MATH: GRAPHING PIECE-WISE...HELP! 15 PTS

(3x-5)/2 = 8

3x - 5 = 2 × 8

3x - 5 = 16

3x = 16 + 5

3x = 21

x = 21/3

x = 7

Answer:

Step-by-step explanation:

Equation

(3x - 5)/2 =  8                         Multiply both sides by 2

2*(3x - 5)/2 = 8 * 2                Combine

3x - 5 = 16                             The 2s on the left cancel. Add 5 to each side

3x - 5 + 5 = 16+5                    Combine

3x = 21                                    Divide both sides by 3

3x/3 = 21/3

x = 7

Answer: x = 7

The probability that the sample proportion is less than 0.80 is mathematically given as P(z<-0.52)

Generally, the equation for probability is  mathematically given as

p=82/100

Therefore

p=0.82

q=1-p

q=1-0.82

q=0.18

[tex]SE=\sqrt{\frac{p(1-p)}{n}}\\\\SE=\sqrt{\frac{0.8(1-0.8)}{100}}\\\\SE=0.03841[/tex]

b)

[tex]P(p < 0.80)=p(\frac{p-0.82}{0.0384} < \frac{0.8-0.82}{0.0384})\\\\P(z < -0.52)[/tex]

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Final answer:

The answer is 10.65.

Step-by-step explanation:

Step 1

Substitute a=1,5 into expression

7.1a, a=1.5

7.1 x 1.5

Step 2

Multiply the numbers

7.1 x 1.5 = 10.65

Answer:

10.65

Step-by-step explanation:

Plug a into the expression

[tex]7.1\times1.5=10.65[/tex]

Hope I helped you in some way!

Answer:

[tex]f^{-1}(x)=x^2+1[/tex]

Step-by-step explanation:

The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y

Original Equation:

[tex]f(x)=\sqrt{x-1}\\[/tex]

write f(x) as y (since that's what it represents)

[tex]y=\sqrt{x-1}[/tex]

Swap x and y

[tex]x=\sqrt{y-1}[/tex]

Square both sides

[tex]x^2=y-1[/tex]

Add 1 to both sides

[tex]x^2+1=y[/tex]

So this gives you the equation:

[tex]f^{-1}(x)=x^2+1[/tex]

The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.

The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.

Mathematically, the point-slope form of a line is given by:

y - y₁ = m(x - x₁)

Where:

In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.

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Answer:

b

Step-by-step explanation:

I do not agree that passing the state math and reading tests will be a predictor of a student's success in college.

The factors that determine a student's success in college include the following:

Do you agree with the board? Mention the factors that determine a student's success in college.

Thus, it is not necessarily true that passing the state math and reading tests will be a predictor of a student's success in college.

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The percentage of a given number in another implies the fraction of the given number to that other number with respect to 100%. Thus the required expression is: [tex]\frac{m}{100}[/tex] x n

When a given number is written in percentage, it implies that the fraction of the number to the total number in relation to 100%. For example, to determine the percentage of a number r in s, -we have:

[tex]\frac{r}{s}[/tex] x 100%

Therefore in the given question, the required expression is;

m% = [tex]\frac{m}{100}[/tex]

So that;

m% of n can be expressed as;

[tex]\frac{m}{100}[/tex] x n

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The required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens

A TV studio has brought in 6 boy kittens and 8 girl kittens for a cat food commercial.

Probability, can be define as the ratio of favorable events to the n number of total events

The director is going to choose 7 of these kittens at random to be in the commercial. the director chooses 4 boy kittens and 3 girl kittens.

Here, probability of to choose 7 of these kittens at random
= c(14,7)

probability to chooses 4 boy kittens and 3 girl kittens
= c(6,4) x c(8,3)

Required probability = [tex]\frac{c(6, 4) * c(8, 3)}{c(14, 7)}[/tex] = 0.012

Thus, The required  required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens.

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Using proportions, her gross pay is given as follows:

d. $779.10.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Her gross pay is divided as follows:

Hence the total pay is:

33 x 14.70 + 2 x 10 x 14.70 = $779.10.

Which means that option d is correct.

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Answer:

159

Step-by-step explanation:

all natural numbers are numbers that go above 0 and etc…

Therefor, 256 - 97

= 159

Answer:

158

Step-by-step explanation:

Between means 97 and 256 are not included

Therefore its should be:

=(256-97)-1

=158

The inequality which represents the number of jeans and sweater which he must purchase is; $17x + $9y >= $75.

It follows from the task content that, to receive free shipping, $75 or more must be spent on the pieces of clothing to receive free shipping.

On this note, it follows that the required inequality is; $17x + $9y >= $75.

This follows from the fact that jeans are $17 each and sweaters are $9 each.

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Considering the volume of a rectangular prism, the capacity of the second sandbox would be of 80 cubic feet.

The volume of a rectangular prism with length l, width w and height h is given by the multiplication of the measures, that is:

V = lwh.

In this problem, the capacity is of 10 cubic feet, that is:

V = lwh = 10.

When each measure is doubled, the volume will be given as follows:

V=  2l x 2w x 2h = (2 x 2 x 2)lwh = 8lwh = 8V = 80 cubic feet.

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It is false that the midpoint is in quadrant IV

The endpoints are given as:

S (1,4) and T (5,2

The midpoint is

(x, y) = 0.5 *(x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 *(1 + 5, 4 + 2)

Evaluate the expression

(x, y) = (3, 3)

The point (3, 3) is located in the first quadrant

Hence, it is false that the midpoint is in quadrant IV

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Answer:

m = 300w OR w = m/300

Step-by-step explanation:

They start with 10k, but that's immediately sold, so they're back at a flat 0. Every week they gain 1000 but lose 700 for a net profit of positive 300.

Therefore, the maximum capacity would be 300 multiplied by the number of weeks. If we know the maximum, then the answer would be m (maximum) divided by 300.

Answer:

801.5625

Step-by-step explanation:

25.65×100/1.6×2=801.5625

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

Simple interest is a method of calculating the interest charge.

Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.

Simple Interest = (Principal × Rate × Time) / 100

25.65 × 100/(1.6 × 2 )

= 801.5625

Therefore, the  principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

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Answer:

Using the formulas

C=2πr

d=2r

Solving for d

d=C

π=8

π≈2.54648

d≈2.55

For convenience sake, I will let [tex]y=f(x)=9e^{x}\sin x[/tex]

First, we evaluate the function at the endpoints of the interval.

[tex]f(0)=9e^{0}\sin(0)=0\\\\f(\pi)=9e^{\pi}\sin(\pi)=0[/tex]

Then, we need to find the critical points.

We can start by taking the derivative using the power rule.

[tex]f'(x)=9e^{x} \frac{d}{dx} \sin x+9\sin x \frac{d}{dx} e^{x}=9e^{x}(\cos x+\sin x)[/tex]

Setting this equal to 0,

[tex]9e^x (\cos x+\sin x)=0[/tex]

Since [tex]9e^x > 0[/tex], we can divide both sides by [tex]9e^x[/tex].

[tex]\cos x+\sin x=0\\\\\sin x=-\cos x\\\\\tan x=-1\\\\x=\frac{3\pi}{4}[/tex]

[tex]f\left(\frac{3\pi}{4} \right)=9e^{3\pi/4}\sin \left(\frac{3\pi}{4} \right)=\frac{9\sqrt{2}e^{3\pi/4}}{2}[/tex]

So, the absolute minimum is [tex]\boxed{\left(\frac{3\pi}{4}, \frac{9\sqrt{2}e^{3\pi/4}}{\sqrt{2}} \right)}[/tex] and the absolute minima are [tex]\boxed{(0,0), (\pi, 0)}[/tex]

Answer:

A turning point is the highest or lowest point on a quadratic graph.

Step-by-step explanation:

A quadratic graph looks something like the graph below.

The equation of a quadratic graph would normally look like

+/- ax^2 + bx + c

An example might be -16x^2 + 5x + 4

Note the negative symbol in front of the 16. The negative means that the graph will be facing downwards, or that the turning point is the highest point. A positive graph will mean that the graph is facing upwards, or that the turning point is the lowest point.

Essentially, it is the location where a graph has its lowest or highest point and where the y-values (can include x-values in horizontal quadratics) "turn" to the direction they originated.

Answer:

Step-by-step explanation:

Hello!

15 < x + 4

We can subtract 4 from both sides, to cancel it out.

15 - 4 is 11.

11 < x

x = {12,13,14,15,16,..........................................................................Infinity}

Hope I Helped!

Using Pythagoras theorem, the top of the ladder will slide down the wall 1.64 ft

The ladder leaning against the wall forms a right-angled triangle of sides 8 ft and 6 ft.

The length of the ladder is y.

Using Pythagoras theorem:

[tex]y = \sqrt{8^{2} + 6^{2}} = 10 \:ft[/tex]

When the ladder is  pulled 1 foot away from the wall, the new height, h the ladder rises up the wall is given below:

[tex]h = \sqrt{10^{2} - 9^{2}} = 4.36 \:ft[/tex]

The top of the ladder will slide 6 - 4.36 ft = 1.64 ft

In conclusion, the length the ladder will slide down is obtained using Pythagoras theorem.

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Answer:

Option A) [tex]\bf{ x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

Step-by-step explanation:

we have

[tex]\sf{\dfrac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}}[/tex]

we know that

[tex]\sf{\sqrt[7]{x^{2}}=x^{\frac{2}{7}}}[/tex]

[tex]\sf{\sqrt[5]{y^{3}}=y^{\frac{3}{5}}}[/tex]

substitute in the expression

[tex]\sf{\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

Answer: 11.4

Step-by-step explanation:

Using the distance formula,

[tex]AC=\sqrt{(-3-1)^2 + (-1-2)^2}}=5\\\\AB=\sqrt{(-3-0)^2 +(-1-3)^2}=5\\\\BC=\sqrt{(1-0)^2 + (2-3)^2}=\sqrt{2} \approx 1.4\\\\\implies P \approx 5+5+1.4=\boxed{11.4}[/tex]

Answer:

1000 times

Step-by-step explanation:

To find out how many times 0.1 can fit into 100, we can just divide 100 by 0.1.

But, we first find out how many times can 1 fit into 100.

No. of times 1 fit into 100 = 100 / 1 = 100 times

Now we know 1 is 10 times of 0.1, so we multiply the above by 10,

so 100 * 10 = 1000 times.

Therefore 0.1 can fit into 100 a 1000 times.

Answer:

1000

Step-by-step explanation:

100 divide by 0.1 the answer is 1000

The object compresses the spring up to 0.8577m.

Potential Energy is the energy possessed by an object at rest.

The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.

The total amount of potential energy at the top of the ramp is given by

Ep=mgh

Ep=3 * 9.81 *5

Ep=147.15 Joules

This is equal to kinetic energy.

From the formula for elastic potential energy

The distance up to which the spring is compressed is determined

The force constant = 400N/m

147.15 =(1/2)k(x²)

294.3=(400)(x²)

0.73575=x²

x=0.8577 m

So, the object compresses the spring up to 0.8577m.

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Answer:

7.  Down 5

8.  Horizontal reflection

9.  Vertical stretch by a factor of 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 7

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=x^3-5[/tex]

Comparing the parent function with the given function, we can see that 5 has been subtracted from the parent function.

Therefore, the transformation is:

[tex]f(x)-5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units down}[/tex]

Question 8

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=-x^3[/tex]

Comparing the parent function with the given function, we can see that the parent function has been multiplied by -1.

Therefore, the transformation is:

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

Question 9

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=5x^3[/tex]

Comparing the parent function with the given function, we can see that the parent function has been multiplied by 5.

Therefore, the transformation is:

[tex]y=5\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:5[/tex]

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Answer:

7. Down 5

8. Horizontal Reflection.

9. Vertical Stretch by a factor of 5.

Explanation:

Parent function: f(x) = x^3

7. f(x)= x^3 - 5

Comparing it with f(x) - d which gives function shifted d units down.

Here the function has shifted 5 units down.

8. f(x)= -x^3

Comparing with -f(x) gives reflection over x-axis (horizontal reflection).

Here the function f(x) = (-1x^3) has been reflected horizontally.

9. f(x)= 5x^3​

Comparing with a(f(x)) gives vertical stretch when |a| > 1 or compression when 0 < |a| < 1 by a factor of a.

Here the function f(x) = 5x^3​ has been vertically stretched by a factor of 5.

Answer:

At Less In Number 20

Step-by-step explanation:

1234567891011121314151617181920

Answer:

[tex]1234567x = [/tex]

The probability that the hacker guesses the password in first go is

[tex]\dfrac{1}{5^5}[/tex]

While statistics examines the frequency of previous events, probability deals with estimating the possibility of future events.

The primary goal of the theoretical branch of mathematics known as the probability is the investigation of the consequences of mathematical concepts. At its core, statistics is a field of mathematics that seeks to explain observations in the actual world.

Both topics are significant, pertinent, and helpful. However, they are distinct, and appreciating this difference is essential to correctly assessing the applicability of mathematical evidence.

Since sample space has 5⁵ possibilities.
The event space has only one possibility which is to successfully hack the password perfectly.
Hence, the probability is

[tex]\dfrac{1}{5^5}[/tex]

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Answer:

[tex]-\frac{8\sqrt{2}+2}{15}.[/tex]

Step-by-step explanation:

1) sin(a+b)=sin(a)cos(b)+sin(b)cos(a);

2) if sin(a)=-0.4, then cos(a)=0.8; if cos(b)=1/3, then sin(b)=-√8/3;

3) finally, sin(a+b)=-0.4*1/3-√8/3*0.8=

[tex]=-\frac{8\sqrt{2}+2}{15}.[/tex]