The lines represented by the equations

12

y

−

4

x

=

84

12y−4x=84 and

y

=

−

3

x

+

8

y=−3x+8 are

Answer:  [tex]132000 \le f(t) \le 264000[/tex]

Explanation:

The domain is [tex]3 \le t \le 6[/tex] to represent the time values between 3 and 6 hours, including the endpoints. This represents the set of possible inputs to the function.

The function f(t) = 44000t is an increasing function. This means the smallest range value corresponds to the smallest domain value.

Plug in t = 3 to find that:

f(t) = 44000t

f(3) = 44000*3

f(3) = 132000

This says he mows 132,000 sq ft of lawn in 3 hours.

Now plug in the largest domain value to find the largest range value

f(t) = 44000t

f(6) = 44000*6

f(6) = 264000

He mows 264,000 sq ft of lawn in 6 hours.

The range is the set of f(t) values between 132,000 and 264,000

We can write that as [tex]132000 \le f(t) \le 264000[/tex]

Answer: 55

Step-by-step explanation: 180-78 to get the complementary angle. 180-157 to get complementary angle. 180-102+23 to get the last angle inside the triangle. 180-125 and get 55

Answer:

proportional!!!!!!

Step-by-step explanation:

The angle in the fourth quadrant associated with trigonometric function is 314.415°. The exact values of the six trigonometric functions are listed below:

In this problem we find the exact form of a trigonometric function and the related quadrant on a Cartesian plane. By definition of the sine function and the features of the sine, the exact value has the following form and conditions:

y / √(x² + y²) = - 5 / 7, x > 0, y < 0

Then,

y = - 5, √(x² + y²) = 7

√[x² + (- 5)²] = 7

x² + 25 = 49

x² = 24

x = √24

x = 2√6

Then, the angle associated to the trigonometric function is:

θ = tan⁻¹ (y / x)

θ = tan⁻¹ (- 5 / 2√6)

θ ≈ 314.415°

And the five other trigonometric functions are:

cos θ = 2√6 / 7

tan θ = - 5 / 2√6

cot θ = - 2√6 / 5

sec θ = 7 / 2√6

csc θ = - 7 / 5

The angle associated with trigonometric function is 314.415°.

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Answer:

x = 15

Step-by-step explanation:

150+3x-15=180 because of same-side interior angles therorem.

Then, we solve the problem to get 15.

Hope this helped! :)

The linear function is y = -3x -5 with f(3)=-4 and f(1)=2.

The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields. The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. Any function with the formula f(x) = mx + b—where m and b are constants—is said to be linear. Because the graphs of these functions are lines in the plane, we refer to them as linear.

Given Data

f(3) = -4

f(1) = 2

The ordered pairs are (3,-4) and (1,2)

The equation of the line :

y - y₁ = [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex](x - x₁)

y + 4 = [tex]\frac{2+4}{1-3}[/tex] (x-3)

y + 4 = -3(x -3)

y + 4 = -3x + 9

3x + y = -5

y = -3x -5

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The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)

Given,

The equation: 8 ( 5 + 2) = (__×___) + (___×__)

Distributive property:

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Here,

8 (5 + 2)

Using distributive property open the brackets:

8 (5 + 2) = (8 × 5) + (8 × 2)

Now,

8 (5 + 2) = 40 + 16

That is,

8 (5 + 2) = 56

So,

The equation using the distributive property is 8 (5 + 2) = (8 × 5) + (8 × 2)

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Answer:

x=62

Step-by-step explanation:

X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.

-Hope this helps

Answer: The daily cost of production in a factory is calculated using

c(x) = 200 +16 x, where x is the number of complete products manufactured.

Complete products manufactured will can not be a decimal or fraction number.

The domain of function c(x) will be the set of  values x can take.x will be a set of whole numbers. Whole numbers are positive numbers, including zero, without any decimal or fractional parts.

Option D) whole numbers is the right answer.

(4) f(1) = 3, f(n+1)=3f(n) - 2

Step-by-step explanation: I hope this helps.

Answer:

See attached worksheet

Step-by-step explanation:

Answer:

nothing but B2. 0 hours

The bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.

Speed can be thought of as the rate at which an object covers distance.

i.e.

Speed = distance traveled/time taken

After arranging the equation we get,

Time taken = Distance traveled/Average speed

Here distance traveled by bus = 90 km

The average speed of the bus = 60 km/hr

So total time taken = 90/60 = 1.5 hours

So the bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.

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One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials. In other words, the results of one trial do not influence those of the others.

An experiment with a fixed number of independent trials and just two results is referred to as a binomial experiment.

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Answer:

1,081 gallons

Step-by-step explanation:

1,119 - 38 = 1,081

Answer:

First, find x.

(12x + 20) + (6x + 70) = 180 (sum of angles on straight line = 180°)

18x + 90 = 180

18x = 90

x = 5

Next, find z.

z = 12x + 20 (vertically opposite angles)

Substitute x = 5 into equation.

z = 12(5) + 20

= 80

The equation of the car can be given as and the price of the car after 8 years is $4445.

What is an exponential function?

A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.

We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.

Let the original price of the car be [tex]P_{0}[/tex]

After two years the price of the car is $11200

Mathematically it can be given as

[tex]11200= P_{0}e^{2x}[/tex]

After 6 years the price of the car is $6100

Mathematically it can be given as

[tex]6100=P_{0}e^{6x}[/tex]

Dividing both equations we get,

[tex]1.83=e^{-4x}[/tex]

Which can also be written as

[tex]e^{4x}=0.54[/tex]

on solving we get,

x=-0.154

Hence the rate at which price of the car is dropping is

[tex]P=P_{0}e^{-0.154t}[/tex]

No we have to find the original price of the car

To do so we substitute t=2 in the equation

we get

11200=[tex]P_0e^{-0.308}[/tex]

On solving we get,

15240=[tex]P_0[/tex]

Now we find the price of the car after 8 years

P=15240·[tex]e^{-1.232}[/tex]

On simplifying we get

P=$4445

Hence the price of the car after 8 years will be $4445

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Answer:

y=3x+14

Step-by-step explanation:

First find the point using slope point form.

y-y₁=m(x-x₁)

Put y value in for y₁, x value in for x₁ and slope in for m.

y-2=3(x+4)

Simplify

y-2=3x+12

Solve for y to get slope intercept form Y=mx+b

y=3x+14

Answer:

Step-by-step explanation:

Approximately, all of the signatures in the sample of 3000 signatures are invalid . We get this outcome by using binomial distribution .

This problem it is said that 30% of 10000 signatures on certain recall petition are invalid . So, here is the two outcomes possible one is the signatures are invalid and other signature are valid .

Probability of Success (signature are valid ) = p = favourable outcomes / total outcomes

Favourable outcomes for Success = 70% of 10,000= 7000

Total number of possible outcomes = 10,000

P = 7000/10,000 = 7/10

Probability of failure (signature are invalid ) = q= 1- p = 1- 7/10 = 3/10

We have to find out probability of getting invalid signature from a sample of 3000 signatures..

Using the binomial distribution,

P(X = x ) = ⁿ C ₓ pˣ (1- p)⁽ⁿ⁻ˣ⁾

n = 3000 , x= 0 for none of signatures from 3000 are invalid.

P(X=0) = ³⁰⁰⁰C ₀ (3/10)⁰ ( 7/10) ³⁰⁰⁰

= 1 . 1 . (7/10)³⁰⁰⁰ = (7/10)³⁰⁰⁰ = 0

Probability of getting invalid signature out of sample 3000 is

1 – ( 7/1000)³⁰⁰⁰ = 1

This implies that all the signatures in sample of 3000 are invalid.

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We cannot conclude that working in a digital workplace caused employees to be happier from the survey.

How is the conclusion from the survey explained?

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Answer:

3x + 5 + (8x - 3) = 180

11x + 2 = 180

11x = 178

x = 16.18

= 16.2

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Solve the problem?

Given that a card is selected from a 52-card deck that has been thoroughly shuffled without being replaced, the following card is drawn.

A: The top card is a 4, and B: The next card is an ace.

Probability =A∩B

After this first card is pulled, if 10is drawn, we have 51 cards left with 4 aces in them. This is the probability we need to discover for

P(A). =  10/52  

P(B) = number of aces in 51 cards divided by 51, thus = 4/51

Hence A∩B =10/52×10/51

=   100/2652

(From this, we can see that, after changing the card count, A and B are independent.

Additionally, we multiply the probability for both.)

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Answer:what photo

Step-by-step explanation:

where

Therefore let us input the values to find the volume of the cone

The answer should be A.

In a sample of 10 nucleotides, the likelihood of drawing 10 consecutive adenines at random is 0.000006.

Probability: The probability of an occurrence is defined as the ratio between the number of favorable outcomes to a certain event and the entire number of potential outcomes.

The following calculation shows the likelihood of picking 10 consecutive adenines at random from a sample of 10 nucleotides:

According to the information provided, there are 10 adenines and a likelihood of 0.30 that DNA contains them. n = 10 and p = 0.30

Therefore, Probability = (0.30)10 = 0.000006

The likelihood of randomly selecting 10 consecutive adenines from a sample of 10 nucleotides is calculated by multiplying the likelihood that DNA contains adenines by 10 times.

Therefore, The probability of picking 10 consecutive adenines at random from a sample of 10 nucleotides is 0.000006.

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Answer:

£94

Step-by-step explanation:

24+ (14×5) = £94

p.s pls give brainliest answer :)

The value of the expression given as 12x^2(y^8)/3xy^7 is 4xy

From the question, the expression is given as

12x^2(y^8)/3xy^7

Start by removing the bracket in the above expression

So, we have the following equation

12x^2(y^8)/3xy^7 = 12x^2y^8/3xy^7

Divide 12 by 3 in the above equation

So, we have the following equation

12x^2(y^8)/3xy^7 = 4x^2y^8/xy^7

Divide x^2 by x

So, we have the following equation

12x^2(y^8)/3xy^7 = 4xy^8/y^7

Divide y^8 by y^7

So, we have the following equation

12x^2(y^8)/3xy^7 = 4xy

Hence, the expression is 4xy

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Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]

Step-by-step explanation:

[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]

8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.

Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as

z = (x - µ) ÷ σ

Where

x = shelf life of a battery in years.

µ = mean shell life

σ = standard deviation

Based on the facts provided,

µ = 8 years

σ = 0.3 years

The z score corresponds to a p-value of 16% in the normal distribution table,

(16 ÷ 100 = 0.16) is - 0.9.

Therefore,

- 0.9 = (x - 9) ÷ 0.3

0.3 × (- 0.9) = x - 8

0.27 = x - 8

x = 0.27 + 8

x = 8.27

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Investor purchased 50 shares of stock in a company for $40.

So, the total initial amount he invested is

Then the rate of return is:

So, the requied rate of return is 10.0%.

Given.

The distance covered by the snail in 4 minutes is 10 cm.

The speed of snail is,

The distance covered by snail in 6 minute is,

Hence, the distance covered by the snail is 15 cm.

Speed :

Speed is defined as the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling.

Hence , speed can be calculated by using the formula,

               Speed = [tex]\frac{Distance-travelled}{Time-taken}[/tex]

Given data :

Distance travelled by the snail = 10 cm = 0.1 m

Time taken by the snail to travel a distance of 10 cm = 4 min = 240 s

Then , speed of the snail = [tex]\frac{10}{4}[/tex] = 2.5 cm/min = 0.0004 m/s

If the time taken by the snail is 6 min = 360 s

Then, the distance travelled by the snail in 6 min

         = speed x time taken

          = 2.5 cm/min  x 6 min

          = 15 cm = 0.15 m.

Therefore, the snail travels a distance of 15 cm in 6 min.

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The price of the car after 15% markup will be $8,280

How to calculate price after 15% of markup ?

The cost price of car for Hanks = $7200

Marking up of price is done by 15%

To find Markup price = Cost price + 15% of cost price

                                  = 7,200 + 7,200 * 15/100

                                  = 7,200 + 1,080 = $8,280

The 15% of car price is $1,080

The price of the car after 15% markup will be $8,280  

What is percentage ?

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