frank bought am math pencil, he used 28% percent off with a QR code, he paid 108$ how much did he save

The slope-intercept definition of the linear function is given as follows:

y = 2x/3 - 5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The line is parallel to:

2x - 3y = 8

3y = 2x + 8

y = 2x/3 + 8/3.

When two lines are parallel, they have the same slope, hence:

y = 2x/3 + b.

When x = 6, y = -1, hence the intercept b is given as follows:

-1 = 2 x 6/3 + b

-1 = 4 + b

b = -5.

Hence the function is:

y = 2x/3 - 5.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The maximum volume of cylinder is 39808.9

Let us consider that, radius of cylinder is r and height is h .

Volume of cylinder is,

V = πr²h

Since, the sum of its height and its circumference is 150 cm.

So,    

h + 2πr = 150

h = 150 - 2πr

Substituting value of h in volume equation of cylinder.

V = πr²(150 - 2πr)      

V = 150πr² - 2π²r³

For maximum volume, differentiate above expression with respect to r and equate with zero.

dv/dr = 300πr - 6π²r²

300πr - 6π²r² = 0

6πr(50 - πr) = 0

6πr = 0

r = 0

50 - πr = 0

r = 50/π  

So, radius of cylinder is,  50/π  

Now,  

h = 150 - 2πr

h = 150 - 2π(50/π)

h = 50

Substituting value of r and h in volume formula of cylinder.

V =  πr²h

V = 3.14(50/3.14)(50/3.14)50

V = 39808.9

Thus, the maximum volume of cylinder is 39808.9

Learn more about volume here

brainly.com/question/6204273

#SPJ4

Answer:

Is there multiple choice or just calculations?

Step-by-step explanation:

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

Learn more about harvest here:

brainly.com/question/16953777

#SPJ11

According to graphical and analytical methods, the value of the input variable associated with point of intersection between f(x) and g(x) is 1.5. (Correct choice: C)

Linear functions are polynomials with a grade of 1 and described by the following form:

y = m · x + b     (1)

Where:

Please notice that horizontal lines have a slope of 0.

There are two forms to estimate the coordinates of the point of intersection of the two functions: (i) graphical, (ii) analytical. According to the first method, the value of the input variable is approximately 1.5.

And according to the second method, we have the functions f(x) = 1 and g(x) = (4/3) · x - 1. Then, we must solve the following formula to determine the input variable of the point of interception:

1 = (4/3) · x - 1

(1/3) · x = 1/2

x = 3/2

x = 1.5

The value of the input variable is approximately 1.5.

According to graphical and analytical methods, the value of the input variable associated with point of intersection between f(x) and g(x) is 1.5. (Correct choice: C)

To learn more on systems of linear equations: https://brainly.com/question/27664510

#SPJ1

Answer: so the total of her percentage will be $28.21

Step-by-step explanation:you have to go like

120.54%

55.99

65.00

1,050,00

and you will find your answer.

The equation to find dimensions of the actualfield is y= 5/2x.

We have,

2 inch = 5 feet

So, the equation can be

y= 5/2 x

Now, width = 10 inch

So, y= 5/2(10)

y= 25 feet

and, length = 20 inch

So, y= 5/2(20)

y= 50 feet

So, the Area of field is

= 10 x 20

= 20 inch²

Learn more about Scale factor here:

https://brainly.com/question/30215119

#SPJ1

The classification of the type of angles are:

Alternate interior angles: ∠4 and ∠2, ∠3 and ∠1

Angles opposite by the vertex: ∠a and ∠4, ∠d and ∠2

Corresponding angles: ∠c and ∠1, ∠d and ∠4, ∠3 and ∠b, ∠2 and ∠a

Adjacent or linear pair: ∠b and ∠a, ∠c and ∠d, ∠3 and ∠2, ∠4 and ∠1

1) The alternating angles are on opposite sides of the horizontal line. Alternating interior angles are alternating angles between two lines intersecting a transverse line. Alternating exterior angles are the exterior alternating angles of two lines intersecting a horizontal line.

2) There are no corresponding interior or exterior angles because the corresponding corners are in the same relative position at the point of intersection. If the traverse crosses two parallel lines, the corresponding angles are congruent.

3) If the traverse crosses two parallel lines, the corresponding interior angles are congruent. In this case there are two identical intersections.

4) Angles opposite by the vertex are called vertically opposite angles.

5) Pair of adjacent angles whose measures add up to form a straight angle is known as a linear pair. They sum up to 180 degrees.

Thus:

∠4 and ∠2 are alternate interior angles

∠3 and ∠1 are alternate interior angles

∠b and ∠a are adjacent or linear pairs

∠c and ∠d are adjacent or linear pairs

∠3 and ∠2 are adjacent or linear pairs

∠4 and ∠1 are adjacent or linear pairs

∠c and ∠1 are corresponding angles

∠d and ∠4 are corresponding angles

∠3 and ∠b are corresponding angles

∠2 and ∠a are corresponding angles

∠a and ∠4 are vertically opposite angles

∠d and ∠2 are vertically opposite angles

Read more about Types of angles at: https://brainly.com/question/28293784

#SPJ1

Answer: 88 1/2

Step-by-step explanation:

easy

Answer:

89

Step-by-step explanation:

We have to find the marginal cost of the function:

for the value t=6. We remember that the marginal cost is defined as the derivative of the function of total cost. So, for finding the value of marginal cost, we will find its function:

Then, using the properties of differentiation,

And then, for finding the last derivative, we use the chain rule:

This means that our marginal cost function is:

Finding the value when t=6

We just have to find the value M(6), by replacing t by 6, as shown:

This means that the marginal cost when t=6 is 0.07 million dollars per year.

Answer:

a. 90

b. 40

c. 55

d. 6

e. 72

Step-by-step explanation:

a: This is a rectangle so all the full corners are 90 degrees. ABC is a corner angle.

b: 1 and 3 are the congruent angles so 3 has the same measure as 1.

C: 1 is a part of the corner, which adds up to 90 degrees. That means angle 2 and angle 1 should add up to 90. They say m<1= 35, so 90-35=55.

d. In a rectangle, the interesecting lines have the same length. AC is 12, so then DB is 12. However, DE is halfway. Half of 12=6.

e. This one has a few steps. Angle 1 is 36, and angle 2 is the other part to the 90 degree corner. 90-36= 54. That gives us angle 2. We know all angles in a triangle add up to 180 degrees. The angle across from angle 2 in the same triangle is the same value, so that is also 54. To find angle 5, it must add up to 180 degrees. 54+54+x=180, in other words. 54+54=108. 180-108=72.

Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

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

The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:

n = 100, p = 0.5.

The mean and the standard deviation are given by:

Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:

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

Z = (59.5 - 50)/5

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

More can be learned about the normal distribution at https://brainly.com/question/24537145

#SPJ1

Radicals expression with variables and exponents can be simplify by:

To help us understand each step better, we will take an example of a radical expression with variables and exponents of: \(\sqrt{16a^{3}b^6c^5 }\)

First, we need to separate the number and variables:

\(\sqrt{16a^3b^6c^5}=\sqrt{16} \sqrt{a^3b^6c^5}\)

Next, we will try to find variables with even exponents:

\(\sqrt{16} \sqrt{a^3b^6c^5} = \sqrt{16} \sqrt{a.a^2.b^6.c^4.c^}\)

Remember that:

(xᵃ)ᵇ = xᵃᵇ; then:

\(\sqrt{16}\sqrt{a.a^2.b^6.c^4.c} =\sqrt{16}\sqrt{a.a^2.(b^3)^2.(c^2)^2.c}\)

We try to breakdown any number into any factor that are perfect square:

\(\sqrt{16}\sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will rewrite both number and the variables into a square exponents:

\(\sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will separate the squared factors into individual radicals:

\(\sqrt{4 ^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c}\)

We take the square root of each radical into:

\(\sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c} = 4|a|.|b^3|.c^2\sqrt{ac}\)

We just need to simplify our last equation into:

\(4|a|.|b^3|.c^2\sqrt{ac} = 4|ab^3|c^2\sqrt{ac}\)

Learn more about Radical Expression here: brainly.com/question/3796764

#SPJ4

Answer:

The answer is option D. Best of luck

Answer:

the last one

the graph increases , then remains constant

Question:

The diagram shows a right -angle and a parallelogram. The area of the parallelogram is 5 times the area of the triangle. The perpendicular height of the parallelogram is h.  Find h

Answer:

\(h =12cm\)

Step-by-step explanation:

Given

Triangle

\(Base = 9cm\)

\(Height = 16cm\)

Parallelogram

\(Base = 30cm\)

\(Height = h\)

Calculate the area of the triangle

\(Area = 0.5 * Base * Height\)

\(Area = 0.5 * 9cm * 16cm\)

\(Area = 72cm^2\)

When multiplied by 5, gives the area of the parallelogram.

So:

The area of Parallelogram is:

\(Area = Base * Height\)

\(Area = 30cm * h\)

This gives:

\(30cm * h = 72cm^2 * 5\)

Make h the subject

\(h = \frac{72cm^2 * 5}{30cm}\)

\(h = \frac{72cm^2}{6cm}\)

\(h =12cm\)

The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Learn more about autocorrelation here:

https://brainly.com/question/14134127

#SPJ4

Answer:

a) -4

Step-by-step explanation: you can either take two points on the graph and calculate the average or count from one point to the next. you'll count 1 to the right and 4 down.

Answer:

I believe its C 1 x 1/12. Hope this helps

Step-by-step explanation:

i. cos 0 =  \(\sqrt{3}\)

ii. tan 0 = 1/ \(\sqrt{3}\)

Trigonometric functions are a set of given functions which are required in determining the value(s) of the sides or internal angle(s) of a given right angled triangle; when the value of one none right angle is given.

In the given question, we have;

sin 0 = 1/2

This implies that;

sin 0 = opposite/ hypotenuse = 1/2

So that;

opposite = 1

hypotenuse = 2

Apply the Pythagorean's theorem so as to determine its adjacent, we have;

adjacent = \(\sqrt{3}\)

Then,

cos 0 = adjacent/ hypotenuse

         =  \(\sqrt{3}\) / 1

cos 0 =  \(\sqrt{3}\)

ii. tan 0 = opposite/ adjacent

            = 1/  \(\sqrt{3}\)

tan 0 = 1/ \(\sqrt{3}\)

Learn more about trigonometric functions at https://brainly.com/question/31068764

#SPJ1

The unknown angles when line BD bisect the angle ABC is as follows:\

An angle bisector divides and angle into 2 equal angles.

Therefore, line BD bisect angle ABC.

Hence,

let's find m∠ABD

if m∠ABD = 6x + 4

m∠DBC =  8x - 4

Therefore,

m∠ABD  = m∠DBC

6x + 4 = 8x - 4

6x - 8x = -4 - 4

-2x = -8

x = -8 / -2

x = 4

Therefore,

m∠ABD = 6x + 4 = 6(4) + 4  = 24 + 4 = 28°

let's find m∠ABC

If m∠ABD = 5y - 3

m∠DBC = 3y + 15

Hence,

m∠ABD = m∠DBC

5y - 3 = 3y + 15

5y - 3y = 15 + 3

2y = 18

y = 18 / 2

y = 9

Therefore,

m∠ABC = m∠ABD +  m∠DBC

m∠ABC = 5(9) - 3 + 3(9) + 15

m∠ABC = 45 - 3 + 27 + 15

m∠ABC = 84°

learn more on angle bisector here: https://brainly.com/question/12896755

#SPJ1

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

for such more question on system of equations

https://brainly.com/question/4262258

#SPJ8

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answer:

67

Step-by-step explanation:

let larger number be x and the other be y.

x - y = 18

x = 18+y

now, x + y = 116

therefore, 18+y+y= 116

18 + 2y =116

2y = 116-18

2y = 98

y = 98/2 = 49

larger number = 49 + 18 = 67

To find the cost of one bottle of water, we need to divide the total cost of the case by the number of bottles in the case, which is 24.

So,

Cost of one bottle of water = Total cost of case / Number of bottles in case

= $2.99 / 24

= $0.1246

Rounding this to two decimal places, we get:

Cost of one bottle of water = $0.12

Therefore, one bottle of water costs $0.12.

Learn more about Cost here:- brainly.com/question/29509552

#SPJ11

\(\stackrel{\textit{\Large morning rate}}{\cfrac{\stackrel{strawberries}{3}}{\underset{minutes}{4}}}~\hspace{7em}\stackrel{\textit{\Large afternoon rate}}{\cfrac{\stackrel{strawberries}{2}}{\underset{minutes}{3}}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\underline{3}}{4}~~ - ~~\cfrac{2}{3}\implies \cfrac{(3)\underline{3}~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{9-8}{12}\implies \cfrac{1}{12}\qquad \impliedby \textit{their difference}\)

The phase II control limits for the T2 control chart, with p = 10 quality characteristics, n = 3 subgroup size, and α = 0.005, can be calculated using the preliminary samples.

The phase II control limits for a T2 control chart are essential in monitoring the quality characteristics of a process. In this case, we have p = 10 quality characteristics and a subgroup size of n = 3. To calculate the control limits, we need to estimate the sample covariance matrix using the available 25 preliminary samples.

The formula to determine the T2 control limits is given by:

T2 = (n - 1)(n - p)/(n(p - 1)) * F(α; p, n - p)

Where T2 represents the control limit value, n is the subgroup size, p is the number of quality characteristics, F(α; p, n - p) is the F-distribution value for a given significance level (α), and (n - 1)(n - p)/(n(p - 1)) is a scaling factor.

By substituting the given values into the formula, we can calculate the T2 control limit. The calculated control limit value should be multiplied by the estimated sample standard deviation, which is obtained from the preliminary samples, to determine the final control limits for each quality characteristic.

Learn more about the T2 control chart

brainly.com/question/28427773

#SPJ11

Answer: -3

Step-by-step explanation: f(-6) =2/3(-6) + 1= -12/3 + 1 = -4 + 1 = -3

Answer:

265°

Step-by-step explanation:

I think we have to minus 200 - 115 = 85

then plus them with 85 and 95 so

85 + 85+ 95 = 265°C

i hope this helps a little bit

The variance of the sample is 6561. The variance measures the spread or dispersion of the data points around the mean. In this case, it represents the average squared deviation from the mean of the 36 observations.

The variance of a sample can be calculated using the formula:

Variance = Standard Deviation^2

Given that the standard deviation of a sample of 36 observations is 81, we can square this value to find the variance.

Variance = 81^2 = 6561

Therefore, the variance of the sample is 6561. The variance measures the spread or dispersion of the data points around the mean. In this case, it represents the average squared deviation from the mean of the 36 observations.

To learn more about  variance click here:

brainly.com/question/2804492

#SPJ11

Answer:

-42

Explanation:

(-6)(-7) = 42

(42)(-1) = -42

Get a calculator homie.

Answer:its negative 42