Determine if each equation represents a linear or nonlinear function. (ignore my original answers)

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

1.9 m

Step-by-step explanation:

1 ft = 30 cm (approximately)

12 in. = 1 ft

100 cm = 1 m

Find the height in ft:

4 in. / 12 in/ft = 1/3 ft

6 ft 4 in. = 6 ft + 1/3 ft = 6 1/3 ft

Convert ft to cm:

6 1/3 ft × 30 cm/ft = 190 cm

Convert cm to m:

190 cm × 1 m / 100 cm = 1.9 m

Answer:

7 units is the distance

Supposing the distribution is uniform, we find that there is a 0.15 = 15% probability that a random selected occupation has an Emotional Health Index Score between 80.5 and 82.

---------------------

Uniform probability distribution:

\(P(c \leq X \leq d) = \frac{d - c}{b - a}\)

In this problem:

The probability between 80.5 and 82 is:

\(P(80.5 \leq X \leq 82) = \frac{82 - 80.5}{85 - 75} = 0.15\)

0.15 = 15% probability that a random selected occupation has an Emotional Health Index Score between 80.5 and 82.

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The solution for the given expression is 14∛x. The correct option is (C).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

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Answer:

2 miles

Step-by-step explanation:

Answer:

11x+2

Step-by-step explanation:

Answer:

11x=+2

Step-by-step explanation:

5x+2(3x-4)+10

5x+(2*3x-2*4)+10

5x+(6x-8)+10

5x+6x-8+10

=11x=2

Answer:

vhil vhil vhil :P

Step-by-step explanation:

hows ur da im kai and i hope u have a lovley day remember u r an awsomw person ly~

Answer:

around  571% or to be more exact, around 571.15384615%

Step-by-step explanation:

468 = 100%

2673 = ?

2673/468 = 297/52 = 5.71153846...≈5.7

468 * 2673/468 = 100%* 2673/468

2673 ≈571.15384615%

% ≈ 571%

Answer:

13. C) The sum of the numerators is incorrect.

14. B) \(-\frac{5}{8}+\frac{1}{8}=\frac{-5+1}{8}=\frac{-4}{8} =-\frac{1}{2}\)

Step-by-step explanation:

13. The reason why it's incorrect.

When dealing with the sum of fractions, denominators must be the same. So allows us to do the sum of the numerator. The image displayed is the incorrect sum of the numerator.

14. \(-\frac{5}{8}+\frac{1}{8}=\frac{-5+1}{8}=\frac{-4}{8} =-\frac{1}{2}\)

Answer:

$657.09

Step-by-step explanation:

The area of the carpet is:

21 × 9 = 189 Square foot

189 foot² = 21 yard²

We know 1 yard² = $31.29

So 21 yard² = 21 × $31.29 = $657.09

Answer:

  32,000

Step-by-step explanation:

In 44 years, it will double to 16,000. In 44 more years (88 years from now), it will double again to 32,000.

The population in 88 years will be 32,000.

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

The probability that the water will run out on a given day is  0.0038.

To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:

where;

x = of 380 million gallons,

µ is the mean daily demand of water = 300 million gallons,

σ is the standard deviation = 30 million gallons.

Substituting the given values:

z = (380 - 300) / 30

z = 2.67

Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.

Therefore, the probability that the water will run out on a given day is  0.0038.

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Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

Answer:

a*n = -8 + (n - 1)6

Step-by-step explanation:

Explicit formula:

a*n = a*1 + (n - 1)d

a*1 = first term

n = nth term or the place

d = difference

Set: -8, -2, 4, 10

-8 ---> -2 = 6 added

Fill it in.

a*1 = -8

n = n

d = 6

Solution:

a^n = -8 + (n -1)6

Answer:

The monthly fee is $30. (400-40 = 360 ; 360/12= 30)

Answer:

30$

Step-by-step explanation:

Answer:

3/5

First you would need to find the greatest common factor of 15 and 25

which is 5

Then divide the numerator and denominator by the GCF

15 divided by 5

25 divided by 5

Then simplify your answer is

3/5

Answer: Quadrant 3

============================================================

Explanation:

pi radians = 180 degrees

If angle \(\theta\) (greek letter theta) is in quadrant 1, then this places the angle in the northeast quadrant. Adding 180 degrees to theta will move it to the third quadrant, which is in the southwest.

Note: when incrementing through the quadrants (1,2,3,4) we move counterclockwise.

The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

a) 10.5 gallons

b) $34.23

Step-by-step explanation:

a) 189 ÷ 18 = 10.5

b) $3.26 * 10.5 =

Answer:

Mode = 7

Median = 6

Mean = 5.2

Range = 7

Step-by-step explanation:

\(3 \: ,7 \:,2 \:,4 \:,7 \:,5, \:7\:,1,8 \:,8\)

a) Write down the mode

Mode is the number that appears the most in a given set of data

\(Mode = \:7\)

7 appears thrice , 8 appears twice and rest appear once.

b) Median

Median is the middle number of a given set of data when arranged in order of least to largest.

\(1,2 , 3 ,4,5, 7,7,7,8,8\\\\=1),2),3),4)5,7,(7,(7,(8,(8\\\\= \frac{5+7}{2}\\ \\= \frac{12}{2}\\ \\= 6\)

c. Mean

Mean is the sum of all values divided by the number of given values

\(\frac{1+2+3+4+5+7+7+7+8+8}{10} \\\\= \frac{52}{10} \\\\= 5.2\)

d)Range

Range is the difference between the highest value and the lowest vale in a given set of data.

\(Highest \:value =8\\Lowest\:value = 1\\\\Range = 8-1\\\\=7\)

\(57=\cfrac{5}{8}z+7\implies 57=\cfrac{5z}{8}+7\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8(57)=8\left( \cfrac{5z}{8}+7 \right)} \\\\\\ 456=5z+56\implies 400=5z\implies \cfrac{400}{5}=z\implies 80=z\)

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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Step-by-step explanation:

70% = 0.7

15% = 0.15

65% = 0.65

x = gallons of the 70% solution.

0.7x + 0.15×20 = 0.65(x + 20)

70% + 15% solution = 65% solution (which has a many gallons as the combination of x and 20 gallons).

0.7x + 3 = 0.65x + 0.65×20

0.05x + 3 = 13

0.05x = 10

x = 10/0.05 = 200 gallons

so, 200 gal of the 70% pesticide solution is needed to make combined with 20 gal of the 15% solution a final solution that is 65% pesticide.

Answer:

11) c = 16.1

12) c = 11.4

Step-by-step explanation:

11)

a² + b² = c²

8² + 14² = c²

64 + 196 = c²

c² = 260

\(\sqrt{c^2} =\sqrt{260}\)

c = 16.1

12)

a² + b² = c²

7² + 9² = c²

49 + 81 = c²

c² = 130

\(\sqrt{c^2} =\sqrt{130}\)

c = 11.4

• Question 1 :-

We see that in a right angled triangle two sides are 8cm and 14cm . We can find the third side using Pythagoras Theorem .

\(\tt \to Hypotenuse^2 = Perpendicular^2+Base^2\\\\\tt \to h^2 = (8)^2+(14) \\\\\to \tt h^2 = 64 + 196 \\\\\tt \to h^2 = 260 \\\\\tt \to h=\sqrt{260} \\\\\tt \to \boxed{\orange{\tt h = 16.12 }}\)

____________________________

• Question 2 :-

\(\tt \to Hypotenuse^2 = Perpendicular^2+Base^2\\\\\tt \to h^2 = (9)^2+(7)^2 \\\\\to\tt h^2 = 81 + 49 \\\\\tt \to h^2 = 130 \\\\\tt \to h=\sqrt{130} \\\\\tt \to \boxed{\orange{\tt h = 11.40}}\)

Answer:

B

Step-by-step explanation:

You would need to convert the fractions to a denominator of 15 because it's the closest denominator for both.

So 1 and 2/5 can be changed to 1 and 6/15

And 1 and 1/3 can be changed to 5/15

So what you do is multiply both the numerator and denominator by how much you need to multiply to get to 15 and the denominator.

You would then add the fractions, leaving the answer to be 2 and 11/15 

So for example 2 * 3 = 6 and 5 * 3 = 15, meaning the fraction would be 6/15

Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

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The true statements are;

1) AB + BC = AC

Length of BC = |6 - 1|

2) ∠JMK = 50°

∠KML = 35°

1) From the given number line interval, we can deduce the interpretation as follows;

AB + BC = AC

Length of BC = 5 units or |6 - 1|

Length of B = 3 Units

2) We can see that ∠JML is an angle triangle. Thus, ∠JML = 85°. Thus;

6x + 2 + 4x + 3 = 85

10x + 5 = 85

10x = 85 - 5

10x = 80

x = 80/10

x = 8°

Thus;

∠JMK = 6(8) + 2

∠JMK = 50°

∠KML = 85° - 50°

∠KML = 35°

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After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.

Using the given exponential growth model, we have:

\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)

Therefore, the population of the rural city in 2030 is approximately 11,014.18.

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