Pizza Palace has a small business loan for 30 months at 6% interest. The expression for the total loan amount to be paid is p (1+r)^t, where:

t is time in years,
r is interest rate as a decimal, and
p is the principal of the loan.

Find the principal of the loan, to the nearest dollar, when the total loan amount to be paid is $404,886 at 30 months.

A manager says, “If the interest rate was cut in half, the difference between the total loan amount and the principal would also be cut in half.”

The statement is not always true.

Provide a specific example to refute the manager’s statement.

Answer:

Inverse Variation

Step-by-step explanation:

Answer: D. F(x)= (x-1)^2+3

Step-by-step explanation:

Answer:

2 and 45/60 which simplifies to 2 and 3/4

Answer:

Step-by-step explanation:

y = f(x) + n - moves the graph n units up

y = f(x) - n - moves the graph n units down

y = f(x + n) - moves the graph n units to the left

y = f(x - n) - moves the graph n units to the right

===================================================

5.5 units to the right

y = f(x - 5.5) = |x - 5.5|

Answer:

[tex]\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).[/tex]

[tex]\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}[/tex]

Answer:

  y = 1/3(x -2) +3

Step-by-step explanation:

The slope of the given line is the coefficient of x, -3. The slope of the perpendicular line will be the negative reciprocal of that: -1/-3 = 1/3. The line through a point (h, k) with slope m can be written in point-slope form as ...

  y = m(x -h) +k

For m=1/3, (h, k) = (2,3), the equation of the line is ...

  y = (1/3)(x -2) +3

Answer:

2/10

Step-by-step explanation:

First you - 20 from 40 (aka 2/10 - 4/10) and you will get 20 (aka 2/10).

To find out what fraction more of the pack Dan used on Saturday compared to Sunday, subtract 2/10 from 4/10.

To find out what fraction more of the pack Dan used on Saturday compared to Sunday, we need to subtract the amount used on Sunday from the amount used on Saturday and express it as a fraction of the original pack.

On Saturday, Dan used 4/10 of the pack. On Sunday, he used 2/10 of the pack. To find the fraction more, we subtract 2/10 from 4/10:

4/10 - 2/10 = 2/10

Therefore, Dan used 2/10 more of the pack on Saturday compared to Sunday.

option A

f(x) = (x – 1)2 + 3

Given in the question a function,

f(x) = 4 + x² – 2x

Step 1

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

Step 2

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

Answer:

2.375 has the same value as 2 and 3/8.

19/8 also has the same value as 2 3/8.

Answer:

[tex]2.05\ miles[/tex]  or  [tex]2\frac{1}{20}\ miles[/tex]

Step-by-step explanation:

we know that

To calculate the total distance Barb walked, add the distance to her friend's house plus the distance to the library.

so

[tex]1.3+\frac{3}{4}[/tex]

Remember that

[tex]1.3=\frac{13}{10}[/tex]

substitute

[tex]\frac{13}{10}+\frac{3}{4}=\frac{13*2+5*3}{20}[/tex]

[tex]=\frac{41}{20}\ miles[/tex]

[tex]=2.05\ miles[/tex]

Convert to mixed number

[tex]\frac{41}{20}=\frac{40}{20}+\frac{1}{20}=2\frac{1}{20}\ miles[/tex]

Answer: 8, 40, 80, 120

1 gallon is equal to 8 pints

The number of pints Jordan needs to fill the fish tank of [tex]15[/tex] gallons is as follow:

gallons :[tex]1 \ \ \ \ \ \ \ \ \ 5\ \ \ \ \ \ \ \ \ \ 10\ \ \ \ \ \ \ \ \ \ \ 15[/tex]

pint       :[tex]8 \ \ \ \ \ \ \ \ \ 40\ \ \ \ \ \ \ \ \ \ 80\ \ \ \ \ \ \ \ \ \ \ 120[/tex]

" Number is defined as the count of a given quantity."

According to the question,

Capacity of fish tank [tex]= 15\ gallons[/tex]

Capacity of a container used to fill the fish tank [tex]= 1 \ pint[/tex]

Standard relation gallons to number of pints

[tex]1 \ gallon = 8\ pints[/tex]

Number of pints required :

[tex]1 \ gallon = 8\ pints[/tex]

[tex]5\ gallon = (8\times 5)\ pints[/tex]

             [tex]= 40 \ pints[/tex]

[tex]10\ gallons = (10 \times 8) \ pints[/tex]

                [tex]= 80\ pints[/tex]

[tex]15\ gallon = (15 \times 8) \ pints[/tex]

               [tex]= 120 \ pints[/tex]

Hence, the number of pints Jordan needs to fill the fish tank of [tex]15[/tex] gallons is as follow:

gallons :[tex]1 \ \ \ \ \ \ \ \ \ 5\ \ \ \ \ \ \ \ \ \ 10\ \ \ \ \ \ \ \ \ \ \ 15[/tex]

pint       :[tex]8 \ \ \ \ \ \ \ \ \ 40\ \ \ \ \ \ \ \ \ \ 80\ \ \ \ \ \ \ \ \ \ \ 120[/tex]

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Answer:

The function f(x) is a geometric sequence

Step-by-step explanation:

If we let the first value of this function be denoted by y, then the second value will grow by;

12% of y

= (12/100)*y = 0.12y

The second value will thus be;

y + 0.12y = 1.12y

The third value will grow by;

12% of 1.12y

= (12/100)*1.12y = 0.12(1.12y)

The third value will thus be;

1.12y + 0.12(1.12y)

= 1.12y(1 + 0.12)

= 1.12y * 1.12 = [tex]1.12^{2}y[/tex]

The function f(x) will thus have the sequence;

y, 1.12y, [tex]1.12^{2}y[/tex], ans so on. This is clearly a geometric sequence since we have a common ratio of 1.12.

Answer: B

Ive done the test before, this was correct. glad i could help

If Tatiana ran the marathon with an average speed of 0.09 miles per minute. 5.4 was her speed to the nearest mile per hour

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

Tatiana ran the marathon with an average speed of 0.09 miles per minute

We know that a hour has 60 minutes.

Speed to the nearest mile per hour we will calculate by multiplying 0.09 with 60

Zero point zero nine times of sixty.

0.09×60

Five point four miles per hour.

5.4 miles/hour

Hence 5.4 miles/hour is Tatiana speed to the nearest mile per hour

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Let x represent those who both football and basketball

The given information can be illustrated in a Venn diagram as shown in the attachment.

We solve the equation below to find the value of x.

[tex](53-x)+x+(24-x)+31=101[/tex]

[tex]\implies -x+x-x=101-53-31-24[/tex]

[tex]\implies -x=-7[/tex]

[tex]\implies x=7[/tex]

From the second diagram;

25. [tex]P(Basketball)=\frac{17}{101}[/tex]

26. [tex]P(Football)=\frac{46}{101}[/tex]

27. [tex]P(Football\: \cap\:Basketball)=\frac{7}{101}[/tex]. This is because 7 play both Football and Basketball.

28. [tex]P(Football\: \cup\:Basketball)=\frac{46}{101}+\frac{17}{101}-\frac{7}{101}=\frac{56}{101}[/tex]. This is because there is intersection.

29. [tex]P(Neither\: \cup\:Both)=\frac{31}{101}+\frac{7}{101}=\frac{38}{101}[/tex]. The two events are mutually exclusive.

The 95% confidence interval for the difference of the two sample means, given a mean difference of 22 and a standard deviation of 10, ranges from 2.4 to 41.6.

The problem provided involves the concept of confidence intervals in statistics. When working with two sample means and you want to find the 95% confidence interval of the difference, the standard deviation of the difference is essential. The difference of two sample means is 22 and the standard deviation of this difference is estimated to be 10.

The 95% confidence interval for a mean can be calculated using the formula:
Confidence Interval = mean difference ± (Z-score * standard deviation).

With a 95% confidence interval, our Z-score (also known as the critical value) is approximately 1.96 (from Z tables or any statistical calculator). Thus, substituting the provided figures into the formula, we have:
Confidence Interval = 22 ± (1.96 * 10).

This gives us a confidence interval range of: 22 - 19.6 to 22 + 19.6, thus the 95% confidence

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The difference of the means of two populations at a 95% confidence interval is between 2.4 and 41.6.

To find the difference of the means of the two populations at a 95% confidence interval, we can use the formula:

CI = (difference of sample means) ± (critical value) × (standard deviation of the difference of sample means)

In this case, the difference of the sample means is 22 and the standard deviation of the difference of the sample means is 10. The critical value for a 95% confidence interval is approximately 1.96.

Using these values, we can calculate the confidence interval as follows:

CI = 22 ± (1.96) × 10

Simplifying the expression, the confidence interval is (2.4, 41.6).

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Answer:  The answers are given below.

Step-by-step explanation:  Given that the graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:.

Part A : We are to find the approximate y-intercept of the line of best fit and state what does it represent.

From the graph, we note that

at x = 0, the value of y is approximately 3.

So, the approximate y -intercept of the line of best fit is 3.

It represents that before starting the matches, the students can win 3 matches without any practice.

Part B : We are to write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice.

From the graph, we note that the line of best fit passes through the points (2, 7) and (9, 18).

So, the slope of the line of best fit will be

[tex]m=\dfrac{18-7}{9-2}=\dfrac{11}{7}.[/tex]

Therefore, the slope-intercept form of the equation of the line of best fit is given by

[tex]y=mx+c\\\\\Rightarrow y=\dfrac{11}{7}x+3.[/tex]

Thus, the number of matches that could be won after 13 months of practice is

[tex]y=\dfrac{11}{7}\times13+3=23.42.[/tex]

That is, students can win 23 matches with 13 months of practice.

The approximate y-intercept is 35.25 and it represents the starting point on the graph. The equation for the line of best fit is y = 0.09x + 35.25. After 13 months of practice, the prediction is that the student could win approximately 36 matches.

Part A: The approximate y-intercept of the line of best fit is 35.25. The y-intercept represents the number of matches a student would have won without any months of practice. In other words, it is the initial starting point on the graph when the number of months practiced is zero.

Part B: The equation for the line of best fit in slope-intercept form is y = 0.09x + 35.25. To predict the number of matches after 13 months of practice, we substitute the value of x (number of months) into the equation. Therefore, y = 0.09(13) + 35.25 = 36.42.

Therefore, the prediction is that the student could win approximately 36 matches after 13 months of practice.

Answer:

a) 1,440 ways

b) 59,280 or 64,000

Step-by-step explanation:

a) Aircraft boarding.

8 people, 2 in first class, boarding first, then 8 economy class.

The 2 people in first class board first, but they can board as AB or BA... so 2 ways here.

For the 6 economy class passengers, we have a permutation of 6 out of 6, so 720, as follows:

[tex]P(6,6) = \frac{6!}{(6 - 6)!} = 6! = 720[/tex]

Since the two are independent, we multiply them to have a global number of ways: 2 * 720 = 1,440 different ways for the 8 passengers to board that plane.

b) combination lock.

Here we do have a little problem... the question doesn't specify if the 3 numbers are different numbers of not.  So, we'll calculate both:

Numbers go from 1 to 40 inclusively... so 40 possibilities.

Normally, in a combination lock, the numbers are different, so let's start with that one:

First number: 40 options available

Second number: 39 options available (cannot take the first one again)

Third number: 38 different options (can't take First or Second number again)

Overall, we then have 40 * 39 * 38 = 59,280 different lock combinations.

If we can pick pick the same number twice:

First number: 40 options available

Second number: 40 options available

Third number: 40 options available

Overall 40 * 40 * 40 = 64,000 different lock combinations

[tex]d. \: y = 6 + 3x \\ \\ 1. \: 3x + 6 = y \\ 2. \: 3x = y - 6 \\ 3. \: \frac{3x}{3} = \frac{y - 6}{3} \\ x = \frac{1}{3} y - 2[/tex]

Answer:

Area of the biggest square: 25 m²

Area of the second biggest square: 16 m²

Area of smallest square: 9 m²

Area of triangle: 6 m²

Answer:

x = 3

Step-by-step explanation:

There are two ways to do this. The simplest way is to realize that the exterior angle (45x) = the sum of the two remote interior angles.

25x and 57 + x

45x = 25x + 57 + x                      Subtract 26x from both sides.

45x - 26x = 25x - 25x + 57   Combine

19x = 57                                Divide by 20

19x/19 = 57/19                     Do the division

x = 3

===================================

Second method.

The supplement of the 45x angle is 180 - 45x

Now add the three angles together.

180 - 45x + x + 57 + 25x = 180     Combine like terms.

180 + 57 - 45x + x + 25x = 180

237 - 19x = 180                              Subtract 237 from both sides.

- 19 x = 180 - 237                           Combine the right side

- 19x = -57

x = 3

Good thing you made me redo it. Sorry!! I made an error. I lost 1 of the xs.

For this case we have the following expression:

[tex]\sqrt {64}[/tex]

We have to:

[tex]64 = 8 * 8 = 8 ^ 2[/tex]

By definition of properties of powers and roots we have to meet:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression we have:

[tex]\sqrt {8 ^ 2} = 8 ^ {\frac {2} {2}} = 8 ^ 1 = 8[/tex]

Thus, we have that the result is a whole number "8".

Answer:

whole number

The perimeter of the shaded region is 39 ft.

The perimeter is the total length of all the sides of the shaded region. To find the perimeter, we need to add up the lengths of all the sides.

The perimeter of the shaded region is the sum of the lengths of all its sides.

Perimeter of a polygon = Sum of the lengths of all its sides

Perimeter of the shaded region = 14 ft + 6 ft + 15 ft + 4 ft

Perimeter of the shaded region = 39 ft

Therefore, the perimeter of the shaded region is 39 ft.

supplementary angles add to equal 180. so x + 57 = 180. solve for x and you get 123.

Answer:

Option 4 is correct

Step-by-step explanation:

If the rate is compounded continuously, the formula used to find the future value is:

A= Pe^rt

Where A = Future Value

P= Principal amount

r = interest rate in decimal

t = time

For the given data:

A=?

P = $5000

r = 7% or 0.07

t = 6

Putting values in the above formula

A= 5000e^(0.07 *6)

A = 7609.81

So, Option 4 is correct.

Answer:

(x+3)² + (y+4)²=25

Step-by-step explanation:

The question is on equation of a circle

The distance formula is given by;

√(x-h)²+ (y-k)²=r

The standard equation of  circle is given as ;

(x-h)²+ (y-k)²=r²

The equation of this circle with center (-3, -4) and radius 5 will be;

(x--3)² + (y--4)²=5²

(x+3)² + (y+4)²=25

ANSWER

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

EXPLANATION

The equation of a circle with center (h,k) and radius r units is given by:

[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

From the given information the center of the circle is (-3,-4) and the radius is r=5 units.

We substitute the known values to obtain:

[tex]{(x - - 3)}^{2} + {(y - - 4)}^{2} = {5}^{2} [/tex]

We simplify to get:

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

Therefore the equation of the circle in standard form is:

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

Using kinematic equations, we determine that the accelerating police car will catch up to the speeding car moving at a constant velocity in 20 seconds.

To solve the problem of when a police car accelerating at 4 m/s² will catch up to a speeding car moving at a constant velocity of 40 m/s, we can use kinematic equations for motion. The speeding car's position over time is given by the equation x = vavgt, where vavg = 40 m/s is the average velocity. Since the police car starts from rest (vo = 0) and has an acceleration of 4 m/s², its position over time is given by the equation x = 0.5at².

We set the displacement of both cars equal to each other to find the time (t) when they are at the same position:
40t = 0.5(4)t².

This simplifies to: 40t = 2t², and by further simplification, we find that t = 20 seconds. Thus, it will take the police car 20 seconds to catch up to the speeding car.

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Answer:

(5, -10)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

-9x - 6y = 15

9x - 10y = 145

Step 2: Solve for y

Elimination

Step 3: Solve for x

Step 4: Check

Graph the systems of equations to verify the algebraically solved solution set is the solution.

Where the 2 lines intersect is the solution set.

We see graphically that we get (5, -10).

∴ (5, -10) or x = 5 and y = -10 is the solution to our systems

Answer:

The measure of angle ERK is 55°

Step-by-step explanation:

step 1

Find the measure of arc EK

we know that

The diameter divide the circle into two equal parts

In this problem

EOR is a diameter

see the attached figure to better understand the problem

so

arc EK + arc RK=180°

substitute the given values

arc EK + 70°=180°

arc EK=180°-70°=110°

step 2

Find the measure of angle ERK

we know that

The inscribed angle is half that of the arc it comprises.

m∠ERK=(1/2)[arc EK]

substitute  

m∠ERK=(1/2)[110°]=55°

The measure of <ERK is 55 degrees

Given the following parameters

arcRK = 70 degrees

Determine the measure of arcEK
arcEK + arcRK + 180 = 360

arcEK + 70 + 180 = 360

arcEK + 250 = 360

arcEK = 110 degrees

<ERK = 1/2 arcEK

<ERK = 1/2(110)
<ERK = 55 degrees

Hence the measure of <ERK is 55 degrees

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An odd function like f(x) = -2x^5 + x^3 − 7x satisfies the property that y(x) = -y(-x), which indicates that the function is symmetric around the origin. The multiplication of odd and even functions results in an odd function, and the integral of an odd function over all space equals zero due to the cancelation of negative and positive areas.

The rule satisfied by the function f(x) = -2x^5 + x^3 − 7x, which is an odd function, is that y(x) = −y(-x). Essentially, what that means is that when you plug -x into the function, the sign of the result will be the opposite of the result of plugging x into the function. This rule manifests itself graphically as a kind of symmetry: odd functions are symmetric around the origin. They are produced by reflecting the graph of y(x) across the y-axis and then the x-axis. In contrast to even functions, which have symmetry around the y-axis, odd functions display this kind of 'rotational' symmetry.

Also worth noting, multiplying an odd function by an even function always yields an odd function. For instance, x*e^-x² is an odd function because x is an odd function and e^-x² is an even function. Additionally, the property of odd functions to integrate over space to zero is particularly useful, as they effectively 'cancel out' negative and positive areas along the x-axis.

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For this case we have that by definition, the associative property states that:

The order in which the factors (or addends) are associated does not alter the product (or the sum).

On the other hand, the commutative property states that:

The order of the factors (or addends) does not alter the product (or the sum).

Answer:

A. 10cm

B. 8 times

Step-by-step explanation:

The question is on volume of a conical container

Volume of a cone= [tex]\pi r^{2} h/3[/tex]

where r is the radius of base and h is the height of the cone

Given diameter= 12 cm, thus radius r=12/2 =6 cm

[tex]v=\pi r^2h/3 \\120\pi =\pi *6*6*h/3\\120\pi =12\pi h\\10=h[/tex]

h=10 cm

B.

If height and diameter were doubled

New height = 2×10 =20 cm

New diameter = 2×12 = 24, r=12 cm

volume = [tex]v=\pi r^2h/3\\v=\pi *12*12*20/3\\v=960\pi[/tex]

To find the number of times we divide new volume with the old volume

[tex]N= 960\pi /120\pi \\\\N= 8[/tex]

Answer: The height of the container is 10 centimeters. If its diameter and height were both doubled, the container's capacity would be 8 times its original capacity.

Step-by-step explanation:

The volume of a cone can be calculated with this formula:

[tex]V=\frac{\pi r^2h}{3}[/tex]

Where "r" is the radius and "h" is the height.

We know that the radius is half the diameter. Then:

[tex]r=\frac{12cm}{2}=6cm[/tex]

We know the volume and the radius of the conical container, then we can find "h":

[tex]120\pi cm^3=\frac{\pi (6cm)^2h}{3}\\\\(3)(120\pi cm^3)=\pi (6cm)^2h\\\\h=\frac{3(120\pi cm^3)}{\pi (6cm)^2}\\\\h=10cm[/tex]

The diameter and height doubled are:

[tex]d=12cm*2=24cm\\h=10cm*2=20cm[/tex]

Now the radius is:

[tex]r=\frac{24cm}{2}=12cm[/tex]

And the container capacity is

[tex]V=\frac{\pi (12cm)^2(20cm)}{3}=960\pi cm^3[/tex]

Then, to compare the capacities, we can divide this new capacity by the original:

 [tex]\frac{960\pi cm^3}{120\pi cm^3}=8[/tex]

Therefore,  the container's capacity would be 8 times its original capacity.