A circle has a diameter with endpoints (-8,2) and (-2,6). What is the equation of the circle?

Answer:

a. 0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.

b. 0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 106 mg/100 ml and standard deviation 8 mg/100 ml

This means that [tex]\mu = 106, \sigma = 8[/tex]

a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml.

This is the p-value of Z when X = 120. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{120 - 106}{8}[/tex]

[tex]Z = 1.75[/tex]

[tex]Z = 1.75[/tex] has a p-value of 0.9599

0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.

b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?

The proportion is the p-value of Z when X = 120 subtracted by the p-value of Z when X = 90. So

X = 120

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{120 - 106}{8}[/tex]

[tex]Z = 1.75[/tex]

[tex]Z = 1.75[/tex] has a p-value of 0.9599

X = 90

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{120 - 106}{8}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

0.9599 - 0.0228 = 0.9371

0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.

Answer:

x = 90

Step-by-step explanation:

If lines A and B were parallel , then

∠ 1 and ∠ 4 are corresponding angles and congruent, so

3x - 160 = x + 20 ( subtract x from both sides )

2x - 160 = 20 ( add 160 to both sides )

2x = 180 ( divide both sides by 2 )

x = 90

Answer:

height ≈ 30 ft

Step-by-step explanation:

The situation is modelled by a right triangle.

let h be the height of the totem pole, then

tan50.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{25}[/tex] ( multiply both sides by 25 )

25 × tan50.1° = h , then

h ≈ 30 ft ( to the nearest foot )

To sketch the graph we have to solve the function with each value of x to get the coordinates.

f(x) = x² − 4x − 5

−2 ≤ x ≤ 6

This inequality represents the domain for x. Therefore x is greater than equal to -2 but less than equal to 6.

The range of x is as follows:

x = -2, -1, 0, 1, 2, 3, 4, 5, 6

We already have the values for x therefore, we must substitute the values of x into the function f(x) = x² − 4x − 5 to find the y values.

Solutions:

For x = -2

f(x) = x² − 4x − 5

= -2² − 4(-2) - 5

= 4 + 8 - 5

= 7

Point = (-2,7)

For x = -1

f(x) = x² − 4x − 5

= -1² - 4(-1) - 5

= 1 + 4 - 5

= 0

Point = (-1,0)

For x = 0

f(x) = x² − 4x − 5

= 0² - 4(0) - 5

= 0 - 0 - 5

= -5

Point = (0,-5)

For x = 1

f(x) = x² − 4x − 5

= 1² - 4(1) - 5

= 1 - 4 - 5

= -8

Point = (1,-8)

For x = 2

f(x) = x² − 4x − 5

= 2² - 4(2) - 5

= 4 - 8 - 5

= -9

Point = (2,-9)

For = 3

f(x) = x² − 4x − 5

= 3² - 4(3) - 5

= 9 - 12 - 5

= -8

Point = (3,-8)

For x = 4

f(x) = x² − 4x − 5

= 4² - 4(4) - 5

= 16 - 16 - 5

= -5

Point = (4,-5)

For x = 5

f(x) = x² − 4x − 5

= 5² - 4(5) - 5

= 25 - 20 - 5

= 0

Point = (5,0)

For x = 6

f(x) = x² − 4x − 5

= 6² - 4(6) - 5

= 36 - 24 - 5

= 7

Point = (6,7)

Coordinates for graph = (-2,7) , (-1,0) , (0,-5) , (1,-8) , (2,-9) ,  (3,-8) ,  (4,-5) , (5,0) ,  (6,7)

These are the points to sketch the quadratic graph.

Answer:

12.5% increase

Step-by-step explanation:

To find the percentage increase ( students joined)

Take the new number minus the original amount

There are 27 students in the class after 3 joined

27 - 24 = 3

Divide by the original amount

3/24 = 1/8 = .125 = 12.5%

Answer:

12.5%

Step-by-step explanation:

Intial number = 27

Final number = 24 + 3 = 27

Percentage change :-

Answer:

Step-by-step explanation:

[tex]C =2\pi r[/tex] and since we have to state the answer to 2 decimal places, that means that we are using the number value for π. In specific, π = 3.1415 is good enough. The other thing we note is that the formula for circumference could also be written in terms of its diameter as opposed to its radius:

C = πd. Let's use that one since we are given the diameter of the tire, not the radius.

C = (3.1415)(.65) so

C = 2.04 m

The circumference of the wheel  is C = 2.04 m.

Given ,

          d = 0.65 m

          π = 3.14

Let's use that one since we are given the diameter of the tire, not the radius.

Use this formula ,     C = πd

                         C = (3.1415)(.65)

                       so, C = 2.04 m

Therefore, the circumference of the wheel  is C = 2.04 m.

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Answer:

I believe that it is the first one.

Step-by-step explanation:

Answer:

(-1,2)

Step-by-step explanation:

hope you find this useful!

https://ncalculators.com/geometry/mid-points-calculator.htm

Answer:

The two INTEGERS are :-

-3 and +4

-3 * (+4) gives us -12

-3 + (+4) gives us 1

hope it helps

have a nice day

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3.

Answer:

1,152

Step-by-step explanation:

So here, we shall be removing random numbers

For ease, since the number is divisible by 45: it is advisable to end the selected number with zero

So we have it that;

we are crossing the first 4, 9 and 7

So, we are left with;

51,840

dividing this by 45 will give 1,152

Answer:

The dependent variable is the amount of money he received for birthday.

Step-by-step explanation:

After his birthday, Benjamin has decided to donate a third of the money he received as a gift from his relatives to a foundation. Considering the variables amount of money received by Benjamin and amount of money that Benjamin will donate. to. What is the dependent variable in this situation.

Here, the money he received for the birthday is x.

So, he donated x/3.

The variable is the money which he gets, so the dependent variable is amount of money he received for the birthday.

Answer:  [tex]6\sqrt{5}[/tex]  miles

This is the same as writing 6*sqrt(5) miles

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

Work Shown:

P = park

C = city hall

Point P is at the location (10,11)

Point C is at the location (7,5)

Apply the distance formula to find the length of segment PC

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\[/tex]

The exact distance between the park (P) and city hall (C) is [tex]3\sqrt{5}[/tex] miles.

This doubles to [tex]2*3\sqrt{5} = 6\sqrt{5}[/tex] miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.

Extra info:

[tex]6\sqrt{5} \approx 13.41641[/tex] so the runner travels a total distance of roughly 13.4 miles.

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Region\ A = 81218576[/tex]

Required

The acres owned by the government

The question is incomplete as the proportion (p) owned by the government is not given.

However, the formula to use is as follows:

[tex]Govt = p * Region\ A[/tex]

Assume the proportion is 28%, the equation becomes

[tex]Govt = 28\% * 81218576[/tex]

[tex]Govt = 22741201.28[/tex]

The acres owned by the government will be 22741201.28

Answer:

P is maximum at I = 2

Step-by-step explanation:

Here is the complete question

The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 100I/(I² + I + 4) where I is the light intensity (measured in thousands of foot candles). For what light intensity P is a maximum?

To find the value of I at which P is maximum, we differentiate P with respect to I and equate it to zero.

So, dP/dI =  d[100I/(I² + I + 4)]/dI

= [(I² + I + 4)d(100I)/dI - 100Id(I² + I + 4)/dI]/(I² + I + 4)²

= [(I² + I + 4)100 - 100I(2I + 1)]/(I² + I + 4)²

= [100I² + 100I + 400 - 200I² - 100I]/(I² + I + 4)²

= [-100I² + 400]/(I² + I + 4)²

=  -100[I² - 4]/(I² + I + 4)²

Since dP/dI = 0,  -100[I² - 4]/(I² + I + 4)² = 0 ⇒ I² - 4 = 0 ⇒ I² = 4 ⇒ I = ±√4

I = ±2

Since I cannot be negative, we ignore the minus sign

To determine if this is a maximum point, we differentiate dP/dI. So,

d(dP/dI)/dI = d²P/dI² = d[-100[I² - 4]/(I² + I + 4)²]/dI

= [(I² + I + 4)²d(-100[I² - 4])/dI - (-100[I² - 4])d(I² + I + 4)²/dt]/[(I² + I + 4)²]²

= [(I² + I + 4)²(-200I) + 100[I² - 4]) × (2I + 1) × 2(I² + I + 4)]/(I² + I + 4)⁴

= [-200I(I² + I + 4)² + 200[I² - 4])(2I + 1)(I² + I + 4)]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I(I² + I + 4) - [I² - 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + I² + 4I - I² + 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + 4I + 8])(2I + 1)]]/(I² + I + 4)⁴

Substituting I = 2 into d²P/dI², we have

= [-200(2² + 2 + 4)[2³ + 4(2) + 8])(2(2) + 1)]]/(2² + 2 + 4)⁴

= [-200(4 + 2 + 4)[8 + 8 + 8])(4 + 1)]]/(4 + 2 + 4)⁴

= [-200(10)[24](5)]]/(10)⁴

= -240000/10⁴

= -24

Since d²P/dI² = -24 < 0 at I = 2,  this shows that it I = 2 is a maximum point.

So, P is maximum at I = 2

Answer:

Sales tax: 402.80 Final cost: 5,702.80

Step-by-step explanation:

Sales price x sales tax rate = sales tax

5300 x .076 (7.6%) = 402.80

Sales price + tax = final cost

5300 + 402.80 = 5702.80

Answer:

using the pythagoras theorem

Step-by-step explanation:

[tex] \sqrt{4 {}^{2} - ( \sqrt{7}) {}^{2} } = 3[/tex]

A.88.2m

Answer:

Solution given:

initial velocity[u]=29.4m/s

g=9.8m/s²

maximum range=?

now

we have

[tex]\theta=90°[/tex]

maximum range =[tex]\frac{29.4²*sin90}{9.8}=88.2m[/tex]

The initial velocity is,

→ u = 29.4 m/s

General assumption,

→ g = 9.8m/s²

→ θ = 90°

Then the maximum range is,

→ (29.4² × sin90)/9.8

→ 88.2 m

Hence, option (A) is answer.

Answer:

26.31

Step-by-step explanation:

Use distance formula

d = [tex]\sqrt{(x_{2}-x_{1)^{2} + (y_{2}-y_ ^{1)^2} } }[/tex]

substitute in points and solve

d =  [tex]\sqrt{(7-3)^2 + (23-(-3))^{2} }[/tex]

d = [tex]\sqrt{4^{2}+26^{2} }[/tex]

d = [tex]\sqrt{16 + 676}[/tex]

d = [tex]\sqrt{692}[/tex]

d = 26.30589288

d = 26.31 rounded

9514 1404 393

Explanation:

The problem statement tells you the meaning of t. It is minutes after Riko leaves. 0 ≤ t < 52.5 is the answer to the question regarding the interval Riko is behind Yuto. It means Riko is behind Yuto for 52.5 minutes after she leaves their house.

t will not be negative because time moves forward. Here, we're only counting time after Riko leaves the house. A negative value for t would refer to a time before Riko leaves the house, which is irrelevant in this problem.*

_____

* One might argue that Riko is behind Yuto for all values of time after Yuto leaves the house, which would be for -21 < t < 52.5. The concept of "behind Yuto" has no meaning except in that interval.

Answer:

again again again hello or merhaba(hello)

speed = path / time

so we can say this;

speed × time = path

note;

two speeds in different directions add up

and

two speeds in the same direction subtract

our speeds are in the same direction so we subtract

0.35 - 0.25 = 0.10 speed

and our path is 5.25 miles because there are 5.25 miles between Yuto and Rico

when will they be in the same place now?

speed × time = path

0.10 × time = 5.25 miles

in this equation we find the time 52.5 minutes

After 52.5 minutes they will be in the same place but before 52.5 minutes Riko will be behind Yuto

0≤ t ≤ 52,5 ( this is our equation of time)

because time cannot take a negative value, as soon as they start moving, time passes and this cannot take a negative value

GOOD LUCK :D

Step-by-step explanation:

greetings from Turkey (≧▽≦)

Answer:

21 + x < 28

Step-by-step explanation:

27 is in fact greater than 28 if you where to input 6 into the x spot, this is the only one that's a true expression.

Answer:

[tex]q=8.5[/tex]

Step-by-step explanation:

The ratio of the side lengths (AB) and (BC) is given. One is also given an expression for the side lengths of each of these sides. Set up a proportion to describe this scenario, then solve using cross products;

[tex]\frac{AB}{BC}=\frac{3}{4}[/tex]

Substitute,

[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]

Cross products,

[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]

[tex](60)(4)=(10q+15)(3)\\\\240=30q+45[/tex]

Inverse operations,

[tex]240=30q+45\\\\195=30q\\\\8.5=q[/tex]

Answer:

It is d

Step-by-step explanation:

[tex]11. \: we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{7 + 11 + 13 + 6 + 8 + x}{6} = 8 \\ = > \frac{45 + x}{6} = 8 \\ = > 45 + x = 8 \: \times 6 \\ = > 45 + x = 48 \\ = > x = 48 - 45 \\ = > x = 2 \\ \\ 12. we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{2 + 5 + 1.3 + 2.2 + x}{5} = 1.8 \\ = > \frac{10.5 + x}{5} = 1.8 \\ = > 10.5 + x = 5 \times 1.8 \\ = > 10.5 + x = 9 \\ = > x = 9 - 10.5 \\ = > x = - 1.5 \\ [/tex][/tex]

This is the answer.

Hope it helps!!

Answer:

Step-by-step explanation:

[tex]\frac{2}{3} * 5 = \frac{2}{3}\frac{3}{2} x \\[/tex]

x = 10/3

Answer: the answer is D. I took the test & got it right

Step-by-step explanation:

The expression is equivalent to 3/2 will be;

⇒ 3y/(2y - 6) + 9/(6 - 2y)

Option D is true.

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

Equivalent expression is 3/2.

Now,

Let the expression is;

⇒ 3y/(2y - 6) + 9/(6 - 2y)

Solve the expression as;

⇒ 3y/(2y - 6) - 9/(2y - 6)

⇒ (3y - 9) / (2y - 6)

⇒ 3 (y - 3) / 2 (y - 3)

⇒ 3/2

So, The expression is equivalent to 3/2 will be;

⇒ 3y/(2y - 6) + 9/(6 - 2y)

Option D is true.

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Answer:

A. Energy (weight)

Step-by-step explanation:

Mark me as brainiest

Answer:

h(x) = 3^(x + 1)

Step-by-step explanation:

The exponential function is;

g(x) = 3^(x)

Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;

g(x) = c•b^(x)

In this question, we are told it is stretched by a factor of 3 along the y-axis.

Thus, new function h is;

h(x) = 3 × 3^(x)

Using law of indices, we have;

h(x) = 3^(x + 1)

Answer:

36,000

Step-by-step explanation:

Rounding Significant Figures Rules

Rounding Rules

When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.

Example: 356 rounded to 2 significant digits is 360

This calculator rounds down if the next digit is less than 5 and rounds up when the next digit is greater than or equal to 5.

In the table below 305.459 is rounded from 0 to 6 significant figures. For comparison the same number is rounded from 0 to 6 decimal places. You can see the difference between rounding for significant figures and rounding to decimal places.