what is the starting number is this puzzle? +7 -4 x3 =30

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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The ratios are not all equal, we can conclude that the cost of the taxi is not proportional to the number of miles driven.

What is proportional?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

To find the cost of hiring a taxi to drive 1, 2, 3, and 4 miles, we can use the formula:

C = 4 + 1.25m

For m = 1, we have:

C = 4 + 1.25(1) = 5.25

For m = 2, we have:

C = 4 + 1.25(2) = 6.5

For m = 3, we have:

C = 4 + 1.25(3) = 7.75

For m = 4, we have:

C = 4 + 1.25(4) = 9

So the table of costs for driving 1, 2, 3, and 4 miles is:

Miles (m) Cost (C)

       1 5.25

       2 6.5

       3 7.75

       4 9

To determine whether the cost of the taxi is proportional to the number of miles driven, we can check whether the ratios of cost to distance are equal. If they are, then the cost is proportional to the number of miles driven.

Let's check the ratios:

C(1)/1 = 5.25/1 = 5.25

C(2)/2 = 6.5/2 = 3.25

C(3)/3 = 7.75/3 = 2.58333...

C(4)/4 = 9/4 = 2.25

Hence, the ratios are not all equal, we can conclude that the cost of the taxi is not proportional to the number of miles driven.

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Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

It is important to use the given standard deviation to construct the control chart.

A control chart is a statistical tool used to monitor and control a process over time. It is a graphical representation of process data over time, with the addition of statistical control limits. Control charts are used to detect any unusual variation in a process and to identify when the process is out of control or deviating from its expected performance.

Yes, you need to use the given process standard deviation of 0.27 to construct the three-sigma control chart for the mean weight.

The control limits for the X-Bar Control Chart with a sample size of n = 4 and a Z-value of 3 can be calculated using the following formula:

UCL = X-Bar + Z(σ/√n)

LCL = X-Bar - Z(σ/√n)

where UCL is the upper control limit, LCL is the lower control limit, X-Bar is the sample mean, σ is the process standard deviation, n is the sample size, and Z is the number of standard deviations.

To construct the control chart, you need to calculate the UCL and LCL for each sample means in your data set using the formula above. Then, plot the sample means on the control chart along with the UCL and LCL.

It is important to use the given standard deviation to construct the control chart.

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Answer

is the B

Step-by-step explanation:

really easy

Answer:

a) Any sample statistic used to approximate a population parameter.

Step-by-step explanation:

An unbiased estimator is any sample statistic used to approximate a population parameter.

In mathematics, the bias of an estimator refers to the difference between the true value of the parameter being estimated and the estimator’s expected value.

If a statistic is not an underestimate or overestimate of the population parameter, then it is unbiased.

That is why an unbiased estimator is an accurate sample statistic used to approximate a population parameter.

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

The formula of the function, where x is entered in radians is   y = -3sin(πx/5) -6

The key components: amplitude, period, phase shift, and vertical shift.

Amplitude is the distance between the midline and max/min points. Midline at (0, -6), so distance to min point (2.5, -9) is 3. Amplitude: 3.

Vertical shift: Displacement along y-axis. Midline at y = -6, vertical shift is -6. Period: distance between max/min points. Graph intersects midline at (0, -6) and minimum point at (2.5, -9).  Period is 5 (2 * 2.5). Freq: Reciprocal of period, 1/5.

Phase shift: Horizontal shift of graph. Graph intersects midline at x=0, no phase shift.

Hence:

The general form of the sinusoidal function is y = A sin (B(x-C)) + D

So, Substituting the known values into the general formula:

y = 3 x  sin((1/5)x - 0) - 6

Hence: Simplifying it will be:

y = 3 x sin(πx/5) - 6

Then, the formula of the function, where x is entered in radians, is: y = -3sin(πx/5) - 6

Based on the image attached, the first given point is one that informs one that the function is a sine (not a cosine) function, and that it is one that has its offset as -6.

Also, the second given point is one that informs you of the first peak is at x=2.5, hence the argument of the sine function is π/2 if x=2.5: (πx/5).

Based on the fact that the peak is 3 units smaller than the midline, the amplitude is said to be -3.

Therefore the  formula for the function is  seen as:  y = -3·sin(πx/5) -6

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Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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Answer:

\(g(x) = x^3+1\\f(x) = x^2\)

Step-by-step explanation:

Answer:

f(x)=x^2 and g(x)=x^3+1

Step-by-step explanation:

to find y=f(g(x))

substitute g(x) into f(x)

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

Answer:

\( {x}^{2} - 4x + 9 = 0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-( - 4)\pm\sqrt{( - 4)^2-4(1)(9)}}{2(1)} \\x=\frac{ 4\pm\sqrt{ 16-36}}{2} \\ x=\frac{ 4\pm\sqrt{ - 20}}{2} \\ x=\frac{ 4\pm2i\sqrt{ 5}}{2} \\ x = 2\pm \: i\sqrt{ 5} \\ D = {b^2-4ac} \\D = { 16-36} \\ = - 20 < 0 \rightarrow \: x \in \: \mathbb{C} \: \\ x \: is \: complex \)

Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

Let's analyze each system of equations and classify them based on the number of solutions they have:

1) y = 11 − 2x

  4x − y = 7

This system of equations represents two lines. The first equation is in slope-intercept form, and the second equation is in standard form. Since the equations have different slopes and different y-intercepts, they intersect at a single point. Thus, the system has a single solution.

2) x = 12 − 3y

  3x + 9y = 24

The first equation represents a line, and the second equation is a linear equation. Since the first equation can be rewritten as 3y = 12 - x or y = 4 - (1/3)x, it indicates that the slope-intercept form can't be satisfied. Both equations are equivalent and represent the same line. Therefore, the system has infinitely many solutions.

3) 2x + y = 7

  -4x = 2y + 14

The first equation represents a line, and the second equation is also a linear equation. If we simplify the second equation, we get y = -2x - 7, which is equivalent to the first equation. Thus, the system has infinitely many solutions.

4) x + y = 15

  2x − y = 15

Both equations are in standard form. By adding the equations, we eliminate y and get 3x = 30, which simplifies to x = 10. Substituting x = 10 into either equation, we find y = 5. Therefore, the system has a single solution.

5) x + 4y = 6

  2x = 12 − 8y

The first equation represents a line, and the second equation is a linear equation. By simplifying the second equation, we get x = 6 - 8y, which is equivalent to the first equation. Therefore, the system has infinitely many solutions.

To summarize:

- System 1: Single solution.

- System 2: Infinitely many solutions.

- System 3: Infinitely many solutions.

- System 4: Single solution.

- System 5: Infinitely many solutions.

12.50

Parallel lines are lines that will never intersect.

Parallel Lines

Parallel lines run opposite of each other without intersecting. For lines to be parallel, they must have the same slope. The equation given to us is written in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. So, the slope from the equation is 12.50.

Finding Parallel Lines

In order to find other lines that are parallel to the line given, all we need to do is write another equation with the same slope. However, 2 lines that are the same are not considered to be parallel. This means that for 2 lines to be parallel they must have the same slope but different y-intercepts. For example, a parallel line could be y = 12.50x + 6.

Answer:

A) (1)/(7)

B) 33

Step-by-step explanation:

For (A), the sequence follows in 1 divided by numbers in a consecutive order, therefore after (1)/(6), the next term is (1)/(7)

For(B), the sequence follows in multiples of three but skips one in between

Example: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

In the sequence, 6, 12, 18 and 24 are skipped, meaning that the next number to be skipped is 30, hence 33 is the next number in the sequence.

Because all the numbers in the sequence are odd numbers we can say that the sequence follows in odd consecutive numbers which are multiples of 3.

The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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Answer:

Step-by-step explanation:

Year 1: $850 * 0.91 = $773.50

Year 2: $773.50 * 0.91 = $704.69

Year 3: $704.69 * 0.91 = $641.95

...

Year 34: (continue the pattern)

We can continue this calculation for each year, but to save time, we can use an exponential decay formula:

Remaining Amount = Initial Amount * (1 - rate)^years

Substituting the values:

Remaining Amount = $850 * (1 - 0.09)^34

Calculating this expression:

Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88

After 34 years, approximately $255.88 will be left with Sally.

Answer:

7.8287

Step-by-step explanation:

Sin(34)=x/14

14 x Sin(34)

Answer:

Step-by-step explanation:

Opposite side of the angle 34  is x & hypotenuse which is opposite to 90 is 14

\(Sin \ 34 = \dfrac{Opposite \ side}{hypotenuse}\\\\0.56 = \dfrac{x}{14}\\\\\\0.56*14=x\)

x = 7.84

Answer:

Step-by-step explanation:

   given equuation      10\(\sqrt{3x\)+4\(\sqrt{3x\)+5\(\sqrt{3x}\)

                                    =19\(\sqrt{3x}\)

the answer is 19\(\sqrt{3x}\)

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(a)Contrapositive: If an object does not have a border, then it is not red.

Converse: If an object has a border, then it is red.

Inverse: If an object is not red, then it does not have a border.

(b)Contrapositive: If an object is not red or does not have a border, then it is not a rectangle.

Converse: If an object is a rectangle, then it is red and has a border.

Inverse: If an object is not red or does not have a border, then it is not a rectangle.

(c)Contrapositive: If an object does not have a border, then it is not red or blue.

Converse: If an object is red or blue, then it has a border.

Inverse: If an object does not have a border, then it is not red or blue.

a) Original Conditional Statement (P - Q): If an object is red, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red.

Converse (Q - P) If an object has a border then it is red.

Inverse (not p → not q) If an object is not red then it does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may have a border but not be red.

b) Original Conditional Statement (P - Q): If an object is a rectangle, then it is red and has a border.

Contrapositive (not Q - not P): If an object is not red and does not have a border, then it is not a rectangle.

Converse (Q - P) If an object is red and has a border, then it is a rectangle.

Inverse (not p → not q) If an object is not a rectangle then it is not red or does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may be red and have a border but not be a rectangle.

c) Original Conditional Statement (P - Q): If an object is red or blue, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red or blue.

Converse (Q - P) If an object has a border then it is red or blue.

Inverse (not p → not q) If an object is not red or blue then it does not have a border.

The contrapositive and converse are true, while the inverse is false. For example, object H may have a border but not be red or blue.

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19 is the median of the numbers

Answer:

900

.........................

Answer:

900

Step-by-step explanation:

30 square is like 30×30=900

Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

Answer:

65 + r = 130

65 + r - 65 = 130 - 65

r = 65

Step-by-step explanation:

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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The limit of the expression is determined as 0.

The limit of the expression is calculated as follows;

The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)

For the given limit in the expression, we have x maps to 9 or x tends to 9.

When x tends to 9, we will have;

x ---->9 = (9 - 9 ) / (√9 - 3)

= (0)/(-3 - 3)

note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.

= 0/-6

= 0

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\(\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ \)

Now , by using Identity:-

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ \)

Answer:

Step-by-step explanation:

a) Total weight comprises of the weight of jar plus weight of Jolly Ranchers

b) When the candy jar is full, it weighs 1224 grams. How many Jolly Ranchers can the jar hold?  

Given w = 1224, then to find j we solve the equation:

The jar can hold 129 Jolly Ranchers

As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

An ordered set of number with a pattern or rule regulating their values is referred to as a sequence in mathematics. A word is used to characterize each number in a sequence. There are many various kinds of sequences, but a few of the most popular ones are as follows: A common differential, or constant number, is added to the respective period to produce an arithmetic series, each term of which is obtained. One arithmetic series with a following differences of three is 1, 4, 7, 10, 13, etc.

given

Given an arithmetic series with a first term (a1) and a common difference (d), the formula for the nth term (an) is as follows:

\(a = a1 + (n - 1) * d\)

In this instance, the common difference (d) is 15, and the first term (a1) is 7. When these values are added to the formula, we obtain:

\(a = 7 + (n - 1) * 15\)

As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

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Answer:

q=6 creates a verticle line at x=6 shaded to the left and encludes the line.

Step-by-step explanation:

9 + q <= 15

q <= 15 - 9 = 6