Daran just retired, and has $670,000 to invest. A very safe Certificate of Deposit (CD) account pays 1.5%, while a riskier bond fund pays 8.5% in interest. Daran figures he needs $40,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk? Round answers to the nearest dollar.

To simplify a polynomial expression, we can expand parentheses by multiplying the terms within with the coefficient outside of them and add like terms.

[tex]3x(-2x + 7) - 5(x - 1)(4x - 3)[/tex]

⇒ Open up the parentheses

[tex]=(3x*(-2x) + 3x*7) - 5(x(4x - 3)-1(4x-3))\\=(-6x^2 + 21x) - 5(4x^2 - 3x-4x+3)\\=-6x^2 + 21x - 5(4x^2 - 7x+3)=-6x^2 + 21x - (20x^2 - 35x+15)\\=-6x^2 + 21x - 20x^2 + 35x-15\\=- 26x^2 + 56x-15[/tex]

[tex]- 26x^2 + 56x-15[/tex]

The altitude of an object with respect to a reference plane or point is termed its height. This includes all parts of the object that add up to its height. Therefore, the height of the wall would be 100.5 inches.

The height of a given object implies the altitude of the object from a reference plane or point.

Therefore given that concrete blocks are 8 inches, then;

total height of mortar required to hold each concrete block = 3/8 inches

Thus, since there are 12 concrete blocks, then 12 sections of mortar would be required to hold 12 blocks starting from the ground.

So that;

total height of mortar required = 3/8 x 12

                                         = 4.5 inches

Total height of all concrete blocks required = 12 x 8

                                                             = 96 inches

Therefore, the height of the wall of 12 courses of concrete blocks = 96 + 4.5

                                                   = 100.5 inches

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Answer:

6 seconds after it is launched

Step-by-step explanation:

h(t) = -4t² + 16t + 48

The balloon is at ground level when it lands.

When it is launched, t = 0, and h(0) = 48

When it lands, at time t, h(t) = 0.

-4t² + 16t + 48 = 0

t² - 4t - 12 = 0

(t - 6)(t + 2) = 0

t = 6 or t = -2

The balloon will hit the ground 6 seconds after it is launched.

Answer:

[tex]\frac{2\sqrt3}{3} = x[/tex]

Step-by-step explanation:

So you want to use PEMDAS to do the equation in order. This means that you'll start by adding 6 and 1 and then multiplying that value by 2

[tex]2(7)-|-10| = 3x^2[/tex]

[tex]14-|-10|=3x^2[/tex]

The absolute value can be defined as the "distance" from 0 which is going to be positive. You can think of it as the positive value of a number so if you have |-b| it will become b, and even if it's already positive, it will remain positive. so the absolute value of -10 is 10 but then it becomes negative again because of the subtraction

[tex]14-10=3x^2[/tex]

[tex]4=3x^2[/tex]

Now you want to solve for x by dividing both sides by 3 and taking the square root of both sides to isolate x

[tex]\frac{4}{3} = x^2[/tex]

[tex]\sqrt{\frac{4}{3}}=x[/tex]

You can distribute the square root across division since [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] and the square root can be defined as [tex]x^{0.5}[/tex] since [tex]a^b * a^c = a^{b+c}[/tex] because if you spread it out it's really just [tex](a * a * a ... b\ amount \ of \ times) * (a * a * a ... c\ amount\ of\ times)[/tex] which can be simplified to (a * a * a... (b + c) amount of times) if that makes any sense. Anyways using this property you'll get [tex]a^{0.50} * a^{0.50} = a^{0.50 + 0.50} = a^1 = a[/tex]. If you look at it you'll notice a^0.50 multiplied by it self gives you a... sounds like the square root, which it is. So now the equation becomes

[tex]\frac{\sqrt{4}}{\sqrt{3}}=x[/tex]

[tex]\frac{2}{\sqrt3}[/tex]

Now if you look at the equation you'll notice there's a radical in the denominator, which can be rationalized by multiplying by sqrt(3)\sqrt(3) which is 1 except it makes the denominator 3 and keeps the original value

[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3}=x\\\frac{2\sqrt{3}}{3} = x[/tex]

The side of the small triangle that will correspond to the side of HI is side IK.

Similar triangles are triangles that have the same shape but different size.

In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are equal.

Therefore, the side of the small triangle that will correspond to the side of HI is side IK.

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Based on the scatter plot on perishable and nonperishable items purchased by customers, the following is true:

Looking at the y-axis which shows the number of nonperishable items bought, the number of dots we find at 5 is 3 which means 3 people bought 5 nonperishable items.

The median of perishable items requires that we order the perishable items bought:

2, 2, 5, 6, 7, 8, 9, 10, 11

The median is 7 perishable items.

The number of people with the same number of perishable and nonperishables are 2 people.

One purchased 8 nonperishables and 8 perishables and the other purchased 9 of both items.

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Answer:

Step-by-step explanation:

The distance in miles between our galaxy and the nearby galaxy is 5.99 * 10^12 miles

Given the following parameters

Distance that light travels = 5.9×10^12 miles

Distance in near galaxy = 5.1×10^6miles

Find the difference

Distance = 5.9×10^12 - 5.1×10^6

Distance = 5.99 * 10^12 miles

Hence the distance in miles between our galaxy and the nearby galaxy is 5.99 * 10^12 miles

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The measure of arc BEC in circle D is 134°

From the question, we are to determine the measure of arc BEC

Measure of arc BEC = 2 × m∠BAC

First, we will determine the measure of angle ACB

From one of the circle theorems,

The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference

∴ m∠ACB = 1/2 × 76°

m∠ACB = 38°

Then,

m∠BAC + m∠ACB + m∠ABC = 180° (Sum of angles in a triangle)

m∠BAC + 38° + 75° = 180°

m∠BAC + 113° = 180°

m∠BAC  = 180°- 113°

m∠BAC = 67°

Then,

Measure of arc BEC = 2 × m∠BAC

Measure of arc BEC = 2 × 67°

Measure of arc BEC = 134°

Hence, the measure of arc BEC is 134°

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The sum is given by -  f(y) = 4(y -1).

We have the following expression -

(y + 5) + (3y - 9)

We have to evaluate the above sum.

Now -

f(x) + g(x) = 3x + 9 - (6 - x)  

f(x) + g(x) = 3x + 10 - 6 + x

f(x) + g(x) =  4x + 4

f(x) + g(x) = 4(x + 1)

According to the question, we have -

(y + 5) + (3y - 9)

Assume that the sum is represented by the function f(y).

Solving, we get -

f(y) = y + 5 + 3y - 9

f(y) = y + 3y + 5 - 9

f(y) = 4y - 4

f(y) = 4(y - 1)

Hence, the sum is given by -  f(y) = 4(y -1).

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In the case above, option b is correct: Marcelina spends the intended amount of money but she bought more than she did intended amount of corn

She  buy 50kg of corn in total

So the equation will be:

C= (20, 50) = 20 white, 50 yellow

But 30 while and 20 yellow is needed.

Since  C = 20 +50 = 70 corns

While 30 + 20 = 50 corns.

This implies that she spends the intended amount of money but she bought more than she did intended amount of corn and as such, option b is correct.

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Answer:

Step-by-step explanation:

f(x)=5x+7

g(x)=-2x-4

g(f(x))=g(5x+7)=-2(5x+7)-4=-10x-14-4=-10x-18

=-10x+(-18)

Answer:

6

Step-by-step explanation:

I believe so because the 20 pole took away six so im guessing the 41 pole will to the same

The length of the shadow cast by the 14-foot pole is 8.4 shadows.

We have,

From the figure given,

The two triangles are similar since the corresponding sides and angles are given equal.

This means,

The ratio of the corresponding sides is equal.

So,

20/14 = 12/x _______(1)

Where x is the length of the shadow cast by the 14-foot pole.

Now,

Solving for x from (1).

20/14 = 12/x

Divide 12 on both sides.

20 / (14 x 12) = 1/x

20/168 = 1/x

Cross multiply.

x = 168/20

x = 8.4 shadow.

Thus,

The length of the shadow cast by the 14-foot pole is 8.4 shadows.

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Using simpler trigonometric identities, the given identity was proven below.

Remember that:

[tex]sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}[/tex]

Then the identity can be rewritten as:

[tex]sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\[/tex]

Now we can multiply both sides by cos⁴(x) to get:

[tex]\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)[/tex]

Now we can use the identity:

sin²(x) + cos²(x) = 1

[tex]1 - cos^2(x) = sin^2(x)*(sin^2(x) + cos^2(x)) = sin^2(x)\\\\1 = sin^2(x) + cos^2(x) = 1[/tex]

Thus, the identity was proven.

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The minimum length Starbucks must build the wheel chair ramp to meet the standards is 23.9ft.

A triangle in which one of the angles is 90 degrees is called a Right angled Triangle.

To find the angle of the ramp, Trigonometric Ratios will be used

As the ramp is forming a right triangle

sin x = 2/22

x = 5.21°

The angle the wheel chair ramp makes with the ground is 5.21°.

If the angle has to be less than 4.8°

Let the length of the wheel chair will be given by y

Then,

2/x < sin4.8

x > 2/sin 4.8

x > 23.9 ft

Therefore the minimum length Starbucks must build the wheel chair ramp to meet the standards is 23.9ft.

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Answer:

Your answer is 31808.6 but if your rounding the answer will be 31809

Step-by-step explanation:

The eqaution would be " v = 3.14 x r^2 x h"

Answer: 294.34 m^3

Step-by-step explanation: The formula for the volume of a hemisphere is 2/3 * 3.14 * radius cubed (r^3). Plugging in the values, we have 2/3 * 3.14 * 5.2^3, and we get roughly 294.339 m^3, or rounded to the nearest hundredth, 294.34 m^3.

Hope this helped!

The maximum height of the pie based on the information given is 124.

From the information given in the table, it can be seen that the time and the height of the pie was given in the table.

In this case, the maximum height of the pie based on the information given is 124. This can be seen at 4 seconds.

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Answer:

y=3/2x + 18

Step-by-step explanation:

So when two lines are perpendicular, that simple means the slope are reciprocals, and the signs are opposite. So for example if one equation had a slope of [tex]\frac{a}{b}[/tex], the equation that is perpendicular, would have a slope of [tex]-\frac{b}{a}[/tex]. So the first step would be to find the slope of 2x+3y=4. To find the slope we can convert it into slope-intercept form which is y=mx+b where m is the slope, and this is done by isolating y, as you can see the y is alone in the slope-intercept form.

Original equation:

2x + 3y = 4

subtract 2x from both equations:

3y = -2x + 4

Divide both sides by 3

y = -2/3x + 4/3

The y-intercept doesn't really matter in this case, what really matters is the slope, and the slope is the coefficient of x, since as x increases by 1, it will increase by the amount of the coefficient, because the slope is rise/run and since the run is 1, if you increase x by 1, the run is the slope, which is the coefficient. The slope in this case is -2/3. So the reciprocal of the slope is 3/2 (notice how the sign is the opposite as well). Now we have the equation

y=3/2x + b

To find the y-intercept, you simply use the point that was given (-2, 15). Plug in -2 as x, and 15 as y to find the value of b

Original equation

y=3/2x + b

Plug in known values:

15 = 3/2(-2) + b

Multiply the fraction:

15 = -6/2 + b

Simplify the fraction:

15 = -3 + b

Add 3 to both sides

18 = b

This gives you the equation

y=3/2x + 18

The value of the investment after 2 years is K2400.00

The given parameters are:

Principal, P = K2,000.00

Rate, r = 10%

Time, t = 2 years

The value is then calculated as:

Amount = P + PRT

So, we have:

Amount = 2000 + 2000 * 10% * 2

Evaluate

Amount = 2400

Hence, the value of the investment after 2 years is K2400.00

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Answer:

10 (x+3/5)= 2y in slope intercept form

simplify

10x+6=2y

subtract by 2

y=5x+3

Hope This Helps!!!

Answer:

Milk and Eggs = 552

Step-by-step explanation:

First add all of the other percentages together. (70%), 100%-70%=30%. 30% of 1840 = 552.

Answer:

H.  552

Step-by-step explanation:

Circle graph information:

Total consumption = 1840 pounds per person

First, calculate the percentage of milk and eggs (the value of x).

Total percentages = 100%

⇒ x + 38 + 10 + 10 + 8 + 4 = 100

⇒ x + 70 = 100

⇒ x = 30

Therefore, 30% of food consumption is milk and eggs.

To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:

= 30% of 1840

= 30% × 1840

[tex]=\sf \dfrac{30}{100} \times 1840[/tex]

= 552

Therefore, the average American consumes 552 pounds of milk and eggs each year.

Answer:

Step-by-step explanation:

3/4 * 1/8 = 3*1 / 4*8

3 / 32 is the solution.

Answer:

h Tu to be a great day of school and

Step-by-step explanation:

great day of school and I have a great day of school and I have a great day of➡ school and I I have a great day of school and I have a great day of school and I have a great yy

The probability of picking a head and a number 4 is 0.25.

Your information is incomplete and the complete information wasn't found. An overview will be given.

A coin has a head and tail and the probability of choosing either is 1/2 or 0.5.

Let the 2 numbers be 1 and 4. The probability of picking either number will be 1/2 or 0.5 as well.

Here, let the probability of picking a head and a number 4 will be:

= 1/2 × 1/2

= 0.5 × 0.5

= 0.25

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The coordinates of the vertex of the parabola are (-6,5).

The coordinates of a vertex of a parabolic equation are those x and y points for which the parabola crosses its axis of symmetry.

The vertex of an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{2}{2(1/6)}}[/tex]

[tex]\mathbf{x_v = -6}[/tex]

From the equation:

[tex]\mathbf{y = \dfrac{1}{6}x^2+2x+11}[/tex]

[tex]\mathbf{y_v = \dfrac{1}{6}(-6)^2+2(-6)+11}[/tex]

[tex]\mathbf{y_v =5}[/tex]

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The type of function is Exponential.

The function whose graph is in the linear straight line then that function is considered a linear function.

An example of this is 2x+3

An exponential function is a model or a relationship in which there is a constant change in the independent variable that gives the same change in proportionality.

The given function is not showing a linear growth which means there is no straight line so the function will be exponential.

When x increases by 1 unit then the growth factor will be 3/1 = 3

So the exponential growth factor is 3.

Exponential growth is like a pattern of data that shows a huge increase with passing time, and by creating the curve for an exponential function.

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1/6 of the people are not elderly or men

The given parameters are:

Men = 1/2

Elderly = 1/3

The number of people that are not elderly or men are:

People = 1 - Men - Elderly

So, we have:

People = 1 - 1/2 - 1/3

Evaluate

People = 1/6

Hence, 1/6 of the people are not elderly or men

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