Aaron just accepted a job at a new company where he will make an annual salary of $52000. Aaron was told that for each year he stays with the company, he will be given a salary raise of $3500. How much would Aaron make as a salary after 6 years working for the company? What would be his salary after t years?

So the range of probability that at least one bond will default next year is between 0% and 80%.

The probability that at least one of two events will occur is the sum of the probability of each event minus the probability that both events will occur. In this case, the probability that at least one bond will default is:

P(A or B) = P(A) + P(B) - P(A and B)

Where P(A) is the probability of bond A defaulting (50%), P(B) is the probability of bond B defaulting (30%), and P(A and B) is the probability that both bonds will default (which we don't know).

So the range of probability that at least one bond will default is:

P(A or B) = 50% + 30% - P(A and B)

The maximum possible probability of both bonds defaulting is (0.5 * 0.3) = 15% and the minimum possible probability of both bonds defaulting is 0%. Therefore, the range of probability that at least one bond will default is:

P(A or B) = 80% - 0% = 80%

So the range of probability that at least one bond will default next year is between 0% and 80%.

It's important to note that the above formula and the range of probability is based on the assumption of independence, i.e the events of Bond A defaulting and Bond B defaulting are independent and don't affect each other.

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It is possible to have a rational function where the denominator can have no zeroes and thus the function itself will have no singularity. Such a function will have no vertical asymptotes.

A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = x / (x - 3). The denominator has only one zero, x = 3.

Given, In a rational function, R(x): = P(x)/Q(x)

p/q is a form of rational function.

q is not zero since divisor cannot be 0.

If we divide any function by 0 the operation is considered as undefined.

A rational function has at most one horizontal or oblique asymptote, and possibly many vertical asymptotes.

First, factor both the numerator and the denominator. Then, cancel out any common factors. A common factor does not give rise to a vertical asymptote, but it does create a hole if the zero of the common factor is real. Next, find the zeros for all of the remaining factors in the denominator after canceling out the common factors. For each zero in the denominator, there will be a vertical asymptote at that zero.

Therefore, The simples example I can give you for such a rational function would the f(X) = X, defined over the real numbers.

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Answer:

By definition, if two angles are complementary, they both will add up to 90 degrees. Knowing this add 18 and (6d-6) together to equal 90.

18+(6d-6)=90

Subtract 18 from both sides, then add 6. This leaves you with 6d equal to 78. Divide by 6 to get 13.

(6d-6)=72

6d=78

d=13 degrees

Make sure of your answer. You know that d is 13, so plug it back into the equation to see if it equals 90 degrees.

18+6(13)-6=90

18+78-6=90

90=90

Answer: Amber has 50 pennies and 10 dime

Step-by-step explanation:

The number of pennies is represented by x, while the number of dimes is represented by y. This means that the statement, "there are five times as many pennies as dimes" can be written as x = 5.

The sum of the coins is $1.50, which can now be written as

0.01x + 0.1y = 1.50

0.01(5y) + 0.1y = 1.50

0.05y + 0.1y = 1.50

0.15y = 1.50

y = 10

Next up:

x = 5y

x = 5(10)

x = 50

Finally, we can conclude that Amber has 50 pennies and 10 dimes

I hope this helps!

The distance-time graphs for the given scenarios have been attached below. The solution has been obtained using distance-time function.

What is distance-time function?

The distance between a person and an object through time is described by distance-time functions. Depending on the kind of movement, a distance-time function may be linear or non-linear, increasing, decreasing, or constant. We need to tell where the object starts, what direction it moves in, how quickly it moves, and whether it is speeding up, slowing down, or travelling at a constant speed in order to explain a distance-time function.

a. The distance-time graph for this scenario is the first graph wherein the line is less steeper than the other graph because the speed is constant.

b.  The distance-time graph for this scenario is the second graph wherein the line is steeper than the first one because the speed is changing from slow to fast.

Hence, the distance-time graphs for the given scenarios have been obtained.

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The required value of x to satisfied the given condition is 1/5.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

We have,

3x (1 + 6) = (3 x 1) + ( 6x)​

3x(7) = 3 + 6x

21x = 3 + 6x

15x = 3

x = 1/5

Thus, required value of x is 1/5.

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In order to satisfy the requirement, x must be 1/5 of the desired value.

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Answer: depending on how much it cost

Step-by-step explanation:

Answer:

Depends on the pizza prices

From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given, In the diagram, ABCD is a square, and R, S, T, and U are the midpoints of the sides of ABCD. Also, RT is perpendicular to SU and SV are equals to VU.

Since, R, S, T, and U are midpoints, and since  RT is perpendicular to SU

in triangle DUT.

UD = TD

UD is also equal to VT  since  RT is perpendicular to SU

UD = TD = VT...(1)

And, From the Pythagorean theorem

UT = √(TD² + UD²)

In TRiangle BSR

BR = BS

BS is also equal to RV  since  RT is perpendicular to SU

BR = BS = RV...(2)

And, From the Pythagorean theorem

SR = √(BR² + BS²)

Since SV is equal to VU.

Thus, RV = VT

From equation 1 and 2

BR = BS = RV = UD = TD = VT

Therefore, From the SSS Property of the triangle, Both triangles BSR and DUT are congruent.

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Answer:

Step-by-step explanation:

78,500 x 0.02 = 1,570--year 1 raise

(78,500 + 1,570) x 0.02 = 1,601.4--year 2 raise

(78,500 + 1,570+ 1,601.4) x 0.02 = 1,633.428--year 3 raise

(78,500 + 1,570+ 1,601.4+1,633.428) x 0.02 = 1666.1--year 4 raise

(78,500 + 1,570+ 1,601.4+1,633.428+1666.1) x 0.02 = 1699.42--year 5 raise

just keep doing this till you get to year 10 and then add up the total of money gained to the initial salary

Answer:

1) False

2)True

3)True

4)False

Answer:

672

Step-by-step explanation:

1. Multiply the length, width, and height of the triangle.

14 x 12 x 8 = 1,344

2. Divide by 2.

1,344/2 = 672

Answer:

672 Feet^3

Step-by-step explanation:

Volume of a triangle = 1/2 (B)(H)(L)

B = base

H = height

L = length

I see you've found the numbers for B, H, and L so great start.

B = 12

H = 8

L = 14

So now its just plug and play

(12)(8) = 96

(96)(14) = 1344

And lastly (1/2)(1344) = 672 cubic feet

Answer: (0, -1)

Step-by-step explanation:

Hello! One method you can use to solve a system of equations is the elimination method.  Here are the steps to use the elimination method in this equation:

 -4y + x = 4               -4y - (-6y) = -4y + 6y = 2y, x -x = 0, 4 - 6 = -2
- (-6y + x = 6)
_________
2y = -2
__    __
2       2

y = -1

You now know that y = -1 for both lines to intersect.  Let's now find x using the substitution method.

Use the equation -4y + x = 4.  Substitute -1 for y in the equation.

-4(-1) + x = 4
4 + x = 4
-4      =  -4
x = 0.  

You now know that x = 0 and y = -1.  Coordinate pairs are represented as (x, y).  Substitute 0 in for x and -1 in for y.  Your answer is (0, -1).

The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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The measure of angle 8 in the figure is given as follows:

m < 8 = 27º.

Alternate interior angles happen when there are two parallel lines cut by a transversal lines.

The two alternate exterior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line.

The alternate interior angles for this problem are given as follows:

2 and 8.

They are congruent, hence the measure of angle 8 is given as follows:

m < 8 = 27º.

The diagram is given by the image presented at the end of the answer.

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The all the measurements that are equivalent to 48 centimeters are (a) 0.48 m and (c) 480 mm.  .

the number is 48 centimeter , we  have to express the number in various units ,

For (a)  and (d) ; we know the conversion that 100 cm = 1 m , so , 48 cm will be = 48/100 = 0.48m .

For (b) and (c) ; we know that 1 cm = 10 mm , so , 48 cm = 48 × 10 = 480 mm

For

For (e) , we know that 100000 cm = 1  km , so , 48 cm = 48/100000 km

= 0.00048 km .

Therefore , the equivalent measurements are (a) 0.48 m and (c) 480 mm.

The given question is incomplete , the complete question is

Select all the measurements that are equivalent to 48 centimeters.

(a) 0.48 m

(b) 4.8 mm

(c) 480 mm

(d) 4,800 m

(e) 48,000 km

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1. The product of 653.2 x 4.6 lie between A. Between 2,612 and 3,265.

2. The value of 147 x 3 will be B. 441

3. The product of 6.84 x 57 will be 389.88.

4. The number of plants in 7 gardens is A. 1652.

5. The value of 16 × 103 to nearest number is B. 1600.

6. The amount for 75 drinks is A. 223.50

7. The option that best describes the estimate for 1.2 x 1.2 is B. The answer will be greater than 1 because the decimals are greater than 1.

8. The product of 2,456 x 38 is B. 93328.

The product of 653.2 x 4.6 will be:

= 653.2 × 4.6

= 3004.72

The value of 147 x 3 will be:

= 147 × 3

= 441

The product of 6.84 x 57 will be:

= 6.84 × 57

= 389.88.

The number of plants in 7 gardens is:

= 236 × 7

= 1652.

5. The value of 16 × 103

= 16 × 103

= 1600 approximately.

The amount for 75 drinks is:

= $2.98 × 75

= $223.50

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The angles of the triangle are ∠Q=59°, ∠R=90°,∠S=31°.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle are less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As sum of all angles of triangles=180°

90+2x+33+5x-34=180

7x=90+1

x=13

Therefore,

                 ∠Q=59°, ∠R=90°,∠S=31°

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The range is 5 feet

The path of the rocket can be modeled by the equation

h(t) = -16t² + 80t

We know that the range of a projectile is nothing but the horizontal distance the projectile travels from the time it is launched to the time it comes back down to the same height at which it is launched.

To find the horizontal distance we find the distance between the points on the horizontal axis.

i.e., to find the value of t for which h(t) = 0

Let us assume that the value of equation h(t) = 0

h(t) = 0

-16t² + 80t = 0

t(-16t + 80) = 0

t = 0   OR   -16t + 80 = 0

t = 0   OR  -16t = -80

t = 0   OR  t = 5

So, the range would be,

R = 5 - 0

R = 5 feet

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The required number of each type of cycles are  25 bicycle and 10 tricycle.

Tricycles will offer better stability and assistance. They can also be applied in a wider variety of circumstances, such as therapy sessions for people with disabilities. The most common vehicle will be a bicycle because they are smaller, lighter, faster, more suited for off-roading, and more widely available.

The seats are counted by 1 for both tricycles and bicycles, so t + b has to equal 35. The only answer choice that has t + b = 35

t = 35 - b

And

3t + 2b = 80

3(35 - b) + 2b = 80

105 - 3b + 2b = 80

105 - b = 80

b = 25

Put value of b in t = 35 - b,we get

t = 35 - 25

= 10

Thus, There are 25 bicycle and 10 tricycle.

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Answer:

B.   (-∞,∞)

Step-by-step explanation:

Function is
[tex]f(x) = \frac{3}{4}\cdot \left|x-3\right|\:+\:1[/tex]

There are no bounds on this function.

x values can range from -∞ to +∞  (but will never reach infinity)

Therefore domain is:
- ∞  < x < ∞

which in interval notation is Option B

Step-by-step explanation:

First one is good, all you have to do is combine like terms

-28x and +4x are like terms because they both have X

Combining those is -28x+4x=+24x

Making #1 7+24x

Answer:

(Their all down there)

Step-by-step explanation:

Okie dokie so! Your answer for 17 is technically correct but you need to imply it further so it would be [tex]7-24x[/tex]

18. [tex]-2(-6+5k)-1[/tex]

do distributive property

[tex]12-10k-1[/tex]   combine like terms (12 and -1)

[tex]-10k+11[/tex]

19. [tex]6(v-5)+1\\[/tex]

do distributive property

[tex]6v-30+1[/tex]    combine like terms (-30 and 1)

[tex]6v-29\\[/tex]

20. [tex]10(n+5)-5n[/tex]

do distributive property

[tex]10n+50-5n[/tex]  combine like terms (10n and -5n)

[tex]5n+50[/tex]

21. [tex]-7(8+8x)-6x[/tex]

do distributive property

-[tex]56-56x-6x[/tex]   combine like terms (-56x and -6x)

[tex]-56-62x[/tex]

22. [tex]6(x-9)+5[/tex]

do distributive property

[tex]6x-54+5[/tex]  combine like terms (-54 and 5)

[tex]6x-49[/tex]

The variance of the ages of this population is equal to 28.33.

Mathematically, the mean for the ages of these siblings (mean age) would be calculated by using this formula:

Mean = [F(x)]/n

Total age, F(x) = 3 + 4 + 6 + 9 + 15 + 17

Total age, F(x) = 54.

Therefore, the mean age is given by:

Mean age = [F(x)]/n

Mean age = 54/6

Mean age = 9

Next, we would calculate the standard deviation by using this formula:

Standard deviation, SD = √(1/n × ∑(xi - u₁)²)

Standard deviation, SD = √(1/6 × [(3 - 9)² + (4 - 9)² + (6 - 9)² + (9 - 9)² + (15 - 9)² + (17 - 9)])

Standard deviation, SD = √(1/6 × [36 + 25 + 9 + 0 + 36 + 64])

Standard deviation, SD = √170/6.

Standard deviation, SD = 5.32

In Statistics, the standard deviation of a data set is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 5.32²

Variance = 28.33.

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Complete Question:

The ages of the siblings in a family are 3, 4, 6, 9, 15, 17. The variance of the ages of this population is?

The value of p from the equation 17.5 - 6.3p = 25 is 1.19

Algebraic expression can be defined as a mathematical expression that are variables, terms, factors, constants and coefficients.

These expressions are also composed of mathematical or arithmetic operations, which includes;

From the information given, we have that;

17.5 - 6.3p = 25

Now, let's take the following steps

collect like terms

-6.3p = 25 - 17.5

subtract the like terms

-6.3p = 7.5

Divide both by the coefficient of p, we get;

p = 7.5/-6.3

p = 1.19

Hence, the value is 1.19

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Complete question:

Solve for P please

17.5 - 6.3p = 25

Answer: -25

Step-by-step explanation:

For f(x) functions, all you do is plug in whatever value that is given in the parenthesis into x.

f(5) = -4(5) - 5

= -20 -5

= -25

Answer:

$337,807.321.

Step-by-step explanation:

every year has 4 quarters, so 19 years = 76 quarters, so it compounds 76 times = (1+5.7%)^76.  so punch into the calculator 1.057 then the "xy"button, then 76, it'll spit out 67.56146111  number. then hit times 5000.  which is $337,807.321.  power of compounding. More than a quarter million $$$.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 5.7\%\to \frac{5.7}{100}\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &19 \end{cases} \\\\\\ A = 5000\left(1+\frac{0.057}{4}\right)^{4\cdot 19} \implies A=5000(1.01425)^{76}\implies A \approx 14655.18[/tex]

The amount of money that will be needed more to buy the amount of cups and napkins by the teacher would be = $57.5

The amount of cups needed = 12 packages

The price per package of cup = $3.50

The total money needed for cup = 12× $3.50 = $42

The amount of napkins needed = 10 package

The price per package of napkins = $4.25

The total money needed for napkins = 10×4.25 = $42.5

The total amount needed = 42+42.5 = $82.5

The difference between the amount available and the total amount = the extra money needed ;

= 82.5-25 = $57.5

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1001 ways are there to distribute the money of Uncle Henry to his nieces and nephews.

He may donate the entire sum to one child (five ways).

He could give each youngster two bucks (one way).

He may offer $0.00, $1.00, $2.00, $3.00, and $4.00 in five different ways.

Henry will put the dividers on the left and the banknotes on the right. Money to the left of the first divider goes to the youngest kid, money between the first and second dividers goes to the child after that, and so on.

For example, the first kid receives $1, the second receives $2, the third receives $1, the fourth receive nothing, and the fifth receives $6.

It is merely a matter of selecting the number of arrangements of 10 bills and four dividers using this model:

[tex]\frac{14 !}{(10 !)(4 !)}=1,001, \text { or: } 14 C 4=1,001[/tex]

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There are 1001 ways to distribute Uncle Henry's money to his nieces and nephews.

He might give one youngster the full amount (five ways).

He could give each child two dollars (one way).

He can make five separate offers of $0.00, $1.00, $2.00, $3.00, and $4.00.

Henry will arrange the banknotes on the right and the dividers on the left. The youngest child receives the money to the left of the first divider, the following child receives the money between the first and second dividers, and so forth.

The first child gets $1, the second gets $2, the third gets $1, the fourth gets nothing, and the fifth gets $6, for instance. Using this model, it is only a matter of choosing the quantity of arrangements of 10 bills and 4 dividers.

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The measure of angle C of the given triangle is 42.8°.

To find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,

sin A / a = sin B / b = sin C / c

where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.

Given ∠A = 61°, c = 35, a = 45

∴( sin A)/a = (sin C)/c

(sin 61° )/ 45 = (sin C) / 35

sin c = ((sin 61°) / 45) × 35

sin c = 0.68

c ≈ 42.8°

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Complete question:

You have given a triangle ΔABC, where ∠A = 61°, c = 35, a = 45. Solve for measurement(s) of angle c.

The given ratio of yes votes to no votes is 3:4

Then,

The ratio of yes votes: to no votes = 3:4  

Yes votes = 2721,

Now,

2721/3 = 907

907 × 4 = 3628.

Hence, there were 3628 no votes.

To calculate the ratio, use this formula:

Ratios equate two numbers, usually by dividing them. If you are comparing one data point (x) to any other data point (y), your formula would be x/y. This means you are dividing information x by information y.

For example, if A is 50 and B is 100, your ratio will be 50/100 the ratio will be 1:2.

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Answer:

A. Total number of Birds: G + D + C + E + S or B + L + F

B. [tex]\frac{L}{B+L+F}[/tex]

C. [tex]\frac{G+D}{B+L+F}[/tex]

Step-by-step explanation:

first divide you duck by one two three and then subtracted by 578