After 12 hours, half of a 16-gram sample of a radioactive element remains. Find the constant k for this element for t hours, then write the equation for modeling its exponential decay

Answer:490

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

The cost of each of the items are calculated as:

Cost of pass = $14

Cost of souvenir = $10.5

Cost of burger = $1.75

Let us define the parameters first:

p = cost of pass

³/₄p = cost of souvenir (which is three quarters of the cost of the pass)

¹/₈p = cost of burger (multiply ³/₄p by ¹/₆)

all costs are in dollars

Adding p, ³/₄p, and ¹/₈p leads to

p + ³/₄p + ¹/₈p

(8p/8) + (6p/8) + (p)/8

(8p + 6p + p)/8

15p/8

This expression represents the total Sammy spent.

We know he started with $28.25 and has $2.00 left over, so he spent 28.25 - 2.00 = 26.25 dollars. Set this equal to 15p/8 and solve for p to get:

15p/8 = 26.25 dollars

15p = 8 * 26.25

15p = 210

p = 210/15

p = $14

³/₄p = cost of souvenir = ³/₄ * 14 = $10.5

¹/₈p = cost of burger = ¹/₈ * 14 = $1.75

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The probability that an arbitrarily chosen adult has an IQ higher than 132.7 is 0.0322, or roughly 3.22%.

Using a standard normal distribution table, we can find the z-score corresponding to an IQ of 132.7:

z = (132.7 - 100.3) / 17.6 = 1.84

The probability of a randomly selected adult having an IQ greater than 132.7 is equal to the area to the right of the z-score of 1.84 on the standard normal distribution curve:

P(Z > 1.84) = 0.0322 (rounded to four decimals)

Therefore, the probability of a randomly selected adult having an IQ greater than 132.7 is 0.0322 or about 3.22%.

The Value of first quartile Q1 is 91.2.

For the second part, we need to find the IQ score that separates the bottom 25% from the top 75%. Using a standard normal distribution table, we can find the z-score corresponding to the 25th percentile:

z = invNorm(0.25) = -0.6745

Now we can solve for the IQ score using the formula:

z = (x - μ) / σ

-0.6745 = (x - 101.8) / 15.7

x - 101.8 = -10.603

x = 91.197

Rounded to one decimal place, the first quartile Q1 is 91.2.

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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

31 is answer !!!!

Answer:

31

Step-by-step explanation:

180-35-23=122

180-122-27=31

It takes 8 blocks with a side length of 1/4 m to fill a rectangular prism with a volume of 1 m3.

The volume of a rectangular prism is calculated by the formula V = l * w * h, where l is the length, w is the width, and h is the height. To calculate the volume of a rectangular prism with 8 blocks (each with a side length of 1/4 m), we need to determine the length, width, and height of the rectangular prism.

Since each block has a side length of 1/4 m, the length, width, and height of the rectangular prism must be a multiple of that. Therefore, the length, width, and height of the rectangular prism must be 4/4 m, 8/4 m, and 8/4 m, respectively.

Substituting this into the formula, the volume of the rectangular prism is (4/4 m) * (8/4 m) * (8/4 m) = 64/64 m3 = 1 m3. Therefore, it takes 8 blocks with a side length of 1/4 m to fill a rectangular prism with a volume of 1 m3.

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There are 20 boys in the park.

Let's use b to denote the number of boys and g to denote the number of girls at the park prior to the arrival of 20 girls.

We can infer from the statistics provided that there are 3:1 more boys than girls when the first 20 girls arrive. This implies:

b/g = 3/1

By multiplying both sides of this ratio by g, we may make it simpler:

b = 3g

Then it is revealed that 20 more girls arrive, changing the ratio to 1:2. As a result, there are now 40 more persons (boys and girls) in the park overall.

Let's use B to stand for the number of boys in the park following the arrival of 20 girls, and G to stand for the number of girls in the park following the arrival of 20 girls.

After the 20 girls arrive, there are 1:2 more guys than girls, thus we know that:

B/G = 1/2

We also know that (b+20) + (g+20) = (B+G) is the total number of persons in the park once the 20 girls arrive.

To replace b in terms of g, we can utilise the first equation we arrived at as a replacement:

b = 3g

Hence, b+g = 3g+g+g = 4g individuals are present in the park overall prior to the arrival of the 20 girls.

After the 20 girls come, we may solve for the total number of individuals by substituting this expression for b+g into the equation:

(3g + 20) + (g + 20) = B + G

If we simplify, we get:

4g + 40 = B + G

So, in order to delete G from this equation, we can replace it with the second equation we derived:

4g + 40 = B + 2B

More simplification results in:

4g + 40 = 3B

When we multiply both sides by 3, we get:

g + 10 = B

Now, we may solve our first problem by substituting the following expression for B:

b/g = 3/1

3g/g = 3/1

3 = 3

We can see that the validity of the equations we derived is unaffected by the amount of g, thus we are free to use any value of g in our calculations. Let's select g=10 (since it makes the math easy).

The equation we previously derived can then be used to determine B:

g + 10 = B

10 + 10 = B

B = 20

20 boys are so present in the park.

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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]

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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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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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.

Tshering's claim is incorrect because the area is not trippled, but it is multiplied by a factor of 9

Given the the side length is

Side length, s = s

So, the area is

Area = s²

When the side length is trippled, we have

New side length, S = 3s

So, the area is

New area = (3s²)

New area = 9s²

Divide the new area by the initial area

Factor = 9s²/s²

So, we have

Factor = 9

This means that the area is multiplied by 9 and not tripled

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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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Answer:

sin57= 30/x

x= 30/sin57

x= 25.16

Step-by-step explanation:

Answer: 1/8

Step-by-step explanation:

The standard normal distribution table used in this course list the cumulative area under the standard normal curve to the left or right of a given z-score.

The standard normal distribution is a probability distribution, so the area under the curve between two points tells you the probability of variables taking on a range of values. Every z score has an associated p value that tells you the probability of all values below or above that z score occuring. The area under the normal curve is equal to 100% that is 1. Normal distributions area denser in the center and less dense in the tails. The z score is the test statistic used in a z test. The z test is used to compare the means of two groups, once you have a z score, you can look up the corresponding probability in a z table. In a z table, the area under the curve is reported for every z value between -4 and 4 at intervals of 0.01.

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In response to the given question, we can state that As a result, at the expressions same pace as automobile A, car B will go 262.5 kilometres in 2 hours and 30 minutes.

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.  

We can use the following formula:

distance = time x speed

We know the distance is 315 km and the time is 3 hours for automobile A. As a result, we can compute its speed as follows:

speed = distance / time = 315 kilometres / 3 hours = 105 kilometres per hour

So we know that car B has the same speed as automobile A, which is 105 km/h. Car B takes 2 hours and 30 minutes, which is comparable to 2.5 hours. Hence, we can apply the same procedure to calculate the distance travelled by automobile B:

Distance is speed multiplied by time = 105 km/h multiplied by 2.5 hours = 262.5 kilometres

As a result, at the same pace as automobile A, car B will go 262.5 kilometres in 2 hours and 30 minutes.

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The construction process for drawing a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measuring its length.

To construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm, follow the steps below:

Draw the two concentric circles with radii of 6 cm and 4 cm, respectively.

Mark a point on the outer circle, which will serve as the point of tangency.

Draw a line from the center of the circle to the point of tangency.

Draw a perpendicular line to the first line, passing through the point of tangency. This line will be the tangent line to the circle.

Measure the length of the tangent line using a ruler.

To verify the measurement of the tangent line, we can use the following formula:

Length of tangent line = sqrt(r^2 - d^2)

where r is the radius of the circle and d is the distance between the center of the circle and the point of tangency.

In this case, r = 4 cm and d = 6 cm - 4 cm = 2 cm.

Therefore, the length of the tangent line is:

sqrt(4^2 - 2^2) = sqrt(12) = 2sqrt(3) cm

Comparing this result with the measured length of the tangent line from the construction, we can see that they match, verifying the measurement.

Complete question:

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

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Answer:

14

Step-by-step explanation:

Answer:

I believe your answer would be 14

Answer: Sorry, I cannot provide visual aids or diagrams. However, I can help with the mathematical calculations and solutions to the given problems.

(a) To construct a trapezium WXYZ, follow the steps below:

Draw a straight line segment WX of length 10.2 cm and draw a line segment YZ of length 5.8 cm parallel to WX, such that the distance between them is 8.3 cm.

Draw a line segment XY of length 5.6 cm perpendicular to both WX and YZ, joining their endpoints.

From the endpoint Z, draw a perpendicular line segment ZN to WX.

Angle LWXY is given as 60°, so mark a point L on WX, such that angle WLY is 60°.

Therefore, the trapezium WXYZ is constructed.

(b) From the diagram, we can see that ZN is perpendicular to WX, so triangles ZWX and ZYN are similar.

Using the similar triangles ZWX and ZYN, we can write:

WX/WY = ZN/XY

10.2/5.6 = ZN/5.8

ZN = (10.2/5.6) * 5.8

ZN ≈ 10.57 cm

(c) Using Pythagoras' theorem, we can find the length of WZ:

WZ² = WX² - XZ²

WZ² = 10.2² - 8.3²

WZ ≈ 4.3 cm

Therefore, |WZ| ≈ 4.3 cm and |ZN| ≈ 10.57 cm.

(a) Let the width of the frame be w and the length be l. Then, according to the problem,

cost ∝ w * √l

cost = k * w * √l, where k is the constant of proportionality.

Using the given information, we can find the value of k as follows:

N115 = k * 10 * √25

k = N115 / 50

k = N2.3

Therefore, the law of variation is cost = N2.3 * w * √l.

(b) For a frame of width 12 cm and length 49 cm,

cost = N2.3 * 12 * √49

cost = N2.3 * 12 * 7

cost = N193.2

(a) Since the range R = {2, 5, 10}, we know that f(x) can take only these three values. Therefore,

x² + 1 = 2 or x² + 1 = 5 or x² + 1 = 10

Solving each of these equations for x, we get:

x = ±√1 or x = ±√4 or x = ±√9

x = ±1 or x = ±2 or x = ±3

Therefore, the domain D = {-3, -2, -1, 1, 2, 3}.

To find f-¹(5), we need to find the values of x for which f(x) = 5. From the equation x² + 1 = 5, we get:

x² = 4

x = ±2

Therefore, f-¹(5) = {-2, 2}.

Step-by-step explanation:

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:

3.7 miles

Step-by-step explanation:

Answer:3.7

Step-by-step explanation:

Answer:

C, D and E

Step-by-step explanation:

2(4f+2g)

8f+4g

so it's C, D and E

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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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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(Sum of the two dice is not 10 and not 7) = 1 - P(3, 4) - P(4, 3) - P(5, 2) - P(2, 5)= 1 - (2/36) - (2/36) - (4/36) - (4/36)= 20/36.

In the rolling of two fair dice, the following probabilities are calculated: P(Sum of the two dice is 8) = 5/36P(Sum of the two dice is 6) = 5/36P(Sum of the two dice is not 4) = 33/36P(Sum of the two dice is 5 or 9) = 10/36P(Sum of the two dice is not 10 and not 7) = 20/36

Note: We can earn partial credit on this problem. We have attempted this problem 0 times. We have unlimited attempts remaining.The step-by-step explanation of how these probabilities are calculated is given below:P(Sum of the two dice is 8) = P(2, 6) + P(3, 5) + P(4, 4) + P(5, 3) + P(6, 2)= (1/36) + (2/36) + (1/36) + (2/36) + (1/36)= 5/36P(Sum of the two dice is 6) = P(1, 5) + P(2, 4) + P(3, 3) + P(4, 2) + P(5, 1)= (1/36) + (1/36) + (1/36) + (1/36) + (1/36)= 5/36P(Sum of the two dice is not 4) = 1 - P(1, 3) - P(2, 2) - P(3, 1)= 1 - (1/36) - (1/36) - (1/36)= 33/36P(Sum of the two dice is 5 or 9) = P(1, 4) + P(2, 3) + P(3, 2) + P(4, 1) + P(3, 6) + P(4, 5) + P(5, 4) + P(6, 3)= (1/36) + (2/36) + (2/36) + (1/36) + (2/36) + (1/36) + (1/36) + (2/36)= 10/36P(Sum of the two dice is not 10 and not 7) = 1 - P(3, 4) - P(4, 3) - P(5, 2) - P(2, 5)= 1 - (2/36) - (2/36) - (4/36) - (4/36)= 20/36.

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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 total area of the painting and frame is 248 inches squared.

Area is the size of a two-dimensional surface, typically defined by its length and width. It is an important concept in mathematics and is used to measure different shapes and figures. Area is also commonly used to measure the size of land, such as a city block or a region of a country. Areas can be measured in square meters, square kilometers, hectares, square feet, and many other units. Knowing the area of a shape or space can be helpful when planning a project or understanding how much space something requires.

Using the given equation, f(x) = x2 + 14x + 40, we can solve for the area of the painting and frame.

f(x) = x2 + 14x + 40
f(x) = (x + 6)2 + 2(x + 6)(2) + 2(2)(2)
f(x) = x2 + 12x + 36 + 4x + 24 + 16
f(x) = x2 + 16x + 56

We are told that the longer side of the frame is 14 inches long, so x = 8.

f(8) = 8^2 + 16(8) + 56
f(8) = 64 + 128 + 56
f(8) = 248 in.2

Therefore, the total area of the painting and frame is 248 inches squared.

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arcST and arcRPT of the given circle are measured at 55 and 208 degrees, respectively.

What is circle?

Every point in a plane that is at a certain distance from the center point forms a circle. In order to go around a curve while maintaining a constant distance from another point, a moving point in a plane must follow a specific path.

The following expression will be used to determine the length of the arc ST:

arcPS = arcPT + arcST

Already given,

• arcPT = 125 degrees

• arc PS = 180 degrees

Putting the value in equation

arcST = arcPS - arcPT

arcST = 180  - 125

arcST = 55 degrees

Following the same steps we can get

arcPR = 180 - arcRS

arcPR = 180 - 97

arcPR = 83 degrees

and also

arcRPT = arcPR + arcPT

arcRPT = 83 + 125

arcRPT = 208 degrees

Hence the measurement of arcST and arcRPT are 55 and 208 degree respectively.

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