Konrad buys a skateboard that costs c dollars. After 7.5% sales tax is added, the total cost can be expressed by the expression c+0.075c . What is this expression written in simplest form?

Answer: the rectangle is 23 x 41

Step-by-step explanation:

x = length

2x - 5 =  width

A = length x width = (x)(2x-5) = 943

2[tex]x^{2}[/tex] - 5x - 943 = 0

use quadratic equation to solve for x:

a = 2, b = -5, c = -943

roots are 23, -20.5

x = 23 (length)

2x - 5 = 2(23) - 5 = 46 - 5 = 41 (width)

Perpendicular bisector passes through midpoint of the line joining the given two points so the equation for this perpendicular bisector of the line segment whose endpoint are (7,-1) and (-9,-5) is 4x-y=29.

To divide a segment or an angle into two congruent sections is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.

A straight line called a bisector divides an angle or a line into two equal pieces. The bisector of a segment always travels through the middle of the segment.

For this problem you have to find the mid point of the line joining

the given points and also the slope of the perpendicular line.

Here, A(7,-1) and B(-9,-5) are the given two points.

let

C is the mid point and CD is the perpendicular through C

Midpoint of AB=[x1+x2)/2,(y1+y2)/2]

C=((7-9)/2,(-1-5)/2)

C=(-1,-3)

Slope of AB=(y2−y1)/(x2−x1)

=(-5+1)/(-9-7)

=4/16

=1/4

Slope of CD=4

Equation of line;

(y−y1)=m(x−x1)

(y+1)=4(x−7)

Y+1=4x-28

4x-y=29

this is our required solution.

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The inequality shown by the graph in the question, found by finding the equation for the line of the inequality and taking note of the dashed line and the shaded region, is; y > 2·x - 4

An equality is a comparison between two expressions that have different values,  by joining them with the use of symbols including '<', '≤', '≥', '>', '≠'

Two points on the graph that can be used to find the equation of the line of the inequality are;

The slope, m, of the line found from the above two  points on the  line is therefore;

m = (0 - 4)/(2 - 4) = 2

The equation of the line in point-slope form is therefore;

y -  0 = 2·(x - 2) = 2·x - 4

The  equation of the line of the inequality is therefore;

y = 2·x - 4

The dashed line and the shaded region indicates that we get;

y > 2·x - 4

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The required solution of the given expression is 1/3 [m²-2m-6].

Given that,
To simplify the [2m⁵ -5m₄ +2m² -8m²]/[m²+1], when  m² + 1 = 3m.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= [2m⁵ -5m₄ +2m² -8m²]/[m²+1]
When substituting the value m² + 1 = 3m in the above expression we get.
= m/3 [m²-2m-6]

Thus, the required solution of the given expression is 1/3 [m²-2m-6].

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The polynomial x³ - 2x² - 13x - 10 divided by x + 2 will have quotient of x² - 4x - 5x and a remainder of zero.

The polynomial x³ - 2x² - 13x - 10 divided by x + 2 as follows;

We divide the first of the polynomial x³ by x to give x²

multiply x - 1 by x² to get x³ + 2x²,

then subtract x³ + 2x² from x³ - 2x² - 13x - 10 to get -4x² - 13x - 10

divide -4x² by x to get -4x

multiply x - 1 by -4x to get -4x² - 8x

then subtract -4x² - 8x from -4x² - 13x - 10 to get -5x - 10

divide -5x by x to get -5

multiply x - 1 by -5 to get -5x - 10,

then subtract -5x - 10 from -5x - 10 to get a remainder of zero.

Therefore, the division of the polynomial x³ - 2x² - 13x - 10 by x + 2 using long division give us the quotient x² - 4x - 5x and a remainder of zero.

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The amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups. So, option D is correct.

A mixed fraction is one that is represented by both its remainder and quotient. Two is the quotient and one is the remainder in the mixed fraction 2/3, for instance.

You can write mixed numbers with or without the word "and," for example, 5 and 3/4 . The mixed number must have a valid fraction as its fractional component. A correct fraction, such as 37, has a numerator that is less than the denominator.

Given,

The amount of orange juice= 3 [tex]\frac{1}{3}[/tex] cups

The amount of grape juice=6 [tex]\frac{1}{2}[/tex] cups

The amount of cherry juice= 4 [tex]\frac{1}{8}[/tex] cups

The amount of club soda=1 [tex]\frac{1}{4}[/tex] cups

So, 3 [tex]\frac{1}{3}[/tex]+6 [tex]\frac{1}{2}[/tex] + 4 [tex]\frac{1}{8}[/tex]

=(10/3)+(13/2)+(33/8)

=(10/3)+(13/2)+(33/8)

=(80+156+99)/24

=335/24

=13.95

≈14 cups approximately

Therefore, the amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups.

So, option D is correct.

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Answer:

48

Step-by-step explanation:

If the area of each square is 16, then each side length has side length of 4 because the area of a square is:

[tex]s^2=A[/tex]

[tex]s^2=16\\s=4[/tex]

Each of the outer edges has 4+4+4 and there are four of them so:

[tex](4+4+4)*4=48[/tex]

Answer:

∠BFC ≅ ∠DFE and DFC (BFC IS CONGRUENT TO DFE AND DFC)

Step-by-step explanation:

∠BFC and DFE are vertical angles which are equal ( OR CONGRUENT)

∠BFC and DFC are supplementry meaning the angles add upp to 180°. The square in ∠BFC shows that it is 90°. So then, angle DFC must be 90° because 180°-90° is 90°.

So ∠DFC and ∠DFE ≅ to ∠BFC

The area of the semicircle table after it is cut in half  [tex]=\frac{9}{2}\pi[/tex] square units.

A semicircle is a 2 -D shape which is obtained by cutting a circle along with its diameter. a circle has 2 semicircles when it is cut along with its diameter.

The formula for finding the area of a semicircle is half of the area of a circle with the same radius.

area of semicircle = [tex]\frac{\pi r^{2} }{2}[/tex] square units

Given:

A table with a round top is cut in half so now its shape is a semicircle.

After it is cut, the edge along the wall is 6 ft means that the diameter of the semicircle is = 6 ft

Diameter = 6 ft

Radius = diameter / 2

Radius = 6/ 2

Radius = 3 ft

Therefore now we can calculate the area of the table after it is cut in half

Area of the semicircle table after it is cut in half =

[tex]=\frac{\pi r^{2} }{2} \\=\frac{\pi 3^{2} }{2} \\=\frac{9\pi }{2}\\= \frac{9}{2}\pi[/tex]

The area of the semicircle table after it is cut in half  [tex]=\frac{9}{2}\pi[/tex] square units.

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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 feet. What is the area of the table after it is cut in half? Give your answer in terms of pi.

If the parlor sold 389389 tattoos and 4343 were arm tattoos, then the probability of next customer does not get an arm tattoos is 0.99

Total number of tattoos sold in this month = 389389 tattoos

Number of arm tattoos = 4343

Number of other tattoos = 389389 - 4343

= 385046

The probability = Number of favorable outcomes / Total number of outcomes

Substitute the values in the equation

The probability of next customer does not get an arm tattoos = 385046 / 389389

Divide the terms

= 0.99

Therefore, the probability of next customer does not get an arm tattoos is 0.99

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The total distance travelled by the particle is 24 units.

What is displacement?

Displacement is defined as a change in an object's position. An object's displacement is defined as how far it has moved from its starting point. The dependent variable in the displacement time graph is displacement, which is represented on the y-axis, and the independent variable is time, which is represented on the x-axis. Position-time graphs are another name for displacement time graphs.

The displacement curve is given for 0 ≤ t ≤ 18.

We need to find the total distance of the curve, it will be the positive sum of all displacements.

So, total distance = (7-0) + (3-0) + (2+3) + (2+4) + (7-4)

                             = 7 + 3 + 5 + 6 + 3

                             = 24

Hence, the total distance is 24 units.

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Answer:

The slope is -6

Step-by-step explanation:

12x+2y=24

We want to find the slope of a line that is parallel to this line.

Parallel lines have the same slope, so we need to find the slope of this line.

We can get this equation in slope intercept form to find the slope

y = mx+b  where m is the slope

Subtract 12x from each side

2y = -12x+24

Divide each side by 2

y = -12x/2 +24/2

y = -6x+12

The slope is -6

The required equation of line is  y = -5x + 2.

The equation of a line in slop intercept form is an equation of the form

y = mx + c . Where m is the slope of the line and c is the intercept of the line on the Y-axis.

Given,

Line passes through (0,2)

Therefore, (2) = m(0) + c

  or               2 = c

Also, the line passes through (1,-3)

Therefore, (-3) = m(1) + 2

or                  m = -3 - 2

                    m = -5

Hence, the required line is y = -5x + 2.

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Answer:

Option (A) and (B)

Step-by-step explanation:

The area under the standard Normal curve corresponding to –0.3 < Z < 1.6 is answer choices 0.3273, and 0.4713.

Area = 0.3273. Ergo, the answer is A.

Step-by-step explanation:

0.9953/2 - 0.3085/2

Answer: No, the ratio between AD and DE is 3:1.

Step-by-step explanation:

The centroid splits the median in a 2:1 ratio from vertex to side.

Answer:

It is letter D; No, the ratio between AD and DE is 3:1.

Step-by-step explanation:

Answer:

I believe the answer is D. 3/8

The rate of change of y with respect to x will be;

⇒ 10

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The table is shown in figure.

Now,

Since, The table is shown in figure.

Let two points from the table as;

(x, y) = (- 8.5 , - 92)  (- 6.5, - 72)

We know that;

⇒ Rate of change = dy/dx = (y₂ - y₁) / (x₂ - x₁)

Substitute all the values we get;

⇒ Rate of change = (- 72 - (-92)) / (- 6.5 - (-8.5))

                            = 20 / 2

                            = 10

Thus, The rate of change of y with respect to x will be;

⇒ 10

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The profit won by Hahid is 28 rupees

Profit is the term used to describe the financial gain experienced when the revenue from a business activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.

There are three main measures of profit. These are gross profit, operating profit and net profit.

According to given question:-

The total amount with which Hahid bought the bananas are

(5/4)*80=100

The total amount with which Hahid sold the bananas are

(8/5)*80=128

The profit got by Hahid is 128-100=28

Hence the solution is 28

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Step-by-step explanation:

Tha answer in standard form is x + 4y = -1

The required bearing angle of town B from Thomas is 65°.

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 125° clockwise, then he faces towards town B,

The bearing angle will be 300+125 = 425°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 425 - 360 = 65

The bearing angle of town B from Thomas is 65°.

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Applying the corresponding angles theorem, the measure of angle 3 is: C. 121°.

Using the figure below that shows that line a is parallel to line b, where angle 1 and angle 2 are corresponding angles, based on the corresponding angles theorem, the measure of angle 1 is equal or congruent to angle 2.

Given the following:

Measure of angle 1 = 9x - 4

Measure of angle 2 = 13x - 32

m<1 = m<2 [corresponding angles theorem]

Substitute

9x - 4 = 13x - 32

Solve for the value of x

9x - 13x = 4 - 32

-4x = -28

x = 7

Measure of angle 3 = 180 - (13x - 32)

Plug in the value of x

Measure of angle 3 = 180 - (13(7) - 32)

m<3 = 121°

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The interest charged for 3 years would be $75 ($500 x 0.05 x 3). The total amount Ariane has to pay back would be $575 ($500 + $75).

Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

To calculate simple interest, multiply the principal sum by the time period, interest rate, and time period. Simple interest is calculated as follows: "Simple Interest = Principal x Interest Rate x Time." This equation provides the simplest method for calculating interest.

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The function y=540(1.04)^x represents exponential growth. The rate of increase can be determined by finding the value of 1.04^x.

For example, if x=1, then the value of 1.04^1 is 1.04, which represents a 4% increase. If x=2, then the value of 1.04^2 is 1.0816, which represents an 8.16% increase. If x=3, then the value of 1.04^3 is 1.1265, which represents a 12.65% increase.

In general, as the value of x increases, the value of 1.04^x increases at a faster rate, resulting in an exponential growth curve. The percentage rate of increase is determined by the value of 1.04. In this case, the percentage rate of increase is 4% per unit increase in x.

Equation in slope intercept form and in standard form for (-2,6) and parallel to x3y=5 will be x + 3y = 10

Given equation =>  x + 3y = 5

3y = -x + 5 so, we have to write it in the equation form,

y = -(1/3)x + 5/3

slope = -1/3     Parallel lines have the same slope.

Now, you have a point and a slope, so use the Point-Slope form of the equation of a line.

y - y1 = m(x - x1) , by using the equation of line

y - 6 = (-1/3)(x - 2), then we get

y - 4 = (-1/3)x + 2/3

y = (-1/3)x + 3 1/3   Slope-intercept Form

(1/3)x + y = 10/3     Multiply both sides by 3.

x + 3y = 10    Standard form

So, the equation is x + 3y = 10

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Answer:

2

Step-by-step explanation:

log_4 (16) is a tiny math problem. It is asking 4^? = 16

See, a log is an exponent. So what power of 4 makes 16? Well, 4^2 = 16. So that means that the log_4(16) = 2

the Pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams: True.

A measure of the degree and direction of relationship between two variables assessed on at least an interval scale is the Pearson product-moment correlation coefficient, or Pearson's correlation.

If you want to determine whether there is a linear relationship between two quantitative variables, you may use Pearson's correlation. The expectation of a linear relationship between those variables is the sole part of the study hypothesis.

This approach finds the precise amount or degree of correlation between any two variables and tells if there is or is not any correlation between them.

Thus, the given statement is true.

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The probability that the student answers exactly 1 question is 0.166.

What is the binomial coefficient?

In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.

There are [tex]3^5 = 243[/tex] possible ways that the student can answer the quiz.

To answer exactly 1 question correctly, the student must answer 4 questions incorrectly and 1 question correctly. There are 5 ways to choose which question the student gets correct, and for each of these ways, there are [tex]3^4 = 81[/tex] ways for the student to answer the remaining questions. Therefore, there are a total of 5*81 = 405 ways for the student to answer exactly 1 question correctly.

Thus, the probability that the student answers exactly 1 question correctly is 405/243 = approximately 0.166.

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Therefore ,A pink gold bracelet weight 60 g has 45.6g of gold .

A fraction of 100 is a percentage, also known as percent. Percentage, which is defined as "per 100," represents a fraction of a total sum. 45 out of 100 is what is meant by 45%, for instance. The share of a whole expressed in terms of 100 is discovered when a percentage is calculated. Calculators online or on paper can be used to determine it.

In addition to "out of 100" and "for every 100," the word "percentage" can also be used. You could, for instance, say "it snowed 20% of the time" or "it snowed 20 days out of every 100 days."

Here,

We know that,

A pink gold bracelet weight 60 g has 76% gold, 18% copper and 6% aluminum.

Therefore,

In order to calculate the weight of gold

First we obtain its percentage in bracelet

It's percentage given in question is 76%

Thus,

mass of gold will be 76% of 60g which is 0.76 * 60=45.6g

Therefore ,In pink gold bracelet has a weight of 60 g has 45.6g of gold .

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The least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.

The smallest multiple that any two numbers have in common is called the lowest common multiple.

It implies that we can divide both numbers by that and that this is the lowest number by which both numbers may be divided.

The LCM of 2 and 8 is 8, for instance.

So, using the two fractions provided:

2/3 + 4/5

15 is the least frequent factor between 3:

(10 + 12)/15

Thus, we used LCM in the first phase.

Therefore, the least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.

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Complete question:
When adding 2/3 + 4/5, what step must be completed first?

A)Finding the least common denominator.

B)Reducing the fractions.

C)Adding the numerators, but keeping the denominators.

D)Adding the denominators, but keeping the numerators.

The equation of the line that passes through the points (2, 15) and (5, 21) is y = 2x + 11

The coordinates of the first point = (2, 15)

The coordinates of the second point = (5, 21)

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (21-15) / (5-2)

= 6 / 3

= 2

The slope intercept form is

y = mx + b

Substitute the values

15 = 2(2) + b

15 = 4 + b

b = 15 - 4

b = 11

Substitute the values in the equation

y = 2x + 11

Therefore, the equation of the line in slope intercept form is y = 2x + 11

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