you invest 1600 in an account that pays an interest rate of 6.5%, what is your balance after 6 years and round your answer to the nearest hundredth.

297 /3 = 99

99-1 = 98

99 +1 = 100

98 + 99 + 100 = 297

 the numbers are 98, 99 , 100

The required function notations for the total law firm charges is expressed as f(t) = 100t + 300

Given the following

Law firm charges = $100 per hour

The amount of charge for "t" hours will be 100t hours

Also, the original fee = $300

In other to get the total charge using function notation;

f(t) = Law firm charges for "t" hours + Original fee

f(t) = 100t + 300

The required function notations for the total law firm charges is expressed as f(t) = 100t + 300

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Answer:

a) 5.2 *10^7 km

Step-by-step explanation:

If we could describe our Solar System, in order of appearance nearer the Sun, it would be like this:

Sun --- Mercury --- Venus --- Earth

Sun --------------------- Venus

1.1 * 10^8 km

Sun -------Mercury

5.8 * 10^7 Km

To find out how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun, all we have to do is simply subtract the distance Sun ---Venus minus Sun ---Mercury

So,

1.1 * 10^8 - 5.8 * 10^7 =

Adjusting the first distance to the same power

110*10^7- 5.8*10^7 =

Subtracting the factors

5.2 * 10^7

Option: A is the correct answer.

        A girl is 9; mom is 27

A girl is now one-third as old as her mother.

i.e. if x is the present age of girl.

and y is the present age of her mother.

Then,

[tex]x=\dfrac{1}{3}y[/tex]

i.e.

[tex]y=3x-----------(1)[/tex]

In three years, she will be two-fifths as old as her mother will be.

This means after three years.

The age of girl will be: x+3

and the age of her mother will be: y+3

This means that:

[tex](x+3)=\dfrac{2}{5}\times (y+3)[/tex]

[tex]5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6[/tex]

i.e.

[tex]5x+15=2\times 3x+6[/tex]

( since on using equation (1) )

i.e.

[tex]5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9[/tex]

and the value of y from equation (1) is:

[tex]y=27[/tex]

The probability of having a baby boy on the fourth child, given that the first three children were all boys, is 0.5. This result is not the same as the probability of getting all boys among four children, which is 0.0625. The conditional probability accounts for the information about the first three births.

To solve this probability problem, let's break it down step by step.

Probability of Having a Boy on the Fourth Child:

Assuming boys and girls are equally likely, the probability of having a boy or a girl is 1/2 or 0.5. When considering each child's gender independently, the probability of having a boy on the fourth child is 0.5, regardless of the genders of the previous children.

However, the question specifies that the first three children were all boys. This information is crucial for the conditional probability calculation.

Conditional Probability:

The probability of having a boy on the fourth child given that the first three children were all boys is denoted as [tex]\( P(B_4 | B_1, B_2, B_3) \)[/tex].

Since the events are assumed to be independent (the gender of one child does not affect the gender of another), the conditional probability is the same as the probability of having a boy on any single birth: 0.5.

Comparison with Getting All Boys:

The probability of getting all boys among four children [tex](\( P(B_1 \cap B_2 \cap B_3 \cap B_4) \))[/tex] is the product of the probabilities of having a boy for each birth.

[tex]\[ P(B_1 \cap B_2 \cap B_3 \cap B_4) = P(B_1) \times P(B_2) \times P(B_3) \times P(B_4) \][/tex]

Given that [tex]\( P(B_4) = 0.5 \)[/tex] and the previous births are all boys, [tex]\( P(B_1 \cap B_2 \cap B_3 \cap B_4) = (0.5)^4 = 0.0625 \)[/tex].

The question probable may be:

Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. Assume boys and girls are equally likely. Is the result the same as the probability of getting all boys among four children?

Answer:

$594.50

Step-by-step explanation:

1. Divide markup into decimal form

45/100 = .45

2. multiply by cost of Refrigerator

.45 x 410 = $184.50

3. Add markup cost to original Refrigerator cost.

184.50 + 410 = $594.50

Answer:

2.828427

Step-by-step explanation:

I looked it up

The probability of selecting at least 7 female students from the sample of 8 students is  0.2797.

To solve this problem, we'll use the binomial probability formula, which calculates the probability of a certain number of successes (in this case, selecting female students) in a fixed number of trials (the sample size).

Given:

Probability of selecting a female student (success), ( p = 0.60 )

Probability of selecting a male student (failure), ( q = 1 - p = 0.40 )

Sample size, ( n = 8 )

We need to calculate the probability of selecting at least 7 female students from the sample.

Calculate the probability of selecting exactly 7 female students:

[tex]\[ P(X = 7) = \binom{8}{7} \times (0.60)^7 \times (0.40)^{8-7} \][/tex]

[tex]\[ = \frac{8!}{7!(8-7)!} \times (0.60)^7 \times (0.40)^{1} \][/tex]

[tex]\[ = 8 \times 0.60^7 \times 0.40 \][/tex]

[tex]\[ = 8 \times 0.0279936 \times 0.40 \][/tex]

[tex]\[ = 0.1119744 \][/tex]

Calculate the probability of selecting exactly 8 female students:

[tex]\[ P(X = 8) = \binom{8}{8} \times (0.60)^8 \times (0.40)^{8-8} \][/tex]

[tex]\[ = (0.60)^8 \][/tex]

[tex]\[ = 0.60^8 \][/tex]

[tex]\[ = 0.16777216 \][/tex]

Add the probabilities from Step 1 and Step 2 to get the final probability:

[tex]\[ P(X \geq 7) = P(X = 7) + P(X = 8) \][/tex]

[tex]\[ = 0.1119744 + 0.16777216 \][/tex]

[tex]\[ = 0.27974656 \][/tex]

So, the probability of selecting at least 7 female students from the sample of 8 students is  0.2797.

Answer: 7 + 7 = 14

8 + 8 = 16

Step-by-step explanation: doubles facts are simply additions where a number is added to it self. The strategy sums up two consecutive numbers when they are next to each other to give their result as given by the question above (8 + 7). We simply add the smaller number together then add one (double-plus-one) OR add the larger number together then subtract one (double-minus-one)

All doubles that can be used in solving 8 + 7 are:

A) 8 + 7 = 7 + (7 + 1) = (7 + 7) + 1 = 14 + 1 = 15 [double-plus-one]

B) 8 + 7 = (8 + 8) - 1 = 16 - 1 = 15 [double-minus-one]

The doubles fact makes use of the associative property of addition —changing the grouping of addends does not change the sum.

The statement which is equivalent to line segment CD is congruent to line segment XY is CD overbar is congruent to XY overbar.

A line is made up of an infinite no. of points it can extend in both directions indefinitely.

We know a line has two subsets they are a ray and a line segment.

A ray is a type of line that has one initial point and the other end can extend indefinitely and a line segment is a type of line which has two endpoints.

Given a line, segment CD is congruent to line segment XY.

∴ [tex]\overline{CD}[/tex] ≅ [tex]\overline{XY}[/tex].

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Answer:

C. The vertex is [tex](-3,-1)[/tex], the domain is all real numbers, and the range is [tex]y\leq -1[/tex].

Step-by-step explanation:

We have been given a function [tex]f(x)=-2(x+3)^2-1[/tex]. We are asked to identify the vertex, domain and range of the given function.

We can see that our given parabola is in vertex form [tex]y=a(x-h)^2+k[/tex], where [tex](h,k)[/tex] represents vertex of parabola.

We can rewrite our given equation as:

[tex]f(x)=-2(x-(-3))^2-1[/tex]

Therefore, the vertex of our given parabola would be [tex](-3,-1)[/tex].

We know that parabola is a quadratic function and the domain of a quadratic function is all real numbers.

We know that range of a quadratic function in form [tex]f(x)=a(x-h)^2+k[/tex] is:

[tex]f(x)\leq k[/tex], when [tex]a<0[/tex] and,

[tex]f(x)\geq k[/tex], when [tex]a>0[/tex]

Upon looking at our given function, we can see that [tex]a=-2[/tex], which is less than 0, therefore, the range of our given function would be [tex]y\leq -1[/tex].

Answer:

1.A  

2.C

Step-by-step explanation:

The end behaviour of the polynomial function y = -2x⁷ + 56x⁶ - 24 will change for a) - x⁸ and c) 5x⁷.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

Given, a polynomial function y = -2x⁷ + 56x⁶ - 24.

So, the given polynomial function has a degree of 7 and its end behavior will be changed by adding or subtracting terms that are of degree 7 and higher.

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Switch the x and y values to find the inverse.

y=x−3x+2

The inverse is given by

x=y−3y+2

Solve for y now:

x(y+2)=y−3

xy+2x=y−3

2x+3=y−xy

2x+3=y(1−x)

2x+31−x=y

The inverse, f−1(x), is given by f−1(x)=2x+31−x.

The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).

For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).

It would take approximately 19 years for Tina's investment to grow from $1100 to $6600 with an annual interest rate of 7.25% if the interest is compounded annually.

This problem deals with the concept of compound interest. To find out how many years it will take for Tina's investment to grow from $1100 to $6600 with an interest rate of 7.25%, we would use the formula for compound interest: A = P(1 + r/n)_(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per time unit (year), t is the time the money is invested for in years.

In Tina's case, she does not make additional contributions, so we assume the interest is compounded once per year (n=1). Our formula becomes A = P*(1 + r)_t. Arranging for t, we get t = log(A/P) / log(1+r).

Using these values: A=$6600, P=$1100, r=7.25/100=0.0725, we can find t = log(6600/1100) / log(1+0.0725). Calculating this, you would get around 19 years.

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