what is the domain and range of this function?
y=|5x|-8

a) The times that the projectile will reach a height of 20.8 ft are 3.643 seconds and 0.357 seconds, respectively.

b) The projectile will hit the ground 4 seconds later of its launch.

Herein we find a physical model known as projectile motion, which considers that the motion of the object is created solely by gravity and effects from Earth's rotation and air viscosity are neglected. The height of the projectile is represented by the following quadratic equation:

s = - 16 · t² + 64 · t

In the first part, we need to determine when the projectile will reach a height of 20.8 feet:

20.8 = - 16 · t² + 64 · t

16 · t² - 64 · t + 20.8 = 0

(t - 3.643) · (t - 0.357) = 0

The times that the projectile will reach a height of 20.8 ft are 3.643 seconds and 0.357 seconds, respectively.

And the time when the projectile hits the ground is found by solving on t in the following quadratic equation:

- 16 · t² + 64 · t = 0

- 16 · t · (t + 4) = 0

The projectile will hit the ground 4 seconds later of its launch.

In the part (a) a dot symbol was omitted, correct part is: Find the time(s) that the projectile will (a) reach a height of 20.8 ft.

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Answer:

4

Step-by-step explanation:

[tex]\sqrt{x} 368640 = 1920[/tex]

The number of digits in 1920 is 4

The number of digits in the square root of 3686400 is 4.

In mathematics, the square root is a component that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.

The square root of 3686400 is,

√3686400 = ±1920

The number of digits in 1920 is 4.

Only four digits make up 4-digit integers; the first digit must be one or higher, and the other three can be any number between 0 and 9. Examples of four-digit numbers include 5693, 1023, and 9825.

Thus, the number of digits in the square root of 3686400 is 4.

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The solution of the expression for a is a = -1 9/40

The expression is given as:

negative a minus five eighths equals three fifths for a.

Rewrite the expression properly as:

-a - 5/8 = 3/5

Collect the like terms in the above expression

So, we have:

a = -5/8 - 3/5

Evaluate the like terms in the above expression

So, we have:

a = -1 9/40

Hence, the solution of the expression for a is a = -1 9/40

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A surveyor asks a friend her opinion and then asks for the names of five friends for obtain additional opinions. This is an example of convenience sampling.

Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.

An elementary illustration of a convenience sampling technique is when businesses hand out their marketing materials and conduct interviews with randomly chosen participants at a mall or on a busy street.

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8. 1,1

9. 5,-5

10. 4, -3

11. 1536, 6144

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

8. 1000, 100, 10,

In this sequence, each term is getting divided by 10,

So, next two terms are, 1, 1

9.  5, -5, 5, -5, ..

In this sequence, each term is alternating with a minus sign,

So, next two terms are 5, -5

10. 34, 27, 20, 13, ...

In this sequence, each term is i getting substracted by 7,

So, next two term  are 4, -3

11. 6, 24, 96, 384, ...

In this sequence each term is getting multiplied by 4,

So, next two terms are 1536 , 6144

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The dimensions of her scale drawing is 9 centimeters high and 101.25 centimeters long.

As we are informed from the question -

Measurement in real = measurement on scale

The 4 feet height measures 3 centimeters on scale

So, height of 12 feet on scale will be = (3/4) × 12

Performing multiplication and division to find the height of scale drawing

Height 12 feet on scale = 9 centimeters

The length of 135 feet will measure on scale = (3/4) × 135

Performing multiplication and division to find the height of scale drawing

Length 135 feet on scale = 101.25 centimeters

So, the dimensions of scale drawing will be 9 centimeters high and 101.25 centimeters long.

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The factor tree diagram is shown below.

========================================================

Explanation:

The first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

These numbers have factors of 1 and themself only.

Divide 405 over the smallest prime (2)

405/2 = 202.5

We don't get a whole number result, so 2 is not a factor of 405

Repeat for the prime next prime (3)

405/3 = 135

We get a whole number result. Therefore, 3 is a factor of 405

405 = 3*135

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

Now focus on 135.

Divide 135 over the smallest prime (2)

135/2 = 67.5

This rules out 2 as a factor of 135

Repeat for the prime number 3

135/3 = 45

So we can see that

135 = 3*45

which shows 3 is a factor of 135.

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

Now focus on 45. The prime 2 isn't a factor since 45/2 = 22.5 isn't a whole number

But 3 is a prime factor because 45/3 = 15 is a whole number. So 45 = 3*15 is the case.

Furthermore, 15/3 = 5 to show that 15 = 3*5

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

We can express all of this as a factor tree as shown below. The primes have been circled in red.

We have the primes of: 3, 3, 3, 3, 5

We can shorten the four '3's into 3^4

Therefore, 405 = 3^4 * 5

The product in terms of prime factor is  3*3*3*3*5.

The factors of a number are numbers that evenly divide into it. A prime factor is a factor that is only divisible by 1 and itself.

Given:

405

On performing prime factorization

405= 3*3*3*3*5

Hence, the prime factors are  3*3*3*3*5.

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Answer:

28.028 cents per ounce
= 28.03 cents per ounce rounded to 2 decimal places
= 28.0 cents per ounce rounded to 1 decimal place
= 28 cents per ounce rounded to nearest cent

Step-by-step explanation:

[tex]\texttt{{Unit Price} = \ensuremath{\dfrac{\texttt{Total Price}}{\texttt{Quantity}}} }[/tex]

Here
Total Price = $3.98
Quantity = 14.2 ounce

[tex]\texttt{{Unit\;Price}\;=\;\ensuremath{\dfrac{\texttt{\$3.98}}{\texttt{14.2 oz}}} }[/tex]

Convert dollars in the numerator to cents for easier calculation

Since one dollar = 100 cents.
$3.98 = 3.98 x 100 = 398¢

Divide 398 by 14.2 to get
[tex]\ensuremath{\dfrac{\texttt{398}}{\texttt{14.2}}} } = \texttt{28.028 cents per ounce}[/tex]

which, you can round off as necessary
Rounding to 2 decimal places it becomes 28.03 cents per ounce
Rounding to 1 decimal place it becomes 28.0 cents per ounce
Rounding to nearest cent it becomes 28 cents per ounce

The algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is  x^2 - 6

Expressions are mathematical statements that are represented by variables, coefficients and operators

The mathematical statement is given as

The difference of a number squared and 6

Represent the number with x

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒ The difference of x squared and 6

x squared implies x^2

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒ The difference of x^2 and 6

difference means minus (-)

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒  x^2 - 6

Hence, the algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is  x^2 - 6

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75% is percentage of undergraduate students are between 36 and 52 years old.

What is percentage and example?

This would be true if k=3, but k=2

because (36-44)/4 = -2 and (52-44)/4 = 2

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The equation of the line in slope-intercept form passing through the points (-4.7 , 2.7) and (1.3 , -7.3) is y = -1.67x - 5.13.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the two points, (-4.7 , 2.7) and (1.3 , -7.3), get the slope of the line using the formula:

m = (y2 - y1)/(x2 - x1)

m = (-7.3 - 2.7)/(1.3 - -4.7)

m = -10/6

m = -5/3

Using the slope-intercept form, plug in the value of the slope and one point to determine the y-intercept, b.

y = mx+ b

2.7 = -5/3(-4.7) + b

b = -77/15

Substitute the value of the slope and y-intercept in the slope-intercept form.

y = -5/3 x -77/15

y = -1.67x - 5.13

Hence, the equation of the line in slope-intercept form is y = -1.67x - 5.13.

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Answer: LCM would be [tex]\sqrt{2}[/tex]

Step-by-step explanation:

First we need to find number of which we need to find lcm

here we dont have any two number but operator (+) is present

so

first we need to solve this operation

=1/[tex]\sqrt{2}[/tex] + 1/[tex]\sqrt{2}[/tex]

=[tex]\sqrt{2}[/tex]

so lcm of  [tex]\sqrt{2}[/tex] would be [tex]\sqrt{2}[/tex].

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The sample proportion, p-hat, of engineers who have master's degrees is   68.5% out of 200 engineers.

p-hat proportion:

In this proportion,  "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.

The general form for calculating p-hat proportion is,

[tex]\hat{p}=\frac{x}{y}[/tex]

where

x  is the number of successes in the sample, and

y is the size of the sample.

Given,

In a random sample of 200 engineers, 137 have a master's degree.

Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees

According to the question,

x = 137 (number of successes in the sample)

and y = 200 (size of the sample)

Now apply the value on the formula then we get,

[tex]\hat{p}=\frac{137}{200}[/tex]

So, the value of p-hat is

[tex]\hat{p}=0.685[/tex]

The results are usually reported as a percentage, which in this case would be

=> 0.685 x 100 = 68.5%

Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.

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Answer:

Terms of a Polynomial

So, each part of a polynomial in an equation is a term. For example, in a polynomial, say, 2x2 + 5 +4, the number of terms will be 3.

Answer:The final balance is $28,043.4.

The total compound interest is $10,043.4.

Step-by-step explanation:

https://www.omnicalculator.com/finance/compound-interest?c=USD&v=var1:1,subject:1138535033,var2:1,subject2:1,FinalBal:20000,FinalBal_adj:20000,apy:1.95!perc,infl:0,PeriodicDep:50,q:1000!!l,type:1,DepositBal:0,PrincipalBal:0,g:0!perc,first_day:19255,select1:1,TableFreq:111,InitialDep:18000,r:3!perc,t:180!yrsmos,m:1,ct1:1,ct2:0,compound_frequency:21,ct3:3,represent:13

Answer:

72

Step-by-step explanation:

7(10) + 2

70 + 2

72

Answer:  No

Explanation:

Apply the derivative

[tex]f(x) = \sqrt{x}\\\\f(x) = x^{1/2}\\\\f'(x) = (1/2)x^{-1/2}\\\\f'(x) = \frac{1}{2x^{1/2}}\\\\f'(x) = \frac{1}{2\sqrt{x}}\\\\[/tex]

Though we run into a problem since f ' (0) is undefined, due to the zero in the denominator.

Therefore, f(x) is not differentiable at x = 0.

The function is continuous, but only on the interval [tex]x \ge 0[/tex] and not over the entire set of real numbers R.

The five number summary for

(a) 0,2,2,4,5,5,5,5,7,11 is minimum=0  , median=5 ,maximum=11 ,Q₁=2 ,Q₃=5  .

(b) 2,2,4,5,5,5,5,7,11 is minimum=2 ,median=5 ,maximum=11 ,Q₁=3 ,Q₃=6 .

Median is defined as the center value of the data.

Part(a)

In the given question

the data is 0, 2, 2, 4, 5, 5, 5, 5, 7, 11

(i)the minimum of the data is 0

(ii) maximum of the data is 11.

(iii) median of the data is 5.

(iv)Q₁ = median of the lower half 0,2,2,4,5 is 2.

(v)Q₃ = median of the upper half 5,5,5,7,11 is 5.

Part (b)

after removing minimum 0 the data becomes 2,2,4,5,5,5,5,7,11

(i)the minimum of the data is 2

(ii) maximum of the data is 11.

(iii) median of the data is 5.

(iv)Q₁ = median of the lower half 2,2,4,5 is 3.

(v)Q₃ = median of the upper half 5,5,7,11 is 6.

Therefore , the five number summary for

(a) 0,2,2,4,5,5,5,5,7,11 is minimum=0 ,median=5 ,maximum=11 ,Q₁=2  ,Q₃=5  .

(b) 2,2,4,5,5,5,5,7,11 is minimum=2 ,median=5 ,maximum=11 ,Q₁=3 ,Q₃=6 .

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Answer:

hoping the equation wasn't cut off. from what i see it started at 1/2.

-3

__

         [tex]\left(4\right)^2=16\\=\frac{1}{2}\cdot \:16-2\left(4\right)-3\\=\frac{1}{2}\cdot \frac{16}{1}\\=\frac{1\cdot \:16}{2\cdot \:1}\\=\frac{16}{2}\\\frac{16}{2}=8\\=8-2\left(4\right)-3\\2\left(4\right)\\2\cdot \:4 = 8\\=8-8-3\\8-8=0\\0-3\\= -3[/tex]

__

Hope this helps!

Answer:

E

Step-by-step explanation:Step-by-step explanation:Step-by-step explanation:Step-by-step explanation:

The original price of a computer was reduced by $250. If p = the computer's original price in dollars. p-250 is algebraic expression represents the reduced price.

The original price of a computer was reduced by $250

p = the computer's original price in dollars

reduced price = original price - reduction

algebraic expression can be written as:

p-250

The complete cost of purchasing an item is known as the original cost. The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.

Listing price, also known as asking price, is the price at which a seller has placed a property on the market, but selling price is the price at which it actually sells. These days, properties that sell for significantly more than their asking or listed price receive a lot of media attention.

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The quotient of 455 ÷ 36 is 12 with a remainder of 23.

It should be noted that the subtraction of 360 from 455 will be 95.

Then after that 72 is subtracted from 95 and this will be 23.

Therefore, the quotient is 12 with a remainder of 23.

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Answer:

Hello,

Step-by-step explanation:

1) Conjecture: The sum of any two odd numbers is even
(2a+1)+(2b+1)=2a+2b+2=2(a+b+1) is even

2) Conjecture: The product of any two odd numbers is ODD
(2a+1)*(2b+1)=4ab+2b+2a+1=2(2ab+a+b)+1 is ODD
1*1=1

1*5=5

7*9=63

9*11=99

13*21=273

3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to the difference of the square of x between 1

(x-1)(x+1)=x²-x+x-1=x²-1

Your answer is x=1/3

Good luck with your test!~ ^^

The value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.

According to the given question.

We have a data set 100, 122, 105, 115, 107, x .

Also, the mean of the data set is 108.

As we know that, mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Therefore, the mean of the data set 100, 122, 105, 115, 107, x is given by

Mean = [100 + 122 + 107 + 115+ 107 + x]/6

⇒ 108  × 6 = (551 + x)

⇒ 648  = 551 + x

⇒ x = 648 - 551

⇒ x = 97

Hence,the value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.

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Error control, flow control, segmentation and reassembly, multiplexing, and connection setup are five tasks that a layer can perform.

Flow control: It is the efficient management of data flow between two or more devices like computers or nodes of a network.

Error control: The identification and correction of errors that occur during the transmission of data is called error control.

Segmentation and reassembly: Data to be transmitted is divided into small parts or chunks for convenience. This process is called segmentation. The combining of these chunks to reform the original data is called reassembling.

Multiplexing: The process of combination of digital data streams in one signal over a shared medium is known as multiplexing.

Connection setup: Establishing a connection between two devices that are connected to the same network is called connection setup.

All these tasks can be duplicated at different layers.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{7 \dfrac{7}{9}}[/tex]

[tex]\mathsf{= \dfrac{7\times9 + 7}{9}}[/tex]

[tex]\mathsf{= \dfrac{63 + 7}{9}}[/tex]

[tex]\mathsf{= \dfrac{70}{9}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{{\dfrac{70}{9}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]