Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest monthly, and to calculate what annual interest rate he needs, he is using the rule of 72. (3 points: Part I – 1 point; Part II – 1 point; Part III – 1 point)

Part I: What is the rule of 72? To represent the annual interest rate, use r.








Part II: What equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires?








Part III: What annual interest rate does Miguel need to double his money by the time he retires?

Answer:

(d)  60°

Step-by-step explanation:

Theorems

Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

⇒ (a + 20) + (a + 10) = (a + 90)

⇒ a + 20 + a + 10 = a + 90

⇒ 2a + 30 = a + 90

⇒ 2a + 30 - a = a + 90 - a

⇒ a + 30 = 90

⇒ a + 30 - 30 = 90 - 30

⇒ a = 60

Answer:

a = 60

Step-by-step explanation:

→ Find the sum of all the angles

2a + 30 + 90 - a = 180

→ Collect the a terms

a + 120 = 180

→ Find a

a = 60

Suppose that a probability is approximated to be zero based on empirical results, this does not mean that the event is​ impossible.

The likelihood that an event will occur is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

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Answer:

m∠C = 38°  (nearest whole number).

Step-by-step explanation:

To find the missing angle, use the Sine Rule.

Sine Rule (for angles)

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

where:

Given:

To find m∠C, substitute the given values into the formula and solve for C:

[tex]\implies \sf \dfrac{\sin 53^{\circ}}{18}=\dfrac{\sin C}{14}[/tex]

[tex]\implies \sf \sin C= \dfrac{14 \sin 53^{\circ}}{18}[/tex]

[tex]\implies \sf C= \sin^{-1} \left( \dfrac{14 \sin 53^{\circ}}{18}\right)[/tex]

[tex]\implies \sf C= 38.40096301...^{\circ}[/tex]

Therefore, m∠C = 38°  (nearest whole number).

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Answer:

y = 49.2x+400

Step-by-step explanation:

He deposits 3% of his monthly pay = 0.03*1640 = $49.2 every month = 49.2x

He put $400 when he opened the account so that needs to be added in = 49.2x+400

The length of the rafter as detailed in the question is approximately; 22.80 yards

The formula for Pythagoras theorem is;

a² + b² = c²

where;

a and b are adjacent and opposite sides of the triangle formed

c is the hypotenuse

Now, a rafter is a sloped member of a roof structure. Thus, if the rafter is raised to a height of 18 yeards, it means that is the vertical height of the top of the rafter to the bottom of the kingpost.

Now, if half the length run is 14 yards, it means that half of the tie beams is 14 yards. Thus, from the base of the rafter to the center of the tie beams is 14 yards. Thus, we will use Pythagoras theorem to find the length of the rafter.

c = √(14² + 18²)

c = √520

c = 22.80 yards

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Answer:

y=-3x-2

Step-by-step explanation:

The slope-intercept form is y=mx+b

where m is slope and b is y-intercept.

Substitute m=-3 and point (x,y)=(1,-5) into the equation:

-5=-3(1)+b

-5=-3+b

b=-5-(-3)=-5+3=-2

Therefore, the required equation:

y=-3x-2

The minimum point on the graph of the equation y=f(x-5) is (-6, -3)

The initial minimum is given as:

(-1, -3)

The transformation y = f(x - 5) means that:

(x, y) = (x - 5, y)

So, we have:

(x, y) = (-1 - 5, -3)

Evaluate

(x, y) = (-6, -3)

Hence, the minimum point on the graph of the equation y=f(x-5) is (-6, -3)

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Answer:

24 people

Step-by-step explanation:

I pizza will feed 3 people

There are 8 pizza's

8 x 3 = 24

The angle is the cosine inverse function because base over hypotenuse. Then the angle will be 37°.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The triangle with base of 4 units and hypotenuse of 5 units.

We know that the angle is given by the cosine inverse function because base over hypotenuse. Then we have

⇒ cos⁻¹ (4/5)

Then the angle will be

⇒ 36.869 ≈ 37°

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The equation of the parabola is y - 1 = (2/3) * (x - 3)².

The general equation of a parabola is: y-k = a(x-h)²

(h, k) - Coordinates of the vertex.

a - Vertex constant

Here:

(h, k) = (3, 1) and (x, y) = (0, 7).

So,

7 - 1 = C · (0 - 3)²

6 = 9 · C

C = 2/3

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Answer:

99.93 [tex]m^{2}[/tex]

Step-by-step explanation:

1.  The area of a circle is defined by the equation: A = [tex]\pi r^{2}[/tex]

2. We can plug in the radius and solve the equation: A = [tex]\pi *5.64^{2}[/tex]

3. A = π * 31.8096

4. A = 99.932

5. A = 99.93

Answer:

(i) -34° C.
(ii) The temperature had fallen by 11° C.

Step-by-step explanation:

(i) As it's a negative number its like we are adding it so 23 + 11 = 34 and as it is a negative number it would be -23 - 11 = -34 which makes it -34° C.

(ii) We know that the temperature now is -45° C, we need to find out how much the temperature had fallen in the 4 hours which had passed. So what we do is essentially add it considering its a negative number so we add -34 by 11 which equals -45. We do this so we can find out how much the temperature had dropped within the 4 hours and as we know that we needed to add 11 to the previous temperature (-34° C) it means that the temperature has dropped by 11° C.

Based on the inscribed angle theorem, the value of x is: 126°.

The inscribed angle theorem states that, the measure of inscribed angle (63 degrees) equals half of the measure of central angle (x).

Thus, we would have:

63 = 1/2(x)

2(63) = x

126 = x

x = 126°

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Answer:

the answer is 0.5

Step-by-step explanation:

The answer for this is 0.5

Answer:

Part A) B

Part B) D

Step-by-step explanation:

Total sweets = 10

Red = 4

Green = 2

Yellow = 3

Purple = 1

A = 2/10 = 1/5

B = 3/10

C = 4/10 = 2/5

D = 1

Yellow sweets = 3

Total = 10

Probability = yellow/total

Hence, B shows the probability of showing a yellow sweet.

Sweets that are not orange = 10 (All sweets are not orange)

Total = 10

Probability = sweets that are not orange / total

Probability = 10 / 10

Hence, D shows the probability of choosing a sweet that is not orange.

[tex]\rule[225]{225}{2}[/tex]

Answer:

There could be 0, 2, or 4 complex solutions

Step-by-step explanation:

The Fundamental Theorem of Algebra states that any polynomial with n degree will have n solutions So since the degree of the polynomial you provided has a degree of 4, that means there are 4 possible solutions. This question specifically asks for complex zeroes. Complex zeroes come in conjugate pairs, so that means if you have one complex zero, there is another complex zero which is it's conjugate. For this reason, there can only be an even number of complex zeroes. And since there's 4 possible solutions, There could be 0, 2, or 4 complex solutions

The slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the given containing ordered paid A(2,-5) and B(-2,6) is:

Slope = 6+5/-2-2 = 11/-4

Hence, the slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.

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An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplification of the given expression can be done as,

[tex]\dfrac{(6x)^2+x-7}{12x^2+14x}\\\\\\=\dfrac{36x^2+x-7}{12x^2+14x}\\\\\\=\dfrac{(6x)^2+x-7}{2(6x^2+7x)}[/tex]

Hence, the simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].

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Using proportions, considering the given ratio, Isabella gets [tex]\frac{4}{7}[/tex] of the total reward.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The ratio of Isabella and Aiden is 4:3, which means that out of 4 + 3 = 7 items, Isabella gets 4 and Aiden gets 3, hence the fraction is given by:

[tex]\frac{4}{7}[/tex].

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Directed numbers are numbers that have either a positive or negative sign, which can be shown on a number line. Therefore, point F is Fifteen-halves of line segment DE.

A number line is a system that can show the positions of positive or negative numbers. It has its ends ranging from negative infinity to positive infinity. Thus any directed number can be located on the line.

Directed numbers are numbers with either a negative or positive sign, which shows their direction with respect to the number line.

In the given question, the distance between points D and E is 9 units. So that dividing 9 units in the ratio of 5 to 6, we have;

[tex]\frac{5}{6}[/tex] x 9   = [tex]\frac{45}{6}[/tex]

          = [tex]\frac{15}{2}[/tex]

Therefore, the location of point F, which partitions the directed line segment from d to E into a 5:6 ratio is    [tex]\frac{15}{2}[/tex]. Thus the answer is Fifteen-halves.

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Answer:

1/11

Step-by-step explanation:

Got it right on assignment

Answer:

456 [tex]cm^{2}[/tex]

Step-by-step explanation:

Find the height of the trapezoid first (QR):

[tex]\sqrt{37^{2} -35^{2} }[/tex] = 12

QR = 12

Area:

[tex]\frac{a+b}{2}[/tex] × h = [tex]\frac{35+41}{2}[/tex] × 12

           = 456 [tex]cm^{2}[/tex]

Answer:

The graph has random dots all over

Step-by-step explanation:

Considering the given quadratic function, it is found that it will take 4.05 seconds for the frog to land on the ground.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The height after t seconds is given by:

h(t) = -16t² + 64t + 3.

it hits the ground when h(t) = 0, hence:

-16t² + 64t + 3 = 0

16t² - 64t - 3 = 0.

The coefficients are a = 16, b = -64, c = -3, hence:

Time has to be positive, hence the frog lands on the ground after 4.05 seconds.

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Answer:

A. 36

Step-by-step explanation:

Because the two angles at the bottom of both the triangles are congruent, the two triangles are similar. Therefore, the corresponding side lengths of the triangles must be proportional to each other

if the area of a triangle is hb/2,

(with h=length of height, b=length of base)

the height of the first triangle is:

25 = 10h/2

50 = 10h

h=5

you can write ratios representing the proportions of the two triangles:

5/x = 10/12 (with x=height of second triangle)

x=6

then find the area of the second triangle with the height (6) and base (12)

(6*12)/2 = 36

The expression that represents the given algebraic tiles is 2x² + 6x + 6

An equation is an expression that shows the relationship between two or more numbers and variables.

The expression for the given algebraic tiles is:

Total = x + x + x + 1 + 1 + 1 + x² + x + x + x + 1 + 1 + 1 + x² = 2x² + 6x + 6

The expression that represents the given algebraic tiles is 2x² + 6x + 6

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Answer: 3.8395025e+12

Lol

3839502493910

Step-by-step explanation:

you will multiple the 6 and the 7 digits and the other digits

Answer:

This is a educated guess, but x is 80 and y is 100.

Step-by-step explanation:

My logic here is that the triangles are the same because of all the congruent lines and stuff. But from there, you know that both the right and the left side are 40 degrees. You know the total degree of a triangle is 180 so 180 - 40 - 40 is 100. So the final angle is 100. If you look at x, its on the outside, but on a line. If you can imagine a circle, its half, so its a 180 degrees total. Then its 180 = x + 100. So x is 80. And then by that same logic its y = 100.

Answer:

B. 1

Step-by-step explanation:

Please see attachment.

Hope this helps!

If not, I am sorry.

Answer:

z= [ 5] VI

that is my answer

Answer: Likely May through August 2023

Step-by-step explanation: It really depends on the college.