Summary
Why are the values V4 and V9 used to approximate the location of values like V5, V6, and V7?

Answer:

Step-by-step explanation:

6^2m × 4^-m÷ (3^m)^2 = \(\frac{6^{2m} * 4^{-m}}{(3^{m})^{2}}\\\)

                                     \(= \frac{(3*2)^{2m}*(2^{2})^{-m}}{3^{2*m}}\\\\=\frac{3^{2m}*2^{2m}*2^{-2m}}{3^{2m}}\\\\\\=3^{2m-2m}*2^{2m-2m}\\\\=3^{0}*2^{0}\\\\=1*1\\= 1\)

Hint:

\(a^{m}*a^{n}= a^{m+n}\\\\(a^{m})^{n}=a^{m*n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\)

Answer:

1811328

Step-by-step explanation:

712 x 212 x 12

Answer and Step-by-step explanation:

To find the volume, multiply the length by the width, then multiply that product by the height.

(We use 7.5 and 2.5 because that is the same as 7 and one half (\(7 \frac{1}{2}\)) and 2 and one half (\(2 \frac{1}{2}\)))

7.5 × 2.5 × 12 = V

18.75 × 12 = V

225 \(in^3\) = V    -- This is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

6

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

\(7j = 91\)

Dividing both sides by 7, we have

\(j = 13\)

Answer:

84

Step-by-step explanation:

just add 84 to 7 and you will get 91.

Statistical methods are the processes of collecting, presenting, analyzing data, and drawing conclusions.

These methods are divided into two groups: descriptive statistics and inferential statistics.

The scope of descriptive statistics includes distributions of random and random variables, discrete and continuous random variables. For inference statistics, including statistical inference from one or two populations, analysis of variance, regression analysis, and analysis of categorical data from both random and normal populations.

Statistical techniques include many ways to collect, present, analyze, and draw conclusions from data. By considering these methods, you can choose which method to use according to the characteristics of your data.

Choosing the right method leads to drawing the right conclusions.

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The key features of this quadratic relation y = -3x² - 24x - 36 include;

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped.

Since the leading coefficient (value of a) in the given quadratic function y = -3x² - 24x - 36 is negative 16, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (-6, 0) and (-2, 0).

When x = 0, the y-intercept can be determined as follows;

y = -3x² - 24x - 36

y = -3(0)² - 24(0) - 36

y = -36

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-24)/2(-3)

Axis of symmetry, Xmax = -4

For the vertex, we have:

y(-4) = -3x² - 24x - 36

y(-4) = -3(-4)² - 24(-4) - 36

y(-4) = 12

In conclusion, the quadratic function has a maximum value at 12.

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Answer:

In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall.

Answer:

125

Step-by-step explanation:

2^2+11^2=c^2

4+121=c^2

125=c^2

c=125 square root

Answer:

8.16 Kg

Step-by-step explanation:

average is calculated as

average = \(\frac{sum}{count}\)

here average = 0.17 and count = 48 , then

0.17 = \(\frac{sum}{48}\) ( multiply both sides by 48 )

8.16 = sum

that is total mass = 8.16 Kg

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Answer: I am 97% sure it's D

Step-by-step explanation:

Step-by-step explanation:

the process is shown in the picture.

From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC

The two column proof to show that ∠BAC ≅ ∠DAC is as follows:

Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD

Reason 1: Given

Statement 2: AB ≅ AD

Reason 2:  Definition of isosceles Triangles

Statement 3: ∠1 and ∠2 are right angles

Reason 3: Definition of perpendicular

Statement 4: AC ≅ AC

Reason 4: Reflexive Property

Statement 5: ΔABC and ΔADC are right triangles

Reason 5: Definition of right triangle

Statement 6: ΔABC ≅ ΔADC

Reason 6: HL Congruency

Statement 7: ∠BAC ≅ ∠DAC

Reason 7: CPCTC

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The statement which has the strongest association is Males prefer thriller movies.

To obtain which statement has the strongest association, we calculate the probability of each given statement and select that which has the highest probability value.

• probability of  Males prefer comedy movies :

n(males who prefer comedy) / n(males)

= 35 / 122 = 0.287

• probability of Females prefer drama movies :

n(Females who prefer drama) / n(females )

= 65 / 129 = 0.504

• probability of Males prefer thriller movies.

n(males who prefer prefer thriller ) / n(males)

= 75 / 122 = 0.615

• probability of Females prefer thriller movies.

n(females who prefer prefer thriller ) / n(females)

= 18 / 129 = 0.140

Comparing the probabilities obtained, Males prefer thriller has the highest probability, thus the strongest association.

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Answer:

i got it right this person above me is correct.

Step-by-step explanation:

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

The safe amount of dose to administer in this situation is 15mL

To solve this problem, we can use the following steps:

Calculate the amount of drug in 1 mL of the solution.

Divide the desired dose by the amount of drug per mL.

The amount of drug in 1 mL of the solution is:

The other options are not safe because they would either deliver too much or too little medication. 20 mL would deliver 1000 mg, which is twice the desired dose. 4 mL would deliver only 60 mg, which is not enough medication. 2 mL would deliver only 30 mg, which is also not enough medication.

Therefore, the correct answer is 15 mL.

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The value of the inequality expression -15<3n + 6 is  n > -7

The inequality expression is given as

-15<3n6

Rewrite the expression properly

So, we have

-15<3n + 6

Subtract 6 from both sides

-15 - 6 < 3n

Evaluate the difference

This gives

-21 < 3n

Divide both sides by 3

So, we have

-21/3 < n

Evaluate the quotient

-7 < n

Rewrite as

n > -7

Express as interval notation

So, we have the following interval notation

(-7, oo)

Hence, the solution is (7, oo) or n > -7

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Answer:

the answer is 16 . the explanation is that because if you have. 200 cm y axis it overcomes the x of other 80

Answer:

9.98- 2.53 = 7.45

7.68 + 13.07 = 20.75

100.03 - 16.28 = 83.75

Step-by-step explanation:

 9.98

- 2.53

_____

7.45

  1   1        - Process of carrying 10's

   7.68

+ 13.07

_______

 20.75

0000 13 ⇔ What the number becomes after carrying

↑↑↑↑↑

100.03

- 16.28

______

83.75

Happy New Year!

Answer:

Step-by-step explanation:

Declarative sentences are those which state a fact, describe something, or make a statement. A declarative sentence is a simple statement that gives some information. It ends with a period and always has a subject and a predicate.

1. Example of a closed declarative statement: A closed declarative sentence is one that has only one answer and cannot be disputed.

An example of a closed declarative statement would be: The capital of France is Paris. This is a closed declarative statement because there is no other city that is the capital of France other than Paris.

2. Example of an open declarative statement: An open declarative sentence is one that may have many possible answers and may be disputed.

An example of an open declarative statement would be: The best pizza topping is pepperoni. This is an open declarative statement because some people may disagree and have their own preferences about pizza toppings.

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Answer:

C. Seasonal variation

Step-by-step explanation:

Distinct pattern around a trend line can be caused by seasonal variation.

Seasonal variation refers to a component of a time series which can be defined as the repetitive and predictable movement around the trend line in a year or less. It is caused by temperature, rainfall, public holiday and cycles of season

Seasonal variation can be detected by measuring the quantity of interest for small time intervals, such as days, weeks, months or quarters.

Firms affected by seasonal variation are usually interested in knowing their performance relative to the normal seasonal variation. They need to identify and measure this seasonality so as to help with planning.

x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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2x +4)° 2x-9)°= 4x  2 +8x−9=3

 Pull out like factors :

  2x + 4  =   2 • (x + 2) (4 • (x + 2) • x) -  9

4x • (x + 2) -  9

Factoring  4x2+8x-9  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  -9  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -9 = -36  

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   8 .

     -36    +    1    =    -35  

     -18    +    2    =    -16  

     -12    +    3    =    -9  

     -9    +    4    =    -5  

     -6    +    6    =    0  

     -4    +    9    =    5  

     -3    +    12    =    9  

     -2    +    18    =    16  

     -1    +    36    =    35

x=3

Answer:

0, -2, 9/2

Step-by-step explanation:

(2x^2 + 4x) (2x-9)

Then Foil

4x^3 + 8x^2 - 18x^2 -36x

Pull out a x

x(4x^2-10x-36)

x=0

(2x-9)(2x+4)=0

X= 9/2 x= -2

Answer:

?

Step-by-step explanation:

what are you trying to convert? This is confusing.

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

\(9^{-0.5}\)  to make the exponent positive, put it over 1.

\(\frac{1}{9^{0.5} }\)  another way to write this is

\(\frac{1}{\sqrt{9} }\)

\(\frac{1}{3}\)