Decimals from greatest to least
.750
.475
-0.123
.675
.253

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 3

b = 6

The factors of 3 and 6 are

a = 1 and 3

b = 1, 2, 3 and 6

So, we have:

Rational roots = ±(1, 2, 3, 6)/(1, 3)

Split the expression

Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3

Evaluate the quotient

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)

Remove the repetition

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)

Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

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The theoretical probability of randomly getting a black counter is P = 2/5.

In this case, we have 8 black counters and 12 white counters, so there is a total of 20 counters.

We assume that all the counters have the same probability of being randomly selected, then the probability of randomly selecting a black counter is just given by the quotient between the number of black counters and the total number of counters.

There are 8 black counters and 20 in total, then the probability is given by:

P = 8/20

Now we can simplify that fraction to get:

P = 2/5

The theoretical probability of randomly getting a black counter is P = 2/5.

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The area of this regular polygon is 46.8 square units

The given parameters are:

Perimeter, p = 54 m

Apothem, a = √3

The area of this regular polygon is then calculated as:

Area = 0.5 * Apothem * Perimeter

Substitute the known values in the above equation

Area = 0.5 * √3 *  54

Evaluate the product

Area = 46.8

Hence, the area of this regular polygon is 46.8 square units

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The surface area of the Spheres is 104.19 cm².

According to the statement

we have given that the

there is a cube with side 10 cm and convert into ten spheres and we have to find the surface area of a sphere.

So,

we know that the cube has a  6 sides, each one 10 x 10 cm

So,

A cube with sides of 10 cm will have a surface area of 600 cm².

And The volume of the cube will be 1,000 cm³  ( = 10 x 10 x 10).

If you melt it down to form ten identical spheres, each of them will have a volume of:

1,000 cm³ / 10  =  100 cm³

And the volume of a sphere is:

[tex]V = 4/3 (pi)r ^{2}[/tex]

So you can calculate the radius of the spheres:

r³ =  3V / 4pi  =  (300) / (12.5664)  =  23.8732 cm³

r  =  2.8794 cm

Now, you can use the radius to find the surface area of the spheres:

As  =  4pi*r² =  (12.5664)(2.8794)^2  =  104.19 cm²

So, The surface area of the Spheres is 104.19 cm².

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Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The total number of students is given by:

26 + 3 + 9 + 10 + 6 + 5 + 7 = 66

Of those, 26 play only football, hence the probability is:

p = 26/66 = 13/33

Which means that option c is correct for question 19.

Of those same 66 students, 9 + 7 = 16 play baseball but not football, hence the probability is:

p = 16/66 = 8/33

Which means that option d is correct for question 20.

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The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

According to the statement

we have given that the Smith family's sprinkler was 25L per hour and

Stewart family's sprinkler was 30L per hour and The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L.

And we have to find the How long was each sprinkler used.

So, For this purpose,

The given statements in the equation form become:

Let Smith family's sprinkler be x

Let Stewart family's sprinkler be y then

The equation become

x + y = 65 -(1)

25x + 30y = 1750 -(2)

Here we use the elimination method.

So, Multiply (1) by 25 and (2) by 1 then

25x + 25y = 1625

25x + 30y = 1750

Now eliminate x from the equations then

-5y = -125

y = 25

then x value becomes

x + y = 65

x + 25 = 65

x = 40.

So, The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

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By solving a quadratic equation we will see that the number can be:

8 or -5.

The product of a number N, and 3 less than the number, is equal to 40.

This is written as:

[tex]N*(N - 3) = 40[/tex]

Now we need to solve this for N.

[tex]N^2 - 3N = 40[/tex]

[tex]N^2 - 3N - 40 = 0[/tex]

Then we need to solve this quadratic equation:

[tex]N = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*1*(-40)} }{2} \\\\N = \frac{3 \pm 13 }{2}[/tex]

Then we have two solutions:

These are the two possible solutions.

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Answer: 4.9

Step-by-step explanation:

[tex]AB=\sqrt{(-4-3)^2 +(6-4)^2}=\sqrt{53}\\\\A'B'=\frac{2}{3}\sqrt{53} \approx \boxed{4.9}[/tex]

The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

= y = -2/1

= y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

= x + 3 = 0

= x = -3

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Step-by-step explanation:

[tex] = \frac{6}{7} \times \frac{2}{3} \\ [/tex]

[tex] = \frac{12}{21} \\ [/tex]

Change into lowest term...

[tex] = \frac{4}{7} \\ [/tex]

...

The value of the evaluation of logarithm e^in4 is 4

Given the expression as;

e^in4

To put in logarithmic form, equate to the power of the "Lin,ln value"

Now, let's equate it to the value of the exponential

e^in4 = 4

We have that'

[tex]loge x = loge 4[/tex]; this is the logarithmic form of the expression but we need to find the value of 'x'

To find the value, let's cancel out the like variables, we have

[tex]x = 4[/tex]

Then we have the value to be

x = 4

Thus, the value of the evaluation of logarithm e^in4 is 4

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Using the normal distribution, there is a 0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching this problem on the internet, the parameters are given as follows:

[tex]\mu = 150, \sigma = 9, n = 10, s = \frac{9}{\sqrt{10}} = 2.85[/tex]

The probability is one subtracted by the p-value of Z when X = 157, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (157 - 150)/2.85

Z = 2.46

Z = 2.46 has a p-value of 0.993.

1 - 0.993 = 0.007.

0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

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there are 12 months in a year, so then 4 months is really 4/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\to \frac{4}{12}years\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (1200)(0.05)(\frac{1}{3})\implies I=20~GHC[/tex]

Answer:

Step-by-step explanation:

9. D

10.D

11.E

12.D

Answer:

9.

[tex]x^2-4\\(x-2)(x+2)[/tex]

10.

[tex]x^2-25\\(x-5)(x+5)[/tex]

11.

[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]

12.

[tex]x^2+100\\[/tex]

This polynomial cannot be factored by using the difference of squares method

Answer:

  no

Step-by-step explanation:

The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.

  tan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600

The angle is found using the inverse relation:

  α = arctan(1/600) ≈ 0.095°

If Emily's aim is off by 0.2°, she will miss the target by several inches.

__

Additional comment

Emily's projectile will miss her aiming point by ...

  (150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in

The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.

The data shows that:

E(x) = 1

E(y) = 2

E(z) = 3

Var(X) = 2² = 4

Var(Y) = 4² = 16

Var(Z) = 5² = 25.

Cov(U, V) = 16

Var(U) = Var(Z - Y)

= 25 - 0 + 16

= 41

The correlation coefficient will be:

= -16/✓(20 × 41)

= -0.5587

The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.

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Based on the distance of the pitcher's mound from the home plate, the path of the ball, and the height the ball was hit, the distance the outfielder threw the ball is C. 183.0 ft.

Based on the shape of a mound, the law of cosines can be used.

The distance the ball was thrown by the outfielder can therefore be d.

Distance is:

d² = 60.5² + 226² - (2 x 60.5 x 226 x Cos(39))

d ²= 33,484.42ft

Then find the square root:

d = √33,484.42

= 182.9874

= 183 ft

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Answer:

83.23%

Step-by-step explanation:

Proportioned Value = 12.9

Total Value = 15.5

Percentage = Proportioned Value / Total Value * 100%

= [tex]\frac{12.9}{15.5}*100[/tex]

= 83.23% (nearest hundredth)

The answer is 83.23%.

To find the percentage, take the ratio between 12.9 and 15.5, and multiply by 100%.

Answer:

7 weeks, £35, and £21.

Step-by-step explanation:

Every week, Suzie saves £5 and gets £3 from her Mum. Altogether, Suzie gets £8 every week. All we need to do is divide 56 by 8, which gives us 7. Suzie will take 7 weeks to collect enough money. To find out how much she has saved and been given by her mum individually, we need only times these values by 7. 5x7=35, and 3x7=21.

The slope of the graph is 1 / 5.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Slope describes the steepness of a line. The slope of any line remains constant along the line.

Therefore,

slope  = y₂ - y₁ / x₂ - x₁

Hence, let's take two coordinates in the graph,

(2, 2)(7, 3)

x₁ =  2

x₂ = 7

y₁ = 2

y₂ = 3

Therefore,

slope = 3 - 2 / 7 - 2

slope = 1 / 5

Therefore, the slope of the graph is 1 / 5.

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The revenue function in terms of q will be 200q - 3q².

The following can be deduced based on the information given:

P(q) = 200 - 3q

C(q) = 75 + 80q - q²

The revenue function in terms of q will be:

= Price × Quantity

= (200 - 3q) × q

= 200q - 3q²

The profit will be:

= Total revenue - Total cost

= (200q - 3q²) - (75 + 80q - q²)

= 200q - 3q² - 75 + 80q + q²

= -2q² + 280q - 75

= 2q² - 280q + 75

The average cost function will be:

= Total cost / Quantity

= (75 + 80q - q²) / q

= 75/q + 80 - q

The marginal cost will be 80 - 2q.

The marginal revenue will be 200 - 6q.

The marginal cost when q = 20 will be:

= 80 - 2q

= 80 - 2(20)

= 80 - 40

= 40

The marginal revenue when q = 20 will be:

= 200 - 6q

= 200 - 6(20)

= 200 - 120

= 80

The company should decrease production from 20 units in order to gain more profit.

The production level that gives the largest profit for the company will be gotten by finding the second derivative for the profit function as illustrated in the question. The profit function is 2q² - 280q. Then the production level will be 4.

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Answer:

[tex]\sf b) \quad \dfrac{y^3}{4x}[/tex]

Explanation:

[tex]\sf \left(\dfrac{6x^2}{5y}\right) \left(?}\right) = \left(\dfrac{3xy^2}{10}\right)[/tex]

cross multiply variables

[tex]\sf ? = \left(\dfrac{3xy^2 (5y)}{10(6x^2)}\right)[/tex]

distribute inside parenthesis

[tex]\sf ? = \left(\dfrac{15xy^3}{60x^2}\right)[/tex]

remove parenthesis and simplify

[tex]\sf ? = \dfrac{y^3}{4x}[/tex]

Answer:

B

Step-by-step explanation:

Every (x,y) pair is equal to each other, thus making them proportional :)

Answer:

1.873

Step-by-step explanation:

Use the exponent rule for roots

[tex]\sqrt[4]{3^{7} } = 3^{\frac{4}{7} }=3^{0.5714} = 1.873[/tex]

Good luck!

Answer:

Step-by-step explanation:

e^-6 = 1/e^6 = about 0.00248

The monetary policy that the Central Bank is using to address the downturn in the economy is the reduction of the reserve requirement from 17% t 14%.

It should be noted that the monetary policy is the set of actions to control money supply in the economy.

The macroeconomic issues resulting from the pandemic on Trinidad and Tobago are that there are less money in circulation and there's a reduction in the standard of living.

The reduction of the reserve requirement will impact the money supply as it will lead to more money in circulation.

Complete question:

1. What form of monetary policy can the Central Bank use to address the downturn in the economy resulting from the pandemic?

2. Identity and explain two macroeconomic issues resulting from the pandemic on Trinidad and Tobago.

3. Identify how the reserve requirement will impact the money supply.

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Answer:60 ml

Step-by-step explanation:20 % of 300 = 60 and snce the rest of the the l are coffee thats 20%

The volume of the solid is which is a cone is 100.48 [tex]km^{3}[/tex].

Given a cone of radius 4 km and height being 6 km.

We are told to find the volume of the cone.

Volume is basically the amount of a substance that a container can hold in its capacity.Its value cannot be equal to zero or negative. It is basically amount of filling in a container.

Volume of cone is 1/3 [tex]\pi r^{2} h[/tex].

Volume =1/3 [tex]\pi 4^{2} *6[/tex]

=1/3 π*16*6

=32π

=32*3.14

=100.48[tex]km^{3}[/tex]

Hence if the radius of the cone is 4 km and height be 6 km then the volume of the cone is 100.48[tex]km^{3}[/tex].

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The measure of the unknown angles are as shown below;

m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

An angle is the point where the two lines meet. From the given diagram, the lines B and D are parallel to each other with a transversal.

Given the following parameters

m<1 = 52 degrees

From the given diagram, the following are true

m<1 = m<3 (corresponding angle)

m<3 = m<8 (vertical angles)

m<1 = m<6 (vertical angles)
m<2 = m<5 (vertical angles)

m<4 = m<7 (vertical angles)

Also;

m<1 + m<2 = 180

m<2 = 180 - m<1

m<2 = 180 - 52
m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

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