As part of his retirement strategy, John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, over time, about 9% per year, while the low risk investments should return about 4% per year. If he wants a supplemental income of $11,400 a year, how should he divide his investments?

Answer:

if it as more

Step-by-step explanation:

no need to thank me just add me on snap wgilpenn

Answer:

-5/3

Step-by-step explanation:

Answer:

Dimension is the square root of 4w-10

Step-by-step explanation:

The length=Breadth=√4w-10

Final answer:

The expression for the area of the rectangle, 4w - 10, can be factored as 2(2w - 5). This implies that one of the rectangle's dimensions could be 2 units and the other could be a linear expression of 2w - 5 units.

Explanation:

To factor the expression 4w - 10 square units, we can find the greatest common factor (GCF) of the two terms. The GCF of 4w and 10 is 2, so we can factor out 2 from the expression:

4w - 10 = 2(2w - 5)

Given the factored form, we can conclude something about the dimensions of the rectangle. The factored expression, 2(2w - 5), suggests that one dimension of the rectangle could be 2 units, and the other is a linear expression of width, specifically 2w - 5 units. This aligns with the area formula for rectangles, A = length × width, where one dimension is considered the length and the other the width for calculation purposes.

The square root of 97 is 8.48857802, but you can round to 8.49 or 8.5 if you so desire.

To model the scenario, we can use the exponential function A = A0 · (1/2)^(t/h), where A is the amount remaining, A0 is the initial amount, t is the time, and h is the half-life. In this case, the initial amount is 100 grams and the half-life is 6 hours. After substituting t = 12 into the function, we find that 25 grams of the isotope remain after 12 hours.

To model the scenario, we can write an exponential function using the formula:

A = A0 · (1/2)t/h

Where:

For this scenario, the initial amount is 100 grams and the half-life is 6 hours. So, the exponential function would be:

A = 100 · (1/2)t/6

To find out how much of the isotope remains after 12 hours, we can substitute t = 12 into the function and solve for A:

A = 100 · (1/2)12/6 = 100 · (1/2)2 = 100 · (1/4) = 25

Therefore, after 12 hours, 25 grams of the isotope would remain.

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Answer:

I would say it is c but im not sure.

Step-by-step explanation:

Well you use distributive property to solve this to get a simplified answer.

[tex]b. \: 5d - 3 \\ \\ 1. \: 2d + 6 + 3(d - 3) \\ 2. \: 2d + 6 + 3d - 9 \\ 3. \: (2d + 3d) + (6 - 9) \\ 4. \: 5d - 3[/tex]

Answer:

A= 20959.52 cm

Step-by-step explanation:

Formula: A= π x r^2

A=  π x 81.68^2

A= 20959.52

Answer:

y=-2/7x+1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-1))/(21-7)

m=(-5+1)/14

m=-4/14

simplify

m=-2/7

y-y1=m(x-x1)

y-(-1)=-2/7(x-7)

y+1=-2/7(x-7)

y=-2/7x+2-1

y=-2/7x+1

The equation of the line in slope-intercept form is: [tex]\[ \boxed{y = -\frac{2}{7}x + 1} \][/tex]

To find the equation of the line in slope-intercept form  y = mx + b that passes through the points 7, -1 and 21, -5 we need to follow these steps:

1. Find the slope  m  of the line.

2. Use the slope and one of the points to find the y-intercept b

3. Write the equation in the form y = mx + b

Step 1: Find the slope m

The formula for the slope between two points [tex]\((x_1, y_1)\) and \((x_2, y_2)\) is:[/tex]

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

For the points 7, -1 and 21, -5

[tex]\[ x_1 = 7, y_1 = -1 \][/tex]

[tex]\[ x_2 = 21, y_2 = -5 \][/tex]

Substitute these values into the slope formula:

[tex]\[ m = \frac{-5 - (-1)}{21 - 7} = \frac{-5 + 1}{21 - 7} = \frac{-4}{14} = -\frac{2}{7} \][/tex]

Step 2: Find the y-intercept b

Use the slope[tex]\( m = -\frac{2}{7} \)[/tex] and one of the points

[tex]\[ -1 = -\frac{2}{7}(7) + b \][/tex]

b = 1

Step 3: Write the equation

Now that we have the slope [tex]\( m = -\frac{2}{7} \)[/tex] and the y-intercept  b = 1 we can write the equation in slope-intercept form:

[tex]\[ y = -\frac{2}{7}x + 1 \][/tex]

Thus, the equation of the line in slope-intercept form is:

[tex]\[ \boxed{y = -\frac{2}{7}x + 1} \][/tex]

Answer:

a = 2 , r = 5

Step-by-step explanation:

The n th term of a geometric progression is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Given the 4 th term is 250, then

ar³ = 250 → (1)

Given the 7 th term is 31250, then

a[tex]r^{6}[/tex] = 31250 → (2)

Dividing the 2 equations gives

[tex]\frac{ar^6}{ar^3}[/tex] = [tex]\frac{31250}{250}[/tex], that is

r³ = 125 ← take the cube root of both sides

r = [tex]\sqrt[3]{125}[/tex] = 5

Substitute r = 5 into (1)

a × 5³ = 250, that is

125a = 250 ( divide both sides by 125 )

a = 2

Answer: a = 2, and r = 5

Step-by-step explanation: What we have been given here is a geometric progression. Every term in the sequence of numbers is derived by multiplying the previous term by a particular number called the common ratio, otherwise known as r. Hence if the first term is 1 for instance, the second term would be derived as 1 x r (which equals 1r), the third term would be derived as 1r x r (which equals 1r squared) and so on.

Having this in mind , we can calculate the Nth term of a geometric progression as

Nth term = a x r{to the power of n - 1}

So if we want to calculate the 4th term for instance, that would be

4th = a x r{to the power of 4 - 1} OR

4th = a x r{to the power of 3}

Similarly to calculate the 7th term would be

7th = a x r{to the power of 7 - 1}

7th = a x r{to the power of 6}

Now that we have been given the 4th (250) and 7th (31250) terms, what we now have is

a x r{to the power of 3} = 250 AND

a x r{to the power of 6} = 31250

a x r{to the power of 6}/a x r{to the power of 3} = 31250/250

After reducing both sides to their simplest form, what we now have is

r{to the power of 3} = 125

If we add the cube root sign to both sides of the equation we would have

r = 5

Having computed r as 5, we can now go back to calculate a as follows;

If a x r{to the power of 3} = 250, then

a x 125 = 250

Divide both sides of the equation by 125

a = 2

Therefore, a = 2 and r = 5

Answer:7 bags

Step-by-step explanation:

Divide 60 by 8 because she has a total of $60 and each bag costs $8. The answer would actually be 7.5 bags but since you can’t buy half a bag your answer would be 7 bags.

Step-by-step explanation:

Hdhcnkcube hxjdje8277ru288xhei8chne

Diicinrhcurnje8f77 8eun3if7 hh8

Answer:

There will be a total 40 jumps.

Step-by-step explanation:

Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].

Now, the piece starts at point A = 7 and jumps to the right.

So, the piece will jump over B = 24  after [tex]\frac{24 - 7}{0.889} = 19.122[/tex] ≈ 20 complete jumps.

Then it switches direction to the left and the piece then stops at point A.

So, there will be a total (20 + 20) = 40 jumps. (Answer)

The game piece took a total of 153/8 jumps.

To determine how many jumps the game piece took, we need to find the total distance it traveled. The piece starts at point A = 7 and jumps to the right, so it covers a distance of 8/9. As soon as it jumps over B = 24, it switches direction and jumps to the left, covering a distance of -8/9. The piece continues this pattern until it reaches point A again.

To find the number of jumps, we can divide the total distance traveled by the distance covered in each jump. The total distance is 24 - 7 = 17. Dividing 17 by 8/9 gives us:

17 / (8/9) = 17 * (9/8) = 153/8

So, the game piece took a total of 153/8 jumps.

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Answer:

B. Square root of 25

Step-by-step explanation:

It is a whole number.

Thus, it is not an irrational number.

The square root of 25 is equal to 5

Therefore

An irrational number is a number that cannot be written as a ratio of two integers. It is a non-terminating and non-repeating decimal.

The given dilation is an isometry dilation.

Step-by-step explanation:

Step 1; First, we need to compare the dimensions of the two figures. We check to see if the side lengths are the same. If the parameters are the same, the dilation could be an enlargement or a reduction. Whereas if the parameters are the same, it could be an isometric dilation or just a reflection.

Step 2; The first shape has a side length of approximately 2.5 units. We compare this to the same side length as the second shape. The second shape has the same side length.

The first shapes side length of the  / same side length of the second shape = 2.5 / 2.5 = 1,

So the scale factor is 1. As the parameters do not change, it could either be a reflection or an isometric dilation.

Step 3; The base side in shape 1 is BC whereas the same base side in shape 2 is [tex]A^{1}[/tex][tex]B^{1}[/tex]. So shape ABCDE has rotated to form the shape  the dilation is isometric and not a reflection with a scale factor of 1.

Answer:

1: Isometry

Step-by-step explanation:

As both the shapes are having equal area hence the scale factor remains 1.

As scale factor remains 1this is neither enlargement or reduction.

It is the isometry that the distance between two pints remains the same.

Answer:

85

Step-by-step explanation:

hello :

if : g(x)= x+7; h(x)= (x-3)²   so : (4g+h)(x)=4g(x)+h(x)  = 4(x+7)+(x-3)²  

(4g+h)(8)=  4(8+7)+(8-3)²  = 60+25=85

Answer:

The value of x is 120°

Step-by-step explanation:

To solve for x, you need to introduce a third line that is parallel to the two parallel lines.

This line should divide the angle at x into two as shown in the attachment.

By the alternate interior angle property, m=70°

and

n=50°

This implies that, x=50+70=120°

Option C 40-2 x

150 square feet

Step-by-step explanation:

Step 1 :

Given that the 3 sides, a,b, and x will be made of 40 feet of fencing,

we have a + b + x = 40

Since this is a rectangular garden , b= x

substituting b= x, we have a + x  + x = 40

=> a+2 x = 40

=> a= 40-2 x

Step 2 :

To find the area in square feet,

when x = 15, a = 40 -  2 * 15 = 40-30 = 10 feet

The length and breadth of the rectangular garden are therefore 5 and 10 feet respectively

Hence, the area of the garden = length  * breadth = 15 * 10 = 150 square feet

Answer: Second option.

Step-by-step explanation:

Below are some transformations for a function  f(x) :

1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.

2. If [tex]f(x)-k[/tex], the function is shifted "k" units down.

3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.

4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.

The Cube root parent function is:

[tex]f(x)=\sqrt[3]{x}[/tex]

By definition, the graph of this function passes through the origin, as you can observe in  the picture attached.

In this case, you need to analize the graph given in the exercise. You can see that the the graph of the function h(x) is like the parent function f(x), but shifted 2 units left.

Therefore, based on the transformations explained above, you can determine that the equation of the function h(x) is the following:

[tex]h(x)=f(x+2)\\\\h(x)=\sqrt[3]{x+2}[/tex]

Answer:

Option B: [tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex]

Step-by-step explanation:

When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:

                     [tex]$ \textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}} $[/tex]

Here, we are given the focus: (h, k) = (0, -2)

Directrix: y = c = -3.

We substitute in the formula to get the equation of the parabola.

[tex]$ (x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y $[/tex]

[tex]$ \implies x^2 + 4 - 9 = 2(- 2 + 3)y $[/tex]

[tex]$ \implies x^2 - 5 = 2(1) y$[/tex]

[tex]$ \implies 2y = x^2 - 5 $[/tex]

Dividing by 2, throughout we get:

[tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex] which is the required answer.

Answer:

4 hours

Step-by-step explanation:

I am not sure, what I did was, if Calvin and Alvin both waxed half the car, their original time would split in half, then I added those values together, which is also the average.

y=mx+b is a pretty safe form to follow

C=3

A=5

if you are doing variables

I tried my best.

Answer:

[tex]\large \boxed{\text{B) 374 mi/day}}[/tex]  

Step-by-step explanation:

The average rate of change from one point to another is the slope of the straight line joining the two points.

[tex]\text{slope} = \dfrac{ y_{2} - y_{1}}{ x_{2} - x_{1}}[/tex]

From Day 1 to Day 3, your points are (1, 383) and (3, 1132).  

[tex]\text{Slope} = \dfrac{1132 - 383 }{3 - 1} = \dfrac{749 }{2} = \textbf{374 mi/day}\\\\\text{The average rate of change from Day 1 to Day 3 was $\large \boxed{\textbf{374 mi/day}}$}[/tex]

The graph below shows the rate of change from Day 1 to Day 3 as a black line. It appears from the graph that Adam and his dad kept the same rate of change for the whole trip.

The answer is.

The Lamp post is 800cm

x = height of lamp post

160/90 = x/450

450 is the length from the base of the lamp post to the end of the shadow (360+90)

cross multiple

90x = 72000

x =800cm

Have a great day!

The lamp post is 800 cm high

From the diagram in the attachment below,

The height of the girl is /AG/ = 160cm

The length of her shadow is /SG/ = 90cm

The height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm

To determine the height of the lamp post, we will calculate the value of x

Consider ΔASG

Determine <ASG = θ

From

[tex]tan\theta = \frac{opposite}{adjacent}[/tex]

Opposite = /AG/ = 160 cm

Adjacent = /SG/ = 90 cm

∴ [tex]tan\theta = \frac{160}{90}[/tex]

Also, Consider ΔLAM

[tex]tan\theta = \frac{/LM/}{/AM/}[/tex]

NOTE: <LAM = θ (Corresponding angles) since line AM is parallel to line SP

∴[tex]\frac{160}{90} = \frac{/LM/}{/AM/}[/tex]

But, /LM/ = x and /AM/ = 360 cm

∴[tex]\frac{160}{90} = \frac{x}{360}[/tex]

[tex]90x = 360 \times 160[/tex]

[tex]x = \frac{360 \times 160}{90}[/tex]

[tex]x = 4 \times 160 \\[/tex]

[tex]x = 640 cm[/tex]

x = 640 cm

Recall that, the height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm

∴ The height of the lamp post is 640 cm + 160cm

The height of the lamp post is 800 cm

Hence, the lamp post is 800 cm high

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Answer: Since 3−5+2=0, then 2

is the additive inverse of 3−5 is 2

 Since 5−3−2=0, then −2is the additive inverse of 5−3. is -2

Step-by-step explanation: additive inverse

The additive inverse of any number

x

is the number that gives zero when added to

x

. Example: the additive inverse of

5 is −5.

Answer:

it's 408,471

Step-by-step explanation:

[tex]400000 \\ + 8000 \\ \: + 400 \\ \: \: + 70 \\ \: \: \: + 1 \\ = 408471[/tex]

Answer:

t = 40

Step-by-step explanation:

Start by breaking the equation down to a simpler form.  To do this you would need to divide 28 by 7.

28 / 7 = x

x = 4

Now we can create a new equation.

4x = t

T would represent the total number of students in the band.  X would be the any number from 1 to 10.  This is because 10 is the highest faction to make the fraction a whole.  Since we a looking for the total we would put ten in place for x.

4 x 10 = t

t = 40

There you go.

Hope this helped.

Answer:

"B"

Step-by-step explanation:

"the median wind speed for country B is greater than the median wind speed for county A"

got it right on the quiz, and good luck ;)

The median wind speed for country B is greater than the median wind speed for county A.

The answer is option B.

A median is a number in the middle of a list of numbers that are sorted, ascended, or descended and can define a set of data. The median is sometimes used in contrast to the definition where there are outsiders in a sequence that may distort the value ratio.

The importance of median value is that it provides an idea about the distribution of data. If the definition and median of the data set are the same, then the data is evenly distributed from the smallest to the highest values.

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Answer:

Try the suggested solution, shown on the picture attached

Step-by-step explanation:

Note, 'm(MNO)' means m(∠MNO), and for issues 2, 4 ,5 - the described angles are angles inside the declared triangle.

Answer:

67º

Step-by-step explanation:

Answer:

The measure of  XY is 79.8 cm.

Step-by-step explanation:

An image of the question is attached here.

Given:

Measure of XT = 39.9

VW is the bisector.

So T is the midpoint of XY .

Note: Bisector divides the line in two equal parts.

According to the question:

⇒ [tex]XT = TY[/tex]           ...as T is the midpoint.

⇒ [tex]XY=XT +TY[/tex] ...Segment addition Postulate

⇒ [tex]XY=XT+XT[/tex]

⇒ [tex]XY=2(XT)[/tex]

⇒ [tex]XY=2(39.9)[/tex]

⇒ [tex]XY=79.8[/tex] cm

The measure of XY in the skateboard design is 79.8 centimeter.