A square has a perimetre of 30.6 cm what is the length of each side

Answer:

-2.8 or -14/5

Step-by-step explanation:

To divide one fraction by another, there is a really cool method called Keep Change Flip

Keep the first fraction

Change the division sign to multiplication

Flip the numbers on the last fraction

Let's try it out.

Keep the 1/5

Change the ÷ to a ×

Flip the -1/14 to a -14/1

1/5 × -14/1

Multiply the top numbers by each other first

1 × -14 = -14

Now the bottom numbers

5 × -1 = -5

The fraction we have now is -14/5

It can also be written as -2.8

Answer:

subtraction

Step-by-step explanation:

$80-$56= $24-$9= $15

Although a bigger random sample can aid in increasing the precision and decreasing the variability of a national opinion poll, it cannot ensure a decrease in bias, which is dependent on the efficacy of the sampling technique and the sample's representativeness.

A nationwide opinion poll's results are often less variable as the random sample size is increased since the bigger sample size more accurately represents the people being sampled.

It does not necessarily lessen bias, which is the term for systemic mistakes in the sampling process or polling methodology that may endure even with a larger sample size.

The accuracy of the poll's results can be improved by reducing random mistakes like sampling and measurement errors with a bigger sample size.

The standard error of the mean, a measurement of the variability of the sample mean from sample to sample, is often less the bigger the sample size.

A national opinion poll's measure of interest, the population mean, can be more accurately estimated with a smaller standard error.

If the sample is not completely random or representative of the population being investigated, bias may still exist in a bigger sample.

For instance, the findings may be biassed if the pollsters oversample a certain demographic group or geographic area.

Non-response bias can also happen if a certain group of people is less likely than others to reply to the survey.

As a result, while a bigger random sample can aid in increasing the precision and decreasing the variability of a national opinion poll, it cannot ensure a decrease in bias, which is dependent on the efficacy of the sampling technique and the sample's representativeness.

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Answer:

(x + 3) - x(x² + 6x + 9)

= (x + 3) - x(x + 3)²

= (x + 3)[1 - x(x + 3)]

= (x + 3)(1 - x² - 3x)

Step-by-step explanation:

Answer:

\((x+3)(1-x^2-3x)\)

Step-by-step explanation:

First, let's factor that quadratic on the right:

\(x^2+6x+9\) happens to factor nicely into \((x+3)^2\), and putting that into our expression gets us

\((x+3)-x(x+3)^2\)

Factoring out an (x + 3) from each term, we get

\((x+3)[1-x(x+3)]\)

Simplifying that expression on the right:

\((x+3)(1-x^2-3x)\)

We can't factor that right-side expression any more, so we can just leave it like that!

Sixteen teachers ordered a book to be used in their classrooms. The book costs $350, which is to be shared equally. The most appropriate representation of how much each teacher will pay is $350 / 16 = $ 21.88.

Since there are a total of sixteen teachers who placed an order for a book and the cost of the book is $ 350.

Thus, in order to determine the amount to be paid by each teacher equally is calculated by dividing the total cost of the book by the number of teachers, as follows

=  $ 350 / 16

=  $  21.875

After rounding off, it is

=   $ 21.88

Thus, each teacher will pay $ 21.88 for the book.

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The price at which the demand drops to 584 units is $20.80 per unit.

The formula given is:

D = 1000 - 20P

To find the price at which the demand drops to 584 units, we can set D equal to 584 and solve for P:

584 = 1000 - 20P

20P = 1000 - 584

20P = 416

P = 416/20

P = 20.8

Therefore, the price at which the demand drops to 584 units is $20.80 per unit.

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Patricia's commission for the month was 4,496.

Patricia's gross pay for the month was 7,146.

To calculate the amount of commission Patricia earned, we need to multiply her sales by the commission rate:

Commission = 8% of 56,200

Commission = 0.08 x 56,200

Commission = 4,496

So Patricia's commission for the month was 4,496.

To calculate Patricia's gross pay, we need to add her salary to her commission:

Gross Pay = Salary + Commission

Gross Pay = 2,650 + 4,496

Gross Pay = 7,146

So Patricia's gross pay for the month was 7,146.

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Answer:

Total ramp system length in feet: Includes the minimum number of 5′ x 5′ resting platforms and the 5′ x 5′ platform at the top of the ramp.

Step-by-step explanation:

hope this helps!

9514 1404 393

Answer:

  3.72 pints

Step-by-step explanation:

The remaining 2/5 of the paint was white. In pints, that is ...

  (2/5)(9.3 pints) = 3.72 pints . . . . white paint used

Answer:

5:2

Step-by-step explanation:

40÷5=8

16÷2=8

hope this helps you!!

The maximum rate of change of function f at the given point occurs in the direction of the gradient vector.

To find the maximum rate of change of a function f at a given point, we need to compute the gradient of the function and evaluate it at that point. The gradient represents the direction of steepest ascent, and its magnitude indicates the maximum rate of change.

By finding the partial derivatives of f with respect to each variable and evaluating them at the given point, we obtain the components of the gradient vector. The maximum rate of change occurs in the direction of this gradient vector. Without the specific function and point, it is not possible to determine the exact maximum rate of change or its direction.

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The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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The surface area of the triangular prism is

To find the surface area of a prism, we use the formula SA=2B+ph, where SA stands for surface area, B stands for the area of the base of the prism, p stands for the perimeter of the base, and h stands for height of the prism. SA=2(lw)+2(l+w)h.

Area of the base 1 = ½bh

= ½ × 6× 4

= 12cm²

Area of base 2 = l×b

= 6×3 = 18 cm²

area of the front = 10×6 = 60cm²

area of the back = 60cm²

area of left = 3×10 = 30cm²

area of the right = 30cm²

total surface area = 60+60+30+30+18+12 = 210cm²

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Answer: 330

Step-by-step explanation:

.

The integer that represents the scenario "Zach hiked 54 feet up the mountain" is the number 54.

A whole number that can be either positive, negative, or zero is known as an integer.In other words, it is a number that has no fractional or decimal part.

Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on.

Mathematical operations like addition, subtraction, multiplication, and division all use integers.

They are also used in everyday life situations, such as counting, measuring, and keeping score.

In this case, since Zach hiked up the mountain, the integer is positive.

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It will take approximately 102.31 years for the population of Humble, TX to reach 500,000 people if it is growing at a rate of 3% per year.

To determine when the population of Humble, TX will reach 500,000 people, we can use the formula for exponential growth: P(t) = P₀ * (1 + r)^t, Where: P(t) is the population at time t, P₀ is the initial population, r is the growth rate, t is the time in years. In this case, we have: P₀ = 13,200 (initial population),r = 3% = 0.03 (growth rate).

We want to find t when P(t) = 500,000, 500,000 = 13,200 * (1 + 0.03)^t. Dividing both sides by 13,200, we get: 500,000 / 13,200 = (1 + 0.03)^t. Approximately: 37.8788 = (1.03)^t. To solve for t, we can take the logarithm of both sides: log(37.8788) = t * log(1.03). Using logarithm properties, we can isolate t: t = log(37.8788) / log(1.03).

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Answer:

Step-by-step explanation:

4x -3(x-2y) + (1/2)(6x -8y)

Let's distribute...

4x-3x+6y+3x-4y

Let's combine like figures...

(4x-3x+3x)+(6y-4y)

4x+2y

Answer:

82 degrees

Step-by-step explanation:

sum of the angles of the triangle = 180 °

first angle is 41°

second one is : 180-123 = 57°

then the measure of the missing angle(x)  is : 57+41 +x = 180

x= 180-98 = 82°

Answer:

radius = 7.5 cm

Step-by-step explanation:

OM is the perpendicular bisector of AB, thus

∠ OMB = 90° and MB = 6 cm with OB being the radius of the circle

Using Pythagoras' identity in right triangle OMB

OB² = MB² + OM² = 6² + 4.5² = 36 + 20.25 = 56.25 ( square root both sides )

OB = \(\sqrt{56.25}\) = 7.5

The radius = OB = 7.5 cm

Answer:

\(\boxed{r = 7.5\ cm}\)

Step-by-step explanation:

If M is the midpoint so AM = BM = AB/2 = 12 / 2 = 6 cm

Let's Consider a ΔOMB which would be a right angled triangle. So, We can use Pythagorean theorem to find the radius of the circle:

\(c^2 = a^2+b^2\)

Where c is hypotenuse (radius) , a is base ( MB = 6 cm ) , b is the perpendicular (OM = 4.5 cm)

\(r^2 = 6^2+4.5^2\\r^2 = 36+20.25\\r^2 = 56.25\)

Taking sqrt on both sides

r ≈ 7.5 cm

Answer:

8

Step-by-step explanation:

2 x 2 x 2

=======================================================

Explanation:

The given equation is in the form of ax^2+bx+c = 0

The coefficients are

According to Vieta's formula, we know that the roots of a quadratic multiply to c/a

In this case, the roots multiply to -3/2

Let p and q be the two roots. We're told that -3 is one of the roots, so p = -3. Let's find q.

pq = c/a

-3q = -3/2

q = (-3/2)*(-3/1)

q = 1/2

q = 0.5

The other root is 0.5

The product of the roots is -3*0.5 = -1.5 = -3/2 to confirm the answer.

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

The longer way to solve would be to plug x = -3 into the equation and solve for k. You should get k = 5

Once you know the value of k, use the quadratic formula to find the two roots. You should get -3 and 1/2 = 0.5 as the two roots.

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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To determine the typical number of points per game in 2008 carefully observe the histogram and identify the number of points that the tallest bar represent.

This is a type of graph that represents frequency by using bars.

Considering the bars differ in height based on the frequencly, the best to identify the typical number of points is:

Note: This questions is incomplete because the histograms were not attached. Due to this, the answer is based on general knowledge.

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The total number of cupcakes packed is 846 cupcakes.

percentage, a relative value indicating hundredth parts of any quantity.

Let's first find out the number of boxes of each size:

40% of 60 boxes = 24 boxes are medium

35% of 60 boxes = 21 boxes are small

The remaining 60 - 24 - 21 = 15 boxes are large

Now we can calculate the total number of cupcakes packed:

24 boxes x 15 cupcakes per medium box = 360 cupcakes in medium boxes

21 boxes x 6 cupcakes per small box = 126 cupcakes in small boxes

15 boxes x 24 cupcakes per large box = 360 cupcakes in large boxes

Therefore, the total number of cupcakes packed is 360 + 126 + 360 = 846 cupcakes.

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The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."

The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.

The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.

The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).

Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.

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Answer:

C, 0.28 x 63 = p

Step-by-step explanation:

Basically, C is getting 28% of 63.

This can be better shown in terms of 100. Let's say you want 28 percent of 100.

0.28 x 100 = 28