Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated

Answer: 1/16

Step-by-step explanation:

4^4*4^(-7)*4

= 4^(-3)*4

=4^(-2)

= 1/16

Answer:

False

Step-by-step explanation:

Since a triangle must contain 3 interior angles all adding to 180°, then there can't be more than one right angle since 2 right angles would add up to 180°.

Answer:

Step-by-step explanation:

Cube

Solve for edge

a= 2

V Volume 8

Answer:

16. 0.57735

17. −0.707107

18. 0.5

19. 0.5

20. 2.61799387

21.  1.15470053

Three different expressions that simplify to x^6​ are

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

Index forms are defined as mathematical expressions used to write numbers too small or large in more convenient forms.

Other names for index forms are standard forms and scientific notations.

Note some rules of indices, they are;

Then, we have;

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

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The equation of the circle x² + y² - 8x - 6y + 16 = 0 in standard form is (x - 4)² + (y - 3)² = 3².

Given the equation of the circle ;

x² + y² - 8x - 6y + 16 = 0

To write the equation of a circle in standard form, we need to express it as:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

To do this, we need to complete the square for both x and y terms in the given equation.

Starting with the x terms:

x² - 8x = x² - 8x + 16 - 16

= (x - 4)² - 16

Similarly, for the y terms:

y² - 6y = y² - 6y + 9 - 9

= (y - 3)² - 9

Substituting these results into the original equation, we get:

x² + y² - 8x - 6y + 16 = 0

(x - 4)² - 16 + (y - 3)² - 9 + 16 = 0

Simplifying, we get:

(x - 4)² + (y - 3)² - 9 = 0

(x - 4)² + (y - 3)² = 9

So the equation of the circle in standard form is:

(x - 4)² + (y - 3)² = 3²

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Answer:

Use the following Financial Ratios to measure financial performance against standards. In addition, analysts compare these ratios to industry averages (benchmarking), industry standards or rules of thumbs and against internal trends (trends analysis). Furthermore the most useful comparison when performing financial ratio analysis is trend analysis They are derived from thethree following financial

statements:

⚫Balance Sheet

•Income Statement

⚫Statement of Cash Flows

.5 Categories

The five (5) major categori in the financial ratios list include the following:

•Liquidity Ratios

•Activity Ratios

•Debt Ratios

•Profitability Ratios

•Market Ratios

Step-by-step explanation:

Sana makatulong

Ratios dealing with short-term debts are Liquidity Ratios; those gauging efficiency in using assets for sales are Activity Ratios, and those scrutinizing long-term debt handling are Leverage Ratios. Along with the calculations, observations and identification of trends and their driving factors are also necessary.

In finance and business, ratio analysis is a tool used for conducting quantitative analysis on a company's financial statements. It involves the calculation and interpretation of various financial ratios. The following are the answers to the question's blanks:

However, only calculating ratios is not enough; you must also observe and identify trends suggested by the analysis, as well as identify the factors that drive these trends. These additional steps provide context and deeper insights into the company's financial performance.

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The coordinates of point A when it is rotated about 180 degrees will be (7,-4).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Given that:-

As it is turned 180 degrees from its initial position ( -7,4) just opposite side of the origin so the new coordinates of the point will be (4,-7).

Therefore the coordinates of point A when it is rotated about 180 degrees will be (7,-4).

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Answer:

a^7

Step-by-step explanation:

a^7

Exponents are added when multiplied

First play = 30 yards gained

Second play = 40 yards lost

Third play = 10 yards gained

Total yards Jason has = +30 -40 +10

= +40 -40

= 0

Answer: 0

Step-by-step explanation:

30 - 40 + 10

30 - 40 = -10

-10 + 10 = 0

0 is your final answer

Answer:

2. x-10=24

Step-by-step explanation:

x is the unknown amount of candy that Charlie has.

He gives ten away (-10).

Now he has 24 pieces.

x-10 = 24

Answer:

7 1/5 cups of flour

Step-by-step explanation:

divide 3/5 which is 0.6 then multiply that by 12, which is 7.2

then convert that into a fraction which is 7 1/5

Answer:

Whole numbers less than 5 may be termed as Rational numbers.

The solution to the given inequality is b ≤ 1.

Inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥.

Given inequality expression is,

7 (b - 1) / b ≤ 0

(7b - 7) / b ≤ 0

(7b / b) - (7 / b) ≤ 0

7 - 7/b ≤ 0

Adding 7/b on both sides,

7 ≤ 7/b

Multiplying b on both sides,

7b ≤ 7

b ≤ 1

Hence the value of b is b ≤ 1.

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Answer:

6.4

Step-by-step explanation:

6.432 rounded to the nearest tenth will be 6.4, the tenth is the first digit after the decimal.

Answer: 6.4

Step-by-step explanation:

6.432 3 < 5

So The 4 Stays The Same

Answer:

inches

Step-by-step explanation:

well depends on how big your foot is

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

Answer: Shown below

Step-by-step explanation:

Since it's a square, we will refer to its values as x. Using that, we can make an equation for the rectangle.
(x + 15) * ( x - 13) = 60

We can expand it and simplify so that we get a zero on one side and a polynomial on the other.

(x + 15)(x - 13) - 60 = 0

x² + 2x - 225 = 0

We simplify the binomial so we get two answers for x.

(x - 15)(x + 17) = 0

x = 15 and -17

Now we have two answers. So which one is right? Well, the sides cannot be negative, therefore we must use 15 and not -17.

15² = 225

Our answer is 225

Answer:

44 students

Step-by-step explanation:

1200 for the first year

a third of that is 400

400 for the second year

a third of that is 133.4

133.4 for the third year

a third of that is 44

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

1 + cot² θ = csc² θ

where angle θ is any angle in standard position in the xy-plane.

Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.

The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:

c² = a² + b² becomes:

r² = y² + x² = 1²

y² + x² = 1

We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:

(sin θ)² + (cos θ)² = 1

1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.

Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:

(sin² θ + cos² θ)/cos² θ = 1/cos² θ

(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ

(sin θ/cos θ)² + 1 = (1/cos θ)²

(tan θ)² + 1 = (sec θ)²

2.) tan² θ + 1 = sec² θ

Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:

(sin² θ + cos² θ)/sin² θ = 1/sin² θ

(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ

1 + (cos θ/sin θ)² = (1/sin θ)²

1 + (cot θ)² = (csc θ)²

3.) 1 + cot² θ = csc² θ

Answer:

the answer is b

step-by-step explanation:

Answer:

1: 0.8461 = 84.61% probability that a randomly selected 1-year old boy from the population will have a weight that is less than 25 lbs.

2: 0.9994 = 99.94% probability that the mean weight for a sample of size 10 1-year-old boys will be less than 25 lbs

3: In part 2, we use the sampling distribution of the sample means, which has more values closer to the mean due to the smaller standard error, so a higher probability of finding a mean less than 25 lbs.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 22.8 lbs and a standard deviation of about 2.15 lbs.

This means that \(\mu = 22.8, \sigma = 2.15\)

Part 1: Find the probability that a randomly selected 1-year old boy from the population will have a weight that is less than 25 lbs.

This is the pvalue of Z when X = 25. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{25 - 22.8}{2.15}\)

\(Z = 1.02\)

\(Z = 1.02\) has a pvalue of 0.8461

0.8461 = 84.61% probability that a randomly selected 1-year old boy from the population will have a weight that is less than 25 lbs.

Part 2: Find the probability that the mean weight for a sample of size 10:

Now \(n = 10, s = \frac{2.15}{\sqrt{10}}\). So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{25 - 22.8}{\frac{2.15}{\sqrt{10}}}\)

\(Z = 3.24\)

\(Z = 3.24\) has a pvalue of 0.9994

0.9994 = 99.94% probability that the mean weight for a sample of size 10 1-year-old boys will be less than 25 lbs

Part 3: Explain the difference between Part 1 and Part 2.

In part 2, we use the sampling distribution of the sample means, which has more values closer to the mean due to the smaller standard error, so a higher probability of finding a mean less than 25 lbs.

The graph of the quadratic function is the one in option A.

Here we want to graph the quadratic function:

y = 2x² + 6x+3

To do so, we can find the y-intercept:

y = 2*0² + 6*0+3 = 3

So the y-intercept is (0, 3).

Also, the x-value of the vertex is at:

x = -6/(2*2) = -6/4 = -3/2

So the vertex is in the left side of the y-axis, with these two things we can conclude that the correct option is A.

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Answer:

Step-by-step explanation:

The area of the rectangle is 48 square feet.

Write an equation you can use to find the value of x.

48 : 4 = x

12 = x

48=4x is the equation which can be used to find the value of x.

Given that area of the rectangle is 48 square feet.

We have to find the value of x.

We know that area of rectangle is length times width.

Area = length × width

Length =x ft

Width = 4 ft

Area = 48 square feet.

Plug in the values of length, width and area in above formula.

48=4x

Divide both sides by 4:

x=12

Hence, 48=4x is the equation which can be used to find the value of x.

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Answer:

\(number = x \\ \frac{x}{4} + 3 = 8 \\ \frac{x}{4} = 5 \\ x = 20 \\ thank \: you\)

Answer:

\(let \: the \: number \: be \: x \: \\ then \: \\ \frac{x}{4} + 3 = 8 \\ \frac{x}{4} = 8 - 3 \\ \frac{x}{4} = 5 \\ x = 5 \times 4 \\ x = 20 \\ \: hence \: 20 \: is \: your \: answer \:hope \: it \: helped\)