2. Use the Rational Root Theorem to list all possible rational roots for the equation.
3x³ +9x-6=0
2
O±1, 12, 13, 16, ±, ± -
6,±3⁄3,±0
T
تانی
O±1, ±3, ±6
2
O±1, ± 2, ±3, ±6, ± -, ± -, ±=
3 3
NI
3
1/3
WIN
112
±1, +2, +3, +9,-,-
, -, ±一,土
13
MIN
3
2

The cheapest option for Jane is to buy from Suttons Shop, as the total cost is £12, whereas, at Greens Garden Shop, the total cost is £9.98.

To determine the cheapest option, we need to calculate the cost of purchasing 140 liters of compost from each shop.

First, we'll calculate the cost at Suttons Shop:

Jane needs 140 liters of compost, so she needs 140 / 20 = 7 bags of compost.

If she buys 1 bag of compost, it will cost her £2.25.

If she buys 2 bags of compost, it will cost her £3.25.

Since she needs 7 bags of compost, she can buy 3 sets of 2 bags (6 bags) and 1 bag.

So the cost of 6 bags will be 3.25 x 3 = £9.75, and the cost of 1 bag will be 2.25.

The total cost of 7 bags at Suttons Shop will be 9.75 + 2.25 = £12.

Next, we'll calculate the cost at Greens Garden Shop:

Jane needs 140 liters of compost, so she needs 140 / 70 = 2 bags of compost.

Each bag at Greens Garden Shop costs £4.99.

So the total cost of 2 bags at Greens Garden Shop will be 4.99 x 2 = £9.98.

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The value of ZE angle is 72 degree and LF is 18 degree.

Complementary and supplementary angles are defined as the addition of two angles. If the sum of two angles is 180 degrees, one is a complementary angle and together they form a linear angle. When the sum of two angles is 90 degrees, they are called complementary angles and together form a right angle.

ZE and LF are complementary. The measure of ZE is 54° more than the measure of LF.

let ZE angle value is x

and ZE is 54 degree more than LF

LF + 54 = ZE  degree  

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

LF +ZE = 90 degree

x+x-54 = 90

2x = 36

x = 18

so ZE angle = 72 degree and LF is 18 degree

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Answer:

7n - 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the missing side and the angles for the right triangle with leg BC = 2.7 cm and hypotenuse AB = 3.1 cm.

The cosine of angle B is given by ...

  Cos = Adjacent/Hypotenuse

  cos(B) = CB/AB = 2.7/3.1

Then the angle is ...

  B = arccos(2.7/3.1) ≈ 29.429°

  B ≈ 29°

Angle A is the complement of angle B:

  A = 90° -29°

  A = 61°

The sine ratio is ...

  Sin = Opposite/Hypotenuse

Then side AC can be found from ...

  sin(B) = AC/AB

  AC = AB·sin(B) = 3.1·sin(29.429°) ≈ 1.523

  AC ≈ 1.5 . . . . cm

The triangle solution is ...

__

Additional comment

The mnemonic SOH CAH TOA is intended to help you remember the trig ratios above, in addition to ...

  Tan = Opposite/Adjacent

Answer:

  36 bottles

Step-by-step explanation:

You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.

The profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.

  profit = selling price - purchase price

  profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle

To make a profit of $120, you need n bottles such that ...

  (10/3)n = 120

  n = 36 . . . . . . . . . multiply by 3/10

The club needs to buy, paint, and sell 36 bottles to raise $120.

Answer:

So the solution to the system of equations is (x,y) = (3,-2).

Step-by-step explanation:

To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.

Starting with the second equation:

4x - 3(-2) = 18

Expanding the -3(-2) using the distributive property:

4x + 6 = 18

Subtracting 6 from both sides:

4x = 12

Dividing both sides by 4:

x = 3

Now that we have x = 3, we can substitute that back into the first equation to find y:

y = -2

So the solution to the system of equations is (x,y) = (3,-2).

Answer:

25/50

will equal to 1/2

a) The missing frequency is 20

b) The modal number of people in a car is 1

c) The median is 3

d) The mean is 0.95

The sum of the frequencies must be 60.

The missing frequency by subtracting the sum of the other frequencies from 60

60 - (28 + 3 + 7 + 1 + 1) = 20

To find the median, we need to arrange the data in order from smallest to largest:

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6

There are 60 numbers in total, so the median is the average of the 30th and 31st numbers:

median = (3 + 3)/2 = 3

The mode is the value with the highest frequency, which is 1.

mean = (1 x 28 + 2 x 20 + 3 x 3 + 4 x 7 + 5 x 1 + 6 x 1) / 60

= (28 + 40 + 9 + 28 + 5 + 6) / 60

= 0.95

Therefore, the missing frequency, mode, median and mean has been found

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The given question is incomplete, the complete question is

Hassan recorded the number of people in 60 passing cars

people 1 2 3 4 5 6

frequency 28 ? 3 7 1 1

a)find the missing frequency

b)median

c)modal

d)mean

Answer:

D. 3/7, 3:7, or 3 to 7

Step-by-step explanation:

To get by what percent the second number (10) is greater than the first number (5), we can use the following formula:

percent increase = ((new value - old value) / old value) x 100%

So, for the pair of numbers 5 and 10:

percent increase = ((10 - 5) / 5) x 100% = 100%

This means that 10 is 100% greater than 5.

To determine by what percent the first number (5) is less than the second number (10), we can use the following formula:

percent decrease = ((old value - new value) / old value) x 100%

So, for the pair of numbers 5 and 10:

percent decrease = ((10 - 5) / 10) x 100% = 50%

This means that 5 is 50% less than 10.

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Percentage profit on a chocolate bar is 150%

Profit percentage is a top-level and the most common tool to measure the profitability of a business. It measures the ability of the firm to convert sales into profits. i.e., 20% means the firm has generated a net profit of $20 for every $100 sale.

%profit = (selling price - cost price)/cost price × 100

%profit =( 1.50-0.6)/0.6 × 100

%profit = 0.9/0.6 × 100

= 1.5 × 100

= 150 %

therefore the percentage profit on a chocolate bar is 150%

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The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54    

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

A ratio can be compared by the division of two numbers. For example, the ratio of a and b can be represented as a: b and read as a is to b. Here a: b can be written as a/b

Here we have  

The ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same. The table shows the number of atoms in different quantities of sulfur dioxide.  

The given table is

Sulfur atoms         6     9     12   ___

Oxygen atoms     12    __   ___   54      

Let x, y, and z be the missing values in the table

Given that ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same.  

=> 12/6 = x/9 = y/12 = 54/z    

Now the x, y, and z values can be calculated as follows

Take 12/6 = x/9  

=> 2 = x/9    

=> x = 18  

Take 12/6 = y/12  

=> 2 = y/12

=> y = 24

Take 12/6 = 54/z  

=> 2 = 54/z

=> z = 54/2

=> z = 27    

Therefore,

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54      

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The complete Question is given in the picture

Answer: 168 in.

Step-by-step explanation:

Feet to inches:

14ft = 168 in.

or

12 x 14 = 168.

Answer: 4 ft 3.8 inches

Step-by-step explanation:

First I converted the measurements to inches to make it easier-

Man - 74in

Tree - 240in

Tree shadow - 168in

240/168 = 74/x

x=51.8

Each week, Desiree earns $925 and pays $149 in payroll tax it will take Desiree at least 4 weeks to earn at least $3000 after taxes.

What is Gross earning ?

Gross earnings refer to the total amount of money that an individual earns before any deductions are taken out. These earnings can include regular salary or wages, as well as any bonuses, tips, or commissions that are earned. Gross earnings are usually reported on a paycheck or pay stub, and may be subject to various taxes and other deductions.

Desiree's net earnings after payroll tax can be calculated by subtracting the tax amount from her gross earnings:

Net Earnings = Gross Earnings - Payroll Tax

Net Earnings = $925 - $149

Net Earnings = $776

To earn at least $3000 after taxes, Desiree needs to earn a total of:

Total Earnings = $3000 + Payroll Tax

Total Earnings = $3000 + $149

Total Earnings = $3149

We can now set up an equation to solve for the number of weeks, x, it will take for Desiree to earn at least $3149:

Net Earnings per week * Number of Weeks = Total Earnings

$776 * x = $3149

Solving for x:

x = $3149 / $776

x = 4.05

Therefore, it will take Desiree approximately 4.05 weeks to earn at least $3000 after payroll tax. Since you can't earn partial weeks, we can round up to 5 weeks to ensure that Desiree has earned at least $3000.

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Answer:

AC = 16 cm

Step-by-step explanation:

given a tangent and a secant from an external point to the circle, then

the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is

AB × AC = AD²

4x = 8² = 64 ( divide both sides by 4 )

x = AC = 16 cm

Answer:

16 cm

Step-by-step explanation:

tan/sec Theorem

a² = b(b+c)

8² = 4(4+c)

64 = 16 + 4c

48 = 4c

12 = c

12 + 4 = 16 cm

The measure of angle DBC is 60 degrees

Any triangle's three angles always sum to 180 degrees. Therefore, if you only have two angles available, add them up, and then take 180 away from the result.

The computation of the measure of angle ABC is shown below:

Given that

Angle ABC is 120 degrees

And, the measure of angle BAC is 60 degrees

So based on the above information

The  measure of angle  is

= Angle ABC - Angle ABD

= 120 degrees - 60 degrees

= 60 degrees

hence, the measure of angle DBC is 60 degrees

Q - Angle ABC is equal to 120 degrees. The measure of angle ABD is 60 degrees. What is the measure of angle DBC?

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Answer:

61.504

Step-by-step explanation:

Answer:

There are £61.50 in 992

Step-by-step explanation:

Here, we shall be doing some currency conversions.Now, £31 = 500 rublesThen;£x = 992 rubles To get c, what we do is simply cross multiply £x * 500 rubles = £31 * 992 rubles £x = (£31 * 992 rubles)/500 rubles £x = £61.504which is £61.50 to two decimal places

hope this helps!!

Jerome saves 337.5$ on the computer.

Jerome buys the computer for 1912.5$.

The total cost of the computer is 2056$ including sales tax.

The total price of the computer not on sale is 2418.75$.

The discount is 15% of the original price:

0.15 x $2250 = $337.50.

If the sales tax is 7.5%,

The price of the computer after the discount is $2250 - $337.50 = $1912.50.

The amount of tax on the computer is 7.5% of $1912.50:

0.075 x $1912.50 = $143.44.

The total cost for the computer is the discounted price plus the tax: $1912.50 + $143.44 = $2055.94.

The total price for the computer not on sale would be the original price plus the tax:

$2250 + $169.13 = $2419.13 (where tax is 7.5% of $2250).

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The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.

In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:

= Number of shirts x Number of pairs of pants

= 2 x 3

= 6 outfits

Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.

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What is Null hypothesis?

The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance. For example, if the predicted earnings for the gambling game are genuinely zero, then any discrepancy between the data's average earnings and zero is due to chance.

(a) The appropriate null and alternative hypotheses for this setting are:

Null hypothesis: The actual mean systolic pressure (μ) of the individual is not greater than 130 (μ ≤ 130).

Alternative hypothesis: The actual mean systolic pressure (μ) of the individual is greater than 130 (μ > 130).

(b) Type I error occurs when the null hypothesis is rejected when it is actually true. In this case, it means that the device recommends that the person seeks medical attention when they do not actually need it. The consequence of this error is that the person may undergo unnecessary medical tests or treatments, which can be costly, time-consuming, and can cause anxiety or other negative effects.

Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, it means that the device does not recommend medical attention when the person actually needs it. The consequence of this error is that the person may not receive the necessary medical attention and treatment, which can lead to serious health problems, including organ damage or failure, stroke, or heart attack.

(c) In this scenario, the cost of making a Type II error is likely to be much higher than the cost of making a Type I error. The reason is that failing to detect high blood pressure in a person can have serious health consequences. Therefore, it is better to make the Type I error probability smaller and the Type II error probability larger. This means that the device should be adjusted to have a higher threshold for recommending medical attention, which would decrease the likelihood of a false alarm, even if it increases the likelihood of missing some cases where medical attention is needed.

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The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge. According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.

A type I error (false-positive) occurs when a researcher rejects a null hypothesis that is actually true in the population; if the researcher does not do this When a null hypothesis is rejected even when it is false in the population, this is known as a type II error (false-negative).

Parameter Hypothesis testing is a second sort of statistical inference.

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The measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠B as follows:

m∠A + m∠B + m∠C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B + 139° = 180°

B = 180° - 139° {subtract 139° from both sides}

m∠B = 41°

12.7/sin90° = a/sin41

a = (12.7 × sin49)/sin90° {cross multiplication}

a = 9.5848

12.7/sin90° = b/sin49

b = (12.7 × sin49)/sin90 {cross multiplication}

b = 8.3319

Therefore, the measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

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The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.

11.2 km = 11,200 meters (1 km = 1000 meters)

Stride length in meters = 70 cm / 100 cm/m = 0.7 m

Now, we can calculate the minimum number of strides as follows,

Minimum number of strides = (Distance covered in meters) / (Stride length in meters)

Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000

Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

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Given the matrix, [tex]\begin{bmatrix}2 & 3 \\3 & 2 \end{bmatrix}[/tex], find its inverse.

First we need to find its determinant which can be done by using the following formula,

[tex]det=\begin{bmatrix}a & b \\c & d \end{bmatrix}=ad-cb[/tex]

Lets call  [tex]\begin{bmatrix}2 & 3 \\3 & 2 \end{bmatrix}[/tex] matrix "A."

So,

[tex]detA=(2)(2)-(3)(3)[/tex]

[tex]\Longrightarrow detA=4-9[/tex]

[tex]\Longrightarrow detA=-5[/tex]

We now have the determinant, we can now use the following formula to determine the inverse matrix,

[tex]A^{-1} =\frac{1}{detA} \begin{bmatrix}d & -b \\-c & a \end{bmatrix}[/tex]

[tex]A^{-1} =-\frac{1}{5} \begin{bmatrix}2 & -3 \\-3 & 2 \end{bmatrix}[/tex]

[tex]\Longrightarrow A^{-1} = \begin{bmatrix}2(-\frac{1}{5}) & -3(-\frac{1}{5}) \\-3(-\frac{1}{5}) & 2(-\frac{1}{5}) \end{bmatrix}[/tex]

[tex]\Longrightarrow A^{-1} = \begin{bmatrix}-\frac{2}{5} & \frac{3}{5} \\\frac{3}{5} & -\frac{2}{5}\end{bmatrix} \therefore \ Sol.[/tex]

*Note* I went a few more steps than the question needed. If you back up two steps on my answer is where they stopped. The last option is correct.

Answer:

287 miles

Step-by-step explanation:

20.95+ .80x =250.55

250.55-20.95=229.6

.80x=229.6

229.6/.80=x

x=287 miles

Answer: B: 15,080

Step-by-step explanation:

Alright, let's convert 20% into a decimal: 0.20

Then multiply 0.20 x 75,400  which gets you to 15080

So she needed to pay $15,080 in taxes

The value of a in the equation a + 2 = 3 is 1.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

a + 2 = 3

Subtract 2 from both sides

a + 2 - 2 = 3 - 2

a = 1

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In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.

Total number of observations = 860

Mean of the observations = 76

Standard deviation = 18

The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -

Z = X - u/a

Calculating the observations -

Where X = 112 u = 76 and a = 18

Z = 112 - 76/18

= 36/18

= 2

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Answer:

He drove 6 hours.

Step-by-step explanation:

distance = rate times time

300 = 50t  Divide both sides by 50

t = 6