Joe invests $3000 in a savings account for a period of 5 years. The account pays simple interest at the rate of 2% per year. Calculate the amount in his savings account after 5 years, assuming he makes no other withdrawls or deposits.

Answer:

D. It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours.

Step-by-step explanation:

From the pair (0, 0) to (2, 26), we can see over a period of two hours, the car moved 26 miles, as the distance went from 0 to 26.

From the pair (2, 26) to (3, 26), we can see over the course of an hour, the car maintained the same distance, 26 miles, the entire time. This means that it stopped. We can rule out options A and B since those include a stop of 3 hours, when the stop is actually only 1.

From the pair (3, 26) to (5, 52), we can see over a time period of 2 hours, the car moved from 26 to 52 miles, so in other words it travelled. We can rule out C because the car only travelled 2 hours, from hour 3 to hour 5.

This leaves us with D as the answer, which perfectly fits the graph.

Answer:

D

Step-by-step explanation:

(It may be wrong) The answer is D because the car's starting point is at the origin (0,0) and goes up and right on both axis by 2 squares and drives for 2 hours (2,26), It then for and hour because only the x axis moves to (3,26) and the y axis doesn't shift then it continues to move up by 2 on both sides meaning that it traveled for another 2 hours.

Answer:

a) S=-6.512t+176

b) 123.904

c) 13.024

Step-by-step explanation:

A glacier covered about 176 acres in 2006

Rate of shrinking is 3.7% per year.

A. The formula for size S as function of years 't' since 2006

               ⇒ S(t)=179(1-0.037)^t

B. Let us take a model were ice ice lost from the glaciers between 2006 to 2014

            S=179(1-0.037)^8

            S=179(0.963)^8

            S=179×0.74

            S =132.4 acres

C. According to the model above area of glaciers lost between 2006 and 2008 is=113 acreacres

       ⇒S=179(1-0.037)^2

      ⇒S=179(0.963)^2

      ⇒S=179×0.90.93

      ⇒S=166 acres

∴glaciers lost between 2006 and 2008 is=179-166=113 acres.

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Answer:

9

Step-by-step explanation:

5x-3= 2x+24

5x=2x+27

3x=27

X=9

Answer: A.  9

Step-by-step explanation:

The diagonal is bisected by the other diagonal.  So the 2 parts of the diagonal are equal

5x - 3 =  2x + 24                 >Bring like terms to 1 side

3x = 27                                >Divide both sides by 3

x = 9

The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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We will have that the volume will be the following:

So, the volume of the volume of the sphere is approximately 2144.7 ft^3.

Answer:

c

Step-by-step explanation:

c

According to the given image, angle AED is angle 4.

It's important to know supplementary angles sum 180°, or they form a straight angle.

In this case, the supplement of angle AED would be the angle DEF because they form a straight angle.

Additionally, another supplementary angle to 4 would be angle 5, for the same reason.

The absolute value of this difference is 18 miles, so the walk diagonally across the rectangle park is approximately 18 miles shorter than walking along the two sides of it.

A rectangle is just a square with four perpendicularly in the Euclidean plane. An equiangular quadrant or a quadrant that appears to have identical angles are other names for it. A straight angle is another choice for the parallelogram. A square has four edges that are the same length. Quadrilaterals with four equal edges and four 90° edges are called rectangles. As a consequence, it is occasionally referred to as a "equirectangular square".

Here,

The length of the diagonal of the rectangle can be found using the Pythagorean theorem:

d = √(8^2 + 6^2) ≈ 10

So the length of the diagonal is approximately 10 miles.

To find the distance of walking along the two sides of the rectangle, we can use the formula for the perimeter of a rectangle:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we have:

P = 2(8) + 2(6) = 28

So the distance of walking along the two sides of the rectangle is 28 miles.

The difference between walking along the two sides and walking diagonally can be found by subtracting the distance of walking along the two sides from the length of the diagonal:

10 - 28 ≈ -18

The absolute value of this difference is 18 miles, so the walk diagonally across the park is approximately 18 miles shorter than walking along the two sides of it.

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Answer:

1404

Step-by-step explanation:

Answer:

Your answer will be 2

Step-by-step explanation:

Hope this help you alot

Answer:

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

CPCTC is commonly used at or near the end of a proof, which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.

Answer:

26

Step-by-step explanation:

9+4+9+4=26

The expression that is equivalent to \(80^{(1/4}\) * x is \(80^{4/x}\)

To determine the equivalent expression to \(80^{1/4}\) * x, let's analyze each option:

\(80/4^{x}\)

This expression simplifies to \(20^{x}\), but it is not equivalent to the original expression.

Applying the power of a power rule, this expression simplifies to \(80^{x/4}\) , which is not equivalent to the original expression.

\(80/x^{4}\)

This expression can be simplified as \(80^{4 x^{4} }\) , which is not equivalent to the original expression.

Therefore, the expression that is option d.

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It is 5%

63-60=3

60 divided by 3 = 5

5%

Answer:

7.5

Step-by-step explanation:

Take the figure apart to make one rectangle and 2 triangles.

the rectangle with the endpoint T has  a width of 3 and a height of 1.

The Area for the rectangle is A = wl = 3 * 1 = 3

The first, smaller triangle with points R and A has a height of 3 and a base of 1.

The Area for the triangle is A = h b/2 = 3 * 1/2 = 1.5

The large triangle with points T and P has a height of 3 and a base of 2.

Using the same formula for the Area of a triangle you get 3

Now add all areas together

3+1.5+3 = 7.5

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} y=2\\x=9 \end{cases} \\\\\\ 2=\cfrac{k}{9}\implies 18 = k\hspace{9em}\boxed{y=\cfrac{18}{x}} \\\\\\ \textit{when x = 6, what's "y"?}\qquad y=\cfrac{18}{6}\implies y=3\)

Hi Student!

Looking at the question provided we are asked to find two integers.  It further specifies that those two integers should be the boundaries around the number that is produced from the square root of 11.  

Now that we know what the question is asking for, we can move onto answering the question.  We know that \(1^2\) is equal to \(1\), \(2^2\) is equal to \(4\), \(3^2\) is equal to \(9\), and \(4^2\) is equal to \(16\).  The number that was provided to us inside of the square root was 11.  That means that it would be between the number 9 and 16 which is given using \(3^2\) and \(4^2\).  

Therefore, the square root of 11 would be between the numbers 3 and 4.  The final answer is option E, 3 and 4

The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

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Answer:

x=45  y=137.5

Step-by-step explanation:

2x=90

x=45

One angle is 45. Another angle is 90.

The total angle sum would be 360

So

45+90+y+(y-50)=360

135+y+y-50=360

85+2y=360

2y=275

y=137.5

Since the two lines with red arrows are parallel, that means the two angles on the left are both 90º angles.  

2x = 90

or x = 45

Now, 2x + 90 + y + (y-50) = 360, since this is a quadrilateral and we know 2x=90.

So 90 + 90 + y + y-50 = 360

or 2y + 130 = 360

or 2y = 230

or y = 115

To check, add up the angles to make sure it adds to 360:

90 + 90 + 115 + 65 = 360.

Answer:

A. $37,395

Step-by-step explanation:

correct on edge! hope it helps :)

The savings from the difference between the 30–year loan at 11%, which

is 6% gives an interest when the mortgage is paid of approximately;

a. $37,395.18

The amount paid is given as follows;

\(Monthly \ payment, \ M = \mathbf{\dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot }\left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}\)

Which gives;

\(M = \dfrac{150000 \times \left(\dfrac{0.11}{12} \right) \cdot \left(1+\dfrac{0.11}{12} \right)^{30 \times 12} }{\left(1+\dfrac{0.11}{12} \right)^{30 \times 12} - 1} \approx \mathbf{1,428.49}\)

Payment in 10 years = $1,428.49 × 120 ≈ $171,418.8

At the lower interest rate the person could have received (11 - 6 = 5)%, we have;

\(M = \mathbf{\dfrac{150000 \times \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{30 \times 12} }{\left(1+\dfrac{0.05}{12} \right)^{30 \times 12} - 1}} \approx 805.23\)

Payment in 10 years = $805.23 × 120 ≈ $92,227.6

Savings = $171,418.8 - $96,627.6 = $74,791.2

The time duration the savings is invested in the account = 30 years - 10 years = 20 years

Which gives;

Simple interest  after 20 years = $74,791.2 × 0.025 × 20 ≈ $37,396.6

Therefore;

The option that best gives the amount of money that would have accumulated in interest is the option a.

a. $37,395.18

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The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

Answer:

A=a2=142=196cm²

Answer: 196 cm²

hope this helps :)

Answer:

196cm²

Step-by-step explanation:

All of a square's sides are congruent which means if one side is 14cm then all the other sides have to be 14cm as well.

To find the area you multiply the length and the width (A=l*w)

l=14, w=14

14*14=196cm²

Answer:

D

Step-by-step explanation:

Answer:hope it helped

Step-by-step explanation:

c answer

Answer:

\(Part = \frac{19}{20}\)

\(Lessons = 23\)

Step-by-step explanation:

Given:

\(Dancing\ Lessons = 24\)

\(April = \frac{3}{4}\)

\(May = \frac{1}{5}\)

Required:

Determine the part she took

To solve this, we simply add up the part she took in April and May.

\(Part = \frac{3}{4} + \frac{1}{5}\)

Take LCM

\(Part = \frac{15 + 4}{20}\)

\(Part = \frac{19}{20}\)

Hence, she took \(\frac{19}{20}\) of the dancing lesson.

However, to calculate the number of lesson.

We have to multiply \(\frac{19}{20}\) by the total dancing lessons.

\(Lessons = \frac{19}{20} * 24\)

\(Lessons = \frac{19* 24}{20}\)

\(Lessons = \frac{456}{20}\)

\(Lessons = 22.8\)

\(Lessons = 23\) ---- Approximated