the grasshopper population in Georgia is currently 4,000. It's growing by 2.3% each year. Write an equation that models the situation.

[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

Answer:

0.5

1 divide by 2 = 0.5

Answer:

-1 and 1

Step-by-step explanation:

Reciprocal means "one divided by...".

1/-1 = -1 and 1/1 = 1

Answer:

Distributive property, addition property

Answer:

additive identity

associative property of addition

distributive property

Step-by-step explanation:

Answer: B. Always

Explanation:

Two points always create a line. The correct answer is option B.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, the two points always create a line. The correct answer is option B.

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Answer:

[tex]\large \boxed{\sf \bf \ \ k=320 \ \ }[/tex]

Step-by-step explanation:

Hello,

The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.

If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?

[tex]64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

81.432 minutes

Step-by-step explanation:

Given the following :

Video Games (Mins) - - - Time with Family(Mins)

40 - - - - - - - - - - - - - - - - - - - 80

55 - - - - - - - - - - - - - - - - - - - 75

70 - - - - - - - - - - - - - - - - - - - 69

85 - - - - - - - - - - - - - - - - - - - 64

Best fit line:

ý = -0.363x +94.5

For someone who spent 36 minutes playing video games, the predicted number of minutes spent with family according to the best fit line will be:

Here number of minutes playing video games '36' is the independent variable

ý is the dependent or predicted variable ;

94.5 is the intercept

ý = -0.363(36) +94.5

ý = −13.068 + 94.5

ý = 81.432 minutes

Which is about 81 minutes to the nearest whole number.

Question

In a study of 100 new cars, 29 are white. Find p and q , where p is the proportion of new cars that are white.

Answer:

p = 0.29  and q = 0.71

Step-by-step explanation:

Given

Total new cars =  100

White new cars = 29

Required

Determine p and q

From the question;

p represents white new cars

Hence;

[tex]p = 29[/tex]

Note that;

[tex]p + q = 100[/tex]

Substitute 29 for p

[tex]29 + q = 100[/tex]

[tex]29 - 29 + q = 100 - 29[/tex]

[tex]q = 100 - 29[/tex]

[tex]q = 71[/tex]

The proportion of p is calculate by dividing p by the total number of new cars (Same process is done for q)

For proportion of p

[tex]Proportion,\ p = \frac{p}{new\ cars}[/tex]

[tex]Proportion,\ p = \frac{29}{100}[/tex]

[tex]Proportion,\ p = 0.29[/tex]

For proportion of q

[tex]Proportion,\ q = \frac{q}{new\ cars}[/tex]

[tex]Proportion,\ q = \frac{71}{100}[/tex]

[tex]Proportion,\ q = 0.71[/tex]

Answer:

v (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?

Step-by-sv (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?tep explanation:

Answer:

C. 47.5%

Step-by-step explanation:

The  summary of the given statistics include:

mean =150000

standard deviation: 1200

The  objective is to use tributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400

The z score formula can be use to calculate the percentage of the buyer who paid.

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

For the sample mean x = 150000

[tex]z = \dfrac{150000 - 150000}{1200}[/tex]

[tex]z = \dfrac{0}{1200}[/tex]

z = 0

For the sample mean x = 152400

[tex]z = \dfrac{152400 - 150000}{1200}[/tex]

[tex]z = \dfrac{2400 }{1200}[/tex]

z  = 2

From the standard normal distribution tables

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5% therefore option C is correct

This question is based on concept of  statistics. Therefore, correct option is C i.e. 47.5% of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.

Given:

Mean is $150,000, and

Standard deviation is $1200.

We need to determined the percentage of buyers who paid: between $150,000 and $152,400 as per given mean and standard deviation.

By using z score formula can be use to calculate the percentage of the buyer who paid,

[tex]\bold{z=\dfrac{x-\mu }{\sigma}}[/tex]

As given in question sample mean i.e. X= 150,000

[tex]z=\dfrac{150000-150000}{1200} \\\\z= \dfrac{0}{1200}\\\\z=0[/tex]

Now for the sample mean X = 152,400 ,

[tex]z=\dfrac{152400-150000}{1200} \\\\\\z= \dfrac{24000}{1200}\\\\\\z=2[/tex]

By using standard normal distribution table,

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5%

Therefore, correct option is C that is 47.5%.

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Answer:

Sum : 65

Step-by-step explanation:

In this notation, n is our starting value, and hence we start at 3 and go to 7. Given the set of values : { 3, 4, 5, 6, 7 }, we can substitute in our expression " 4n - 7 " for n and solve. The sum of these values is our solution.

4( 3 ) - 7 = 12 - 7 = 5,

4( 4 ) - 7 = 16 - 7 = 9,

4( 5 ) - 7 = 20 - 7 = 13,

Our remaining values for n = 6 and n = 7 must then be 17 and 21. This is predictable as we have an arithmetic series here, the common difference being 4. As you can see 9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4, 21 - 17 = 4.

Therefore we have the series { 5, 9, 13, 17, 21 }. This adds to an answer of 65.

Answer:

542

Step-by-step explanation:

We are required to find the sample size at 98% confidence interval in this question

E = 0.04

P* = 20% = 0.20

n = p* x (1-p)(Zα/2÷E)²

α = 1 - 0.98

= 0.02

To get Critical value

= 0.02/2 = 0.01

The critical value at 0.01 is 2.33

Inserting values into formula:

O.2 x 0.8(2.33/0.04)²

= 0.8 x 0.2 x 58.25²

= 542.89

The value of n must be an integer therefore the answer is 542.

Answer:

B. ​No, because the probability of success is different for each trial.

The experiment is not binomial.

Step-by-step explanation:

The trials are not independent  because they are chosen without replacement.

There are successes and failures but the trials are dependent.

So it is not binomial.

When the balls are not replaced the probability of success becomes different for each ball.

Suppose  we have 10 balls and we pick out 1 so the p1 = 1/10

but when we again pick out another without replacement the p2= 1/9

This explains why it is not binomial. In binomial the n is fixed.

Answer:

ig

Step-by-step explanation:

[tex](9-\sqrt{-8} )- (5 + \sqrt{-32} ) \\(9-5) + (-\sqrt{-8}- \sqrt{-32} )\\4 - \sqrt{-8} -\sqrt{-32} \\4-2i\sqrt{2} -4i\sqrt{2} \\4-6i\sqrt{2}[/tex]

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

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

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

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

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

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

Answer:

its [c] if Bradley serves 4 tables he will earn an average of $25

Step-by-step explanation:

Answer: Find answer in the attached files

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, just apply the instructions as below.

[tex]3(x-2)^2(x+5)^3[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

3 years

Step-by-step explanation:

Use the formula I = prt, where I is the interest money made, p is the starting amount of money, r is the interest rate as a decimal, and t is the time the money was borrowed.

Plug in the values and solve for t:

108 = (1200)(0.03)(t)

108 = 36t

3 = t

= 3 years

Answer:

A. 55, 89

Step-by-step explanation:

In a Fibonacci sequence, you start with 2 given numbers. Then each subsequent number is the sum of the last two numbers.

12, 21, 34

12 + 21 = 34

34 + 21 = 55

55 + 34 = 89

Answer: 55, 89

Answer:

√(x)

Step-by-step explanation:

(1)/(x^-(1/2)) that's 3 goes into -3 leaving 1 and goes into 6 leaving 2

1/2 is same as 2^-1

so therefore we can simplify the above as

x^-(-1/2)

x^(1/2)

and 4^(1/2)

is same as √(4)

so we conclude as

√(x)

Answer:

Hey there!

The slope is -1/3, because the rise over run is -1/3.

Let me know if this helps :)

Answer:

A. 120

Step-by-step explanation:

The rest of the answers are acute.

120 is the only one that matches the type of angle <V is.

Always pay attention to the type of angle it is.

Answer:

3.416, bar above 6

Step-by-step explanation:

41/12 = 3.4166666666666

41/12 = 3 & 5/12

Answer:

66

Step-by-step explanation:

41/12 = 3.4166

Answer:

3,069

Step-by-step explanation:

The sequence is doubling, so terms 1 through 10 are:

3, 6, 12, 24, 48, 96, 192, 384, 768, 1,536

3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1,536 = 3,069

Answer: А.

The function f intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

In the graph we can see f(x), first let's do some analysis of the graph.

First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.

The arms of the graph go up, so the leading coefficient of f(x) is positive.

The vertex of f(x) is near (-0.5, -2)

The roots are at x = -2 and x = 1. (intersects the x-axis at two points)

Now, we know that:

g(x) has a positive leading coefficient, and a vertex at (0, 3)

As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.

As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.

so:

f(x) intersects the x-axis at two points

g(x) does not intersect the x-axis.

The correct option is A.

Answer:

The answer is A.) The function f  intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

I took the test and got it right.

Answer: C

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the markers on QP and PR, we know that QS and SR are equivalent.

To find the value of n, we set QS and SR equal to each other.

6n+3=4n+11                     [combine like terms]

2n=8                                 [divide both sides by 2]

n=4

Now that we know n=4, we know that A is incorrect. What we can do is use the value of n to solve for QS, SR, and QR.

QS

6(4)+3=13

Since the length of QS is 13, we know B is incorrect.

SR

4(4)+11=27

Since SR is 27, C is a correct answer.

QR

13+27=40

Since QR is 40, the only correct answer is C.

Answer:

True

Step-by-step explanation:

The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.

Answer:

A=108 cm²

Step-by-step explanation:

length (l)=3w

perimeter=2l+2w

P=2(3w)+2w

48=6w+2w

width=48/8

w=6

l=3w=3(6)=18

Area=l*w

A=18*6

A=108 cm²

Answer:

Step-by-step explanation:

Hello, the slope of the tangent is the value of the derivative.

f'(x) = 2*0.2x + 5 = 0.4x + 5

So we are looking for

[tex]-1\leq f'(x) \leq 1 \\ \\<=> -1\leq 0.4x+5 \leq 1 \\ \\<=> -1-5=-6\leq 0.4x \leq 1-5=-4 \\ \\<=> \dfrac{-6}{0.4}\leq 0.4x \leq \dfrac{-4}{0.4} \\\\<=> \boxed{-15 \leq x\leq -10}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).

It is given by the derivative at x = x_0, that is:

m = f'(x_0)

In this problem, the function is:

f(x) = 0.2x^2 + 5x − 12

Hence the derivative is:

f'(x) = 0.4x + 5

For a slope of -1, we have that,

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that,

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval is (-15,-10).

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