0.04 less than 1.38​

Answer:

D. y =  √(x - 12)

Step-by-step explanation:

x  = y² + 12

y² = x - 12

y = √(x - 12)

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.

Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.

We are required to find the number of bacteria present after 10 weeks.

let the number of bacteria present at t is x.

So,

dx/dt∝x

dx/dt=kx

1/x dx=k dt

Now integrate both sides.

[tex]\int\limits {1/x} \, dx[/tex]=[tex]\int\limits{k} \, dt[/tex]

log x=kt+log c----------1

Put t=0

log [tex]x_{0}[/tex]=0 +log c    ([tex]x_{0}[/tex] shows the population in beginning)

Cancelling log from both sides.

c=[tex]x_{0}[/tex]

So put c=[tex]x_{0}[/tex] in 1

log x=kt+log [tex]x_{0}[/tex]

log x=log [tex]e^{kt}[/tex]+log [tex]x_{0}[/tex]

log x=log [tex]e^{kt}x_{0}[/tex]

x=[tex]e^{kt}x_{0}[/tex]

We have been given that the population triples in a week so we have to put the value of x=2[tex]x_{0}[/tex] and t=1 to get the value of k.

2[tex]x_{0}[/tex]=[tex]e^{k} x_{0}[/tex]

2=[tex]e^{k}[/tex]

log 2=k

We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.

x=[tex]e^{20log 2}[/tex][tex]x_{0}[/tex]

x=[tex]e^{0.30*2}[/tex][tex]x_{0}[/tex]

x=[tex]e^{6}x_{0}[/tex]

x=403.42[tex]x_{0}[/tex]

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.

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The given question is incomplete as the question incudes the following:

Calculate the population after 20 weeks.

Answer:

x = 19

Step-by-step explanation:

You would use vertical angles to move the 8x - 14 so that we could use the Consecutive Interior angles theorem. Which says that consecutive angles equal 180. So, you would set up your equation: 8x-14+2x+4 = 180. Add the 8 and 2 = 10. Add the -14 and 4 = -10. You get 10x-10 = 180. 180+10 = 190. 190/10 = 19. X = 19

money paid by employer to Alan is $ 155.09

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

money paid for dinner by employer=$20.20

money paid for lunch by employer =$10.70

money paid for breakfast by employer =$6.93

according to question,

in this problem we will simply multiply quantity of dinners with amount

to get our answer.

so as given in problem  Alan scheduled 4 dinners , 5 lunches and 3 breakfast

(4×$20.20)+(5×$10.70)+(3×$6.93)

80.8+53.5+20.79

=$ 155.09

hence money paid by employer to Alan is $ 155.09

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The second bus is traveling at a speed of 33.3 miles per hour.

Given that the speed of first bus is 60 miles per hour , distance between both the buses is 700 miles after 8 hour.

We are required to find the speed of second car which is heading towards south.

If first car is travelling at a speed of 60 miles per hour then the distance of first car after 8 hours is 60*8=480 miles.

We have been given that the distance between both the cars after 8 hours is 700 miles,So,

Distance of second car after 8 hours=700-480=220 miles.

We know that the speed is equal to distance divided by time.

We know that we have calculated distance after 8 hours so the speed of second car will be =20/6

=33.3 miles per hour

Hence the speed of second car which is heading towards south is 33.3 miles per hour.

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The values of x and y from the given diagram are 47 ad 86 degrees respectively

From the given circle, the triangle HJL is a right triangle.

Determine the value of y

43 = 1/2 <y

<y = 43 * 2

<y = 86 degrees

Since the sum of angle on a straight line is 180 degrees, such that;

x+90+43 = 180

x + 133 = 180

x = 47 degrees

Hence the values of x and y from the given diagram are 47 ad 86 degrees respectively

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Answer:

see explanation

Step-by-step explanation:

to find the zeros let f(x) = 0

1

f(x) = 0 , that is

x(x + 10) = 0

equate each factor to zero and solve for x

x = 0

x + 10 = 0 ⇒ x = - 10

2

f(x) = 0 , that is

x(x - 3) - 4(x - 3) = 0 ← factor out (x - 3) from each term on the left side

(x - 3)(x - 4) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

Answer:

1) x₁ = 0, x₂ = -10

2) x₁ = 3, x₂ = 4

Step-by-step explanation:

Given functions:

[tex]1)\ f(x)=x(x+10)[/tex]

[tex]2)\ f(x)=x(x-3)-4(x-3)[/tex]

.................................................................................................................................................

Zero Product Property: If m • n = 0, then m = 0 or n = 0.

Distributive Property: a(b + c) = ab + ac.

Standard Form of a Quadratic: ax² + bx + c = 0.

.................................................................................................................................................

The Zero Product Property

1) f(x) = x(x + 10)

Step 1: Set the function to zero.

[tex]\implies 0=x(x+10)[/tex]

Step 2: Apply the Zero Product Property.

[tex]\boxed{x_1=0}[/tex]

[tex]x+10=0\implies \boxed{x_2=-10}[/tex]

The solutions to this quadratic are: [tex]x_1=0,\ x_2=-10[/tex].

.................................................................................................................................................

The Zero Product Property

2. f(x) = x(x - 3) - 4(x - 3)

Step 1: Set the function to zero.

[tex]\implies 0 = x(x - 3) - 4(x - 3)[/tex]

Step 2: Factor out [tex]x- 3[/tex].

[tex]\implies 0 = (x - 3)(x - 4)[/tex]

Step 3: Apply the Zero Product Property.

[tex]x-3=0\implies \boxed{x_1=3}[/tex]

[tex]x-4=0 \implies \boxed{x_2=4}[/tex]

The solutions to this quadratic are: [tex]x_1=3,\ x_2=4[/tex].

.................................................................................................................................................

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Answer:

probability of choosing two women over people in a community=⅔

Answer:

7/100000000

Step-by-step explanation:

to find this out we can start by saying that 0.7 is 7/10

every 0 in front of 7 after that is adding another 0 to 10

so

0.07 is 7/100

0.00000007 is 7/100000000

There are [tex]\frac{30!}{(3!)^{10} }[/tex] ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.

A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.

A whole number's "n" factororial is the sum of that number and each whole number up to one.

When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.

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Answer:

A.

Step-by-step explanation:

i'm 99% sure!

Answer:

B

Step-by-step explanation:

Plug in the coordinates.

The transformation that produces same image are:

The transformation that produces different image are:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation, reflection and rotation are rigid transformation which produces same image while dilation produces similar shapes.

The transformation that produces same image are:

The transformation that produces different image are:

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TRUE

The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.

An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.

Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.

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Answer:

x=17

Step-by-step explanation:

Since they are intersecting lines, 3x=51

x=17

Answer:

x = 17

Step-by-step explanation:

When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".

3x = 51

x = 17

Answer: (-4,2)

Step-by-step explanation:

To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint

So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)

To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B

The statements that are true about the angle include:

x > y

w = y

y < v

From the information, the first has legs 529m and 229m. Then tan x = 529/229. Also tan y = 529/347.

It can be seen that tan x is greater than tan y. Angles x, v, y, and w are alternate angles. Therefore, the correct options are A, C, avd D.

A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress. Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true

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Answer:

D (the last choice)

Step-by-step explanation:

Taking the fourth root of each element individually:

49^(1/4) = sqrt(7)

(d^8)^(1/4) = d^2

(e^2)^(1/4) = sqrt(e)

Multiplying them back together:

sqrt(7) * d^2 * sqrt(e) = d^2 * sqrt(7e)

Answer:

The last bubble (that of which is cut from the screen) is simplified.

Step-by-step explanation:

The provided equation is simplified by following these steps:

[tex](49d^{8}e^2)^\frac{1}{4}[/tex]

= [tex](49)^\frac{1}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]

[tex](7)^\frac{2}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]

=[tex]\sqrt{7} (d^2)(\sqrt{e})[/tex]

Answer:

A, C, E, F

Step-by-step explanation:

since nothing else was said, it is a general triangle. nothing special about it.

so, the only rules are that the sum of any pair of sides must be longer than the 3rd side (otherwise, if the 3rd side is longer, the sides could not connect).

A. 10.

so, we have

6 + 9 > 10 true

6 + 10 > 9 true

9 + 10 > 6 true

therefore this is a possible 3rd side.

B. 2.

so, we have

6 + 9 > 2 true

6 + 2 > 9 false

9 + 2 > 6 true

therefore this is NOT a possible 3rd side.

C. 4.

so, we have

6 + 9 > 4 true

6 + 4 > 9 true

9 + 4 > 6 true

therefore this is a possible 3rd side.

D. 15.

so, we have

6 + 9 > 15 false

6 + 15 > 9 true

9 + 15 > 6 true

therefore this is NOT a possible 3rd side (this triangle is a special case as 6+9 = 15 : it can only exist as a completely flat line and is therefore not a triangle).

E. 12.

so, we have

6 + 9 > 12 true

6 + 12 > 9 true

9 + 12 > 6 true

therefore this is a possible 3rd side.

F. 7.

so, we have

6 + 9 > 7 true

6 + 7 > 9 true

9 + 7 > 6 true

therefore this is a possible 3rd side.

The Surface Area of the sphere is 1017.16 unit^2.

what is the surface area of the sphere?

The surface area of the sphere is 4*pi*r^2.

where, r is the radius

Calculation :

given  radius is 9 units

putting value in the formula of the sphere

S(area)=4*pi*r^2

            =4*3.14*9^2

            =4*3.14*81

            =1017.16 UNIT^2

The Surface Area of the sphere is 1017.16 unit^2.

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The Surface Area of the sphere is 1017.16 unit^2.

The surface area of the sphere is 4*pi*r^2.

where, r is the radius

Calculation :

given  radius is 9 units

putting value in the formula of the sphere

S(area)=4*pi*r^2

           =4*3.14*9^2

           =1017.16 UNIT^2

The Surface Area of the sphere is 1017.16 unit^2.

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Based on the graph of the function (F(x) = log6x), the following facts are true:

A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).

This ultimately implies that, the following facts are true:

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Complete Question:

Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x

A. It is increasing.

B. The range is y > 0.

C. The x-intercept is (1, 0).

D. It is decreasing.

E. The y-intercept is (0, 6).

F. The domain is x > 6.

Answer:

$29.75

Step-by-step explanation:

If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757

it is a relatively easy way to draw a sample while ensuring randomness is the answer.

Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.

These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.

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The answer choice which best fits the function described in the task content is; Choice A; time(length).

It follows from the task content that the function takes the length of a race and returns the time needed to complete it.

On this note, it follows that the time taken is a function of the length of the race.

Hence, the appropriate name of the function is; Choice A.

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The proof to show that at least 80% of students who study both art and science, also study math is illustrated below.

From the information given, it was stated that at least 80% of students study both math and art and that at least 80% of students study both math and science.

Therefore, about (100 - 80) 20% doesn't study the combination of both subjects.

Here, those students who study both art and science, and also study math will be:

= 100% - 20%

= 80%

Therefore, at least 80% study the subjects.

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The table represents an exponential function:

[tex]f(x) = 3^x[/tex]

Then the correct option is B.

Here we have the table:

x       y

1       3

2      9

3      27

4      81

5      243

You can see that each time that x increases by one unit, the value of is multiplied by 3. This is clearly an exponential function.

The function actually is:

[tex]f(x) = 3^x[/tex]

Evaluating it we get:

[tex]f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\...[/tex]

So the correct option is B, exponential.

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Answer:

10. Area: ((6+4) * 8)/2 = 40 ft^2

Perimeter: 6 + 4 + 8 + 12.8 = 30.8 ft

8. 22 + 22 + 22 + 38 + 27.2 = 131.2 ft

m∠ AEM = 20°

From the given figure, we can see that m∠ AEM is alternate to m∠ ACE

Note that m∠ ACE = 20°

Alternate angles are equal.

If m∠ ACE is alternate to m∠ AEM

Then, m∠ AEM = 20°

Hence, m∠ AEM = 20°

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