Dina is shipping a wall map to a collector. When the map is rolled up, it measures
7 ft long. She will use a box that is a right rectangular prism with a base that is 3 ft
by 3 ft. Which whole number could be the shortest height of the box that will hold
the map?
A 4 ft
B 5 ft
C 6 ft
D 7 ft

Answer:

  5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

__

In navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

  N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

__

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

The final position is the sum of these two changes in position:

  3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

  = 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

__

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

  a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

  a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

  a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

Additional comment

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

  (0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

  OB = √(1.434² +5.048²) ≈ 5.248

Answer:

21 liters

Step-by-step explanation:

14 liters + 7 liters = 21 liters

Hope this helped :)

Answer:

Triangle ABC is not a Right Triangle

Step-by-step explanation:

The perimeter of a triangle is all of the sides added together so we can model our equation like so:

AB + BC + CA = P

or

8 + 5 + CA = 22

We first combine like terms

13 + CA = 22

Then make the variable have no numbers on its side

13 + CA = 22

-13          -13

CA = 9

So now that we know what CA is, we can determine whether or not its a right triangle

We can use the Pythagorean Theorem for this:

a^2 + b^2 = c^2   (the '^' symbol means 'to the power of')

or

5^2 + 8^2 = 9^2

Now we Solve

5^2 = 25

8^2 = 64

9^2 = 81

25 + 64 =? 81

89 does not equal 81

So Triangle ABC is not a Right Triangle

Answer:

the missing angle is 30 and the missing exterior angle is 150

Step-by-step explanation:

180-90=90-60=30

180-30=150

Answer: Exterior angle = 150 degrees

Step-by-step explanation:

Hope that helps!

:)

Answer:

time=t= 9.36 months.........

The money was in the SACCO for a time of 0.78125 years.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Amount of money deposited or principal amount = 56,800

Rate of interest = 12% = 12/100 = 0.12

Final amount = 62,125

The formula for simple interest is,

A = P(1 + rt), where A is the final amount, P is the principal amount, r is the interest rate and t is the time.

Substituting,

56800 (1 + 0.12t) = 62125

1 + 0.12t = 1.09375

0.12t = 0.09375

t = 0.78125 years

Hence the time that the money kept for is 0.78125 years.

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Answer:

(2,-4)

Step-by-step explanation:

Here, h=2 and k=-4, so the center is (2,-4)

1 year or less is at the first quartile mark in the box plot, therefore, the number of schools that participated for a year and less is: A. 6 schools.

The data point at the beginning of the edge of the rectangular box in a box plot is the first quartile mark of the data, which is 1/4 or 25% of the data.

1 year or less is at the first quartile mark in the box plot. That is 1/4 of the total number of schools.

Therefore, schools that participated for a year and less = 1/4(24) = 6 schools.

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Answer:

? = x = 12

Step-by-step explanation:

Remark

This is a proportion question. A proportion is 2 equal ratios. The two triangles are similar, which means that a proportion can be set up.

Givens

? = x

x + 8

9

9 + 6

Equation

x/(x + 8) = 9 / (9 + 6)       Combine

Solution

x/(x + 8) = 9/15                Cross multiply

15x = 9(x + 8)                  Remove the brackets

15x = 9x + 72                  Subtract 9x from both sides

15x - 9x = 72                   Combine

6x = 72                            Divide both sides by 6

6x/6 = 72/6

x = 12

Answer x = 12

Using the slope concept, it is found that the distance from point A to point B is of 465 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

To find the horizontal position at point A, we have that:

tan(10º) = 107/dA

dA = 107/tan(10º)

dA = 607.

For the horizontal position at point B, we have that:

tan(37º) = 107/dB

dB = 107/tan(37º)

dB = 142.

Hence the distance is given by:

D = dA - dB = 607 - 142 = 465.

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Answer:

see explanation

Step-by-step explanation:

to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule

to find the 10th term substitute n = 10 into the rule

(a)

a₁ = 1² + 3 = 1 + 3 = 4

a₂ = 2² + 3 = 4 + 3 = 7

a₃ = 3² + 3 = 9 + 3 = 12

a₄ = 4² + 3 = 16 + 3 = 19

a₁₀ = 10² + 3 = 100 + 3 = 103

(b)

a₁ = 2(1)² = 2(1) = 2

a₂ = 2(2)² = 2(4) = 8

a₃ = 2(3)² = 2(9) = 18

a₄ = 2(4)² = 2(16) = 32

a₁₀ = 2(10)² = 2(100) = 200

Step-by-step explanation:

un is the balance of the loan after n years.

so,

u12 is the balance of the loan after 12 years.

Answer:

slope = 1/3

Step-by-step explanation:

slope,m = vertical change/ horizotal change

that means (-3)-2/(-5)-10 or 2-(-3)/10-(-5)

and we got -5/-15 or 5/15.

So the answer is 1/3.

Based on the table, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

In the first week, there's 9.5 pounds. This can be illustrated using the arithmetic progression. The formula will be:

= a + (n - 1)d

where,

a = first term

d = common difference

3rd term = a + 2d

13 = 9.5 + 2d

2d = 13 - 9.5

2d = 3.5

d = 3.5/2

d = 1.75

Therefore, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

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Answer:

11 hope this helps you and write

Answer:

y = (1/3)*x + 5

Step-by-step explanation:

Step 1: determine slope or m

m = change in y-coordinates ÷ change in x-coordinates

m = (4-7)/(-3-6) = -3/-9 = 1/3

Step 2: determine y-intercept or b

y = m*x + b

y = (1/3)*x + b

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

4 = -1 + b

b = 5

Step 3: substitute values for m and b into the slope intercept equation

y = (1/3)*x + 5

For pumpkins

Total 12mins sets

earnings

For apples

Total 12 mins

Earnings

Total earnings

Answer:

$37.60

Step-by-step explanation:

Eve earns:

Money earned from picking pumpkins:

1 hour = 60 minutes

[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 60\:minutes\\\\& = \sf \$4.00\:per\:12\:minutes \times 60\:minutes\\\\& =\sf \dfrac{\$4.00}{12\:minutes} \times 60\:minutes\\\\ & = \sf \$4.00 \times \dfrac{60\:minutes}{12\:minutes}\\\\ & = \sf \$4.00 \times 5\\\\ & = \sf\$20.00\end{aligned}[/tex]

Money earned from picking apples:

[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 48\:minutes\\\\& = \sf \$4.40\:per\:12\:minutes \times 48\:minutes\\\\& =\sf \dfrac{\$4.40}{12\:minutes} \times 48\:minutes\\\\ & = \sf \$4.40 \times \dfrac{48\:minutes}{12\:minutes}\\\\ & = \sf \$4.40 \times 4\\\\ & = \sf\$17.60\end{aligned}[/tex]

Total earned:

= money earned from picking pumpkins + money earned from picking apples

= $20.00 + $17.60

= $37.60

The probability that a randomly selected makeup item from her bag will be an eye shadow is 1/5 or 20%.

The probability of selecting an eye shadow from Gabby's bag can be calculated by dividing the number of eye shadows in the bag by the total number of cosmetics in the bag.

There are 4 eye shadows in Gabby's bag, and a total of 20 cosmetics. Therefore, the probability of selecting an eye shadow is:

P(eye shadow) = 4/20 = 1/5

This means that there is a 1 in 5 chance, or a 20% chance, that a randomly selected makeup item from Gabby's bag will be an eye shadow.

The probability can be expressed as a fraction or a whole number, depending on the context of the problem. In this case, we can express the probability as the fraction 1/5, which means that out of 20 possible cosmetics, only 4 are eye shadows.

We can also express the probability as the whole number 0.2 or 20%, which represents the proportion of eye shadows in Gabby's bag.

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speed = distance/time

speed = 180/2

speed = 60km/hr

hope it helps...!!!

Answer:

first one

Step-by-step explanation:

because its cheap as for 1 NM it would be 10$ which is 2.5 AED so yehh

Answer:

x = (y - b)/m.

Step-by-step explanation:

y=mx+b      

Subtract b from both sides :-

y - b = mx

Divide both sides by m:-

(y - b) /m = x.

Answer:

The airplane flies 95 miles.

Step-by-step explanation:

Question:

An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.

Answer:

The plane flew 91 miles.

Step-by-step explanation:

City 1 - City 2

---------------------------------------------------------------------------------------------------------

[tex]d_{1}[/tex] = [tex]\sqrt{(33 - 0)^{2} + (56 - 0)^{2}[/tex]

[tex]d_{1}[/tex] = [tex]\sqrt{33^{2} + 56^{2}[/tex]

[tex]d_{1[/tex] = [tex]\sqrt{1089 + 3136[/tex]

[tex]d_{1}[/tex] = [tex]\sqrt{4225}[/tex]

[tex]d_1[/tex] = [tex]65[/tex]

---------------------------------------------------------------------------------------------------------

City 2 - City 3

[tex]d_2[/tex] = [tex]\sqrt{(33 - 23)^2 + (56 - 32)^2[/tex]

[tex]d_2[/tex] = [tex]\sqrt {10^2 + 24^2}[/tex]

[tex]d_2[/tex] = [tex]\sqrt{676}[/tex]

[tex]d_2[/tex] = 26

---------------------------------------------------------------------------------------------------------

[tex]d_1 + d_2 = 65 + 26[/tex]

[tex]d_1 + d_2 = 91[/tex]

---------------------------------------------------------------------------------------------------------

Therefore, the airplane flew a total of 91 miles through every city

---------------------------------------------------------------------------------------------------------

Key words: the airplane, 91 miles, through, every, city, flies, City 1, City 2, City 3, total, number, unit, represent, mile.

<3 Lots of love!

-The Book Worm.

The axis of symmetry of h(x) = 5x2 + 40x + 64 = -4

The formula for calculating the axis of symmetry is expressed as:

Axis of symmetry x = -b/2a

h(x) = 5x^2 + 40x + 64

a = 5 and b = 40

Answer:

  x ≈ 95.6

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. Here, the hypotenuse of the triangle and the side adjacent to the given angle are marked, so the relationship of choice is ...

  Cos = Adjacent/Hypotenuse

__

Using the values shown, we have ...

  cos(15°) = x/99

Solving for x gives ...

  x = 99·cos(15°) ≈ 95.6

The length of the side marked x is about 95.6 units.

Answer:

y = -2x - 6

Step-by-step explanation:

We know that the slopes of the lines are equal when the lines are parallel to each other.

So, the equation of the given line is y = -2x + 2.

Here,

y = mx + c

y = -2x + 2

slope ⇒ m ⇒ -2

Therefore, the slope of the new line will be ( - 2 ).

And now we have to find the y-intercept ( c ).

For that let us use the given coordinate.

( -6 , 6 ) ⇒ ( x , y )

To find the y-intercept we have to make c the subject of the equation y mx + c.

Also, we have to replace m with ( - 2 ) as the slope of the new line is -2.

Let us solve it now.

y = m x + c

6 = -2 × -6 + c

6 = 12 + c

6 - 12 = c

-6 = c

Now we have found that,

m ⇒ - 2

c ⇒ -6

And now let us write the equation of the line.

y = m x + c

y = -2x - 6

The system of equations of two unknowns is formulated and solved.

      [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ x\times y = 4 \\ x^2+y^2 = 17 \end{matrix}\right. \ \Longrightarrow \ y=\dfrac{4}{x}} \end{gathered}$}[/tex]

        [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+\left (\dfrac{4}{x} \right )^2=17\ \Longrightarrow\ x^4+16=17x^2 } \end{gathered}$}[/tex]

                                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} 0&=(x^2)^2-17(x^2)+16\\ =(x^2-16)(x^2-1) \\ \ \ \ \ \ \ \ \ \ \ =(x+4)(x-4)(x+1)(x-1) \end{gathered}$}[/tex]

Possible number pairs are 4, 1 and -4, -1 .

Step-by-step explanation:

mean value is always the sum of all data divided by the number of data points.

we can see just by looking at the numbers that team B is way below team A.

mean team A : 1529/8 = 191.125

mean team B : 1141/8 = 142.625

so, clearly, team B had to make dinner.

the median is the value of all the data points, where half of the others are smaller, and the other half are bigger.

in case of an even number of data points (like here with 8), we find the 2 middle values and calculate the mean value of these 2 :

median team A : (180+189)/2 = 184.5

median team B : (143+134)/2 = 138.5

the mode is the number in the set of data that occurred must often. if they are all unique, then they ALL are the mode. it is NOT 0 or empty. it is then really all the data points.

mode team A : 212

mode team B : 99, 102, 105, 134, 143, 145, 202, 211

a) Recall the integration by parts formula:

[tex]\displaystyle \int u \, dw = uw - \int w \, du[/tex]

Then with [tex]u = x[/tex] and [tex]dw = e^x\,dx[/tex] we have

[tex]\displaystyle v = \int e^x x \, dx = xe^x - \int e^x \, dx[/tex]

[tex]\implies \boxed{v = xe^x - e^x + C}[/tex]

since [tex]w=\int e^x\,dx=e^x[/tex] and [tex]du=dx[/tex]. (C is of course an arbitrary constant that can be determined exactly if you know the velocity at some given value of x.)

b) No?

[tex]\displaystyle \int e^xx\,dx = \int xe^x\,dx[/tex]

because multiplication is commutative. I get the feeling I'm missing something here...

Answer:

h=70°

Step-by-step explanation:

h + 110° = 180° {linear pair angles}

h = 180° - 110°

h = 70°

Answer:

h=70

pa brainliest po kuya/ate

Step-by-step explanation:

pa brainliest po

Answer:

-17.25

Step-by-step explanation: