five more than a half number is 6. find the number.

Answer:

Arc CB is equals to 160

Step-by-step explanation:

Add all of those numbers and subtracted by 360

Answer:

Step-by-step explanation:

Remark

Be very careful that you understand which arc you are asking for. Arc CB could be the arc made up of 53 + 79 + 68 = 200.

Somehow I get the idea that is not what you want. You want the arc that is not divided up so it is

Arc CB = 360 - Sum of the minor arcs

Arc CB = 360 --  200

Arc CB = 160

result is 31+i in where 31 is real part and i is complex part as given i= √-1 and i²= -1

In mathematics complex number is an element which has two parts one is called real part and the remaining is termed as imaginary part. An example is 41+6i

here, 41 is real part, 6i is imaginary part

A real number cannot be added or subtracted with an imaginary number, but a real number can be multiplied or divided with an imaginary number.

We are given, (2+3i) (5-7i)

    at first, we expand it by removing parenthesis

2x5-2x7i+3ix5-3ix7i

10-14i+15i-21i²

now like term is added

10+i+21   as we are given i²= -1

    31+i

hence, we get 31+i

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Answer:

y = 5/3x + 4

Step-by-step explanation:

First, you need to find the slope. Use the slope formula of (y^2-y^1) / (x^2 - x^1).

Plug the numbers in.

(4 - (-1)) / (0 - (-3))

5 / 3

Slope is 5/3

Now, you have an equation of y = 5/3x + b.

Since one of the points shows you what y equals when x=0, that is your y intercept.

A random sampling method could be used to find the percentage of students in your grade who eat five servings of fruit and vegetables each day.

This method involves selecting a random sample of students from the entire population of your grade and surveying them about their eating habits.

In other word, its involves randomly selecting a subset of students from the entire grade population and collecting data on their eating habits. By selecting students at random, the sample is more likely to be representative of the entire grade. This cam provide accurate insights into the percentage of students meeting the desired dietary recommendation.

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The curvature at the point (1, 1, 1) is: k = ||r'(1) x r''(1)|| / ||r'(1)||^3 = (2sqrt(58)) / (sqrt(14))^3 = 58 / 14sqrt(14) ≈ 3.18.

The curvature of a curve in three-dimensional space is given by the formula: k = ||r'(t) x r''(t)|| / ||r'(t)||^3

where r(t) is the position vector function of the curve, r'(t) and r''(t) are its first and second derivatives, and ||v|| denotes the magnitude of vector v.

In this case, we have: r(t) = (t, t^2, t^3)

r'(t) = (1, 2t, 3t^2)

r''(t) = (0, 2, 6t)

So, at the point (1, 1, 1), we have: r'(1) = (1, 2, 3), r''(1) = (0, 2, 6), ||r'(1)|| = sqrt(1^2 + 2^2 + 3^2) = sqrt(14)

r'(1) x r''(1) = (-12, 0, 2)

||r'(1) x r''(1)|| = sqrt(12^2 + 2^2) = 2sqrt(58)

Therefore, the curvature at the point (1, 1, 1) is: k = ||r'(1) x r''(1)|| / ||r'(1)||^3 = (2sqrt(58)) / (sqrt(14))^3 = 58 / 14sqrt(14) ≈ 3.18.

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Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

There are total 576 numbers.

What do you mean by factorial?

The product of all positive integers less than or equal to a given non-negative integer, n!, is known as the factorial of that number in mathematics. The product of the factorial of n! with the following smaller factorial also equals the factorial of n!:

n! = n × (n-1) × (n-2) × (n-3) ..........3 × 2 × 1

Total number of digits = 7

Digits = 1,2,3,4,5,6,7

Number of odd digit = 4

Number of even digit = 3

Consider the 4 odd digits as a single unit. Number of ways in which the odd digits can be arranged within the unit = 4!

Take the unit of four odd digits with 3 even digits. So, there are 4 units. Number of possible arrangements of these 4 units= 4!

So, total number of 7-digit numbers that can be made = Number of ways in which the off digits can be arranged within the unit x Number of possible arrangements of 4 units

= 4! × 4!

= 24 × 24

= 576

Therefore, there are total 576 numbers.

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On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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A 95% confidence interval for the population mean of the surgery durations for all heart valve patients is (4.022, 5.398). This contradicts the medical group's claim that the population mean is 5.42 hours. So,  medical group's claim cannot be rejected.

Sample size = 32

Point estimate for the population mean = 4.71

Population standard deviation = 1.92

Critical value (from the table of critical values provided) for 95% confidence interval = 1.96

Using the formula for a confidence interval for a population mean with known population standard deviation, we get

Confidence interval = (point estimate - margin of error, point estimate + margin of error)

Margin of error = critical value * (population standard deviation / sqrt(sample size))

= 1.96 * (1.92 / sqrt(32))

= 0.688

Therefore, the 95% confidence interval for the population mean of the surgery durations for all heart valve patients is

(4.71 - 0.688, 4.71 + 0.688) = (4.022, 5.398)

Since the claimed population mean of 5.42 hours falls within this confidence interval, we cannot reject the medical group's claim at the 95% confidence level based on this sample.

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--The given question is incomplete, the complete question is given

" A prominent medical group claims that the population mean of the surgery durations for all heart valve patients is 5.42 hours. You are a data analyst for a health insurance company and want to test that aim. To do so, you select a random sample of 32 heart valve surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all heart valve surgeries is 192 hours Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the surgery durations for all heart Valve patients. The state whether the confidence interval you construct contradicts the medical group's claim. (If necessary, consulta list of formulas. (w)

Click on "Take Sample to see the results from your random sample of 32 heart valve patients Sample standard deviation 1.43 Sample mean 4.71 Population standard deviation 1.92 Number of patients 32 Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 95% confidence interval (Choose the correct critical value from the table of critical values provided.) Critical value: 0.95 70.00 2.576 20.019-2326 20.025 1.960 70.050 1.645 "--

George's current age is 10.

Let's break down the information given:

1. Tim is twice as old as his brother George.

2. George is 6 years older than his sister Leah.

3. In 4 years, Tim will be three times older than Leah.

Let's assign variables to the unknown ages. Let's say George's current age is G.

According to the given information:

1. Tim's age is twice George's age, so Tim's current age is 2G.

2. George is 6 years older than Leah, so Leah's current age is G - 6.

3. In 4 years, Tim will be three times older than Leah, so we can set up the equation: 2G + 4 = 3(G - 6 + 4).

Simplifying the equation:

2G + 4 = 3(G - 2)

2G + 4 = 3G - 6

Subtracting 2G from both sides:

4 = G - 6

Adding 6 from both sides:

10 = G

Therefore, George's current age is 10.

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The statement which is true of the growth rate of the functions over the interval 0 ≤ x ≤ 1 is that: B. The exponential grows at the same rate as the quadratic.

The rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity.

Mathematically, the rate of change can be calculated by using this formula;

\(Rate = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Rate = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

From the given interval and graph (see attachment), the data point for the exponential function would be as follows:

Next, we would calculate the rate of change of the exponential function over the given interval:

Rate of change = (2 - 1)/(1 - 0)

Rate of change = 1/1

Rate of change = 1.

From the given interval and graph (see attachment), the data point for the quadratic function would be as follows:

Next, we would calculate the rate of change of the quadratic function over the given interval:

Rate of change = (1 - 0)/(1 - 0)

Rate of change = 1/1

Rate of change = 1.

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Answer:

207 cubic cm

Step-by-step explanation:

3x3^2x11/3 = 99

4/3x3x3^3 = 108

108+99=207

Answer:

Step-by-step explanation:

The rule is that opposite angles are supplementary. Therefore, angle A plus angle C = 180:

angle A + 43 = 180 and

angle A = 180 - 43 so

angle A = 137

Answer:

4.25+8=17/4+32/4=49/4 or 12.25

Answer:

B. obtuse triangle

Step-by-step explanation:

Obtuse triangles are triangles with one obtuse angle and two acute angles. Define obtuse angles as angles over 90 degrees and acute angles as angles less than 90 degrees.

In this triangle:

118 degrees - obtuse angle

19 degrees - acute angle

43 degrees - acute angle

Thus, this triangle is an obtuse triangle.

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

1. The value can be read from the graph. At 3 units to the right of the vertical axis, the line is 3 units above the horizontal axis. The independent variable has a value of 3 at that point.

__

2. The dependent variable has a value of -5 at the next grid line just below the bottom of the graph shown. The value of the independent variable is -1 at that point.

we have the following:

Therefore, the answer is (x + 27, x + 1)

Answer:

Step-by-step explanation:

In a parallelogram, the two opposite sides are parallel and equal

WR = 2 (6x - 7.7)

221 = 2( 6x - 7.7)

Answer:

(a) (7, -3)

(b) (-7, 3)

Step-by-step explanation:

Michael's opportunity cost of a sculpture is 2 paintings per sculpture.

According to the table, Michael can produce either 3 sculptures or 6 paintings in a day. Therefore, the opportunity cost of producing one sculpture for Michael is 2 paintings, as he could have produced 2 additional paintings instead of the sculpture.

Opportunity cost represents the trade-off between two options and helps decision makers understand the benefits and drawbacks of different choices. In this case, by choosing to produce a sculpture, Michael is forgoing the opportunity to produce 2 paintings.

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The solution is Option A.

The point B ( -8 , 1 ) reflected over y-axis is B' ( 8 , 1 )

What is Reflection?

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of the point (x, y) across the y-axis is (-x, y).

Given data ,

Let the point be B ( x₁ , y₁ ) = B ( -8 , 1 )

Now , when the point B is reflected , we get

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

So , B' ( x₂ , y₂ ) is the reflection of point B ( -8 , 1 ) over y axis

And , B' ( x₂ , y₂ ) = B' ( 8 , 1 )

Therefore the point B' is B' ( 8 , 1 )

Hence , The point B ( -8 , 1 ) reflected over y-axis is B' ( 8 , 1 )

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Answer:

Step-by-step explanation:

Let x be the number of pants and y be the number of shirts

x + y = 6

20x + 15y = 100

multiply the first equation by -20

-20x -20y = -120

20x + 15y = 100

subtract the equations

-5y = -20

y = 4

replace y in equation 1

x + 4 = 6

x = 2

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The slope of the function showing by table is,

⇒ m = - 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table represents a linear function.

Let Two points on the line are (- 2, 8) and (- 1, 2).

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 8) / (-1 - (-2))

m = - 6 / 1

m = - 6

Thus, The slope of the function showing by table is,

⇒ m = - 6

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Answer: The angle of depression would be 26.57°

Step-by-step explanation: Please refer to the attached picture for further details.

What harry has done has effectively led to the formation of a right angled triangle. As shown in the diagram, the camera has been mounted at a height of 8 feet above the ground. Also he mounts the camera at a horizontal from the entrance, which puts the camera at 16 feet away from the entrance (not from the ground). In order to capture every movement at the entrance, the camera range would be determined by an angle which covers everything from top to bottom of the entrance. That gives you the angle of depression which is at the point labelled CAMERA in the triangle.

Having determined two sides and an angle (unknown) in a right angled triangle, we shall use the trigonometric ratios as follows;

Tan ∅ = Opposite/Adjacent

Where the opposite is 8 (side facing the reference angle) and the adjacent is 16 (side that lies between the reference angle and the 90 degree angle)

Tan ∅ = 8/16

Tan ∅ = 0.5

By use of a calculator,

∅ = 26.5650

∅ ≈ 26.57

Therefore the angle of depression of the surveillance camera should be 26.57°

Answer:

y = –3 is the answer since the y-coordinate is –3 and y = lines are horizontal.

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The equation of the horizontal line through (-7,-3) is \(y = x - 3\).and this can be determined by using the two-point form of a line.

Given :

The line is horizontal and passes through (-7,-3).

The following steps can be used in order to determine the equation of a line that passes through (-7,-3):

Step 1 - According to the given data, the line is horizontal which means it is parallel to the x-axis.

Step 2 - So, the horizontal line also passes through (0,-3).

Step 3 - So, the equation of a line that passes through the points (-7,-3) and (0,-3) is:

\(\dfrac{y+3}{x-0}=\dfrac{-3+3}{-7-0}\)

Step 4 - Simplify the above expression.

\(y = x - 3\)

So, the equation of the horizontal line through (-7,-3) is \(y = x - 3\).

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Answer:

(x² - 3)(x² + 3)(\(x^{4}\) + 9)

Step-by-step explanation:

\(x^{8}\) - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

\(x^{8}\) - 81

= (\(x^{4}\) )² - 9²

= (\(x^{4}\) - 9)(\(x^{4}\) + 9) ← \(x^{4}\) - 9 is also a difference of squares

= (x² - 3)(x² + 3)(\(x^{4}\) + 9)

Answer:B

Step-by-step explanation:

(x2 − 3)(x2 + 3)(x4 + 9)