analyzing stem and leaf plots

Answer:

The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

9 ± √89 /4 = 2x² - 9x - 1.

4 ± √22 /2 = 2x² - 8x - 3.

Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5.                                                  x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4.     24 can also be written as 4 × 6 and √4 = 2. So                                                                                     x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3.                                                   x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So                                                                              x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3.                                                    x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4.     88 can also be written as 4 × 22 and √4 = 2. So                                                                             x = 8 ± 2√22 / 2×2 = 4± √22/2.

2x² - 9x - 1, here a = 2, b = -9, c = -1.                                                     x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4.                                          x = 9 ± √89 / 4.

2x² - 9x + 6, here a = 2, b = -9, c = 6.                                                    x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4.                                                                             x = 9 ± √33 / 4 .

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Answer:

.4

Step-by-step explanation:

2.80/7=.4

7 x 0.4 = 2.8

The given formula V₂ = Vmax [S] / (Km + [S]) can be rearranged as 1 / V₂ = (Km + [S]) / (Km Vmax [S]) + 1 / V₁ max.

Here's how to algebraically rearrange the formula:

Start with the given formula:

V₂ = Vmax [S] / (Km + [S])

Multiply both sides of the equation by Km / Km:

V₂(Km) = Vmax [S] / (Km / Km + [S] / Km)

Simplify the denominator on the right-hand side:

V₂(Km) = Vmax [S] / (1 + [S] / Km)

Rewrite the denominator as a single fraction:

V₂(Km) = Vmax [S] / ((Km + [S]) / Km)

Invert the denominator and multiply:

V₂(Km) = Vmax [S] x Km / (Km + [S])

Rearrange the terms:

Vmax [S] x Km / (Km + [S]) = V₂(Km)

Divide both sides by Vmax [S]:

Km / (Km + [S]) = V₂(Km) / Vmax [S]

Subtract this term from both sides:

1 - (Km / (Km + [S])) = 1 - (V₂(Km) / Vmax [S])

Simplify the left-hand side:

[S] / (Km + [S]) = 1 - (V₂(Km) / Vmax [S])

Multiply both sides by Vmax:

Vmax [S] / (Km + [S]) = Vmax - V₂(Km)

Factor out [S] on the left-hand side:

Vmax ([S] / (Km + [S])) = Vmax - V₂(Km)

Rearrange the terms:

Vmax / (Km + [S]) x [S] = Vmax - V₂(Km)

Multiply both sides by Km:

Km Vmax [S] / (Km + [S]) = Vmax Km - V₂(Km) [S]

Divide both sides by Vmax Km V₁ max :

1 / V₂ = (Km + [S]) / (Km Vmax [S]) + 1 / V₁ max

Therefore, the given formula V₂ = Vmax [S] / (Km + [S]) can be rearranged as 1 / V₂ = (Km + [S]) / (Km Vmax [S]) + 1 / V₁ max.

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Answer:

2400

Step-by-step explanation:

2244 is the final price. it includes the VAT based on the actual sale price. and that is then actually 15% lower than the originally marked price.

so, let's calculate backwards :

2244 = 100% sale price + 10% VAT = 110%

1% = 2244 / 110 = 20.40

100% (actual sale price) = 20.40×100 = 2040

now, because of the 15% discount, these 2040 are only 85% of the originally marked price.

2040 = 85%

1% = 2040 / 85 = 24.00

100% (the original marked price) = 24×100 = 2400

Answer: If you have 80% of 5 it would be 4 if you have 120% its six

Step-by-step explanation:

Answer:

1).  The constant of variation is 7

2).  w = 6 for the given values of x and y

Step-by-step explanation:

"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w.  We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.

We are given one data point:  y=-42 where x is 2 and w is -3.  Let's put those values into our trrial expression:

y=Kxw

-42=K(2)(-3)

-42 = -6K

K = 7

The constant of variation is 7.

The value of w for y=3 and x=(1/14) would be:

  y=7xw

  3 = 7*(1/14)*w

3 = (1/2)*w

Answer:

1)  k = 7

2)  w = 6

Step-by-step explanation:

Joint variation equation

If y varies jointly with x and w:

\(\boxed{y \propto xw \implies y=kxw}\)

for some constant k.

Given:

Substitute the given values into the joint variation equation and solve for k:

\(\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}\)

Therefore, the equation is:

\(\boxed{y=7xw}\)

To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:

\(\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}\)

The solution for the absolute value equation is x = 10 and x = -14

In this question,

Two thirds times the absolute value of the quantity x plus 2 end quantity minus 8 equals 0. The equation for this statement is 2/3 lx + 2l -8 =0.

The solution for the equation is

\(\frac{2}{3}\) lx + 2l -8 =0

\(\frac{2}{3}\) lx + 2l = 8

Multiply by 3/2 on both sides,

\(\frac{2}{3}\) lx + 2l = 8

\(\frac{2}{3}\) ×\(\frac{3}{2}\)lx + 2l =8×\(\frac{3}{2}\)

=> x +2 = 12

Case 1: Take as positive value

=> x + 2 = 12

=> x = 12 - 2

=> x = 10

Case 2: Take as negative value

=> -(x +2) = 12

=> -x - 2 = 12

=> -x = 12 + 2

=> -x = 14

=> x = -14

Hence, we can conclude that the solution for the absolute value equation is x = 10 and x = -14 is the correct answer

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Answer:

\(\boldsymbol{2.5}\)

Step-by-step explanation:

Hi student! Let me help you out on this question.

____________

- - - - - - - - - - - - - - -

 When rounding numbers, it's important that you remember these two rules:

  \(\boldsymbol{3.51=== > 3.5}\) (Rounded to 1 D.P.)

     2. If the digit you are asked to round is followed by a digit

          greater than or equal to 5, you round up. An example is given

             below.

\(\boldsymbol{6.25=== > 6.3}\)

\(\boldsymbol{2.16=== > 2.2}\)

                                     ↪

Now that we know these two rules, let's round the given number.

\(\boldsymbol{2.51=== > ?}\)

The digit we are asked to round to (5) is followed by a number less than 5.

\(\sf{\therefore,\:we\:round\:down.}\)

Thus,

\(\boldsymbol{2.51=== > \not? \:2.5}\). Which is our answer.

Hope that this helped you out! Have a nice day ahead.

Best Wishes!

◈◈-Greetings!-◆◆

- - - - - - - - - - - - - -

___________________

4.) is 3. Acute

5.) is 4. 77°

Answer:

1. 75%

2. 0%

3. 0.1

4. one half

5. six tenths

6. 0.75

7. 64%

Step-by-step explanation:Answer 1:

The spinner has a total of 8 sections, out of which there are 2 yellow sections. Therefore, the probability of not getting a yellow section when the spinner is spun once is 6/8 or 3/4, which is equal to 75%.

Answer 2:

The spinner has only three sections and none of them is colored yellow. Therefore, the probability of getting a yellow section when the spinner is spun once is 0%.

Answer 3:

The total number of students surveyed is:

1 + 3 + 2 + 5 + 9 + 7 + 3 = 30

The number of students who studied for 1 hour is 3. Therefore, the probability of a student studying for 1 hour is 3/30, which simplifies to 1/10 or 0.1.

Answer 4:

Since the coin is fair and has one side colored yellow and the other side colored green, the probability of getting a yellow side when the coin is tossed is 1/2 or one half.

Answer 5:

The set of cards has 10 letters, out of which 4 are vowels (A, I, U). Therefore, the number of consonants in the set is 10 - 4 = 6. The probability of drawing a consonant is therefore 6/10, which simplifies to 3/5 or 0.6.

Answer 6:

The number cube has 8 sides, numbered 1 through 8. The probability of getting a number greater than 2 is the same as the probability of getting any number from 3 to 8. There are 6 such numbers out of 8 total numbers, so the probability is 6/8 or 3/4, which is equal to 0.75.

Answer 7:

The total number of marbles in the bag is:

2 + 4 + 10 + 9 = 25

The number of marbles that are not purple is:

2 + 4 + 10 = 16

Therefore, the probability of not getting a purple marble when one marble is chosen from the bag is 16/25, which is equal to 64%.

The Inequality that is equivalent to  Ix - 4| < 9 is given as;  -9 < x - 4 < 9

We are given the inequality;

Ix - 4| < 9

Now, what the given inequality represents is;

x - 4 < 9 or x - 4 < -9

-9 < x - 4 < 9

This is because the specific bracket means absolute value.

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Answer:

x = 8b + 3

Step-by-step explanation:

BRAINLIST PLZ

Answer:

x = 8b + 3

Step-by-step explanation:

x = 8b + 3

You can kick "b" balls in 2 minutes. There are 8 two-minute intervals in 16. So 8 is multiplied by "b" soccer balls. 3 is the extra number of balls kicked after the break. x is the total number of soccer balls kicked.

The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.

To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.

When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.

Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).

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Answer:b

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

150 diveded by 30 is 5

Answer:

It sounds like 5 months, but the wording you chose is a little strange. What are the other wording options?

Step-by-step explanation:

150/30=5.

I hope this helps.

Answer:

Step-by-step explanation:

Given:

s = b + 7

=> 11 = b + 7

=> b = 4

a = 15 + b

=> a = 15 + 4

=> a = 19

Therefore, the equation is 'a = 15 + 4' and the answer is 'a = 19'.

Hoped this helped.

I apologize if this was incorrect or un-helpful.

So

As z=11

\(\\ \rm\Rrightarrow y+7=11\)

\(\\ \rm\Rrightarrow y=4\)

My age=

Answer:

\(x=14\)

Step-by-step explanation:

Since lines \(\overrightarrow{f}\) and \(\overrightarrow{g}\) are parallel, the angles labelled in the diagram must be supplementary (add up to \(180^{\circ}\)). Therefore, we have the following equation:

\(4x+(7x+26)=180,\\11x+26=180,\\11x=154,\\x=\boxed{14}\)

Step-by-step explanation:

25. (+10)-(-6) = 10+6 = 16

26. (-14)-(+7) = -14-7 = -21

27. (-3)-(-9) = -3+9 = 6

28. 0-(-9) = 0+9 = 9

29. (-3)-(+6) = -3-6 = -9

30. (+8)-(-9) = 8+9 = 17

31. (+13)-(+7) = 13-7 = 6

32. (-6)-(-12) = -6+12 = 6

In summary the equivalence relation on the set of real numbers is:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

To show that the relation {(x, y) | x − y ∈ Q} is an equivalence relation on the set of real numbers, we need to verify three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any real number x, we have x - x = 0, which is a rational number (0 ∈ Q). Therefore, (x, x) ∈ {(x, y) | x − y ∈ Q} for all x, and the relation is reflexive.

2. Symmetry: If (x, y) ∈ {(x, y) | x − y ∈ Q}, then x - y is a rational number. Since the negation of a rational number is still a rational number, -(x - y) = y - x is also a rational number. Therefore, (y, x) ∈ {(x, y) | x − y ∈ Q}, and the relation is symmetric.

3. Transitivity: If (x, y) ∈ {(x, y) | x − y ∈ Q} and (y, z) ∈ {(x, y) | x − y ∈ Q}, then x - y and y - z are both rational numbers. The sum of two rational numbers is also a rational number, so (x - y) + (y - z) = x - z is a rational number. Therefore, (x, z) ∈ {(x, y) | x − y ∈ Q}, and the relation is transitive.

Since the relation satisfies all three properties (reflexivity, symmetry, and transitivity), it is an equivalence relation on the set of real numbers.

Now, let's determine the equivalence classes [1], [1/2], and [π].

The equivalence class [1] consists of all real numbers x such that x - 1 ∈ Q. In other words, [1] = {x ∈ R | x - 1 ∈ Q}. This means that any real number x in the form x = 1 + q, where q is a rational number, belongs to [1].

Similarly, the equivalence class [1/2] consists of all real numbers x such that x - 1/2 ∈ Q. Therefore, [1/2] = {x ∈ R | x - 1/2 ∈ Q}, which means that any real number x in the form x = 1/2 + q, where q is a rational number, belongs to [1/2].

Finally, the equivalence class [π] consists of all real numbers x such that x - π ∈ Q. Thus, [π] = {x ∈ R | x - π ∈ Q}. This means that any real number x in the form x = π + q, where q is a rational number, belongs to [π].

In summary:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

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The graph of the system of inequalities is the one in the bottom left corner.

Here we have the following system of inequalities:

y ≤ 2x+1

y > −2x−3

The first inequality has the symbol "≤", then the liine should be a solid line, and we need to have the region below the line shaded. Also notice that this line has a positive slope, so it goes up.

The second line has the symbol ">", so here we have a dashed line and the region shaded must be above the line, this line has a negative slope.

Then the graph of the system of inequalities is the one in the bottom left.

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Answer:

Cannot be determined.

Step-by-step explanation:

The triangle has three different angles which are not congruent. The sides of the two triangle are not equal therefore these triangle are not determined to be congruent. These triangles share their three angles but not the three sides.

There are two distinct sorts of angles created by two intersecting lines or rays: vertical angles and neighboring angles.

Vertical angles are a pair of opposing angles with different rays on their sides but a same vertex. In other words, they are generated by the intersection of two opposing lines or rays. The measurements of vertical angles are equivalent, therefore if one angle is x degrees, the other will also be x degrees.

On the other hand, adjacent angles are two angles that have a similar vertex and side. In other words, they share a side but do not overlap since they are created by two lines or rays that intersect.

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The correct form of the particular solution for fn = -6fn-1 + 7fn-2 + 6n is d. n(an+b). To determine the particular solution, we need to first find the characteristic equation, which is r^2 + 6r - 7 = 0. The roots of this equation are r = -7 and r = 1. Therefore, the homogeneous solution is of the form fn = A(-7)^n + B(1)^n.

To find the particular solution, we look at the non-homogeneous term, which is 6n. Since this is a linear function, we can assume that the particular solution is of the form Pn = an + b. We substitute this into the original equation and solve for a and b.

f n = -6fn-1 + 7fn-2 + 6n
(a n +b) = -6(an-1+b) + 7(an-2+b) + 6n
an + b = -6an-1 + 7an-2 + 6n + 6b
an + b = 6(an-2 - an-1 + b) + 6n

Comparing coefficients, we get:
a = 6a - 6a + 0 = 0
b = 6b + 6n

Solving for b, we get b = n. Therefore, the particular solution is Pn = an + n.

Combining the homogeneous and particular solutions, we get:
fn = A(-7)^n + B(1)^n + an + n

Note that we can further simplify this by setting A and B based on initial conditions, if given.

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Answer:

Option 2 is correct .

Step-by-step explanation:

A inequality is given to us , and we need to find the solution set for it. The given inequality is :-

⇒ 3(8 - 4x) < 6(x - 5)

⇒ 24 - 12x < 6x - 30

⇒ 24 +30 < 6x + 12x

⇒ 54 < 18x

⇒ x > 54/18

⇒ x > 3

This means that x can have all values Greater than 3 . Hence x can have all real numbers greater than 3 . Hence the Solution set will be x ∈ ( 3, ∞ ) . From the number lines given in the option second option is correct .

I have also attached the graph . The red area shows the possible values of x.

The solution is : Option 2 is correct .

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

A inequality is given to us , and we need to find the solution set for it. The given inequality is :-

⇒ 3(8 - 4x) < 6(x - 5)

⇒ 24 - 12x < 6x - 30

⇒ 24 +30 < 6x + 12x

⇒ 54 < 18x

⇒ x > 54/18

⇒ x > 3

This means that x can have all values Greater than 3 . Hence x can have all real numbers greater than 3 .

Hence the Solution set will be x ∈ ( 3, ∞ ) . From the number lines given in the option second option is correct .

The solution set is x ∈ ( 3 , ∞ ) .And the second option is correct.

Here, attached the graph . The red area shows the possible values of x.

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Answer:

a = -4

a = 3

Step-by-step explanation:

Hope that helps

Mr. Wilkinson needs more than 11 years to get more than 800 profit.

Compound interest refers to the interest added to a loan or deposit. It is the concept that we use every day the most regularly. Compound interest is calculated for an amount based on both the principal and cumulative interest. The significant distinction between compound and simple interest is this.

The profit is 3000 × \((1+(2.2/100))^t\) - 3000

= 3000 [\((1+ 0.022)^ t\) -1]

The given profit is 800.

So,

800 = 3000 [\((1+ 0.22)^ t\) -1]

\(1.022^t\) – 1 = 800/3000

\(1.022^t\) = 8/30 + 1

\(1.022^t\)  = 38/30

T = \(log_{1.022}\) (98/30)

= 10.86

So, he needs more than 11 years to get more than 800 profit.

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Answer:

x=1

Explanation:

Given the equation:

To solve for x, follow the steps below.

Step 1: Subtract 2 from both sides of the equation.

Step 2: Divide both sides by 3.

The value of x (that is the solution to the equation) is 1.

The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Compound interest accrued at a rate of 3.6% per year, compounded 12 times per year over a period of 3.5 years, on a principal of $5,000.00, resulting in a total value of $5,670.34.

The interest earned on a deposit is known as compound interest because it is computed using both the original principle and the interest accrued over the course of prior periods. Compound interest is just interest that is earned on interest, to put it another way. Interest can be compounded daily, monthly, or yearly, among other frequency plans.

A = $5,670.34

A = P + I where

P (principal) = $5,000.00

I (interest) = $670.34

convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.036/12)(12)(3.5)

A = 5,000.00(1 + 0.003)(42)

A = $5,670.34

The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 3.6% per year compounded 12 times per year over 3.5 years is $5,670.34.

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