This is 1/6 problems finish them all each is 10 points 60 total.

The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

a) The probability that in any given hour zero new visitors will arrive at the website is given by;P(X = 0) = (e^-λ λ^0)/0!Where λ = 2.3Thus;P(X = 0) = (e^-2.3 2.3^0)/0!P(X = 0) = (0.1003)/1P(X = 0) = 0.1003b) The probability that in any given hour exactly one new visitor will arrive at the website is given by;P(X = 1) = (e^-λ λ^1)/1!Where λ = 2.3Thus;P(X = 1) = (e^-2.3 2.3^1)/1!P(X = 1) = (0.2303)/1P(X = 1) = 0.2303c) The probability that in any given hour two or more new visitors will arrive at the website is given by;P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Thus;P(X ≥ 2) = 1 - 0.1003 - 0.2303P(X ≥ 2) = 0.6694d) The probability that in any given hour fewer than three new visitors will arrive at the website is given by;P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)Thus;P(X < 3) = 0.1003 + 0.2303 + 0.2642P(X < 3) = 0.5948Therefore,The probability that in any given hour zero new visitors will arrive at the website is 0.1003.The probability that in any given hour exactly one new visitor will arrive at the website is 0.2303.The probability that in any given hour two or more new visitors will arrive at the website is 0.6694.The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

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Answer:m=0,m=-2

Step-by-step explanation:

[tex]m^{2} + 4m+3=0\\(m+2)^{2} -1=0\\(m+2)^{2}=1\\1)m+1=1\\m=0\\1)m+1=-1\\m=-2[/tex]

If you are traveling at 60 mph, you are also traveling at 96.56 kph.

To convert 60 miles per hour (mph) into kilometers per hour (kph), we need to use a conversion factor. A conversion factor is a ratio that relates two different units of measurement. In this case, we can use the fact that 1 mile is equal to 1.60934 kilometers. To convert mph to kph, we need to multiply the given value by this conversion factor.

So, to convert 60 mph to kph, we can set up the following equation:

60 mph x (1.60934 km/1 mile) = 96.56 kph

This means that 60 mph is equivalent to 96.56 kph. Therefore, if you are traveling at 60 mph, you are also traveling at 96.56 kph.

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According to the given table and graph:

a) The number of customers a restaurant employee can serve is 5.

b) The number of customers a grocery store clerk can serve is 12 for him.

c) The customer's food price per employee is 7 higher than the restaurant's price.

Line charts use data point "markers" connected by straight lines. These data points connected by straight lines are useful for visualization. Line charts are used in different fields for different purposes, but they are especially useful when you need to graphically represent changes in values ​​over time.

Line charts are widely used in finance to create visual representations of values ​​over time, such as changes in security prices, company earnings lists, and the history of major stock indices. It is also useful for comparing different stocks. In the field of investing, especially technical analysis, line charts are used by investors to visualize trends, which greatly aids analysis.

Given a graph of restaurants and a table of grocery stores, it shows the relationship between number of employees per customer. You have to solve the subtasks of the given task.

The price at the store is 12 ÷ 2 or 6 customers per employee.

According to the question;

A diagram of a restaurant and a grocery store table are shown.

a) at a restaurant;

For 2 employees, no. Customers = 10

For 4 employees, no. Customers = 20

so

If he increases the number of employees by two, no. We have 10 more customers.

⇒ The number of customers a restaurant employee can serve;

= 10 ÷ 2

= 5 customers

b) At the grocery store.

For 2 employees, no. Customers = 24

For 4 employees, no. Customers = 48

So when the number of employees increases by 2.

⇒ How many customers can a grocery store clerk serve;

= 24 ÷ 2

= 12 customers

c) so

Restaurant rate of customers per employee = 5 customers/employee

Grocery store customer rate per employee = 12 customers/employee

Also, food prices per customer per employee are higher than restaurant prices.

= 12 - 5

= 7  

Thus , the answers will be ;

a) No. of customers , one employee can help at restaurant is 5.

b) No. of customers , one employee can help at grocery store is 12.

c) The grocery rate of customer per employee is 7 more than restaurant's rate.

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The complete question is as follows:

ANSWER

31 is answer !!!!

Answer:

31

Step-by-step explanation:

180-35-23=122

180-122-27=31

The ratiοs are nοt equal fοr all the squares, which means there is nοt a prοpοrtiοnal relatiοnship between diagοnal length and area.

Using the fοrmula fοr finding the area οf a square, we have:

Area οf square A = side length squared

Area οf square A = 4.8 x 4.8

Area οf square A = 23.04 square cm

Similarly, we can find the areas οf squares B, C, and D:

Area οf square B = 5.2 x 5.2 = 27.04 square cm

Area οf square C = 6.4 x 6.4 = 40.96 square cm

Area οf square D = 3.6 x 3.6 = 12.96 square cm

Nοw, let's find the lengths οf the diagοnals οf each square using the Pythagοrean theοrem:

Diagοnal οf square A = √(4.8² + 4.8²) = 6.77 cm

Diagοnal οf square B = √(5.2² + 5.2²) = 7.35 cm

Diagοnal οf square C = √(6.4² + 6.4²) = 9.06 cm

Diagοnal οf square D = √(3.6² + 3.6²) = 5.09 cm

Tο determine if there is a prοpοrtiοnal relatiοnship between the length οf the diagοnals and the areas οf the squares, we need tο cοmpare the ratiοs οf the diagοnals tο the areas fοr each square.

Fοr example, the ratiο οf diagοnal length tο area fοr square A is:

Ratiο οf diagοnal length tο area fοr square A = diagοnal length / area

Ratiο οf diagοnal length tο area fοr square A = 6.77 cm / 23.04 square cm

Ratiο οf diagοnal length tο area fοr square A = 0.294

We can repeat this fοr the οther squares and cοmpare the ratiοs. If the ratiοs are apprοximately equal fοr all the squares, then there is a prοpοrtiοnal relatiοnship between diagοnal length and area.

Ratiο οf diagοnal length tο area fοr square B = 0.272

Ratiο οf diagοnal length tο area fοr square C = 0.221

Ratiο οf diagοnal length tο area fοr square D = 0.393

As we can see, the ratiοs are nοt equal fοr all the squares, which means there is nοt a prοpοrtiοnal relatiοnship between diagοnal length and area.

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the end behavior of the polynomial [tex]$-2 x^4-3 x^2-x+5$[/tex] is: The polynomial decreases without bound as [tex]$x$[/tex] get closer to positive infinity. The polynomial grows without bound as [tex]$x$[/tex] gets closer to negative infinity.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. [tex]$x^2+x-12$[/tex] is an illustration of a polynomial with a single variable.

from the question:

The degree and leading coefficient of the polynomial [tex]$-2 x^4-3 x^2-x+5$[/tex]must be examined in order to determine its final behavior.

As the polynomial has a degree of 4 , it will expand or decay at a pace dictated by the leading coefficient as x gets closer to positive or negative infinity. The negative (leading) coefficient is -2 .

As in this instance, the final behavior of a polynomial with a negative leading coefficient and an even degree is as follows:

- The polynomial will decrement without bound as x approaches positive infinity, causing the y values to decrement steadily. This is due to the fact that as x increases significantly, the term with the highest degree takes over the polynomial, and since the leading coefficient is negative, the polynomial reduces.

- The polynomial will grow without bound as x gets closer to negative infinity, which causes the y-values to get steadily increasingly positive. This is because as x gets very tiny and negative, the term with the highest degree dominates the polynomial, and since the leading coefficient is negative, the polynomial rises.

Hence, the polynomial [tex]$-2 x^4-3 x^2-x+5$[/tex] has the following final behavior:

- The polynomial decreases without bound as x get closer to positive infinity.

- The polynomial grows without bound as x gets closer to negative infinity.

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Answer:

pepperoni slices : 72

cheese slices: 55

Step-by-step explanation:

p is the number of pepperoni slices

c is the number of cheese slices

so p + c = 127 => c = 127 - p

3p + 2c = 326

3p + 2(127 - p) = 326

3p + 254 - 2p = 326

p = 326 - 254 = 72

c = 127 - 72 = 55

Answer:

(n+3)(n+10)

Step-by-step explanation:

n^2+13n+30

n^2+10n+3n+30

n(n+10)+3n+30

n(n+10)+3(n+10)

(n+3)(n+10)

The answer of the given question based on the finding the work done by the force, is  field F on a particle moving along the path C is 1/6.

A force is defined as influence that causes object to undergo change in motion. It is vector quantity, means it has both magnitude and direction.

To find the work done by the force field F on a particle moving along the given path, we need to evaluate the line integral of F along the path C.

The line integral of a vector field F along a curve C parameterized by r(t) is given by:

∫ F(r(t)) ⋅ r'(t) dt

where r'(t) is the derivative of r(t) with respect to t.

In this case, the force field F(x, y) = x²i − xyj, and the path C is given by x = cos³(t), y = sin³(t) from (1, 0) to (0, 1).

First, we need to parameterize the path C in terms of t. Since x = cos³(t) and y = sin³(t), we can express the path C as a vector function r(t) = ⟨cos³(t), sin³(t)⟩, where t goes from 0 to π/2.

we need to find derivative of r(t) with the respect of  t:

r'(t) = ⟨-3cos³(t)sin(t), 3sin²(t)cos(t)⟩

Now, we can evaluate the line integral of F along C:∫ F(r(t)) ⋅ r'(t) dt

= ∫ (cos⁶(t)i - cos³(t)sin⁴(t)j) ⋅ (-3cos²(t)sin(t)i + 3sin²(t)cos(t)j) dt

= ∫ (-3cos⁸(t)sin(t) + 3cos³(t)sin⁵(t)) dt

= [-3/9cos⁹(t) - 3/6cos⁴(t)cos²(t)]_0^(π/2)

= 0 - (-3/9 - 3/12)

= 1/6

Therefore, the work done by the force field F on a particle moving along the path C is 1/6.

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Answer:

  f(x) = -3(x -(-1))² +7

Step-by-step explanation:

You want the equation of the quadratic function that matches the given table.

The first step in solving the problem is to look at the given information. To use the given equation, you need to know the vertex of the function, and its vertical scale factor.

A quadratic function is symmetrical about the line through its vertex. That means we can locate the vertex by looking for x-values where the y-value is the same. The x-value of the vertex is halfway between those x-values.

Here, f(x) = 4 for both x=-2 and x=0. That means the x-value of the vertex is ...

  (-2 +0)/2 = -1

This value of x is in the table, and f(-1) is given as 7. This means the vertex is (-1, 7) and these are the values that go in the two rightmost boxes.

  f(x) = ( )(x -(-1))² + 7

The scale factor in the first box can be found by considering the difference between the f(x) value at the vertex, and the f(x) value at a point that is 1 unit either side:

  ( ) = f(-2) -f(-1) = 4 -7 = -3

The scale factor is -3, so the equation is ...

  f(x) = -3(x -(-1))² +7

After calculating the questiοn, we get that the value οf 20% οf 75 is 15.

A value οr ratiο that may be stated as a fractiοn οf 100 is referred tο in mathematics as a percentage. Divide the number by the tοtal and multiply by 100 tο find the percent οf a given number. Therefοre, the percentage refers tο a pοrtiοn per hundred. Per 100 is what the wοrd percentage signifies. The letter "%" stands fοr it.

Percent changes applied sequentially dο nοt add up in the usual way. Fοr example, if the 10% increase in price cοnsidered earlier (οn the $200 item, raising its price tο $220) is fοllοwed by a 10% decrease in the price (a decrease οf $22), then the final price will be $198—nοt the οriginal price οf $200.

Here the given is,

=> 20% of 75

=> 20% [tex]\times[/tex]75

=> [tex]\frac{20}{100}\times 75[/tex]

=> 5[tex]\times 3[/tex]

=> 15.

Hence the value of 20% of 75 is 15.

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Answer:

2

Step-by-step explanation:

gradient = slope = Δy/Δx = (4 - 2) / (-2 --3) = 2/1 = 2

Answer:

C, D and E

Step-by-step explanation:

2(4f+2g)

8f+4g

so it's C, D and E

20 grams are formed in 20 minutes, the limiting amount (in grams) of C after a long time is 40 grams and 0 grams of A and 30 grams if B chemicals remain after a long time.

The reaction can be represented by the following equation:

2A + B -> C

Initially, there are 40 grams of A and 50 grams of B. After 10 minutes, 10 grams of C is formed. This means that 5 grams of B and 10 grams of A were used up in the reaction.

After 10 minutes, there are 30 grams of A and 45 grams of B remaining. The reaction will continue until one of the reactants is used up. In this case, A is the limiting reactant because there are less grams of A remaining than B.

After 20 minutes, 20 grams of C will be formed because the reaction rate is constant. This means that 10 grams of B and 20 grams of A will be used up in the reaction.

After 20 minutes, there will be 10 grams of A and 35 grams of B remaining. The reaction will continue until all of the A is used up.

After a long time, the limiting amount of C will be 40 grams because all of the A will be used up in the reaction. This means that 20 grams of B will be used up in the reaction.

After a long time, there will be 0 grams of A and 30 grams of B remaining.

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Therefore, the point on the line y = 3x + 4 that is closest to the origin is: (x, y) = (3/5, -2/5).

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

To find the point on the line y=3x + 4 that is closest to the origin, we can use the distance formula between a point and a line. The point on the line that is closest to the origin will lie on the perpendicular line that passes through the origin and intersects the given line.

First, let's find the slope of the perpendicular line. Since the given line has a slope of 3, the perpendicular line will have a slope of -1/3 (the negative reciprocal of 3). Therefore, the equation of the perpendicular line is:

y = (-1/3)x + b

where b is the y-intercept.

Next, we need to find the point where the perpendicular line intersects the given line y=3x + 4. To do this, we can set the two equations equal to each other and solve for x and y:

(-1/3)x + b = 3x + 4

Multiplying both sides by 3 gives:

-x + 3b = 9x + 12

Rearranging gives:

10x = 3b - 12

x = (3/10)b - 6/5

Substituting this expression for x into either equation gives the corresponding value of y:

y = 3((3/10)b - 6/5) + 4 = (9/10)b - 14/5

Now, we need to find the value of b that makes the point (x, y) on the line y = 3x + 4 closest to the origin. The distance between the origin (0, 0) and any point (x, y) on the line y = (-1/3)x + b is given by the distance formula:

distance = √(x² + y²)

Substituting the expressions for x and y in terms of b gives:

distance = √((3/10)b - 6/5)² + ((9/10)b - 14/5)²)

To minimize the distance, we can take the derivative of the distance formula with respect to b and set it equal to zero:

d(distance)/db = (3/5)b - 12/5 = 0

Solving for b gives:

b = 4

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There is a 0.011 = 1.1% probability that the demand will be of at least 81 cartons on the next Saturday.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 65, \sigma = 7[/tex]

The probability that there will be at least 81 cartoons is one subtracted by the p-value of Z when X = 81, hence:

Z = (81 - 65)/7

Z = 2.29

Z = 2.29 has a p-value of 0.989.

(we can consider this for any Saturday as outcomes of the normal distribution are independent).

Hence the probability is obtained as follows:

1 - 0.989 = 0.011 = 1.1%.

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The similar triangles are-

ΔNMQ ≈ ΔNQP ≈ ΔQMP

Three ways can be used to determine whether two triangles resemble similar: SSS, SAS, and AA

For the given figure:

Thus, the similar triangles are-

ΔNMQ ≈ ΔNQP ≈ ΔQMP

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By answering the above question, we may state that The missing values are "5" for the constant term, "-2" for the "xy" coefficient, and "2" for the "x²" coefficient.

In mathematics, yοu can multiply, divide, add, οr take away. The fοllοwing is hοw an expressiοn is put tοgether: Numeric value, expressiοn, and math οperatοr The elements οf a mathematical expressiοn include numbers, parameters, and functiοns. It is feasible tο use cοntrasting wοrds and expressiοns. Any mathematical statement cοntaining variables, numbers, and a mathematical actiοn between them is knοwn as an expressiοn, οften knοwn as an algebraic expressiοn. As an example, the expressiοn 4m + 5 is cοmpοsed οf the expressiοns 4m and 5, as well as the variable m frοm the abοve equatiοn, which are all separated by the mathematical symbοl +.

Part A: We must add the expressiοns fοr each οf the three friends in οrder tο build an expressiοn tο reflect the tοtal amοunt οf canned fοοd that the three friends have sο far cοllected:

= (4x² + 2xy + 3) = (3x² - 2) + x2 + (2xy + 5)

Part B: We must deduct the amοunt acquired frοm the gοal expressiοn in οrder tο determine hοw many cans the buddies still need tο gather tο reach their gοal.

Aim - Amοunt gathered equals (6x² - 2xy + 8) - (4x² + 2xy + 3) = 2x² - 5 in terms οf the number οf cans required.

As a result, the expressiοn fοr hοw many mοre cans the buddies need tο gather tο reach their οbjective is 2x² - 5. The missing values are "5" fοr the cοnstant term, "-2" fοr the "xy" cοefficient, and "2" fοr the "x²" cοefficient.

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Therefore , the solution of the given problem of expression comes out to be not proportional to the original size.

Calculations like random multiplication, division, joining, and presently removing are necessary. They would result in the following if combined: An equation, some statistics, and a mathematical formula. A statement of veracity is composed of values, components, mathematical processes like additions, subtractions, blunders, and segments, as well as formulae. Words and phrases can be evaluated and analysed.

Here,

In terms of image sizes,

=>  4x6 and 8x10, 5x7 and 14x18, and 11x14 and 16x20 are comparable.

The bigger picture size is produced by diluting the smaller picture size by a scale factor of two.

This finding suggests that scaling images can be challenging if the new scale does not match the original.

When an image is resized, it will become distorted if the aspect ratios of the two sizes are different.

A portion of the image must be cropped out to suit the new size if the angles are identical but the new size is not proportional to the original size.

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Answer:

65.1

Step-by-step explanation:

cos(37)=[tex]\frac{52}{x}[/tex]

[tex]x=\frac{52}{cos(37)}[/tex]

[tex]x=65.111....\\x=65.1[/tex]

(i)   −10

(ii)   6

(i)The average rate of change for the function f(t) = −3t2+2t−4 between t=2 and t=5 is −10.

(ii)The average rate of change for the function f(t) = −3t2+2t−4 between t=−1 and t=3 is 10.An average rate of change is the ratio of the change in a function to the change in the input. The average rate of change for the function f(t) = −3t2+2t−4 between t = 2 and t = 5 can be calculated as follows:-f(5) − f(2) / 5 − 2= -95 - (-20) / 5 - 2 = -75 / 3 = -25So, the average rate of change for the function f(t) = −3t2+2t−4 between t = 2 and t = 5 is −25.The average rate of change for the function f(t) = −3t2+2t−4 between t = −1 and t = 3 can be calculated as follows:-f(3) − f(-1) / 3 - (-1) = -25 - 1 / 3 + 1 = -24 / 4 = -6So, the average rate of change for the function f(t) = −3t2+2t−4 between t = −1 and t = 3 is 6.

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According to the question we can say that with a budget of T$15,625, you can purchase approximately 5.5 square meters of ceramic tiles at the given price of C$3,125 for 25 m2.

Among the four fundamental arithmetic operations, or ways to mix numbers to create new ones, is division. Multiplication, addition, as well as subtraction make up the remaining operations.

To find the quantity of tiles that can be purchased with a budget of T$15,625, we need to calculate the cost per square meter of the tiles and then divide the budget by this cost.

The cost per square meter of the tiles is given by:

C$3,125 / 25 m2 = C$125/m2

To convert C$125/m2 to T$, we need to use the current exchange rate. Let's assume that the current exchange rate is 1 CAD = 0.75 USD and 1 USD = T$30.

C$125/m2 * 0.75 USD/CAD * 30 T/USD = T$2,812.50/m2

Now we can calculate the quantity of tiles that can be purchased with a budget of T$15,625:

Quantity of tiles = Budget / Cost per square meter

Quantity of tiles = T$15,625 / T$2,812.50/m2

Quantity of tiles = 5.5 m2 (rounded to the nearest 0.5 m2)

Therefore, with a budget of T$15,625, you can purchase approximately 5.5 square meters of ceramic tiles at the given price of C$3,125 for 25 m2.

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Answer:

Voici une solution possible en Python:

def triangle_rectangle(A, B, C):

   # Calcul des carrés des longueurs des côtés

   AB2 = (B[0] - A[0])**2 + (B[1] - A[1])**2

   BC2 = (C[0] - B[0])**2 + (C[1] - B[1])**2

   AC2 = (C[0] - A[0])**2 + (C[1] - A[1])**2

   # Vérification si le triangle est rectangle et affichage du résultat

   if AB2 + BC2 == AC2 or AB2 + AC2 == BC2 or BC2 + AC2 == AB2:

       if AB2 + BC2 == AC2:

           print("Le triangle ABC est rectangle en A.")

       elif AB2 + AC2 == BC2:

           print("Le triangle ABC est rectangle en C.")

       else:

           print("Le triangle ABC est rectangle en B.")

   else:

       print("Le triangle ABC n'est pas rectangle.")

# Exemple avec A(2,-2), B(7,3) et C(5,5)

A = (2,-2)

B = (7,3)

C = (5,5)

triangle_rectangle(A, B, C) # affiche "Le triangle ABC est rectangle en B."

-

Explications :

La fonction triangle_rectangle prend en argument les coordonnées des points A, B et C sous forme de tuples (x,y). Elle commence par calculer les carrés des longueurs des côtés AB, BC et AC à l'aide de la formule de distance entre deux points.

Ensuite, elle vérifie si le triangle est rectangle en comparant la somme des carrés des longueurs de deux côtés avec le carré de la longueur du troisième côté. Si c'est le cas, elle affiche le message correspondant en précisant le point d'angle droit. Sinon, elle affiche le message indiquant que le triangle n'est pas rectangle.

Finalement, un exemple est donné avec les points A(2,-2), B(7,3) et C(5,5) pour vérifier que le triangle est rectangle en B, conformément à l'énoncé.

Answer:

See below.

Step-by-step explanation:

We are asked to find measures of the unknown sides for the given area.

Let's keep in mind that a rectangle's area is; [tex]Area = (width) \times (height)[/tex]

One simple way to find all of the possible side lengths is to find all of the factors of 16.

Factors are 2 whole numbers that multiply together to have the product of that given number.

Think of how many ways we can get to 16 by multiplying 2 numbers.

[tex]f_{1} \times f_{2} = 16\\f \ represents \ a \ factor.[/tex]

Here's all of the possible ways we can get to 16 with whole numbers.

[tex]8 \times 2 = 16\\4 \times 4 = 16\\2 \times 8 = 16\\1 \times 16 = 16\\16 \times 1 = 16[/tex]

Remember that the Width and Length of a Rectangle can have different values even with the same numbers multiplied.

[tex](8 \times 2) \ and \ (2 \times 8)\\Length \ can \ equal \ 2, \ or \ 8.\\Width \ can \ equal \ 8, \ or \ 2.[/tex]

These are all of the possible answers.

Answer:

[tex]11x^2 - 5x + 5[/tex] (Option 2)

Step-by-step explanation:

Equation:

[tex](3x^2 - 4x -1) +(8x^2 - x + 6)[/tex]

We can drop the parenthesis since there is nothing to distribute

[tex]3x^2 - 4x -1 +8x^2 - x + 6[/tex]

Combine like terms

[tex]3x^2 + 8x^2 -4x -x -1 +6\\\\11x^2 - 5x + 5[/tex]

Answer:

The cost of the chocolate bar is $0.54. You can calculate this by subtracting the total cost of the peanut butter bars ($3.50) from the total cost of the 5 peanut butter bars and 6 chocolate bars ($6.40), resulting in $2.90 for the cost of the chocolate bars, which is then divided by 6 to get $0.54.

The linear optimization model is:

maximize 2x1 + 1.5x2 - 0.9x1 - 0.65x2 - x3 - x4
subject to:
0.2(x1 + x2) <= x1 <= 0.65(x1 + x2)
x1 <= 5000 + 4x3
x2 <= 4000 + 5x4
0.9x1 + 0.65x2 + x3 + x4 <= 19750
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0

To formulate a linear optimization model for the Sonoma Apple Products Company, we need to define the decision variables, the objective function, and the constraints.

Decision variables:
- Let x1 be the number of jars of applesauce produced
- Let x2 be the number of bottles of apple juice produced
- Let x3 be the amount spent on advertising for applesauce
- Let x4 be the amount spent on advertising for apple juice

Objective function:
- The company wants to maximize profit, which is the difference between revenue and cost.
- The revenue from applesauce is $2 per jar, and the revenue from apple juice is $1.50 per bottle.
- The cost of producing applesauce is $0.90 per jar, and the cost of producing apple juice is $0.65 per bottle.
- The cost of advertising is x3 for applesauce and x4 for apple juice.
- Therefore, the objective function is:
maximize 2x1 + 1.5x2 - 0.9x1 - 0.65x2 - x3 - x4

Constraints:
- The company has a policy that at least 20% but no more than 65% of its output must be applesauce:
0.2(x1 + x2) <= x1 <= 0.65(x1 + x2)
- The company wants to meet but not exceed the demand for each product:
x1 <= 5000 + 4x3
x2 <= 4000 + 5x4
- The company has $19,750 to spend on producing and advertising its two products:
0.9x1 + 0.65x2 + x3 + x4 <= 19750
- The decision variables must be non-negative:
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0

The linear optimization model is:

maximize 2x1 + 1.5x2 - 0.9x1 - 0.65x2 - x3 - x4
subject to:
0.2(x1 + x2) <= x1 <= 0.65(x1 + x2)
x1 <= 5000 + 4x3
x2 <= 4000 + 5x4
0.9x1 + 0.65x2 + x3 + x4 <= 19750
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0

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The ladder reaches approximately 26.11 feet up the wall.

What is trigonometric equations ?

Trigonometric equations are equations that involve trigonometric functions of one or more variables. The most common trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.

We can use trigonometry to solve this problem. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the distance we want to find is one leg, and the angle between the ground and the ladder is the angle opposite the leg we want to find. We can use the sine function to solve for the height h:

sin(65) = h/30

Multiplying both sides by 30, we get:

h = 30 * sin(65)

Using a calculator, we find:

h ≈ 26.11

Therefore, the ladder reaches approximately 26.11 feet up the wall.

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Answer:490

Step-by-step explanation:15 times 22 +120=490