The Earth's human population is approximately 7,900,000,000 people.
Express this number using scientific notation.

Answer: B

Step-by-step explanation:

English: 0.25^5=0.001

Science:0.5^7=0.008

English is harder to get 100% on, since the probability 0.001 is lower than 0.008.

The weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is (A + 4B + C) / 6.

To find the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively, we first need to multiply each point by its corresponding weight and then add them together.

Finally, we divide the sum by the total weight.

The weighted sum of the points is:

(1 × A) + (4 × B) + (1 × C) = A + 4B + C

The total weight is:

1 + 4 + 1 = 6

Therefore, the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is:

(A + 4B + C) / 6

Note that the weight of B is four times that of A and C.

Therefore, the weighted average will be closer to B than A or C, reflecting the fact that B has a larger weight.

For example, if A = 3, B = 5, and C = 4, then the weighted average is:

(A + 4B + C) / 6 = (3 + 4 × 5 + 4) / 6 = 26 / 6 = 4.33.

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The fraction of the money the youngest boy does get is 5x/22.

Given that, three brothers share some money. The oldest 5/11 of the money.

Let the total money be x.

Share of oldest boy = 5/11 ×x

= 5x/11

Remainder = x-5x/11

Remainder = 6x/11

The next boy gets 7/12 of the remainder.

Share of next boy = 7/12 × 6x/11

= 7x/22

Share of youngest boy = 6x/11 - 7x/22

= (12x-7x)/22

= 5x/22

Therefore, the fraction of the money the youngest boy does get is 5x/22.

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The external circumference of the metal pipe is approximately 31.4 centimeters.

We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We are given that  internal radius is 5cm and the thickness of the metal is 6mm.

The circumference of the external circle = 2πr

= 2 x 3.14 x 5

= 31.4

The circumference of the metal pipe is approximately 31.4 centimeters.

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The perimeter of the triangle ABC is 146.

Given that a triangle we need to find it perimeter,

We know that the tangents from a common point to the circle are equal,

Therefore,

DB = BE

EC = FC

FA = AD

So,

FA = AC - FC

FA = 52-13 = 39

Therefore,

FA = AD

AD = 39

Now,

9x-56 = 17x - 120

8x = 64

x = 8

DB = BE = 16

AB = 16 + 39 = 55

BC = 16+13 = 29

AC = 52

Perimeter = AC + BC + AB = 55 + 29 + 52 = 146

Hence the perimeter of the triangle ABC is 146.

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Im sorry but I dont see a Box Plot.

Answer:

provide more data

Step-by-step explanation:

no solution

The function for the concentration of the drug in the bloodstream indicates;

a. The concentration will be 0.5 mg/L when t = 20 - 6·√(11) and t = 20 - 6·√(11) hours

b. Please find the completed table of values in the following section

c. The domain is all positive values of t, including t = 0, which is [0, ∞)

d. The patient should receive the drug after about 19.78 hours

e. The shape of the concentration graph are similar, but the concentration of the oral drug is higher than the concentration of the drug administered intravenously

A function is a rule that maps input variables to output values.

a. The function modelling the concentration of the drug in the bloodstream after t hours indicates;

c(t) = 20·t/(t² + 4)
When the concentration is 0.5 mg/L, we get;

c(t) = 20·t/(t² + 4) = 0.5

(t² + 4) × 0.5 = 20·t

t² + 4 = 20·t ÷ 0.5 = 40·t

t² - 40·t + 4 = 0

t = (40 ± √((-40)² - 4 × 1 × 4))/(2 × 1) = (40 ± 12·√(11))/(2) = 20 ± 6·√(11)

The concentration will be 0.5 mg/L when t = 20 + 6·√(11) and t = 20 - 6·√(11)

b. The completed table of values, obtained using MS Excel can be presented as follows;

t     [tex]{}[/tex]  0      2      4      6      8       10      12       14      16      18       20

c(t)   [tex]{}[/tex]0      5      4      3      2.35  1.92   1.62    1.4     1.23   1.09    0.99

c. The denominator, t² + 4, indicates that the denominator is positive for all values of x, whereby the time is a natural, a possible domain for the function is the set [0, ∞)

d. The values in the table indicates that to maintain a concentration above 1 mg/L and below 8 mg/L, the patient must receive the next intravenous dose between the values obtained as follows;

The maximum value of the function is 5 mg/L when t = 2 hours, therefore, when c(t) = 1 mg/L, we get;

c(t) = 20·t/(t² + 4) = 1, which indicates that t = 10 ± 4·√6, which indicates that the time at which the concentration reduces to 1 mg/L again in the bloodstream is 10 + 4·√6 ≈ 19.78 hours

The patient should receive the next dose, after about 19.78 hours

e. The concentration of the oral drug, obtained from a similar question on the website, indicates that the maximum concentration is 64 mg/L, which is higher than the maximum concentration of the drug administered intravenously, which has a maximum concentration of 5 mg/L

However, the maximum bloodstream is reached at about the same period for both drugs administration methods

The concentration of the drug administered by oral administration in the first part is about four times the drug administered intravenously after 20 hours.

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Step-by-step explanation:

y= rad(x+3)

y²=x+3

x= y²-3

change the variables

y= x²-3

The value of the missing coefficient is 12

Lets explain how to factorize the difference of two cubes

- The factorization of the difference of two cubes like a³ - b³, is a

 product of a binomial and trinomial

- The binomial is the cube root of the first term and the second term

∵ The ∛a³ = a and ∛b³ = b

∴ The binomial is (a - b)

- We will find the trinomial from the binomial by square the 1st term

of the binomial and multiply the 1st term and the 2nd term of the

binomial with opposite sign of the binomial and square the 2nd

term of the binomial

∴ The trinomial is (a² + ab + b²

∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)

* Lets solve the problem

∵ 8f³ - 216g³ is the difference of two cubes

∵ ∛(8f³) = 2f

∵ ∛(216g³) = 6g

∴ The binomial is (2f - 6g)

- Lets make the trinomial

∵ (2f)² = 4f²

∵ (2f)(6g) = 12fg

∵ (6g)² = 36g²

∴ The trinomial = (4f² + 12fg + 36g²)

∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)

∴ The value of the missing coefficient is 12.

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complete question:

Find the value of the missing coefficient in the factored form of 8f^3-216g^3

8f^3-216g^3=(2f-6g) (4f^2+?fg+36g^2)

The value of ? =

Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, Functions are,

⇒ y = 2ˣ

And, Its inverse function is,

⇒ y = log₂ x

Thus, The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.

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cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.

Therefore, the exact value of cos 30° is (√3)/2.

Answer:

cos30 = √3 / 2

or cos30 ≈ 0.8660254037

[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]

The number that belongs in the green box, using the law of cosines, is given as follows:

15.97º.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:

c² = a² + b² - 2abcos(C)

For this problem, the parameters are given as follows:

c = 11, a = 12, b = 20.

Hence the missing angle measure is given as follows:

11² = 12² + 20² - 2 x 11 x 20cos(C)

440cos(C) = 423

cos(C) = 423/440

C = arccos(423/440)

C = 15.97º.

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the next two terms in the sequence would be 12 and 17.

Answer:

150°

Step-by-step explanation:

Measure of and interior angle of 12-gon:

  [tex]\sf \boxed{\text{\bf Sum of all angles of n-polygon = (n -2) * 180}}[/tex]

n is the number of sides.

  Sum of all angles of 12-gon     = (12 - 2) * 180

                                                     = 10 *180

                                                     = 1800°

In a regular 12-gon, all the interior angles will be equal.

    [tex]\text{\bf Measure of each interior angle = $\bf \dfrac{Sum \ of \ all \ the \ angles}{number \ of \ sides}$}[/tex]

                                                            [tex]\sf = \dfrac{1800}{12}\\\\=150^\circ[/tex]

The standard deviation for this set of data is approximately 2.85.

To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.

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Answer:

6

Step-by-step explanation:

To find the mean you've got to add 7, 9,4,3,9 and 4 (which gives you 36) and divide that by the number of figures/numbers (which is 6 numbers in total) and it gives you 6

Answer: x = 11

Step-by-step explanation:

     We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.

128° = 8x + 40°

8x + 40° = 128°

8x = 88°

x = 11

Answer:

$762.53

Step-by-step explanation:

think of 710.98 as the whole.

then 7.25% = an increase of 0.0725.

710.98 X (1 + 0.0725)

= $762.53 (to nearest cent)

The median will be greater than the mean in a left-skewed distribution

We have,

In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.

A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.

When the data is skewed left, it means that the distribution is being pulled towards the left side.

This is because there are a few extreme values on the left side that are pulling the mean in that direction.

In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.

For a left-skewed distribution,

The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.

In a data distribution that is skewed left, the mean will be less than the median.

This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.

Therefore,

The median will be greater than the mean in a left-skewed distribution

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Answer: 8

Step-by-step explanation:

      We see that each term is 5 less than the previous one. We will subtract 5 from 13 to find the next term in the sequence.

                    13 - 5 = 8

Answer:

m = 25 + 6n

Step-by-step explanation:

To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.

let's recall that whenever omitted, the base is assumed to be 10.

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_{10}(2)=m\implies \log(2)=m\hspace{5em}\log_{10}(3)=n\implies \log(3)=n \\\\[-0.35em] ~\dotfill\\\\ \log_{10}(24)\implies \log(24)\implies \log(8\cdot 3)\implies \log(2^3\cdot 3) \\\\\\ \log(2^3)+\log(3)\implies 3\log(2)+\log(3)\implies 3m+n[/tex]

The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.The correct answer is c.

The interest rate of a loan is one of the most important factors to consider when shopping around for loans because it directly affects the cost of borrowing money. The interest rate determines the percentage of the loan amount that the borrower will have to pay back to the lender as interest over the loan's term.

A higher interest rate means that borrowers will have to pay more in interest over the life of the loan, increasing the total cost of borrowing. Conversely, a lower interest rate will result in lower interest payments and a reduced overall cost of the loan.

For example, in the case of a mortgage, which is a long-term loan, even a small difference in the interest rate can have a significant impact on the total amount paid to the lender. Over the course of a 30-year mortgage, a higher interest rate could result in thousands of dollars in additional interest payments.

Therefore, it is important to compare and consider different loan offers to find the best interest rate available. This can help borrowers save money and make more informed decisions about their borrowing options. The correct answer is c.

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Answer:

AB ≈ 8.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{6.2}{AB}[/tex] ( multiply both sides by AB )

AB × cos40° = 6.2 ( divide both sides by cos40° )

AB = [tex]\frac{6.2}{cos49}[/tex] ≈ 8.1 ( to the nearest tenth )

The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.

To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.

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