A rabbit is 4m away from its burrow. Each hop takes it 0.4m farther from the burrow. The following diagram shows that there is a tasty plant that is 6m from the burrow. Which equation can we use to determine h, the number of hops it takes the rabbit to reach the plant?
A 6h+0.4=4
B 4h+0.4=6
C 4+0.4h=6
D 6+0.4h=4

To estimate the difference between 17/18 and 3/7, one could use benchmark figures. These fractions are approximated as 1 and 1/2 respectively. Therefore, the estimated difference is typically around 1/2 or 0.5.

The student is asking for help to estimate the difference between the fractions 17/18 and 3/7. To estimate this, we first need to understand fractions and benchmark values. A benchmark value is a value that's easy to handle in calculations. For fractions, often 0, 1/2, and 1 are used as benchmarks.

Looking at the given fractions, 17/18 is close to 1 (our benchmark) and 3/7 is about 1/2 (another benchmark). Therefore, to estimate the difference, we subtract our rough approximation of 1/2 from 1, giving us an estimate of 1/2 or 0.5 as the difference.

This is a fairly quick way to estimate the difference between two fractions using benchmark values. It won't provide you with the exact answer, but it will give you a ballpark figure that's usually quite close to the actual result.

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30 days. This is because everyday, the magician only climbs 1 foot since 3-2=1

-5, -4 -1, 3, 5,  if i am correct

Lildude216001,

In order to solve this question you an just order them from least to greatest.

Remember when dealing with negative numbers the one that is usually greater then the other number is shorter.

Therefore your answer is "-5, -4, -1, 3, and 5."

Hope this helps!

X= cost of each bracelet

9x+9=72

9x+9-9=72-9

9x=63

9x/9=63/9

X=7

The answer to the first part is $7 / each bracelet.

Given expression in exponential form : [tex]a^{\frac{4}{9} }[/tex].

We need to convert it into radical form.

Please note: When we convert an exponential to radical form, the top number goes in the exponent of the term and bottom number of the fraction goes in the radical sign to make it nth radical.

We can apply following rule:

[tex](a)^{\frac{m}{n}}= \sqrt[n]{x^m}[/tex].

Therefore,

[tex]a^{\frac{4}{9} }= \sqrt[9]{a^4}[/tex].

Therefore, correct option is : D. ninth root of a to the fourth power.

Hey there!

Given equation :

... 0.2 ( x + 50 ) - 6 = 0.4 ( 3x + 20 )

Using the distributive property.

... 0.2x + 10 - 6 = 1.2x + 8

... 0.2x + 4 = 1.2x + 8

Subtract 4 on both sides.

... 0.2x = 1.2x + 4

Subtract 1.2x on both sides.

... - x = 4

... x = -4

Hence, the answer is -4.

Hope it helps!!

To solve this problem you would distribute the 0.2 and 0.4 inside of the parentheses first. Then you would combine like terms and solve from there on. We are solving for the variable x.

Start by distributing (multiplying) 0.2 and 0.4 inside the parentheses that they are "attached" to (parentheses on their right). After distributing, rewrite the problem.

0.2x + 10 - 6 = 1.2x + 8

1] Combine like terms on the left side of the equation.

0.2x + 4 = 1.2x + 8

2] Subtract 4 from both sides of the equation.

0.2x = 1.2x + 4

3] Subtract 1.2x from both sides of the equation.

-x = 4

4] Divide both sides of the equation by -1 to make the variable x a positive.

4.9 convert it fraction = 49/10

QUESTION 1

Let [tex]n[/tex] represent the number of years.

Then each year the number of people added is given by the function

[tex]N(n)=8.7\times 10^5(n)[/tex]

Therefore after [tex]25[/tex] years,

[tex]N(25)=8.7\times 10^5(25)[/tex]

[tex]N(25)=21750000[/tex]

In scientific notation,

[tex]N(25)=2.175\times 10^7[/tex]

ANSWER TO QUESTION 2

The population after 25 years can be calculated by adding the increment in population to the initial population.

The initial population

[tex]P_0=9.7\times 10^7[/tex]

The population  after 25 years

[tex]P(25)=9.7\times 10^7+2.175\times 10^7[/tex]

[tex]P(25)=(9.7+2.175)\times 10^7[/tex]

[tex]P(25)=(11.875)\times 10^7[/tex]

[tex]P(25)=1.1875\times 10^1 \times 10^7[/tex]

[tex]P(25)=1.1875\times 10^1 \times 10^7[/tex]

[tex]P(25)=1.1875\times 10^8[/tex]

Answer:

1. [tex]2.175*10^{7}[/tex]

2. [tex]1.1875*10^{8}[/tex]

Step-by-step explanation:

We are given that population of a country is [tex]9.7*10^{7}[/tex] , and is increasing by [tex]8.7*10^{5}[/tex] people each year.

1. To find number of people added after 25 years we will multiply 25 by [tex]8.7*10^{5}[/tex].

[tex](2.5\cdot 10^{1})\cdot (8.7\cdot 10^{5})[/tex]

[tex](2.5\cdot 8.7)\cdot (10^{1+5})[/tex]

[tex](21.75)\cdot (10^{6})=(2.175)\cdot (10^{7})[/tex]

Therefore, [tex]2.175\cdot 10^{7}[/tex] will be added after 25 years.

2. To find out population after 25 years we will add population added in 25 years to initial population.

[tex]9.7*10^{7}+2.175\cdot 10^{7}[/tex]

[tex]11.875\cdot 10^{7}[/tex]

[tex]1.1875\cdot 10^{8}[/tex]

Therefore, population after 25 years will be [tex]1.1875\cdot 10^{8}[/tex].

81 1/4 should be the answer

let the wigth =x

then the length =2x

You can get

2·(2x+x)=60

2·(2x+x)÷2=60÷2

2x+x=30

3x=30

x=10

So 2x=2×10=20

The width of the garden is 10 feet, the length is 20 feet and the area is 200 square feet.

Final answer:

To find the dimensions of the garden, set up equations based on the perimeter formula and the given relationship between length and width. Solve to find that the width is 10 feet, and therefore the length is 20 feet.

Explanation:

To find the dimensions of a rectangular garden with a perimeter of 60 feet where the length is twice the width, we first need to set up two equations based on what we know about perimeters and the relationship between the garden's length and width. The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that P = 60 feet and the length is twice the width (l = 2w), we can substitute the latter into the perimeter formula and get 60 = 2(2w) + 2w, simplifying to 60 = 4w + 2w, which further simplifies to 60 = 6w. Dividing both sides by 6 gives us w = 10 feet. Therefore, the width is 10 feet and since the length is twice the width, the length is 20 feet.

A ray is a line with one end. It starts at a given point and goes off in a certain direction forever to infinity. The point where the ray starts is called the endpoint.

Answer:

any of a set of straight lines passing through one point.

Step-by-step explanation:

3445 divided by 13 is 265.

Answer:

is it 1.50? I got it wrong tho

When the price of bus tickets is raised, Alphonso's new budget constraint will be affected and he will be able to purchase fewer bus tickets. The opportunity cost of bus tickets increases as Alphonso has to give up more burgers to purchase bus tickets.

When the price of bus tickets is raised to $1 per trip, Alphonso's new budget constraint will be affected. The new budget line will have a steeper slope, indicating that he can purchase fewer bus tickets for the same amount of money. The opportunity cost of bus tickets increases because now Alphonso has to give up more burgers in order to purchase bus tickets.

For exercise a), f and g are the same function. So,

[tex] f(g(x)) = g(f(x)) = f(f(x)) = f\left(\dfrac{2}{x}\right) = \dfrac{2}{\frac{2}{x}} = x [/tex]

This means that f and g are inverse (i.e., f is the inverse of itself). In fact, if f(g(x)) = g(f(x)) = x, then f and g are inverse.

As for exercise b), you have

[tex] f(g(x)) = f(6x-1) = 6(6x-1)+1 = 36x-6+1 = 36x-5 [/tex]

[tex] g(f(x)) = g(6x+1) = 6(6x+1)-1 = 36x+6-1 = 36x+5 [/tex]

So, f and g are not inverse of each other.

Solution

Here we have to use compound interest formula for half year.

6 months = 1/2 years

Amount = [tex]P(1 + \frac{r/2}{100})^2n[/tex]

R = Rate

P = Principle

n = number of years

Here P = 6000, r/2 = 3.5/2 = 1.75, n = 1/2

Plug in the given values into the formula, we get    

A  = 6000(1 + 1.75/100)^2(1/2)

A = 6000(1 + 0.0175)^1

A = 6000(1.0175)

A = $6105

Compound interest = A - P

= $6105 - $6000

Interest = $105

Thank you :)

3(x+4)

Three times -> 3()

the sum of a number and four x+4

3(x+4)

Answer:

3(x+4)

D is correct

Step-by-step explanation:

If you want each side it will equal to 18 in. 18*4=72

turn it into a fraction for example (i know i am making it harder than it seems with variables) x:y you turn it into [tex]\frac{x}{y}[/tex] then you take the top number in the fraction and put it in the "house"

                         y  ⟌x

-hope this helps

÷

Answer:

Step-by-step explanation:

Factor 125[tex]x^{3}[/tex]-64

5³ₓ³ -  64

2.1      Factoring: 125[tex]x^{3}[/tex]-64

Theory : A difference of two perfect cubes [tex]a^3 - b^3[/tex] ,can be factored into

(a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =

           [tex]a^3+a^2b+ab^2-ba^2-b^2a-b^3 =[/tex]

           [tex]a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3 =[/tex]

           [tex]a^3+0+0-b^3 =[/tex]

           [tex]a^3-b^3[/tex]

Check :  125  is the cube of  5

Check :  64  is the cube of   4

Check :  x³ is the cube of   x¹

Factorization is :

(5[tex]x[/tex] - 4)  •  (25[tex]x^{2}[/tex] + 20[tex]x[/tex] + 16)

2.2     Factoring  25[tex]x^{2}[/tex] + 20[tex]x[/tex] + 16

The first term is,  25[tex]x^{2}[/tex]  its coefficient is  25 .

The middle term is,  +20[tex]x[/tex]  its coefficient is  20 .

The last term, "the constant", is  +16

Step-1 :

Multiply the coefficient of the first term by the constant   25 • 16 = 400

Step-2 :

Find two factors of  400  whose sum equals the coefficient of the middle term, which is 20 .

                       -400     +     -1    =     -401

                     -200     +     -2    =     -202

                     -100      +     -4    =      -104

                      -80      +     -5    =      -85

                      -50      +     -8    =      -58

                      -40      +    -10   =      -50

For tidiness, printing of 24 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

[tex](5x - 4) • (25x^2 + 20x + 16)[/tex]

first side is 7cm

second is 12cm

third is 14cm

The lengths of the sides are 7 cm, 12 cm, and 14 cm, respectively.

Let's denote the lengths of the sides as follows:

First side: x centimeters

Second side: y centimeters

Third side: z centimeters

According to the problem, we can set up a system of equations based on the given information:

The perimeter is the sum of all three sides, so:

x + y + z = 33

The first side is 5 centimeters shorter than the second:

x = y - 5

The third side is twice the first:

z = 2x

Now, we can use these equations to solve for the lengths of the sides. Substituting the second and third equations into the first, we get:

(y - 5) + y + 2(y - 5) = 33

y - 5 + y + 2y - 10 = 33

4y - 15 = 33

4y = 48

y = 12

Plugging y back into the second equation, we find:

x = 12 - 5

x = 7

And using the third equation:

z = 2x

z = 2(7)

z = 14

So, the lengths of the sides are:

x = 7 centimeters

y = 12 centimeters

z = 14 centimeters.

To learn more about lengths

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Answer:

number x = 3.

Step-by-step explanation:

Given : Three times the sum of a number and 4 is the same as 18 more than the number.

To find : what is the number.

Solution : We have given a statement

According to question :

Let the number= x

Sum of the number and 4 = x + 4

Three times the sum of the number and 4 = 3 ( x +4).

18 more than a number = 18 + x .

Three times the sum of a number and 4 is the same as 18 more than the number.

3 (x+4) = 18 + x

On distributing 3 over ( x+4)

3x + 12 = 18 + x

On subtracting both sides by 12

3x = 18 -12 +x

3x = 6+x

On On subtracting both sides by x

3x -x =6

2x = 6

On dividing both sides by 2

x = 3.

To verify plug x = 3 in 3x + 12 = 18 + x

3(3)+12 =18+3

9+12 = 18+ 3

21 =21

Therefore, number x = 3.

Amount of chemical A mixed in medicine = 9.357 g

Amount of chemical B mixed in medicine = 12.082 g

Amount of chemical C mixed in medicine = 7.502 g

We have to determine the total amount of medicine he prepared in grams.

Total amount of medicine

= 9.357 + 12.082 + 7.502

= 28.941 grams

So, he prepared 28.941 grams of medicine.

Now, we have to round each chemical to the nearest tenth.

Amount of chemical A mixed in medicine = 9.357 g

Rounding to nearest tenth = 9.4 grams

Amount of chemical B mixed in medicine = 12.082 g

Rounding to nearest tenth = 12.1 grams

Amount of chemical C mixed in medicine = 7.502 g

Rounding to nearest tenth = 7.5 grams

By adding the amounts of Chemical A, B, and C after rounding to the nearest tenth, we find that Dr. Manion made a total of approximately 29 grams of medicine.

To find the total amount of medicine made by Dr. Manion, we need to add the amounts of Chemical A, Chemical B, and Chemical C. But before that, we must round each of these to the nearest tenth of a gram.

So, Chemical A is about 9.4g, Chemical B is approximately 12.1g, and the Chemical C is about 7.5g.

Adding these together: 9.4g + 12.1g + 7.5g = 29.0 gragramsms.

This implies that Dr. Manion made a total of approximately 29.0 grams of medicine.

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ANSWER

[tex]\frac{3}{7}(-21x-49)= -9x- 21[/tex]

EXPLANATION

To expand

[tex]\frac{3}{7}(-21x-49)[/tex], we use the distributive property of multiplication over subtraction.

According to the distributive property of multiplication over subtraction, if we have any three real numbers,

[tex]a,b,\:and\:c[/tex].

Then;

[tex]a(b-c)=a\times b-a\times c[/tex]

Applying this property to the given expression, we obtain;

[tex]\frac{3}{7}(-21x-49)= \frac{3}{7}\times (-21x)- \frac{3}{7}\times (49)[/tex]

If we cancel out common factors we obtain;

[tex]\frac{3}{7}(-21x-49)= 3\times (-3x)- 3\times (7)[/tex]

If we simplify further, we obtain;

[tex]\frac{3}{7}(-21x-49)= -9x- 21[/tex]

The sale price is $425

hope this helps

Answer: The point A is 26m above from the ground.

Explanation:

It is given that the maximum drop Is 65m over a horizontal distance of 65m in two sections. So, the maximum value is (65,65) and the value is (0,0) when it stops.

From the given information it is noticed that the first section has a gradient of 3 and the second section has a gradient of 1/2.

The equation of line passing through the point [tex](x_1,y_1)[/tex] with slope m is define as,

[tex]y-y_1=m(x-x_1)[/tex]

For first section the slope is 3 and the point is (65,65).

[tex]y-65=3(x-65)[/tex]

[tex]y=3x-130[/tex]    ..... (1)

For second section the slope is 1/2 and the point is (0,0).

[tex]y=\frac{1}{2}x[/tex]  .....(2)

Put [tex]y=\frac{1}{2}x[/tex] in equation (1), we get,

[tex]\frac{1}{2}x=3x-130[/tex]

[tex]\frac{5}{2}x=130[/tex]

[tex]x=52[/tex]

Put this value in equation (2)

[tex]y=26[/tex]

Therefore, the point A is 26m above the ground and the horizontal distance is 52m from the endpoint.

If l correctly understand your question, you would subtract 18 - 12 to get 6. Was this the answer you were looking for??

The t procedure can be used to construct a confidence interval for the mean of a population, even if the population is not normally distributed.

The correct statement is c. You may use the t procedure because it is robust to nonNormality.

The t procedure can be used to construct a confidence interval for the mean of a population, even if the population is not normally distributed. As long as the sample size is sufficiently large (usually considered to be at least 30), the t procedure provides reliable results. It is important to note that the t procedure assumes that the sample is random and that the observations are independent.

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