What is the area of a circle with a radius of 6 inches?

9 pi in^2
12 pi in^2
36 pi in^2
81 pi in^ 2

An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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Answer:

a

Step-by-step explanation:

The possible trigonometric function is option (C) \(sec \theta = \frac{3}{\sqrt{5} }\) and \(tan \theta = \frac{-2}{\sqrt{5} }\) is the correct answer.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The trigonometric function, sin θ = -2/3

We know that \(sin \theta = \frac{opposite}{hypotenuse}\)

So, opposite = -2, hypotenuse = 3

The other side of the right triangle adjacent side can be found by using the Pythagoras theorem,

\(adjacent=\sqrt{hypotenuse^{2} -opposite^{2} }\)

⇒ \(adjacent=\sqrt{3^{2} -(-2)^{2} }\)

⇒ \(adjacent=\sqrt{9-4 }\)

⇒ \(adjacent=\sqrt{5}\)

Now, \(cos \theta = \frac{adjacent}{hypotenuse}\) and \(tan \theta = \frac{opposite}{adjacent}\)

Then, \(cos \theta = \frac{\sqrt{5} }{3}\)

\(sec \theta = \frac{1}{cos \theta}\)

⇒ \(sec \theta = \frac{1}{\frac{\sqrt{5} }{3} }\)

⇒ \(sec \theta = \frac{3}{\sqrt{5} }\)

\(tan \theta = \frac{-2}{\sqrt{5} }\)

Hence we can conclude that the possible trigonometric function is option (C) \(sec \theta = \frac{3}{\sqrt{5} }\) and \(tan \theta = \frac{-2}{\sqrt{5} }\) is the correct answer.

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Answer:

if you convert inches to cm...

Step-by-step explanation:

9inch=22.86cm

12inch=30.48cm

V=TTr²h

TT= 3.14

V= 3.14×22.86²×30.48

V= 50014.6cm³

if you don't convert inches to cm...

V=TTr²h

V=3.14 ×9×12

V=339.12cm³

1064 x

19

________

20216 legos

Sharon has 20216 legos

Answer:

D for sure

Step-by-step explanation:

i dont know if you have time for this so i explain it in the comments if you need it

Answer:

the answer is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

b0 = 5.83

b1 = 52.23

Step-by-step explanation:

Given the data:

X:

2

4

5

6

Y

70

65

78

95

General form of a linear regression equation :

y = b1x + b0

b1 = slope ; b0 = intercept

Using an online regression calculator, the regression equation obtained is :

y = 5.8286 + 52.2286x

Comparing the equation ;

b1 = 52.23

b0 = 5.83

The point that is on the graph of the function \(F(x) = 5^x\) is given by:

D. (1,5).

The function is defined by:

\(F(x) = 5^x\)

When x = 0, \(F(x) = 5^0 = 1\), hence point (0,1) is on the graph of the function.

When x = 1, \(F(x) = 5^1 = 5\), hence point (1,5) is on the graph of the function, which means that option D is correct.

When x = 5, \(F(x) = 5^5 = 3125\), hence point (5,3125) is on the graph of the function.

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Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

Answer:

The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = \(\sqrt{13}\) , -  \(\sqrt{13}\) , x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i .

Given equations ,

\(x^{2}\) + 81 = 0  ,\(x^{2}\)-22 = -26 , 3\(x^{2}\)-18=21 ,2\(x^{2}\) +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a\(x^{2}\)+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

\(x^{2}\) +81 = 0

\(x^{2}\) = -81

x = 9i , -9i

\(x^{2}\) - 22 = -26

\(x^{2}\) = -26 + 22

\(x^{2}\) = -4

x = 2i,-2i

3\(x^{2}\) - 18 = 21

3\(x^{2}\) = 18+21

3\(x^{2}\) = 39

\(x^{2}\) = 13

x = \(\sqrt{13}\) , -  \(\sqrt{13}\)

2\(x^{2}\) +15 = -13

2\(x^{2}\)  = -13-15

2\(x^{2}\)  = -28

\(x^{2}\)  = -14

x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = \(\sqrt{13}\) , -  \(\sqrt{13}\) , x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i .

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Answer:

The dinner date

Step-by-step explanation:

Answer:

x= -3

Step-by-step explanation:

i hope its right

The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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259.25π in² is the surface area of the cone

The surface area of a cone can be calculated using the formula SA = πr² + πrl

where r is the radius and l is the slant height.

Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.

The slant height (l) is given as 22 inches.

Substituting these values into the formula:

Surface Area = π(8.5)² + π(8.5)(22)

= 72.25π + 187π

= 259.25π

Therefore, the surface area of the cone is 259.25π in²

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Answer: the teacher is 43

Step-by-step explanation: if you take 11 and multiply it by 15 you get 165 if you take 208 and divide it by 16 you get 13.

so basically you subtract 208 from 165 to get 43

Answer:

1st evening = 7 + 20 = 27 calls

2nd evening = 3 (20 ) = 60 call

3rd evening = 20 calls

Step-by-step explanation:

total calls for the last three evenings = 107 phone calls

2nd evening = 3x as many calls as the 3rd evening

1st evening = 7 more calls than the 3rd evening.

find:

how many calls did she receive each evening?

let T (total) = 107

let x = 3rd evening.

let 2nd = 3x

let 1st = (7 + x)

T = 1st + 2nd + 3rd

107 = (7 + x) + 3x + x

107 - 7 = 5x

100 = 5x

x = 100 / 5

x = 20

therefore,

1st evening = 7 + 20 = 27 calls

2nd evening = 3 (20 ) = 60 call

3rd evening = 20 calls

Answer:

1st  = 27 calls

2nd  = 60 call

3rd = 20 calls

Step-by-step explanation:

total calls = 107 phone calls

2nd  = 3x

1st = 7 + 3x

T (total) = 107

T = 1st + 2nd + 3rd

107 = (7 + x) + 3x + x

107 - 7 = 5x

100 = 5x

x = 100 / 5

x = 20

so,

1st = 7 + 20 = 27 calls

2nd  = 3 (20 ) = 60 call

3rd  = 20 calls

Answer:

The answer would be 536 cones.

Step-by-step explanation:

You have to subtract 164 from 700.

700-164=536.

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Answer:

(a) less than 1 year =0.751488

(b) more than 2 years but less than 4 years = 0.2458

(c) at least 5 years= 0.760331

Step-by-step explanation:

f(t) = 1 λ e−t/λ, [0, [infinity])

First we calculate the probability for an exponential random variable X with parameter λ

P (X= t) = ∫ 1 λ e−t/λ, dt

P (x=t) =  e−t/λ,

λ = 3.5

Now P (X< 1 ) = ∫ 1 λ e−t/λ, dt        [the limits are (-∞ to 1)]

                         = e−1/3.5= 0.751488

P ( 2<X< 4 ) =  ∫ 1 λ e−t/λ, dt         [ the limits are (2 to 4)]

                     =e−2/3.5- e−4/3.5

                  = e-0.57142-e-1.142857  

                  = 0.5647-0.31890

                  = 0.2458

P (at least 5)  = 1- P (x=5)

                   = 1-∫ 1 λ e−t/λ, dt           [ the limits are (∞ to 5)]

                     = 1- e−5/3.5

                     = 1 - e-1.4285

                     = 1-0.239

                        = 0.760331

Answer:

The point estimate for the true difference between the population means is 0.13.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

Step-by-step explanation:

To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.

This means that:

\(\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325\)

A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.

This means that:

\(\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753\)

Difference between the true mean ages for cars owned by students and faculty.

Distribution s - f. So

\(\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13\)

This is also the point estimate for the true difference between the population means.

\(s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912\)

90% confidence interval for the difference:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Now, find the margin of error M as such

\(M = zs = 1.645*0.2912 = 0.48\)

The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years

The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

Answer:

5

Step-by-step explanation:

The height of the largest triangle = √(9 * 25) = 3 * 5 = 15

y is the square root of (25^2 + 15^2)

y = √(625 + 225)

y = √850

y = √(2 * 5*5 * 17)

y = 5 * √34

5 goes in the box.

Answer:

222 [ft²].

Step-by-step explanation:

1. the required area can be calculated according to the formula:

A=0.5*b*c*sin(A);

2. after substitution of b=32; c=19 and sin(A)≈0.7313537:

A=0.5*32*19*0.7313537=222.3315248 [ft²].

Answer:

4-2 = 2

2x5+9 = 19

2^19 = 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 = 524288

Answer:

29

Step-by-step explanation:

Use PEMDAS

P- Parenthesis

E- Exponents

M- Multiply

D- Divide

A- Add

S- Subtract

(4-2)^2×5+9 first you do parenthesis which is (4-2)=2

(2)^2×5+9 next the exponents (2)^2=4

4×5+9 now the multiplication, 4×5=20

20+9 And now finish it off with the addition

So the answer ends up being 29.

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Answer:

3 whole but 3.4 as a decimal

Step-by-step explanation:

In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.

The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.

In general, the choice of significance level depends on the specific application and context of the statistical analysis.

The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.

The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.

A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.

A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.

For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.

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Answer: (2, 3)

Step-by-step explanation: This graph depicts a parabola. The vertex of a parabola is the point at the intersection of the parabola, and it is the line of symmetry. In other words, it is the point where the parabola crosses its axis of symmetry. Therefore, the ordered pair of (2, 3) represents the vertex of this graph.