can 24 be the output

The exponential function graphed in this problem is given as follows:

\(y = e^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The graphed function has an intercept of 1, hence the parameter a is given as follows:

a = 1.

The function has the base e, hence it is given as follows:

\(y = e^x\)

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The interest that will be paid in 10 years is = $2,925

The total amount of money deposited as savings (p)

= $4,500,

The annual simple interest rate (r) = 6.5%.

The time to collect the interest expected (t) = 10 years.

There the simple interest generated =

\( \frac{p \times t \times r}{100} \)

\( \frac{4500 \times 10 \times 6.5}{100} \)

\( \frac{292500}{100} \)

Therefore simple interest = $2,925

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Answer:

x=7

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

constant monomial

Step-by-step explanation:

the 8 is a constant number and has one term.

Answer:

$280

Step-by-step explanation:

7•40=$280

Jenny's Average swimming speed is 1.5 km/h.

Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.

We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.

Thus, the distance she swam is S * 1 = S km.

Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.

Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.

Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.

She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.

The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.

Therefore, we can write the equation:

S + 8S + 28S = 55.5.

Simplifying the equation, we get:

37S = 55.5.

To solve for S, we divide both sides of the equation by 37:

S = 55.5 / 37 = 1.5.

Thus, Jenny's average swimming speed is 1.5 km/h.

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Answer:

she scored 76 percent in the test

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

Answer:47 X=16

Step-by-step explanation:

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

Use the following formula:

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

Let:

\((x_1 , y_1) = (-2 , -8)\\(x_2 , y_2) = (6 , -4)\)

Plug in the corresponding numbers to the corresponding variables:

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-8)}{6 - (-2)} = \frac{-4 + 8}{6 + 2} = \frac{4}{8}\)

Simplify the slope:

\((\frac{4}{8} )/(\frac{4}{4}) = \frac{1}{2}\)

\(\frac{1}{2}\) is your answer.

Answer:

A. 25.7°

Step-by-step explanation:

the sum of straight angle is 180°.

so, i subtract 154.3 from 180.

i get 25.7 °

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

\(\dfrac{1}{6}:6=\dfrac{1}{6}\cdot\dfrac{1}{6}=\dfrac{1\cdot1}{6\cdot6}=\dfrac{1}{36}\)

Answer:

1.Many pairs of triangles designed into a building, for example as roof ends, would be congruent, so the roof beam and the top edges of the walls are horizontal.

2.The congruent triangle is used in most of the building that are design to stay in bad conditions and Strong winds for Example the Sydney Bridge.

3.in real life two triangles are rarely exactly congruent. However they are crucial in the construction of large man-made structures. This is because a triangle is the most stable shape and the congruence is needed to create even surfaces.

Answer:

w=-9

Step-by-step explanation:

Yes, the relationship is proportional and the slope is 1000/3. The unit rate is also 1000/3. So, slope is directly proportional to the unit rate. Since, slope=unit rate.

When the ratio is expressed as a quotient, the same number is provided for every pair of distinct points on the same line ("rise over run"). In a diagram that shows a roof or a road as a description or a plan, the line may be practical as determined by a road surveyor; on a falling line, there is a negative "rise."

The slope's absolute value can be used to estimate a line's steepness, incline, or grade. The slope of a line in the plane that includes the x and y axes is commonly represented by the letter m and is defined as the difference between the y coordinate and the equivalent difference in the x coordinate between two distinct points on the line.

The sales are directly proportional to the number of days

The slope of the lines is given by (3, 1000), (6, 2000)

Slope=(2000-1000)/(6-3)

Slope=1000/3

From the graph given,

$1000 is obtained on 3 days.

Therefore, the unit rate is 1000/3

Therefore, Slope=unit rate=1000/3

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On simplifying the values obtained for the fractions are - 3 / 3/4= 4, 5 / 3/4= 6.66, 8 / 4/7= 14, 6 / 3/5= 10, 2 / 5/8= 3.2 and 4 / 8/9= 4.5.

What is fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The first fraction is 3/(3/4).

The denominator will reciprocate.

Simplify, the fraction -

3 × 4/3 = 4

The second fraction is 5/(3/4).

The denominator will reciprocate.

Simplify, the fraction -

5 × 4/3

20/3 = 6.66

The third fraction is 8/(4/7).

The denominator will reciprocate.

Simplify, the fraction -

8 × 7/4 = 14

The fourth fraction is 6/(3/5).

The denominator will reciprocate.

Simplify, the fraction -

6 × 5/3 = 10

The fifth fraction is 2/(5/8).

The denominator will reciprocate.

Simplify, the fraction -

2 × 8/5

16/5 = 3.2

The sixth fraction is 4/(8/9).

The denominator will reciprocate.

Simplify, the fraction -

4 × 9/8

9/2 = 4.5

Therefore, the values of fractions are 4, 6.66, 14, 10, 3.2 and 4.5.

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Step-by-step explanation: We may determine the range of potential further miles Charlie will run by deducting his present mileage from the maximum mileage if he has already run 17 miles and will only cover 35 miles this week.

Maximum mileage - current mileage = potential extra miles.

17 miles minus 35 miles equals 18 miles.

As a result, Charlie may run somewhere between 0 and 18 additional miles.

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Answer:

18 possible numbers

Step-by-step explanation:

If Charlie has already run 17 miles and he will run at most 35 miles this week.

We can calculate the possible numbers of additional miles he will run by subtracting the distance he has already run from the maximum distance he can run.

Maximum distance Charlie can run = 35 miles

Distance Charlie has already run = 17 miles

Possible additional miles he will run = Maximum distance - Distance already run

                              = 35 miles - 17 miles

                              = 18 miles

Therefore, there are 18 possible numbers of additional miles Charlie will run.

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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The answer is 12πn.

To find this answer we can proceed as follows:

1. We have that the circular painting is surrounded by a circular frame, and its radius is n - 3.

2. The radius of the circle formed by the frame is n + 3.

3. Then if we have that the area of a circle is given by:

And we have that:

Answer:

x = 20, y = -3

Step-by-step explanation:

Set both equations equal to each other

\(\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3\)

Answer:

(2+n)-3

That's how you write if that is what you want.

The mode of the textbooks thicknesses is,

⇒ 1 cm

Since, The most frequent number which is, the number that occurs the highest number of times is called Mode of data set.

Here, We have to given that;

The librarian measured the thickness of the textbooks in the school library.

And, Among a selection of 6 books, he recorded the following thicknesses:

⇒ 4 cm, 1 cm, 1 cm, 1 cm, 5 cm, 2 cm

Hence, By definition of mode we get;

Here, Most often number in data set is, 1 cm

So, The mode of the textbooks thicknesses is,

⇒ 1 cm

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Answer:

57

Step-by-step explanation:

this is the boybfiend

= 3 pages per hour

Showing Work

This is a fraction equal to

9 pages ÷ 3 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 3

Answer:

1.3 hours



Step-by-step explanation:

It looks like it'd end up being \(16^3+4x-1\) given that you meant \(1+4x(4x^2+1)-2\)

(Willing to redo if wrong