Express 48 as a percentage of 155.

After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.

To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.

Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.

The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.

To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.

Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.

To find the value of s, we take the square root of both sides. So, s = √(7√3).

Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.

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The surface integral ∫∫aw F. dà directly is zero.To evaluate the surface integral ∫∫aw F.

dà directly, we need to compute the flux of the vector field F across the boundary surfaces of the solid unit cube W.

Let's consider the six faces of the cube: x=0, x=1, y=0, y=1, z=0 and z=1.

For the face x=0, the outward unit normal is -i. So, the flux of F across this face is given by:

∫∫S F. dà = ∫∫D F(-i). dA

where D is the region of the face projected onto the yz plane, which is the square [0, 1] × [0, 1], and dA is the area element on the face.

Thus, we have:

∫∫S F. dà = ∫∫D (-y)i. dA = -∫∫D y dA = -½

Similarly, we can compute the flux across the other faces as follows:

For the face x=1, the outward unit normal is i. So, the flux of F across this face is given by ∫∫D F(i). dA = ½.

For the face y=0, the outward unit normal is -j. So, the flux of F across this face is given by ∫∫D F(-j). dA = -½.

For the face y=1, the outward unit normal is j. So, the flux of F across this face is given by ∫∫D F(j). dA = ½.

For the face z=0, the outward unit normal is -k. So, the flux of F across this face is given by ∫∫D F(-k). dA = -½.

For the face z=1, the outward unit normal is k. So, the flux of F across this face is given by ∫∫D F(k). dA = ½.

Therefore, the total flux of F across the boundary surfaces of the solid unit cube W is:

∫∫aw F. dà = (-½ + ½ - ½ + ½ - ½ + ½) = 0

Hence, the surface integral ∫∫aw F. dà directly is zero.

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Answer:

A and B

Step-by-step explanation:

simplify both sides of the equation

add 4x to both sides subtract 3 from both sides. Divide both sides by 9 and that's it

If the equation given a unique and single value of variable after solving then the equation is said one solution equation.

The equation which has only one solution are,

\(5x+3=-2(2x+3)\)

Thus, the option C is the correct option.

How to find one solution of equation?

If the equation given a unique and single value of variable after solving then the equation is said one solution equation.

Such equation gives exactly one solution.

Given information-

To find the equation we have to solve each equation one by one.

\(-7x+2&=-3(x-3)-4x-7\\\)

Solve it further,

\(-7x+2&=-3x+9-4x-7\\-7x+2&=-7x+2\\.\;\;\;\;\;\;\;\;\;\;\;0=0\)

Thus this equation has no solution. Hence the option A is the incorrect option.

\(14x&=7(2x+2)\)

Solve it further,

\(14x&=14x+14\\.\;\;\;0=14\)

Thus this equation has no solution. Hence the option B is the incorrect option.

\(5x+3=-2(2x+3)\)

Solve it further,

\(5x+3=-(4x+6)\\5x+3=-4x-6\)

Bring the same variable terms one side.

\(5x+4x=-6-3\\9x=-9\\x=-1\)

As the expression of equation gives the value of variable which is -1.Thus this equation has one solution.

Hence the option C is the correct option.

\(3(4x+2)-9=12x-3\)

Solve it further,

\(12x+6-9=12x-3\\2x-3=12x-3\\.\;\;\;\;\;\;\;0=0\)

Thus, this equation does not has one solution.

Hence the option D is the incorrect option.

Hence the equation which has only one solution are,

\(5x+3=-2(2x+3)\)

Thus, the option C is the correct option.

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The mean absolute deviation of the given scores of Robin as shown in the diagram atatched is: 5.2.

The mean absolute deviation of a data set is determined by finding the average of the distance of each data point from the mean of the data set.

Given that the distance from the mean are: 8, 1, 5, 0, 12,

Mean absolute deviation = (8 + 1 + 5 + 0 + 12)/5

Mean absolute deviation = 26/5

Mean absolute deviation = 5.2.

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Given :

The points P (2, -3) & Q (-5, -3) whose ordinates are same.

To Find :

To which axis the line PQ is parallel.

Solution :

In given points the ordinates are same.

Therefore, the line is parallel to the x- axis.

Hence, this is the required solution.

Answer:

Step-by-step explanation:

Use Pythagorean theorem,

Base² + altitude² =hypotenuse²

x² + 19² = 21²

x² + 361 = 441

         x² = 441 - 361

          x² = 80

          \(x =\sqrt{80}=\sqrt{2*2*2*2*5}=2*2*\sqrt{5}=4\sqrt{5}\)

Answer: 4/10 (÷2) => 2/5

Answer:

2/5 or 4/10

Step-by-step explanation:

2  (x2) =    4

-----       -------

5  (x2) =  10

Answer:

it will be $80.00 and your saving $20.00

Step-by-step explanation:

The option (c) 40 + 360n, for any integer, n is correct for the given angle.

It is given that the options given below represent the measures of all angles coterminal with a 400° angle.

It is required to find the correct option given below:

a) 360 + 40n, for any integer, n

b) 360 + 40n, for any whole number, n

c) 40 + 360n, for any integer, n

d) 40 + 360n, for any whole number, n

For the given terminal angle the coterminal angles are defined as the different angle measures with the same terminal side and vertex side.

The given angle = 400°

If we subtract 360° from it, we will get:

= 400-360 = 40°

If we add 360° to a given angle: we get:

=400+360 = 760°

Here option (c) is correct because if we put n=0,1,2...., we get:

=40° (if n = 0)

= 400° (if n= 1)

=760 (if n=2)

Thus, option (c) 40 + 360n, for any integer, n is correct for the given angle.

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Answer:

its C

Step-by-step explanation:

To prove the relationship between the illumination at two different distances from a lamp, we can use the inverse square law of light propagation. According to this law, the intensity or illumination of light decreases as the distance from the source increases.

The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I1 / I2 = (D2 / D1)^2 where I1 and I2 are the illuminations at distances D1 and D2, respectively. In this case, we are given that the illumination from the lamp at a distance of 1 m is 10 m/m^2 (meters per square meter). Let's assume that the illumination at a distance of 0.5 m is I2.

Using the inverse square law, we can write the equation as:

10 / I2 = (1 / 0.5)^2

Simplifying the equation, we have:

10 / I2 = 4

Cross-multiplying, we get:

I2 = 10 / 4 = 2.5 m/m^2

Therefore, we have proven that the illumination at a point 0.5 m away from the lamp is 2.5 m/m^2, not 40 m/m^2 as stated in the question. It seems there may be an error or inconsistency in the given values.

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The range of the miles biked data set is 14.

The range of a set of data is the difference between the largest and smallest values in the data set. To find the range of the miles biked data set of 11, 15, 20, 25, and 25, we need to first find the largest and smallest values.

The largest value is 25, and the smallest value is 11. To find the range, we subtract the smallest value from the largest value: 25 - 11 = 14. This means that the difference between the largest distance biked and the smallest distance biked is 14 miles.

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The mean and standard deviation of a normal population are called parameters, and the mean and standard deviation of a random sample in the population are called statistics.

Normally distributed data:

In a normal distribution, data is distributed symmetrically without asymmetry the data are probabilities whose distribution is symmetrical with respect to the mean.

The normal distribution is symmetric, unimodal and asymptotic, and the mean, median and mode are all equal.

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wide range.

For solving the problems are :

The average of the data is the average of the given data. The standard deviation of the data is half the difference between the highest value in the data set and the mean.

These numbers that summarize information about a sample are called statistics.

The numbers that summarize information about a population are called parameters.

Numbers that summarize information about a sample are called statistics.

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Answer:

(B) Parameters

(A) Statistics

Step-by-step explanation:

egg 2023

Answer:

Answer: x=15

This is my answer

isosceles trapezoid, the two angles on the legs are the same size, so the other two angles are also equal.

the sum of all the angles is 360°

3x+3x+9x+9x = 360°

24x = 360°

x = 15

Answer:

50

Step-by-step explanation:

trust me bro

The height of the kite is 47.5 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 95

h = 47.5 feet

Therefore the height of the kite is 47.5 feet.

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A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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Answer:

25%.

Step-by-step explanation:

88 - 66 = 22

22/88 = 0.25

0.25 * 100 = 25%.

Answer:

The only graph that is fully shown.

Step-by-step explanation:

I did the math and the points check out.

The materials price variance for January can be calculated using the following formula: Materials Price Variance = (Actual Quantity Purchased x Standard Price) - (Actual Quantity Purchased x Actual Price).

In this case, the actual quantity purchased is 29,300 grams and the actual price is $8.00 per gram. The standard price is given as $7.90 per gram. Plugging these values into the formula, we get: Materials Price Variance = (29,300 grams x $7.90 per gram) - (29,300 grams x $8.00 per gram).

To calculate the specific value of the variance, you would need to subtract the product of the actual quantity purchased and actual price from the product of the actual quantity purchased and standard price. The resulting value will determine whether the materials price variance is favorable or unfavorable, indicating whether the actual price paid for the material was higher or lower than the standard price set by the company.

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This retirement planning scenario involves saving a fixed amount per year, earning a specified interest rate, and determining the final retirement account balance, lump-sum investment amount, annual withdrawal in retirement, and required interest rate for a specific savings goal. The details are as follows:

a. retirement account balance of approximately $536,144.37

b. The lump sum required would be approximately $60,319.79.

c. With an account balance of $536,144.37, the annual withdrawal would be approximately $46,914.90.

d.  It would take approximately 16 years until the savings are depleted.

e. Through trial and error, it can be determined that an interest rate of approximately 10.47% is needed to achieve the desired savings goal.

a. The retirement account balance on the day of retirement can be calculated by using the formula for the future value of an ordinary annuity. In this case, saving $4,500 per year for 35 years with an annual interest rate of 5.5% will result in a retirement account balance of approximately $536,144.37.

b. To achieve the same retirement savings goal with a lump-sum investment today, the present value of an ordinary annuity formula can be used. The lump sum required would be approximately $60,319.79.

c. Assuming a retirement duration of 17 years and a desire to exhaust the savings with the 17th withdrawal, the annual withdrawal can be calculated using the formula for the annuity payment. With an account balance of $536,144.37, the annual withdrawal would be approximately $46,914.90.

d. If the decision is made to withdraw $90,000 per year in retirement, the number of years until the savings are exhausted can be determined using the formula for the number of periods in an annuity. It would take approximately 16 years until the savings are depleted.

e. If the maximum affordable annual saving is $900 and the goal is to retire with $1,000,000, the required interest rate can be calculated using the formula for the rate of return. Through trial and error, it can be determined that an interest rate of approximately 10.47% is needed to achieve the desired savings goal.

These calculations provide insights into the financial aspects of retirement planning and can help individuals make informed decisions about their savings, investments, and withdrawal strategies based on their specific goals and constraints.

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The weighted-average unit contribution margin is $46.20.

The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin of each model by its respective sales mix percentage, and then summing up the results.

To find the weighted-average unit contribution margin, we first calculate the unit contribution margin for each model by subtracting the unit variable costs from the selling price:

For Model A12:

Unit contribution margin = Selling price - Unit variable cost

                     = $60 - $42

                     = $18

For Model B22:

Unit contribution margin = Selling price - Unit variable cost

                     = $120 - $84

                     = $36

For Model C124:

Unit contribution margin = Selling price - Unit variable cost

                     = $480 - $360

                     = $120

Next, we multiply each unit contribution margin by its respective sales mix percentage:

Weighted contribution margin for Model A12 = 60% * $18 = $10.80

Weighted contribution margin for Model B22 = 15% * $36 = $5.40

Weighted contribution margin for Model C124 = 25% * $120 = $30.00

Finally, we sum up the weighted contribution margins:

Weighted-average unit contribution margin = $10.80 + $5.40 + $30.00 = $46.20. Therefore, the weighted-average unit contribution margin is $46.20.

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-4 is not included, that is why the open interval and the symbol of ) are used

Answer:

B. 48.

Step-by-step explanation:

16, 23,  55, 64, 49

Range = highest value - least

= 64 - 16

= 48.

Answer:

29

Step-by-step explanation:

5^2 = 5x5

=25+4

=29

Answer:

29

Step-by-step explanation:

Here, b=5

Now a= b^2+4

= (5)^2+4

=25+4

=29 Ans

A combination is a rearrangement of items in which the order does not make a difference.

In mathematics, both permutations and combinations are used to count the number of ways to arrange or select items. However, they differ in terms of whether the order of the items matters or not.

A permutation is an arrangement of items where the order of the items is important. For example, if we have three items A, B, and C, the permutations would include ABC, BAC, CAB, etc. Each arrangement is considered distinct.

On the other hand, a combination is a selection of items where the order does not matter. It focuses on the group of items selected rather than their specific arrangement. Using the same example, the combinations would include ABC, but also ACB, BAC, BCA, CAB, and CBA. All these combinations are considered the same group.

To determine whether to use permutations or combinations, we consider the problem's requirements. If the problem involves arranging items in a particular order, permutations are used. If the problem involves selecting a group of items without considering their order, combinations are used.

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The change left when Susan buys lotion for $2.33 and gives the bill is $8.

Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. The total amount will be:

= $10 + (3 × 0.1) + (3 × 0.01)

= $10.33

The change left will be:

= Total amount - Cost of lotion

= $10.33 = $2.33

= $8

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if it has a diameter of 6, that means its radius is half that or 3.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\pi (3)^2(7)\implies V\approx 197.92\)

Answer:

V=197.92

Step-by-step explanation:

Diameter (d) =6

Height (h) =7

Solution:

V=π(d/2)^2

H=π(6/2)^2 . 7=197.92034

Increasing each phrase inside a bracket even by expression outside of the bracket is referred to as expanding it: 2a + 2d

Mathematical expressions consist of a minimum of two integers or variables, at least one arithmetic operation, and a statement. Any one of the following mathematical operations can be used. An expression's basic components are as follows: The formula becomes (Number/Variable, Math Operator, Number/Variable).

An expressions is just a mathematical term that combines variables, operators, and numbers to indicate the value about something.

Increasing each phrase inside a bracket even by expression outside of the bracket is referred to as expanding it.

to expand 2(a+d):

= 2a + 2d

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Answer:

Step-by-step explanation:

A negative number raised to an even exponent gives a positive result so it is the same as 3 raised to 6. That is 3 x 3 x 3 x 3 x 3 x 3 = 729

The (-3) to the sixth power, (-3)⁶, is equal to 729.

To express (-3) to the sixth power in exponential form, we write it as (-3)⁶.

Now, let's calculate (-3)⁶ properly:

(-3)⁶ = (-3) * (-3) * (-3) * (-3) * (-3) * (-3)

Multiplying -3 by itself six times:

(-3) * (-3) * (-3) * (-3) * (-3) * (-3) = 729

Therefore, (-3) to the sixth power, (-3)⁶, is equal to 729.

By raising -3 to the power of 6, we obtain the result of 729.

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