Six out of 40 is equivalent to

Answer:

3/4 of a foot.

Step-by-step explanation:

In order to find how many feet are in 9 inches, we simply divide 9 by 12. We use the number 12, because that is how many inches are in a foot. 9 divided by 12 = 0.75 or 3/4 of a foot.

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Answer:

The car gets 25 miles per gallon.

It means that for each gallon of gas the car uses, it will travel a distance of 25 miles.

Step-by-step explanation:

"Miles per gallon" is calculated by dividing the number of miles by the number of gallons.

mpg = (335 miles)/(13.4 gallons) = 25 miles per gallon

Answer:

The car gets 25 miles per gallon.

It means that for each gallon of gas the car uses, it will travel a distance of 25 miles.

Answer:

25

Step-by-step explanation:

You need to divide 335 miles by 13.4 to find the miles per gallon. 335 miles divided by 13.4 gallons is 25. So for every 25 miles you use 1 gallon.

The factored form of an equation is done by rewriting the equation in simpler forms.

The completely factored form of \(8x^2 - 50\) is \(2(2x-5)(2x + 5)\)

The expression is given as:

\(8x^2 - 50\)

Factor out 2 from the expression, \(8x^2 - 50\)

\(8x^2 - 50 = 2(4x^2-25)\)

Express 25 as 5^2

\(8x^2 - 50 = 2(4x^2-5^2)\)

Express 4 as 2^2

\(8x^2 - 50 = 2(2^2x^2-5^2)\)

Rewrite the expression as:

\(8x^2 - 50 = 2((2x)^2-5^2)\)

Express the expression as a difference of two squares

\(8x^2 - 50 = 2(2x-5)(2x + 5)\)

Hence, the completely factored form of \(8x^2 - 50\) is \(2(2x-5)(2x + 5)\)

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Answer:

Firstly we will divide all 8 marbles into 2 sections. Each section contains 4 marbles.

Then we balance each section and find that one section is lighter than other.

Then we take lighter section and further divide it into 2 sections and each section contains 2 marbles.

Then we balance them again and we find the lighter section further divide it into 2 sections and each section contains 1 marble, balance them and we get the lightest marble.

0.765

answer is 0.764758824 and because there is a 7 after the 4 we round up

The equations for parts A and B are 170 = 60x + 50 and 210 = 75x + 35 - 10x, respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

A) It is stated that Maci once earned $170 by grooming dogs.

For each appointment, she charges $60, and she received $50 in tips. Consequently, the equation to illustrate this is;

170 = 60x + 50

the number of appointments is x.

B) Logan earned $210.00 in profit. He charged $75.00 for each session and got $35.00 in gratuities. In addition, he had a $10.00 truck rental fee per appointment. In order to represent this, the equation is;

210 = 75x + 35 - 10x

the number of appointments is x.

C) The quantity of tips they will receive even without an appointment varies between the formulae.

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Answer:

the triangle is not right angle triangle

Answer:

No

Step-by-step explanation:

Using the converse of Pythagoras' identity

If the square on the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

longest side = 8 , and 8² = 64

4² + 5² = 16 + 25 = 41

Since 41 ≠ 64

Then triangle is not right

Answer:

logically cp =25%less than mp

The length of the rectangle is (10+x) cm and the width of the rectangle is x cm.

According to the question,

We have the following information:

The width of the rectangle = x cm

Now, the length of the rectangle is given to be 10 cm more than the width of the rectangle.

So, this can be converted in the following mathematical expression:

Length of the rectangle = 10+x cm

(More to know: the area of the rectangle is given by the formula l*b where l is the length and b is the breadth of width of the rectangle.)

Hence, the length of the rectangle is (10+x) cm and the width of the rectangle is x cm.

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100 + 75x > 700: This inequality represents the condition where Lawrence charges clients more than $700.

Let's represent the typical number of hours worked by Lawrence as "x" (in hours). Based on the information provided, we can set up the inequality to represent the range of fees charged by Lawrence: 100 + 75x < 250 or 100 + 75x > 700. Let's explain these inequalities: 100 + 75x < 250: This inequality represents the condition where Lawrence charges clients less than $250. The initial fee of $100 plus the product of $75 per hour (75x) should be less than $250.

100 + 75x > 700: This inequality represents the condition where Lawrence charges clients more than $700. The initial fee of $100 plus the product of $75 per hour (75x) should be greater than $700. These inequalities provide the boundaries for the range of fees charged by Lawrence, based on the number of hours worked (x). The exact value of "x" that satisfies either inequality depends on the specific rates charged by Lawrence and would need further information to determine.

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The probability of randomly selecting a student who sometimes sleeps in socks given they are ambidextrous is 0.6

First, P(sometimes sleep in socks | ambidextrous)

= P(sometimes sleep in socks and ambidextrous) / P(ambidextrous)

From the given table, we can see that there are 21 students who sometimes sleep in socks and 46 ambidextrous students.

So, P(sometimes sleep in socks and ambidextrous) = 3/75

P(ambidextrous) = 5/75

Now, P(sometimes sleep in socks | ambidextrous)

=3/75 x 75/5

= 3/5

≈ 0.6

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The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.

The interquartile range(IQR) = third quartile(Q3) - first quartile(Q1)

The third quartile of in the box plot given is : 56 pounds

The third quartile of the data as represented in the box plot given :

39 pounds

The interquartile range(IQR) of ken's data = 56 - 39

= 17 pounds

Hence, The interquartile range(IQR) of the recorded weight of ken is calculated as 17 pounds.

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There are no real values for X and Y that satisfy the given equations X + Y = 17 and XY = 164.

To find the values of X and Y in the given equations, we can use a system of equations approach.

Let's start by solving the first equation, X + Y = 17, for one variable in terms of the other. We can choose to solve for X:

X = 17 - Y

Now, substitute this expression for X in the second equation, XY = 164:

(17 - Y)Y = 164

Expanding the equation gives us:

17Y - Y^2 = 164

Rearranging the equation to a quadratic form, we have:

Y^2 - 17Y + 164 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

Y = (-(-17) ± √((-17)^2 - 4(1)(164))) / (2(1))

Simplifying further:

Y = (17 ± √(289 - 656)) / 2

Y = (17 ± √(-367)) / 2

Since the expression under the square root is negative, there are no real solutions for Y. This means that there are no real values for X and Y that satisfy both equations simultaneously.

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Answer: The answer would be C

Step-by-step explanation:

You want to divide. 15/3= 5 and then a^3 is basically being divided by 1 so your completed answer would be 5a^3

Answer:

The third one

Step-by-step explanation:

CAD is preferred over traditional methods of drafting because it is less time-consuming, more accurate, and saves a lot of effort.

The tool which has replaced traditional tools like T-squares, triangles, paper, and pencils is CAD (Computer-Aided Design).

CAD is the most popular software used in industries like engineering, architecture, construction, etc. for drafting.

It provides a high degree of freedom to the designer to make changes as per the need and requirement of the design.

In CAD software, we can create, modify, and optimize the design without starting from scratch again and again.

Also, we can save different versions of the same design.

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Answer:

3rd choice

Step-by-step explanation:

y = mx + b

Look at where the line crosses the y-axis. That is the y-intercept. It is 2, so b = 2, and you have

y = mx + 2

Now we need the slope, m.

Start at (0, 2). Go up 1 and right 2.

slope = m = rise/run = 1/2

Now you have

y = 1/2 x + 2

Answer: 3rd choice

Answer:

\(c)y=\frac{1}{2}x+2\)

Step-by-step explanation:

\(We\ know\ that,\\The\ equation\ of\ a\ graph\ is\ given\ by\ the\ formula:\\y=mx+b,\ where\ m\ is\ the\ slope\ of\ the\ graph,\ and\ b\ is\ the\ y-intercept;\\Here,\\First,\\Lets\ calculate\ the\ slope\ of\ the\ graph:\\We\ also\ know\ that,\\Slope(m)=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}\\Lets\ consider\ any\ two\ points\ which\ lie\ on\ the\ line:\\(2,3),(-2,1)\\Hence,\\The\ slope\ of\ the\ given\ line=\frac{1-3}{-2-2}=\frac{-2}{-4}=\frac{1}{2}\\Hence,\\m=\frac{1}{2}\\\)

\(Now,\\The\ y-intercept\ is\ the\ point\ at\ which\ the\ graph\ intersects\ the\ whole\ y-axis.\\Hence,\\Here,\\The\ line\ of\ the\ graph\ cuts\ the\ y-axis\ at\ (0,2).\\The\ y-intercept\ of\ the\ line=2\\Hence,\\The\ equation\ of\ the\ line:\\y=(\frac{1}{2})x+(+2)\\y=\frac{1}{2}x+2\)

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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The probability of winning first prize in the chess tournament is approximately 0.2667 or 26.67%.

To calculate the probability of winning first prize in a chess tournament given odds of 4 to 11, we need to understand how odds are related to probability.

Odds are typically expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds are given as 4 to 11, which means there are 4 favorable outcomes (winning first prize) and 11 unfavorable outcomes (not winning first prize).

To convert odds to probability, we need to normalize the odds ratio. This is done by adding the number of favorable outcomes to the number of unfavorable outcomes to get the total number of possible outcomes.

In this case, the total number of possible outcomes is 4 (favorable outcomes) + 11 (unfavorable outcomes) = 15.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Probability = 4 / 15 ≈ 0.2667

Therefore, the probability of winning first prize in the chess tournament is approximately 0.2667 or 26.67%.

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The kinetic energy change of the block is 4.05 J

Kinetic energy is energy due to motion of an object

Since two forces, of magnitudes F1 = 95.0 N and F2 = 50.0 N, act in opposite directions on a block, which sits atop a frictionless surface, as shown in the figure.

If Initially, the center of the block is at position xi = -3.00 cm. At some later time, the block has moved to the right, and its center is at a new position, xf = 6.00 cm.

To determine the change Kf−Ki in the kinetic energy of the block as it moves from xi = -3.00 cm to xf = 6.00 cm, we use the work-kinetic energy principle.

So, Fd = ΔK where

Given that

So, substituting the values of the variables into the equation, we have that

ΔK = Fd

= ( F₂ + F₁)(x₂ - x₁)

.= [95.0 N + (-50.0 N)](0.06 m - (-0.03 m)

=  [95.0 N - 50.0 N)](0.06 m + 0.03 m)

= 45.0 N × 0.09 m

= 4.05 Nm

= 4.05 J

So, the kinetic energy change is 4.05 J

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The variable assigned to strgrade when intscore equals 90 would likely be 'A'.

When the variable intscore equals 90, the corresponding value assigned to the variable strgrade would typically be 'A'. This suggests that a score of 90 is associated with the highest grade achievable in the given context. The specific mapping between integer scores and letter grades may vary depending on the grading system or criteria in place. It is important to note that without further information about the grading scale or specific rules defined within the system, it is difficult to determine the exact value of strgrade assigned to intscore of 90.

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Answer:

$4,608.00

Step-by-step explanation:

Subtract 36% from 7,200 and you get 4,608.

Answer: 163 & 8

Step-by-step explanation:

Given equation f(x) =\(2x^3+3x^2-4x+3\) to solve for f(4) and f(-1)

First for f(4) in synthetic substitution;

We have to take down the first number 2 then multiply with 4 and add. Again keep repeating the process till the last number.

(4)        2     3     -4      3                    

                   8     44    160

            2     11    40    163

So the answer for f(4) is 163

Again for f(-1)

(-1)             2    3     -4      3

                     -2     -1       5

                2    1      -5      8

So the answer for f(-1) is 8.

If you want to recheck try the simple, direct method of putting the values instead of x.

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Answer:

F(x) = (x + 3)^2 -87

Step-by-step explanation:

Here, we want to rewrite the function by completing the square.

Firstly, we move the c term(-78) to the right hand side of the equation and that becomes

x^2 + 6x = 78

Then, we can complete the square on the right hand side here, to be

Let’s add 9 to both sides

That would be;

x^2 + 6x + 9 = 78 + 9

x^2 + 6x + 9 = 87

(x+3)^2 = 87

or simply

(x+3)^2 -87 = 0

So our F(x) becomes

F(x) = (x + 3)^2 -87

Answer:

The expression after completing the square is:

\(f(x) = (x+3)^{2} -87\)

Step-by-step explanation:

The function is rewritten after making algebraic manipulation:

\(f(x) = x^{2} + 6\cdot x +9 - 9 - 78\)

The expression after completing the square is:

\(f(x) = (x+3)^{2} -87\)

\(\huge\underline\color{skyblue}{Answer ☘}\)

let the number be x.

according to Question...

\( \frac{1}{8} x \leqslant 3 \\ x \leqslant 3 \times 8 \\ x \leqslant 24\)

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The probability of drawing two jacks in a row from a deck of 52 cards without replacement is equal to option(B) 0.005.

Total number of cards in a deck = 52

Number of Jack in deck of cards = 4

Probability of getting a jack on the first draw is

= 4/52

Now, there are only 3 jacks remaining in a deck of 51 cards.

This implies,

Probability of drawing another jack on the second draw given that the first card was a jack

= 3/51

Probability of drawing two jacks in a row,

Multiply the probability of drawing

= (a jack on first draw by another jack on second draw given first card was a jack)

⇒ P(two jacks)

= (4/52) × (3/51)

= 1/13 × 1/17

= 1/221

= 0.00452489

= 0.005 (rounded to three decimal places).

Therefore, the probability of drawing two jacks in a row is equal to option(B) 0.005.

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The probability of drawing two jacks in a row from a deck of 52 cards without replacement is equal to option(B) 0.005.

Total number of cards in a deck = 52

Number of Jack in deck of cards = 4

Probability of getting a jack on the first draw is

= 4/52

Now, there are only 3 jacks remaining in a deck of 51 cards.

This implies,

Probability of drawing another jack on the second draw given that the first card was a jack

= 3/51

Probability of drawing two jacks in a row,

Multiply the probability of drawing

= (a jack on first draw by another jack on second draw given first card was a jack)

⇒ P(two jacks)

= (4/52) × (3/51)

= 1/13 × 1/17

= 1/221

= 0.00452489

= 0.005 (rounded to three decimal places).

Therefore, the probability of drawing two jacks in a row is equal to option(B) 0.005.

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Answer:  just want points tbh

Step-by-step explanation:

For some reason it didnt let me upload as text so here you go.

Answer:

D. n= 0 or n= 4/5

Step-by-step explanation:

Factor and set each factor equal to zero.

n

=

0

,

4

5

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

n

=

0

,

4

5

Decimal Form:

n

=

0

,

0.8

The area of the Triangular pen is  roughly 118.99 square  bases.        

   The area of the triangular pen, we can use Heron's formula, which allows us to calculate the area grounded on the lengths of the sides of the triangle.  Heron's formula states that the area( A) of a triangle with side lengths a, b, and c is given by  A =  √( s( s- a)( s- b)( s- c))  where s is

the semiperimeter of the triangle, calculated as  s = ( a b c)/ 2  For the given side lengths of the triangular pen( 15 ft, 11 ft, and 9 ft), we can plug these values into Heron's formula to find the area.  s = ( 15 ft 11 ft 9 ft)/ 2 = 17.5 ft  Now, let's substitute the values into the formula  A =  √(17.5 ft *(17.5 ft- 15 ft) *(17.5 ft- 11 ft) *(17.5 ft- 9 ft))  

Simplifying the expression  A =  √(17.5 ft *2.5 ft *6.5 ft *8.5 ft)  A =  √(14137.5 ft ²)  A ≈118.99 ft ²  

thus, the area of the triangular pen is  roughly 118.99 square  bases.

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Answer:

2. Necklace

Discount : 95.19 x 0.75 = 71.25

Selling prices: 95.19 - 71.25 = 23.94

4. Book

Markup: 39 x 0.075 = 2.93

Selling price 39 + 39(0.075) = 41.93

6. Car

Markup: 15558 x 0.28 = 4356.24

Selling price: 1558 + 1558(0.28) = 19.914.24

8. 37.99 x 0.076 = 2.89

10. 219 + 219(0.30) = 284.7

12. 479 + 479(0.08) = 517.32

Step-by-step explanation:

2. Necklace

Discount : 95.19 x 0.75 = 71.25

Selling prices: 95.19 - 71.25 = 23.94

4. Book

Markup: 39 x 0.075 = 2.93

Selling price 39 + 39(0.075) = 41.93

6. Car

Markup: 15558 x 0.28 = 4356.24

Selling price: 1558 + 1558(0.28) = 19.914.24

8. 37.99 x 0.076 = 2.89

10. 219 + 219(0.30) = 284.7

12. 479 + 479(0.08) = 517.32