Maria invests $6,154 in a savings account with a fixed interest rate of 8% compounded continuously. What will the account balance be after 10 years?

Answer:

Eli has saved $10

Step-by-step explanation:

Let us use the first letters of their names to represent them.

A for Angela and E for ELi

So, from the first statement, we can write out an equation: E = [tex]\frac{1}{3}[/tex]A + 8, that is, one-third of Angela's savings + $8 will give us Eli's savings

From the second statement, we can write out: E + 10 = (A + 10) + 4 which means that if $10 is added to both their savings, Eli will still have $4 more than Angela.

So, we can solve both equations;

Equation 1: E = [tex]\frac{1}{3}[/tex]A + 8

Equation 2: E + 10 = (A + 10) + 4; which can be rewritten as E + 10 = A + 14

and then E = A + 4

The two equations (in bold), can then be solved simultaneously.

Let us carry out this operation to eliminate the E: Subtract equation 1 from equation 2, so that;

A + 4 - ( [tex]\frac{1}{3}[/tex]A + 8) = E - E

[tex]\frac{2}{3}[/tex]A - 4 = 0

[tex]\frac{2}{3}[/tex]A = 4

A = 4 × [tex]\frac{3}{2}[/tex] = 6

So, if A is 6, and E = A + 4 (from equation 2, that means that E = 6 + 4 = 10

So, Eli has saved $10, while Angela has saved $6.

If we check what was said in the question about their savings, which is what we have represented using the equations, the answers can be confirmed.

Answer:

Eli has saved $10

Step-by-step explanation:

 Let us denote Angela's saving by "x".

  If Eli's saving is $8 more than one-third of Angela's saving, then Eli's saving   is:

 [(1/3 × x) + 8 = x/3 + 8]

 We will make x/3 + 8 to have a common denominator:

 x/3 + 8 = (x+24)/3

 If Eli and Angela each saved $10 more, then their respective savings would have been:

(x+24)/3  +  10 for Eli

x+10 for Angela.

At this savings, Eli would have been $4 richer than Angela.

i.e   [((x + 24)/3) + 10] -  (x+10) = $4

 We will make [(x+24)/3] + 10 to have common denominator.

(x + 24 + 30)/3

= (x + 54)/3

 Then:

  [(x+54)/3]  -  [(x+10)/1] = 4

   [x+54-(3x+30)]/3 = 4/1

    (-2x + 24)/3 = 4

    cross multiply

  -2x + 24 = 12

    -2x = -12

       x = -12/-2

       x = 6

  Since Eli's saving = x/3 + 8

Then his actual saving

  = 6/3 + 8

  = 2 + 8

  = $10

Final answer:

The approximate square root of 48 is found by locating it between the perfect squares of 36 (6²) and 49 (7²), leading to a closer estimation of about 6.9 when considering 48 as 16 * 3 and simplifying.

Explanation:

The question asks to find the approximate square root of 48. To do this, we first recognize that the exact square root of 48 is not a whole number, and therefore, we need to find two perfect squares between which 48 lies. The perfect squares closest to 48 are 49 (7²) and 36 (6²). Since 48 is closer to 49, we can estimate that the square root of 48 is slightly less than 7. A more refined method involves thinking of 48 as 16 * 3, which then gives us √16 * √3 = 4√3. Knowing that √3 is approximately 1.732, we can multiply this by 4 to get an approximation of 6.928. Therefore, a good approximation for the square root of 48 is approximately 6.9.

Answer: 6 in ^2

Step-by-step explanation:

The shapes are congruent, so all the given values have to apply to both shapes. Keeping this in mind, the only answer that works is 6in^2.

Answer:

The translation rule is (x , y) → (x - 12 , y - 4)

Step-by-step explanation:

Let us revise the translation of a point

An object is translated from A (-6, -4) to A' (-18, -8)

∵ A is (-6 , -4)

∵ A' is (-18 , -8)

∴ x-coordinate = -6

∴ x'-coordinate = -18

- By using the translation rule above

∵ x' = x + h

∴ -18 = -6 + h

- Add 6 to both sides

∴ -12 = h

∴ h = -12

∵ h is a negative value

- That means A translated to the left 12 units

∴ The rule is (x , y) → (x - 12 , y)

∵ y-coordinate = -4

∴ y'-coordinate = -8

∵ y' = y + k

∴ -8 = -4 + k

- Add 4 to both sides

∴ -4 = k

∴ k = -4

∵ k is a negative value

- That means A down 4 units

∴ The rule is (x , y) → (x , y - 4)

The translation rule is (x , y) → (x - 12 , y - 4)

Answer:

hot dogs- $1.25

hamburgers- $1.50

Step-by-step explanation:

let hot dogs be x and hamburgers be y∀

five hot dogs and two hamburgers cost $9.25

5x + 2y = $9.25 (eq. 1)

5x=9.25-2y

divide both sides by 5x

x= 1.85-0.4 (insert this in eq. 2)

two hotdogs and five hamburgers cost $10.00

2x + 5y = $10.00 (eq. 2)

2×(1.85-0.4) +5y=10.00

3.7 - 0.8 + 5y = 10.00

-0.8+5y=10.00-3.7

4.2y=6.3

divide both sides by 4.2 to evaluate the variable

6.3 divided by 4.2

y=1.50

now find x

x=1.85-0.4×1.5

x=1.85-0.6

x= 1.25

Answer:

1109

Step-by-step explanation:

you can subtract the terms to see the difference between them

-11-(-27)=16

The sequence is increasing by 16

you can plug that 16 in the formula for d

a_n=a_1+(n-1)d

a_n=a_1+(n-1)16

n represents the term you want to find in this case the 72nd

a sub 1 is the first term of the sequence in this case -27

a_72=-27+(72-1)16

a_72=-27+(71)16

a_72=-27+1136

a_72=1109

The 72nd term of the given arithmetic sequence is 1109.

A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.

The given arithmetic sequence is -27, -11, 5...

The common difference of the arithmetic sequence is:

d = -11 - (-27)

d = 16

The nth term of an arithmetic sequence is:

aₙ = a₁ + (n-1)d

   = -27 + (n-1)16

   = -27 +16n -16

   = 16n - 43

To find the 72nd term, substitute n = 72 into the above equation:

a₇₂ = 16(72) -43

a₇₂ = 1109

Hence, the 72nd term of the given arithmetic sequence is 1109.

Learn more arithmetic sequences here:

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Answer:

x=115 y=65

Step-by-step explanation:

You get 115 for X because angle x is vertical to 115 degrees.

You get 65 because y is supplementary to x, and 180-65=115.

Answer:

x = 115 degree and y = 65 degree

Step-by-step explanation:

Here we can see

x = 115 ( being vertically opposite angles )

So Now

x + y = 180 ( being linear pair )

115 + y = 180

y = 180 - 115

Therefore  y = 65

Hope this helps

Answer:

-12

Step-by-step explanation:

2 - -4 = 6 --> y + 6 = x

x = -6, so subtract 6 from x to find y

-6 - 6 = -12

y = -12

Does that help?

To find y when x = -6, given that y varies directly with x and y = -4 when x = 2, we first calculate the proportionality constant k, and then use it to find the new value of y.

If y varies directly with x, this means that y can be expressed as y = kx, where k is the proportionality constant. Given that y = -4 when x = 2, we can first find the value of k by substituting these values into the direct variation equation:

-4 = k(2)

From this, we can solve for k:

k = -2

Now, to find y when x = -6, we substitute -6 for x in the original direct variation equation y = kx, using our found value of k:

y = (-2)(-6)

y = 12

Therefore, when x = -6, y will be 12.

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Answer:

16/48

Step-by-step explanation:

When you look for a pattern from frequency to probability, it is clear that the frequency will become the numerator for the probability and the denominator will remain 48. This appears to be the rule of the probability distribution table, so using this established rule, we can use 16 as the numerator for the probability, and then remember that 48 is always the numerator, which gives you 16/48 in result.

Answer:

6%

Step-by-step explanation:

we know that

To find out the percentage chance that Karissa has of winning the necklace, divide the number of tickets purchased by the total number of tickets

so

[tex]\frac{9}{150}=0.06[/tex]

Convert to percentage (multiply by 100)

[tex]0.06(100)=6\%[/tex]

Answer:

2/3

Step-by-step explanation:

Answer: 2/3

Step-by-Step:

divide 10 by 5 = 2, then divide 15 by 5 =3, so 2/3

Answer:              

2322

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer: the speed of the plane in still air is 101.2 mph

Step-by-step explanation:

Let x represent the speed of the plane in still air.

The pilot flew his​ single-engine airplane 60 miles with the wind from City A to above City B. If the wind was a constant 30 miles per​ hour, it means that the total speed at which he flew the plane while going is (x + 30) mph.

Time = distance/speed

Time spent while going is

60/(x + 30)

He then turned around and flew back to City A against the wind. it means that the total speed at which he flew the plane while returning is (x - 30) mph.

Time spent while returning is

60/(x - 30)

If the total time going and returning was 1.31.3 ​hours, it means that

60/(x + 30) + 60/(x - 30) = 1.3

Cross multiplying, it becomes

60(x - 30) + 60(x + 30) = 1.3(x - 30)(x + 30)

60x - 1800 + 60x + 1800 = 1.3(x² + 30x - 30x - 900)

120x = 1.3x² - 1170

1.3x² - 120x - 1170 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 1.3

b = - 120

c = - 1170

Therefore,

x = [- - 120 ± √(- 120² - 4 × 1.3 × - 1170)]/2 × 1.3

x = [120 ± √(14400 + 6080)]/2.6

x = [120 ± √20480]/2.6

x = (120 + 143.1)/2.6 or x = (120 - 143.1)/2.6

x = 101.2 or x = - 8.9

Since the speed cannot be negative, then x = 101.2 mph

The angle that must also measure 130° is angle 4.

Angle 4 must also measure 130°. When two lines intersect, the vertically opposite angles are congruent, meaning angle 1 and angle 4 are equal. Therefore, if angle 1 measures 130°, angle 4 must also measure 130°.

If angle 1 measures 130°, angle 3 must also measure 130°.

When two lines intersect, they form pairs of angles known as vertical angles or vertically opposite angles. These angles are congruent, meaning they have the same measure. The key property of vertical angles is that they are formed by opposite rays.

In the given scenario:

Angle 1 and angle 3 are vertically opposite angles because they are formed by the intersecting lines and share the same vertex.

Since angle 1 measures 130°, according to the properties of vertical angles, angle 3 must have the same measure.

This is a fundamental property of vertical angles: they are always congruent. Therefore, if angle 1 measures 130°, angle 3 must also measure 130°.

For complete question refer to image:

The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is calculated using the midpoint formula and is (-3.5, 1.5).

The question seems to be asking for the midpoint of a segment with given endpoints. However, the numbers provided (-1, 5, -6, -2) do not clearly define a specific segment in a conventional two-dimensional coordinate system. Typically, a line segment in two-dimensional space is represented by the coordinates of its endpoints, such as (x₁, y₁) and (x₂, y₂).

If we assume the numbers are pairs of coordinates, we could interpret them as the endpoints (-1, 5) and (-6, -2). To find the midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂), you use the midpoint formula: Midpoint M = [tex](\frac{x_1 + x_2}{ 2}, \frac{y_1 + y_2}{2})[/tex]

Applying this to the given points: M = [tex](\frac{-1 + (-6)}{ 2}, \frac{5 + (-2)}{ 2} = (\frac{-7}{ 2}, \frac{3 }{ 2})[/tex] = (-3.5, 1.5).

The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is (-3.5, 1.5).

Answer:

P43=4!(4–3)!=241=24 24 possible choices

Step-by-step explanation:

There are four choices you can make for the lead reindeer. For each possible choice, there are then three remaining you can choose to fly second, making 4×3=12 choices for the lead pair. For each possible choice there are two remaining reindeer to take up the back position, making 12×2=24 choices for the team of three.

This type of problem is called a permutation problem, and we write Pnr for the number of ways of choosing r items from n possibilities when the order of the items matters. In this case we are choosing 3 reindeer from 4 possibilities, and the order they appear in the flying line does matter, so the answer we want is P43. The general formula is Pnr=n!(n−r)!. For the answer we are looking for we therefore have:

P43=4!(4–3)!=241=24

Brainliest?

Answer: Twiddle dee dee can type 3960 words per hour.

Step-by-step explanation:

There are 3600 seconds in an hour.

3600 ÷ 20 = 180

Therefore, she/he can type 22 words 180 times during the hour.

22 · 180 = 3960

So, twiddle dee dee can type 3960 words per hour. (or 66 words per minute). This is my first answer, but I do hope this helps!

Her typing rate per hour is 3,960 words.

To determine Twiddle Dee Dee's typing rate per hour, we first need to convert the rate from words per second to words per hour. Twiddle Dee Dee types 22 words in 20 seconds. To find out how many words she types in one minute, we divide the number of seconds in a minute by the time it took her to type those 22 words:

60 seconds / 20 seconds = 3

Now we multiply this factor by the number of words:

22 words × 3 = 66 words per minute

Now to find the rate per hour, we multiply the words per minute by the number of minutes in an hour:

66 words/minute × 60 minutes/hour = 3,960 words/hour

Therefore, Twiddle Dee Dee's typing rate per hour is 3,960 words.

Answer: The area of the square is increasing at a rate of 90.4 m2/min (square meters/minute)

Step-by-step explanation: Please see the attachments below

Answer:

The area of the square is increasing at 90.51m^2/min

Step by step explanation:

Given;

Change in diagonal length ∆d = 8m/min

Length l = 8m

When l = 8m

d^2 = 2l^2 = 2×8^2 = 128

d = √128

Area of a square = l^2 = (d^2)/2

d = diagonal

Change in area = ∆A = dA/dd

∆A = 2 × d/2 × ∆d = d×∆d

∆A = √128 × 8 = 90.51m^2/min

Answer:

80 ft

Step-by-step explanation:

Answer:

A. 80 ft.

Step-by-step explanation:

Triangle ABC is similar to Triangle DFG so they are proportional. 20/4=5; 25/5=5; so 7*5=35.

20+25+35=80

A horizontal translation is expressed by transforming

[tex]f(x)\mapsto f(x+k)[/tex]

If [tex]k[/tex] is positive, the function is translated to the left. If [tex]k[/tex] is negative, the function is translated to the right.

So, a 3-units left shift is given by [tex]k=3[/tex]. So you have

[tex]f(x)=2x^2-1 \implies f(x+3)=2(x+3)^2-1[/tex]

Answer:

Multiply by 100

Step-by-step explanation:

There are 100 centimeters in a meter, so multiply your value for meters by 100

100 i learned this before so if you have 2 meters there are 200 centimeters

Answer:

The width is 23cm

Step-by-step explanation:

9*2 = 18

64-18 = 46

46/2 = 23

Answer:

a=bh

Step-by-step explanation:

the answer is 70

im sorry if thats not right

Answer:

The answer to your question is Area = 70 cm²

Step-by-step explanation:

Data

height = 5 cm

base = 14 cm

side = 13 cm

To solve this problem just look for the formula and substitute the values. It is not necessary the length of the short side.

Formula

Area = base x height

-Substitution

Area = 14 x 5

-Result

Area = 70 cm²

Answer:

try 45

Step-by-step explanation:

The water level rises at a rate of approximately 2.83 cm per minute. Therefore, the water level would be approximately 34 cm after 12 minutes.

This problem involves the concept of linear relationships and slopes in mathematics. Given that the water level rises by 17 cm every 6 minutes, we can find the rate of increase per minute by dividing 17 cm by 6 minutes. This value, approximately 2.83 cm/minute, is the slope of the linear relationship.

This means each additional minute increases the water level by about 2.83 cm. If we denote the time as x and the water level as y, the linear equation expressing this relationship can be written as y = 2.83x.

To find the value of y when x (time) is 12 minutes, we substitute x = 12 into this equation. So, y = 2.83 * 12 = 33.96 cm. Therefore, the water level would be close to 34 cm after 12 minutes.

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Answer:

Rational,   0.424242... =  42/99

Step-by-step explanation:

let x = 0.4242424242....

We can convert this to a fraction

100x = 42.424242....

100x - x = 42

99x = 42

x = 42/99  a rational number

Answer: 0.424242424242 is a rational number

Step-by-step explanation:

Answer: the equation is x/2=18.8

Step-by-step explanation: you start with x because that’s the number and you divide it by 2 because that’s the same as halving then you write =18.8.

Final answer:

To form the equation based on the information provided, use the fact that Dan halves the number and gets 18.8. Solve by applying basic algebra to find the original number Dan was thinking of.

Explanation:

Equation: Let the original number that Dan was thinking of be represented by x. Given that Dan halves the number and gets 18.8, we can form the equation:

x / 2 = 18.8

Solving for x: Multiply both sides by 2 to find that the original number Dan was thinking of is x = 18.8 x 2 = 37.6.

Answer:

For a quadratic function in standard form, y=ax2+bx+c

the axis of symmetry is a vertical line x=−b2a .

Step-by-step explanation:

Hope this helps !

Answer:

  29.7°

Step-by-step explanation:

In a right triangle representing the geometry of the problem, the side opposite the angle is the height of your observation (400 ft). The side adjacent to the angle is the distance from shore (700 ft).

You know the tangent ratio is ...

  Tan = Opposite/Adjacent

so your angle of depression satisfies ...

  tan(angle of depression) = (400 ft)/(700 ft)

Using the inverse function, we find ...

  angle of depression = arctan(4/7) ≈ 29.745°

The angle of depression is about 29.7°.

Answer:

The correct option is;

21 ft

Step-by-step explanation:

The equation of the parabolic arc is as follows;

y = a(x - h)² + k

Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)

We therefore have;

y = a(x - 20)² + 25

Whereby the parabola starts from the origin (0, 0), we have;

0 = a(0 - 20)² + 25

0 = 20²a + 25 → 0 = 400·a + 25

∴a = -25/400 = -1/16

The equation of the parabola is therefore;

[tex]y = (-\frac{1}{16})(x-20)^2 + 25[/tex]

To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28

Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;

[tex]y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft[/tex].

Final answer:

By creating and solving the equation of a parabola which matches the description of the arch, it is found that the height of the arch 8 feet from the center is 21 feet.

Explanation:

To determine how high the parabolic arch is 8 feet from each side of the center, we can use the properties of a parabola to set up an equation. The vertex of the parabola (the highest point) is in the center of the arch, so we know that the parabola is symmetrical about the vertex.

The general form of a parabolic equation is y = ax^2 + bx + c. In this scenario:

The vertex is at the origin (0,25).

The arch has a span (width) of 40 feet, so its x-intercepts, or roots, are at (-20,0) and (20,0).

To find the parabolic constant, a, we use the x-intercepts to establish the equation 0 = a(20)^2, which simplifies to a = -25/400 = -1/16 because we know that the height at the x-intercepts is 0.

The parabolic equation for the arch is then y = -1/16x^2 + 25. To find the height 8 feet from the center, we substitute x with 8:

y = -1/16(8)^2 + 25 = -1/16(64) + 25 = -4 + 25 = 21

Therefore, the arch is 21 feet high 8 feet from each side of the center.