Four cookies cost $7.00. At this rate, how much will 9 cookies cost?

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

Learn more on quadratic equations ; https://brainly.com/question/30164833

#SPJ1

Answer:

They should not be exactly the same but they should be close.

Step-by-step explanation:

The first thing that we must take into account is the following:

Experimental probability is the result of an experiment, and theoretical probability is based on the mathematical model developed in probability theory. With the above, we can affirm that the precision of the results of the experiments depends directly on the sample size of the experiment and the precision is greater when the sample size is greater.

This means that the odds are most likely not the same, they must be very close since it has been repeated a considerable number of times and the more times it is done the closer they will be to being the same.

Answer:

a_n = 47 - 8n

Step-by-step explanation:

a_1 = 39

a_2 = 31

a_3 = 23

31 - 39 = -8

23 - 31 = -8

This is an arithmetic sequence with constant difference -8.

a_1 = 39

a_2 = 39 - 8

a_3 = 39 - 8 - 8 = 39 - 2(8)

a_4 = 39 - 8 - 8 - 8 = 39 - 3(8)

...

a_n = 39 - (n - 1)(8)

a_n = 39 - 8(n - 1)

a_n = 39 - 8n + 8

a_n = 47 - 8n

Answer:

\(a_n=47-8n\)

Step-by-step explanation:

Given sequence:

Calculate the differences between the terms:

\(39 \underset{-8}{\longrightarrow} 31 \underset{-8}{\longrightarrow} 23\)

As the differences are constant (the same), this is an arithmetic sequence with:

\(\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\end{minipage}}\)

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

\(\implies a_n=39+(n-1)(-8)\)

\(\implies a_n=39-8n+8\)

\(\implies a_n=47-8n\)

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

For similar questions on area of the circle

https://brainly.com/question/12269818

#SPJ8

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

Learn more about volume at:
#SPJ1

The regression equation is y = 14.57 + 2.22x₁ + 1.73x₂    and   The estimated regression coefficients indicate that the cost of shipping a package is affected by the type of cargo, with an average base cost of $14.57. Fragile shipments cost an additional $2.22 per package, while semi fragile shipments cost an additional $1.73 per package. Durable shipments are the least expensive, with no additional cost.  

We can use the least squares method to estimate the regression equation. The equation is in the form of y = a + b₁x₁ + b₂x₂, where a is the intercept, b₁ is the coefficient for the fragile cargo type, and b₂ is the coefficient for the semi fragile cargo type. We can calculate the coefficients by first calculating the sum of squares of x₁ and x₂, which is 4. The coefficient for x1 (b1) can be calculated by:

 b1 = (∑xy1 - (∑ x₁∑y/n))/(∑ x₁₂ - (∑ x₁²/n))

= (76.62 - (20*94.07/15))/(17 - (20^2/15))  

= (76.62 - 63.47)/(17 - 400/15)  = 13.15/ (-383.33/15)  = -2.22  

The coefficient for x2 (b2) can be calculated by:  

b2 = (∑xy₂ - (∑x₂∑y/n))/(∑x₂₂ - (∑x₂²/n))

 = (71.59 - (11*94.07/15))/(14 - (11^2/15))  

= (71.59 - 40.47)/(14 - 121/15)  = 31.12/ (-107.33/15)  = 1.73

The intercept (a) can be calculated by:

  a = (∑y/n) - (b₁(∑x₁/n)) - (b₂(∑x₂/n))

    = (94.07/15) - (-2.22(20/15)) - (1.73(11/15))  = 14.57

To know more about  regression coefficient refer to the link brainly.com/question/14313391

#SPJ4

Answer:

Step-by-step explanation:

1) angle 5 and 8

2) perimeter = 20 + 48 +52 = 120 m

3) area = 1/2 * 20 * 48 = 480 m^2

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

For more such information on: rates

https://brainly.com/question/25720319

#SPJ8

Answer: 102 dollars/4.5x+75

Step-by-step explanation: Your question isn't really straightforward, x x snacks for everybody to share? Please elaborate, and are they talking about the total cost, or just the cost of 6 snacks?

First, we have to take into account that if SADIE is taking her FOUR kids, there will be 5 people.

Cost of tickets is equal to $15 per one, and

5x (where x=15, per 5)

5(15)=75, and now onto the snacks

4.5x2=9, and 6/2=3, so 9x3=27, or 4.5x6=27

75+27=102

then for x snacks, if 1 snack costs 4.5 dollars than it'd be 4.5x (x number of snacks)+75 to find the total cost with tickets and all.

Answer:

0.675

Step-by-step explanation:

Option-C is correct, The product of the numbers 4.5 x 10⁵ and 2.4 x 10² is 108000000.

Given that,

The numbers are 4.5 x 10⁵ and 2.4 x 10²

The product of the numbers must be determined.

Multiplication is a representation of the underlying idea of adding the same number repeatedly. The product of two or more numbers is the result of the multiplication of the factors, which are the amounts being multiplied. It is easier to continually add the same number after the numbers have been multiplied.

Take the numbers,

4.5 x 10⁵ and 2.4 x 10²

=4.5 x 10⁵ × 2.4 x 10²

=108000000

Therefore, Option-C is correct, The product of the numbers 4.5 x 10⁵ and 2.4 x 10² is 108000000.

To learn more about product visit: https://brainly.com/question/22852400

#SPJ9

The product of the numbers 4.5 x 10⁵ and 2.4 x 10² is 108000000. Option-C is correct.

Given that,

The numbers are 4.5 x 10⁵ and 2.4 x 10²

The product of the numbers must be determined.

Multiplication is a representation of the underlying idea of adding the same number repeatedly. The product of two or more numbers is the result of the multiplication of the factors, which are the amounts being multiplied. It is easier to continually add the same number after the numbers have been multiplied.

From the numbers,

=4.5 x 10⁵ × 2.4 x 10²

=108000000

Therefore, The product of the numbers 4.5 x 10⁵ and 2.4 x 10² is 108000000. Option-C is correct,

To learn more about number visit: https://brainly.com/question/17429689

#SPJ9

Answer:

\(y-9=-\dfrac{8}{3}(x-7)\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}\)

Define the given points:

Substitute the defined points into the slope formula:

\(\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}\)

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Substitute the found slope and one of the points into the point-slope formula:

\(\implies y-9=-\dfrac{8}{3}(x-7)\)

Answer:

C

Step-by-step explanation:

The slope of a horizontal line, such as that of y= 3, is equal to 0.

This can be proved using the slope formula.

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

Let's choose 2 points on the line y= 3:

(0, 3) and (2, 3)

Slope

\( = \frac{3 - 3}{2 - 0} \)

\( = \frac{0}{2} \)

= 0

Thus, the line has a slope of zero.

On the other hand, vertical lines have an undefined slope.

Additional:

To learn more about horizontal lines and their slopes, do check out the following!

The diagram in the question is an example of two intersecting chords. The length of the unknown portion can be gotten by applying the intersecting chord theorem.

The Intersecting Chord Theorem states that the products of the lengths of the line segments on each chord are equal.

Following this theorem, we have that

Solving, we can get the value of x to be

The correct option is the SECOND OPTION (3).

Answer:

Answer:

2/3

Step-by-step explanation:

Given:

Number of eclairs = 3

Number of humbugs =2x+6=2(x+3)  

Number of mints =  x

Therefore, total number of sweets in the jar is,

s=3+2x+6+x=3x+9=3(x+3)

Now, probability of selecting a sweet to be humbug is given as:

 p(humbug)= number of humbugs/number of sweets

p(humbug)=2(x+3)/3(x+3)=2/3

Therefore, the probability that it is a humbug is 2/3

Step-by-step explanation:

Both E and F are sets.

E = {w | w ≤ 2}

means that E is the set of all numbers w satisfying the condition that w ≤ 2. In other words, E contains all real numbers less than and including 2.

Similarly,

F = {w | w > 9}

is the set of all real numbers strictly greater than 9.

The intersection of E and F, denoted E ∩ F, is the set that contains the overlap of the two sets, or all the numbers that are common to both sets. In this case, E ∩ F is the empty set; this is because all numbers small than 2 cannot be larger than 9, so E ∩ F = ∅.

The union of E and F, written as E ∪ F, is the set containing all elements from both sets. In interval notation, E = (-∞, 2] and F = (9, ∞), so E ∪ F = (-∞, 2] ∪ (9, ∞).

The unknown number will be 75.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given that the product of two numbers is 50. If one of the numbers is 2/3.

Let the other number be ‘y’. The number will be calculated as below:-

‘y’ x ( 2/3 )= 50

Divide both sides by 2/3 to make y the subject and you would end up with the equation

y= 50 / 2/3

Solve the above expression for the value of y.

y= 50 / 2/3

y=75

Therefore, the unknown number will be 75.

To know more about multiplication follow

brainly.com/question/10873737

#SPJ2

This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can be simplified, evaluated, or manipulated using algebraic rules and properties.

Let x be the number of miles Mr. Smith drove. Then, the number of miles Mr. Stein drove is \(140 - x\)  , since they drove a total of 140 miles and Mr. Smith already drove x miles.

the algebraic expression for how many miles Mr. Stein drove is:

\(140 - x\)

Therefore, This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

Learn more about expression here:

brainly.com/question/14083225

#SPJ1

Answer:

The best buy is the 16-ounce drink

Step-by-step explanation:

here, we see that,

12 ounce = 3/4 (16 ounce)

So, the price should reflect that,

i.e,

price of 12 ounce drink = 3/4 (price of 16 ounce drink)

By this metric,

Price of 12 ounce drink = 3/4 ( 1.19)

Price of 12 ounce drink = $0.8925

So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,

So, it is more expensive than it should be,

So, the best buy is the 16-ounce drink

Answer:

B) y - 2 = (-1/4)(x - 2)

Step-by-step explanation:

Start with the equation of the given line: y = 4x + 7.

Determine the slope of the given line, which is 4.

Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.

Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).

Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.

Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.

Simplify further: y = (-1/4)x + 5/2.

The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.

Answer:

4 + ( -7 X 2 ) = -10

Step-by-step explanation:

Check work:

-7 times 2 is -14.

4 + -14 = -10

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Answer:

140

Step-by-step explanation:

P = 2(L + w) = 2 x (54 + 16) = 140

Hope this helps :D

Answer:

x = 11/4 or 2.75

Step-by-step explanation:

Perimeter: 43

Perimeter: L + L + W + W

L = 4x + 3

W = 2x + 2

(4x + 3) + (4x + 3) + (2x + 2) + (2x + 2) = 43

4x + 4x + 2x + 2x + 3 + 3 + 2 + 2 = 43

8x + 4x + 6 + 4 = 43

12x + 10 = 43

12x = 43 - 10

12x = 33

12x/12 = 33/12

x = 33/12

Answer:

x = 2

Step-by-step explanation:

1. The perimeter is the distance around a 2D shape, meaning to find the perimeter we have to add: 2x + 2 + 2x + 2 + 4x + 3 + 4x + 3. Or, we could write it as 2(2x+2) + 2(4x+3).

2. Since we're already given the perimeter, 34, we can set up an equation of: \(2(2x+2) + 2(4x+3) = 34\)

3. (Solving)

Step 1: Simplify both sides of the equation.

Step 2: Subtract 10 from both sides.

Step 3: Divide both sides by 12.

4. To check if our answer correct, let's plug in the value of x into our equation!

Therefore, x = 2! I hope this helped you.

The numbers in table are in proportion. Therefore, option B is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Here,

From the table A:

1/5 = 3/15 = 5/20 = 7/28

1/5 = 1/5 ≠ 1/4 = 1/4

Here, numbers are not in proportion.

From the table B:

3/9 = 5/15 = 7/21 = 8/24

1/3 = 1/3 = 1/3 = 1/3

The numbers are in proportion.

From the table C:

4/12 = 6/18 = 7/28 = 9/36

1/3 = 1/3 ≠ 1/4 ≠ 1/4

The numbers are not in proportion.

From the table D:

2/8 = 3/12 = 4/16 = 5/30

1/4 = 1/4 = 1/4 ≠ 1/6

The numbers are not in proportion.

Therefore, option B is the correct answer.

To learn more about the proportional relationship visit:

brainly.com/question/12917806.

#SPJ1

Answer:

first find the value of 3 squared.

3 x 3

now multiply.

It would be 9.

Now multiply by 2.

2 x 9 = 18

Finally, subtract.

18 - 8 = 10

▬▬▬▬▬▬▬▬

Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)