Chapter 6: Review page 2
For problems 7, 8 and 9, determine whether each of the numbers is a solution to the
inequality.
3x2 < 2 - 2x. (Yes or No)
7) 1
9)
113
8) 1/2

Option C is the table of values representing a proportional relationship in the context of this problem.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For item c, we have that the output is equals to the input, hence the proportional relationship is given as follows:

y = x.

The problem asks for which table represents a proportional relationship.

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Answer:

Hope this saved you ^^

Step-by-step explanation:

To determine the number of babies we can expect among the next 12 children to enroll, we need to calculate the proportion of babies based on the current enrollment data.

Out of the total enrollment so far, there are 3 babies and 6 children of other ages, making a total of 9 children.

Proportion of babies = (Number of babies / Total number of children) = 3 / 9 = 1/3

Now, to estimate the number of babies among the next 12 children, we multiply the proportion of babies by the total number of children to be enrolled:

Number of babies expected = Proportion of babies * Total number of children to enroll

Number of babies expected = (1/3) * 12 = 4

Therefore, based on the current enrollment data, we can expect approximately 4 out of the next 12 children to be babies.

Answer:

what is all that?!

floor plan => It is the scale drawing that show the relationship between rooms, spaces, and physical features viewed from the above

THIS PIC WILL ALSO HELP U

Yes, because it is practical to obtain that many aspirin because the number is relatively small. The correct option is B.

The minimum sample size required to be 99% confident that the sample standard deviation (s) is within 10% of the population standard deviation (σ) is 336, according to the table provided.

This means that in order to have a high level of confidence (99%) that the sample standard deviation is within a reasonable range of the population standard deviation, a minimum sample size of 336 is needed.

In this case, the sample size requirement is met with a relatively small number, 336, compared to the larger values provided in the table for higher levels of confidence.

Therefore, it can be considered practical to obtain that many aspirin tablets for the purposes of this study.

Thus, the correct option is B.

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If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk, she has more than the required amount, so she has sufficient buttermilk for the recipe.

1.2 To determine if Erin has enough buttermilk for the recipe, we need to convert the given quantities to a common unit.

150 ml of buttermilk is equivalent to 0.15 liters (since 1 liter = 1000 ml).

Now, let's convert 0.25 cups to liters. Since 1 cup is approximately 0.2366 liters, we have:

0.25 cups ≈ 0.25 * 0.2366 liters = 0.05915 liters.

Comparing the amount of buttermilk Erin has (0.15 liters) with the amount required by the recipe (0.05915 liters), we can see that Erin has enough buttermilk. She has more than the required amount, so she has sufficient buttermilk for the recipe.

1.3.1 To determine the total mass of the ingredients, we need to convert the given quantities to a common unit, kilograms.

0.8 kg of flour is already in kilograms.

650 g of sugar is equivalent to 0.65 kg (since 1 kg = 1000 g).

900,000 mg of butter is equivalent to 900 g (since 1 g = 1000 mg), which is 0.9 kg.

Adding up the masses of the ingredients:

0.8 kg (flour) + 0.65 kg (sugar) + 0.9 kg (butter) = 2.35 kg.

Therefore, the total mass of the ingredients is 2.35 kilograms.

1.3.2 If sugar comes in 150 g bags at a cost of R5.95 per 150 g, we can calculate the total cost of the sugar needed for the recipe.

The recipe requires 650 g of sugar. Since each bag contains 150 g of sugar, we divide the required amount by 150 g:

650 g / 150 g = 4.3333 bags.

Since we cannot purchase a fraction of a bag, we need to round up to the nearest whole number. So, we'll need to buy 5 bags of sugar.

The total cost of the sugar is calculated by multiplying the number of bags by the cost per bag:

5 bags * 5.95 per bag = 29.75.

Therefore, the total cost of the sugar needed for the recipe is 29.75.

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The expression x²x²x²√x when evaluated is [tex]x^{6\frac{1}{2}}[/tex]

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

x²x²x²√x

The above expression can be evaluated using the law of indices

Using the above as a guide, we have the following:

x²x²x²√x = x⁶√x

So, we have

x²x²x²√x = x⁶ * √x

When evaluated, we have

x²x²x²√x =  [tex]x^{6\frac{1}{2}}[/tex]

Hence, the expression when evaluated is [tex]x^{6\frac{1}{2}}[/tex]

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Complete question

Evaluate x²x²x²√x

AnswerTherefore, Jennifer traveled for 2 hours.

Step-by-step explanation:

Let x be the time Jennifer traveled.

Kristin traveled for 2 hours at 33 km/h, so she had traveled 66 km when Jennifer started traveling.

After x hours, Jennifer had traveled 45x km.

The total distance between them was 156 km.

So, we have:

66 km + 45x km = 156 km

Simplifying the equation, we get:

45x km = 90 km

x = 2 hours

Therefore, Jennifer traveled for 2 hours.

Answer:

x = 1 or x = 7

Step-by-step explanation:

-x² + 8x - 7

= -(x² - 8x) - 7

= - [(x - 4)² - 16] - 7

= -(x - 4)² + 16 - 7

= -(x - 4)² + 9.

-(x - 4)² + 9 = 0

-(x - 4)² = -9

(x - 4)² = 9

x - 4 = ±√9

x - 4 = ±3

x = 3 + 4 or x = -3 + 4

x = 7 or x = 1

Answer:

76.5 hours

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

Part 1 of 2:

(a) The equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the number of hours, y, worked at the second job can be written as:

P = (10x) + (9.25y + 0.7 * 9.25y) - 0.2[(10x) + (9.25y + 0.7 * 9.25y)]

Simplifying the equation:

P = 10x + 9.25y + 0.7 * 9.25y - 0.2(10x + 9.25y + 0.7 * 9.25y)

Part 2 of 2:

(b) If Winona is committed to working 30 hours per week at the first job, let's assume x = 30. We need to find the number of hours per week, y, she would need to work at the second job to reach a biweekly take-home pay of $800.

Using the simplified equation from part (a), we substitute x = 30 and solve for y:

800 = (10 * 30) + (9.25y + 0.7 * 9.25y) - 0.2[(10 * 30) + (9.25y + 0.7 * 9.25y)]

800 = 300 + (9.25y + 0.7 * 9.25y) - 0.2(300 + (9.25y + 0.7 * 9.25y))

Now, we can solve for y:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2(300 + 9.25y + 0.7 * 9.25y)

Simplify the equation:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2 * 300 - 0.2 * 9.25y - 0.2 * 0.7 * 9.25y

Combine like terms:

800 = 300 - 60 + 9.25y - 1.85y - 0.1295y

800 = 240 + 7.32y

Subtract 240 from both sides:

560 = 7.32y

Divide both sides by 7.32:

y ≈ 76.5

Therefore, Winona would need to work approximately 76.5 hours per week at her second job to reach a biweekly take-home pay of $800.

The measure of unknown angle of triangle is 28.2°.

From the given triangle, we have sides 11 units, 12 units and 20 units.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Here, 11²=12²+20²-2×12×20·cosA

121=144+400-480·cosA

121=544-480·cosA

121-544=-480·cosA

-423=-480·cosA

cosA= 423/480

cosA= 0.88125

A=28.2°

Therefore, the measure of unknown angle of triangle is 28.2°.

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Answer:

To calculate the value of (-3/4)^-4, we need to apply the exponentiation rules.

When a negative number is raised to an even power, the result is positive. Thus, we can rewrite (-3/4)^-4 as (4/-3)^4.

Now, let's evaluate the expression:

(4/-3)^4 = (4^4)/(-3)^4 = 256/81

So, the value of (-3/4)^-4 is 256/81

Step-by-step explanation:

When matched, the prompts on asymptotes would be:

The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.

This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.

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The probabilities of getting eagles in different quantities, given the number of coins would be:

There are 8 possible outcomes when tossing 3 coins: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

The probability of getting 2 eagles is 3/8 because the ways of getting eagles HHH, HHT, and HTH.

The probability of getting at least 1 eagle is 7 / 8. There are 7 ways to get at least 1 eagle: HHH, HHT, HTH, THH, TTH, THT, and HTT.

The probability of getting no eagles is 1/8 / . There is only 1 way to get no eagles: TTT.

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The measure of the marked central angle for the given circle is 160°.

Given a part of a circle.

This part is 4/9 of the full circle.

We have to find the marked central angle.

We know that,

Total circle can be represented as,

Total circle = 360°

Since the given figure is 4/9 part of the total circle, the marked central angle will be 4/9 of the total central angle.

Marked central angle = 4/9 × 360

                                    = 160°

Hence the marked central angle is 160°.

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The minimum y-value of g(x) is -3 and g(x) has the smallest possible y-value.

The function  f(x) = 32 - 3 is a constant function, as there is no variable term involving x. It simplifies to f(x) = 29.

Regardless of the value of x, the function f(x) will always have a y-value of 29.

Therefore, option A is incorrect because there is no minimum y-value for f(x); it is a constant.

g(x) = 7x² - 3 is a quadratic function in the form of ax² + bx + c, where a = 7, b = 0, and c = -3.

The coefficient a (7) is positive, indicating that the parabola opens upward.

Since there is no linear term (bx), the vertex of the parabola is located at the point (0, -3), which corresponds to the minimum y-value of the function.

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The reasoning of the student is wrong because the claim doesn't abide by the sine rule and formula.

The sine rule states that in a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.

That is;

a/sinA= b/sinB = c/sinC

Therefore, the proper equation to find X = 5/sin98° = X/sin20°

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Answer:

16x^2 - 1.6x - 5

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

x+2 | 16x^3 + 31.6x^2 - 6.8x - 12

- (16x^3 + 32x^2)

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

-0.4x^2 - 6.8x

+(-0.4x^2 - 0.8x)

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

-6x - 12

+(-6x - 12)

----------

0

Answer:   = 16x²-.4x-6

Step-by-step explanation:

divide 16x³+31.6x²-6.8x-12 by x+2​

Using synthetic division:  Carry first 1 down.  Multiply that by outside -2 and put it under 2nd number.  Add.  Then multiply and repeat until you get to end.

-2    |   16            31.6             -6.8           -12

      |                  -32                  .8             12        

           16              -.4             -6                0

Put back into equation form.  Last number is 0 so remainder is 0

= 16x²-.4x-6

The two mathematical symbols that William Oughtred introduced are "×" for multiplication and "::" for proportion.

Given is a statement about William Oughtred.

William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols.

We have to find those symbols.

William Oughtred is actually an English priest who basically teaches the students in mathematics subject.

He did invent other famous things like slide rule.

But the most famous invention of him is two mathematical symbols which are "×" for multiplication and "::" for proportion which are still widely used symbols.

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On July 20, the journal entry to record the reissuance of treasury stock is: Debit Cash for $4,140 and credit Treasury Stock for $4,140.

To record the reissuance of treasury stock on July 20, the company needs to make the following journal entry:

Date: July 20

Account Debit Credit

Cash $4,140

Treasury Stock $4,140

Explanation:

Debit to Cash ($46 per share * 90 shares) to record the cash received from the reissuance of 90 shares of treasury stock: $46 * 90 = $4,140.

Credit to Treasury Stock to remove the cost of the 90 reissued shares from the treasury stock account.

This journal entry reflects the cash inflow from the reissuance of treasury stock and reduces the balance in the treasury stock account, indicating a reduction in the number of shares held by the company as treasury stock.

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Answer:

49pi cm^2

Step-by-step explanation:

The area of a circle is pi(r)^2

To find our radius, we need to divide the diameter by 2.

14 / 2 = 7

Lets plug that into our equation:

pi(7)^2

Simplify:

pi(49)

rearrange:

49pi

WAIT, we need units!

49pi cm^2

~~~Harsha~~~

The percentage is 26%, so the number is 26.

Here we know that the x% of the number 800,000 is equal to 208,000.

Remember that the x% of a number N, is given by the product:

(x%/100%)*N

So in this case we can solve the equation:

(x%/100%)*800,000 = 208,000

Solving that equation for the percentage, we will get:

x% = 100%*(208,000/800,000)

x% = 26%

That is the missing number.

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Altogether they have 85 marbles.

Given,

Randy's marbles = 50

Randy's marbles is 5/2 of Andy's marbles.

Randy's marbles is 10/3 of Peter's marbles.

Now form the linear equations,

Let Andy has x marbles.

So,

5/2 × x = 50

x = 20

Andy's marbles = 50

Let Peter has y marbles.

So,

10/3 × y = 50

y = 15

Peter's marbles = 15

Thus total marbles of Randy , Andy , Peter is 85.

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Answer:

85 marbles

Step-by-step explanation:

Andy has 20

Randy has 50

Peter has 15

Answer:

To summarize:

√3 - 6x: Domain is all real numbers (-∞, +∞).

√13 - (13 - 2x): Domain is all real numbers (-∞, +∞).

1/√x - 2: Domain is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).

Step-by-step explanation:

To find the domain of each expression, we need to identify any restrictions or limitations on the variables that would result in undefined values.

√3 - 6x:

Since square roots are defined for non-negative numbers, the expression is defined as long as the value inside the square root (√3) is non-negative. The square root of 3 is a positive value, so there are no restrictions on the domain of this expression. Therefore, the domain is all real numbers (-∞, +∞).

√13 - (13 - 2x):

Similar to the previous expression, the square root (√13) is defined for non-negative values. However, we also need to consider the expression (13 - 2x) inside the parentheses. This expression does not have any limitations since it is defined for all real numbers. Therefore, the domain of this expression is all real numbers (-∞, +∞).

1/√x - 2:

For this expression, we need to consider both the square root (√x) and the denominator (1/√x). The square root (√x) is defined for non-negative values of x. However, the denominator 1/√x will become undefined if the value of x is zero because division by zero is undefined. Therefore, we need to exclude x = 0 from the domain. For all other non-zero values of x, the expression is defined. Therefore, the domain of this expression is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).

The numeric value of the expression in this problem is given as follows:

-77.

The expression in the context of this problem is defined as follows:

[tex]2^5[/tex] x (-2) - 4 x 5 + 7.

Considering the PEMDAS acronym, the power operation has the precedence over the remaining operations, hence:

[tex]2^5[/tex] x (-2) - 4 x 5 + 7 = 32 x (-2) - 4 x 5 + 7.

Then, following the same acronym, we have that the multiplication operation has precedence over the addition/subtraction operations, hence:

32 x (-2) - 4 x 5 + 7 = -64 - 20 + 7.

Finally, we can just subtract and add the numbers to obtain the numeric value of the expression as follows:

-64 - 20 + 7 = -77.

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Answer:

Table B was created using the equation y = 4x-1.

Explanation:

The equation y = 4x-1 means that for any given value of x, the corresponding value of y can be found by multiplying x by 4 and then subtracting 1.

Table B shows input values of x and output values of y that are consistent with this equation. For example, when x = 3, y = 11 (4 * 3 - 1), and when x = 4, y = 15 (4 * 4 - 1), and so on.

Therefore, we can conclude that Table B was created using the equation y = 4x-1.

Answer:

One method that a person can use to send money to another person who does not have a bank account is through a money transfer service like Western Union or MoneyGram. These services allow individuals to send money to recipients who can then collect it in cash from designated locations. The sender can visit a local agent or use an online platform to initiate the transfer, providing the recipient's name and other required details. The recipient can then go to a nearby agent location with proper identification to receive the cash. This method provides a convenient way to send money to individuals who may not have access to traditional banking services.

Step-by-step explanation:

Person 1 takes money out of wallet, gives money to person 2.

BOOM!

Answer:

Θ ≈ 103°

Step-by-step explanation:

using the Cosine rule in Δ ABC

cosB = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]

where a is the side opposite ∠ A , b the side opposite ∠ B and c the side opposite ∠ C

here a = 42 , b = 78 and c = 57 , then

cos B = [tex]\frac{42^2+57^2-78^2}{2(42)(57)}[/tex]

          = [tex]\frac{1764+3249-6084}{4788}[/tex]

          = [tex]\frac{5013-6084}{4788}[/tex]

         = [tex]\frac{-1071}{4788}[/tex] , then

B = Θ = [tex]cos^{-1}[/tex] ( - [tex]\frac{1071}{4788}[/tex] ) ≈ 103° ( to the nearest degree )