Find the maximum value of the objective function and the values of x and y for which it occurs.
F=5x+2y
x+2y<6. x>0 and y>0
2x+y<6

The first mechanic wοrked fοr 10 hοurs, and the secοnd mechanic wοrked fοr 15 - 10 = 5 hοurs.

Let x be the number οf hοurs the first mechanic wοrked, then the number οf hοurs the secοnd mechanic wοrked wοuld be (15 - x).

The tοtal cοst οf the first mechanic wοuld be 65x, and the tοtal cοst οf the secοnd mechanic wοuld be 45(15 - x) = 675 - 45x.

Tοgether, their tοtal cοst wοuld be 65x + (675 - 45x) = 20x + 675.

We knοw that their tοtal cοst was $875, sο we can set up the equatiοn:

20x + 675 = 875

Subtracting 675 frοm bοth sides, we get: 20x = 200

Dividing bοth sides by 20, we get: x = 10

Therefοre, the first mechanic wοrked fοr 10 hοurs, and the secοnd mechanic wοrked fοr 15 - 10 = 5 hοurs .

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Gabe or Gabriel is a new child in the novel, "The Giver" and was described as a symbol of hope and new beginnings.

As a new child, Gabe is not yet fully indoctrinated into the rules and customs of the community, making him more open to the memories transmitted by Jonas.

This presentation of Gabe's character aligns with the novel's recurring motif of babies symbolizing hope and regeneration in literature.

The novel "The Giver" was authored by Lois Lowry. It is set in a futuristic society that has eliminated all pain, fear, war, and hatred and appears to be utopian at first glance.

The story is written from the point of view of Jonas, an eleven-year-old boy, selected to be the new Receiver of Memory.

Through training, Jonas learns about the joys and pains of life and becomes increasingly disillusioned with the society he lives in.

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Answer:

n=15.1

Step-by-step explanation:

14.8=n-0.3

14.8+0.3=n

15.1=n

Answer:

x=120 and y=60

Step-by-step explanation:

As we know, a straight line is 180 degrees.

To find x, you would do 180= 60 + x to get 120.

I forget how but I know y= 60 because its the same angle as 60 degrees.

The expression −25(y-x) can be expanded by multiplying -25 to each term inside the parentheses:

-25(y - x) = -25y + 25x

Therefore, the expanded form of the expression is -25y + 25x.

The probability of getting exactly one tail would be = 1/2

Probability can be defined as the possibility of an event occuring or an outcome of an event.

The number of time the fair coin was tossed = 2 times

From the sample space, the total number of samples = 4.

The number of single heads = 2

The probability of getting a single head (H) = 2/4 = 1/2

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Answer:

Decimal: 0.25

Fraction: 1/4

Step-by-step explanation:

2 / 3 * 3/8

2/3 X* 3/8

=  

2 × 3

3 × 8

=  

6/ 24

=  

6 ÷ 6

24 ÷ 6

=  

1/4

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ΔTUV is not congruent to ΔT'U'V', as the transformation involved a rotation and translation, but they have similarities.

ΔABC and ΔDEF have the same angles but different side lengths, so they are similar but not congruent triangles.

What are the similarities?

The situations that describe similar but not congruent triangles are given below:

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Part 1: Triangles are similar by Side-Side-Side similarity.

Part 2: Triangles are similar angle-Angle (AA) similarity.

Part 1: Ratios must be equal for triangle similarity.

Taking the ratios of the sides:

17/37.4  = 20/44 = 25/55

On solving

0.4545 = 0.4545 = 0.4545

As the ratios are equal, triangles are similar.by Side-Side-Side similarity.

Part 2:

∠F = ∠H (given)

∠EGF = ∠JGH (vertically opposite)

By Angle-Angle (AA) similarity.

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The correct question is 1 and 2.

The probability that at least nine flashlights will work is 0.3874 or 0.387 to three decimal places.

Given: A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages.

Suppose that 90% of all batteries from a certain supplier have acceptable voltages. Among ten randomly selected flashlights,

Let p be the probability that any single battery has an acceptable voltage.

Let X be the number of flashlights out of 10 that work.

Then X has a binomial distribution with n=10 and p=0.9.

The probability that at least nine of the ten flashlights work is P(X≥9).

We have

[tex]P(X=9)= 10C_9 \times 0.9⁹ \times 0.1 = 0.3874

P(X=10)= 10C_10 \times 0.9¹⁰ \times 0 = 0[/tex]

P(X≥9)  = P(X=9) + P(X=10)

            = 0.3874 + 0

            = 0.3874

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(a)   1

(b)  0.3

(c)  0.15
(d)  0.27

(a) The cumulative probability distribution of the random variable X for the year 2020 is:
X = 0, P(X<=0) = 0.2
X = 1, P(X<=1) = 0.6
X = 2, P(X<=2) = 0.9
X = 3, P(X<=3) = 1
Graph:


(b) P(1 ≤ X < 3) = P(X<=2) - P(X<=1) = 0.9 - 0.6 = 0.3

(c) The joint probability distribution of the variables X and Y for the year 2020 is:
X = 0, Y = 0, P(X=0, Y=0) = 0.15
X = 0, Y = 1, P(X=0, Y=1) = 0.25
X = 0, Y = 2, P(X=0, Y=2) = 0.05
X = 1, Y = 0, P(X=1, Y=0) = 0.2
X = 1, Y = 1, P(X=1, Y=1) = 0.4
X = 1, Y = 2, P(X=1, Y=2) = 0.2
X = 2, Y = 0, P(X=2, Y=0) = 0.3
X = 2, Y = 1, P(X=2, Y=1) = 0.3
X = 2, Y = 2, P(X=2, Y=2) = 0.2
X = 3, Y = 0, P(X=3, Y=0) = 0.15
X = 3, Y = 1, P(X=3, Y=1) = 0.15
X = 3, Y = 2, P(X=3, Y=2) = 0.15

(d) Treating the answer from question 3(c) as the joint probability distribution in the population, the correlation between X and Y is 0.27.

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Where the above H0 : p1 = 0.65, p2 = 0.70, p3 = 0.75, note that there is not sufficient evidence to conclude that the proportion of adherence differs between the age groups at the 0.05 level of significance.

Level of significance is the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05 or 0.01, indicating a 5% or 1% chance of a Type I error, respectively.

To test whether there is sufficient evidence to reject the null hypothesis, we can use the χ2 goodness of fit test. The null hypothesis is that the proportion of adherence is the same in each age group, with p1 = 0.65, p2 = 0.70, and p3 = 0.75.

The alternative hypothesis is that the proportion of adherence is different in at least one of the age groups.

To apply the χ2 goodness of fit test, we need to calculate the expected frequencies for each age group under the null hypothesis.

The expected frequency for each group is the total sample size (100) times the hypothesized proportion of adherence for that group. Therefore, the expected frequencies for each age group are:

Young: 100 * 0.65 = 65

Medium: 100 * 0.70 = 70

Old: 100 * 0.75 = 75


We can now calculate the test statistic χ2 by summing over the three age groups the squared difference between the observed and expected frequencies divided by the expected frequency:

χ² = ((0.64-65)²/65) + ((0.68-70)²/70) + ((0.70-75)²/75)

= 1.81

The degrees of freedom for the χ2 goodness of fit test are the number of categories minus one, which in this case is 3 - 1 = 2. Using a chi-square distribution table with 2 degrees of freedom and a significance level of 0.05, we find the critical value to be 5.99.

Since the calculated χ2 value of 1.81 is less than the critical value of 5.99, we fail to reject the null hypothesis.

Thus, there is not sufficient evidence to conclude that the proportion of adherence differs between the age groups at the 0.05 level of significance.

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Step-by-step explanation:

the acorn falls from the height of 25 feet above the ground, it means the initial time when it falls is t = 0. The time when it lands on the ground is t = 1.25

So the acorn was in the air for 1.25 seconds

Given that individual is a non-physics major, the probability of choosing a freshman is around [tex]0.2342[/tex].

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.

Calculating a result or the likelihood that an event would ever occur is known as simple probability. Probability statistics are used by insurance firms to calculate the likelihood of having to pay out using a claim. By dividing one possible outcome by all other possible possibilities, one may determine a basic probability.

P(Non-Physics Major) [tex]= (19+19+17+12) / 122 = 0.7049[/tex]

P(Freshman) [tex]= (15+19) / 122 = 0.2951[/tex]

P(Non-Physics Major / Freshman) [tex]= 19 / (15+19) = 0.5588[/tex]

All of these values may now be entered into Bayes' theorem:

P(Freshman / Non-Physics Major)[tex]= 0.5588 * 0.2951 / 0.7049 ≈ 0.2342[/tex]

Therefore, the probability of selecting a freshman given that the student is a non-physics major is approximately [tex]0.2342[/tex].

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Answer:

New naira note scarcity

The value of [tex]\( \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right] \)[/tex] is:
[tex]\ln \sqrt{x^{3}} - \ln \left(2 \cdot \sqrt[3]{(4 x+1)^{7}}\right)\][/tex]

To find the value of \[tex]( \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right] \)[/tex], we can use the following steps:

1. Factor out [tex]\( \left(x^{3}-2\right)^5 \)[/tex]:
[tex]\[ \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right][/tex] = [tex]ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}}{1}\right]\][/tex]

2. Use the product rule for logs:
[tex]\[ \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}}{1}\right] = \ln \left(x^{3}-2\right)^5 + \ln \left(\frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right)\][/tex]

3. Evaluate each logarithm separately:
[tex]\[ \ln \left(x^{3}-2\right)^5 = 5\ln \left(x^{3}-2\right) \]\[ \ln \left(\frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right)[/tex] = [tex]\ln \sqrt{x^{3}} - \ln \left(2 \cdot \sqrt[3]{(4 x+1)^{7}}\right)\][/tex]

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For the given figure, the area of the shaded region is obtained as 100 m².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of shaded region can be obtained as -

Area of shaded region =  Area of rectangular concrete path - Area of rectangular lawn

The formula for area of rectangle is -

Area of rectangle  =  Length × width

The area of rectangular concrete path is -

Length  =  (30+2) m  =  32 m

width  =  (18+2) m  =  20 m

Area of rectangular concrete path  =  32 × 20

Area of rectangular concrete path  =  640 m²------(1)

The area of rectangular lawn is -

Length  =  30 m and width  =  18 m

Area of rectangular lawn  =  30 × 10

Area of rectangular lawn  =  540 m²------(2)

To find the are of shaded region subtract equation (2) from (1) =

Area of shaded region = (1) - (2)

Area of shaded region =  (640 – 540) m²

Area of shaded region =  100 m²

Therefore, the total area of concrete is 100 m².

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A rectangular lawn 18 m by 30 m is surrounded by a concrete path 1 m wide. Draw a diagram of the situation and find the total area of concrete.

The probability that the battery lasts less than 25 hours is 0.3446.

The probability of P(Z > -1.5) is 0.9332. The value of -1.5 has to be positive for this computation because the normal distribution curve is symmetrical about the z = 0 line. The probability of being at z = -1.5 is the same as being at z = +1.5. Thus, the probability is found by referencing the z-table for the area under the curve to the right of the mean: 0.9332.

The probability of P(Z < 1.15) is 0.8749. The area below z = 1.15 is needed for this calculation. The probability that the standard normal random variable is less than 1.15 is 0.8749.iii) The probability of P(Z > 0.35) is 0.3632. The area under the curve to the right of the mean is needed. The probability that the standard normal random variable is greater than 0.35 is 0.3632.

Given that, the amount of time the battery lasts in a toy racing car is normally distributed with a mean of 26 hours and a standard deviation of 2.5 hours. Let X denote the time a battery lasts, which is a normally distributed random variable. Find the following probabilities:a) P(25 < X < 29)To calculate the probability,

we first standardize the values of 25 and 29 using the formula below:

z1 = (25 - 26) / 2.5 = -0.4 and z2 = (29 - 26) / 2.5 = 1.2 Now, we find the probability as shown:P(-0.4 < Z < 1.2) = P(Z < 1.2) - P(Z < -0.4) = 0.8849 - 0.3446 = 0.5403 Thus, the probability that the battery lasts between 25 and 29 hours is 0.5403.b) P(X > 29)

To find the probability, we first standardize the value of 29 using the formula below:z = (29 - 26) / 2.5 = 1.2 Now, we find the probability as shown:P(Z > 1.2) = 1 - P(Z < 1.2) = 1 - 0.8849 = 0.1151 Thus, the probability that the battery lasts longer than 29 hours is 0.1151.c) P(X < 25)To find the probability, we first standardize the value of 25 using the formula below:z = (25 - 26) / 2.5 = -0.4 Now, we find the probability as shown:P(Z < -0.4) = 0.3446

Thus, the probability that the battery lasts less than 25 hours is 0.3446.

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Two of the following statements about the results of a screening test are correct are:

a. Sensitivity is the proportion of people who fail the screening test who are aspirators, and

d. Specificity is the proportion of people who pass the screening test who are not aspirators.

Option A: Sensitivity is the proportion of people who fail the screening test who are aspirators

The sensitivity is the proportion of people who fail the screening test and who are actually sick. Sensitivity is the proportion of people who have the disease who test positive in the screening test. Sensitivity, in other words, is the test's capacity to recognize the condition. Sensitivity is calculated as follows: True positive / (True positive + False negative).

Option D: Specificity is the proportion of people who pass the screening test who are not aspirators

Specificity is the proportion of people who pass the screening test and who are actually not sick. Specificity is the proportion of people who are healthy who test negative in the screening test. Specificity, in other words, is the test's capacity to correctly identify non-sick persons. Specificity is calculated as follows: True negative / (True negative + False positive).

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A circular park of radius 14 m has a road of 7 m width all around on its outside then the  area of the road is approximately 153.943 square meters.

The circular park has a radius of 14 m. This means that the diameter of the park is 2 x 14 = 28 m. The road around the park has a width of 7 m. This means that the total width of the park and the road is 28 + 7 + 7 = 42 m. The area of the circular park can be found using the formula for the area of a circle: Area of park =[tex]π x r^2 = π x 14^2 = 615.752 m^2[/tex] (rounded to 3 decimal places)

The area of the park and the road can be found by calculating the area of the larger circle and subtracting the area of the park: Area of park and road =[tex]π x (r+7)^2 - π x r^2 = π x (14+7)^2 - π x 14^2 = π x 21^2 - π x 14^2 = π x (441 - 196) = π x 245 = 769.695 m^2[/tex] (rounded to 3 decimal places)

To find the area of just the road, we need to subtract the area of the park from the area of the park and road: Area of road = Area of park and road - Area of park = 769.695 - 615.752 =[tex]153.943 m^2[/tex] (rounded to 3 decimal places)

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The answer is d. While it is possible for a parallelogram to be a square, it is not a valid conclusion given only the information that ABCD is a parallelogram and has diagonals AB and BD.

A parallelogram is a four-sided plane figure with two pairs of parallel and equal sides. Opposite sides of a parallelogram are of equal length and the opposite angles are of equal measure. The area of a parallelogram is determined by multiplying the length of one side with the height of the parallelogram. Parallelograms are quadrilaterals, which means they have four sides, and are classified by their angles and sides.

To determine if the parallelogram is also a square, additional information such as the length of the sides or angles of the parallelogram would need to be known.

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Complete questions as follows-

Which of the following is not a valid conclusion given parallelogram ABCD with diagonals AB and BD?
a
AB=CD
b
AC=BD
c
d
m

By using the "acosd" function in MATLAB, you can easily calculate the angles of obtuse triangles in real-life objects.

The shapes of obtuse triangles occur in real-life objects such as kites and architectural designs. An obtuse triangle is a type of triangle that has one obtuse angle, which means that one of its angles is greater than 90 degrees.

These types of triangles can be seen in many real-life objects, such as kites, which often have an obtuse angle at the top where the two sides of the kite meet. Similarly, architectural designs often include obtuse angles in order to create unique and interesting shapes.

In terms of using MATLAB to calculate the angles of an obtuse triangle, you can use the "acosd" function to calculate the angle in degrees. For example, if you have a triangle with sides of length 3, 4, and 5, you can use the following code to calculate the angle between the sides of length 3 and 4:

angle = acosd((3^2 + 4^2 - 5^2)/(2*3*4));

This will give you an angle of 90 degrees, which is a right angle. However, if you change the lengths of the sides to create an obtuse triangle, such as a triangle with sides of length 3, 4, and 6, you can use the same code to calculate the obtuse angle:

angle = acosd((3^2 + 4^2 - 6^2)/(2*3*4));

This will give you an angle of approximately 98.13 degrees, which is an obtuse angle. By using the "acosd" function in MATLAB, you can easily calculate the angles of obtuse triangles in real-life objects.

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The statement "Two chords in the same circle are congruent if and only if the associated central angles are supplementary" is false because  two chords in the same circle are congruent if and only if they are equidistant from the center of the circle

Two chords in the same circle are congruent if and only if they are equidistant from the center of the circle. However, two chords having associated central angles that are supplementary will always be equal in length only if the chords are diameters of the circle.

For any other pair of chords with supplementary central angles, their lengths will depend on their distance from the center of the circle. Therefore, the statement "Two chords in the same circle are congruent if and only if the associated central angles are supplementary" is not true in general.

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The equatiοn that represents the given ellipse is[tex](x-6)^2 /49 + (y-2)^2 / 9 = 1[/tex].

This is because the equatiοn οf an ellipse with centre (h, k), hοrizοntal axis length 2a, and vertical axis length 2b are given by:

[tex](x-h)^2 / a^2 + (y-k)^2 / b^2 = 1[/tex]

In this case, the centre οf the ellipse is (6, 2), the hοrizοntal axis length is 2 * 7 = 14, and the vertical axis length is 2 * 3 = 6. Therefοre, we have:

a = 7, b = 3, h = 6, k = 2

Substituting these values intο the general equatiοn οf an ellipse, we get:

[tex](x-6)^2 / 7^2 + (y-2)^2 / 3^2 = 1[/tex]

Simplifying this equatiοn, we get:

[tex](x-6)^2 /49 + (y-2)^2 / 9 = 1[/tex]

Therefοre, the equatiοn that represents the given ellipse is[tex](x-6)^2 /49 + (y-2)^2 / 9 = 1.[/tex]

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Answer:

The answer is A on edge :)

Step-by-step explanation:

goodluck <3

Answer:

5 bags will cost 36.25

Step-by-step explanation:

We can use a proportion to solve. Put the price over the number of bags.

[tex]\dfrac{21.75}{3 \ bags} =\dfrac{x}{5 \ bags}[/tex]

Using cross products

[tex]21.75\times 5 = 3x[/tex]

[tex]108.75 = 3x[/tex]

Divide each side by 3

[tex]108.75\div3 = 3x\div3[/tex]

[tex]36.25 =x[/tex]

5 bags will cost 36.25

The starting price of the toys was $7.50.

What is addition?

Addition is a basic arithmetic operation that combines two or more numbers to get a sum or a total. It is represented by the "+" symbol. When we add numbers, we are finding the total amount when we combine them.

Let's assume the starting price of the toys as "x".

After the first hour, the price of the toys will be "x - 0.25".

After the second hour, the price of the toys will be "x - 0.25 - 0.25 = x - 0.5".

Similarly, after the third hour, the price of the toys will be "x - 0.75".

We can see that the price of the toys decreases by $0.25 every hour. So, after the 8th hour, the price of the toys will be:

x - (0.25 + 0.25 + 0.25 + 0.25 + 0.25 + 0.25 + 0.25 + 0.25)

= x - (8 x 0.25)

= x - 2

We know that after the 8th hour, the price of the toys is $5.50. So we can write:

x - 2 = 5.50

Adding 2 to both sides:

x = 7.50

Therefore, the starting price of the toys was $7.50.

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The area οf οnly the frame is apprοximately 50.27 square inches.

The area οf a circle is the amοunt οf surface inside the bοundary οf a circle. It is a measure οf hοw much space the circle takes up in twο-dimensiοnal space. The fοrmula tο calculate the area οf a circle is:

[tex]A = \pi r^2[/tex]

where A is the area οf the circle and r is the radius οf the circle.

The diameter οf the mirrοr with the frame is 17 inches, and the diameter οf οnly the mirrοr (withοut the frame) is 15 inches.

Therefοre, the width οf the frame is:

17 inches (diameter οf mirrοr with frame) - 15 inches (diameter οf οnly mirrοr) = 2 inches

Sο the radius οf the mirrοr withοut the frame is:

r₁= (15 inches / 2) = 7.5 inches

The area οf the mirrοr withοut the frame is:

A₁= π(7.5)² square inches ≈ 176.71 square inches

The radius οf the mirrοr with the frame is:

r₂= (17 inches / 2) = 8.5 inches

The area οf the mirrοr with the frame is:

A₂= π(8.5)² square inches ≈ 226.98 square inches

The area οf οnly the frame is the difference between these twο areas:

=A₂-A₁

=π(8.5)²- π(7.5)² square inches

≈ 50.27 square inches

Therefοre, the area οf οnly the frame is apprοximately 50.27 square inches.

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By answering the presented question, we may conclude that Kayden surface area used 116.4 square centimeters of wrapping paper as a result.

The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional form (a three-dimensional shape is a shape that has height, width, and depth).

Then, we must establish the size of the pyramid's square base. The net shows that the base has a side length of 6 cm.

sqrt((5.7 cm)2 + (3 cm)2) = 6.7 cm slant height (rounded to one decimal place)

Each triangle face has the following area:

(1/2) x width x height

(half) × 6 cm x 6.7 cm

= 20.1 cm2 4 times 20.1 cm2 = 80.4 cm2

The area of the square face is:

6 cm × 6 cm = 36 cm2 side x side

As a result, the total surface area of the net (together with the amount of wrapping paper used by Kayden) is:

80.4 cm2 plus 36 cm2 equals 116.4 cm2.

Kayden used 116.4 square centimeters of wrapping paper as a result.

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