Carmen drew line A and line B in the two scatter plots shown. one scatter plot contains 12 points indicating a negative correlation and line A, which passes through the middle of points, with 6 above and 6 below, touching none of them; the other scatter plot contains 12 points indicating a positive correlation and line B, which passes through four of the points and sits above the other 8 points. Which statement is true? Both line A and line B are well-placed lines of best fit. Only line A is a well-placed line of best fit. Only line B is a well-placed line of best fit. Neither line A nor line B are well-placed lines of best fit.

Step-by-step explanation:

f.g(x) = f(x+2)

         =(x+2)2 -1

         =(x2+2*x*2+4)-1

         =x2+4x+4-1

         =x2+4x+3

Answer:

D

Step-by-step explanation:

Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.

The amount that Lydia has earned on her investment is $198 on the stock paying the 11% dividend and $252 on the stock paying 14% interest for a total earned of $450 on her $3600 investment.

Let x represent half of her total investment.

The total annual interest earned is $450.

This is represented by the following equation:

0.11x + 0.14x= 450

Collect the like terms together

0.25x = 450

x= 1800

Therefore, half of her total investment is $1800 so her total investment is $3600.

Check the solution:

0.11∗1800 + 0.14 ∗ 1800 = 450

198 + 252 = 450

Therefore, she earned $198 on the stock paying the 11% dividend, and $252 on the stock paying 14% interest for a total earned of $450 on her $3600 investment.

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Step-by-step explanation:

the distance between 2 points is per Pythagoras

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle, which is the direct distance between the points). a and b are the legs (the x and y coordinate differences).

so,

AB² = (3-6)² + (1-2)² = 9+1 = 10

AB = sqrt(10) = 3.16227766...

BC² = (6-6)² + (2 - -2)² = 0² + 4² = 16

BC = sqrt(16) = 4

CD² = (6-3)² + (-2 - -3)² = 3² + 1² = 10

CD = sqrt(10) = 3.16227766...

DA² = (3-3)² + (-3 - 1)² = 0² + 4² = 16

DA = sqrt(16) = 4

so, the perimeter is

2×4 + 2×sqrt(10) = 8 + 6.32455532... = 14.32455532... ≈

≈ 14.3

(a.i) If [tex]a_1,a_2,a_3,\ldots[/tex] are in arithmetic progression, then there is a constant [tex]d[/tex] such that

[tex]a_{n+1} - a_n = d[/tex]

for all [tex]n\ge1[/tex]. In other words, the difference [tex]d[/tex] between any two consecutive terms in the sequence is always the same.

[tex]a_2-a_1 = a_3-a_2 = a_4-a_3 = \cdots = d[/tex]

Now, we can expand the target expression into partial fractions.

[tex]\dfrac1{a_na_{n+1}} = \dfrac{\alpha}{a_n} + \dfrac{\beta}{a_{n+1}}[/tex]

Combining the fractions on the right and using the recursive equation above, we have

[tex]\dfrac1{a_na_{n+1}} = \dfrac{\alpha (a_n + d) + \beta a_n}{a_n(a_n+d)} = \dfrac{(\alpha+\beta) a_n + \alpha d}{a_n a_{n+d}} \\\\ \implies \begin{cases}\alpha + \beta = 0 \\ \alpha d = 1 \end{cases} \implies \alpha = \dfrac1d, \beta = -\dfrac1d[/tex]

and hence

[tex]\dfrac1{a_n a_{n+1}} = \dfrac1{da_n} - \dfrac1{da_{n+1}}[/tex]

as required.

(a.ii) Using the previous result, the [tex]n[/tex]-th term [tex](n\ge1)[/tex] in the sum on the left is

[tex]\dfrac1{a_n a_{n+1}} = \dfrac1d \left(\dfrac1{a_n} - \dfrac1{a_{n+1}}\right)[/tex]

Expand each term in this way to reveal a telescoping sum:

[tex]\dfrac1{a_1a_2} + \dfrac1{a_2a_3} + \dfrac1{a_3a_4} + \cdots + \dfrac1{a_{99}a_{100}} \\\\ ~~~~~~~~ = \dfrac1d \left(\left(\dfrac1{a_1} - \dfrac1{a_2}\right) + \left(\dfrac1{a_2} - \dfrac1{a_3}\right) + \left(\dfrac1{a_3} - \dfrac1{a_4}\right) + \cdots + \left(\dfrac1{a_{99}} - \dfrac1{a_{100}}\right)\right) \\\\ ~~~~~~~~ = \dfrac1d \left(\dfrac1{a_1} - \dfrac1{a_{100}}\right) = \dfrac{a_{100} - a_1}{d a_1 a_{100}}[/tex]

By substitution, we can show

[tex]a_n = a_{n-1} + d = a_{n-2} + 2d = \cdots = a_1 + (n-1)d \\\\ \implies a_{100} = a_1 + 99d[/tex]

so that the last expression reduces to

[tex]\dfrac{(a_1 + 99d) - a_1}{d a_1 a_{100}} = \dfrac{99d}{d a_1 a_{100}} = \dfrac{99}{a_1 a_{100}}[/tex]

as required. More generally, it's easy to see that

[tex]\dfrac1{a_1a_2} + \dfrac1{a_2a_3} + \dfrac1{a_3a_4} + \cdots + \dfrac1{a_na_{n+1}} = \dfrac{n}{a_1a_{n+1}}[/tex]

(b) I assume you mean the equation

[tex]\dfrac1{3\times7} + \dfrac1{7\times11} + \dfrac1{11\times15} + \cdots + \dfrac1{k(k+4)} = \dfrac2{25}[/tex]

Note that the distinct factors of each denominator on the left form an arithmetic sequence.

[tex]a_1 = 3[/tex]

[tex]a_2 = 3 + 4 = 7[/tex]

[tex]a_3 = 7 + 4 = 11[/tex]

and so on, with [tex]n[/tex]-th term

[tex]a_n = 3 + (n-1)\times4 = 4n - 1[/tex]

Let [tex]a_n=k[/tex]. Using the previous general result, the left side reduces to

[tex]\dfrac1{3\times7} + \dfrac1{7\times11} + \dfrac1{11\times15} + \cdots + \dfrac1{a_na_{n+1}} = \dfrac n{3a_{n+1}} \\\\ \implies \dfrac{\frac{k+1}4}{3(k+4)} = \dfrac2{25}[/tex]

Solve for [tex]k[/tex].

[tex]\dfrac{k+1}{12k+48} = \dfrac2{25} \implies 25(k+1) = 2(12k+48) \\\\ \implies 25k + 25 = 24k + 96 \implies \boxed{k=71}[/tex]

Answer:

no

Step-by-step explanation:

Prime factorization of 66

[tex]66=[/tex][tex]2[/tex] × [tex]3[/tex] × [tex]11[/tex]

the perfect cubes are the numbers that possess exact cubic roots

[tex]\sqrt[3]{66}[/tex] ≈ [tex]4.04[/tex]

66 is not a perfect cube

Hope this helps

Answer:

AB: y=2x+2

CB: y=-2x+6

CD: y=1/2x-1.5

DA: y=-3x+2

Step-by-step explanation:

Answer:

AB: [tex]y=2x+2[/tex]

CB: [tex]y=-2x+6[/tex]

CD: [tex]y=\frac{1}{2}x -1.5[/tex]

DA: [tex]y=-3x+2[/tex]

Step-by-step explanation:

So when it's saying y = __ x + __ it's asking for the slope-intercept form. This is given as y=mx+b where m is the slope and b is the y-intercept. m is the slope because as x increases by 1, the y-value will increase by m, which is by definition what the slope is [tex]\frac{rise}{run}[/tex] how much the function "rises" as x "runs".

AB: See how it "rises" by 2 and only "runs by 1", thus the slope is 2/1 or 2. the last part is the y-intercept, which is the value of y when the line crosses the y-axis. If you look at the graph when it "crosses" the y-axis it's y-value is 2. So you have the equation: [tex]y=2x+2[/tex]

CB: See how it "goes down" by 4 and "runs" by 2, thus the slope is -4/2 or -2. The y-intercept isn't shown on the graph but you can calculate that by substituting known values into the slope-intercept form. So we know so far y=-2x+b since the slope was calculated, and we can take any point on the line to calculate b, for this example I'll take the point C which is (3, 0) which is (x, y) and I'll plug that in

Plug values in:

0 = -2(3) + b

0 = -6 + b

6 = b

This gives you the complete equation: [tex]y=-2x+6[/tex]

CD: see how it only "rises" by 1 but "runs" by 2, thus the slope is 1/2. The y-intercept isn't shown on the graph but you can calculate it by substituting a point into the equation For this example I'll use point C (3, 0)

0 = 3(1/2) + b

0 = 1.5 + b

-1.5 = b

This gives you the complete equation: [tex]y=\frac{1}{2}x - 1.5[/tex]

DA: see how it "decreases" by 3 but "runs" by 1, thus the slope is -3/1 or -3. The y-intercept is known and is at (0, 2) so now we plug these values in to get the equation: [tex]y=-3x+2[/tex]

The distance from ships to the submarine is AX=1084.20

                                                                      BX=1270.69

Let X be the submarine position.

The length between a and b is AB=1425

             and the angle point a is at 59 degrees

                    the angle point b is at 47 degrees

The calculating angle at X:

∠X+∠A+∠B = 180

∠X+59°+47°=180°

∠X=180°-59°-47°

∠X=74°

Then the distance between boat A and the submarine will be found using sine law

Sine law is the ratio of each side of a plane triangle to the sine of the opposite angle is the same for all three sides and angles.

[tex]\frac{a}{sinA}=\frac{b}{sin B} = \frac{c}{sin C}[/tex]

so for Boat A and submarine, we use

[tex]\frac{AB}{sin X}=\frac{AX}{sin B}[/tex]

[tex]\frac{1425}{sin (74)} = \frac{AX}{sin (47)}[/tex]

When AX is the subject

AX=[tex]\frac{1425}{sin(74)}*sin(47)[/tex]

=[tex]\frac{1425}{0.9613}*0.7314[/tex]

AX=1042.245/0.9613

AX=1084.20

The distance between ship B and the submarine

The sine formula we use is

[tex]\frac{AB}{sin X}=\frac{BX}{sin A}[/tex]

[tex]\frac{1425}{sin 74}=\frac{BX}{sin 59}[/tex]

When BX is the subject

BX=[tex]\frac{1425}{sin 74}*sin(59)[/tex]

= 1425/0.9613 * 0.8572

=1221.51/0.9613

=1270.69

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Answer:

Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59°, and the angle of depression from ship B to the submarine is 47°.

How far away is the submarine from the two ships? Round to the nearest hundredth of a foot.

The distance from ship A to the submarine is about

✔ 1,084.18

feet.

The distance from ship B to the submarine is about

✔ 1,270.69

feet.

Step-by-step explanation:

For the given systems the answers are:

1) "Replace one equation with a multiple of the other equation".

2) The systems are not equivalent.

Here we have the systems of equations:

A:

4x + 16y = 12

x +2y = -9

B:

4x + 16y = 12

x + 4y = 3

Notice that the first equation is the same in both systems, but the second is different.

In A we have:

x + 2y = -9

In B we have:

x + 4y = 3

So we need to add 2y on the left side of A, and 12 on the right side of A to get the equation in B.

Or we can just take the other equation in A, divide it by 4, and replace it.

So we need to replace the second equation in A for other equation, then the correct option is:

"Replace one equation with a multiple of the other equation".

Because we are replacing an equation in A by other to get system B, we conclude that systems are not equivalent.

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Answer:

khan

Step-by-step explanation:

Answer: C. 0.0225

Step-by-step explanation:

The distance is 0.03 - 0.02 = 0.01.

1/4 of this is 0.0025.

Adding this to 0.02, we get 0.00225.

The value of F(G(x)) is 2x^2 - 13

The functions are given as:

F(x)=2x+1

G(x)=x^2-7

To find (FxG)(x), we make use of

(FxG)(x) = F(G(x))

So, we have:

F(G(x))=2G(x)+1

Substitute G(x)=x^2-7

F(G(x))=2(x^2-7)+1

Expand

F(G(x))=2x^2 - 14 + 1

Evaluate the like terms

F(G(x))=2x^2 - 13

Hence, the value of F(G(x)) is 2x^2 - 13

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Answer:

2¹²

Step-by-step explanation:

one expression equivalent to 16³ is 2¹²

think about it like this: we know that 2 to the power of 4 is 16

(2 x 2 = 4, x 2 = 8, x 2 = 16)

So for every "16" we already have 2⁴; meaning that 16³ is the same thing as 3 groups of 2⁴ -- which is 2¹²

hope this helps! have a lovely day :)

Answer:

[tex]2.20b + 3.60m = 44.20\\2.50b + 3.40m = 44.70[/tex]

Step-by-step explanation:

So in this systems of equations, we know the prices of the items, so the coefficients will represent how many Mary is getting of that item. So you can represent amount of bread as the variable b and the amount of milk as the variable m. On the right will be the total amount spent, since multiplying the price by how much you buy should get you the price

So since at store A, she spends 44.20 and bread costs 2.20 and milk costs 3.60 you get

[tex]2.20b + 3.60m = 44.20[/tex]

Since at store B, she spends 44.70 and bread costs 2.50 and milk costs 3.40 you get the equation:

[tex]2.50b + 3.40m = 44.70[/tex]

Answer:

Option A

2.20b + 3.6m = 44.20

2.5b + 3.4m = 44.70

Explanation:

For store A, bread costs $2.20 and milk costs $3.60 and she pays $44.20

Equation created: 2.20b + 3.6m = 44.20

For store B, bread costs $2.50 and milk costs $3.40 and she pays $44.70

Equation created: 2.5b + 3.4m = 44.70

It will take the roller coaster 171.652 seconds to pass over the hill and reach ground level

The function is given as:

h = –.025t^2 + 4t + 50

Set h = 0.

So, we have:

–.025t^2 + 4t + 50 = 0

Using a graphing calculator, we have:

t = -11.652 and t = 171.652

Time cannot be negative.

So, we have:

t = 171.652

Hence, it will take the roller coaster 171.652 seconds to pass over the hill and reach ground level

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Assuming [tex]z_1=5[/tex] and [tex]z_2=-6i[/tex], as well as [tex]z_3=3i z_1[/tex] and [tex]z_4 = z_2-2[/tex], we have

[tex]z_3 - z_4 = 3iz_1 - (z_2-2) = 3i\times5 - (-6i-2) = 15i + 6i + 2 = 2 + 21i[/tex]

Since both the real and imaginary parts are positive, [tex]z_3-z_4[/tex] belongs to the first quadrant.

[tex]frequency = \frac{24 \: osc}{60 \: sec} = 0.4 \: osc \: per \: sec[/tex]

[tex]period = \frac{1}{frequency} = \frac{1}{0.4} = 2.5 \: sec \: per \: osc[/tex]

[tex]t = 2\pi \sqrt{ \frac{l}{g} } \\ 2.5 = 2\pi \sqrt{ \frac{l}{9.8} } \\ \frac{2.5}{2\pi} = \sqrt{ \frac{l}{9.8} } \\ ( \frac{2.5}{2\pi} ) {}^{2} = \frac{l}{9.8}[/tex]

[tex]l = ( \frac{2.5}{2\pi} ) {}^{2} \times 9.8 = 1.55148 \: meters[/tex]

Answer:

Step-by-step explanation:

A bit late, but better than never.

24. For [tex]x\neq1[/tex], we have

[tex]\dfrac{9x^2 - x - 8}{x - 1} = \dfrac{(x-1)(9x+8)}{x-1} = 9x+8[/tex]

Then as [tex]x[/tex] approaches 1, we have

[tex]\displaystyle \lim_{x\to1} f(x) = \lim_{x\to1} (9x+8) = 17 \neq 0[/tex]

so the function is not continuous at [tex]x=1[/tex]. It is thus continuous on the interval union [tex](-\infty,0)\cup(0,\infty)[/tex]. You can also write this as "[tex]x<0[/tex] or [tex]x>0[/tex]".

25. When [tex]x[/tex] approaches 2 from the left (when [tex]x<2[/tex]), we have

[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} (5-x) = 3[/tex]

When [tex]x[/tex] approaches 2 from the right [tex](x>2)[/tex], we have

[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (2x-3) = 1[/tex]

so the function is not continuous at [tex]x=2[/tex]. Thus it's continuous on [tex](-\infty,2)\cup(2,\infty)[/tex], or "[tex]x<2[/tex] or [tex]x>2[/tex]".

Answer:1,3,5

Step-by-step explanation:

Answer:

  B.  (5x+5)/(x²-2x)

Step-by-step explanation:

As with numerical fractions, division by a rational expression is equivalent to multiplication by its reciprocal.

  [tex]\dfrac{5}{x-2}\div\dfrac{x}{x+1}=\dfrac{5}{x-2}\times\dfrac{x+1}{x}[/tex]

As with numerical fractions, the product is the product of numerators, divided by the product of denominators.

  [tex]=\dfrac{5(x+1)}{x(x-2)}=\boxed{\dfrac{5x+5}{x^2-2x}}[/tex]

Answer:

12x+6y+5

Step-by-step explanation:

expand this: 3(4x+2y)=12x+6y

then add 5

12x+6y+5

Answer:

Hello! The answer is 12x + 6y + 5

Step-by-step explanation:

3(4x + 2y) + 5

Distribute:

3(4x + 2y) + 5

= 12x + 6y + 5

All like terms are combined/non-existent so the equivalent expression is: 12x + 6y + 5

Answer: C

Step-by-step explanation:

The line is dotted, so eliminate B and D.

Also, the line has a y-intercept of 1, so this eliminates A.

This means the answer must be C.

The length of the arc in the image given is approximately: A. 3.5 cm

Length of arc = ∅/360 × 2πr

The missing parts of the question is shown in the image below, where we are asked to find arc length of JH.

Thus, we would have the following:

∅ = 25°

Radius (r) = 16/2 = 8 cm

Substitute the values into the formula:

Arc length JH = 25/360 × 2π(8)

Arc length JH ≈ 3.5 cm

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The value of the underlined digit (8) in the number given is; Choice B; Eighty million.

The underlined digit in the task content is 8. On this note, it follows that the since, the number can be pronounced as; Five billion, Six hundred and Eighty-two million, Four hundred and fifty thousand, and three.

It is evident, that the place value occupied by the underlined number is; Eighty million.

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The value of z in the equation evaluation as given in the task content is; 3/5.

It follows from the task content that the value of z as in the task content can be evaluated as follows;

2 4/15-z= 1 2/3

34/15 - z = 5/3

Hence, z = 34/15 - 5/3

z = (34-25)/15 = 9/15

z = 3/5

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The probability of being 25-35 years and having a haemoglobin level above 11 is 34%.

The probability of having a haemoglobin level above 11 is 36%.

Being 25-35 years and having a hemoglobin level above 11 are not dependent on each other.

Probability determines the odds that a random event would occur. The odds of the event happening lie between 0 and 1.

The probability of being 25-35 years and having a haemoglobin level above 11 = number of people between 25 - 35 that have a level above 11 / total number of people between 25 - 35

44 / 128 = 34%

The probability of having a haemoglobin level above 11  = number of people with a level above 11 / total number of respondents

153 / 429 = 36%

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Answer: 4.8

Step-by-step explanation:

Corresponding sides of similar figures are proportional, so

[tex]\frac{x}[4}=\frac{6}[5}\\\\x=4\left(\frac{6}{5} \right)=\boxed{4.8}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

Let the number of pistachios be x then the number of almonds = x-100.

The number of cashews = 1000 - x - (x - 100) = 1100-2x.

From the info given

3(1100-2x) + 4x + 5(x - 100) = 3700

3300 - 6x + 4x + 5x - 500 = 3700

3x = 3700 - 3300 + 500

3x = 900

x = 300

So there are 300 pistachios, 200 almonds and 500 cashews in the bag.

There are 300 pistachios, 200 almonds, and 500 cashews in the bag of mixed nuts.

To find the number of each type of nut in the bag, we can set up a system of equations based on the given information.

Let's assume there are x pistachios in the bag. According to the problem, there are 100 fewer almonds than pistachios, so the number of almonds will be (x - 100).

Now, the total number of nuts is 1,000:

x (pistachios) + (x - 100) (almonds) + cashews = 1000

The total weight of the nuts in the bag can be calculated as follows:

3g (cashews) * number of cashews + 4g (pistachios) * x + 5g (almonds) * (x - 100) = Total weight in grams.

Since we know that the bag weighs 3.7 kg, we need to convert the total weight to grams and set it equal to 3.7 kg * 1000g/kg = 3700g.

Now we have two equations:

x + (x - 100) + cashews = 1000

3g * cashews + 4g * x + 5g * (x - 100) = 3700

Let's simplify equation 1:

2x - 100 + cashews = 1000

2x + cashews = 1100

cashews = 1100 - 2x

Now, let's substitute the expression for cashews in equation 2:

3g * (1100 - 2x) + 4g * x + 5g * (x - 100) = 3700

Now, distribute the weights:

3300g - 6g * x + 4g * x + 5g * x - 500g = 3700

Combine like terms:

-6g * x + 4g * x + 5g * x = 3700 - 3300 + 500

3g * x = 900

x = 900 / 3

x = 300

Now that we have the value of x (number of pistachios), let's find the number of almonds:

almonds = x - 100

almonds = 300 - 100

almonds = 200

Now, let's find the number of cashews using the total nut count:

cashews = 1000 - (pistachios + almonds)

cashews = 1000 - (300 + 200)

cashews = 1000 - 500

cashews = 500

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Answer:

The answer is ninth term is -32