simplify this expression: 54 - c + 3c by the power of 2 - 10

The dimensions of the container of least cost are 15 inches by 15 inches by 3 inches, and the least cost of the container is $990.

Let the side of the square base of the rectangular container be x, and the height be y. The volume of the container can be expressed as xy² = 2250. From this, we can solve for x in terms of y using x = (2250/y²) as shown in equation (1).

Next, let's consider the cost of the sides (C). The cost of the sides is directly proportional to the surface area of the sides of the container, which is given by 2xy + 4y². Therefore, we can express the cost of the sides as C = k(2xy + 4y²) in equation (2), where k is a constant.

Since we are looking for the dimensions of the container of least cost, we need to minimize the cost function. To do this, we can differentiate the cost function with respect to y and set it equal to zero. This will give us the critical point where the cost is minimized.

Differentiating C with respect to y, we get dC/dy = 2k(x + 4y). Setting this equal to zero, we have 0 = 2k(x + 4y). Simplifying this equation, we get y = x/4 as shown in equation (3).

From equations (1) and (3), we have x = 15 and y = 3 inches. Therefore, the dimensions of the container of least cost are 15 inches by 15 inches by 3 inches.

To find the total cost, we calculate the cost of the top and bottom of the container (2xy) which is $2(15²) = $450, and the cost of the sides (4y²) which is $3(4*15*3) = $540. The total cost is the sum of these costs, which is $450 + $540 = $990.

In conclusion, the dimensions of the container of least cost are 15 inches by 15 inches by 3 inches, and the least cost of the container is $990.

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Answer:

8. C

9. B

10. C

11. B

Step-by-step explanation:

Two events A and B are mutually exclusive if they cannot occur together, that is, P(A∩B) = 0.P(A∩B) = 0.42

P(A∩B) ≠ 0

Therefore, A and B are not mutually exclusive.

1. Probability of A or B or both occurring P(A∪B) = P(A) + P(B) - P(A∩B)0.42 = 0.4 + 0.3 - P(A∩B)

P(A∩B) = 0.28

Therefore, probability of either A or B or both occurring is P(A∪B) = 0.28

2. Probability of both A and B occurring

P(A∩B) = P(A) + P(B) - P(A∪B)P(A∩B) = 0.4 + 0.3 - 0.28 = 0.42

Therefore, the probability of both A and B occurring is P(A∩B) = 0.42

3. Probability of A occurring but not B P(A) - P(A∩B) = 0.4 - 0.42 = 0.14

Therefore, probability of A occurring but not B is P(A) - P(A∩B) = 0.14

4. Probability of both A and B occurring when C occurs, if A, B and C are statistically independent

P(A∩B|C) = P(A|C)P(B|C)

A, B and C are statistically independent.

Hence, P(A|C) = P(A), P(B|C) = P(B)

P(A∩B|C) = P(A) × P(B) = 0.4 × 0.3 = 0.12

Therefore, probability of both A and B occurring when C occurs is P(A∩B|C) = 0.12

5. Two events A and B are statistically independent if the occurrence of one does not affect the probability of the occurrence of the other.

That is, P(A∩B) = P(A)P(B).

P(A∩B) = 0.42P(A)P(B) = 0.4 × 0.3 = 0.12

P(A∩B) ≠ P(A)P(B)

Therefore, A and B are not statistically independent.

6. Two events A and B are mutually exclusive if they cannot occur together, that is, P(A∩B) = 0.P(A∩B) = 0.42

P(A∩B) ≠ 0

Therefore, A and B are not mutually exclusive.

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Answer:

\(\frac{\text{2csc(2t)}}{\text{sec(t)}}\)

Step-by-step explanation:

\(\frac{\text{cot(t)+tan(t)}}{\text{sec(-t)}}\)

~Use the identity [ sec(-x) = sec(x) ]

\(\frac{\text{cot(t)+tan(t)}}{\text{sec(t)}}\)

~Simplify

\(\frac{\text{2csc(2t)}}{\text{sec(t)}}\)

Best of Luck!

The correct option is a) (-7, 3) which is the midpoint of the segment.

To find the midpoint of a segment, we need to use the midpoint formula:

Midpoint = ( \((x1 + x2)/2 , (y1 + y2)/2\) )

The midpoint of a segment is the point that lies exactly halfway between the two endpoints of the segment.

It is calculated using the midpoint formula, which involves finding the average of the x-coordinates and y-coordinates of the endpoints.

Using the coordinates given in the diagram, we can substitute them into the formula:

Midpoint = ( (-9 + 5)/2 , (3 + 3)/2 )

Midpoint = ( (-4)/2 , 6/2 )

Midpoint = ( -2 , 3 )

However, it means that if we were to draw a line segment connecting (-9, 3) and (5, 3), the midpoint would be exactly in the middle of that line.

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The required additional information for a quadrilateral ABCD is a parallelogram with AB ∥ CD is given by AB ≅ CD.

In quadrilateral ABDC,

AB ∥ CD

Additional piece of information for a quadrilateral ABCD to be a parallelogram if and only if it satisfies any of the following conditions,

Opposite sides are parallel,

If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram.

Opposite sides are equal in length,

If both pairs of opposite sides of a quadrilateral are equal in length, then it is a parallelogram.

Opposite angles are equal,

If both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram.

Diagonals bisect each other,

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

One pair of opposite sides is both parallel and equal,

If one pair of opposite sides of a quadrilateral are both parallel and equal in length, then it is a parallelogram.

Here AB ∥ CD

Additionally if we have ,

AB ≅ CD

⇒ Quadrilateral ABCD is a parallelogram.

Therefore, the additional information for quadrilateral ABCD to be a parallelogram is AB ≅ CD.

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The above question is incomplete, the complete question is:

In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram? AB ≅ CD AC ≅ BD AB ⊥ BD CD ⊥ BD.

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

The reason for which HK={1,(1 2),(2 3), (1 3 2)} is HK = {hk | h in H and k in K}.

We are given that;

G = S3, H = {(1 2)} and K ={(2 3)},

Now,

The set HK is defined as the set of all products of the form hk, where h belongs to H and k belongs to K. In other words,

HK = {hk | h in H and k in K}. To find HK, we need to multiply every element of H by every element of K and simplify the result using the rules of permutation multiplication. Here are the calculations:

\($$1 \cdot 1 = 1$$\)

\($$1 \cdot (2 3) = (2 3)$$\)

\($$(1 2) \cdot 1 = (1 2)$$\)

\($$(1 2) \cdot (2 3) = (1 3 2)$$\)

Therefore, by algebra the answer will be HK = {hk | h in H and k in K}.

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Match the Data Visualisation terms as follows:

1. Numpy: Working with arrays and matrices.

2. Bar chart: Representing categorical data with rectangular bars.

3. Pip: Package installer for Python.

4. S: Statistical library for Python.

The following are the meanings of the given terms:

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It is proved that Point A is situated equal distance from Triangle PQA and RQA.

It is a line that divide an angle or a line in two equal parts.  In the given figure, QA is a bisector as it divides the angle PQR.

Triangles are called congruent when they have equal corresponding sides and equal corresponding angles. As shown in figure, the bisector QA creates two congruent triangle PQA and RQA.

it is given, QA is bisector of angle Q, so point A lies equal distance from P and R. According to the figure, APQ and ARQ are right angle.

As per the rules of congruence theorem, triangle PQA and Triangle RQA are two congruent triangles.

hence, A is the same distance from P and R

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Statement                                                                  Reason

1. QA is the bisector of ∠PQR                                   Given

2. ∠PQA   ≅ ∠RQA                                          Definition of bisector

4. ∠QXA ≅ ∠QYA                                   All right angles are congruent

5. QA ≅ QA                                                                Given

6.△PQA ≅ △RQA                                            AAS Postulate

8. Point A is equidistance                              Definition equidistance

from the side of ∠PQR        

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given that point A is lie on the bisector of ∠PQR.

When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.

Therefore QA is the bisector of ∠PQR

Then ∠PQA   ≅ ∠RQA  

Since ∠QXA and ∠QYA are right angle, therefore they are congruent.

∠QXA ≅ ∠QYA

QA ≅ QA

AAS postulate: The triangles are congruent if two angles and the excluded side of one triangle match two angles and the excluded side of another triangle.

According to AAS postulate,

△PQA ≅ △RQA  

Point A is equidistance from ∠PQR.

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Answer:

7. 22 2/5   8. 10 8/10

Step-by-step explanation:

7. 7x3=21 + 7x1/5= 22 2/5

8.  2x5=10 + 2x4/10= 10 8/10

Answer:

394 km

Step-by-step explanation:

197 is 197/60 times as much as 60

so the distance is also that much more: 120 km * 197/60 = 394

The slope of the line parallel to the function: y = 50 - 0.5x include the following: C. -0.5.

In Mathematics and Geometry, parallel lines simply refers to two (2) lines that are always the same or equal distance apart and never meet.

Generally speaking, two (2) lines are considered as parallel under the following standard conditions:

Slope, m₁ = Slope, m₂.

From the function, we have:

y = 50 - 0.5x

Slope, m = -0.5

In this context, we can reasonably infer and logically deduce that the slope of the two lines would be equal and the same:

Slope of line 1 = Slope of line 2

-0.5 = -0.5

In conclusion, we can logically deduce that the slope of the given line is equal to -0.5.

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Answer:

false

Step-by-step explanation:

Answer:

0.2222222...

Step-by-step explanation:

Long division or just googl

Answer:

.2 with a bar on top of the 2

Step-by-step explanation:

Whenever we have a number over 9 (Ex. 1/9, 2/9, 4/9), we can write it as a . and then that number, with a bar on top (Which basically tells you that it is repeating).

Answer:

15

if you are happy with my answer, please give brainliest :)

Step-by-step explanation:

You do 4 times 2 first

so

7+8 equals 15

Answer:

Step-by-step explanation:

=7+8

=15

Hope it helped you.

Plz mark me brainliest.

The percent change in size from 983 to 2,349 square feet was 138.8%.

The average American home swelled from 983 square feet in 1950 to 2,349 square feet in 2004, representing a change of 1366 square feet. This change can be expressed as a percent change by dividing the change (1366 square feet) by the starting value (983 square feet). The resulting percent change is 138.8%.

To calculate the percent change, we can use the following equation:
Percent Change = (Ending Value - Starting Value) / Starting Value x 100
Using this equation, the percent change in the size of the average American home is calculated as follows:
Percent Change = (2349 - 983) / 983 x 100 = 138.8%

This means that the average American home increased by 138.8% in size between 1950 and 2004. This is an impressive rate of growth and may be attributed to a number of factors. In 1950, the United States was in the midst of a period of rapid economic growth, and this may have allowed people to buy larger homes and upgrade to more luxurious accommodations. In addition, advances in technology and manufacturing may have made larger homes more affordable for more people.

Whatever the cause of the growth in home size, it is clear that the average American home saw a substantial increase in size between 1950 and 2004. The percent change in size from 983 to 2,349 square feet was 138.8%.

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The vertical component of the initial velocity will basically decide where the vertices will be. that is how the initial velocity is related to the vertex of the parabola.

A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone, where the plane is parallel to one of the cone's generating lines. The shape of a parabola is similar to that of a U-shaped curve, but with a sharper curve near the bottom of the U.

The parabola has several important properties, including a focus and a directrix. The focus is a point on the axis of symmetry of the parabola that is equidistant from every point on the curve. The directrix is a line that is perpendicular to the axis of symmetry and is equidistant from every point on the curve.

The equation of a parabola in standard form is y = ax² + bx + c, where "a" determines the direction and shape of the parabola, "b" determines the horizontal shift of the parabola, and "c" determines the vertical shift of the parabola.

The initial velocity will have two component basically, a horizontal component and a vertical component. The vertical component will decide how high the object will go, or in other words the vertical component of the velocity will decide the position of the vertex of the parabolis path which the object is going to follow.

When the vertical component of the velocity becomes 0, the object will be at it's maximum height (i.e the object will be at the vertex of the parabola)

The vertical component of the initial velocity will basically decide where the verties will be. that is how the initial velocity is related to the vertex of the parabola.

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Answer:

389 hours and 23 minutes

Step-by-step explanation:

16x24=384

384+=5=389

and 23 minutes

The difference in the interest that the account will have earned at the end of 10 years is of:

D. $3.01.

The amount of interest earned, in compound interest, after t years, is given by:

\(I(t) = P\left(1 + \frac{r}{n}\right)^{nt} - P\)

In which the variables are listed as follows:

In the context of this problem, these parameters are given as follows:

P = 250, r = 0.016, n = 12, t = 10.

Hence the interest earned by account 1 is:

\(I(10) = 250\left(1 + \frac{0.016}{12}\right)^{12 \times 10} - 250 = 43.35\)

For simple interest, the amount of interest earned is:

I(t) = Prt.

Hence:

I(10) = 250 x 0.016 x 10 = 40.

Hence the difference is:

43.35 - 40 = $3.35.

Which is closest to option D.

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Answer:

Slope = \(-\frac{1}{6}\)

Step-by-step explanation:

Slope = \(\frac{Rise}{Run}\)

Slope = \(\frac{6-10}{24-0}\)

Slope = \(-\frac{1}{6}\)

Answer:

-1/6

Step-by-step explanation:

Just use the formula Y2-Y1/X2-X1.

In this case if you substitute the coordinates of those numbers, then it would be 6-10/24-0 which is 24/-4 and if you simplify it, then you get the slope -1/6.

Answer:

day eight!!

Step-by-step explanation:

Josh --> starts with $40, saving $10

Sal --> starts with $160, spending $5

day one: josh: $50, sal: $155

day two: josh: $60, sal: $150

day three: josh: $70, sal: $145

day four: josh: $80, sal: $140

day five: josh: $90, sal: $135

day six: josh: $100, sal: $130

day seven: josh: $110, sal: $125

day eight: josh: $120, sal: $120

Answer:

120 Miles in 1 hour.

Step-by-step explanation:

Sorry if I'm wrong but, that's my calculation.

Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.

To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.

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The total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

1 mass of a paperclip = 8.0 × 10−4 mg

But there are 7.68 × 104 paperclips = x mg

cross multiply

x = 7.68 × 104 × 8.0 × 10−4 mg

Multiply through

x = 61. 44 × 10^ 4 -4

x = 61. 44 × 1

x = 6. 144 × 10^1 mg

Thus, the total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

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To find the probability that someone who tests negative for opium use does not use opium, we need to use Bayes' theorem.

Let's assume that the prevalence of opium use in the population is 5%. This means that out of 100 people, 5 people use opium.

Now, let's say that the test for opium use has a sensitivity of 95% and a specificity of 98%. This means that out of 100 people who use opium, 95 will test positive, and out of 100 people who do not use opium, 98 will test negative.

Using Bayes' theorem, we can calculate the probability that someone who tests negative for opium use does not use opium as follows:

P(Not using opium | Negative test) = P(Negative test | Not using opium) * P(Not using opium) / P(Negative test)

P(Negative test | Not using opium) = 0.98 (specificity)
P(Not using opium) = 0.95 (complement of the prevalence)
P(Negative test) = P(Negative test | Not using opium) * P(Not using opium) + P(Negative test | Using opium) * P(Using opium)
P(Negative test | Using opium) = 1 - 0.95 = 0.05 (false negative rate)
P(Using opium) = 0.05 (prevalence)

P(Negative test) = 0.98 * 0.95 + 0.05 * 0.05 = 0.0935

P(Not using opium | Negative test) = 0.98 * 0.95 / 0.0935 ≈ 0.994

Therefore, the probability that someone who tests negative for opium use does not use opium is approximately 0.994, or 0.994 in decimal format rounded to three decimal places.
In this case, we want to find the probability of not using opium, given that someone tests negative.

Let's define the events as follows:
- A: Person does not use opium
- B: Person tests negative for opium

We want to find P(A|B), which is the probability of event A occurring given that event B has occurred. Using the conditional probability formula:

P(A|B) = P(A ∩ B) / P(B)

Unfortunately, without specific data on the probabilities of A, B, and A ∩ B (not using opium and testing negative), we cannot provide a numeric answer. However, if you have this information, you can simply plug the values into the formula and divide P(A ∩ B) by P(B) to obtain the probability in decimal format. Finally, round the result to three decimal places.

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Answer:

Step-by-step explanation:

Using the ratio and Isla's counters' number, find the total number of counters.

Let the multiplier be x, then the ratio is 6x : 5x : 7x, where Isla's number is 6x, which is 12.

Total number of counters is:

Find the multiplier using initial ratios:

Find the initial number of counters Isla had:

Answer:

Peyton's reasoning is incorrect because the sum of two opposites always equal 0.

Step-by-step explanation:

Ex.

-1+1=0   -1 and 1 are opposites

-2+2=0    -2 and 2 are opposites

The given number \(\frac{16}{11}\) is an improper fraction.

Proper fraction = A fraction with a smaller numerator than denominator is said to be a correct fraction. A fraction whose numerator is the same as or bigger than its denominator is said to be inappropriate. Proper fractions include 3/4, 2/11, and 7/19.

Improper fraction = A fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc.

When we divide 16 by 11 we get a quotient of 1 and a remainder of 5.

This fraction after solving can be represented as \(11\frac{1}{6}\) which is a mixed fraction.

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