If $a:b = 1:3$ and $b$ is a positive, one-digit integer, what is the greatest possible value of $a$?

The value of x will be -7. The expression is solved using the identity.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

\(\rm log_2(\frac{1}{128}) = x\)

The expression is solved using the identity as;

\(\rm log_e1 = x\\\ e^x=1\)

Apply the identity;

\(\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7\)

Hence the value of x will bed -7.

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Question:

Four inches of heavy, wet snow are equivalent to an inch of rain. Estimate the water content in 17 inches of heavy, wet snow.

Solution:

Consider the following diagram (also named "rule of tree"):

by cross-multiplication and solving for x, we get:

so that, the correct answer is:

Answer:

1/3(x-10) = 40

(x-10) = 120

x= 130

Based on the given triangle, we can find that:

First, we will focus on the triangle NLP. NLP is a right triangle, then we can use the formula of sinus to find the length of NP, where:

Sin ∠NLP = NP / LP

Sin 35° = NP / 20

0.57 = NP / 20

NP = 11.47

NP ≈ 11

Next, we will focus on triangle GLP. GLP is a right triangle with hypotenuse of 52 and the base of 20. Using the Phytagoras theorem we can try to find the triangle's height.

GL² = GP² + LP²

52² = GP² + 20²

2704 = GP² + 400

GP² = 2304

GP = 48

GP = GN + NP

48 = GN + 11

GN = 37

To find the size of angle ∠GLN, we have to find the size of angle ∠PGN first. We will use the Sines Law:

LP / sin ∠PGN = GL / sin ∠GPN

20 / sin ∠PGN = 52 / 1

sin ∠PGN = 20/52

∠PGN = 22.5°

∠PGN ≈ 23°

∠GLP + ∠GPL + ∠PGN = 180°

∠GLP + 90° + 23° = 180°

∠GLP = 67°

∠GLP = ∠GLN + ∠NLP

67° = ∠GLN + 35°

∠GLN = 32°

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Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Problem N 25

we know that

C=132 in

Remember that

The formula to calculate the circumference is given by

using pi=3.14

C=132 in

substitute given values in the formula

The diameter D=42.04 in ( with pi=22/7 the diameter is 42 in exact)

Find out the radius r

r=D/2=42.04/2=21.02 in -----> the radius is half the diameter

Find out the area of the circle

The area is given by the formula

we have

r=21.02 in

pi=3.14

substitute

therefore

The slope of the least-squares line is 0.3

Given:

r = correlation between X and Y = 0.9

J = mean of the values of X = 6.5

M = mean of the values of Y = 6.6

sJ = standard deviation of the values of X = 3.6

sM = standard deviation of the values of Y = 1.2

To find the slope of the least-squares line in this case, you can use the following formula:

Slope = r × (sM / sJ)

Substituting the given values for r, sJ, and sM:

Slope = 0.9 × (1.2 / 3.6) = 0.3

Thus, the slope of the least-squares line is 0.3. This tells you the rate at which the average weight of children changes as their age increases by one month

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The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

198 1/3

Step-by-step explanation:

arithmetic sequence formula for the nth term:

aₙ = a₁ + (n-1)d

d = the common difference between each term

a₇ = a₁ + (7-1)d

34 = 5 + 6d

subtract 5 from both sides to isolate d and its coefficient

29 = 6d

divide both sides by 6 to isolate d

d = 29/6

a₄₁ = a₁ + (n-1)d

    = 5 + (41-1)d

    = 5 + 40d

    = 5 + 40(29/6)

    = 198 1/3

Answer:

3 to 8

Step-by-step explanation:

There are 24 total shapes, 9 of which are circles. So we have the ratio 9 to 24, or 3 to 8.

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

The formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

Step-by-step explanation:

To obtain the formula for the function g(x) when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units, we can use the following transformations:

A vertical shift up by 1 unit is represented by adding 1 to the function: f(x) + 1

A horizontal shift to the left by 6 units is represented by replacing x with (x + 6): f(x + 6)

Therefore, the formula for the function g(x) is:

g(x) = f(x + 6) + 1

Substituting the expression for f(x), we get:

g(x) = √(x + 6) + 1

So, the formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

Answer:

3x+12

Step-by-step explanation:

Triple is 3 times a number which we will call “x” and sonce it is the sum, it is addition :)

Answer:

Step-by-step explanation:

The factors of the function graphed in the given graph is option (C) (x-1)(x+5)

The function is the mathematical statement that shows the relationship between the dependent variable and independent variable

From the given graph

The given graph is a parabola and the equation of the graph will be a quadratic function

x intercepts of the lines are

x = -5 and x = 1

Then to find the factors of the function graphed

x = -5

x + 5 = 0

Similarly the second equation will become

x = 1

x-1 = 0

Then the factors function will be

(x+5)(x-1)

Therefore, the factors are option (C) (x-1)(x+5)

I have solved the question in general, as the given question is incomplete

The complete question is

Which of the following are the most likely factors of the function graphed above?

A. (x+1)(x-5)

B. (x)(x-5)

C. (x-1)(x+5)

D. (x)(x+5)

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Answer:

The probability that the student answers at least seventeen questions correctly is \(8.03\times 10^{-10}\).

Step-by-step explanation:

Let the random variable X represent the number of correctly answered questions.

It is provided all the questions have five options with only one correct option.

Then the probability of selecting the correct option is,

\(P(X)=p=\frac{1}{5}=0.20\)

There are n = 20 question in the exam.

It is also provided that a student taking the examination answers each of the questions with an independent random guess.

Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.

The probability mass function of X is:

\(P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...\)

Compute the probability that the student answers at least seventeen questions correctly as follows:

\(P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)\)

\(=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}\)

Thus, the probability that the student answers at least seventeen questions correctly is \(8.03\times 10^{-10}\).

To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

Answer:

1/6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.1666666 (6 repeating)  is 1/6

The value of n in terms of b is given as 42%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

And to convert a fraction or a decimal into percentage, they are multiplied by 100.

Given that,

n = 14m.

And, m = 3% of b.

From the given expressions, n can be written in terms of b as follows,

n = 14m

=> n = 14 × 3% of b

=> n = 14 × 3/100 × b

=> n = 42/100 × b

The conversion of 42/100 into percentage is 42%.

Hence, the value of n is 42 percentage of b.

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The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Answer:

2440

Step-by-step explanation:

1,000+686 =

1,686

1686+ 754

= 2440

Answer:

x =6.0

The base is 6x  = 35.8

The side is 3x =  17.9

Step-by-step explanation:

We can use the pythagorean theorem

a^2 + b^2 = c^2

(6x)^2 +(3x)^2 = 40^2

36x^2 + 9x^2 = 1600

Combine like terms

45x^2 = 1600

Divide each side by 45

45x^2 /45 =1600/45

x^2 =35.555555555

Take the square root of each side

sqrt(x^2) = sqrt(35.555555555)

x =5.96284794 = 6.0

The base is 6x = 6*5.9628479 =35.77708 = 35.8

The side is 3x = 3*5.9628479 =17.88854382= 17.9

Answer:

x = 6.0

3x = 17.9

6x = 35.8

Step-by-step explanation:

Using pythagoras theorem

40² = (3x)² + (6x)²

1600 = 9x² + 36x²

1600 = 45x²

x² = 320/9

x = 5.96284794

3x = 17.88854382

6x = 35.77708764

Answer:

2√73 or 17.09 inches

Step-by-step explanation:

The small red square at the corner of the triangle symbolizes that the triangle is a right triangle. Therefore, to find the hypotenuse of the triangle, we can use the Pythagorean Theorem: a² + b² = c²

a = 6

b = 16

c = ?

Plug these values into the equation.

(6)² + (16)² = c²

Evaluate the exponents.

36 + 256 = c²

292 = c²

Take the square root of both sides to find c.

√292 = √c²

17.09 ≈ c

This is your answer.

You can also simplify the radical without using decimals.

4 • 73 = 292

Therefore,

√4 • √73 = √292

Which also means,

2•√73 = √292

So your answer is: 2√73

Hope this helps!

Answer:

We use the pythagorean theorem a²+b²=c² and in this question

a = 6

and

b = 16

so

36 + 256 = c²

so

c² = 292 so now we take the square root of it to get \(\sqrt{292}\)

Hope this helps!

The expression that represents the combined inventory of these two stores is given as follows:

A. 7g²/2 - 4g/5 + 15/4.

The combined inventory is obtained adding the inventories for each store, combining the like terms.

The addition of the like terms for g² is given as follows:

1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².

The term with g is given as follows:

-4g/5.

The constant like terms are combined as follows:

7/2 + 1/4 = 14/4 + 1/4 = 15/4.

Hence the simplified expression is given as follows:

7g²/2 - 4g/5 + 15/4.

Meaning that the correct option is given by option A.

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Answer:

  x = -4, -1, 9

Step-by-step explanation:

The zeros of f(x) will be found from the factors of f(x). Like factoring numbers, you reduce the problem in stages by factoring out the given factor. You can do this using polynomial long division, or its simpler cousin, synthetic division.

The attachment shows the synthetic division required to determine that the remaining quadratic factor is (x^2 -8x -9). That is ...

  f(x) = (x +4)(x^2 -8x -9)

The quadratic can be factored by looking for two numbers that have a product of -9, but have a sum of -8. Those numbers are +1 and -9. These are the values of the constants in the remaining factors you need.

  f(x) = (x +4)(x +1)(x -9)

The zeros of f(x) are the values of x that make these factors zero. (When a factor is 0, f(x) is 0.) The values of interest are the opposites of the constant in each factor, -4, -1, 9.

The zeros of f(x) are x = -4, -1, 9.

_____

Additional comment

In regular division, the divisor is multiplied by the (partial) quotient, and the product is subtracted from the dividend to get a new dividend. In synthetic division, the divisor is presumed to be a binomial of the form (x -r), where r is the zero of this binomial term. (x=r gives r-r = 0) It is this r value that appears in the upper left corner of the synthetic division table.

Answer:

97°

Step-by-step explanation:

The angles of any quadrilateral will add up to 360°. Since we already know 3 out of the 4 angles (the bottom two are both 90°), we can easily find the measure of x.

\(90 + 90 + 83 +x = 360\)

\(263 + x = 360\\\\x = 97\)

Hope this helped!

Answer:

Value of x = 97 degrees

Step-by-step explanation:

In the given quadrilateral

One angle = 83

2 other angles = 90 degrees each

Sum of all the four angles in a quadrilateral = 360 (Angle Sum Property of     quadrilaterals)

=>90+90+x+83= 360

=>180+83+x = 360

=> 263+x= 360

=>x= 360-263

=>x=97