A car left Town A for Town b. Another car left Town B for Town A at the same time. The ratio of the speeds of the two cars was 6:5 initially. After the two cars passed each other, Car A's speed was reduced by 1/6 and car B's speed was reduced by 25%. When car A arrived at Town B, Car B was still 54 km away from Town A. Find the distance between Town A and Town B. Please I need the answer quickly :]

Answer: \(x=\dfrac{3240}{83}\)

Step-by-step explanation:

Given: 83 : 45 :: 72 : ?

Let unknown quantity (?) be x.

Now, x : y :: a : b

\(\Rightarrow\ \dfrac{x}{y}=\dfrac{a}{b}\)

83 : 45 :: 72 : x

\(\Rightarrow\ \dfrac{83}{45}=\dfrac{72}{x}\\\\\Rightarrow\ x=\dfrac{72}{83}\times45\\\\\Rightarrow\ x=\dfrac{3240}{83}\)

Hence, \(x=\dfrac{3240}{83}\)

Answer: 0.864

Step-by-step explanation:

0.6 x 0.8 x 1.8 = 0.864

Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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\(\large\boxed{Formula: V= \frac{wl}{2}×h}\)

Let's solve!

First, let's multiply width and height.

\(6×6\)

\(= 36\)

Now, we'll have to divide the answer by 2.

\(\frac{36}{2}\)

\(= 18\)

Then, multiply the answer by length.

\(18×10\)

\(\large\boxed{V= 180 \: {units}^{3}}\)

Hence, the volume of the given triangular prism is 180 cubic units.

1/2×6×6×10

=180 units^3

hope this helps

The range is the best measure of variability, and it equals 3.

Since the data is discrete and there are relatively few unique values, the best measure of variability would be the range, which is the difference between the largest and smallest values.

The largest value in the data is 4, and the smallest value is 1,

so the range is 4-1=3.

Therefore, the answer is "The range is the best measure of variability, and it equals 3."

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Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

To calculate the probability of selecting a six-digit number with digits summing up to 52 and being divisible by 11, we need to determine the number of valid numbers meeting these criteria and divide it by the total number of six-digit numbers with digits summing up to 52. The resulting probability will depend on the specific calculation.

To find the probability, we first need to calculate the number of six-digit numbers whose digits sum up to 52. This involves finding all possible combinations of digits that add up to 52. However, without further information about restrictions or patterns, it is challenging to provide an exact count.

Next, we need to determine how many of these numbers are divisible by 11. A six-digit number is divisible by 11 if the difference between the sum of its odd-positioned digits and the sum of its even-positioned digits is either 0 or a multiple of 11.

By calculating the count of six-digit numbers satisfying these divisibility conditions, we can then divide it by the total count of six-digit numbers with digits summing up to 52 to obtain the probability. The specific probability will vary depending on the calculations involved, but it is expected to be relatively low due to the specific conditions required for both the digit sum and divisibility by 11.

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Answer:

30,324

Step-by-step explanation:

30,000 x 4.5 = 135.00

135.00 x 4 + 540.00 four quarters in a year

6 years  x 540 = 3,240

30,000 + 3,240 = 33. 240

We can conclude that for experiments 1, 2, and 4, we fail to reject the null hypothesis, indicating that the observed proportion of six's is not significantly different from 1/6. However, for experiment 3, we reject the null hypothesis, suggesting that the observed proportion of six's is significantly different from 1/6.

To perform the test, we can calculate the test statistic and compare it to the critical value or calculate the p-value. Since the question asks for the critical/acceptance region approach, we will use critical values.

Assuming a significance level (alpha) of 0.05, we can calculate the critical values for a two-tailed test. Since we have four separate experiments, we will conduct four separate tests.

To calculate the critical values, we will use a two-tailed test. We want to find the z-values corresponding to the adjusted significance level of 0.0125/2 = 0.00625 in each experiment.

Using a standard normal distribution table or a calculator, the critical z-values for an adjusted significance level of 0.00625 are approximately ±2.878.

For each experiment, we can compare the test statistic (the number of "six's" observed) to the critical values to make a decision:

Experiment 1:

Number of tosses: 100

Number of "six's": 19

Decision: Fail to reject the null hypothesis since 19 is not outside the critical values.

Experiment 2:

Number of tosses: 500

Number of "six's": 90

Decision: Fail to reject the null hypothesis since 90 is not outside the critical values.

Experiment 3:

Number of tosses: 1000

Number of "six's": 142

Decision: Reject the null hypothesis since 142 is outside the critical values.

Experiment 4:

Number of tosses: 10000

Number of "six's": 1508

Decision: Reject the null hypothesis since 1508 is outside the critical values.

Based on these results, we can conclude that for experiments 1, 2, and 4, we fail to reject the null hypothesis, indicating that the observed proportion of six's is not significantly different from 1/6. However, for experiment 3, we reject the null hypothesis, suggesting that the observed proportion of six's is significantly different from 1/6.

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Answer:

21.4

Step-by-step explanation:

a^2+b^2=c^2

13^2+17^2=c^2

169+289=c^2

458=c^2

squrt 458=c^2

21.4=c

Answer:

Length = x feet = 104 feet

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Length = x feet

Width = 102 feet

Perimeter of a rectangle = 412 feet

Perimeter of a rectangle = 2(length + width)

412 = 2(x + 102)

412 = 2x + 204

412 - 204 = 2x

208 = 2x

x = 208/2

x = 104 feet

Answer:Question 135184: Find the equation of the line with slope 6 that goes through the point (6,4). Write your answer in slope-intercept form. b=-32 ANSWER FOR THE Y INTERCEPT. Y=6X-32 LINE EQUATION

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

Answer:

the fourth one: 36.25

Step-by-step explanation:

the 3 in 20.342 is in the tenths place.

0.3*100=30

the three in 36.25 is in the tens place

There is only one point of inflection on the interval 0 < x < π for the function f(x).

To find the points of inflection of a function, we need to find the points where the concavity of the graph changes. Let's start by finding the second derivative of the given function f(x):f(x) = ∫[sin(3t) - cos(t)]dt. The first derivative of the function is: f'(x) = sin(3x) - cos(x)

Now, let's find the second derivative: f''(x) = 3cos(3x) + sin(x)For the points of inflection, we need to find where the concavity changes. This means that we need to find where the second derivative changes sign.Let's solve for when f''(x) = 0:3cos(3x) + sin(x) = 0. Solving for x, we get: x = (π/6) + n(2π) or x = (7π/18) + n(2π), where n is an integer.Since we are only interested in the interval 0 < x < π, we need to find the values of x that fall within this interval. We can see that (7π/18) + n(2π) is outside of this interval for all values of n, so we can ignore these solutions. The only solution that falls within the interval is x = π/6.

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Answer:

-0.4 or -2/5

:) hope this helped!

Answer:

y = 1, x = 11

Step-by-step explanation:

Let's solve your system by elimination.

x+6y=17;x−3y=8

Multiply the second equation by -1, then add the equations together.

(x+6y=17)

−1 (x−3y=8)

Becomes:

x+6y=17

−x+3y=−8

Add these equations to eliminate x:

9y=9

y = 1

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

x+6y=17

Substitute1foryinx+6y=17:

x+(6)(1)=17

x+6=17  (Simplify both sides of the equation)

x+6+−6=17+−6  (Add -6 to both sides)

x=11

Tasha is correct, we can rewrite the difference of given two numbers as the product of GCF of the two numbers and another difference

Greatest Common Factor: The greatest common factor is the largest factor which is common to two or more numbers. For example, the factors of 4 are 1, 2, and 4, and factors of 16 are 1, 2, 4, 8, and 16. We can see that 1, 2, and 4 are the common factors and in these 4 is the largest common factor as compared to 1 and 2. Therefore, 4 is the greatest common factor of 4 and 16.

given in the question that Tasha believes that she can rewrite the difference 84-60 as a product of the GCF of the two numbers and another difference

   84-60=24

we can write this as,

=12(7-5)  where 12 is the greatest common factor of 84 and 60

=12(2)

= 24

She is correct

we can rewrite the difference of given two numbers as the product of GCF of the two numbers and another difference

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The width and length of the rectangle is 27 cm and 36 cm. respectively.

To solve the problem, we can use the Pythagorean theorem since the diagonal, width, and length of the rectangle form a right triangle. The Pythagorean theorem states that:
a² + b² = c²
where a and b are the legs of the right triangle and c is the hypotenuse (diagonal of the rectangle).

Let's denote the width of the rectangle as w, the length as l, and the diagonal as d. According to the problem, we have:
d = w + 18
l = w + 9

Substituting these equations into the Pythagorean theorem, we get:
(w + 9)² + w² = (w + 18)²

Expanding and simplifying the equation, we get:
w² - 18w - 243 = 0

We can solve for w by factoring the expression:
(w - 27)(w + 9) = 0

w = 27 or w = -9

The positive solution for w is 27. We can use this value to find the length of the rectangle:
l = w + 9
l = 27 + 9
l = 36

Therefore, the width of the rectangle is 27 cm, and the length of the rectangle is 36 cm.

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False. The range of a linear transformation is a subset of the codomain, not the domain.

The domain is the set of inputs to the transformation, while the codomain is the set of possible outputs. The range is the set of actual outputs produced by the transformation. The statement "The range of a linear transformation must be a subset of the domain" is false. The range of a linear transformation is a subset of the codomain, not the domain. The domain is the set of input vectors, while the codomain contains the possible output vectors after applying the linear transformation.

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To fill the rectangular prism we need 1 cube.

To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of a single cube.

The volume of the rectangular prism is given by the formula:

Volume = Length × Width × Height

Substituting the given values:

Volume = 8 in. × 4 in. × 21 in.

Volume = 672 in³

The volume of a cube is given by the formula:

Volume = Edge Length³

Substituting the given edge length:

Volume of a cube = (14 in.)³

Volume of a cube = 2744 in³

Now, we can divide the volume of the prism by the volume of a single cube to find the number of cubes needed:

Number of cubes = Volume of prism / Volume of a single cube

Number of cubes = 672 in³ / 2744 in³

Calculating this division gives:

Number of cubes ≈ 0.245

Since we cannot have a fraction of a cube, we need to round up to the nearest whole number. Therefore, we would need 1 cube to fill the rectangular prism.

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Answer:

they would both be at the depot again at 8:35 am.

Step-by-step explanation:

no point in explaining cause ur a noob at math

The difference between the highest and lowest temperatures in the data set. In this case, the highest temperature is 9.5°C and the lowest temperature is -5.4°C. The range of temperatures for the first 10 days in January is 15.9°C.

To calculate the range, we need to find the difference between the highest and lowest temperatures in the data set. In this case, the highest temperature is 9.5°C and the lowest temperature is -5.4°C.

The range is obtained by subtracting the lowest temperature from the highest temperature: 9.5 - (-5.4) = 9.5 + 5.4 = 15.9.

Therefore, the range of temperatures for the first 10 days in January is 15.9°C. The range represents the span of temperatures in the data set, indicating the variability or spread of the temperatures during that period.

In this case, the range tells us that the temperatures ranged from -5.4°C to 9.5°C, with a difference of 15.9°C between the highest and lowest recorded temperatures.

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Answer:

  (x/9)² +(y/3)² = 1 . . . P = (x, y)

Step-by-step explanation:

You want the equation of the locus of a point P that is 3 cm from the x-axis end of a 12 cm rod whose ends are on the x- and y-axes.

Let the x- and y-intercepts of the rod ends be represented by 'a' and 'b', respectively. The fixed length of the rod tells us ...

  a² +b² = 12²

according to the Pythagorean theorem.

The location of point P is 3/12 = 1/4 of the way from the x-intercept to the y-intercept. Its coordinates in terms of 'a' and 'b' are ...

  P = 3/4(a, 0) +1/4(0, b) = (3a/4, b/4)

If we define the point P as having coordinates (x, y), then we have ...

  3a/4 = x   ⇒   a = 4/3x

  b/4 = y   ⇒   b = 4y

Using these values in the above relation between 'a' and 'b', we have ...

  (4/3x)² +(4y)² = 12²

We can divide by 12² to get the following equation of the ellipse that is the locus of P.

  (x/9)² +(y/3)² = 1 . . . . . . useful domain/range: 0≤x≤9; 0≤y≤3.

Starting points = 7,985

Doubling the points: 7,985 x 2 = 15,970

Subtracting 3,500 points: 15,970 - 3,500 = 12,470

Adding 4,972 points: 12,470 + 4,972 = 17,442

Therefore, Daniel has 17,442 points at the end of the game.

Answer:

B

Step-by-step explanation:

half × base × height

height × length

Answer: B

Step-by-step explanation:

Triangle)

25 - 7 = 18

\(A=\frac{1}{2}(b)(h)\\A=\frac{1}{2}(18)(17)\\A=153cm^2\)

Rectangle)

\(A=b(h)\\A=7(17) = 119cm^2\)

Total)

\(153+119=272 cm^2\)

Answer:

4.54 rad.

Step-by-step explanation:

360° = 2π rad

260° =

260° * 2π/360°

x= 4.54 rad

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The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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