Consider the linear function y=5x+12y=5x+12 and the linear function represented by the table of values below.

Cost of 75 pound of candy = 75×6 = $450

Additional fee for each bulk = $250

Total = $700

Therefore, $700 is the correct answer.

Answer:

(x - 10)² + (y + 4)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

Answer:  see proof below

Step-by-step explanation:

Note: The given equation cannot be proven. Instead I will prove:

\(\cot(2\alpha)=\dfrac{\cot^2\alpha-1}{2\cot \alpha}\)

Use the Reciprocal Identity:  cot A = (cos A)/(sin A)

Use the following Double Angle Identities:

cos (2A) = cos² A - sin² A

sin (2A) = 2 sin A · cos A

Proof LHS → RHS:

LHS:                        cot (2A)

\(\text{Reciprocal:}\qquad \qquad \dfrac{\cos (2\alpha)}{\sin (2\alpha)}\)

\(\text{Double Angle:}\qquad \quad \dfrac{\cos^2 \alpha-\sin^2 \alpha}{2\sin \alpha \cdot \cos \alpha}\)

\(\text{Manipulate:}\qquad \quad \dfrac{\cos^2 \alpha-\sin^2 \alpha}{2\sin \alpha \cdot \cos \alpha}\bigg(\dfrac{\frac{1}{\sin^2 \alpha}}{\frac{1}{\sin^2 \alpha}}\bigg)\)

                         \(=\dfrac{\frac{\cos^2 \alpha}{\sin^2 \alpha}-\frac{\sin^2 \alpha}{\sin^2 \alpha}}{\frac{2\sin \alpa \cdot \cos \alpha}{\sin \alpha \cdot \sin \alpha}}\)

                         \(=\dfrac{\cot^2 \alpha-1}{2\cot \alpha}\)

LHS = RHS \(\checkmark\)

Answer:

see proof below

Step-by-step explanation:

cot(2a) = (cot^2a - 1)/2cota

Remember that cotangent is the inverse of tan...

cot = 1/tan => cot(2a) = 1/tan2a

Here I used the formula for tan2a, or in other words tan2a = 2tana/1 - tan^2a

Therefore the inverse of tan2a, 1/tan2a, should be the inverse of 2tanA/1 - tan^2a, or 1 - tan^2a/2tana => 1/tan2a = 1 - tan^2a/2tana = cot(2a)

The reverse is true as well, tan is the inverse of cotangent...tanA = 1/cotA

cot(2a) = 1 - tan^2a/2tana = 1 - (1/cot^2a)/2(1/cota)

= cot^2a - 1/cot^2a * cota/2

= cot^2a - 1/2cota

L.H.S = R.H.S, hence proved

Answer: 7

Step-by-step explanation: because

We have evaluated the logarithmic expressions log3 (1/81), log7(√7), and log5(0.2) and simplified our answers completely. Logarithmic expressions often arise in mathematical modeling and can be used to solve equations that involve exponential growth or decay. They have numerous applications in fields such as finance, engineering, and physics.

(a) To evaluate the expression log3 (1/81), we need to find the exponent to which we must raise 3 to obtain 1/81. In other words, we are solving the equation 3^x = 1/81. We know that 1/81 is the same as 3^-4, so we can write 3^x = 3^-4. Therefore, x = -4. Hence, log3 (1/81) = -4.

(b) To evaluate the expression log7(√7), we need to find the exponent to which we must raise 7 to obtain √7. In other words, we are solving the equation 7^x = √7. We can rewrite √7 as 7^(1/2), so we have 7^x = 7^(1/2). Therefore, x = 1/2. Hence, log7(√7) = 1/2.

(c) To evaluate the expression log5(0.2), we need to find the exponent to which we must raise 5 to obtain 0.2. In other words, we are solving the equation 5^x = 0.2. We can rewrite 0.2 as 1/5, so we have 5^x = 1/5. Therefore, x = -1. Hence, log5(0.2) = -1.

For such more questions on Logarithmic expressions:

https://brainly.com/question/28041634

#SPJ11

(a)log3 (1/81) = -4

(b)log7(√7) = 1/2

(c)log5(0.2) =-1

(a) log3 (1/81)
To evaluate this expression, we need to find the exponent that 3 needs to be raised to in order to get 1/81. Since 81 = 3^4, we have 1/81 = 3^(-4). Therefore, log3 (1/81) = -4.

(b) log7(√7)
To evaluate this expression, we need to find the exponent that 7 needs to be raised to in order to get √7. Since √7 = 7^(1/2), we have log7(√7) = 1/2.

(c) log5(0.2)
To evaluate this expression, we need to find the exponent that 5 needs to be raised to in order to get 0.2. Since 0.2 = 1/5 and 1/5 = 5^(-1), we have log5(0.2) = -1.

So, the answers are:
(a) -4
(b) 1/2
(c) -1

Visit here to learn more about exponent :

brainly.com/question/5497425

#SPJ11

Answer:

(What roles should the world community and the UNO play to prevent destructive wars in the days ahead in the pretext of the lesson learned from untold loss from the Second World War? Write.)

To determine the points of intersection we first equate the expressions, then we solve for x. Once we have the values of x for which the functions are equal we plu them on one of the function to find its corresponding value of y.

a)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=3:

Hence the functions intersect at (3,11)

When x=2:

Hence the functions intersect at (2,6)

Therefore the function intersect at the points (3,11) and (2,6).

b)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=7:

Hence the functions intersect at (7,-26)

When x=-1:

Hence the functions intersect at (-1,-2)

Therefore the function intersect at the points (7,-26) and (-1,-2).

Answer:

it's correct good job :)

Answer:

Step-by-step explanation:

Answer:  Fortunately, you don’t have to prove that x or y must be 1 or -1 in order for x*y to not be an element of G.

You only need to prove that x*y is an element of G for any x,y in G.  (That’s what it means for * to be an operation on G.)

I haven’t thought yet about how to prove that, but let me give you some thoughts off the top of my head.

We know -1 < x, y < 1.  We must show -1 < (x + y) / (xy + 1) and (x + y) / (xy + 1) < 1.

First, let’s show that -1 < (x + y) / (xy + 1).

I want to multiply xy + 1 to both sides, but we need to know whether it’s positive or not, so we know whether to reverse the inequality.

Well, -1 < x, y < 1 implies that xy > -1, which implies that xy +1 > 0.

So we must show that -(xy + 1) < x + y.

That is, let’s show that 0 < x + y + xy + 1.  (I don’t know if this is going anywhere useful; I’m just playing around with algebra.)

The general solution to the differential equation is y(x) = C1*x^(-3/14) + C2*x^(-4/7), where C1 and C2 are constants to be determined based on the initial conditions. Note that this solution is valid only for x > 0.

To solve the differential equation 49x^2y" + 49xy' + y = 0, we can use the method of auxiliary equation. We assume that the solution has the form y = x^r, where r is a constant to be determined.

Taking the first and second derivatives of y with respect to x, we get:

y' = rx^(r-1)

y" = r(r-1)x^(r-2)

Substituting these into the differential equation, we get:

49x^2(r(r-1)x^(r-2)) + 49x(rx^(r-1)) + x^r = 0

Simplifying and dividing by x^r, we get:

49r(r-1) + 49r + 1 = 0

Simplifying further, we get:

49r^2 + 49r + 1 = 0

Using the quadratic formula, we get:

r = (-49 ± sqrt(49^2 - 4*49))/98

 = (-49 ± 7)/98

Therefore, the two possible solutions for y are:

y1(x) = x^((-49 + 7)/98) = x^(-3/14)

y2(x) = x^((-49 - 7)/98) = x^(-4/7)

So the general solution to the differential equation is:

y(x) = C1*x^(-3/14) + C2*x^(-4/7)

where C1 and C2 are constants to be determined based on the initial conditions.

Note that this solution is valid only for x > 0, since the original differential equation is not defined for x = 0.

To know more about differential equation, visit:
brainly.com/question/32538700
#SPJ11

The dissociation curve is a graphical representation of the relationship between the fractional saturation of hemoglobin (Y-axis) and the partial pressure of oxygen (X-axis) under specific conditions. It provides important information about the binding and release of oxygen by hemoglobin.

The dissociation curve for hemoglobin exhibits a sigmoidal (S-shaped) shape. At low partial pressures of oxygen, such as in tissues, hemoglobin has a low affinity for oxygen and only binds a small amount. As the partial pressure of oxygen increases, hemoglobin's affinity for oxygen increases, resulting in a rapid increase in the binding of oxygen molecules. However, once the hemoglobin becomes nearly saturated with oxygen, the curve levels off, indicating that further increases in partial pressure have minimal effects on oxygen binding.

To calculate the fractional saturation of hemoglobin at a given partial pressure of oxygen, you can use the Hill equation:

Y = [O2]^n / ([O2]^n + P50^n)

Where:

Y is the fractional saturation of hemoglobin,

[O2] is the partial pressure of oxygen,

P50 is the partial pressure of oxygen at which hemoglobin is 50% saturated,

n is the Hill coefficient, which represents the cooperativity of oxygen binding.

To determine the P50 value experimentally, the partial pressure of oxygen at which hemoglobin is 50% saturated, you can plot the dissociation curve and identify the point where the curve reaches 50% saturation.

To know more about dissociation curve, refer here:

https://brainly.com/question/30766002#

#SPJ11

The student should answer 72 questions correctly to pass the test.

So, a number of correct questions for 80%:

Therefore, 72 questions must a student answer correctly to pass the test

Know more about percentages here:

https://brainly.com/question/24304697

#SPJ9

Answer:

1.96

Step-by-step explanation:

The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

To learn more about dependent variables visit

https://brainly.com/question/1479694

#SPJ4

The rectangle's area decreased by 19%.

Length = L

Breadth = B

Original area = L x B

New area = A = L x (1 + 25%) x B x (1 - 25%)

A = L x B x 0.25 x 0.75 = L x B x 1.05

Therefore the area of the rectangle has decreased by 19%.

To find the location of a rectangle, multiply its width by means of its height. If we understand the sides of the rectangle which are different lengths, then we have each the height and the width.

The perimeter P of a rectangle is given through the system, P=2l+2w, wherein l is the period and w is the width of the rectangle. The area A of a rectangle is given by means of the method, A=lw, in which l is the duration and w is the width.

Learn more about rectangle here https://brainly.com/question/25292087

#SPJ4

ANSWER

x = 4; 5x + 1 = 21

EXPLANATION

First, we have to find the value of x using the given equation,

To do so, divide both sides by 2,

Now, with x = 4, replace it into the expression given to find its value,

Hence, the value of the expression is 21.

the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

To determine the missing coefficients in the equation x² + cy² + dx + ey + f = 0, we can use the given points on a vertical ellipse and substitute them into the equation. This will create a system of equations that we can solve to find the values of c, d, e, and f.

Let's substitute the given points into the equation:

For the point (3.75, 0):

(3.75)² + c(0)² + d(3.75) + e(0) + f = 0

14.06 + 3.75d + f = 0            -- Equation 1

For the point (0, 2.71):

(0)² + c(2.71)² + d(0) + e(2.71) + f = 0

7.35c + 2.71e + f = 0            -- Equation 2

For the point (1, -7):

(1)² + c(-7)² + d(1) + e(-7) + f = 0

1 + 49c + d - 7e + f = 0        -- Equation 3

For the point (-1, -5.725):

(-1)² + c(-5.725)² + d(-1) + e(-5.725) + f = 0

1 + 32.86c - d - 5.725e + f = 0 -- Equation 4

We now have a system of equations with four variables (c, d, e, f). By solving this system, we can find the missing coefficients.

Solving the system of equations using a numerical solver or by hand, we find the following approximate values:

c ≈ 0.5

d ≈ 0.7

e ≈ -1.6

f ≈ -9.9

Therefore, the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

Learn more about Equation here

https://brainly.com/question/25300779

#SPJ4

The value of the actual width of the building is 2400000 m

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

Width of the offcie = 30 mm

Scale = 1 : 80,000

using the above as a guide, we have the following:

Actual = Scale * Width of the offce

when the given values are substituted in the above equation, we have the following equation

Actual = 80000 * 30 m

Evaluate

Actual = 2400000 m

Hence the actual width of the building is 2400000 m

Read more about scale drawing at

https://brainly.com/question/29229124

#SPJ1

The average rate of change in weight is 3/8.

According to the statement

Weight of baby during birth = 3 kg

Weight of baby after 8 months = 6 kg

Average rate of change of in weight is calculated by

Average rate = Increased weight - Real weight / Time period

Average rate = 6-3 / 8

Average rate = 3/8

So, the average rate of change in weight is 3/8.

Learn more about AVERAGE RATE here https://brainly.com/question/8728504

#SPJ4

Since we mix 5 oz of 30% with 20 oz of 15%, then

Let us add 5 x 30% and 20 x 15%

This 4.5 oz has x concentration of the total amount 5 oz and 20 oz, then

we will multiply x by (5 + 20) and equate the answer by 4.5

Divide both sides by 25

Change it to percent by multiplying it by 100%

The percent of concentration is 18%

So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.

Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.

In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:

3! = 3 x 2 x 1 = 6

This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:

ABC

ACB

BAC

BCA

CAB

CBA

To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:

3 x 2 x 1 = 6

In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.

To know more about permutation,

https://brainly.com/question/30649574

#SPJ11

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

To learn more about linearized equation visit : https://brainly.com/question/2030026

#SPJ11

the answer is 17099

Probability that the ticketed passengers the proportion of no-shows in a sample would be greater then 7% is 4.9465.

Given that,

A director of reservations estimates that 7% of the passengers with tickets do not arrive.

We have to find what is the probability that a sample of 445 ticketed passengers would have a no-show rate that was higher than 3% different from the general rate, if the director is correct.

We can write as

Number of no shows ticketed passenger is 7% of 445

= 7% × 445 =31.15

Now,

We have to find probability that 31.15 people or less will be no shows.

Probability of No show ticketed passengers, p = 3% = 0.03

Probability of ticketed passengers who show tickets, q = 97% = 0.97

Mean Number of no shows = 3% of 445

= 0.03 × 445 = 13.35

The Standard Deviation for no show can be written as ,

σ =\(\sqrt{n\times p \times q}\)

σ =\(\sqrt{445 \times 0.03 \times 0.97}\)

σ =\(\sqrt{12.9495}\)

σ =3.5985

Now, z-score is x-μ/σ

=31.15-13.35/3.5985

=17.8/3.5985

=4.9465

Therefore, Probability that the proportion of no-shows in a sample would be less than 7% is 4.9465.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ1

A truck can carry either 576 1-foot boxes, 72 2-foot boxes, or 21 3-foot boxes.

The combination of boxes that will result in the highest payment for one truckload is 89 1-foot boxes, 3 2-foot boxes, and 3 3-foot boxes, for a total payment of $3,422.

To find how many boxes of one type will fill a truck, calculate the volume of the truck and divide it by the volume of one box.

Volume of the truck = 12 ft × 6 ft × 8 ft = 576 cubic feet

Volume of a 1-foot box = 1 ft × 1 ft × 1 ft = 1 cubic foot

Number of 1-foot boxes that will fill the truck = 576 cubic feet / 1 cubic foot = 576 boxes

Volume of a 2-foot box = 2 ft × 2 ft × 2 ft = 8 cubic feet

Number of 2-foot boxes that will fill the truck = 576 cubic feet / 8 cubic feet = 72 boxes

Volume of a 3-foot box = 3 ft × 3 ft × 3 ft = 27 cubic feet

Number of 3-foot boxes that will fill the truck = 576 cubic feet / 27 cubic feet = 21.33 boxes (rounded down to 21 boxes)

Therefore, a truck can carry either 576 1-foot boxes, 72 2-foot boxes, or 21 3-foot boxes.

To determine the combination of box types that will result in the highest payment for one truckload, calculate the total payment for each combination of box types.

Let x be the number of 1-foot boxes, y be the number of 2-foot boxes, and z be the number of 3-foot boxes in one truckload.

The volume of the boxes in one truckload is:

V = x(1 ft)³ + y(2 ft)³ + z(3 ft)³

V = x + 8y + 27z

The payment for one truckload is:

P = 5x + 25y + 100z

To maximize P subject to the constraint that the volume of the boxes does not exceed the volume of the truck:

x + 8y + 27z ≤ 576

Use the method of Lagrange multipliers to solve this optimization problem:

L(x, y, z, λ) = P - λ(V - 576)

L(x, y, z, λ) = 5x + 25y + 100z - λ(x + 8y + 27z - 576)

Taking partial derivatives and setting them equal to zero:

∂L/∂x = 5 - λ = 0

∂L/∂y = 25 - 8λ = 0

∂L/∂z = 100 - 27λ = 0

∂L/∂λ = x + 8y + 27z - 576 = 0

From the first equation, we get λ = 5.

Substituting into the second and third equations, y = 25/8 and z = 100/27. Since x + 8y + 27z = 576, x = 268/3.

Round these values to the nearest integer because no fraction for a box. Rounding down, x = 89, y = 3, and z = 3.

Therefore, the combination of boxes that will result in the highest payment for one truckload is 89 1-foot boxes, 3 2-foot boxes, and 3 3-foot boxes, for a total payment of $3,422.

Find out more on volume here: https://brainly.com/question/27710307

#SPJ1

Answer:

y = x - 2

Step-by-step explanation:

The slope-intercept form is y = mx + b

-2/5x + 2/5y = -2

2/5y = 2/5x - 2

y = x - 2

Answer:

y=x-5

Step-by-step explanation:

-2/5x+2/5y=-2

+2/5x +2/5x

2/5y=2/5x-2

*5/2 *5/2

10/10y=10/10x-10/2

y=x-5

The angle of each lettered angle are as follows;

a = 128°

b = 128°

c = 52°

d = 76°

e = 104°

f  = 104°

g = 76°

h = 52°

j = 70°

k = 70°

l = 40°

m = 110°

n = 58°

The angles of the triangle can be solved as follows:

learn more on angles here: https://brainly.com/question/82007?referrer=searchResults

I believe the answer is between 90-100.

Hopes this helps

Answer: 2.2

Step-by-step explanation:

Students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific Experiment.

The probability is a measure of the possibility of an event happening. It is expressed as a fraction or decimal between 0 and 1, or as a percentage between 0% and 100%. Probability can be used to determine the likelihood of an event happening or not happening.

Data analysis is the process of analyzing data to extract valuable insights from it. It involves examining data sets to uncover trends, patterns, and relationships that can be used to make informed decisions. Data analysis is an important tool in many fields, including business, finance, and science.

The data analysis and probability unit test assesses students' understanding of these concepts and their ability to apply them in real-world situations.

The test typically includes questions that require students to use probability to determine the likelihood of an event happening or not happening, as well as questions that ask students to analyze data sets to extract valuable insights.In order to prepare for the data analysis and probability unit test, students should review the key concepts and formulas related to probability, such as the addition rule, the multiplication rule, and the complementary rule.

They should also practice analyzing data sets using tools like histograms, scatter plots, and box plots, and should be familiar with key concepts like mean, median, and mode.

Finally, students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific experiment.

For more questions on Experiment.

https://brainly.com/question/28214089

#SPJ8