Which expressions are equivalent to z + (z + 6)z+(z+6)z, plus, left parenthesis, z, plus, 6, right parenthesis ?

Answer:

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Step-by-step explanation:

Recall the MacLaurin series for sin(x)

\(\displaystyle \sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\)

Substitute 3t²

\(\displaystyle \displaystyle \sin(3t^2)=3t^2-\frac{(3t^2)^3}{3!}+\frac{(3t^2)^5}{5!}-...=3t^2-\frac{3^3t^6}{3!}+\frac{3^5t^{10}}{5!}-...\)

Use FTC Part 1 to find degree 7 for F(x)

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx\frac{3x^3}{3}-\frac{3^3x^7}{7\cdot3!}\\\\\int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Hopefully you remember to integrate each term and see how you get the solution!

Using a system of equations, it is found that:

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

In a triangle, the sum of the interior angles is of 180º, thus:

\(x + y + z = 180\)

The second angle of the triangle  has a measure equal to the sum of two times the other two angles, then:

\(y = 2(x + z)\)

\(x + z = 0.5y\)

Replacing into the first equation, we find the second angle:

\(x + y + z = 180\)

\(0.5y + y = 180\)

\(1.5y = 180\)

\(y = \frac{180}{1.5}\)

\(y = 120\)

The measure of the second angle is of 120º.

Now, working to find the measures of the first and of the third angles:

\(x + z = 0.5y \rightarrow x + z = 60 \rightarrow x = 60 - z\)

The third  angle has a measure equal to ten less than the first angle, then:

\(z = x - 10\)

Since \(x = 60 - z\)

\(z = 60 - z - 10\)

\(2z = 50\)

\(z = \frac{50}{2}\)

\(z = 25\)

And

\(x = 60 - z = 60 - 25 = 35\)

The measure of the first angle is of 35º.

The measure of the third angle is of 25º.

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Answer:

16-7x

Step-by-step explanation:

10x-3x+7-6-4x+5

16-7x

Upper

daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.

(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.

Given:

Mean (μ) = 5 days

Standard deviation (σ) = 0.5 days

The confidence interval can be calculated as follows:

Lower limit = Mean - (1.96 * Standard deviation)

Upper limit = Mean + (1.96 * Standard deviation)

Lower limit = 5 - (1.96 * 0.5)

= 5 - 0.98

= 4.02 days

Upper limit = 5 + (1.96 * 0.5)

= 5 + 0.98

= 5.98 days

Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.

(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.

(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.

(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:

Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.

Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.

Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.

No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.

These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.

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Answer:

Step-by-step explanation:

Answer:

y = 7x

Step-by-step explanation:

y = px

21 = p(3)

÷3

7 = p

Ann has 21, Deandre has 31, and Bob has 42 in their wallets.

Let's start by using variables to represent the amount of money each person has:

Let A be the amount of money Ann has.

Let B be the amount of money Bob has.

Let D be the amount of money Deandre has.

We can then translate the problem into a system of equations:

A + B + D = 94 (the total amount of money they have is 94)

B = 2A (Bob has twice what Ann has)

A = D - 10 (Ann has 10 less than Deandre)

We can use the third equation to substitute A in terms of D in the first two equations:

A = D - 10

B = 2A = 2(D - 10) = 2D - 20

A + B + D = 94 => (D - 10) + (2D - 20) + D = 94 => 4D - 30 = 94 => 4D = 124 => D = 31

So Deandre has 31. We can use the third equation again to find that Ann has 21, and then we can use the second equation to find that Bob has 42.

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Answer:

The youngest sister would be 4 years old

Step-by-step explanation:

Answer:

48 in³

Base Area:

\(\hookrightarrow \sf \dfrac{1}{2} *base*height\)

\(\hookrightarrow \sf \dfrac{1}{2} *3*8\)

\(\hookrightarrow \sf 12 \ in^2\)

Volume:

\(\hookrightarrow \sf 12 * 4\)

\(\hookrightarrow \sf 48 \ in^3\)

Answer:

12x-6

Step-by-step explanation:

9-3(5-4x) distribute

9-15+12x subtract

-6+12x rearrange

12x-6

hi

technique is  to decompose both part of the fraction ( in prime numbers if possible )

 8 * 5/6   =     2*4*5  / 3*2   =   20/3

Answer:

3*81/100

Step-by-step explanation:

The linear approximation of the function f(x) at x = -1 is given by:

L(x) = f(-1) + f'(-1)(x+1)

To find f'(-1), we first need to find the derivative of f(x):

f'(x) = -7 - 33x^0

f'(-1) = -7 - 33(-1)^0 = -7 + 33 = 26

Substituting this value into the linear approximation formula, we get:

L(x) = f(-1) + 26(x+1)

Now, to approximate f(-0.8), we simply plug in x = -0.8 into our linear approximation formula:

L(-0.8) = f(-1) + 26(-0.8+1)

L(-0.8) = f(-1) + 26(-0.2)

L(-0.8) = f(-1) - 5.2

Since we want to approximate f(-0.8), we set L(-0.8) equal to our desired value:

f(-0.8) ≈ L(-0.8) = f(-1) - 5.2

We don't know f(-1), but we can find it by simply plugging in x = -1 into the original function:

f(-1) = -7(-1) - 33(-1)^1 = 26

Substituting this value into our approximation formula, we get:

f(-0.8) ≈ 26 - 5.2 = 20.8

Therefore, our conclusion is that the linear approximation of f(x) at x = -1 is L(x) = f(-1) + 26(x+1), and using this approximation, we estimate that f(-0.8) is approximately equal to 20.8.

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Therefore, using the linear approximation, we can approximate function f(-0.8) as -14.2.

To find the linear approximation of the function f(x) = -7x - 33x^2 at x = -1, we can use the formula for linear approximation:

L(x) = f(a) + f'(a)(x - a)

where a is the point of approximation.

First, let's calculate the derivative of f(x):

f'(x) = -7 - 66x

Now, evaluate the function and its derivative at x = -1:

f(-1) = -7(-1) - 33(-1)^2

= 7 - 33

= -26

f'(-1) = -7 - 66(-1)

= -7 + 66

= 59

Using the linear approximation formula at x = -1:

L(x) = f(-1) + f'(-1)(x - (-1))

= -26 + 59(x + 1)

Now, we can approximate f(-0.8) using the linear approximation:

f(-0.8) ≈ L(-0.8)

= -26 + 59(-0.8 + 1)

= -26 + 59(0.2)

= -26 + 11.8

= -14.2

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Answer:

Rational numbers...

Step-by-step explanation:

Any number that can be written in the form a/b where a and b are integers and b unequal to 0, is called rational number

Step-by-step explanation:

5 people.

how many ways can they line up in general ?

5 choices for the 1st position, then no matter what we picked, 4 remaining for the second, then 3 for the 3rd, 2 for the 4th and 1 for the 5th :

5×4×3×2×1 = 5! = 120 ways.

but we have restrictions. we don't want the girls not just anywhere in the line, we want them to be at the end points of the line.

and none of the boys should ever be at one of the ends.

so, we actually have only

2×1 for the endpoints and 3×2×1 for the 3 boy positions in the middle.

in total

2×1×3×2×1 = 12

under these constrictions they have actually only 12 different ways to line up.

Answer: 1/4, 1/8, 1/16, 1/32, 1/64

Answer:

The answer should be a. 1/4, and b. 2^6 * 2^-8

hope this helps

Answer:

A) and b)

Step-by-step explanation:

\((2^{-3} * 2^{4})^{-2} = (\frac{1}{2^{3}} *16)^{-2} = (\frac{1}{8} *16)^{-2} = \frac{1}{2^{2}} = 1/4\)

a) 1/4

b) \(2^{6}*2^{-8} = 64 * \frac{1}{2^8} = 64 * \frac{1}{256} = 1/4\)

c) \(2^{-5} *2^{2} = \frac{1}{2^{5}} *4 = \frac{1}{32} *4 = 1/8\)

d) 4

Answer: its the 3 answer where the two are switiched

Step-by-step explanation:

Answer:

it is because 8 is twice 4 and any number minus twice itself is the numbers opposite and the opposite of 4 which is -4 when multiplied by itself is -4 times -4 which equals 16 or the same as 4 squared

Answer:

40°

Step-by-step explanation:

Ratio of two supplementary angles = 2 : 7

The angles are 2x , 7x

2x + 7x = 180  {Supplementary}

       9x = 180

         x = 180/9

x = 20

Acute angle = 2x = 2*20 = 40

Answer:

-120/169

Step-by-step explanation:

Sin2theta = 2sintheta costheta

Given that tan theta = -12/5

Opposite = -12

Adjacent = 5

Using Pythagoras theorem

Hyp = √(-12)²+5²

Hyp = √144+25

Hyp = √169

Hyp = 13

Cos theta = adj/hyp

Cos theta = 5/13

Sin theta = opp/hyp

Sin theta = -12/13

Substitute

Sin2theta = 2(-12/13)(5/13)

Sin2theta = -120/169

Hence sin 2theta = -120/169

Step-by-step explanation:

(1) The radius of sphere is 4.5 units.

The volume of volume of sphere is given by :

\(V=\dfrac{4}{3}\pi r^3\)

\(\pi=3.14\ , r=4.5\)

So,

\(V=\dfrac{4}{3}\times 3.14\times (4.5)^3\)

Option C is correct.

(2) If we solve the plugged values, then we get :

\(V=\dfrac{4}{3}\times 3.14\times (4.5)^3\)

\(V=381.5\ \text{units}^3\)

Option C is correct.

Answer:

2.78

Step-by-step explanation:

you could have used a calculator

Answer:

23.2 times 0.14 is 3.248

Using a t-table or calculator, the t-distribution for an upper tail area of 0.025 with 15 degrees of freedom. The final answer (a) -2.021 and 2.021 (b) -1.675 (c) 0.873, (d) -2.845 and 2.845. (e) -2.021 and 2.021,

a. Using a t-table or calculator, the t-distribution for an upper tail area of 0.025 with 15 degrees of freedom is 2.131. T-values, where 95% of the area falls between, are -2.021 and 2.021.

b. Using a t-table or calculator, the t-value for a lower tail area of 0.05 with 55 degrees of freedom is -1.675.

c. Using a t-table or calculator, the t-value for an upper tail area of 0.20 with 35 degrees of freedom is 0.873.

d. The t-values corresponding to 0.01 and 0.99 quantiles for a t-distribution with 20 degrees of freedom are -2.845 and 2.845, respectively. Therefore, the t-values where 98% of the area falls between are -2.845 and 2.845.

e. The t-values corresponding to 0.025 and 0.975 quantiles for a t-distribution with 40 degrees of freedom are -2.021 and 2.021, respectively.

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Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

The line plot shows the favorite color of the students in the class. Option A, 9 students liked red or blue.

The line plot presents four columns with red, blue, orange, and yellow colors at the bottom. The number of students liking the color is represented by the x variable. The line plot presents five x in the column of red and four x in the column of blue. Therefore, a total number of students liking the color red and blue are option 9.

A line plot or line chart presents a chart along the number line. Line dots are often used in the line chart but variables can be presented by alphabet as well. It presents the frequency of the number of times the variable is presented in the data. If the data is big in numbers, the legend is used to present the variable. For instance, the legend of the line plot is x. Therefore, x = 5 students.

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Answer:

A

Step-by-step explanation:

I think its B about 8.6 units

Answer:

x=18

Step-by-step explanation:

The angles are supplementary, meaning that they will equal 180.

4x+5x=10x

10x=180

x=18