Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 5% each year. In other words, if you have $1 this year, next year it will only buy you $0.95 worth of stuff. How much will $100 buy you in 25 years?

The lengths of the right-angled triangle are 6 and 8.

A right-angled triangled is a triangle that has one of its angles equal to 90°. The sum of the other two interior angles is also equal to 90°.

The Pythagoras theorem relates the three sides of a right-angled triangle through a simple equation. According to the Pythagoras theorem,

hypotenuse^2 = base^2 + opposite^2

Let base = b, so opposite = b + 2

So,

10^2 = b^2 + (b+2)^2

100 = b^2 + b^2 + 4b + 4

100 = 2b^2 + 4b + 4

50 = b^2 + 2b + 2

b^2 + 2b - 48 = 0

solving this quadratic equation gives, b = 6 and b = -8. Since length cannot be negative, the base is 6 feet and the opposite is 8 feet.

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Answer:

The smallest square number  that can be written using five different  Roman numerals is 10,000.

The result of the number divided by 24 is \(416 \dfrac{2}{3}\)

Step-by-step explanation:

The lowest digit which can be written using five different Roman numerals is 10,000.

Therefore, the smallest square number must be greater than or equal to 10,000.

\(\sqrt{10,000} =100\)

Therefore, the smallest square number  that can be written using five different  Roman numerals is 10,000.

Next, we divide the number by 24.

\(10,000 \div 24 =416 \dfrac{2}{3}\)

The result of the number divided by 24 is \(416 \dfrac{2}{3}\)

The simplified value  of expression -36/(27/3*2) is -8.

Given an expression -36/(27/3*2).

We are required to find the simplified value of given expression. To simplify the expression we need to use addition,subtraction,multiplication, division, brackets, etc. We can say that we have to use BODMAS in order to find the simplified value of expression.

Expression is combination of numbers, symbols, coefficients, determinants, indeterminants, fraction,algebraic operations,etc.  usually not found in equal to form.

The given expression :

=-36/(27/3*2)     (Multiplying 3 and 2 first)

=-36/(27/6)

=(-36*2)/9   (Invert the fraction given in denominator)

=-72/9          (Multiplying -36 to 2)

=-8

Hence the simplified value of expression -36/(27/3*2) is -8.

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The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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Answer:

7 schools have fewer than 50 classrooms.

To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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The equation to show the perimeter of the rectangle is P = 2(2w + 5)

From the question, we have the following parameters that can be used in our computation:

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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upload the picture...

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.

1. First, we need to find the vector-valued function r(t) using the given parameter.

2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:

y = √(4 − (1+sin t)2 − (1 − sin t)2).

3. We can now substitute this expression into the vector-valued function to obtain:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k

4. The space curve represented by the intersection of the surfaces is a helix in a graph.

The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.

The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.

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Answer:

4/24

Step-by-step explanation:

\(\frac{1}{6} = \frac{1*4}{6*4}=\frac{4}{24}\)

The polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.

In this problem we have three shapes related to circle-like and ellipse-like arcs (circle, semicircle, ellipse) and a regular polygon.

Circles are closed figures created by a arc whose radius of curvature is the same at every point and ellipses are closed figures created  by a arc whose radius of curvature varies in the following interval: a ≤ r ≤ b, where a, b are the lengths of the semiaxes.

Polygons are closed figures created by a finite number of line segments and therefore the concept of radius of curvature is not applicable.

Therefore, the polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.

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Answer:

sh 90,000

Step-by-step explanation:

let x be the total amount left , then

x = \(\frac{1}{3}\) x + \(\frac{2}{5}\) x + 24,000

multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions

15x = 5x + 6x + 360,000

15x = 11x + 360,000 ( subtract 11x from both sides )

4x = 360,000 ( divide both sides by 4 )

x = 90,000

the total amount left was sh 90,000

Player B is the more consistent player, determined by the variability.

Range measures the difference between the highest and lowest numbers, whereas the IQR measures the difference between the first and third quartiles.

Range and IQR are both measures of variability that measure how spread out the data is.

Player B has a lower range and IQR than Player A, which indicates that Player B was more consistent.

Since Player B had a lower range and IQR than Player A, this indicates that Player B is the more consistent player.

This shows that Player B is more consistent because the data points are closer together.

This is because Player B had fewer outliers, which made the data points more consistent.

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Answer:

32 gallons

Step-by-step explanation:

c'mon this is simple, but thx for the points

Answer:

H) 24

Step-by-step explanation:

24 is the only number that is divisible by 3.

CHECK:

3 x 8 : 4 x 8

24:32✔

(You can try dividing '3' by the other numbers to also check your answer)

Hope this helped ^^

Answer: 6/7

Step-by-step explanation:

Answer:

\(-\frac{9}{1}\)

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

The correct statements are: A, B and F, for the equations f(x) = (1.4)x + 2, g(x) = 2x − 5.

What are the correct statements ?

To determine the answer, we can look at the slopes of the two lines. The slope of f(x) is 1.4, and the slope of g(x) is 2. Since the slope of g(x) is larger than the slope of f(x), the value of g(x) will increase faster than the value of f(x) as x increases. Therefore, options A and F are incorrect.

Next, we can set f(x) equal to g(x) and solve for x:

(1.4)x + 2 = 2x − 5

0.6x = -7

x = -35/3

Therefore, the equation f(x) = g(x) will be true for exactly one value of x, so option B is correct.

Option D is incorrect because there is only one solution to f(x) = g(x). Option E is incorrect because we have already found one solution to f(x) = g(x). Option C and G are incorrect because the graphs of f and g will never cross since the slope of g(x) is larger than the slope of f(x).

Therefore, the correct statements are:

B. The equation f(x) = g(x) will be true for exactly one value of x.

A. The graphs of f and g will never cross because the value of g(x) will continually increase faster than the value of f(x).

F. The graphs of f and g will never cross because the value of g(x) will continually increase faster than the value of f(x).

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Complete question is: The correct statements are: A, B and F, for the equations f(x) = (1.4)x + 2, g(x) = 2x − 5.

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

Quadrilateral: 20.5 units

Triangle: 8.6 units

Step-by-step explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

\(AB = \sqrt{(-3 - (-3))^2 + ((-1) - 3)^2} = \sqrt{16} = 4\)

\(BC = \sqrt{(-3 - 2)^2 + ((3) - 3)^2} = \sqrt{25}= 5\)

\(CD = \sqrt{(2 - 4)^2 + ((3) - (-1))^2} = \sqrt{4+16} = 2\sqrt{5}\)

\(DA = \sqrt{(4 - (-3))^2 + ((-1) - 1)^2} = \sqrt{49} =7\)

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

= \(4+5+2\sqrt5+7=20.5\) units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

\(EF = \sqrt{(-4 - (-2))^2 + ((1) - (3))^2} = 2\sqrt{2}\)

\(FG = \sqrt{(-2 - (-2))^2 + ((3) - (4))^2} = 1\)

\(EG = \sqrt{(-4 - (-2))^2 + ((1) - (4))^2} = \sqrt{4 + 9} = \sqrt{13}\)

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 + \(\sqrt{13}\)

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units

Answer:

5

Step-by-step explanation:

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

−2k+7=−3

Step 1: Subtract 7 from both sides.

−2k+7−7=−3−7

−2k=−10

Step 2: Divide both sides by -2.

−2k/-2 = -10/-2

k=5

Answer:

Natural numbers

Step-by-step explanation:

the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.

Answer:

The number is 23

Step-by-step explanation:

23-10=13

Answer:

I think that 1 x 2 x 8 units³ is the correct one because the base, height, and length are multiplied. And when they are  multiplied together we get volume.

Step-by-step explanation:

Answer:

15.5027 ft

Step-by-step explanation:

Step 1: Find conversion

1 m = 3.281 ft

Step 2: Use Dimensional Analysis

\(4.725 \hspace{3} m(\frac{3.281 \hspace{3} ft}{1 \hspace{3} m} )\) = 15.5027 ft

Answer:

The slope of function A is greater than the slope of function B

hope it is helpful to you

Answer:

x < 5

x > -3

Step-by-step explanation:

I didn't see the graph you mentioned, but this is the graph I did.

|x - 1| < 4

x-1 < 4    ,  -(x-1) < 4

x < 5

x > -3