Use the next of a rectangular prism to answer the question

Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches

Step-by-step explanation:

Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 17 3/4= 71/4 inches

d = 103/12 inches

n = 3 weeks

the height in inches, of the pile after 3 weeks, T3. Therefore,

T3 = 71/4 + (3 - 1)103/12

T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6

T3 = 419/12 inches = 34 11/12 inches

Answer:C) 4 feet and 12 feet

Step-by-step explanation:

The diagram of the first mural is shown. The formula for determining the perimeter of a rectangle is expressed as

Perimeter of rectangle = 2(L + W)

The length of the first mural is given as 8ft while the width of the first mural is given as 6 ft. The perimeter becomes

P = 2(8 + 6) = 2×14 = 28ft

The area of a rectangle is expressed as L×W

The area if the first mural would be

6 × 8 = 48ft^2

The second mural has the same area as the first mural but has a different perimeter. The side lengths of the second mural are

4 ft and 12ft

Area = 4×12 = 48 ft^2

Perimeter = 2(12+4) = 32ft

So area is the same and perimeter is different.

Answer:

y equals one fourth times x minus 16

y = 4x − 16

Step-by-step explanation:

this is because you're taking the time it took to get there minus 16 because of the delay

Answer:

Answer is three because it is one fourth of the time don't listen to the other person's.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diameter equals the side length of the outer square. The radius of the circle is √2. The diameter of the circle would be

2 × radius = 2 × √2 = 2√2

The area of a square is expressed as length^2. This means that the area of the outer square would be

( 2√2)^2 = 4×2 = 8

The area of the circle is expressed as πr^2. Therefore, the area of the circle would be

π×√2^2 = 2π = 2×3.14 = 6.28

Looking at the inner square, to find the length of the base, we would apply Pythagoras theorem.

√2^2 = base^2 + 1^2

2 = base^2 + 1

base^2 = 2 -1 = 1

base = √1

Area of the inner square would be

√1^2 = 1

Total shaded area would be

6.28 - 1 = 5.28

The probability that the dart will land on the shaded area is

5.28/8 = 0.66

Answer:

per person$15.71

Answer:

AE = 70

Step-by-step explanation:

Given that ACE is a triangle and B , D , F are mid-points of AC, CE, AE respectively.

⇒ BF, FD, BD are mid-segments.

Mid-segment is a line segment joining mid points of two sides of a triangle,

And it as two properties :

1) mid-segment is always parallel to the third side

2) mid-segment is half in length of the third side

⇒ Here, BD is the mid-segment and is parallel to third side AE

And also BD is half of AE

⇒ AE = 2×BD = 2×35

⇒ AE = 70.    

Answer:

a=2

Step-by-step explanation:

Well, first let us find product of the first 8 positive integers, which is 1*2*3*4*5*6*7*8=40320. It can also be written as 40320=[tex]2^{7}[/tex]*3²*5*7. From the formula above, it can be extracted that if a=2, n can be any number from 3 to 7 (considering that a and n are not equal and greater than 1).

In (1) a^n=64 and in (2) n=6 so it can be written as 2^6=64 so a=2 and n=6. So the value of a is 2. a=2

Answer:

c

Step-by-step explanation:

Answer:

64 square inches

Step-by-step explanation:

The base is square, and there are 16 cupcakes, so there are 4 cupcakes along the width and 4 cupcakes along the length.

Each cupcake is 2 inches, so the base is 8 inches by 8 inches.  Therefore, the area is 64 square inches.

Answer:

Step-by-step explanation:

Answer:

B. [tex]\displaystyle y = -2x + 7[/tex]

Step-by-step explanation:

The y-intercept is given to us, which is [tex]\displaystyle [0, 7],[/tex]and Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −2 remains the way it is.

I am joyous to assist you anytime.

Answer:

108 feet long

Step-by-step explanation:

You know that to find the perimeter you have to add up all the sides. A rectangle has 4 sides, so 30+30 is 60 and 24+24 is 48. Add 60 and 48 up and you get 108 as the perimeter. Since Madhu is hanging a string of flowers on the PERIMETER, the flower string will need to be 108 feet long.

Hope this Helped!

Answer:

6 hours

Step-by-step explanation:

Suppose Madison spent x hours on her social project,

then the number of hours spent on other project will be 1/3 of x=x/3

Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e

x + x/3 = 4x/3

It si given that this is 8 hours, therefore

4x/3=8

Multiplying both sides by 3:

4x=24

Dividing across board by 4:

x= 6 hours

Answer:

  (x, y) = (-3 5/8, 1 5/16)

Step-by-step explanation:

Add y+14 to the second equation to get ...

  3.5x +14 = y

Substitute this for y in the first equation:

  2.5x -3(3.5x +14) = -13

  2.5x -10.5x -42 = -13

  -8x = 29

  x = -29/8 = -3 5/8

Using this in the formula for y, we get ...

  3.5(-29/8) +14 = y

  -203/16 +14 = y = 21/16 = 1 5/16

Answer : The value of x and y is, 4 and 27 respectively.

Step-by-step explanation :

The given equations are:

[tex]2.5x-3y=-13[/tex]       ...........(1)

[tex]3.25x-y=-14[/tex]      .........(2)

or,

[tex]y=3.25x+14[/tex]     ..........(3)

Now put equation 3 in 1, we get the value of 'x'.

[tex]2.5x-3y=-13[/tex]

[tex]2.5x-3(3.25x+14)=-13[/tex]

[tex]2.5x-9.75x-42=-13[/tex]

[tex]-7.25x=-13+42[/tex]

[tex]-7.25x=29[/tex]

[tex]x=-\frac{29}{7.25}[/tex]

[tex]x=-4[/tex]

Now put the value of 'x' in equation 3, we get the value of 'y'.

[tex]y=3.25x+14[/tex]

[tex]y=3.25(4)+14[/tex]

[tex]y=13+14[/tex]

[tex]y=27[/tex]

Therefore, the value of x and y is, 4 and 27 respectively.

Answer:

  AB = DC = 12

  AD = BC = 10

Step-by-step explanation:

For ABCD to be a parallelogram, opposite side pairs must be congruent. That will be the case when ...

  AB = DC

  x+4 = 12 . . . . substitute expressions for length

  x = 8 . . . . . . . subtract 4

Then the lengths of AD and BC must be ...

  BC = AD = x+2 = 8+2 = 10

___

The figure will be a parallelogram when x=8 and sides have lengths ...

  AB = DC = 12

  AD = BC = 10

_____

Comment on the problem

Of course, if x ≠ 8, or BC ≠ AD, the figure will not be a parallelogram. You are asked to show the figure IS a parallelogram, but all you can really show is that the figure CAN BE a parallelogram. In order to do anything useful with the given expressions for side lengths, you must assume the figure is a parallelogram.

Answer:

$32,000

Step-by-step explanation:

Yearly investment = $3,000

Number of years = 20

Investments earned an average of 8 percent a year.

Total invested amount = $3,000 × 20 = $60,000

Current value of investment = $92,000.

We need to find the total earnings on the investment.

Earnings = Current value of investment - Total invested amount

Earnings = $92,000 - $60,000

Earnings = $32,000

Therefore, the total earnings is $32,000.

To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.

This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.

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Final answer:

It takes 30 minutes for the moon's shadow to travel 1150 miles during a solar eclipse based on the speed of 2300 miles per hour.

Explanation:

The question asks us to calculate the amount of time it takes the moon's shadow to travel a certain distance during a solar eclipse, based on given speeds and distances. We know that the shadow travels 2300 miles in one hour, so the speed of the shadow is 2300 miles per hour. In the first 20 minutes, the shadow traveled 766 ⅓ miles. To find the time it takes the shadow to reach 1150 miles, we set up a proportion since the motion of the shadow is at a constant speed.

First, let's convert the 20-minute travel time to hours by dividing by 60, which is ⅓ of an hour (20 / 60 = ⅓). Then we can set up the proportion as follows:

766 ⅓ miles is to ⅓ hour, as 1150 miles is to T hours. Which gives us:

(766 ⅓ / 2300) = (⅓ / 1)

(1150 / 2300) = (T / 1)

Now, we solve for T:

⅓ = 1150 / 2300

T = ⅓

So, T is ⅓ of an hour, which means that it takes ⅓ of an hour for the shadow to reach 1150 miles. We can convert ⅓ of an hour to minutes by multiplying by 60, thus:

T = ⅓ × 60

T = 30 minutes

Therefore, it takes 30 minutes for the shadow to reach 1150 miles.

Final answer:

To calculate the percent error, subtract the actual attendance from the predicted attendance, take the absolute value, divide by the actual attendance, and multiply by 100%. Sheila's prediction has a percent error of 37.14%.

Explanation:

The question is asking for the calculation of the percent error between Sheila's prediction for concert attendance and the actual attendance. To find the percent error, you subtract the actual value from the predicted value, take the absolute value of the difference, divide by the actual value, and then multiply by 100 to convert it to a percentage.

Steps to Calculate Percent Error

The percent error in Sheila's prediction is 37.14%.

The highest point for the dollhouse will be 3.12 feet

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

His house is 28 feet wide and 36 feet tall at the highest point of the roof.

And, The dollhouse will be 2.5 feet wide.

Now,

Let the highest point for the dollhouse = x

So, By definition of proportion, we get;

⇒ 28 / 36 = 2.5 / x

Solve for x as;

⇒ x = 2.5 × 36/28

⇒ x = 3.12 feet

Thus, The highest point for the dollhouse = 3.12 feet

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Step-by-step explanation:

Length of  automobile = 16 feet = 4.88 m

Length of truck = 28 feet = 8.53 m

Speed of truck = 30 mph = 48 km/h = 13.33 m/s

Time in which automobile to pass truck = 4 s

Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m

Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of  automobile, length of truck and distance traveled by truck in 4 seconds.

Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33

Distance which need to cover by automobile in 4 seconds = 66.74 m

Distance = Speed x Time

66.74 = Speed x 4

Speed = 16.69 m/s = 60 km/h = 96 mph

Automobile must travel at 96 mph to pass the truck in 4 seconds.

Answer:

a) ΔL = 80mm

b) h = 600 - 10w mm

Step-by-step explanation:

a. From the time when 7 L have been removed to the time when 15 L have been removed, the change in the volume has been 8L and how the height of the water decreases 10mm per liter removed, then the acumulate change in the height of water has been (8lt)(10mm/lt) = 80 mm

b) If w liters have been removed, then the change in the height of water is (10mm/lt)(wlt) = 10w mm and thus the water's height at this precise point in time is 600 - 10w mm

The question is incomplete. Here is the complete question:

Two roads that cross at right angles are used as coordinate axes for a map. A library is  located at point L.

Use the drop-down menus to complete the statements about the location of the library.

(a) The library is located at point (_,_).

(b) The library is __  miles from Road X and __  miles from Road Y.

Answer:

(a) The library is located at point (3.25, -1.5).

(b) The library is 1.5 miles from Road X and 3.25 miles from Road Y

Step-by-step explanation:

Given:

The roads are at right angles to each other. Point 'L' is the location of the library.

(a)

From the graph, we can conclude that,

The length of each square in the graph is 0.5 miles. So,

The coordinates of point L are (3.25, -1.5).

The 'x' value is 3.25 and the 'y' value is -1.5.

Since the point 'L' is the location of library, therefore, the library is located at point (3.25,-1.5).

(b)

The distance of point L from road X is obtained by moving vertically up from point L till we reach the road X. In other words, the perpendicular distance between point L and horizontal x axis is the required distance.

The perpendicular distance is the absolute value of the y-coordinate of point L. The absolute value of 'y' of point L is |-1.5| = 1.5 miles.

Hence, the library is 1.5 miles from road X.

Similarly, the distance of point L from road Y is the perpendicular distance of point L to the road Y.

The perpendicular distance is the absolute value of the x-coordinate of point L. The absolute value of 'x' of point L is |3.25| = 3.25 miles.

Therefore, the library is 3.25 miles from road Y.

So, the library is 1.5 miles from Road X and 3.25 miles from Road Y

The productivity of labor increases by 5% would cause the firm to increase hiring capital and decrease hiring of labor

Step-by-step explanation:

A company can convert input data to output data. So, it gets divided the data into broad categories called production factors. Productivity variations, or more precisely the marginal products of labour, work in the same way as differences in real wages. Remember that marginal prices depend on both - real wages and the productivity.

If in case, productivity increases, perhaps because the company has increased its capital base, thereby marginal costs will decrease. Companies will produce more products and employ more employees. Conversely, if productivity drops, companies will produce less and destroy jobs.

When a firm faces union demands for higher wages, they may increase hiring of capital and decrease hiring of labor. This can result in increased labor productivity. In the United States in the 1970s, firms shifted towards more capital and less labor due to union demands for higher wages.

When a firm is confronted with union demands for higher wages, they may choose to increase hiring of capital and decrease hiring of labor. This is because using more physical capital and less labor can result in increased labor productivity.

For example, if the cost of machines increases relative to labor, the firm may shift towards using less capital and more labor to minimize costs. In this situation, the firm would hire more capital and decrease hiring of labor.

In the United States in the 1970s, this situation occurred where firms faced union demands for higher wages, causing a shift towards more capital and less labor in production methods.

Answer:

it is option a

Step-by-step explanation:

. f(x) = (4x + 1)(4x − 1) is the correct answer overall you have the check it and just make sure you fully to your capability of those steps

The equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).

A function assigns the value of each element of one set to the other specific element of another set.

As the function is given to us that f(x)=16x²-1, therefore, the equivalent function that best shows the x-intercepts on the graph can be written as,

[tex]f(x)= 16x^2-1\\\\f(x)=16x^2-1^2\\\\f(x)=(4x-1)(4x+1)[/tex]

If we solve the roots of the given function,

(4x-1)=0

x = 1/4 = 0.25

(4x+1)=0

x = -1/4 = -0.25

Thus, the x-intercept of the function is 0.25 or -0.25.

Thus, the equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).

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Answer:

.006%

Step-by-step explanation:

Answer:

The vertex is the point  [tex](4,11)[/tex]

Step-by-step explanation:

we know that

The equation of the absolute value in vertex form is equal to

[tex]y=a\left|x-h\right|+k[/tex]

where

a is a coefficient      

(h,k) is the vertex

In this problem we have

[tex]y=-2\left|x-4\right|+11[/tex]

so

[tex]a=-2[/tex] ---> the vertex represent a maximum

[tex]h=4[/tex]

[tex]k=11[/tex]

therefore

The vertex is the point  [tex](4,11)[/tex]            

Answer:

∆AKM is a right triangle for it is inscribed in semicircle O.

AM = diameter of semi-circle O = 2R = 2(2) = 4

%22AK%22%2F%22AM%22=cos%2833%5Eo%29

AK+=+AM%2Acos%2833%5Eo%29

AK+=+4cos%2833%5Eo%29

%22KM%22%2F%22AM%22=sin%2833%5Eo%29

KM+=+AM%2Asin%2833%5Eo%29

KM+=+4sin%2833%5Eo%29

The perimeter of a triangle is the sum of the three sides.

perimeter=AK%2BKM%2BAM

perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4

Approximately 9.533238412

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:

Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.

Answer:

[tex]8y^{50}[/tex]

Step-by-step explanation:

This expression is equal :

[tex]{(64y^{100})}^{\frac{1}{2}}[/tex]

Here we can use this rule :

[tex](a^mb^n)^y=a^{my}b^{ny}[/tex]

Now, 64 we can write like : [tex]8^2[/tex]

[tex](8^2y^{100})^{\frac{1}{2}}[/tex]

Now we can use our rule :

[tex]8^{2*\frac{1}{2}}y^{100*\frac{1}{2}[/tex]

When we simplify, we have :

8y^{50}

Answer:

b

Step-by-step explanation: