Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?

Answer:

segment I'm and segment ad

Answer:

The answer is B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Two congruent chords in a circle have the same distance from the center.

If two chords in a circle are congruent, then they are the same distance from the center of the circle .

The properties of Equal Chords of a Circle are:

According to the question

If two chords in a circle are congruent, then they are

Now,

By properties of Equal Chords of a Circle

The equal chords will be equal distance from the center of the circle .

Hence, If two chords in a circle are congruent, then they are the same distance from the center of the circle .

To know more about  properties of equal chords of a circle here:

https://brainly.com/question/14539317

#SPJ3

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

Learn more about BODMAS rule here:

https://brainly.com/question/16738857

#SPJ4

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

Answer:

  -5

Step-by-step explanation:

The value of x that gives f(x) = 3 is -5.

  [tex]f^{-1}(3)=-5[/tex]

Step-by-step explanation:

y = 0.8x+ 7.2   ..........(1)

20x + 32y = 48 .........(2)

Substitute (1) in (2)

20x +32*(0.8x+7.2) = 48     expand

20x + 25.6x+230.4 = 48     add

45.6x+230.4 = 48                transpose and simplify

45.6x = 48-230.4 = -182.4

x = -182.4 / 45.6

x = -4

Answer:

x=-4, Y=4

Step-by-step explanation:

20x+32(0.8x+7.2)=48

45.6x =48-230.4

x=-4

substitute x=-4 in y eqn

y=-3.2+7.2

y=4

Answer:

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Step-by-step explanation:

Given that:

[tex]sin(A)=-\dfrac{20}{29}\\cos(B)=\dfrac{12}{13}[/tex]

A is in 3rd quadrant and B is in 1st quadrant.

To find: sin(A+B)

Solution:

We know the Formula:

1. [tex]sin(A+B) = sinAcosB+cosAsinB[/tex]

2. [tex]sin^{2} \theta+cos^{2} \theta=1[/tex]

Now, let us find the values of cosA and sinB.

[tex]sin^{2} A+cos^{2} A=1\\\Rightarrow (\frac{-20}{29})^2+cos^{2} A=1\\\Rightarrow cos^{2} A=1- \dfrac{400}{941}\\\Rightarrow cos^{2} A=\dfrac{941-400}{941}\\\Rightarrow cos^{2} A=\dfrac{441}{941}\\\Rightarrow cos A=\pm \dfrac{21}{29}[/tex]

A is in 3rd quadrant, so cosA will be negative,

[tex]\therefore cos A=-\dfrac{21}{29}[/tex]

[tex]sin^{2} B+cos^{2} B=1\\\Rightarrow sin^{2} A+(\frac{12}{13})^2=1\\\Rightarrow sin^{2} B=1- \dfrac{144}{169}\\\Rightarrow sin^{2} B=\dfrac{169-144}{169}\\\Rightarrow sin^{2} B=\dfrac{25}{169}\\\Rightarrow sinB=\pm \dfrac{5}{13}[/tex]

B is in 1st quadrant, sin B will be positive.

[tex]sinB =\dfrac{5}{13}[/tex]

Now, using the formula:

[tex]sin(A+B) = sinAcosB+cosAsinB\\\Rightarrow -\dfrac{20}{29} \times \dfrac{12}{13}-\dfrac{21}{29}\times \dfrac{5}{13}\\\Rightarrow -\dfrac{20\times 12+21\times 5}{29\times 13} \\\Rightarrow -\dfrac{240+105}{29\times 13} \\\Rightarrow -\dfrac{345}{377}[/tex]

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Answer: 5/26

Step-by-step explanation: 6/13 x 5/12

Answer:

49 people

Step-by-step explanation:

Take the amount of candy and divide by the amount in a serving

2 3/4 ÷ 1/18

Change to an improper fraction

(4*2+3)/4 ÷ 1 /18

11/4 ÷ 1/18

Copy dot flip

11/4 * 18/1

198/4

49.5

Round down since people do not want half a serving

49 people

Answer: 2 29/36

Step-by-step explanation:

Answer:

to find the dimension I would get 3.6/4.5=x/70 amd u get 3.6*70=4.5x and u get 252=4.5x and x=56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the width of logo printed on canvas = x inches

Dimensions are in proportion

[tex]\frac{70}{x}=\frac{3.6}{4.5}\\[/tex]

Cross multiply

70 * 4.5 = x * 3.6

x * 3.6 = 315

[tex]x=\frac{315}{3.6}\\\\=\frac{3150}{36}\\\\x=87.5inches[/tex]

Answer:

The discount is 36 dollars

The sale price is 44 dollars

Step-by-step explanation:

First find the discount by multiplying the original price by the discount rate

80*45%

Change to decimal form

80*.45

36

The discount is 36 dollars

The sale price is the original price minus the discount

80-36

44

The sale price is 44 dollars

Answer:

[tex]\dfrac{65}{81}[/tex] or 80.25%

Step-by-step explanation:

Number of blue Marbles = 4

Number of Red Marbles = 5

Total Number of marbles =4+5=9

[tex]P(B)=\dfrac49\\\\P(R)=\dfrac59[/tex]

In the experiment, two marbles are chosen one after the other with replacement.

The possible outcomes are: BB, BR, RB and RR

The probability of getting at least 1 red

=P(BR or RB or RR)

=P(BR)+P(RB)+P(RR)

[tex]=\left(\dfrac49\times\dfrac59\right) + \left(\dfrac59\times\dfrac49\right)+\left(\dfrac59\times\dfrac59\right)\\\\=\dfrac{20}{81}+\dfrac{20}{81}+\dfrac{25}{81}\\\\=\dfrac{65}{81}[/tex]

Expressed as a percentage, we have:

[tex]\dfrac{65}{81}\times100=80.25\%[/tex]

The probability of getting at least 1 red is 80.25%.

Answer:

1/5

Step-by-step explanation:

Gradient is another word for slope. To find the gradient, we have to use a formula.

The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer:

(A⋂B) U (A⋂C) = {d, e}

Step-by-step explanation:

U= {a,b,c,d,e,f,g,h}

A = {b,d,e}

B = {a,d,e}

C={a,c,f,g,h}

=> A⋂B = {d,e}

=> A⋂C = ∅

=> (A⋂B) U (A⋂C) = {d, e}

Answer:

(A) 1199.168

(B) 1503.372

(C) 159.17728

Step-by-step explanation:

(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.

Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 30th percentile,

X = 1261 + (-0.524)(118)

X = 1261 - 61.832 = 1199.168

(B) The number of chocolate chips that make up the middle 98% of chips in the bag is

X = 1261 + (2.054)(118)

X = 1261 + 242.372 = 1503.372

(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.

This is within 1.34896 standard deviations of the mean.

IQR = (1.34896)(118)

IQR = 159.17728

Answer:

B is a function of A

Step-by-step explanation:

If you do something to another thing, it is a function of that.

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]

I hope this helps!

Answer:

P(0,4)

Q(2,0)

Step-by-step explanation:

We khow that both P and Q are lying in the line : 4x+2y=8

Answer:

Step-by-step explanation:

The independent variables are the input values which are not dependent on the other value.

The dependent variables are the output values whose values depends on the value of some other number.

The independent variable in this case is the data on the set of distances she measured out.

The dependent variable in this case is the the time (measured by the stopwatch) it takes for the ball to roll.

The control variable in this case study is the size of ball, slope of hill, weight of ball etc.

Answer:

Step-by-step explanation:

hello

[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]

hope this helps

Answer:

3

Step-by-step explanation:

12 is divisible by: 1, 2, 3, 4, 6, 12

Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.

Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.

Answer:

с.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g

Step-by-step explanation:

The given options

a.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to g 70

b. if yt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/1

с.i fyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g  

d. if yt grows at a rate of g percent per year, then the number of years it takes yt to triple is approximately equal to 70/g  

е.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is exactly equal to 70/g

The rule of 70 refers to the time period in which the investment you make is doubled. It analyzed that in how many years it took for doubling the amount by considering the specific rate of return  

Now we go through the options and as we can see that the option c meets the requirement as the g represents the growth rate and it fits to the above explanation

Step-by-step explanation:

36 ÷ (4 x 3)

36 ÷ 12

= 3

54 - 48 - (16 ÷ 4)

54 - 48 - 4

= 2

So first one is greater

Answer:

y=15; y=5

Step-by-step explanation:

y=x2+2x

plug in x as 3:

y=3 2+ 2*3

y=9+6

y=15

Next problem:

y=x3-3

plug in x as 2:

y=2 3-3

y=8-3

y=5

Answer:

7.2

Step-by-step explanation

plug the values in in the distance formula

the points are -3,3 and 1, -3

sqrt((-3-1)^2+(3-(-3))^2)

sqrt(16)+(36)

sqrt(52)

approximately 7.2

Answer:

its its 12.

Step-by-step explanation:

=8÷4×6+2-2

=2×6+2-2

=12+2-2

=14-2

=12 is answer..

Answer:

12

Step-by-step explanation:

8÷4×6+2-2

=2×6+2-2

=12+2-2

14-2

=12