Answer:
7 stations
19 stations
199 stations
Step-by-step explanation:
We can model the stage number as \(x\), and the number of modules as \(y\). We can write this as a linear equation, where the initial number of modules is 1, and the number of modules increases by 2 every station. This is \(y=2x+1\), but since if you plug in 1 into the equation, you get 3, which is the station number for the next number, you have to edit that into x - 1:
\(y=2(x-1)+1\)
Expanding, we have 2x - 2 + 1, which is 2x - 1:
\(y = 2x - 1\)
Now, plugging 4 into the equation, we have 7.
Plugging 10 into the equation, we have 19.
Plugging 100 into the equation, we have 199.
Using diagonals from a common vertex, how many triangles could be formed from the polygon pictured below?
Answer:
i can help you
Step-by-step explanation:
mabey its hard for you
The depth of a local lake averages 38 ft, which is represented as |−38|. In February, it measured 6 ft deep, or |−6|, and in July, it was 25 ft deep, or |−25|. What is the difference between the depths in February and July?
A32 feet
B 31 feet
C 19 feet
D 13 feet
The difference between the depths in February and July is 31 feet.
How to measure depth?The method of measuring depth depends on what we are trying to measure the depth of. Here are some general methods for measuring different types of depth:
Depth of water: The depth of water can be measured using a sounding device such as a sonar or a simple depth gauge. A sonar uses sound waves to determine the distance from the water's surface to the bottom. A depth gauge is a simple device that measures the distance from the surface of the water to the bottom using a weight and a line.
Depth of a hole: The depth of a hole can be measured using a tape measure or a ruler. Simply insert the measuring device into the hole and measure the distance from the top of the hole to the bottom.
Depth of a trench: The depth of a trench can be measured using a measuring tape or a surveyor's level. Place the measuring device at the edge of the trench and measure the distance from the top of the trench to the bottom.
Depth of a pool: The depth of a pool can be measured using a pool depth marker or by using a measuring tape. A depth marker is usually located on the side of the pool and indicates the depth at various points. Alternatively, you can use a measuring tape to measure the distance from the surface of the water to the bottom of the pool.
Depth of a well: The depth of a well can be measured using a well sounder or a tape measure. A well sounder is a device that sends a signal down the well and measures the time it takes for the signal to bounce back. The time it takes is then used to calculate the depth of the well. Alternatively, a tape measure can be used to measure the distance from the surface of the water to the bottom.
Given, In February, it measured 6 ft deep, or |−6| and in July, it was 25 ft deep, or |−25|.
The difference between the depths in February and July is:
|−6| − |−25| = 6 − (−25) = 6 + 25 = 31
Therefore, the correct choice is B) 31 feet.
Learn more about depth here:
brainly.com/question/20070144
#SPJ1
A farmer has 1804 feet of fencing available to enclose a rectangular area bordering a river. If no fencing is required along the river, find the dimensions of the fenced
area that will maximize the area. What is the maximum area?
What is the length of the fenced area?
Answer:
length: 601 1/3 area: 361601 7/9
Step-by-step explanation:
the maximum area would be a square, and we only need 3 sides, so we can divide the amount of fencing by 3
1804/3=601 1/3
the length is 601.(3)
square to find the area
(1804/3)^2
361601 7/9
area is 361601 7/9
y = 2x + 7
y = -3x - 33
Solve using the Substitution Method
Answer:
-8
Step-by-step explanation:
A rectangular poster is 50 centimeters long and 25 centimeters wide. If 1 centimeter is approximately 0.4 inches, which of the following best represents the area of the poster in inches?
The area of the poster in inches is,
⇒ A = 4 inches²
We have to given that;
A rectangular poster is 50 centimeters long and 25 centimeters wide.
Here, 1 centimeter is approximately 0.4 inches
Hence, Lenght = 50 cm
Lenght = 50 x 0.4
= 2 inches
Width = 25 cm
= 25 x 0.4
= 1 inches
Thus, The area of the poster in inches is,
⇒ A = 1 x 4
⇒ A = 4 inches²
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
for such more question on temperature
https://brainly.com/question/14820864
#SPJ8
HELP I GIVE 15 POINTS
Please helpppp!!! Find the area of the irregular figure
Answer:
The area of the figure is 143 sq in
Step-by-step explanation:
10 in * 7 in = 70 sq in
12 in * 4 in = 48 sq in
5 in * 5 in = 25 sq in
A = 70 sq in + 48 sq in + 25 sq in
A = 143 sq in
Find the area of the triangle with vertices: Q(4,4,-1), R(5,7,-2), S(3,2,-4).
Answer:
The area of the triangle is 5.875 square units.
Step-by-step explanation:
First, we need to calculate the lengths of the triangle by means of Pythagorean Theorem:
\(a = \|\overrightarrow {QR}\| = \sqrt{(5-4)^{2}+(7-4)^{2}+(-2+1)^{2}}\)
\(a \approx 3.317\)
\(b = \|\overrightarrow {RS}\| = \sqrt{(3-5)^{2}+(2-7)^{2}+(-4+2)^{2}}\)
\(b \approx 5.745\)
\(c = \|\overrightarrow {QS}\| = \sqrt{(3-4)^{2}+(2-4)^{2}+(-4+1)^{2}}\)
\(c \approx 3.742\)
Now, we can use the following formula to fid the area of the triangle (\(A\)), measured in square units:
\(A = \sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}\)
Where:
\(s\) - Semiperimeter of the triangle, dimensionless.
\(a\), \(b\), \(c\) - Sides of the triangle, dimensionless.
The semiperimeter can be determined by this:
\(s = \frac{a+b+c}{2}\)
If we know that \(a \approx 3.317\), \(b \approx 5.745\) and \(c \approx 3.742\), the area of the triangle is:
\(s = \frac{3.317+5.745+3.742}{2}\)
\(s = 6.402\)
\(A = \sqrt{(6.402)\cdot (6.402-3.317)\cdot (6.402-5.745)\cdot (6.402-3.742)}\)
\(A \approx 5.875\)
The area of the triangle is 5.875 square units.
Can someone please help super short
Answer:
542, 543, 544, 545.
Step-by-step explanation:
Divide 2174 by 4 = 543.5
(because there are 4 integers) 543.5 is not an integer.
However, one of the four integers is 543.
Write down four consecutive numbers that include 543 and add them:
like 541+542+543+544 =. if that is 2174, you have the answer, if it's too low, try moving up one number, like
542+543+544+545 = if it's still too low, move up one number again
543+544+545+546=
You only have to do that a max of 3 times to get the answer.
The four consecutive integers are
542, 543, 544, 545.
good luck, hope this helps :)
A website developer wished to analyze the clicks per day on their newly updated website. Let the mean number of clicks per day be μ. If the website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average, what are the null and alternative hypotheses?
Answer:
Null Hypothesis, \(H_0\) : \(\mu\) = 200 clicks a day
Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 200 clicks a day
Step-by-step explanation:
We are given that a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
Let \(\mu\) = mean number of clicks per day.
So, Null Hypothesis, \(H_0\) : \(\mu\) = 200 clicks a day
Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 200 clicks a day
Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.
On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.
Hence, this is the correct null and alternative hypotheses.
Answer: Null Hypothesis \(H_0:\mu=200\)
Alternate Hypothesis\(H_a:\mu\neq200\)
Step-by-step explanation:
Let \(\mu\) be the mean number of clicks per day.
Given, a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
i.e. he wants to check either \(\mu=200\text{ or }\mu\neq 200\)
Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.
So, Null Hypothesis \(H_0:\mu=200\)
Alternate Hypothesis\(H_a:\mu\neq200\)
Hence, the required null and alternative hypotheses.
Null Hypothesis \(H_0:\mu=200\)
Alternate Hypothesis\(H_a:\mu\neq200\)
Differentiate 4x^2sinx-3x^2cosx
Answer:
(3x² + 8x)sin x + (4x² - 6x)cos x
Step-by-step explanation:
d/dx (4x^2sin x - 3x^2cos x) =
= 4x² × d/dx sin x + sin x × d/dx 4x² - (3x² × d/dx cos x + cos x × d/dx 3x²)
= 4x² × cos x + sin x × 8x + 3x² × sin x - cos x × 6x
= 4x² cos x + 8x sin x + 3x² sin x - 6x cos x
= (3x² + 8x)sin x + (4x² - 6x)cos x
Write the equation of the line that passes through the given points.
(0,6) and (5,14)
The equation of the line is ?
Answer: 8x-5y+30=0
Step-by-step explanation:
in slope intercet form y= 8/5x + 6≈1.6x + 6
Amanda brought a 6-cup of bag of shredded cheese for $6.89. She used 2.25 cups to make lasagna and 1.25 cups to make pizza. How much cheese is left?
Answer:
There is 2.5 cups of cheese left.
Step-by-step explanation:
Write a number in the blank to make the statement true.
Each child is riding on a pony with a saddle
Each saddle has exactly two saddle bags on it.
Each saddle bag has exactly three water bottles in it.
Twenty-two riders altogether are in the group.
________ = total number of water bottles
The total number of water bottles is 132 .
In the question ,
it is given that
there are 22 riders ,
each rider has 2 saddle bags on the pony ,
and each saddle bag has 3 water bottles in it ,
So According to the question
total number of water bottles = ( number of rider ) * ( number of saddle bag on each pony ) * ( number of water bottles in each saddle bag )
Substituting the values from above , we get ,
= 22*2*3
On simplifying we get ,
= 44*3
= 132 .
Therefore , the total number of water bottles is 132.
Learn more about Multiplication here
https://brainly.com/question/1796107
#SPJ1
The figure is cut into 15 equal pieces. Shade 2/5 of the figure
Answer: Shade 6 pieces
Step-by-step explanation:
Because 2/5 of 15 is 6
How much interest is earned if $5800 is put into a savings account that pays 2.5% interest for four years?
ANSWER:
$580
STEP-BY-STEP EXPLANATION:
We have that the simple interest formula is the following:
\(I=P\times R\times t\)Where, I is the interest money created, P is the principal starting amount of money, R is the interest rate per year and t is the time the money is invested.
Replacing, we calculate the interest earned in 4 years:
\(\begin{gathered} I=5800\cdot0.025\cdot4 \\ I=\text{ \$580} \end{gathered}\)The interest earned is $580
Write 40 cm as a fraction of 2.4 m. Give your answer in its simplest form.
40cm as a fraction of 2.4m is 1/6
What are fractions?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. In a proper fraction, the numerator is less than the denominator. e.g . 2/7, 4/5, 3/10 e.t.c
An improper fraction had it's numerator higher than it's denominator .Example is 5/2 , 7/3 e.tc.
By expressing 40 cm as a fraction of 2.4m. The first thing we have to do is making both of thesame unit. therefore ;
2.4m = 2.4×100 = 240cm
40 as a fraction of 240 = 40/240
divide through by 40
= 1/6
therefore the fraction of 40 in 240 is 1/6 i.e 240×1/6 = 40
learn more about fractions from
https://brainly.com/question/78672
#SPJ1
On the domain of [0,2π), for which of the following values of x will cosx=secx? Choose all answers that apply.
Answer Choices In Pic
Answer:
\(cos(\pi )=-1\)
Step-by-step explanation:
\(f(x)=cos(x)\)
State that the values where cos x is minimum:
\(x=\pi +2\pi n,n\)∈ℤ
\(cos(0)=1\\cos(\frac{\pi}{4} )=\frac{\sqrt{2} }{2} \\cos(\frac{\pi }{2} )=0\\cos(\pi )=-1\\cos(\frac{3\pi }{2})=0\)
Which of the following sentences show correct verb tense usage? Check all that apply. When the facilitator announced a bathroom break, the seminar participants took out their iPhones and begun checking their messages a The overall outlook is favorable, so I wrote to the board chair to inform him. She has wrote him an e-mail
The sentence which show correct verb tense usage is The overall outlook is favorable.
Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.
Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.
Learn more about Verb usage:
https://brainly.com/question/15276178
#SPJ4
Question 3 (1 point)
Julie drives by a stop light near her home once every morning. The stop light has red,
yellow and green lights. She wants to know the probability of the light being red on
two mornings.
Which list represents the sample space for two mornings at the stop light?
O {red, yellow, green}
O {red/red,red/yellow,red/green}
O {red/yellow, red/green, yellow/green, yellow/red,green/yellow, green/red}
{red/red,red/yellow,red/green,yellow/red,yellow/yellow,yellow/green,green/red,green/yellow,green/green}
The sample space for the two mornings at the stop light would be D. {red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}.
How to find the sample space ?In probability theory, the sample space constitutes the collection of all potential results that could ensue from an experiment. Symbolized by S, it encompasses every plausible outcome that can arise when such a test is conducted.
The sample space would therefore be :
{red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}
This includes all the possible lights that could be seen on the two mornings by Julie.
Find out more on sample space at https://brainly.com/question/29719992
#SPJ1
If the balance at the end of eight years on an investment of $196 that has been invested at a rate of 9% is $337.12, how much was the interest
Answer:
$141.12
Step-by-step explanation:
Initial investment = $196
After 8 years with 9% interest rate it becomes: $337.12
The amount of interest will be:
= $337.12 - $196
= $141.12
answered Which number line represents the solution to the inequality 4x +20 <40
Answer:
the one that has a hollow dot on 5 with the line pointing left
Step-by-step explanation:
4x+20<40
-20 -20
4x<20
/4 /4
x<5
:) ur welcome
Choose the graph that matches the following system of equations: x + y = 4 2x + 3y = 18 Group of answer choices Picture of coordinate plane with line y equals negative x plus 4 and line y = equals negative 2 thirds x plus 6. They intersect at negative 6, 10. Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x plus 6. They intersect at 6, 2. Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x minus 6. They intersect at negative 1.2, negative 5.2. Picture of coordinate plane with line y equals x plus 4 and line y equals negative 2x plus 6. They intersect at 0.67, 4.67.
Answer: y = 1 2 x + 3
Step-by-step explanation:
They intersect at 4.71, negative 10.43 picture of coordinate plane with line y equals 1 third x plus 4 and line y equals 2x minus 1.
Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0. Then plot the point. (2, -3)
Answer:
X = 2
Y = -3
Step-by-step explanation:
Go on the Y axis and count up to 2Then go to the X axis and count down -3 / 0.3Now you have 2, -3
Convert the rectangular coordinates to polar coordinates
(1, -9)
The polar coordinates of (1, -9) are (9.06, -1.47 radians).
To convert from rectangular coordinates to polar coordinates, we can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:
r = √(1² + (-9)²) = √82 ≈ 9.06
θ = tan⁻¹((-9)/1) ≈ -1.47 radians
Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).
learn more about polar coordinates here:
https://brainly.com/question/31904915
#SPJ1
Write the equation for the line that goes through (3.18) and has a slope of 2.
Answer:
y=2x+12 or 18=2(3)+12
12=b
hope this helps =3
sorry if im wrong
PLEASE HELP TODAY!!!! WILL GIVE BRAINLIST
Hello!
We will go tu use the pythagorean theorem!
So:
BA² = BC² + AC²
AC² = BA² - BC²
AC² = 52² - 20²
AC² = 2304
AC = √2304
AC = 48
A
B
C
D
37. What is the length of side P in the figure below?
6.7 cm
11 cm
15 cm
45 cm
20 cm
25 cm
P
The length of the side P is 15 cm. And the right option is C.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
To calculate the length of side P we use Pythagoras theorem's formula
Pythagoras formula:
a² = b²+c²......................... Equation 1Where:
a = Diagonal of the rectangleb = Length of the rectanglec = Width of the rectangleFrom the diagram,
Given:
a = 25 cmb = 20 cmc = p cmSubstitute these values into equation 1
25² = 20²+p²p² = 25²-20²p² = 225p = √225p = 15 cmHence, the right option is C 15 cm.
Learn more about Pythagoras theorem here: https://brainly.com/question/27997683
#SPJ1
What graph would best display the data shown in the frequency table?
A. line plot
B. vertex-edge graph
C. histogram
D. stem-and-leaf graph
Answer:
histogram
Step-by-step explanation: