(√x + 2)(√x - 2) = 0
X =

The initial population at time t = 0 is 1406.25.

The size of the bacterial population after 3 hours is 720,000.

The bacterial population would grow at an exponential rate. The equation that can be used to determine the bacterial population in 3 hours is

Bacterial population = initial population x ( 1 + 1)^t

Where

t = time = total number of minutes / 20 minutes

t = 120 / 20 = 6

Initial population:

90,000 / (2^6) = 1406.25

Population in 3 hours = 1406.25 ( 1 + 1)^9 = 720,000

t = (3 x 60) / 20

180 / 20 = 9

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A circle graph is attached.

A circle graph, also known as a pie chart, is used to visualize information and data. A circle graph is commonly used to show the results of an investigation in a proportional manner. The arcs of a circle graph are proportional to the percentage of the population who answered a specific question.

Given data

Top-selling US kids magazine as of 2002

Seventeen      2.352

Ym                      2.242

Teen              1.729

Teen people      1.625

Boys              1.280

First, we have to add up the dataset

Total = 2.352 + 2.242 + 1.729 + 1.625 + 1.280

= 9.228

The proportion of each magazine is then calculated.

This is calculated by dividing each magazine's frequency by the total frequency.

Mathematically, the formula is represented as:

Proportion = issue sold/ Total magazines sold

So we have

Seventeen= 2.352/9.228

= 25.5%

Seventeen= 2.242/9.228

= 24.3%

Seventeen= 1.729/9.228

= 18.7%

Seventeen= 1.625/9.228

= 17.6%

Seventeen= 1.280/9.228

= 13.9%

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Answer: range 14 IQR 12

Step-by-step explanation:

took the exam got it right

If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

In the question ,

it is given that

the when the object is dropped from height h then the velocity with which it hits the ground is given by the formula

v = √(19.6×h)

to find the height it was dropped , and it hits the ground with velocity 25.7 meter per second ,

we substitute v = 25.7 in the equation v = √(19.6×h) ,

we get ,

25.7 = √(19.6×h)

squaring both the sides , we get

19.6 × h = 25.7²

19.6 × h = 660.49

h = 660.49/19.6

h = 33.698

h ≈ 33.7

Therefore ,If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

The given question is incomplete , the complete question is

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v = √(19.6×h) . If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?

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The x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.

In the given question we have to find the x- and y-intercepts of the graph of x +6y= 10.

The given equation is x +6y= 10.

To find the x intercept we have to put y=o and to find the y intercept we have to put x=0.

Firstly finding the x intercept by putting y=0 in the equation.

x +6×0= 10

x+0=10

x=10

Now finding the y intercept by putting x=0 in the equation.

0 +6y= 10

6y = 10

Divide by 6 on both side

6/6 y =10/6

y=5/3

Hence, the x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.

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Answer:

30

Step-by-step explanation:

240/ 8 = 30.

alternatively, you can say 30 multiplied by 8 is 240. or you divide 240 by 30 and get 8.

Answer:

Yes correct so what is the question

240/8=30

Step-by-step explanation:

Her monthly payment is $88.64

The total of her monthly payments is $2,127.39

The finance charge is $127.39

Given, Melissa wants to check the accuracy of the finance charge on her promissory note.

She has a $2,000, two-year loan at a APR of 6%.

As, she has a $2,000 loan for two year at a APR of 6%.

Then, the total amount she has to pay is $2,127.39

(a) So, the monthly payments be

$2,127.39/24 = $88.64

(b) Now, she has to pay monthly payments for 24 months

So, the total of her monthly payments is $2,127.39.

(c) the finance charge she has to pay is,

$2,127.39 - $2,000 = $127.39

Hence, her monthly payment is $88.64

the total of her monthly payments is $2,127.39

the finance charge is $127.39

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Probability that the sample mean would differ from the true mean by more than 162 dollars if a sample of 71 persons is randomly selected is 50%

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation 805 , the zscore of a measure X is given by:

Z = (X - μ)/σ

s = σ/√n

In this problem, we have that:

μ = 21053, n = 71, σ = 805

s = 805/√71 = 95.53

Eiher it differs by 162 or less dollars, or it differs by more than 162 dollars. The sum of the probabilities of these events is decimal 1. So

Probability it differs by 160 or less dollars.

pvalue of Z when X = 21053 + 162 = 21215 subtracted by the pvalue of Z when X = 21053 - 162 = 20891.

X = 21215

Z = (X-μ)/σ

Z = (21215-21053)/95.53

Z = 1.69

has a pvalue of 0.091

X = 21568

Z = (X-μ)/σ

Z = (21215-21053)/95.53

Z = 1.69

has a pvalue of 0.041

0.091 -  0.041 = 0.05098

p + 0.50 = 1

p = 0.50

Thus, Probability that the sample mean would differ from the true mean by more than 162 dollars if a sample of 71 persons is randomly selected is 50%

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The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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The solution to the expression is -180

From the question, we have the following parameters that can be used in our computation:

(-6)(15)(-2)(-1)

Remove the brackets in the expression

So, we have the following product expression

(-6)(15)(-2)(-1) = -6 * 15 * -2 * -1

Evaluate the products using a calculator

This gives

(-6)(15)(-2)(-1) = -180

Hence, the solution is -180

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Answer:

[tex]2x^{2} +17x+21[/tex]

Step-by-step explanation:

multiply the 2x by x and 7 and then multiply 3 by x and 7. you will get 2[tex]x^{2}[/tex]+14x+3x+21. combine like terms so add 14x to 3x and thats the only like trerms in the equation. so 2x^2+17x+21

Answer:Smallest + Middle + Largest = 53

M= S + 2

L = 2S

Substitute M= S +2 and L = 2S into S + M + L =53

S + S + 2 + 2S = 53

4S + 2 = 53

4S/4 = 51/4

S = 12.75

M = 12.75 + 2

M = 14.75

L = 2 (12.75)

L = 25.5

Step-by-step explanation:

The average rate of change of the function g(x) = x² – 1 from x = 3 to x = 6 is 9.

What is the average rate of change of a function?

The average rate of change function describes the average rate at which one quantity changes in proportion to another's change.

We can write the Average Rate of Change of a function f from a to b as follows using function notation:

                                   [tex]r = \frac{g(b)-g(a)}{b-a}[/tex]

The given function is g(x) = x² – 1.

Then the rate of change of a function from x = 3 to x = 6.

so the value of a =  3 and b = 6, using the above formula, we get

                                           [tex]r = \frac{g(b)-g(a)}{b-a}\\r = \frac{g(6)-g(3)}{6-3}\\r = \frac{(36-1)-(9-1)}{6-3}\\\\r = \frac{35-8}{3}\\r = \frac{27}{3}\\\\r = 9[/tex]

Hence, The average rate of change of the function g(x) = x² – 1 from x = 3 to x = 6 is 9.

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Answer:

false

Step-by-step explanation:

x+2<-9

x<-9-2

x<-12

Answer is : 5a + 4b

Answer:

isosceles triangle

Step-by-step explanation:

first by using corresponding angle theorem:

<A=<C

<A=50°

then by using exterior angle theorem:

<A+<C=<B(the outer angle)

50°+<C=<B,<B=180°-80°(angle B lies in a staight line)

<B=100°

50°+<C=100°

<C=50°

The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)

The list of options represents the given parameter

All ordered pairs are relations but not all ordered pair are functions

For an ordered pair to be a function, the following must be true:

The y values on the ordered pair must have  different x values

Using the above as a guide,

This means that the ordered pair in option (b) represents a function

Hence, the ordered pair that is a function is (b)

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C:

3500(0.93)^d

Exponential functions have the form a·b^x, where:

   a is the initial amount

   b is the percent remaining after each time period

a = 3500, since that's the original volume.

Since 7% is lost each day, 93% remains, so b=0.93.

Answer:

3 hours and 44 minutes

Answer:

65 good sir.

Step-by-step explanation:

The Area of the fabric required is 3.6 square feet

The square's side length is 3 feet.

Due to the fact that Lin is creating a window covering for a window that is half circle-shaped on top of a square.

The window covering must therefore be a semicircle with a 3-feet diameter.

thus the semicircle's radius is equal to d/2 = 3/2 feet

Now, the Area of the semicircle,

[tex]A =\frac{1}{2} \pi r^{2} \\[/tex]

Putting the value of the radius in the equation, we have,

[tex]A =\frac{1}{2} \pi (\frac{3}{2} )^{2} \\\\A = \frac{1}{2} *\frac{22}{7} *\frac{3}{2} *\frac{3}{2} \\\\A = \frac{99}{28} = 3.53 = 3.6[/tex]

Hence, The Area of the fabric required = 3.6 square feet

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Answer:

Use the Intermediate Value Theorem to prove that every cubic function has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

Using corresponding and alternating angle theorem. The values of the angles in the figure are m∠1 = 47, m∠2 = 133, m∠3 = 139, m∠4 = 41, m∠5 = 139 degrees respectively.

The corresponding angle postulate states that the corresponding angles are congruent if the transversal intersects two parallel lines. In other words, if a transversal intersects two parallel lines, the corresponding angles will be always equal.

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

a. m∠1 = m∠7

Reason : Corresponding angles are equal

m∠1 = 47°

b. m∠2 = 180 - m∠1

Reason: Angles on a straight line

m∠2 = 180 - 47

m∠2 = 133°

c. m∠3 = m∠16

Reason : alternating angles are equal

m∠ = 139°

d. m∠4 = 180 - m∠3

Reason : Angles on a straight line

m∠4 = 41°

e. m∠5 = 180 - m∠4

Reason: Angles on a straight line

m∠5 = 139°

n. m∠17 = 180 - m∠6

m∠17 = 41°

f. m∠ 6 = m∠15

m∠15 = m∠17

Reason : Opposite angles are equal

m∠ 6 = m∠ 17

Reason : Alternating angles are equal

m∠ 6 = 41°

g. m∠8 = m∠1

m∠ 8 = 47°

h. m∠ 9 = m∠2

m∠9 = 133°

m. m∠15 = m∠ 17

m ∠ 15 = 41°

o. m∠ 18 = 360 - (m∠15 + m∠16  m∠ 17)

m∠18 = 360 - (41 + 139 + 41)

m∠18 = 139°

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As per the given sales tax, the total cost of the bicycle is $1056.194

Sales tax:

Sales tax is defined as the amount of money, calculated as a percentage, that is added to the cost of a product or service when purchased by a consumer at a retail location.

Given,

DeShawn buys a bicycle that costs $129.95. The sales-tax rate in his city is 712%.

Here we need to find the total cost of the bicycle.

Let us consider the 712% is applied as the tax for $129.95.

So, the amount of tax is calculated as,

=> 712% of 129.95

=>  712/100 x 129.95

=> 7.12 x 129.95

=> 926.244

Therefore, the total amount is obtained by adding the tax amount plus the cost of bicycle,

Then,

=>  129.95 + 926.244

=> 1056.194.

Therefore, the total cost of the bicycle is $1056.194.

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16, 14, 12

80, 70, 60

Step-by-step explanation:

16×5 = 80

14×5 = 70

12×5 = 60

Answer:

16, 14, 12

80, 70, 60

Step-by-step explanation:

16×5 = 80

14×5 = 70

12×5 = 60

Hope it helps! :)

Answer:

Table B

Step-by-step explanation:

To determine whether or not something is linear, we find the slope between two different coordinates and see if that slope remains consistent throughout the data. To find the slope between two points, use the equation (y2-y1)/(x2-x1)

Table A -->  (-1-5)/(3-2) = -6/1 = -6

Now we have to see if the slope remains consistent in "Table A" by finding the slope using two other coordinates:

(6-3)/(5-4) = 3/1 = 3

We see that the slope is not consistent in Table A, so we repeat the same steps with the other Tables to find one with a consistent slope.

Table B --> (0- -3)/(5-3) = 3/2

                  (6-3)/(9-7) = 3/2

Table B's data creates a consistent slope, so Table B represents a linear function.

The integrals in this problem are given as follows:

a) 18 units².

b) 18π units².

c) (18π + 4.5) units².

d) (9π + 9) units².

To obtain the integrals in this problem, we need to have knowledge of the meaning of the integrals, which is that they represent the area of the function over the interval.

For item a, the area is obtained as follows:

Hence the integral is of 18 units².

For item b, the figure is a semicircle of radius 6, hence the area is given as follows:

A = 0.5πr² = 18π units².

For item c, the area is composed as follows:

Hence the area is of:

A = (18π + 4.5) units².

For item d, the area is given as follows:

Hence the area is of:

A = (9π + 9) units².

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The required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct.

Given that,
To determine the equation that has the solution x = all real numbers.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Equation 1
5(3-x)+7x = 3x + 15 - x
15 - 5x + 7x = 3x +15 - x
2x = 2x
Since it implies the variable x solution as all real numbers,
While all other equation has a distinct unique solution,

Thus, the required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct

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The slope of the line  passing through the points ( -8,8) and ( 2,8) is 0.

What is slope?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols y and x stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is given by m = change in y/change in x = y/x. where'm' denotes a line's slope

Here the given points are,

[tex](x_1,y_1)=(-8,8)\\(x_2,y_2)=(2,8)[/tex]

Now using slope formula ,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m= [tex]\frac{8-8}{2+8}[/tex]

=> slope m = 0

Hence slope of the given points is 0.

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