Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.0. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?

Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence

[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]

Differentiating [tex]f(x)[/tex] gives

[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]

Then

[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]

[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]

[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]

which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.

Answer:

log x to the base 2 +log x to the base 4 =2

or log x/ log 2+ log x /lig 4 =2

or log x /log2 + log x /2.log 2 = 2

or log x/log 2(1+1/2)= 2

or log x/log 2 = 4/3

or 3.log x =4.log2

or logx^3=log 2^4

or x^3= 2^4

or x =(2)^4/3 or 2.(2)^1/3 ,Answer.

hope this helps

Step-by-step explanation:

Answer:

(-4,-3)

Step-by-step explanation:

The point where those 2 equations intersect is (-4,-3)

The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

We have a scatter plot shown in the table:

1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:

Standard deviation = SD

6SD(x) = 40

SD(x) = 40/6 = 6.67

6SD(y) = 20

SD(y) = 20/6 = 3.37

2) Slope of the line:

= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5

3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.

Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

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Answer:

(π2,15)(π2,15) is a local maximal

(3π2,9)(3π2,9) is a local minimal

Step-by-step explanation:

C is the right answer.

hope it helps...

Answer:

C.

Step-by-step explanation:

Calculating this in Desmos, the closest equation to the points on the graph will have to be c

Answer:

512? xd

Step-by-step explanation:

Answer:

128

Step-1by-step explanation:

An easy way of solving these sort of problems is to set up an equation

Since we have a total, that being 512 burgers, we can set an equation equal to that number.

We can say that hamburgers is represented by x. Since we sold 3 times more cheeseburgers than the amount of hamburgers, we can represent this as 3x.

Since these totals are combined, we can represent this via an equation:

512 = x + 3x

Solve for x accordingly, and we are given 128, which is equal to the amount of hamburgers.

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The correct option is B.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Since the graph of the equation is a line, therefore, it can be concluded that the relationship is linear as a result y varies directly with x.

Therefore we can write the relationship as,

y ∝ x

y = k x

The line goes through the point (-2,3), thus, substitute the points in the equation formed above,

3 = k × (-2)

k = -3/2

Now, substitute the value of k in the equation,

y = -(3/2)x

Hence, the correct option is B.

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H(x) = 4(x - 7)^2 - 19

Hope you find it usefull

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Answer:

answer D    ( if i interpreted your question correctly )

Step-by-step explanation:

Sqrt (c^2)  = √(c^2) = C

Answer:

The answer is 64

Step-by-step explanation:

If you find this answer helpful pls mark it the brainliest answer

it's easy 64 the key is in the pic.

Answer:

24

Step-by-step explanation:

the question translates to asking how many times does 7/8 fit in 21, so 21 divided by 7/8.

when we divide by a fraction, we can multiply by it's inverse, so 21 divided by 7/8, is 21 multiplied by 8/7. so:

21×8/7 = (21×8)/7 = (21/7)×8 = 3×8 = 24

Answer:

B.) 2x¹⁰y¹²

Step-by-step explanation:

To begin, because all of the terms in the top and bottom are combined (right next to each other being multiplied), the coefficients can be divided like any normal number. When you divide variables with powers, you need to subtract the denominator powers from the numerator powers.

Therefore,

60 / 30 = 2

x²⁰ / x¹⁰ = x²⁰ ⁻ ¹⁰ = x¹⁰

y²⁴ / y¹² = y²⁴ ⁻ ¹² = y¹²

Combined, the simplified expression is 2x¹⁰y¹².

Answer:

(144)^1/2

(12^2)^1/2

12 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

12

Step-by-step explanation:

Rewrite 144 as 12²

(12²)^1/2

Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].

12^2(1/2)

Cancel the common factor of 2.

Cancel the common factor.

Rewrite the expression

12^1

Evaluate the exponent.

12

Answer: Two pounds of beef costs $7.38.

Step-by-step explanation:

Multiply the cost for one pound by the amount of pounds you need.

$3.69×2=$7.38

I hope this helps!!

Answer:

325

Step-by-step explanation:

10 is 3^2 + 1

37 is 6^2 + 1

82 is 9^2 + 1

145 is 12^2 +  1

226 is 15^2 + 1

325 is 18^2 + 1

325 is the next number in the sequence and is also the answer.

The graph is attached with the answer.

When two algebraic expressions are equated using an inequality operator , The statement formed is called In equality.

The given Inequality is 2x + y ≤ 2

in slope intercept form can be written as

y ≤  -2x +2 , here slope is -2 and intercept is 2

As an equation it will be

y = -2x +2

x         y

0 ,       2

1 ,       0

2         -2

The graph is plotted

The area is shaded and the test for the origin is applied , and it lies in the shaded region.

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Answer:

the answer to this problem is 703.7 in^2

Answer:

2a² + 2b²

Step-by-step explanation:

(a - b)² + (a + b)² ← expand both factors using FOIL

= a² - 2ab + b² + a² + 2ab + b² ← collect like terms

= 2a² + 2b²

Step-by-step explanation:

Expand both classic quadratics and combine like terms to find the sum:

(a−b)2+(a+b)2

Answer:

yessss

Step-by-step explanation:

yessssssss

The condition that distinguishes organism from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to the environment through changes originating internally.

The control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.

According to the information, the researcher wants to seek whether singing to plants causes them to grow taller.

The explanatory variable is singing. Therefore, the researcher can control some of the variables to determine the explanatory variable on the growth of the plant.

Hence, the control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.

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Answer:

either it's 7 and 3 but not sure

Step-by-step explanation:

7x3 =21

now for the negative -10 it would basically be -7+-3=-10

Answer:

6.708.

Step-by-step explanation:

hope this helps

Answer:

A = 13 degrees

B = 65.3 degrees

C = 180 - (13 + 65.3) = 101.7 degrees

Side a = 35 km

Side b = 141.4 km

Side c = 152.4 km

Answer:

115

Step-by-step explanation:

You solve this by factoring.

12140 = x^2-10x+65

0 = x^2-10x-12075

0=(x+105)(x-115)

The only positive solution is x=115

Answer:

The first graph

Step-by-step explanation:

The second graph does not have a point at (1, -2).

y=[tex]\frac{1}{2}[/tex]x+0.5

Hope it helps!

Answer:

A. -6

D. 3

Step-by-step explanation: