To build a new skate park, a community board must have at least 30% of the voters agree to the build. At a recent voters meeting, 125 voters were asked if they would vote for the new skate park and 47 responded yes. Should the community board go ahead and start planning the park? Yes, they should plan for the skate park because the sample had about 37. 6% people vote yes. Yes, they should plan for the skate park because the sample had about 53. 2% people vote yes. No, they should not plan for the skate park because the sample had about 37. 6% people vote no. No, they should not plan for the skate park because the sample had about 53. 2% people vote no

Answer:

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Answer:

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Answer:

17.5

Step-by-step explanation:

The ratio of "pure drug" to liquid is 35:150

Therefore to evaluate for 75 mls we get the ratio 75/2150 or simply 1/2

we can then multiply 35 by the ratio 1/2

35/2=17.5

State the answer

In 75 mls there are 17.5 grams of pure drug

The amount of the pure drug in 75 ml will be 17.5 grams.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The ratio of the two proportional items will remain the same.

The amount of the drug is directly proportional to the contained liquid.

If 35 gms of the pure drug are contained in 150 ml.

Then the amount of the pure drug in 1 ml will be

⇒ 35 / 150

⇒ 0.2333 grams per ml

Then the amount of the pure drug in 75 ml will be

⇒ 0.2333 x 75

⇒ 17.5 grams

The amount of the pure drug in 75 ml will be 17.5 grams.

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Answer:

x = -7

Step-by-step explanation:

4(2x + 14) = 0

Isolate the variable (x)

2x + 14 = 0 ÷ 4

2x + 14 = 0

2x = 0 - 14

2x = -14

x = -14 ÷ 2

x = -7

Answer:

Richard would charge you $117 for working from 11:00am to 2:30pm.

Step-by-step explanation:

Answer:

-25

Step-by-step explanation:

Answer:

2(5−12)

Hope this helps!

Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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Answer:

The answer is a. 96

Step-by-step explanation:

53+31+x=180

84+x=180

(84-84)+x=180-84

x = 96

Answer:

Step-by-step explanation:

Since the plumber charges $50 regardless of how many hours he works, then the equation must be 50 + ....

Since the plumber charges $80 for each hour, then the equation will be y = 50 + 80x.

Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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Answer:

5 is -20

7 is -5

Answer:

\(5. \: -8/ -2 × -5 = -20\)

\(7. \: \\ -25/5 × -40/8 = - 25\)

\(have \: a \: safe \: life\)

Answer:

(x, y) = (1, 4) is the solution to the graph.

Step-by-step explanation:

Given the system of the equations

\(y=3x+1\)

\(y=5x-1\)

The solution graph is attached below.

From the attached solution graph,

From the graph, it is clear that both lines intersect at x=1 and y=4.  So, the point where two lines intersect or meet is called the solution to the graph.

Thus, the point of intersection is (x, y) = (1, 4)

Therefore, (x, y) = (1, 4) is the solution to the graph.

"If I miss a dose, I can take a double dose the next day to make up for it." This statement by the client reflects the need for further teaching.

Taking a double dose of warfarin sodium to make up for a missed dose is not appropriate and can lead to an increased risk of bleeding. It is important for the client to understand that consistency in taking the medication is crucial and any missed dose should be discussed with the healthcare provider.

Warfarin sodium is an anticoagulant medication used to prevent blood clots. It works by inhibiting the synthesis of certain clotting factors in the liver. It is important for clients taking warfarin to adhere to a consistent dosing schedule as prescribed by their healthcare provider. Missing a dose or taking an incorrect dose can disrupt the balance of anticoagulation in the body and increase the risk of bleeding or clotting.

Therefore, the client should be educated on the importance of taking the medication as prescribed and the potential risks associated with improper dosing.

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Answer:

15 cm²

Step-by-step explanation:

The formula for the area of a triangle:

area = 1/2 × a × b × sin(c)

where a = 6√2, b = 5, c = sin(45)

area = 1/2 × 5 × 6√2 × sin(45) = 15

The measure of angle p in this problem is given as follows:

m < p = 58º.

p is combined with an angle of a right triangle of sides 5 and 6, hence we consider that:

The trigonometric ratios for a right triangle are given as follows:

Then the measure of the internal angle ip is calculated as follows:

tan(ip) = 5/8

ip = arctan(5/8)

ip = 32.

Then the measure of angle p is calculated as follows:

32 + m<p = 90

m < p = 58º.

The problem is given by the image shown at the end of the answer.

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The catcher has to throw a ball to get out a runner trying to steal second base about 127.3 ft away.

Given is a figure of baseball field, we are asked to find the distance between home plate and second base,

Since, the field is a square so all the sides will be equal,

So, using the Pythagorean theorem,

The distance between home plate and second base = √90²+90²

= √8100+8100

= √16200

= 127.3

Hence the catcher has to throw a ball to get out a runner trying to steal second base about 127.3 ft away.

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Answer:

Width = x mile = 4 4/9 mile

J.4 4/9

Step-by-step explanation:

Area of a rectangle = length × width

Area of the rectangular plot = 8/3 square miles

Length = 3/5 mile

Width = x mile

Area of a rectangle = length × width

8/3 = 3/5 * x

8/3 = 3/5x

x = 8/3 ÷ 3/5

Multiply 8/3 by the reciprocal of 3/5

x = 8/3 × 5/3

= (8*5) / (3*3)

x = 40/9

x = 4 4/9 mile

Width = x mile = 4 4/9 mile

The statement the most frequently used graphic in reports is the table is false because tables are not typically the most frequently used graphic in reports.

While tables are commonly used in reports to present structured and detailed information, they are not typically the most frequently used graphic. Instead, other types of visuals such as charts, graphs, and diagrams are often employed to present data and communicate information more effectively.

Graphical representations like bar charts, line charts, pie charts, and scatter plots are widely used in reports to visualize patterns, trends, comparisons, and relationships in the data. These visualizations offer a concise and visually appealing way to convey information, making it easier for readers to understand complex data.

Tables, on the other hand, are more suitable for presenting precise numerical values, categorical information, or detailed breakdowns. They are useful for displaying large datasets or providing specific values for reference. However, their format can be dense and may require closer scrutiny, making them less visually impactful compared to graphical representations.

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To determine the number of ways to select a committee of three faculty members and two students from a group of five faculty and seven students, we need to calculate the combination of faculty members and students separately and then multiply the results.

The number of ways to select three faculty members from a group of five is given by the combination formula:

C(5, 3) = 5! / (3!(5 - 3)!) = 10

Similarly, the number of ways to select two students from a group of seven is given by:

C(7, 2) = 7! / (2!(7 - 2)!) = 21

To find the total number of ways to select a committee consisting of three faculty members and two students, we multiply these two values:

Total ways = 10 * 21 = 210

Therefore, there are 210 ways to select a committee of three faculty members and two students from the given group.

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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The statement is false. Adding non-significant terms to a model does not reduce the mean square for pure error in a replicated factorial design.

In a replicated factorial design, the mean square for pure error measures the random variation or unexplained variation in the data. This variation is unaffected by the addition of non-significant terms to the model. Non-significant terms do not contribute to explaining the response variable and are considered noise in the analysis. Including non-significant terms may even increase the error variation because they introduce additional sources of variability without improving the model's ability to explain the data. Therefore, adding non-significant terms to a model does not lead to a reduction in the mean square for pure error in a replicated factorial design.

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Answer:

x = 0 or x = 1/4

Step-by-step explanation:

You are able to factor out 3x² from 12x³ - 3x² to get 3x²(4x-1).

Set everything to zero and solve.

Hey there!

First, we are given:

\(\frac{1\frac{1}{4}}{1\frac{3}{8}}\)

To make this easier, I am going to change the fractions in to decimals.

\(\frac{1.25}{0.375}\)

To get the unit rate, we can use proportions:

\(\frac{1.25}{0.375} = \frac{x}{1}\)

Using cross products, we know that...

\(1.25 * 1 = 0.375 * x\)

Now, we solve for \(x\):

\(1.25 * 1 = 0.375 * x\\ 1.25 = 0.375x\\ 3 \frac{1}{3} = x\)

Therefore, the unit rate is \(\frac{3\frac{1}{3} }{1}\)

Now, do the same with the other problem, and the unit rate is \(\frac{1\frac{4}{5} }{1}\)

Have a terrificly amazing day!!!

Answer:

\(\huge\boxed{\sf 14\ times}\)

Step-by-step explanation:

\(\displaystyle Probability = \frac{Possible \ no. \ of\ events}{Total \ number\ of \ events}\)

If we roll a die 1 time, the probability of obtaining a 3 is:

= 1 / 6

Because a die has total 6 faces, out of which 3 is only 1.

But, if we roll it 84 times, it becomes:

= \(\displaystyle \frac{1}{6} \times 84\)

= 84/6

\(\rule[225]{225}{2}\)

Answer:

Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513

Step-by-step explanation:

Answer:

The square root of 73

Step-by-step explanation:

The square root of 37 squared is 37

6^2=36

36+37=73

The square root of 73 is an irrational number, so just leave it as the square root of 73

Answer:

x = \(\sqrt{73}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 6² + (\(\sqrt{37}\) )² = 36 + 37 = 73 ( take the square root of both sides )

x = \(\sqrt{73}\)

To show that the vector field F(x,y,z)=〈7ycos(−9x),−9xsin(7y),0〉 is not a gradient vector field, we need to compute its curl.

The curl of a vector field is defined as the cross product of the del operator with the vector field. In other words, curl(F)=∇×F. When we compute the curl of F, we get 〈63cos(7y), 0, 63sin(9x)〉. Since the curl is not zero, we can conclude that F is not a gradient vector field. This is because a vector field is a gradient vector field if and only if its curl is zero.

Therefore, the non-zero curl of F shows that it cannot be expressed as the gradient of a scalar function. In summary, we can conclude that F is not a gradient vector field since its curl is not zero.

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Answer:

\(\textsf{(a)} \quad -4 < x\leq 1\)

\(\textsf{(b)} \quad [3, 19)\)

Step-by-step explanation:

Given compound inequality:

\(\dfrac{9+x}{5} < 5+x\leq 6\)

\(\textsf{If\: $a < u\leq b$ \:then\: $a < u$ \:and\: $u\leq b$}.\)

\(\textsf{Therefore \:$\dfrac{9+x}{5} < 5+x$ \:and\: $5+x\leq 6$}\)

Solve the inequalities separately:

Inequality 1

\(\begin{aligned}\dfrac{9+x}{5} & < 5+x\\9+x & < 5(5+x)\\9+x & < 25+5x\\9+x -5x& < 25+5x-5x\\9-4x & < 25\\ 9-4x-9 & < 25-9\\-4x & < 16\\-x & < 4\\x & > -4\\ \end{aligned}\)

Inequality 2

\(\begin{aligned} 5+x & \leq 6\\ 5+x-5 & \leq 6-5\\x & \leq 1 \end{aligned}\)

Combine the intervals:

\(-4 < x\leq 1\)

Given equation:

\(y=x^2+3\)

As the domain is restricted to  -4 < x ≤ 1, the range is also restricted.

The vertex (minimum point) of  \(y = x^2 + 3\)  is when x = 0.

As x = 0 lies within the restricted domain, y = 3 is the lowest value of the range.

\(x=-4 \implies y=(-4)^2+3=19\)

Therefore, the range is:

Answer:

she swam 1500 meters in 1/4 of the time and he swam 750 in half of his time. Hope this helps

Answer:

5 un^2

Step-by-step explanation:

the liens from (0, 0) to (1, 3) and (1, 3) to (4, 2) are perpendicular meaning that the angle at (1, 3) is a right angle

to find the lengths of the sides we must use the pythagorean theorem

a^2 + b^2 = c^2

for the leftmost side

we have 1^2 + 3^2 = c^2

1 + 9 = 10

c^2 = 10

c = sqrt(10)

for the top side

we have

the same thing

1^2 + 3^2 = c^2

1 + 9 = 10

c^2 = 10

c = sqrt(10)

you must multiple sqrt(10) by sqrt(10) and then by 1/2

sqrt(10) * sqrt(10) is 10

10 * 1/2 is 5

the area is 5 un^2