Answer:
The constants are 7 and 1
Step-by-step explanation:
A spherical balloon is being inflated at a rate of 8 cm³s-1. Find the rate of change of the surface area when the radius is 10 cm.
Answer:
1.6
Step-by-step explanation:
Firstly, we know the rate of change of volume [tex]v'=8[/tex].
The equation for surface area is: [tex]A = 4\pi r^2[/tex].
The derivative (rate of change) is then: [tex]A'=8\pi r*r'[/tex]
The equation of the volume of a sphere is: [tex]V=\frac{4}{3}\pi r^3[/tex].
The derivative (rate of change) is then: [tex]V' = 4\pi r^2 * r'[/tex].
This means that [tex]r'=\frac{V'}{4\pi r^2}[/tex].
We can then plug that into our equation for [tex]A'[/tex] and get:
[tex]A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}[/tex]
After that, we can just plug in:
[tex]2*\frac{8}{10}=1.6[/tex]
In triangle XYZ, m∠Y = 71.02° and m∠Z = 29.6°. Determine the measure of the exterior angle to ∠X.
18.98°
60.4°
100.62°
79.38°
The measure of exterior angle to ∠X is 79.38°. So, option 4 is correct.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.
Given,
In ΔXYZ, m∠Y=71.02° and m∠Z=29.6°
We know that,
The angles sum in a triangle is 180°.
m∠X+m∠Y+m∠Z=180°
m∠X+71.02°+29.6°=180°
m∠X=180°-100.62°
m∠X=79.38°
Therefore, the measure of exterior angle to ∠X is 79.38°.
So, option 4 is correct.
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When planning a more strenuous hike, Brett figures that he will need at least 0.5 liters of water for each hour on the trail. He also plans to always have at least 1.80 liters of water as a general reserve. If x represents the duration of the hike (in hours) and y represents the amount of water needed (in liters) for a hike, the following inequality describes this relation: y> 0.5x + 1.8 Which of the following would be a solution to this situation?
a.) Having 3 liters of water for 4.5 hours of hiking
b.) Having 2 liters of water for 2.5 hours of hiking
c.) Having 4.5 liters of water for 4 hours of hiking
d.) Having 2.5 liters of water for 3 hours of hiking
Option C is correct,4.5 is greater than 3.8, so this solution does work.
If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.
Inequality
In mathematics, an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
The first option is having 0.5 liters of water for 4.5 hours of hiking. So will plug 3 in for y and 4.5 in for x:
y > 0.5x + 1.8
3 > 0.5(4.5) + 1.8
3 > 4.05
But 3 is not greater than 4.05, this solution does not work.
The next option is having 2 liters of water for 2.5 hrs of hiking:
2 > 0.5(2.5) + 1.8
2 > 3.05
But 2 is not greater than 3.05, so this solution does not work.
Option c is having 4.5 liters of water for 4 hours of hiking:
4.5 > 0.5(4) + 1.8
4.5 > 3.8
So 4.5 is greater than 3.8, this solution does work.
The last option is having 2.5 liters of water for 3 hours of hiking:
2.5 > 0.5(3) + 1.8
2.5 > 3.3
2.5 is not greater than 3.3, so this solution does not works
Option c is correct,4.5 is greater than 3.8 so this solution does work.
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y > 0.5x + 1.8
3 > 0.5(4.5) + 1.8
3 > 4.05
But 3 is not greater than 4.05, this solution does not work.
2 > 0.5(2.5) + 1.8
2 > 3.05
But 2 is not greater than 3.05, so this solution does not work.
4.5 > 0.5(4) + 1.8
4.5 > 3.8
2.5 > 0.5(3) + 1.8
2.5 > 3.3
2.5 is not greater than 3.3, so this solution does not works
Option c is correct,4.5 is greater than 3.8 so this solution does work.
Finley mows 1 lawn every 12 minutes. If his rate of lawn mowing remains the same, which method could be used to determine the number of minutes for him to mow 6 lawns? Responses
Answer:
6(12), multiplication
Step-by-step explanation:
Since it takes 12 minutes to mow one lawn, multiplying would give you the answer of how long 6 lawns would take, which is 72
−1+log 6 (2x+3)−log 6 (2x)=0
Answer:
Step-by-step explanation:
Let us solve the equation for X-
-1+log 6 (2x+3)-log 6 (2x)=0
adding +1 to both sides-
-1+1+log 6(2x+3)-log 6 (2x)=0+1
log 6(2x+3)-log 6 (2x)=1 . . . (1)
using logarithmic rule,
log a - log b= log(a/b)
equation (1) becomes,
log [6(2x+3)/6(2x)]=1 . . .(2)
equation (2) becomes,
log[(2x+3)/2x]=1....(3)
Again using the logarithmic rule,
log a = b
is equivalent to 10∧b = a
hence equation 3 becomes,
10∧1= (2x+3)/2x
i.e. 10 = (2x+3)/2x. . .(4)
multiplying both sides by 2x, considering x is not 0.
equation( 4) becomes
20x = 2x+3. . .(5)
subtracting 2x from both sides
equation (5) becomes,
18x=3
dividing both sides by 3,
we get,
x=6
Hence value of x is 6.
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Find the fifth power of the following transition matrix. Then find the probability that state 2 changes to state 4 after five repetitions of the experiment. Compute A5. A =O (Type an integer or decimal for each matrix element. Round to three decimal places as needed.) 0.4 0.1 0.1 0.2 0.2 0.1 0.3 0.2 0.1 0.3 A= 0.2 0.1 0.2 0.1 0.4 0.4 0.1 0.1 0.2 0.2 0.1 0.3 0.2 0.1 0.3
Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.
To find the fifth power of the matrix A, we can simply multiply A by itself five times:
A^5 = A * A * A * A * A
= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)
= (0.22 0.12 0.14 0.14 0.34)
To find the probability that state 2 changes to state 4 after five repetitions of the experiment, we need to look at the element in the fifth power matrix A^5 that corresponds to state 2 and state 4. This element is located in the second row and fourth column of the matrix, which is 0.14.
Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.
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A^5 = A * A * A * A * A
= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)
= (0.22 0.12 0.14 0.14 0.34)
Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.
QUESTION DOWN BELOW! PLASE HELP DUE SOON!
Answer: its 18 im pretty sure
Step-by-step explanation:
A carnival game gives variety bags as prizes. The game operator uses 100 balloons and 68 stickers to put into a certain number of bags. How many balloons and how many stickers can go in each bag if they make the greatest number of bags possible so that each bag has the same number of balloons and the same number of stickers?(1 point)
Responses
25 stickers and 17 balloons
25 stickers and 17 balloons
25 balloons and 17 stickers
25 balloons and 17 stickers
4 balloons and 4 stickers
4 balloons and 4 stickers
50 balloons and 34 stickers
50 balloons and 34 stickers
Answer:
D is the answer
Step-by-step explanation:
Using bags that will make the balloon and the stickers have the same number in each bag, mere looking at the answers, 100/2 gives you 50 while 68/2 gives you 34. it means that it was splitted equally into the two bags.
An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. Now there are concerns that if the true mean is actually higher than this they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set significance level = :05, test to see if the insurance company should be concerned.
So, the insurance company should be concerned that they could potentially lose money.
To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.
The null hypothesis for this test is that the true mean claim amount is equal to the original estimate of $1,800, and the alternative hypothesis is that the true mean claim amount is greater than the original estimate.
The t-statistic for this test is calculated as follows:
t = (sample mean - null mean) / (standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.
We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.
Since the calculated t-value of 2.5 is greater than the critical value, we can reject the null hypothesis and conclude that the true mean claim amount is significantly greater than the original estimate of $1,800.
Therefore, the insurance company should be concerned that they could potentially lose money.
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To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.
t = (sample mean - null mean) / (standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.
We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.
Therefore, the insurance company should be concerned that they could potentially lose money.
how did the ancient greeks represent numbers and
why are their symbols so enduring today
Step-by-step explanation:
the ancient Greeks used the system know as the attic numerals
What should be calculated first when finding the value of the following expression?
[(-3) (-8)+6)-(-6 + (-2))
A.8+6
B. (-3) (-8)
C.6+ (-2)
D.-6 -(-6)
Answer:
A
Step-by-step explanation:
The problem is a little unclear with its format(random bracket) but given the following it should be A even though a parenthesis is missing but with going from left to right with parenthesis first depending on where the extra parenthesis is placed it is either A or B but it looks like there should be one grouping ((-8)+6) so it should be A
A one-factor ANOVA is used to evaluate the mean differences among four treatment conditions with a sample of n = 12 participants in each group. For this study, what is dfwithin treatments?
In this case, with four treatment groups and n = 12 participants in each group, dfwithin treatments would be equal to 3, because there are 4 - 1 = 3 treatment groups.
In a one-factor ANOVA, dfwithin treatments refers to the degrees of freedom within the treatment groups, which is a measure of the amount of variability that is present within each group.
The degrees of freedom within the treatment groups is used to calculate the mean square within treatments (MSwithin), which is a measure of the variability within each group. MSwithin is calculated by dividing the sum of the squared differences between each participant's score and the group mean by dfwithin. This value is then used to determine the statistical significance of the treatment effects, by comparing it to the mean square between treatments (MSbetween), which is a measure of the variability between the treatment groups.
In a one-factor ANOVA, the total degrees of freedom is equal to the number of participants in all of the groups combined (4 groups * 12 participants per group = 48) minus the number of groups (48 - 4 = 44). The degrees of freedom between treatments is equal to the number of groups minus 1 (4 - 1 = 3), and the degrees of freedom within treatments is equal to the total degrees of freedom minus the degrees of freedom between treatments (44 - 3 = 41).
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1. Let C be a nonsymmetric n x n matrix. For each of the following, determine whether the given matrix must necessarily be symmetric or could possibly be nonsymmetric:
(a) A= C+CT
(b) B = C-CT
(c) D = CTC
(d) E = CTC - CCT
(e) F = (I +C)(I + CT
(f) G = (I +C)(I -CT)
Option of the matrices a, b, and d are non symmetric.
What are Symmetric matrices ?Symmetric matrices are those matrices that have equal dimensions, i.e. the number of rows is same as the number of columns. They are also known as square matrices.
It is provided that A and B are symmetric n × n matrices.
To multiply two matrices of different order, the number of rows of the first matrix must be same as the number of columns of the second matrix.
Suppose X is a 2 × 3 matrix and Y is a 3 × 2.
Then the product AB will be a n × n matrix.
(a) A= C+CT
Thus the sum of matrix A and B will be a n × n matrix.
Thus, the matrix A is non symmetric.
(b) B = C-CT
So, matrix D will also be a n × n matrix.
Thus, the matrix D is non symmetric.
(c) D = CTC = (CT) × C
Then the product CT will be a n × n matrix.
The next step would be to multiply CT and C.
Both are n × n matrices.
Thus, the matrix D is symmetric.
(d) E = CTC - CCT
Then he product CT will be a n × n matrix.
Similarly, the product CT will be a n × n matrix.
Thus, the matrix E is non symmetric.
Similalry,
(e) F = (I +C)(I + CT
Thus, the matrix F is symmetric.
(f) G = (I +C)(I -CT)
Thus, the matrix G is symmetric.
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A textbook store sold a combined total of 412 chemistry and math textbooks in a week. The number of chemistry textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold?
Answer:
309 chemistry textbooks and 103 math textbooks.
Step-by-step explanation:
Let c be the number of chemistry textbooks sold and m be the number of math textbooks sold. We know that c + m = 412, because the total number of textbooks sold is 412. We also know that c = 3m, because the number of chemistry textbooks sold is three times the number of math textbooks sold.
We can substitute 3m for c in the first equation to get 3m + m = 412. This simplifies to 4m = 412. Dividing both sides by 4 gives us m = 103.
Since we know that c = 3m, the number of chemistry textbooks sold is 3 * 103 = 309. Therefore, the store sold 309 chemistry textbooks and 103 math textbooks.
how is the circumference of a circle related to the length of its diameter?
Answer:
"the circumference divided by the diameter"
Step-by-step explanation:
Circles are all similar, and "the circumference divided by the diameter" produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).
Please help! on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?
Answer: 4/3 of a mile
Step-by-step explanation:
To find the distance that Pepe and Paula ran in 60 minutes, we need to first determine their individual pace in miles per minute. Pepe ran 2/3 of a mile in 5 minutes, so his pace was 2/3 / 5 = 2/15 of a mile per minute. Paula ran 1/4 of a mile in 2 minutes, so her pace was 1/4 / 2 = 1/8 of a mile per minute.
We can now use these values to determine the distance that each of them ran in 60 minutes. Pepe ran at a pace of 2/15 of a mile per minute, so he ran 2/15 * 60 = 8/15 of a mile in 60 minutes. Paula ran at a pace of 1/8 of a mile per minute, so she ran 1/8 * 60 = 3/8 of a mile in 60 minutes.
To find the total distance that Pepe and Paula ran in 60 minutes, we can add their individual distances: 8/15 + 3/8 = 35/60 + 45/60 = 80/60 = 4/3 of a mile. Therefore, Pepe and Paula cumulatively ran a total of 4/3 of a mile on their 60-minute training run.
The base of a triangular piece of fabric is 6 in more than the height. The area is 600 in2. Find the base and height of the triangle
Answer:
Below in bold.
Step-by-step explanation:
Let the height be h in.
Area of a triangle = 1/2 * base * height
= 1/2 * (h + 6) * h = 600
Multiply both sides by 2:
h(h + 6) = 1200
h^2 + 6h = 1200
(h + 3)^2 - 9 = 1200
(h + 3)^2 = 1209
h + 3 = +/- sqrt(1209
h = -3 +/-sqrt(1209)
= 31.77 in (we ignore the negative root).
So, the height is 31.77 in and the base is 37.77 in
find the values of the variable, giving brief reasons for your answers.
please help me with the answer. thank you.
Answer:
a= 108 degrees
b=88 degrees
c= 90 degrees
d= 90 degrees
Step-by-step explanation:
For a degrees since 72 degrees and a degrees make a straight angle:
180-72= a
So, a=108 degrees
Same goes for b degrees:
180-92=b
So, b=88 degrees
For c degrees, you need to know that the sum of the angles in a quadrilateral equal to 360 degrees.
So, 74+a+b+c=360
= 360- (74+108+88)=c
= 90 degrees= c
So since d degrees and c degrees make a straight angle,
180-90=d
90 degrees= d
Think of two numbers that multiply to -24, but add to -14.
Answer:
x = -7 + √(73)
y = -7 - √(73)
Step-by-step explanation:
Product p = x × y = -24
Somme s = x + y = -14
Then
x and y are solutions to the equation:
z² - sz + p = 0
Then
x and y are solutions to the equation:
z² + 14z - 24 = 0
Using the quadratic formula:
x = ( -14 + √[(14² - 4×(1)×(-24)] ) / ( 2×(1) ) = -7 + √(73)
and
y = ( -14 - √[(14² - 4×(1)×(-24)] ) / ( 2×(1) ) = -7 - √(73)
In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were:
Men Women
Voted 2366
3611
Didn't Vote 1499
2524
If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)]
a) [p-value = 0.019, RH0]
b) [p-value = 0.140, RH0]
c) [p-value = 0.019, FRH0]
d) [p-value = 0.010, RH0]
e) [p-value = 0.140, FRH0]
An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.
Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."
Give the null hypotheses a name.
Negative hypothesis:
H. There is no correlation between gender and election participation.
Other possibilities:
H: Gender and participation in the most recent election are linked.
Rule of rejection:
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pls help i will mark brainliest
Determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths.
y ≥ 0
y ≤ 0
y is greater than or equal to negative 1 over 40
y is less than or equal to negative 1 over 40
The value of y of the inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.
How to Solve an Inequality?Inequalities can be solved the way a normal algebraic equation is being solved. It is solved by isolating the value of the variable.
The inequality given is, 4y + 1/5 ≤ 4/5. Solve as shown below:
Subtract both sides by 1/5:
4y + 1/5 - 1/5 ≤ 4/5 - 1/5 [subtraction property of equality]
4y ≤ 3/5
Divide both sides by 4:
4y/4 ≤ 3/5 / 4
y ≤ 3/5 × 1/4
y ≤ 3/5 × 1/4
y ≤ (3 × 1) / (5 × 4)
y ≤ 3/20
The value of y is: y ≤ 3/20.
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Alfonso is making chili for a get-together.
His recipe calls for 1 1/2 cups of diced tomatoes for every 3 cups of chili.
He wants to make 13 cups of chili.
How many cups of diced tomatoes should he put in the chili?
Answer is a mixed number
The cups of diced tomatoes the Alfonso should put in the chili is 6 1/2 cups.
How to calculate the number of cups?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Let the number of cups be x.
Based on the information, this will be illustrated as:
1.5 / x = 3/13
Cross multiply
3x = 13 × 1.5
3x = 19.5
Divide
x = 19.5 / 3
x = 6 1/2
The cups needed is 6 1/2 cups.
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A block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest. What is their velocity after the collision ?
Answer:
When a block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest, their velocity after the collision is equal to the original velocity of the first block. This is because, in a collision where the two objects stick together, the final velocity of the combined system is equal to the initial velocity of the first object.
To calculate the final velocity of the combined system, we can use the formula vf = vi + (2mv)/(m1+m2), where vf is the final velocity, vi is the initial velocity, m is the mass of the first object, v is the velocity of the first object, and m1 and m2 are the masses of the two objects. Plugging in the values from the problem, we get:
vf = V + (2 * M * V)/(M + 2M) = V + (2 * M * V)/(3M) = V + (2/3) * V = (5/3) * V
Therefore, the final velocity of the combined system is (5/3) * V, which is equal to the original velocity of the first block.
The velocity of the mass 2M after the collision will be V/2 which is half of the velocity of mass M.
What is elastic collision?An elastic collision is one during which the system does not experience a huge reduction of kinetic energy as a result of the collision. In elastic collisions, mass and kinetic energy are both preserved. Imagine two trolleys that resemble one another moving in the same direction at the same pace.
A block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest.
Let 'v' be the velocity after the collision. Then the velocity of the mass 2M after the collision will be calculated as,
MV = 2Mv
v = V / 2
Thus, the velocity of the mass 2M after the collision will be V/2 which is half of the velocity of the mass M.
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Which of the following number sentences is true?
A. 40 -2 × 3² = 4
C. 40 -2 × 3² = 114
B. 40-2 × 3² = 22
D. 40 -2 × 3² = 360
Answer:
B
Step-by-step explanation:
First, we compute the exponent (3² = 9).
Next, we compute the multiplication and division (from left to right), so we have (40 - 2 × 9) = (40 - 18) = 22.
Thus, the number sentence 40 -2 × 3² = 22 is true.
B is true .22 is the real answer
The expense function for a manufacturer can be modeled using the equation
E = 1.43q + 43, 123
What is the cost for producing 200 units (q)?
Answer:
The cost of producing 200 units can be calculated by plugging in 200 for q in the equation E = 1.43q + 43,123. This gives us E = 1.43*200 + 43,123 = 286 + 43,123 = $43,409.
Makayla wants to make 200 ml of a 18% saline solution but only has access to 8% and 24% saline mixtures. Which of the following system of equations correctly describes this situation if x represents the amount of the 8% solution used, and y represents the amount of the 24% solution used?
O a.) 0.24x +0.08y= 0.18(200) x+y = 200 O b.) 0.08x +0.24y = 200 x+y=0.18(200) O c.) 0.08x+0.24y = 0.18(200) x+y=200 O d.) 0.24x +0.08y = 200 x+y=0.18(200)
The formulae that specify how much 8% solution and how much 24% solution were utilized are [tex]x+ y=200 and x+3y=450.[/tex]
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.
The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: [tex]x +y=200[/tex]
Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:
[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]
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i rlly need help with these questions someone please help
The perimeter of the shape is 12.82 units
How to determine the perimeter of the shape?From the question, we have the following parameters that can be used in our computation:
A = (0, 2.76)
B = (3.65, 2.76)
C = (3.65, 0)
D = (0, 0)
Because the point D is at the origin, and the shape is a rectangle.
The perimeter of the shape can be represented as
P = 2 * (Bx + By)
Substitute the known values in the above equation, so, we have the following representation
P = 2* (3.65 + 2.76)
Evaluate
P = 12.82
Hence, the perimeter is 12.82 units
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find a direct relationship between x and y.
x=t-5 and y=t^2-6t
The direct relationship of the variables is y = (t^2 - 6t)/(t - 5) * x
How to determine the direct relationship?From the question, we have the following parameters that can be used in our computation:
x = t - 5 and y = t^2 - 6t
The direct relationship between x and y is calculated using
Y = (y/x) * X
Substitute the known values in the above equation, so, we have the following representation
y = (t^2 - 6t)/(t - 5) * x
Hence, the direct relationship is y = (t^2 - 6t)/(t - 5) * x
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A solution in a book demonstrates the following:
79z = 92x + 9y (values for z, x and y are in between 0 and 10)
Modulo 9, this gives -2z ≡ 2x and by multiplying both sides by 5 gives -z ≡ x. Since 1 ≤ x ≤ 9, we have z = 9 - x.
Can someone please explain how taking Modulo 9 of the equation above leads to these results in detail. Thanks.
Answer:
In modular arithmetic, the modulo operation is used to find the remainder when one number is divided by another. For example, the expression "9 % 3" would evaluate to 0 because 9 divided by 3 leaves a remainder of 0.
In the given equation, taking the modulo 9 of both sides gives:
79z % 9 ≡ 92x + 9y % 9
The modulo operation distributes over addition, so we can simplify this to:
(79z % 9) ≡ (92x % 9) + (9y % 9)
Since any number divided by 9 has a remainder of itself, we can simplify this further to:
(z % 9) ≡ (2x % 9) + (y % 9)
This gives us the result:
-2z % 9 ≡ 2x % 9
Multiplying both sides by 5 gives:
(-2z % 9) * 5 ≡ (2x % 9) * 5
Which simplifies to:
-z % 9 ≡ x % 9
Since x is between 0 and 10, we know that x % 9 is between 0 and 9. Therefore, we can conclude that z = 9 - x.
How many factor pairs does the number 84 have?