An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.


The amount of cardboard required to make one box is___square inches.
a)130
b)111
c)109
d)84

Answer:

2(a - 3). = 4

_______

3

Cross multiply.

2(a- 3) = 12

2a - 6 = 12

2a = 12 + 6

2a = 18

a = 18 ÷ 2

a = 9

Answer:

a = 9

Step-by-step explanation:

Given

[tex]\frac{2(a-3)}{3}[/tex] = 4 ( multiply both sides by 3 to clear the fraction

2(a - 3) = 12 ( divide both sides by 2 )

a - 3 = 6 ( add 3 to both sides )

a = 9

As a check substitute a = 9 into the left side of the equation and if equal to the right side then it is the solution.

[tex]\frac{2(9-3)}{3}[/tex] = [tex]\frac{2(6)}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4 = right side

Thus solution is a = 9

Answer:

The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵

Step-by-step explanation:

The given parameters are;

Mean = 34 cm

The standard deviation = 8 cm

The mean

The Z score is [tex]Z=\dfrac{x-\mu }{\sigma }[/tex], which gives;

For x  = 30 we have;

[tex]Z=\dfrac{30-34 }{8 } = -0.5[/tex]

P(x>30) = 1 - 0.30854 = 0.69146

For x = 40, we have

[tex]Z=\dfrac{40-34 }{8 } = 0.75[/tex]

P(x < 40) = 0.77337

Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;

P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191

The probability that a randomly selected group of four trees can be used as timber is given as follows;

Binomial distribution

[tex]P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}[/tex]

Answer:

y = 4

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross-  multiply )

y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

y = 4

Answer:

y=4

Step-by-step explanation:

If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.

So, by the law of sines we can say that:

[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]

Solving for y, we get:

[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]

Answer:

B

Step-by-step explanation:

Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )

Then the sum of the roots = - [tex]\frac{b}{a}[/tex]

A 2x² - 3x + 6 = 0

with a = 2 and b = - 3

sum of roots = - [tex]\frac{-3}{2}[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3

B - x² + 3x - 3 = 0

with a = - 1 and b = 3

sum of roots = - [tex]\frac{3}{-1}[/tex] = 3 ← True

C [tex]\sqrt{2}[/tex] x² - [tex]\frac{3}{\sqrt{2} }[/tex] x + 1

with a = [tex]\sqrt{2}[/tex] and b = - [tex]\frac{3}{\sqrt{2} }[/tex]

sum of roots = - [tex]\frac{-\frac{3}{\sqrt{2} } }{\sqrt{2} }[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3

D 3x² - 3x + 3 = 0

with a = 3 and b = - 3

sum of roots = - [tex]\frac{3}{-3}[/tex] = 1 ≠ 3

Thus the equation with sum of roots as 3 is B

Answer:

32

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)

                 = 9 + 9

                 = 18

Answer:

18

Step-by-step explanation:

Answer:

Hey there!

We have the slope is equal to -2.5, and the y intercept  is 3.

Thus, the equation is y=-2.5x+3

Hope this helps :)

Answer:

a = 11.71 ; b = 15.56

Step-by-step explanation:

For this problem, we need two things.  The law of sines, and the sum of the interior angles of a triangle.

The law of sines is simply:

sin(A)/a = sin(B)/b = sin(C)/c

And the sum of interior angles of a triangle is 180.

45 + 110 + <C = 180

<C = 25

We can find the sides by simply applying the law of sines.

length b

7/sin(25) = b/sin(110)

b = 7sin(110)/sin(25)

b = 15.56

length a

7/sin(25) = a/sin(45)

a = 7sin(45)/sin(25)

a = 11.71

Answer:

C

Step-by-step explanation:

Using Parts Whole Postulate we can write:

∠LQP = ∠LQR + ∠PQR

We know that ∠LQP = 77° and ∠LQR = 35° so we can write:

77° = 35° + ∠PQR

Therefore the answer is 77 - 35 = 42°.

Answer:

167.55

Step-by-step explanation:

so it varies jointly so

A-area if cylinder

so

[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]

so

[tex]a = k\pi \: r^{2}h[/tex]

where k is the constant

so apply the first set of values to get k=2/3

then substitute the k with the second set of values

Answer:

[tex]|7m- 56| = 56 - 7m[/tex]

Step-by-step explanation:

Given

[tex]|7m- 56|[/tex]

[tex]m < 8[/tex]

Required

Rewrite the expression without absolute values

The first step is to check if the expression in |...| is positive or negative;

The question says m < 8,

This means the value of m could be 7, 6 ...

Let's assume m is 7

[tex]7m - 56 = 7 * 7 - 56 = 49 - 56 = -7[/tex]

This means that the expression [tex]|7m- 56|[/tex] will give a negative value if [tex]m < 8[/tex]

So,

[tex]|7m- 56| = -(7m - 56)[/tex]

Open bracket

[tex]|7m- 56| = -7m + 56[/tex]

Rearrange

[tex]|7m- 56| = 56 - 7m[/tex]

The expression can't be further simplified

Answer:

97

Step-by-step explanation:

5 * 85 - 4* 82 = 97

Answer:

[tex] \frac{5x + 11}{3(x + 8)} [/tex]

Step-by-step explanation:

[tex] \frac{5x + 11}{3(x + 8)} [/tex]

Five times the sum of a number and eleven, divided by three times the sum of the number and eight

Five times the sum= 5(_+_)

a number and eleven= x+11

divided= ÷ or /

3 times the sum of= 3(_+_)

the number and eight.

Together it will be

[tex]the \: \: one \: written \: in \: the \: answering \: section[/tex]

Hope this helps ;) ❤❤❤

Answer:

Third option is the right choice.

Step-by-step explanation:

y = -4x + 11       (Slope = m = -4)

3 = -4(2) + 11

3 = -8 + 11

3 = 3

True.

Answer:

To solve for the zeros of the function equate f(x) = 0

That's

- 2x² + x + 5 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a = - 2 b = 1 c = 5

And from the question

b² - 4ac = 41

So we have

[tex]x = \frac{ - 1± \sqrt{41} }{2( - 2)} = \frac{ - 1± \sqrt{41} }{ - 4} [/tex]

[tex]x = \frac{1± \sqrt{41} }{4} [/tex]

We have the final answer as

[tex]x = \frac{1 + \sqrt{41} }{4} \: \: \: \: or \: \: \: \: x = \frac{1 - \sqrt{41} }{4} [/tex]

Hope this helps you

Answer:

The CORRECT answer is A.

Step-by-step explanation:

just did it.

Answer:

He should expect to be stopped a total of 16 times

Step-by-step explanation:

What the question is saying is that out of every 5 intersections, he would be stopped at 2.

Now, for forty times in which he passes through an intersection , we want to know the number of times in which he would be stopped

In this case we only need to multiply the probability by the number of times in which he passes an intersection and that would be 2/5 * 40 = 16 times

Answer:

16

Step-by-step explanation:

Answer:

100 students on each bus

Step-by-step explanation:

100*4 is 400 so there might be just 4

Answer:

Hey there!

It's possible that there are 200 busses, and each  bus carries only 2 people, there are 10 busses and each bus carries 40 people, or there are 5 busses and each bus carries 80 people.

Hope this helps :)

Answer:

480 liters of natural oil

Step by step Explanation:

ratio of natural to synthetic oil

= 5:3

If 440 liters have to be made then,

Add 5 + 3 = 8

So, 5/8 of 768 liters will be = 480 liters of natural oil

and, 3/8 of 768 liters will be = 288liters of synthetic oil

Therefore, 480 liters of natural oil will be needed

Answer:

The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)

Step-by-step explanation:

The coordinates of quadrilateral EFGH are;

Point E has coordinates (-1, 1)

Point F has coordinates (0, 4)

Point G has coordinates (3, 1)

Point H has coordinates (3, 0)

The coordinates of the translation are;

Point E' has coordinates (0, -3)

Point F' has coordinates (1, 0)

Point G' has coordinates (4, -3)

Point H' has coordinates (4, -4)

The change in the y-coordinate values (y values) are;

From point E to point E', we have;

(-3 - 1) = -4 which is four units down

The change in the x-coordinate values (x values) are;

From point E to point E', we have;

(0 - (-1)) = 2 which is two units to the right

The total change in translation is [tex]T_{(2, -4)}[/tex].

Answer:

d = 8.5

Step-by-step explanation:

The following data were obtained from the question:

Angle D = 100°

Opposite D = d

Opposite E = e = 6

Opposite F = f = 5

Thus, we can obtain the value of d by using the cosine rule as shown below:

d² = e² + f² – 2ef Cos D

d² = 6² + 5² – 2 × 6 × 5 × Cos 100°

d² = 36 + 25 – 60 × Cos 100°

d² = 61 – – 10.419

d² = 61 + 10.419

d² = 71.419

Take the square root of both side.

d = √71.419

d = 8.5

Therefore, the value of d is 8.5

The probability that student chose running is 9/49 .

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Consider the information as that 49 students choose to attend one of three after-school activities: football, tennis, or running.

11 students choose football,  29 students choose tennis.

The students choose running = 49 - 11 - 29 = 9.

The students choose running = 0

This means out of 49 students 9 choose running.

P(E) = 9/49

Hence, the probability that student chose running is 9/49 .

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ2

Answer:

Total possible outcomes = 6×6 = 36

a) P(5) = 1/9

b) P(11) = 1/18

c) P(two and six) = 1/36

Step-by-step explanation:

A black die and a white die are thrown at the same  time.

Each die has six sides so total possible outcomes are

Total possible outcomes = 6×6 = 36

The possible outcomes are given below:

(1, 1)  (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

a) Find the  probability of obtaining a total of 5

Number of ways to get a total of 5 = (1, 4) (2, 3) (3, 2) (4, 1)

Number of ways to get a total of 5 = 4

The probability is given by

P = Number of desired outcomes/total number of outcomes

P(5) = 4/36

P(5) = 1/9

b) Find the  probability of obtaining a total of 11

Number of ways to get a total of 11 = (5, 6) (6, 5)

Number of ways to get a total of 11 = 2

The probability is given by

P(11) = 2/36

P(11) = 1/18

c) a 'two' on the black die and a six' on the white die.

There is only one way to get a two on the black die.

Probability of obtaining a two on the black die = 1/6

There is only one way to get a six on the white die.

Probability of obtaining a six on the white die = 1/6

P(two and six) = 1/6×1/6

P(two and six) = 1/36

Answer:

350 meters cubed.

Step-by-step explanation:

If you visualize it, there are two rectangular prisms: one flat one on the top, and one large one on the bottom.

The width of the top one is 5 meters. The length is 7 meters. The height is 8 - 5 = 3 meters. So, one prism has a volume of 5m x 7m x 3m.

The width of the bottom one is 7 meters. The length is 7 meters. The height is 5 meters. So, the bottom prism has a volume of 7m x 7m x 5m.

(5 * 7 * 3) + (7 * 7 * 5)

= (35 * 3) + (49 * 5)

= 105 + 245

= 350

So, the volume of the figure is 350 meters cubed.

Hope this helps!

Answer:

3.90%

Step-by-step explanation:

Relevant Data provided as per the question below:

Annual dividend = $0.28 and $0.16

Current per share = $11.27

According to the given situation, the calculation of the current yield of the stock is shown below:-

Current yield is

[tex]= \frac{Annual\ dividend}{Current\ share\ price} \times 100\\\\ = \frac{0.28 + 0.16}{11.27} \times 100[/tex]

[tex]= \frac{0.44}{11.27} \times 100[/tex]

= 3.90%

Therefore for computing the current yield of the stock we simply applied the above formula.

Answer:

c.

Step-by-step explanation:

90 degrees clockwise is (x,y)-(y,-x)

Answer:

The answer is A

Step-by-step explanation:

Took the test

Answer:

Below

Step-by-step explanation:

r us the radius of the base and h is the heigth of the cylinder.

The volume of a cylinder is given by the formula:

V = Pi*r^2*h

V/Pi*r^2 = h

We can write a function that relates h and r

Answer:

One of the cylinders is short and wide, while the other is tall and thin.

Step-by-step explanation:

sample answer given on edmentum

Answer:

k = 5

Step-by-step explanation:

The equation of proportionality is

y = kx ← k is the constant of proportionality

Given

y = 5x , then k = 5

Answer:

(2, −1) and (−4, 17)

Step-by-step explanation:

I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).

Answer:(2, −1) and (−4, 17) Its C on Edge 2023

Step-by-step explanation: Its (C) after an extensive research

Answer:

f ( x ) = -3*cos ( x ) -2                    

Step-by-step explanation:

Solution:-

The standard generalized cosine function is given in the form:

                             f ( x ) = a* cos ( w*x - k ) + b

Where,

                   a: The magnitude of the waveform

                   w: the frequency of the waveform

                   k: The phase difference of the waveform

                   b: The vertical offset of central axis from the origin

To determine the amplitude ( a ) of the waveform. We will first determine the central axis of the waveform. This can be determined by averaging the maximum and minimum values attained. So from graph:

                   Maximum: 1

                   Minimum: -5

The average would be:

                  Central axis ( y ) = [ 1 - 5 ] / 2

                                              = -4 / 2

                                         y   = -2

The amplitude ( a ) is the difference between either the maximum value and the central axis or minimum value and the central axis. Hence,

                   a = Maximum -  Central value

                   a = 1 - (-2)

                   a = 3  

The waveform is inverted for all values of ( x ). That means the direction of amplitude is governed to the mirror image about x-axis. Hence, a = -3 not +3.

The offset of central axis from the x - axis ( y = 0 ) is denoted by the value of ( b ).

                   b = ( y = -2 ) - ( y = 0 )

                   b = -2   ... Answer

The frequency of the waveform ( w ) is given as the number of cycles completed by the waveform. The peak-peak distance over the domain of [ 0, 2π ]. We see from the graph is that two consecutive peaks are 2π distance apart. This means the number of cycles in the domain  [ 0, 2π ] are w = 1.

The phase difference ( k ) is determined by the amount of "lag" or "lead" in the waveform. This can be determined from the x-distance between x point value of peak and the origin value ( x = 0 ). The peak and the origin coincides with one another. Hence, there is no lag of lead in the waveform. Hence, k = 0.

The waveform can be written as:

                      f ( x ) = -3*cos ( x ) -2