q is euidistant fromt he of tsr. find the value of x. the diagram is not to scale. 3x+18=24

Mary has left with a 1 kilometer  i.e. \(\frac{2}{7}\) of the journey is incomplete

Given that Mary is going for a 3.5 km walk. So far she’s walked 1.55 km through the park, 0.6 km across the bridge, and 0.35 km up the hill and asked to find the  fraction of the walk she has left

Total journey distance = 3.5 kilometers

Distance walked by mary on the bridge=0.6 kilometers

Distance walked by mary through the park=1.55 kilometers

Distance walked by mary up the hill=0.35 kilometers

Total distance traveled by mary=(0.6+1.55+0.35)kilometers

Total distance traveled by mary=2.5 kilometers

The distance left=3.5 kilometers-2.5 kilometers

The distance left=1 kilometer

1 kilometer is  \(\frac{2}{7}\) of the journey by assuming 3.5 kilometer will complete the jouney

Therefore, Mary has left with a 1 kilometer  i.e. \(\frac{2}{7}\) of the journey is incomplete

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Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

2174.93879228

Step-by-step explanation:

\(A = P(1 + \frac{r}{n})^{nt}\)

=2000(1+0.004/12)²⁴

=200(1.0035)²⁴

=2000x1.08746939614

=2174.93879228

hope this helps

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The interest would be $171.53 if $2,000 earn, compounded annually, in two years at the rate of 4.2%.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

\(\rm A = P(1+\dfrac{r}{n})^{nt}\)

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

From the data given in the question:

P = $2,000

r = 4.2% = 0.042

n = 1

t = 2 years

A = 2000(1 + 0.042)²

A = 200(1.0035)²

A = $2,171.53

I = A - P = $2,171.53 - $2,000 = $171.53

Thus, the interest would be $171.53 if $2,000 earn, compounded annually, in two years at the rate of 4.2%.

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Answer:

increases by 30

Step-by-step explanation: its right

Answer:

5.7 units

Step-by-step explanation:

The distance from point P to QS is the distance from point P (1, 1) to the point of interception R(-3, 5).

Use distance formula to calculate distance between P and R:

\( PR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( P (1, 1) = (x_1, y_1) \)

\( R(-3, 5) = (x_2, y_2) \)

Plug in the values into the formula.

\( PR = \sqrt{(-3 - 1)^2 + (5 - 1)^2} \)

\( PR = \sqrt{(-4)^2 + (4)^2} \)

\( PR = \sqrt{16 + 16} \)

\( PR = \sqrt{32} \)

\( PR = 5.7 units \) (to nearest tenth)

Answer:

a(31) = 84

Step-by-step explanation:

The first term, a(1) is 204, and the common difference is 4.  That is, each new term is 4 less than the previous term.

The rule governing this arithmetic sequence is

a(n) = 204 - 4(n - 1)

and so the 31st term is

a(31) = 204 - 4(30) = 84

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:

Step-by-step explanation:

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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To solve this question we must know the difference between discrete and continuous variables.

Discrete variables are the ones we count using the fingers:

n = 0, 1, 2, 3, 4,... and so on

We can also use negative numbers to do so:

n = ...-4, -3, -2, -1, 0

Continuous variables can't be count using our fingers. For instance, we can take a small interval, say, from 0 to 1 and give some examples of numbers that lie in that interval:

interval = 0 to 1

The number 1/2 = 0.5 lies in the interval

The number 1/3 = 0.333 lies in the interval too

The number 0.9998 lies in the interval too

And so on.

What do I mean with that? There are inifity numbers that we can't count, all of them that lies on the interval.

Let's go to the problem:

a)

The number of hits on a website can be count: 1, 2, 3,...., 1,458, ..., 1,506,897 and so on. So it is a discrete variable.

Answer: option D.

b)

The ammount of rain can be meaured by the height of the water that has poured down on that day. Let's say we measure using milimeters (mm). Then the ammount of water could be 125 mm, or even 189.6 mm. There is a infinite set of numbers that could be used. So we have a continuous variable.

Answer: option B

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.

The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:

Output = (6 * x) - 80

The problem states that the input and output are the same. Therefore, we can set up the equation:

x = (6 * x) - 80

To solve for x, we'll rearrange the equation and isolate the variable:

x - 6 * x = -80

Combine like terms:

-5 * x = -80

Divide both sides by -5:

x = (-80) / (-5)

Simplifying the division:

x = 16

Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.

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Answer:

c

Step-by-step explanation:

Answer:

Let's start by writing the given statement as an equation.

Twice the sum of −4 and a number is the same as the number decreased by 5/2:

2(-4 + x) = x - 5/2

Where x represents the unknown number.

Now, let's simplify and solve for x:

-8 + 2x = x - 5/2

Adding 8 and 5/2 to both sides, we get:

2x + 8.5/2 = x + 1.5/2

Simplifying, we get:

2x + 17/2 = x + 3/2

Subtracting x and 3/2 from both sides, we get:

x + 17/2 = 3/2

Subtracting 17/2 from both sides, we get:

x = -7

Therefore, the number is -7.

To check our answer, we can substitute x = -7 into the original equation:

2(-4 + (-7)) = (-7) - 5/2

-2 = -2.5

The left-hand side does not equal the right-hand side, so our solution is incorrect. However, this equation has no solution, because the left-hand side is always an even number, while the right-hand side is always an odd number. Therefore, the original statement is inconsistent, and there is no solution to the equation.

Answer:

A=πr2=π·82≈201.06193ft²

Answer:

Step-by-step explanation:

r = 8

pi = 3.14

Area = pi * r^2

Area = pi * r * r               That's what the 2 means.

Area = 3.14 * 8 * 8

Area = 200.96 square feet

Answer:

-0.38

Step-by-step explanation:

0.6-(0.7)(1.4)

0.6-0.98

-0.38

Answer:

0.10 + 0.10 + 0.10 + 0.10 + 0.10 equal to 5 dimes or a half of dollar.

Step-by-step explanation:

0.10 + 0.10 + 0.10 + 0.10 + 0.10 = 0.50 (half of a dollar)

Answer: 50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

300(2) bcuz 300 guests and each person gets 2

600(12) bcuz 300(2) is 600 and a dozen is 12

=50

The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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The total time taken for the entire journey is 2.8 hours.

To calculate the total time taken for the entire journey, we can use the formula:

Time = Distance / Speed

For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:

Time1 = 112 km / 70 km/h = 1.6 hours

For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:

Time2 = 60 km / 50 km/h = 1.2 hours

To find the total time for the entire journey, we sum up the times for both parts:

Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours

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Clara can reach a height of 2.57 meters when she jumps.

Given information:

The ceiling in Clara’s basement is 2.75 meters high.

When Clara jumps she is 18 centimeters short of being able to touch the ceiling.

We can start by converting the height of the ceiling and Clara's jump to the same units, either meters or centimeters. Let's convert Clara's jump to meters:

18 centimeters = 0.18 meters

Now we can subtract Clara's jump from the height of the ceiling to find how high she can reach:

2.75 meters - 0.18 meters = 2.57 meters

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Answer:

x = 0 , y = -2

Step-by-step explanation:

Answer:

For the first group we have the pairs:

year           population

0                20

1                 80

2                320

3                 1,280

4                 5,120

5                 20,480

Here we can see that the population quadruples each year

(4*20 = 80, 80*4 = 320, 320*4 = 1,280, etc...)

then the population equation is:

P(0) = 20

P(1) = 20*4

P(2) = (20*4)*4 = 20*4^2

We already can see the pattern, then we can write this relationship as:

P(t) = A*(4)^(t)

Where:

t represents time in years, and A is the initial population, that we know it is 20, then:

P(t) = 20*(4)^t

This is the function that represents the table.

B) Now we have a group of 20 squirrels and the population triples each year, with the same reasoning than before we can write the equation that models this situation as:

Q(t) = 20*(3)^t

C) Now, if the initial population of the second group is 40, the equation becomes:

Q(t) = 40*(3)^t

The population by year 3 is given by replacing t by 3, then:

Q(3) = 40*(3)^3 = 1080

And the population of the other group in year 3 is seen in the table, it is 1,280, then the population of the first group is bigger by year 3, and it is greater by:

1,280 - 1,080 = 200

So the first group is larger by 200 squirrels.

Step-by-step explanation:

Just using the Pythagoras theorem

Answer:

Following are the complete solution to the given question:

Step-by-step explanation:

The two main elements are geometry. One of them is analyzing the form of something. The second element is distance thinking. Four dominant sides are united into the triangle. Its sides can be of any height, however, the biggest side can be even more than and equal to a sum of the other two sides. Also, there are two concentric angles in a triangular, with the overall amount of three angles being 180 °.

Answer:

120

Step-by-step explanation:

370m - (65 x 2) = 240

240 divided by 2 = 120

The value of y for the inequality is y  >  0

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

The inequality 2 times the quantity y plus one third end quantity is greater than two thirds can be written as:

2(y + 1/3) > 2/3

To determine the value of y in the inequality, you need to solve for y. That is:

2(y + 1/3) > 2/3  

y + 1/3 > 1/3     (Divide both sides by 2)

y > 1/3 - 1/3     (Collect like terms)

y > 0

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The sheet decreased by 1.5 meters and is now at 2.5 meters.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, s=−0.25t + 4 represents the thickness of the ice over t weeks. To find the thickness at 6 weeks, substitute t=6.

s = -0.25(6)+4

s = 2.5 meters

It started at t= 0 at 4 meters. So it decreased by (4 - 2.5) = 1.5 meters.

The start of spring has 4 meters because when t= 0, s= -0.25(0)+4 = 4

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During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt.

The variable s models the ice sheet's thickness (in meters) t

weeks after the beginning of spring.

s=−0.25t+4s=-0.25t+4

s=−0.25t+4

By how much does the ice sheet's thickness decrease every 6 weeks?