Esther gave the storekeeper a twenty dollar bill for a purchase of $14.51. How
much change should she have received?

The equation of the scatter plot is (a) y = 100x + 2

The line of best fit of the scatter plot passes through the points

(x,y) = (0,2) and (1,102)

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{102 - 2}{1 - 0}[/tex]

m = 100

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 100(x -0) + 2

Evaluate

y = 100x + 2

Hence, the equation of the scatter plot is (a) y = 100x + 2

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Answer:

Here,

[tex](a + b) [(a + b)(a + b)][/tex]

[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]

[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]

[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]

[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]

Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]

Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.

Answer:

9 feet, 108 inches, 274.32 cm, 2.7432 meters

Step-by-step explanation:

Not enough information is given to answer.

You didn't provide the list of "these" to choose from, but I can just list some potential answers I could see being an option.

3 yards = 9 feet [1 yard = 3 feet. 3 yards = 9 feet]

             9 feet is also 108 inches [1 foot = 12 inches. 9 feet = 108 inches]

3 yards = 108 inches

{There are 91.44 cm in a yard} (1 yard = 91.44 cm. 3 yards = 274.32 cm),

3 yards = 274.32 cm

3 yards = 2.7432 meters (1 yard = 0.9144 meters; 3 yards = 2.7432 meters)

Answer:

Area of the circle = 227.0095 cm^2

Step-by-step explanation:

Given:

To Find:

Area of the circle

Soln:

We know that,

Area of the circle: πr²

where:

But we don't know the radius,as the diameter is given.We could use the formula of diameter & plug the value of it do find the radius.

[tex] \rm \: Diameter = 2(r)[/tex]

Where

Substitute the value of Diameter:

Diameter = 2r

17 = 2r

17/2 = r

8.5 = r

r = 8.5

Now we got the radius, so substitute radius onto the formulae:

[tex]\text{Area of circle} = \pi\cdot \text{Radius}^2\\\\\\~~~~~~~~~~~~~~~~~~=\pi~ \left( \dfrac{\text{Diameter}}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=3.142 \left(\dfrac{ 17}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=227.0095~ \text{cm}^2[/tex]

Answer:

yes

Step-by-step explanation:

yes, because there is a 99/1 chance. also, you can put 50 2010 coins in.

Given the radius of the regular hexagon, its area is approximately 42in².

Hence, option B) is the correct answer.

Given that;

Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.

Angle of one triangle in the regular hexagon = 360°/6 = 60°.

To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.

We find the perpendicular height using Pythagoras theorem

h = √( (4)² - (2)² )

h = √( 16 - 4 )

h = √( 12 )

h = √( 2² × 3 )

h = 2√3

Now, we determine the area of a single triangle.

Area = (1/2) × base × height

Area = 0.5 × 4 × 2√3

Area = (4√3)in²

Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6

Area of regular hexagon = 6 × (4√3)in²

Area of regular hexagon = 24(√3)in²

Area of regular hexagon = 41.57in² ≈ 42in²

Given the radius of the regular hexagon, its area is approximately 42in².

Hence, option B) is the correct answer.

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Answer: b

Step-by-step explanation:

Answer:

12 ft

Step-by-step explanation:

We assume right triangle ABC with the right angle being at B. We are given that the ratio of AB/CB = 8/7, and one leg is 10.5.  Let's call the other leg is X. We don't know which leg is which so assume both. Then

(a) assume the X leg is the longer

8 / 7 = X / 10.5

(8 * 10.5) / 7= X

X = 12

OR (b) assume the X leg is the shorter

8/7 = 10.5 / X

(8X / 7) = 10.5

8X = 10.5 * 7

8X =  73.5

X = 9.1875

(a) is the greater so (a) wins

The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].

A slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.

The slope of a line that passes through points ( p,q) and (x,y)

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

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Answer:

(5*10^3)*(9*10^7) = 4.5*10^11

(7*10^5) / (2*10^2) = 3.5*10^3

Step-by-step explanation:

calculate 5 multiply by 9

5*9=45

the multiple of the power in the same base of number is calculated by using addition(+)

(10^3)*(10^7) = 10^(3+7)

= 10^10

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

45*(10^10)

= (4.5*10^1) * (10^10)

= 4.5*10^(1+10)

= 4.5*10^11

calculate 7 divide by 2

7/2=3.5

the dividing of the power in the same base of number is calculated by using subtraction(-)

(10^5)/(10^2)

= 10^(5-2)

= 10^3

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

3.5*10^3

Answer:

Step-by-step explanation:

(5×10³)×(9×10⁷)

= 5×10³×9×10⁷

= 5×9×10³×10⁷      (commutative property)

= (5×9)×(10³×10⁷)  (associative property)

= 45 × 10³⁺⁷

= 45 × 10¹⁰.           (Exponent property)

= 4.5 × 10¹¹

…………………………………………

(7×10⁵) / (2×10²)

= (7/2) × (10⁵/10²)

= 3.5 × 10⁵⁻²

= 3.5 × 10³

Answer:

Circumference: 25.12m

Area: 50.24 [tex]m^{2}[/tex]

Step-by-step explanation:

Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius

C=3.14*2*4=3.14*8=25.12

Formula for area of a circle: A=[tex]\pi r^{2}[/tex]

A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24

The value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length which is 8 units.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

Here the diagram and some data are missing.

But using Pythagoras or trigonometric ratio we can find the length.

We have:

17sinA-15-0

sinA = 15/17

Using Pythagoras theorem:

Base length = √(17² - 15²) = 8 units

= tanA = 15/8

= 1 - cosA = 1 - 8/17 = 9/17

We can find the rest of the trigonometric ratio.

Thus, the value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length, which is 8 units.

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The graphed cosine function can either be:

cos(x + pi) or cos(x - pi).

We know that this function is a cosine function with a phase shift, so the general form is:

f(x) = cos(x + P).

Where P is the phase shift.

In the graph we can see that when x = 0, f(0) = -1

And we know that cos(pi) = -1 = cos(-pi)

Then we must have that:

f(0) = cos(P) = -1

By what we wrote above, we know that P can be either -pi or pi (because of the parity of the cosine). Let's say that P = pi, then the cosine function is:

f(x) = cos(x + pi).

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Answer:

the function is only increasing.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this question, we can use the formula [tex]S=\theta r[/tex], where [tex]S[/tex] is the arc length, [tex]\theta[/tex] is the central angle of the sector in radians, and [tex]r[/tex] is the radius.

In this situation, we know that [tex]S=55[/tex] and [tex]\theta=5[/tex]

This means that [tex]55=5r \longrightarrow \boxed{r=11}[/tex]

Answer:

Step-by-step explanation:

-5x+4y=-3

-6(-5x+4y)=-6×(-3)=18

Answer:

Mean = 3.125 ≈ 3.13

Step-by-step explanation:

Mean = Sum of numbers =  1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13

           Amount of number                     8                             8

Based on the calculations below, the weekly gross pay of John Pelson is $1,339.90.

Let G represents weekly gross pay. The gross pay can now be calculated as follows:

Net pay = G – FIT – SIT – CIT - Health insurance – Charity ……………….. (1)

Substitute all the relevant values into the equation (1) and solve as follows:

$972.11 = G – $185.00 – 0.05G – 0.02G – $64.00 – $25.00

$972.11 + $185.00 + $64.00 + $25.00 = G – 0.05G – 0.02G

$1,246.11 = (1 – 0.05 – 0.02)G

$1,246.11 = 0.93G

G = $1,246.11 / 0.93

G = $1,339.90

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Answer:

0.341

Step-by-step explanation:

Multiply the probabilities: 0.55 * 0.62 = 0.341

Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]

Step-by-step explanation:

Adjacent angles of a parallelogram are always supplementary.

Answer: 2

Step-by-step explanation:

     We will first pull the data values.

0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3

     Now, we will find the middle data value. This is the median.

0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3

/,  /,  /, /, /, 2,  /,  /,  /,  /,  /

     Our median is 2.

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Answer:

the class earned $722059884

Step-by-step explanation:

because each person sold 444 tickets and there was 232323 students

=232323×444

=103151412

because 103151412 tickets were sold and a ticket cost $7

=103151412×7

=722059884

Answer:

$12

Step-by-step explanation:

x+2y=82........(1)

3x+y=96.........(2)

y=96-3x...........(3)

x+2y=82

x+2(96-3x)=82

x+192-6x=82

-5x=82-192

-5x=-110

x=-110÷-5

x=22

y=96-3x

y=96-3(22)

y=96-66

y=30

Therefore,x=22 and Y=30

so silver= x =22

gold= y = 30

y=30;x=22

=30-22

-12

Therefore $12

well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]

Answer:

Zoe's number is 6

Step-by-step explanation:

Let the number be 'n'

a) Multiply 'n' by 3 ⇒ n*3 = 3n

  Add 4 to '3n' ⇒ 3n + 4

Add 5 to 'n' ⇒  n +5

Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10

    3n + 4 = 2n + 10

b) 3n + 4 = 2n + 10

Subtract 4 form both sides

       3n = 2n + 10 - 4

       3n = 2n + 6

Subtract 2n from both sides

    3n - 2n = 6

          [tex]\sf \boxed{\bf n = 6}[/tex]

Answer:

21 is probably the best answer

Finding the correlation coefficient, it is found that the regression line shows a:

negative trend line with a strong relationship.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.

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Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,

The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.

Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.

It is an index that measures the correlation between two variables, assuming values between -1 and 1.

If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.

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Answer:

=> Apply law of cosine

[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]

=> input value

[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]

=> simplify

[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]

=> calulcation

[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]

=> apply rule: Distance must be greater than 0

which is about 14.51828

Answer:

the answer is D

hope it will help

Answer:

x = 3

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve for x.

The value of x is 3.

We can plug it back in to check if it works.

Correct!

Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

9 - 2(x - 5) = x + 10

Distribute

9 - 2x + 10 = x + 10

Subtract 10 to both sides

9 - 2x = x

Add 2x to both sides

9 = x + 2x

9 = 3x

Divide 3 to both sides

9/3 = 3x/3

3 = x

OR

[tex]\rule[225]{225}{2}[/tex]

Answer:

-12

Step-by-step explanation:

What you have to do is plug -4  into the function as a puzzle. So, replace all x with -4.

f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12

f (-4) = 7x ( 1-4 ) - 4 (-4)

       = -28 + 16

      = -12

An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.

A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.

Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

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