Solve the formula for the radius of a sphere Solve for ANeed help Literal equations

Answer:

The 95% confidence interval for the average number of years until the first major repair is (3.1, 3.5).

Step-by-step explanation:

The (1 - α)% confidence interval for the average using the finite correction factor is:

\(CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}}\)

The information provided is:

\(N=1500\\n=183\\\sigma=1.47\\\bar x=3.3\)

The critical value of z for 95% confidence level is,

z = 1.96

Compute the 95% confidence interval for the average number of years until the first major repair as follows:

\(CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}}\)

     \(=3.3\pm 1.96\times\frac{1.47}{\sqrt{183}}\times\sqrt{\frac{1500-183}{1500-1}}\\\\=3.3\pm 0.19964\\\\=(3.10036, 3.49964)\\\\\approx (3.1, 3.5)\)

Thus, the 95% confidence interval for the average number of years until the first major repair is (3.1, 3.5).

Answer:

Step-by-step explanation:

\((15 + 15) + (21 + 21) + - 5 \\ 30 + 42 - 5 \\ 67\)

I hope that is useful for you :)

Answer:

The LCD is 3x²

The other two denominators can be factors of 3x²

Step-by-step explanation:

To get the equivalent fractions, divide the original denominator into the LCD, then multiply the original numerator by the quotient.

For the first term: 1/x²

3x² ÷ x² = 3 3×1=3 The equivalent is 3/3x²

Second term: Leave it as it is.

For the third term: 15x

The implied denominator is 1

3x² ÷ 1 = 3x² 3x² × 15 = 135x²

The equivalent is 135x²/3x²

To check the validity, substitute a value for x and calculate the numbers.

For example let x = 3

The original expression becomes

1/3² + 4/3(3²) - 15(3)

1/9 + 4/27 - 45

With the LCD it is

3/27 + 4/27 - 1215/27

Answer:

3x^2(x+5)

Step-by-step explanation:

hope this helps

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

The first step is to find the values of x and y. From the information given,

x is the cost of an adult ticket and y is the cost of a child ticket. The system of equations is shown below

3x + 5y = 50

x + 5y = 31

From the second equation,

x = 31 - 5y

We would substitute x = 31 - 5y into 3x + 5y = 50. We have

3(31 - 5y) + 5y = 50

By expanding the parentheses, we have

93 - 15y + 5y = 50

- 15y + 5y = 50 - 93

- 10y = - 43

Dividing both sides of the equation by - 10,

- 10y/- 10 = - 43/- 10

y = 4.3

Substituting y = 4.3 into x = 31 - 5y, we have

x = 31 - 5 * 4.3 = 31 - 21.5

x = 9.5

If an adult ticket costs $9.5, then the cost of 4 adult tickets is

4 x 9.5 = $38

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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Answer:

-13/-5 is the opposite of 13/5. Hope this helps :)

By algebraic handling, the expression 9 / 6 - 4 · (2 / 3 - 7 / 6)² is equivalent to the expression 1 / 2.

In this problem we must simplify an expressions involving powers and rational numbers by algebra definitions and theorems:

9 / 6 - 4 · (2 / 3 - 7 / 6)²                                Given

9 / 6 - 4 · [[(2 · 6) - (3 · 7)] / (3 · 6)]²              Subtraction of fractions with different denominators

9 / 6 - 4 · [(12 - 21) / 18]²                               Definition of multiplication

9 / 6 - 4 · (- 9 / 18)²                                       Definition of subtraction

3 / 2 - 4 · (1 / 2)²                                           Definition of simplification

3 / 2 - 4 · (1 / 4)                                             Power properties

3 / 2 - 1                                                         Definition of division / Existence of multiplicative inverse

3 / 2 - 2 / 2                                                   Definition of division / Existence of multiplicative inverse

1 / 2                                                               Subtraction of fractions with same denominator / Result

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Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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The amount earned, calculated using the formula for geometric progressions are as follows;

(A) The income on day 31 =$1,073,741,824

(B) Total income for 31 working days = $2,147,483,647

A geometric progression is one in which each subsequent term is a constant multiple of the previous  term

(A) The function that indicates the amount earned on the nth day is the formula for a geometric progression , which can be presented as follows;

\(a_n = a_1\cdot r^{n-1}\)

The sum is presented as follows;

\(S_n =a_1\cdot \dfrac{1 - r^n}{1 - r}\)

Therefore;

The common ratio, r = 2

The first term, a₁ = 1

The amount received on day 31 is therefore;

\(a_{31} = 1\times 2^{31-1} = 1,073,741,824\)

Income on day 31 = $1,073,741,824

(B) The total income in 31 days is therefore;

\(S_{31} =a_1\cdot \dfrac{2^{31} - 1}{2- 1}== 2,147,483,647\)

The total income in 31 working days = $2,147,183,647

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Mr. X reduces his weight in a ratio of 4:17. This means that for every 4 units of weight he loses, his initial weight was divided into 17 equal parts.

To determine the ratio by which Mr. X reduces his weight, we need to compare his initial weight of 85 kg with his target weight of 65 kg.

The reduction in weight is calculated as the difference between the initial weight and the target weight, which in this case is 85 kg - 65 kg = 20 kg.

The ratio can be expressed as a fraction, where the numerator represents the reduction in weight and the denominator represents the initial weight:

Reduction in weight / Initial weight

Substituting the values, we have:

20 kg / 85 kg

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case:

(20 kg / 5) / (85 kg / 5) = 4/17

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The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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Answer: it the first one

Step-by-step explanation:

Answer:

44 in^2

Step-by-step explanation:

Area of rectangle = 5 x 10 = 50 in^2

High of trapezoid = 10 - 6 = 4 in

Area of trapezoid = (7+15) x 4 / 2 = 22 x 4 / 2 = 22 x 2 = 44 in^2

The expression that gives the area of the rectangular flag is presented as follows:

5x + 7.5.

The area of a rectangle of length l and width w is obtained by the multiplication of these dimensions, as follows:

A = l x w.

The flag in this problem is composed by three rectangles, as follows:

The total area is obtained by the sum of the areas of each part of the flag, hence:

Area = 2x + 2 x 1.5 + 3(x + 1.5)

Area = 2x + 3 + 3x + 4.5

Area = 5x + 7.5.

The area of each part was obtained by the multiplication of the dimensions, which is the standard procedure to obtain the area of a rectangle.

The flag is given by the image at the end of the answer.

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2.73

1.3x2.1=2.73

1.3

x2.1

13

+26

2.73

Answer:

To multiply 1.3 by 2.1, we need to use the distributive property of multiplication, which states that:

a × (b + c) = a × b + a × c

Using this property, we can break down 2.1 as the sum of 2 and 0.1:

1.3 × 2.1 = 1.3 × (2 + 0.1)

= 1.3 × 2 + 1.3 × 0.1

= 2.6 + 0.13

= 2.73

Therefore, 1.3 multiplied by 2.1 equals 2.73.

Answer:

15 black marbles

Step-by-step explanation:

So its. A ratio (basically a fraction)

3/2

we add them up so we know how much marbles but not which kind

so we get 5

now we know for every 5 batches there is 3 black and 2 red

so we divide 25/5 to get 5

now we know there are 5, 5 batches of black ad red marbles.

now black is 3 of them so we multiply 5(3) which is 15

Now red is 2 of them so we multiply 5(2). Which is 10

now to check, if we add them up, they equal to 25 which is correct.

basically add the fraction, divide that by the original number, time the quotient by each number in the fraction.

Answer:

There are a total of 15 black marbles in the bag.

Step-by-step explanation:

Well, we know that for every 3 black marbles, there are 2 red marbles. In order to solve this problem, we just need to keep adding equivalent ratios with a proportional relationship until the sum of both numbers is 25.

3:2, 6:4, 9:6, 12:8, 15:10

Since 15 + 10 = 25, we can stop here.

Since the number in front of the colon is the amount of black marbles, then there are a total of 15 black marbles in the bag.

Hope this helps! :D

Answer:

5 Weeks

Step-by-step explanation:

50% of $60. Sawyers gift card covers $30.

.5 x $60 = $30

That means Sawyer's mom needs to cover the remaining cost:

$60 - $30 = $30

Sawyer will pay his mom back 20% of that amount each week. To find out how much that is, we can multiply:

0.2 x $30 = $6

So Sawyer will pay his mom back $6 each week. To figure out how many weeks it will take to pay her back, we can divide the toatal amount he owes her (/30) by the amount he pays her each week (/6):

$30 ÷ $6 = 5

There were 18 time trials recorded during the experiment.

To determine the number of time trials recorded during the experiment, we count the total number of dots on the dot plot.

According to the given information, we have:

- Two dots over 15

- Three dots over 17

- Two dots over 19

- Two dots over 20

- One dot over 21

- Four dots over 23

- One dot over 24

- Three dots over 25

By adding up these counts, we get:

2 + 3 + 2 + 2 + 1 + 4 + 1 + 3 = 18

Therefore, there were 18 time trials recorded during the experiment.

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Answer:

10.27

Step-by-step explanation:

10.2719 rounded to the nearest hundredth is 10.27, because to round up, the thousandths place has to be 5 or greater, but since the thousandths place is 1, you need to change the number to 10.27

Hope this helps!

The number 10.2719 rounded to the nearest hundredth is; 10.27

While considering place values of numbers,

Numbers on the left side of the decimal are ordered from right to left as unit, tens, hundreds, thousands and so on respectively.

While Numbers on the right side of the decimal are ordered from left to right as tenth, hundredth, thousandth and so on respectively.

Therefore, according to the question, the digit with occupies the hundredth position is 7.

As such, to round off the number 10.2719, the digit which is after the digit 7 is considered.

If the digit is less than 5, it is rounded to 0, and if greater or equal to 5, it is rounded to 1 and ultimately added to the preceding number.

In this case, the number is 1 and since 1 is less than 5, it is rounded to 0 and added to 7.

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Answer:

363

Step-by-step explanation:

0.66*550=363

Option B

sqrt(60) = sqrt(4 x 15) = sqrt(4) x sqrt(15)

Answer:

25 units

Step-by-step explanation:

use the distance formula to get the square root of 24² + 7²

this will give you the square root of 625, which is 25

Answer:

slope=0

hope this helps

have a good day :)

Step-by-step explanation: