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W. If f(x)=4, find x.

X. If f(x)=-3, find x.

Answer:

-4 degrees

Step-by-step explanation:

You subtract 14-18

Let's begin by listing out the information given to us:

The general formula for growth or decay is given by:

y = ab^x

For growth: b = 1 + r

For decay: b = 1 - r

1.

y = ⅓(4^x)

When we compare this equation with the general formula, we will see that

The feature that distinguishes the growth from decay is the value of b, whether it is 1 + r for growth or 1 - r for decay

Step-by-step explanation:

x^2 + (4+3)X + 12

x^2 + 4x + 3X + 12

X (X + 4) + 3 ( X + 4)

( X + 3) (X +4)

Solving steps:

\(\sf \rightarrow x^2\:+\:7x\:+\:12\)

breakdown the following

\(\sf \rightarrow x^2\:+\:3x + 4x\:+\:12\)

break the expressions into groups

\(\sf \rightarrow \left(x^2+3x\right)+\left(4x+12\right)\)

factor the following

\(\rightarrow \sf x\left(x+3\right)+4\left(x+3\right)\)

factor the common term: (x+3)

\(\rightarrow \sf \left(x+3\right)\left(x+4\right)\)

False. The triple exponential smoothing method does consider seasonality variations in the analysis of the data, along with trend and level components, to provide accurate forecasts.

The statement is false. Triple exponential smoothing, also known as Holt-Winters method, is a time series forecasting method that incorporates trend and seasonality variations in the analysis of the data, but it does not specifically use seasonality variations.

Triple exponential smoothing extends simple exponential smoothing and double exponential smoothing by introducing an additional component for seasonality. It is commonly used to forecast data that exhibits trend and seasonality patterns. The method takes into account the level, trend, and seasonality of the time series to make predictions.

The triple exponential smoothing method utilizes three smoothing equations to update the level, trend, and seasonality components of the time series. The level component represents the overall average value of the series, the trend component captures the systematic increase or decrease over time, and the seasonality component accounts for the repetitive patterns observed within each season.

By incorporating these three components, triple exponential smoothing can capture both the trend and seasonality variations in the data, making it suitable for forecasting time series that exhibit both long-term trends and repetitive seasonal patterns.

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Answer:

ok

Step-by-step explanation:

Answer:

9.5 * 10^23 molecules of HCl

Step-by-step explanation:

just a note this might be better to put in the chem section next time since this is a stoichiometry question

the molar mass of HCL is 1.007 + 35.45 = 65.457 g/mol

to find the number of moles, divide 100 by 65.457

then multiply the number of moles by 6.22 * 10^23 to get the number of molecules

\(100.00g * \frac{1 mol}{65.457g} * \frac{6.22 * 10^{23} molecules }{1 mol} = 9.502 * 10^{23} molecules\)

Answer:

6) yes

7) no

Step-by-step explanation:

yes Step-by-step explanation:

The given relation in the mapping diagram represents a function.

A function in mathematics is an expression with a independent variable (x) in it. The variable is called independent because it is not dependent on any value to get its value. Function also has a dependent variable (y) whose value depend on x. Ex -

y = f(x) = ax + d

We have a relation as shown in the figure.

The given relation is a function as all the values of [x], has independent values of [y]. Two or more values of [x] can have same value of y.

Therefore, the given relation in the mapping diagram represents a function.

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The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

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Answer:

Step-by-step explanation:

Draw a diagram of a vertical wall with a ladder leaned against it.

You can say that the ladder is 8 meters long and the distance from the bottom of the ladder to the base of the wall is 2 meters..

Then ask the question At what height on the wall is the top of the ladder?

This is calculated using the Pythagoras theorem - the ladder is the hypotenuse used of the right angled triangle formed by the wall, ladder and the ground.

8^2 = x^2 + 2^2      where x is the required height.

x^2 = 8^2 - 2^2

x^2 = 60

x = sqrt60

= 7.75 meters to nearest hundredth.

Answer:

negative because any positive number multiplied by a negative number will be negative, the only way to make it positive is to multiply a negative number by another negative number.

Step-by-step explanation:

The correct answer is, C.) The population is increasing by 19,597 people per year.

To find how fast the population is changing in 2013, we need to find the derivative of P(t) with respect to time (t) and evaluate it at t=13 (since we're looking at 2013, which is 13 years after 2000).

The derivative of P(t) = 200(1.052)^t is:
P'(t) = 200 * ln(1.052) * (1.052)^t

Evaluating this at t=13:
P'(13) = 200 * ln(1.052) * (1.052)^13

Using a calculator, we get:
P'(13) = 19,597

So the population is increasing by 19,597 people per year in 2013.

Therefore, the answer is, C.) The population is increasing by 19,597 people per year.

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The value of $m$ is $43$.

The equation $6^{-1}\equiv 6^2\pmod m$ implies that $6^{-1}$ is a valid inverse of $6$ modulo $m$. This means that multiplying $6^{-1}$ by $6$ must result in the remainder $1$ when divided by $m$.

To find the value of $m$, we can then set up the equation:

                                $0\equiv 215\pmod m$

and find all possible values of $m$ that make this equation true.

Multiplying $6^{-1}\equiv 6^2\pmod m$ by $6$, we get $1\equiv 6^3\pmod m$, so $0\equiv 215\pmod m$. So, $m$ must be a divisor of $215$. The only 2-digit divisor of $215$ is $43$.

Therefore, $m$ is a two-digit number, the only possible value of $m$ is $43$.

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By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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The measure of the smallest angle in the triangle is 10.8°

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

The corresponding angles of the two equal lengths in an isosceles triangle are equal. This means that if we represent the two angles by x and the the third angle by y , then 2x+y = 180.

using cosine rule c² = a²+b²+2abcosC

a = 8, b = 8 and c = 3

3² = 8²+8²+2×8×8cos C

9 = 64+64+128cos C

128cosC = 9- 128

cos C = -119/128

cos C = -0.93

C = cos^-1 0.93

C = 158.4°

therefore 158.4 + A+ B = 180

A= B

2A = 180-158.4

2A = 21.6

A = 21.6/2

A = 10.8°

therefore A = B = 10.8°. This means the value of the smallest angle is 10.8°

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I did not get Your Question Probably But the way I see it the answer is:

The equation of a circle with center (h, k) and radius r can be written as:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -6). To find the radius, we can use the distance formula between the center and the given point (-√28, 3):

r = √((x₂ - x₁)^2 + (y₂ - y₁)^2)

Plugging in the values:

r = √((-√28 - 0)^2 + (3 - (-6))^2)

Simplifying:

r = √(28 + 81)

r = √109

Therefore, the equation of the circle with center (0, -6) and containing the point (-√28, 3) is:

(x - 0)^2 + (y + 6)^2 = (√109)^2

Simplifying further:

x^2 + (y + 6)^2 = 109

Answer:

The equation of the circle with center (0, -6) containing the point (-√28, 3) is x^2 + (y + 6)^2 = 109.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by the formula:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -6), which means that h = 0 and k = -6. We also know that the circle contains the point (-√28, 3), which means that this point is on the circle and satisfies the equation above.

To find the radius r, we can use the distance formula between the center of the circle and the given point:

r = sqrt((0 - (-√28))^2 + (-6 - 3)^2) = sqrt(28 + 81) = sqrt(109)

Substituting h, k, and r into the equation of the circle, we get:

x^2 + (y + 6)^2 = 109

Therefore, the equation of the circle is x^2 + (y + 6)^2 = 109.

Its D or A But im pretty sure its A! Hope you do Great!

Let me know if its wrong!

Answer:  14 inches of wire can be bought for 42 cents.

Given, 19 inches of wire costs 57 cents.

We need to find out how many inches of wire can be bought for 42 cents.

Let x be the number of inches of wire that can be bought for 42 cents.

As we know, wire costs at the same rate, we can set up a proportion to solve for x:

19/57 = x/42

Simplifying, we get:

x = (19 × 42)/57

x = 798/57

x = 14

Therefore, 14 inches of wire can be bought for 42 cents.

To solve the given problem, we can use the concept of proportionality. Since the cost of the wire remains the same, we can assume that the rate of change between the cost and the length of the wire is constant. By setting up a proportion using this idea, we can solve for the length of wire that can be bought for a given cost. Thus, 14 inches of wire can be bought for 42 cents.

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Answer:

Value of 8x -5y + 7 is 4.

Step-by-step explanation:

Given that:

8x-5y = -3     Eqn 1

It is a true equation.

Now we have to find the value of the given expression

8x -5y + 7

Putting value of 8x-5y from Eqn 1 in the given expression

8x - 5y + 7

-3 + 7

4

Therefore,

8x - 5y + 7 = 4

Hence,

Value of 8x -5y + 7 is 4.

Answer:

576'' squared

Step-by-step explanation:

When y = 12, the value of x is 3.

When two variables, x and y, vary inversely, it means that as one variable increases, the other variable decreases in such a way that their product remains constant.

In this case, we are given that x and y vary inversely. We are also given a specific pair of values: when x = 4, y = 9. We can use this information to find the constant of variation, which will allow us to determine the value of x when y is given as 12.

Let's denote the constant of variation as k. According to the inverse variation relationship, we have:

x * y = k

Substituting the given values, we have:

4 * 9 = k

36 = k

Now that we have determined the constant of variation, we can find x when y = 12. Using the same relationship:

x * y = k

Substituting y = 12 and k = 36, we have:

x * 12 = 36

To solve for x, we divide both sides of the equation by 12:

x = 36 / 12

x = 3

Therefore, when y = 12, the value of x is 3.

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The value of [x] in the triangle is 36.25°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a right angled triangle.

We can write -

tan(x°) = (22/30)

x° = tan⁻¹(22/30)

x° = 36.25°

Therefore, the value of [x] in the triangle is 36.25°.

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Congruent angles simply refer to those angles that are the same size.

The rules for congruent angles with parallel lines and transversal are that the angles must be:

1) Alternate Interior Angles

2) Alternate Exterior Angles

3) Corresponding Angles

4) Vertical Angles.

Now, let us check each option individually:

OPTION A: Angles 1 and 7

Angles 1 and 7 are alternate exterior angles.

Therefore, they are CONGRUENT.

OPTION B: Angles 3 and 5

Angles 3 and 5 are alternate interior angles.

Therefore, they are CONGRUENT.

OPTION C: Angles 4 and 6

Angles 4 and 6 are corresponding angles.

Therefore, they are CONGRUENT.

OPTION D: Angles 2 and 5

Angles 2 and 5 do not have any particular relationship with each other.

Therefore, they are NOT CONGRUENT.

Hence, OPTION D is correct.

Answer:

k = 7

Step-by-step explanation:

Applying,

S = (y₂-y₁)/(x₂-x₁)................ Equation 1

Where S = slope of the line.

From the question,

Given: y₂ = 10, y₁ = 4, x₂ = k, x₁ = 1, S = 1

Substitute these values into equation 1

1 = (10-4)/(k-1)

crossmultiplying,

(k-1) = (10-4)

k-1 = 6

k = 6+1

k = 7

Answer:

x=24

y=58

Step-by-step explanation:

5x+20=6x-4

5x-6x=-20-4

-x=-24 /:(-1)

x=24

5×24+20+y-18=180

122+y=180

y=180-122

y=58

Answer:

50 in. 48 in. 14 in.

Step-by-step explanation:

you didn't attach the figure....

Answer:

2.6 or 2.66

Step-by-step explanation:

multiply 8 x 2 = 16

divide 16 ÷ 6

there i guess