Han earned $850 over the summer working odd jobs. He wants to put his money into a savings account for when he is ready to buy a car. His bank offers a simple interest account at 5%, how much interest will Han have earned after 2 years?

the left-hand limit and the right-hand limit are not equal, the limit of f(x) as x approaches 0 does not exist.

To find the left-hand and right-handof f(x) at a = 0, we need to evaluate the limit as x approaches 0 from the left and right sides of 0 separately.

For the left-hand limit, we need to consider values of x that are negative and approach 0. Since f(x) is defined differently for negative and non-negative values of x, we only need to look at the first part of the function, f(x) = e^x. Thus:

\(lim_{ x=0^-}f(x) = lim _{x=0^-} e^x\)

Using the continuity of the exponential function, we can see that this limit is equal to e^0 = 1. Therefore, the left-hand limit of f(x) at a = 0 is 1.

For the right-hand limit, we need to consider values of x that are positive and approach 0. Since f(x) is defined differently for negative and non-negative values of x, we only need to look at the second part of the function, f(x) = x^4. Thus:

lim x→0+ f(x) = lim x→0+ x^4

Using the fact that the limit of a polynomial function at a point equals the value of the function at that point, we can see that this limit is equal to 0^4 = 0. Therefore, the right-hand limit of f(x) at a = 0 is 0.

Overall, we have:

lim x→0− f(x) = 1
lim x→0+ f(x) = 0

Since the left-hand limit and the right-hand limit are not equal, the limit of f(x) as x approaches 0 does not exist.

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Answer:

161

Step-by-step explanation:

145+318=463. 624-463=161

The required number that comes in place of "What" is given as 161.

Given that,
what + 145 + 318 = 624

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
What = 624 - 318 - 145
what = 161

Thus, the required number that comes in place of "What" is given as 161.

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The station of Point of Curvature (PC) is 319+50.

A horizontal curve on a 4-lane highway (i.e., 2-lanes in each direction) has a superelevation of 6% and central angle of 40 degrees. The pt and pi are located at stations 322 50 and 320 08, respectively. The roadway has 10 feet lanes and 8 feet shoulders on both sides with high retaining walls going up immediately next to shoulders.

What is the highest safe speed of this curve and at what station is the PC located? Solution:The following is a solution to the problem discussed above.

We know that, Maximum Safe Speed = Vmax = √Rf Where,Rf = G x f (Radius of Flair)G = 32.2 ft/s2 (Acceleration due to Gravity)

f = Superelevation of the RoadwayVmax = √RfG= √(160f) ft/s

Equation 1 Where

Now, Maximum Safe Speed = Vmax = 3.10 ft/s The Central Angle is given to be 40 degrees.

The Station of the PT and PI is given to be 322+50 and 320+08 respectively. Also, the roadway has 10 feet lanes and 8 feet shoulders on both sides with high retaining walls going up immediately next to shoulders.

To calculate the station of the Point of Curvature (PC), let's use the following formula:

PC = PI - (LC x sin ∆)

Where,

PC = 320+08 - (LC x sin 0.698)

Equation 2Let's calculate the Length of Curve (LC) for the curve.

LC = (Deg. of Curvature/ 360°) x 2πRWhere, 2L = Width of Pavement= 10 x 2 + 8 x 2= 36 feet

R = (2L/ sin ∆) + (2L/ tan 2∆)R = (18/ sin 0.698) + (18/ tan 1.397)R = 362.61 feet

LC = (40/ 360) x 2π x 362.61 feet= 80.14 feet

Now, substitute the value of LC and ∆ in Equation 2 and calculate the value of PC.

PC = 320+08 - (80.14 x sin 0.698)= 320+08 - 58.12= 319+50Hence, the station of Point of Curvature (PC) is 319+50.

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\( \sf \: 1. \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 - 5}{ - 2 - 3} \bigg]\bigg[ \frac{14 - 21}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{ - 1}{ - 5} \bigg]\bigg[ \frac{ - 7}{ - 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{1}{ 5} \times \frac{ 7}{ 6} \\ \)

\( \sf \longrightarrow \: \frac{7}{30} \\ \)

C) 7/30 ✅

________________________________

\( \sf \: 2. \bigg[ \frac{7+ ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 + ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 - 6}{ - 4 - 9} \bigg]\bigg[ \frac{20 - 45}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 4 - 9} \bigg]\bigg[ \frac{ - 25}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 13} \bigg]\bigg[ \frac{ -25}{ 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{ - 25}{ - 78} \\ \)

\( \sf \longrightarrow \: \frac{ 25}{ 78} \\ \)

A] 25 / 78 ✅

________________________________

\( \sf \: 3. \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4 - 5}{ - 2 - 4} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{-18}{ 4} \bigg] \\ \)

\( \sf \longrightarrow \frac{18}{ - 24} \\ \)

\( \sf \longrightarrow -\frac{6}{ 8} \\ \)

\( \sf \longrightarrow -\frac{3}{ 4} \\ \)

C] -3/4 ✅

________________________________

\( \sf \: 4. \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7- 3}{ - 6 - 2} \bigg]\bigg[ \frac{18 - 6}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 6 - 2} \bigg]\bigg[ \frac{12}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 8} \bigg]\bigg[ \frac{12}{ -1} \bigg] \\ \)

\( \sf \longrightarrow \frac{48}{ 8} \\ \)

\( \sf \longrightarrow \frac{6}{ 1} \\ \)

\( \sf \longrightarrow 6 \\ \)

D] 6 ✅

________________________________

\( \sf \: 5. \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8 - 2}{ - 5- 6} \bigg]\bigg[ \frac{40 - 48}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 5- 6} \bigg]\bigg[ \frac{-8}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 11} \bigg]\bigg[ \frac{-8}{ 1} \bigg] \\ \)

\( \sf \longrightarrow \frac{-48}{ - 11} \\ \)

\( \sf \longrightarrow \frac{48}{ 11} \\ \)

B] 48/11 ✅

________________________________

The inequality that best describes the width of the garden is

Width ≤ 6 yards

Area ≤ Length* Width

Length = 5 yards

Width = ??

Area = 30 square yards

From the formula of the area of rectangle we have

Area = Length * Width

Let the width be x

Substitute

30 = 5 * x

30 = 5x

Divide both sides by 5

x = 30/5

x = 6 yards

Hence the with should be less than or equal to 6 yards

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The best name for the quadrilateral K.J. graphed is a parallelogram.

A parallelogram is a quadrilateral with opposite sides parallel to each other. Looking at the slopes of opposite sides, we see that AB and CD both have a slope of -4/3, while BC and DA both have a slope of 0. This means that opposite sides are parallel.

Additionally, we can see that opposite sides have equal length. AB and CD both have a length of 5, while BC and DA both have a length of 4. This is another characteristic of a parallelogram.

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Answer:

R

Step-by-step explanation:

The solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=5/2 x.

Substitute x=0, 1, 2, 3, 4,......

When x=0

y=0

When x=1

y=5/2=2.5

When x=2

y=5

When x=3

y=7.5

Therefore, the solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

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"Your question is incomplete, probably the complete question/missing part is:"

Use the equation y=5/2 x to complete the table. Is y proportional to x? Explain why or why not.

Answer:

b. $3,000.00

Step-by-step explanation:

Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture.

Grath Oil bonds are selling at 120.514

Ombor Medical Supplies bonds are selling at 90.773

Dwyn Horticulture bonds are selling at 101.180.

These values have nothing to do here as we only have to find the face value.

The face value of 1 bond is $1000 so, the face value of 3 bonds will be =  dollars.

Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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Answer:

-Entire triangle region : 120 sq.cm

-Area of semi circle : 100.53 sq.cm

-Entire composite figure : 220.53 sq.cm

Step-by-step explanation:

Area of triangle = ½ × base × height

= ½ × (8+8) × 15

=½ × 16 × 15

= 120 sq.cm

\(area \: of \: semi \: circle = \frac{1}{2} \pi {r}^{2} \\ = \frac{1}{2} \times \pi \times {8}^{2} \\ = \frac{1}{2} \times \pi \times 64 \\ = 32\pi\)

=100.530.......

=100.53 sq.cm (rounded to 2 decimal place)

Area of entire figure = 120 + 100.5353

= 220.53 sq.cm

Hope I could help:))

Answer:

$80.75 dollars

Step-by-step explanation:

Given the following question:
Initial price = $95
15% discount

In order to find the answer, we have to find 15% of 95.

\(\frac{15\times95}{100} =15\times95=1425\div100=14.25\)
\(95-14.25=80.75\)
\(g=80.75\)

The guitar (after a 15% discount) costs "$80.75 dollars."

Hope this helps.

In order to have a function, each value of x in the set of points can have only one corresponding value of y.

Looking at the set of points, the value of x = 2 has two different values of y: 0 and 2.

Therefore this relation is not a function.

Graphing these points, we can see that the point (2, 2) is above the point (2, 0), that is, they are in the same value of x, showing that one value of x has two values of y, therefore we don't have a function in this case.

Answer:

A. (4, 18)

Step-by-step explanation:

The "y" coordinate of the midpoint will be equal to the average of the y coordinates of the endpoints, and the x coordinate of the midpoint will be equal to the average of the x coordinates of the endpoints, and so we get that...

The x coordinate of the midpoint = (5 + 3) / 2 = 8 / 2 = 4

The y coordinate of the midpoint = (21 + 15) / 2 = 36 / 2 = 18

So the right answer is A (4, 18)

We have here four linear functions, and we have to compare the slopes of them as well as their y-intercept. For this, it is important to remember the general equation for the line in the slope-intercept form:

Where

• m is the slope of the line

• b is the y-intercept of the line (0, b)

The y-intercept is the point where the line passes through the y-axis, and at this point, we have that x = 0.

We have in this case that the function passes through the points:

• (0, 5), (1, 1)

We can find the equation of this line using the two-point form of the line equation:

Using the points above, we can label them as follows:

• (0, 5) ---> x1 = 0, y1 = 5

• (1, 1) ---> x2 = 1, y2 = 1

Then we have:

Therefore, the slope for this line is m = -4, and the y-intercept is (0, 5).

For Function 2 we need to do the same procedure as before. We have to select two points of the function to find its equation:

We can select the following points: (0, 1), (1, 6).

Then we can proceed as we did in the previous part:

• (0, 1) ---> x1 = 0, y1 = 1

• (1, 6) ---> x2 = 1, y2 = 6

Therefore, the slope in Function 2 is 5, m = 5, and the y-intercept is (0, 1).

We can see that Function 3 has already its line equation in slope-intercept form:

Then the slope for Function 3 is m = -1, and its y-intercept is (0, -2).

From the question, we have:

The efficiency of the Zumba class system is approximately 69.2%, and its utilization is approximately 54.5%.

To calculate the efficiency of the system, we can divide the actual output (number of employees trained) by the designed capacity (maximum number of employees that can be trained per month) and multiply by 100 to get a percentage.

Efficiency = (Actual Output / Designed Capacity) * 100

Efficiency = (600 / 850) * 100 = 70.6%

Therefore, the efficiency of the system is approximately 70.6%.

To calculate the utilization of the system, we can divide the actual output (number of employees trained) by the capacity (maximum number of students per month) and multiply by 100.

Utilization = (Actual Output / Capacity) * 100

Utilization = (600 / 1100) * 100 = 54.5%

Therefore, the utilization of the system is approximately 54.5%.

The Zumba class system at the local gym has an efficiency of approximately 69.2% and a utilization rate of approximately 54.5%. The efficiency indicates how well the system is performing relative to its designed capacity, and in this case, it suggests that the system is operating at a reasonably high level. The utilization rate, on the other hand, indicates how much of the available capacity is being utilized, and in this case, it suggests that the system is operating at around half of its maximum capacity. This information can be used by the gym to evaluate the performance of their Zumba class program and make informed decisions regarding resource allocation and potential improvements.

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Answer:

Odel has sold 84 Pizzas and Sam has sold 42

Step-by-step explanation:

:p

Answer:

18x^2y^2 3√3xy^2

Step-by-step explanation:

the ^ = exponent

the 3 (the one that is after 2) is the tiny number that is by √

Answer:

B

Step-by-step explanation:

HJ, IJ

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer:

20

Step-by-step explanation:

if the cat is 8, and the parrot is 12 years older, then add the 12 to the 8 and you get 20 as the parrots age

\(\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1\) is the equation of the ellipse.

The equation of an ellipse is given by

\(\rm \dfrac{ (x-h)^2 }{a^2} + \dfrac{ (y-k)^2}{b^2} = 1\)

here

(h,k) is the center

c = is the distance between center to focus

c = \(\rm \sqrt{a ^2 - b^2}\)

as the a = 10 , component length

and c = 8

8 = \(\rm \sqrt{10 ^2 - b^2}\)

8² = 10² -b²

b² = 36

b = 6

h = 0 ,k = 0

Substituting the values given

\(\rm \dfrac{ (x-0)^2 }{10^2} + \dfrac{ (y-0)^2}{6^2} = 1\)

\(\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1\)

Therefore the equation of the ellipse has been determined.

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Answer:

----------------------

Find the hypotenuse c of the base using Pythagorean theorem:

Lateral surface area, three rectangular faces, is:

Find base area, the area of two right triangles:

Find total surface area:

The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Answer:

9

Step-by-step explanation:

-3 x -2 (aka x) gives you a positive 6 obviously because when you do a negative times a negative you get a positive

6 to the power of 2 is 36, and 36 + 4 = 40.

40/4 = 10 and 10-1=9

I HOPE IT GOT THIS RIGHT FOR YOUUU <3 .

Answer:

57 1/10

(14× 3/4)+(4× 1/2)+(8× 1/2)+(10× 2/5)+(10× 2/5)+(12× 4/5)= 571/10 or 57× 1/10

Answer:

4 hours

Step-by-step explanation:

120 ÷ 30 = 4

Hope this helps. Pls give brainliest.