Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one
day. It is reasonable to assume that the population is approximately normal.

4.754 4.372 4.174 4.678 4.424 4.227
4.123 4.254 3.951 4.291 4.414


(a) Construct a 95% confidence interval for the mean rate. Round the answer to at least four decimal places.
A 95% confidence interval for the mean rate is < M

1) The scatter plot at the right most likely represents the number of siblings a person has and the person’s GPA.

2) The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is; 17 gallons

1) Scatter plots are defined as the graphs that present the particular relationship between two variables in a data-set.

A scatter plot is also defined as a chart type that is usually used to observe and visually display the relationship between variables.

From the given scatter plot, we can say that the scatter plot at the right would most likely be used to represent the number of siblings a person has and the person’s GPA.

2) From the given scatter plot, we can see that the x-axis shows the number of days left since filling up while the y-axis represents the gallons of gas.

Now, we want to find out the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up. We will trace 3 on the x-axis and the corresponding value on the y-axis would be approximately 17 gallons.

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Answer:1/5

Step-by-step explanation:

it correct

Answer:

Step-by-step explanation:

Second part to the answer is 3/20

The number of subsets that the set S , seasons of the year is 16  .

In the question ,

it is given that

the Set S have elements as the seasons of the year , that is

Set S [tex]=[/tex] { Summer , Spring , Fall , Winter }

So , the number of elements that are present in the  set S = 4 ,

we know that the number of subsets of the set having n elements is = 2ⁿ .

So , the number of subsets of the set S having 4 elements is =  2⁴ = 16

Therefore , The number of subsets that the set S , seasons of the year is 16  .

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The equation if a=4 represents the number of people who can go to the park is 8.75 + 26.50a = C.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

a formula that expresses the connection between two expressions on each side of a sign.

Typically, it has a single variable and an equal sign.

Like this: 2x - 4 = 2.

In the above example, the variable x exists.

So, the equation represents the number of people who can go to the park:

The total budget is $114.75.

Parking costs $8.75.

The cost of a ticket per person is $26.50.

So form the equation:

Let, a be the number of people and C be the total cost.

8.75 + 26.50a = C

Now, let a be 4.

8.75 + 26.50a = C

8.75 + 26.50(4) = C

8.75 + 106 = C

114.75 = C

Therefore, the equation if a=4 represents the number of people who can go to the park is 8.75 + 26.50a = C.

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Answer:

Step-by-step explanation:

You have segment RT of length 77 with point S on it dividing it into segments RS=6y+3 and ST=5y+8. You want to know the value of y and the lengths of segments RS and ST.

The segment sum theorem tells you the whole is the sum of the parts:

  RS +ST = RT

  (6y +3) +(5y +8) = 77 . . . . . use given values

  11y +11 = 77 . . . . . . . . . . . . collect terms

  y +1 = 7 . . . . . . . . . . . . . . . divide by 11

  y = 6 . . . . . . . . . . . . . . . . . subtract 1

The lengths of the parts are ...

  RS = 6y +3 = 6(6) +3 = 39

  ST = 5y +8 = 5(6) +8 = 38

The speed of the wave is 2 m/s.

Given,

Time taken by wave to travel back and forth=25 seconds

Length of the pool = 25 meters

As given, the wave travels the length of pool and returns back then,

distance covered by wave is twice the length of pool i.e. [tex]2*25=50[/tex] meters

To find speed of the wave, use formula

[tex]Speed=\frac{Distance covered }{time taken}\\\\Speed=\frac{50}{25} \\\\Speed=2 m/s[/tex]

Thus, the speed of the wave is 2 meter/sec.

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Using the given information, the length of LM is and the length of LN is 12

From the question, we are to determine the length of LM and LN.

From the given information,

M is the midpoint of LN

Therefore,

LM = MN

Also,

From the given information,

LM = 3x

MN = 2x + 2

Thus,

3x = 2x + 2

Solving for x

3x = 2x + 2

3x - 2x = 2

x = 2

Then,

Substitute the value of x in the equation

LM = 3x

LM = 3(2)

LM = 6

Also,

LN = LM + MN

LN = 3x + 2x + 2

LN = 5x + 2

Substitute the value of x

LN = 5(2) + 2

LN = 10 + 2

LN = 12

Hence, the value of LM is 6 and the value of LN is 12

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Answer:

b) 9m + 20

Step-by-step explanation:

Given expression,

→ 5m - (2m - 8) + 12 + 6m

Simplifying the expression,

→ 5m - (2m - 8) + 12 + 6m

→ 5m - 2m + 8 + 12 + 6m

→ (5m - 2m + 6m) + (8 + 12)

→ 9m + 20

Hence, answer is 9m + 20.

Answer:

D

Step-by-step explanation:

The coefficient is the number before the varaible x.

The Two Consecutive integers are 7 and 8.

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

Let the first Integer be x

Since the two numbers are consecutive

therefore the second number will be x+1

Now given:

square of the second integer added to 6 times the first is equal to 106.

( x+1 )²+6x=106

Expand  ( x+1 )² using [tex](a+b)^2=a^2+2ab+b^2[/tex]

x²+2x+1+6x=106

x²+8x+1-106=0

x²+8x-105=0

Factor the expression

(x-7)(x+15)=0

x-7=0,  x+15=0

x=7, x=-15

Now we get 2 values of x which is 7 and -15.

Since it is given that number is a positive Integer hence the number will be 7.

and the other number would 7 + 1 = 8.

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The other points (7.3, 2.2) are on a line that includes points (-5, 4) and (4, 1).

What is the equation of a line?

The equation of a line is written as axe + by + c = 0, which is its conventional form. In this equation, the variables x and y are the constant term, while the coefficients a and b are the coefficients. It is a first-order equation with the variables x and y.

Slope using the formula:

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

We have two points, (-5, 4) and (4, 1).

m = (1 - 4) ÷ (4 - (-5))

m = −1/3

m = -0.3

Line Equations with Slope : y - y1 = m(x - x1)

Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point-slope form.

Let's use a point from the original example above  (4, 1). and the slope we calculated as -0.3. Put those values in the point-slope format to get an equation of that line in the point-slope form:

y - 1 = -0.3(x - 4)

y = -0.3x + 2.2

Using the equation y = -0.3x + 2.2, set x=0 to find the y-intercept.

y = -0.3(0) + 2.2

y = 2.2

The y-intercept is 2.2

Using the equation y = -0.3x + 2.2, set y=0 to find the x-intercept.

0 = 3x - 6

0 = -0.3x + 2.2

0.3x  = 2.2

x = 7.3

The x-intercept is 7.3.

Hence, the other points (7.3, 2.2) are on a line that includes the points (-5, 4) and (4, 1).

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Answer: 1- 26%

Step-by-step explanation:

just divide 100 by 100 and remove the % sign :)

The component form of the vector that translates C to D is <7, -3>

A translation is a movement in a straight line.

In order to determine the component form of the vector that translates C to D, we have to subtract the coordinate values of point C from the coordinate values of the image C:  

(x, y) = D - C  

The movement from C to D on the x-axis is 7 units to the right (positive 7) while movement on the y-axis is 3 units down (negative -3). Thus:

(x, y)  = (7, -3)

In vector form, <x, y> = <7, -3>

Therefore, the vector that translates C to D is <7, -3>

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The measure of angle CDE ( ∠CDE) is 55°. The correct option is the first option  55°

From the question, we are to determine the measure of angle CDE.

From one of the circle theorems, we have that

"The measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs"

Thus,

m ∠CDE = 1/2(measure of arc CBE - measure of arc CE)

From the given information,

Measure of arc CE = 125°

Then,

Measure of arc CBE = 360° - 125°

Measure of arc CBE = 235°

Therefore,

m ∠CDE = 1/2(235° - 125°)

m ∠CDE = 1/2(110°)

m ∠CDE = 55°

Hence, the measure of ∠CDE is 55°

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Answer:

Guys this answer is wrong

Step-by-step explanation:
when you are coming from the center point of the circle it mirrors the arc wich is 125 degrees
But when we are trying to figure out the angle which is CDE its always half of the arc of the circle
So you would do 125/2
wich gives you 62.5
therefore your answer is 62.5
No hate to the other guy but plsssss make sure you read the question before answering

Step-by-step explanation:

secx - 2=0

secx= 2

x= π/3

that's it

The x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.

To verify the given equation, we need to find the value(s) of x that satisfy the equation Sec(x) - 2 = 0.

Sec(x) represents the secant function, which is the reciprocal of the cosine function.

The equation can be rewritten as follows:

Sec(x) = 2

To find the solutions, we can take the reciprocal of both sides:

1 / Cos(x) = 2

Next, we can invert the equation to get the cosine function alone:

Cos(x) = 1/2

The cosine function has a value of 1/2 at two specific angles in the interval [0, 2π]: π/3 and 5π/3.

These angles correspond to the inverse cosine function (arccos), so we have:

x = arccos(1/2) = π/3 or x = arccos(1/2) + 2π = 5π/3

Therefore, the x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.

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Answer:

Slope = 1/3

Y-intercept = 0

Step-by-step explanation:

Hello!

Slope - Intercept Form: y = mx + b

The slope is the coefficient before the x-variable. Which means that the slope would be 1/3.

The y-intercept is the constant term after the x-term. In this case, there is no term, so the y-intercept is 0.

Answer:

Slope: 1/3

y-intercept: 0

Step-by-step explanation:

y=mx+b

the coefficient (m) of x is always the slope, so therefore the slope is 1/3

the y-intercept (b) is not here in this equation, so the y-intercept is 0

Answer:

4

Step-by-step explanation:

3/1=3

hence 3/(3/4 )= 3 x4/3=4

Answer:

4

Step-by-step explanation:

keep switch flip

3/1 * 4/3 = 12/3 = 4

The value of m is equal to 7√5 using the Pythagoras' theorem.

What is are Right Angled Triangle?

According to the definition of a right triangle, if one of the triangle's angles is a right angle (90°), the triangle is referred to as a right-angled triangle or just a right triangle. Triangle ABC is a right triangle in the example image, and its components are the base, altitude, and hypotenuse. Here, the base is represented by AB, the altitude by AC, and the hypotenuse by BC. The largest side and side opposite to the right angle of a right triangle, the hypotenuse, is the side that needs to be considered.

The sum of any two sides of a triangle's three sides is always more than the sum of its third side, making it a regular polygon. A triangle only possesses this quality.

In the figure

From Pythagoras' theorem, we have, h² = p²+b²

Now we can write 3 equations from the figure i.e

m²=7²+n²

m²=35²-x²

x²=n²+28²

So we have m²=35²-n²-28²

⇒m²=35²-28²-m²+7²

⇒2m²=35²-28²+7²

⇒2m²= 490

⇒m²= 490/2

⇒m= 7√5

Hence, the value of m in the figure is 7√5

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The amount of milliliters of acid that are in the resulting mixture is 522 ml and the percentage of the resulting mixture is 83.6%.

a. Milliliters of acid:

Milliliters of acid = ( .18 x 125ml) +500 ml

Milliliters of acid = 522.5ml

b. Percentage of the resulting mixture

Percentage of the resulting mixture = 522.5ml /(125ml + 500 ml)

Percentage of the resulting mixture = 522.5ml  / 625 ml × 100

Percentage of the resulting mixture =83.6%

Therefore the milliliters of acid is 522.5ml.

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The function that can easily be seen when a quadratic function is given

in the form: y = a (x − ℎ)^2 + K are

A parabola is given in factored form when it is in the form

y = a (x − ℎ)^2 + K

the factored form can be rearranged

(y - k) = a (x − ℎ)^2

The vertex is v(h, k)

the axis of symmetry of the parabola when the parabola is written in the form as in the question is of the formula x = -b/2a.

this says that the axis of symmetry is a vertical line

the focus is given by f(h, k + 1/4a)

"a" curve opens up when a is positive and down when a is negative. when (x − ℎ) = a (y − k)^2, a opens left or right

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The value of the equation (2a^2 +a + 3) divided by (a - 1) is 2a + 3.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the equation is illustrated as:

(2a² +a - 3) divided by (a - 1). This will be

(2a² +a - 3) / (a - 1)

It should be noted that (2a² +a + 3) will be:

(2a² +a + 3)

= 2a² - 2a + 3a - 3

= 2a(a - 1) + 3(a - 1)

= (2a + 3)(a - 1)

This will be:

= (2a + 3)(a - 1) / (a - 1)

= 2a + 3

The value is 2a + 3.

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Complete question

(2a^2 +a - 3) divided by (a - 1)

Supplier which gives the best deal of selling light bulbs for the electrician is ZZZ LIGHTING with the total selling amount of

$ 30676.2.

As given in the question,

Different suppliers sells energy saving light bulbs with different deals,

Number of bulbs  required by an electrician = 250

Different deals of selling amount are as follow:

1. ELECTRA :

123 (250) + 350

=$31100

2. ZZZ LIGHTING :

140(250) + 260

= $35260

13% discount on final amount

= 13% of 35260

= 4583.8

Total amount to pay = 35260 - 4583.8

                                  = $30676.2

3. SPARX :

Offer of Buy one get one and no delivery fee

Total amount to be pay for 125 light bulbs.

255 (125)

= $31875

4. BRIGHTEX :

190(250) + 100

= $47600

With a third off on the final amount

(1/3) of 47600

= $15866.666..

= $15867 (approximately)

Final payment = 47600 - 15867

                        = $31733

$31875 > $31733 > $31100 >  $30676.2

Therefore, supplier which gives the best deal of selling light bulbs for the electrician is ZZZ LIGHTING with the total selling amount of

$ 30676.2.

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Prime factors  from the factors of the given numbers are as follow :

a. 256 = { 2 }

b. 361 = { 19 ]

c. 225 = { 3, 5 }

As given in the question,

Given numbers are as follow:

a. 256     b. 361     c. 225

Prime numbers are those numbers which has only two factors 1 and number itself.

Simplify given numbers to get the prime factors from the factors of the followings  are as follow:

a. 256 = 16 × 16

      = 2⁴ × 2⁴

      = 2⁸

Prime factor of 256 = { 2 }

b. 361 = 19 × 19

19 itself is prime number.

Prime factor of 361 = { 19 }

c. 225

225 = 15 × 15

      = ( 3 × 5 )²

Prime factors are { 3, 5 }

Therefore, prime factors from the factors of the given numbers are as follow :

a. 256 = { 2 }

b. 361 = { 19 ]

c. 225 = { 3, 5 }

The complete question is :

Find the prime factorization of the following:

a. 256     b. 361     c. 225

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The width of the original rectangular slate is 14 inches.

A rectangle is an object that has four sides. The opposite sides are of equal length. A rectangle has two diagonals that are of equal length that bisect each other at right angles.

The area of a rectangle = length x width

Area of the new rectangular slate = (16 - 2) x (w - 2) = (16 x w) - 56

Area of the new rectangular slate = 14 x (w - 2) = 16w - 56

Area of the new rectangular slate = 14w - 28 = 16w - 56

In order to determine the value of w, take the following steps:

Combine similar terms together: 56 - 28 = 16w - 14w

Add similar terms together: 28 = 2w

Divide both sides of the equation by 2 : w = 28 / 2

w = 14

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Answer:

10

Step-by-step explanation:

You take 10,000 and divide it by 10 leaving 1,000. Then, you multiply 1,000 by 0.001 resulting in 10.

The customer will rent 4 bikes per dollar

Keller's bike deal with renting of bikes

At the Keller's bike rentals it costs $16 to rent a bike for 4 hours

Therefore the number of bikes per dollar can be calculated as follows

16= 4

x= 1

Cross multiply

4x= 16

x= 16/4

x= 4

Hence it costs a customer 1 dollar to get 4 bikes

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a. The function that models the population t years after 2000  is

Pf = 15600(1.04)^t

b. The estimate of the fox population in the year 2008 is  21349.67.

Given,

A fox population in a certain region has a continuous growth rate of 4% per year.

It is estimated that the population in the year 2000 was 15600.

we are asked to determine a function that models the popualtion t years after 2000 (t = 0 for 2000)

Pf = Pi(1 + r)^t  where Pf is the final population, Pi is the initial population, r is the annual growth rate in decimal (not %), and t is the time in years.

a.  Pf = 15600(1.04)^t

b.  Pf = 15600(1.04)⁸ = 24497.386

= 21349.67

hence we get the required answers.

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The probabilities, using the normal distribution, are given as follows:

a. P(0 < x < 0.5) = 0.1915.

b. P(-1.42 < x < 0) = 0.4222.

c. P(x > 0.46) = 0.3228.

d. P(x > -0.5) = 0.6915.

e. P(x < 2.05) = 0.9798.

f. P(x < -0.70) = 0.2420.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

For a standard normal random variable, the mean and the standard deviation are given as follows:

[tex]\mu = 0, \sigma = 1[/tex]

Hence each value of x is it's own z-score.

For item a, the probability is the p-value of Z = 0.5 subtracted by the p-value of Z = 0, hence:

P(0 < x < 0.5) = 0.6915 - 0.5 = 0.1915.

For item b, the probability is the p-value of Z = 0 subtracted by the p-value of Z = -1.42, hence:

P(-1.42 < x < 0) = 0.5 - 0.0778 = 0.4222.

For item c, the probability is one subtracted by the p-value of Z = 0.46, hence:

P(x > 0.46) = 1 - 0.6772 = 0.3228.

For item d, the probability is one subtracted by the p-value of Z = -0.5, hence:

P(x > -0.5) = 1 - 0.3085 = 0.6915.

For item e, the probability is the p-value of Z = 2.05, hence:

P(x < 2.05) = 0.9798.

For item f, the probability is the p-value of Z = -0.70, hence:

P(x < -0.70) = 0.2420.

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