 5.26
And
f(2.9, 1.1) = √((2.9)² + 16(1.1)²) = 5.27 (Rounding up to 2 decimal places)
So we can approximate using the linear function.
Hence, the linearization of the function is L(x,y) = 5 + 3(x-3)/5 + 16(x-1)/5 and the approximation of f(2.9.1.1) is 5.26.
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Determine the vertex of a parabola represented by the equation f (x ) = x2 - 2x - 8, with two symmetric points on the parabola (2, -8) and (0, -8).
The two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The vertex of a parabola in standard form, f(x) = a(x - h)² + k, is at the point (h, k).
We can rewrite the given equation, f(x) = x² - 2x - 8, in standard form by completing the square:
f(x) = x² - 2x - 8
= (x² - 2x + 1) - 1 - 8
= (x - 1)² - 9
So the vertex of the parabola is at the point (1, -9), where h = 1 is the x-coordinate of the vertex, and k = -9 is the y-coordinate of the vertex.
To verify that points (2, -8) and (0, -8) are symmetric about the vertex, we can calculate the axis of symmetry, which is x = h, or x = 1 in this case.
The distance between the vertex (1, -9) and the point (2, -8) is the same as the distance between the vertex and the point (0, -8), since these points have the same y-coordinate:
d((1, -9), (2, -8)) = d((1, -9), (0, -8))
Using the distance formula, we can calculate the left-hand side:
d((1, -9), (2, -8)) = √((2 - 1)² + (-8 - (-9))²)
= √(1 + 1)
= √(2)
Using the distance formula again, we can calculate the right-hand side:
d((1, -9), (0, -8)) = √((0 - 1)² + (-8 - (-9))²)
= √(1 + 1)
= √(2)
Hence, the two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).
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Please answer this friends ?
Answer: Rs. 6075
40500×(15/100)= 6075
Step-by-step explanation:
three cards are drwan at random, without replacement, from a standard deck of 52 playing cards. compute the (conditional) probability that the first card drawn is spade, given that the second and third cards have spades.
If the second and third cards have a spade then the probability that the first card drawn is a spade is 21.2%.
Probability can be described as a field of mathematics that determines how likely a thing is to happen. When there is uncertainty about the outcome of an event we consider the probabilities of certain results or outcomes.
There are a total of 13 spades in a deck of 52 playing cards. So if the second and third cards have spades then there are 11 spades remaining.
The formula for probability can be given as;
probability = number of favorable outcomes or events ÷ total number of outcomes or events
probability = 11 / 52 = 0.212
Converting it into percentage;
probability = 0.212 × 100 = 21.2%
Therefore, the probability that the first card drawn is a spade is calculated to be 21.2%.
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Mislabeled seafood In 2013 the environmental group Oceana (usa.oceana.org) analyzed 1215 samples of seafood purchased across the United States and genetically compared the pieces to standard gene fragments that can identify the species. Laboratory results indicated that 33% of the seafood was mislabeled according to U.S. Food and Drug Administration guidelines.
Construct a 95% confidence interval for the proportion of all seafood sold in the United States that is mislabeled or misidentified.
Using the z-distribution, it is found that the 95% confidence interval for the proportion of all seafood sold in the United States that is mislabeled or misidentified is (0.3036, 0.3564).
z-distribution interval:In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).For this problem:
1215 samples, hence \(n = 1215\).33% was mislabeled or misidentified, hence \(p = 0.33\).95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so \(z = 1.96\). The lower limit of this interval is:\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.33 - 1.96\sqrt{\frac{0.33(0.67)}{1215}} = 0.3036\)
The upper limit of this interval is:\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.33 + 1.96\sqrt{\frac{0.33(0.67)}{1215}} = 0.3564\)
The 95% confidence interval for the proportion of all seafood sold in the United States that is mislabeled or misidentified is (0.3036, 0.3564).
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Use any problem stragey
A farm planter corn. Wheat and grass in total of 88 fields he planted twice as many fields in corn than in wheat and half as many in grass than in corn how many fields did he plant each
Answer:
He planted 44 fields do corn, and 22 each for wheat and grass.
Step-by-step explanation:
There are three subjects. If we have something that was 2x as much as wheat, and then something half as much as that, we know that the wheat and grass are equal. Then, you just need to think about how a 50 25 25 split would work out of 88.
is this correct HURRY I HAVE LIKE 3 MINS
Answer:
Yes its 20.9
Step-by-step explanation:
On friday night, the owner of chez pierre in downtown chicago noted the amount spent for dinner for 28 four-person tables. 110 118 124 185 129 128 122 139 120 95 119 99 191 130 84 110 149 123 76 175 143 83 110 76 165 67 102 151. click here for the excel data file.
(a) Find the mean, median, and mode. (Round your answers to 2 decimal places.) NOTE - (It also asks for the count)
(b) Are the data symmetric or skewed? If skewed, which direction?
multiple choice
a. Symmetric
b. Skewed right
c. Skewed left
- Mean: 119.43- Median: 118.50- Mode: 110 - Count: 28
To find the mean, we add up all the values and divide by the number of observations. In this case, the sum of the values is 3342, and since there are 28 observations, the mean is 3342/28 = 119.43.
The median is the middle value when the data is arranged in ascending order. In this case, there are 28 observations, so the median is the average of the 14th and 15th values. When the data is ordered, the 14th value is 118 and the 15th value is 124. Therefore, the median is (118 + 124)/2 = 118.50.
The mode is the value that appears most frequently in the dataset. In this case, the value 110 appears three times, which is more than any other value. Hence, the mode is 110.
The count simply refers to the number of observations in the dataset, which is 28 in this case.
(b) The data is skewed right.
When data is symmetric, it means that the values are evenly distributed around the mean, resulting in a bell-shaped curve. In this case, the data is not symmetric. Looking at the dataset, we can observe that there are several smaller values on the left side, while the right side has a few larger values. This indicates a right skew or positive skewness.
Skewness refers to the asymmetry of a distribution. In a right-skewed distribution, the tail of the distribution extends towards the right, indicating a longer right tail. Therefore, the correct answer is b. Skewed right, indicating that the data is positively skewed.
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B. Write S if the expression is a sum of two cubes, D if a difference of two cubes, and N if neither.
1. 27x⁶ + y³=
2. 81 - b¹⁵=
3. 64x³ - 9z⁹=
4. 36m¹² - n⁶
5. 1 - d¹²=
6. 729 - y²⁹=
7. 343 - y⁶=
8. 4x³ + 8 =
9. 144 -125y² =
10. 64j⁶- k⁹=
Answers:
SNNNDNDNND==========================================================
Explanation:
Question 1
27x^6 = (3x^2)^3 which is one cube and y^3 is another cube
Therefore 27x^6+y^3 is a sum of two cubes.
It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.
----------------------------------------
Question 2
81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.
We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.
----------------------------------------
Question 3
64x^3 = (4x)^3 is a perfect cube
but 9z^9 is not a perfect cube
We can see this if we computed 9^(1/3) and the result is a non-whole number.
The answer here is the same as the previous question.
----------------------------------------
Question 4
36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension 36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.
----------------------------------------
Question 5
1 is a perfect cube since 1 = 1^3
d^12 is a perfect cube because d^12 = (d^4)^3
Therefore, we have a difference of two cubes.
----------------------------------------
Question 6
729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.
However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.
The overall expression is "neither".
----------------------------------------
Question 7
343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube
y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.
We have a difference of cubes.
----------------------------------------
Question 8
4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.
----------------------------------------
Question 9
144^(1/3) isn't a whole number, so we get a similar result to problem 8.
----------------------------------------
Question 10
64j^6 = (4j^3)^3 is one cube
k^9 = (k^3)^3 is another cube
We have a difference of cubes
Model Real Life The Elephant
Building is 335 feet high. A real
Asian elephant is 12 feet tall. If
29 real elephants could stand on
top of each other, would they reach
the top of the building?
Answer:
Yes
Step-by-step explanation:
The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?
They are asking if 29 12' elephants are as tall as as a 335' building:
29 × 12' = 348' elephant stack
because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.
Mrs. Holt writes the expression 6/4 + 5/8 . She ask her students to simplify the expression and write the answer as a percentage. The table shows the responses of four students. Which student correctly simplifies Mrs. Holt ‘s expression into percentage?
Answer:
I don't see the table, but if you do 6/4 + 5/8 = 12/8+5/8 = 17/8.
17/8 = 2.125 = 212.5%
Step-by-step explanation:
The student who correctly simplifies the expression should have an answer
of 212.5%
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Mrs. Holt writes the expression 6/4 + 5/8 .
She asks her students to simplify the expression which is,
= (6/4 + 5/8).
= (2×6 + 1×5)/8.
= (12 + 5)/8.
= 17/8.
And write the answer as a percentage which is,
= (17/8)×100%.
= 212.5%
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Can some help me I’m in a hurry
Answer:
a. No
b. 2.25 days
Step-by-step explanation:
The answer is NO due to two different variables in the equation.
When Carla looked out at the school parking lot, she noticed that for every 2 minivans, there were 5 other types of vehicles. If there are 161 total vehicles in the parking lot, how many of them are minivans?
Answer:
46 of the total vehicles are minivans
Step-by-step explanation:
Let the number of minivans be x
and the number of other types of vehicles be y
From the question,
Carla noticed that for every 2 minivans, there were 5 other types of vehicles.
This means the ratio of minivans to other types of vehicles is 2:5.
Therefore,
x:y = 2:5
We can then write that
x/y = 2/5
∴ 5x = 2y ...... (1)
Also from the question,
There are 161 total vehicles in the parking lot
That is
x + y = 161 ...... (2)
From equation (2), we can write that
y = 161 - x
Put this into equation (1)
5x = 2y
Then
5x = 2(161-x)
5x = 322 -2x
5x+2x = 322
7x = 322
x = 322/7
x = 46
Since x represent the number of minivans
Hence, 46 of the total vehicles are minivans.
You buy a sheet with 10 stamps. Some are 45 cents and some are 30 cents. If it cost $4. 20 how many of each did you get
You bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.
Let's assume you bought x stamps that cost 45 cents each and y stamps that cost 30 cents each.
From the given information, we can create two equations:
The total number of stamps is 10: x + y = 10.
The total cost is $4.20: 45x + 30y = 420 (since the cost is given in cents).
Now we can solve this system of equations to find the values of x and y.
We can multiply the first equation by 30 to eliminate y:
30x + 30y = 300.
Now we have a system of equations:
30x + 30y = 300,
45x + 30y = 420.
Subtracting the first equation from the second equation, we get:
45x + 30y - (30x + 30y) = 420 - 300,
15x = 120,
x = 120/15,
x = 8.
Substituting the value of x back into the first equation:
8 + y = 10,
y = 10 - 8,
y = 2.
Therefore, you bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.
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Multiply
(-4) • (-8)
A. -32 B. -12 C. 12 D. 32
Answer:
D. 32
Step-by-step explanation:
= ( -4 ) x ( -8 )
= 32