Both and are in direct proportion, then and are ________. (a) in direct proportion

(b) in inverse proportion

(c) neither in direct nor in inverse proportion

(d) sometimes in direct proportion and sometimes in inverse proportion

Answer:

Step-by-step explanation:

=276.45/3

=92.15

each share is for 92.15

Answer:

Step-by-step explanation:

To determine if the true average stopping distance of the truck exceeds the maximum value of 30, a hypothesis test is conducted using the given data. With an alpha level of 0.01, the test is performed assuming the stopping distances are normally distributed. The probability of a type II error is calculated for two scenarios: when sigma is 0.65 and mu is 31, and when sigma is 0.80 and mu is 31. Finally, the sample size required to achieve α = 0.01 and β = 0.10, with μ = 31 and σ = 0.65, is determined.

To test the hypothesis, we set up the null and alternative hypotheses as follows:

Null hypothesis (H0): The true average stopping distance is less than or equal to 30.

Alternative hypothesis (Ha): The true average stopping distance exceeds 30.

Using the given data and assuming normal distribution, we calculate the sample mean, sample standard deviation, and standard error. With the given alpha level of 0.01, we compare the test statistic (calculated from the sample mean and standard error) to the critical value from the t-distribution to determine if we reject or fail to reject the null hypothesis.

To calculate the probability of a type II error, we need to specify the alternative value of mu. For mu = 31 and sigma = 0.65, we can calculate the corresponding z-score and find the probability of observing a value less than the critical value for alpha = 0.01.

Repeating the calculation with mu = 32 and sigma = 0.65, we determine the probability of a type II error.

In the third part, when sigma is changed to 0.80, we recalculate the probability of a type II error forμ = 31.

To find the sample size needed to achieve α = 0.01 and β = 0.10 with μ = 31 andσ = 0.65, we can use power analysis formulas or statistical software to determine the required sample size based on the desired significance level and power of the test.

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The exact forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:

Tuesday: 389.1

Wednesday: 368.7

Thursday: 326.5

Friday: 510.9

To forecast the number of customers served on each of the next five business days using Winters' method, we need to follow these steps:

Calculate the seasonal factor for each day by multiplying the seasonal index by the level.

Monday: 1.10 × 20 = 22

Tuesday: 0.95 × 20 = 19

Wednesday: 0.90 × 20 = 18

Thursday: 0.80 × 20 = 16

Friday: 1.25 × 20 = 25

Update the level and trend using the following formulas:

New Level = α × (Actual Value / Seasonal Factor) + (1 - α) × (Previous Level + Previous Trend)

New Trend = β × (New Level - Previous Level) + (1 - β) * Previous Trend

For Tuesday:

New Level = 0.2 × (30 / 22) + 0.8 × (20 + 1) = 20.3636

New Trend = 0.1 × (20.3636 - 20) + 0.9 × 1 = 0.0364

Forecast the number of customers served on each subsequent day using the formula:

Forecast = (New Level + Forecasted Trend) × Seasonal Factor

Tuesday Forecast = (20.3636 + 0.0364) × 19 = 389.0909

Wednesday Forecast = (20.3636 + 0.0364) × 18 = 368.7273

Thursday Forecast = (20.3636 + 0.0364) × 16 = 326.5455

Friday Forecast = (20.3636 + 0.0364) × 25 = 510.9091

Therefore, the forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:

Tuesday: 389.1

Wednesday: 368.7

Thursday: 326.5

Friday: 510.9

The question should be: A local bank is using Winters' method with α = 0.2, β= 0.1, and γ = 0.5 to forecast the number of customers served each day. The bank is open Monday through Friday. At the end of the previous week, the following seasonal indexes have been estimated: Monday, 1.10; Tuesday, 0.95; Wednesday, 0.90; Thursday, 0.80; Friday, 1.25. Also, the current estimates of level and trend are 20 and 1. After observing that 30 customers are served by the bank on this Monday, forecast the number of customers who will be served on each of the next five business days. Round your answers to one decimal place, if necessary.

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Answer:

see below

Step-by-step explanation:

a) 1 = 4 they are corresponding angles when j and k are parallel

b) 3 + 4 = 180 these just lies on same straight line and they add up to 180 so none

c) 5 + 7 = 180 are consecutive interior angles when k and l are parallel

d) 6 = 7 they are alternate interior angles when k and l are parallel

and refer this link for theory on this topic

https://www.ixl.com/math/lessons/transversals-of-parallel-lines

Let ABC be the equilateral triangle inscribed in a circle of radius r. The area of the equilateral triangle ABC is:A1 = (sqrt(3) / 4) × (2r)² = (sqrt(3) / 4) × 4r² = sqrt(3) × r²The radius of the circle inscribed in equilateral triangle ABC is r / sqrt(3).

Therefore, the altitude h of the triangle ABC is:h = sqrt(3) / 2 × 2 × r / sqrt(3) = rThe smaller equilateral triangle is ADE, which is inscribed in the region bounded by the base of the equilateral triangle and the lower part of the circle in such a way that the heights of each triangle are on the same line. Let AD = x be the side of the smaller equilateral triangle. The altitude of the smaller equilateral triangle is h – x.The radius of the circle inscribed in the smaller equilateral triangle ADE is (r – h + x) / 2.

The ratio of the area of the shaded region to the area of the smaller triangle is:((1 / 6) × πr² - (sqrt(3) / 4) × x²) / [(sqrt(3) / 4) × x²]Thus, we have the following equivalent ratios:

(sqrt(3) × r²) / [(sqrt(3) / 4) × x²] = ((1 / 6) × πr² - (sqrt(3) / 4) × x²) / [(sqrt(3) / 4) × x²]

After multiplying both sides by 4x² and simplifying, we obtain the following quadratic equation in x:πr² / 6x² - 1 = sqrt(3)After solving the quadratic equation, we obtain the following result:x = r × (2 - sqrt(3))The ratio of the area of the larger triangle to the area of the smaller triangle is:

(sqrt(3) × r²) / [(sqrt(3) / 4) × x²]= 4(2 + sqrt(3)).

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Answer:

65

tep-by-step explanation:

Brainliest tysmmm you are my 5000 points tysmmmmm

The equation of the tangent plane to the given surface at the point (4, 10, 9) is x - 12y + 6z = 79. The equation of the normal line to the given surface at the point (4, 10, 9) is given parametrically as \(\(x(t) = 4 + t, y(t) = 10 - 6t, z(t) = 9 - 3t\)\).

The tangent plane to a surface can be determined by finding the partial derivatives of the equation with respect to x, y, and z. We start by differentiating the equation \(\(2(x - 3)^2 + (y - 8)^2 + (z - 7)^2 = 10\)\) with respect to x, y, and z. Evaluating these partial derivatives at the point (4, 10, 9), we get the coefficients of the tangent plane equation as 1, -12, and 6 respectively, giving us the equation x - 12y + 6z = 79.

To find the equation of the normal line, we use the gradient vector of the surface, which is perpendicular to the tangent plane. The gradient vector is given by \(\(\nabla f(x, y, z) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)\)\), where f(x, y, z) is the equation of the surface. Evaluating the gradient vector at the point (4, 10, 9), we obtain (1, -12, 6). Thus, the parametric equations of the normal line are \(\(x(t) = 4 + t\), \(y(t) = 10 - 6t\), and \(z(t) = 9 - 3t\)\).

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the number 6 is in the hundredths place and 4 is in the ones place

Answer:

3

Step-by-step explanation:

2

The area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

To find the area enclosed by the curve r=2sin(θ) 3sin(9θ), we first need to determine the limits of integration for θ.

Since the curve is periodic with period 2π/9 (due to the 9 in the second term), we only need to consider the portion of the curve in the interval [0, 2π/9].

Next, we need to convert the polar equation to rectangular coordinates, which can be done using the formulas x = r cos(θ) and y = r sin(θ).

Plugging in the given equation, we get:

x = 2sin(θ) cos(θ) + 3sin(9θ) cos(θ)
y = 2sin(θ) sin(θ) + 3sin(9θ) sin(θ)

Now we can find the area enclosed by the curve by integrating over the given interval:

A = ∫[0,2π/9] (1/2) [x(θ) y'(θ) - y(θ) x'(θ)] dθ

Using the formulas for x and y, we can find the derivatives x'(θ) and y'(θ):

x'(θ) = 2cos(θ) cos(θ) - 2sin(θ) sin(θ) + 27cos(9θ) cos(θ) - 27sin(9θ) sin(θ)
y'(θ) = 2cos(θ) sin(θ) + 2sin(θ) cos(θ) + 27cos(9θ) sin(θ) + 27sin(9θ) cos(θ)

Substituting these expressions into the formula for A and evaluating the integral, we get:

A = (243π/64) - (3√3/16)

Therefore, the area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

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Answer:

5 pictures

Step-by-step explanation:

Just solve the equation: 50+8p=96

-96on both sides

8p=46

divide by 8 on both sides

p=5.75 or 5 3/4, so 5 because it hasnt reached the number 6 yet so 5

Answer:10th?

Step-by-step explanation:

8 + two = 10????

Answer:

what grade are you in

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

32+14 = 46

46 ppl study spanish

Answer:

A = the Venn diagram and the middle section is 41 because :

14 + 25 = 39

80 - 39 = 41

B = 25 ( because of diagram )

C = the number of kids who studied both and only studied it which is:

41 + 14 = 55 (so C = 55).

Answer:

\(m(BC) = 72^\circ\)

\(m\angle EBC = 168^\circ\)

Step-by-step explanation:

Given

\(m\angle BAC = 72\)

\(m(BE) = 96\)

See attachment for circle

Required

Determine

(a) Measure of BC

(b) Measure of EBC

(a) Measure of BC

From the attachment, we can see that:

\(m(BC) = m\angle BAC\) because they belong to the same sector

This gives:

\(m(BC) = 72^\circ\)

(b) Measure of EBC

From the attachment, we can see that:

\(m\angle EBC = m(EB) +m(BC)\)

Where

\(m(EB) = m(BE) =96^\circ\)

So, we have:

\(m\angle EBC = 96^\circ + 72^\circ\)

\(m\angle EBC = 168^\circ\)

Other answers are possible.

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

Explanation:

The normal vector is n = (a,b,c) = (2,3,4)

The point on the plane is (p,q,r) = (2,4,-1)

Plug those values into the template below and simplify

a(x-p) + b(y-q) + c(z-r) = 0

2(x-2) + 3(y-4) + 4(z-(-1)) = 0

2(x-2) + 3(y-4) + 4(z+1) = 0

2x-4 + 3y-12 + 4z+4 = 0

2x+3y+4z-12 = 0

2x+3y+4z = 12

This is one way to express the cartesian form of the equation.

The unit tangent vector T(t) is i / √2 + j / √2, the normal vector N(t) is -sin t i + cos t j, and the binormal vector B(t) is - (sin t + cos t) k / √2.

To find T(t), N(t), and K(t) for the space curve r(t) = (et cos t) i + (et sin t) j + 4k, we'll need to calculate the unit tangent vector, normal vector, and binormal vector.

Unit Tangent Vector (T(t)):

The unit tangent vector T(t) is the derivative of the position vector r(t) with respect to t, divided by its magnitude.

r(t) = (et cos t) i + (et sin t) j + 4k

Taking the derivative of r(t) with respect to t, we get:

r'(t) = (et (-sin t) + et cos t) i + (et cos t + et sin t) j

To normalize the vector, we divide r'(t) by its magnitude:

T(t) = (1 / |r'(t)|) * r'(t)

| r'(t) | = √[(et (-sin t) + et cos t)² + (et cos t + et sin t)²]

Simplifying the magnitude, we get:

| r'(t) | = √[\(e^{2t\)(cos² t + sin² t) + \(e^{2t\)(cos² t + sin² t)]

| r'(t) | = √(2\(e^{2t\))

Therefore, the unit tangent vector is:

T(t) = (1 / √(2\(e^{2t\))) * [(et (-sin t) + et cos t) i + (et cos t + et sin t) j]

Simplifying further, we get:

T(t) = (1 / √(2\(e^{2t\))) * et(cos t i + sin t j + cos t i + sin t j)

T(t) = (1 / √(2\(e^{2t\))) * 2et(cos t i + sin t j)

T(t) = (1 / √2) (cos t i + sin t j)

Thus, T(t) = i / √2 + j / √2.

Normal Vector (N(t)):

The normal vector N(t) is the derivative of the unit tangent vector T(t) with respect to t, divided by its magnitude.

N(t) = (d/dt)(T(t)) / |(d/dt)(T(t))|

N(t) = (d/dt)(T(t)) / |(d/dt)(T(t))|

N(t) = (d/dt)[(1 / √2)(cos t i + sin t j)] / |(d/dt)[(1 / √2)(cos t i + sin t j)]|

N(t) = (1 / √2)(-sin t i + cos t j) / (1 / √2)(-sin t i + cos t j)

N(t) = -sin t i + cos t j

Thus, N(t) = -sin t i + cos t j.

Binormal Vector (B(t)):

The binormal vector B(t) can be calculated by taking the cross product of T(t) and N(t).

B(t) = T(t) × N(t)

B(t) = (i / √2 + j / √2) × (-sin t i + cos t j)

B(t) = (-sin t / √2) k - (cos t / √2) k

B(t) = - (sin t + cos t) k / √2

Thus, B(t) = - (sin t + cos t) k / √2.

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Answer:

1. 3-D Shapes
2. To find the area of all 2-D Shapes that make up the 3-D shape who's surface area we are trying to find
3. 160ft^2
4. 213.53cm^2
5. 239.3in^2
6.490.87km^2
7.75.4cm^2
8.1724.9mi^2

Step-by-step explanation:

In question 1 surface area means the final surface area of all 2-d shapes on a 3-D shape, so it is 3-D Shapes

In question 2,  it is simply the last questions explanation as an answer

All the questions up to question 8 are explained in the attached

20 oz soda bottle for $1.80

Explanation

to solve this , find the unit rate and compare

Step 1

unit rate 1

then

Let

total cost=$1.80

number of ounces=20

replace

Step 2

now, for option 2

Let

cost=1.25 dollars

number of ounces=12

replace

the better deal is teh cheapest option,

Hence, the better deal is option one

20 oz soda bottle for $1.80

I hope this helps you

Step-by-step explanation:

the intercept with the y axis is the y value for x = 0 (only for x = 0 is the line "hitting" the y axis).

and the intercept with the x axis ? well, that is the x value leading to y = 0.

so,

y = -6x - 2

x = 0

y = -6×0 - 2 = -2

so, the y intercept point is (0, -2)

and for what x is y = 0 ?

0 = -6x - 2

2 = -6x

x = -2/6 = -1/3

so, the x intercept point is (-1/3, 0)

Answer:

y = \(3^{x}\)

Step-by-step explanation:

the standard form of an exponential function is

y = a\(b^{x}\)

Use ordered pairs from the table to find a and b

Using (0, 1 ) , then

1 = a\(b^{0}\) [ \(b^{0}\) = 1 ] , so

1 = a × 1 , that is a = 1

y = \(b^{x}\)

Using (1, 3 )

3 = \(b^{1}\) ⇒ b = 3

y = \(3^{x}\) ← required exponential function

After converting \(4.5 * 10^4\) to decimal format, one gets 45,000 as an answer. Thus, option (A) is the correct answer.

To convert numbers multiplied by 10 with having an exponent number to decimal format, one first needs to check the sign on the exponent.

If the sign is positive, we must shift the decimal to the right with each power of 10. The exponent indicates the number of zeros added after the number in case no decimal is used.

And if the sign is negative, we have to shift the decimal to the left with each power of 10. One has to divide the number by the number one gets after multiplying 10 by itself as many times as the exponent.

Therefore, to convert \(4.5 * 10^4\) to decimal format, we shift the decimal by 4 places and we get 45,000 as the answer.

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Answer:

12.5%

Step-by-step explanation:

\(\frac{10}{80} =\frac{x}{100}\)

Cross multiply

80x = 1000

Divide both sides by 80

80x/80 = 1000/80

x = 12.5

Hope this helps and pls do mark me brainliest if you can:)

Answer: hey girl hal is north west west of north west west north west of north north

Step-by-step explanation:

The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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The line of the best fit would pass through (a) (1,9) and (9,5)

From the question, we have the following parameters that can be used in our computation:

The graph

A good line of best fit would have equal number of points on either sides

To plot the graph, we draw a line that divides the points on the graph evenly

This line when drawn on the scattered points divided the points approximately evenly

The line of the best fit when drawn using the above properties would pass through (a) (1,9) and (9,5)

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Answer:

AC is the longest side

AB is the shortest

Step-by-step explanation:

Generally, the side that faces the smallest angle has the smallest side while the side that faces the largest angle has the largest side

The measure of the third angle C is 180 - 55 -75 = 50

Kindly note that A faces BC

B faces AC

C faces AB

So while AC is the longest side, AB is the shortest

So the correct answers are;

AC is the longest side

AB is the shortest side

Answer:

given,

ratio= 2:3:5 , smallest part length=6

let x be the common multiple then,

first number (smallest) =2x

6cm =2x

6/2=x

therefore, x=3

now,

1st part=2x=2*3=6

2nd part=3x=3*3=9

3rd part=5x=5*3=15

again,

total length = sum of all part

=6+9+15

=30

therefore 30cm is the answer

John and Mar need 14 minutes complete shovel their driveway together, to the nearest minute.

You can use this computation to determine the hourly value of each employee's job, allowing you to more effectively and efficiently plan your staffing needs in the future.

This is crucial because it enables you to determine the ideal workforce size based on your average hourly wage.

According to the question;

by calculating the fraction of unit work that each individual can finish in a given amount of time together work is estimated.

Mary can clear 1/20 of a driveway in a minute, but John can clear 1/50 of it in that time.

The both will do the same job in;

= (1/20) + (1/50)

= (5/100) + (2/100)

= 7/100

They'll be finished when they've cleared 100 percent of the driveway, therefore the equation we must finally solve is:

7x = 100.

x = 100/7

x = 14.28

Therefore, when John and Mar will work together, they will shovel the driveway in 14 minutes (to the nearest minute).

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