On a photograph an ant is enlarged at a scale 25:1. In the photo, the ant's leg is 15 cm. What is the actual length of the ant's leg?

11=5(x-2)+2x

11-2x=5(x-2)

(11-2x) / 5 = x-2

11/5=2.2

2.2-0.4x = x-2

4.2-0.4x=x

4.2=1.4x

x=3

Answer: x = 3

Step-by-step explanation:

5x -10 +2x = 11

7x = 21

x=3

Hope that helps!

Answer:

10miles I think

Step-by-step explanation:

The required distance between, Nate's house and the restaurant is 7.5 miles.

From the graph,

Consider point C on the graph, which is 6  and 8 units apart from A and B respectively.

The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units

Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles

Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.

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The percentile of Tomijia's scores is her score as a percentage

If Tomijia received an 89 on the test, she is in the 70th percentile

The score of the tests are given as:

42, 44, 56, 71, 74, 83, 89, 90, 90, 92

From the above list of scores, the score 89 is at the 7th position.

So, we have:

Tomijia = 7/10

Express as percentage

Tomijia = 70%

Hence, if Tomijia received an 89 on the test, she is in the 70th percentile

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Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

The solutions for the quadratic equation:

x^2 - 8x = -3

Are:

Here we want to solve the quadratic equation:

x^2 - 8x = -3

First we can move all the terms to the left side so we get:

x^2 - 8x + 3 = 0

Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:

\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)

Then the two solutions for the quadratic equation are:

x = (8 + 7.2)/2 = 7.6

x = (8 - 7.2)/2 =0.4

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Answer:

Either a pie chart or a bar graph

Step-by-step explanation:

THIS THE CORRECT ANSWER

Answer:

17287180

Step-by-step explanation:

hope this helps

Answer: I think it is 17,287,180

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = 10 - 5/2y

Answer:

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. hope that helps love!

Answer:

Step-by-step explanation:

(4,8)..Its the only one in which x doesnt repeat

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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the answer to your question is -67.424

Answer:

I'm stuck to.

Step-by-step explanation:

is there suppose to be an angle or a triangle?

Answer:

$160                0.4/lemon

Step-by-step explanation:

5 per car wash

12 cars in 3 hours

4 cars per hour times 8= 32 cars in 8 hours

32 times 5= 160

5 lemons for 2.00

Unit cost= 0.4 per lemon

Answer:

The total number of times Eva performed the experiment is 19. Out of these 19 times, a pineapple chew was selected 7 times, and a lemon chew and watermelon chew were selected 6 times each.

Therefore, the probability of selecting a flavor other than pineapple can be found by adding the number of times a lemon chew or watermelon chew was selected and dividing by the total number of times Eva performed the experiment:

P(selecting a flavor other than pineapple) = (number of times a lemon or watermelon chew was selected) / (total number of times the experiment was performed)

P(selecting a flavor other than pineapple) = (6 + 6) / 19

P(selecting a flavor other than pineapple) = 12 / 19

P(selecting a flavor other than pineapple) ≈ 0.63 (rounded to the nearest hundredth)

Therefore, the probability that the next chew Eva removes from the bag will be a flavor other than pineapple is approximately 0.63.

Step-by-step explanation:

Answer:we can’t help if it is barely readable

Step-by-step explanation:

Check the picture below.

9514 1404 393

Answer:

  (i) 55.59 km/h

  (ii) 3600 nautical miles ≈ 6670.8 km

  (iii) 30°N 29.3°E

Step-by-step explanation:

(i) The speed in km/h requires a units conversion.

  (30 kt/h)(1.853 km/kt) = 55.59 km/h

__

(ii) Here, we assume we're interested in the distance traveled. If the course is "due east", we presume that means it follows the 30° latitude line, so is not the shortest route between A and B. That is, the distance from A to B will be different from the distance traveled. (The shortest route from A to B is along a great circle.)

  distance = speed × time

  distance = (30 kt/h)(120 h) = 3600 nautical miles

  = (55.59 km/h)(120 h) = 6670.8 km

__

(iii) The radius of the 30° latitude line is ...

  (6370 km)(cos(30°)) = 3185√3 km ≈ 5516.58 km

The relationship between arc length (s) and central angle (α) is ...

  s = rα

So, the change in the vessel's longitude is ...

  α = (6670.8 km)/(5516.58 km) ≈ 1.20923 radians ≈ 69.28°

Then town B has longitude ...

  40°W -69.3° = -29.3°W = 29.3°E

The position of town B is about 30°N 29.3°E.

_____

Additional comment

The route supposedly taken by this sea vessel is from the middle of the North Atlantic to a town in northern Egypt, through the northern Sahara desert. The eastern end point is shown in the attachment.

Some spherical trigonometry is involved if you want to find the end point of the great-circle route of the same length.

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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1.) 1

Let's start with 18 degrees and then subtract 12 degrees from it

18-12=6

Now let's take 6 degrees and subtract 5 from it

6-5=1

At 2 pm the temperature was 1 degree.

2.) $125

Start with the total amount John had ($250) and then subtract his remaining amount ($125) to find out how much he withdrew.

$250-$125=$125

Answer:

89 and d is               DEEZ NUT.S

Step-by-step explanation:

Answer:

89xd, but if you meant equation it would be 89xd=89d

Step-by-step explanation:

Product is the word for the number that results from multiplication.

Answer:

-b^14 i think this is te answer but i am also consused

Answer: :)

Step-by-step explanation:

To find the angle that the ramp makes with a horizontal line, we need to use trigonometry. The angle we are looking for is the angle between the ramp and the ground, which is the same as the angle between the hypotenuse of a right triangle (the ramp) and its adjacent side (the ground).

We can use the tangent function to find this angle:

tan(theta) = opposite/adjacent

In this case, the opposite side is the height of the ramp (4.1 feet) and the adjacent side is the length of the ramp along the ground (6 feet). So we have:

tan(theta) = 4.1/6

Using a calculator, we can solve for theta:

theta = tan^-1(4.1/6)

theta ≈ 34.3°

Therefore, to the nearest tenth of a degree, the measure of the angle that the ramp makes with a horizontal line is 34.3°.

Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.

(a) The process is not a statistical process .

b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.

(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74

and Tolerance = 0.01 USL LSL = 0.01

After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995

cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686

(ii) Cp = min (Cpu, CP).

Cpu = 37.005-37 0.073 = 0.06849

CPL = 0.06859

Срк = 2 × 0.06849 = 0.024

The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).

This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).

The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.

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The smoothed forecast for this year depends on last years forecast and

observation, as well as the value of alpha.

Response:

The given parameter are;

α = 0.2

From a similar question online, we have the following possible values;

Last year's smoothed forecast, F₄ = 15,000

Last years actual value, A₄ = 20,000

Required:

The forecast this year

Solution:

The exponential smoothing relationship is expressed as follows;

F₅ = F₄ + α·(A₄ - F₄)

Which gives;

F₅ = 15,000 + 0.2 × (20,000 - 15,000) = 16,000

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Answer:

240

Step-by-step explanation:

According to law of exponential growth,

\(y=y_0e^{kt}\)

Here, \(y_0\) denotes the initial amount and k is the rate constant of the equation.

Now, the initial population is 240 bacteria.

Put \(y_0=240\)

So,

\(y=240e^{kt}\)

The population after 12 hours is double the population after 1 hour.

\(y(12)=2y(1)\)

\(240e^{12k}=240e^{k} \\e^{12k}=e^{k} \\e^{12k-k}=1\\e^{11k}=1\\11k=log 1=0\\k=0\)

(Formulae used: \(\frac{e^x}{e^y}=e^{x-y}\,,\,log 1=0\))

So,

\(y=240e^{0}=240\\y=240\)

Therefore,

Number of bacteria after 3 hours = 240

The correct option is A, we have a translation of 7 units to the right.-

To find it, we need to analyze two correspondent vertices.

We can see that vertex A is at (1, 5), while the correspondent vertex A' is at (8, 5)

Taking the difference between that, we will get:

A' - A = (8, 5) - (1, 5) = (8 - 1, 5 - 5) = (7, 0)

The first value gives the horizontal translation and the second the vertical one

So,we have a translation of 7 units to the right, the correct option is A.

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Answer:

2/3

Step-by-step explanation:

5/6 - (1/8÷3/4)

=5/6 - (1/8 × 4/3)

=5/6 - ( 1/6)

=4/6

=2/3

Answer:

2/3

Step-by-step explanation:

The sales tax on telephone is 1 percent.

Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.

Given that, after sales tax, a $27 telephone costs $27.27.

Here, sales tax =27.27-27

= 0.27

Now, tax rate is 0.27/27 ×100

= 1%

Therefore, the sales tax on telephone is 1 percent.

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