Find the interest earned and the future value of an annuity with semiannual payments of $1,500 for 16 years into an account that pays 9% interest per year compounded semiannually.

Answer:

The probability is  0.977

Step-by-step explanation:

We know that the average [tex]\mu[/tex] is:

[tex]\mu=500[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=100[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(x>300)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{300-500}{100}[/tex]

[tex]Z=-2[/tex]

The score of Z = -2 means that 300 is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 1 deviations from the mean has percentage of  2.35% for Z<-2

So

[tex]P(z>-2)=1-P(Z<-2)[/tex]

[tex]P(z>-2)=1-0.0235[/tex]

[tex]P(z>-2)=0.9765[/tex]

Final answer:

The probability of a randomly chosen exam score being above 300, given a normal distribution with a mean of 500 and a standard deviation of 100, is approximately 97.5%.

Explanation:

To find the probability that a randomly chosen exam score is above 300 on a college entrance exam with a mean score of 500 and a standard deviation of 100, we first calculate the z-score. A z-score is a measure of how many standard deviations an element is from the mean. Using the formula z = (X - \\(mu\\))/\\(sigma), where X is the score, \\(mu\\) is the mean, and \\(sigma\\) is the standard deviation, we get:

z = (300 - 500) / 100 = -2.

The z-score of -2 means the score is 2 standard deviations below the mean. The symmetry of the normal curve and the empirical rule tell us that approximately 95% of the scores lie within 2 standard deviations of the mean, or between 300 and 700 in this case. Given that 95% of the scores are between 300 and 700, and the curve is symmetrical, we find that roughly 2.5% of the scores are below 300. Therefore, the probability of a score being above 300 is 100% - 2.5% = 97.5%.

You would need to add 0.25 from t to get the number of hours ( this would be the total number of hours she has raced) and then multiply that by her speed.

The equation would be d = 35(t+0.25)

Answer:

x = -2 and y = 2

Step-by-step explanation:

We have the following system of linear equations;

y=x+4

y=-2x-2

To solve the above system, we shall be equating the right hand sides of the two equations since we have y's on the left hand side of both equations;

x + 4 = -2x - 2

add 2x on both sides of the equation;

x + 4 + 2x = -2x - 2 + 2x

3x + 4 = -2

subtract 4 on both sides of the equation;

3x + 4 - 4 = -2 - 4

3x = -6

x = -2

We can use the first equation y=x+4 to determine the value of y;

y = -2 + 4

y = 2

The solution to the system of linear equations is thus;

x = -2 and y = 2

Answer: y= -6

Step-by-step explanation:

because you know the slope is 0, you simply plug in from there

y=mx+b

y=0x (no slope) -6 (where it intersects the y axis)

y= -6

The answer is:   " y = - 6 " .

_________________________________________________

Step-by-step explanation:

_________________________________________________

To start, We find the equation of the given line ;  (in "blue" ; within the "image attached");

in the slope-intercept form:  

  " y = mx + b " ;

in which:

   "m = the slope = 0 " ; since there is no "slope";

   "b" = the "y-intercept" ;  or more precise, the value of the "y-coordinate" of the [point of the "y-intercept" — that is; the point at which the graph crosses the "y-axis" .].

    Note:  From the graph shown (Refer to image attached);  the "y-intercept" is:  " (0, 4) " ;  

    As such:  " b = 4 " .

_____________________________

So,  the equation;  in "slope intercept format" ; that is:  " y = mx + b " for the original line;  is:   "y = 0x + 4 " .

Let us simplify this equation:

    " y = 0x + 4 " ;    Note:  " 0x = 0 " ;

      {since:  "0" ; multiplied by "any value" ;  results in:  "0" .}.

_____________________________

We are are left with " y = 4 " ;  

_____________________________

Now, we are asked to find the equation of the line that is "parallel" to this line and that passes through the point:  " (-4, 6) ".

If such a line is "parallel" to the original line, the slope would be the same, which is "0" .

So, " y = 0x + b" ;

_____________________________

Also, note the formula:

 y - y₁  = m(x - x₁) ;

in which we consider the point:  " (- 4, - 6) " ;

 in which:  " y₁ = -6 " ;  and:  " x₁ = -4 " ;

→  y - (-6) = m (x - (-4)) ;

→  y + 6  = m (x + 4) ;

Note:  " m = 0" ;

  So;  " m(x + 4) " =  (0)* (x + 4) = "0" ;  

      {since:  "0" ; multiplied by "any value" ;  results in:  "0" .}.

→  We have:

    y + 6 = 0 ;  

→ Let us subtract "6" from each side of the equation;

          to isolate "y" on one side of the equation;

          & to write the equation for the 'perpendicular line' ; as follows:

→   y + 6 - 6 = 0 - 6 ;

to get:  

→   y  =  - 6  ;

____________________________________________

The answer is:   " y = - 6 " .

____________________________________________

Hope this helps!

    Wishing you the best in your academic endeavors

             — and within the "Brainly" community!

____________________________________________

Answer:

d+e =6       d=5 and e=1

d-e=4

Step-by-step explanation:

5+1=6

5-1=4

simple math you have to think hard to get it right might look easy but it is not

Answer:

the solution is (1, 5)

Step-by-step explanation:

If d - e = 4, then d = e + 4.  Substitute e + 4 for d in the first equation:

d + e = 6 →  e + 4 + e = 6.  Then 2e = 2, and e = 1.

Subbing 1 for e in the second equation, we get d + e = 6, or d + 1 = 6.

Thus, d = 5, and the solution is (1, 5)

Answer:

Step-by-step explanation:

Givens

Formula

V = (a * b)/2  * h

Solution

V = (10 * 11)/2   * 10

V = 110/2  * 10

V = 55 * 10

V = 550

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

[tex]A_ {b} = \frac {b * h} {2}[/tex]

Where:

b: It is the base of the triangle

h: It's the height of the triangle

Substituting the values:

[tex]A_ {b} = \frac {10 * 11} {2}\\A_ {b} = 55 \ cm ^ 2[/tex]

Then, the volume is:

[tex]V = 55 * 10\\V = 550 \ cm ^ 3[/tex]

ANswer:

550

y < -1/2 x + 2

I will try the first-two points. You can then finish.

Let x = 2 and y = 3.

3 < (-1/2)(2) + 2

3 < -1 + 2

3 < 1

False statement. Choice A is not the answer.

Let x = 2 and y = 1

1 < (-1/2)(2) + 2

1 < -1 + 2

1 < 1

False statement. Choice B is not the answer.

Do the same thing with the remaining points. One of the points will make the given inequality a true statement.

The point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

The inequality is given as:

y < 1/2x + 2

Next, we test the options

A. (2, 3)

3 < 1/2 * 2 + 2

3 < 3 ---- false

B. (2, 1)

1 < 1/2 * 2 + 2

1 < 3 ---- true

Hence, the point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

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Answer: -0.52

Step-by-step explanation:

From the given scatter plot, it can be seen that there is a moderate negative correlation between the variables as variable X increases variable Y decreases.

i.e. the value of correlation coefficient must be negative.

Also, the value of weak correlation coefficient r, lies between the absolute value of 0.40 to 0.59.

From all the given options -0.52  is the value which is contained in interval  0.40 to 0.59 .

Therefore, the best estimate of the correlation coefficient for the variables in the scatter plot = -0.52

Answer:

2x < 600 or x < 300

Step-by-step explanation:

x = Johnny's current amount of records.

Answer:

look at the calculator.

ANSWER

EXPLANATION

We want to graph the inequality:

[tex]3y - 5x \: < \: - 6[/tex]

To this inequality, we must first of all graph the corresponding linear equation:

[tex]3y - 5x = - 6[/tex]

When x=0, we have

[tex]3y - 5(0) = - 6[/tex]

[tex]3y = - 6[/tex]

y=-2

We plot the point (0,-2)

When y=0,

[tex]3(0) - 5x = - 6[/tex]

[tex]x = \frac{6}{5} [/tex]

[tex]( \frac{6}{5} ,0)[/tex]

We plot the points and draw a dashed straight line through them.

We test for (0,0).

[tex]3(0)- 5(0)\: < \: - 6[/tex]

[tex]0 < \: - 6[/tex]

This is false hence we shade the lower half plane. See attachment.

Answer:

√(A/4π) = r

Step-by-step explanation:

A = 4πr²

r² = A/4π

r = √(A/4π)

Answer:

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

Step-by-step explanation:

Given

A = 4πr² ( isolate r² by dividing both sides by 4π )

r² = [tex]\frac{A}{4\pi }[/tex]

Take the square root of both sides

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

well, do a payments table of values, just like before for each mont hmm let's see

1st month.......................3500 + p(1)

2nd month....................3500 + p(2)

3rd month.....................3500 + p(3)

4th month.....................3500 + p(4)

5th month.....................3500 + p(5)

36th month..................3500 + p(36)

[tex]\bf \stackrel{\textit{total value}}{17900}=\stackrel{\textit{down payment}}{3500}+\stackrel{\stackrel{\textit{payments for}}{\textit{36 months}}}{36p} \\\\\\ 14400=36p\implies \cfrac{14400}{36}=p\implies 400=p[/tex]

Answer:

The value of P( A and B ) is 0.08.

Step-by-step explanation:

When two events are independent then the probability of both occurring is equal to the product of probabilities of both events individually,

That is, If X and Y are independent events,

Then, P(X∩Y) = P(X) × P(Y),

or P(X and Y) = P(X) × P(Y),

Here, P(A) = 0.40 and P(B) = 0.20,

Hence, P(A∩B) = P(A) × P(B)

= 0.40 × 0.20

= 0.08

The value of [tex]\( P(A \text{ and } B) \)[/tex] is 0.08. So option(a) is correct.

To determine[tex]\( P(A \text{ and } B) \)[/tex] for two independent events ( A ) and ( B ) with given probabilities ( P(A) = 0.40 ) and ( P(B) = 0.20 ), follow these steps:

Step 1: Understand the Concept of Independence

For independent events, the probability of both events occurring together (the intersection of A and B, denoted as [tex]\( P(A \cap B) \))[/tex] is the product of their individual probabilities.

Step 2: Apply the Independent Event Formula

Since (A ) and (B ) are self-contained,

[tex]P(A) \times P(B) = P(A \cap B)[/tex]

Step 3: Substitute the Given Probabilities

Insert the given probabilities [tex]\( P(A) = 0.40 \)[/tex] and [tex]\( P(B) = 0.20 \)[/tex] into the formula:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 \][/tex]

Step 4: Perform the Multiplication

Calculate the product of 0.40 and 0.20:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 = 0.08 \][/tex]

Step 5: Interpret the Result

The probability that both events ( A ) and ( B ) occur is 0.08.

Therefore, the correct answer is (a) 0.08.

Complete Question:

A and B are independent events. P(A)=0.40 and P(B)=0.20 . What is P(A and B) ?

A. 0.08

B. 0.60

C. 0

D. 0.80

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{8.4\times 8.4}{70.56}\\ h\approx& 8.6 \end{cases}\implies V=\cfrac{1}{3}(70.56)(8.6) \\\\\\ V=202.272\implies \stackrel{\textit{rounded up}}{V=202.3}[/tex]

Answer:

OPTION A

Step-by-step explanation:

The exponential growth functions has the following form:

[tex]y=a(b)^x[/tex]

Where "a" is the principal coefficient and  "b" is the base greater than 1.

To know which of the functions shown has exponential growth, identify which one has a base greater than 1.

[tex]\frac{4}{3}=1.33>1[/tex]

Therefore, the exponential growth function is the function shown in the option A.

The answer is:

The correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

To identify which of the given functions is an exponential growth function, we need to remember the form of the exponenial growth or decay functions.

We can define the exponential growth or decay function by the following way:

[tex]P(x)=y=StartValue*(rate)^{x}[/tex]

Where,

P(x) or y, is the function

Start value is the starting amount or value

Rate, is the growth or decay rate

x, is the variable (time)

Now, we can identify if the function is a exponential growth or decay function by the following way:

If [tex]rate>1[/tex] the function is an exponential growth function.

If [tex]rate<1[/tex] the function is an exponential decay function.

Now, we are given the function first function, A)

[tex]y=(\frac{4}{3})^{x}[/tex]

Where,

[tex]rate=\frac{4}{3}=1.33[/tex]

and we have that:

[tex]rate>1\\1.33>1[/tex]

So, the function is an exponential growth function.

Hence, the correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

Have a nice day!

Answer:

(x + 2)² + (y - 5)² = 7²

Step-by-step explanation:

Incomplete question.  I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.

That would be:

(x + 2)² + (y - 5)² = 7²

The equation of the circle with center (-2,5) and radius 7 is (x+2)² + (y-5)² = 49.

The question is asking for the equation of a circle with center at (-2,5) and radius 7. The general equation for a circle is (x-h)² + (y-k)² = r², with (h,k) as the center and r as the radius. In this case, h = -2, k = 5, and r = 7, so substituting these into the equation gives us the solution:

(x-(-2))² + (y-5)² = 7², which simplifies to (x+2)² + (y-5)² = 49.

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Answer:

 94.18                            

Step-by-step explanation:

Given in the question a semi circle and a right angle triangle

Step 1

Find the diameter of the semi circle

To find the diameter we will use pythagorus theorem

here,

hypotenuse will be diameter of semicircle

height = 9

base = 4

Plug values in the formula above

diameter = √(9²+4²)

diameter = √97

Step 2

Find radius

Step 3

Area

π(√97/2)²

= 76.18

Step 4

Total surface area = area of circle + area of right angle triangle

                               = 76.18 + 1/2(9)(4)

                               = 94.18

Answer:

2

Step-by-step explanation:

512^(1/9)

Write 512 as power of 2:

(2^9)^(1/9)

Multiply the exponents:

2^(9 × 1/9)

2^1

2

Answer:

2

Step-by-step explanation:

The answer is:

The average speed for the total trip is 753.19 mph.

To calculate the average speed for the total trip, we need to calculate the time of travel for both distances according to their speeds.

So, calculating we have:

- First distance and speed: 3334 miles at 760 mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{3334miles}{760mph=4.39hours}[/tex]

Therefore, we have that the first distance was covered in 4.39 hours.

- Second distance and speed: 2244.7 miles at 740mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{2244.7miles}{740mph=3.03hours}[/tex]

Therefore, we have that the second distance was covered in 3.03 hours.

Now, calculating the average speed, we have:

[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]

Substuting we have:

[tex]AverageSpeed=\frac{3344miles+2244.7miles}{4.39hours+3.03hours}[/tex]

[tex]AverageSpeed=\frac{5588.7miles}{7.42hours}=753.19mph[/tex]

Hence, we have that the average speed for the total trip is 753.19 mph.

Have a nice day!

Answer:

6

Step-by-step explanation:

Q1 is 3, Q2 is 5, Q3 is 6, which is the upper quartile.

It is important to do the same thing to both sides of an equation because in the end, both sides will be equivalent, or equal, therefor making the problem true. If you didn't do the same thing on both sides of an equation, one side would be incorrect and not equal to the other side. Hope this helps! Please mark brainliest. Thank you v much! :)

It's necessary to do the same thing to both sides of an equation to maintain balance and allow valid operations. This basic principle is crucial for solving and simplifying equations in mathematics.

In mathematics, it is necessary to do the same thing to both sides of an equation to perform valid operations. An equation represents a balance; what is done to one side must also be done to the other to maintain this balance. For instance, if you add, subtract, multiply, or divide a value from/to one side of an equation, you have to do the same to the other side. This principle is essential for solving and simplifying equations. For example, in the equation 5x + 3 = 18, to solve for x, you would subtract 3 from both sides, establishing the new equation 5x = 15, maintaining the balance.

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Answer:

Required system of equation is

4s+3c=26 and 5s+2c=29.

Step-by-step explanation:

Let cost of 1 sundaes = s

Let cost of 1 cone = c

Then statement "Marcus is treating his family to ice cream he buys 4 Sundaes and 3 cones for the total of $26", gives equation:

4s+3c=26...(i)

And statement "Brian also buy ice cream for his family his total is 29 for purchasing 2 cones and 5 Sundaes " gives equation:

5s+2c=29...(ii)

Hence required system of equation is

4s+3c=26 and 5s+2c=29.

Answer:

4s+3c=26

5s+2c=29.

Step-by-step explanation:

b and c is the answer .

Number 7 - Second answer

Number 8 - Third answer

Answer:

49b^2 -36 = (7b -6)(7b +6)

so because there you missed some signs in these wrote choices  

hope helped  

Step-by-step explanation:

Answer:

[tex](b+1)^2(b+6)[/tex]

Step-by-step explanation:

The given rational expression is:

[tex]\frac{b}{b^2+2b+1}-\frac{6}{b^2+7b+6}[/tex]

We factor the denominators to get:

[tex]\frac{b}{(b+1)^2}-\frac{6}{(b+1)(b+6)}[/tex]

The least common denominator is the product of the highest powers of the common factors of the denominators.

Therefore the least common denominator is:

[tex](b+1)^2(b+6)[/tex]

Answer:

d

Step-by-step explanation:

The scale is simply the ratio between the distances in the plan and the actual distances. So, first of all, let's convert all lengths to the same unit measure:

[tex]18\text{ ft} = 216\text{ in}[/tex]

So, the scale is

[tex]\dfrac{216}{6.4} = 33.75[/tex]

which means that one inch in the plan is the same as 33.75 inches in the real world.

Answer:

1 : 33.75

Step-by-step explanation:

6.4 inches ⇒ 18 feet

6.4 inches ⇒ 18 x 12 = 216 inches

scale used

= 6.4 : 216

= 1 : 216 ÷ 6.4

= 1 : 33.75

Answer:

V =91.125 in ^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3  where s is the side length

V= 4.5 ^ 3

V =91.125 in ^3

Given : Length of side of a cube = 4.5 inches.

We know that,

Volume of cube = (side)³ cu. units

= (4.5)³ inches³

= 91.125 inches³

Hence,

Volume of a cube = 91.125 inches³

Answer: More bees were observed on both trees from 12:00 p.m. to 6:00 p.m. than from 6:00 p.m. to 9:00 p.m.

Step-by-step explanation:

12:00 p.m. to 6:00 p.m: 135 bees

6:00 p.m to 9:00 p.m: 28 bees

Answer:

The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

Step-by-step explanation:

In the real world, length and width only make sense when they are positive. For that to be the case, the width must be greater than 2. There is nothing in the description that restricts the values to integers.

Answer:

C) the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

Step-by-step explanation: