S
A national park in Florida is approximately x 108 square meters in area. A New York State Park
is approximately 2 x 10?square meters in area. Based on these areas, how many times larger is the
national park than the state par?

can be simplified to

[tex]-\frac{3p^8}{4q^3}[/tex]

Hopes this helps

if not then I'm sorrr

The quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\) is \(-\frac{3p^8}{4q^3}\). This is found by dividing the numerical coefficients and subtracting the exponents for variables of the same base (negative exponents indicate reciprocals).

To find the quotient in simplified form for \(\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}\), we perform division of the coefficients (15 divided by -20) and subtraction of the exponents for variables with the same base (p's and q's exponents) according to the rules of exponents. First, simplify the numerical coefficients:

\(\frac{15}{-20} = -\frac{3}{4}\)

Now, subtract the exponents for p (applying the formula x^p \cdot x^q = x^{(p+q)}):

\(p^{-4} - p^{-12} = p^{-4 + 12} = p^8\)

Next, apply the same process to the exponents of q:

\(q^{-6} - q^{-3} = q^{-6 + 3} = q^{-3}\)

Combine the results to get the simplified quotient:

\(-\frac{3}{4} × p^8 × q^{-3}\)

Remember that a negative exponent indicates a reciprocal, so we can write \(q^{-3}\) as \(\frac{1}{q^3}\). Therefore, the final answer is:

\(-\frac{3p^8}{4q^3}\)

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Answer:

1170

Step-by-step explanation:

Answer:

The future value of investment at 6 % compounded quarterly is                $ 4782.472  

Step-by-step explanation:

Given as :

The principal amount = $ 4000

The rate of interest compounded quarterly = 6 %

The time period = 3 years

Let The future amount = A

From Compounded method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{4\times \textrm time}[/tex]

Or, Amount = 4000 × [tex](1+\dfrac{\textrm 6}{4\times 100})^{4\times \textrm 3}[/tex]

Or, Amount = 4000 × [tex](1.015)^{12}[/tex]

Or, Amount = 4000 × 1.195618

∴ Amount = $ 4782.472

Hence The future value of investment at 6 % compounded quarterly is  $ 4782.472  Answer

Answer:

0

Step-by-step explanation:

Answer:

The answer would be 0

1. r closest to 1: figure

2. No linear relationship: Figure 1

3. r equal to 1: Figure 3

Step-by-step explanation:

Correlation is the link between two variables or things"

Now for the scatter plot of a correlation:

Correlation coefficient closest to 1:

We can see in figure 4 that the data points are gathered across a line but not a perfect line and both the quantities are increasing so the correlation coefficient is close to 1.

Least Evidence of linear relationship:

Figure 1 can be observed to conclude that the data points are scattered on whole scatter plot hence creating no relationship

Correlation coefficient equal to -1:

We can see in figure 3 that one quantity is increasing and the other is decreasing and the data points are forming a line so the correlation coefficient will be -1

Keywords: Correlation, Scatter plot

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Answer:

48pi or about 150.8 cm^3

Step-by-step explanation:

volume of cone = 1/3 * pi * r^2 * h

r = 12/2 = 6

1/3 (6^2) (4) pi = 48pi

48pi ~= 150.8 cm^3

Answer: 150.8 cm^3

Step-by-step explanation: The volume formula is V=πr^2(h/3). Once you plug in the radius (half the diameter) and the height, you solve the equation and get the answer of 150.8 cm^3

Answer:

(1, - 2 )

Step-by-step explanation:

Given the 2 equations

y = - 4x + 2 → (1)

y = 6x - 8 → (2)

Substitute y = 6x - 8 into (1)

6x - 8 = - 4x + 2 ( add 4x to both sides )

10x - 8 = 2 ( add 8 to both sides )

10x = 10 ( divide both sides by 10 )

x = 1

Substitute x = 1 into (2) for corresponding value of y

y = 6(1) - 8 = 6 - 8 = - 2

Solution is (1, - 2 )

Answer:

Step-by-step explanation:

Scott has ridden 12% of the course.

Step-by-step explanation:

Length of bike course = 50 miles

Distance covered = 6 miles

Distance covered in percentage = [tex]\frac{Distance\ covered}{length\ of\ bike\ course}*100[/tex]

Distance covered in percentage = [tex]\frac{6}{50}*100\\[/tex]

Distance covered in percentage = [tex]\frac{600}{50}[/tex]

Distance covered in percentage = 12%

Scott has ridden 12% of the course.

Keywords: percentage, distance

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Answer:

-1.6

Step-by-step explanation:

Simple division but with a negative number. Positive ÷ Negative = Negative and vice versa

Answer:

-1.6

Step-by-step explanation:

edge-

Answer:

1. HL

2. SAS

3. SSS

Step-by-step explanation:

Triangles ABR and ACR share side AR (hypotenuse of two right triiangles).

Angles ABR and ACR are right angles.

Sides AB and AC are congruent.

Sides BR and CR are congruent.

1. You can use HL theorem, because two triangles have congruent pair of legs and congruent hypotenuses.

2. You can use SAS theorem, because two triangles have two pairs of congruent legs and a pair of included right angles between these legs.

3. You can use SSS theorem, because two triangles have two pairs of congruent legs and  congruent hypotenuses.

Answer

1. HL

2. SAS

3. SSS

Step-by-step explanation:

just took the test aced it

Answer:

ln|sec θ + tan θ| + C

Step-by-step explanation:

The integrals of basic trig functions are:

∫ sin θ dθ = -cos θ + C

∫ cos θ dθ = sin θ + C

∫ csc θ dθ = -ln|csc θ + cot θ| + C

∫ sec θ dθ = ln|sec θ + tan θ| + C

∫ tan θ dθ = -ln|cos θ| + C

∫ cot θ dθ = ln|sin θ| + C

The integral of sec θ can be proven by multiplying and dividing by sec θ + tan θ, then using ∫ du/u = ln|u| + C.

∫ sec θ dθ

∫ sec θ (sec θ + tan θ) / (sec θ + tan θ) dθ

∫ (sec² θ + sec θ tan θ) / (sec θ + tan θ) dθ

ln|sec θ + tan θ| + C

Answer:

Length n = 5 cm

Step-by-step explanation:

Given:

Each angle measure is of 60° for the triangle given in the figure.

Equilateral Triangle:

If all the angles measure of the triangle is 60° then the triangle is said to be an Equilateral Triangle.

Therefore, the triangle given in the figure is an Equilateral Triangle.

Another property of an Equilateral Triangle is

All the Three sides of an equilateral triangles are equal.

Here,

measure of each angle is 60° ...... { Given}

length of one side = 5 cm       ........{Given}

∴  Length n = 5 cm

Answer:

4200

Step-by-step explanation:

In an arithmetic sequence equation t=a + (n-1)d, a is the starting value. In this case, a=3000.

Although, since the initial investment is not considered the first month, the equation is t = a + dn.

d is the rate of change. In this case, the rate of change is 100 for every month, n.

Substitute these values from the problem to get an equation:

t = 3000 + 100n

t means the total amount of money we have for the amount of months (n) that passed.

Sub n for 12.

t = 3000 + 100n

t = 3000 + 100(12)

t = 4200

You will have $4200 after 12 months of investment.

Answer:

(B) The inequality that represents this relationship is [tex]3x  < x^2 +15[/tex]

Step-by-step explanation:

Let us assume the given number = x

⇒ 3 times the given number = 3 (x)  = 3x

Square of the given number = [tex](x)^2  = x^2[/tex]

Now, According to the question:

The difference of (3 x) and 15 is no less than [tex] x^2[/tex]

⇒ [tex]3x - 15 < x^2\\ \implies 3x  < x^2 +15[/tex]

or, [tex]3x  < x^2 +15[/tex]

Hence, the given inequality is represented as [tex]3x  < x^2 +15[/tex]

Answer:

3x - 15 > [tex]x^{2}[/tex]

Step-by-step explanation:

Let the number be x

⇒3 times the number is 3x and square of the number is [tex]x^{2}[/tex]

Difference of 3 times a number and 15 is 3x -15

⇒This difference is no less than the square of the number

⇒The difference is greater than or equal to square of the number

⇒ 3x - 15 ≥ [tex]x^{2}[/tex]

Answer:

B is the correct answer

Step-by-step explanation:

use your calculator and or in the problem and it should give you a decimal just go to math. and click 1 and click enter again and it should give you a fraction

Answer:

[tex]x\leq -27[/tex]

Step-by-step explanation:

Given:

[tex]\frac{x}{-9}\geq 3[/tex]

Multiplying both sides by -9, we get

[tex]-9\times \frac{x}{-9}\leq -9\times 3\\x\leq -27[/tex]

On multiplying both sides of an inequality by a negative number, the sign of the inequality changes as evident in the above equation.

So, the value of [tex]x[/tex] varies as:

[tex]x\leq -27[/tex]

The right answer is Option C.

Step-by-step explanation:

A. 9/17 and 27/50

Using cross product;

[tex]\frac{9}{17}=\frac{27}{50}\\9*50=17*27\\450=459[/tex]

The ratio does not form proportion.

B. 12/35 and 24/75

[tex]\frac{12}{35}=\frac{24}{75}\\12*75=24*35\\900=840[/tex]

The ratio does not form proportion.

C. 15/55 and  33/121

[tex]\frac{15}{55}=\frac{33}{121}\\15*121=33*55\\1815=1815[/tex]

The ratio form a proportion.

D. 12/35 and 20/70​

[tex]\frac{12}{35}=\frac{20}{70}\\12*70=20*35\\840=700[/tex]

The ratio does not form proportion.

The right answer is Option C.

Keywords: ratio, proportion

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Answer:

9.5

Step-by-step explanation:

The cost of movie tickets is $9.50 per person.

Now, if the variable x represents the number of people and t represents a total cost in dollars, then we can write the equation that models the above situation as

t = 9.5x ......... (1)

From this above two-variable linear equation it is clear that the slope of the line is 9.5. And its unit is dollars per person. (Answer)

Answer:

975 girls

Step-by-step explanation:

To find 65% of 1500, multiply 1500 by .65 (to convert percentages to decimals, just move a decimal point over two spaces).

1500*.65=975

You can check that this answer is right with logic. Most of the students will be girls (more than 50%) and 975 makes up most of 1500.

Someone else asked this same question a while ago, and you can find their explanation here https://brainly.com/question/969975

Answer:

minerals

Step-by-step explanation:

Rocks are either SEDIMENTARY , IGNEOUS, or METAMORPHIC. Almost all rocks made of minerals, but different rocks contain different mixtures of minerals.

hope this helps :)

Answer:

sand

Step-by-step explanation:

sand because sand is made of different substance and for a lon

g time it starts to sit and without water its hard for them to sit, and sand has more similar substance between some that was one living and mineral.

Answer:

see explanation

Step-by-step explanation:

To find the x- intercept let y = 0 in the equation and solve for x

x + 0 = 9

x = 9 ← x- intercept ⇒ (9, 0 )

To find the y- intercept let x = 0 in the equation and solve for y

0 + y = 9

y = 9 ← y- intercept ⇒ (0, 9 )

Translation

Rigid motion occurs when you move figures without affecting the size or shape in order for the figure to be congruent in a new location.

The types of rigid motions are:

In this problem, you haven't provided any figure, but I've attached one below. As you can see, we have a triangle ΔABC that has been translated to a new location in order to match triangle ΔDEF. So any point (x, y) on the triangle is mapped following this rule:

[tex](x,y) \rightarrow (x+8,y+2)[/tex]

So the new vertices D,E,F will be:

[tex]A(-6,2) \rightarrow D(-6+8,2+2)=\boxed{D(2,4)} \\ \\ B(-6,6) \rightarrow E(-6+8,6+2)=\boxed{E(2,8)} \\ \\ C(-2,2) \rightarrow F(-2+8,2+2)=\boxed{F(6,4)}[/tex]

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Option C. (A’UB') is the correct answer

Step-by-step explanation:

If A and B are two sets

Then

We can say the the elements that are not in set a can only be obtained by finding its complement

So,

all of the elements which are not in set  A = A'

Similarly

those elements not in set B = B'

Combining these means that elements of both sets will be : A'UB'

Hence,

Option C. (A’UB') is the correct answer

Keywords: Sets, complements

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The bakery made 3 batches of cookies and a total of 180 cookies.

To determine the number of batches of cookies the bakery made, we divide the total amount of flour used by the amount of flour used in each batch. The bakery used 5.25 cups of flour in total, and each batch requires 1.75 cups of flour. Therefore, the number of batches made is:

[tex]\[ \text{Number of batches} = \frac{\text{Total flour used}}{\text{Flour per batch}} = \frac{5.25}{1.75} \][/tex]

[tex]\[ \text{Number of batches} = 3 \][/tex]

Since there are 5 dozen cookies in each batch, we multiply the number of batches by the number of cookies per batch to find the total number of cookies made:

[tex]\[ \text{Total number of cookies} = \text{Number of batches} \times \text{Cookies per batch} \][/tex]

[tex]\[ \text{Total number of cookies} = 3 \times (5 \times 12) \][/tex]

[tex]\[ \text{Total number of cookies} = 3 \times 60 \][/tex]

[tex]\[ \text{Total number of cookies} = 180 \][/tex]

Thus, the bakery made 3 batches of cookies, resulting in a total of 180 cookies."

Answer: 6 gallons

Step-by-step explanation:

1/3 = 2/6. 1/2 = 3/6

2/6 already + 3/6 = 5/6, it

To determine the total capacity of Goran's gas tank, we set up and solved an algebraic equation, finding that the total capacity of the tank is 18 gallons.

The student's question is about figuring out the total capacity of Goran's gas tank based on the information given. To solve this problem, we can set up a simple algebraic equation based on the proportions of the tank's capacity that are filled. Since filling the tank with 3 gallons of gas takes it from being 1/3 full to 1/2 full, we know that these 3 gallons represent the difference between 1/3 and 1/2 of the tank's total capacity.

Let's denote the total capacity of the tank as 'T' gallons. According to the question:

We can now set up the equation:

1/3 * T + 3 = 1/2 * T

To find 'T', we need to solve for T:

1/2 * T - 1/3 * T = 3

This simplifies to:
(3T - 2T) / 6 = 3
T/6 = 3

Now multiply both sides by 6 to solve for T:
T = 18

Therefore, the total capacity of Goran's gas tank is 18 gallons.

Answer:

57=12+3d

d=number of days worked

Answer:

(57-12)3/x=15 days

x=57-12

Answer:

a. 10x + 2y = 23

b. 4x - y + 3 = 0

c. y + 8 = 0

d. 2x - y + 4 = 0

Step-by-step explanation:

a.

Slope of the line 'm' is [tex]\frac{36.5-1.5}{-5-2}[/tex] = [tex]\frac{35}{-7}[/tex] = -5

Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)

⇒y-1.5 = -5·(x-2)

⇒y = -5x + 10 + 1.5

⇒5x + y = 11.5 (or) 10x + 2y = 23

b.

Slope of the line 'm' = 4

Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)

⇒y-15 = 4·(x-3)

⇒y = 4x -12 + 15

⇒4x - y + 3 = 0

c.

Line is parallel to y = 1

Equations of parallel lines only differ by constant. So the required line equation has the form y = c where c is any real number.

But, it is given that the line passes through the point (3,-8)

⇒c=-8

⇒y = -8 (or) y + 8 = 0

d.

Equation of a line with slope 'm' and y-intercept of (0,c) is of the form y = mx + c

⇒y = 2x + 4

⇒2x - y + 4 = 0

Answer:

1. A is d=1.75

Step-by-step explanation:

Answer:

1a) 10.50=6d

1b) d= 1.75

2a) w is less than or equal to 35

2b) It would not make sense to have a bag that weighed zero or below.

3a) The tree grows 15 ft for every since it was planted.

3b) h(t)=70+15x