The equation of the dilated line is 9x + 15y = 10.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object or equation based on a specific scale factor of 3 is given by this mathematical expression:
(x, y) → (SFx, SFy)
Where:
x and y represents the data points.SF represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (3x, 3y)
3(3x + 5y) = 10
9x + 15y = 10.
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The volume of a cone is 109.95 cubic inches and the height is 4.2 inches. What is the radius of the cone?
The calculated radius of the cone is 5 inches
What is the radius of the cone?From the question, we have the following parameters that can be used in our computation:
Volume = 109.95 cubic inches
Height = 4.2 inches.
The volume is calculated as
V = 1/3 * 3.14 * r^2h
So, we have
1/3 * 3.14 * r^2 * 4.2 = 109.95
So, we have
r^2 = 3 * 109.95/(4.2 * 3.14)
So, we have
r^2 = 25.01
Take the square roots
r = 5
Hence, the radius is 5 inches
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The function f(x) = 1.85x^2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answer:
I helped you last time so I'll help you again.
Step-by-step explanation:
We can find the average rate of change of f(x) over the interval [10, 20] using the formula:
average rate of change = (f(b) - f(a))/(b - a)
where a = 10 and b = 20.
So, we have:
f(a) = f(10) = 1.85(10)^2 = 185
f(b) = f(20) = 1.85(20)^2 = 740
average rate of change = (740 - 185)/(20 - 10) ≈ 55.5
Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.
Find the tangent of the smaller acute angle in a right triangle with side lengths 8, 15, and 17
Answer: the tangent of the smaller acute angle in this right triangle is 8/15.
Step-by-step explanation:
Since the side lengths of the correct triangle are given as 8, 15, and 17, able to see that the sides with lengths 8 and 15 are the legs of the proper triangle, and the side with length 17 is the hypotenuse.
We know that the littler intense point θ is inverse the shorter leg of length 8. Hence, the digression of θ is:
tan(θ) = opposite/adjacent = 8/15
3 dependent events. A bag contains ten balls. Six of the balls are green. A ball is chosen at random. The ball is replaced and then a second ball is chosen at random. Work out the probability that: a)both balls are green b)neither ball is green
The Probability of both balls being green is 0.36 or 36%
b) The Probability of neither ball being green is 0.16 or 16%
What is the Probability about?Based on question A, To find the probability that both balls are green, we use the equation below:
P (both green) = P (first green) x P (second green)
= (6/10) x (6/10)
= 36/100
= 9/25
=0.36
b) To find the probability that neither ball is green, we use the formula below:
P (neither green) = P (first not green) x P (second not green)
= (4/10) x (4/10)
= 16/100
= 4/25
=0.16.
Therefore, the statement will be: The Probability of both balls being green: 0.36 and the probability of neither ball being green is 0.16
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picture look in the picture
Answer:
The measure of angle E is 56°.
Dingaka receives R12650R12650 when taking out a loan with an annual simple discount rate of 12,5%12,5%. The loan has to be repaid in eight months’ time. The amount that he has to repay is?
Dingaka took out a loan of R12650 with a simple annual discount rate of 12.5%. He has to repay R11595.83 in eight months, after deducting the simple discount of R1054.17.
To find the amount that Dingaka has to repay, we can use the formula for simple discount
Simple Discount = Principal * Rate * Time
Where Principal is the original amount borrowed, Rate is the annual simple discount rate, and Time is the time period in years.
We know that Dingaka received R12650 as the principal amount and the annual simple discount rate is 12.5%, which is equivalent to 0.125 as a decimal. The time period is 8/12 = 2/3 years, since the loan has to be repaid in eight months' time.
Plugging these values into the formula, we get
Simple Discount = 12650 * 0.125 * 2/3
= 12650 * 0.08333333
= 1054.166625
Therefore, the amount that Dingaka has to repay is the principal minus the simple discount, which is
Amount to Repay = Principal - Simple Discount
= 12650 - 1054.166625
= 11595.833375
So, Dingaka has to repay R11595.83 after eight months.
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Match these values of r with the accompanying scatterplots:
−0.405,
−0.998,
−1,
−0.743,
and
0.743.
The matching table is given in the image below:
What is a Scatter Plot?A scatter plot, an undeniably essential chart for visualizing the correlation between two variables, is constructed by putting one variable on the x-axis and another one alongside the y-axis, with each individual data point symbolizing both associated values.
Scatter plots are not only indispensable when inspecting trends and peculiarities in a given set of data but can likewise be applied to examine the relationship or link between the two components.
Essentially imperative to fields such as economics, engineering, and statistics, these diagrams are efficiently drawn up through popular software applications like Excel or Python.
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QUESTION ONE
(a) If the mean of five values is64, find the sum of the values
(b) If the mean of five values is 8.2 and four of the values are 6, 10, 7, and 12, find the fifth vaue.
(c) Find the mean of 10, 20, 30, 40, and 50.
i) Add 10 to each value and find the mean.
ii) Subtract 10 from each value and find the mean.
iii) Multiply each value by 10 and find the mean.
iv) Divideeach value by 10 and find the mean.
v) Make a general statement about each situation.
QUESTION TWO
a)Find the mean deviation for these data. 5, 9, 10, 11, 11, 12, 15, 18, 20, 22
b)The mean marks in statistics of 100 students in a class was 72 per cent. The mean marks of boys
was 75 per cent, while their number was 70 per cent. Find outthe mean marks of girls in the
cass.
c)The weighted geometric mean of the four numbers 20, 18, 12, and 4 is 11.75. If the weights of
the first three numbers are 1, 3, and 4, respectivey, find the weight of the fourth number
QUESTION THREE
a)For a group of 50 male workers, the mean and standard deviation of their monthly wages
are $6300 and $900 respectively. For a group of 40 female workers, these are $ 5400 and $
600 respectively. Find the standard deviation of monthly wages for the combined group of
workers.
b)A study of the age of 100 persons grouped into intervals 20–22, 22–24, 24–26..., revealed
the mean age and standard deviation to be 32.02 and 13.18 respectivey. While checking it
was discovered that the observation 57 was misread as 27. Cacuate the correct mean age and standard deviation
QUESTION FOUR
The weekly sales of two products A and B were recorded as given below:
Product A : 59 75 27 63 27 28 56
Product B : 150 200 125 310 330 250 225
Find out which of the two shows greater fluctuation in sales
(a) Sum of values = Mean × Number of values = 64 × 5 = 320
(b) Sum of values = Mean × Number of values = 8.2 × 5 = 41
Fifth value = Sum of values - sum of known values = 41 - (6 + 10 + 7 + 12) = 41 - 35 = 6
How to solve(c) The resulting middle number when computing 10, 20, 30, 40, 50;that is (10 + 20 + 30 + 40 + 50)/5, totals up to 150 and dividing that number by 5 reflects a mean of 30.
i) Forming an average of 20, 30, 40, 50, 60;that is (20 + 30 + 40 + 50 + 60)/5 provides an outcome of 200 and divided by 5 reveals a mean of 40.
ii) With 0, 10, 20, 30, 40 used, (0 + 10 + 20 + 30 + 40)/5 practices calculation yielding a total of 100 which, split into five parties, imparts a mean of 20.
iii) Taking into consideration the input of 100, 200, 300, 400, 500;whereby (100 + 200 + 300 + 400 + 500)/5 develops a collective of 1500, cut in half produces a mean of 300.
iv) Calculating 1, 2, 3, 4, 5's mean; namely (1 + 2 + 3 + 4 + 5)/5 ascertains a collective amount of 15, divide that figure by five culminates with a mean of 3.
v) Accordingly, the following general assumptions can be made:
i) Introducing a constant to each value augments the mean by that very same constant.
ii) Extracting a constant from all values decrements the mean by such said constant.
iii) Multiplying every value by one constant multiplies the mean by the same specific constant.
iv) Dividing all values by a particular constant divides the mean by that given constant.
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please tell methe cords of the answer
Answer:
(- 2, - 4 )
Step-by-step explanation:
4x - 3y = = 4 → (1)
3x + 3y = - 18 → (2)
adding the equations term by term will eliminate y
(4x + 3x) + (- 3y + 3y) = 4 - 18
7x + 0 = - 14
7x = - 14 ( divide both sides by 7 )
x = - 2
substitute x = - 2 into either of the 2 equations and solve for y
substituting into (2)
3(- 2) + 3y = - 18
- 6 + 3y = - 18 ( add 6 to both sides )
3y = - 12 ( divide both sides by 3 )
y = - 4
solution is (- 2, - 4 )
b) Find the value of w. Sive each answer as an integer or as a fraction in its simplest form 4 cm A 7 cm 12 cm 3 cm B W cm 9 cm
The calculated value of w from the similar triangles is 21/4
Calculating the value of wFrom the question, we have the following parameters that can be used in our computation:
Similar triangles A and B
Also from the similar triangles, we have the following proportional relation
4 7 12
3 W 9
Using the above as a guide, we have the following equation
4/3 = 7/W = 12/9
So, we have
W * 12 = 7 * 9
Evaluate the products and divide both sides by 12
W = 21/4
Hence, the value of W is 21/4
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HELP ME ASAP PLS. If 19,432 divided by x equals 48 with a remainder of 232. What is X?
The value of x, given that when it divides a number, there is a quotient and a remainder, is 400
How to find the value of x?To find the value of divisor, we can use a variant of the division algorithm formula :
Divisor = ( Dividend - Remainder ) / Quotient
x is the divisor
Dividend = 19, 432
Remainder = 232
Quotient = 48
This means that the value of x is:
x = ( 19, 432 - 232 ) / 48
x = 19, 200 / 48
x = 400
In conclusion, x is 400.
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Hurry up please (time limit)
State the domain and range and tell if the graph is a function yes or no?
What’s the domain and range?
The graph in this problem is not a function, as it contains vertically aligned points.
The domain and the range are given as follows:
Domain: -3 ≤ x ≤ 3.Range: 1 ≤ y ≤ 3.When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.
When we trace a vertical line through the circle, it would cross the circle at two points, meaning that the graph contains vertically aligned points, and thus, is not a function.
The domain and the range are defined as follows:
Domain: -3 ≤ x ≤ 3. -> values of x on the graph.Range: 1 ≤ y ≤ 3. -> values of y on the graph.More can be learned about graphs and functions at https://brainly.com/question/12463448
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Please help me solve questions 14,15, & 16.
=================================================
Explanation for problem 14
There are 4 aces and 4 copies of "9".
4+4 = 8 cards we want to select out of 52 total
8/52 = (4*2)/(4*13) = 2/13 which points to choice D as the final answer
---------------
Explanation for problem 15
4 kings gives a probability of 4/52 = 1/13.
After the king is chosen, there are 52-1 = 51 cards left since we aren't replacing it. The probability of getting a queen on the second selection is 4/51
(1/13)*(4/51) = 4/663 is the probability of a king, then a queen, with no replacement. We arrive at choice C as the final answer.
----------------
Explanation for problem 16
face card = picture card
face card = Jack, Queen, King
aces are not considered a face card
3*4 = 12 face cards in total
A = 12/52 = (4*3)/(4*13) = 3/13 is the probability of selecting a face card.
That card is then put back (aka replacement) and we still have 52 cards in the deck. We don't drop down to 51.
13 hearts ---> B = 13/52 = 1/4 is the probability of getting a heart
A*B = (3/13)*(1/4) = 3/52 is the probability of getting a face card, then a heart, when replacement is done. The final answer is choice B
What is the meaning of "the equation ax = b has a solution for every b ∈ H"?
In the given image, H is a non-empty set of complex numbers, a and b are complex numbers, and x is a variable.
"The equation ax = b has a solution for every b ∈ H" means that for any complex number b in the set H, there exists a complex number x such that the product of a and x is equal to b.
In other words, for every numbers of b in H, there exists a solution for x that satisfies the equation ax = b.
This statement has important implications in linear algebra and functional analysis, where it is used to define the concept of a surjective linear transformation in numbers. It also has applications in many areas of mathematics and science, including engineering, physics, and computer science.
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Using the picture, give the term that best describes
each of the following.
C.
1.
E
D
B
G
F
H
BC
3. DH
4. EH 5. OG 6. GF
7. B
2. Term not applicable to this diagram
The labelled parts are described as follows
1. BC - Tangent
3. DH - Chord
4. EH - Diameter
5. G - center of the circle
6. GF Radius of the circle
7. B. a point of tangency
What is tangent and chord of a circleTangent: Referenced as a point of tangency, a tangent to a circle is a line that meets the circumference at one solitary area while never penetrating inside its bounds. To explain further, this line is perpendicular to the radius of the circle right at the tip of contact.
Chord: Referring to such an element, a chord of a circle is a straight piece between two areas that lay along the circumference. Without having any relation to the middle of the target object, it has both of its extremities on the peripheral border.
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(ILL GIVE YOU 100 POINTS!!)
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
a Step 2; 8x − 4 = 2(6 + x + 6)
b Step 2; 8x − 16 = 16 + 2x
c Step 3; 6x − 2x = 16 − 8
d Step 3; 6x + 2x = 16 + 8
Answer:
step 2 is wrong
Step-by-step explanation:
4 multiply by 2x = 8x4 multiply by -4 = -16CORRECT STEP4(2x - 4) = 8 + 2x + 88x - 16 = 8 + 2x + 88x - 16 = 2x + 16 6x = 32x = 32/6 = 5 ( approximately )Here, The work of a student to solve the equation :
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
The steps for calculating the value of x are :
Step 1: [tex]4(2x - 4) = 8 + 2x + 8[/tex]
Step 2: [tex]6x - 8 = 16 + 2x[/tex]
Step 3: [tex]6x - 2x = 16 + 8[/tex]
Step 4: [tex]4x = 24[/tex]
Step 5: [tex]x = 6[/tex]
Step 2 is incorrect, as the student instead of multiplying, adds the number as:
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
Here, the correct step is:
[tex]\boxed{\bold{8x - 16 = 16 + 2x}}[/tex]
[tex]6 x = 32[/tex]
[tex]x = 5.33[/tex]
So, the error is in STEP 2 and the correct option is (B).
8 cupcakes in 1 box = 16 cupcake in X boxes
Answer:
2 boxes
Step-by-step explanation:
8 cupcakes in 1 box = 16 cupcake in x box
We Take
16 ÷ 8 = 2 boxes
So, the answer is 2 boxes.
i want to find inverse laplace help me pls.
Answer:
MY OPINION IS (REALLLLLL)
Step-by-step explanation:
cant be that hard but i didnt pay attention
∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.
option A.
What is a supplementary?Supplementary angles are the two angles that sum up to 180 degrees.
That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.
From the given diagram we can form the following equation;
∠ AFE + ∠ AFB = 180 (supplementary angles or sum of angles on a straight line )
∠ AFE = 180 - ∠ AFB
∠ AFE = 180 - 78
∠ AFE = 102⁰.
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Is anyone good with Math or History
The probability of passing at least one will be 0.70.
We know that,
Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
here, we have,
Probability of passing history course = 0.59
Probability of passing math course = 0.60
Probability of passing both courses = 0.49
so, we get,
Probability of passing at least one will be
⇒ 0.59 + 0.60 – 0.49
⇒ 0.70
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complete question:
A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?
What is the sum of 3.0 x 4.1 x 5.5
Answer: 67.65
Step-by-step explanation:
Multiply 3.0*4.1 and you get 12.3
Then take that sum and multiply it by the 5.5
So 12.3*5.5=67.65
What is the area of the reduced rectangle? 0.18 square units 1.8 square units 18 square units 180 square units
The area of the reduced rectangle is 1.8 unit²
The correct answer is an option (b)
Here the length of the rectangle is 15 units.
And the width of the rectangle is 12 units.
The rectangle has been reduced by a scale of 1/10
so, the new length of the rectangle is:
l = 1/10 × 15
= 1.5 units
And the new width of the rectangle is:
w = 1/10 × 12
= 1.2 units
We need to determine the area of the reduced rectangle.
Using the formula for area of rectagle, the area of the reduced rectangle would be:
A = l × w
A = 1.5 × 1.2
A = 1.8 unit²
Therefore, the correct answer is an option (b)
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The complete question is:
The rectangle below has been reduced by a scale of StartFraction 1 over 10 EndFraction. A rectangle has a length of 15 and width of 12. [Not drawn to scale] What is the area of the reduced rectangle?
a) 0.18 square units
b) 1.8 square units
c) 18 square units
d) 180 square units
A sack of rice wieghs 50 kilos. What is the weight of 85 sacks of rice?
Answer:
4250 kilos
Step-by-step explanation:
Enter the correct answer in the box.
What is the factored form of this expression?
2x^3+5x^2+6x+15
Write all factors in standard form.
Answer:
(2x + 5)(x² + 3)------------------
Given expression:
2x³ + 5x² + 6x + 15Group the expression as below and factorize:
2x³ + 5x² + 6x + 15 = (2x³ + 5x²) + (6x + 15) =x²(2x + 5) + 3(2x + 5) = (2x + 5)(x² + 3)Hence the factored form of the expression is (2x + 5)(x² + 3).
The factored form of the expression is,
⇒ (2x + 5)(x² + 3).
Given that;'
The expression is,
⇒ 2x³ + 5x² + 6x + 15
Now, Group the expression as below and factorize:
2x³ + 5x² + 6x + 15
(2x³ + 5x²) + (6x + 15)
x²(2x + 5) + 3(2x + 5)
(2x + 5)(x² + 3)
Hence, the factored form of the expression is (2x + 5)(x² + 3).
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Classify the following into finite and infinite set
(i) The set of months in a year
(ii)The set of stars in the galaxy
(iii)The set of even integers
(iv)The set of odd integers
(v)The set of alphabets
i) finite set, ii) infinite set, iii) infinite set, iv) infinite set, and v) finite set are the required solutions.
A Set is a collection of objects with similar properties. There are different types of set two of them are finite and infinite set.
Finite set- A set is called a finite set when the elements inside the set are countable or where we can know the starting and the ending of the elements. For example- A set of players in a cricket team.
Infinite set- A set is called an infinite set when the elements inside the set are uncountable or where the ending of the elements is not known. For Example- A set of positive numbers.
Here in the question the option (i) and (v) are finite sets because the no.of months in the year and no.of alphabets are countable or finite. Option (ii), (iii), and (iv) are infinite sets as no.of stars in the galaxy, even integers, and odd integers are uncountable.
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Answer:
the set of months in a year is finite
the set of star in the Galaxy is finite
the set of even integers is infinite
the set of odd integers is infinite
the set of alphabet is finite
Step-by-step explanation:
1) the set of month in a year is finite because they are limit and we can count them easily
2) the set of star in the galaxy is finite cause there are zillions of stars
3) the set of even integer is infinite because numbers are unlimit or infinite
4) the set of odd integers is infinite cause numbers are infinite ir they have not limit
5) the set of alphabet is finite because we can count them limitedly
A hippopotamus weighs 2 tons and a crocodile weighs 20 lbs.
How many times as much as the hippopotamus does the crocodile weigh?
The crocodile weighs 0.005 times as much as the hippopotamus.
To determine how many times as much as the hippopotamus a crocodile weighs, we need to compare the weights of both animals. However, they are currently in different units, so we need to convert them to a common unit.
We can convert the weight of the hippopotamus from tons to pounds by multiplying by 2,000, since there are 2,000 pounds in a ton. This gives us:
Hippopotamus weight = 2 tons × 2,000 pounds/ton = 4,000 pounds
Now that both weights are in pounds, we can compare them. To determine how many times as much as the hippopotamus the crocodile weighs, we can divide the weight of the crocodile by the weight of the hippopotamus. This gives us:
Crocodile weight / Hippopotamus weight = 20 pounds / 4,000 pounds = 0.005
Alternatively, we could say that the hippopotamus weighs 200 times as much as the crocodile.
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Ms. Monti bought * adult tickets and y
children's tickets to an ice-skating show. She spent a total of $145. The equation below describes the relationship
between x and y.
25x + 15y = 145 The ordered pair (4, 3) is a solution of the equation. What does the solution
(4, 3) represent?
A Ms. Monti bought 4 adult tickets and
3 children's tickets. B Adult tickets cost $4 each and
children's tickets cost $3 each. C Ms. Monti spent $4 on adult tickets
and $3 on children's tickets. D The cost of 4 adult tickets equals the
cost of 3 children's tickets.
Vocabulary
1. The remainder is the number that remains after the division is
complete. Use an R to indicate the remainder.
Tia has 26 walnuts. She gives 7 walnuts to each friend. How many friends get
7 walnuts? How many walnuts are left over?
Use the array to find 26+7. Circle the groups of 7.
There are
groups of 7.
left over.
There are
2647-
friends each get 7 walnuts.
walnuts left over.
000000
000000
0.0
000
O
There are
2. Juan puts 57 oranges in bags. Each bag holds 6 oranges. Use the array to divide.
To find 57 +6, circle groups of
5746-
How many full bags of oranges are there?
How many oranges are not in bags?
How many bags does Juan need to put all the oranges in bags?.
3. How many craft sticks will be left over if 9 friends equally share a
package of 85 craft sticks?
000000
OOO
000
000
O
000000
000000
000000
000000
4. A group of 43 people are going to a concert. If 6 people fit in each
car, how many cars will they need to take?
000000
000000
On the Back!
6. Find the number of equal groups and the number left over for
88 +3. Show your work.
bags
000
5. Bess has 19 sunflowers that she is putting into vases. She will put 4 sunflowers in
each vase. How many vases will have 4 flowers?
The number of friends that get 7 walnuts is 3 and there are 5 walnuts are left over
Sharing walnuts among friendsHere, we have
Walnuts = 26Walnuts to each friend = 7So, we have
Friends = 26/7 = 3 R 5
This means that 3 friends get 7 walnuts and there are 5 walnuts are left over
Putting oranges in bagsHere, we have
Oranges = 57
Oranges in each bags = 6
So, we have
Bags 57/6 = 9 R 3
This means that there are 9 full bags of oranges, 3 oranges are not in the bag and Juan needs 10 bags in total
Crafts in sticksHere, we have
Craft sticks = 85
Friends = 9
So, we have
Sticks left = 85\9
Evaluate
Sticks left = 4
Hence, there will be 4 sticks left
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Look at the picture
According to the information, we can infer that the area of the triangle is: 19 1/4ft²
How to calculate the area of the triangle?To calculate the area of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) x base x heightwhere,
Base = 5 1/2 ftHeight = 7 ft.How to find the height of the triangle?To find the height of the triangle, we need to use the Pythagorean theorem, which relates the slant height, height, and half the base:
(slant height)^2 = (height)^2 + (1/2 base)^2Substituting the given values, we get:
(1/3)^2 = (7)^2 + (1/2 x 5 1/2)^2(1/9) = 49 + (15/4)(1/9) = (196/4 + 15/4)(1/9) = (211/4)Multiplying both sides by 36, we get:
4 = 844.44...So the height of the triangle is approximately 2.04 ft.
Now we can plug in the values for the base and height into the formula for the area:
Area = (1/2) x 5 1/2 x 7Area = 19.25 square feetArea = 19 1/4ft²Therefore, the area of the triangle is approximately 19.25 square feet.
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A show box measures 15 in. by 7 in. by 4 1/2 in. What is the surface of the box?
The surface area of the box is 408 square inches whose dimensions of the box are 15 in. by 7 in. by [tex]4\frac{1}{2}[/tex] in.
The formula for the surface area of a rectangular box is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the box.
Given that the dimensions of the box are 15 in. by 7 in. by [tex]4\frac{1}{2}[/tex] in., we have:
l = 15 in.
w = 7 in.
h = [tex]4\frac{1}{2}[/tex] in. = 9/2 in.
Substituting these values into the formula, we get:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(15)(7) + 2(15)(9/2) + 2(7)(9/2)
Surface Area = 210 + 135 + 63
Surface Area = 408
Therefore, the surface area of the box is 408 square inches.
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