Lita,Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4:1. If Rose typed 48 words, how many words did Lita type?

Answer:

[tex]6000x=135000[/tex]

23 fire extinguisher.

Step-by-step explanation:

Let x be the number of fire extinguishers.

We have been given that one fire extinguisher be available for every 6,000 square feet in a building. So the total area covered by x extinguisher will be 6,000x.

Since the building has an area of 135,000 square feet. This means that that total area covered by x extinguisher is 135,000 square feet. We can represent this information in an equation as:

[tex]6000x=135000[/tex]

Therefore, the equation [tex]6000x=135000[/tex] represents the number of fire extinguishers needed for a building that has 135,000 square feet.

Now we will solve for by dividing both sides of our equation by 6000.

[tex]\frac{6000x}{6000}=\frac{135000}{6000}[/tex]

[tex]x=\frac{135}{6}[/tex]

[tex]x=22.5[/tex]

Since we can not have 0.5 of a fire extinguisher, so we will round up our answer as:

[tex]x\approx 23[/tex]

Therefore, 23 fire extinguisher are needed for the building.

Answer:

2:5!

Step-by-step explanation:

Have a great day!

Answer:

The answer is 140 miles 100x42 is 4200 divide that by 30= 140Step-by-step explanation:

Answer:

30.28

Step-by-step explanation:

just did the k12 test so i thought i would help out:)

Answer:

92 is correct

Step-by-step explanation:

Answer:

640 m

Step-by-step explanation:

We can consider 4 seconds to be 1 time unit. Then 8 more seconds is 2 more time units, for a total of 3 time units.

The distance is proportional to the square of the number of time units. After 1 time unit, the distance is 1² × 80 m. Then after 3 time units, the distance will be 3² × 80 m = 720 m.

In the additional 2 time units (8 seconds), the ball dropped an additional

... (720 -80) m = 640 m

_____

Alternate solution

You can write the equation for the proportionality and find the constant that goes into it. If we use seconds (not 4-second intervals) as the time unit, then we can say ...

... d = kt²

Filling in the information related to the first 4 seconds, we have ...

... 80 = k(4)²

... 80/16 = k = 5

Then the distance equation becomes ...

... d = 5t²

After 12 seconds (the first 4 plus the next 8), the distance will be ...

... d = 5×12² = 5×144 = 720 . . . meters

That is, the ball dropped an additional 720 -80 = 640 meters in the 12 -4 = 8 seconds after the first data point.

Answer:

Because f+e=c

Therefore ,[tex]a^2+b^2=c^2[/tex]

Step-by-step explanation:

Given A right triangle ABC as shown in figure  where CD is an altitude of the triangle.

To prove that [tex]a^2+b^2=c^2[/tex]

Proofe: Given [tex]\triangle ABC\; and\; \triangle CBD[/tex] both are right triangle and both triangles have common angle B si same.

Therefore , two angles of two triangles are equal .

Hence, [tex]\triangle ABC \sim\triangle CBD[/tex] by using AA similarity.

Similarly , [tex]\triangle ABC \sim \triangle ACD[/tex] by AA similarity property . Because both triangles are right triangles therefore, one angle of both triangles is equal to 90 degree and both triangles have one common angle A is same .

[tex]\therefore[/tex] [tex]\frac{b}{c} =\frac{e}{b}[/tex]

The corresponding parts of two similar triangles are in equal proportion  therefore , two proportion can be rewrite as

[tex]a^2=cf[/tex] (I equation)

and  [tex]b^2=ce[/tex] (II equation)

Adding [tex]b^2[/tex] to  both sides of firs equation

[tex]a^2+b^2=cf+b^2[/tex]

Because [tex]b^2=ce[/tex] and ce can be substituted into the right side of equation wevcan write as

[tex]a^2+b^2=ce+cf[/tex]

Applying the converse of distributive property we can write

[tex]a^2+b^2=c(f+e)[/tex]

Distributive property: a.(b+c)= a.c+a.b

[tex]a^2+b^2=c^2[/tex]

Because f+e=[tex]c^2[/tex]

Hence proved.

Final answer:

Paul needs to buy 1 carton of eggs, as there are 6 teams needing 1 egg each, and one carton contains 6 eggs.

Explanation:

Paul needs to calculate how many cartons of eggs to buy for the egg toss at the world egg day fair.

With 48 people participating in teams of 8, we have a total of 48/8 = 6 teams, and each team needs 1 egg.

Since each carton contains 6 eggs, Paul needs to buy 6/6 = 1 carton to provide one egg for each team.

Answer:

21.8

Step-by-step explanation:

Leo painted for 2/3 of an hour each day on Monday, Tuesday, Thurday, and friday. Thus, the total time of the week for which he painted is 1.58% of the total time.

A fraction represents a part of a whole number or, more commonly, any number of equal parts. A fraction can be defined as the parts of a certain size, for example, one-half, eight-fifths, three-quarters, etc.

The time for which Leo painted in this week can be calculated as:

Leo painted 2/3 of an hour each day for monday, tuesday, thursday, and friday

Therefore, the time of painting in an hour = 40 minutes

2/3 × 60 = 120/ 3 = 40 minutes = 40 × 4 = 160 minutes

The number of minutes in a day,

1 day = 60 × 24 = 1,440 minutes

The number of minutes in seven days,

7 days = 1440 × 7 = 10,080 minutes

Therefore, the total time for which Leo painted = time for which he painted in minute divided by total time in minutes

Total time for which Leo painted = 160/ 1440 = 0.0158 or 1.58%

Therefore, total time for which he painted in this week is 0.0158 of total time

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Answer:

The correct answer is: A:  x(y – 5) = 2

Step-by-step explanation:

edge2021

If line AB is parallel to line CD and line CD is perpendicular to line EF, we can conclude that line AB is also perpendicular to line EF.

If line AB is parallel to line CD and line CD is perpendicular to line EF, we can conclude that line AB is also perpendicular to line EF.

The reason for this is that if two lines are parallel to the same line, they are parallel to each other. In this case, we have line AB and line CD both parallel to line EF. Then, because line CD is perpendicular to line EF, line AB must also be perpendicular to line EF.

Answer: [tex](gof)(-1)=-2[/tex]

Step-by-step explanation:

By definition, a composite function is a function formed by substituing one function into another function.

Given the composite function:

[tex](gof)(-1)[/tex]

You can rewrite it in the following form:

[tex]g(f(-1))[/tex]

In order to evaluate it, follow these steps:

- Based on the table of the function f(x), the ouput value for [tex]x=-1[/tex] is [tex]y=3[/tex]. Then:

[tex]f(-1)=3[/tex]

- This will be the input of the function g(x).

- Notice in the table of the function g(x) that the output value when [tex]x=3[/tex] is [tex]y=-2[/tex]:

[tex]g(3)=-2[/tex]

Therefore:

[tex]g(f(-1))=-2[/tex] or [tex](gof)(-1)=-2[/tex]

Answer:

The value of [tex]\rm{gof(-1)}[/tex] is -2.

Step-by-step explanation:

Given,

The table contains the functional value of f(x) and g(x).

To find:   [tex]\rm{gof(-1)}[/tex]

[tex]\rm{fog(-1)}[/tex] is a composite function of f(x) and g(x).

[tex]\rm{gof(-1)}=\rm{g[f(-1)}][/tex]

Clearly from the table, the value of f(x) when [tex]x=-1[/tex] is 3.

Therefore,

[tex]f(-1)=3[/tex]

Now,

[tex]\rm{gof(-1)}=\rm{g[f(-1)}]\\\rm{fof(-1)}=\rm{g(3)}[/tex]

Clearly from the table, the value of g(x) when [tex]x=3[/tex] is -2.

Thus,

[tex]\rm{gof(-1)}=-2[/tex]

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Answer:

The answer is 7,000

Your welcome ;)

Using the Chain Rule of differentiation, we can solve for ∂z/∂s and ∂z/∂t given the functions for z, x, and y. The Chain Rule is fundamental for calculus by finding the derivative of composite functions.

To solve for ∂z/∂s and ∂z/∂t with z = x5y7, x = s cos(t), and y = s sin(t), we'll employ the use of the Chain Rule of differentiation. First, we consider ∂z/∂s. As z is x raised to the power of 5 then multiplied by y to the power of 7, we can express ∂z/∂x and ∂z/∂y. Proceeding using the chain rule, which in simpler terms could be stated as 'the derivative of the outside times the derivative of the inside', we get the values of ∂z/∂s and ∂z/∂t. The chain rule in calculus is an important tool when differentiating composite functions.

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Answer:

1

Step-by-step explanation:

Answer:

To solve this problem, you need to remember that an exponential function has the following form:

f(x)=a^x

"a" is the base and "x" is the exponent.

2. It is important to know that the logarithmic functions  and the exponential functionsare inverse. Then, you have:

y=ln x

e^y=e^(lnx)

e^y=x

3. Therefore, the answer is:

Step-by-step explanation:

Final answer:

To find the position vector r(t) given its derivative and an initial condition, we integrate each component of the derivative and apply the initial condition to solve for constants of integration. The final position function is r(t) = t³i + t⁴j + (0.5t² - 0.5)k.

Explanation:

To find r(t) given that r'(t) = 3t²i + 4t³j + tk and r(1) = i + j, we integrate each component of r'(t) with respect to t. The integral of a derivative returns the original function plus a constant of integration, which we can solve using the initial condition provided.

For the i component: ∑ 3t² dt = t³+ C1

For the j component: ∑ 4t³ dt = t⁴ + C2

For the k component: ∑ t dt = 0.5t² + C3

Applying the initial condition r(1) = i + j, we substitute t = 1 into r(t) to solve for the constants of integration:

(1) + C1 = 1, so C1 = 0

(1) + C2 = 1, so C2 = 0

0.5(1) + C3 = 0, so C3 = -0.5

Therefore, the position function r(t) is given by t³i + t⁴j + (0.5t² - 0.5)k.

r(t) = t^3i + t^4j + ((1/2)t^2 - 1/2)k.

To find r(t) given r'(t) = 3t^2i + 4t^3j + tk and r(1) = i + j, we need to integrate r'(t) with respect to t.

Step 1: Integrate each component of r'(t) separately:

∫3t^2 dt = t^3 + C1 (integration with respect to t)

∫4t^3 dt = t^4 + C2 (integration with respect to t)

∫tk dt = (1/2)t^2k + C3 (integration with respect to t)

Step 2: Combine the results to get r(t):

r(t) = (t^3 + C1)i + (t^4 + C2)j + ((1/2)t^2k + C3)

Step 3: Use the given initial condition r(1) = i + j to find the values of the constants C1, C2, and C3:

r(1) = (1^3 + C1)i + (1^4 + C2)j + ((1/2)(1)^2k + C3)

i + j = i + j + (1/2)k + C3

Comparing the coefficients of k, we get:

(1/2) + C3 = 0

C3 = -1/2

Therefore, r(t) = (t^3 + C1)i + (t^4 + C2)j + ((1/2)t^2 - 1/2)k

Answer:

2/5

Step-by-step explanation:

1 to 10, it is 10 numbers

and there are 4 numbers which are 7,8,9,10 are bigger than 6

so P =4/10=2/5