Eli made a wooden box in the shape of a rectangular prism. The box has a length of 5 inches, a width of 3 1/2 inches, and a height of 7 inches.
Part A. Eli wants to paint the entire box green and give the box to his dad as a gift. What is the total area that he will paint? Explain how you found your answer.
Part B. Can the box hold 22 cubic inches of packing peanuts? Explain how you know.

Answer:

A= 10.5

Step-by-step explanation:

Answer:10.5 yards

Step-by-step explanation:3 x 7 / 2

Answer:

l = 65 – 15d; discrete

Step-by-step explanation:

15 is the centimeters he cuts off every day, you have to multiply that by D that´s the nomber of days, in order to calculate how much baguette does he have left.

If 4 days have passed, the anser would be 5 centimeters:

I=65- 15(4)= 65-60= 5

Answer:

[tex]l=65-15d[/tex]; discrete.

Step-by-step explanation:

Let d represent number of days.

We have been given that for lunch every afternoon, Diep cuts 15 centimeters of bread for his  sandwich. The length of loaf cut in d days would be [tex]15d[/tex].

Diep bought a baguette loaf of bread 65 centimeters long. The length of loaf of bread after d days would be initial length minus amount of loaf cut in d days that is:

[tex]65-15d[/tex]

Since [tex]l[/tex] represents length of bread, so our equation would be: [tex]l=65-15d[/tex]

Therefore, the expression [tex]l=65-15d[/tex] represents the given scenario.

The variable d represents number of days and days cannot be fractional. We can take only whole number of days, therefore, the graph of the equation would be discrete.

Answer:

37

Step-by-step explanation:

To start out, if you know that the digits add to 10, then the number must me around 46-37, as 28 and 82 wouldn't make sense, and 55 is a palindrome.

37-->73, 73-37=36.

Step-by-step explanation:

10y + x = 10x + y + 36

x+y = 10

so we have to find y and x

10y - y = 10x - x + 36

9y = 9x + 36

Answer:

[tex]\large\boxed{z=\dfrac{15\sqrt3}{2}}[/tex]

Step-by-step explanation:

We have the right triangle 30° - 60° - 90°. The sides are in ratio

1 : √3 : 2. Look at the picture.

[tex]15=2x\to2x=15[/tex]         divide both sides by 2

[tex]\dfrac{2x}{2}=\dfrac{15}{2}\\\\x=\dfrac{15}{2}[/tex]

[tex]z=x\sqrt3\to z=\dfrac{15}{2}\sqrt3=\dfrac{15\sqrt3}{2}[/tex]

To calculate the area Tia needs to waterproof, find the perimeter of the triangular base and multiply it by the height of the prism.

To find the area Tia will waterproof, we need to calculate the lateral surface area of the triangular prism. The lateral surface area is given by the formula:

Lateral Surface Area = Perimeter of Base × Height

First, find the perimeter of the triangular base by adding up the lengths of all three sides. Then, multiply this perimeter by the height of the prism. This will give you the area Tia needs to waterproof.

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To determine the area Tia needs to waterproof for her triangular prism tent with base dimensions 14 ft, 8 ft, and side lengths 8 ft, the total area is calculated as the sum of the areas of the two triangular bases.

To find the area that Tia needs to waterproof, we can calculate the surface area of the triangular prism. The formula for the surface area of a triangular prism is given by:

A = 2B + Ph

where:

- B is the area of the triangular base,

- P is the perimeter of the base, and

- h is the height of the prism.

First, calculate the area of one triangular base (either base 1 or base 2). The area B of a triangle is given by:

[tex]\[ B = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

For base 1:

[tex]\[ B_1 = \frac{1}{2} \times 14 \times 8 = 56 \, \text{ft}^2 \][/tex]

Now, find the perimeter P of the base, which is the sum of the three sides:

[tex]\[ P = \text{side}_1 + \text{side}_2 + \text{side}_3 \][/tex]

[tex]\[ P_1 = 8 + 8 + 14 = 30 \, \text{ft} \][/tex]

Now, substitute these values into the formula for the surface area:

[tex]\[ A_1 = 2 \times 56 + 30 \times h \][/tex]

Similarly, calculate the area [tex]\( A_2 \)[/tex] for base 2.

Tia needs to waterproof both bases, so the total area to be waterproofed is [tex]\( A_1 + A_2 \).[/tex]

Answer:

[tex]\frac32 \pi[/tex]

Step-by-step explanation:

If you realize that the sin is actually the y coordinate of a (unit) circle when you travel around it, you will know that it is -1 when you are 3 quarters round, assuming you started at (1,0).

The circumference is measured in radians, where one round is 2π.

So 3/4 of 2π is 3/2 π.

In degrees, the answer is 3/4 of 360°, which is 270°.

Answer:

C

Step-by-step explanation:

Answer:

361x ÷ 19 = 19x

Answer:

18/x = 19

18=19x

Step-by-step explanation:

The answer is:

According to the picture, the angle that the boat should head upstream is 19° north of west.

From the figure, we can see that there is a right triangle formed, and since we know its hypothenuse and its opposite side, we can use the following trigonometric relation:

[tex]Sin(\alpha)=\frac{opposite}{hypothenuse}[/tex]

We are given that:

[tex]opposite=6\\hypothenuse=18[/tex]

So, substituting and calculating, we have:

[tex]Sin(\alpha)=\frac{6}{18}[/tex]

[tex]Arcosin(Sin(\alpha))=Arcsin(\frac{6}{18})\\\\\alpha =19.47\°[/tex]

Therefore the angle that the boat should head upstream is 19°, but since speeds and direction and involved, we need to look for the direction, we can see that the vertical speed is due to north, and the horizontal speed is due to west, knowing that, we can conclude that the resultant speed will be due to north of west.

Hence,  according to the picture, the angle that the boat should head upstream is 19° north of west.

Have a nice day!

The sum of the first four terms of the arithmetic series 4+8+12+... is calculated using the sum formula for arithmetic series, resulting in a sum of 40.

The question seeks the expression for the sum of the first four terms of the arithmetic series 4+8+12+... To solve this, we utilize the formula for the sum of the first n terms of an arithmetic series, which is Sn = n/2 [2a + (n-1)d], where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

For the series 4+8+12+..., the first term a = 4, the common difference d = 4, and the number of terms n = 4. Plugging these values into the formula gives us:

S4 = 4/2 [2(4) + (4-1)4] = 2 [8 + 12] = 2 × 20 = 40.

Therefore, the sum of the first four terms of the arithmetic series 4+8+12+... is 40.

This expression sums from [tex]\( (k-1)^4 \) to \( 4n \),[/tex] which doesn't represent the arithmetic series either.

None of the given expressions seem to represent the arithmetic series [tex]\(4 + 8 + 12 + ... \)[/tex] for four terms correctly.

An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the series given is:

[tex]\[ 4 + 8 + 12 + ... \][/tex]

The common difference between consecutive terms is (8 - 4 = 4).

The general formula for the sum of an arithmetic series is:

[tex]\[ S_n = \frac{n}{2}(a_1 + a_n) \][/tex]

Where:

[tex]- \( S_n \)[/tex] is the sum of the first ( n ) terms,

[tex]- \( a_1 \)[/tex]is the first term,

[tex]- \( a_n \) is the \( n \)[/tex]-th term.

To find the sum of the first four terms, we can use this formula.

Now, let's look at each option:

[tex]a. \( \sum\limits_{(a-1)^4}^{(2n+4)} \)[/tex]

[tex]b. \( \sum\limits_{(s=1)}^{4} (1+4n) \)[/tex]

[tex]c. \( \sum\limits_{(k=1)}^{4} (n+4) \)[/tex]

[tex]d. \( \sum\limits_{(k-1)^4}^{4n} \)[/tex]

We need to choose the expression that correctly represents the sum of the arithmetic series.

Using the formula for the sum of an arithmetic series, we have:

[tex]\[ a_1 = 4 \][/tex]

[tex]\[ a_n = 4 + (4 \times (n-1)) \][/tex](since the common difference is 4)

Now, let's plug these values into the formula:

[tex]\[ S_4 = \frac{4}{2}(4 + (4 + 4 \times (4-1))) \][/tex]

[tex]\[ S_4 = \frac{4}{2}(4 + 4 + 16) \][/tex]

[tex]\[ S_4 = \frac{4}{2}(24) \][/tex]

[tex]\[ S_4 = 2 \times 24 \][/tex]

[tex]\[ S_4 = 48 \][/tex]

So, the sum of the first four terms of the series is 48.

Now, let's see which expression correctly represents this sum.

a. [tex]\( \sum\limits_{(a-1)^4}^{(2n+4)} \)[/tex]

  - This expression doesn't seem to represent an arithmetic series.

b. [tex]\( \sum\limits_{(s=1)}^{4} (1+4n) \)[/tex]

  - This expression doesn't seem to represent an arithmetic series either.

c.[tex]\( \sum\limits_{(k=1)}^{4} (n+4) \)[/tex]

  - This expression sums[tex]\( n+4 \) for \( k = 1 \) to \( k = 4 \)[/tex], but it doesn't seem to correctly represent the arithmetic series.

d. [tex]\( \sum\limits_{(k-1)^4}^{4n} \)[/tex]

  - This expression sums from [tex]\( (k-1)^4 \) to \( 4n \),[/tex] which doesn't represent the arithmetic series either.

None of the given expressions seem to represent the arithmetic series [tex]\(4 + 8 + 12 + ... \)[/tex] for four terms correctly. If none of the options are correct, it's possible that there might be a typo or a mistake in the options provided.

2. Which expression defines the arithmetic series 4+8+12+.. for four terms? a.sumlimits _(a-1)^4(2n+4)

b.sumlimits _(s=1)^4(1+4n)

c.sumlimits _(k=1)^4(n+4)

d.sumlimits _(k-1)^44n

Answer:

20 and 56

Step-by-step explanation:

76/2 = 38

38 - 18 = 20

38 + 18 = 56

20 + 56 = 76

Answer:

p=m/v

v=9 x 4 x 4=144cm

m=1267.2g

p=1267.2/144

p=8.8 g/cm^3

Answer:

8.8

Step-by-step explanation:

Density = Mass / Volume

Volume = 9 × 4 × 4  = 144

Mass = 1267.2

Density = 1267.2 / 144 = 8.8

Answer:

$15116.28

Step-by-step explanation:

Given data:

interest rate, r= 4%

time, t= 18 years

Final investment, A= $26000

Principle investment, P=?

As per the formula of interest

A= P (1+rt)

Putting the values:

26000= P(1+ 0.04(18))

P= 26000/(1+ 0.04(18))

P= 15116.28 !

Answer:

P(face | Black) = 3/13

Step-by-step explanation:

total number of cards in standard deck of cards = 52

Total number of face cards = 12

Then P(face cards) = 12/52

Total number of black cards = 26

Then P(black cards) = 26/52

Total number of cards that are both black and face cards = 6

Then P(black and face cards) = 6/52

Then conditional probability of getting face card given that the card is black is given by:

P(face | Black) = P( face & Black) / P(Black)

P(face | Black) = (6/52) / (26/52)

P(face | Black) = 6/26

P(face | Black) = 3/13

Answer:

The probability of a face card given that the card is black = 3/26

Step-by-step explanation:

Points to remember

There are total 52 cards. It is divided into 4 suites, 13 each.

Spades, Clubs, Hearts and Diamonds

Spades and  Clubs are black.

Hearts and Diamonds are red

In each suites there are 3 face cards.

To find the probability

There are total 52 cards. And 6 black face cards

The  probability of a face card given that the card is black =6/52

 = 3/26

Answer:

[tex]R^{2}=0.7744[/tex]

Step-by-step explanation:

r represents the correlation coefficient between two sets of data. It is a measure of the degree of association between the two sets of data and gives insight into the strength and direction of the relationship.

On the other hand, [tex]R^{2}[/tex] is the coefficient of determination for a given data set. It is a measure of the predictive power of a linear model.

Given r, [tex]R^{2}[/tex] is simply the square of r;

in this case we are given, r = 0.88. Therefore, [tex]R^{2}=0.88^{2}\\\\R^{2}=0.7744[/tex]

Answer:

C. 9

Step-by-step explanation:

Matrix is an arranged array of rows and columns. The number of rows are represented by m and number of columns by n. Hence the elements of matrix is denoted by small letter with it's row number and column number in subscript.

Like elements belonging to A matrix will be written as:

[tex]a_{mn}[/tex]

In the given matrix, we have to tell the element b_23 which means we have to point out the element in row 2 and column 3.

Looking at the matric we can see that the number at the position of 2nd row and third column is 9.

Hence Option C is the correct answer ..

Answer:

Opposite sides of parallel are just like diagonal and the other diagonal going the other way.

Step-by-step explanation:

ANSWER

Quadrant IV

EXPLANATION

The given point have the x-coordinate to be positive and the y-coordinate to be negative.

In general, the point P(x,-y) lies in the fourth quadrant.

The reason is that, this quadrant contains the positive x-axis and the negative y-axis.

See attachment for diagram.

Answer: II and IV

Step-by-step explanation:

To show Lin's elevation at 3:00 p.m on a graph, mark a point below her starting altitude at 2:00 p.m, given that she was climbing downwards. The exact placement will depend on her descent rate, for which we have no data.

The question refers to Lin climbing downwards in the period from 2:00 p.m. to 3:00 p.m. In order to plot Lin's movement on a graph, we need to define the vertical axis as her altitude and the horizontal axis as time. Since Lin was moving downward, her altitude at 3:00 p.m. should be less than her altitude at 2:00 p.m.

For example, if she started at an altitude of 4,000 meters at 2:00 p.m., when adding a point to the graph at 3:00 p.m., it should be below the 4,000-meter altitude point, since Lin was descending. The exact point will depend on the speed of her descent, which we don't have information on, but it would be somewhere below the starting point.

It's similar to the thrown rock example where the rock rises and then falls. Lin, like the rock, started at a higher point (instead of airborne, she was high on a cliff or a hill), but then moved downwards, decreasing her altitude over time.

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The point is placed at -50 feet to represent a possible elevation halfway between 0 feet and -100 feet. However, it is important to note that her actual elevation could be anywhere within this range.

Assuming Lin started climbing from an elevation of 0 feet at 2:00 p.m., she could have reached a negative elevation at 3:00 p.m. This is because the graph shows that she was descending at a constant rate.

To determine her possible elevation, we need to consider the following:

The slope of the graph represents the rate of change in elevation. A negative slope indicates that Lin is descending.

The y-intercept of the graph represents Lin's elevation at 2:00 p.m. Since she started at 0 feet, the y-intercept is 0.

The time interval from 2:00 p.m. to 3:00 p.m. is one hour.

Using this information, we can determine that Lin's elevation at 3:00 p.m. could be anywhere from 0 feet to -100 feet. This is because the slope indicates that she is descending at a rate of -100 feet per hour.

Answer:

Negatively skewed

Step-by-step explanation:

Arrange this data in ascending order:

46, 50, 57, 58, 59, 59, 65, 66, 77, 80

and draw the bar chart as shown in attached diagram.

The data distribution appears to be negatively skewed (or left skewed), because the scores fall toward the higher side of the scale and there are very few low scores. The mean is also to the left of the peak.

Answer:

Negatively skewed

Step-by-step explanation:

Arrange this data in ascending order:

46, 50, 57, 58, 59, 59, 65, 66, 77, 80

and draw the bar chart as shown in attached diagram.

The data distribution appears to be negatively skewed (or left skewed), because the scores fall toward the higher side of the scale and there are very few low scores. The mean is also to the left of the peak.

Applying the definition of negative exponents, we have

[tex]3^{-2}\cdot 27 = \dfrac{1}{3^2}\cdot 27 = \dfrac{27}{9} = 3[/tex]

B. 900 inches squared

Work is shown in IMG

Answer:

y=36°

z=54°

Step-by-step explanation:

3y+2y -> 5y=180 y=36

90-36= 54

5/8 paper chains used more than 2 containers but less than 2 3/4 containers of glitter.

Answer:

1218.75

Step-by-step explanation:

7.5 x 5 = 37.5

37.5 x 3250 = 121875

121875 ÷ 100 = 1218.75

Answer:

Step-by-step explanation:

A(1,4), B(4, -2), C(-1, 2)

In the first transformation, we multiply each x coordinate by -2, and each y coordinate by 1/2.

A(1*-2, 4/2) = A(-2, 2)

B(4*-2, -2/2) = B(-8, -1)

C(-1*-2, 2/2) = C(2, 1)

In the second transformation, we take each new x coordinate and subtract 2, and each new y coordinate and add 3:

A(-2-2, 2+3) = A(-4, 5)

B(-8-2, -1+3) = B(-10, 2)

C(2-2, 1+3) = C(0, 4)

Answer:

-15

Step-by-step explanation:

(-2/7) = 5

(5/-8) = -3

5 x -3 = -15

Answer:

0.17 or 5/28

Explanation:

(-2/7)=-0.28

(5/-8)=-0.62

(-0.28)(5/-8)=0.17

Answer:

1: It's I think 2+2

2: If I got your accent right then it's 4

3: count 2 and 2 makes 4

4: YAYYY YOU GOT IT PRACTICE MORE

Step-by-step explanation:

PLZZZZ MARK BRAINLIST!! REALLY FUNNY QUESTION AND MADE MY DAY!!!

The value of x in the equation sin 40 = x/12 is found by multiplying both sides by 12 and then by the sine of 40 degrees, resulting in x being approximately 7.7136.

To find the value of x in the equation sin 40 = x/12, we need to isolate x on one side of the equation. To do this, we multiply both sides of the equation by 12 to get x on its own. So, the steps are as follows:

Multiply both sides of the equation by 12 to eliminate the denominator on the right side, which gives us 12 * sin 40 = x.

Calculate sin 40 using a calculator.

Finally, multiply the value of sin 40 by 12 to find the value of x.

Carrying out these steps:

sin 40 approximately equals 0.6428 (rounded to four decimal places).

Then we calculate 12 * 0.6428 = 7.7136 (rounded to four decimal places).

Therefore, the value of x is approximately 7.7136.

7776pi since the volume of a sphere can be found by V=4/3pi(r)^3

V=4/3pi(18)^3

V=7776pi

Answer:

[tex]\large\boxed{972\pi\ cm^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{We have the diameter of the sphere.}\ D=18cm.\\\\D=2R\to R=\dfrac{18}{2}\ cm=9cm.\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(9^3)=\dfrac{4}{3}\pi(729)=(4)\pi(243)=972\pi\ cm^3[/tex]

Answer:

a. 84 students

b. 12

Step-by-step explanation:

a.

From the information given, we see that 7 out of 12 practice every day. Now we want to know how many (let it equal x) would we expect to practice everyday given there are total 144 martial artists?

we set up a ratio and cross multiply and solve for x:

[tex]\frac{7}{12}=\frac{x}{144}\\7*144=12*x\\1008=12x\\x=\frac{1008}{12}=84[/tex]

So 84 students practice everyday

b.

The sample size is a "proportion" of the whole population. Here, there are a total of 144 martial artists. And we took 12 of them to figure out how many practice everyday (from these 12). So , clearly, the sample size is 12