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Answer:

Step-by-step explanation:

density is mass divided by volume

15 divided by 9 is

1.6666666666

so its 1.666 repeating g/cm^3

Answer:

(1,0)

Step-by-step explanation:

\(\boxed{midpoint = ( \frac{x1 + x2}{2}, \frac{y1 + y2}{2}) }\)

Thus, midpoint of the line segment is

\( = ( \frac{3 - 1}{2} , \frac{1 - 1}{2} ) \\ = ( \frac{2}{2} , \frac{0}{2} ) \\ = (1,0)\)

This student performed better than 68% of the other test-takers in the verbal part and better than 27% in the quantitative part.

Given,

Test-taker scored at the 68th percentile for their verbal grade and at the 27th percentile for their quantitative grade .

Now,

68% percentile : 68% scores equal or less .

27% percentile : 27^ scored equal or less .

Thus option D

This student performed better than 68% of other test taker in verbal and better than 27% in quantitative part .

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To find the unit price that maximizes revenue, we need to maximize the given revenue function: \(R = 0.25(36950 - 0.02p^3)^2\). The revenue function R is dependent on the unit price p.

To maximize the revenue, we need to find the value of p that corresponds to the maximum point on the revenue curve.

To determine this, we can take the derivative of the revenue function with respect to p and set it equal to zero to find the critical points. Let's calculate the derivative:

\(dR/dp = 2 * 0.25 * (36950 - 0.02p^3) * (-0.02) * 3p^2 = -0.015 * p^2 * (36950 - 0.02p^3)\)

Setting this derivative equal to zero, we have:

\(-0.015 * p^2 * (36950 - 0.02p^3) = 0\)

Since we are interested in finding the unit price, we can solve this equation numerically using methods like graphing, Newton's method, or a calculator. The resulting value of p will be the unit price that maximizes revenue. Remember to round the answer appropriately based on the precision required.

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The average waiting time for a tourist who isn't served immediately is approximately 0.9375 minutes, which is closest to option d. 0.333 minutes.

To calculate the average waiting time for a tourist who isn't served immediately, we need to consider the arrival rate of tourists, the service rate of the employees, and the number of employees available.

The arrival rate is given as one tourist every 60 minutes, which means that the arrival rate (λ) is 1/60 tourists per minute. The service rate (μ) is the reciprocal of the average service time, which is 1/30 tourists per minute.

Since we have 8 employees available, the effective service rate (μ') is 8 times the individual service rate, which gives us 8/30 tourists per minute.

To calculate the average waiting time (W), we can use the formula:

W = (ρ / (μ - λ)) * (1 / μ),

where ρ is the traffic intensity, which is equal to λ / μ'.

Substituting the values into the formula:

ρ = (1/60) / (8/30) = 0.25,

W = (0.25 / (8/30)) * (1 / (8/30)) = 0.25 * (30/8) = 0.9375 minutes.

Therefore, the average waiting time for a tourist who isn't served immediately is approximately 0.9375 minutes, which is closest to option d. 0.333 minutes.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer: y= 0.64 is the answer

For the notation of average the expression {{1, 1, 0} [0, 1] 0} is evaluates to  0.3889 approximately.

To evaluate the expression {{1, 1, 0} [0, 1] 0}, we need to follow the notation,

[a, b] denotes the average of a and b.

{a, b, c} denotes the average of a, b, and c.

Let's break down the expression step by step

[0, 1]

= (0 + 1) / 2

= 1/2

= 0.5

Now we have {{1, 1, 0} 0.5 0}. We can evaluate the inner expression first.

{1, 1, 0}

= (1 + 1 + 0) / 3

= 2/3

≈ 0.6667

Now we have {0.6667 0.5 0}. We can apply the same notation to find the average,

{0.6667, 0.5, 0}

= (0.6667 + 0.5 + 0) / 3

= 1.1667 / 3

≈ 0.3889

Therefore, the expression {{1, 1, 0} [0, 1] 0} for the notation of average evaluates to approximately 0.3889.

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The minimum value is 0.5 and the maximum value is 3.5.

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If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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To specify the orientation of the plane of a paper, the following single line can be used: "Hold the paper such that the plane of the paper is perpendicular to the direction of the gravity.

This means that if you hold the paper and drop a plumb line, the line should be parallel to the edge of the paper. This way, anyone can hold the paper in the same or a parallel plane, thus ensuring that the orientation is consistent.An alternate line to specify the orientation of the plane of a paper is: "Hold the paper such that the plane of the paper is parallel to the surface of the earth." This means that if you hold the paper and look at it from the top, the surface of the paper should appear to be parallel to the ground. By using either of these lines, one can specify the orientation of the paper's plane.

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If the number of checks are greater than 25, the Simple Checking plan cost​ less.

We have two checking account plans at Parson's bank.

We have to determine for what number of checks per month will the Simple Checking plan cost​ less.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Let for x number of checks per month the simple checking plan cost less.

For No frills plan -

Charge per check - $0.25

Therefore, for x checks, it will cost - $0.25x

For Simple Checking plan -

Fixed monthly charges - $5

Charges per check - $0.50

Therefore - for x checks - $5 + $0.50x

Now - for Simple Checking plan to cost​ less than No frills plan -

5 + 0.05x < 0.25x

5 < 0.25x - 0.05x

5 < 0.2x

x > 25

Hence, if the number of checks are greater than 25, the Simple Checking plan cost​ less.

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The range of values of x which satisifies both of the inequalities is:

(-3, 2)

Here we have two inequalities:

3 + x < 5

8 + x > 5

And we want to see which range of values of x satisfie both of these inequalities.

If we isolate x on both inequalities, we will get:

3 + x < 5

x < 5 - 3

x < 2

And the other one is:

8 + x > 5

x > 5 - 8

x > -3

Then we havethe compound inequality:

x < 2

x > -3

Then the range of values that satisfies both inequalities is (-3, 2)

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The angle measure of x is given as follows:

x = 46.2º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of x, we have that:

Hence the value of x is obtained applying the cosine ratio as follows:

cos(x) = 9/13

x = arccos(9/13)

x = 46.2º.

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The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.

To find out how long each sprinkler was used, we can set up a system of equations. Let's say the Alexander family used their sprinkler for x hours, and the Chen family used their sprinkler for y hours.

From the given information, we know that the water output rate for the Alexander family's sprinkler is 30 liters per hour. Therefore, the total water output from their sprinkler is 30x liters.

Similarly, the water output rate for the Chen family's sprinkler is 40 liters per hour, resulting in a total water output of 40y liters.

Since the combined total water output from both sprinklers is 2250 liters, we can set up the equation 30x + 40y = 2250.

We also know that the families used their sprinklers for a combined total of 65 hours, so we can set up the equation x + y = 65.

Now we can solve this system of equations to find the values of x and y, which represent the number of hours each sprinkler was used.

By solving the equation we get,

The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.

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Answer is the following:

B

The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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After answering the provided question, we can conclude that As a result, the total surface area of the cake that will be frosted is 24+36+54 = 114 square inches.

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

The surface area of the frosted cake is the total of the areas of all the sides of the rectangular prism, omitting the bottom.

The aggregate area of the two 6-inch by 2-inch sides is 262 = 24 square inches.

The aggregate area of the two 9-inch by 2-inch sides is 292 = 36 square inches.

The cake's top, which is similarly 6 inches by 9 inches, has a surface area of 6*9 = 54 square inches.

As a result, the total surface area of the cake that will be frosted is 24+36+54 = 114 square inches.

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Each part will be approximately 8.04 inches long.

We can express this as:

Length of each part = Total length of ribbon / Number of parts

In this case, the total length of the ribbon is 4 feet, and we want to divide it into six equal parts. So, we can substitute these values into the above formula:

Length of each part = 4 feet / 6 parts

To solve this division problem, we can either use a calculator or do long division:

4 / 6 = 0.6666666667

So, each part will be approximately 0.67 feet long. Alternatively, we can convert this to inches, which is a more common unit of measurement for small lengths:

0.67 feet x 12 inches/foot = 8.04 inches

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Answer:

B. 20

Step-by-step explanation:

First, 20% of 20 is 4.

36 decreased by 4 (36-4) is 32.

The equation is N (160%)=32    or    1.6n=32

160% because it was already 100%, and its increased by 60% (100+60)

Divide  both sides by 1.6.

You get n=20

I hope this helps!

Answer:

Step-by-step explanation:

One winter day, the temperature at noon was -9°F.

The temperature then rose by ​1/2 degree each hour for 3 hours:

The temperature then dropped by 2 1/4 degrees each hour for 2 hours:

Now add up all three values to find the final value:

Answer:

x=-7/4

3x+1=7x+8

-3x     -3x

1=      4x+ 8

-8            -8

-7/4=x

Answer:

You can't make a triangle with those solutions.

Answer:

0

Step-by-step explanation:

A trianlge cannot be formed

3x+y=-1 is the equation for slope as -3 and point as (-1,2).

Algebraic expressions are used to express mathematical expressions, and algebraic expressions are used to express mathematical expressions. For example, 3x + 5 = 14 is an equation containing two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

slope=-3

point=(-1,2)

(y-y1)=m(x-x1)

y-2=-3(x+1)

y-2=-3x-3

3x+y=-1

The equation for slope as -3 and point as (-1,2) is 3x+y=-1.

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Answer:

\( \boxed{13}\)

Step-by-step explanation:

Arranging the data in ascending order:

8 , 8 , 10 , 11 , 13 , 13 ,13 , 14 , 14 , 15 , 16 , 17 , 18 , 18 ,

In the case of discrete data, mode can be found just by inspection, i.e just by taking an item with highest frequency.

Here, 13 has the highest frequency

So, Mode = 13

Extra information

Mode

The mode of a set of data is the value with the highest frequency. A distribution that has two modes is called bimodal. The mode of a set of data is denoted by Mo.

Hope I helped!

Best regards!

9514 1404 393

Answer:

  13

Step-by-step explanation:

Let n represent that number.

  (2 +n)/(5 +n) = 5/6 . . . . . . . . n is added to numerator and denominator

  6(2 +n) = 5(5 +n) . . . . . . . . . multiply by 5(5+n)

  12 +6n = 25 +5n . . . . . . . . . eliminate parentheses

  n = 13 . . . . . . . . . . . subtract 5n+12

Adding 13 to each term will give 5/6.

__

Check

  (2 +13)/(5 +13) = 15/18 = (3·5)/(3·6) = 5/6

_____

Alternate solution

The difference of denominator and numerator in 2/5 is 5-2 = 3. The difference of denominator and numerator in 5/6 is 6-5 = 1. In order to make the latter difference 3, we must have (3/3)(5/6) = 15/18. We can get 15/18 from 2/5 by adding 13 to numerator and denominator.

The required measure of length of the rectangle is 8 feet.

As given, the length of a rectangle is 5 feet more than the width. The perimeter is 22 feet.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,

Let the length of the rectangle be l and the width be w,
According to the question,
l = w + 5
The perimeter of the rectangle = 22
2 [w + 5 + w ] = 22
2 [2w + 5] = 22
4w + 10 = 22
w = 3
Now,
l = 5 + 3 = 8

Thus, the required measure of the length of the rectangle is 8 feet.

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Answer:

the answer is A

Step-by-step explanation:

If you draw it then the height of the building (x) is the opposite, the adjacent is 75 (it's in between a 90 degree angle and the 58 degree angle). With this you have tan (58) = x/75

Then you add multiply 75 on the other side

75 tan (58) = x

After putting it in a DEG calculator, x = 120.03.

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17