During science class, groups measure out different volumes of vinegar. The line plot below shows the amount of vinegar used by 12 1212 groups, rounded to the nearest 1 2 mL 2 1 ​ mLstart fraction, 1, divided by, 2, end fraction, start text, space, m, L, end text. 4 4 4 1 2 4 2 1 ​ 5 5 5 1 2 5 2 1 ​ 6 6 6 1 2 6 2 1 ​ 7 7 7 1 2 7 2 1 ​ 8 8 A line plot labeled 4 to 8 with tick marks every one-half unit labeled with a tick mark and number. Above tick mark four and one-half there is a column of two dots. Above tick mark 5 there is a column of three dots. Above tick mark six and one-half there is a column of two dots. Above tick mark 7, there is a column of two dots. Above tick mark seven and one-half, there is a column of three dots. What is the total amount of vinegar, in milliliters, used by the 3 33 groups that used the most? mL mL

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer:

2x - y _> 2 = 4 / y<4 3.2

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

You are going a distance of 3/2 to the right, to get 3/2. You are going the same distance of 3/2 to the left, to get -3/2. Same distance traveled on a number line, just in different directions making it positive/negative.

If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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the coordinates of the vertices of D2(WXYZ) are;

W' ( 2, 3)

X' ( 3, -1)

Y' ( -2, -2)

Z'(−1, −2)

It is important to note that the general formula for finding the transformation of the coordinates is;

M ( h, k) = M' ( k, -h)

Where

For the quadrilateral WXYZ we have to find the transformed coordinates

For W, we have

W(−3, 2)

h = -3

k = 2

Substitute the values

W' ( 2, 3)

For X,

X(1, 3)

h = 1

k = 3

Substitute the values

X' ( 3, -1)

For Y

Y(2, −2)

h = 2

k = -2

Substitute the values

Y' ( -2, -2)

For Z

Z(−1, −2)

h = -1

k = -2

Z'(−1, −2)

Thus, the coordinates of the vertices of D2(WXYZ) are;

W' ( 2, 3)

X' ( 3, -1)

Y' ( -2, -2)

Z'(−1, −2)

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Answer:

of what

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Robert's dimes are anywhere between 17 and 19.

Nickels

are worth 5 cents, and

dimes

are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.

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Answer:

6.6

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The sum of interior angles in a triangle is 180°.

We can write the sum as ...

  A + 98° +46° = 180°

Then solve for A by subtracting the sum (98° +46°) from both sides of the equation:

  A = 180° -(98° +46°)

The result of evaluating that expression is ...

  A = 36°

Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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The key here is to not worry too much and just follow PEMDAS.

Here we have the expression \((5\cdot 7)^2\).  Following PEMDAS, we complete the expression inside the parentheses first, or \(5\cdot 7 = 35\). This gives us \((35)^2\) or just \(35^2.\)

Hope this helps.

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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The total amount of money Carol originally invested is £22,000 in the bank account.

Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.

This results in exponential growth or accumulation of interest over time.

Let X be the amount that Carol originally invested in the account.

After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).

After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.

After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).

We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:

(X(1.025) - £1000)(1.025) = £23,517.60

Expanding the left-hand side and simplifying, we get:

X(1.025)² - £1000(1.025) = £23,517.60

X(1.025)² = £24,567.63

Dividing both sides by (1.025)², we get:

X = £22,000 (rounded to the nearest pound)

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The complete question is -

On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?

The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.

Let's start the proof:

1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.

2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.

3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).

5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.

6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.

7. Now, we need to show that arc DE + arc FG = 360∘.

8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.

9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.

10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.

11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.

12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.

13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.

14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.

15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.

16. Simplifying, we have 90∘ = 180∘, which is a true statement.

17. Therefore, we have proven that m∠D + m∠F = 180∘.

Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

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Answer:

5,009.206

Explanation:

The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

Answer:

$5.20

Step-by-step explanation:

divide 5 dollars by 26 miles.

26 miles÷ $5 = $5.20

Step-by-step explanation:

terms such as 1 , 3, 5 (odd numbers) obtained orderly by multiplying 2 , 3, 4 ,........

terms such as 2,4,6 (even numbers) obtained by subtracting 3 from previous term

By direct multiplication of fractions, we will see that she uses 1/30 of the original container of applesauce to bake the muffins.

Remember that the product of two fractions is just:

\(\frac{x}{y} \frac{a}{b} = \frac{x*a}{y*b} \)

Now, we know that Sasha gets 1/3 of the applesauce, and she uses 1/10 of what she gets to make the muffins. So the fraction that she uses is just the product of these two:

\(\frac{1}{3}* \frac{1}{10} = \frac{1}{30} \)

This means that she uses 1/30 of the original container of applesauce to bake muffins.

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Answer:

B! Pls mark brainiest!

Step-by-step explanation:

Answer:

Theyre right the answer is B. expirment

Step-by-step explanation:

Took the test just confirming

Answer:

B. 103°

Step-by-step explanation:

Supplementary angles add up to 180°, so we can find the measure of angle 2 by subtracting 77 from 180

180 - 77

= 103

So, m∠2 is 103°

Answer:

y = 3x + 4

Step-by-step explanation:

✔️First, find the slope using any two given pairs form the table, say (2, 10) and (5, 19):

Slope (m) = ∆y/∆x = (19 - 10) / (5 - 2) = 9/3

m = 3

✔️Find y-intercept (b) by substituting (x, y) = (2, 10) and m = 3 into y = mx + b

10 = 3(2) + b

10 = 6 + b

10 - 6 = b

4 = b

b = 4

✔️Write the equation by substituing m = 3 and b = 4 into y = mx + b

y = 3x + 4

The option that is unique to only skeletal muscle is Option(B.) They can fatigue with too much movement or exercise.

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1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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