What is the equation of the line graphed below?

Answer:

Length of the arc LM = 15.7 cm

Step-by-step explanation:

To determine the length of the arc LM we have to find the circumference of the the big circle then divide by the ratio of the angle or go straight to use the radians as the angle and look for the length.

Radius= 30cm

π= 3.142

Value of the angle is in radians

360° = 2π

π = 180

π/6 = 180/6

π/6= 30

Value of the angle is 30°

Length of the arc = 2πr * 30/360

Length of the arc = 2πr/12

Length of the arc = πr/6

Length of the arc = 30π/6

Length of the arc =5π

Length of the arc = 5*3.142

Length of the arc = 15.71

Approximately Length of the arc

= 15.7cm

Answer:

B. 15.7cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

We khow that the volume of a prism the product of the base and the height

We have a hole inside it so we must khow what is the geometrical form of this whole to calculate its volum then substract from the total volume

Sample Answer:

I found the volume of the large rectangular prism. Then I found the volume of the small rectangular prism. I subtracted the volume of the smaller prism from the volume of the larger prism.

Answer:

The  UCL  is  [tex]UCL = 0.054[/tex]

The LCL  is  [tex]LCL \approx 0[/tex]

Step-by-step explanation:

From the question we are told that  

     The quantity of each sample is  n =  30

     The  average of defective products is  [tex]p = 0.025[/tex]

Now  the upper control limit [UCL] is  mathematically represented as

      [tex]UCL = p + 3 \sqrt{\frac{p(1-p)}{n} }[/tex]

substituting values  

      [tex]UCL = 0.025 + 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]

      [tex]UCL = 0.054[/tex]

The  upper control limit (LCL) is mathematically represented as

       [tex]LCL = p - 3 \sqrt{\frac{p(1-p)}{n} }[/tex]

substituting values  

      [tex]LCL = 0.025 - 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]

       [tex]LCL = -0.004[/tex]

        [tex]LCL \approx 0[/tex]

Answer:

Step-by-step explanation:

A, B and C must be real numbers, and A and B are not both zero (which would cause division by zero in the calculation of the slope).

Answer:

Presumably the first graph solely based on its shape.

Graph A is showing the exponential function. Then the correct option is A.

The mathematical expression f(x)= [tex]e^x[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data. In graph A we can see that the values are varying exponentially from the second quadrant to the first quadrant.

Hence, the correct option is A.

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Answer:

The probability that the weight of a randomly selected steer is between 920 and 1730 lbs

P(920≤ x≤1730) = 0.7078

Step-by-step explanation:

Step(i):-

Given mean of the Population = 1100 lbs

Standard deviation of the Population = 300 lbs

Let 'X' be the random variable in Normal distribution

Let x₁ = 920

[tex]Z = \frac{x-mean}{S.D} = \frac{920-1100}{300} = - 0.6[/tex]

Let x₂ = 1730

[tex]Z = \frac{x-mean}{S.D} = \frac{1730-1100}{300} = 2.1[/tex]

Step(ii)

The probability that the weight of a randomly selected steer is between 920 and 1730 lbs

P(x₁≤ x≤x₂) = P(Z₁≤ Z≤ Z₂)

                  = P(-0.6 ≤Z≤2.1)

                  = P(Z≤2.1) - P(Z≤-0.6)

                 = 0.5 + A(2.1) - (0.5 - A(-0.6)

                 =  A(2.1) +A(0.6)               (∵A(-0.6) = A(0.6)

                 =  0.4821 + 0.2257

                 = 0.7078

Conclusion:-

The probability that the weight of a randomly selected steer is between 920 and 1730 lbs

            P(920≤ x≤1730) = 0.7078

Answer:

0.7975

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diagonal of the parallelogram ABCD divides it into 2 equal triangles. Considering triangle ABC, it means that the area of the parallelogram would be

2 × area of triangle ABC

Writing the vertices of triangle ABC,

A(−1,3,3), B(0,5,7), C(1,2,6)

We would determine the length of each side of the triangle.

AB = √(0 - - 1)² + (5 - 3)² + (7 - 3)^2

AB = √(1 + 4 + 16) = √21

BC = √(1 - 0)² + (2 - 5)² + (6 - 7)²

BC = √(1 + 9 + 1) = √11

AC = √(1 - - 1)² + (2 - 3)² + (6 - 3)²)

AC = √(4 + 1 + 9) = √14

We would apply the heron's formula for determining the area of a triangle

Area = √s(s - a)(s - b)(s - c)

Where

s = (a + b + c)/2

a = AB, b = BC, c = AC

s = (√21 + √11 + √14)/2 = 5.82

s - a = 5.82 - √21 = 1.24

s - b = 5.82 - √11 = 2.5

s - c = 5.82 - √14 = 2.08

Area = √(5.82 × 1.24 × 2.5 × 2.08) = 6.126

Therefore, area of parallelogram ABCD is

6.126 × 2 = 12.252

Answer:

410 bagels

Step-by-step explanation:

If the weights of the moving averages are 0.6, 0.3, 0.1. We will determine the forecast for week 8 using week seven's sales with a 0.6 weight, week six's sales with a 0.3 weight, and week five's sales with a 0.1 weight:

[tex]S_8=0.6S_7+0.3S_6+0.1S_5\\S_8=0.6*400+0.3*430+0.1*410\\S_8=410\ bagels[/tex]

The forecast for week 8 is 410 bagels.

Answer:

6

Step-by-step explanation:

=> -x+4

Given that x = -2

=> -(-2)+4

=> 2+4

=> 6

Answer:

6

Step-by-step explanation:

You just have to input -2 into the statement and then solve

= -(-2) + 4

= 2+ 4

= 6

Answer:

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distribution with a mean of 1 crack per 100 ft.

So [tex]\mu = \frac{ft}{100}[/tex], in which ft is the length of the pavement.

What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement

500ft, so [tex]\mu = \frac{500}{100} = 5[/tex]

This is P(X = 8).

[tex]P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653[/tex]

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

Answer:

C. -3/2

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes.

We know that line m is perpendicular to line l.

Line l has a slope of 2/3. To find the slope of line m, find the negative reciprocal of 2/3.

Negative: switch the sign

2/3 --> -2/3

Reciprocal: switch the numerator (top number) and denominator (bottom number)

-2/3 --> -3/2

Line m has a slope of -3/2 and C is correct.

Answer:

C

Step-by-step explanation:

perpendicular lines have negative reciprocal slope

Answer:

180 fb*lb

45 ft*lb

Step-by-step explanation:

We have that the work is equal to:

W = F * d

but when the force is constant and in this case, it is changing.

 therefore it would be:

[tex]W = \int\limits^b_ a {F(x)} \, dx[/tex]

Where a = 0 and b = 30.

F (x) = 0.4 * x

Therefore, we replace and we would be left with:

[tex]W = \int\limits^b_a {0.4*x} \, dx[/tex]

We integrate and we have:

W = 0.4 / 2 * x ^ 2

W = 0.2 * (x ^ 2) from 0 to 30, we replace:

W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)

W = 180 ft * lb

Now in the second part it is the same, but the integral would be from 0 to 15.

we replace:

W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)

W = 45 ft * lb

Following are the calculation to the given value:

Given:

[tex]length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\[/tex]

To find:

work=?

Solution:

Using formula:

[tex]\to W=fd[/tex]

[tex]\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\[/tex]

[tex]= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180[/tex]

Therefore, the final answer is "[tex]180\ \frac{ lb}{ft}[/tex]".

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Answer:

C. -2

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply use 2 xy values and plug them into the formula:

m = (-4 - 0)/(5 - 3)

m = -4/2

m = -2

Answer:

-2

Step-by-step explanation:

Since we have two points we can use the slope formula

m = (y2-y1)/(x2-x1)

  = (10-6)/(-2-0)

  =4/-2

  -2

Answer:

There will be no transaction

Step-by-step explanation:

Given:

Displayed ask price = $20.05 for 100 shares

Displayed bid price = $20 for 150 shares

Explain:

If a limit order to buy = 50 shares for $20.02

Computation:

Displayed bid will be not accepted because, displayed bid price is for 150 shares not 100 shares

Limited order will be also not accepted.

So, there will be no transaction.

Answer:

Five

Step-by-step explanation:

Pivot columns are said to be columns where pivot exist and a pivot exist in the first nonzero entry of each row in a matrix that is in a shape resulting from a Gaussian elimination.

Suppose A = 5 × 7 matrix

So; if A columns span set of real numbers R⁵

The number of pivot columns that A must have must be present in each row. In a  5 × 7 matrix ; we have 5 rows and 7 columns . So , since A must be present in each row, then :

The matrix must have five pivot columns and we can infer that about  the statements that "A has a pivot position in every row"  and "the columns of A spans R⁵" are logically equivalent.

Answer:

(A)4 + 4 + 4 = 12

Step-by-step explanation:

Each of Nika's cake needed 17/4 cups of flour. Now, we know that:

[tex]\dfrac{17}{4}=4.25 \approx 4[/tex]

Therefore, for three loaves of bread, the best estimate of the number of cups of flour Nika used is:

4 + 4 + 4 = 12

The correct option is A.

Answer:

The correct answer is A.)4 + 4 + 4 = 12

Answer:(x+1)(x+2)(x-3)

Because..

Answer:

C. c = (xv - x) / (v - 1).

Step-by-step explanation:

v = (x + c) / (x - c)

(x - c) * v = x + c

vx - vc = x + c

-vc - c = x - vx

vc + c = -x + vx

c(v + 1) = -x + vx

c = (-x + vx) / (v + 1)

c = (-x + xv) / (v + 1)

c = (xv - x) / (v + 1)

So, the answer should be C. c = (xv - x) / (v + 1).

Hope this helps!

Answer:

a. A completely randomized design experiment

Step-by-step Explanation:

An experiment that is completely randomised is practically an effective way of controlling and reducing the influence of the confounding variables in a research study, especially when you have a sample that is large enough.

Randomisation will ensure that both the group that will wear the new shoe (treatment group) and the group that will not wear the new shoe (control group) will have averagely the same values for age and height. This will eliminate the chances of these confounding variables of correlating with the independent variable in the study, as there would be no difference, in terms of characteristics, between both groups.

Answer:

12/25

Step-by-step explanation:

Answer:

AD = 23

Step-by-step explanation:

Answer:

Required probability is 0.9748

Step-by-step explanation:

given data

mean [tex]\mu[/tex] = 117.7-cm

standard deviation [tex]\sigma[/tex] = 2.2-cm

sample size n = 29

solution

we consider here random variable which represents here length of rod= x

so get here first z that is express as

[tex]Z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]    

put here value with x value 118.5-cm

[tex]Z = \dfrac{118.5-117.7}{\dfrac{2.2}{\sqrt{29}}}[/tex]

Z = 1.9582

p value is 0.9748

so required probability is 0.9748

Answer:

The answer is

Step-by-step explanation:

f(x) = 2x² + 1

g(x) = 3x - 5

To find f - g(x) subtract g(x) from f(x)

That's

f-g(x) = 2x² + 1 - (3x - 5)

= 2x² + 1 - 3x + 5

= 2x² - 3x + 6

Hope this helps you

Answer:

Step-by-step explanation:

f(x)=-x+4

f(-2)=-(-2)+4

f(-2)=+2+4

f(-2)=6

Answer:

6

Step-by-step explanation:

-(-2)+4=___

+(+2)+4=6

Answer:

3

Step-by-step explanation:

f(x) = 4x^3 – 13x^2 + 9x + 2

This looks complicated but all we need to find are the Roots

We are looking for when y=0

So given each part of the information, we can label how many times it happens

The function starts from the bottom of quadrant 3: Starts lower left

and goes up through the x-axis at (0, negative 0.25) : This is ONE ROOT

and then through the y-axis at (0, 2). : It's now on the 2nd quartile

It then starts to curve down at (0.5, 4): It's moving towards y=0

until it reaches (1.75, negative 0.5).: It has now passed y=o and there are TWO ROOTS

It then curves up and crosses the x-axis at (2, 0) and goes up approaching x = 3: It has passed y=0 again, so there are THREE ROOTS

This polynomial function has 3 ROOTS

Answer:

The first for the graph is crosses and then it is touches for the second.

Step-by-step explanation:

Answer:

11.3 cm

Step-by-step explanation:

(see attached for reference)

using the Pythagorean theorem

hypotenuse ² = length ² + length ²

16² = L² + L²

16² = 2L²   (express 2 = (√2)²

16² = (√2)²L²  

16² = (√2L)²  

16 = √2L

L = 16 /√2

L = 11.3 cm

11.3

use Pythagoras theorem give each side is "a"

a^2+a^2=16^2

2*a^2=256

a^2=256/2=128

a=sqrt(128)=11.3 sqrt=square root

Answer:

Option I and II

Step-by-step explanation:

I. Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean.

II. Because they're robust, t procedures are justified in this case.

The t procedures are utilized because they are used as a hypothesis testing tool, which allows for testing of an hypothesis applicable to a population where in this case we are testing the null hypothesis about the population mean.

Answer:

So then our significance level is [tex]\alpha=0.05[/tex] and we need to remember these two conditions:

1) If the p value [tex]p_v <\alpha[/tex] we have enough evidence to reject the null hypothesis at the significance level given

2) If the p value [tex]p_v \geq \alpha[/tex] we have enough evidence to FAIL reject the null hypothesis at the significance level given

And baed on the options we see that the only possibility would be:

d. 0.015

Step-by-step explanation:

We want to know for which value we would REJECT the null hypothesis.

So then our significance level is [tex]\alpha=0.05[/tex] and we need to remember these two conditions:

1) If the p value [tex]p_v <\alpha[/tex] we have enough evidence to reject the null hypothesis at the significance level given

2) If the p value [tex]p_v \geq \alpha[/tex] we have enough evidence to FAIL reject the null hypothesis at the significance level given

And baed on the options we see that the only possibility would be:

d. 0.015