You roll a six sided dice four times, what is the probability of rolling four sixes?

Answer:

[tex]\frac{2}{5}[/tex]-pound of sand

Step-by-step explanation:

We have been given that Amber has [tex]\frac{4}{5}[/tex]-pound bag of colored sand. She uses 1/2 of the bag for the project.

We need to find 1/2 'of' the 4/5 as:

[tex]\frac{4}{5}\times \frac{1}{2}[/tex]

[tex]\frac{4\times1}{5\times2}[/tex]

[tex]\frac{2\times1}{5\times1}[/tex]

[tex]\frac{2}{5}[/tex]

Therefore, Amber used [tex]\frac{2}{5}[/tex]-pound of sand for the project.

The family has been members of the swimming pool for 8 months. This was calculated by setting up an equation with the formula for the total cost, C = 55m + 25, and solving for the number of months (m), with C set to the amount paid of $465.

To determine how many months a family has been members of a swimming pool with a membership cost of $55 per month plus a one-time registration fee of $25 and a total payment of $465, we need to set up an equation and solve for the number of months.

Let's denote the number of months as m. The total cost of the membership for m months is the monthly rate times the number of months plus the registration fee.

The equation representing the total cost (C) is:
C = 55m + 25

We know that the total cost is $465, so we substitute this value into the equation:

465 = 55m + 25

To solve for m, we first subtract 25 from both sides:

440 = 55m

Then, we divide both sides by 55 to find the number of months:

m = 440 / 55

m = 8

So, the family has been members for 8 months.

The answer to the statement is:

                     TRUE

In order for a segment to form a triangle.

The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining third side of the given triangle.

Here we have three segments of length:

7 units, 9  units and 12 units.

Also, for any two pair:

7 and 9 we have:

7+9=16> 12

for 9 and 12 we have:

9+12=21>7

and for 7 and 12 we have:

7+12=19>9

Hence, the segments could form a triangle.

width = w

 length = w+8

perimieter = 256 feet

formla for perimeter is p=2L+2w

so you have: 256 =2(w+8) +2w =

256 = 2w+16 +2w

256= 4w+16

240=4w

w=240/4 = 60

 width is 60 feet

length = 60+8 = 68 feet

Final answer:

To find vertical asymptotes of a function, factor the denominator, set each factor equal to zero, and solve for x.

Explanation:

To find vertical asymptotes of a function, we need to determine the values of x that make the function approach infinity or negative infinity. Vertical asymptotes occur when the function approaches these values but never reaches them.

To find the vertical asymptotes, follow these steps:

Factor the denominator of the function.

Set each factor equal to zero and solve for x.

The values of x obtained in step 2 are the vertical asymptotes.

For example, let's find the vertical asymptotes of the function f(x) = 1/x. The denominator is x, which is already factored. Setting x = 0, we find that x = 0 is the vertical asymptote.

a) The radius of the navy pier wheel is 70 feet.

b) The radius of the first ferris wheel is 125 feet.

c) The speed of the wheel is 87.2 ft/sec

Given data:

The circumference of circle = 2πr

The area of the circle = πr²

a)

The circumference = 2πr

where π = 3.142

r = radius

Therefore, 2πr = 439.6

(2 * 3.142 * r) = 439.6

6.284r = 439.6

On simplifying the equation:

Radius = 439.6/6.284

Radius = 69.9

≈ 70 feet

b)

The Navy Pier Ferris Wheel in Chicago has a circumference that is ​56% of the circumference of the first Ferris wheel.

So, 56% of f = 439.6

0.56f = 439.6

f = 439.6/0.56

f = 785

The circumference of the first wheel is 785 feet.

Now, 2πr = 785

r = 785/2π

r = 785/(2×3.142)

r = 785/6.284

r = 124.9

≈ 125ft

c)

The first ferris wheel took nine minutes to make a complete revolution.

So, the speed of wheel is determined as:

s = 785/9

s = 87.2 ft/sec

To learn more about circle, refer:

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The complete question is attached below:

If the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893.

a. What is the radius of the navy pier wheel?

b. what was the radius of the first ferris wheel?

c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?

C=439.6 ft.

The tip of the minute hand moves approximately (8/3)π inches in 20 minutes, using the circumference of the circular path it follows and the proportion of the path covered in that time.

The student is asking about the distance traveled by the tip of the minute hand of a clock over a 20-minute period. To find the distance, we'll consider the movement of the minute hand as part of a circular path, which is described by the arc length of the circle segment.

The length of the minute hand, which is 4 inches, acts as the radius (r) of the circle. The minute hand completes one full rotation around the clock face in 60 minutes, so in 20 minutes, it covers one-third of a full rotation. We can find the arc length of the minute hand's path using the formula for the circumference of a circle (C = 2πr), multiplied by the fraction of the rotation:

Circumference: C = 2π(4 inches) = 8π inches

Arc Length for 20 minutes: (1/3) × 8π inches = (8/3)π inches

Therefore, the tip of the minute hand moves approximately (8/3)π inches in 20 minutes.

Answer:

A. 64π cubic centimeters

D. Gold (19300 kg per cubic meter)

The height of the cylinder is 3.04 unit

Step-by-step explanation:

A waffle cone for ice cream has a diameter of 8 centimeters and a height of 12 centimeters. What is the volume of the cone, in cubic centimeters?

A. 64π cubic centimeters

B. 32π cubic centimeters

c. 256π cubic centimeters

D. 192π cubic centimeters

EXPLANATION

Volume of a cone is given by the formula  V=[tex]\frac{\pi*r^{2}*h }{3}[/tex]

V = [tex]\frac{\pi *4^{2}*12 }{3}[/tex]   = 64π

The correction option is A

Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25 cubic meters. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins.

What kind of metal are the coins made of?

Bronze (8700 kg per cubic meter)

Silver (10500 kg per cubic meter)

Lead (11300 kg per cubic meter)

Gold (19300 kg per cubic meter)

the formula for Density is density = mass/volume

The density of the metal = 4825/0.25 = 19,300kg.

Therefor the coins are made of Gold

The correction option is D

A cylinder with radius 3 units is shown. Its volume is 86 cubic units.

Find the height of the cylinder.

Use 3.14 for π and round your final answer to the nearest hundredth.

The volume of a cylinder is given as V= πr^2h

86 =3.14 * 3^2*h

Make h the subject of the formula h =86/(3.14*9) =86/28.26 =3.04 unit

The height of the cylinder is 3.04 unit

Indication "12/10, n/30" (or "12/10 net 30") on an account represents a cash (sales) discount provided by the seller to the buyer for swift payment.

The term 12/10, n/30 is a classic credit term and means the following:

The discount date begins at August 9 and the last day would be August 19.

The '12/10, n/30' term means a 12% discount is given if payment is made within 10 days of the invoice date, and the entire invoice must be paid within 30 days. As such, the discount date is August 19.

The sale terms 12/10, and n/30 in the question denote a sale transaction where the seller is offering the buyer a 12% discount if they pay the invoice within 10 days of the invoice date. The 'n/30' part means that the rest of the invoice amount needs to be paid within 30 days. So, if the manager of the new business opts to take the cash discount, the discount date falls on August 19 (the invoice date - August 9 plus 10 days).

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Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.

10x - 2y = 3

-2y = -10x + 3

-2y/-2 = -10x / -2 + 3/-2

y = 5x - 3/2

The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.

point slope form =  y – y1 = m(x – x1)

Remember m = slope = 5. Now plugin our x and y cord  from the point (0,1) and our slope of 5

y - y1 = m(x - x1)

y - 1 = 5(x - 0)

y - 1 = 5x - 0

y - 1+1 = 5x + 1

y= 5x + 1

So the point (0,1) passes through y = 5x + 1

Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.

8) 

Point = (5,8)

Slope = 7

y - y1 = m(x - x1) 

y - 8 = 7(x - 5) 

y =  7x - 27

So for number 8 the point (5,8) passes through y = 7x - 27

(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.

Point = (-4, 6)

Slope = 2/5 

perpendicular slope = 5/2

y - 6 = 5/2(x - (-4))

y = 5/2 x + 16

So point (-4, 6) passes through y = 5/2 x + 16

(10) Point (4,1) passes through y = 7/5 x - 23/5

Answer:

Step-by-step explanation:

First, let's formulate an equation. Let the independent variable be x to denote the number of hours. The dependent variable is y to denote the total cost. The equation should be:

y = 25x + 50

The table and graph is shown in the picture. Just use values of x as 1, 2, 3 and 4, find y and plot the points.

To find how much the temperature fell, we created an equation using the given temperatures at 5 P.M. and 10 P.M. We subtracted the temperature at 10 P.M. from the one at 5 P.M. and found the temperature fell by 25 degrees.

The subject of this question is Mathematics and this question is for the Middle School grade level.

To solve this problem, we can create an equation using the given information about the temperature at two different times. At 5 P.M., the temperature (let's assume T1) is 20∘F. At 10 P.M., the temperature (let's assume T2) is -5∘F. Therefore, to find how much the temperature fell, we subtract the temperature at 10 P.M. from the temperature at 5 P.M., so the equation would be T1 - T2.

Substitute the temperatures into the equation: 20 - (-5) = 20 + 5 = 25.

Therefore, the temperature fell by 25 degrees.

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Answer:

x - 2y = -1

this is correct

Answer: Congruent angles have the same measure

Step-by-step explanation:

The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].

Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:

ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]

The area of a trapezoid is given by:

Area = [tex]\frac{1}{2}[/tex] * base * height

For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:

Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]

We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:

Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]

Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]