Composition of two functions:Basic

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: d

Step-by-step explanation:

The graph is increasing, so the base must be more than 1.

Also, the y-intercept is 2.

This leaves d.

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 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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Answer: 48 doghouses

Step-by-step explanation:

We will look at the details given, then we will perform the necessary operations to solve the problem.

     16 bundles of plywood * 12 sheets in a bundle = 192 sheets

     192 total sheets / 4 sheets to build a dog house = 48 doghouses

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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]

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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Answer:

the answer is 86,016

Step-by-step explanation:

i took the test

Answer:

The answer is 4.

Step-by-step explanation:

8(-1)^4 - 3(-1) - 7

    8 + 3 - 7

      11 - 7

         4

Answer:

■ Sales tax: $52.75

■ Cost/Price before ST: $540.99

■ Total Cost/Price including ST: $593.74

Step-by-step explanation:

540.99 x 0.0975

= 52.75

Total

= 540.99+52.75

=593.74

The probability that a randomly selected member did not volunteer for the recent activity is 19/43.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered

1 - 24/43

(43/43) - (24/43) = 19/43

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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:

[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]

a. The changes in each four-month period are as follows:

Month and       Prices       Absolute      Relative

Year              in Dollars     Change       Change

Apr-20              1.841             n/a                n/a

Aug-20            2.183         $0.342        18.58%

Dec-20            2.195            0.012         0.55%

Apr-21             2.858          0.663         30.21%

Aug-21             3.158          0.300        10.50%

Dec-21            3.307           0.149          4.72%

Apr-22            4.109          0.802        24.25%

b. The change in gas prices has been relatively unstable.

c. Using the inflation calculator, the costs of gas in April 2020 in 2022 dollars terms should be $2.08.

d. The inflation-adjusted cost of gas in April 2020 when compared to April 2022 as absolute and relative changes are as follows:

Absolute change = $2.268 ($4.109 - $1.841)

Relative change = 123.2% ($2.268/$1.841 x 100)

e. The two most drastic rises in gasoline prices in April 2021 and April 2022 can be attributed to spikes in demand relative to supply.

Gasoline prices rise when there is an increased demand relative to supply.

Increasing prices in gasoline prices can also be attributed to cuts in production and supply by the oil cartel.

An absolute change is a dollar change from one period to another.

A relative change is an absolute change expressed in percentages.

The calculations of absolute change and relative change are demonstrated below.

Month and       Prices       Absolute      Relative

Year              in Dollars     Change       Change

Apr-20              1.841             n/a                n/a

Aug-20            2.183         $0.342        18.58% ($0.342/$1.841 x 100)

Dec-20            2.195           0.012         0.55% ($0.12/$2.183 x 100)

Apr-21             2.858          0.663        30.21% ($0.663/$2.195 x 100)

Aug-21             3.158          0.300        10.50% ($0.3/$2.858 x 100)

Dec-21            3.307           0.149          4.72% ($0.149/$3.158 x 100)

Apr-22            4.109          0.802        24.25% ($0.802/$3.307 x 100)

Absolute Change for Aug-20 = $0.342 ($2.183 - $1.841)

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The spread of the disease will take a time 100 days to reach 2,500 infected people.

In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)

2,500 = 250 · √t

√t = 2,500 / 250

√t = 10

t = 10²

t = 100

The spread of the disease will take a time 100 days to reach 2,500 infected people.

The statement is poorly formatted and presents typing mistakes, correct form is shown below:

The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?

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Compute the divergence of [tex]\vec F[/tex].

[tex]\mathrm{div}(\vec F) = \dfrac{\partial(2x^3+y^3)}{\partial x} + \dfrac{\partial (y^3+z^3)}{\partial y} + \dfrac{\partial(3y^2z)}{\partial z} = 6x^2 + 3y^2 + 3y^2 = 6(x^2+y^2)[/tex]

By the divergence theorem, the integral of [tex]\vec F[/tex] across [tex]S[/tex] is equivalent to the integral of [tex]\mathrm{div}(\vec F)[/tex] over the interior of [tex]S[/tex], so that

[tex]\displaystyle \iint_S \vec F\cdot d\vec S = \iiint_{\mathrm{int}(S)} \mathrm{div}(\vec F)\,dV[/tex]

The paraboloid meets the [tex]x,y[/tex]-plane in a circle with radius 3, so we have

[tex]\mathrm{int}(S) = \left\{(x,y,z) \mid x^2+y^2\le3 \text{ and } 0 \le z \le 9-x^2-y^2\right\}[/tex]

and

[tex]\displaystyle \iiint_{\mathrm{int}(S)} \mathrm{div}(\vec F) \,dV = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_0^{9-x^2-y^2} 6(x^2+y^2)\,dz\,dy\,dx[/tex]

Convert to cylindrical coordinates, with

[tex]\begin{cases}x = r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]

so that [tex]x^2+y^2=r^2[/tex], and the domain of integration is the set

[tex]\left\{(r,\theta,\zeta) \mid 0 \le r \le 3\text{ and } 0 \le \theta\le2\pi \text{ and } 0 \le \zeta \le 9-r^2\right\}[/tex]

Now compute the integral.

[tex]\displaystyle \int_0^3 \int_0^{2\pi} \int_0^{9-r^2} 6r^2\cdot r\,d\zeta\,d\theta\,dr = 12\pi \int_0^3 \int_0^{9-r^2} r^3\, d\zeta \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \int_0^3 r^3 (9 - r^2) \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \int_0^3 (9r^3 - r^5) \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \left(\frac94 r^4 - \frac16 r^6\right)\bigg|_0^3 = 12\pi \left(\frac94\cdot3^4-\frac16\cdot3^6\right) = \boxed{729\pi}[/tex]

Answer:

45.7 kilometers = 45,700 meters

Explanation:

Hi!
Okay, so basically, in one kilometer, there are 1000 meters.
Using this problem, all you have to do is multiply 45.7 by 1000, which is 45,700.

Whatever value is used for kilometers (ex. 2), just multiply by 1000, and you’ll get the value as meters (ex. 2 x 1000 = 2000 meters).

Hope this helps!

To convert kilometers to meters, multiply the kilometer value by 1000 meters which is equal to 1 km.

Convert 45.7 kilometers to meters:

               [tex]\boldsymbol{\sf{Therefore \ \ \longmapsto \ \ 45.7\not{km}*\left(\dfrac{1000 \ m}{1\not{km}}\right)=45700 \ m }}[/tex]

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Total 8 triangles are formed in figure and 4 edges used to make triangles and The area of all triangle is 1 square unit.

According to the statement

we have given that a figure and we have to the number of triangle present in it and the area of each square and the number of edges used in all triangles.

So, For this purpose, we know that the

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

So,

A. The number of triangles present in figure:

There is a rectangle provided with two diagonals and due to this structure

Firstly 4 triangles are formed with 2 diagonals (big size).

And 4 triangles are formed in diagonals because diagonals cut each other (small size).

So, Total 8 triangles are formed in figure.

B. Edges used to form triangle :

there are 4 edges used to form triangles because of presence of overall shape of rectangle because triangles are formed in a rectangle shape.

So, 4 edges used to make triangles.

C. Area of the triangle:

If the area is 1 square unit and area of all triangles are same

So, The area of all triangle is 1 square unit.

So, Total 8 triangles are formed in figure and 4 edges used to make triangles and The area of all triangle is 1 square unit.

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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]

Answer:

B

Step-by-step explanation:

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

Based on the given current and the given resistance, the voltage of the current is 14 + j8

From the question, we have the following parameters

current of 4+j2 amps and a resistance of 2-j3 ohms.

This can be rewritten as:

Current (I) = 4+j2 amps

Resistance (R) = 2-j3 ohms.

The formula to calculate voltage is given as

Voltage=(current) × (resistance)

Rewrite as:

V = I * R

Substitute the known values in the above equation

V = (4 + j2) * (2 - j3)

Expand the brackets

V = 8 - j4 + j12 + 6

Collect the like ters

V = 8 + 6 - j4 + j12

Evaluate the like term

V = 14 + j8

Based on the given current and the given resistance, the voltage of the current is 14 + j8

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The FOIL method is a method of expanding two given brackets by following the required steps. Thus using the FOIL method, the required answer is: -7

Expansion of brackets may be done using different methods, but these methods would give the same answer. Some methods that can be used are the binomial expansion method, FOIL method, etc.

The FOIL method is a shortened form of the steps required for the process. These required steps are First, Outside, Inside, and last.

Thus to expand the given brackets in the question, we have;

(5+2)(4-5) = 5(4 - 5) + 2(4 - 5)

                = 20 - 25 + 8 - 10

                = 28 - 35

(5+2)(4-5) = -7

Thus using the FOIL method, the answer to the question is -7.

Quick check: (5+2)(4-5) = (7)(-1)

                             = -7

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Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.

Therefore, the correct answer is option A. The mean is less than the median.

Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.

Half the students scored 87.

The next highest score exists at 71.

Then the median will be (71+ 87) / 2 = 79

A few students scored 52, so the mean exists a little lower than the mean of 71 and 87.

Therefore, the correct answer is option A. The mean is less than the median.

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The complete question is:

In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?

A. The mean is less than the median.

B. The mean and the median is the same.

C. The mean is greater than the mode.

D. The mean is greater than the median.

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:

1/4 ,- 4, 1/2 2 1/2 4 1/4

Step-by-step explanation:

1/4, 4 1/2, 2,1/2,4, 1/4,

Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angle triangle. Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other.

From triangle MNL and triangle QNL, in triangle MNL:

∠M + ∠N + ∠L = 180° (sum of angles in a triangle)

90 + 58 + ∠L = 180

∠L = 32°

Hence Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.

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The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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The vector in component form is given by:

V = i - j.

A vector is given by the terminal point subtracted by the initial point, hence:

(3,-4) - (2, -3) = (3 - 2, -4 - (-3)) = (1, -1)

A vector (a,b) in component form is:

V = a i + bj.

Hence, for vector (1,-1), we have that:

V = i - j.

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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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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

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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