in triangle abc, angle b is 120∘ . it contains bisectors aa1, bb1 and cc1. prove that the angle a1b1c1 is 90∘

correlation coefficient,r = 0.5497

Standard Error,[tex]SE_{r} = 0.1477[/tex]

Dopamine, also known as DA or 3,4-dihydroxyphenethylamine, is a neuromodulatory chemical with a variety of crucial functions in cells. It is an organic substance that belongs to the phenethylamine and catecholamine families. About 80% of the catecholamines in the brain are made up of dopamine. It is an amine produced by removing a carboxyl group from a molecule of L-DOPA, which is used as a precursor and is produced in the kidneys and brain. Plants and the majority of animals can produce dopamine as well. Dopamine performs the role of a neurotransmitter in the brain, which is a substance secreted by neurons (nerve cells) to communicate with other nerve cells. Although neurotransmitters are only produced in some parts of the brain, they have a systemic impact on numerous areas.

Let the random variable, X = % of dopamine receptors blocked and Y= subject's ratings of cocaine high.

The correlation coefficient, r

Given:

[tex]SS_{XY}[/tex] = 957.5

[tex]SS_{X}[/tex] = 8145.441

[tex]SS_{Y}[/tex]= 372.5

The correlation coefficient between the variables, X and Y is obtained using the following formula,

[tex]r=\frac{SS_{XY} }{\sqrt{SS_{X} \times SS_{Y} } }[/tex]

[tex]r=\frac{957.5 }{\sqrt{{8145.441} \times372.5 } } }[/tex]

r = 0.5497

The standard error for the estimate of the correlation coefficient is obtained using the following formula,

[tex]SE_{r} = \sqrt{\frac{1-r^{2} }{n-2} }[/tex]

From the scatterplot, the sample size, n = 34

[tex]SE_{r} = \sqrt{\frac{1-(0.5497)^{2} }{34-2} }[/tex]

[tex]SE_{r}=0.1477[/tex]

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The total number of times 7 can occur as the sum on rolling two cubes for 180 times is 30. It is gained by applying the knowledge of probability to the given problem.

What is probability?

Probability depicts the number of possibilities of how many times an event can occur. The probability of happening of an event invariably lies between 0 and 1. For a sure event, it is always 1. Its formula is given as P(E) = No. of favourable outcomes / Total no. of outcomes

Calculation of the total number of times 7 can appear as a sum on rolling two cubes for 180 times

Number of cubes rolled = 2

Total number of outcomes on rolling two cubes = 36

Total possibility of getting 7 as sum = 6

The probability of getting 7 as a sum on rolling two dice only once is given by P(E1)

P(E1) = 6 / 36

         = 1 / 6

She repeated the process 180 times  so the needed probability, P(E) is obtained by multiplying 180 by P(E1)

P(E) = 180 × (1 / 6)

P(E) = 30

Hence, the required probability of getting 7 as the sum is given by 30.

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[tex]\%( \alpha ) = \frac{cardinality( \alpha )}{cardinality( \omega) } \times 100 \\ [/tex]

[tex]\%(pennies) = \frac{12}{60} \times 100[/tex]

[tex]\%(pennies) = \frac{1}{5} \times 100 = \frac{100}{5} = 20 \% \\ [/tex]

Answer:

20%

Step-by-step explanation:

are the three items that need to be addressed in the coding quality plan that will help achieve the KPI of 98 accuracy.

KPI:

KPI = Key Performance Indicator

A performance indicator or key performance indicator is a type of performance measurement. It basically evaluate the success of an organization or of a particular activity in which it engages.

Given,

Here we need to find the 3 items that need to be addressed in the coding quality plan that will help achieve the KPI of 98 accuracy.

The following are the 3 major pillars that are helps to achieve the KPI of 98 accuracy.

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Answer: Enlargement with a scale factor 4

Step-by-step explanation:

      Since shape B is four times as long as shape A, this is an enlargement with a scale factor of 4.

      What is scale factor?

Scale factor is a ratio between the original and transformed objects. Here, it is 4.

The equation: [tex]\frac{x^{2}}{6^{2}}={y^{2}+z^{2}[/tex],  represents a circle with radius r = y = x/6, and the surface that results is a cone, as obtained with the help of surface of revolution.

Now,

If we consider the point (6y, y, 0) in the xy plane, it appears to be a circular path that is a cone when the curve is rotated about the x axis. The cone's equation takes the following form:

[tex]\frac{x^{2}}{c^{2}}=\frac{y^{2}}{a^{2}}+\frac{z^{2}}{b^{2}}[/tex]

Given that x = 6y, we square x = 6y to give the equation the form shown above, which results in:

x² = (6y)²

x² = 36y²

Circular paths go parallel to the y-axis, hence the equation should be circular in nature. 36z² needs to be added, so:

x² = 36y² + 36z²

=> [tex]\frac{x^{2}}{6^{2}}={y^{2}+z^{2}[/tex]

Hence, This equation represents a circle with radius r = y = x/6, and the surface that results is a cone, as obtained with the help of surface of revolution.

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The answer is -√125

Step-by-step explanation:

-√125 does not simplify to an integer as -√125 = -5√5

Answer:

Each person would get 80% of a bag

Answer: look at the screenshot

Answer: $22

Step-by-step explanation:

47- 25= 22

Answer:

3/25

Step-by-step explanation:

0.12 multiplied by 100 equals 12

which means 12/100 is 0.12

now simplify

6/50

3/25

Answer:

Hi, it's 8^9

Step-by-step explanation:

[tex]8^5\cdot \:8^4\\8^5\cdot \:8^4=8^{5+4}\\8^{5+4}\\=8^9\\[/tex]

Answer:

An exponent is a power to a given number that will multiply the given number by itself the number of times the exponent's value represents. Exponents are represented by small, floating numbers that go after the given value in an equation.

Example A:

[tex]5^2 = 5 \times 5 = 25[/tex]

Example B:

[tex]x^4 + 8 = y[/tex]

Answer:

4725 Students

Step-by-step explanation:

First, multiply 4500 by 0.05 (which is 5% in decimal format.) You should get 225. Next, add 225 to the original value of 4500; you should get the answer, which is 4725 :)

Answer:

4725 Students

Step-by-step explanation:

To find the total enrollment of the community college this year, all we have to do is add the previous year's enrollment to 5% of the same value.

So...

Previous enrollment: 4500

5% of Previous enrollment = 0.05 * 4500 = 225

This year's enrollment = 4500 + 225 = 4725

So the final answer is 4725 students.

Answer:

y=3x-8

Step-by-step explanation:

Slope -intercept form is y=mx+b.

M represents the slope; b represents the y-intercept.

First, let's find the y-intercept.

It'll be found on the y-axis on the graph.

If you go down the y-axis, you'll see that -8 is the only point to be directly on the y-axis, so we can assume that that's the y-intercept.

Thus, the B in the equation is -8.

Now, let's find the slope.

You can think of it as rise over run. The rise is how many numbers the y-intercept either goes up or down until it can cross over to the x-axis. Crossing sideways is the run that's located on the x-axis.

You can begin from -8 and either count downward or upward.

For the sake of this graph, we'll go upward.

Do you see the dot on the coordinate (1,-5)?

Count upward and go to the side to get to that coordinate.

I count three upward and one to the right.

So as a fraction that would be 3 over 1 or 3/1.

But you can simplify that to just 3.

Thus, the M in the equation is 3.

Hence, y=3x-8.

Hope this helps.

Answer:

M is (-5,6)

N is (1,0)

P is (-4,2)

Step-by-step explanation:

We have to move all our coordinates in the same position and distance so we add and subtract the x and y values

M (-6,1) we add 1 to the x value and add 5 to the y value

M (-6+1,1+5)

So M prime is (-5,6 and we do that for the rest

Answer:

Here, I might have messed up one part , I think ;-;

Step-by-step explanation:

Answer:

I think it’s 6x^3 + 16x^2 - 4x

After simplify of this equation 2x (3x + 4) - (3x ² + 8x - 2). We get, the two factors which are +√(-2/3), -√(-2/3).

Given Equation:

2x (3x + 4) - (3x ² + 8x - 2)

2x (3x + 4) - 3x ² - 8x + 2

6x² + 8x - 3x ² - 8x + 2

3x ² + 2

To find the factors

3x ² + 2 = 0

x ² = -2/3

x = ±√(-2/3).

Therefore, the factors of given equation are +√(-2/3), -√(-2/3).

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Answer C :

[tex](5 {}^{ - 3} ) {}^{6} = 5 {}^{ - 3 \times 6} = 5 {}^{ - 18} = \frac{1}{5 {}^{18} } [/tex]

Answer:

C is correct.

Step-by-step explanation:

(5^-3)^6

= 5 ^(-3*6)

= 5^-18

= 1 /5^18.

The value of the lesser integer is 5

From the information given, we have the following deductions;

The expression can be represented as;

8(x + 1) - x = 43

expand the bracket, we have;

8x + 8 - x = 43

collect like terms

8x - x = 43 - 8

Subtract like terms

7x = 35

Make 'x the subject of formula

Divide both sides by 7

7x /7 = 35/7

x = 5

The lesser integer is x = 5

Thus, the value of the lesser integer is 5

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Answer:

6 units

Step-by-step explanation:
To find out how far apart two points are on a graph, we must count the spaces that separate them along the x and y axis

Counting on the x-axis, Point A is 2 units to the left of Point B

On the y-axis, Point A is 4 units below Point B.

Add the two to get the total units

Answer:

The root of 27 would be 5.196

Step-by-step explanation:

Answer:

4x^2−5x+11

Step-by-step explanation:

combine like terms

Answer:

linear

Step-by-step explanation:

y is always 1 behind x

Answer:

62-4=58

April is 58 much warmer than December and 62 is the farthest from 0

Answer:

I Can only tell you the temperature part, sorry...

Step-by-step explanation:

Basically 62 is actually farther away, and essay writers stink

I'm a bumblebee who likes to eat KFC - Ash the Fox

We can conclude that 10 percentage of the students voted for yellow.

Total number of students = 738 + 82 = 820

As we can notice that total number is 820 and the number of students that voted for yellow is 82.

So, 82/820 = 10%

Therefore, we can conclude that 10 percentage of students voted for yellow.

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The temperature at an altitude of 11,000 feet will be 47.6°F

From the question, we are to calculate the temperature at an altitude of 11,000 feet

From the given information,

There is a 1.1°F drop in temperature for every thousand feet

and

The temperature on the ground is 59.7°F

Now,

We are to determine the temperature at an altitude of 11,000 feet

Since the temperature  drops by 1.1°F for every thousand feet,

Then,

At an altitude of 11,000 feet, the temperature would have dropped by 1.1°F 11000/1000 times

That is, the temperature would have dropped by that magnitude 11 times

Thus,

The temperature at an altitude of 11,000 feet = 59.7°F - 11×1.1°F

The temperature at an altitude of 11,000 feet = 59.7°F - 12.1°F

The temperature at an altitude of 11,000 feet = 47.6°F

Hence, the temperature at an altitude of 11,000 feet will be 47.6°F

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Answer:

The Answer is -3x+15

Answer:

Step-by-step explanation:

25= (3x+10)

25-10 =

15=3x

15/3= 3x/3

5=x

Answer:

x = -3

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

Answer:

(a)  3.5

(b)  x = 4

(c)  -¹/₂

(d)  -¹/₂

Step-by-step explanation:

f(1) is the value of y when x = 1.

To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line. Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.

Therefore, f(1) = 3.5.

To solve f(x) = 2, find the value of x when y = 2.

To find the value of x from a given value of y, find the position of y on the y-axis, then trace horizontally until you meet the line. Once you meet the line, trace vertically to the x-axis to find the corresponding value of x.

Therefore, the solution of f(x) = 2 is x = 4.

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  2 ≤ x ≤ 4

Therefore:

[tex]\implies \dfrac{f(4)-f(2)}{4-2}=\dfrac{2-3}{4-2}=-\dfrac{1}{2}[/tex]

The average rate of change between any interval of the given function will be the same as the graph is linear.  Therefore, the average rate of change from 0 to 8 is the same as the rate found in part (c):  -¹/₂.

Proof

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  0 ≤ x ≤ 8

Therefore:

[tex]\implies \dfrac{f(8)-f(0)}{8-0}=\dfrac{0-4}{8-0}=-\dfrac{4}{8}=-\dfrac{1}{2}[/tex]