Which graph represents y= ^3 square root x + 2?

The equation of a parabola can be drawn given a focus of (5, 3 ) and a directrix of x = − 1.

The equation of the parabola is:

x² - 10x - 8y + 17= 0

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

The equation of a parabola:

y = a(x-h)^2 + k

We have,

The standard form:

(x - h)² = 4p (y - k)

where the focus is (h, k + p) and the directrix is y = k - p.

Now,

(h, k + p) = (5, 3)

h = 5

k - p = -1

k + p = 3

Now,

k - p = -1

k = -1 + p

substituting

k + p = 3

-1 + p + p = 3

-1 + 2p = 3

2p = 3 + 1

2p = 4

p = 2

k = -1 + 2

k = 1

Now,

The equation of the parabola.

(x - h)² = 4p (y - k)

(x - 5)² = 4 x 2 (y - 1)

(x - 5)² = 8 (y - 1)

x² - 10x + 25 = 8y - 8

x² - 10x - 8y + 25 - 8 = 0

x² - 10x - 8y + 17= 0

Thus,

The equation of the parabola is

x² - 10x - 8y + 17= 0

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1) The number of points that they scored is;

Michaela scored; 28 points

Aleah scored; 14 points.

2) The speed of the current is; 2.79 km/ hr

1) Let s represent the team score and as such we have;

Michaela scored s/5 (one fifth of the team's points)

Aleah scored s/10 (one tenth of the team's points)

These total scores is 42. Thus;

s/5 + s/10 = 42

Multiply through by 10 to get;

2s + s = 420

3s = 420

s = 420/3

s = 140

The team scored 140 points.

Thus;

Michaela scored;

140/5 = 28 points

Aleah scored;

140/10 = 14 points.

2) Let the speed of current be x km/ hr

Thus;

Upstream speed  = ( 6.5 - x) km/ hr

Downstream speed = ( 6.5 + x) km/ hr

Distance = Speed * Time

Thus;

5(6.5 - x) = 2(6.5 + x)

32.5 - 5x = 13 + 2x

7x = 19.5

x = 2.79 km/ hr

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The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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The average velocity for the time period from t = 1 to t = 4 is 6 feet/s.

The distance driven in a car is shown by

s(t) = t^2 + t

The distance driven in a car at t = 1

s(1) = (1)^2 + 1

s(1) = 1 + 1

s(1) = 2

The distance driven in a car at t = 4

s(4) = (4)^2 + 4

s(4) = 16 + 4

s(4) = 20

Let at t = 1, it is t(1) and at t = 4 it is t(2)

Displacement of car between t(1) and t(4) = s(2) - s(1)

Displacement of car between t(1) and t(4) = 20 - 2

Displacement of car between t(1) and t(4) = 18 feet

Time travel between t(1) and t(4) = 4 - 1

Time travel between t(1) and t(4) = 3

Now,

Average velocity = Displacement of car between t(1) and t(4)/Time travel between t(1) and t(4)

Average velocity = 18/3

Average velocity = 6 feet/s

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The detailed steps how the algorithm implemented in the identified procedure works is:

i. Outlines the two instances of the method that were mentioned in written response 3c. Each call must take a separate argument(s) that direct the algorithm to run a different section of code.

ii. Specifies the condition(s) each call to the process is testing.

iii. Shows the outcome of each call.

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Answer:

5

Step-by-step explanation:

The first says 4 and 4

They added 4 to the previous cumulative, which was nothing and thru got the cumulative of 4+0=4

The second says 10 and 14

Same thing. Adding 10 to the previous cumulative, which was 4, you get 4+10=14

Let's follow the rules for this next one

We have ? and 19

Adding ? to the previous cumulative, which was 14, you get 14+?=19

Making ? = 5 because that what 19-14 is

Mary is 5 feet tall and her shadow is 12 feet long flagpole. She is standing next to cast a shadow 42 feet. The height of the flag pole is 17.5 feet.

Mary is 5 feet tall and her shadow is 12 feet long flagpole.

She is standing next to cast a shadow 42 feet.

ΔABC ≅ ΔADE

Using the Similarity Theorem

BC/ED = AC/AD

From the diagram the value of BC = x, ED = 5 feet, AC = 42 feet and AD = 12 feet

Now putting the value

x/5 = 42/12

Multiply by 5 on both side, we get

x = 210/12

x = 17.5

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The complete question is:

Mary is 5 feet tall and her shadow is 12 feet long flagpole. She is standing next to cast a shadow 42 feet. The height of the flag pole is.

Answer: A

Step-by-step explanation:

Option A is the correct answer. The probability of the nearest hundredth of the pointer landing on a non-shaded area is 0.66.

An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle. It contains a total of 360° degrees all the way around the center.

To know the Probability of the non-shaded area first we have to add the shaded area.

The sum of the shaded angles 48°+45°+122°+52° =145°.

As we know that the total angle of a  circle=360°.

Now divide the sum of the shaded angles by the total angle of the circle.

i.e=145°/360°

non-shaded area=0.66

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On integrating the function ∫4/(2x-1) dx, the value is obtained as 2 ln (2x + 1) + C.

What is Integration?

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

The integral is given as - ∫4/(2x-1) dx

Substitute u = (2x - 1) → du/dx = 2 → dx = 1/2 du -

⇒ 2 ∫ 1/u du

The standard integral is -

⇒ ln (u)

Plug in solved integrals -

⇒ 2 ∫ 1/u du

⇒ 2 ln (u)

Undo the substitution u = (2x - 1) -

⇒ 2 ln (2x + 1)

Apply the absolute value function to arguments of logarithm functions in order to extend the antiderivative's domain -

⇒ 2 ln (2x + 1) + C

Therefore, the value is obtained as 2 ln (2x + 1) + C.

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Answer:

Step-by-step explanation:

L=3W

P=2L+2W

40= 2 (3W)+2W

40=6W+2W

8W=40

W=40/8

W=5 in

L=15 in (3W= 3*5=15)

Someone can't pay exactly 87 to have their windows washed.

A company charges a 5 flat fee plus 3 per window to wash windows. Therefore, let's find if someone can pay exactly 87 units to have there window washed.

Hence, using equation,

y = 5 + 3x

where

Using the equation, let's find if someone can use exactly 87 units for the service.

87 = 5 + 3x

87 - 5 = 3x

82 = 3x

divide both sides by 3

x = 82 / 3

x = 27.33

Therefore, someone can't use exactly 87 units because the number of windows washed is in decimal.

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a) The number of widgets that Widgets"R'U must sell to reach the break-even point is 2,082 units.

b) Using the expense and revenue equations, if Widgets'R'Us sells 5,430 widgets, their profit will be $8,745.

The profit equation is total revenue minus total costs.

The profit equation shows that profit is a function of the difference between the total revenue realized from sales and services less the total costs involved in rendering the services or delivering the goods.

At the break-even point, the total revenue equals the total costs.  Therefore, there is no profit or loss.

The total cost function, E = 1.48q + 4,830

The total revenue function, R = 3.98q

To break even, the quantity to be sold, q, 1.48q + 4,830 = 3.98q

-2.32q = -4,830

q = 2,082

When q = 5,430:

Profit = 3.98q - (1.48q + 4,830)

= 3.98(5,430) - (1.48 x 5,430 + 4,830)

= 21,611.4 - (12,866.4

= 8,745

= $8,745

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If the two sides of isosceles triangle are (x+2) cm and third side is (x+6) cm. if perimeter is 385 cm, then the value of x is 125 .

We know that the Perimeter of the triangle is equal to the sum of the lengths of all its sides.

the two sides of isosceles triangle are = (x+2) cm ;

the length of third side of triangle is = (x+6) cm ;

So , we have:

⇒ x + 2 + x + 2 + x + 6  = 385

Simplifying and solving for x:

⇒ 3x + 10 = 385 ;

⇒ 3x = 385 - 10 ;

⇒ 3x = 375 ;

⇒ x = 375/3 = 125

Therefore , the value of x for the isosceles triangle is 125 .

The given question is incomplete , the complete question is

The two equal sides of an isosceles triangle are given as (x+2) cm and the third side is (x+6) cm. if the perimeter of the triangle is 385cm, find the value of x.

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(a). Revenues = $6,600.

(b). Expenses = $10400

(c). Net income = $3800

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

For the year ending April 30,

Urology Medical Services Co. mistakenly omitted to adjust entries for (1) $1,400 of supplies that were used,

(2) unearned revenue of $6,600 that was earned,

and (3) insurance of $9,000 that expired.

(a). Revenues = $6,600.

(b). Expenses = ($1,400 + $9,000).

= $10400

(c). Net income =

($10,400 – $6,600).

= $3800

Therefore, all the required values are given above.

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Answer:

Step-by-step explanation:

The correct interpretation of the 95% confidence level is (D) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the mean size of farms in the United States.

In other words, if we repeatedly take random samples of size 30 from the population of farm sizes in the United States and construct 95% confidence intervals for the mean size in each sample, approximately 95% of those intervals will contain the true mean size of farms in the United States. The interval (367, 558) is just one of those intervals, and it is not a statement about the farm sizes in the sample or the farm sizes in the entire population.

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The probability of earning a total of exactly 10 points in 2 turns is 1/8.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:

(4, 6) or (6, 4)

The probability of getting a 4 in first try and 6 in second try is:

(4, 6) = 1/4 * 1/4 = 1/16

The probability of getting a 6 in first try and 4 in second try is:

(6, 4) = 1.4 * 1/4 = 1/16

The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:

(4, 6) or (6, 4) = 1/16 + 1/ 16 = 2/16 = 1/8

Hence, the probability of earning a total of exactly 10 points in 2 turns is 1/8.

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Answer:

1109

Step-by-step explanation:

4563 = 4b + 127  Subtract 127 from both sides

4436 = 4b  Divide both sides by 4

1109 = b

If the radius of a circle is multiplied by 1/4, then its area is multiplied by 1/16.

The formula for the area of a circle is given by:

A = πr²

Where:

r = the radius of the circle.

Notice that the area is directly proportional to the square of the radius, or:

A ∝ r²

Let:

r₁ = initial radius of the circle

r₂ = final radius of the circle

A₁ = initial ara of the circle

A₂ = final area of the circle

It is mentioned that: r₂ = 1/4 r₁

A ∝ r²

A₂/A₁  = (r₂/r₁  )²

A₂/A₁  = (1/4 )²

A₂/A₁  = 1/16

Hence, the area is multiplied by 1/16.

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Answer:

39 ckfiffiofods9odoxdo

The system does not have any solution 0=2, The one solution exactly has one solution is, [tex]x=2[/tex] and the infinity many solutions is, [tex]y=2-x\end{aligned}$$[/tex].

The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1, then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

A system consisting of exactly one equation can have no solution. for example.

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

on we solve this, we get,

[tex]$$\begin{aligned}& 2 x=\frac{1}{2}(4 x+2)+1 \\\Rightarrow & 2 x=2 x+1+1 \\\Rightarrow & 2 x-2 x=2 \\\Rightarrow & 0=2\end{aligned}$$[/tex]

which is not true.

hence the system does not have any solution.

One Solution: -

Consider the system.

[tex]$$3x+3=9$$[/tex]

On sowing we get,

[tex]$$\begin{aligned}& 3 x+3-3=9-3 \\& \Rightarrow 3 x=6 \\& \Rightarrow \frac{3 x}{3}=\frac{6}{3} \\& \Rightarrow x=2\end{aligned}$$[/tex]

which has exactly one solution.

infinity many solutions: -

Consider the system of two variables.

[tex]$$2x+2 y=4$$[/tex]

On solving we get,

[tex]$$\begin{aligned}& 2 x+2 y=4 \\\Rightarrow & 2 x+2 y-2 x=4-2 x \\\Rightarrow & 2 y=4-2 x \\\Rightarrow & \frac{2 y}{2}=\frac{4-2 x}{2} \\\Rightarrow & y=2-x\end{aligned}$$[/tex]

Now, we can choose any value of [tex]$x$[/tex] and we will get the corresponding value of [tex]$y$[/tex]. So, there exists infinitely many solutions to the system.

Therefore, the system does not have any solution is 0=2, The one solution exactly has one solution is [tex]x=2[/tex] and the infinity many solutions is [tex]y=2-x\end{aligned}$$[/tex].

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The value of common difference, d is equals to the one. The value of common ratio, r is equals to the 4/3.

We have, an arithmetic sequence and second is geometric sequences. The common difference between the two consecutive terms of AP sequence is "d" and d ≠ 0 and the common ratio between two consecutive terms of geometric sequence is "r". Let the AP sequence is represented by aₙ and G.P sequence is represented by Tₙ. First term of both sequences = 9 , i.e., a₁ = a = T₁ = 9

The nth term of A.P is written as

aₙ = a + (n - 1)d so, a₄ = a + 3d and a₈ = a + 7d

The nth term of G.P is , Tₙ = ar⁽ⁿ⁻¹⁾

so, T₂ = ar , T₃ = ar²

Now, a₄ = T₂ => ar = a + 3d

=> 9r = 9 + 3d --(1)

a₈ = T₃ => ar² = a + 7d

=> 9r² = 9 + 7d --(2)

from(1) and (2) , 3(r - 1) = d , 9r² = 9 + 7(r -1)3

=> 9r² = 9 + 21r - 21

=> 9r² = 21r - 12

=> 9r² - 21r + 12 = 0

=> r = 1, 4/3

then, plugging the value of r in equation (1),

d = 3( r - 1)

=> d = 3( 0) when r = 1

=> d = 0, but it is not possible as d≠0

and d = 3( 4/3 - 1) = 1 when r = 4/3

So, required values of d and r are 1 and 4/3.

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The radius of the pencil is 3.32mm

The formula for determining the volume of a cylinder is expressed as;

V = πr²h

Given that the parameters are;

From the information given, we have that;

The volume of the cylinder = 110 π mm³

The height of the cylinder = 10mm

Now, substitute the values, we get

110π = πr² × 10

Multiply the values

110π = 10πr²

Divide both sides by the coefficient of r², we get;

r² = 110π/10

r² = 11

Find the square root of both sides

r = 3. 32mm

Hence, the value is 3.32mm

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In 71.12 centimeters, there are 28 inches.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

We have a measurement in centimeters,

= 71.12

And we know 1 inch = 2.54 centimeters

So,

In inches, the mesurement = 71.12/2.54

= 28 inches.

Therefore, the required result is 28 inches.

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Variance and standard deviation are measures of variability that are appropriate and possible to calculate for variables measured on an interval or ratio scale of measurement.

Interval scales have a true zero point, meaning that a difference of zero on the scale represents a lack of the characteristic being measured (e.g. temperature measured in degrees Celsius). Ratio scales are similar to interval scales, but also have a meaningful zero point, meaning that a value of zero on the scale represents a complete absence of the characteristic being measured (e.g. height measured in meters).

Variance and standard deviation can be calculated for interval and ratio variables because these scales provide meaningful differences and ratios between values. The calculation of variance involves finding the average squared difference between each value and the mean of the values, while standard deviation is the square root of the variance. Both variance and standard deviation provide information about how spread out the values of a variable are and are useful in statistical analysis.

On the other hand, nominal and ordinal scales only provide categories or rank order for values, without any meaningful differences or ratios between values. As such, it is not appropriate or possible to calculate variance or standard deviation for variables measured on nominal or ordinal scales.

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Answer: The quotient of 60 divided by k is 60/k.

Step-by-step explanation:

The quotient of 60 divided by k refers to the result of dividing the number 60 by another number k. The division operation can be represented mathematically as 60/k.

In other words, the quotient of 60 and k is a mathematical expression that returns the number that results from dividing 60 by k. The result of this division is a single value which can be a fraction or a whole number, depending on the value of k.

D) 15 tablespoons of parsley she needs.

Let's call the number of tablespoons of parsley she needs "x". We know the recipe uses 5 parts thyme to 3 parts parsley, so the total number of parts is 5 + 3 = 8.

Since she's making 40 tablespoons of the mix, each part is equal to 40 / 8 = 5 tablespoons.

So x, the number of tablespoons of parsley, is equal to 3 parts * 5 tablespoons/part = 15 tablespoons.

The answer is D) 15 tablespoons of parsley she needs.

Therefore, we can say she needs 15 tablespoons of parsley.

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The present value of your winnings is $20.07 million.

Present value is the value right now of some amount of money in the future.

For example, if you are promised $110 in one year, the present value is the current value of that $110 today.

Given:

The present value of an annuity is determined by:

PV = P [ 1- [tex](1+ r)^{-n[/tex] / r]

With annual payments (P) of $1.75 million, for a period (n) of 20 years at a discount rate (r) of 6 percent, the present value is:

PV = 1.75  [ 1- [tex](1+ 0.06)^{-20[/tex] / 0.06]

PV = 1.75 [ 1- 0.31180472688 / 0.06]

PV = 1.75 x 11.4699

PV = $20.07 million

Hence, the present value is $20.07 million.

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Answer: t= -6

Step-by-step explanation:

-3(t+6)=0

-3t+-18=0

-3t=18

-t=6

t= -6