treasury securities are issued and backed by the u.s. government and, therefore, are considered to be the lowest-risk securities on the market. as an investor looking for protection against inflation, you are considering the purchase of inflation-adjusted bonds known as u.s. treasury inflation-protected securities (tips). with these securities, the face value (which is paid at maturity) is regularly adjusted to account for inflation; however, the semiannual interest payment (called the bond dividend) remains the same. you purchased a 10-year $10,000 tips bond with dividend of 4% per year payable semiannually (i.e., $200 every 6 months). assume there is no inflation adjustment for the first 5 years, but in years 6 through 10, the bond face value increases by $1150 each year. you use an expected investment return of 14% per year compounded semiannually. note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. what is the net amount of money that you will have received during the 10-year life of the bond without any consideration of dividend reinvestment? the total net amount of money that you would have received is $

Answer:

the 2nd option

Step-by-step explanation:

given a quadratic in standard form : y = ax² + bx + c (a ≠ 0 )

• if a > 0 then minimum turning point

• if a < 0 then maximum turning point

the graph here has a minimum turning point , so

the function has a positive leading coefficient.

the function is symmetrical about the y- axis , so is of even degree

the function has 1 turning point at (0, 2 )

the graph does not cross the x- axis so has 0 x- intercepts

Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:

2x² + 5x + 1.

In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:

8, 26, 19 and 3.

The divisor is found as follows:

4x + 3 = 0

4x = -3

x = -3/4

x = -0.75.

The resulting coefficients of the quotient are given as follows:

8, 20, 4 and remainder of 0.

Hence the quotient is:

8x² + 20x + 4.

Which can be simplified as:

2x² + 5x + 1.

The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.

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Emma's actual height is found to be 42 inches.

For the given question:

In a photograph,

Let 'x' be the actual height of Emma.

Thus,

2.5 / 1.5 = 70 / x

x = 70*1.5 / 2.5

x = 42

Thus, Emma's actual height is found to be 42 inches.

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Answer:

is this from a text book

Step-by-step explanation:

Answer:

The correct answer is D. Enough to feel rested.

a) The height of the frisbee each second it is in the air are 5, 29, 45, 53, 53, 45, 29, 5, -27 and -67.

b) The frisbee is in the air for a total of 8 seconds.

To find the height of the frisbee each second it is in the air, we need to substitute different values of t into the equation \(h = -16t^2 + 40t + 5\) and calculate the corresponding height.

a) Let's substitute t = 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 into the equation:

When t = 0: \(h = -16(0)^2 + 40(0) + 5 = 5\)

When t = 1: \(h = -16(1)^2 + 40(1) + 5 = 29\)

When t = 2: \(h = -16(2)^2 + 40(2) + 5 = 45\)

When t = 3: \(h = -16(3)^2 + 40(3) + 5 = 53\)

When t = 4: \(h = -16(4)^2 + 40(4) + 5 = 53\)

When t = 5: h = \(-16(5)^2 + 40(5) + 5 = 45\)

When t = 6: h = \(-16(6)^2 + 40(6) + 5 = 29\)

When t = 7: h = \(-16(7)^2 + 40(7) + 5 = 5\)

When t = 8: h = \(-16(8)^2 + 40(8) + 5 = -27\)

When t = 9: h =\(-16(9)^2 + 40(9) + 5 = -67\)

b) The frisbee is in the air as long as its height is greater than 0. From the calculations above, we can see that the frisbee is in the air from t = 0 to t = 7, inclusive.

Note: The table you provided shows the height of the frisbee at each second it is in the air, but it seems to be cut off. However, based on the calculations above, the height values at each second should be as follows:

0 seconds: 5 feet

1 second: 29 feet

2 seconds: 45 feet

3 seconds: 53 feet

4 seconds: 53 feet

5 seconds: 45 feet

6 seconds: 29 feet

7 seconds: 5 feet

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Answer:

The length of the rectangle, L = 2.5 units

Step-by-step explanation:

Given the following data;

Length of rectangle =?

Width of rectangle = 10 units.

Note:

The formula for calculating the perimeter of a rectangle is;

\(P = 2L + 2W\)  ........equation 1

Substituting into equation 1, we have;

P = 2L + 2(10)

P = 2L + 20

The formula for calculating the area of a rectangle is given by;

\(A = L * W\) ..........equation 2

Substituting into equation 2, we have;

A = 10L

Since, the perimeter of the rectangle is equal to its area;

Perimeter = Area

2L + 20 = 10L

20 = 8L

L = 20/8

L = 2.5 units.

Valerie paid a total amount of $124 this year for her movie club membership and the 14 movies she rented.

In math, the total amount typically refers to the final sum or result of a calculation involving multiple numbers or quantities.

Valerie pays a fixed fee of $40 annually, and she rented 14 movies at a cost of $6 each. Thus, the total amount she paid this year can be calculated as follows:

Total cost of movie rentals = 14 x $6 = $84

Adding the fixed annual fee to the rental costs:

Total amount paid by Valerie this year = $40 + $84 = $124

Therefore, Valerie paid a total of $124 this year for her movie club membership and the 14 movies she rented.

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Answer: vertical angles

these angles are also congruent

hope this helps!

Answer:

vertical lines

Step-by-step explanation:

that's answer choice

Answer:

average speed of sprinter will be 10.42m/s

Step-by-step explanation:

distance covered=s=100m

time taken=t=9.67m/s

average speed=10.42m/s

Answer:

c

Step-by-step explanation:

all real values of x where 1 < x < 4

Answer:

c

Step-by-step explanation:

trust me

cscθ is the same as 1/sinθ

Explanation:

csc stands for cosec which is equivalent to   1/sinθ

The expression is thus equal to 1/[sin⁡(4π/3)]

Since we know by consulting the unit circle that  sin⁡(4π/3) = - [(√3)/2]

we get the expression  1/[sin⁡(4π/3)] = 1/(-√3/2)  

which can be simplified to 1/(-√3/2) = 2/(-√3) = (-2√3)/3

Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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Answer:

70 * 2.5 = 175

80 * 3.5 = 280

175 + 280 = 455 miles all together

Step-by-step explanation:

I hope this helps :)

Answer:

A

Step-by-step explanation:

A, is the only answer with the correct slope, and when you plug the coordinates in, you get 1=1

Answer:

the answer is B $6 per quart

Answer: 2x+6xy+5y+11

Step-by-step explanation:

Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm

#1

\(\\ \sf\longmapsto \left(\dfrac{4+8}{2},\dfrac{3+8}{2}\right)\)

\(\\ \sf\longmapsto \left(\dfrac{12}{2},\dfrac{11}{2}\right)\)

\(\\ \sf\longmapsto \left(6,\dfrac{11}{2}\right)\)

#2

\(\\ \sf\longmapsto \left(\dfrac{7+1}{2},\dfrac{2+5}{2}\right)\)

\(\\ \sf\longmapsto \left(\dfrac{8}{2},\dfrac{7}{2}\right)\)

\(\\ \sf\longmapsto \left(4,\dfrac{7}{2}\right)\)

#3

\(\\ \sf\longmapsto \left(\dfrac{-5+1}{2},\dfrac{6-3}{2}\right)\)

\(\\ \sf\longmapsto \left(\dfrac{-4}{2},\dfrac{3}{2}\right)\)

\(\\ \sf\longmapsto \left(-2,\dfrac{3}{2}\right)\)

#4

\(\\ \sf\longmapsto \left(\dfrac{-7-5}{2},\dfrac{-1-9}{2}\right)\)

\(\\ \sf\longmapsto \left(\dfrac{-12}{2},\dfrac{-10}{2}\right)\)

\(\\ \sf\longmapsto \left(-6,{-5}\right)\)

The proportional relationship between the cost and the weight is c = 2.2w.

A proportional relationship is used to show the constant od proportionality between the variables.

One bag weighs 2.4 pounds and costs $5.28. The constant will be:

= 5.28/2.4

= 2.2

This can be expressed as c = 2.2w

where c = cost

w = weight

This shows the relationship.

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Answer:

The Equation would be $4 + $3.50x = y

Step-by-step explanation:

Answer: 52=y and 15=x

Step-by-step explanation:

Since we know m and n are parallel that means alternate exterior angles are equal to each other.

The angle with 8x+8= the angle above the one that says 3x+7

Two angles on a line add up to 180 so 8x+8+3x+7=180

Now we can solve

\(8x+8+3x+7=180\\(8x+3x)+(8+7)=180\\11x+15=180\\11x+15-15=180-15\\11x=165\\\frac{11x}{11} =\frac{165}{11} \\x=15\)

Now we know that x=15

The angle y and the angle of 3x+7 are corresponding angles. Corresponding angles are congruent. Subbing in 15 for x we can solve for y

\(3(15)+7=y\\45+7=y\\52=y\)

The definite integral in this problem has the value given as follows:

B. 42.

The definite integral in the context of this problem is given as follows:

\(\int_0^2 (x^7 + 5) dx\)

Applying the power of x integral rule, the result of the integral is given as follows:

\(\frac{x^8}{8} + 5x\)

At x = 2, the numeric value of the integral is given as follows:

\(\frac{2^8}{8} + 5(2) = 42\)

At x = 0, the numeric value of the integral is given as follows:

0.

(as both terms involve a multiplication by x and x = 0).

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

42 - 0 = 42.

Hence option B is the correct option in the context of this problem.

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The value of x is 14 and the value of y is 7√3.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

We know sin is opposite/hypotenuse

∴ sin30° = 7/x.

1/2 = 7/x.

x = 14.

We also know that tan is opposite/adjacent.

tan30° = 7/y.

1/√3 = 7/y.

y = 7√3.

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The correct net that represents a Square pyramid is Option B.

A net is a two-dimensional pattern that can be folded into a three-dimensional figure. To draw a net of a square pyramid, we need to create a two-dimensional pattern that includes a square base and four triangular faces that meet at a common vertex.

Option A: This net has a square base, but it has three triangular faces and one trapezoidal face. Therefore, it does not represent a square pyramid.

Option B: This net has a square base and four triangular faces that meet at a common vertex. Therefore, it represents a square pyramid.

Option C: This net has a triangular base, so it does not represent a square pyramid.

Option D: This net has a square base, but it has six triangular faces that do not meet at a common vertex. Therefore, it does not represent a square pyramid.

Therefore, the correct net that represents a square pyramid is Option B.

It's important to note that there may be different ways to draw a net for a square pyramid, as long as the net includes a square base and four triangular faces that meet at a common vertex. However, Option B is a valid net for a square pyramid and represents the figure accurately.

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Answer:

52 weeks are there in a year

Step-by-step explanation:

365/7

Answer:

6

Step-by-step explanation:

smallest x value is -3

largest x value is 3

so distance between them is 6

3- (-3)=6

Answer:

Step-by-step explanation:

The expression that is equivalent to the given expression is 125y⁵.

The given expression is:

\(\frac{5y^{3} }{(5y)^{-2} }\)

Some important power rules applicable to this problem are:

1)\((ab)^m=a^mb^m\)

2)\(\frac{1}{a^{-n} } =a^n\)

So, \(\frac{5y^{3} }{(5y)^{-2} } =\frac{5y^{3} }{5^{-2} y^{-2} }\).....by power rule (1)

\(=(\frac{5}{5^{-2} } )(\frac{y^3}{y^{-2} })\)

\(=5^3y^5\).....by power rule(2)

\(=125y^5\)

Hence, the expression that is equivalent to the given expression is 125y⁵.

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Since the volume of the sphere V = 36π cm³is greater than that of the cone, V' = 21π cm³ the ice cream will overflow.

The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere

Now if the ice cream above is going to melt when it does, will it fit in the cone or will it overflow? Since the ice cream is a sphere, the ice cream will not overflow if the volume of the ice cream equals the volume of the cone. If is greater than the volume of the cone, it will overflow.

Now, since the ice cream is a sphere, its volume is given by V = 4πr³/3 where r = radius of sphere = 3 cm

So, substituting this into the equation, we have that

V = 4πr³/3

V = 4π(3 cm)³/3

V = 4π × 27 cm³/3  

= 4π × 9 cm³

= 36π cm³

Also, since the volume of the cone is given by V' = 1/3πr²h where r = radius of cone = 3 cm and h = height of cone = 7 cm

So, substituting the value of the variables into the equation, we have that

V' = 1/3πr²h

V' = 1/3π(3 cm)² × 7 cm

= 1/3π × 9 cm² × 7 cm

= 3π cm² × 7 cm

= 21π cm³

We see that V = 36π cm³ > V' = 21π cm³

Since the volume of the sphere is greater than that of the cone, the ice cream will overflow.

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