3n^2+4m+5
A. 2
B. 3
C. 4
D. 5

Step-by-step explanation:

The curve represented by this polar equation is a vertical line with angle  = /6 passing through the point (r, /6). To sketch this curve, simply draw a vertical line at an angle of /6 on the polar plane.

In conclusion, the curve with the given polar equation  = /6 is a vertical line passing through the point (r, /6).
To sketch the curve with the given polar equation  = -/6, follow these steps:
To sketch the curve with the given polar equation  = /6, we first need to understand what this equation represents. In polar coordinates, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis ().
1. Understand the polar equation: The equation  = -/6 tells us that the angle  is constant and equal to -/6 radians, or -30 degrees.

2. Convert to degrees (optional): By converting -/6 radians to degrees, we get -30 degrees.
In this equation,  is constant at /6, which means that all points on the curve have the same angle of /6. This creates a vertical line passing through the point (r, /6) on the polar plane.

3. Sketch the curve: Since  is constant at -30 degrees, the curve is a straight line (or ray) that extends from the origin (the pole) and makes an angle of -30 degrees with the positive x-axis.

4. Label the curve: label the curve with the given polar equation θ = -π/6.

In summary, the curve described by the polar equation  = -/6 is a straight line (or ray) extending from the origin and making an angle of -30 degrees with the positive x-axis.

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Answer:

correct / incorrect / incorrect

Step-by-step explanation:

5a - 8 + 2a² + 2a - 1 ← collect like terms

= 2a² + 7a - 9 ← correct

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

b² + 6b - 4 - (3b + b²) ← distribute parenthesis by - 1

= b² + 6b - 4 - 3b - b² ← collect like terms

= 3b - 4 ≠ 2b² + 3b - 4

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

9c - 4c² - (2c² + c) ← distribute parenthesis by - 1

= 9c - 4c² - 2c² - c ← collect like terms

= - 6c² + 8c ≠ - 6c² + 10c

Answer:

correct

incorrect

incorrect

Step-by-step explanation:

\(\begin{aligned}(5a-8)+(2a^2+2a-1)&=5a-8+2a^2+2a-1\\& = 2a^2+5a+2a-8-1\\ & = 2a^2+7a-9\end{aligned}\)

\(\implies (5a-8)+(2a^2+2a-1)=2a^2+7a-9\quad\textsf{is correct}\)

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

\(\begin{aligned}(b^2+6b-4)-(3b+b^2) &=b^2+6b-4-3b-b^2\\ & = b^2-b^2+6b-3b-4\\& = 3b-4\end{aligned}\)

\(\implies (b^2+6b-4)-(3b+b^2)=2b^2+3b-4\quad\textsf{is incorrect}\)

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

\(\begin{aligned}(9c-4c^2)-(2c^2+c) &=9c-4c^2-2c^2-c\\ & = -4c^2-2c^2+9c-c\\& = -6c^2+8c\end{aligned}\)

\(\implies (9c-4c^2)-(2c^2+c)=-6c^2+10c\quad\textsf{is incorrect}\)

Each part of the question is answered above and the angles are given below.

Given are the angles as mentioned in the question.

[1] -

Since, angle [1] and angle [4] are vertically opposite angles, we can write-

3x + 14 = 5x - 52

14 + 52 = 5x - 3x

2x = 66

x = 33

∠1 = 3x + 14 = 3 x 33 + 14 = 99 + 14 = 113°

∠1 = 113°

[2] -

Since, angle [A] and angle [B] are supplementary angles, we can write-

(3x + 8) + {(2/3)x + 62} = 180

3x + 8 + 62 + (2/3)x = 180

3x + (2/3)x = 110

x{3 + 2/3} = 110

x{(9 + 2)/3} = 110

(11/3)x = 110

x = (110 x 3)/11

x = 30

∠A = 3x + 8 = 3 x 30 + 8 = 98°

∠A = 98°

∠A = (2/3)x + 62 = 2/3 x 30 + 62 = 82°

∠B = 82°

[3] -

Since, angle [2] and angle [3] are  vertically opposite angles, we can write -

13x + 27 = 9x + 59

13x - 9x = 59 - 27

4x = 32

x = 8

∠2 = 13x + 27 = 13 x 8 + 27 = 104 + 27 = 131°

∠2 = 131°

∠3 = 9x + 59 = 9 x 8 + 59 = 72 + 59 = 131°

∠3 = 131°

Therefore, each part of the question is answered above and the angles are given above.

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Answer:

we will do it by Trigonometry

Step-by-step explanation:

sin45⁰=root2 over 2

x/8=root 2 over 2

x=4root 2

SOLUTION

To solve this, we get the Z for 81 and 89

We will use the formula

Z for 81, we have

Z for 89, we have

Using the Zscore calculator for probability between two Zscores, we have

Hence the answer is 0.68 to the nearest hundredth

Or 68.27% to the nearest hundredth

Fallacies of relevance are types of logical fallacies that occur when an argument is presented without a relevant connection to the subject matter.

Rather than addressing the topic, these fallacies are aimed at the listener's feelings, emotions, or biases.There are many different types of fallacies of relevance, but some of the most common are ad hominem, straw man, appeal to authority, and red herring. Ad hominem, for example, is a type of fallacy that attacks the speaker rather than addressing the argument they are presenting.. It can undermine the quality of your argument and make you seem less credible.

However, if you want to describe a time when you used these fallacies, you might think back to a situation where you were arguing with someone and felt like you were losing the argument. In this case, you might have resorted to a fallacy of relevance to try to regain control of the conversation. In conclusion, it is important to avoid using fallacies of relevance in your arguments. Instead, focus on addressing the topic at hand and presenting logical, evidence-based arguments.

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Answer:

8.. answer 31/8 = 3 7/8

9 ... answer : 189/15 = 12 9/12

10 answer : 43/12 = 3 7/12

Hope this will helpful for you and plz mark me as brainlist plzzzz

We can choose c₂ = 1, as 1 is a positive constant. For any x ∈ R, we have:

c₁ ||x||₁ ≤ ||x||₂ ≤ c₂ ||x||₁

This proves the equivalence of the norms ||·||₁ and ||·||₂ with respect to convergence.

To prove that all norms on R (the set of real numbers) are equivalent with respect to convergence, we need to show that any two norms on R, let's say ||·||₁ and ||·||₂, are equivalent.

To show equivalence, we need to demonstrate that there exist positive constants c₁ and c₂ such that for any real number x:

c₁ ||x||₁ ≤ ||x||₂ ≤ c₂ ||x||₁

Let's proceed with the proof:

Existence of c₁:

For any x ∈ R, since ||x||₁ and ||x||₂ are norms, they satisfy the properties of positivity and homogeneity. This implies that for any x ≠ 0, we have:

||x||₁ > 0

||x||₂ > 0

Therefore, we can choose c₁ = 1, as 1 is a positive constant.

Existence of c₂:

For any x ≠ 0, we have:

||x||₁ = ||x||₁ * 1 ≤ ||x||₁ * ||1||₂

= ||x||₁ * ||1||₂

= ||x * 1||₂

= ||x||₂

Hence, for any x ≠ 0, we have ||x||₁ ≤ ||x||₂.

Therefore, we can choose c₂ = 1, as 1 is a positive constant.

Thus, we have shown that for any x ∈ R, we have:

c₁ ||x||₁ ≤ ||x||₂ ≤ c₂ ||x||₁

This proves the equivalence of the norms ||·||₁ and ||·||₂ with respect to convergence.

In general, this proof can be extended to any norms on R, demonstrating that all norms on R are equivalent with respect to convergence.

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The chord of a circle is defined as the line segment connecting any two points on its circumference.

VU is not a radius it is a chord.

The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.

A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.

A radius is a segment with ends at the center and circumference of a circle. VU, on the other hand, is a chord because it has both endpoints on the circle.

Therefore, VU is not a radius it is a chord.

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Answer: do you still need help

Step-by-step explanation:

Answer:

a) 1/2

b) 7

Step-by-step explanation:

COS 60° = 1/2

COS 60° = 8 squared + 5 squared - b square = 1/2

2 x 8 x 5

a) 1/2

b) 7

The solution to the given inequalities will be x≤2 and x≤4.

The relation between two expressions that are not equal employs a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than. The greater than and less than sign is used to represent inequalities.

Given inequalities are x-0.8>0 and -5x<10. The inequalities will be solved as:-

(I) 2 - x ≤ 0

Take negative -x to the right.

x ≤ 2

(II) x -4 ≤ 0

Solve the inequality x - 4 ≤ 0.

x ≤ 4

Therefore, the solution to the given inequalities will be x≤2 and x≤4.

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In a nonexperimental method, relationships between variables are studied by making observations or measures of the variables of interest.

Research without either the manipulation of an independent variable, the random assignment of individuals to conditions or orders of conditions, or both, is referred to as non-experimental research.

The non-experimental study is entirely dependent on variables that the researcher has no control over. By whatever means, they cannot manipulate, control, or change the subjects. Thus, all they can do is continue their research while monitoring and interpreting their subjects.

It is safe to assume that a non-experimental research design is used when there is no specific cause-effect study problem and the researcher simply wants to grasp a topic in depth without constraining it with variables. They examine the natural phenomena as they take place.

Therefore, in a nonexperimental method, relationships between variables are studied by observing or measuring the variables of interest.

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The median and quartiles fall in the middle age classes.

The median is the middle value in a set of data, meaning that half of the data falls below the median and half falls above it. The quartiles divide the data into four equal parts, with the first quartile (Q1) being the 25th percentile, the second quartile (Q2) being the median or 50th percentile, and the third quartile (Q3) being the 75th percentile.

In terms of age classes, the median and quartiles would fall in the middle age classes. For example, if the age classes were 0-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, and 81-90, the median and quartiles would fall in the 21-30, 31-40, and 41-50 age classes.

It is important to note that the specific age classes that the median and quartiles fall in will depend on the distribution of the data. However, they will always fall in the middle age classes, as they represent the middle values of the data set.

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Answer:

Step-by-step explanation:

55*9%= 4.95 or 5.00

If you start at 10% you get 5.50. Go down a % to get the 4.95.

Answer:

answer is C

average speed=distance÷time=120÷4=30

Answer:

D

Step-by-step explanation:

Recall that the area of a rectangle is given by the formula:

\(A=\ell w\)

Where l is the the length and w is the width.

If we increase our length by 20%, this means that we add 20% or 0.2 of our old length to our old length. So, our new length will be:

\(\ell_{\text{new}}=\ell + 0.2\ell = 1.2\ell\)

Similarly, if we increase our width by 10%, this means that we add 10% or 0.1 of our old width to our old width. So, our new width is:

\(w_{\text{new}}=0.1w+w = 1.1w\)

Therefore, our new area will be:

\(A_{\text{new}}=(\ell_{\text{new}})\left(w_{\text{new}}\right)\)

By substituting:

\(A_{\text{new}}=\left(1.2\ell\right)\left(1.1w\right)\)

Multiply:

\(\displaystyle A_{\text{new}}=1.32\ell w\)

Recall that the old area is given by:

\(\displaystyle A_{\text{old}} = \ell w\)

So, our area increased by a factor of 1.32. In other words, our area increased by 0.32 or 32%.

Therefore, our answer is D.

Answer:

D) 32

Step-by-step explanation:

\(\textsf {The original equation would be :}\)

\(\implies \mathsf {area = length \times width}\)

\(\textsf {Now, length has been increased by 20 percent and} \\\textsf {width has been increased by 10 percent.}\)

\(\textsf {Hence, new length and width will be :}\)

\(\implies \textsf {new length = length + 0.2(length) = 1.2(length)}\)

\(\implies \textsf {new width = width + 0.1(width) = 1.1(width)}\)

\(\textsf {Now the new area will be :}\)

\(\implies \mathsf {area' = 1.2(length) \times 1.1(width)}\)

\(\implies \mathsf {area' = 1.32 \times length \times width}\)

\(\textsf {Now finding the percent change in area, 'a' :}\)

\(\implies \mathsf {a = \frac{1.32 \times length \times width - 1 \times length \times width}{1 \times length \times width}}\)

\(\implies \textsf {a = 0.32 = 32 percent}\)

The correct option is D) 32 .

The cartons hold 1305 blocks.

What are Comparing quantities?

- Finding an unknown quantity that has a relationship with a certain condition associated to it is the process of comparing quantities.

- One or more quantities with their units will be provided to us, and we will   be required to determine the value of the same quantity in other units (i.e.  in higher values or in lower values).

We given that,

A carton holds 87 blocks.

It means, 1 carton holds = 87 blocks

So find 15 cartons holds how much of blocks.

15 cartons holds = 15 * 87

                            = 1305 blocks

Hence, we can say that the cartons hold 1305 blocks.

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To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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Answer:

1/36

Step-by-step explanation:

1/6 * 1/6 = 1/36

The statements that must be true about the graph of the function include the following:

B. the function has two (2) asymptotes.

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

By critically observing the graph of this function, we can reasonably infer and logically deduce the following vertical and horizontal asymptotes;

Vertical asymptote is x = -2.

Horizontal asymptote is y = -3.

In conclusion, if x⁻ is equal to -2, then f(x) tends towards negative infinity.

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The statement that best describes the Central Limit Theorem is (a) The distribution of means of random samples pulled from a population will be normally distributed if the sample size is large enough.

The Central Limit Theorem (CLT) states that if repeated random samples is taken from a population with a finite mean and standard deviation, then the distribution of the sample means will approach a normal distribution, even if the original population is not normally distributed.

The larger the sample size, the more closely the sample means will approximate a normal distribution.

which means that, for example, if we take multiple samples of size 100 from a population and calculate the average of each sample, the distribution of those sample means will be approximately normally distributed, regardless of the original shape of the population.

The given question is incomplete , the complete question is

Which best describes what the Central Limit Theorem states ?

(a) The distribution of means of random samples pulled from a population will be normally distributed if the sample size is large enough.

(b) All distributions have the same mean.

(c) The distribution of standard deviations of random samples pulled from a population will be normally distributed if the sample size is large enough.

(d) All distributions are close enough to normally distributed to use the normal distribution as a approximation.

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A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high, the work done in pulling the rope to the top of the building is 1785 ft-lb.

To calculate the work done in pulling the rope to the top of the building, we need to use the formula:

W = F x d

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

In this problem, we can calculate the force required to pull the rope as the product of its weight per unit length (0.7 lb/ft) and the length of the rope (30 ft). Thus, the force required is:

F = 0.7 lb/ft x 30 ft = 21 lb

To calculate the distance over which the force is applied, we need to calculate the total length of the rope that needs to be lifted. This can be found using the Pythagorean theorem, as follows:

l = √(30^2 + 80^2) = 85 ft

So the distance over which the force is applied is 85 ft.

Now we can substitute the values for F and d into the formula for work to get:

W = F x d = 21 lb x 85 ft = 1785 ft-lb

This calculation shows how the formula for work can be used to calculate the energy required to lift an object against gravity over a given distance.

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These agencies use statistics to provide reliable and timely information that supports evidence-based decision-making, policy formulation, economic planning, and monitoring of global and national development goals.

1. United States Census Bureau: The U.S. Census Bureau is a federal agency responsible for collecting and analyzing demographic, social, and economic data about the United States. It conducts the decennial census, as well as numerous surveys and studies that provide statistical information for policy-making, research, and decision-making purposes.

2. National Center for Health Statistics (NCHS): NCHS is a division of the U.S. Centers for Disease Control and Prevention (CDC) that collects and disseminates vital health statistics for the country. It conducts surveys, gathers data from various sources, and produces reports on topics such as mortality, morbidity, birth rates, and health behaviors, which help inform public health policies and programs.

3. Eurostat: Eurostat is the statistical office of the European Union (EU), responsible for collecting and publishing statistical information on various aspects of the EU member countries and their economies. It provides data on areas such as population, economy, agriculture, environment, and social conditions, facilitating evidence-based decision-making and monitoring of EU policies.

4. Australian Bureau of Statistics (ABS): The ABS is Australia's national statistical agency, collecting, analyzing, and disseminating a wide range of statistical data on the country's population, economy, and society. It conducts regular surveys and censuses, providing insights into areas like labor market, population trends, housing, and social well-being, to support informed decision-making by government, businesses, and the public.

5. Statistics Canada: Statistics Canada is the national statistical agency of Canada, responsible for gathering and analyzing statistical data on various aspects of the country. It conducts surveys, censuses, and administrative data collection to produce information related to population, economy, agriculture, and social conditions. The data generated by Statistics Canada is used to inform government policies, business strategies, and research activities.

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Answer:

Circumference of S = T/4

I didn't quite catch your question though, could you elaborate a bit more?

Answer: 10.9, about 11 ft

Step-by-step explanation:

a^2 + b^2 = c^2

a^2 + (5)^2 = (12)^2

Answer:

The ladder is the hypotenuse and one side equals 5 feet.

From the Pythagorean Theorem we can calculate the other side:

other side^2 = 12^2 -5^2

other side^2 = 144 -25

other side^2 = 119

other side = 10.9087121146

Rounding, we get 11 feet.

Step-by-step explanation:

The radius of the table top, rounded to 1 dp is 5.6 cm

From the question,

We are to determine the radius of the table top

First, we will determine the volume of the cylindrical wooden table

From the given information

Density = 0.42 g/cm³

Mass = 0.25 kg = 250 g

Using the formula

\(Volume = \frac{Mass}{Density}\)

∴ \(Volume = \frac{250}{0.42}\)

Volume = 595.238 cm³

Now, for the radius of the table top

Using the formula for volume of a cylinder

\(V = \pi r^{2}h\)

Where V is the volume

r is the radius

and h is the height or depth

From the given information

h = 6cm

Putting the parameters into the formula

\(595.238 = \pi r^{2} \times 6\)

∴ \(r^{2} = \frac{595.238}{6\pi }\)

\(r^{2} =31.57835667\)

\(r =\sqrt{31.57835667}\)

r = 5.6 cm

Hence, the radius of the table top, rounded to 1 dp is 5.6 cm

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We can expect 10 rolls of 2 in the new experiment.

We have,

The total number of rolls.

Adding up all the frequency.

We get,

= 60 trials

Now,

The number of 2 rolls.

= 8

The percentage of 2 rolls.

= 8/60 x 100

= 13.33%

Now,

New experiment total rolls = 75 trials.

So,

The expected number of 2 rolls.

= 13.33/100 x 75

= 9.99

= 10

Thus,

We can expect 10 rolls of 2 in the new experiment.

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There can be 8 rolls of 2 in a new experiment with 75 trials.

In the given experiment, the frequency of rolling a 2 is 8 out of a total of 75 rolls.

So, the probability of rolling a 2 in one trial is 8/75.

To find the expected number of rolls of 2 in the new experiment with 75 trials, we multiply the probability by the number of trials:

Expected number of rolls of 2

= (8/75) x 75

= 8

Therefore, based on the experimental results, we would expect to get 8 rolls of 2 in a new experiment with 75 trials.

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