Compare your response to the sample response. Which of these did your response include? Check all of the boxes that apply.

The real number is on the number line, but the complex number is in the complex plane.

Both are distances.

Both are positive values.

The distance formula or the Pythagorean theorem is used to calculate the absolute value of a complex number.

The value of diameter and radius of circle is 7 cm and 3.5cm.

According to the statement

we have given that the a figure of circle and we have to find the radius and the diameter of the circle.

So, We know that the

The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.

Here from the figure it is clear that the

Diameter of circle = 7cm

and the radius of circle we have to find

So,

Radius of circle = Diameter /2

Substitute the values in it then

Radius of circle = 7cm /2

Radius of circle = 3.5 cm.

So, The value of diameter and radius of circle is 7 cm and 3.5cm.

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Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:

[tex]v = \frac{12}{t}[/tex]

Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:

[tex]v + 6 = \frac{12}{3 - t}[/tex]

[tex]v = \frac{12}{3 - t} - 6[/tex]

Then:

[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]

[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]

[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]

18t - 6t² = 24t - 36

6t² + 6t - 36 = 0

t² + t - 6 = 0

(t + 3)(t - 2) = 0. -> t = 2 hours.

Hence her jogging rate in mph is given as follows:

[tex]v = \frac{12}{2} = 6[/tex]

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The graph showing the temperature over the 5-day period will look exactly like the attached. On the y-axis, we have the Temperature and the x-axis the number of days.

Graphs and charts are useful visual aids because they make information accessible and easy to understand.

Therefore, it is not unexpected that print and electronic media frequently employ graphs.

When data is displayed as a graph rather than a table, it can often be easier to understand since the graph might show a pattern or comparison.

The graph shows the forecasted data against the actual data. It is to be noted that the data for the actual 5-day temperatures are made-up to help the analyst understand the differences between the forecasted and the actual data.

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The answer is p = -8/15


Proportion can simply be defined as equating two ratios

The proportion of 3/2 = 4/p +9 can be calculated as follows

3/2 - 9/1 = 4/p

-15/2 = 4/p


cross multiply both sides together to find the value of p

-15×p= 4×2

-15p= 8

p= -8/15

Hence the answer is p= -8/15

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Answer:

x=10 and x=-4

Step-by-step explanation:

When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.

| x - 3 | = 7

x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.

Here is the second equation:

x - 3 = -7

It is the left side copied, without the bars, but the right side has the opposite sign.

Solve these both separately to find the answers.

x-3=7 and x-3=-7

x=10 and x=-4

Answer:

b = 2a

Step-by-step explanation:

a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )

2a = b

Answer: b = 2a

Step-by-step explanation:

Original equation

a = (1/2) b

Multiply 2 on both sides

a * 2 = (1/2) b * 2

[tex]\Large\boxed{b=2a}[/tex]

Hope this helps!! :)

Please let me know if you have any quesitons

Step-by-step explanation:

there are

1 red marble

3 blue marbles

4 green marbles

in the box.

that means there are 8 marbles in the box. which gives us 8 different outcomes for pulling randomly 1 marbles.

the probability for each of these 8 outcomes is equal : 1/8.

remember, the probability is always the number of desired cases over the number of total possible cases.

so, the probability of pulling a red marble is :

1 desired case

8 total cases

->

1/8 or 0.125

the probability of pulling a blue marble is :

3 desired cases

8 total cases

->

3/8 or 0.375

the probability of pulling a green marble is :

4 desired cases

8 total cases

->

4/8 = 1/2 or 0.5

now the experiment is pulling 2 marbles in a row, but the first pulled marble is put back into the box again.

this makes this a combined event, where the first AND the second event must fulfill the desired over total cases.

if the 2 events are independent (not overlapping or influencing each other), then we can simply multiply the probabilities. which is the case here, because the first marble is put back.

why ?

because now we have 8 possible outcomes for the first ball, and again 8 possible outcomes for the second ball, and when we combine all possibilities from the first with all possibilities from the second pull, we get 8×8 = 64 possible outcomes :

red. red

red. blue1

red. blue2

red. blue3

red. green1

...

green4 green4

so, the probability to pull a blue ball first is

3/8

and the probability to pull a blue ball second is

3/8 too

the combined probability of the combined event is

3/8 × 3/8 = 9/64

we have 3×3 = 9 desired outcomes of combining 3 blue and 3 blue balls out of the total of 64 possible outcomes.

Answer:

8√2 cm²

Refer to the attached page,I've shown the complete calculation over there

Answer:

Area under the graph = 6 sq.units

I've shown the complete calculation over the attached page

Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct

The quotient is given as:

4.2/5

Kerris reasoning is that

4.2/5 is approximately 0.8

We start by calculating the actual value of the quotient 4.2/5

Using a calculator, we have:

4.2/5 = 0.84

Approximate to the nearest tenth

4.2/5 = 0.8

This means that Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct

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f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure. This can be obtained using the formula of f(x) = P(X)/Q(X) by vertical asymptotes and factors of the polynomial.

Let  where P(X) and Q(X) are polynomial function.

The function has the following:

This means that, -3 and 2 are roots of the denominator. Thus, the equation of the denominator is:

⇒ Q(X) = (x + 2)(x - 3)

Let a be the leading coefficient of P(X)

⇒ P(X) = a(x - 1)

Now for finding the value of a we can rewrite the equation as,

⇒ f(x) = P(X)/Q(X)

⇒ f(x) = a(x - 1)/[(x + 2)(x - 3)]

⇒ f(0) = a(0 - 1)/[(0 + 2)(0 - 3)]

Since from the graph we can say that the y-intercept is (0, - 2), this means that when x = 0, y = -2, f(0) = - 2

⇒ - 2 = -a/[(2)(- 3)]

⇒ a = - 2 × 2 × 3

⇒ a = - 12

By putting a = -12 in f(x) we get,

⇒ f(x) = 12(x - 1)/[(x + 2)(x - 3)]

Hence f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure.

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Answer:

15 quarters and 10 nickels

Step-by-step explanation:

[tex]q+n=25[/tex]

[tex]0.25q+0.05n=4.25[/tex]

multiply the first equation by -0.25 and add the second equation to it

[tex]-0.25q-0.25n=-6.25\\0.25q+0.05n=4.25[/tex]
________________
                [tex]-0.2n=-2[/tex]

[tex]n=\frac{-2}{-0.2} =10[/tex]   has 10 nickels

[tex]q=25-n=25-10=15[/tex]  has 15 quarters

10(.05) +15(0.25) = 0.5 + 3.75 = 4.25

Hope this helps

Total of 24.03% of boys choose Niagara falls.

A frequency table is a list of objects with the frequency of each item shown in the table.

The quantity of times that an event or value occurs is its frequency.

A frequency table, then, is a table that contains some facts and their frequency.

Given,

Total number of boys

56 + 74 + 103 = 233

Number of boys who chose Niagara falls = 56

Percentage of 56 out of 233

(56/233) × 100⇒ 24.03%

Hence the percent of the boys chose Niagara Falls will be 24.03%.

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The value of 'x' from the expression is 9/ 11

Given the expression;

3 x +14 (3x-4) +3 x ( 6) +3 (х+2 )=4

First, we expand the bracket

3x + 42x - 56 + 18x + 3x + 6 = 4

collect like terms

3x + 42x + 18x + 3x - 56 + 6 = 4

Add up like terms

66x - 50 = 4

66x = 4 + 50

66x = 54

Make 'x' the subject of formula

x = 54/ 66

x = 9/ 11

Thus, the value of 'x' from the expression is 9/ 11

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Step-by-step explanation:

sin(90-A) = sin90cosA-sinAcos90

= cosA*1-0*sinA

= cos90

hence proved

Step-by-step explanation:

sin(90-A)=cosA

sin(90-A)=sin(90-A)

90-A=90-A

-A+A=90-90

=0

The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2

The number of wholesalers Sue has sourced = 4

Terms of two suppliers = 30 days credit

Amount of stock Sue has = $15000

Amount of stock on credit = $10000

Operating cash reserve of the business = $20000

Required:

The number of wholesalers that require terms of cash on delivery

Solution:

Given that the number of wholesalers = 4

The number number of suppliers (wholesalers) that supply on 30-day credit = 2

Therefore;

The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2

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The maximum volume of the cylinder in exact form is; V_max = 2560π/27

Let us define the variables as:

Radius of cone = r

Radius of cylinder = x

Height of Cone = h

Height of Cylinder = y

The general equation for volume of the cylinder is;

V = πx²y  

Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:

Height of triangle above cylinder/Base of Triangle above cylinder   =   Height of full triangle/Base of full triangle

This gives;

(h - y)/2x  = h/2r

Making y the subject gives us;

h – y = hx/r

y =  h – hx/r

y = h(1 – x/r)

Plug in y into our Volume equation:

V(x) = πx²h(1 – x/r)

V(x) = πh(x²  - x³/r)

To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:

V'(x) = πh(2x  - 3x²/r)

V'(x) = 0

Thus;

(2x  - 3x²/r) = 0

x( 2r – 3x) = 0

Thus;

x = 0 or x = 2r/3

Put x = 2r/3 in our volume equation to find V_max

V_max  = πh((2r/3)² – (2r/3)³/r)

V_max = πh(4r²/9 - 8r²/27)

V_max = πh(12r²/27 - 8r²/27)

V_max = 4πhr²/27

Thus, at r = 8 and h = 10, we have;

V_max = 4π(10)8²/27

V_max = 2560π/27

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Answer:

5

Step-by-step explanation:

The midpoint of segment AB is (1, 1).

Substituting these coordinates into the equation of the line,

[tex]2(1)+3(1)-k=0 \\ \\ 5-k=0 \\ \\ k=5[/tex]

Answer:

2.52 m

Step-by-step explanation:

let the height be h m.

let the shorter ladder be x m away from the base of wall.

(x+1.96)²+h²=5.6²

x²+h²=4.2²

subtract

(x+1.96)²-x²=5.6²-4.2²

(x+1.96+x)(x+1.96-x)=31.36-17.64

(2x+1.96)(1.96)=13.72

2x+1.96=13.72/1.96=7

2x=7-1.96=5.04

x=5.04/2=2.52

Answer:

Step-by-step explanation:

The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.

Let w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...

  P = 2(L +W)

  1040 = 2((3w-120) +w)

Dividing by 2 and simplifying, we have ...

  520 = 4w -120

  130 = w -30 . . . . . . divide by 4

  160 = w . . . . . . . . . add 30

  3w-120 = 3(160) -120 = 360 . . . the field's length

The dimensions of the field are 160 feet long by 360 feet wide.

Answer: 120

Step-by-step explanation:

There are 5 digits that are odd, 1 3 5 7 9

There are 5 possibilities for the first digit, 4 for the second, 3 for the third, and 2 for the last, so there are 5 x 4 x 3 x 2 = 120

The proof that the line AE bisects the segment can be seen below.

Let us have

Γ1  and 2 are the two intersecting circles. to be the circumcircle of the shape ADE. Then we can see that  Γ1 is tangent to the line DB.

A common tangent would have to touch T1 at A and also touch T2 at B

Such that what we would have would be

<ADB = 180◦ − 2<ABD = <ABC = <AEC

This would then tell us that the line is tangent to the segment.

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Step-by-step explanation:

if , X>4

---> y= x-4

if , X<4

---> y= -(x-4)

y= 4- X

because , the value of |x-4| is Always positive ....

The speed ratio of the two trains is 4:3, that is, for every 4 hours that one train is delayed, the other is delayed 3.

To find the speed ratio of the trains we must do the following operation:

Note: This question is incomplete because there is some information missing. Here is the complete information in:

A train started from Howrah for Allahabad another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9hours and 16 hours respectively after they meet each other. Find the ratio of speed of the two trains.​

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Based on the given diagram (see attachment), the statement which is missing in the proof is: D. m∠7 ≅ m∠5.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

From the given diagram (see attachment), we can logically deduce that line m is parallel to line n (m || n) and a transversal line intersects both of them.

Based on these reasons, we can prove the following statements:

In conclusion, we can logically deduce that the statement which is missing in the proof is m∠7 ≅ m∠5.

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Answer:

here you go

Step-by-step explanation:

Due to the higher z-score, the correct option regarding the highest relative score is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean, hence the higher the z-score, the higher the score X is relative to other scores.

The respective z-scores for this problem are given by:

Hence the correct option is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

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Answer:

0.524

Step-by-step explanation:

That is the answer not really sure tho

The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.

According to the statement

We have given that the A rancher’s herd of 250 sheep grazes over a 40-acre pasture.

And we have to find the how many sheep are grazing on each acre.

So, For this purpose If we assume that the sheep are equally distributed, to see how many sheep there are in each acre we just divide the number of sheep by the number of acres. So,

we have to find the average of number of sheep in per acre.

We know that

The total area of the rancher’s herd = 40 acre

The number of sheep grazes in the land = 250 sheep

Now, we have to find the Average number

Average number of sheep grazed in per acre = 250/40

Average number of sheep grazed in per acre = 6 approx.

So, The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.

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Answer:

2.8 metres each

Step-by-step explanation:

14/5

2.8