The cost of a pair of boots was $66. The sales tax rate is 5% of the purchase price.

Answer:

1/5

Step-by-step explanation:

20% = 20/100 = 2/10 = 1/5

Answer:

20%

\( = \frac{20}{100} \\ \\ = \frac{2}{10} \\ \\ = \frac{1}{5} \)

# be careful #

The solution is : The measure of angle ADC is 115°.

Here, we have,

Let A, B, C represent the vertex angle measures of ΔABC.

Then the sum of angles in ΔADC is ...

 A/2 +∠ADC + C/2 = 180°

Multiplying by 2 gives ...

 A + C + 2×∠ADC = 360°

From the given information, we know ...

 A + C + 50° = 180° . . . . . sum of angles in ΔABC

This lets us write an expression for (A +C):

 A + C = 130° . . . . . . . . subtract 50° from the previous equation

Substituting for A+C, we get ...

 130° + 2×∠ADC = 360°

 2×∠ADC = 230° . . . . . . . . . subtract 130°

 ∠ADC = 115° . . . . . . . . . . . divide by 2

The measure of angle ADC is 115°.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

complete question:

The measure of an angle ABC is 50°,AD bisects angle BAC, and DC bisects angle BCA. The measure of angle ADC is what?​

\(\frac{3}{y}=18 \\ \\ 3=18y \\ \\ y=1/6 \\ \\ \implies y+2=\boxed{13/6}\)

Answer:

the ant would have traveled 2.045 miles

1) The probabilities are given as follows:

a) More than 75: 0.0301 = 3.01%.

b) Between 60 and 73: 0.4484 = 44.84%.

c) Less than 50: 0.1057 = 10.57%.

2) The proportion of students who fail the module is of: 0.0062 = 0.62%.

3) The measures are given as follows:

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

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

The mean and the standard deviation in this problem are given as follows:

\(\mu = 60, \sigma = 8\)

The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:

Z = (75 - 60)/8

Z = 1.88

Z = 1.88 has a p-value of 0.9699.

1 - 0.9699 = 0.0301 = 3.01%.

The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:

Z = (73 - 60)/8

Z = 1.63

Z = 1.63 has a p-value of 0.9484.

Z = (60 - 60)/8

Z = 0

Z = 0 has a p-value of 0.5.

Then:

0.9484 - 0.5 = 0.4484 = 44.84%.

The probability of an score less than 50 is the p-value of Z when X = 50, hence:

Z = (50 - 60)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

The proportion who might fail the test is the p-value of Z when X = 40, hence:

Z = (40 - 60)/8

Z = -2.5

Z = -2.5 has a p-value of 0.0062.

Then the statistical measures are obtained as follows:

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

Answer:0.05 is the answer

Step-by-step explanation:

Answer:

A) 0.1

Step-by-step explanation:

√398=19.9

2/19.9=0.1005

The closest answer to that is 0.1

Please give brainliest if I helped! :)

The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

Learn more about polygon on

https://brainly.com/question/1592456

#SPJ1

9514 1404 393

Answer:

Step-by-step explanation:

Usually, a table of this nature is written with the "input" (independent variable) on the left, and the "output" (dependent variable) on the right. If we assume that is the case here, then ...

  h is the independent variable

  e is the dependent variable

__

We notice that the ratio e/h is the constant 11, so the equation expresses that proportional relationship.

  e = 11h

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

learn more on angles here:https://brainly.com/question/25779160

#SPJ1

Answer:

A) g(x) has a greater absolute maximum.

Step-by-step explanation:

Given graph of g(x) which is a Parabola

1. Opens downwards

2. The absolute maximum (vertex) is at around (3.5, 6)

i.e. value of absolute maximum is 6.

Another function:

\(f(x) =-x^{2}+4x-5\)

Let us convert it to vertex form to find its vertex.

Taking - sign common:

\(f(x) =-(x^{2}-4x+5)\)

Now, let us try to make it a whole square,

Writing 5 as 4+1:

\(f(x) =-(x^{2}-4x+4+1)\\\Rightarrow f(x) =-((x^{2}-2 \times 2\times x+2^2)+1)\\\Rightarrow f(x) =-((x-2)^{2}+1)\\\Rightarrow f(x) =-(x-2)^{2}-1\)

Please refer to attached graph of f(x).

We know that, vertex form of a parabola is given as:

\(f (x) = a(x - h)^2 + k\)

Comparing the equations we get:

a = -1 (Negative value of a means the parabola opens downwards)

h = 2, k = -1

Vertex of f(x) is at (2, -1) i.e. value of absolute maximum is -1

and

Vertex of g(x) is at (3.5, 6)

i.e. value of absolute maximum is 6.

Hence, correct answer is:

A) g(x) has a greater absolute maximum.

Answer:

g(x) has a greater absolute maximum.

Answer:

Strong positive correlation

Step-by-step explanation:

The given scatterplot, where the data points are sloping upward:

The stronger the association of the two variables, the closer the Pearson correlation coefficient, r, will be to either +1 or -1 depending on whether the relationship is positive or negative, respectively.  

If the value of the correlation coefficient is 0 < r < 1 then there is a positive linear trend and the data points are scattered around the line of best fit; the smaller the absolute value of r, the less well the data can be visualized by a single linear relationship. The closer the value of r to 0 the greater the variation around the line of best fit.

In the attached screenshot, where I've drawn a line across the graph: it shows that the data points are clustered around the line. It is easier to estimate that the value of r is closer to 1, which implies a strong positive relationship between two variables. My estimate is that r = 0.8.

Therefore, the correct answer is Strong Positive association.

Please mark my answers as the Brainliest, if you find this helpful :)

Answer:

23 cubic units

Step-by-step explanation:

1st layer: 8 units
2nd layer: 7 units
3rd layer: 5 units
4th layer: 3 units

8+7+5+3 = 23
See the attachments below

Hope this helps :)

Answer:B

Step-by-step explanation:

So an irrational number is a decimal that repeats the same number or numbers  over and over again so it would be B.

The given equation have only one solution, x = 1.75

Given,

The equation; 5x + 3x - 4 = 10

We have to find the number of solutions for this equation;

Solve the equation first;

That is,

5x + 3x - 4 = 10

8x - 4 = 10

Add 4 to both sides

8x - 4 + 4 = 10 + 4

We get,

8x = 14

Now divide with 8 on both sides

8x/8 = 14/8

We get,

x = 1.75

That is,

The equation 5x + 3x - 4 = 10 has only one solution.

Learn more about number of solutions here;

https://brainly.com/question/12734349

#SPJ1

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

For more questions on Law of Cosines, click on:

https://brainly.com/question/30766161

#SPJ8

The figure for the given question is provided here :

Answer:

angle 1 is 105degrees and angle 2 is 75degrees

Step-by-step explanation:

The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.

Answer:

look below

Step-by-step explanation:

(7.25 * 2) + 5.50 + (3 * 1.80) + 4.85

Lets combine

(7.25 * 2) + (3 * 1.8) + 10.35

7.25 * 2 is 14.50

3 * 1.8 is 5.4

14.50 + 5.4 + 10.35

is $30.25 before tip

(Tip should be 6.05 minimum, 20% of 30.25 is 6.05)

Answer:

3-4i

Step-by-step explanation:

Answer:

56/48

Step-by-step explanation:

Multiply both sides by 8.

Answer:

56/48

Step-by-step explanation:

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.

In this case you have a clue which is 48, correct?

Okay well 6 times 8 = 48

Then you would want to take the 8 and times it by the numerator which is 7

So 7 times 8 = 56

Hope this helpsss

Answer:I only see one graph my guy but that is leaner

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

x/3x-1 divided by x-2/2x

= x/3x-1 * 2x/x-2

= 2x^2/(3x-1)(x-2).

If we expand the denominator it is

2x^2/(3x^2-7x+2).

Answer:

the probability is 0.0067

Step-by-step explanation:

The computation of the probability of receiving no e-mails during an hour is shown below;

Let us assume x be the number of emails received during an hour

Now the probability of receiving no e-mails is

= e^-5 × 5^0÷ 0!

= e^-5 × 1  ÷ 1

= e^-5

= 0.00674

= 0.0067

Hence, the probability is 0.0067

Answer:

8

Step-by-step explanation:

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

Read more about exponential function at

brainly.com/question/2456547

#SPJ1

Answer:

3.34, 3 1/3 300%

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

Learn more about Pythagorean formula here:

https://brainly.com/question/28981380

#SPJ1