If $4,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is: (a) 7% simple interest: $ (b) 7% compounded annually: $ (c) 7% compounded quarterly: $ (d) 7% compounded monthly: $ Round your answers to the nearest cent.

So the correct statement is:

" The GCF of the numbers in each term in the expression is 2"

Here we have the expression:

12d - 26c

To rewrite ti as a product, we need to find the greatest common factor between 12 and 26.

The decomposition of these two numbers is:

12 = 2*2*3

26 = 2*13

The greatest common factor between the two numbers is 2, then we can rewrite:

12d - 26c = 2*(6d - 13c)

So the correct statement is:

" The GCF of the numbers in each term in the expression is 2"

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The domain f the function is (-∞, 1/3) U (1/3, ∞)

The composite functions are also known as function of a function

Given the following functions

f(x) = √2-6x

g(x) = -1/x

In order to determine the composite function g(f(x))

g(f(x)) = g(√2-6x)

Replace x with √2-6x in g(x)

g(f(x))  = -1/√2-6x

The expression does not exist when √2-6x = 0

2-6x = 0

x = 1/3

The values shows that the domain of the function exists on all real numbers except 1/3.

Hence the domain f the function is (-∞, 1/3) U (1/3, ∞)

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See below for the response to each question

The study is experimental.

This is so because, the administer surveyed random college students

This is the total number of students in the college

Hence, the population of interest is the students in the college

This is the value that gives the required information.

Hence, the parameter of interest is the proportion of college students that work part-time

This is the students that were randomly surveyed

Hence, the sample in the study is the  2,512  students that were randomly surveyed

The statistic is the sample mean

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The probability is illustrated below.

1) Raffles game is a gambling competition in which people get numbered tickets and each number has an equal chance of winning.

2) When two dice are rolled then there will be totally 36 outcomes. Of those the outcomes with sum 8 are (2,6),(3,5),(4,4),(5,3),(6,2).

These are 5 in number.

So,P( sum =8)= 5/36.

3)This is a true statement.

4) Here win, lose, or tie is just the outcomes where their probabilities are different from each other and those values depend upon different situations.

5) Tossing a coin is a random experiment which means that the result of the experiment (ie head or tail) cannot be predicted.

6) If 60% said yes to " study during the week" then 40% will say yes to "either won't study or study at weekend".

7) When two coins are tossed, the outcomes are as follows

H,H

H,T

T,H

T,T.

So, P( head, tail ) =2/4 =1/2

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The reasons for each incorrect statement are as follows;

The term probability put simply is the ratio of the desired outcome to the possible outcomes. It therefore follows that probability as the name implies is used to predict the chance of an occurrence.

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Answer:

[tex]\huge\boxed{\sf \{-3, 1/2\}}[/tex]

Step-by-step explanation:

4x² + 10x = 6

Take 2 common

2(2x² + 5x) = 6

Divide 2 to both sides

2x² + 5x = 3

Subtract 3 to both sides

2x² + 5x - 3 = 0

Using mid-term break

2x² + 6x - x - 3 = 0

Take common

2x(x + 3) - 1(x + 3) = 0

Take (x + 3) common

(x + 3)(2x - 1) = 0

Either,

x + 3 = 0      OR     2x - 1 = 0

x = -3           OR       2x = 1

x = -3            OR     x = 1/2

[tex]\rule[225]{225}{2}[/tex]

Answer: x = 3 or (-1/2)

Step-by-step explanation:

Given equation

4x² + 10x = 6

Subtract 6 on both sides

4x² + 10x - 6 = 6 - 6

4x² + 10x - 6 = 0

Use cross-multiplication to factorize the quadratic

Starting with:

2x             -6

2x             1

This gives us:

(2x - 6) (2x + 1) = 0

Assume each value in the parenthesis to be 0

PART I:

2x - 6 = 0 ⇒ Given equation

2x - 6 + 6 = 0 + 6 ⇒ Add 6 on both sides

2x / 2 = 6 / 2 ⇒ Divide 2 on both sides

[tex]\boxed{x=3}[/tex]

PART II:

2x + 1 = 0 ⇒ Given equation

2x + 1 - 1 = 0 - 1 ⇒ Subtract 1 on both sides

2x / 2 = -1 / 2 ⇒ Divide 2 on both sides

[tex]\boxed{x=-\frac{1}{2} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It is proportional.  When You graph it, it will go through the origin.  The slope is 5.  The y intercept is 0.

Step-by-step explanation:

When a linear function is proportional, the slope will be in the form of y/x.

So, say we put 2 in for x, then y would be 10.  2 is the x and 10 is the y.  What is 10/2? 5 (the slope)

If we put in 6 for x, then y would be 30.  5 is the x and 30 would be the y.  What is 30/5? 5 (the slope)

if we put in -3 for x, then y would be -15.  -3 is the x and -15 would be the y.  What is -15/-3? 5 (the slope).

We could not find the slope this way, if the line was not proportional.

For example, if the y intercept is not zero, like

y = 5x + 2.  If I put 3 in for the x, then the y would be 17.  Is 17/3 equal to 5?  No, because the line is not proportional.

The conclusion is P(pass l morning) = 0.56

P(pass l afternoon) = 0.72

Conclusion: a student taking the test in the afternoon has a greater probability of passing than a student taking the test in the morning.

Probability is the odds that a random event would happen. The odds that the event would happen lies between 0 and 1. The closer the probability is to one, the more likely it is for the event to happen.

P(pass l morning) = number of students who took the test in the morning and passed / total number of students that took the exam in the morning

28 / 50 =  0.56

P(pass l afternoon) = number of students who took the test in the afternoon and passed / total number of students that took the exam in the afternoon  = 36 / 50 = 0.72

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Answer:

C

Step-by-step explanation:

Just took the quiz

The graphed function is: y = (x + 2)(x − 1)(x − 3).

Option (a) is correct.

From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.

From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.

The critical points for a function are obtained by substituting the function to be equal to zero.

So, (x + 2)(x − 1)(x − 3) = 0

That is, x= -2, x = 1 and x = 3.

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a. central angle is ∠QPR

b. semicircle is QRS

c. major arc is arc QTS

d. m∠QPR = 130° [central angle theorem]

e. arc QTS = 180°

The central angle theorem states that the measure of the intercepted arc will always be equal to the central angle.

a. A central angle is ∠QPR

b. A semicircle is QRS

c. A major arc is arc QTS

d. Measure of arc QR = m∠QPR = 130° [central angle theorem]

e. arc QTS = semicircle = 180°

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Using the z-distribution, the p-value would be of:

b) 0.0086.

At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, we test if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

For the distribution of differences, it is given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

z = -2/0.76

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

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Answer:

-129

Step-by-step explanation:

good luck

The distance are

a. 42.42

b. 15. 52

80 = 65 + <ABC

<ABC = 80 - 65

= 15

Through the use of sine rule we would have

By using sine rule,

Sine 15/a = sine 135/b =

sin 30/30.

Next we have to solve b by cross multiplying

b = (30× sin135) / sin 30

= 21.21/0.5

b = 42.42 km

Also, the value of a will be:

= (42.42 × sin 15) / sin 135

= 10.98/0.7071

= 15.52

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Step-by-step explanation:

you need to use the ruler to measure the lengths of it, like place the ruler from A to B and look at the measurement of it

Answer:

36

Step-by-step explanation:

81 x (4/9) =

36

The equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

A line is the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given that m=1, b=-3, the required equation will be y = x - 3 or x - y = 3

For the parameter m=1, (-1,2)

y - 2 =1(x+1)

y - 2 = x+1

y =x + 3

Hence the equation of the line for the parameters m=1, (-1,2)  is y = x + 3

For the coordinates (-2,3),(-3,4)

Slope = 4-3/-3+2
Slope = -1

For the intercept;

4 =-1(-3) + b

b = 4 - 3

b = 1

Hence the equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

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[tex]a {}^{2} + ab - 2 {b}^{2} [/tex]

[tex] = (a - b) {}^{2} [/tex]

[tex]\square[/tex] The function is continuous. [False]

Both pieces of the function are continuous, so the overall continuity of [tex]g(x)[/tex] depends on continuity at [tex]x=0[/tex].

We have

[tex]\displaystyle \lim_{x\to0^-} g(x) = \lim_{x\to0} \left(\frac1{2^x} + 3\right) = 1 + 3 = 4[/tex]

and

[tex]\displaystyle \lim_{x\to0^+} g(x) = \lim_{x\to0} (-x^2+2) = 2[/tex]

The one-sided limits do not match, so [tex]g[/tex] is not continuous at [tex]x=0[/tex].

[tex]\square[/tex] As [tex]x[/tex] approaches positive infinity, [tex]g(x)[/tex] approaches positive infinity. [False]

[tex]g(x)[/tex] is a large negative number when [tex]x[/tex] is very large, so [tex]g(x)[/tex] is approaching negative infinity.

[tex]\boxed{\checkmark}[/tex] The function is decreasing over its entire domain. [True]

This requires [tex]g'(x) \le 0[/tex] on the entire real line. Compute the derivative of [tex]g[/tex].

[tex]g'(x) = \begin{cases}-\ln(2)\left(\dfrac12\right)^x & x<0 \\\\ ? & x=0 \\\\ -2x & x>0 \end{cases}[/tex]

• [tex]\left(\frac12\right)^x > 0[/tex] for all real [tex]x[/tex], so [tex]g'(x)<0[/tex] whenever [tex]x<0[/tex].

• [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so [tex]-x^2\le0[/tex] and [tex]-x^2+2\le2[/tex]. Equality occurs only for [tex]x=0[/tex], which does not belong to [tex]x>0[/tex].

Whether the derivative at [tex]x=0[/tex] exists or not is actually irrelevant. The point is that [tex]g(b) < g(a)[/tex] if [tex]b>a[/tex] for all real [tex]a,b[/tex].

[tex]\boxed{\checkmark}[/tex] The domain is all real numbers. [True]

There are no infinite/nonremovable discontinuities, so all good here.

[tex]\boxed{\checkmark}[/tex] The [tex]y[/tex]-intercept is 2. [True]

When [tex]x=0[/tex],

[tex]g(0) = -0^2 + 2 = 2[/tex]

The quadratic equation has the following results: (p, q) = (8, 15), minimum point: (h, k) = (1, 4), range of values: - 4 < x < - 3

In this question we have a quadratic equation of the form y = x² + p · x + q , whose missing coefficients can be found by solving on the following system of linear equations:

- 5 · p + q = - 25

- 3 · p + q = - 9

(p, q) = (8, 15)

The vertex represents the minimum point, which is found by changing the form of the equation from standard form into vertex form:

y = x² + 8 · x + 15

y + 1 = x² + 8 · x + 16

y + 1 = (x + 4)²

(h, k) = (1, 4)

And lastly we must solve for x in the following inequality:

x² + 8 · x + 15 < x + 3

x² + 7 · x + 12 < 0

(x + 3) · (x + 4) < 0

- 4 < x < - 3

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Using proportions, the property tax on a house with an assessed value of $762,000 is of $8,890.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate, as a proportion, is:

7280/624000 = 0.011667.

Hence, the property tax on a house with an assessed value of $762,000 is of:

0.011667 x 762,000 = $8,890.

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The equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

Simple harmonic motion can be defined as a periodic motion of a point in a straight line, such that its acceleration is towards a fixed point and is proportional to its distance from that point to the line.

It is derived from the projection to the axis of a circle of a point in constant speed on the circumference

Displacement is represented thus;

d ( t ) = A sin⁡ ( 2 π f t )

T = 1/f

Where,

Note that there is no phase shift

d (t) = 7 sin ( 2π × 1/ 6 t)

d (t) = 7 sin ( 2π/6 t)

d (t) = 7 sin ( 3π t)

Thus, the equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

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Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.

In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

[tex]mPn=\frac{m!}{(m-n)!}[/tex]

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

In this case, you have:

Then, you know that:

Replacing in the definition of permutation:

[tex]7P6=\frac{7!}{(7-6)!}[/tex]

Solving:

[tex]7P6=\frac{7!}{1!}[/tex]

7P6= 5040

Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

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Answer:

x=1

Step-by-step explanation:

[tex] \sqrt{( - 3 - x) ^{2} + {( - 2 - 3)}^{2} } = \\ \sqrt{ {(4 - x)}^{2} + {(5 - 3)}^{2} } \\ \\ 9 + 6x + {x}^{2} + 25 = \\ 16 - 8x + {x}^{2} + 4 = = = > \\ 34 + 6x = 20 - 8x = > \\ 14 = 14x = = = > x = 1[/tex]

Done

The value of x that makes up the coordinate of B is -1

To find the value of x, we need to determine the coordinates of point B.

Since A to (B) = B to (C), the distance from point A to point B is equal to the distance from point B to point C. The distance between two points in a coordinate plane can be calculated using the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distances:

Distance A to (B):

x₁ = -3 (x-coordinate of point A)

y₁ = -2 (y-coordinate of point A)

x₂ = x (x-coordinate of point B)

y₂ = 3 (y-coordinate of point B)

Distance A to (B) = √((x - (-3))² + (3 - (-2))²)

Distance A to (B) =√((x + 3)² + 5²)

Distance A to (B) = √(x² + 6x + 9 + 25)

Distance A to (B) = √(x² + 6x + 34)

Distance B to (C):

x₁ = x (x-coordinate of point B)

y₁ = 3 (y-coordinate of point B)

x₂ = 4 (x-coordinate of point C)

y₂ = 5 (y-coordinate of point C)

Distance B to (C) = √((4 - x)² + (5 - 3)²)

Distance B to (C) = √((4 - x)² + 2²)

Distance B to (C) = √((4 - x)² + 4)

Distance B to (C) = √(x² - 8x + 20)

Since A to (B) = B to (C):

√(x² + 6x + 34) = √(x² - 8x + 20)

Now, we can square both sides to get rid of the square root:

x² + 6x + 34 = x² - 8x + 20

Next, move all the x terms to one side of the equation:

x² - x² + 6x + 8x = 20 - 34

Combine like terms:

14x = -14

Finally, solve for x:

x = -14 / 14

x = -1

So the value of x is -1. Point B is located at (-1, 3).

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The maximum height of the object is 15.4 m and occurs at 0.295 sec. The object touches ground at 2.06 seconds

An equation is an expression that shows the relationship between two or more variables and numbers.

A ball is thrown upward from the top of a building 15 meters high, at a velocity of 2.8m/sec. Hence:

s = -4.9t² + 2.8t + 15

The maximum height is at s'(t) = 0, hence:

-9.8t + 2.8 = 0

t = 0.295 s

s = -4.9(0.295)² + 2.8(0.295) + 15 = 15.4 m

The object reaches ground when s = 0, hence:

0 = -4.9t² + 2.8t + 15

t = 2.06 seconds

The maximum height of the object is 15.4 m and occurs at 0.295 sec. The object touches ground at 2.06 seconds

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The graph that best corresponds to the situation is graph 4; option C

Number of pages read is on the y - axis

Time taken is on the x - axis

Therefore, graph 4 represent the situation

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The probability of picking a ticket that is green or has a number greater than four is 3/5

The given parameters are:

Yellow = 1 - 5

Green = 1 - 5

Total = 10

There are 2 cards whose numbers are greater than 4 i.e. Yellow 5 and Green 5

So, we have:

P(Number greater than 4) = 2/10

There are 5 green cards.

So, we have:

P(Green) = 5/10

Also, 1 green card is numbered greater than 4

So, we have:

P(Green greater than 4) = 1/10

The required probability is:

P = P(Green) + P(Number greater than 4) - P(Green greater than 4)

This gives

P = 5/10 + 2/10 - 1/10

Evaluate

P = 6/10

Simplify

P =3/5

Hence, the probability of picking a ticket that is green or has a number greater than four is 3/5

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Answer:

$17.2

Step-by-step explanation:

120 + 16*100 = 120 + 1600 = 1720

The member pays $1720 annually for 100 classes and membership fee combined.

1720/100 = 17.2

The student pays $17.2 per class on average.

Answer:

- Please see the attached picture for full solution!:)

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based on the given area for the six habitats, Dullinger and his colleagues can find the p-value to be 0.0018.

a chi-squared test is the best test for to find the p-value and when the data given is put through a chi-square model, the observed values are:

= 7, 9, 2, 11, 2, 0

the expected values should be:

= 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

the p-value will be 0.001819

df = 5

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Answer: The base graph vertically stretched by a factor of 6.

Step-by-step explanation:

See attached image.