f(x) = 4 - 2x – 2x3
g(x) = x² + 7x-9
Find f(x) + g(x).

Answer:

Step-by-step explanation:

A y = -3.6x + 12.8

The line of best fit is,

⇒ y = - 3.6x + 12.8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, Given that;

⇒ y = ax + b.

And, the best fitting line has values of a = - 3.6 and b = 12.8.

Hence, All you need do is put that into the general equation and try different values for it.

So you have y = - 3.6 x + 12.8

Now Let's run a couple of numbers.

The table shows 1 and 9 for the first entry. This means when x = 1, y should come pretty close to nine.

y = - 3.6(1) + 12.8

y = 9.2

Which is not a bad result for x = 1

You might want to check to see if anything else comes closer in your choices. If it does, then you have to try other points.

C

-0.998 = -3.6(1) + 12.8

This answer cannot work. We've already shown that x =1 will leave us close to 9  not -998

So, C is incorrect.

B

y = 12.8x - 3.6

Let x = 1

y = 12.8(1) - 3.6

y = 9.2 is right by coincidence. We must try another value. The hardest one is going to be 5 and - 5

y= 12.8*5 - 3.6

y = 64 - 3.6 which is no where's near - 5.

So B is wrong.

A

y = -0.998(1) + 12.8 Does this give 9 or anywhere near it? 11.802 You might argue that that is not a bad result. So let's try another pair.

x = 3. y should come to somewhere near 2.

y = -0.998 * 3 + 12.8 which comes to roughly nine. You can check this out.

It is not close enough to 2 to be acceptable.

Thus, The correct option is,

⇒ y = - 3.6x + 12.8

Learn more about the mathematical expression visit:

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#SPJ7

Step-by-step explanation:

ejdjbd x bxbx k wbu y DJ UK j HK JM dz

nb

Step-by-step explanation:

I have no idea but here's thiss

Given:

In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].

To find:

The length of the hypotenuse.

Solution:

It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the given triangle,

[tex]\sin A=\dfrac{a}{c}[/tex]

Substituting the given values, we get

[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]

By cross multiplication, we get

[tex]1\times c=4\times 2[/tex]

[tex]c=8[/tex]

Therefore, the length of the hypotenuse is 8 units.

the answer is in the picture

Answer:

Cross sectional study

Step-by-step explanation:

Cross sectional study, also known as traverse or prevalence study caloukdnbe defined as a form of observational study which involves analysing a certain sample of data which is selected based on a variable of interest. This data is collected at a given point in time across the sample population. In the scenario described above, the record of viewing habit of 7500 household smoke obtained today(point in time) will be used to determine the proportion tuned to a particular sport programme. (data collected is based on the variable to be analyzed).

Answer:

9 basketballs

15 footballs

Step-by-step explanation:

The number of basketballs will be y.

The number of basketballs will be y + 6.

y + y + 6 = 24

2y + 6 = 24

2y + 6 - 6 = 24 - 6

2y = 18

2y ÷ 2 = 18 ÷ 2

y = 9

y + 6

9 + 6 = 15

Answer:

Step-by-step explanation:

there are a total of 16+8+8=32 coins in bag

16 out of 32 are red

player wins by pulling a red coin

assume it is a single pull, the winning probability = 16/32 = 1/2

so it is 50/50 chance n hence a fair game

Step-by-step explanation:

yes it is a fair game because any one don't know what the coin will get, it is based on luck

Answer:

(-4/3, 2]

Step-by-step explanation:

f(x)= sqrt (4-x^2)

g(x) = sqrt (3x+4)

domain of f(x)/ g(x)

The domain of the numerator is

4-x^2 ≥ 0

4 ≥x^2

Taking the square root of each side

-2 ≤x≤2

The domain of the denominator

3x+4 > 0  ( the denominator cannot be zero)

3x>-4

x > -4/3

Combine the restrictions to make it most restrictive

-4/3<x≤2

In interval notation

(-4/3, 2]

Answer:

0.3233

0.09

Step-by-step explanation:

Given that :

Mean, λ = 0.25 for a 100,000 per week

For a population of 800,000 :

λ = 800,000 / 100,000 * 0.25 = 8 * 0.25 = 2 orders per week

Probability that technician is required after one week ;

After one week, order is beyond 2 ; hence, order, x ≥ 3

P(x ≥ 3) = 1 - [p(x=0) + p(x= 1) + p(x =2)]

P(x ≥ 3) = 1 - e^-λ(1 + 2¹/1! + 2²/2!)

P(x ≥ 3) = 1 - e^-2(1+2+2) = 1 - e^-2*5 = 1 - e^-10

P(x ≥ 3) = 1 - e^-2 * 10

P(x ≥ 3) = 1 - 0.6766764

P(x ≥ 3) = 0.3233

B.)

Mean, λ for more than 2 weeks = 2 * 2 = 4

P(x < 2) = p(x = 0) + p(x = 1)

P(x < 2) = e^-4(0 + 4^1/1!)

P(x < 2) = e^-4(0 + 4) = e^-4(5)

P(x < 2) = e^-4(5) = 0.0183156 * 5 = 0.0915

P(x < 2) = 0.09

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Answer:

  y = 21/x

Step-by-step explanation:

The inverse variation relation means ...

  y = k/x

For the given values, we can determine the constant k:

  3 = k/7

  3×7 = k = 21

Then the function is ...

  y = 21/x

Answer: [tex]32.36\ ft[/tex]

Step-by-step explanation:

Given

Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]

Electric box is 30 ft up the ground.

Suppose x is the length of ladder

From the figure, we can write

[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.

The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,

[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]

Hence, the length of the ladder is 32.356 feet.

Learn more about Sine:

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Answer:

10

Step-by-step explanation:

let the distance = d

d² = (x2-x1)² + (y2-y1)²

=>

10²= (x-4)²+(1+7)²

100 = (x-4)²+64

(x-4)²=100-64

= 36

x-4 = √36

x-4=6

x= 6+4

x= 10

Answer:

216 yd³

Step-by-step explanation:

Volume of a rectangular prism

= product of the three orthogonal sides

= 6yd * 6yd * 6yd

= 216 yd³

Answer:

216

Step-by-step explanation:

:)

[tex]HOLA!![/tex]

Answer:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=e^{\frac{1}{3} } }}[/tex]

Explanation:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]

For this we have to take into account:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{x^{n} }{n!} =e^{x} }}[/tex]

Using the properties of factorials and exponents we have:

          [tex]n!=(n-1)n![/tex]  Also.    [tex]\frac{n^{x} }{ n^{y} }=n^{x-y}[/tex]  

We replace:

[tex]{\boxed{ \sum_{n=1}^{\infty}\ \frac{1}{3^{n-1}.(n-1)! } }}[/tex]

Shape it:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} }}[/tex]

Finally:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} =e^{\frac{1}{3} } }}[/tex]

Answer:

(S, FS, FFS, FFF)

Step-by-step explanation:

According to the Question,

So, the sample space for this random experiment is

{S, FS, FFS, FFF}

The person stops trying when he successfully enters the code or when he has failed at all 3 attempts .

9514 1404 393

Answer:

  D.  (x² -2x -3) +(-x² +4x +2)

Step-by-step explanation:

The tiles on the first row model (x² -2x -3).

The tiles on the second row model (-x² +4x +2).

If the difference is being modeled, it will show as ...

  (x² -2x -3) -(-x² +4x +2) = (x -2x -3) +(x² -4x -2) . . . . . matches none

If the sum is being modeled, it will show as ...

  (x² -2x -3) +(-x² +4x +2) . . . . . matches D

_____

Additional comment

As is often the case, you can select the correct answer without even any understanding of the question. You can do that because the correct answer is the only one that is a true statement. All of the other answer choices are incorrectly "simplified."

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Answer:

  (a) -7

Step-by-step explanation:

You are given f(x) = -3. Look for -3 in the f(x) column. (You will find it in the first row.)

You want the corresponding value of x. It will be in the first row of the x column. The value there is -7.

The value of x for f(x) = -3 is -7.

[tex]w - (14) < 8 \\ = w < 8 + 14 \\ \\ w = < 22[/tex]

Step by Step Explanation:

#CarryOnLearning

Step-by-step explanation:

Starting out with the Taylor series,

[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]

where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:

[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]

Expanding this series up to the 1st 3 terms at a = 0,

[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]

Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:

[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]

[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]

We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as

[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]

Answer:

Here we know that:

[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } }[/tex]

Where V is the speed, C = 3*10^8 m/s

We want to solve:

[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]

We can just isolate V from the above equation, so we will get:

[tex]\frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]

[tex]\frac{1}{\sqrt{1 - \frac{V}{C} } } = 2[/tex]

[tex]1 = 2\sqrt{1 - \frac{V}{C} }[/tex]

[tex](1/2)^2 = 1 - \frac{V}{C}[/tex]

[tex]V = (1 - (1/4))*C = (3/4)*C = (3/4)*3*10^8 m/s = (9/4)*10^8 m/s[/tex]

That is the velocity such that the effective mass is twice the rest mass.

Answer:

Baguette. :)

Step-by-step explanation:

Answer:

I don't know you lollollollll

Answer:

72

72

96

120

Step-by-step explanation:

The arcs are in the ratio:

3 : 3 : 4 : 5

Add all numbers in the ratio:

3 + 3 + 4 + 5 = 15

In the ratio, the sum of all numbers is 15.

In the real circle, the sum of the measures of all the arcs is 360.

360/15 = 24

Multiply all numbers in the ratio by 24.

72 : 72 : 96 : 120

Answer:

72

72

96

120

Answer:

p > 9

Step-by-step explanation:

First let's note down-

George- has 23$

Total cost of m+p= more than $14

Second, let's subtract 23 and 14 to get what the glue costs.

23 - 14 = 9

So now we can cross out choice A and D.

Third, now earlier I said  more than $14, this is the key part to find what we are going to choose.

more than = >

now we just plug in the variable,

p > 9

Hope this helps!

Please reach out to me if you still don't understand :)

9514 1404 393

Answer:

  the end of the whole number and the beginning of the fraction

Step-by-step explanation:

The word "and" means the whole part and the fractional part should be considered together as having a value equal to their sum. It signifies the separation between the whole-number part and the fractional part.

__

It has the same meaning as when used in a decimal mixed number:

1.2 = "one and two tenths"

Answer:

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Step-by-step explanation:

Tem.Before    Tem.After       diff.      

103.7                   102.6            1.1

103.7                   102.7             1

100.7                     98.8             1.9

102.7                    103.5            -0.8

100.7                      99.4             1.3

102.4                      101.41           (Mean)

1.4                             1.9              0.9       Std. Dev.

n =  6

df  =  6  -  1  =  5

CI we propose to be 95 %

Then  α  = 5 %  α = 0.05    

The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever

Hypothesis test

Null Hypothesis                      H₀         μd  = 0

Alternative Hypothesis          Hₐ         μd > 0

(NOTE:)   μd (average) = Temp Before  -  Temp. after

Therefore if   μd >  0   means that there is a statistical difference between values before ( bigger ) and after  or that the aspirin will reduce a child´s fever

To find t(c)  from t-student table  df = 5  and α = 0.05

t(c)  =  2.015

To compute  t(s)

t(s)  =  μd/ sd/√n      t(s)  =  0.98/ 0.9/√6

t(s)  =  2.66

Comparing  t(s) and  t(c)

t(s) > t(c)    

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Answer:

1.) We don't reject the null

2.) We reject the Null

3.) We do not reject the null

Step-by-step explanation:

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0

A.)

Left tail , Z = - 1.32 ; α = 0.10

We can use the Pvalue calculator from Z score :

Pvalue = 0.934

Pvalue > α ; Hence, we fail to reject the null, H0

B.)

Right-tailed test, z = 2.46, α = 0.01

Pvalue from Zscore calculator ;

Pvalue = 0.0069

Pvalue < α ; Hence, we reject the null, H0

C.)

Two-tailed test, z = -1.68, α = 0.05

Pvalue from Zscore calculator ;

Pvalue = 0.093

Pvalue > α ; Hence, we fail to reject the null, H0

Answer:

3000 text messages can be sent without breaking the budget.

Step-by-step explanation:

Since each month your cell phone company charges $ 50 for your plan plus 3 cents for each text you send, and you have $ 140 budgeted for cell phone expenses for the month, to make a determination about the number of texts you can send each month the following calculation must be performed:

(140 - 50) / 0.03 = X

90 / 0.03 = X

3000 = X

Therefore, 3000 text messages can be sent without breaking the budget.

Answer: [tex]\frac{3}{5} x+10[/tex]

Step-by-step explanation:

three-fifths of a number means multiply three-fifths by a variable [tex]\frac{3}{5} x[/tex]

increased by 10 means addition +10

together it is [tex]\frac{3}{5}x +10[/tex]