Suppose Amanda wants to have $800,000 in her IRA at the end of 30 years. She chooses to invest in an annuity that pays 5% interest, compounded annually. How much of IRA is interest at the end of 30 years?

Answer:

  x^4 +2 +x^-4

Step-by-step explanation:

The square of a binomial is a form worthy of memorization.

  (a +b)² = a² +2ab +b²

Here, you have a binomial with a=x² and b=1/x². Using these values in the pattern, we have ...

  [tex]\left(x^2+\dfrac{1}{x^2}\right)^2=(x^2)^2+2(x^2)\dfrac{1}{x^2}+\left(\dfrac{1}{x^2}\right)^2\\\\=\boxed{x^4+2+\dfrac{1}{x^4}}[/tex]

Using proportions, it is found that the boat can go 6 m/s in still water.

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

In this problem, we have that:

He goes twice as fast down the river, hence:

v + 2 = 2(v - 2).

v + 2 = 2v - 4

2v - v = 2 + 4

v = 6.

The boat can go 6 m/s in still water.

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Answer:

  (d)  f(x) = -x²

Step-by-step explanation:

For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...

  f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)

  f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)

Of the offered answer choices, the only one with a vertex at the origin is ...

  f(x) = -x² . . . . . a=-1

The friend's probability of beating the next level on her first attempt are 22.5 percent.

Describe probability.

To forecast how likely occurrences are to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment.

This idea is used to discuss the probability or likelihood of an event happening.

The frequency of the number 8 is seven.

The frequency of the number 9 is 11.

The full list of frequencies is provided as

10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80

7 + 11 = 18

18/80 is the probability.

= 0.225 x 100

22.5 percent

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a) The fire is out of the reach of helicopter 1.

b) Only helicopter 3 can be sent to stop the fire.

We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:

The distance is found by the straight line distance formula, an application of Pythagorean theorem:

a) [tex]d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}[/tex]

[tex]d = \sqrt{4^{2}+9^{2}}[/tex]

[tex]d = \sqrt{97}[/tex]

d ≈ 9.849

The fire is out of the reach of helicopter 1.

b) Helicopter 2

[tex]d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}[/tex]

[tex]d = \sqrt{1^{2}+8^{2}}[/tex]

[tex]d = \sqrt{65}[/tex]

d ≈ 8.062

Helicopter 3

[tex]d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}[/tex]

[tex]d = \sqrt{7^{2}+3^{2}}[/tex]

[tex]d = \sqrt{58}[/tex]

d ≈ 7.616

Only helicopter 3 can be sent to stop the fire.

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the probability that the sample mean will be smaller than m = 22 is 0.02275.

For the given question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Here sample size, n = 4

mean, μ = 30

standard deviation, σ = 8

The probability that the sample mean will be smaller than m = 22 is

z = [tex]\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ z =[tex]\frac{22-30}{\frac{8}{\sqrt{4} } }[/tex]

⇒ z = [tex]\frac{22-30}{\frac{8}{2} }[/tex]

⇒ z = [tex]-\frac{8}{4}[/tex]

⇒ z = -2

Refer the Z table for p value,

Thus for P(z < -2) is 0.02275.

Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.

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#1

#b

#c

#f

#i

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

Binary to Decimal Conversion (Positional Notation Method)

For a binary number with 'n' digits:

For example, to convert the binary number 111001₂ into a decimal:

[tex]\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}[/tex]

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

[tex]=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)[/tex]

[tex]= 32+16+8+0+0+1[/tex]

[tex]= 57[/tex]

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

Question (a)

[tex]\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}[/tex]

Therefore, 11₂ = 3₁₀

Question (b)

[tex]\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}[/tex]

Therefore, 110₂ = 6₁₀

Question (c)

[tex]\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}[/tex]

Therefore, 111₂ = 7₁₀

Question (f)

[tex]\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}[/tex]

Therefore, 10011₂ = 19₁₀

Question (i)

[tex]\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181[/tex]

Therefore, 10110101₂ = 181₁₀

The measure of side c is 9 cm. The correct option is the last option 9 cm

From the question, we are to determine the measure of side c

From the law of sines, we have that

[tex]\frac{c}{sinC} =\frac{b}{sinB}[/tex]

From the given information,

b = 11 cm

B = 80°

C = 54°

Putting the parameters into the equation, we get

[tex]\frac{c}{sin54^\circ} =\frac{11}{sin80^\circ}[/tex]

[tex]c =\frac{11\times sin54^\circ}{sin80^\circ}[/tex]

c = 9.03647

c ≈ 9 cm

Hence, the measure of side c is 9 cm. The correct option is the last option 9 cm

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Answer:

Step-by-step explanation:

For the frequency distribution, count the numbers that satisfy each category.

79 to 83: 4 (81, 82, 83, 81)

84 to 88: 3 (87, 88, 86)

89 to 93: 7 (92, 93, 93, 93, 90, 90, 91)

94 to 98: 1 (97)

For the historagram, raise the bars at the bottom of the histogram to the numbers above (4, 3, 7, 1; in this order)

Answer:

Answer should be 15

Step-by-step explanation:

25 divided by 15 is 1.6666666667 so if use that multiply 9 you'll get 15.

Answer:

Step-by-step explanation:

A^2 + B^2=C^2

30^2 -25^2= 16.5

answer= 16.5

An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program: TRUE

Therefore, the statement "an integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program" is TRUE.

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Complete question:

An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program. TRUE or FALSE

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.

Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]

Lets simplify the equation:

[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]

Expression:

An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.

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Answer:

statement 1(one)

Step-by-step explanation:

For the expression to be equal to the original one, we have;

[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]

We are given the algebraic expression;

(5x² + 25x + 20)/(7x)

Now, looking at the numerator, a common factor to all terms is 5. Thus, we will factorize it out to get;

5(x² + 5x + 4) = 5((x + 1)(x + 4))

Now, we see that the expression that simplifies the algebra is given as;

[(x² + 2x + 1) * ( )]/[( ) * (7x² + 7x)]

Now, the numerator and denominator can be factorized to get;

[(x + 1)(x + 1) * ( )]/[( ) * 7x(x + 1)]

Thus, x + 1 will cancel out to get;

[(x + 1) * ( )]/[( ) * 7x]

For the expression to be equal to the original one, we have;

[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]

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The coefficient of (3y² + 9)5 is 15.

A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.

Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.

a₀ is the leading coefficient.

In the question, we are asked to identify the coefficient of (3y² + 9)5.

First, we expand the given expression:

(3y² + 9)5

= 15y² + 45.

Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.

Thus, the coefficient of (3y² + 9)5 is 15.

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If Angle A ≅ Angle T, then the triangles would be congruent by ASA

If Angle B ≅ Angle P, then the triangles would be congruent by AAS.

We are told that;

Sides AC and TQ are congruent.

Angles BCA and  PQT are congruent.

Thus, we can say that;

Side AC and side TQ are congruent.

Angle BCA and angle PQT are congruent too.

Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.

Lastly, if angle B were to be congruent to angle P,  it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.

The missing options are;

A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.

B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.

C) If all the angles are acute, then the triangles would be congruent.

D) If AngleC and AngleQ are right angles, then triangles would be congruent.

E) If BC ≅ PQ, then the triangles would be congruent by ASA.

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He has to sell in a month $26616.67.

Given that a local salesman receives a base salary of $975 monthly and he also receives a commission of 6% on all sales over $1200.

A numerical assertion wherein two articulations are delivered equivalent to each other is known as an algebraic condition.

Let the Sales amount be s.

We have:

Sales over 1,200 is written as

s-1200

6% is also 0.06  as a decimal,

so according to question, we have

0.06(s - 1200) + 975=2500

Now, we will apply the distributive property a(b+c)=ab+ac, we get

0.06s-0.06×1200+975=2500

Further, we want to simplify the left-hand side, we get

0.06s-72+975=2500

0.06s+903=2500

Furthermore, we will subtract 903 from both sides, we get

0.06s+903-903=2500-903

0.06s=1597

Now, we will divide both sides with 0.06, we get

0.06s/0.06=1597/0.06

s=26616.67

Hence, he have to sell in a month if he needed to have a monthly income of $2500 is $26616.67.

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Answer:

probability of all the four women chosen over people needed in a committee=4 over 4 =1

Answer:

The class and exam medians are almost the same.

Step-by-step explanation:

The median of a box-and-whisker plot is the line inside the box.

• As we can see, the medians of  class and median are very similar, both around 85. This is why the first option is correct.

•The second option is incorrect because the exam median is not much higher than the class median; the difference is very small.

• The third option is incorrect because exam does not have the lowest median. In fact, exam median is slightly higher than class median.

• The fourth option is incorrect because outliers do not affect the median.

Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

Answer: (8,10)

Step-by-step explanation:

To go from A to C, we go right 2 units and up 6 units.

So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.

Therefore, the answer is (8, 10).

Answer:

B. Yes, because it passes the vertical line test.

Step-by-step explanation:

Vertical line test - if a vertical line passes through more than one pone, the relation is not a function

Any vertical line will only pass through one point, so this relation is a function

The relation is a function because it passes the vertical line test

Answer:

The answer is B) b

Step-by-step explanation:

According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.

So d+(a+b)/2=d+b

(a+b)/2=b

a+b=2b

a=b

hope this helps <3

Answer:

B is the answer

Step-by-step explanation:

See below for the solution to each expression

Expression 1

The expression is given as:

(x-y)(y-z)(x+z)/(2x^2+4yz+6)

Expand the numerator

(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)

Further, expand the numerator

(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Evaluate the like terms

(x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Expression 2

The expression is given as:

4(x+y)(x-y)(y-x)

Apply the difference of two squares

4(x^2 - y^2)(y - x)

Expand the expressions in the brackets

4(x^2y - x^3 - y^3 + xy^2)

Open the bracket

4x^2y - 4x^3 - 4y^3 + 4xy^2

Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2

Expression 3

The expression is given as:

(√25+√9/2) + √21675

Take the square roots of 25, 9 and 21675

(5 +3/2) + 5√867

Evaluate the sum

13/2 + 5√867

Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867

Expression 4

The expression is given as:

(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z

Factor out 3 and 2 from the numerator

3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z

This gives

18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

The expression cannot be further simplified.

Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

Expression 5

The expression is given as:

(x^2+6x+5)/(x+2)(x+6)

Factorize the numerator

(x + 1)(x + 5)/(x + 2)(x + 6)

Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)

Expression 6

6) (xy/m) + (xm/y) - (m/x) = 63

Factor out x

x(y/m + m/y) - m/x = 63

Evaluate the sum

x(y^2 + m^2)/y - m/x = 63

Multiply through by xy

x^2(y^2 + m^2) - my = 63xy

Add my to both sides

x^2(y^2 + m^2)  = 63xy + my

The above implies that the variable x cannot be isolated from the equation

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[tex]\textbf{Heya !}[/tex]

basic math tips -»

"of" means multiply

[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]

multiply the numerators and denominators times each other -»

[tex]\sf{\cfrac{5}{10}}[/tex]

reduce:-

[tex]\sf{\cfrac{1}{2}}[/tex]

`hope it was helpful to u ~

Jake travel to the coffee shop by bike with speed of [tex]8mph[/tex] is  [tex]56mile[/tex] and when bike got a flat so Jake walked [tex]4mile[/tex]

How to find the speed by biking and walking ?

let [tex]b[/tex] = time spent biking

then   [tex]8-b[/tex] =time spent walking

Write distance equation

[tex]dist=speed *time[/tex]

So bike distance [tex]+[/tex] walk distance [tex]=60mile[/tex]

[tex]8b+4(8-b)=60\\8b+32-4b=60\\4b=60-32\\b=28/4\\\\b=7hrs[/tex]

Then [tex]8-7=1 hrs[/tex] spent walking.

For cross check the answer find that actual distance for each

[tex]8(7)=56mi\\4(1)=4mi\\-------\\total distance=60mile[/tex]

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Answer:

1. a = 32, c = 24

Step-by-step explanation:

a = c+8

a-20 = 3(c-20)

(c+8)-20 = 3c-60

c = 24

a = 24+8

a = 32

2. t = 15, j = 9

t-3 = 2(j-3)

t-3 = 2j-6

t = 2j-3

t + 2 + j + 2 = 28

(2j-3)+ 2 + j + 2 = 28

3j + 1 = 28

3j = 27

j = 9

t-3 = 2(9-3)

t-3 = 2(6)

t-3=12

t = 15

3. b=36, s=31

b = s + 5

b+s = 67

(s+5)+s = 67

2s+5 = 67

2s = 62

s = 31

b = 31+5

b = 36

4. 231

h + t + u = 6

(with h=hundreds digit, t=tens digit, u=units digit)

h = 2u

t = h+u

t = (2u) + u

(2u) + (2u +u) + u = 6

6u = 6

u = 1

h = 2

t = 3

the number is 231

5. 48

u = 2t

the 2-digit number is 10t+u

2(10t+u) = 10u+t+12

2(10t + 2t) = 10(2t) + t + 12

20t + 4t = 20t + t + 12

24t = 21t + 12

3t = 12

t = 4

u = 2*4

u = 8

the number is 48

Using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.

According to the question,

One cupcake weighs 3 1/2 ounces. In order to find the number of cupcakes are there in 28 ounce package.

1 cupcake = 7/2 ounces

x cupcakes = 28 ounces

28 = 7/2 * x [cross multiplication]

x = (28*2)/7     [Using division]

x = 8

Hence, using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.

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