Katherine is going to invest in an account paying an interest rate of 5.8%
compounded monthly. How much would Katherine need to invest, to the nearest ten
dollars, for the value of the account to reach $960 in 16 years?

Answer:

116

Step-by-step explanation:

The diameter of the circle is 396 units.

The length of the arc is 0.83π units.  

The length of an arc of a circle is given by the formula:

L = θ/360 * πd

where θ is the measure of the angle and is the diameter of the circle

Given: θ = 80° and L = 88π

L = θ/360 * πd

88π = 80/360 * π * d

88 = 80/360 * d

80 * d = 88 * 360

80d = 31680

80d = 31680/80

d = 396 units

PART 2

If  θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12

L = θ/360 * πd

L = 25/360 * π * 12

L = 0.83π units

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Answer:

If the probability of an event is 0.20, the odds in favor of the event can be calculated as follows:

- Divide the probability of the event occurring by the probability of the event not occurring:

0.20 / (1 - 0.20) = 0.20 / 0.80

- Simplify the fraction:

0.20 / 0.80 = 1 / 4

Therefore, the odds in favor of the event are 1 to 4.

Step-by-step explanation:

The odds in favor of an event with a probability of 0.20 is a ratio of 1 to 4.

The question is about calculating the odds in favor of an event with a probability of 0.20. The odds in favor of an event is defined as the ratio of the probability that the event will happen to the probability that it will not happen.

In this case, the probability of the event is 0.20, therefore the probability that it will not happen is 1 - 0.20 = 0.80. So, the odds in favor of the event are 0.20 to 0.80 or it can be simplified to 1 to 4.

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The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.

It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.

By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).

So,

5/6 × 6/5

= 30/30

= 1

Hence, 6/5 is the multiplicative inverse of 5/6

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The  algebraic expression represents loga 75 is st²

An algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

The statement reads:

loga 2=r,

loga 3=s, and

loga 5=t

Log 75 Log(3*5*5)

That log3*log5*log5

= s*t*t = st²

Therefore the expression is st²

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The position of an object is determined as  (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j.

None of above is the correct answer.

The position of an object is defined as the product of velocity of the object and the time of motion of the object.

So to obtain the position of the particle, we will integrate the velocity of the particle as follows;

The velocity is given as;

v(t) = t²i/(1 + t³)  +  sin 2t j

Integrate i component as;

Let u = 1 + t³

du/dt = 3t².

dt = du / (3t²)

∫ t²/(1 + t³) dt =∫ (1/u) x (t²/3t²) du

= (1/3) ∫ (1/u) du

= (1/3) ln |u| + C

= (1/3) ln|1 + t³| + C

Integrate j component as follows;

∫ sin(2t) dt = - ¹/₂cos(2t) + C

∫ v(t) dt = (1/3) ln|1 + t³|)i - ¹/₂cos(2t)j

So finally, we add the initial position of 2i + 3j, as follows;

x = (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j

So none of the options matches this solution, the closet is B.

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In the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.

We have a right triangle with an unknown angle θ (measured in degrees), the opposite side length of 16 units, and a hypotenuse length of 21 units. We're given the formula for calculating the sine of an angle:

sin(θ) = opposite / hypotenuse

By substituting the values we know, we get:

sin(x) = 16 / 21

x = sin⁻¹(16 / 21)

x ≈ 49.6°

Therefore, in the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.

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The surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm is 507 cm².

We know that the area of the square base is 169 cm², so we can solve for the length of one side.

To find the length, we use the formula for the area of a square:

Area = length x length

169 = length²

Taking the square root of both sides, we get:

length = √169

        = 13 cm

Now we can use the formula for the surface area of a square pyramid:

Surface area = area of base + (1/2)perimeter of base x slant height

The perimeter of the base is 4 times the length of one side, so it is:

perimeter of base = 4 x length = 4 x 13 cm = 52 cm

Plugging in the values we have:

Surface area = 169 cm² + (1/2)(52 cm)(13 cm)

Surface area = 169 cm² + 338 cm²

Surface area = 507 cm²

Therefore, the surface area of the right square pyramid is 507 cm².

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The equation is writen in the quatradtic form as [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]

Quadratic equation is of the form

[tex]f(x) = ax^2 + bx + c[/tex]

the transformations

Reflect it in the x-axis: To reflect a function in the x-axis, we change the sign of the function.

[tex]g(x) = -ax^2 - bx - c[/tex]

Shift it horizontally to the right by 2 units: Our function becomes:

[tex]g(x) = -a(x - 2)^2 - b(x - 2) - c[/tex]

Stretch the function by a factor of 3: To stretch a function vertically, we multiply the function by the stretch factor, k.

[tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]

So, the final transformed quadratic function is: [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]

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The value of ||w - u || = 3 sqrt 2

Given:

u = 2i - 3j

w = - i - 6j

w - u = ( - i - 2i ) + ( - 6j - (-3j))

w - u = - 3i - 3j

|| w - u || = sqrt [ - 3^2 + - 3^2 ]

||w - u || = 3 sqrt 2

The concept of a radical in mathematics refers to the symbolic representation (√) of finding the roots of an expression or a number.

The widely known and frequently used kind is the square root (√), which reveals a positive value that, when multiplied by itself at once, generates the radicand.

Other forms may include cube roots (∛) or fourth roots (∜). To simplify radicals, one can factor out those factors within it that result in perfect cubes or squares from their corresponding radicands.

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The time required for the amount to double and triple are 19.53 and 30.95 respectively.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]f(t) = P_{0}e^{rt}[/tex]

Where:

Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;

[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]

Taking the natural log (ln) of both sides of the equation, we have:

0.0355t = ln(2)

Time, t = 19.53

Similarly, a function for the time required for the amount to triple is given by;

[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]

Time, t = 30.95

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The solution is, Option 4 is correct., the graph represents the following system of inequalities.

Explanation:

We are given two inequality y<-x-4 and y>2x-3.

We need to choose correct graph from given choices.

First we draw the graph of each equation

Equation 1: y<-x-4

We draw the graph using slope intercept form.

Slope=-1 and y-intercept (0,-4)

Test point (0,0). Put (0,0) into equation 1 y<-x-4

We get . This is false statement. Graph will shade away from point (0,0).

Equation 2: y<2x-3

We draw the graph using slope intercept form.

Slope=2 and y-intercept (0,-3)

Take test point (0,0). Put (0,0) into equation 2, y>2x-3

We get . This is true statement. Graph will shade towards the point (0,0).

Please take a look attachment for the graph.

Option 4 is correct.

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complete question:

Which graph represents the following system of inequalities?

y < -x - 4

y > 2x - 3

The expected profit for the first mall is $1,750,000

Given data ,

Let the probability be represented as A and B

Now , For Event A:

Probability of success at the first mall (P(A)) = 2 (given)

Profit if successful (P(A) * Profit | Success) = 2 * $1,050,000 = $2,100,000

Loss if unsuccessful (Loss | Failure) = -$350,000

For Event B:

Probability of success at the second mall (P(B)) = unknown (to be calculated)

Profit if successful (P(B) * Profit | Success) = P(B) * $700,000

Loss if unsuccessful (Loss | Failure) = -$210,000

Expected Profit for Event A = P(A) * Profit | Success + (1 - P(A)) * Loss | Failure

Expected Profit for Event A = 2 * $1,050,000 + (1 - 2) * -$350,000

Expected Profit for Event A = $2,100,000 - $350,000

Expected Profit for Event A = $ 1,750,000

Hence , the profit is $ 1,750,000

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Answer:

The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.

The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.

Step-by-step explanation:

The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.

The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.

The value of the radius of the cone is, 5 inches

We have to given that;

The volume of a cone is 35π cubic inches.

And, the height is 4.2 inches.

Now, We know that;

Volume of cone is,

V = πr²h/3

Hence, We get;

35π = π × r² × 4.2 / 3

105 = 4.2r²

r² = 105/4.2

r² = 25

r = 5 inches

Thus, The value of the radius of the cone is, 5 inches

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The simple interest after 4 years with the given principal and rate is $120.

Given that, principal =$600, rate=5% and time=4 years.

We know that, simple interest=(Principal×Rate×Time)/100.

Simple interest = (600×5×4)/100

= $120

Therefore, the simple interest after 4 years with the given principal and rate is $120.

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Answer:

x= -18

Step-by-step explanation:

-2/3x + -21/4 = 27/4

-8x-63=81

-8x-63+63=81+63

-8x=144

-8x/-8 = 144/-8

x=-18

The variables to the parallelogram OPQR are;

1. coordinates of points M is (1, 2.5)

2. The length of PQ is 4

3. The length of QR is 5.4

4. The length of PM is 3.9

5. The length of OM is 2.7

6. The perimeter of the parallelogram OPQR is approximately  18.8

7. if m ∠QMR = 120° m ∠ QMP = 60°

8. If m ∠ QRO = 80°  m ∠ROP =  100°

To calculate for every listed length of parallelogram OPQR it will be helpful to list all the coordinate for this diagram and they are;

O (0, 0)

p (-2, 5)

R (4, 0)

Q (2, 5)

To find for M, we could just get it from the diagram by looking at the points for x and then y. This is (1, 2.5). You can also calculate it like this

Mx = (Px + Rx)/2 = (-2 + 4)/ 2 = 2/2 = 1

My = (Py + Ry)/2 = ( 5 + 0)/2 = 2.5

To calculate for the length of any side, we say

LPQ = √(Qx -Px)² + (Qy - Py)² = √(2 - -2)² + (5-5)² = √8 = 4

LQR = √(Rx -Qx)² + (Ry - Qy)²

LPM = √(Mx -Px)² + (My - Py)²

LOM = √(Mx -Mx)² + (Oy - My)²

if m∠QMP = 180° - m∠QMR = 180° - 120° = 60°

The question below is as seen in the pictures provided.

The diagonals of parallelogram OPQR intersect at point M.

What are the coordinates of points M?

Find PQ

Find QR

Find PM

Find OM

Find permeter of parallelogram OPQR

if m ∠QMR = 120° what is m ∠ QMP

If m ∠ QRO = 80°  what is m ∠ROP

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Answer:

D

Step-by-step explanation:

A dot plot would be the best representation for this data, because the number of scores reported individually is small and a dot plot is ideal for displaying individual data points.

Answer:translation, 12^2+35^2, squre root the answer, thgen add it to 12

Step-by-step explanation:

The figures that complete the two-way frequency table are attached accordingly.

Let represent the table like this:


                      Chcken       Veggie             Tuna               Total

Seltzer            38                 45                     A                    90
Iced Tea           B                  C                        D                    E
Total                 75                 F                       G                    160

NOte that:

A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2

D=11

Thus C = 22
F = 45 + C
F = 45 + 22
F = 22


G = A + D = 18

?thus, the completed two-way frequency table is:


                    Chcken       Veggie             Tuna               Total

Seltzer            38                 45                     7                    90
Iced Tea           B                  22                     11                    70
Total                 75                 67                    18                    160

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The area of the entire space is 38.57 units².

We have,

From the figure,

Total area.

= Semicircle + Rectangle + Trapezium + Rectangle

Now,

Semicircle:

Radius = 2 units

Rectangle:

Length = 4 units

Width = 3 units

Trapezium:

Parallel sides = 5 units and 3 units

Height = 1 unit

Rectangle:

Length = 2 units

Width = 5 units

Now,

Area of the entire space.

= πr² + 4 x 3 + 1/2 x 1 x (5 + 3) + 2 x 5

= 22/7 x 2 x 2 + 12 + 1/2 x 1 x 8 + 10
= 88/7 + 12 + 4 + 10

= 12.57 + 12 + 4 + 10

= 12.57 + 26

= 38.57 units²

Now,

1 unit = 7 feet

So,

= 38.57 X 7² feet²

= 1889.93 feet²

Thus,

The area of the entire space is 38.57 units².

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The probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train is 0.5 or 50%.

To calculate the probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train from the terminal to the rental car and long term parking center, we need to find the probability of each event separately and then add them together.

The probability of waiting less than 2 minutes can be calculated as the ratio of the time interval from 0 to 2 minutes (2 minutes) to the total time interval of 8 minutes;

P(waiting less than 2 minutes) = (2 minutes) / (8 minutes) = 0.25

The probability of waiting more than 6 minutes can be calculated as the ratio of the time interval from 6 to 8 minutes (2 minutes) to the total time interval of 8 minutes;

P(waiting more than 6 minutes) = (2 minutes) / (8 minutes) = 0.25

Now, to find the probability of waiting less than 2 minutes or more than 6 minutes, we can add the two probabilities together;

P(waiting less than 2 minutes or more than 6 minutes) = P(waiting less than 2 minutes) + P(waiting more than 6 minutes)

= 0.25 + 0.25

= 0.5

Therefore, the  probability of waiting less than 2 minutes or more than 6 minutes will be 0.5 or 50%.

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The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

We have,

To calculate the cost of leasing the car, we first need to determine the total amount paid over the lease term:

= (Monthly payment x Number of months) + Down payment

= ($473 x 60) + $2,420

= $28,780

To determine the cost of buying the car, we first need to calculate the total loan amount:

= Cost of car - Down payment + Residual value

= $34,000 - $5,000 + $16,400

= $45,400

Now,

Total loan cost = (Monthly payment x Number of months) + Down payment

Total loan cost = ($623 x 60) + $5,000

Total loan cost = $42,380

So,

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

To determine which option is less expensive, we can subtract the cost of leasing from the cost of buying:

Cost of buying - Cost of leasing = $42,380 - $28,780

Cost of buying - Cost of leasing = $13,600

So,

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

Thus,

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

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The  vector-valued function is continuous at t=2,

are

A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

We are required  to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the  vector-valued function is continuous at t=2.

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Jay's score for the last quiz is 14.

Let's use the formula for finding the mean:

Mean = (Sum of all scores) / (Number of scores)

We can rearrange this formula to solve for the unknown score:

Unknown score = (Mean x Number of scores) - (Sum of all other scores)

Given that Jay's mean score for four quizzes is 9, we have:

Mean = 9

Number of scores = 4

Jay's scores for the first three quizzes are 8, 5, and 9. The sum of these scores is:

Sum of first three scores = 8 + 5 + 9 = 22

Using the formula above, we can find Jay's score on the fourth quiz:

Unknown score = (Mean x Number of scores) - (Sum of all other scores)

Unknown score = (9 x 4) - 22

Unknown score = 36 - 22

Unknown score = 14

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