You want to put a 6 inch thick layer of topsoil for a new 24 ft by 25 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.

Answer:

800

Step-by-step explanation:

16,000 x 0.05 = 800

We solve the system of equations -5x - 5y = 0 and y = 8x using the substitution method. Substituting y = 8x into the first equation, then solving for x and y, we find that x = 0, y = 0.

To solve the system of equations -5x - 5y = 0 and y = 8x we will use substitution method. The substitution method involves substituting the expression from one equation into the other equation. Here, we are given that y is equal to 8x, so we can substitute 8x in place of y in the first equation. That gives us:

-5x - 5*(8x) = 0

Solve this equation, we get x = 0. Now, substitute x = 0 in the second equation to find y. That gives us:

y = 8*0

So, y = 0. Therefore, the solution to the system of equations is x = 0, y = 0.

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The equation of the parabola opening up or down with a vertex at the origin and passing through the point (4,2) is y = 0.125x².

The equation of a parabola in vertex form is represented by y = a(x-h)² + k, where (h, k) is the vertex of the parabola, and 'a' is a coefficient that determines the direction and steepness of the parabola.

Since the vertex of the parabola in this case is at the origin (0, 0), the equation simplifies to y = ax²

We know the curve passes through the point (4,2), so we can substitute these values into the equation 2 = a(4)², which simplifies to 2 = 16a. Solving for 'a' gives us a = 2/16 or a = 0.125.

Thus, the equation of the parabola is y = 0.125x²

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The equation of a parabola with vertex at (0,0) passing through (4,2) is y = (1/8)x². This is derived by using the vertex form and solving for 'a'.

Equation of a Parabola in Vertex Form

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k, where (h, k) is the vertex.

In this case, the vertex of the parabola is at (0, 0), so the equation simplifies to:

y = ax²

Since the parabola passes through the point (4, 2), we can substitute this point into the equation to find the value of 'a':

Substitute x = 4 and y = 2:

2 = a(4)²

2 = 16a

Solve for 'a': a = 2/16 = 1/8

Therefore, the equation of the parabola in vertex form is: y = (1/8)x²

Answer:

Step-by-step explanation:

The given quadratic equation is expressed as

4x² + 2x = 7

The first step is to divide both sides of the equation by 4. It becomes

4x²/4 + 2x/4 = 7/4

x² + x/2 = 7/4

The next step is to add the square of half of the coefficient of x to both sides of the equation. It becomes

x² + x/2 + (1/4)² = 7/4 + (1/4)²

(x + 1/4)² = 7/4 + 1/16

(x + 1/4)² = 29/16

Taking square root of both sides of the equation, it becomes

x + 1/4 = ±√29/4

x = - 1/4 ± √29/4

x = (- 1 + √29)/4 or x = (- 1 - √29)/4

x = (- 1 + 5.385)/4 or x = (- 1 - 5.385)/4

x = 1.09625 or x = - 1.59625

Answer:

It is not reasonable

Step-by-step explanation:

We have a population of 150 and the person takes 10 data from the raccoons, if we take the average of these values, we are left with:

(17 +19 +20 +21 +23 +27 +28 +28+ 28 + 32) / 10 = 24.3

Therefore the inference of the average weight is to approximate up to 25.

This is NOT correct, since it cannot be approximated in this way first and also that the sample is not representative. 10 sample data of 150, which is the population, will give results with a very large margin of error and with a minimum level of confidence.

Therefore it is not reasonable.

Answer:

No

Step-by-step explanation:

Here we have the weights as follows

17, 19, 20, 21, 23, 27, 28, 28, 28, 32

Sum = 243 pounds

Sample size = 10

Which gives the average as 243/10 = 24.3

Therefore, since the average is a point estimate, and measure of central tendency, to give the average rounded up in error will impact on the description of the data as the average is closer to 24 than to 25.

Answer:

6

Step-by-step explanation:

8(.25)-1+.5(10)

2-1+5

1+5

6

It will take about 11.55 years to double his money.

Important information:

The formula for the amount in continuous compound interest is:

[tex]A=Pe^{rt}[/tex]

Where A is the amount, P is the principal, r is the rate of interest and t is time in years.

Substitute [tex]A=10000, P=5000,r=0.06[/tex].

[tex]10000=5000e^{0.06t}[/tex]

[tex]\dfrac{10000}{5000}=e^{0.06t}[/tex]

[tex]2=e^{0.06t}[/tex]

Taking ln on both sides, we get

[tex]\ln 2=\ln e^{0.06t}[/tex]

[tex]\ln 2=0.06t[/tex]

[tex]\dfrac{\ln 2}{0.06}=t[/tex]

[tex]t=11.55245[/tex]

[tex]t\approx 11.55[/tex]

Therefore, it will take about 11.55 years to double his money.

Find out more about 'Continuous compound interest' here:

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Answer:

$268.80

Step-by-step explanation:

#first convert the patio's dimensions to feet:

[tex]1 \ Yd= 3 \ ft\\\\4\frac{2}{3}\times 3=14\ ft\\\\5\frac{1}{3}\times 3=16\ ft[/tex]

#We now calculate the patio's area in sq ft:

[tex]A=lw\\\\=14\times 16\\\\=224\ ft^2[/tex]

#To determine the total cost of the pavers, we multiply by the cost  per sq foot;

[tex]Cost=Area \times Cost/sq \ ft\\\\=224\times 1.2\\\\=268.80[/tex]

Hence, the pavers cost a total of $268.80

Answer:

The true average mileage of the Libra  Using Null hypothesis is as ;

H0:μ≤26

(Ha):μ >26

Step-by-step explanation:

Given:

Libra, will average better than 26 miles per gallon in the city

To Find:

Average mileage of the Libra.

Solution:

This problem is related to the null hypothesis  and alternate hypothesis.

i.e Null Hypothesis is the statement which is true and statement which contradictory is called alternate hypothesis.

“reject H0” if the sample information favors the alternative hypothesis.

“do not reject H0” / “decline to reject H0” if the sample information is insufficient to reject the null hypothesis

So given that condition is libra will have average better than 26

So it will include 26 and above values .

i.e. True  condition is called as null hypothesis (H0)

so true average will be greater than 26

So H0:μ≤26

And the Alternate hypothesis will be the contradictory to true condition

(Ha):μ >26 .

The rounded number is 0.01.

To round 0.00706 to 2 significant figures, we first need to identify the non-zero digits and any zeros between them. The non-zero digits in this number are 7 and 6. There are no zeros between them.

Since the second significant digit is 6, which is greater than or equal to 5, we round the first significant digit up. Therefore, the rounded number is 0.01.

Here is a table of the rounding rules:

| Digit to the right of the last significant digit |

| Less than 5 | Round the last significant digit down |

| 5 or greater | Round the last significant digit up |

For such more question on number

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Answer:

b = 10

Step-by-step explanation:

We know

x^2 / (24^2)  -    y^2/ ( b^2) = 1

equation:  directrix   x  =  a^2 / c  = 576/26

a = 24

24^2/ c =  576/26

c = 26

so     a^2 + b^2 = c^2

so   24^2  + b^2 =  26^2

b^2 =  26^2 - 24^2 =  100

b = 10

you gave us nothing to go off of..no details or anything i was gonna say 7 until i realized b has no values

0.694 rounded to the nearest hundredth remains 0.69 because the third digit after the decimal is 4, which is less than 5.

The question asks for 0.694 to be rounded to the nearest hundredth.

To round to the nearest hundredth, you look at the third digit after the decimal point.

If this digit is 5 or greater, you round the second digit after the decimal up.

In this case, the third digit is 4, which is less than 5.

Therefore, when rounding 0.694 to the nearest hundredth, it remains 0.69.

Answer:

¢42 per game

¢1.11 per minute

Step-by-step explanation:

Please refer to the attached image for explanations

LeBron James earns approximately $0.42 per game and $0.01 per minute based on the given salary and total games and minutes played for the season.

The student has asked two questions about calculating earnings per game and per minute for LeBron James, based on a given salary for a season and the total number of games and minutes played.

To calculate the earnings per game, we divide the total salary for the season by the number of games played. If LeBron James was paid $31 for the season and played 74 games, his earnings per game would be: $31 ÷ 74 games = $0.4189 per game, which rounds to $0.42 per game to the nearest cent.

For the earnings per minute, we divide the total salary for the season by the total number of minutes played. With $31 for the season and 2,796 minutes played, his pay per minute would be: $31 ÷ 2,796 minutes = $0.0111 per minute, rounding to $0.01 per minute to the nearest cent.

Answer:

She got a 76

Step-by-step explanation:

All you have to do is divide 19/25. You'll get your answer. Hope you understand. If you have any concerns, contact me! Also, a fraction is a division problem! The number on the top goes first!

Answer:

28.3 square inches

Step-by-step explanation:

In the question, we are asked to calculate the portion of the area of the cake eaten by Ellie’s sister.

To calculate this, the first thing to do is to calculate the area of the cookie cake. Now, since it’s a round cake, then it must be circular in shape.

Hence we calculate the area.

mathematically the area of a circle can be calculated using the formula;

A = pi * r^2

here our r =6 inches

Substituting this, we have

A = 22/7 * 6 * 6 = approximately 113 sq. inches

we now move on to calculate the portion ate, which is a quarter

That would be 1/4 * 113 = 28.3 sq. inches was eaten

Answer:

28 Square inches

Step-by-step explanation:

Since the cookie is round, it is in a circular shape.

Radius of the Cookie Cake, r= 6 Inches

Area of a Circle [tex]=\pi r^2[/tex]

Therefore, the area of the whole cookie cake [tex]=\pi X 6^2 =113.097 \:Square\: Inches[/tex]

Since Ellie's Sister ate 1/4 of the cookie cake,

Area of cake eaten by Ellie's Sister

[tex]\frac{1}{4} X 113.097\\ =28.27[/tex]

Ellie's Sister ate approximately about 28 Square inches of cake.

Answer:

It B and C

Step-by-step explanation:

the equation in Pythagorean theorem is  a^2+b^2=c^2

so the answer for B would be 5^2*5^2=50,which is correct sine 5^2=25,and 25+25=50

The answer for C would be like 9^2+12^2=225

the square root of 225 is 15 which is correct.

but A is wrong because 5^2+6^2=31 is wrong.

Answer:

its A and C

Step-by-step explanation:

khan academy

Answer:

(Area of circle a)/5

Step-by-step explanation:

(Area of circle b) = (1/5)* (Area of circle a)

What is the area of circle a?  There is not enough given information

Answer:

area of circle a/5

Step-by-step explanation:

The equation: 1/5(a) = b

multiply 1/5(a)

We get the area of circle a/5

Answer:

50

Step-by-step explanation:

v = the original speed of the cruise

d = 225 km the distance passed

t = d/v = 225/v the total time of the travel

v*1.5 + (v + 10)(d/v - 1.5 - 0.5) = d (using the formula distance = speed*time)

1.5v + (v + 10)(225/v - 2) = 225

Look at the images to see the solved equation

Answer:

sqrt(15)/ sqrt(3)

sqrt(5)

sqrt(25)/ sqrt(5)

Step-by-step explanation:

Sqrt(100)/sqrt(20)

We know sqrt(a)/sqrt(b) = sqrt(a/b)

Sqrt(100/20)

sqrt(5)

sqrt(100)/sqrt(20)

10 / sqrt(4) sqrt(5)

10/2 sqrt(5)

5/ sqrt(5)

Rewriting 5 as sqrt(25)

sqrt(25)/ sqrt(5)

We can also look at

sqrt(15)/ sqrt(3)

We know sqrt(a)/sqrt(b) = sqrt(a/b)

sqrt(15/3)

sqrt(5)

There are 3 choices that are equal to sqrt(100)/ sqrt(20)

Joseph and Wilson will each have ridden 45 kilometers to meet halfway, and it will take each of them 5 hours to do so.

Joseph and Wilson are biking towards each other. Joseph has already traveled 10 kilometers and is moving at a constant speed of 7 kilometers per hour. Wilson has just started and rides at a speed of 9 kilometers per hour. To determine how far each boy will have ridden to meet halfway and how long that will take, we need to use the relation between distance, speed, and time.

Let's assume the total distance between their houses is 2d kilometers. Meeting halfway means each boy will cover d kilometers. We already know Joseph has covered 10 kilometers, so he has d - 10 kilometers left to travel. Since Wilson just started, he has the entire d kilometers to cover.

The time it will take for each to travel the remaining distance can be calculated using the formula:

Time = Distance ÷ Speed

For Joseph:
Time = [tex]\frac{d - 10}{ 7}[/tex]

For Wilson:
Time = [tex]\frac{d }{ 9}[/tex]

Since they meet halfway at the same time, the times for each to travel the remaining distance must be equal.
[tex]\frac{d - 10}{ 7} = \frac{d }{ 9}[/tex]

By solving this equation cross-multiplying, we get:
9(d - 10) = 7d

9d - 90 = 7d

2d = 90

d = 45

Each boy will ride for 45 kilometers to meet halfway. Joseph has already covered 10 kilometers, so he will ride an additional 35 kilometers (45 km - 10 km).

Now to find out how long it will take:

For Joseph:
Time = 35 ÷ 7 hours = 5 hours

For Wilson:
Time = 45 ÷ 9 hours = 5 hours

So, both boys will have ridden for 5 hours to meet each other halfway.

Answer:

  ƒ(a + h) = 2(a^3 + 3a^2h + 3ah^2 + h^3)

Step-by-step explanation:

Put (a+h) in place of x and "simplify" the expression.

  f(x) = 2x^3

  f(a +h) = 2(a +h)^3 = 2(a^3 +3a^2h +3ah^2 +h^3) . . . . matches 1st choice

_____

It helps to know the expansion of a binomial:

  (a +b)^3 = a^3 +3a^2b +3ab^2 +b^3

Even if you don't, you can multiply it out.

 (a +b)^3 = (a +b)(a^2 +2ab +b^2) = a^3 +2a^2b +ab^2 +a^2b +2ab^2 +b^3

  = a^3 +3a^2b +3ab^2 +b^3

Answer:

b or d

Step-by-step explanation:

they have the same answers bruh

Answer:

The missing number is either 1 or 2.

1/6 and 2/6 are both less than 1/2.

Answer: Cross-Section of the prism perpendicular to base is equal to base area so the  base area is equal to 2*2=4 ft^2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:right

Answer:

64

Step-by-step explanation:

The first thing we should know is the equivalence between pound and ounce.

1 pound equals 16 ounces. Which means that Rhada has a total of:

3 * 16 = 48 ounces of clay.

We are told that for every 3 ounces of clay you can make 4 ornaments., therefore:

48 * 4/3 = 64 ornaments

Which means that you can with the amount of clay you have can make 64 ornaments.

Answer:

64

Step-by-step explanation:

Answer:

33 Points

Step-by-step explanation:

We can figure out that the total number of points scored by the team is 38+45+49=132. Since we know that Caitlin scored 1/4 of these total points, and 1/4 of 132=33, then she scored 33 points during the first three games.

Answer:

Any number above 85.6

Step-by-step explanation:

To calculate the mean you add all of the scores together then divide by how many scores you added

So in this case you would add 84 + 72 + 90 + 87 + 95 = 428

Then you would Divide 428 by five because you are adding 5 numbers

428/5 = 85.6

It says the score increased so as long as then score is greater than 85.6 it is an option.

Answer:

90, 86, 89, and 92

Step-by-step explanation:

Basically anything above 85.6