A 100​-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

Step-by-step explanation:

WHats the question here bud

Answer:

x = 1000

Step-by-step explanation:

5,350 ÷ x = 5.35

To find this you should divide 5,350 by 5.35.

5,350 ÷ 5.35 = 1000

x = 1000

Answer:

5.35

Step-by-step explanation:

Divide 5,350 by 5.35

\(5350 \div 5.35\)

you'll get 1000

Check your answer by dividing 5350 by 1000

\(5350 \div 1000 = 5.35\)

Answer:

For every 1 vote cast for Candidate D, there were 4 votes for candidate C.

Step-by-step explanation:

Hope this helps! Have a good day!

Answer:

For every 1 vote cast for Candidate D, there were 4 votes cast for Candidate C.

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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To solve this problem, we can use the trigonometric functions sine, cosine, and tangent.

First, let's draw a diagram:

             A (top of the mountain)

            /|

           / |

         /    |  h (height of mountain)

       /      |

     / θ     |

B /_____|

   d (distance from base)

We are given that the distance from the base of the mountain to point B is 1/2 mile, or 2640 feet (since there are 5280 feet in a mile). We are also given that the angle of elevation from point B to point A is 65 degrees, and that the angle between the ski lift and the ground is 15 degrees.

Let's start by finding the height of the mountain h. We can use the tangent function, since we know the opposite (h) and the adjacent (d) sides of the right triangle formed by points A, B, and the foot of the mountain (call it point C):

tan(65) = h / d

h = d * tan(65)

Plugging in the values, we get:

h = 2640 * tan(65)

h ≈ 7855 feet

Next, let's find the length of the ski lift. We can use the cosine function, since we know the adjacent (d) and hypotenuse (L) sides of the right triangle formed by points B, the foot of the mountain, and the base of the ski lift (call it point D):

cos(15) = d / L

L = d / cos(15)

Plugging in the values, we get:

L = 2640 / cos(15)

L ≈ 2736 feet

Therefore, the length of the ski lift from the beginning to the end is approximately 2736 feet.

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

4th one is correct

Step-by-step explanation:

it perfectly matches all the given condition

Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Using equivalent angles, the solutions to the equation are given as follows:

\(\theta = 255^\circ, \theta = 285^\circ\)

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

\(\sin{\theta} = -0.966\)

Applying the inverse relation:

\(\theta = \arcsin{-0.966} = 255^\circ\)

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

\(270^\circ + (270^\circ - 255^\circ) = 285^\circ\)

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Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

Answer:

  n² -10 = 6

Step-by-step explanation:

If n represents a positive number, then "the square of a positive number" is represented by n². When that value is decreased by 10, it becomes ...

  n² -10

and if that value is 6, the math expression is ...

  n² -10 = 6

__

Additional comment

Increasing the value by 10 gives ...

  n² = 16

and taking the positive square root gives us the value of the number:

  n = √16 = 4

in this question we have to multiply 4 with 4 then we have to minus 16 with 10 we get the answer 6

= 4 × 4 = 16

= 16 - 10

= 6

Answer:

x - 9 = -1

Step-by-step explanation:

When you see less than you switch the numbers. So, for instance, it says 9 less than x means x-9

The joint probability density function for the random variables Y1 and Y2 E(Y1+Y2) and V(Y1+Y2) is 41/144.

To find E(Y1+Y2), we need to integrate the sum of Y1 and Y2 over their joint probability density function:

E(Y1+Y2) = ∫∫ (y1 + y2) f(y1,y2) dy1 dy2

= ∫∫ (y1 + y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 <=1

= ∫\(0^1\) ∫\(0^{(1-y1)}\)(y1 + y2) (2) dy2 dy1

= ∫\(0^1\) (2y1 + 1) (1-y1)² dy1

= 5/12

To find V(Y1+Y2), we can use the formula V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]².

First, we need to find E[(Y1+Y2)^2]:

E[(Y1+Y2)²] = ∫∫ (y1+y2)² f(y1,y2) dy1 dy2

= ∫∫ (y1² + y2² + 2y1y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 = 1

= ∫\(0^1\) ∫\(0^{(1-y1)}\) (y1² + y2² + 2y1y2) (2) dy2 dy1

= ∫\(0^1\) (1/3)y1³ + (1/2)y1² + (1/2)y1

(1/3)y1 + (1/4) dy1

= 7/12

Next, we need to find [E(Y1+Y2)]²:

[E(Y1+Y2)]² = (5/12)² = 25/144

Therefore, V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]² = (7/12) - (25/144) = 41/144.

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Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

The current stock price is $54.15.

Given that  RLX Company just paid a dividend of $2.85 per share on its stock and dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely.

Stock valuation alludes to the valuation of the natural worth per portion of an organization's stock which can help the organization in deciding its reasonable worth in case of twisting up or consolidation. One of the models used to esteem the stock cost is the profit development model. It expects the cost of the stock to be the current worth representing things to come profits of the stock accepted to develop at a consistent rate.

Dividend (D0) = $2.85

Growth rate (g) = 4.5%

Required return (r) = 10%

Firstly, we have to calculate the value of the current stock price.

The current stock price can be calculated by using the dividend growing model.

\(\begin{aligned}\text{Current stock price}&=\frac{D_{0}\times(1+g)}{r-g}\\ &=\frac{2.85\times (1+0.045)}{0.10-0.045}\\ &=\frac{2.85\times 1.045}{0.055}\\ &=\frac{2.97825}{0.055}\\ &=54.15\end\)

Hence, the current stock price when dividend of $2.85 are expected to grow at a constant rate of 4.5 percent per year, indefinitely is $54.15.

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Answer:

The simple pendulum should be 15.9 m long.

Step-by-step explanation:

Approximately (for small amplitudes), the period of a simple pendulum is

T = 2*pi * sqrt (L/g), L=length

using pi = 22/7, and g=9.8 m/s^2

8 = 2* 22/7 * sqrt(L/9.8)

solve for L

L = (8*7/(2*22))^2 * 9.8

= 15.874 m

That's quite a long pendulum!

Answer:

2(3/2)^2+2(3)^2+4(3)-3=0

Step-by-step explanation:

3(4)^2+4(2)=0

The data are discrete because the data can only take on specific values, So correct option is B.

Discrete data refers to data that can only take on specific, separate values. It is a type of data that can be counted or enumerated, but not measured. In other words, the values can't be expressed as fractions or decimals between two whole numbers. Some examples of discrete data include the number of siblings in a family, the number of pets owned by an individual, and the number of correct answers on a test. Discrete data is distinct from continuous data, which can take on any value within a certain range.

The data are discrete because the data can only take on specific values (e.g. a time of 20 minutes, 21 minutes, 22 minutes, etc.). They cannot take on any value in an interval, such as 20.5 minutes. Discrete data represent a countable number of values, while continuous data can take on any value within a given range.

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Answer:

Step-by-step explanation:

Answer:

Option E, two-proportion z test  should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same as the proportion of shoppers in the large downtown shopping area who had been to a movie in the past month

Step-by-step explanation:

The complete question is

In a random sample of 60 shoppers chosen from the shoppers at a large suburban mall, 36 indicated that they had been to a movie in the past

month. In an independent random sample of 50 shoppers chosen from the shoppers in a large downtown shopping area, 31 indicated that

they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient

evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same

as the proportion of shoppers in a large downtown shopping area who had been to a movie in the past month?

A one-proportion z interval B two-proportion z interval

B two-proportion z interval

C two-sample t test D one-proportion z test

D one-proportion z test

E two-proportion z test

Solution

Two proportion z test is used to compare two proportions. In this test the null hypothesis is that the two proportions are equal and the alternate hypothesis is that the proportions are not the same. The random sample of populations serve as two proportions.

Hence, option E is the best choice of answer

Answer: 11 people like vanilla.

Step-by-step explanation: There are 50 people in this question. Since 22% of them like vanilla, multiply 0.22 and 50. That gives you 11. Therefore, 11 people out of 50 like vanilla.

Answer: pi/3

Step-by-step explanation:

correct on edge 2020

The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

sin⁻¹ ( √3/2 ) = θ

Now , the value of θ is calculated by

In a triangle , sin θ = opposite / hypotenuse

So , sin θ = √3/2

The value of θ = 60°

So , the measure of 60° in radians is θ = π/3

Hence , the value of θ from the trigonometric relation is π/3

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Answer:

\(a = \frac{2 - b}{5(3 - b)} \: \: b = \frac{15a - 2}{5a - 1} \)

Step-by-step explanation:

There's two options check your question and answer

\(1. \: \frac{ \frac{2 - b}{3 - b} }{5} = a \\ 2. \frac{2 - b}{5(3 - b)} = a \\ 3. \: a = \frac{2 - b}{5(3 - b)} \\ \\ \\ 1. \: 2 - b = 5a(3 - b) \\ 2. \: 2 - b = 15a - 5ab \\ 3. \: - b = 15a - 5ab - 2 \\ 4. \: - b + 5ab = 15a - 2 \\ 5. \: 5ab - b = 15a - 2 \\ 6. \: b(5a - 1) = 15a - 2 \\ 7. \: b = \frac{15a - 2}{5a - 1} \)

Answer:

LCM of 12 and 3 is 12

Step-by-step explanation:

hope it helps you vhprince

Answer:

x   ≤ 3/2

Step-by-step explanation:

4x −7 ≤ −1

Add 7 to each side

4x −7+7 ≤ −1+7

4x  ≤ 6

Divide by 4

4x/4  ≤ 6/4

x   ≤ 3/2

Answer:

\(x\leq \frac{6}{4}\)

Step-by-step explanation:

Solve for the equation and that's what you'll get

Answer:

x=75/4

Step-by-step explanation:

4x+3=8x-9

4x+3= -72

4x= -72-3

4x= -75

x=75/4