Start with a square piece of cardboard to produce a box that is 8 cm deep and whose capacity is exactly 1 liter. how large must the original square be

The hikers are 2064 m apart

The situation forms two right angle triangle.

A right angle triangle has one of its sides as 90 degree.

Therefore,

First hiker distance

tan 37 = opposite / adjacent

tan 37° = 525 / x

x = 525 / tan 37

x = 696.711059326

x = 696. 711 m

Second Hiker distance:

tan 21 = 525 / y

y = 525 / tan 21

y = 1367.68613557

y = 1367.686 m

Distance apart = 696.711 + 1367.686 = 2064.39713557 = 2064 m

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The value of x is 13.

The problem at hand has a quadrilateral shape. The problem depicts four angles and sides, with the only known angle being X.

The graphic depicts four sides (quad), and the stick drawn in the center of each side explains the length relationship.

One stick is equal to two sticks, and two sticks are equal to one stick.

Angles Assumed:

X=102 deg

W=(7x+4) deg

Y=(5x-4) deg

Because angle X is 102 degrees, angle Z must also be 102 degrees. A quadrilateral has a total angle of 360 degrees.

So, to find x, do the following:

102 + 102 + 7x + 4 + 5x - 4 = 360

Add the constant terms: 102 + 102 + 4 - 4 = 204

Combine x terms: 7x + 5x = 12x

Substitute the combined terms:

204 + 12x = 360

Isolate x:

12x = 360 - 204

12x = 156

x = 156 / 12

Simplify:

x = 13

Therefore, the solution is x = 13.

Answer:

f(-2 ) =2

f(0) = 3

f(4) = -1

Step-by-step explanation:

Clearly by looking at the graph of the given function f(x) we could observe that the function f(x) is increasing in the interval (-∞,0] and then decreasing in the interval (0,∞).

Also, the function is discontinuous at x=0.

( Since, there is a break in a graph and also the left and right hand limit of the function are not equal at x=0)

Hence, from the graph we could directly say that:

                 f(-2 ) =2

                 f(0) = 3

                  f(4) = -1

The values of the function values are:

f(-2 ) =2, f(0) = 3 and f(4) = -1

On the graph, the value of the function when x = -2 is 2

Hence, the value of f(-2) is 2

On the graph, the values of the function when x = 0 are 1 and 3.

However, the line that has a closed circle (i.e f(0) = 3) will take precedence over the line that has an open circle (i.e f(0) = 1)

Hence, the value of f(0) is 3

On the graph, the value of the function when x = 4 is -1

Hence, the value of f(4) is -1

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Answer: Volume of cylinder is 1152.38 m³.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 10 m

Height of cylinder = 11 m

Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.

So, Volume of an oblique cylinder is given by

[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]

Hence, Volume of cylinder is 1152.38 m³.

Because C is the centroid, therefore:

Segments PZ = ZR;  RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer:      PC = 20      PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer:      ZC = 5        ZQ = 15

C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:      PQ = 40

Answer:

The answer is the 2 and 5 ones. :)

Step-by-step explanation:

The samples that fairly represent the population are measuring every fiftieth person's height on the school roster, calling every third person on the soccer team's roster, and taking a poll in the lunchroom.

The samples that fairly represent the population are:

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Answer: [tex]-3^x +4[/tex]

Step-by-step explanation:

The equation for the vertical reflection of a function f(x) across the x-axis is given by :-

[tex]y=-f(x) [/tex]

The vertical shift of 'k'  units of a function g(x) is given by :-

 [tex]y=g(x)+k [/tex]

Now, the equation for the vertical reflection of a function [tex]f(x)=3^x[/tex] across the x-axis is given by :-

[tex]-f(x)=-3^x [/tex]

Then , the equation for the vertical shift of 4 units of function [tex]-3^x[/tex] is given by :-

[tex]y=-3^x +4[/tex]

Hence, the function represents transforming [tex]f(x)=3^x[/tex] with a reflection over the x-axis and a vertical shift of 4 units

[tex]y=-3^x +4[/tex]

Answer:

800 is 1.74

700 is 1.54

Step-by-step explanation:

i just took the assignment and it was right

The weight of each tire in pounds is  1.76 pounds for the full steel bead tire and 1.54 pounds for the lighter wheel.

To find the weight of each tire in pounds, we'll first convert the weights from grams to pounds using the conversion factor provided (1 pound = 453.592 grams). Then, we'll round the answers to two decimal places.

Let's denote:

Weight of full steel bead tire = 800 grams

Weight of lighter wheel = 700 grams

Convert the weight of the full steel bead tire from grams to pounds:

[tex]\(800 \, \text{grams} \times \frac{1 \, \text{pound}}{453.592 \, \text{grams}} = 1.763698 \, \text{pounds}\)[/tex]

Rounded to two decimal places, the weight of the full steel bead tire is approximately 1.76 pounds.

Convert the weight of the lighter wheel from grams to pounds:

[tex]\(700 \, \text{grams} \times \frac{1 \, \text{pound}}{453.592 \, \text{grams}} = 1.543235 \, \text{pounds}\)[/tex]

Rounded to two decimal places, the weight of the lighter wheel is  1.54 pounds.

So, the weight of each tire in pounds is  1.76 pounds for the full steel bead tire and 1.54 pounds for the lighter wheel.

It is given that:

The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.

Ques 1)

We are asked to find the probability that the second player will also win a small prize given that the first player wins a small prize.

That is we need to find the conditional probability.

Let A denote the event that first player wins the small prize.

B denote the vent that the second player wins the small prize.

A∩B denote the event that both the player wins the small prize.

Let P denote the probability of an event.

We are asked to find:

P(B|A)

[tex]P(B|A)=\dfrac{P(B\bigcap A)}{P(A)}[/tex]

Now we know that:

[tex]P(A)=\dfrac{25}{100}[/tex]

( Since out of 100 marbles 25 are silver)

Also,

[tex]P(A\bigcap B)=\dfrac{25_C_2}{100_C_2}\\\\\\P(A\bigcap B)=\dfrac{25\times 24}{100\times 99}[/tex]

Hence,

[tex]P(B|A)=\dfrac{24}{99}[/tex]

Hence, the probability that the second player will also win a small prize is:

0.242424

Ques 2)

The probability that the first player will win a large prize is:

5/100

( But the first player draws a silver marble and wins)

The probability that the second player will win a large prize is:

5/99

( Since one marble has been taken out by the first player so the second player is left with 99 choices and here also the second player draws a silver and wins the game)

Similarly,

The probability that the third player will win a large prize is:

5/98

( Since one more marble has been taken out by the second player so the third player is left with 98 choices and here also the third player draws a silver and wins the game)

The probability that the fourth player will win a large prize is:

5/97

Hence, the greatest probability of winning a gold marble is by:

Player 4. ( Since, 5/97 is greater than the rest three probabilities)

Ques 3)

The game can be made fair for each player if all have the equal choices of drawing a marble and this can be done by replacing the marbles that have been drawn out by the previous player.

straight line = 180 degrees

180-92 = 88

 so angle 1 = 88 degrees

there are 5 ways for 1st place, then there would be 4 ways for 2nd place, then 3 ways for third

5*4*3 = 60 different ways

Answer:  The required number of ways is 60.

Step-by-step explanation:  Given that there are five automobiles entered in a race and there are no ties.

We are to find the number of ways in which the first three finishers come in.

Since there are 5 automobiles entered in the race, so the number of ways in which first finisher come in is 5.

Now, there are no ties, so the number of ways in which second and third finisher come in are 4 and 3 respectively.

Therefore, the total number of ways in which the first three finishers come in is

[tex]n=5\times4\times3=60.[/tex]

Thus, the required number of ways is 60.

Answer:

35

Step-by-step explanation:

In rise over run value ( or slope ),

Rise is the unit that moved up or down while the run is the unit that moved from right to left or from left to right.

In the coordinates plane the difference between the y coordinates shows rise and difference in x coordinates shows run,

Thus, the rise over run value from (2,70) to (3,105) is,

[tex]m=\frac{105-70}{3-2}[/tex]

[tex]=\frac{35}{1}[/tex]

[tex]=35[/tex]

In the given graph a line represents the relation between distance and time,

We know that the rise over run value for a line is same as the rise over run value for any two points in the line.

Hence, the rise-over-run value for the relationship represented in the graph is 35.

Third option is correct.

L = lemon drops

J = jelly beans

L +J = 100

L=100-J

1.90L + 1.20J=1.48*100

1.90(100-j) +1.20J =148

190-1.90J+1.20J=148

190-0.7J=148

-0.7J=-42

J = 60

L=100-60 = 40

40 pounds of Lemon Drops are needed

Final answer:

40 pounds of lemon drops are needed.

Explanation:

To find out how many pounds of lemon drops are needed to make a 100-pound mix that costs $1.48 per pound, we can set up a system of equations. Let L represent the number of pounds of lemon drops and J represent the number of pounds of jelly beans.

Since the total weight of the mix is 100 pounds:

L + J = 100

Given the cost of lemon drops is $1.90 per pound and jelly beans cost $1.20 per pound, and the entire mix should cost $1.48 per pound:

1.90L + 1.20J = 100 * 1.48

We already have that L + J = 100, so J can be expressed as 100 - L. Substituting J in the second equation we get:

1.90L + 1.20(100 - L) = 148

Solving for L:

1.90L + 120 - 1.20L = 148

0.70L = 28

L = 28 / 0.70

L = 40

Therefore, 40 pounds of lemon drops are needed for the mix.

The image crosses the x-axis at the points where the function f(x) = (x + 8)(x - 4) equals zero. The points are (-8, 0) and (4, 0).

To identify the points where the image of the parabolic lens crosses the x-axis, we should find the roots of the function f(x) = (x + 8)(x - 4). A function crosses the x-axis at its roots, the points where f(x) is equal to zero.

Setting the function equal to zero gives us (x + 8)(x - 4) = 0. We can see the polynomial is already factored. The roots of the equation are x = -8 and x = 4, since these values of x will make the equation equal to zero.

So, the graph of the function crosses the x-axis at the points (-8, 0) and (4,0). This means the correct option is: (–8, 0) and (4, 0)

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perimeter = 4s

56=4s

s=56/4 = 14

diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm

round answer as needed

Answer:

The approximate length of diagonal is:

19.796 cm.

Step-by-step explanation:

We are given the perimeter of a square as 56 cm.

Let 's' be the side of the square.

We know that the perimeter of square is given as:

[tex]Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14[/tex]

Hence, the side of square is 14 cm.

Now, the length of a diagonal(D) is given as:[tex]D=\sqrt{2}s[/tex]

( Since it could be proved with the help of Pythagorean Theorem )

Hence, as s=14 cm

Hence, the length of diagonal is:

[tex]D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm[/tex]

Hence, the approximate length of diagonal is:

19.796 cm.

To cover 50 windows with coverings that are 15 windows long, at least 4 window coverings are needed to span all the windows.

The question asks how many window coverings are necessary to span 50 windows, given that each window covering is 15 windows long. To find out how many window coverings are required, you divide the total number of windows by the length of one window covering. So, we do 50 ÷ 15 which equals approximately 3.33. Since you can't have a fraction of a window covering, you'll need at least 4 full window coverings to span all 50 windows.

x = 50 * tan(60) = 50sqrt(3) =86.6 feet

tower is 93.6 feet tall

Answer:

The value of k is 4.

Step-by-step explanation:

Given,

f of x equals 1 over 3 x minus 3,

[tex]\implies f(x)=\frac{1}{3}x-3[/tex]

Also, g of x equals 1 over 3 x plus 1,

[tex]\implies g(x)=\frac{1}{3}x+1[/tex]

Since, g(x) = f(x) + k,

By substituting the values,

[tex]\frac{1}{3}x+1=\frac{1}{3}x-3+k[/tex]

[tex]1=k-3[/tex]

[tex]\implies k = 1+3 = 4[/tex]

Hence, the value of k is 4.

Answer:

a

Step-by-step explanation: