CALCULUS:
The position in feet of a race car along a straight track after t seconds is given by s(t) = t^2 − 4t + 4. Find its instantaneous velocity at t = 2 seconds.

Answer:

0.4oz

Step-by-step explanation:

conversion factor 1oz = 28.35g

(10g/1)(1oz/28.35g) cross out grams

    10/28.35oz = 0.3|527 = 0.4oz

Answer:

I took the time to graph the image onto the image that you had used, I hope this helps! <3

Step-by-step explanation:

Dilating by 1/2, is a contraction, it makes the pre-image smaller than the image.

The car's fuel consumption is 1.6 gallons per 62.50 miles

The mathematical operation that would be used to solve this question is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

The first step is to convert litres to gallons. To convert to gallons, divide 7.0 liters by the unit of conversion.

7 / 4.5 = 1.6 gallons

The second step is to convert kilometer to mile. To do this, divide 100 by the unit of conversion

100 / 1.6 = 62.50 miles

The car's fuel consumption is 1.6 gallons per 62.50 miles

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Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given the data in the question;

To determine the with of the rectangular prism, plug the given values into the formula above and solve for w.

V = w × h × l

528 ft³ = w × 11ft × 6ft

528 ft³ = w × 66ft²

Reorder the equation and divide both sides by 66ft²

w × 66ft = 528 ft³

( w × 66ft )/66ft² = 528 ft³ / 66ft²

w = 528 ft³ / 66ft²

w = 8ft

Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.

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Answer:

Step-by-step explanation:kfn

Step-by-step explanation:

for positive numbet (2, 4, 6, 8, 10, 12, 14)

 2, 4, 6, 8, 10, 12, and 14.

Step-by-step explanation:

even number is 2,4,6,8.....

odd number is 1,3,5,7.......

wish you have a great day

The solution set in interval notation [7, ∝)

The compound inequality is given as:

x+8 ≥ 9 and 2x − 6 ≥ 8

Take the like terms

x ≥ 9 - 8 and 2x ≥ 8 + 6

Evaluate the like terms

x ≥ 1 and 2x ≥ 14

Divide by 2

x ≥ 1 and x ≥ 7

The solution set of x ≥ 7 is greater than x ≥ 1

So, we have

x ≥ 7

In interval notation, it is [7, ∝)

Hence, the solution set in interval notation [7, ∝)

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The  ratio of frogs to flies in simplest form., 4 frogs and 8 flies​  in simplest form is 2:4.

A ratio  can be described as the ordered pair of numbers in mathematics which do comes in form of a and b, and this can be written as a / b  as well as a:b  which is the ratio of two terms where both of them is not equal to zero.

In the case above, 4 frogs and 8 flies =4:8 =2:4

Therefore, the  ratio of frogs to flies in simplest form., 4 frogs and 8 flies​  in simplest form is 2:4.

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Complete question:

Write the ratio of frogs to flies in simplest form., 4 frogs and 8 flies​  in simplest form.

The required polynomial function is x^4 + 8x³ + 22x² + 24x + 9

In this question,

We have been given  the zeros of a polynomial and the degree of a polynomial.

We need to find the polynomial of degree 4 and has zeros x = -3, -1

If a polynomial function f(x) has zeros x = -3, x = -1, then it has factors

(x + 3), (x + 1).

If these were its only factors, then polynomial would be a quadratic.

This means, both the zeros must be of multiplicity 2.

So, the roots of the polynomial must be of the form f(x) = (x + 3)²(x + 1)²

f(x) = (x + 3)²(x + 1)²

f(x) = (x² + 6x + 9)(x² + 2x + 1)

f(x) = x^4 + 8x³ + 22x² + 24x + 9

Therefore, the required polynomial function is x^4 + 8x³ + 22x² + 24x + 9

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The factors of the polynomial 3x² + 4x - 4 are (3x - 2) and (x + 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

Polynomial is an expression that involves the operations of addition, subtraction, multiplication of variables.

Given the polynomial:

3x² + 4x - 4

Factorizing the polynomial gives:

= 3x² + 6x - 2x  - 4

= 3x(x + 2) - 2(x + 2)

= (3x - 2)(x + 2)

The factors of the polynomial 3x² + 4x - 4 are (3x - 2) and (x + 2)

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Approximately 7.4 is 1.9 times larger than 3.9.

[tex]10^{-8}[/tex]  is 3 times smaller than [tex]10^{-5}[/tex] .

7.4 x [tex]10^{-8}[/tex] is 1.9 x x [tex]10^{-3}[/tex] smaller than 3.9 x [tex]10^{-5}[/tex].

Scientific notation is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, when 100 is written in scientific notation it becomes 1 x 10².

For negative numbers, the sign in front of the power would be negative. For example, 0.0012 becomes 1.2 x [tex]10^{-3}[/tex] in scientific notation.

0.000039 becomes 3.9 x [tex]10^{-5}[/tex]

Difference between 7.4 and 3.9 : 7.4 / 3.9 = 1.9

Difference between [tex]10^{-8}[/tex] and x [tex]10^{-5}[/tex]

= [tex]10^{-8 - (-5)}[/tex]

= [tex]10^{-8 + 5}[/tex]

= [tex]10^{-3}[/tex]

[tex]10^{-8}[/tex]  is three times smaller than  [tex]10^{-5}[/tex]

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Step-by-step explanation:

the €300 as current price is 125% relative to the original price. in other words : 1.25 times the original price.

to get the amount of the increase we need to get the original price first and then subtract the original price from the current price.

to get the original price we need now to divide the actual price by 1.25 to undo the increase.

the original price

OP = 300/1.25 = €240

the price increase (of 25%) was then

300 - 240 = €60

A) The amount that the retailer should charge for each candle in order to maximize its profit is; $27

B) The domain of the function is; x ≥ 120

The range of the function is; P(x) ≥ 3645

A) Let the total sales be represented by P(x).

Let the number of candles sold be x.

Now, since the retailer  120 jar candles at $30 per candle and estimated that or each $2 decrease in price, they will sell 10 additional candles.. Thus;

P(x) = (30 - 2 * (x - 120)/10)x

P(x) = 30x - x²/5 + 24x

P(x) = - x²/5 + 54x

Using -b/2a, we can get the number of candles that maximizes profit as;

-54/(2 * -1/5) = 135 candles

Plugging 135 for x into the P(x) equation gives;

P(135) = $27

B) The domain of the function is; x ≥ 120

The range of the function is; 135 * 27 = 3645

P(x) ≥ 3645

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The value of the given expression is 16. The correct option is the fourth option 16

From the question, we are to find the value of the given expression

The given expression is

|-8| + 4(-5 + 9) ÷ 2

Simplifying by applying PEMDAS

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Simplifying

|-8| + 4(-5 + 9) ÷ 2

8 + 4(4) ÷ 2

8 + 16 ÷ 2

8 + 8

= 16

Hence, the evaluation of the expression is 16

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Answer:

no

Step-by-step explanation:

4 33/100 is equal to 4.33, it is 4.33, not 4.33 with the dot on it, it means recurring decimal. It is jot a recurring decimal. :)

The solution of the equation 12x + 31 = 15 is x = -4/3

In this question we have been given an equation.

12x + 31 = 15

We need to find the solution of the given equation.

12x + 31 = 15

12x + 31 - 31 = 15 - 31                 ..............(Subtract 31 from each side)

12x = -16

x = -16/12                                   .............(Divide each side by 12)

x = -4/3

Therefore, the solution of the equation 12x + 31 = 15 is x = -4/3

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Answer:

$5,864

Step-by-step explanation:

If you subtract all of the monthly costs from her monthly income, it will drop down to $733 and multiply that by 8.

Answer:

16 + n

Step-by-step explanation:

Whenever something says "more" it typically includes addition.

It says 16 more than a number, meaning that you add 16 to an number (n)

*Please mark brainliest

Answer:

16 + n

Step-by-step explanation:

I got 100% on the test

Answer:

C.

Step-by-step explanation:

• C. No, because two points with the same x-value have different y

values. Points with coordinates (7;4) and (7;6).

The missing steps of the expression are as follows;

The expression can be solved as follows:

step 1

[tex](\frac{3^{2} + 4 }{|-0.25|} ) - 10.4[/tex] ÷ 4

Step 2

The absolute value will remove the minus sign of the denominator.

[tex](\frac{3^{2} + 4 }{0.25} ) - 10.4[/tex] ÷ 4

Step 3

We have to find the square of the 3 in the numerator. Therefore, the step 3 will be as follows:

[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷ 4

Step 4

We have simplify the numerator.

[tex](\frac{13 }{0.25} ) - 10.4[/tex] ÷ 4

Step 5

52 - 10.4 ÷ 4

Step 6

Using PEMDAS rule, we have to solve the division sign. Therefore, the step 6 is as follows;

52 - 2.6

Step 7

49.4

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each numbered angle is

1. right angle

2. obtuse angle

Road signs, often known as traffic signs, are posted along the side of roadways or above them to inform and direct drivers. Simple wooden or stone milestones were the oldest types of signs. Later, directional signs with arms were developed, such as the fingerposts used in the United Kingdom and their wooden equivalents in Saxony. Since the 1930s, as traffic volumes have increased, many nations have adopted pictorial signs or have similarly standardized and simplified their signs in an effort to overcome linguistic barriers and improve traffic safety. Such pictorial signals are typically based on international norms and use symbols (often silhouettes) in place of words. These signs were initially created in Europe and have since been adopted in varied degrees by the majority of nations.

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The complete question is attached below

Answer:5/3

Step-by-step explanation:

first u need to change is mixed fraction in to normal fraction

3 1/3-5

3 1/3 means 3*3+1 =10

therefor 10/3-5

u need to find the lcm or the common for the two factor (3 and 1 )

the lcm is 3

so 10-5/3 =5/3

Answer:By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) The shape of the data remains the same

(b) The mean and median are increased by $1,000

(c) The standard deviation and interquartile range remain the same

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

Therefore, following an increase of $1,000, we have;

Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, , are increased by $1,000, the median salary, , is also increased by $1,000

Therefore;

The correct response is that the median is increased by $1,000

(c) The standard deviation, σ, is given by ;

Where;

n = The number of teaches;

Given that, we have both a salary, , and the mean, , increased by $1,000, we can write;

Therefore;

; The standard deviation stays the same

Interquartile range;

The interquartile range, IQR = Q₃ - Q₁

New interquartile range, IQR = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR

Therefore;

The interquartile range stays the same

Step-by-step explanation:

The ordered pair that represents a function is:

⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

The given points are;

(-3, -3), (-2, 2), (1, 1), (2, -2)

(-3, 3), (-3, -3), (-1, 1), (1, 4)

(-4, 4), (-4, 1), (-2, 1), (2, 1)

(-3, 3), (-3, -3), (1, -4), (1, 1)

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

Each x-value have exactly one corresponding y-value.

More than one x-values have the same corresponding y-values.

And, If any of the following conditions is true, then the ordered pair is not a function,

One x-value have multiple corresponding y-values.

More than one x-values have the multiple corresponding y-values.

From the given options, only ordered pair (-3, -3), (-2, 2), (1, 1), (2, -2) satisfies the condition to be a function.

Because none of its x-values have multiple corresponding y-values.

And, Other ordered pairs are either one-to-many or many-to-many.

So, The ordered pair that represents a function is:

⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)

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Answer:

19

Step-by-step explanation:

Arrange into parentheses and start at the innermost parentheses

[tex]5 + (2 \times (6 + (3 \div 3)))[/tex]

Start with 3 ÷ 3

[tex]3 \div 3 = 1[/tex]

Continue with the other parts of the equation in order

[tex]1 + 6 = 7\\7 \times 2 = 14\\14 + 5 = 19\\= 19[/tex]

Hope this helped you understand better, have a great day!

Answer:

2

Step-by-step explanation:

2^2 is 4 and two more than 2, which is 4, is 16 when squared. 16+4=20

The value of KM is equal to 5.

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within.

Consider a point L on a line segment KM such that:

We have the values,

KL = 3x ;

LM = 2

Now, we know,

KL + LM = KM

KM = 3x + 2                                                                                ---------(1)

Now, KM = x + 4                                                                         ---------(2)

Equating the equations (1) and (2),

We get,

3x + 2 = x + 4

Now, subtract 2 from each side of the equation.

3x + 2 - 2 = x + 4 - 2

3x = x + 2

Subtracting x from each side of the equation.

3x - x = x + 2 - x

2x = 2

Dividing each side of the equation by 2.

( 2x / 2 ) = ( 2 / 2)

x = 1

Therefore,

KM = x + 4

KM = 1 + 4

KM = 5

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