Heidi contributes 11% of her monthly salary towards her 401(k) and her employer matches her contribution up to 6% of her salary. If the interest rate of her 401(k) is 6. 25% compounded monthly and her monthly salary is $3,250, determine the amount in her account after 15 years. Round to the nearest cent. A. $164,146. 52 b. $165,001. 45 c. $112,585. 20 d. $113,171. 58.

Answer:

x = 21

Step-by-step explanation:

7x - 3 + 2x - 6 = 180       {Linear pair}

7x + 2x - 3 -6  = 180          {combine like terms}

       9x - 9 = 180

           9x  = 180+ 9

           9x = 189

             x = 189/9

x = 21

The Task objective chosen is: A Measuring Task

The Objective is: To investigate the fairness of a local athlete's track for runners starting on different lines.

To carry about the investigation, follow the steps given below.

Lastly, make a crossword puzzle that includes mathematical vocabulary in a clever manner.

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```Class IX```

*Mathematics Project work*

*Do any one*

1. *A Measuring Task*

To investigate your local athletes track to see whether it is worked fairly for runners who start on different lines.

2. *Design a crossword puzzle with mathematical terms*

To review mathematics vocabulary, to give the opportunity for creative expression in designing puzzles, to act as a means of motivating the study of a given unit and to given recreation .​

Given:-

\( \: \)

\( \: \)

Solution:-

By combining the expression nd setting them equal to 180°

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:

x = 47

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The angles given are,

→ x - 2

→ 3x - 6

We know that,

→ Sum of angles in a straight line is 180°.

Formula we use,

→ Total sum of angles = 180°

Forming the equation,

→ (x - 2) + (3x - 6) = 180

Then the value of x will be,

→ (x - 2) + (3x - 6) = 180

→ x - 2 + 3x - 6 = 180

→ (x + 3x) + (-2 - 6) = 180

→ (4x) + (-8) = 180

→ 4x - 8 = 180

→ 4x = 180 + 8

→ 4x = 188

→ x = 188 ÷ 4

→ [ x = 47 ]

Hence, the value of x is 47.

Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

---------------------------

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

If p(1) represents the probability of the opposite outcome, then we can estimate it as the relative frequency of the opposite outcome.

To find p(0), we need to know the context of the problem, specifically what variable p represents. Without this information, we cannot provide an answer. However, assuming p represents the probability of a certain outcome in a data set, we can use the relative frequency of that outcome to estimate p.

If we know that there are 200 students in the data set and that 30 of them had a certain outcome, then the relative frequency of that outcome is 30/200 = 0.15.

Assuming that p represents the probability of this outcome, we can estimate that p(0) = 0.85, since p(1) would be the probability of the opposite outcome.

It's important to note that this estimate is based on the assumption that the relative frequency of the outcome in the data set is a good approximation of its probability in the population.

In reality, this may not always be the case, and additional statistical techniques may be needed to make more accurate estimates.

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Answer:

1. 6

Step-by-step explanation:

500 – 350 = 150

150/25 = 6

Answer:

6 lawns

Step-by-step explanation:

She needs $500 and already has $350 saved

500-350=150

She still needs $150 to reach her goal

150/25 = 6  ($25 for each lawn)

\([Hello,BrainlyUser]\)

Answer:

19.5

Step-by-step explanation:

Given that;

Recipe calls for 5.25 grams of chocolate

Question Ask;

If you have 102.375 grams of chocolate, how many batches,of the recipe can you make?

Note;

102.375 ÷ 5.25 = b

102.375 ÷ 5.25 = Solution

Solve;

\(\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:100\)

\(\frac{10237.5}{525}\)

\(\mathrm{Write\:the\:problem\:in\:long\:division\:format}\)

\(\begin{matrix}525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(Divide\;1023\;by\;525\;to\;get\;1\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace5\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace9\emptyspace8\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(Divide\;4987\;by\;525\;to\;get\;9\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace19\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace5\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace9\emptyspace8\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\:\:\:\:\:\:\:\:\:\underline{\emptyspace47\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace6\emptyspace2\emptyspace5\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(Divide\;2625\;by\;525\;to\;get\;5\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace19.5\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 525\overline{|\smallspace10237.5}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace5\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace9\emptyspace8\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\:\:\:\:\:\:\:\:\:\underline{\emptyspace47\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace6\emptyspace2\emptyspace5\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\:\:\:\:\:\:\:\:\:\underline{\emptyspace26\emptyspace2\emptyspace5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\:\:\:\:\:\:\:\:\:\emptyspace\emptyspace\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

\(\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{102.375}{5.25}\:\mathrm{is}\:19.5\)

[CloudBreeze]

Answer:

Taxes: 16%

Clothing: 13%

Insurance: 7%

Step-by-step explanation:

The value of the variable based on the triangle given is 5.5 units.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Add each side of the triangle.

3z + z + 1 + 4z - 3 = 8z - 2

8z - 2 is equivalent to the  perimeter.

Since you know the perimeter is 38 units, you can set 8z-2 to 38.

8z -2 = 38

Solve for z. Subtract 2 from each side.

8z = 36

Divide each side by 8.

z = 4.5

Now solve for side WX.

WX = z + 1

WX = 4.5 + 1

WX = 5.5

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Answer:

D because we just distribute the 0.5

Hope this helps and brainliest please

Answer:

0.5x + 1.5

Step-by-step explanation:

0.5(x+3)

on opening bracket : 0.5 * x = 0.5x

+

0.5* 3 = 1.5

∴ 0.5x+1.5

y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

In the perpendicular lines the product of slopes will be -1

m1m2=-1

y=x+4 is the given line, it has slope of 1, so the perpendicular line will have slope -1.

The line is passing through (8,2)

2=-1(8)+b

2=-8+b

2+8=b

10=b

Hence, y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4

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The dimensions of the rectangle are 7 feet by 9 feet.

Let's use algebra to solve this problem.

Let x be the width of the rectangle in feet. Then, according to the problem, the length of the rectangle is 2 feet longer than the width, or x + 2 feet.

The area of a rectangle is given by the formula\(A = length x width.\) So, we can write:

A = (x + 2) x x

Simplifying this expression, we get:

A = x^2 + 2x

We know from the problem that the area of the rectangle is 63 square feet. So, we can substitute this value for A and solve for x:

63 = x^2 + 2x

Rewriting this equation in standard form:

x^2 + 2x - 63 = 0

Now, we can use the quadratic formula to solve for x:

x = (-2 ± sqrt(2^2 - 4(1)(-63))) / (2(1))

x = (-2 ± sqrt(4 + 252)) / 2

x = (-2 ± sqrt(256)) / 2

x = (-2 ± 16) / 2

x = -9 or x = 7

Since the width of the rectangle cannot be negative, we reject the solution x = -9. Therefore, the width of the rectangle is 7 feet.

The length of the rectangle is 2 feet longer than the width, or x + 2 = 7 + 2 = 9 feet.

So, the dimensions of the rectangle are 7 feet by 9 feet.

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Answer:

1

Step-by-step explanation:

Distance between x's (Δx)

0

This field is calculated automatically, you cannot change it's value manually.

Distance between y's (Δy)

1

d = √(Δy2 + Δx2) = √(12 + 02) = √1 = 1

Answer:

Step-by-step explanation:

can you get a bigger picture pls

Answer: There are no solutions.

Step-by-step explanation: Hope this help :D

Answer: A. 3 ways: k, DE, ED (both DE and ED have line markers over top)

To name a line, we just need two points on the line. We list them in any order because the line extends forever in both directions. Contrast this with a ray where order does matter. The little k is another way to name a line, potentially simplifying things.

Choice B is close, but it mentions ray DE instead of line DE. Choice C is missing line ED. Choice D is a similar story as choice B. These facts allow us to rule out B through D.

A. Z + W = 12 + 6i.

B. The Argand diagram for z = -√3 + i would show z in the fourth quadrant, with modulus |z| = 2 and argument arg(z) = -π/6.

A. To find Z + W, we can simply add the real and imaginary parts of z and w separately:

z = 5 + 5i

w = 7 + i

Adding the real parts, we get:

5 + 7 = 12

Adding the imaginary parts, we get:

5i + i = 6i

Therefore, Z + W = 12 + 6i.

B. To draw an Argand diagram for z = -√3 + i, we plot z as a point on the complex plane. The real part is -√3, and the imaginary part is 1.

The modulus (or absolute value) of z is given by the distance from the origin to the point representing z. Using the Pythagorean theorem, we can calculate it as:

|z| = √((-√3)^2 + 1^2) = √(3 + 1) = 2.

The argument of z (also known as the angle or phase) is the angle formed between the positive real axis and the line connecting the origin to the point representing z. We can calculate it using the arctan function:

arg(z) = arctan(imaginary part / real part) = arctan(1 / -√3) = -π/6.

Therefore, the Argand diagram representing z would have z as a point in the fourth quadrant, with modulus |z| = 2 and argument arg(z) = -π/6.

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Answer:

Its A $0.50 per mile

Step-by-step explanation:

In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.

This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).

Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.

Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.

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Answer:

this is the  answer \(x\geq 40\)

hope this helps!

Answer:

x is greater than or equal to 40

Step-by-step explanation:

30-90

-3/2x <-60

x>40

Answer:

I'm pretty sure its b but I'm not sure I'm sorry if it's wrong

The answer is  A.) 3n - 8

The height of the water tank of the air cooler brought by Anu is 40 cm.

Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.

given,

Length = 50 cm

Width = 20 cm

Maximum tank volume = 40 liters = 40,000 cm3

Tank height?

Steps,

Tank volume = length x width x height

40,000 = 50 x 20 x height

40,000 = 1000 x height

Tank height = 40,000 : 1000

Tank height = 40 cm

So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.

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The zeros of f(x) are x = 3, x = -5, and x = 1/2.

To find the zeros of the given polynomial functions, we can use different methods such as factoring, synthetic division, or the quadratic formula. Let's apply these methods to each polynomial function:

For f(x) = x^3 + x^2 - 10x + 8:

To check for rational roots, we can use synthetic division with possible factors of 8 (the constant term). By testing x = 1, we find that it is indeed a root.

Applying synthetic division with x = 1:

      1   |   1    1    -10    8

            |__________

              1    2    -8   -2

The resulting quotient is x^2 + 2x - 8. Now we can factor this quadratic equation:

      (x + 4)(x - 2) = 0

So, the zeros of f(x) are x = -4, x = 1, and x = 2.

For f(x) = 6x^3 - 18x^2 - 7x + 21:

Given that one of the factors is (x - 3), we can perform synthetic division by dividing f(x) by (x - 3):

      3   |   6    -18    -7    21

            |____________

              6    0     -7   0

The resulting quotient is 6x^2 - 7. Now we can solve the quadratic equation:

      6x^2 - 7 = 0

      6x^2 = 7

      x^2 = 7/6

      x = ±√(7/6)

So, the zeros of f(x) are x = 3, x = √(7/6), and x = -√(7/6).

For f(x) = 2x^3 + 4x^2 - 33x - 15:

Given that one of the factors is (x - 3), we can perform synthetic division by dividing f(x) by (x - 3):

      3   |   2    4    -33    -15

            |___________

              2   10    -3     12

The resulting quotient is 2x^2 + 10x - 3. Now we can factor this quadratic equation:

      (x + 5)(2x - 1) = 0

So, the zeros of f(x) are x = 3, x = -5, and x = 1/2.

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Answer:

see below

Step-by-step explanation:

s = r theta   where r is the radius  and theta is  the central angle in radians

theta = 80 * pi/180 =  4 pi/9

PQ = 10 * 4 pi/9

      = 40 pi/9 ft

To find the area of the sector, first find the area of the circle

A = pi r^2

  = pi ( 10)^2

  = 100 pi

The sector is 80/360 = 2/9 so the sector is 2/9 of the circle

Multiply the area by the fraction of the circle that the sector is

100 pi* 2/9 = 200 pi /9  ft^2

Answer:

\(\huge \boxed{\mathrm{a. \ 13.96 \ ft}} \\ \\ \\ \huge \boxed{\mathrm{b. \ 69.81 \ ft^2 }}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

Arc length = θ/360 × 2πr

80/360 × 2π(10)

40/9π ≈ 13.96

Area of sector = θ/360 × πr²

80/360 × π(10)²

200/9π ≈ 69.81

\(\rule[225]{225}{2}\)

Answer:

15.75

Step-by-step explanation:

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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