8.
If a principal of $2500 was invested at a rate of 5% compounded semiannually and terminates
with a balance of $5509.39, how long was the money invested for? hint: use table A11 or log calculations

4 yrs

8 yrs

16 yrs

32 yrs

The value of x is 60.

The Midpoint theorem states that :

The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side

By Midpoint theorem

DE = 30

AC = x

DE = [tex]\frac{1}{2}[/tex] AC

30 = [tex]\frac{x}{2}[/tex]

x = 60

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Answer:

5 sin 38 should be the length.

I’m pretty sure it’s the last answer. 5 sin 38

To evaluate 16+j⋅4 for j=8, substitute j with 8, multiply the result by 4, and add it to 16 to get the final result of 48.

To evaluate 16+j⋅4 for j=8, follow these steps:

16 + j * 4 = 16 + 8 * 4 = 16 + 32 = 48

After performing these steps, we find that the expression 16+j⋅4 for j=8 is equal to 16+32, which is 48.

Answer:

15.00 once you add percent

Answer:

The increase from $3.50 to $8.50 was 243%.

Step-by-step explanation:

The increase from $3.50 to $12.00 was $8.50.

We need to compare this to the original $3.50 by writing the following ratio, evaluating it and converting the result to a percentage:

$8.50

--------- = 2.43

$3.50

Multiply this result by 100%:  (100%)(2.43) = 243%

The increase from $3.50 to $8.50 was 243%.

Answer:

interest earned= 1436.143

the future value of an annuity= 2836.143

Step-by-step explanation:

Given Data:

Interest rate= 4%

time,t = 18 years

Annual payment, P= 1400

At the end of 18 years, final investment A= ?

As per the interest formula for interest

A= P(1+r)t

Putting the values in above equation

= 1400(1+0.04)^18

= 2836.143

Interest earned = A-P

                           = 2836.143-1400

                          = 1436.143 !

Answer:

Step-by-step explanation:

1.5

Answer:

If x and y are independent events;

[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]

If x and y are dependent events then;

[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]

Step-by-step explanation:

The expression;

P(x|y)  in probability represents the conditional probability of an event x occurring given that an event y has already occurred. An example of such would be; the probability that a student passes the examination given that he attempted all the assignments.

If x and y are independent events, that is the occurrence of y does not in any way influence the occurrence of x, then;

[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]

If x and y are dependent events then;

[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]

[tex]P(xny)[/tex] represents the probability of both x and y occurring together;

n denotes intersection

Answer:

Josh won the race 5 seconds ahead of Rafael

Step-by-step explanation:

The winner of the race is the individual who completes the race in the shortest time. From the graph, Josh reaches the finish line at the 15 seconds mark while Rafael finishes at the 20 seconds mark.

The difference in the time is thus;

20 - 15 = 5 seconds.

Therefore, Josh won the race 5 seconds ahead of Rafael

Answer:

y - 5 = 3(x - 2)

Step-by-step explanation:

Point Slope Form: y – y1 = m(x – x1)

y1 represents the y-coordinate

x1 represents the x-coordinate

m represents the slope

Answer:

9

Step-by-step explanation:

The median is the middle entry of the data set in ascending order. If there is no exact middle then it is the average of the values either side of the middle.

Arrange the data in ascending order

4, 8, 8, 9, 11, 13, 17

            ↑

The median = 9

Answer:

9

Step-by-step explanation:

Order the numbers from least to greatest, then find the number that is in the middle. If there are two numbers that are in the middle then add the two numbers together and then divide by 2.

Answer:

Domain is (0,∞)

Step-by-step explanation:

We need to find the domain of the function graphed

Domain are the values of x for which the function is defined.

For domain, we look at the x values of the graph.

We have graph for x values greater than 0. the graph goes close to y axis but does not cross y axis.

For x values greater than 0 there is a value for y.

There is no graph for negative value of x

So , domain is set of all x values greater than 0

Domain is (0,∞)

Answer:

4x²  +  12x  +  18

Step-by-step explanation:

This would be the trinomial.

Answer:

if you mean to factor it, it would be, (2x + 3)(2x + 3) but if you do mean the trinomial, that is already the answer.

Step-by-step explanation:

4x^2 + 12x + 9

you can split 12x into 6x + 6x so now it's

4x^2 + 6x + 6x + 9

then simplify it into:

2(2x + 3) + 3(2x + 3)

then into:

(2x + 3)(2x + 3)

Answer:

[tex]G(x)=\frac{1}{2}(x-3)^3+2[/tex]

Step-by-step explanation:

The given function is

[tex]F(x)=x^{3}[/tex]

The transformations to this graph are  in the form;

[tex]G(x)=a(x-b)^3+c[/tex]

where [tex]a=\frac{1}{2}[/tex] is the vertical compression by a factor of [tex]\frac{1}{2}[/tex]

b=3 is a shift to the right by 3 units.

c=2 is an upward shift by 2 units.

Therefore [tex]G(x)=\frac{1}{2}(x-3)^3+2[/tex]

Answer:

The equation is

[tex]G(x)=-\frac{1}{2}(x-3)^3 +2[/tex]

Step-by-step explanation:

If the graph of the function [tex]G(x)=cf(x+h) +b[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <|c| <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

If [tex]b> 0[/tex] the graph moves vertically upwards.

If [tex]b <0[/tex] the graph moves vertically down

If [tex]h <0[/tex] the graph moves horizontally h units to the right

If [tex]h >0[/tex] the graph moves horizontally h units to the left

In this problem we have the function [tex]G(x)[/tex] and our parent function is [tex]f(x) = x^3[/tex]

We know that G(x) is equal to f(x) but reflected on the x-axis ([tex]c <0[/tex]), compressed vertically by a multiple of 1/2 ([tex]0 <|c| <1[/tex] and [tex]c = -\frac{1}{2}[/tex]), displaced 2 units upwards ([tex]b = 2>0[/tex]) and moved to the right 3 units ([tex]h = -3<0[/tex])

Then:

[tex]G(x)=-\frac{1}{2}f(x-3) +2[/tex]

[tex]G(x)=-\frac{1}{2}(x-3)^3 +2[/tex]

Answer:

Step-by-step explanation:

Well, we can divide 399 and 75 so it would be 5.32. Round that and it would be about 5 items per page

The required average number of items per page is 5.32.

A rate with a second term of one is referred to as a unit rate. To put it another way, a unit rate compares two quantities, with the second number being expressed as 1. Unit rates, such as price per item, speed per hour, or cost per pound, are frequently used to describe a rate per unit of measurement.

Here,
To find the average number of items per page, we need to divide the total number of items by the number of pages:

The average number of items per page = Total number of items / Number of pages

Substitute the given values, and we get:

The average number of items per page = 399 / 75

Simplifying the expression, we get:

The average number of items per page = 5.32 (rounded to two decimal places)

Therefore, the average number of items per page is 5.32.

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Answer:

x=1 or x=−9

Step-by-step explanation:

Let's solve your equation step-by-step.

x(x+8)=9

Step 1: Simplify both sides of the equation.

x2+8x=9

Step 2: Subtract 9 from both sides.

x2+8x−9=9−9

x2+8x−9=0

Step 3: Factor left side of equation.

(x−1)(x+9)=0

Step 4: Set factors equal to 0.

x−1=0 or x+9=0

x=1 or x=−9

Hey there!

(x + 8) = 9

➡️ x + 8 = 9

SUBTRACT 8 to BOTH SIDES

x + 8 - 8 = 9 - 8

CANCEL out: 8 - 8 because that gives you 0

KEEP: 9 - 8 because it helps solve for the x-value

x = 9 - 8

9 - 8 = x

9 - 8 = 1

Therefore your answer is: x = 1

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

B) 20

Step-by-step explanation:

Subtract  10  from both sides of the equation.

6 a = 130 - 10

Subtract  10  from  130 .

6a=120

Divide each term by  6  and simplify.

6 a/ 6  = 120 /6

Reduce the expression by cancelling the common factors.

a=120/6

Divide  120  by  6 .

a  =  20

Hope this helps.

The value of a is 20.

Parallelogram's characteristics

Given

6a + 10 = 130 [The opposing angles congruent.]

6a = 120

a = 20

Therefore, The value of a is 20.

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Answer:

4n²+2n as a factorial is given as:

[tex]= (2n+1)!/(2n-1)![/tex]

Step-by-step explanation:

We are given an expression which has to be converted into factorial form.

The expression is as follows:

[tex]4n^{2} + 2n\\ = 2n(2n+1)\\ = (2n+1)2n\\[/tex]

Now we know that 2n+1 and 2n differs by '1' and the next smaller term is '2n-1'.

Hence, multiplying and dividing by '(2n-1)!'; we get:

[tex]= ((2n+1)(2n)(2n-1)!)/(2n-1)![/tex]

we know that x(x-1)(x-2)! = x!, so:

[tex]= (2n+1)!/(2n-1)![/tex]

Answer:

1600

Step-by-step explanation:

first, 1.6 m is 160 cm.

160 cm is 1 in 1:100

converting the proportion into a fract., it is 1/100.

160=1/100x

1600=x

To find the width of the model car in centimeters, we need to follow a different approach, because the information given doesn't include the width of the actual car or the ratio of length to width. Since only the scale of the model and the length of the model car are given, without additional information about the actual car or its dimensions, we cannot directly calculate the width of the model car.
However, I can explain the general process of how to calculate the width of the model car if the necessary information was provided:
1. **Find the width of the actual car**: If the width of the actual car (in meters or any other units) is given, we could proceed to the next step. Without this information, we cannot continue, so let's assume hypothetically that this information is available.
2. **Convert the width of the actual car to centimeters**: Since the dimensions of the model car are sought in centimeters, we need to convert the actual car's width from meters to centimeters by the following conversion:
  \[ \text{width in centimeters} = \text{width in meters} \times 100 \].
3. **Apply the scale ratio**: After converting the actual car's width to centimeters, we need to apply the scale ratio to calculate the width of the model car. The scale is 1:100, which means that one unit of measurement on the model represents 100 of the same units on the actual car.
4. **Calculate the width of the model car**: Divide the width of the actual car in centimeters by the scale ratio (which is 100 in this case) to calculate the width of the model car in centimeters:
  \[ \text{width of model car in centimeters} = \frac{\text{width of actual car in centimeters}}{100} \].
If we suppose that the actual car is twice as long as it is wide, and we have the model's length (1.6 m), we could assume that the actual car's length is 160 m (since 1.6 m times the scale factor of 100). With an assumption of the actual car being twice as long as wide, we can deduce that the actual car's width would be 80 m (160 m divided by 2). Converting that to centimeters would be 8000 cm (since 80 m times 100 cm/m). Dividing that by 100 (scale factor) would yield a result of 80 cm for the width of the model car.
However, please note, without the essential information about the actual car's width or its length-to-width ratio, this is just a hypothetical scenario. To proceed with a real calculation, you would need to clarify the actual width of the car or provide the proportional dimensions.

The graph of f(x) is shifted k units above the graph of g(x). Therefore, the option C is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x) = 2ˣ and f(x) = 2ˣ+k

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: g(x)=2x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Vertical Compression or Stretch: None

So, from graph of g(x) to the graph of f(x), it shifted k units up.

Therefore, the option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

The function g(x) = 2ˣ. The f(x) = 2ˣ+k and k < 0. Which of the following statements is true?

A) The graph of f(x) is shifted k units to the left of the graph of g(x).

B) The graph of f(x) is shifted k units to the right of the graph of g(x).

C) The graph of f(x) is shifted k units above the graph of g(x).

D) The graph of f(x) is shifted k units below the graph of g(x).

Answer:

The answer is D

Step-by-step explanation:

In D, all of the multiplacative parts of the problems add up to the factoring of 185 • 12, and the others don't. I really hope this helps!

Answer:

D. [tex]12\cdot 100 + 12 \cdot 80 + 12 \cdot 5[/tex]

Step-by-step explanation:

A possible solution of the expression is:

[tex]12\cdot (185)[/tex]

[tex]12\cdot (100 + 80 + 5)[/tex]

[tex]12\cdot 100 + 12 \cdot 80 + 12 \cdot 5[/tex]

The right answer is D.

Step-by-step explanation:

To find the answer you have to put it into y=mx+b format.

This means that it will be 5y=-30x+15

So it will simplify to y=-6x+3

This means that:

If y=2

You substitute then…

2=-6x+3

So x would equal 1/6.

The rate of change in y per unit change in x for the function 30x+5y=15 is 1/6.

Suppose that the considered linear equation is of the form y=mx+c

Then, when we change x by 1 unit, then:

[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]

where[tex]\delta[/tex] y  shows the change in y as x changes by 1 unit. We found that this change is the value of 'm'. It is called slope of the line this equation represents (each linear equation represents a line).

To find the answer we have to put it into y=mx+b format.

Given the function 30x+5y=15

This means that it will be;

5y = -30x+15

So it will simplify and gives;

y=-6x+3

If y=2

substitute then;

2=-6x+3

x  =1/6

Thus x would equal 1/6.

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Answer:

Step-by-step explanation:

The first step will be to make y the subject of the formula, by multiplying both sides of the equation by -1.

y = x - 1

This is simply the equation of a line with a slope of 1 and y-intercept (0,-1)

To determine the three points that solve the equation, we can let x be;

0, 1, 2

When x =0, y = 0-1 = -1

When x = 1, y = 1-1 = 0

When x = 2, y = 2 - 1 = 1

Therefore, we have the following three sets of points that can be used to graph the given linear equation;

(0, -1)

(1, 0)

(2, 1)

Find the attached for the graph

Answer:

The correct answer option is: True.

Step-by-step explanation:

Its true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.

For example, for the given non linear equation, start by dividing both sides by coefficient of the variable.

Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.

Answer: true

Step-by-step explanation: A pex

Final answer:

The sum of the absolute deviations for the given data set is 14.

Explanation:

To find the sum of the absolute deviations of a data set, you need to find the absolute value of the difference between each data point and the mean, and then add them up. Here is the calculation for the given data set:

Absolute deviations: |8-10| + |5-10| + |15-10| + |12-10| + |10-10| = 2 + 5 + 5 + 2 + 0 = 14

So, the sum of the absolute deviations for this data set is 14.

Answer:

"The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis."

Step-by-step explanation:

:)

Final answer:

The y-intercept is the point where a graph crosses the y-axis, while the x-intercept is the point where a graph crosses the x-axis.

Explanation:

The y-intercept is the point where a graph crosses the y-axis. It is represented by the coordinate (0, b), where b is the y-coordinate of the intercept. The y-intercept can be found by analyzing the equation of the line y = mx + b, where b is the y-intercept.

The x-intercept, on the other hand, is the point where a graph crosses the x-axis. It is represented by the coordinate (a, 0), where a is the x-coordinate of the intercept. To find the x-intercept, set y equal to 0 in the equation y = mx + b and solve for x.

Answer:

Option C. 6

Step-by-step explanation:

we know that

If NM bisects the angle ENL

then

∠MNL=∠MNE

In the right triangle MLN

sin(∠MNL)=ML/MN -----> equation A

In the right triangle MEN

sin(∠MNE)=6/MN -----> equation B

equate equation A and equation B

ML/MN=6/MN

Simplify

ML=6

Answer:

degree of vertex B = 2

degree of vertex g = 4

Step-by-step explanation:

Using given picture we need to find about what is the degree of vertex B and G.

In graph theory, we know that the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex.

So we just need to count how many edges are incindent on vertex B and G.

From picture we see that number of edges incident on vertex B = 2

Hence degree of vertex B = 2

From picture we see that number of edges incident on vertex G = 4

Hence degree of vertex g = 4

A dilation with a scale factor greater than 1 and then a translation is correct.

Dilation of a figure will leave its sides to get scaled (multiplied) by the same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due to the involvement of coordinates, it involves a center of a dilation, which is like a pinned point that stays at the same place after dilation.

It's like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

Dilation totally depends on the scale factor.

We need to find the composition of similarity transformations maps A

LMN to AL'M'N'.

If the absolute value of the scale factor is more than 1, then it represents the enlargement and if the absolute value of the scale factor lies between 0 to 1, then it represents the compression.

Therefore, a dilation with a scale factor greater than 1 and then a translation is correct.

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Answer:

D.a dilation with a scale factor greater than 1 and then a translation.

Answer:

A=2(wl+hl+hw)

2·(4·7+15·7+15·4)

386

Step-by-step explanation:

Answer:

1 2 3 1

Step-by-step explanation:

To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam!

Answer:

The GCF is [tex]u^3v^2[/tex]

Step-by-step explanation:

The given monomials are:

[tex]u^3v^6[/tex]

and

[tex]u^6v^2[/tex]

The greatest common factor is the product of the least powers of the common factors.

The least of the powers of the common factors are:

[tex]u^3[/tex] and [tex]v^2[/tex].

Their product is [tex]u^3v^2[/tex]

Therefore the Greatest Common Factors is [tex]u^3v^2[/tex]