What is the circumference of the given circle in terms of [tex]\pi[/tex]?

a. 14[tex]\pi[/tex] in.
b. 28[tex]\pi[/tex] in.
c. 42[tex]\pi[/tex] in.
d. 196[tex]\pi[/tex] in.

Answer:

The rate at which the distance between the cars increasing two hours later=52mi/h

Step-by-step explanation:

Let

Speed of one car, x'=48 mi/h

Speed of other car, y'=20 mi/h

We have to find the rate at which the distance between the cars increasing two hours later.

After 2 hours,

Distance traveled by one car

[tex]x=48\times 2=96 mi[/tex]

Using the formula

[tex]Distance=Time\times speed[/tex]

Distance traveled by other car

[tex]y=20\times 2=40 mi[/tex]

Let z be the distance between two cars after 2 hours later

[tex]z=\sqrt{x^2+y^2}[/tex]

Substitute the values

[tex]z=\sqrt{(96)^2+(40)^2}[/tex]

z=104 mi

Now,

[tex]z^2=x^2+y^2[/tex]

Differentiate w.r.t t

[tex]2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}[/tex]

[tex]z\frac{dz}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}[/tex]

Substitute the values

[tex]104\frac{dz}{dt}=96\times 48+40\times 20[/tex]

[tex]\frac{dz}{dt}=\frac{96\times 48+40\times 20}{104}[/tex]

[tex]\frac{dz}{dt}=52mi/h[/tex]

Hence, the rate at which the distance between the cars increasing two hours later=52mi/h

Answer:

( x - 3.5)² - 29/4

Step-by-step explanation:

Given :-

Writing in ( x - a)² - b form ,

Answer:

8^2+12x

Step-by-step explanation:

4x(2x+3)

=4x times 2x+4x times 3

=4 times 2xx+4 times 3x

Answer:

8x^2 +12x

Step-by-step explanation:

Step 1) Multiply each term in the parentheses by 4x

4xx2x+4xx3

Step 2) Calcuate the product

8x^2 +12x

Answer:

95°Fahrenheit

hipe this helps you

Answer:

Here's your answer .

hope it helps you

Answer:

a) The probability that none of the lines experiences a surface finish problem in 41 hours of operation is 0.0498.

b)The probability that all three lines experience a surface finish problem between 24 and 41 hours of operation is 0.0346.

Step-by-step explanation:

[tex]Mean = \frac{1}{\lambda} = 41\\P(X\leq x)= 1-e^{-\lambda x}[/tex]

[tex]P(X>x)= e^{-\lambda x}[/tex]

a)

[tex]P(x> 41, y>41, Z>41) = (P(X>41))^{3}\\\\P(X>41)=e^{^{-\frac{41}{41}}}=e^{-1}[/tex]

[tex]P(x> 41, y>41, Z>41) = \left (e^{-1} \right )^{3}\\\\P(x> 41, y>41, Z>41) = e^{-3} = 0.0498.[/tex]

b)

[tex]\lambda =\frac{24}{41}\\P(X=1)=e^{-\lambda }\cdot \lambda =\left ( e^{-0.585} \right )\left ( 0.585 \right )\\P(X=1)=0.326[/tex]

For 3 where, P(X=1, Y==1, Z=1)

                     [tex]= (0.326)^{3} \\\\= 0.0346[/tex]

Answer:

13

Step-by-step explanation:

1. Round 19.625 up to 20.

2. Round 6.77 up to 7.

3. Calculate the equation. Ans is 13.

Step-by-step explanation:

2x+60°= 110°

2x= 110-60

2x= 50

x= 25°

Answer:

a. A linear pattern exists in the data.

b. The parameters for the line that minimizes MSE for this time series are as folows:

ß1 = Estimated slope = 1.4567

ß0 = Estimated intercept = 4.7165

Also, we have:

MSE = Mean squared error = 0.4896

c. Forecast for year 10 is 19,280.

Step-by-step explanation:

a. What type of pattern exists in the data?

Note: See Sheet1 of the attached excel file for the line graph.

From the line graph, it can be observed that a linear pattern exists in the data.

b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.

Note: See Sheet2 of the attached excel file for all the calculations to obtain the following:

Sample size = 9

Total of X = 45

Total of Y = 108

Mean of X = Total of X / Sample size = 45 / 9 = 5

Mean of Y = Total of X / Sample size = 108 / 9 = 12

SSxx = Total of (X - Mean of X)^2 = 60

SSyy = Total of (Y - Mean of Y)^2 = 130.74

SSxy = Total of (X - Mean of X) * (Y - Mean of Y) = 87.40

Therefore, we have:                

ß1 = Estimated slope = SSxy/SSxx = 87.4 / 60  = 1.4567

ß0 = Estimated intercept = Mean of Y – (ß1 * Mean of X) = 12 - (5 * 1.4567) = 4.7165

Therefore, the parameters for the line that minimizes MSE for this time series are as folows:

ß1 = Estimated slope = 1.4567

ß0 = Estimated intercept = 4.7165

Regression equation which also used in the attached excel is as follows:

Y = ß0 + ß1X =

Y = 4.7165 + 1.4567X …………………. (1)

SSE = Sum of squared error = Total of (Y - Y*)^2 = 3.4273

Therefore, we have:

MSE = Mean squared error = (SSE/(n-2)) = (3.4273 / (9 - 2)) = 0.4896

c. What is the forecast for year 10?

This implies that X = 10

Substitute X = 10 into equation (1), we have:

Y = 4.7165 + (1.4567 * 10) = 19.28

Since it is 1,000s, we have:

Y = 19.28 * 1,000 = 19,280

Therefore, forecast for year 10 is 19,280.

Answer:

6x + y

Step-by-step explanation:

6x + 3y/3​

6x + y

Answer:

6x + y

Step-by-step explanation:

6x + 3y / 3

cancel 3y by 3

6x + y

Answer:

56600 cars

Step-by-step explanation:

Below is the calculation of number of cars produced.

The percentage of cars that is defected = 3%

Number of cars that are defective = 1698 cars

The number of cars produced in a year = 1698 / 3%  

The number of cars produced in a year = 56600 cars

Answer:

Step-by-step explanation:

A=45

Answer:

4,a

5.d

6.c

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Step-by-step explanation:

Answer:

1. A

2. C

3. A

Step-by-step explanation:

all the explanations are In the image above

Hi there!

[tex]\large\boxed{12/5}}[/tex]

tan (angle) = Opposite side / Adjacent side, so:

Tan (A) = opposite side / adjacent side

= 24 / 10

Simplify:

= 12 / 5

Answer:

sorting;

greatest = 2,700

least = 2,250

HAVE A NİCE DAY

Step-by-step explanation:

GREETINGS FROM TURKEY ツ

Answer:

0.924

Step-by-step explanation:

R² = 0.854

R = √0.854

R = 0.924

Hence, the correlation Coefficient of electricity tarrif is 0.924 ; this correlation Coefficient value, depicts a strong positive correlation between machine hours and cost of electricity. And can he interpreted to mean that ; Electricity tarrif increases as machine hours increases and also decreases as machine hours decreases.

Answer:

The original graph was shifted 2 units to the left and 5 units down.

Step-by-step explanation:

y = |x|

From this, we go to: y = |x - 2|.

When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.

y = |x - 2|.

From this, we go to: y = |x - 2| - 5.

Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.

Answer:

absolute value of the determinant, adjacent to, equal to

Step-by-step explanation:

The absolute value of a determinant  of the [tex]\text{matrix whose}[/tex] columns are the vectors and they define the [tex]\text{sides}[/tex] of a [tex]\text{parallelogram}[/tex] which is adjacent to  one another and is equal to the [tex]\text{area}[/tex] of the [tex]\text{parallelogram}[/tex].

The determinant is a real number. They are like matrices, but we use absolute value bars to show determinants whereas to represent a matric, we use square brackets.

9514 1404 393

Answer:

  b. No; the domain values are not at regular intervals although the range values have a common factor.

Step-by-step explanation:

The differences between x-values are ...

  -1, -1, -1, -2 . . . . not a constant difference

The ratios of y-values are ...

  2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference

The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.

Answer: 0.108

Step-by-step explanation:

Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:

= 1 - 21.6%

= 78.4%

The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:

= 5% × 21.6%

= 0.05 × 0.216

= 0.108

Answer:

What function?

Step-by-step explanation:

9514 1404 393

Answer:

  5/8

Step-by-step explanation:

The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.

Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.

The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.

Answer:

79.8

Step-by-step explanation:

math

Answer:

A. (4,4.5)

Step-by-step explanation:

Midpoint={x1+x2/2,y1+y2/2}

M={4+4/2,1+8/2}

M={8/2,9/2}

M={4,4.5}

Answer:

the car travels 10km then 15km 60* north of east

Step-by-step explanation:

Answers:

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

Explanation:

The angle theta is between pi and 3pi/2, excluding both endpoints.

This places theta in the third quadrant (Q3) between 180 degrees and 270 degrees. The third quadrant is in the southwest.

Plot point A at the origin. 12 units to the left of this point, will be point B. So B is at (-12,0). Then five units lower is point C at (-12,-5). Refer to the diagram below. Notice how triangle ABC is a right triangle.

The angle theta will be the angle BAC, or simply angle A.

Since cos(theta) = -12/13, this indicates that

AB = -12 = adjacent

AC = 13 = hypotenuse

Technically, AB is should be positive, but I'm making it negative so that we can then say

cos(angle) = adjacent/hypotenuse

cos(theta) = AB/AC

cos(theta) = -12/13

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

If you apply the pythagorean theorem, you should find that BC = 5, which I'll  make negative since we're below the x axis. Then we can say

sin(theta) = opposite/hypotenuse

sin(theta) = BC/AC

sin(theta) = -5/13

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

If you divide sine over cosine, then you'll get 5/12. The 13's cancel out. This is the value of tangent.

Or you could say

tan(theta) = opposite/adjacent

tan(theta) = BC/AB

tan(theta) = (-5)/(-12)

tan(theta) = 5/12

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

To find csc, aka cosecant, you apply the reciprocal to sine

sin = -5/13 which means csc = -13/5

sec, or secant, is the reciprocal of cosine

cos = -12/13 leads to sec = -13/12

and finally cotangent (cot) is the reciprocal of tangent

tan = 5/12 leads to cot = 12/5

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

Note: everything but tan and cot is negative in Q3.

Answer:

Hence, the roots of the polynomial equation are:

-2, 1, 4

Step-by-step explanation:

We are asked to find the roots of the polynomial equation:

We can also equate this equation to y to obtain a system of equation as:

and

Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.

Hence, the point of intersection of the two graphs are:

(-2,4), (1,-5) and (4,40)

Hence, the roots of the polynomial equation are:

-2, 1, 4